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Vadose zone processes affecting water table fluctuations :
b conceptualization and modeling considerations
h [electronic resource] /
by Nirjhar Shah.
[Tampa, Fla.] :
University of South Florida,
ABSTRACT: This dissertation focuses on a variety of vadose zone processes that impact water table fluctuations. The development of vadose zone process conceptualization has been limited due to both the lack of recognition of the importance of the vadose zone and the absence of suitable field data. Recent studies have, however, shown that vadose zone soil moisture dynamics, especially in shallow water table environments, can have a significant effect on processes such as infiltration, recharge to the water table, and evapotranspiration. This dissertation, hence, attempts to elucidate approaches for modeling vadose zone soil moisture dynamics. The ultimate objective is to predict different vertical and horizontal hydrological fluxes. The first part of the dissertation demonstrates a new methodology using soil moisture and water table data collected along a flow transect.The methodology was found to be successful in the estimation of hydrological fluxes such as evapotranspiration, infiltration, runoff, etc. The observed dataset was also used to verify an exponential model developed to quantify the ground water component of total evapotranspiration. This analysis was followed by a study which analyzed the impact of soil moisture variability in the vadose zone on water table fluctuations. It was found that antecedent soil moisture conditions in the vadose zone greatly affected the specific yield values, causing a broad range of water table fluctuations for similar boundary fluxes. Hence, use of a constant specific yield value can produce inaccurate results. Having gained insight into the process of evapotranspiration and specific yield, a threshold based model to determine evapotranspiration and subsequent water table fluctuation was conceptualized and validated.A discussion of plant root water uptake and its impact on vadose zone soil moisture dynamics is presented in the latter half of this dissertation. A methodology utilizing soil moisture and water table data to determine the root water uptake from different sections of roots is also described. It was found that, unlike traditional empirical root water uptake models, the uptake was not only proportional to the root fraction, but was also dependent on the ambient soil moisture conditions. A modeling framework based on root hydraulic characteristics is provided as well. Lastly, a preliminary analysis of observed data indicated that, under certain field conditions, air entrapment and air pressurization can significantly affect the observed water table values. A modeling technique must be developed to correct such observations.
Dissertation (Ph.D.)--University of South Florida, 2007.
Includes bibliographical references.
Text (Electronic dissertation) in PDF format.
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Title from PDF of title page.
Document formatted into pages; contains 214 pages.
Advisor: Mark A. Ross, Ph.D.
Shallow water table.
Root water uptake.
Variable specific yield.
x Civil Engineering
t USF Electronic Theses and Dissertations.
Vadose Zone Processes Affecting Water Fluctuations: Conceptualization and Modeling Considerations by Nirjhar Shah A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Civil and Environmental Engineering College of Engineering University of South Florida Co-Major Professor: Mark A. Ross, Ph.D. Co-Major Professor: Mahmood H. Nachabe, Ph.D. David M. Sumner, Ph.D. Mark Rains, Ph.D. Rafael Perez, Ph.D. Date of Approval: October 18, 2007 Keywords: shallow water table, evapotranspiration, extinction depth, variable specific yield, root water uptake Copyright 2007, Nirjhar Shah
Dedication To my grandfather, the late Mr. L.D. Shah, a great teacher, who from very childhood instilled in me a sense of appreciation of science and a never ending pursuit of understanding it. Dadaji this is for you.
Acknowledgements First and foremost I would like to thank my family, especially my parents, who worked very hard to ensure that I received an excel lent education. Their constant love, support, patience, and encouragement guided me and helped me to successfully reach my goals. I am grateful to all of my friends and relat ives for being there whenever I needed them. I would also like to express the deepest appreciat ion to Dr. Mark Ross, Dr. Mahmood Nachabe, and all my committee members for t heir constant support and guidance throughout my tenure at the university. I am thankful that Dr. Ken Trout was always there to listen to my grievances and for off ering constructive ideas. I also want to thank all of my CMHAS colleagues, especially Jeff V omacka, Lisa Foster, Dr. Jing Zhang, Ken Nilsson, and Makhan Virdi, for all of th eir useful input, problem solving expertise, and overall assistance. Finally, I want to thank my lovely fianc, and soo n to be wife, Swarna. I cannot express how grateful I am for all the encouragement love, and friendship she has provided me with throughout this journey.
i Table of Contents List of Tables..................................... ................................................... ............................vii List of Figures.................................... ................................................... .............................ix Abstract........................................... ................................................... ..............................xiv Chapter 1: Overview................................ ................................................... ........................1 Chapter 2: Estimation of Evapotranspiration and Wat er Budget Components Using Concurrent Soil Moisture and Water Table Monitoring ................................................... ..8 2.1 Introduction................................... ................................................... .........................8 2.2 Materials and Methods.......................... ................................................... ...............11 2.2.1 Study Site................................... ................................................... ...................11 2.2.2 Instrumentation.............................. ................................................... ...............14 2.2.3 Point Scale Modeling of Evapotranspiration... ................................................16 2.2.4 One Dimensional Transect Model............... ................................................... .19 126.96.36.199 Estimation of Hydraulic Conductivity....... ...............................................25 2.2.5 Estimation of Lateral and Vertical Fluxes.... ................................................... 27 188.8.131.52 Interception Capture ( Ic).................................................. .........................27 184.108.40.206 Effective Precipitation ( PE).................................................. .....................28 220.127.116.11 Upstream Runoff Infiltration ( URI ).................................................. ........28
ii 18.104.22.168 Infiltration ( I ).................................................. ..........................................28 22.214.171.124 Depression Storage ET ( DS ET ).................................................. .............29 126.96.36.199 Total ET ( TET ).................................................. ........................................30 188.8.131.52 Total Rainfall Excess ( TRE ).................................................. ...................30 184.108.40.206 Saturation Excess Runoff ( SER ), Hortonian Runoff ( HR ), and Net Runoff ( NR ).................................................. ................................................... ..................30 2.2.6 Assumptions.................................. ................................................... ................33 2.3 Results and Discussion......................... ................................................... ...............33 2.3.1 Point Scale Model............................ ................................................... .............37 220.127.116.11 Comparison with Pan Evaporation............ ...............................................39 2.3.2 One Dimensional Transect Model............... ................................................... .40 2.3.3 Error Estimates.............................. ................................................... ................53 2.4 Conclusions.................................... ................................................... ......................55 Chapter 3: Extinction Depth and Evapotranspiration from Ground Water under Selected Land Covers........................................ ................................................... ...........................57 3.1 Introduction................................... ................................................... .......................57 3.2 Background..................................... ................................................... .....................57 3.2.1 Objectives and Scope......................... ................................................... ...........60 3.3 Methods........................................ ................................................... .......................61 3.3.1 Numerical Simulations........................ ................................................... ..........61 3.3.2 Data Processing and Analysis................. ................................................... ......64 3.3.3 Field Estimation of GWET ................................................... ............................67 3.4 Results and Discussion......................... ................................................... ...............69
iii 3.4.1 Influence of Soil Properties and Land Cover.. .................................................71 3.4.2 Variability in Extinction Depths............. ................................................... ......75 3.4.3 Fitting a Model for ET and GWET Variation with dWT...................................77 18.104.22.168 Field Assessment of Proposed Equations..... ............................................78 3.5 Conclusions.................................... ................................................... ......................82 Chapter 4: Conceptualization of Vadose Zone Process es to Account for Evapotranspiration Distribution.................... ................................................... .................84 4.1 Introduction................................... ................................................... .......................84 4.2 Specific Yield................................. ................................................... .....................85 4.2.1 Background................................... ................................................... ................85 4.2.2 Objectives and Scope......................... ................................................... ...........88 4.2.3 Materials and Methods........................ ................................................... ..........89 22.214.171.124 Numerical Model............................ ................................................... .......89 126.96.36.199 Soil Hydraulic Properties.................. ................................................... .....90 188.8.131.52 Initial and Boundary Conditions............ ................................................... 91 184.108.40.206.1 Initial Conditions....................... ................................................... .....91 220.127.116.11.2 Boundary Conditions...................... ................................................... 91 18.104.22.168 Root Water Uptake Model.................... ................................................... .92 4.2.4 Specific Yield Calculation................... ................................................... .........92 22.214.171.124 Calculation of Equilibrium Specific Yield.. .............................................96 4.3 Results and Discussion......................... ................................................... ...............98 4.3.1 Drying Specific Yield........................ ................................................... ...........99 4.3.2 Specific Yield under Pumping Conditions...... ..............................................101
iv 4.3.3 Specific Yield under Wetting Conditions...... ................................................104 4.4 Comparison with Other Studies.................. ................................................... .......105 4.5 Conclusions.................................... ................................................... ....................110 Chapter 5: Vadose Zone Evapotranspiration Distribut ion and Conceptualization for Integrated Modeling................................ ................................................... .....................112 5.1 Introduction................................... ................................................... .....................112 5.1.1 Objectives and Scope......................... ................................................... .........114 5.2 Materials and Methods.......................... ................................................... .............114 5.2.1 Initial and Boundary Conditions.............. ................................................... ...........114 5.2.2 Three-Layer/Two Zones Concept................ ..................................................1 15 5.3 Results and Discussion......................... ................................................... .............118 5.3.1 Numerical Simulation......................... ................................................... ........118 5.3.2 ET Thresholds Conditions............................. ................................................119 126.96.36.199 Case A..................................... ................................................... .............119 188.8.131.52 Case D..................................... ................................................... .............120 184.108.40.206 Case B and Case C.......................... ................................................... .....121 5.4 Limitations.................................... ................................................... .....................123 5.5 Conclusions.................................... ................................................... ....................125 Chapter 6: Determination of Root Water Uptake: Cal culation from Soil Moisture Data and Conceptualization for Modeling................. ................................................... ..........127 6.1 Introduction................................... ................................................... .....................127 6.2 Background..................................... ................................................... ...................128
v 6.2.1 Objectives and Scope......................... ................................................... .........130 6.3 Theory......................................... ................................................... .......................130 6.3.1 Root Water Uptake Model...................... ................................................... ....132 6.4 Materials and Methods.......................... ................................................... .............135 6.4.1 Study Site................................... ................................................... .................135 6.4.2 Methodology.................................. ................................................... .............135 220.127.116.11 Saturated and Residual Water Content....... ............................................139 18.104.22.168 Saturated Hydraulic Conductivity........... ................................................139 22.214.171.124 van Genuchten Parameters................... ................................................... 139 126.96.36.199 Calculation of Root Water Uptake........... ...............................................141 6.5 Results........................................ ................................................... ........................143 6.6 Incorporation of Plant Physiology.............. ................................................... .......150 6.6.1 Root Distribution............................ ................................................... ............150 6.6.2 Hydraulic Characterization of Roots.......... ................................................... 151 6.6.3 Development of a Physically Based Root Water Uptake Model...................153 6.7 Conclusions.................................... ................................................... ....................157 Chapter 7: Long Term Air Entrapment Affecting Runof f and Water Table Observations....................................... ................................................... ..........................159 7.1 Introduction................................... ................................................... .....................159 7.2 Background..................................... ................................................... ...................159 7.2.1 Objectives and Scope......................... ................................................... .........162 7.3 Study Site and Data Collected.................. ................................................... .........163 7.4 Methodology.................................... ................................................... ..................163
vi 7.4.1 Numerical Model.............................. ................................................... ..........164 188.8.131.52 Model Setup................................ ................................................... .........166 184.108.40.206 Soil Hydraulic Properties.................. ................................................... ...167 220.127.116.11 Initial and Boundary Conditions............ .................................................16 8 18.104.22.168.1 Initial Conditions....................... ................................................... ...168 22.214.171.124.2 Boundary Conditions...................... .................................................16 9 7.4.2 Calibration to Observed Period of Record..... ................................................170 7.4.3 Calculation of Excess Pressurization Using Id eal Gas Law..........................172 126.96.36.199 Implementation of the Spreadsheet Model.... .........................................173 7.5 Results........................................ ................................................... ........................176 7.5.1 Calibration and Validation Results........... ................................................... ..176 7.5.2 Numerical Solution........................... ................................................... ..........177 7.5.3 Spreadsheet Analysis......................... ................................................... .........182 7.6 Discussion of Results.......................... ................................................... ...............191 7.6.1 Implications for Ground Water Modeling....... ..............................................193 7.7 Conclusions.................................... ................................................... ....................195 Chapter 8: Summary and Conclusions................. ................................................... ........197 References......................................... ................................................... ...........................202 About the Author................................... ................................................... .............End Page
vii List of Tables Table 2.1 Notations Used in the 1D Transect Model A long with Description and Units of Each Symbol............................... ................................................... ......22 Table 2.2 Values of Hydraulic Conductivity Obtained from Permeameter Analysis Done on Soil Core Samples Taken at Different Depths Below Land Surface [Adapted from Thompson (2003)]..................... ................................................26 Table 2.3 Pan Coefficients Used to Obtain Pasture E vapotranspiration for Different Months............................................. ................................................... ...............37 Table 2.4 Total Annual Water Budget for 2002 (a) ET Runoff, and (b) Other Water Budget Components.................................. ................................................... ......48 Table 2.5 Total Annual Water Budget for 2003 (a) ET Runoff, and (b) Other Water Budget Components.................................. ................................................... ......49 Table 2.6 Semi-Annual Water Budget for 2004 (a) ET Runoff, and (b) Other Water Budget Components.................................. ................................................... ......50 Table 3.1 Extinction Depths for Different Soils and Land Covers....................................75 Table 3.2 Parameters for Equation 3.16............. ................................................... .............81 Table 3.3 Parameters for Equation 3.17............. ................................................... .............82 Table 6.1 Soil Parameters for Study Locations in (a ) Grassland and (b) Forested Area.140
viii Table 7.1 Differences in Observed Maximum Water Con tent (Water Table at the Land Surface) for Different Period of Records...... ..........................................165 Table 7.2 Calibrated Parameters and Extent of Soil Layers Below the Land Surface....173
ix List of Figures Figure 2.1 Location of the Study Site in Hillsborou gh County, Florida............................11 Figure 2.2 Soil Stratiagraphy of Cores Taken from L ocation Adjacent to (a) PS-39 and (b) PS-43...................................... ................................................... ..........13 Figure 2.3 Soil Moisture Probe on the Left Showing the Mounted Sensors Along with Schematics on the Right............................ ................................................... ....15 Figure 2.4 Total Soil Moisture is Estimated in Two Soil Columns..................................18 Figure 2.5 Total Soil Moisture versus Time in the ( a) Ground Water Discharge Area and (b) Ground Water Recharge Area................. ............................................20 Figure 2.6 One Dimensional Transect Model for Well Transect PS-39 to PS-43 (Not to Scale).......................................... ................................................... ..............21 Figure 2.7 Process Flow Diagram Showing the Sequenc e of Calculation of the Water Budget Components.................................. ................................................... ....32 Figure 2.8 Variation of Soil Moisture Storage Due t o Different Stresses.........................35 Figure 2.9 Monthly Average of Evapotranspiration ( ET ) Daily Values in Forested (Diamonds) and Pasture (Triangles) Areas........... ...........................................38 Figure 2.10 Evapotranspiration Estimates for Pastur e by the Pan and Point Scale Model.............................................. ................................................... ............40 Figure 2.11 Variation in Total ET for Grass and Forest Land Covers.................. .............42
x Figure 2.12 Variation in ET Derived from Soil Moist ure Changes for Grass and Forest Land Covers................................. ................................................... ....42 Figure 2.13 Variation of Depression Storage ET for Grass and Forest Land Covers........43 Figure 2.14 Variation of Infiltration for Grass and Forest Land Covers...........................43 Figure 2.15 Rainfall Excess for Grass and Forest La nd Covers........................................44 Figure 2.16 Saturation Excess Runoff Variation for Grass and Forest Land Covers........44 Figure 2.17 Net Runoff for Grass and Forest Land Co vers............................................... 45 Figure 2.18 Variation in Depth to the Water Table f or Grass and Forest Land Covers....45 Figure 2.19 Precipitation versus Infiltration for ( a) Grassed Land Cover and (b) Forested Land Cover................................ ................................................... ...46 Figure 3.1 Water Table and Total Soil Moisture (TSM ) Diurnal Variation with Time [Adapted from Nachabe et al. 2005]................. ...............................................60 Figure 3.2 Simulated ET in Sandy Clay with Forest Land Cover.............. .......................70 Figure 3.3 GWET and VZET in Sandy Clay Soil with Forested Land Cover....... .............71 Figure 3.4 Variation of Ratio of GWET with Water Table Depth for Two Soils.............. 72 Figure 3.5 Variation in GWET for Different Land Covers in Sandy Clay........... .............74 Figure 3.6 Estimated GWET/PET versus DTWT from White (1932)..................... ..........80 Figure 4.1 Median Values of the Observed Soil Water Retention Data Along with Best-Fit Brooks and Corey Model.................... ...............................................89 Figure 4.2 Variation of Specific Yield in Response to Different Stresses.........................98
xi Figure 4.3 ET Contribution from Direct Ground Water (Water Table ) and from the Non-Coupled Soil Water Storage Above the Water Tabl e............................100 Figure 4.4 Available Free Vadose Zone Storage for V ariable Depth to Water Table.....101 Figure 4.5 Actual Water Content Profile for Pumping and Equilibrium After (a) 60 and (b) 100 Days of Pumping........................ ................................................103 Figure 4.6 Wetting Front and the Equilibrium Water Content Profile After (a) 20 and (b) 40 Days of the Pulsing Soil Column with 5cm/hr Rainfall Infiltration for One Hour....................................... ................................................... ........106 Figure 4.7 Departure of Drying Water Content Profil e from the Equilibrium with Increasing Water Table Depths...................... ................................................109 Figure 5.1 Three-Layer Water Content Concept Used i n IHM.......................................116 Figure 5.2 Thresholds Used in IHM for Distribution of ET Between Vadose Zone and Ground Water....................................... ................................................... .......119 Figure 5.3 Water Content Profiles for Equilibrium a nd Dry Conditions After 10 Days of ET with Water Table at the Extinction Depth.......... .................................120 Figure 5.4 Variation of Total Soil Moisture above t he Water Table under Different Initial Water Table Depths or Initial Water Content Conditions at (a) Equilibrium (b) Wetter than Equilibrium............ ..........................................124 Figure 6.1 Water Stress Response Function as Concep tualized by (a) Feddes et al. (1978) and (b) van Genuchten (1980) [Adapted from S imunek et al. 2005].............................................. ................................................... .............134 Figure 6.2 Schematics of the Vertical Soil Column w ith Location of the Soil Moisture Sensors and Water Table............................ ................................................... 138
xii Figure 6.3 Schematics of a Section of Vertical Soil Column Showing Fluxes and Change in Storage.................................. ................................................... .....142 Figure 6.4 Root Water Uptake from Sections of Soil Corresponding to Each Sensor on the Soil Moisture Instrument for (a and b) Grass Land and (c and d) Forest Land Cover.................................. ................................................... .....144 Figure 6.5 Root Water Uptake Variation Due to an In ch of Rainfall Event....................147 Figure 6.6 Daily Root Water Uptake Variation from O ctober to November 2003 for (a) Grass Land Cover and (b) Forested Land Cover... ...................................149 Figure 6.7 Observed and Fitted Root Distribution fo r Different Type of Land Covers [Adapted from Jackson et al. 1996]................. ..............................................151 Figure 6.8 Vulnerability Curves for Various Species [Adapted from Tyree 1999].........152 Figure 6.9 Observed Values and Fitted Vulnerability Curve for Roots and Stem Sections of Different Eucylaptus Trees [Adapted fro m Pammenter and Willigen 1998]..................................... ................................................... .......154 Figure 6.10 Variation of Ratio of Actual to Potenti al ET with Location of the Critical Stress Level....................................... ................................................... ........156 Figure 6.11 Variation in the Vertical Distribution of Root Water Uptake, at Different Times [Adapted from Jarvis 1989]................... ...........................................157 Figure 7.1 Snapshot of Water Content Variation Alon g the Vertical Soil Profile..........167 Figure 7.2 Snapshot of Calibration ResultsÂ…Â…Â…Â…Â…Â…Â…Â…Â… Â…Â…Â…Â…Â… .Â…Â…Â….178 Figure 7.3 Actual dWT Calculated from HYDRUS Plotted Against Observed dWT for (a) May 2002-June 2002, (b) April 2003-May 2003.... .................................180 Figure 7.4 Rainfall and Infiltration Plotted Along with Excess Pressure for (a) May 2002-June 2002, (b) April 2003-May 2003............ .......................................184
xiii Figure 7.5 Excess Pressure as Calculated from Sprea dsheet Model and HYDRUS Solution........................................... ................................................... ............185 Figure 7.6 Variation of Water Content Values as Obt ained from the Sensors Located at 10, 20, and 30 cm Below Land Surface............ .........................................188
xiv Vadose Zone Processes Affecting Water Table Fluctua tions: Conceptualization and Modeling Considerations Nirjhar Shah ABSTRACT This dissertation focuses on a variety of vadose z one processes that impact water table fluctuations. The development of vadose zone process conceptualization has been limited due to both the lack of recognition of the importance of the vadose zone and the absence of suitable field data. Recent studies have however, shown that vadose zone soil moisture dynamics, especially in shallow water tabl e environments, can have a significant effect on processes such as infiltratio n, recharge to the water table, and evapotranspiration. This dissertation, hence, attem pts to elucidate approaches for modeling vadose zone soil moisture dynamics. The ul timate objective is to predict different vertical and horizontal hydrological flux es. The first part of the dissertation demonstrates a new methodology using soil moisture and water table data collected along a flo w transect. The methodology was found to be successful in the estimation of hydrolo gical fluxes such as evapotranspiration, infiltration, runoff, etc. The observed dataset was also used to verify an exponential model developed to quantify the grou nd water component of total evapotranspiration. This analysis was followed by a study which analyzed the impact of soil moisture variability in the vadose zone on wat er table fluctuations. It was found that
xv antecedent soil moisture conditions in the vadose z one greatly affected the specific yield values, causing a broad range of water table fluctu ations for similar boundary fluxes. Hence, use of a constant specific yield value can p roduce inaccurate results. Having gained insight into the process of evapotranspirati on and specific yield, a threshold based model to determine evapotranspiration and subsequen t water table fluctuation was conceptualized and validated. A discussion of plant root water uptake and its im pact on vadose zone soil moisture dynamics is presented in the latter half o f this dissertation. A methodology utilizing soil moisture and water table data to det ermine the root water uptake from different sections of roots is also described. It w as found that, unlike traditional empirical root water uptake models, the uptake was not only p roportional to the root fraction, but was also dependent on the ambient soil moisture con ditions. A modeling framework based on root hydraulic characteristics is provided as well. Lastly, a preliminary analysis of observed data in dicated that, under certain field conditions, air entrapment and air pressurization c an significantly affect the observed water table values. A modeling technique must be de veloped to correct such observations.
1 Chapter 1: Overview Vadose zone processes are recognized for controlli ng both short term dynamics in watershed hydrology and long term water balances of hydrologic basins. The soil moisture variability in the vadose zone also determ ines the functional type of vegetation that grows in a particular area (Rodriguez-Iturbe a nd Porporato 2004). In shallow water table environments (depth to the water table < 2 m) the vadose zone not only impacts the surface hydrological processes but also affects the ground water system by influencing processes such as (a) the time scale of recharge to the water table, (b) actual recharge to the water table, (c) evapotranspiration from the so il, and (d) water table fluctuations. Despite its significance, vadose zone process conc eptualization and modeling capabilities are not as developed as those of groun d water and/or surface water modeling is (Harter and Hopman 2004). Traditionally the vado se zone has been treated as a lower boundary for the surface water models like HSPF (Bi cknell et al. 2001), acting primarily as a sink term to simulate evapotranspiration and r echarge or treated as an upper boundary for ground water models like MODFLOW (Harb augh et al. 2005) where it is conceptualized as a source term thorough which an e mpirically generate recharge is applied. The treatment of the vadose zone as a lumped sourc e or sink term, instead of a separate hydrologic system with its own dynamics, c an be attributed primarily to two reasons. The first and foremost reason is the absen ce of suitable data to develop and test
2 conceptualizations for modeling vadose zone process es, while the second reason lies in the desired output from any modeling exercise. Be i t surface water or ground water modeling, the objectives are to either simulate run off or stream flow, or potentiometric surface, and in the process empirical relationships are used to simulate the expected vadose zone behavior. For instance, the value of re charge is arbitrarily assumed to be some fraction of rainfall and the whole time scale and actual amount of recharge that is influenced by the antecedent vadose zone condition is ignored. Over last decade or so, however, with an increase in computation power and the need for more accurate modeling, the focus of hydro logical modeling has shifted from separate surface and ground water models to an inte grated modeling approach wherein both surface and ground water models are run simult aneously and the output of one is used as the input to the other. The critical compon ent of integrated modeling philosophy is the vadose zone which forms the vital link betwe en the surface and ground water models. Hence, it is of real importance to advance the modeling and predictive capabilities for all the vadose zone process. This dissertation focuses on data collection and c onceptualizations to enhance the understanding and modeling of vadose zone processes which ultimately impact the fluctuation of the water table. This document is d ivided into eight chapters, including this overview chapter. The majority of the text for each chapter is adapted from a corresponding journal article written on the topic. The following chapter describes a data collection effort in which continuous soil moisture data along with water table elevation data is recorded along a flow transect. The chapter which is adapted in large part from Nachabe, Shah et al. (2005) and Rahgozar, Shah et a l. (2007), talks about how the
3 collected data can be analyzed at a point scale or a along transect to determine evapotranspiration and other water budget component s. The approach helps in developing a comprehensive dataset involving time s eries, spanning approximately two and half years, of all the water budget components. This dataset can prove ideal for constructing and testing modeling considerations as demonstrated in Chapters 3, 4, 6, and 7. The third chapter, which derives its content from Shah et al. (2007a), talks about a very important problem about extinction depth and p artitioning of evapotranspiration between vadose zone and ground water. In many land scapes, vegetation extracts water from both the unsaturated and saturated zones. The partitioning of evapotranspiration ( ET ) into vadose zone ET and ground water ET is complex because it depends on land cover and subsurface characteristics. Traditionally the ground water ET fraction is assumed to decay with increasing depth to the water table, attaining a value of zero at what is termed the extinction depth. A simple assum ption of linear decay with depth is often utilized, but has never been rigorously exami ned using unsaturated-saturated flow simulations. Furthermore, it is not well understoo d how to relate extinction depths to characteristics of land cover and soil texture. Variable saturation flow theory is utilized to sim ulate ground water ET for three land covers and a range of soil properties under dr ying soil conditions. For a water table within a half a meter of the land surface, nearly a ll ET is extracted from ground water due to the close hydraulic connection between the unsat urated and saturated zones. For deeprooted vegetation, the decoupling of ground water a nd vadose zone was found to begin at water table depths between 30 and 100 cm, depending on the soil texture. The decline of
4 ET with depth to the water table is better simulated by an exponential decay function than the commonly used linear decay. A comparison with field data is consistent with the findings of this study. Tables are also provided t o vary the extinction depth for heterogeneous landscapes with different vegetation cover and soil properties. In Chapter 4, which is based on Shah and Ross (200 7), an investigation is provided concerning the variable behavior of specif ic yield ( SY) under shallow water table conditions. Traditionally, specific yield has been defined as the volume of water released per unit area from pumping of a phreatic aquifer do wn by a unit head. It is often used as a fixed value in ground water flow models. The chapte r seeks to elucidate SY variability due to natural processes of evapotranspiration and rech arge. SY variability is of fundamental importance for modeling hydrologic response from st resses and for determination of the water budget of a catchment. HYDRUS 1D Â– a numerica l model solving RichardÂ’s equation for saturated Â– unsaturated flow in one di mension was used to simulate the behavior of specific yield for a soil type represen tative of west-central Florida. It was found, that for various cases examined (e.g., ET and infiltration), the magnitude of specific yield varied with depth to the water table For infiltration response, the variation in the specific yield exhibited strong dependence o n the inter-event time. For ET stress, the specific yield first increased rapidly to attai n a maximum value and then declined steadily to ultimately become less than specific yi eld at equilibrium moisture conditions. The results indicated that assumptions of constant specific yield for different stresses can yield erroneous results especially in shallow water table environments. For deeper water tables, it was found that specific yield variation was not that pronounced and a constant
5 value of specific yield can be used as an approxima te value for simulating water table fluctuations. Chapter 5, adapted from Shah et al. (2007b), talks about use of HYDRUS-1D, to analyze evapotranspiration ( ET ) contributions from different regions of the vados e zone. This analysis was based on solving RichardÂ’s equati on for a soil column subject to ET stress and analyzing the changes in the soil water content along the column. The results of the analysis can be used in developing and valid ating integrated surface and ground water models. Fundamental to integrated modeling is the concept to allocate ET demand within the saturated and unsaturated zones. A compa rison of the approach of the Integrated Hydrologic Model (IHM) with the solution derived by the one dimensional analysis is presented. The simulation results match ed those derived from the IHM threelayer concept. The results validated three of the f our thresholds that control ET distribution demand along a soil column, as defined in IHM. The fourth threshold matched, but to lesser degree, due to the differenc e of capillary fringe definitions between the two models. Chapter 6, adapted from Shah et al. (2007c), descr ibes a dynamic model of water uptake from plants growing in naturally vegetated a reas subjected to a rainfall and evaporation time series. The model results are comp ared and contrasted with popular preexisting models. Also, the effects of the uptake pa ttern on the movement of water across multiple soil layers are also analyzed. The results showed that contrary to common modeling approaches, root water uptake is both a fu nction of root distribution and variability in water content.
6 Following the comparison of derived root water upt ake with the traditionally used models, a modeling framework based on physical root distribution and hydraulic characteristics of xylems is presented. The framewo rk using empirical data is found to provide results that closely match the observed roo t water uptake values. The results greatly increased the confidence in the framework a nd warrant a more detailed future investigation. Chapter 7, adapted from Shah et al. (2007d), talks about air entrapment which plays a significant role in controlling infiltratio n and depth to water table in shallow water table environments. The chapter describes use of fi eld data and numerical modeling, using HYDRUS-1D to quantify the variation of air pr essurization values. It was found that lateral flow of air and evapotranspiration bet ween precipitation events have significant effects on soil air pressures. The obse rvations of water table in the field data depart significantly on occasions from the theoreti cal values using a calibrated RichardÂ’s equation solution. Antecedent conditions were also found to be very important in controlling air pressurization. A simple analysis b ased on the Ideal Gas Law was also done to help understand air pressurization effects. Results indicate that there is a high sensitivity of pressure changes with small air volu me changes. Also, an assumption of uniform air pressure over the vadose zone over pred icts the pressure decline. The significant contribution of the current analysis is the adaptation of an approach which incorporates multi-event field measurements with va rying antecedent conditions. Also, observed and model predicted ET volume recovery is explored providing strong evide nce of long duration excess air pressures in shallow wa ter table environments.
7 Chapter 8 concludes the dissertation with summariz ing all the important results, their implications on the current state of vadose z one modeling, and talks about the future work needed.
8 Chapter 2: Estimation of Evapotranspiration and Wat er Budget Components Using Concurrent Soil Moisture and Water Table Monitoring 2.1 Introduction It is often useful in modeling or other hydrologic al studies to quantify components of a water budget. For upland and wetland settings, water budgets are driven principally by precipitation ( P ) and evapotranspiration ( ET) Given the magnitude of ET relative to other processes e.g., infiltration and runoff, quan tification of ET for different land cover types is critical to transient hydrologic analysis (Sumner 2006). Understanding of the contribution of ET from different sources (e.g., interception, shallo w, and deep soil) is very valuable for simulation modeling (Ross et al. 2005). Accurate measurement of ET components is, however, difficult and unreliable (N achabe et al. 2005). In humid regions such as west-central Florida, ET is estimated to be 70% of precipitation on an aver age annual basis (Bidlake et al. 1993; Knowles 1996; Su mner 2001). Despite its significance, ET is traditionally inferred from values of potential ET ( PET ) or reference ET (Doorenbos and Pruitt 1977). PET data are more readily available and can be compute d from either pan evaporation or from energy budget m ethods (e.g., Penman 1948; Thornthwaite 1948; Monteith 1965; Priestly and Tayl or 1972). The above methodologies, though simple, suffer from the fact that meteorolog ical data collected in the field for PET are mostly under non-potential conditions, renderin g ET estimates as erroneous (Brutsaert 1982; Sumner 2006).
9 Lysimeters can be used to determine ET from mass balance, however, for shallow water table environments, they are found to give er roneous readings due to air entrapment (Fayer and Hillel 1986), as well as fluctuating wat er table (Yang et al. 2000). Remote sensing techniques used in studies such as Kite and Droogers (2000) and Mo et al. (2004) are especially useful for large scale studies. Howe ver, in case of highly heterogeneous landscapes, the resolution of ET may become problematic owing to the coarse resolut ion of the data (Nachabe et al. 2005). The energy budge t or eddy correlation methodologies are also limited to computing net ET and cannot resolve ET contribution from different sources. Recently, Sumner (2006) provided a detailed review of the approximations used in the calculation of ET and based on eddy correlation measurements recomm ended values of vegetation coefficients to be used to red uce PET to ET The coefficients though simple to use in hydrologic models are more a funct ion of ambient water content and particular seasonal rainfall pattern at the time of measurement rather than actual plant tendencies. Hence, during periods of excessive rain fall they may under predict the actual ET Therefore, the use of these coefficients is prima rily restricted to areas with similar climatic pattern and water table conditions. For shallow water table environments, continuous s oil moisture measurements have been found to accurately determine ET (Nachabe et al. 2005; Fares and Alva 2000). Past studies, e.g., Robock et al. (2000), Mahmood a nd Hubbard (2003), and Nachabe et al. (2005), have clearly shown that soil moisture m onitoring can be successfully used to determine ET from a hydrologic balance. The objective of this c hapter is to describe two methodologies, one based on estimation of lateral f low, from water table fluctuations, to
10 determine daily evapotranspiration on non rainy day s at a point scale and the second methodology which involves a one dimensional transe ct model and its use in calculating evapotranspiration along with other components of w ater budget such as lateral flow, infiltration, interception capture, surface runoff and other fluxes. Specifically, the objectives of this chapter are to: (a) introduce a methodology to estimate the spatiotemporal distribution of ET as a function of fluctuating water table measureme nts, (b) develop a hydrologic model to quantify constitu ents of the water budget, and (c) study variation of hydrologic fluxes with changes in land use. The approach herein involves use of soil moisture and water table data collected at different locations along a flow path. For the f irst model, soil moisture and water table observations from individual wells were used to det ermine ET values on non rainy days while the second model is based on a set of wells a long a flow transect and attempts to comprehensively resolve other components of the wat er budget at the study site. The two approaches show that point scale soil moisture and water table observation may be sufficient to resolve evapotranspiration; however, to get a handle at other components of water budget, transect modeling is needed.
11 Figure 2.1 Location of the Study Site in Hillsborou gh County, Florida. 2.2 Materials and Methods 2.2.1 Study Site The site for this particular study was located in the sub basin of Long Flat Creek, a tributary of the Alafia River, adjacent to the Ta mpa Bay regional reservoir in Lithia, Florida. Figure 2.1 shows the regional and aerial v iew of the site location. Two sets of monitoring well transects were installed on the wes t side of Long Flat Creek. One set of wells designated as PS-39, PS-40, PS-41, PS-42, and PS-43 ran from east to west while the other set consisting of two wells was roughly p arallel to the stream (Long Flat Creek), running in the North-South direction. The wells wer e designated as USF-1 and USF-3. The topography of the area slopes towards the str eam with PS-43 being located at roughly the highest point for both transects. The v egetation varied from ungrazed Bahia grass in the upland areas (in proximity of PS-43, U SF-1, and USF-3), to alluvial wetland forest composed of slash pine/ hardwood trees near the stream. The area close to PS-42 is
12 characterized as a mixed zone. Horizontal distance between the wells is approximately 16, 22, 96, 153 m from PS-39 to PS-43, with PS-39 b eing approximately 6 m from the creek. Horizontal distance between USF-1 and USF-3 was 33 m. All wells were surveyed and land surface elevations were determined with re spect to National Geodetic Vertical Datum 1927 (NGVD). Extensive soil investigations were performed on th e soil cores taken from the study site. The soil in the study area is primarily Myakka fine sand (of marine origins) with high permeability (10-1 to 10 m/d) in the surface and subsurface layers (C arlisle et al. 1989). Figure 2.2(a and b) shows sample soil st ratiagraphy obtained from two cores taken from the study site close to wells PS-39 and PS-43. The results of soil sampling at a number of locations along the East-West as well as North-South transect showed that the soil was primarily sand with the presence of a clay layer at a depth, that varied from 4m below land surface in the upland regions to about 2 .5 m below land surface near the stream region. Detailed information on soil and sit e characteristics can be found in Thompson (2003) and Trout and Ross (2005). Apart fr om the study specific tests, information about extent of the confining clay laye r, hydraulic conductivity values of the confinement, head differences between surficial and intermediate aquifer, were obtained from the geotechnical and site characterization rep ort (HDR and Tampa Bay Water 1999) prepared as a part of the construction of Tampa Bay regional reservoir. The report indicates (Refer to volume 1 section 3) that thickn ess of the clay layer averages around 35 m with average head differences between the surfi cial and intermediate aquifer being
13 LS(m)0.62.6 2.03.34.0 1.3 Sand; fine tomedium Sand; fine tomedium,yellowish greyto greyish slightly silty Clay; banded, slightly sandy Clay; slightlysandy (a) LS(m) 0.62.6 2.03.3 4.0 1.3 Organic matter,some silt and sand Sand; fine tomedium, slightlysilty Clay; sandy, lightolive gray, silty Sand;medium fine,silty, some organics Sand; fine tomedium Sand; fine tomedium, light olivegray, silty (b) Figure 2.2 Soil Stratiagraphy of Cores Taken from L ocations Adjacent to (a) PS-39 and (b) PS-43. Notice that Soil at Both Locations is Pr imarily Sandy Bounded by a Clay Layer.
14 approximately 6 m. The hydraulic conductivity value s Â– as determined by slug test and deep aquifer performance test Â– for the confining c lay layer varied from 10-4 m/day to 10-5 m/day. The lower confining layer can hence be assu med as an impermeable layer. Data collection for the study was done from January 2002 through June 2004. 2.2.2 Instrumentation All transect wells housed Instrumentation Northwes t (Kirkland, WA) 0-34 kPa (05 psi) submersible pressure transducers, accurate t o 0.034 kPa (0.005 psi). Adjacent to each well, an EnviroSMART soil moisture probe (Sentek Pty. Ltd., Adelaide, A ustralia) carrying eight sensors was installed (see Figure 2. 3). The soil moisture sensors allowed measurement of moisture content along a vertical pr ofile at different depths from land surface. The sensors were deployed at 10, 20, 30, 5 0, 70, 90, 110, and 150 cm from the land surface. The sensors work on the principle of frequency domain reflectometery (FDR) to convert electrical capacitance shift to vo lumetric water content ranging from oven dryness to saturation with a resolution of 0.1 % (Buss 1993). Default factory calibration equations were used for calibrating the se sensors. Fares and Alva (2000) and Morgan et al. (1999) found no significant differenc e in the values of observed recorded water content from the sensors when compared with t he manually measured values. In addition to pressure transducers and soil moistu re probes, stream gages were placed at three locations in the adjacent perennial creek (Lo ng Flat Creek). Two tipping bucket and two manual rain gages were also installed to record the amount of precipitation.
15 M 0.20.40.60.81.01.21.6 1.42.2 1.82.02.4 20 cm 10 cm30 cm90 cm 50 cm70 cm150 cm 110 cmSensor Locations Figure 2.3 Soil Moisture Probe on the Left Showing the Mounted Sensors Along with Schematics on the Right. All equipments were installed according to Nationa l Weather Service or USGS standards where applicable. The data were collected on a 5 minute interval (instantaneous) and were averaged to hourly values.
16 In case of missing water table elevation data from a particular location, interpolation of water table heads from the adjacen t station was used to complete the record. For soil moisture data, however, no attempt was made to simulate the missing data. Instead, a different methodology, relying on water table observations and a variable specific yield calculation, calibrated for the site based on the results of Said et al. (2005), was used to derive storage changes. Data gaps were, however, infrequent and comprised less than 5% of the data record. During the entire study period the water table was found to fluctuate between land surface and a maximum dep th of about 140 cm for all of the well locations. 2.2.3 Point Scale Modeling of Evapotranspiration At any given well location, variation in total soi l moisture on non-rainy days can be due to (a) subsurface flow from or to the one di mensional soil column (0Â–155 cm below land surface) over which soil moisture is mea sured and (b) evapotranspiration from this soil column. Mathematically it can be exp ressed as ET Q t TSM = (2.1) where t is time (h), Q is subsurface flow rate (m/h), and ET is evapotranspiration rate (m/h). TSM is total soil moisture, determined as below =Vqdz TSM (2.2) where [L3L-3] is the measured water content, z [L] is the depth below land surface [L] is the depth of monitored soil column (155 cm).
17 The negative sign in front of ET in Equation 2.1 indicates that ET depletes the TSM in the column. The subsurface flow rate can be ei ther positive or negative. In a ground water discharge area, the subsurface flow ra te, Q is positive because it acts to replenish the TSM in the soil column (Freeze and Cherry 1979). Obvio usly, this flow rate is negative in a ground water recharge area. Figure 2.4 illustrates the role of subsurface flow in replenishing or depleting total soil moistu re in the column. To estimate both ET and Q in Equation 2.1, it was important to decouple these fluxes. In this model the subsurface flow rate was estimated from the diurnal fluctuation in TSM Assuming ET is effectively zero between midnight and 0400h, Q can be easily calculated from Equation 2.3 using: 4 TSM TSM Qmidnight h 0400= (2.3) where TSM0400h and TSMmidnight are total soil moisture measured at 0400 h and midnight, respectively. The denominator in Equation 2.3 is 4h, corresponding to the time difference between the two TSM measurements. The as sumption of negligible ET between midnight and 0400h is not new, but was adop ted in the early works of White (1932) and Meyboom (1967) in analyzing diurnal wate r table fluctuations. It is a reasonable assumption to make at night when sunligh t is absent.
18 Figure 2.4 Total Soil Moisture is Estimated in Two Soil Columns. The First is in a Ground Water Recharge Area (Pasture), and the Secon d is in a Ground Water Discharge Area (Forested). In the Ground Water Discharge Area Subsurface Flow Acts to Replenish the Total Soil Moisture. Taking Q as constant for a 24h period (White 1932; Meyboom 1967), the ET consumption in any single day was calculated from t he following equation Q 24 TSM TSM ET1 j j + = + (2.4) where TSMj is the total soil moisture at midnight on day j and TSM j+1 is the total soil moisture 24h later (midnight the following day). Q is multiplied by 24 as the Equation 2.4 provides daily ET values. Figure 2.5(a and b) show a sample observat ions for 5 day period showing the evolution of TSM in a ground water discharge and recharge area respectively. Also marked on the graphs are differe nt quantities calculated to determine ET from the observations. Equation 2.1 applies for dry periods only, because it does not account for the contribution of interception storage to ET on rainy days. Also, the changes in soil moisture on rainy days can occur due to other proce sses like infiltration, upstream runoff
19 infiltration (as will be discussed later), etc. The results obtained from the above model were averaged based on the land cover of each well and are presented as ET values for grass or forested land cover. The values for the gr assed land cover were also compared against ET values derived from pan evaporation measurements. The model results, as well as comparison graphs are discussed in the resu lts section. 2.2.4 One Dimensional Transect Model In an attempt to comprehensively determine other c omponents of water budget for both rainy or non rainy days two separate transect models were developed, one for wells PS-39 to PS-43 and one for wells USF-1 to USF-3. T he first model was setup with five grid cells, with the location of the observation we lls being the center of each of the grid cells and the observed values representative of the whole grid. TransectÂ’s upland flow divide comprised one boundary (no flow) and the str eam with variable stage comprised the other (stage boundary). The second model, howev er, had just two cells with USF-1 and USF-3 representing the two internal storage mea surements. Flows at each internal cell boundary were derived from nodal (cell centere d) observed records and a simple Darcian flow calculation. Figure 2.6 shows the tran sect model for wells PS-39 to PS-43 with details about land surface elevation, distance s between the wells, etc. For both the models, the upper boundary was the la nd surface and the lower boundary was conceptualized as a no-flow boundary c ondition, quite appropriate for the surficial aquifer at the site (Trout and Ross 2005; HDR and Tampa Bay Water 1999). The
20 Figure 2.5 Total Soil Moisture versus Time in the ( a) Ground Water Discharge Area and (b) Ground Water Recharge Area. The Subsurface Flux is the Positive Slope of the Line between Midnight and 4 AM. (a) (b) Total soil moisture (m)
21 flow thickness was determined by the depth to the w ater table and the local depth to the underlying clay confinement. The flow occurring alo ng the transect was assumed to be uniform (non-convergent) across the width of the mo del. For each grid cell the equivalent hydraulic conduc tivity obtained from the laboratory measurements (refer to section 188.8.131.52) was used in the application of the mass balance equations. The following paragraphs summari ze the basis of the one dimensional transect model used to derive ET Table 2.1 lists the notation with description and dimensions of each of the symbols used. Figure 2.6 One Dimensional Transect Model for Well Transect PS-39 to PS-43 (Not to Scale).
22 Table 2.1 Notations Used in the 1D Transect Model A long with Description and Units of Each Symbol. Notation Description Units P Precipitation [LT-1] dwt Depth to the water table [L] ET Evapotranspiration [LT-1] I Infiltration [LT-1] IS Daily soil infiltration [L3L-2]* SMET Evapotranspiration from soil moisture [LT-1] q Specific lateral discharge [L3L-1T-1] S Water storage in the soil column per unit width [L3L-1] Water content [L3L-3] Xi Lateral dimension of ith grid cell [L] K Hydraulic conductivity [LT-1] i Effective flow thickness in the ith grid cell [L] PE Effective rainfall [L3L-2]* IC Interception capture [L3L-2]* URI Upstream runoff infiltration [L3L-2]* DS ET Evapotranspiration from depression storage [L3L-2]* TET Total evapotranspiration [L3L-2]* TRE Total rainfall excess [L3L-2]* NR Net runoff [L3L-2]* HR Hortonian runoff [L3L-2]* SER Saturation excess runoff [L3L-2]* SI Soil infiltration [LT-1] *Accumulated on daily time step
23 The water budget equation for the model can be wri tten as: [SI Â–SMET]X = S/t+ q (2.5) where SI [L3L-2T-1] represents soil infiltration, SMET [L3L-2T-1] is soil moisture evapotranspiration from the soil column, X is the lateral dimension of a grid cell (see Figure 2.6) q [L3L-2T-1] is net lateral flow from the adjoining cell(s), S is change in total storage of water in the grid cell [L3L-1] per unit width, and t [T] represents the time step (one hour). As the maximum depth to the water table ( dWT) was 140 cm, changes in the water storage in any grid cell can be effectively inferre d by integrating the observed soil moisture through the soil profile (0-155 cm), and s ubtracting the consecutive storage values in time. The trapezoidal rule of numerical i ntegration was used to calculate the total soil moisture from the observed values from t he sensors. Mathematically, the changes in storage per unit width at any timeÂ‘ t + tÂ’ from timeÂ‘ t Â’ for a given grid cell Â‘ i Â’ of lateral dimension Xi [L] can be computed as i 0 0 iX dz)t,z( dz)t t,z( )t t(SD l q l D q D D + = + (2.6) where [L] is a fixed depth of soil which for all the wel ls was 155 cm. From recorded values of dWT and known land surface elevations, water table hea d, hi (at any cell Â‘iÂ’ ), with respect to NGVD can be computed. Hence, usi ng DarcyÂ’s Law with computed values of equivalent hydraulic conduc tivity, iK [LT-1], for a given grid cell Â‘iÂ’, flow from cell Â‘i-1Â’ to cell Â‘iÂ’ ,1 iq-at any time Â‘tÂ’, can be computed as : n r =i t 1 i t i i i 1 ih h K qDC t (2.7)
24 where it[L]is the effective flow thickness for the cell, wh ich is the difference between the water table elevation and the elevation of the confining clay layer at each time step. Other symbols are as previously defined. By simply changing the parameters, flow from cell i to cell i+1, iq can be similarly computed. For the fifth cell (PS39), however, the stream stage was used as the head value to compute the lateral flow going into or coming from the stream.Net lateral flow into cell Â‘iÂ’ can thus be calculated as in Equation 2.8. t i t 1 i t iq q q =-D (2.8) In a given time step (hourly), depending on the al gebraic sum of terms on the right hand side of Equation 2.5, either soil infilt ration or soil evapotranspiration is assumed to be occurring. An inherent assumption mad e here is that, during the small time interval (hourly) of the analysis, either soil surf ace evaporation or infiltration can take place. SMET is representative of direct soil evaporation and/or plant transpiration from the soil column. SMET values from soil moisture change, for each cell, ar e summed up over a 24 hour period (midnight to midnight) to get an estimate of daily soil moisture ET (SMET) from that grid cell. To determine total ET (TET), depression storage ET (DS ET,) and interception ET (IC ET) (explained in sections 184.108.40.206 and 220.127.116.11 respec tively) are also added to daily SMET. On the other hand, the soil infiltration values w ere associated directly with precipitation and/or upstream runoff infiltration (refer to section 18.104.22.168). Like the SMET, values soil infiltration, were further aggregated over 24 hours to determine net Infiltration (IS), which is used to find other water budget compone nts such as total rainfall excess, runoff, etc. (refer to se ction 2.2.5)
25 22.214.171.124 Estimation of Hydraulic Conductivity To get a good idea about the soil conditions at th e study site several undisturbed soil samples, using a hydraulic coring machine (Geo Probe), were obtained. The samples were then analyzed to determine the stratiagraphy. The section of soil cores corresponding to each stratum were then cut and wet ted for two days to saturate them completely. Falling head permeameter analysis was d one to determine the saturated hydraulic conductivity (K) of the samples. For spec ific details about permeameter tests and other soil analyses please refer to Thompson (2 003). Table 2.2 shows the depths and corresponding values of hydraulic conductivity valu es obtained for samples close to different well locations. Each soil strata was assu med to be isotropic and hence within a given strata of soil, vertical hydraulic conductivi ty will be same as the horizontal hydraulic conductivity. Using this assumption equiv alent horizontal saturated hydraulic conductivity can be determined using the thickness weighted average of individual hydraulic conductivity values (Equation 2.9) = dz dz K Ki (2.9) where dz is the depth of each strata, Ki is the corresponding values of saturated hydraulic conductivity and K as defined above, is the equivalent hydraulic cond uctivity. At any time step depending on the depth to the water table the zone of saturation is determined and, based on the saturated soil layers, the equiva lent value of hydraulic conductivity is calculated for each time step. Apart from the permeameter test, in situ slug test s were done to estimate the general hydraulic conductivity of the surficial aqu ifer. The results of the slug tests were
26 analyzed using the Bower-Rice as well as the Hvorsl ev methods. The results indicated the horizontal hydraulic conductivity of the aquifer va ried between around 0.5 m/day to 0.1 m/day which is within 10-15% of the laboratory obta ined values. For further details about the results please refer to Thompson (2003). Table 2.2 Values of Hydraulic Conductivity Obtained from Permeameter Analysis Done on Soil Core Samples Taken at Different Depths Belo w Land Surface [Adapted from Thompson (2003)]. Location (Closest Well) Mean Depth Below LS (m) Hydraulic Conductivity (m/day) 0.76 1.33 1.11 0.084 USF-1 1.675 2.72E-04 0.61 0.44 1.11 0.08 1.98 2.20E-04 USF-3 2.27 1.67E-04 0.45 5.60E-02 1.675 3.30E-01 2.89 4.10E-01 PS-43 3.5 3.79E-04 0.45 1.23E+00 0.99 3.50E-01 1.145 4.20E-02 PS-42 2.34 3.30E-02 0.54 2.00E-01 1.15 1.27E-03 PS-41 2.36 1.05E-04 0.125 1.03 0.3 0.64 2.89 4.74E-04 PS-39/PS-40 3.12 1.40E-04
27 2.2.5 Estimation of Lateral and Vertical Fluxes The one dimensional transect model was run on hour ly time steps to calculate the lateral flow, soil infiltration and soil moisture ET. Soil moisture evapotranspiration and infiltration were then aggregated over 24 hours to determine the values of daily SMET and daily soil infiltration (IS). Using these aggregated daily values and the proc edure described in the following subsections, other water budget components were calculated on a daily time step. 126.96.36.199 Interception Capture (IC) Interception capture is the initial extraction fro m a rainfall event. If there is no runoff accompanied with of a given rainfall event, than, theoretically, it can be estimated by subtracting the observed rainfall from the obser ved infiltration. In absence of any direct measurement of runoff, in terception capture can be estimated by selecting isolated events with intensi ty less than the hydraulic conductivity of the surface soil layers, occurring after dry ant ecedent conditions (deep water table conditions); for such events, runoff can be assumed to be negligible. For this particular study, for a particular land cover, individual rain fall events, which satisfied the above mentioned criteria, were manually selected and were plotted against the observed soil infiltration during the time the event lasted. Assu ming that the interception capture is same for all the events for a given land cover the intercept of the best fit line on the precipitation versus infiltration curve will give t he value of the interception capture (IC). To avoid any bias arising out of small precipitatio n events (smaller than interception
28 capture), all the precipitation events for which no soil infiltration was observed were ignored during the linear regression to get equatio n of the best fit line. 188.8.131.52 Effective Precipitation (PE) On a daily time step effective precipitation (PE) is defined as the difference between the cumulative precipitation (from midnight to midnight) and the interception capture C hrs 24 EI P P = (2.10) where, P [LT-1] is the recorded precipitation, and IC [L] is the interception capture. 184.108.40.206 Upstream Runoff Infiltration (URI) For any well location if daily soil infiltration (IS) is greater than the effective precipitation (PE), the difference between the two is assumed to cor respond to upstream runoff infiltration (URI). Mathematically, it can be written as > = Otherwise 0 P I if P I URIE S E S (2.11) 220.127.116.11 Infiltration (I) Daily infiltration (I) is defined as the difference between daily soil i nfiltration and upstream runoff infiltration. The value indicates h ow much of the water from the rainfall actually went in to the ground and is useful when q uantifying runoff. I = IS Â– URI (2.12)
29 18.104.22.168 Depression Storage ET (DS ET) It is known that when the water table is close to the land surface, such that the capillary fringe (zone of tension saturation) start s intersecting the land surface (i.e. dWT < capillary fringe), the evapotranspiration occurs at potential (Shah et al. 2007). Hence, to calculate the depression storage ET under these conditions, potential ET values needs to be estimated. Subtracting interception capture and daily SMET from the potential ET will hence result in DS ET. To estimate the potential ET several methods can be used. For this particular study, the Jensen and Haise (1963) method was used to estimate PET. The equation (Equation 2.13) used is n r + =) 08.0 ) 025 .0 (( 2450 &ave S H JT R ETP (2.13) The input parameters to get hourly values of ETPJ&H are solar radiation (RS) (kJ/m2/hr) and average temperature (Tave) (C). The hourly values were accumulated over one day to get daily ETPJ&H. At the site, USGS standard class A pan and a wea ther station measuring solar radiation, temperature and relative humidity were installed and monitored. The site measured data was further suppl emented with National Weather Service (NWS) Ona station [NWS station # 086539-4] record. A constant pan factor of 0.7 was used to reduce the ETPJ&H values to potential ET values appropriate for the study site (Ross et al. 2005). During these brief, shallo w water table periods, the sum of interception capture and soil moisture ET were than subtracted from the calculated potential ET to estimate the depression storage ET.
30 From a field study, Said et al. (2005) found that, on average, the capillary fringe value for the soils in the study area (for all land covers) was uniform and approximately 0.3 m. Therefore, the depth to the water table thre shold for assumption of evapotranspiration being at potential was set for a ll times when daily average depth to the water table 0.3 m. Mathematically, for depth to the water tabl e less than 0.3 m, DS ET can be calculated by DS ET = PET Â– IC Â– daily SMET (2.14) 22.214.171.124 Total ET (TET) Total ET (TET) was determined on a daily basis by summing up the value of daily SMET, DS ET and the interception capture (Ic). The underlying assumption being that all the interception capture evaporates within one day, considered reasonable for the subtropical west-central Florida conditions at the stu dy site (Nachabe et al. 2005). 126.96.36.199 Total Rainfall Excess (TRE) Total rainfall excess (TRE) is defined as the amount of effective precipitati on that is not reflected as infiltration. Mathematically, f or any time step, TRE can be computed as TRE = PE Â– I (2.15) 188.8.131.52 Saturation Excess Runoff (SER), Hortonian Runoff (HR), and Net Runoff (NR) As mentioned previously in section 184.108.40.206, the ca pillary fringe depth for the study site was found to be 0.3 m. Therefore, if the dWT is less than this value, then all of
31 the rainfall excess is assumed to be contributing t o Saturation Excess Runoff (SER). TRE is otherwise assumed to be associated with Hortonia n Runoff (HR). Mathematically, > Â£ = m 3.0 d if HR m 3.0 d if SER TREWT WT (2.16) On a daily basis, total rainfall excess goes into filling up surface depressions as well as part of it runs off downstream. Hence the a mount of rainfall excess that runs off from a particular well (Net Runoff NR), and infiltr ates downstream (as URI for a downstream well) and/or flows into the stream can b e quantified using Equation 2.19. If total rainfall excess was found to be smaller than DS ET, than NR was assumed to be zero NR = TREDS ET ( 2.17) The results presented in this paper were then aver aged to obtain quarterly values, i.e., four values per year. In the results and disc ussion section, the winter quarter represents the months of January to March, spring r epresents April through June, the summer quarter goes from July through September and fall ranges from October to December. On a quarterly basis, to check the perfor mance of the model, mass balance was done on quarterly values of all the water budge t components. Figure 2.7 shows a flow chart which shows the whol e process of calculation of different components of the water budget.
32 q )t / S ( D DD D D DD D D DD D + ++ + q )t / S ( D DD D D DD D D DD D + ++ + q )t / S ( D DD D D DD D D DD D + ++ + hrs 24SI q D DD D S D DD D Figure 2.7 Process Flow Diagram Showing the Sequenc e of Calculation of the Water Budget Components. Th e Gray Boxes Show the Computed Components. The Area Marked Out by the Dashed Line Represent the One Dimensional Transect Model Running on Hourly Time Step. 32
33 2.2.6 Assumptions Before discussing the results obtained from the an alysis it is very important to categorically define the important assumptions in t he methodology. This will help the reader in deciding which of the assumptions hold tr ue as well as which assumptions have to be adapted for successful extension of the abov e methodology at a site different that the study area for this paper. (a) For any given small time step (hourly), it was assumed that there was either net infiltration into or a net evapotranspiration o ut of soil grid cell. (b) The interception capture values for the land c over adjacent to a given well were assumed to be constant for all the quarters. (c) On a daily basis, interception capture is the initial extraction from total rainfall which is bounded by an upper limit controlled by th e vegetation. (d) On a daily basis interception capture is assum ed to be totally evaporated before the start of the next day. (e) Owing to the low value of permeability of the confining clay layer leakage to intermediate aquifer was neglected. 2.3 Results and Discussion An important aspect to be considered for the succe ss of this framework is the time scale of variation of the soil moisture storage wit h respect to external stresses. Figure 2.8(a) to (d) shows the response of the soil moistu re storage to different external factors; water table fluctuations, rainfall, and solar radia tion. The figures show that soil moisture changes are very responsive (time scale of minutes) to imposed stresses. Also, integrated
34 storage changes accumulated over time are very cons istent with observed rainfall fluxes. Figure 2.8(b) shows that even at sub-hour time step s, changes in the solar radiation (due to passing clouds, etc.) caused variations in the s oil moisture storage (root water uptake). Figures 2.8(c) and (d) show the contrasting diurnal fluctuations of the soil moisture changes along with the water table for two location s, one in a forested area (PS-41) and the other in a grassed area (PS-43). Finally, Figur e 2.8(a) shows the intuitive, yet important process of soil moisture increase due to rainfall and decrease in its absence. It is noted that, repeatedly, the magnitude of integra ted soil moisture change is consistent with the observed rainfall totals (minus intercepti on capture). Overall, Figures 2.8(a) to 2.8(d) conclusively show that the soil moisture mea surements can be used as an effective indicator (with high reliability) of soil moisture changes at the time scale of hours. Thus, a high degree of confidence in the use of soil mois ture observations for deriving soil moisture fluxes can be expected.
35 Figure 2.8 Variation of Soil Moisture Storage Due t o Different Stresses. (a) Rainfall, (b) Solar Radiation, (c) Water Table for PS-41, and (d) Water Table for PS-43. Change in storage (cm) x 10 3 Solar radiation (100 W/m 2 ) Soil moisture storage (cm) Cumulative rainfall (cm) (b) (a)
36 Figure 2.8 (Continued) Soil moisture storage (cm) Water table elevation (m) above NGVD (c) (d)
37 2.3.1 Point Scale Model The results of the point scale model are shown in Figure 2.9 with graph showing the monthly variability in the values of ET for a period of about a year and half. It can be seen from Figure 2.9 that the method was successful in capturing spatial variability in the ET rates based on the changes in the land cover, as t he ET rate of forested land cover was found to be always higher than that of the grasslan d. In addition to spatial variability, the method seemed to capture well the temporal variabil ity in ET. The temporal variability for this particular analysis existed at two time sc ales, a short-scale daily variation associated with daily changes in atmospheric condit ions (e.g., local cloud cover, wind speed, etc.) and a long term, seasonal, climatic va riation. The short-scale variation tends to be less systematic and is demonstrated in Figure 2.9 by the range marks. The seasonal variation is more systematic and pronounced and is clearly captured by the method. Table 2.3 Pan Coefficients Used to Obtain Pasture E vapotranspiration for Different Months. Month Coefficient January 0.4 February 0.45 March 0.55 April 0.64 May 0.7 June 0.7 July 0.7 August 0.7 September 0.7 October 0.6 November 0.5 December 0.5
38 Figure 2.9 Monthly Average of Evapotranspiration ( ET ) Daily Values in Forested (Diamonds) and Pasture ( Triangles) Areas. The Gap in the Graph Represents a Period of Missing Dat a. Standard Deviations of Daily Values are also Sho wn in the Range Limits. ET (mm/day) 38
39 220.127.116.11 Comparison with Pan Evaporation To assess the robustness of the model, the estimat ed ET values for pasture were compared with ET estimated from the evaporation pan. The measured p an evaporation was multiplied by a pan coefficient for pasture to estimate ET for this vegetation cover. A monthly variable crop coefficient was adopted (Door enbos and Pruitt, 1977) to account for changes associated with seasonal plant phenolog y (see Table 2.3). The consumptive water use or the crop evapotranspiration is calcula ted as: ETC = EP KC (2.18) where EP is the measured pan evaporation, KC is a pan coefficient for pastureland, and ETC is the estimated evapotranspiration (mm/d) by the pan evaporation method. Figure 2.10 compares the ET estimated by both the evaporation pan and moisture sensors for pasture. Although the two methods are fundamentally different, on ave rage, estimated ET agreed well with an r2 coefficient of 0.78. This supported the validity o f the soil moisture methodology, which further captured the daily varia bility of ET ranging from a low of 0.3 mm/d to a maximum of 4.9 mm/d. The differences betw een the two methods can be attributed to fundamental discrepancies that should be obvious. The pan results are based on atmospheric potential with crude average monthly coefficients while the TSM approach inherently incorporates plant physiology a nd actual moisture limitations. Indeed, both methods suffer from limitations. The p an coefficient is generic and does not account for regional variation in vegetation phenol ogy or other local influences such as soil texture and fertility. Similarly, the accuracy of the soil moisture method proposed in this study depends on the number of sensors used in monitoring total moisture in the soil column.
40 Figure 2.10 Evapotranspiration Estimates for Pastur e by the Pan and Point Scale Model. Data Points Represent the Daily Values of ET from both Techniques. 2.3.2 One Dimensional Transect Model Water budget components, calculated from the one d imensional transect model using soil moisture and water table observations in 2002 Â– 2004 revealed that almost all components display a consistent seasonal behavior. Quarterly averaged observed fluctuations in SMET (soil moisture ET), DS ET (depression storage ET), TET (Total ET), I (infiltration), TRE (Total rainfall excess), SER (Saturation excess runoff), and the dWT (depth to the water table) are shown in Figures 2.1 1 to 2.18. Figure 2.19(a) and (b) shows sample plots of preci pitation versus infiltration for two of the wells (PS-43 and PS-41 respectively) alo ng with the equation of the best fit ET (mm/day) [TSM Method] ET (mm/day) [Pan Method]
41 line. The intercept obtained from the best fit line was used for the determination of interception capture. The average value of daily ma ximum interception capture from the y-intercept was found to be 1.3 mm for grassland an d 2.5 mm for the flat-woods forested land cover. The values of interception capture foun d using the described methodology is consistent with literature values (e.g., Viesman an d Lewis 2002, pg. 132). From the annual water budget tables (Table 2.4-2.7) the annu al value of interception capture varied from 106 to 221 mm.
42 Figure 2.11 Variation in Total ET for Grass and Forest Land Covers. Figure 2.12 Variation in ET Derived from Soil Moisture Changes for Grass and F orest Land Covers. Total ET (mm) Rainfall (mm) Soil moisture derived ET (mm)
43 Figure 2.13 Variation of Depression Storage ET for Grass and Forest Land Covers. Figure 2.14 Variation of Infiltration for Grass and Forest Land Covers. Depression storage ET (mm) Infiltration (mm)
44 Figure 2.15 Rainfall Excess for Grass and Forest La nd Covers. Figure 2.16 Saturation Excess Runoff Variation for Grass and Forest Land Covers. Rainfall excess (mm) Rainfall (mm) Saturation excess runoff (mm)
45 Figure 2.17 Net Runoff for Grass and Forest Land Co vers. Figure 2.18 Variation in Depth to the Water Table f or Grass and Forest Land Covers. Net runoff (mm) Depth to water table (cm)
46 Figure 2.19 Precipitation versus Infiltration for ( a) Grassed Land Cover and (b) Forested Land Cover. The Equation Shown is the Equation of the Best Fit Line. Comparison of quarterly values of water budget com ponents for different years shows some interesting behavior. Derived ET components vary in a similar manner in corresponding quarters. Infiltration and runoff com ponents, on the other hand, varied significantly depending on available precipitation and quarterly ET. For instance, rainfall Precipitation (mm) Infiltration (mm) (a) (b)
47 magnitude in summer 2002 was about 200 mm more than that observed during summer 2003 (see Figure 2.11). However, the corresponding ET magnitudes for both grassland and forest cover stayed pretty much the same. This shows that under normal or wet conditions ET is strictly a function of ambient atmospheric cond itions, while runoff is directly proportional to both the amount of precipi tation occurring during a particular quarter and the magnitude of the ET in that period. This conclusion holds significance for predictive modeling, wherein models of runoff behav ior must be expected to reproduce strong seasonally varying ET behavior to insure predictive capability. Annual observed water budget components in the two land cover environments in 2002, 2003 and 2004 are summarized in Tables 2.4, 2 .5, and 2.6 respectively. A clear trend in seasonal and annual behavior of the water budget components is observed for the upland versus near stream region. The upland grassl and, with corresponding lower ET, exhibits higher runoff annually than the down-slope forested land cover. This result is supported by the shallower dWT exhibited by the grassed upland (Figure 2.18).
48 Table 2.4 Total Annual Water Budget for 2002 (a) ET, Runoff, and (b) Other Water Budget Components. (a) Total Annual Water Budget 2002 Land Use Wells Rain (mm) ET (mm) Runoff (mm) ID P Ic SMET DS ET TET TRE SER HR URI NR Grass USF-3 1914 147 514 344 1005 1231 1113 118 282 888 Grass USF-1 1914 147 516 287 950 1143 1111 32 235 856 Grass PS-43 1914 147 521 195 863 1235 1050 185 220 1040 Mixed PS-42 1914 121 746 145 1012 1034 908 126 303 889 Forest PS-41 1914 221 690 171 1082 1055 904 151 300 884 Forest PS-40 1914 197 877 8 1082 816 383 433 396 808 Forest PS-39 1914 197 882 17 1096 819 404 415 399 802 (b) Total Annual Water Budget 2002 (Contd.) Land Use Wells Lateral Flow Infiltration Depth to Water Table Change in Storage Mass Balance Error (mm) (mm) (cm) (mm) (mm) ID q I dWT S e Grass USF-3 0* 536 45 212 0 Grass USF-1 0* 624 41 223 0 Grass PS-43 23 532 71 247 45 Mixed PS-42 13 759 77 307 -20 Forest PS-41 14 638 70 237 2 Forest PS-40 9 900 109 374 -9 Forest PS-39 -2 898 93 374 -18 Insignificant
49 Table 2.5 Total Annual Water Budget for 2003 (a) ET, Runoff, and (b) Other Water Budget Components. (a) Total Annual Water Budget 2003 Land Use Wells Rain (mm) ET (mm) Runoff (mm) ID P Ic SMET DS ET TET TRE SER HR URI NR Grass USF-3 1350 128 411 314 853 862 790 72 64 547 Grass USF-1 1350 128 458 374 960 799 782 17 167 426 Grass PS-43 1350 128 550 228 906 801 759 42 69 573 Mixed PS-42 1350 106 896 91 1093 604 533 71 190 513 Forest PS-41 1350 192 784 162 1138 592 531 61 104 430 Forest PS-40 1350 171 1042 9 1222 437 219 218 153 428 Forest PS-39 1350 171 1016 13 1200 436 250 186 159 423 (b) Total Annual Water Budget 2003 (Contd.) Land Use Wells Lateral Flow Infiltration Depth to Water Table Change in Storage Mass Balance Error (mm) (mm) (cm) (mm) (mm) ID q I dWT S e Grass USF-3 0* 361 35 -6 1 Grass USF-1 0* 423 26 65 0 Grass PS-43 26 421 48 -75 55 Mixed PS-42 14 640 62 -106 -16 Forest PS-41 19 565 56 -141 14 Forest PS-40 -11 741 107 -174 -59 Forest PS-39 -5 742 85 -175 13 Insignificant
50 Table 2.6 Semi-Annual Water Budget for 2004 (a) ET, Runoff, and (b) Other Water Budget Components. (a) SemiAnnual Water Budget 2004 Land Use Wells Rain (mm) ET (mm) Runoff (mm) ID P Ic SMET DS ET TET TRE SER HR URI NR Grass USF-3 502 42 382 127 551 182 129 53 86 55 Grass USF-1 502 42 388 124 554 142 49 93 126 18 Grass PS-43 502 42 384 25 451 112 71 41 134 87 Mixed PS-42 502 34 499 27 560 98 51 47 162 71 Forest PS-41 502 62 437 28 527 93 34 59 133 64 Forest PS-40 502 56 538 0 594 35 0 35 176 35 Forest PS-39 502 56 525 0 581 35 1 34 177 34 (b) SemiAnnual Water Budget 2004 (Contd.) Land Use Wells Lateral Flow Infiltration Depth to Water Table Change in Storage Mass Balance Error (mm) (mm) (cm) (mm) (mm) ID q I dWT S e Grass USF-3 0* 278 46 195 0 Grass USF-1 0* 319 45 58 0 Grass PS-43 10 348 84 135 20 Mixed PS-42 7 370 82 20 -7 Forest PS-41 7 347 87 42 0 Forest PS-40 -4 412 132 5 -21 Forest PS-39 -3 412 111 6 3 *Insignificant
51 Various components of ET also revealed variability corresponding to land us e regime. During dry periods, a relatively uniform ma gnitude of total ET (TET) is observed across the transect wells for each land cover. The highest magnitude of TET was observed in the spring, followed by summer periods regardless of the land use covers. DS ET magnitude was considerably higher for the upland a rea (exhibiting shallower dWT) than near the stream region. This behavior was most pronounced in the summer (wet season) across transect wells and can be attributed to shallower dWT in corresponding periods. Concerning results obtained from the current analy sis, it can be stated that evapotranspiration, to a significant degree, contro ls all the subsurface fluxes. Forest land cover has higher consumptive use of water resulting in lower elevation of the water table, as compared to the water table in the upland region This condition, supported by the observed values, causes the initiation of lateral f lux, whose magnitude is governed by the head difference between the upland and wetland (nea r stream) water table. At the same time, due to deep water table and dryer conditions in the vadose zone, the infiltration value is higher for forested land cover, thereby de creasing the total rainfall excess and runoff. Also, interesting observations can be made concern ing the diurnal behavior. In the night, as ET subsides, the lateral (and small vertical upward) flow is still observed and tends to partially replenish the water table as wel l as the vadose zone. Interestingly, from Figure 2.8(c) and (d) it can be seen that during th e night time the water table elevation in the well in the forested area (PS-41) rises, while in PS-43 (grassed upland section) the water table, due to lateral flux out of the column, still shows decline. This observation is
52 typical of the observation between the recharge and discharge regions (as previously noted by Nachabe et al. 2005; Trout and Ross 2005; Freeze and Cherry 1979). The values of ET obtained from the current study are consistent wit h the numbers found by other studies, also done in Florida, inclu ding Sumner (2006), Sumner (2001), Bidlake et al. (1993), and Knowles (1996), for land covers similar to the ones present at the study site. On an average, ET was found to vary between 60-70% of the long term average precipitation occurring in the area. Howeve r, as pointed out earlier, for higher than normal precipitation, the ET rates do not necessarily increase, hence, for years that are wetter than normal, the percentage of ET can be substantially lower. In the current study, 2002 was an abnormally wet year with annual recorded precipitation of about 2000 mm as compared to average annual values of 1300-150 0 mm. This resulted in the percentage fraction of ET dropping from 70% to about 50%. However the absolu te magnitude of ET was very consistent. The consistency of the results across different ye ars coupled with similarities to previous studies validates the current methodology. The small mass balance errors as can be seen from the water budget table (Table 2.4-2.6) can be attributed to error in the measurements as well as assumption of impermeable l ower boundary conditions. However, the error is really small as compared to t he values of other components of the water budget (see the following section for discuss ion on the error estimates). The biggest advantage of this method lies in comp rehensiveness with which one can estimate water budget components and determine seasonal or shorter time-scale variation. Another advantage is that very small lan d cover/soil type regions can be analyzed. Observations of ET components, derived plant coefficients and other v ariables
53 should prove extremely useful for predictive compre hensive surface and ground water models. 2.3.3 Error Estimates Finally, it is very important to also comment abou t the error ranges of the equipment as well as error estimates of other hydro logic properties determined for the study site and their possible effects on the magnit ude of the hydrologic components. Section 2.2.2 mentions that the soil moisture obse rvations as well as water table measurements are good to 0.1% water content and hav e been tested by manual measurements hence assuming the error to be random the net effect on the final results is expected to be negligible. This leaves the values o f hydraulic conductivities and its effect on the lateral flow calculations. Section 18.104.22.168 d iscusses the determination of hydraulic conductivity. Both permeameter analysis and slug te st gave values which were within 1015%. As a matter of fact, apart from the wells in c onsiderations, forty two other soil cores were taken and analyzed (Thompson 2003) and the res ults were very consistent, further increasing our confidence in the calculated numbers Due to real small value of lateral flow, even if the hydraulic conductivity is assumed to be variable around 10-15% the final water budget (Table 2.4-2.6) will only change by less than 10 mm, which wonÂ’t affect the annual or seasonal variation of the othe r water budget components. Another factor that has the potential to introduce error is the choice of an equation for calculation of potential evapotranspiration. Th e selection of Jensen and Haise (1963) method was done primarily in lieu of the availabili ty and quality of weather data. Use of standardized Penman Monteith equation requires a wh ole suite of weather parameters and
54 for this particular study the data were not consist ently and continuously available. Apart from that problem, use of net radiation and wind sp eed from a supplemental dataset used from Ona weather station was thought to be fraught with error and hence only temperature and solar radiation data were used, lim iting the choice of ET methods. Imrak et al. (2003) compared different methods of ET estimation versus the standardized Penman Monteith method and found that Jensen and Ha ise method fluctuated on either side with an error of 15%. Hence, the depression st orage ET as well as net runoff is expected to be off by a maximum 15%. However the du e fractional contribution towards total ET estimates, the values of TET can be easily expected to be put within a confiden ce bound of 5%. As far as total rainfall excess, infi ltration, etc. are concerned none of the other water budget component is expected to be effe cted. Similarly, the fluctuation in the value of interce ption capture which is around 10% of total ET values is not expected to change the numbers that much. Hence, instead of quantifying on a seasonal basis, a constant average value for each vegetation cover was assumed. Overall we can be pretty confident that the result s obtained from the aforesaid analysis are with in acceptable errors (~5-10%) give n that that methodology attempts to comprehensively determine all the water budget comp onents. The consistency in the values of ET and other components calculated for other similar environments e.g., Sumner (2006), Sumner (2001), and Bidlake (1996) fu rther increases our confidence in the results obtained.
55 2.4 Conclusions A one dimensional point and transect models couple d with precise and highly resolved soil moisture profile and water table moni toring were developed to determine the magnitude and variation of different components of the water budget. Two and a half years of observed soil moisture and water table ele vation data were used to derive all lateral and vertical fluxes comprising evapotranspi ration components. The results successfully showed the variation of different flux es with varying land cover and ambient weather conditions. Results also indicate a long te rm consistency in seasonality of different fluxes with short time scale differences occurring due to differences in antecedent conditions. ET was found to be a dominant factor controlling surf ace and sub surface fluxes including runoff and water table rec harge, second only to precipitation. Lateral sub-surface flow was found to be less than 2% of the precipitation in the annual water budget. Thus, it remains to be seen how the m ethodology will function in higher lateral flow (and vertical leakage) settings. This aspect of the investigation is ongoing and results will be forthcoming. The methodology used in the study, unlike other me thods, such as eddy correlation or solar radiation based methods, gives a direct estimate of the soil moisture extracted by the roots and, hence, is expected to y ield better plant based ET parameters, such as plant coefficients. The method excels at de termining component fluxes such as ET, lateral flow, and rainfall excess (runoff). Even though the current study considered land cover variations, it did not take into account plant specifics like rooting depths, leaf area index, etc., which are known to affect the lat eral and vertical fluxes for a given land cover and are key modeling parameters. Some attempt needs to be made to incorporate
56 these variables in the observations. The main drawb ack of the above methodology is that if the water table gets deeper than the deepest soi l moisture sensors, errors in the calculation of storage changes can over or under pr edict fluxes. This could be a problem in deep water table environments. Another limitati on occurs at the other end, when the water table is very shallow. While setting ET equal to potential ET is an acceptable assumption for water table at or near land surface (Shah et al. 2007), actual PET measurement is always problematic (Allen et al. 200 5). Also, resolution of soil ET flux cannot be made during these times. Thus, reliabilit y of the method is only achieved if sensors penetrate the deepest depths of soil moistu re uptake and several methods are used to estimate PET during the wet conditions. Another important aspec t that is relevant for the application of this methodology, especially in a different hydrogeological setting is the determination of vertical leakage. For the stud y site as the confining layer separating the surficial aquifer with the intermediate is thic k and has very low permeability, assuming the boundary to be impermeable is appropri ate; however, in high leakage environments, vertical leakage should be explicitly measured and accounted for in the mass balance equation.
57 Chapter 3: Extinction Depth and Evapotranspiration from Ground Water under Selected Land Covers 3.1 Introduction Chapter 2 concluded that continuous soil moisture and water table observations can help estimate evapotranspiration and other comp onents of the water budget. An important question, from the modeling perspective, which remains unanswered, is how much of the evapotranspiration comes from vadose zo ne and how much comes directly from ground water? Also, of importance to modeling, is the determination of the extinction depth, defined as the depth to the water table at which the contribution of ground water to the total evapotranspiration become s negligible. The current chapter is aimed at answering the abov e said questions about extinction depths, ground water, and vadose zone co ntribution to evapotranspiration as well as, developing some equations that can be used depending on the land cover and soil type, to model the aforesaid processes. 3.2 Background Evapotranspiration (ET) is a major component of the water budget in veget ated soils and shallow ground water systems. The impact of ET on ground water flow was recognized in the early works of White (1932) and M eyboom (1967) who attributed diurnal fluctuation in a shallow water table to gro und water consumption by
58 phreatophytes. Phreatophytes, such as willow and c ottonwood, flourish in riparian zones fringing streams, and their significant ET consumption influences the behavior of interconnected surface-ground water systems (Woessn er 2000; Sophocleous 2002). In landscapes where the water table is within or sligh tly below the root zone, the vegetation can uptake water both from a thin unsaturated vados e zone and saturated ground water (water table). The partitioning of ET into Vadose Zone ET (VZET) and Ground Water ET (GWET) is challenging because it is controlled by many v ariables including soil hydraulic properties, depth to water table (dWT), and root distribution. In particular, the management and modeling of shallow ground water sys tems requires an understanding of how the depth to water table impacts evapotranspira tion, often a significant sink term in shallow ground water systems. In ground water modeling, an early version of MODF LOW (McDonald and Harbaugh 1988) assumed that GWET decays linearly with increasing water table depth, with GWET reaching a value of zero at a depth designated as the extinction depth. The extinction depth can vary considerably as a functio n of the presence of phreatophytes, and seasonal and long term climatic conditions among ot her factors (Anderson and Woessner 1992). Surprisingly, few formal attempts (e.g., Blu m et al. 2001) have challenged this linear decay approach. Banta (2000) revised the ori ginal evapotranspiration module in MODFLOW to allow a piece-wise linear decline of ET with increasing depth to the water table. This new approach is flexible and can better capture the exponential decay behavior that was proposed earlier by Gardner (1958 ). Recently, different MODFLOW modules have been released that have subroutines to simulate surface evaporation and root transpiration (Unsaturated-Zone Flow (UZF) pac kage (Niswonger et al. 2006),
59 Variably Saturated Flow package (VSF) (Thoms et al. 2006), and Farm Process (FMP1) package (Schmid et al. 2006)). However, no common g uidelines or functions are recommended for setting extinction depth for differ ent soils or vegetative covers. Regardless of the parametric function adopted: line ar, piece-wise linear, or exponential, the parameters of the ET module should vary over the spatial domain to refl ect heterogeneities in soil and vegetative covers. Regi onal models for ground water management simulate large aquifer areas with varyin g vegetation covers on the land surface. Because ground water ET can be a significant component of the ground water budget, resolving the variability over the spatial domain is a necessity for managing interconnected surface-ground water systems. In shallow ground water systems, the ET demand of plants is supported by two hydraulically connected domains: the shallow unsatu rated soil (vadose zone) and the deeper saturated ground water system (Anderson and Woessner 1992; Thompson 2003). Previous studies by Nachabe (2002) and Nachabe et a l. (2005) suggested that temporal fluctuations in a shallow water table control soil moisture conditions, associated rootwater uptake, and ET across the ground water-vadose zone-atmosphere con tinuum. Figure 3.1 shows the variability of water table and soil moisture for a 5 day period in a ground water discharge zone. The water table, which declines rapidly during daylight due to ET, recovers partially at night. The partial recovery in the evening and night hours is attributed to lateral and vertical ground water flo w to the discharge area as noted in earlier studies (e.g., Meyboom 1967; McWhorter and Sunada 1977). Interestingly, the soil moisture in the unsaturated zone above the wat er table displays similar diurnal fluctuation. The soil moisture partially recovers a t night by upward flow from the
60 saturated zone. Although the soil moisture recovery lags by about two hours the recovery of the water table, the synchronization of soil moi sture and water table indicates a close hydraulic connection between the two domains in sha llow water table environments (Nachabe et al. 2005). Figure 3.1 Water Table and Total Soil Moisture (TSM ) Diurnal Variation with Time [Adapted from Nachabe et al. 2005]. The TSM was Cal culated by Integrating the Observed Water Content in the Top 1.5 m of Soil [NG VD Refers to National Geodetic Vertical Datum]. 3.2.1 Objectives and Scope The objectives for this chapter are thus: (a) to s tudy the relationships of total ET and GWET to dWT using saturated/unsaturated flow simulations, (b) to introduce new analytic expressions to capture this relationship, (c) to assess if the proposed expressions are consistent with field data, and (d) to determin e the impact of varying soil properties Total soil moisture (m) Water table elevation (m above NGVD)
61 and land cover on GWET and extinction depth. Three land covers will be co nsidered: bare soil, shallow rooted vegetation (e.g., shrubs and grasses), and deep rooted vegetation (trees and forested landscapes). The primary findin g is that an exponential decay function better describes the decline of GWET with water table depth. New equations are introduced to express the decline of GWET with variation in land cover and soil properties. 3.3 Methods 3.3.1 Numerical Simulations Evapotranspiration extracts water from both the sa turated and vadose zones. Water flow is driven by head gradients from the dry ing of the soil close to plant roots (root water uptake) and evaporation at the surface. In this study, HYDRUS, a variable saturation flow model (Simunek et al. 1998), is use d to simulate the evapotranspiration process. Introduced by the U.S. Salinity Lab, this model has been previously used and verified in a number of studies (e.g., Hernandez et al. 2003; Simunek and van Genuchten 1999). Also, an independent team of hydrologists s crutinized HYDRUS and found the model to be reliable and highly capable (Diodato 20 00). The HYDRUS-1D model simulates variably saturated f low by solving RichardÂ’s equation written as: S x h K x t + = ] cos [b q (3.1) where h [L] is the water pressure head, q [L3L-3] is the volumetric water content, t [T] is time, x [L] is the spatial coordinate, b [-] is the angle between the flow direction and th e
62 vertical axis (for vertical columns b = 0o), K [LT-1] is the unsaturated hydraulic conductivity, and S [L3L-3T-1] represents the sink term. Soil hydraulic properti es characterizing volumetric water content q (h) and hydraulic conductivity K(h) are assumed to be described by the van Genuchten (1980) model as:  < + + = 0 0 ) ( 1 ) ( h h h hs m n r s rq f q q q q (3.2) < = 0 h K 0 h ] ) S 1( 1 [ S K ) h ( KS 2 m m /1 e l e S (3.3.1) r s r eh Sq q q q= ) ( (3.3.2) where m = 1 Â– 1/n for n > 1, Se [-] is the effective water content, KS [LT-1] is the saturated hydraulic conductivity of the soil column qr [L3L-3] and qs [L3L-3] denote the residual and saturated water contents respectively, l [-] is the pore connectivity parameter assumed to be 0.5 as an average for most soils, an d f [L-1], n [-] and m [-] are the van Genuchten empirical parameters. The soil column sim ulated in HYDRUS varied from 3 to 9 m in length depending on soil type and vegetat ive cover. The column was divided into 1000 elements to provide good spatial resoluti on. Increasing the number of elements did not change or improve the results of the numeri cal simulations presented here. Evapotranspiration is simulated as a sink term, S [ L3L-3T-1], on the right side of Equation 3.1. This sink term is distributed through the soi l profile reflecting the plant root distribution in the domain as follows: S(x) = a (h) Sp(x) (3.4)
63 where a (h) [-] is the root water uptake stress response fu nction (0 < a (h) <1) as defined by Feddes et al. (1978), and Sp(x) [L3L-3 T-1] is the spatial distribution of the potential transpiration rate over the soil profile as a funct ion of depth x [L]. The potential rate represents the water uptake rate when the plant is not experiencing any water stress, that is a (h) = 1. For vegetated covers, the upper surface wa s set as a no-flux boundary and the potential ET rate was distributed through the root system in th e subsurface according to the function: Sp(x) = bÂ’(x) Tp (3.5) where Tp [LT-1] is the potential rate and bÂ’(x) [L-1] is the relative fraction of roots at any depth x. Jackson et al. (1996) analyzed the distri bution of roots for a large number of vegetation and found that the model proposed by Gal e and Grigal (1987) was successful in describing root distribution. This model of root distribution is adopted in this study and the root distribution is assumed as: Y = 1 gd (3.6) where Y is the cumulative fraction of roots from th e surface to depth d, and g is a numerical index of rooting distribution which depen ds on vegetation type. This relationship was used in the numerical simulations with g equals 0.975 for forest and 0.952 for grass (Jackson et al. 1996). The root zon e thickness ( xRZ) of 1 meter was assumed for grass (shallow rooted vegetation) and 2 meters for trees (Jackson et al. 1996). Throughout the study, the only differentiati ons that were considered concerning land cover were differences in rooting depths and d istributions. Other physiological characteristics affecting ET such as the leaf area index were not considered.
64 For bare soil, the potential ET rate is applied as a surface evaporation boundary condition. In all simulations, the potential ET rate ( PET ) is assumed to follow a semisinusoidal function with a frequency of 12 hours to capture the diurnal variation in PET The area under the rate curve is 0.5 cm, representi ng an average potential daily ET of 0.5 cm/day which is a reasonable average for many regio ns in the U.S (e.g., Nachabe et al. 2005; Linsley and Franzini 1972). These 12 hours of active ET are followed by 12 hours of zero potential ET to reflect night hours. Representing a day, this 2 4-hour cycle of upper boundary condition is repeated for the entire duration of the numerical simulation, which was also set as the model output time step. I n all simulations, a no-flux boundary condition was defined at the column bottom. The ini tial depth to the water table (dWT) was assumed zero, i.e., the water table coincided w ith the land surface. No further constraints were placed on the evolution of the wat er content profiles or location of the water table. To assess the influence of soil texture, simulatio ns for twelve texture classes were carried out for each land cover; van Genuchten para meters f n and m for the standard USDA twelve soil texture classes were adopted from the database of HYDRUS (Carsel and Parrish 1988). 3.3.2 Data Processing and Analysis The numerical model solves for the pressure head a nd water content distributions in the domain subject to the PET conditions described above. The model results were used to track the evolution of the water table decl ine by tracking the location of the zero
65 pressure head with time. The partitioning of evapot ranspiration ( ET ) into VZ and GW fractions was subsequently determined from mass bal ance relationships. The first processing step included calculation of the model simulated total soil moisture (TSM) across the entire soil profile for a ll specified time steps. The TSM (in cm of water) is the total depth of water in the soil c olumn and is calculated by integrating the water content along the soil column. The ET is a loss of water from the soil column and is determined by subtracting two sequential values of TSM. Mathematically the ET loss (expressed as a positive value) in a time step is c alculated as: =-SS t el mod t el mod ti 1 i idz dz ETLDDq q (3.7) where ETL is total ET loss in a time step, model is the simulated water content at depth z from the land surface at time ti with i being a running index for time, and S [L] is the length of soil column. The ET rate is then calculated as follows: t ETL ET D = (3.8) where: 1-= Di it t t is the time step. Mathematically, the ETL in Equation 3.7 was calculated using the trapezoidal rule of integratio n and the simulated water content. ()() ()() i t 0 S j 1 j j Z 1 j Z 2 1 1 i t 0 S j 1 j j Z 1 j Z 2 1 ETL + + + + + + =D q q D q q (3.9) At the end of a time step, the return of the press ure and water content distributions to hydrostatic equilibrium indicates that upward fl ow has replenished the unsaturated vadose zone and there is no further upward flow. In this case, ET is supported by ground water alone without a vadose zone contribution. Wit h increasing depth to the water table,
66 however, the hydraulic connection between ground wa ter and the vadose zone weakens, causing the vadose zone to lose water at a rate tha t exceeds the upward replenishment from the saturated zone. Hence, the vadose zone con tribution (VZC) to ET in a time step 1-= Di it t t was calculated from consecutive departure at time ti and ti-1 of the water content profile from hydrostatic equilibrium. Math ematically, i 1 it el mod eq t el mod eq) TSM TSM ( ) TSM TSM ( VZC =(3.10) where at any given instant in time, TSMeq is the total soil moisture in the column for the corresponding depth to water table under hydrostati c equilibrium condition and TSMmodel is the total soil moisture computed from the water content values simulated by HYDRUS for the corresponding time. The vadose zone ET rate can therefore be found as: t VZC VZET D = (3.11) From mass balance, the ground water contribution (G WC) can be written as: VZC ETL GWC = (3.12) and ground water ET rate (GWET) is: t GWC GWET D = (3.1 3) Theoretically, the water table extinction depth is reached when GWET becomes zero. It was observed, however, that GWET approaches zero only asymptotically. Thus, for practical consideration, the depth of water tab le is said to reach extinction when GWET is only 0.5% of the PET imposed at the boundary. The simulation time to re ach extinction ranged from one month to a year dependin g on soil type and land cover.
67 3.3.3 Field Estimation of GWET To assess the appropriateness of the proposed mode l, water table data from a ground water observation well in Hillsborough Count y, Florida were used. The depth to the water table in the well was measured at five-mi nute intervals with a submersible pressure transducer 0 to 5-psi (Instrumentation Nor thwest Inc., Kirkland, WA), accurate to 0.005 psi. This site is covered with shallow gra ss and the soil is predominantly sand with pockets of fines deposited as described in Tro ut and Ross (2004) and Said et al. (2005). A methodology introduced by White (1932), and scru tinized recently by Loheide et al. (2005), was used to estimate the GWET from water table fluctuations. The equation to estimate GWET is (White 1932): ) R 24 s ( S GWETY =D (3.14) where GWET is ground water evapotranspiration (cm/day), SY is the specific yield [-], s is the daily change in the water table elevation (c m/day), and R is the net ground water inflow rate (cm/hour). The change in water level s is calculated as the difference between water levels over one day. Depending on the direction of hydraulic gradient, the ground water inflow rate, R, can be either a rechar ge or discharge term (Freeze and Cherry 1979). As recommended by White (1932), the g round water inflow rate, R, was determined from the slope of the water table hydrog raph between midnight and 4 AM. Despite the simplicity of the methodology by White (1932), Equation 3.14 has serious limitations as noted recently by Loheide et al. (20 05). This method assumes a constant ground water inflow rate for the entire day. Also, the specific yield, SY, is difficult to estimate because it varies non-linearly with dWT due to the capillary fringe above the
68 water table (Duke 1972; Nachabe 2002). At this par ticular site, the equation introduced by Duke (1972) was calibrated by Said et al. (2005) to capture the specific yield variation with dWT. This equation takes the form: n r =lFWT a r Yd h 1 ) S ( S (3.15 ) where [-] and ha [L] are the pore size distribution index and soil air-entry (or bubbling) pressure head of the Brooks and Corey water retenti on model (Brooks and Corey 1966), dWT [L] is depth to water table, Sr is the soil specific retention [L3L-3] and f is the porosity [L3L-3]. For this site, values of (f-Sr) = 0.12, = 0.7, ha = 33 cm were used in Equation 3.15 (Said et al. 2005; Nachabe 2002). Equation 3.15 can be applied two or three days fol lowing rainfall, after infiltration and moisture redistribution have ceased in the unsa turated zone above the water table (Nachabe 2002; Said et al. 2005). Therefore, for ea ch rainfall storm, three days were removed from the one year water table record. This step reduced considerably the data that can be used to estimate GWET, but it was necessary to have a reasonable estimat e of specific yield values (Nachabe 2002; Said et al. 2005). To determine values of potential evapotranspiratio n (PET), a USGS Class A pan housed in the weather station at the study site was used to measure pan evaporation (Nachabe et al. 2005). The difference in water leve l observed in the pan for a period of one day was multiplied by a pan coefficient of 0.7 (Doorenbos and Pruitt 1977) to get a reference value of evapotranspiration for pasture g rass, representing the type of vegetation around the observation well.
69 3.4 Results and Discussion The ET rates are plotted versus depth to water table in F igure 3.2 for the simulation with forest cover in a sandy clay soil. The simulated ET was normalized by the potential ET so ET/PET varied between 0 and 1. The figure shows that the ET is equal to its potential until the water table reaches a de pth dÂ’ defined here as the Â‘transition depthÂ’. At the transition depth, ET shifts from atmospheric controlled (ET is equal to PET) to soil moisture controlled. For water table cond itions deeper than the transition depth dÂ’, ET is limited by the available moisture in the column While Figure 3.2 shows total ET from both ground water and vadose zone, we are int erested in estimating the ground water fraction (GWET) because of its influence on the ground water budg et. Therefore it is important to partition the ET into GWET and VZET components. Figure 3.3 demonstrates the partitioning of ET into the GWET and VZET fractions for a typical simulation. As shown in Figure 3.3, a ll evapotranspiration will be provided by the ground water if the water table is at a dept h less than dÂ’Â’ referred here as the Â‘decoupling depthÂ’. For water table less than the d ecoupling depth, all the evapotranspiration is borne by ground water, and th e vadose zone acts as a conveyor being continuously replenished to hydrostatic equil ibrium from the ground water below. Clearly, the vadose contribution to ET is zero for water table depth less than the decoupling depth. As the water table (dWT) becomes deeper than the decoupling depth, the vadose zone loses moisture at a rate that excee ds the replenishment rate from ground water. This can be attributed to the weakening of t he hydraulic coupling as dWT increases beyond dÂ’Â’. After the water table reaches the decou pling depth, the VZET contribution increases with further increase in the depth to the water table, reaching a maximum
70 contribution at the transition depth dÂ’ (the depth at which ET is controlled by soil moisture availability). Obviously dÂ’ and dÂ” are imp ortant parameters in describing the ET decline with dWT both physically and mathematically. Figure 3.2 Simulated ET in Sandy Clay with Forest Land Cover. The Diamonds are the Simulated Values while the Solid Line is Curve Fitt ed using Equation 3.16. The Transition Depth, dÂ’, is the Depth at which ET becomes Limited by Available Water. xRZ is the Maximum Root Depth (= 200 cm) for Forest La nd Cover. Clearly, the decline of GWET with increasing dWT is not linear. This relationship is better fitted with an exponential decay function with parameters reflecting soil hydraulic properties and land cover. This observati on concurs with the early work of Gardner (1958) and Gardner and Fireman (1958) who, based on laboratory experiment of evaporation from bare soils, proposed an exponentia l relationship for steady-state evaporation from a shallow water table. Depth to the water table (cm) ET/PET
71 This study, however, extends the early findings to (a) transient conditions where the vadose zone, in addition to ground water, may c ontribute to ET and (b) vegetated landscapes where the sink is not limited to the lan d surface boundary but distributed through a root system in the unsaturated zone. Jur y et al. (1991) and Hillel (1980) discuss the early work of Gardner (1958) and some o f the inherent limitations, such as assumption of water evaporation as a steady-state p rocess. Figure 3.3 GWET and VZET in Sandy Clay Soil with Forested Land Cover. The Diamonds and Circles are the Simulated Values while the Solid Line is Curve Fitted with Equation 3.17. dÂ’ and dÂ” Represent the Transition and Decoupling Depth Respectively. xRZ is the Maximum Root Depth (= 200 cm) for Forest La nd Cover. 3.4.1 Influence of Soil Properties and Land Cover For a given distribution of roots the decoupling d epth is not only a function of capillary fringe height (as defined by Carsel and P arrish 1988) but also the unsaturated hydraulic conductivity of the soil matrix. Under lo w suction pressure, sufficient upward Depth to the water table (cm) Ratio
72 flow from the water table will occur to support ET on a daily time scale. However, as the time scale of water flow within the capillary fring e is lot less than the time scale across unsaturated media, capillary fringe height tends to be a dominating factor in deciding the decoupling depth. Thus, soils with thicker capillar y fringe have greater decoupling depth as compared to coarser soils (refer to Figure 3.4). Figure 3.4 Variation of Ratio of GWET with Water Table Depth for Two Soils. Height of Capillary Fringe for Sandy Clay and Sandy Loam i s 30 cm and 15 cm, Respectively (Carsel and Parrish 1988). Once the water table becomes deeper than the decou pling depth, the GWET starts declining rapidly in a fine textured soil. As shown in Figure 3.4, after the decoupling depth, the decline of GWET in sandy clay is faster than sandy loam. However, GWET in sandy clay is more persistent than GWET in sandy loam so the extinction depth is greater Depth to the water table (cm) GWET/PET
73 in sandy clay than it is in sandy loam. This condit ion can be readily explained by the variation of hydraulic conductivity with increasing suction pressure has to be considered. When the water table is deeper than the root zone, water extracted by the roots from the unsaturated zone is replenished by upward flow from the water table. This flow depends on the unsaturated hydraulic conductivity of the me dia. It is well known (Jury et al. 1991, pg. 89; Hillel 1998, pg. 237) that the hydraulic c onductivity of fine textured soil (sandy clay) is much less (e.g., two orders of magnitude) than that of coarse textured soils (sandy loam) for low suction pressures, which explain the rapid decrease in GWET after the decoupling depth for sandy clay. After some critica l pressure, however, the unsaturated hydraulic conductivity of the fine textured soil be comes greater than that of the coarse textured soil. Therefore, in a relatively deep wate r table environment, a fine textured soil can sustain a greater upward flux than a coarse soi l for the same head gradient, resulting in fine textured soils having a greater extinction depth. A similar observation was made by Gardner and Fireman (1958) for evaporation from bare soil.
74 Figure 3.5 Variation in GWET for Different Land Covers in Sandy Clay. Normalize d Depth (Depth to Water Table / Extinction Depth) is Used on the Vertical Axis to Facilitate Comparison. To address the variability with land covers, Figur e 3.5 shows GWET with dWT for three land covers on the same soil. The dWT on the ordinate is normalized by the extinction depth to capture the relative variation of the GWET for different land covers. As expected, the decoupling depth was the shallowes t for bare soil, and deepest for the landscape with deep rooted vegetation. Obviously, d eep roots support GWET from deeper water table depths. After the decoupling depth is r eached, however, the behavior of the decline of GWET is similar for all land covers because the soils h ave the same conductivity. Normalized Depth GWET/PET
75 Table 3.1 Extinction Depths for Different Soils an d Land Covers. Depths are Rounded up to Nearest 5 cm. Maximum Rooting Depth (xRZ) for Grassland and Forest was Assumed to be 100 and 200 cm, Respectively. Land Cover -------------cm-------------Soil Type Bare Soil Grassland Forest Sand 50 145 250 Loamy Sand 70 170 270 Sandy Loam 130 230 330 Sandy Clay Loam 200 300 400 Sandy Clay 210 310 410 Loam 265 370 470 Silty Clay 335 430 530 Clay Loam 405 505 610 Silt Loam 420 515 615 Silt 430 530 630 Silty Clay loam 450 550 655 Clay 620 715 820 3.4.2 Variability in Extinction Depths Extinction depths for different soils and land cov ers were rounded to the nearest 5 cm and presented in Table 3.1. Two trends are obvio us from a close examination of this table. First, fine textured soils have larger extin ction depth than coarse textured soils for a similar land cover. Secondly, extinction depth inc reased with increase in rooting depths. For shallow and deep rooted vegetation, the increas e in extinction depth was almost the same as the increase in rooting depths.
76 The cause for this almost equal increase can be ex plained by the fundamentals of soil physics and the soil-root water interaction. R oots can extract water from the vadose zone only up to wilting point, which is normally as sumed as the water content at 15 bar suction pressure (Hillel 1998, pg. 622). Hence, com parison of water content profiles when the water table is at extinction depth reveale d that the presence of roots translates downward the bare soil drying profile by a depth ap proximately equal to the rooting depth. The value of 0.5 cm/day used in the original simul ations might be considered a reasonable PET rate for many regions in the U.S. (e.g., Nachabe et al. 2005; Linsley and Franzini 1972). To test the sensitivity of extinct ion depths to potential ET rates, additional simulations with PET values of 0.25 cm/day and 1.0 cm/day were performe d. The behavior of ET, along with the transition and decoupling depths, changed slightly with changes in PET values. Lower PET rates caused less drying of the vadose zone, facilitating its replenishment by upward flow from the water table. Therefore, ET was closer to its potential for lower PET. Conversely, higher PET rates shortened the decoupling depth by permitting a higher contributio n from the vadose zone (VZET). In addition, for a given PET rate, the maximum values of VZET for each combination of soil type and land cover were averaged. It was found tha t for a PET of 0.25 cm/day the average maximum VZET was around 28% of the PET, and for a PET of 1 cm/day this value rose to 45%. Extinction depths, however, did not seem to be sensitive to PET. An increase of PET rates by a factor of four resulted in less than a 15% reduction in extinction depths.
77 3.4.3 Fitting a Model for ET and GWET Variation with dWT As suggested by Figure 3.2, the decline of ET with depth to the water table seemed to follow an exponential decay function afte r the water table depth reached dÂ’, the transition depth Therefore a simple model of the form ' 1)' (d d for d d for e PET ETd d b> Â£ =(3.16) was fitted to the data, where dÂ’ is the transition depth, d is the depth to water table and b is a decay coefficient. Table 3.2 showed the value s for the two parameters dÂ’ and b of this model for the different land covers and soils. The model fit the data well with r2 values exceeding 95% for most cases, suggesting tha t the exponential model captured well the relationship between ET and depth to water table. The transition depth ran ged between 18 cm for bare sand to a maximum of 186 cm for clay with forested land cover. As expected, the exponential decay coefficient b decreased with an increase in rooting depth. A smaller coefficient b indicates that higher vegetation evapotranspiratio n can be supported by accessing moisture from deeper soil la yers. Equation 3.16 was used again to simulate the decli ne of ground water evapotranspiration, GWET/PET, with decline in the water table. An analysis of t he regression fit, however, revealed that the curve fi tted well for shallow water tables but the fit was poor for deep water tables. For deep water tables, the regression fit was enhanced substantially by introducing a correction parameter yo to the equation. Thus, the model that captured the decline of GWET with water table depth was: " 1") (d d for d d for e y PET GWETd d b o> Â£ + =(3.17)
78 where dÂ” is the decoupling depth for the GWET, y0 is a correction and b is the decay coefficient. Table 3.3 compiles values of the param eters for all the thirty-six cases. The small correction y0 enhances the fit of the curve substantially at dee p water table close to the extinction depth. Figure 3.3 shows an example f it of the regression equation to the generated data. The r2 exceeded 95% for most cases considered here. The new equations introduced in this study provide a mean to simulate GWET decline with water table in ground water models. Th e piece-wise-linear ET module in MODFLOW (Banta 2000) is flexible, and the parameter s of the piece-wise-linear relationship can be adjusted to capture the exponen tial decay function introduced here. Hence, in absence of field data, the exponential re lations in Equations 3.16 and 3.17 with parameters from Tables 3.2 and 3.3 can be used by n umerical modelers simulating ground water flow under landscapes with heterogeneo us vegetative cover. 22.214.171.124 Field Assessment of Proposed Equations While total ET can be estimated reasonably well with existing (e. g., Priestly and Taylor 1972) and newly proposed (e.g., Nachabe et a l. 2005) techniques, resolving the GWET fraction can be a challenge. The GWET estimated by WhiteÂ’s method was normalized by the PET and plotted against the dWT in Figure 3.6. The solid line in this figure is the plot of Equation 3.17 with parameters from Table 3.3 for loamy sand and grass (shallow rooted) land cover. These conditions best reflected soil type and vegetation at our site. Equation 3.17 captures reas onably well the decline of GWET/PET with dWT. Two observations are worthy of note. First, the n umber of field data points available was limited for this study due to the lar ge number of storms in west-central
79 Florida. This restricted significantly the number o f days of data that can be analyzed with WhiteÂ’s equation. Secondly, though a pattern of dec line of GWET/PET with dWT can be identified, data points generated with WhiteÂ’s equa tion are scattered widely. The scatter on Figure 3.6 can be attributed to a n umber of factors. Recently, Loheide et al. (2005) did a comprehensive analysis of the ground water ET estimates obtained using the White (1932) methodology. The au thors found that the largest source of error in the White (1932) equation is the uncert ainty in the specific yield. Specific yield which is a non-linear function of dWT is influenced by hysteresis and transient pore drainage (Nachabe 2002). While the non-linear depe ndence of specific yield on dWT is captured in Equation 3.15 (Said et al. 2005), hyste resis is more difficult to estimate because it stems from the cycles of wetting and dry ing during shallow water table diurnal fluctuations. The specific yield also is transient (varies with time) because pore drainage (during water table decline), or imbibition (during water table surge), are time dependent processes. In other words, these processes are not instantaneous with observed water table fluctuation. Recognized as Â‘delayed yieldÂ’ in the literature (e.g., Nachabe 2002), the relation calibrated by Said et al. (2005) does not account for the transient as pect of specific yield.
80 Figure 3.6 Estimated GWET/PET versus DTWT from White (1932). The Solid Line is the Proposed Theoretical Model, Equation 3.17, with Parameters from Table 3.3 for Loamy Sand with a Grass Land Cover. In summary, while total ET can be estimated reasonably well using various methodologies, partitioning ET into GWET fraction and VZET can be a challenge because of the non-linear hydraulic connection between the two domains, the complex root distribution system, and hysteresis. Despite the la rge scatter of the data, the method by White (1932) did show the decline of GWET with increasing dWT. This decline was captured reasonably well with the equations and par ameters suggested in this study. Thus, this initial assessment indicates that an exponenti al decay relationship is consistent with the field data. Depth to the water table (cm) GWET/PET
81 Table 3.2 Parameters for Equation 3.16. The r2 Shows the Goodness of Fit of the Exponential Model to Simulated Results. Land Cover Type Bare Soil Grassland Forest Soil Type dÂ’ cm b cm-1 r2 % dÂ’ cm b cm-1 r2 % dÂ’ cm b cm-1 r2 % Sand 18 0.170 99 30 0.043 99 39 0.017 99 Loamy Sand 22 0.115 99 38 0.041 99 51 0.017 99 Sandy Loam 40 0.074 99 60 0.039 99 82 0.016 99 Sandy Clay Loam 35 0.055 99 70 0.031 99 102 0.014 9 9 Sandy Clay 26 0.078 98 66 0.028 97 145 0.016 99 Loam 55 0.04 97 85 0.026 99 128 0.014 99 Silty Clay 37 0.030 97 90 0.026 98 181 0.018 97 Clay Loam 50 0.032 98 92 0.020 98 159 0.012 99 Silt Loam 72 0.034 97 110 0.019 99 167 0.012 99 Silt 70 0.038 96 104 0.017 98 109 0.012 99 Silty Clay Loam 50 0.040 97 94 0.018 97 182 0.011 9 9 Clay 54 0.130 88 88 0.014 95 186 0.011 97
82 Table 3.3 Parameters for Equation 3.17. The r2 Shows the Goodness of Fit of the Exponential Model to Simulated Results. Land Cover Type Bare Soil Grassland Forest Soil Type dÂ” cm y0 b cm-1 r2 % dÂ” cm y0 b cm-1 r2 % dÂ” cm y0 b cm-1 r2 % Sand 16 0 0.171 97 27 -0.012 0.036 99 31 -0.052 0.0 13 99 Loamy Sand 21 0.002 0.13 99 29 -0.018 0.031 98 36 -0.048 0.013 98 Sandy Loam 30 0.004 0.065 99 35 -0.013 0.022 97 50 -0.044 0.01 1 97 Sandy Clay Loam 30 0.006 0.046 98 31 -0.003 0.020 98 56 -0.014 0.01 2 98 Sandy Clay 20 0.005 0.042 99 35 0.005 0.028 99 87 0 0.017 99 Loam 33 0.004 0.028 98 39 -0.007 0.015 97 66 -0.017 0.010 98 Silty Clay 37 0.007 0.046 91 78 0.003 0.020 90 158 0.004 0.035 91 Clay Loam 33 0.008 0.027 98 35 0.004 0.014 99 84 0.001 0.011 99 Silt Loam 38 0.006 0.019 99 40 -0.003 0.011 98 82 0.008 0.010 99 Silt 31 0.007 0.021 97 49 0.009 0.021 95 94 0.006 0 .010 99 Silty Clay Loam 40 0.007 0.021 97 49 0.009 0.017 95 94 0.006 0.013 99 Clay 45 0.006 0.019 96 70 0.007 0.017 83 96 0.006 0 .012 98 3.5 Conclusions The process of ET extinction was studied in detail and a quantitativ e evaluation of the factors affecting it (considering soil retentio n and vegetative rooting depths) was carried out. Simulations of variable saturation flo w suggested that an exponential decay better describes the decline of ET and ground water ET with increasing depth to the water table than the commonly used linear relationships. The exponential functions derived here can be easily used to describe the ET characteristics for different soil and vegetation
83 types. The soil and root parameters in the study, h owever, represent average conditions that can be used in the absence of site-specific da ta. The simulations conducted here assumed continuous drying, and thus the vadose zone contribution was determined assuming a dry cli mate. An intermittent precipitation event or wetter antecedent moisture conditions woul d increase the vadose zone contribution. Hence the results of this study are m ainly applicable for arid or semi-arid areas with little irrigation or rainfall. Another limitation for this study is that the extinction depth was assumed to be reached when ET/PET is 0.5%. Most vegetation will wilt if transpiration is too low. For these cases, the plant physiological response should be considered before setting a threshold value for ext inction. Equations 3.16 and 3.17 can be easily adopted as t hey require just two and three parameters respectively. Hence, these equations ca n guide numerical ground water modelers in simulating GWET. A field assessment of one equation showed that i t was consistent with the field data. More field testing, however, should be carried out to evaluate the robustness of the model for different soil types and a variety of land covers.
84 Chapter 4: Conceptualization of Vadose Zone Process es to Account for Evapotranspiration Distribution 4.1 Introduction From Chapter 3, it is evident that depending on th e water table depth (shallower than the extinction depth), contributions from the vadose zone and ground water are highly variable. For watershed scale models, numeri cal solution of RichardÂ’s equation may help in solving vadose zone soil moisture dynam ics. However, for regional scale models use of RichardÂ’s equation becomes both compu tationally and data intensive. Hence, the use of RichardÂ’s equation for large regi onal scale hydrological models is infeasible. Vadose zone moisture dynamics and its a ffect on the water table, hence, need to be modeled using a more simplistic methodology. Depending on the final objectives, modeling effort s may be aimed either at determining water table fluctuations without detail ed modeling of vadose zone soil moisture or, in other cases, involve determination of both soil moisture in the unsaturated zone as well as the water table fluctuations. For t he former type of modeling requirements, conceptualization of specific yield v ariability, incorporating effects of the vadose zone, needs to be made. The latter type of m odeling can, however, be done using a threshold based approach. The following sections focus on the concept of spe cific yield, its traditional use and development of variable specific yield curves f or different types of boundary
85 conditions such as evapotranspiration, rainfall, an d pumping. The next chapter discusses development and validation of a threshold based mod eling approach to account for variable vadose zone and ground water contribution to evapotranspiration, which can be used for regional scale modeling. 4.2 Specific Yield 4.2.1 Background Modeling of water table fluctuations is very impor tant for predicting runoff and ET in coastal plain environments such as west-central Florida (Ross et al. 2005). Highly transient and complex flow patterns that result fro m water table variations have a significant effect on the transport of solutes (Nov akowski and Gillham 1988). Therefore, a prerequisite for the success of any hydrologic mo deling of shallow water table systems is the efficient and accurate representation of the dynamics of the water table. Water table fluctuations and associated recharge t o the water table are most commonly estimated using a parameter known as the s pecific yield (SY) (Healy and Cook 2002; Crosbie et al. 2005). The definition of speci fic yield, which can be found in any ground water hydrology text, is the volume of water that an aquifer releases from storage per unit surface area of aquifer per unit decline i n the water table (e.g., Todd 1959; Freeze and Cherry 1979). Mathematically it can be w ritten as Z A V Sw YD= (4.1) where A [L2] is the aquifer area and Vw [L3] is the volume released/stored resulting from Z [L] water table fluctuation (in either direction).
86 As pointed out by Duke (1972), the above definitio n is misleading as it renders the specific yield as a constant, by making it inde pendent of soil water pressure. Several studies have acknowledged and described the spatiot emporal variability of specific yield in great detail (Gillham 1984; Jayatilika and Gillh am 1996; Nachabe 2002; Said et al. 2005; Sumner 2007). Variable distribution of water content in the unsaturated zone of a soil column, results in variable available fillabal e pore space and, depending on the depth to water table, this space may cause differential w ater table fluctuations for the same amount of soil water added or removed. For instance if the tension saturated zone, referred to as the capillary fringe, is within clos e proximity of land surface, adding a small amount of water will cause a sudden surge in the water table elevation as compared to a little or no elevation rise in deeper conditio ns (Barlow et al. 2000). Another important factor in the specific yield det ermination concerns the time frame of fluxes and observations. A column of soil, if allowed to drain for a day will release more water than when it is allowed to drain for couple of hours. This is known as delayed yield (Nwankwor et al. 1992). Nwankwor et a l. (1984) found in a field experiment, that the specific yield values obtained by the type curve fitting to timedrawdown curves were an order of magnitude lower th an laboratory derived values. Overall, corroborating the observation of Duke (19 72), it can be concluded that specific yield is not just a function of porous med ia, but is also a function of depth to water table (dWT), duration of drainage and the antecedent moisture conditions. Said et al. (2005) showed that variability in SY is apparent in field data and indicated that an apparent different behavior was exhibited for wetti ng versus drying.
87 Over the last decade the specific yield behavior h as been widely studied, however, only a few hydrologic models have incorporated the variable dWT behavior and the associated dynamics from flow processes (Jayatilika and Gillham 1996, Ross et al. 2004). Most ground water models such as MODFLOW (Harbaugh 2005) use a constant parameter in modeling water table fluctuations in r esponses to natural fluxes such as recharge and evapotranspiration (ET) or vice-versa. The models inadvertently assume a constant specific yield value for any dWT and ignore any early time or delayed drainage process. Ross et al. (2004) attempted to add variab le SY in an integrated MODFLOWHSPF application. They considered the SY to vary with dWT and relative moisture conditions based on simple conceptualization of moi sture retention. However, they acknowledge that more field and theoretical studies are needed to help elucidate this behavior. Adding to this knowledge gap is the fact that the studies on variable specific yield have been primarily restricted to the variation in water released from an aquifer (Newman 1987; Nwankwor et al. 1992) and very few formal att empts (e.g., White 1932; Meyboom 1967; Sophocleous 1984; Loheide et al. 2005; Crosbi e et al. 2005; Sumner 2007) have been made to identify its variation in response to different natural processes such as from evapotranspiration and recharge. In natural enviro nments, especially in humid regions with shallow water table, such as west-central Flor ida, the dynamics of the water table control important fluxes including root water uptak e, evaporation, and recharge to the ground water table (Troch et al. 1992; Nachabe et a l. 2005). Studies by Gillham (1984) and Sophocleous (1984) have reported an error, rang ing from 30 to 330 times the actual value, for cases when a constant value of specific yield was used for simulating recharge.
88 From the foregoing discussion it is clear that sou nd understanding of the variable specific yield behavior is fundamental to an accura te estimation of natural and anthropogenic stresses including pumping or transpi ration uptake by plants (Novakowski and Gillham 1988; Loheide et al. 2005). Different s tudies have analyzed the role of recharge (Crosbie et al. 2005), evapotranspiration (Loheide et al. 2005) and proximity of the capillary fringe (Gillham 1984) to land surface in isolation and no efforts have been made to compare the relative magnitudes of specific yield variation for different combinations of depth to water table and variable s tress boundary conditions. 4.2.2 Objectives and Scope This section aims at improving understanding of th is variability in specific yield for different anthropogenic and natural stresses. T he scope of the present work involves analysis of the specific yield behavior using satur ated/unsaturated flow simulations. The objectives of this paper are to: (a) analyze the va riability of specific yield due to evapotranspiration, pumping, and recharge; (b) anal yze the impact of redistribution time on the specific yield variations; and, (c) analyze and comment on the validity of a constant and/or equilibrium specific yield assumpti on. The basic approach of the study is to perform nume rical simulations on a conceptual one dimensional column and, from mass ba lance, determine the volume of water added or removed by a corresponding change in the water table elevation. Using different sets of boundary conditions, various flux es including ET, water table recharge, and pumping can be simulated. The analysis results in a better understanding of specific yield for different depths to water table and for d ifferent imposed fluxes.
89 4.2.3 Materials and Methods 126.96.36.199 Numerical Model HYDRUS-1D (Simunek et al. 2005) was used to simula te changes in soil water content under saturated/unsaturated vertical ground water flow (Refer to Chapter 2) for further details about HYDRUS-1D). For this investigation, a homogenous, vertical, conceptual soil column 300 cm long was setup in HYDRUS-1D. The column was subdivi ded into 1001 (maximum number) zones to obtain the finest possible discret ization. Three different sets of simulations were made incorporating the processes o f evapotranspiration (ET), precipitation and pumping, individually. Each set w as carried out by changing the initial and boundary conditions (described under the sectio n of Initial and Boundary Conditions). 0 50 100 150 200 250 300 350 010203040 Water Content (%) Brooks and Corey Fit Median Values Plot Layer1: Upper Gravity Zone Layer 2: Intermediate Capillary Zone Layer 3: Capillary Fringe Figure 4.1 Median Values of the Observed Soil Water Retention Data Along with BestFit Brooks and Corey Model. Suction pressure (cm) Water content (%)
90 188.8.131.52 Soil Hydraulic Properties Water retention data (soil water content versus ca pillary pressure) for the soils found in west-central Florida was obtained from a s oil characterization survey published by the Institute of Food and Agricultural Sciences (IFAS), University of Florida (Carlisle et al. 1989). From this survey the median values of soil water content at different capillary pressures were derived (Figure 4.1). The idea behind selecting the median values is to get parameters which are most represen tative of soils found in west-central Florida (Figure 4.1) The median soil data were described with an analyt ical model Brooks and Corey model, as given by Equations 4.2.1 and 4.2.2. < = =a a a r s r eh h for 1 h h for h h ) h ( ) h ( Slq q q q (4.2.1) ) 2 l 2 ( e S eS K ) S ( K+ +=l (4.2.2) where Se [L3L-3] is effective water content, Ks [LT-1] is saturated hydraulic conductivity, qr [L3L-3]and qs [L3L-3] denotes residual and saturated water contents, re spectively; ha [L] is the air-entry pressure value (or bubbling pressu re), [-] is a model parameter ,h [L]is the capillary pressure head and l [-] is a pore connectivity parameter assumed to be 1.0 as an average for many soils (Mualem 1976). The IFAS data (Carlisle et al. 1989) do not list t he water content for capillary pressures between 20 and 3.5 cm. From Figure 4.1, i t can be inferred that the air entry pressure for the simulated soil lies somewhere betw een this range. Based on field experience for Florida fine sands (Trout and Ross 2 004), the air entry pressure was
91 empirically set at 15 cm. Also, similar to the wate r content values, saturated hydraulic conductivity was set as the median of the saturated hydraulic conductivity values observed from the survey data. The parameter values used in the model were qs = 0.385; qr = 0.02; ha = 15; = 0.95; Ks = 9.5 cm/hr. 184.108.40.206 Initial and Boundary Conditions 220.127.116.11.1 Initial Conditions Numerical simulations using HYDRUS-1D for no pondi ng boundary conditions do not converge when the soil column is fully satur ated. Hence, water table depths less than air entry pressure cannot be simulated. Theref ore, the initial dWT for ET and pumping stresses was defined at 20 cm below the lan d surface. For the case of infiltration and recharge simulation, the initial water table de pth was set at 250 cm below land surface. Initial pressure distribution for all simu lations was set as hydrostatic. 18.104.22.168.2 Boundary Conditions In all three scenarios (ET, recharge, and pumping) the upper boundary conditi on was assumed to have no surface runoff and no pondin g. A Â‘no-flow conditionÂ’ (flux = 0) was defined at the lower boundary of the soil colum n for ET and precipitation scenarios. However, in order to simulate pumping, a lower boun dary flux was set equal to the imposed pumping rate. Additionally, a uniform root zone of depth of 100 cm was defined to simulate transpiration out of the soil column. As an average number for many regions in the U.S d uring the growing season, an ET of 0.5 cm/day was applied as a constant potential flux (e.g., Nachabe et al. 2005;
92 Linsley and Franzini 1972). Pumping rates were also set up at the same value to allow easy comparison and contrasting of the specific yie ld for different flux types. For the wetting phase, however, precipitation pulses of 5 c m and 2.5 cm for one hour were simulated with a prolonged redistribution time of 2 0 and 40 days. In Figure 4.2, the labels for wetting show pulse rate for one hour and the as sociated redistribution time (e.g., 2.5 cm/hr@40d means 2.5 cm pulse with redistribution ti me of 40 days). The purpose of simulating different redistribution times was to st udy the dependence of both rainfall intensity and redistribution time on the specific y ield variability. All simulation sets were carried out independently, implying that only one o f the three fluxes was active in any given simulation. 22.214.171.124 Root Water Uptake Model The Sink term, S, as defined in HYDRUS-1D as: pS) h ( ) h (Sa= (4.3) where S(h) [L3L-3T-1] is the actual root water uptake (RWU) from roots subjected to capillary pressure head Â‘hÂ’, and Sp [L3L-3T-1] is the potential RWU rate. For uniform root zone, Sp is defined as the ratio of potential transpiration rate and length of root zone. The (h) is a root water uptake stress response function defined by Feddes et al. (1978). The values of a varies between 0 and 1 depending on the capillary pressure head Â‘hÂ’. 4.2.4 Specific Yield Calculation The HYDRUS-1D model solves for the pressure head a nd water content distributions in the domain subject to the boundary conditions described above. The
93 model results were used to track the evolution of t he water table dynamics by tracking the elevation of the zero pressure head with time. The specific yield was subsequently determined from mass balance relationships and wate r table variation. The first processing step included calculation of the simulated total soil moisture (TSM) across the entire soil profile for all specif ied time steps. The TSM is the total depth of water in the soil column and is calculated by integrating the water content along the soil column. Subtracting two sequential values of TSM at corresponding time steps yields the net volume of water (per unit area) leav ing or entering the soil column. Equation 4.4 describes the mathematical form of the relation: =-00 t t ti 1 i idz) ( dz) ( NetVolumezzq q (4.4) where [L3L-3] is the simulated water content at depth z [L] from the land surface at time ti [T], with i being a running index for time and [L] is the depth of soil profile. Depending on the direction of flow, net volume can be positive (water leaving the soil column) or negative (water entering the soil column ). As the simulations involve a one dimensional vert ical column, the horizontal cross sectional area can be considered as unity. Th e specific yield can thus be computed by finding the ratio of net volume and water table elevation difference determined for the corresponding time steps as: Z NetVolume Y SD= (4.5) where Z=Zi-1-Zi with Zi [L] being the water table depth at any time ti. At any given dWT, the most stable water content distribution occurs when there are no net fluxes in the soil column, in other words wa ter content profile reaches equilibrium.
94 If this condition is disturbed by addition (e.g., i nfiltration) or removal (e.g., ET) of soil water, the soil column tends to equilibrate through redistribution of soil water content vertically, which ultimately involves water table m ovement. However, in field conditions (Rahgozar et al. 2006 ) on a day to day basis, some limited variability in moisture content (departure from equilibrium) exists with no perceptible change in the water table elevation. Th us, the condition of a limited variability of actual water content profile with re spect to equilibrium, be it dry or wet, will give an estimate of how much water can be adde d or removed (respectively) from the soil column without bringing about any signific ant changes in the dWT. Stressing the moisture content beyond this limit rapidly (period of hours to days) manifests itself as a water table change as the profile progresses to reequilibration. This limited departure from equilibrium hence quantifies storage that is n ot manifested as a water table change (over timescales of days to weeks), and herein is r eferred to as Â“Free Vadose Zone StorageÂ” (). Starting at any instant in time with a declining w ater table, if is zero or constant it means that all of water that is transpired out o f the soil column is reflected as a water table change. On the other hand if the increases it means that the storage above water table is also contributing to ET and this contribution is not reflected as a water table change. The magnitude of thus gives an indication as to how much water can be cumulatively released from the storage above the wa ter table without resulting in a water table fluctuation (within a limited time scale, e.g ., a couple to tens of days). By subtracting the consecutive Â’s, the loss of water from the vadose zone occurrin g within a given time can be estimated. Thus, the actual flux going out of the soil column can be
95 partitioned into that part which causes ground wate r fluctuation and that part which would not. As the latter flux is not contributed to directly (i.e., no vertical flux) from the water table, we will refer to it as the non-ground water flux (). The non-ground water flux () results from ET drying of the vadose zone moisture beyond equilibr ium down to the limit where no resulting water table decline oc curs. To quantify the change in the Free Vadose Zone Storage () must be evaluated. The change in can be mathematically defined as )t( TSM )t( TSM )t(el mod eqD D g D= (4.6) where: TSMeq is the total soil moisture above water table under equilibrium conditions, and TSMmodel is the total soil moisture as calculated from the HYDRUS-1D model output i.e. the actual water content distribution. The eqTSM D and el modTSMD are defined as: -=-0 d 1 t eq t 0 d eq eqWT WTdz dz TSMq q D (4.7) =0 d 1 t el mod t 0 d el mod el modWT WTdz dz TSMq q D (4.8) The contribution to total ET from the non-ground water flux can thus be calculated using Equation 4.9: t )t( )t(D g D h= (4.9) From mass balance, ground water contribution (GWC) to ET and ground water flux () can be found using Equations 4.10 and 4.11 g D = NetVolume GWC (4.10 )
96 t GWCD y= (4 .11) Any flux occurring in the vadose zone, be it non g round water flux () or ground water flux (), is governed by DarcyÂ’s Law, and hence its magnit ude is directly proportional to the hydraulic conductivity of the u nsaturated media. As the unsaturated hydraulic conductivity declines with increasing suc tion potential (see Equation 4.2) and, as the depth to water table increases, the time sca le of soil water dynamics (e.g., water table recharge) increases dramatically (Hillel 1998 ). This results in what is known as delayed yield or release of more water from the aqu ifer as the time scale of observation is increased (Nwankwor et al. 1992). Hence, the time s cale of observation for determining specific yield is very important. Past studies anal yzing different natural processes have tackled this issue by fixing the time scale of calc ulations. Loheide et al. (2005), studying evapotranspiration by phreatophytes used the concep t of Â‘readily available specific yieldÂ’, introduced by Meyboom (1967) in which the time step of calculation was kept to less than 12 hours. Crosbie et al. (2005), in a differen t study calculated Â‘apparent specific yieldÂ’ by assuming equilibrium conditions in the va dose zone 15 hours after a recharge event. For the current study, the time step of asse ssment was set at 24 hours for the simulation with boundary conditions of evapotranspi ration and pumping. For recharge boundary conditions, two different time steps were used (20 and 40 days) to analyze the sensitivity of the time of redistribution on specif ic yield values. 126.96.36.199 Calculation of Equilibrium Specific Yield Equilibrium specific yield is defined herein as th e amount of water released/stored per unit decline or rise in the water table conside ring the water content profile remains at
97 equilibrium at all times. To determine equilibrium specific yield for any water table depth, equilibrium total soil moisture (n) for the whole column was calculated using as dz)z(0 eq =zq F (4.12) where, is the depth of soil profile, eq(z) represents the equilibrium soil moisture content at any depth z, corresponding to a particular water table depth (dWT). The ratio of the difference between the n and the difference in the corresponding water tabl e depths yields the equilibrium specific yield value. Mathem atically, this is expressed as i 1 i eqWT WT i 1 i Yd d S =--F F (4.13) One important thing to note is that for the curren t study, as water table variations were not large, the specific yield obtained for a p air of initial and final water table conditions was assigned to the final water table de pth. Another point is that the drying simulation was ca rried out until the ratio of actual ET (calculated from Equation 4.4) and assumed potenti al ET (PET) became less than one percent. This value was arbitrarily chosen as the l imit of effective ET. Also, the dWT decline shows an asymptotic behavior with time. Thu s, the simulation involving pumping of ground water was terminated at the same dWT. Before considering the results and inferences draw n from them, it is important to point out the reliability of the model to the field conditions. Shah et al. (2007) and Desilva et al. (2007) performed extensive calibrati on and verification of the HYDRUS model to west-central Florida field data with Myakk a fine sand as the dominant soil type at their study site. Both studies showed that the H YDRUS simulation was highly
98 successful in mimicking observed water table and so il moisture profiles for multiple-year records. The reader is directed to those studies fo r demonstration of model validity, calibration and sensitivity. 4.3 Results and Discussion Specific yield obtained by carrying out different simulations is shown in Figure 4.2. It becomes clear that specific yield varies wi th water table depth for all stresses: wetting, drying or pumping, as well as no stress co ndition, i.e., equilibrium. What follows is a detailed discussion on the evolution of variab le specific yield and the soil physics governing this variation for different types of flu xes. 0 50 100150200250300 00.050.10.150.188.8.131.520.40.45 Eq. Drying Pumping wet2.5cm/hr@40d wet2.5cm/hr@20d wet5cm/hr@20d wet5cm/hr@40d Figure 4.2 Variation of Specific Yield in Response to Different Stresses. Depth to the water table (cm) SY
99 4.3.1 Drying Specific Yield Investigation of variability of the specific yield under drying conditions shows irregular behavior. To understand this behavior, th e non-ground water flux (), ground water flux (), and the actual ET flux going out of the column were plotted against the depth to water table (Figure 4.3). Initially when a ll ET is coupled to the water table (all ground water ET), the specific yield corresponds to equilibrium sp ecific yield (which is also very small). However, as the depth to water ta ble increases, free vadose zone storage () commences to contribute to the net ET from the soil column keeping the ET at potential. This implies that, for this period, the ET flux is still at potential but due to decrease in the the rate of water table decline decreases, causing a sharp increase in specific yield (as calculated from Equation 4.5). A s decreases, the continuously increases to maintain the net ET flux at potential. Since, the water content in the vadose zone is limited, after reaching a maximum, ultimately declines as moisture content approaches residual water content value. This cause s the actual ET to decline below the imposed potential value (Figure 4.3). From this poi nt onwards as actual ET values start to decrease the net volume leaving the soil column als o declines, causing the specific yield values to decline.
100 0 50 100150200250 00.10.20.30.40.50.6 Total Actual ET Direct Groundwater ET (GCF) ET Contribution from non-groundwater storage (NGF) Figure 4.3 ET Contribution from Direct Ground Water (Water Table ) and from the NonCoupled Soil Water Storage Above the Water Table. Figure 4.4 shows the variability of free vadose zo ne storage versus depth to water table. With increasing dWT, the free storage in the soil column continuously increases indicating the contribution of and justifying relatively higher values of SY as compared to the equilibrium values. However at approximately 170 cm below the land surface becomes constant showing zero contribution from non -ground water flux. From Figure 4.3 it can be seen that this is the point where the drying specific yield values coincides with the equilibrium value. From this point onward s saturated ground water is fully contributing to the actual ET (see Figure 4.3). However, as the soil moisture co ndition is much drier than the equilibrium condition, the flux from the soil is small and effectively negligible (Figure 4.3). This has been shown to be a practical limit of extinction (Shah et Depth to the water table (cm) Moisture leaving the soil column (cm/d) ET contribution from non-ground water storage (NGF) Direct ground water ET (GCF) Total actual ET
101 al. 2007). This causes the drying specific yield va lues to decrease with respect to the equilibrium SY values. 0 50 100150200250 00.511.522.533.544.55Myakka Fine Sand Figure 4.4 Available Free Vadose Zone Storage for V ariable Depth to Water Table. 4.3.2 Specific Yield under Pumping Conditions For pumping simulation, the explanation for having the specific yield values less than equilibrium, is more straightforward. Initiall y, when the water table is shallow (the water table is strongly coupled to with the vadose zone), the moisture condition is near equilibrium and the specific yield of pumping corre sponds to the equilibrium specific yield. However, with increasing time and decreasing water table this coupling weakens. As water is continuously withdrawn from the water t able via pumping, it takes increasingly more time for soil moisture in the vad ose zone to redistribute vertical head gradients and non-equilibrium conditions persist. T he net result under pumping is that, Depth to the water table (cm) Free vadose zone storage (cm 3 cm 2 ) Myakka fine sand
102 the moisture conditions in the vadose zone are alwa ys elevated, with respect to the equilibrium (see Figure 4.5). This means less moist ure (as compared to equilibrium conditions) is removed from the soil column renderi ng a specific yield value less than the corresponding equilibrium value. Over time, however a sort of quasi-equilibrium is established with the amount of moisture uptake and moisture addition to an expanding vadose zone due to water table decline become rough ly equal. Hence the specific yield over time becomes a constant value even though it r emains less than equilibrium value. The simulation with a higher pumping rate shifts th e specific yield values slightly to the left (further reduction). However this effect is mi nor and can be neglected, indicating that specific yield is not especially sensitive to the p umping rate. For pumping conditions a common assumption is that specific yield values always follow the equilibrium specific yield curve (McWhor ter and Sunada 1977; Nachabe 2002). However, contradicting this assumption, the current study clearly indicates that the specific yield values for pumping (in this case 0.5 cm/day) followed an equilibrium curve only until the dWT of is about 50 cm. Beyond this depth the pumping SY was consistently smaller than the equilibrium specific yield.
103 0 20406080 100120140 00.050.10.150.184.108.40.2060.40.45 Pumping W.C. Profile Eq. W.C. Profile A 0 20406080 100120140160180200 00.050.10.150.220.127.116.110.40.45Pumping W.C. Profile Eq. W.C. Profile B Figure 4.5 Actual Water Content Profile for Pumping and Equilibrium After (a) 60 and (b) 100 Days of Pumping. Depth below land surface (cm) Water content (cm 3 cm 3 ) (a) (b)
104 4.3.3 Specific Yield under Wetting Conditions In this set of simulations, the initial depth to water table was set to 250 cm below the land surface and the evolution of specific yiel d from dWT equal to 250 cm up to the land surface was examined from infiltration wetting When the water table is deep (250 cm), due to weak coupling, the wetting fronts take considerable time (~10-15 days) to make it to the zone of saturation. Hence, within th is time frame of couple of weeks the water table rise is primarily due to redistribution of earlier wetting fronts. However, once the water table rises to a certain level (<1 m), th e vadose zone and water table get strongly coupled again. With rising water table ele vation, infiltration fluxes increasingly create more responsive recharge behavior. The reaso n for this is simply that the wetting front has to travel a shorter distance and also the rising water table encounters (and helps maintain) elevated moisture conditions in the vados e zone (Figure 4.6). Hence, the specific yield values again decrease with shallower water table and the profile appears more like the equilibrium distribution as can be in ferred from Figure 4.2. The time to redistribute can be considered analogo us to the time for complete drainage which is also called delayed drainage (Nwa nkwor et al. 1992). Nachabe (2002) quantitatively defined this time as a function of s oil properties and found it to decrease with decrease in water table depth. It is for this reason that the curves corresponding to greater redistribution time are closer to the equil ibrium specific yield for both rainfall rates. It also appears that redistribution time is not a function of rainfall depths (rate). An interesting fact can be seen from the wetting curve s in Figure 4.2. For the same redistribution time, even if the precipitation rate is doubled, specific yield behavior remains essentially the same. This suggests specif ic yield variability is just a function of
105 redistribution time. However, if a simulation is ma de with very high infiltration rates (~10cm/hr) the water table rise is so great within the time frame of observation that the model is not able to capture the actual variability of specific yield. Anything short of this critical threshold high rainfall rate results in es sentially similar specific yield behavior. 4.4 Comparison with Other Studies Variability in the specific yield is not a new con cept; however, such detailed analysis of its variability does not exist in the l iterature. The ensuing paragraphs describe the current study put in perspective with the past studies on this topic. A discussion about how the current results corroborates or contradicts previous studies is also provided. Healy and Cook (2002) in their thorough review of field and laboratory methods for determining specific yield pointed out that the estimate of specific yield suggested by dos Santos and Youngs (1969) and Duke (1972) provid es a good starting point, to which further adjustments have to be applied to account f or hysteresis, field scale heterogeneity and other variables. The suggested relationship is ) ( h SYq f= (4.14) where f [L3L-3] is the saturated water content and q(h) [L3L-3] is the water content at the land surface for any given depth to water table h [ L] and SY is the specific yield value. A big limitation of this relationship is that Equatio n 4.14 is valid only when the initial and final water contents are at equilibrium value. Com parison of Equation 4.14 with the equilibrium specific yield values calculated using Equation 4.13 showed an exact overlap in the calculated specific yield values for the ent ire range of water table depths. This
106 0 50 100150200250 00.050.10.150.18.104.22.1680.40.45 Wetting Front Eq. W.C. Profile A 0 50 100150200250 00.050.10.150.22.214.171.1240.40.45 Wetting Front Eq. W.C. Profile B Figure 4.6 Wetting Front and the Equilibrium Water Content Profile After (a) 20 and (b) 40 Days of the Pulsing Soil Column with 5cm/hr Rain fall Infiltration for One Hour. supports the premise that if the conditions are in equilibrium this simple equation can be effectively used for specific yield calculation. Ho wever, as can be seen from Figure 4.2, for imposed wetting, drying, and pumping boundary c onditions, the specific yield values Below land surface (cm) Water content (cm 3 cm 3 ) (a) (b)
107 depart from the equilibrium specific yield (in some cases considerably) as the water table becomes deep. Therefore, assuming equilibrium specific yield valu es for all stresses can cause, in some cases, considerable error in the estimation of water table fluctuations or fluxes such as evapotranspiration (Loheide et al. 2005). Loheid e et al. (2005) referred to the above relationship (Equation 4.14) as depth compensated s pecific yield, while Crosbie et al. (2005) called the same relationship apparent specif ic yield. As the initial and final conditions, warranting the validity of the above eq uations have to be equilibrium water content and the results match exactly to equilibriu m specific yield values (Equation 4.13) derived from comprehensive mass balance analysis, i t is more intuitive to refer to Equation 4.13 as equilibrium specific yield (eqYS) and use it as a common terminology for all the processes such as recharge and evapotra nspiration. A more common method used for calculation of speci fic yield, especially for deep water table environments (dWT >2 m), is the difference between the saturated wat er content (S) and the water content at field capacity (fc) (e.g., McWhorter and Sunada 1977). r s Y0Sq q= (4.15) The field capacity is often defined as the moistur e retention for drained soil at 1/3 bar pressures (Jamison and Kroth 1958). For the soi l used in the HYDRUS investigation 0YS is about 0.34, which is the value of the equilibri um specific yield at water table depth of about 200 cm below the land surface. Thus, it is clear that using a constant value of specific yield for analysis involving shallow water table will result in significant error
108 and dampened ground water fluctuation. For deep wat er table environments, however, Equation 4.15 is a reasonable estimate of specific yield value for normally mild soil fluxes (< 1 cm/day). Also, further supported by thi s study is the case of SY for a very shallow water table, when the capillary fringe inte rsects the land surface. Due to limitation of HYDRUS, and the use of Brooks and Cor ey moisture retention model, specific yield values were not calculated for water table shallower than capillary fringe value. However, results of Crosbie et al. (2005) an d Gillham (1984) can be easily used to show that the specific yield continues to decline w ith decreasing water table depths and ultimately becomes zero as the capillary fringe com es up to the land surface. For conditions of dWT shallower than capillary fringe, a negligible rele ase or addition of water would be required to significantly change water lev el. The latter phenomenon, known as the reverse Wieringermeer effect, was first modeled by Gillham (1984) and later observed in the field by Helitois and Dewitt (1987) The water content profiles by Loheide et al. (2005 ) present an interesting contradiction when compared to the water content pr ofiles obtained under drying conditions. Figure 4.7(a and b) show the simulated water content under drying to be smaller than the equilibrium water content, which i s totally contrary to what Loheide et al. (2005), simulated (see Figure 9 in Loheide et a l. 2005). The reason for this discrepancy is that root water uptake in the curren t study is both from the vadose zone and ground water as opposed to just ground water in Loheide et al. (2005). Therefore, the simulated root uptake conditions for their study co rrespond to a pumping simulation where all the demand is met from ground water. Henc e, the water content profiles for pumping (Figure 4.6) closely match those obtained b y Loheide et al. In other words the
109 specific yield values obtained by Loheide et al. (2 005) for evapotranspiration will always be lower than the equilibrium specific yield, contr ary to the corresponding specific yield values obtained in the current study. 0 102030405060 00.050.10.150.126.96.36.1990.40.45 Eq. W.C. Profile Dry W.C. Profile 0 20406080 100120140160180200220240 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 Eq. WC Profile Dry W.C.Profile Figure 4.7 Departure of Drying Water Content Profil e from the Equilibrium with Increasing Water Table Depths. (a) Near Equilibrium for Shallow Water Table (b) Following Water Table Decline. Water content (cm 3 cm 3 ) Depth below land surface (cm) (a) (b)
110 One of the biggest implications of this observation is that the specific yield values calculated by Loheide et al. may be only applicable to phreatophytes and the tri-linear diagram obtained by them will be valid only if the roots are extracting water solely from the ground water. 4.5 Conclusions Numerical simulations were done to analyze the var iability in specific yield under different stresses: wetting, drying, and pumping, a s well as equilibrium. It was found that there is significant variation in the specific yiel d values depending on the water table depth and the stresses involved. The value of speci fic yield was found to be lower than equilibrium for wetting conditions while for drying it was higher. ET rate as well as redistribution time was found to play a major role in deciding the value of specific yield for any depth to the water table An important conclusion that comes from this analy sis and corroborates previous theories is that the assumption of a constant speci fic yield is erroneous and may cause large error in the calculation, especially in shall ow water table environments (dWT < 2m). For pumping scenarios it was found that, contrary t o the assumption of most models (e.g., MODFLOW), SY deviated from equilibrium conditions substantially In addition, for wetting scenarios it was observed that the redistri bution time was the main factor governing the specific yield variability and that r echarge and the corresponding water table response can lag behind the infiltration even t significantly (> 40 days) even in modest water table depths (< 2 m). In a field setti ng with plant water demand, most of the
111 delayed recharge would undoubtedly be taken up by t he ET during inter event periods throughout the root zone. From the point of view of potential error introduc ed, it can be concluded that the for deep water table conditions (> 2m) the SY values tend to converge within 10-15% of equilibrium, implying that the assumption of consta nt/equilibrium specific yield can be used as a good approximation for simulating water t able fluctuation under these conditions. It should be noted that hysteresis was not simulated in the HYDRUS-1D runs, yet strong specific yield variability was obtained. Therefore, it can be concluded that variability in specific yield is not just an artifa ct of hysteresis; its presence, however, will enhance variability in SY. The above sets of simulations were done only for f ine sandy soil characteristic of the coastal plain and in particular, west-central F lorida. The main objective was to discuss the qualitative behavior of the specific yi eld with water table stress. Depending on the site and specific soil parameters, the quant itative behavior may change significantly. However the implications for and po ssible errors in, predictive models of the water table in alluvial, wetland and other shal low water table settings is significant.
112 Chapter 5: Vadose Zone Evapotranspiration Distribut ion and Conceptualization for Integrated Modeling 5.1 Introduction The vadose zone is an intrinsic part of the hydrol ogic cycle, essentially controlling interrelationships between precipitatio n, infiltration, surface runoff, evapotranspiration (ET) and ground water recharge. The vadose zone regula tes the transfer of water from the land surface to ground w ater and vice versa, while providing protection, screening, filtering, transfer, and att enuation of potential ground water contaminants that are delivered via the land surfac e. Yet, unlike the ground water below and surface water resources above, the dynamics of the vadose zone have not been quantified as well (Harter and Hopmans 2004). The p otential for continuous capillary rise maintains ET at potential rates long after other parts of the l andscape dry out (Gardner 1958). The vadose zone receives water from rainfall and c apillary rise, and delivers water through ET. ET is an important element of the hydrologic cycle an d is the dominant component of the annual rainfall of a region (e.g., 70 or 80 percent in Florida Bidlake et al. 1993; Knowles 1996; Sumner 2001). Unfortunately ET can be the most difficult hydrologic process to analyze.
113 Of several different approaches of quantifying the distribution of ET stress (e.g., Bicknell et al. 2001; Banta 2000) in the unsaturate d and saturated zone, the approach involving solution of RichardÂ’s equation for unsatu rated flow can provide a more precise method of determining water movement between the so il surface and the ground water table. However, due to the computational burden and data requirements of this approach, most of the watershed models use simple approximati ons or empirical algorithms to allocate evapotranspiration to different regions in the vadose zone. ET distribution plays a critical role in integrated models which combine th e surface water and ground water processes via vadose zone. The uncertainties in th e source of ET, whether supported by water table, or the vadose zone, can introduce erro r in simulations of water table in recharge and base flow. A number of integrated models have been developed in the past 10 to 20 years including, FHM (Ross et al. 1997), WASIM-ETH (Schul la and Jasper 2000) and the Integrated Hydrologic Model (IHM) (Ross et al. 2003 ). Different integrated models use different approaches to partition ET stress between saturated and unsaturated zones. Fo r instance, IHM distributes ET using a three-layer soil water concept (Ross et al 2005). The three-layer concept defines four thresholds con trolling vadose zone and ground water contribution to ET. Based on these thresholds, ET demand from the vadose zone/ground water (water table) can be satisfied: (a) entirely by the vadose zone, (b) partially from both vadose zone and ground water, (c) by direct ev aporation from the soil, or (d) entirely by ground water at open-water evaporation rates.
114 5.1.1 Objectives and Scope Though the origin of the above mentioned three-lay er soil water concept lies in the conceptualization of ET processes in one of the most commonly used surface water model, Hydrologic Simulation Program-FORTRAN (HSPF) (Bicknell et al. 2001), it has never been rigorously tested using the saturated-un saturated theoretical flow equations. The objectives of this chapter are thus: (a) To use a theoretical framework to determine the distribution of ET stress between the vadose zone and ground water an d (b) compare and contrast the results obtained with the three la yer concept used in IHM. 5.2 Materials and Methods The simulation technique and the type of soil used are same as that used in Chapter 5 on specific yield. However, as the intere st now is to find out thresholds that control vadose zone and ground water components of the total ET flux, different initial and boundary conditions were defined. 5.2.1 Initial and Boundary Conditions Two simulations were done by changing the initial and boundary conditions to simulate the process of evapotranspiration in as mu ch detail as possible. The first simulation was set initially to have depth to the w ater table (dWT) at 20 cm below land surface, while dWT of 250 cm below land surface was set up for the se cond simulation. To facilitate easy reference, the simulations can be n amed as simulation A and simulation B, respectively. The initial conditions in the soil co lumn were set up to be hydrostatic in both sets. In both scenarios, the upper boundary wa s assumed to have no surface runoff
115 and the land surface was open to the atmosphere. In addition, a no flux boundary (constant flux = 0) was assumed as the lower bounda ry of the soil column. A 100 cm uniform root zone was assumed for the sim ulations to facilitate transpiration out of the soil column. As an average number for many regions in the U.S during the growing season, an ET of 0.5 cm/day was applied as a constant potential stress (e.g., Nachabe et al. 2005; Linsley and Franzini 19 72). The post processing of the HYDRUS output was carri ed out in the exact same steps as described in Chapter 4. Free vadose zone s torage, non-ground water flux and ground water flux were consequently determined for both simulations A and B. What follows is a brief discussion about the three -layer concept used in IHM for ET partitioning. The purpose of the discussion is to provide a background to help in the discussion of results. Detailed information about I HM and/or ET conceptualization in IHM can be found in (Ross et al. 2005). 5.2.2 Three-Layer/Two Zones Concept The Integrated Hydrologic Model (IHM) was develope d to simulate surface and ground interaction especially in shallow water ta ble systems (Ross et al., 2005). IHM couples surface and ground water processes in a uni que integration of the Hydrological Simulation Program-FORTRAN (HSPF) (Bicknell, et al. 2001) and MODFLOW (McDonald and Harbaugh 1996) respectively. In HSPF (Bicknell et al. 2001), the unsaturated zo ne between the land surface and water table is divided into two regions, the upper zone (top 10-15 cm) and the lower zone (remainder of the vadose zone) as shown in Figure 5 .1. The upper zone is comprised of
116 Â‘AÂ’ horizon (shallow soil), and surface depressions, including small isolated wetlands, ponds, and small lakes, not Â“routedÂ” in the model. The lower zone represents the remainder of unsaturated zone down to the shallower of the extinction elevation or the water table elevation. It is the lower zone which i s responsible for sustained moisture availability and dry period root zone evapotranspir ation (Bicknell et al. 2001). Layer1: Upper ConstantMoisture Region Layer 2: IntermediateCapillary Zone Layer 3: LowerCapillary Fringe DryProfile WetProfile EquilibriumProfile ZCZZCFZWT (z) Upper Zone Lower ZoneMean Land Surface ZRZ Ground Level Figure 5.1 Three-Layer Water Content Concept Used i n IHM. IHM partitions the water within the saturated and u nsaturated zones using a three layer soil water retention profile. This assumption is considered to be a significant improvement over the simple uniform moisture profil e assumption of the integrated models (e.g., MIKE-SHE (Ross et al. 1997)), in the approach of integrated modeling. The three-layer concept has lead to four threshold cond itions that illustrate transition points in
117 the distribution of ET. Based on these thresholds, ET demand from the vadose zone/ground water can be satisfied: (a) entirely by the vadose zone, (b) from both vadose zone and ground water, (c) from the soil (direct ev aporation), or (d) entirely from ground water at fractional potential evaporation rates. In IHM, for analyzing soil water variability, the lower zone is divided into three layers; the upper gravity region, the intermediate capillary zone, and the lower capillary zone (capillary fringe) as shown in Figure 5.1. Low er zone storage as defined in IHM is the moisture available to the root zone for any giv en water table elevation that is above the wilting point, or driest profile. For deep wate r table conditions, the lower zone storage can exhibit the largest values incorporating a rang e of variable soil water retention to an effective depth below the root zone (assumed to be the soil intermediate capillary zone thickness). This follows the plant behavior within the root zone, i.e., the ability of plants to reduce soil water content to near wilting value and indirectly bringing about a reduction in the soil water content. The deepest layer, right above the water table, re presents the near-saturation capillary fringe. This layer is followed by the int ermediate layer of capillary rise. This intermediate layer shows maximum variation of soil water with depths. Both layers are assumed to be fixed by the soil type. For deep wate r table conditions (dWT > x), the uppermost layer (close to land surface) represents the nearly uniform soil water region above the capillary rise (capillary zone). For shal lower conditions of water table this layer of uniform soil water content may be totally absent Three profiles are shown in Figure 5.1, corresponding to dry, equilibrium and wet soil moisture conditions of a mildly sorptive soil (e.g., loamy sand). The thick lines o n the figure represent the actual profiles
118 in a uniform soil and the thin lines represent a st epwise, linear approximate profile developed for computational efficiency. Because evapotranspiration (ET) represents a dominant process in the water cycle (second only to rainfall) and controls the partitio ning of energy and water fluxes at the land surface, it is used in this study to test the three-layer approach. Four threshold conditions (case a-case d), shown in Figure 5.2, il lustrate transition points in the distribution of ET from one region of vadose zone or ground water to another. All elevations, z, are relative to a common datum (e.g. the National Geodetic Vertical Datum of 1927, NGVD) including land surface (zLS), capillary zone (zCZ), capillary fringe (zCF), root zone (zRZ), and water table (zWT). 5.3 Results and Discussion 5.3.1 Numerical Simulation Results from the HYDRUS-1D model that were used to determine the actual ET leaving the soil column simulation showed that the extinction depth was about 250 cm (based on ET/PET of 0.5%) for the root zone of 100 cm. Based on the Brooks and Corey function fitted to retention data for Myakka fine s and, the thickness of the capillary zone (a region of pronounced elevated retention) comes o ut to be approximately 150 cm. Thus, the extinction depth is consistent with the IHM def inition of capillary zone plus root zone. On looking closely at Figure 4.1 and comparin g it with Figure 5.1, distinct threelayer behavior for the soil types found in west-cen tral Florida can be easily observed. Also shown in Figure 4.1, the capillary zone of the median water retention characteristics is approximately 150 cm. Thus, HYDRUS 1D solutions support the IHM definition of
119 extinction depths and also the three layer soil wat er retention behavior can be clearly observed. Figure 5.2 Thresholds Used in IHM for Distribution of ET between Vadose Zone and Ground Water. 5.3.2 ET Thresholds Conditions 188.8.131.52 Case A As conceptualized in IHM that if water table is at or below extinction, all the contribution will be from the vadose zone, i.e., al l the ET will be supported by free vadose zone storage. The simulation of HYDRUS-1D wi th water table at 250 cm below
120 land surface with initial conditions being hydrosta tic showed that even after 10 days of ET stress, the water table did not decline further an d all flux came from the storage above the water table (vadose zone ET). Figure 5.3 shows that the initial equilibrium pr ofile has shifted over to the dry profile. However, there was no movement in the water table and the actual ET rate declined very fast to a value below 0.5% of PET after 10 days, the working definition of extinction depths. 0 50 100150200250 00.050.10.150.184.108.40.2060.40.45 Initial Eq. W.C.Profile W.C. Profile after 10 days Figure 5.3 Water Content Profiles for Equilibrium a nd Dry Conditions after 10 Days of ET with Water Table at the Extinction Depth. 220.127.116.11 Case D To validate case D, the simulation was done starti ng with the water table depth of 20 cm below ground water. However, as in Figure 4. 3, the ground water supports all the ET at potential rate, up to a depth of around 60 cm, which is about four times the magnitude of capillary fringe (15 cm). The reason f or this can be explained by the Depth below land surface (cm) Water content (cm 3 cm 3 ) W.C. Profile After 10 Days Initial Eq. W.C. Profile
121 weakening of the hydraulic connection with the wate r table for depth below 60 cm, where the water transpired by roots cannot be replenished at the same rate by ground water. Deep roots can extract water directly from the grou nd water up to greater depths, thus ground water contribution remains at potential to a greater vertical extent. Therefore, depth to water table at capillary fringe depth is a reasonable threshold for complete ground water PET support (all ground water ET) however, HYDRUS 1D solution indicate that the potential ET is satisfied from ground water contribution up to 60 cm. 18.104.22.168 Case B and Case C For cases B and C, for dWT greater than 60 cm the contribution from the stora ge in the vadose zone becomes important and hence, as sho wn in Figure 4.3 in Chapter 4, as the ground water contribution decreases the free va dose zone ET flux increases. The combined vadose zone plus ground water flux support s the PET rate to a depth of 1 m. If water table continues to drop (from case D to cases B and C) after the initial transition, ET will be supported by ground water ET and partially vadose zone ET contribution as conceptualized in IHM. Once the water table drops b elow the root zone, the free vadose zone flux will start to decrease and rapidly tend t o zero. As mentioned earlier due to the kind of boundary c onditions set up the simulation renders the vadose zone conditions to be driest pos sible state for any dWT at the given ET stress. To determine the effect of wetter vadose zo ne conditions on the ET distribution simulations with different initial dWT under hydrostatic conditions were done, the result s were compared with the original simulation. Figure 5.4(a) shows total soil moisture above the water table plotted versus corresponding dWT. The change in the TSM above
122 the water table can be considered as an indicator o f the contribution from the vadose zone while the water table decline shows the saturated g round water contribution. From Figure 5.4(a) it is clear that the equilibrium and the soi l moisture values obtained from the initial simulation sort of blanket out the soil moisture va riation in the vadose zone, hence corroborating the earlier statements about driest c ondition and maximum (Free vadose zone storage). Two main characteristics as seen in Figure 5.4(a) are, (a) at any dWT the initial conditions starts from the equilibrium (as set up i n the model) and ultimately transitions to the moisture profile of the original simulation and (b) the rate of decline of the dWT in the transitions keeps on decreasing as the initial dWT keeps on increasing. These observations indicate that non-coupled flux increas es proportionally with the degree of wetness of vadose zone profile. A close analysis of Figure 5.4(a) show the above 60 cm vadose zone conditions donÂ’t play a role as they ar e always at equilibrium. Around 100 cm, both the vadose zone and the ground water stora ge are actively supporting the ET stress however the loss of vadose zone soil moistur e now is clearly greater than the initial simulation, showing greater magnitude of (Non ground-water flux). For deeper water table (dWT >150) it can be seen that all the ET stress is supported by vadose zone until the soil moisture conditions transitions to the driest possible profile after which the water table contribution becomes active. At or beyond ex tinction all the extra moisture of vadose zone is lost and then ET virtually stops without bringing about any changes in the dWT (as previously noted in Figure 5.3). The above obs ervations prove that the thresholds of ET remain unchanged for different antecedent moisture conditions; however the magnitude of contribution coming from saturated gro und water and vadose zone is highly
123 dependent on prior conditions. To test for water co ntent profile wetter than equilibrium two different simulations involving rainfall for so me time, followed by the ET stress were done. The results are plotted in Figure 5.4(b). As expected from the concept all the extra moisture beyond equilibrium was first dried up with out any water table change and then the transition to the driest profiles begins exactl y similar to what was observed in earlier simulation (Figure 5.4(a)). 5.4 Limitations Although the above results and discussion showed t hat the concept of the three layer model can be verified using the HYDRUS-1D mod el, there are certain limitations to this verification as well as some differences betwe en the two models. Rigorous threelayer concept in IHM is a simple approach requiring no flux-stress model. The problem with Brooks and Corey model is that the thickness of the capillary fringe layer that has to be defined explicitly. In this study, a thickness of 15 cm was predefined. The comparisons between the two models sho wed that the qualitative definition for the layer thicknesses can lead to overestimatio n or underestimation of the threshold thicknesses as in case D.
124 0 50 100150200250300 051015202530WT@ 50 cm WT@125 cm WT@100 cm WT@150 cm WT@200 cm WT@225 cm Total Soil Moisture @ Equilibrium Total Soil Moisture under Driest Conditions 0 50 100150200250300 05101520253035WT @100 cm WT @200 cm Total Soil Moisture @ Equilibrium Total Soil Moisture under Driest Conditions Figure 5.4 Variation of Total Soil Moisture above t he Water Table under Different Initial Water Table Depths or Initial Water Content Conditions at (a) Equilibrium (b) Wetter than Equilibrium. Depth to the water table (cm) Total soil moisture above water table (cm) (a) (b) Total Soil Moisture under Driest Conditions
125 The three-layer model verification using the theore tical equations is a sort of qualitative analysis dealing with the thresholds co ntrolling the ET partitioning to the vadose zone and ground water. The calculation of ex act quantitative description is difficult as it is highly dependent on the antecede nt moisture conditions, which are really dynamic in nature. 5.5 Conclusions The HYDRUS-1D model was used to numerically solve the RichardÂ’s equation, with imported plant ET stress and was subjected to several Â“what ifÂ” inve stigations. The Brooks and Corey and van Genuchten models were fitt ed to the median water retention characteristics curve of the soil types found in we st-central Florida. The Brooks and Corey model was found to be superior to the van Gen uchten retention model, reproducing observed data and describing the observation well f rom the raw record. The simulated and fitted data clearly support the approach of IHM. The definition of the extinction depth is not strict and depends o n soil type and retention character. However, in this paper, the extinction depth was de fined as the depth at which ET rate declined to become less than 0.5% of its initial va lue. Comparing the observed data and fitted data indicates similar three layer behavior. Four thresholds cases were checked for validity us ing HYDRUS-1D model. In the first three cases (deep water table, root zone clos e to water table, and transition to direct ground water evaporation), there were close matches between the two models. In the fourth case (ground water evaporation at open water ), potential ET can be satisfied from ground water contribution for a depth greater than capillary fringe.
126 Although there are similarities in both HYDRUS-1D and IHM, the two models have a different perspective at representing the va dose zone. While HYDRUS-1D can be applied for small-scale cases, site-scale, IHM is t ypically applied at regional or watershed scales. The three-layer model used in IHM and the t hreshold conditions presented appear to be theoretically sound and simplify the approach
127 Chapter 6: Determination of Root Water Uptake: Calc ulation from Soil Moisture Data and Conceptualization for Modeling 6.1 Introduction Simulating root water uptake is an integral compon ent of modeling evapotranspiration using any hydrological model. Tr aditionally used models and concepts, however, make over simplifying assumption s about plants (Shah et al. 2007b), hence casting a doubt on the model results. Hence, what needs to be done is to try and combine land cover characteristics in the root wate r uptake models to produce more reliable results. The current chapter discusses a new branch of stud y called Â‘Eco-HydrologyÂ’ which aims at progressing the interdisciplinary wor k on ecology and hydrology with an objective of improving hydrological modeling capabi lities. The chapter also presents a methodology involving use of soil moisture and wate r table data to calculate root water uptake and how the observation of root water uptake contradict the assumptions commonly used root water uptake models. The second part of the chapter will take a step further and propose a modeling framework wherein la nd cover characteristics can be used to model root water uptake.
128 6.2 Background Over the past two centuries, rapid increase in hum an population coupled with unplanned water management activities has resulted in severe degradation of ecosystems on a global scale (Zalewiski 2000). Several studie s have shown that the mechanisms of interaction of the biota with their surroundings co ntribute to their spatiotemporal patterns (Rodriguez-Iturbe and Porporato 2004). Hence, knowl edge about species specific interaction with its environment is of utmost impor tance for successful restoration efforts. Historically, hydrology and ecology have evolved a s two distinct sciences with little or no connection with each other (Baird and Wilby 1999). As an example, for a hydrologist, plants on the river bed have never bee n more than a ManningÂ’s roughness coefficient; similarly for an ecologist, the soil i s no different than a reservoir of water. It is this difference in perspectives that has limited our ability to forecast changes, assess impacts and develop mitigation strategies. Traditio nal relationships used for quantifying hydrological processes, though very useful, are bas ed more on empiricism rather than actual experimental approaches. Estimating evapotra nspiration from pan measurements (Doorenbos and Pruitt 1977), specifying extinction depths based on qualitative rules (Anderson and Woessner 1991), and estimation of rec harge to ground water as a calibration parameter (e.g., MODFLOW (Harbaugh et a l. 2000)) are some of the relationships that have been in use in hydrology pr imarily because the plants physiology has been ignored. Recent studies, like that of Shah et al. (2007) and Nachabe et al. (2005), have shown that processes like evapotranspi ration, recharge, etc. are strongly a function of the type of vegetation cover and climat e. Ignoring the land cover effects can hence lead to erroneous estimate of these fluxes.
129 To cater to this need, interdisciplinary work in e cology and hydrology has been initiated. Zalewiski et al. (1997), Rodriguez-Iturb e and Porporato (2004) have shown promising results from seminal research in this new area called Â‘Eco-hydrologyÂ’, thereby increasing confidence in the use of ecohydrological framework for understanding species dynamics. Despite the recent progress, our knowled ge about species interaction, especially that of plants in ecotones and response of an ecosystem to the change in ambient conditions remains limited. An important gap that remains in the eco-hydrologi cal framework is the ability to successfully simulate the spatial and temporal patt erns of root zone soil moisture. Fundamental to the modeling of the soil moisture dy namics in the root zone is the knowledge of the water uptake patterns by roots. T wo major classes of root water uptake models that are in use are the microscopic scale mo dels (Steudle 2000), where water movement along single root hair is modeled, and the other is the macroscopic model where instead of a root hair, a section of roots is considered (e.g., Feddes et al. 1978). The former class of models, even though more accura te, require more information and hence become infeasible while modeling on the water shed scale (~10 km2); the latter class of models are empirical and even though they can be applied on large scales do not consider plant physiology and hence cannot be used with confidence for modeling purposes. Analytical watershed scale models based on soil ph ysics have the capability to simulate the moisture conditions in the unsaturated vadose zone, incorporating variability in soil and atmospheric conditions. However, empiri cal conceptualization of root water uptake in these models cast a doubt on the validity of the model results.
130 6.2.1 Objectives and Scope The objective of this paper is thus to: (a) discus s the empirical root water uptake models used, (b) to describe a methodology involvin g field data to calculate root water uptake, (c) use field data to compute root water up take values, (d) compare and contrast the model derived estimated from those derived from field data, and (e) propose a modeling framework involving plant physiological ch aracteristics to model root water uptake 6.3 Theory The governing equation for soil moisture dynamics in the unsaturated soil zone is the RichardÂ’s equation (Richard 1931). RichardÂ’s eq uation is derived from DarcyÂ’s law and the continuity equation. What follows is a brie f description of RichardÂ’s equation and how can it incorporates root water uptake. For more detailed information about the formulation of RichardÂ’s equation, including its de rivation in three dimensions, the readers are directed to any text book on soil physi cs e.g., Hillel (1998). Due to ease of measurement and conceptualization, energy of water (E) is represented in terms of height of liquid column and is called the hydraulic head (h). It is defined as the total energy of water per unit weigh t. Mathematically hydraulic head, h, can be represented as g E hWr= (6.1) where W is the density of water and g is the acceleration due to gravity. The flow of water always occurs along decreasing head. In soil physics, the fundamental equation
131 used to model the flow of water along a head gradie nt is known as DarcyÂ’s Law (Hillel 1998). Mathematically the equation can be written a s l h K q D = (6.2) where q [L3L-2T-1] is known as the specific discharge and is defined as the flow per unit cross-sectional area, K [LT-1] is termed as the hydraulic conductivity, which in dicates ease of flow, h [L] is the head difference between the points of i nterest and l [L] is the distance between them. DarcyÂ’s Law is analogous to OhmÂ’s law with head gradient being analogous to the potential difference and, current being analogous to specific discharge and hydraulic conductivity being similar to the con ductance of a wire. The second component of RichardÂ’s equation is the equation of continuity. The continuity equation is based on the law of mass con servation, and for any given volume it states that the net increase in storage in the give n volume is inflow minus the sum of outflow and any sink present in the volume of soil. Mathematically it is this sink term that allows the modeling of water extracted from th e given volume of soil. In one dimension, for flow occurring in the vertic al direction (z axis is positive downwards), RichardÂ’s equation can be written as S 1 z h K z t + = q (6.3) where is the water content, defined as the ratio of volu me of water present and total volume of the soil element t is time, S represents the sink term while other terms are as defined before.
132 If flow in lateral directions is also considered, RichardÂ’s equation in three dimensions can be derived. Solution of the partial differential equation derived above can, hence, theoretically provide the spatial and t emporal variability of moisture in the soil. However, due to the high degree of non linear ity of the equation, no analytical solution exists for RichardÂ’s equation and numerica l techniques are used to solve it. For a numerical solution of RichardÂ’s equation, two ess ential properties that need to be defined a-priori are, (a) relationship between soil water content and hydraulic head, also known as, soil moisture retention curves and (b) a model that relates hydraulic head to root water uptake. While much of literature and fie ld data exist describing the soil moisture retention curves, relatively less informat ion exists about root water uptake models. The root water uptake models generally used especially on a watershed scale, are mostly empirical and lack any field verificatio n. The main reason for this can be attributed to the fact that, until recently, plant physiology was ignored in hydrological modeling. Details about the soil moisture retention curves and numerical techniques used to solve RichardÂ’s equation can be found in Simunek et al. (2005). The focus of this paper will be on root water uptake models and field data that contradict the existing models. 6.3.1 Root Water Uptake Model The most common approach used to model root water uptake is to define sink term S as a function of hydraulic head using the fo llowing equation pS) h ( ) h (Sa= (6.4)
133 where S(h) [L3L-3T-1] is the actual root water uptake (RWU) from roots subjected to hydraulic or capillary pressure head Â‘hÂ’. On the right hand side of the equation Sp [L3L3T-1] is the maximum (also known as potential) uptake o f water by the roots. The (h) is a root water uptake stress response function, with it s values varying between 0 and 1. The idea behind the conceptualization of Equation 6.4 is based on three basic assumptions. The first assumption being that as the soil becomes dryer, the amount of water that can be extracted decreases proportionall y. Secondly, the amount of water extracted by the roots is affected by the ambient c limatic conditions. Drier and hotter conditions result in more water loss through the st omata of leaves, hence, initiating more water extraction from the soil. The third and final assumption is that the uptake of water from a particular section of a root is directly pro portional to the amount of roots present. The root water stress response function () is a result of the first assumption. Two models commonly used to define are the Feddes model (Feddes et al. 1978) and the van Genuchten model (van Genuchten 1987). Figure 6.1(a and b, respectively) show the variation of with decreasing hydraulic head, which is same as d ecreasing water content or increasing soil dryness. Both models for are empirical and do not involve any plant physiology to define the thresholds for the water s tress response function. An interesting contrast, due to empiricism that is clearly evident is the value of during saturated conditions. While the Feddes model predict the valu e of to decrease to zero van Genuchten model predicts the opposite response with rising to become unity under saturated conditions.
134 Figure 6.1 Water Stress Response Function as Concep tualized by (a) Feddes et al. (1978) and (b) van Genuchten (1980) [Adapted from S imunek et al. 2005]. Recently a couple of different models (Li et al. 2 001; Li et al. 2006) have been presented to overcome the empiricism in ; however, these models are more a result of observation fitting and fail to bring in the plant physiology, which is what causing the changes in the water uptake rate due to variation i n soil moisture conditions. Combining the second and the third assumptions in Equation 6.4 results in the definition of Sp. Sp for any section of roots is defined as the product of root fraction in that section and the maximum possible water loss by the plant which is also known as the potential evapotranspiration. Potential evapotransp iration is a function of ambient atmospheric conditions and standard models like Pen man-Monteith (Allen et al. 1998) are used to calculate the potential evapotranspirat ion rate. For any given value of potential evapotranspiration rate, limiting the val ue of Sp by the fraction of roots restricts the amount of water that can be extracted from a pa rticular section. This, as will shown Water Response Function () (a) (b)
135 later using field data, is a big limitation especia lly during dry period when the top soil with maximum roots get dry while the deep soil laye r with lesser root mass still has soil moisture available for extraction. 6.4 Materials and Methods 6.4.1 Study Site For the current chapter, field data from the study site described in Chapter 2 is used. Soil moisture and water table data from well location PS-43 and PS-40 were used to determine root water uptake from forested versus gr assed land cover. The well PS-43 is referred to as Site A while PS-40 will be called Si te B. Hourly averaged data at a four hour time step were used for the analysis in this c hapter. Extensive soil investigations including in situ an d laboratory analysis were performed for the study site. The soil in the study area is primarily sandy marine sediments with high permeability in the surface and subsurface layers. Detailed information about soil and site characteristics can be found in Said et al. (2005), and Trout and Ross (2005). Data for the period of recor d January 2003 to December 2003 were used in this analysis. 6.4.2 Methodology Soil matrix has voids which can be filled with wat er or air. In soil physics, the ratio of the volume of voids and total volume of so il matrix is defined as porosity. If all the pores (or voids) are filled with water the soil matrix is termed as saturated and the water content in the soil matrix is called saturate d water content and is represented as s.
136 As the soil starts drying up the water content () in the soil matrix starts reducing below s. It is known that as the small pores in the soil m atrix do not necessarily make a continuous network not all of the water can be remo ved from the soil under natural conditions (Hillel 1998). Hence, even under extreme ly dry conditions, soils do not get completely dry. The minimum water content that rema ins is called the residual water content and is represented by r. A common technique used to represent the observed water content is to normalize it using Equation 6.5, hence confining the values b etween 0 and 1. r s r eSq q q q= (6.5) Here Se is called the normalized water content, varying be tween 0 and 1. is the observed water content, while r and s are the residual and saturated water content values, respectively. An important implication of varying water content, which greatly affects the soil moisture dynamics, is the fluctuations in the value of hydraulic conductivity of soil. When the soil is saturated all the pores are well c onnected and hence the water can flow thorough the soil matrix easily. However, as the so il starts drying, the path gets blocked due to intermittent air pockets that develop due to evaporation of water from the pores. The net result is that the water carrying capacity of soil is reduced, which is manifested as the reduced hydraulic conductivity (Jury et al. 199 1). Hence, with increasing soil dryness, which increas es soil suction head, both water content and hydraulic conductivity are reduced. van Genuchten (1980) proposed a model
137 relating the water content and hydraulic conductivi ty with the suction head and is represented by the following equations f qn 1 m 1 e)1 S ( ) (h = (6.6) < = 0 h K 0 h ) S 1( 1 [ S K ) h ( KS m m /1 e l e S (6.7) where m = 1 Â– 1/n for n > 1, Se [-] is the normalized water content, KS [LT-1] is the hydraulic conductivity when the soil matrix is satu rated, l [-] is the pore connectivity parameter assumed to be 0.5 as an average for most soils (Mualem 1976), and f [L-1], n [-] and m [-] are the van Genuchten empirical param eters. Negative values of hydraulic head means the water content in the soil matrix is less that saturated water content while the positive values indicate saturated conditions. From Equations 6.6 and 6.7, it is clear that for each type of soil, five parameters, namely KS, n, f, r and s have to be determined to uniquely define the relationship of h ydraulic conductivity and water content with soil suction head. Before the discussion about the how the parameters values were determined, it is essential to get a grasp of the system we are deali ng with. Figure 6.2 show the schematics of the vertical soil column which is monitored usin g eight soil moisture sensors and a pressure transducer measuring water table elevation at each of the two locations. Shown also in Figure 6.2 is the zone of influence of each sensor along with the elevation of water table and arrows showing possible flow directions.
138 Sensor @ 10 cm Sensor @ 20 cm Sensor @ 30 cm Sensor @ 50 cm Sensor @ 70 cm Sensor @ 90 cm Sensor @ 110 cm Sensor @ 150 cm WT Figure 6.2 Schematics of the Vertical Soil Column w ith Location of the Soil Moisture Sensors and Water Table. For the purpose of defining moisture retention and hydraulic conductivity curves, each section is treated as a different soil layer a nd was independently parameterized. Hence, for each of the two locations for this parti cular study eight, soil cores from depths corresponding to the zone of influence of each sens or were taken and analyzed using the methods described below.
139 22.214.171.124 Saturated and Residual Water Content Actual water content measurements for all the eigh t locations were available for each of the two sites, for around two years, with w ell pronounced wet and dry seasons. Hence, from the observed data, the maximum and mini mum water content was set up as saturated and residual water content, respectively. 126.96.36.199 Saturated Hydraulic Conductivity Saturated hydraulic conductivity (KS) for different soil layers at the study locations was calculated using falling head permeam eter analysis as described in Das (2002). Falling head permeameter test is a standard technique to determine the saturated hydraulic conductivity. Multiple tests were done an d the results were averaged to determine the most appropriate value of saturated h ydraulic conductivity for each of the soil layers at both the study locations. 188.8.131.52 van Genuchten Parameters To determine the values of parameters n,f the soil cores taken out were saturated and rotated in a centrifuge. Rotating the sample co res generated outward centrifugal force that created suction forces in the soil sample and caused the loss of water from the sample. For each revolution per minute (RPM) settin g, the soil sample was weighed and depending on the saturated weight and water content the new water content value was determined. Moisture retention curves from the meas ure data were then plotted and fitted with Equation 6.6 and the best fit values of n,f, were taken as the parameter value for the respective soil layer.
140 The method to determine moisture retention curve h as been used in the past by Carlisle et al. (1989) as a part of comprehensive s oil survey of Floridian soils. Table 6.1(a) and (b) shows the parameters values that wer e obtained following the all the soil tests. Table 6.1 Soil Parameters for Study Locations in (a ) Grassland and (b) Forested Area. (a) Sensor Location below land surface (cm) s (%) r (%) (cm-1) n (-) KS (cm/hr) 10 38 3 0.02 1.35 0.0100 20 34 3 0.03 1.35 0.0100 30 31 3 0.03 1.35 0.0100 50 31 3 0.07 1.90 0.0100 70 31 3 0.20 2.20 0.0100 90 31 3 0.20 2.20 0.0004 110 33 3 0.20 2.20 0.0004 150 35 3 0.20 2.10 0.0012 (b) Sensor Location below land surface (cm) s (%) r (%) (cm-1) n (-) KS (cm/hr) 10 35 3 0.03 1.85 4.212 20 35 3 0.07 1.7 2.520 30 32 3 0.07 1.7 2.520 50 34 3 0.03 1.6 0.803 70 31 3 0.03 1.6 0.005 90 32 3 0.05 1.9 0.005 110 32 3 0.05 1.8 0.005 150 30 3 0.05 1.8 0.001
141 184.108.40.206 Calculation of Root Water Uptake Once the soil parameterization is complete, root w ater uptake from each section can be calculated. For any given soil layer in the vertical soil column (Figure 6.2), above the observed water table, observed water content an d Equation 6.6 can be used to calculate the hydraulic head. For soil layers below the water table, hydraulic head is the same as the depth of soil layer below the water tab le due to assumption of hydrostatic pressure. Similarly using Equation 6.7, hydraulic conductivity can be calculated. Hence, at any instant in time, hydraulic head in each of t he eight soil layers can be calculated. To determine total head, gravity head, which is the he ight of the soil layer above a common datum, has to be added to the hydraulic head. For t his particular study, the datum was arbitrarily selected as 2000 cm below the land surf ace. Water flow along decreasing head, hence, depending on total head values of the adjace nt layers and the direction of water flow for a given soil layer is determined. To quantify flow across each soil layer, DarcyÂ’s L aw (Equation 6.2) is used. Average head values between two consecutive time st eps are used to determine the head difference. Also, flow across different soil layers is assumed to be occurring between the midpoints of one layer to another, hence, to determ ine the head gradient (h/l) the distance between the midpoints of each soil layer i s used. The last component needed to solve DarcyÂ’s Law is the value of hydraulic conduct ivity. For flow occurring between layers of different hydraulic conductivities equiva lent hydraulic conductivity is calculated by taking the harmonic mean of the hydraulic conduc tivities of both the layers (Freeze and Cherry 1979). Hence, for each time step, harmon ically (Equation 6.8) averaged hydraulic conductivity values were used to calculat e the flow across soil layers.
142 2 1 2 1 eqK K K K 2 K + = (6.8) where K1 [LT-1]and K2 [LT-1]are the two hydraulic conductivity values for any two adjacent soil layers and Keq [LT-1]is the equivalent hydraulic conductivity for flow occurring between those two layers. Figure 6.3 Schematics of a Section of Vertical Soil Column Showing Fluxes and Change in Storage. Figure 6.3 shows a typical flow layer with inflow and outflow marked. Now using simple mass balance, changes in water content at tw o consecutive time steps can be attributed to net inflow minus the root water uptak e (assuming no other sink is present). Equation 6.9 can hence be used to determine root wa ter uptake from any given soil layer with thickness Z cm ) q q ( Z) ( RWUin out 1 t t=+q q (6.9) Using the described methodology, one can determine the root water uptake from each soil layer at both study locations (site A and site B).
143 Time step for calculation of the root water uptake was set as four hours and the root water uptake values obtained were summed up to get a daily value for each soil layer. The results section describes the finding of the study. 6.5 Results Using the above methodology, root water uptake was calculated from each section of roots for tree and grass land cover from January to December 2003 at a daily time step. Figure 6.4(a and c) shows the variation of root wat er uptake for a representative period from May 1st to May 15th, 2003. This particular period was selected as the conditions were dry and there was no rainfall. Graphs in Figur e 6.4(a and c) show the root water uptake variation corresponding to each section. Als o plotted on the graphs is the normalized water content, which gives an indication of water, lost from the section. Figure 6.4(a) shows the root water uptake from gra ssed site while the panel of graphs in Figure 6.4(c) plots RWU from the forested area. From Figure 6.4(a and c) it can be seen that in both the cases of grass and forest the root water uptake varies with water content and when the top layers starts to get dry, then the water uptake from the lower layer increases so as to keep the root water uptake constant clearly indicating that compensation do take place and hence the models nee d to account for it. Another important point to note is that, in Figure 6.4(a), root water uptake from the top three layers accounts for the almost all the water uptake while in Figure 6.4(b) the contribution from fourth and fifth layers is also significant. Also, as will be shown later (Figure 6.6), in the case of forested land cover, root water upta ke is observed from the sections that are even deeper than 70 cm below land surface. This is expected owing to the differences in
144 Sensor @ 10 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 RWU (cm/day) Se Sensor @ 20 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 Sensor @ 50 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 Sensor @ 30 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 Sensor @ 70 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 Sensor @ 90 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 Sensor @ 10 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 RWU (cm/day) Se Sensor @ 20 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 Sensor @ 50 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 Sensor @ 30 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 Sensor @ 70 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 Sensor @ 90 cm0.00 0.10 0.20 0.30 0.40 0.50 5/1/035/6/035/11/03 0 0.2 0.4 0.6 0.8 1 (a) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 5/15/35/55/75/95/115/135/15 PET / RWU (cm/day) 0123456789 Rainfall (cm) PET (cm/day) RWU (cm/day) Rainfall (cm) (b) Figure 6.4 Root Water Uptake from Sections of Soil Corresponding to Each Sensor on the Soil Moisture Instrument for (a and b) Grass La nd and (c and d) Forest Land Cover. Se Root water uptake (cm/day)
145 Sensor @ 10 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 RWU (cm/day ) Se Sensor @ 20 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 Sensor @ 30 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 Sensor @ 50 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 Sensor @ 70 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 Sensor @ 90 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 Sensor @ 10 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 RWU (cm/day ) Se Sensor @ 20 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 Sensor @ 30 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 Sensor @ 50 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 Sensor @ 70 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 Sensor @ 90 cm 0.00 0.10 0.20 0.30 5/1/035/6/035/11/03 0 0.4 0.8 1.2 (c) 0 0.2 0.4 0.6 0.8 1 1.2 5/15/35/55/75/95/115/135/15 RWU/PET (cm /day) 00.511.522.533.544.55 Rainfall (cm) PET RWU Rainfall (d) Figure 6.4 (Continued) Root water uptake (cm/day) Se
146 the root systems of both land cover types. While gr asses have shallow roots, forest trees tend to put their roots deeper into the soil to mee t their high water consumptive use. Figure 6.4(b and d) shows the values of potential ET (PET) plotted along with the observed values of root water uptake. On comparing grass versus forested graphs it is evident that the grassland is still evapotranspirin g at values close to PET, root water uptake from forested land covers is occurring at le ss than potential. This behavior can be explained by the fact that water content in the gra ssed region (as shown by the normalized water content graph), due to shallower w ater table (not shown in the figure), is more than that of the forest and even though the 70 cm sensor shows significant contribution the uptake is still not sufficient to meet the potential demand. Figure 6.5 shows an interesting scenario when a ra infall event occurs right after a long dry stretch that caused the upper soil layers to dry out. Figure 6.5(a) shows the root water uptake profile on May 18th, 2003 for the forested land cover with maximum wat er being taken from section of soil profile correspond ing to 70 cm below the land surface. A rainfall event of 1inch took place on May 19th, 2003 and, as can be clearly seen in Figure 6.5(b), the maximum water uptake shifts right back up to 10 cm below the land surface, clearly showing that the ambient water content dire ctly and instantaneously affects the root water uptake distribution. Figure 6.5(c) shows the snapshot on May 20th, 2003 a day after the rainfall where the root water uptake star ts redistributing and shifting toward deeper wetter layers. In fact this kind of behavior was observed for all the data analyzed for the period of record for both the grass land an d forested land cover. With roots taking water from deeper wetter layers and, as soon as the shallower layer becomes wet the uptakes shift to the top layers. Figure 6.6(a and b ) show a long duration of record
147 5/18/20030 20406080 100120140 0.00.10.20.3RWU (cm/day) Below Land Surface (cm) Contribution to RWU Water Table Figure 6.5 Root Water Uptake Variation Due to an In ch of Rainfall Event (a) ( b ) (c) 5/19/20030 20406080 100120140 0.00.20.40.60.8 Contribution to RWU Water Table 5/20/20030 20406080 100120140 0.00.20.40.60.8 Water Table Contribution to RWU Below land surface (cm) Root water uptake (cm/day)
148 spanning two months (starting October to end Novemb er), with the whiter shade indicating higher root water uptake. From both the figures it is reiterated that water uptake significantly shifts away from drier soil la yers, especially in the case of forest land cover (Figure 6.6(b)), while in the case of the gra ss land, uptake is primarily concentrated in the top layers. As a quick summary, the results indicate that: (a) Assuming RWU as directly proportional to root densi ty may not be a good approximation. (b) Plants adjust to seek out water over the root zone. (c) In case of wet conditions, preferential RWU from up per soil horizons may take place. (d) In case of low ET demands, the distribution of ET was found to be occurring as per the root distribution, assuming an exponenti al root distribution. Hence, traditionally used models are not adequate as such, to model this behavior. Changes in regard to the modeling techniques as wel l as conceptualizations, hence, need to be done. Plant physiology is one area that needs to be looked into to see what plant properties affect the water uptake and how can they be modeled mathematically. The next section discusses a modeling framework based on pla nt root characteristics which can be employed to model the aforesaid observations.
149 Figure 6.6 Daily Root Water Uptake Variation from O ctober to November 2003 for (a) Grass Land Cover and (b) Forested Land Cover. Below land surface (cm) (a) (b)
150 6.6 Incorporation of Plant Physiology Any framework to model root water uptake dynamical ly, will have to explicitly account for all the four points listed above. The d ynamic model should be able to adjust the uptake pattern based on root density as well as available water across the root zone. The model should use physically based parameters s o as to remove empiricism from the formulation of the equations. For a given distribut ion of water content along the root zone (observed or modeled), knowledge of root distr ibution as well as hydraulic characteristics of roots is hence essential to deve lop a physically based root uptake model. The following two sections will describe how root distributions can be modeled as well as how do roots need to be characterized to mo del uptake from rootÂ’s perspective. 6.6.1 Root Distribution Schenk and Jackson (2002) expanded an earlier work of Jackson et al. (1996) to develop a global root database having 475 observed root profiles from different geographic regions of the world. It was found that by varying parameter values the root distribution model given by Gale and Grigal (1987) can be used with good accuracy to describe the observed root distributions. Equation 6.10 describes the root distribution model. Y = 1 bd (6.10) where Y is the cumulative fraction of roots from th e surface to depth d, and b is a numerical index of rooting distribution which depen ds on vegetation type. Figure 6.7 shows the observed distribution (shown by data poin ts) versus the fitted distribution using Equation 6.10 for different vegetation types. The f igure clearly indicates the goodness of
151 fit of the above model. Hence, for a given type of vegetation a suitable b can be used to describe the root distribution. Figure 6.7 Observed and Fitted Root Distribution fo r Different Type of Land Covers [Adapted from Jackson et al. 1996]. 6.6.2 Hydraulic Characterization of Roots Hydraulically, soil and xylem are similar as they both show a decrease in hydraulic conductivity with reduction in soil moist ure (increase in soil suction). For xylem, the relationship between hydraulic conductiv ity and soil suction pressure is called the Â‘vulnerability curveÂ’ (Sperry et al. 2003) (see Figure 6.8). The curves are drawn as a percentage loss in conductivity rather than absolut e value of conductivity due to the ease
152 of determination of former. Tyree et al. (1994) and Hacke et al. (2000) have described methods for determination of vulnerability curves f or different types of vegetation. Commonly, the stems and/or root segments are spun t o generate negative xylem pressure (as a result of centrifugal force) which results in loss of hydraulic conductivity due to air seeding into the xylem vessels (Pammenter and Willi gen 1998). This loss of hydraulic conductivity is plotted against the xylem pressure to get the desired vulnerability curve.For different plant species the vulnerability curve follows an S-Shape function, see Figure 6.8 (Tyree 1999). Figure 6.8 Vulnerability Curves for Various Species [Adapted from Tyree 1999]. In Figure 6.8, y-axis is percentage loss of hydrau lic conductivity induced by the xylem pressure potential Px, shown on the x-axis. C= Ceanothus megacarpus, J = Juniperus virginiana, R = Rhizphora mangel, A = Ace r saccharum, T= Thuja occidentalis, P = Populus deltoids.
153 Pammenter and Willigen (1998) came up with an equa tion to model the vulnerability curve by parametrizing the equation f or different plant species. Equation 6.11 describes the model mathematically. ) P P .(aPLC 50e 1 100 PLC-+ = (6.11 ) where PLC denotes the percentage loss of conductivi ty P50PLC denotes the negative pressure causing 50% loss in the hydraulic conducti vity of xylems, P represents the negative pressure and a is a plant based parameter. Figure 6.9 shows the model plotted against the data points for different plants. Olive ras et al. (2003) and references cited therein have parameterized the model for different types of pine and oak trees and found the model to be successful in modeling the vulnerab ility characteristics of xylem. The knowledge of hydraulic conductivity loss can b e used analogous to the water stress response function (Equation 6.4) by scaling PLC from 0 to 1 and converting the suction pressure to water head. The advantage of us ing vulnerability curves instead of the Feddes or van Genuchten models is that vulnerabilit y curves are based on xylem hydraulics and hence can be physically characterize d for each plant species. 6.6.3 Development of a Physically Based Root Water Uptake Model The current model development is based on the mode l conceptualization proposed by Jarvis (1989); however, the parameters for the c urrent model are physically defined and include plant physiological characteristics. For a given land cover type, Equations 6.10 and 6. 11 can be parameterized to determine the root fraction for any given segment i n root zone and percentage loss of
154 conductivity for a given soil suction pressure. For consistency of representation, percentage loss of conductivity will be hence forth represented by (scaled between 0 and 1) and will be called stress index. Figure 6.9 Observed Values and Fitted Vulnerability Curve for Roots and Stem Sections of Different Eucylaptus Trees [Adapted from Pamment er and Willigen 1998]. Percentage loss of conductivity Water potential (MPa)
155 For any section of root zone, say ith section, the root fraction can be written as Ri and the stress index, determined from vulnerability curve and ambient soil moisture condition, can be written as i. The average stress level a over the root zone can be defined as the i n 1 i i _Ra a== (6.12) where n represents the number of soil layers and other sy mbols as previously defined. Thus, as can be seen from Equation 6.12, the averag e stress level a combines the effect of both root distribution and available water conte nt (via vulnerability curve). As shown in Figure 6.6(b), if there is available m oisture in the root zone, plants can transpire at potential by increasing the uptake from the lower wetter section of the roots. In terms of modeling it can be conceptualize d that above a certain critical average stress level ( Ca ), plants can transpire at potential and below Ca the value of total evapotranspiration decreases. The decrease in the ET value can be modeled linearly as shown by Liao et al. (2001). The graph of average s tress level versus ET (expressed as a ratio with potential ET rate) can hence be plotted as shown in Figure 6.10 In 6.10, ETa is the actual ET out of the soil column while ETp is the potential value of ET. Figure 6.10 can be used to determine the value of actual ET for any given average stress level. Once the actual ET value is known, contributions from individual sect ion can be modeled depending on the weighted stress index usin g the relationship defined by =a a Di i i a iR Z E S ( 6.13)
156 where Si defined as the water uptake from the ith section, Zi is the depth of ith section and other symbols are as previously defined. a Figure 6.10 Variation of Ratio of Actual to Potenti al ET with Location of the Critical Stress Level. Jarvis (1989) used empirical values to simulate th e behavior of the above function and Figure 6.11 shows the result of root water upta ke obtained from his simulation. The values next to each curve in Figure 6.11 represent the day after the start of simulation and actual ET rate as expressed in mm/day. On comparison with Fi gure 6.6, the model successfully reproduced the shift in root water upt ake pattern with the uptake being close to potential value (ETP = 5.0 mm/d) for about a month from the start of si mulation. The decline in ET rate occurred long after the start of the simulati on in accordance with the ETA/ETP
157 observed values. The model hence was successful not only in simulating peak but also in the observed magnitude of the root water uptake. The advantage of the above described approach in m odeling root water uptake is that the parameters and the characteristics are phy sically based and hence less susceptible to empiricism and, unlike the traditionally used mo del, it takes into account not only the root distribution but also the available water cont ent in determining the root water uptake. Figure 6.11 Variation in the Vertical Distribution of Root Water Uptake at Different Times [Adapted from Jarvis 1989]. 6.7 Conclusions The methodology presented here elucidates the non linear variation of root water uptake. It also revealed that the water uptake is n ot just directly proportional to amount of the roots but also depends on the ambient water con tent and under dry conditions roots can easily take water from deeper wetter soil layer s. Below land surface (cm)
158 Traditionally used models are not adequate as such to model this behavior. Changes in regard to the modeling techniques as wel l as conceptualizations, hence, need to be done. Plant physiology is one area that needs to be looked into to see what plant properties affect the water uptake and how can they be modeled mathematically. Also discussed is a framework which makes use of x ylem vulnerability curves to provide a physical basis to model root water uptake Simulation results have shown promise for the framework to provide a robust model of root water uptake. However further work needs to be done to determine the vuln erability curves and root distributions for Site A and Site B and then use the recommended model to validate observed versus simulated values. The methodology described in this chapter involves initial laboratory analysis to determine the hydraulic characteristics of plant xy lems; however, once a particular plant species is characterized then the parameters can be used for that specie elsewhere under similar conditions. The eco-hydrological framework approach has great potential for improving predictive hydrological modeling.
159 Chapter 7: Long Term Air Entrapment Affecting Runof f and Water Table Observations 7.1 Introduction This final chapter discusses a phenomenon that exi sts in shallow water table environments and may under intense rainfall effect the water level observed in observation well that are screened below the water table elevation. The phenomenon is the air entrapment, which occurs when an intense ra infall event effectively seals the surface soil layer thus trapping the soil air below the advancing wetting front. Due to the compression of air the pressure at the surface of w ater table becomes greater than atmospheric and hence the observation wells that ar e vented to atmosphere show a sudden jump in water levels, hence erroneously indi cating recharge even though the wetting front is still way above water table. A mod eling strategy using vertical soil moisture profiles and some preliminary results are discussed in this chapter. 7.2 Background The role of air entrapment in inhibiting infiltrat ion has long been recognized (e.g., Adrian and Franzini 1966; Morel-Seytoux and Khanji 1974; Vachaud et al. 1974; Parlange and Hill, 1979). Several theoretical and e xperimental studies e.g., Youngs and Peck (1964) and McWhorter (1971), have quantitative ly defined the impact of air compression on infiltration. These studies found t hat, air compression ahead of a wetting
160 front, in some water table conditions, brings abou t a sharp decrease in the infiltration rate. However, as pointed out by Parlange and Hill (1979) and observed by Wang et al. (1998), air compressibility has been generally cons idered negligible, when the air is free to move ahead of the wetting front. Hence, the impo rtance of air compression in an unconfined aquifer with deep water table is conside red negligible. However, for shallow water table environments (depth to water table <2 m ) air compression plays a significant role in determining infiltration in many soils (Tou ma et al. 1984). Another phenomenon found in shallow water table en vironments is a rapid rise in the water level of observation wells screened below the water table during high intensity rainfall events. The process, known as the Lisse Ef fect (Weeks 2002), as the wetting front advances, pressurization of the soil air occurs. A s a result of this increased air pressure, observation wells which are screened below the wate r table show a rapid rise in their water level, despite the fact that the actual water table (elevation of saturation) is essentially unchanged. As mentioned in Weeks (2002) the effect was noted as early as 1932 by Thal Larsen in the village of Lisse, Hollan d and was given its name by Hooghoudt (1947). Heliotis and DeWitt (1987) and Meyboom (1967) have reported observations of Lisse effect in water table hydrographs; however, t heir explanation is more from the point of view of identifying anomalies in water table obs ervations rather than a way to quantify air pressurization. Weeks (2002) attempted to mathe matically link air pressurization to the anomalous water level rise in observation wells but his analysis was overly simplistic and proved useful only for calculating the maximum possible water level rise for a
161 specific soil type Nonetheless the effort provides a background relat ing air entrapment and water table fluctuations. Because air entrapment in shallow water table envi ronments reduces infiltration and causes artificial rise in the water table, it h as significant implications for estimating ground water recharge. Healy and Cook (2002) presen ted a thorough review of methodologies to estimate recharge using ground wat er levels, but commented that one of the major limitations of any method for shallow unc onfined aquifer was the Lisse effect. As the artificial rise in the water table is diffic ult to identify and it can easily be mistaken for recharge (Healy and Cook 2002). Accurate estimation of soil air pressure is thus o f great importance for modeling runoff and water table recharge. Mathematical solut ions derived from laboratories studies e.g., Wang et al. (1997, 1998) provide very useful insight into the process of air entrapment, however the use of the laboratory deriv ed equations have not been adequately tested under field conditions. Latifi et al. (1994) concluded that air pressure buildup was more pronounced in soil columns of two layers than in a soil monolith. Zhang and Ross (2007) discuss the importance and pr evalence of soil layering in most coastal plane soils. Natural soil layering introduc es uncertainty in the applicability of laboratory results, derived under homogenous soil c onditions. Another important aspect to note is that most of t he theoretical/experimental work or field observations have been limited to an event based approach wherein the effects of single rainfall event on air pressurization/ water table fluctuation are noted and analyzed for only short duration. For the purpose of long te rm modeling of stream flow and aquifer recharge a continuous monitoring and analysis is ne eded. For field conditions subjected
162 to multiple events and varying antecedent condition s, air effects may become compounded and/or prolonged. Recently, Crosbie et a l. (2005) proposed a time series approach to infer ground water recharge using a wat er table fluctuation method. The approach tried to overcome the limitations mentione d in Healy and Cook (2002) and was reported to be applicable to long term records of p recipitation and water table elevation. Even though the proposed model by Crosbie et al. (2 005) was innovative in its and accounting for air pressurization, the model elimin ated all water level rise, if the assumed criteria for Lisse effect (see Crosbie et al. 2005, Equation 2) is satisfied. This may, during long continual rainfall events, neglect the actual water table rise due to wetting fronts reaching the water table. 7.2.1 Objectives and Scope The above discussion clearly illustrates the need for a more physically based analysis of air entrapment over long term (multi-ev ent) records. The current study attempts to address this need by using shallow wate r table elevation records in conjunction with observed soil water content profil es that were measured during a field study. The specific objective of the investigation is to: (a) detect the presence of Lisse effect, (b) quantify the air pressurization values in field data, (c) use quantified air pressurization values to determine the location of true elevation of the water table, and (d) to elucidate the overall implication on modelin g runoff and recharge. The approach used in the study is to calibrate a R ichardÂ’s equation model to observed water content profile and derive depth to water table from resultant pore water tension pressure, as it is unaffected by the air pr essurization. The soil moisture behavior
163 can then be used to determine the true depth to wat er table. The difference between the observed and the true depth to water table will hen ce give the value of air pressurization. 7.3 Study Site and Data Collected For the current study, field data were obtained fr om a study site described in Chapter 2. Soil moisture and water table data from well PS-43 located in the grassed area of the study site was used for the analysis. Hourly data from both soil water content probe and pressure transducer was used for analysis in th is study. Rainfall data were obtained from a tipping bucket rain gauge housed in a weathe r station established in the study area. 7.4 Methodology Due to air entrapment traditional rainfall infiltr ation models like Green and Ampt (1911), tend to over predict infiltration with phys ical soil parameters in shallow water table environments. In this case, infiltration can be derived from volume changes since soil water content was explicitly measured. Assumin g a one dimensional soil column, integration of the soil water content values will g ive the total water content (TWC) per unit area of soil column at any instant in time. Su btraction of two consecutive values will, hence, give an estimate of net infiltration or net evapotranspiration (ET) (depending on the algebraic sign of the difference) in units of l ength. For the purposes of this study, net infiltration or net ET refers to all inflow and outflow respectively (inc luding lateral flows) for details of the approach one is directed to Rahg ozar et al. (2005). Nachabe et al. (2005) used a similar approach to determine ET and found the methodology to give a very good match with calculated values from other methods. Fo r this particular study, given the
164 spatial distribution of the soil moisture sensors, a simple numerical integration (trapezoidal rule) was done to calculate TWC for th e soil column of length 1.5 m. The mathematical equation used is =8 1 i iz TWCq (7.1) where zi [L] is the depth associated with each sensors (see Table 7.2 ), and qi [L3L-3]is the water content values at the corresponding sensor. 7.4.1 Numerical Model Soil water content profiles were modeled using a s ingle phase, one dimensional RichardÂ’s equation model known as HYDRUS -1D (versi on 3) (Simunek et al. 2005). HYDRUS was previously used by Hammecker et al. (200 3) to try and quantify the effect of air compression. The approach they used was to a pply Dirichlet conditions, namely the upper boundary given by the ponding water level in the plot and the lower boundary given by the depth of the water table as the two bo undary conditions. The lack of match with the observed data was attributed to the air co mpression, as all the other processes were assumed to be accounted for in HYDRUS. No furt her analysis was done to quantify the air entrapment from the numerical solution. As described in Hillel (1998), due to air entrapmen t, the soil water content does not attain total saturation but some maximal value lower than saturation, which he called satiation. Satiation can be taken into account by c onsidering that the maximum water content in a soil only reaches to a value smaller t han porosity, more commonly referred to as natural saturation or effective porosity (Charbe neau 2000). Hence, laboratory
165 determination of soil saturation water content norm ally overestimates the values found in situ. This phenomenon was considered in the calibra tion of soil parameters. For the current investigation data for two months (May and June) in 2002 and another two months (April and May) in 2003 were ana lyzed, and modeled numerically using HYDRUS. This period of record was selected be cause it represented the transitional months when conditions changed from ve ry dry to very wet. Hence, a good contrast between the conditions with and without ai r pressurization can be expected. Due to hysteresis, the effective porosity shows a long term seasonal behavior as listed in Table 7.1. Hence, for calibration purposes, saturated wat er content values that are used correspond to the maximum water content values obse rved during the period of record. As expected the values were found to be less than t he laboratory determined porosity, by as much as 7-8%. Table 7.1 Differences in Observed Maximum Water Con tent (Water Table at the Land Surface) for Different Period of Records. Sensor Location Below Land Surface (cm) Maximum Water Content for Period (20012004) % Maximum Water Content (May-June 2002) % Maximum Water Content (April Â–May 2003) % 10 42.3 33.9 37.3 20 37.6 34.8 32.9 30 31.4 31.3 29.5 50 30.8 29.3 29.4 70 30.3 28.3 29.3 90 30.9 28.7 29.5 110 32.7 29.9 32.0 150 36.9 36.6 34.4
166 220.127.116.11 Model Setup It is known that under heterogeneous conditions ai r pressure buildup is more pronounced than under homogenous conditions (Latifi et al. 1994). Field observations of water content values obtained from the soil moistur e sensors show that the soil profile is far from homogenous even at a vertical scale of 1.5 m. (Figure 7.1), also noted by Zhang and Ross (2007). Hence, with the purpose of making the model representative of actual soil column at the study location, the simulated so il column was setup with eight different soil layers, each corresponding to a soil moisture sensor. It is worth noting that the objective of the model setup is to mimic as closely as possible the observed water content. To make the numerical model highly resolve d, it was discritized into 1001 numerical nodes, which corresponds to maximum spati al discretization allowed in HYDRUS. HYDRUS calculates the value of pressure hea d and water content at each of the nodal location. Hence, an almost smooth water c ontent profile can be obtained from this highly resolved discretization. Of special interest is the actual depth to water t able which, due to air pressurization, can be lower than observed. Therefo re, a conservative column length of 200 cm was used even though the observed maximum va lue of observed depth to water table (dWT) never exceeded approximately 140 cm. For the give n sensor distribution the depth and location of each soil layer is given in T able 7.2.
167 Figure 7.1 Snapshot of Water Content Variation Alon g the Vertical Soil Profile. 18.104.22.168 Soil Hydraulic Properties For the purposes of numerical solution of RichardÂ’ s equation, the relationship between soil water content and suction pressure hea d has to be defined. Out of many different models found in literature, the Brooks an d Corey (1964) model was selected. Mathematically the model is defined by Equations 7. 2 and 7.3. < = =a a a r s r eh h for h h for h h h h S 1 ) ( ) (lq q q q (7.2) 2 2) (+ +=l e s eS K S Kl (7.3) where Se [L3L-3] is effective water content, Ks [LT-1] is saturated hydraulic conductivity, qr [L3L-3]and qs [L3L-3] denotes residual and saturated water contents, re spectively; ha [L] is the air-entry pressure value (or bubbling pressu re), [-] is a model parameter, h [L]is Water Table Depth to the water table (cm) Water content (%) Water Content
168 the capillary suction pressure and l [-] is a pore connectivity parameter assumed to be 1.0 as an average for many soils (Mualem 1976). The soi l parameters thus needing to be defined in HYDRUS are the residual and saturated wa ter content, bubbling pressure, saturated hydraulic conductivity and the model para meter Soil parameters, taken from a soil survey published by the Institute of Food and Agricultural Science, University of Florida (Carlis le et al. 1989), for an area very close to the study site serve as the base for calibration of soil hydraulic properties. From the soil survey data it was clear that the soil profile in t he region (in and around the study area) comprises of six to eight different horizons charac teristic of Myakka fine sand with the thickness closing matching to the ones observed in the field and assumed in the numerical model. 22.214.171.124 Initial and Boundary Conditions As part of the model setup, initial and boundary c onditions were defined based on observed field data. As mentioned before, two perio ds from May 4th to June 30th, 2002, and April 1st to May 30th, 2003 were analyzed. To accomplish this, two sets of simulations with similar initial and boundary condi tions were setup. 126.96.36.199.1 Initial Conditions As both period of records were preceded with very dry conditions (more than 10 days of no rainfall), no initial air pressurization was assumed and soil water content distribution was assumed to be at equilibrium (i.e. water pressure distribution was assumed hydrostatic). Hence, the observed value of dWT can be assumed to closely match
169 the zero water pressure elevation (i.e., true depth to water table). For the first simulation starting from May 4th, 2002, the initial dWT was thus set at 100 cm. For the second simulation, starting on April 1st, 2003, the initial dWT was established at 80 cm. 188.8.131.52.2 Boundary Conditions The 1D numerical soil column (for both simulations ) was set up with a no-flow boundary condition at the bottom. At the top, atmos pheric boundary conditions with no surface runoff were defined. Changes in observed TW C were used to define the imposed stress of rainfall and potential evapotranspiration The variable boundary conditions (defining the stresses) were set up at an hourly in terval with, depending on the result of Equation 7.1, either net ET or net precipitation defined one at a time. HYDRUS -1D does not allow specification of actual evapotranspiratio n explicitly. Instead, the code determines values and contribution from the soil pr ofile using the specified potential transpiration values (see the following paragraph f or details). The net ET was later compared to the actual ET that was observed in the field. This served as a v alidation that the imposed boundary conditions were similar to tha t observed in the field. Further details are discussed in the results section. Evapotranspiration is simulated via the sink term S [L3L-3T-1] shown on the right side of RichardÂ’s equation. This sink term modeled as modeled in HYDRUS-1D is distributed through the root zone to reflect the pl ant root distribution in the domain as follows: S(x) = a(h) Sp(x) (7.4)
170 where a(h) [-] is root water uptake stress response function (0 a(h) 1), as defined by Feddes et al. (1978), and Sp(x) [T-1] is the spatial distribution of the potential tran spiration rate over the soil profile as a function of depth x [L]. The potential transpiration rate is the water uptake rate when the plant is not experiencin g any water stress; a(h) = 1. For vegetated cover, the potential ET is distributed through the subsurface root system according to a distribution function. The distribu tion function used is: Sp(x) = bÂ’(x) Tp (7.5) where Tp [LT-1] is the potential ET and bÂ’(x) [L-1] is the relative fraction of roots at any depth x. Jackson et al. (1996) compiled data on th e distribution of roots as determined by large number of field studies and found that the mo del proposed by Gale and Grigal (1987) was very successful in describing the root d istribution. The model of root distribution is: Y = 1 gd (7.6) where Y is the cumulative fraction of roots from the land surface to depth d, and g is a numerical index of rooting distribution which depen ds on vegetation type. This relationship was used in the numerical simulation, to specify relative root density at each node, with g equals to 0.952 for grass (Jackson et al. 1996), t he predominant land cover at the study location. The root zone thickness was sp ecified as 1 meter consistent for grass in this environment (Jackson et al. 1996). 7.4.2 Calibration to Observed Period of Record The whole calibration process was done as a two st ep process. In the first step hydraulic characteristics of top three soil layer w ere calibrated using the inverse solution
171 tool in HYDRUS 1D, while the parameters for other s oil layers were kept at the values given in Carlisle et al. (1989). Secondly the para meters of the bottom layers were adjusted manually to get the best match to the soil water content variation. The inverse solution tool in HYDRUS uses the Marqu ardt-Levenberg algorithm to determine the best fit soil parameters, based on specified observed values. The limitation with the inverse tool is that it can acc ept only about 7000 records as observed values, and 15 parameters as the maximum that can b e calibrated. Owing to this limitation, parameters for only top three soil laye rs were calibrated using the inverse solution tool, with about a month of data (May 4th-May 30th, 2002)). The remaining parameters of soil layers values were manually cali brated, and some fine adjustment was made to the earlier calibrated parameters, for anot her month of data (May 30th-June 30th, 2002). Overall for this analysis, observed water co ntent values from the period of record for the first simulation (i.e., May 4th-June 30th, 2002) were used as input values. As previously discussed, from observation of maximum v alues, it is clear that, as a result of air entrapment, saturated water content in the fiel d data averages lower than ultimate porosity. As a result, the only constraint that was placed in the inverse solution was that saturated water content value be fixed as the maxim um observed water content at the corresponding sensor location for the period of rec ord. Apart from saturated water content, other soil hydraulic properties are mostly unaffected by air entrapment. As such, the calibrated values from the first period of reco rds were used unaltered for the second simulation. This was considered a simple validation for the calibrated soil hydraulic variables. Similar to the first simulation, the sat urated water content values for the second run were also specified based on the maximum value (corresponding to water table at or
172 above land surface) observed for the period of reco rd of the simulation. Table 7.2 lists the soil parameters used for the theoretical solution o f RichardÂ’s equation. 7.4.3 Calculation of Excess Pressurization Using Id eal Gas Law The difference between the dWT obtained from theoretical solution (HYDRUS1D) and field observations, gives a quantitative es timate of air pressurization. If the pressure of the entrapped air is atmospheric then t he observed and the actual dWT will be at the same location, void pressures above atmosphe ric will cause the two water table depth values to depart (observation will be higher) The pressure of the compressed air in excess of atmospheric, herein denoted as Â“excess pr essureÂ”, is defined as the difference between the observed dWT and the HYDRUS-1D generated dWT. It is expressed in terms of depth of water column. In an attempt to quantify the amount of excess pre ssure and, potential thresholds for air eruption, a simple spreadsheet-air-excess-p ressure-analysis was set up. The maximum saturated water content for every sensor fr om the entire period of data collection was found. To this value 7.5% (Nachabe e t al. 2004) was added to account for the residual air, crudely representing the actual s oil porosity at each sensor. Multiplication of porosity by the depth associated with each sensor (as shown in Table 7.2) gives the available pore space in the soil col umn (per unit cross sectional area). Subtracting total soil water content obtained by in tegrating water content values along the soil profile (like in Equation 7.1) from the porosi ty gives the amount of pores filled with air in the soil column.
173 Table 7.2 Calibrated Parameters and Extent of Soil Layers Below the Land Surface. Saturated Water Content Soil Hydraulic Parameters for Brooks and Corey Model Layer /Sensor No. Depth Below Land Surface (cm) 2002 (%) 2003 (%) Residual Water Content (%) [-] hb (cm) Ks (cm/hr) l [-] 1 0-15 33.9 37.3 1 1.1 25 20 1 2 15-25 34.8 32.9 1 1.1 25 20 1 3 25-40 31.3 29.5 1 1.2 25 20 1 4 40-60 29.3 29.4 5 0.7 25 10 1 5 60-80 28.3 29.3 5 0.7 25 10 1 6 80-100 28.7 29.5 5 0.7 25 10 1 7 100-125 29.9 32.0 5 0.7 25 10 1 8 125-200 36.6 34.4 5 0.7 25 10 1 It is important to know the inherent assumptions involved in the spreadsheet calculation of excess pressure. The fir st and possibly most important assumption is that all the entrapped air present be tween the wetting front and the water table has the same pressure. This limitation will b e discussed later. The second assumption is that continuous counter flow of air d uring an event is neglected. Therefore, the only way the soil air can leave the soil column is via air eruption. Finally, the temperature is assumed to be constant and the Ideal Gas Law behavior is assumed under adiabatic conditions. 184.108.40.206 Implementation of the Spreadsheet Model Morel-Seytoux and Khanji (1975) proposed a model f or quantifying air compression using BoyleÂ’s law. As BoyleÂ’s law assu mes the mass of the gas to be
174 constant, this methodology becomes invalid in case of air eruption. It is for this reason the Ideal Gas Law is used for the spreadsheet analy sis, with the underlying assumption that air behaves like an ideal gas. Consistent with the HYDRUS solution, hourly time steps were used for pressure calculations. Thus, ho urly values of total soil water content were used to determine the changes in the volume fr om which the void air pressure is derived. Mathematically, the Ideal Gas Law can be defined a s PV = nRT (7.7) where P is the absolute pressure (N/cm2), T is absolute temperature (K) assumed constant at 298K, V is volume of the void air (cm3), n is the number of moles, and R is the gas constant (= 831.41 N-cm / (mol/ K)). As mentioned earlier, both the simulation periods were preceded by dry conditions. Therefore, the initial pressure of the entrapped air is assumed to be atmospheric, P0, i.e. 10.13 N/cm2. The initial volume V0 of entrapped air was determined by subtraction of observed total soil water content (initial value) from the total pore space (constant =68.92 cm3). At the next hour the new volume of air (V1) is similarly calculated, using the corresponding observed total soil water content. Assuming a constant temperature T, Equation 7.7, is used to determine the initial nu mber of moles (n0). Using n0 and the volume at the next hour V1 the pressure P1 was found again using Equation 7.7.From this approach excess pressure (in centimeter of water column) is determined as follows g P P Pr0 1= D (7.8)
175 where P is the excess pressure (cm), r is the density of water, and g is the acceleration due to gravity, and rg is assumed as 0.00981 N/cm3.Between consecutive time steps two processes are possible. First, due to net ET, the new volume of air is greater than the previous volume or secondly, due to net infiltratio n, voids are reduced and excess pressure ensues. It is important to note that at an hourly time step sufficient infiltration can occur to cause the excess pressure to become qu ite large. Therefore excess pressure may reach an upper limit where by rapid air eruptio n occurs. This breaking value (as defined in Wang et al. (1997) results in eruption a nd a lowered air pressure values is produced. Consider the ET case where the volume of air increases. In this ca se the new value of air pressure will decrease, except that there is no wetting front to preclude air uptake by the soil from the atmospheric boundary. As a res ult the pressure cannot significantly decrease below atmospheric. Thus, during the spread sheet analysis the new pressure value is made atmospheric if the solution of the Eq uation 7.7 results in sub atmospheric pressure during drying conditions. However, no adju stment is made if the new pressure comes out to be greater than atmospheric. One probl em that remains is that Ideal Gas Law cannot be used to determine the air eruption th resholds. Also, as a consequence of air eruption, undeterminable numbers of moles of ai r are lost. Hence, for the infiltration case, to incorporate air breaking values threshold pressures must be set through observation of the data to constrain the maximum pr essure. In the absence of any other indicators, excess pre ssure determined from comparison of the HYDRUS solution with the field ob servation, was used to limit the excess pressure values calculated in the spreadshee t. Air eruption was evident in the
176 several events in both periods requiring constraini ng the maximum pressure. Thus, if the excess pressure calculated from Equation 7.8 exceed ed the thresholds for air breaking derived by HYDRUS, the excess pressure was set at t he threshold and the numbers of moles lost were calculated using Ideal Gas Law. As will be seen later in the results section the e xcess pressures calculated using HYDRUS show large variations depending on the infil tration magnitude and the antecedent conditions. However critical thresholds were more consistent. This implies that, in order to determine air eruption for each e vent, different thresholds have to be set. To avoid this cumbersome approach, the analysis was done only on the events occurring in the month of May of 2002 and 2003. 7.5 Results 7.5.1 Calibration and Validation Results The numerical soil column model, calibra ted for 2002 and validated against 2003 data, gave values very close to the observed soil w ater content. Figure 7.2(a-d) shows observed and simulated water content values for bot h the simulations, during dry and wet conditions. The observed dWT and HYDRUS dWT are also plotted. As expected, during wet conditions the observed dWT departs from the HYDRUS dWT while they match almost exactly during the drying conditions. To compare th e observed boundary conditions with those simulated in HYDRUS, the water content values obtained from the simulations were integrated using Equation 7.1 and plotted vers us the observed total water content values. The data points were found to lie along a f orty five degree line with and coefficient of regression value (r2) of 0.997. The high value of r2 indicates that the
177 numerical model is reasonably calibrated to the con ditions and soil types observed in situ, thereby increasing confidence in numerical simulati on results. 7.5.2 Numerical Solution HYDRUS -1D was used to derive pressure head and wa ter content values at each node in the soil column, continuously in time. The model was run at an hourly time step, but due to limitations in the maximum number of out put, model results were saved every six hours. From the pressure distribution along the soil column, the dWT was determined by noting the location of zero pressure head (Freez e and Cherry 1979). It has been deduced from the calibration and validation results that the model describes the soil characteristics reasonably well and successfully re produces the water content profiles and dWT during drying periods. Therefore, dWT determined above should represent the actual dWT in absence of air pressurization. Figure 7.3(a) and (b) show the variations of the observed dWT and the HYDRUS dWT with time. Also plotted on the secondary Y axis is the net infiltration (as obtained from Equation 7.1). As Figure 7.3 illustrates, the HYDRUS solution was very successful (given a tolerance of 3 cm) in describing the wate r table during the drying periods and many wet periods. Therefore, departures from the a ctual (HYDRUS) dWT during large infiltration events clearly indicate air entrapment and pressurization.
178 0 20406080 100120140160 152025303540 0 20406080 100120140160 0510152025303540 Figure 7.2 Snapshot of Calibration Results. Crosses Represent the Observed Water Content Values, while the Circles are the Calibrate d Values. The Dashed Lines Represent the Observed dWT and Solid Line Represents the dWT calculated from HYDRUS. Water Content Distribution from 2002 (a) Wet Conditions ( b) Dry Conditions, and 2003 (c) Wet Conditions (d) Dry Conditions. Water content (%) Below land surface (cm) (a) (b)
179 0 20406080 100120140160 152025303540 0 20406080 100120140160 0510152025303540 Figure 7.2 (Continued) Below land surface (cm) Water content (%) (c)(d)
180 0 20406080 100120140160 5/4/025/11/025/18/025/25/026/1/026/8/026/15/026/22/ 026/29/02012345678Equipment Failure Observed dWTHYDRUS dWT Infiltration A 0 20406080 100120140160 4/1/034/8/034/15/034/22/034/29/035/6/035/13/035/20/ 035/27/03012345678HYDRUS dWT Observed dWT Infiltration B Figure 7.3 Actual dWT Calculated from HYDRUS Plotted Against Observed dWT for (a) May 2002-June 2002, (b) April 2003-May 2003. From the results above, the magnitude of the exces s pressure was found to be a function of actual dWT. For example, the April 7th, 2003 1.4 cm infiltration event shown in Figure 7.4(b) produced an excess pressure of aro und 40 cm, while a May 19th, 2003 Depth to the water table (cm) Infiltration (cm) (a) (b)
181 infiltration event of similar magnitude only produc ed 7 cm of excess pressure. As can be seen from the graph the antecedent conditions were very similar with the only difference being the dWT. For the two events, dWT, in former case was 60 cm while for the latter period it was 100 cm. In fact (from Figure 7.4) in 2002 on June 15th, 2002 an infiltration event of around 2.25 cm did not produce any excess pressure as the water table was deep at around 140 cm. Overall both graphs show that the actual water table fluctuations are smooth. However, due to the excess air pressure, th e observed water table fluctuations appear more responsive. To evaluate the role of air entrapment in controll ing the runoff process, infiltration, as calculated using Equation 7.1, was plotted along with observed rainfall and the calculated excess pressure for the period of si mulation in 2002 and 2003 (Figure 7.4(a) and (b)). From the graphical analysis it was found that the magnitude of the maximum excess pressure for both the simulations re mained at around 45-47 cm, yet some differences in the periods existed. In 2002, t he two months of simulation definitely produced some runoff, contrary to 2003 where all th e rainfall infiltrated. The 2002 and 2003 simulations while representing similar seasona l period exhibit some notable difference in soil response reflecting difference i n antecedent moisture condition (AMC). Several specific events from 2002 and 2003 are offe red for discussion. On April 26th, 2003 and on June 25th, 2002 the excess pressure maximum was found to be around 45 cm. However, on April 26th, 2003 all rainfall infiltrated contrasting June 25th, 2002 where negligible infiltration took place. These differenc es are attributed to difference in AMC. From Figure 7.4 and 7.5 if the AMC prior to the rai nfall events is considered, on April 26th, 2003 the actual dWT was around 85 cm with dry antecedent condition (< 0.05 cm of
182 rainfall in previous 10 days) while on June 25th, 2002 the water table was high at 46 cm reflecting much wetter AMC. Another noteworthy obs ervation is that on June 25th, 2002 the sizable infiltration event resulted in water ta ble rise from 85 to 50 cm (below land surface) with excess pressure build of 45 cm, as ag ainst April 26th, 2003 where the water table remained pretty much stable. The most obvious question that results from these observations is how can one be so sure that the run off produced is due to air pressurization? To address this question the intensity of rainfall from the data were calculated and compared with the saturated hydraulic conductivity of the top layer of the soil. It was found that the during all four months of analysis t he rainfall intensity was never greater than the infiltration capacity theoretically given by soil physics (i.e., RichardÂ’s equation neglecting air effect) as the vertical hydraulic co nductivity and predicted by simple models such as Green and Ampt (1911) model. The cle ar conclusion is that runoff resulted solely due to air entrapment, investigated below through simple spreadsheet analysis of air pressurization. 7.5.3 Spreadsheet Analysis Figure 7.5(a-d) shows the variation of excess pres sure calculated from spreadsheet analysis of void air pressures using Id eal Gas Law along with the HYDRUS solution, and the observed dWT. The number and variation of air moles are also in cluded in the figure to demonstrate air eruption. A review of Figure 7.5(a) and (b) shows that rate of pressure decline calculated from the spread sheet is significantly more than the decline calculated from HYDRUS. The results from th e spreadsheet analysis hence raise
183 a big question, what is going on with air pressure in shallow dWT and why are the air excess pressure periods so prolonged. Another concl usion might be that RichardÂ’s equation solution may not represent dWT and infiltration behavior well enough in shallow water table settings to reasonably quantify runoff (Hortonian or saturation excess) and recharge processes. In an attempt to answer, this q uestion and the bold statement, basic processes in porous gas behavior (i.e., spreadsheet ) and soil moisture physics (neglecting air effects) needs to be examined. RichardÂ’s equation as solved by HYDRUS ignores void air pressurization. Hence for all boundary conditions and soil moisture varia tion it solves for dWT, from which the excess pressure is derived. The spreadsheet solutio n on the other hand is highly dependent on the soil air volume changes from which the excess pressure is calculated. While, HYDRUS calculations incorporate soil propert ies from which pore water pressure distribution is calculated and dWT determined, spreadsheet solution do not take any s oil property into account. The only driving variable in the spreadsheet solution is the change in void air volume, which is inherently assumed to be occurring between the wetting front and the water table. The following paragraph tries to numerically explore the differences that are created due to the aforesaid d ifference in methodologies involving either HYDRUS or spreadsheet (Ideal Gas Law).
184 0 5 10 15 20 25 30 35 40 45 50 5/4/025/11/025/18/025/25/026/1/026/8/026/15/026/22/ 026/29/020 5 10 15 20 25 30 35 40 45 50 Equipment FailureCumulative Rainfall Cumulative Infiltration Excess PressureA 0 5 10 15 20 25 30 35 40 45 50 4/1/034/8/034/15/034/22/034/29/035/6/035/13/035/20/ 035/27/030 5 10 15 20 25 30 35 40 45 50Cumulative Infiltration Cumulative Rainfall Excess PressureB Figure 7.4 Rainfall and Infiltration Plotted Along with Excess Pressure for (a) May 2002-June 2002, (b) April 2003-May 2003.Excess pressure (cm) Cumulative rainfall/infiltration (cm) (a) (b)
185 30405060708090 100110120 5/18/03 5/19 / 0 3 5 / 2 0 / 0 3 5 / 2 1 /03 5 / 2 2 / 0 3 5/23/03 5/24 / 0 3 5 / 2 5 / 0 3 5 / 2 6 / 0 3 5/27/03 5/28 / 0 3 5 / 2 9 / 0 3 0 10 20 30 40 50 60 70 80 90 Observed d WT Excess Pressure Derived From HYDRUS Spreadsheet Solution 90 100110120130140150 5 / 18/02 5/19/02 5 / 20/02 5 /21/02 5 / 22/02 5 / 23/ 02 5 / 24/02 5/25/02 5 / 26/02 5 /27/02 5 / 28/02 5 / 29/ 02 5 / 30/02 0 10 20 30 40 50 60 Observed dWTExcess Pressure Derived From HYDRUS Spreadsheet Solution Figure 7.5 Excess Pressure as Calculated from Sprea dsheet Model and HYDRUS Solution. (a) Shows the Variation of Pressure for M ay 2003, (b) Shows Variation of Pressure for May 2002, (c) and (d) Shows the Variat ion in the Number of Moles as Predicted from the Spreadsheet Model for 2003 and 2 002, Respectively.Observed depth to the water table (dWT) (cm) Excess pressure (cm) (a) (b)
186 5.0 5.5 6.0 6.5 7.0 7.5 8.0 0 5 /1 8 /03 05/19/03 05/20 / 03 05 / 21 / 03 05 /2 2 /0 3 05 /2 3 /0 3 05/24/03 05 / 25 / 03 05 / 26 / 03 05 / 27 / 03 0 5 /2 8 /0 3 05/29/03 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 5/1 8/02 5/19/02 5/20/02 5/21/02 5/22/02 5/23/02 5/24/02 5/25 /02 5/26/02 5/27 / 0 2 5/28/02 5 /29/02 5/30/02 Figure 7.5 (Continued) Number of moles (X 10 4 ) (c) (d)
187 Assuming no counter flow (i.e., the number of mole s remain constant), a decline of excess pressure from 47 cm (the maximum observed in the HYDRUS analysis) to zero involves a change of 1.15 cm3 of soil air, using Equation 7.7. This translates t o about one percent change in soil water content of the sensors In other words, even if the soil water content value of the top two sensors changes by a c ouple of percent the spreadsheet solution will result in major loss of excess pressu re. Figure 7.6 shows the variation of the water conten t values of top three sensors for portion of May 2003. From the graphs, the occurrenc e of infiltration events and the propagation of the wetting front can easily be seen In response to the event on May 18th 2003, the soil moisture sensor at 10 cm shows a sud den spike while the soil moisture sensors at 20 and 30 cm show a much more subdued in crease. From the events on May 19th and May 23rd, 2003 it can be easily seen that the wetting front continued to propagate downward as the water content values at 20 cm and 3 0 cm below land surface keep on increasing. After May 23rd the 10 and 20 cm sensors show decline and the 30 cm sensor is mostly unchanged indicating that the location of wetting front has progress to at or below 30 cm below the land surface. Thus the soil v oids generating excess air pressures will be those entrapped below 30 cm from the land s urface. However due to rapidly declining water content val ues of the moisture sensors at 10 cm and 20 cm below land surface, the soil air pr essure above the wetting front probably recovers to near atmospheric levels. The i nherent assumption of uniform pressures in the soil voids in the spreadsheet mode l thus results in considerable difference in the excess pressure predicted versus the water t able departure observed. Figure 7.6, indicates that the water content in the top sensors especially at 10 cm, can change by a
188 couple of percent within one or two days after any event without affecting the wetting front, and hence the spreadsheet solution, will cau se the excess pressures to dissipate within a day or so after the event, as observed in Figure 7.5(a) and (b). This contrasts the field data which show it takes several days for air pressures to dissipate. 12 17 22 27 32 37 5/18/035/20/035/22/035/24/035/26/035/28/035/30/0305010015020025030020 cm sensor 10 cm sensor 30 cm sensor Observed dWTHYDRUS dWT Figure 7.6 Variation of Water Content Values as Obt ained from the Sensors Located at 10, 20, and 30 cm Below Land Surface. Also Plotted in the Figure is the Observed and Actual dWT. The foregoing analysis suggests that the spreadshe et analysis may be overly simplifying the air entrapment behavior in the dryi ng phase. Nevertheless Figure 7.6 presents another indication of air pressurization t hrough observation in the variation in water content values. From the calibrated soil prop erties (Table 7.2) the thickness of the capillary fringe (zone of tension saturation) is 25 cm. This implies that at any dWT, water content values in a region up to 25 cm above the wa ter table should be at or very near saturated values. Therefore if the observed dWT was correct than on May 23rd, 2003 when Water content (%) Depth to the water table (cm)
189 the observed dWT was around 30 cm all soil moisture sensors should have been saturated. However, only the sensor at 30 cm is close to satur ation indicating that the observed dWT is higher than the true dWT. An important feature of the spreadsheet analysis, assuming the HYDRUS solution is a good approximation of the moisture retention p hysics, is the determination of air eruption and its associated loss of air mass. Figur e 7.5(c) and (d) can be used to identify air loss by noting instances when the pressure sudd enly decline. Determination of the mass loss during an eruption showed that the loss w as consistently about 10-12% of the total mass. Adaptation of Ideal Gas Law has been us ed in studies (e.g., Sabeh 2004) to quantify air entrapment and have been found to prod uce good results for single event analysis. However, due to its sensitivity to the so il air volume measurements, multi-event analysis greatly over predicts the loss of excess p ressures during drying. This makes the use of perfect gas law, at least assuming uniform v oid pressure, for long term analysis questionable. Nonetheless, the amount of air loss can be estimated from the thresholds of eruption. As speculated by Peck (1965) and confirmed by Wang et al. (1997), after air eruption, which takes place at air breaking values (breakthrough threshold), the post aireruption soil air pressure approaches an excess pre ssure value called Â‘air closing valueÂ’. In the absence of any data on the location of wetti ng front, equations for finding air breaking and air closing pressure heads suggested b y Wang et al. (1997, 1998) cannot be rigorously applied or validated. However, if a shar p wetting front with its depth equal to infiltration depth is assumed, the air closing valu es can be estimated to compare these values to the pressure thresholds obtained from HYD RUS. For example, given that on
190 May 19th, 2003 net infiltration event was about 3 cm, the d ifference between rainfall and infiltration was observed to be approximately 1 cm. Assuming this to be the ponding depth, the water bubbling pressure for sandy loam t ype soil was found to be approximately 7 cm (van Genuchten et al. 1991; Cars el and Parrish 1988). Using a relationship for air closing head Hc [L] suggested by Wang et al. (1997) Hc = h0 + w + hwb (7.9) where, h0 [L] is the ponding depth, w [L] is the depth of the wetting front, which is th e minimum depth in case the wetting front is not shar p, and hwb [L] is the water bubbling pressure of the soil, the value of air closing is a pproximately 11 cm. This suggests that the value of soil air excess pressure after air eru ption should be equal to 11 cm, as opposed to 20 cm as observed from HYDRUS difference Similarly for the rainfall event on May 23rd, 2003 the value of air closing pressure predicted by Equation 7.9 came out to be 12.5 cm as opposed to a value of 30 cm observed. One possible explanation for the difference can be attributed to the consideration o f the isolated event where by the depth of wetting front was defined just on the correspond ing infiltration event and no consideration was given for the previous even on Ma y 18th, 2003. Considering the overlapping events it is likely that the wetting fr ont depth would be much longer. The discrepancy again emphasizes the differences that m ay arise between long term and short term analysis. This is also evident and supported b y the prolonged (multiple days) excess air pressures observed in the field data.
191 7.6 Discussion of Results The results described above clearly provide field evidence of long term air entrapment and false water table observations as re corded by an observation well cased down through the vadose zone. Analysis showed the i mportance of antecedent conditions in deciding the amount of excess pressure and the r eduction in infiltration, and hence calls for a physically based model to describe the air entrapment process under in situ stresses. Contrasting previous lab experiments, the field conditions are much more variable in space and time and hence the applicabil ity of theoretical relationships obtained from experiments may be questionable. For instance equations given from experiments, (e.g., Wang et al. 1997, 1998), are th eoretically and mathematically rigorous, however, the boundary conditions (single continuous event) under which they are derived and validated are seldom observed in th e field. The most obvious process that is unaccounted for in laboratory analysis is ET recovery of soil air volume. This process was found to play a significant role in the reducti on of excess pressure using Ideal Gas Law analysis. For column experiments generating air confining co nditions, the only way soil air can escape is through air eruption from the top, ca using a sudden reduction in the excess pressure. The pressure conditions after air eruptio n were found to be constant and stable, however as can be seen in Figure 7.4, after reachin g a peak (at which air eruption may have taken place) the excess pressures in field con ditions continue to decline in absence of any rainfall event perhaps responding to ET. Root Zone ET can bring about changes in the soil column by reducing the length of the wetti ng front through redistribution of soil water content vertically. Also, near surface root s tructure includes macro pores which
192 may cause some air to escape during build up. Anoth er process that is very evident in field but cannot be simulated via soil column is th e lateral redistribution of excess pressures due to field scale variability in root zo ne conditions. Not accounting this condition in practical modeling exercise could over predict excess pressures. The field study by Hammecker et al. (2003) suggested a simila r conclusion whereby the authors found that the equations suggested by Wang et al. ( 1997) greatly over predicted excess pressures. They concluded that a small constant val ue of excess pressure was found to do a better job. The processes of ET and lateral air flow thus significantly reduces in stances of air eruption, however, during period of heavy ra infall as in June of 2002, the conditions observed in the field become similar to a soil column experiment with the top layer of the soil being saturated and almost contin uous infiltration. This period exhibits sudden rises and drops in air excess pressures sugg esting repeated occurrences of air eruption. The time scale of the air entrapment process is al so important especially for multievent simulation involving a time series of intermi ttent rainfall and ET (e.g., Crosbie et al. 2005). From the current analysis it was found t hat the time scale of excess pressure or Lisse effect ranged from several days to a week and varied depending on the frequency of infiltration events consistent with what was observ ed in a previous field study by Meyboom (1967). However the more extensive observat ion of the present study indicates that dWT also played a big role is determining the occurren ce and duration of Lisse effect. For dWT values shallower than a meter below land surface, infiltration events almost always cause some degree of air pressurization. How ever at dWT around 140 cm an infiltration event of 2.25 cm did not cause any air pressurization. This implies existence
193 of threshold below which air pressurization does no t take place. Heliotis and Dewitt (1987) and Weeks (2002) found this value to be arou nd 1 to 1.3 m below land surface. This analysis further corroborates that the above l ength scale may be a practical threshold. A significant departure in the current approach fr om the previous studies on Lisse effect and air entrapment (e.g., Heliotis and Dewit t 1987 and Sabeh 2004) is the observation and analysis of a time series of events to determine the excess pressures contrary to single events studied by previous resea rchers. Inherent in this approach is the inclusion of highly variable antecedent soil water and water table conditions in the analysis which significantly affect air pressurizat ion and infiltration. Secondly, multievent approaches are important when the water table fluctuations are used for estimating ground water recharge and when accurate determinati on of air pressurization is needed (Healy and Cook 2002; Crosbie et al. 2005). The ana lysis is also novel from the point of view of marrying the two facets of vadose zone air entrapment, the first one dealing with its effect on reduction in infiltration and the oth er dealing with its effect on the water table observations. 7.6.1 Implications for Ground Water Modeling Water table observations are important for ground water modeling aimed at quantifying surface and ground water interactions a nd for estimating head gradients controlling deeper aquifer recharge. Traditionally ground water models like MODLFOW 2000 (Harbaugh et al. 2000) rely heavily on ground water heads for model calibration and subsequent determination of vertical and horizo ntal fluxes in the model. Constructed
194 water table wells are generally cased (no screen) t hrough the vadose zone to prevent short circuiting of percolation, causing erroneous observ ations. Given this construction practice in shallow water table environments it becomes impe rative to carefully screen the water table data for Lisse effect before using it for mod el calibration. The water table heads, if directly taken from the observation wells and used in the model will significantly overestimate heads and therefore recharge estimates to the water table and deeper aquifer (Weeks 2002; Healy and Cook 2002). Ground water pro cesses like the ET, lateral flux, leakage to deep aquifer, etc. as described in the g round water model are directly a function of dWT (e.g., Banta 2000) and hence error in water table observation can bring about large errors in the estimation of these fluxe s. In the literature, methods like the one described by Sophocleous (1991) have been used to estimate natural ground water recharge. The se methods were found to give consistent results in deep water table conditions ( Sophocleous 1991) as air entrapment would not likely play any role. However, if applied for shallow water table conditions proper care should be taken to apply corrections fo r excess air pressures. The model proposed by Crosbie et al. (2005) to estimate groun d water recharge, provides an innovative method to account for Lisse effect. Howe ver, the model parameter accounting for Lisse effect time scale will have to be adjuste d depending on the in situ soil conditions, dWT and the time series of meteorological stresses. Ai r entrapment has also been found to have implication of wetlands used for wastewater treatment. Detailed discussion about the impacts can be found in Heliot is and Dewitt (1987).
195 7.7 Conclusions Theoretical one dimensional modeling using field d ata were utilized to detect and quantify long term air entrapment and Lisse effect. It was found that the air entrapment was dominant only in shallow water table environmen ts (dWT < 1.4 m) however, limited observation were available for deeper conditions to rigorously confirm the statement. Also the time scale of observed excess pore pressur e ranged from a couple of days to a week. From the analysis it was concluded that ante cedent conditions of soil moisture and dWT play a significant role in determining excess pres sure and infiltration values. The analysis on continuous multi-event observations fou nd prolonged excess air pressures compounded by successive events, suggesting some us eful insights as compared to single event based analysis. It was also concluded that du e to restrictive boundaries and the type of stresses applied, the results obtained from soil column experiments may provide adequate prediction of field occurrences of air ent rapment. The ratio of water table change to rainfall magnitude resulted in an average value of 45 for both years which was found to be consistent with the range of values rep orted by Weeks (2002) and Heliotis and Dewitt (1987). The implications of the air entr apment on ground water modeling were also discussed. An attempt was also made to mo del the excess pressures using Ideal Gas Law and uniform air pressure assumption. Howeve r, due to the unpredictable dependency of externally defined air eruption thres holds and sensitivity to soil air volume change, it was not found to provide a satisfactory estimation method at this time. The main limitation is believed to be the scale of vert ical variability in air pressurization. The limitation of this kind of analysis is that it cannot be applied as yet to larger, basin-scale modeling. Further observations of soil moisture profiles, coupled with vertical
196 measurement of pore pressure variability can provid e further understanding of the governing processes. Only following this effect can a simplified predictive model be developed to facilitate regional modeling of the na tural system. Overall, contrary to the conclusion by Weeks (2002 ), it was found that the Lisse effect is not a rarity but is a common occurrence i n shallow water table environments. Furthermore, field data incorporating sufficiently accurate water content measurement can be used to help correct water table observation s and provide useful data to reformulate infiltration, percolation and recharge models.
197 Chapter 8: Summary and Conclusions The main objective of this dissertation was to tal k about the importance of vadose zone soil moisture dynamics in impacting various hy drological processes. First, an innovative way to collect data along a flow transec t was discussed. It was shown that water table and soil moisture data when analyzed at a point scale was successful in estimation of spatial and temporal variability of e vapotranspiration. The methodology when extended to a flow transect scale resolved not only evapotranspiration variability but was also able to determine the magnitude of oth er water budget components. The data collection efforts were hence successful in develop ing a dataset that which compiled time series of all the hydrological processes in a water shed for different land covers. The dataset as used subsequently in Chapter 3, Chapter 6, and Chapter 7 shows its potential to be used as a validating dataset for different model ing concepts for vadose zone processes. Chapter 3 to Chapter 5 talked about extinction dep th, specific yield variability, partitioning of evapotranspiration between vadose z one and ground water, and their effects on the water table fluctuations. Using vari able saturation flow theory and field data it was shown that the empirically derived rela tionships were not adequate to model these concepts. For instance, it was found that an exponential model for decline of ground water component of evapotranspiration was more suit able than using a linear model. Similarly, instead of defining extinction depth arb itrarily, combination of land cover and
198 soil type can be used to make a more appropriate de cision about the extinction depths at a given study site. In case of usage of specific yield to model water table fluctuation for a given flux rate, it was concluded that for shallow water table environments, neither the assumption of constant specific yield nor the variation of spe cific yield based on equilibrium conditions in the vadose zone was valid. In additio n to this, the commonly used assumption of calculating recharge as a fixed perce ntage of rainfall was also found to be erroneous. It was shown that the values of specific yield, depending on the antecedent soil moisture conditions and the type of boundary f lux vary greatly for different water table elevations. To incorporate vadose zone soil m oisture dynamics terms such as free vadose zone storage and non-ground water coupled fl ux were defined along with the methodology to determine their values. Chapter 4 el ucidated details on how the free vadose zone storage and non coupled need to be util ized to correctly model processes such as recharge to the water table, evapotranspira tion from ground water or vadose zone etc. Building upon the concepts discussed in Chapters 2 3, and 4, Chapter 5 described a simple thresholds based model dependent on soil c haracteristics and depth to the water table, to determine evapotranspiration. Comparison of theoretical solutions for a given soil type with the results determined from the thre sholds based model showed a high degree of match in the values. Such close match bet ween the model and the theoretical solution increases confidence of application of thr esholds based models on regional scale modeling where application of RichardÂ’s equation to model vadose zone moisture conditions becomes infeasible.
199 The focus of Chapter 6 in the dissertation shifted to plant roots which are the main cause of moisture variability in vadose zone. Soil moisture and water table data from the study site described in Chapter 2 was used to deter mine the root water uptake from different sections of the root zone. It was found t hat the traditionally used models to determine root water uptake were not accurate as th ey assumed root water uptake to be directly proportional to the relative root fraction The results clearly indicated that the root water uptake was a function of relative root f raction and ambient soil moisture. Any new model should hence take into account both of th ese factors. Also, it was found that both grass and trees transpired at potential but ta king more water from the bottom wetter layers. Based on the observations from the calculat ed root water uptake in the first half Chapter 6, a novel concept of using root hydraulic characteristics to develop a framework to model root water uptake was conceptualized. The relationship that was suggested was found to yield results that were similar to the roo t water uptake calculated from the field data, however additional work to further characteri ze roots need to be done. The major implication of such analysis for regional scale mod eling is the determination of the coefficients that are used to determine actual evap otranspiration from potential value. Unlike using coefficient based on empiricism such a nalysis can help determine the values which are physically based or measured. Chapter 7 concluded with description of an interes ting concept of air entrapment and a methodology to determine it. Preliminary fie ld observations coupled with numerical and spreadsheet solutions were used to de rive the magnitude and duration of air entrapment which cause artificial water table r ise in the observation wells. It was found that the air pressurization effect was respon sible at time up to 40 cm of water table
200 rise being recorded by the observation well and the excess pressurization was found to last some where between a day to a week in some cas es. The observations are however preliminary and more data need to be collected to c onfirm about the magnitude and duration of the process and then find out ways to m odel it. On the whole the dissertation was successful in sh owing the importance of the vadose zone in hydrological modeling. It talked abo ut ways to collect data and model different hydrological processes. Moisture variabil ity in the vadose zone was found to be primary factor affecting all the fluxes and hence a ll modeling efforts need to be concentrated at describing and predicting its behav ior. The role of plant roots in impacting the moisture variability in the vadose zo ne cannot be ignored and hence physically based root water uptake model accounting for roots characteristics, such as distribution and vulnerability, need to be develope d and used integrally with any hydrological model. Alternatively, plant coefficien ts based on roots characteristics and ambient soil moisture conditions need to be develop ed to facilitate accurate land cover response in regional scale modeling. This dissertation hence provides a platform on whi ch robust and more comprehensive modeling conceptualizations can be de veloped. Future work from this point onwards will be to collect similar data from other sites differing in hydrometrological conditions than the current field site and test the models developed from the current dataset. Having recognized the importance o f plant roots, greater efforts needs to be made to sample roots of as many plant types as p ossible and develop a root distribution as talked about in Chapter 6. Vulnerab ility characteristics for each vegetation type needs to be determined and then a physically b ased model as suggested in Chapter 6
201 needs to be constructed and tested using the root w ater uptake values calculated from the study site. The process of root characterization th ough tedious will provide physically based root parameters that can be used with confide nce in the future modeling efforts for similar land cover without repeating the whole proc ess.
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About the Author Nirjhar Shah received his BachelorÂ’s Degree in Civ il Engineering from the Indian Institute of Technology, Roorkee, India in 2003. Ri ght after getting BachelorÂ’s Nirjhar joined the direct PhD program at the Department of Civil and Environmental Engineering, in the University of South Florida (US F), Tampa. Working with Dr.Mahmood Nachabe and Dr.Mark Ross, Nirjhar has sp ecialized in the field of hydrological modeling specially modeling of vadose zone soil moisture dynamics. His research interests include Eco-Hydrology, integrate d surface and ground water modeling and application of GIS in water resources. During l ast four years during his stint at USF, Nirjhar has co-authored more than eight journal art icles and presented more than ten papers in various conferences. Apart from academics, Nirjhar has been also involv ed in dramatics, and has been a part of more than fifteen professional level play s. He likes to play badminton, squash, racquetball, and of course cricket (one game which every Indian likes).