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Cost/effectiveness analysis of obtaining operational estimates of reference evapotranspiration, Peninsular Florida, USA

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Title:
Cost/effectiveness analysis of obtaining operational estimates of reference evapotranspiration, Peninsular Florida, USA
Physical Description:
Book
Language:
English
Creator:
Kittridge, Michael G
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University of South Florida
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Tampa, Fla.
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Subjects / Keywords:
FAO Penman-Monteith equation
ASCE Penman-Monteith equation
Priestly-Taylor equation
Radiation/Tmax equation
Simple equation
Hargreaves equation
Dissertations, Academic -- Geology -- Masters -- USF   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Abstract:
ABSTRACT: The objective of this study is to conduct a cost/effectiveness analysis of the computation of reference evapotranspiration (ETo) in the peninsular of Florida. A meteorological station on the Fort Meade Mine in Polk County, Florida was used to provide data for the calculation of ETo. Five ETo equations were tested to determine the accuracy and cost/effectiveness to the fully measured ASCE Penman-Monteith (Full ASCE-PM) equation on daily, monthly, and annually time steps. The ETo equations ranged in amounts of parameters from the Full ASCE-PM to the Hargreaves. The energy terms accounted for approximately 90% of the total ETo flux. Solar radiation alone also accounted for approximately 90% of the total ETo flux. The highest cost-effectiveness ratios were equations that were able to accurately estimate values without relying on expensive meteorological equipment and/or omitted terms that had a lesser influence on the magnitude of ETo. The seasonal variability in the climate and consequently the emphasis of each meteorological parameter on ETo will create seasonal errors in the reduced sets of the ETo equations. Large seasonal errors were associated with temperature based ETo equations, while solar radiation based ETo equations accurately preserved the seasonal trends. At least in Florida, solar radiation is the key driving force in both the magnitude and the seasonality of ETo.
Thesis:
Thesis (M.S.)--University of South Florida, 2007.
Bibliography:
Includes bibliographical references.
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Statement of Responsibility:
by Michael G. Kittridge.
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Title from PDF of title page.
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Document formatted into pages; contains 81 pages.

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Cost/effectiveness analysis of obtaining operational estimates of reference evapotranspiration, Peninsular Florida, USA
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ABSTRACT: The objective of this study is to conduct a cost/effectiveness analysis of the computation of reference evapotranspiration (ETo) in the peninsular of Florida. A meteorological station on the Fort Meade Mine in Polk County, Florida was used to provide data for the calculation of ETo. Five ETo equations were tested to determine the accuracy and cost/effectiveness to the fully measured ASCE Penman-Monteith (Full ASCE-PM) equation on daily, monthly, and annually time steps. The ETo equations ranged in amounts of parameters from the Full ASCE-PM to the Hargreaves. The energy terms accounted for approximately 90% of the total ETo flux. Solar radiation alone also accounted for approximately 90% of the total ETo flux. The highest cost-effectiveness ratios were equations that were able to accurately estimate values without relying on expensive meteorological equipment and/or omitted terms that had a lesser influence on the magnitude of ETo. The seasonal variability in the climate and consequently the emphasis of each meteorological parameter on ETo will create seasonal errors in the reduced sets of the ETo equations. Large seasonal errors were associated with temperature based ETo equations, while solar radiation based ETo equations accurately preserved the seasonal trends. At least in Florida, solar radiation is the key driving force in both the magnitude and the seasonality of ETo.
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i Cost/Effectiveness Analysis of Obtaining Operational Estimates of Reference Evapotranspiration, Peninsular Florida, USA by Michael G. Kittridge A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science Department of Geology College of Arts and Sciences University of South Florida Major Professor: Mark C. Rains, Ph.D. Mark Stewart, Ph.D. Mark A. Ross, Ph.D. Date of Approval: July 20, 2007 Keywords: FAO Penman-Monteith equation, AS CE Penman-Monteith equation, PriestlyTaylor equation, Radiation/Tmax equati on, Simple equation, Hargreaves equation Copyright 2007, Michael G. Kittridge

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ii ACKNOWLEDGMENTS This project was funded by the Florida Institute of Phosphate Research project 0303-150s. I would like to thank Mosaic for allowing us to use their site and facilities. I would like to thank my graduate advisor Mark Rains for his continued support and tutelage. I would like to thank the following people for their help: Jeffrey S. DeSimone and Arcadii Z. Grinshpan for advice related to the cost/effectiveness analysis, David Sumner for support on ET concepts, Sasha Ivan s for Campbell Sci. tech support, and my other committee members Mark Stewart and Mark Ross. And finally, I would like to thank my family for all their support throughout my entire academic career.

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i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv ABSTRACT viii 1. INTRODUCTION 1 2. SITE DESCRIPTION 5 2.1. Location and Hydrological Setting 5 2.2. Vegetation 7 2.3. Climate 7 3. METHODS 13 3.1. Instrumentation and Measurement 13 3.2. ET o Equations 15 3.3. ET Analysis 16 4. RESULTS 18 4.1. ET o by the Full ASCE Penman-Monteith Equation 18 4.2. Comparisons on Daily Time Steps 20 4.3. Comparisons on Monthly Time Steps 30 4.4. Comparisons on an Annual Time Step 40

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ii 4.5. Seasonality 42 4.6. Cost/Effectiveness Analysis on Daily Time Steps 52 4.7. Cost/Effectiveness Analysis on Monthly Time Steps 52 4.8. Cost/Effectiveness Analysis on an Annual Time Step 53 5. DISCUSSION 58 5.1. Accuracy 58 5.1. Cost/Effectiveness 59 5.1. Obtaining ET from ET o 58 6. CONCLUSIONS 62 7. REFERENCES 63 8. APPENDICES 65

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iii LIST OF TABLES Table 1. Average Daily meteorological values for 2006. 9 Table 2. Meteorological parame ter with the associated sy mbol and instrumentation. 14 Table 3. Final cost/effectiveness analysis with average daily ET o and SEE values for 2006. 54

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iv LIST OF FIGURES Figure 1. Site location at the Ft. Meade mine clay storage area (CSA) in Polk County, FL. 6 Figure 2a. Mean monthly temperature a nd precipitation for Bartow, FL from 1892-2006. 10 Figure 2b. Mean monthly temperature and precipitation for Bartow, FL for 2006. 11 Figure 2c. Mean monthly temperature and precipitation for the CSA for 2006. 12 Figure 3. Daily ET o values for 2006 calculated fro m the Full ASCE-PM. 19 Figure 4a. Daily leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rn, G, T ). 21 Figure 4b. Daily least-sq uares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs U, RH, T ). 22 Figure 4c. Daily least-sq uares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs, T ). 23 Figure 4d. Daily least-sq uares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (T ). 24 Figure 4e. Daily least-sq uares regression of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rn, G, T ). 25 Figure 4f. Daily least-sq uares regression of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rs, T ). 26

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v Figure 4g. Daily least-sq uares regression of ET o from the Full ASCE-PM for 2006 calculated by the Radiation/Tmax. 27 Figure 4h. Daily least-sq uares regression of ET o from the Full ASCE-PM for 2006 calculated by the Simple. 28 Figure 4i. Daily least-sq uares regression of ET o from the Full ASCE-PM for 2006 calculated by the Hargreaves. 29 Figure 5a. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rn, G, T ). 31 Figure 5b. Monthly least-squares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs U, RH, T ). 32 Figure 5c. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs, T ). 33 Figure 4d. Monthly least-squares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (T ). 34 Figure 5e. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rn, G, T ). 35 Figure 5f. Monthly least-squares regression of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rs, T ). 36 Figure 5g. Monthly least-squares regression of ET o from the Full ASCE-PM for 2006 calculated by the Radiation/Tmax. 37 Figure 5h. Monthly least-squares regression of ET o from the Full ASCE-PM for 2006 calculated by the Simple. 38 Figure 5i. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006

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vi calculated by the Hargreaves. 39 Figure 6. Annual comparison of the various ET o equations from the Full ASCE-PM for 2006. 40 Figure 7a. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rn, G, T ). 43 Figure 7b. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs U, RH, T ). 44 Figure 7c. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs, T ). 45 Figure 7d. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (T ). 46 Figure 7e. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rn, G, T ). 47 Figure 7f. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rs, T ). 48 Figure 7g. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the Radiation/Tmax. 49 Figure 7h. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the Simple. 50 Figure 7g. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the Hargreaves. 51 Figure 8a. Cost/effectivene ss plot of all of the ET o equations with the optimum cost/effectiveness line at a daily time step. 55

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vii Figure 8b. Cost/effectiveness plot of all of the ET o equations with the optimum cost/effectiveness line at a monthly time step. 56 Figure 8c. Cost/effectivene ss plot of all of the ET o equations with the optimum cost/effectiveness line at an annual time step. 57

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viii Cost/Effectiveness Analysis of Obtaini ng Operational Estimates of Reference Evapotranspiration, Peni nsular Florida, USA Michael G. Kittridge ABSTRACT The objective of this study is to conduct a cost/effectiveness analysis of the computation of reference evapotranspiration (ET o ) in the peninsular of Florida. A meteorological station on the Fort Meade Mi ne in Polk County, Florida was used to provide data for the calculation of ET o Five ET o equations were tested to determine the accuracy and cost/effectiveness to the fully measured ASCE Penman-Monteith (Full ASCE-PM) equation on daily, monthly, and annually time steps. The ET o equations ranged in amounts of parameters from the Fu ll ASCE-PM to the Hargreaves. The energy terms accounted for approximately 90% of the total ET o flux. Solar radiation alone also accounted for approximately 90% of the total ET o flux. The highest cost-effectiveness ratios were equations that were able to accurately estimate values without relying on expensive meteorological equipment and/or om itted terms that had a lesser influence on the magnitude of ET o The seasonal variability in the climate and consequently the emphasis of each meteorological parameter on ET o will create seasonal errors in the reduced sets of the ET o equations. Large seasonal e rrors were associated with temperature based ET o equations, while sola r radiation based ET o equations accurately

PAGE 11

ix preserved the seasonal trends. At least in Flor ida, solar radiation is the key driving force in both the magnitude and the seasonality of ET o

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1 INTRODUCTION Groundwater extraction exceeds groundwat er recharge by ~200 billion cubic meters per year in aquifers used for wate r resources supply throughout the world (Postel, 1999). As Growth continues, already-stressed water supplies will be increasingly stressed to satisfy the continually-growing number of thermoelectric, agricultural, municipal, industrial, and environmental water users. Therefore, wa ter managers are increasingly operating at the margins, where small errors in projections can cause proportionally-large changes in actual water deliver y to these many water users. Evapotranspiration (ET) is the primary outflow in terrestr ial water budgets. Globally, annual ET is ~65% of annual precipitat ion (Trenberth et al., In Press), while in peninsular Florida, annual ET is ~75% of annual precipitation (B idlake et al., 1996). Unfortunately, ET cannot be directly measured and must therefore be indirectly measured or computed. Because ET fluxes are so large, small errors in the in direct measurement or computation of ET can result in large diffe rences in projected runoff and groundwater recharge. Therefore, accurate projections necessitate accurate yet cost-effective methods to indirectly measure or compute ET. Evaporation requires energy to vaporize the water and a mass transfer mechanism to transfer the water vapor fr om the saturated boundary layer to the atmosphere. Most of the energy available to vaporize water comes from sensible heat originating from solar radiation (Penman, 1948; Mont eith, 1965; Priestly and Taylor, 1972). The saturated

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2 vapor is then transported from the boundary layer to the atmosphere by diffusion down vapor pressure grad ients and/or by advection from wind. Penman (1948) developed the first equation for computing ET by combining energy and mass transfer terms in the first so-called combination equation. Monteith (1965) later modified this equation by repl acing empirical coefficients with canopy and aerodynamic resistance terms. However, th e Penman-Monteith (P M) equation requires physical measurements of the vegetation in the computation of the canopy and aerodynamic resistance terms. Physical measur ements of vegetation can be difficult to obtain if the site is remote the vegetation changes seasona lly, and/or the vegetation is structurally complex. This has led to the development of nume rous empirically-deriv ed equations that compute potential ET (PET) from a variety of land covers using only meteorological parameters as variables. PET, though inconsiste ntly defined in the l iterature, is typically defined as the amount of ET from a uniform s hort crop surface with soil water at field capacity (Irmak and Haman 2003). Priestly and Taylor (1972) assumed that the computation of ET is more sensitive to the energy terms than to the mass transfer terms and therefore developed the Priestly-Taylor equation to compute PET using net radiation, soil density heat flux, and a coefficient that varies as a function of humidity. Other researchers have used similar reasoning. For example, Abtew (1996) developed two equations to compute PET from wetlands in South Florida, with the Radiation/Tmax equation using solar radiation and maximum temperature, the Simple equation using only solar radiation, and Hargreaves (1975) and Ha rgreaves and Samani (1985) developed the Hargreaves equation to compute PET usi ng only minimum and ma ximum temperature.

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3 As the need for accurate yet inexpensive methods to compute ET equations grew, so did the quantity of equations calibrate d to provide potential ET from different land covers. This created a lack of comparab ility between results from the various PET equations as many were developed for and perform best for specific land covers in specific regions due to the general definition of PET (Winter and Rosenberry 1995). This also created a difficulty in converting PET from one of these different land covers into actual ET for a specific land cover of inte rest. Consequently, reference ET (ET o ) was introduced and further developed to serv e as a standard ET calculation method (Doorenbos and Pruitt, 1977; Allen et al., 1994; Hargreaves 1994; Allen et al., 2005). First defined by the United Nations Food and Agriculture Organization (FAO) in 1977 (Doorenbos and Pruitt, 1977), updated by the FAO in 1998 (Allen et al. 1998), and recently adopted by the American Society of Civil Engineers in 2005 (ASCE; Allen et al., 2005), ET o has come to be defined as the ET from a hypothetical grass reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s/m and an albedo of 0.23 in which the reference surface clos ely resembles an extensive surface of green, well-watered grass of uniform height, activ ely growing and completely shading the ground. With functional and structural characteris tics fixed to the reference surface, the PM equation has been modified to require just energy and mass transfer terms. The final formulation was the FAO-PM equation (Allen et al. 1998). This has become the standard around the world, and it has been shown that FAO-PM ET o is nearly identical to lysimeter ET o data in a variety of environments throughout the world (Allen et al., 1994b; Allen et al., 1998; Ventura et al., 1999; Hargreaves and Allen, 2003; Irmak and Haman, 2003). The ASCE-PM equation is becoming the e quivalent standard in the U.S. (Allen et

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4 al., 2005). Standardization has allowed rese archers to focus resources on developing a wide variety of crop coe fficients to convert ET o to actual ET for a specific land cover of interest. The Full ASCE-PM equation requires the m easurement of energy terms (i.e., net radiation, soil heat flux density, and temper ature) and mass transfer terms (i.e., wind speed and humidity). However, complete data sets are not always readily available or cannot always be afforded. In these cases, ET o can be estimated by one of two basic approaches; (a) ET o can be computed using the ASCE -PM equation with some computed or estimated meteorological parame ters (Allen et al., 2005), (b) ET o can be computed using one of the numerous empirically-derived ET o /PET equations that accurately reproduce values close to the Full ASCE -PM (Allen et al., 1998). Though these approaches provide cost savings, they may also reduce accuracy. The objective of this study is to conduct a cost/effectiveness analysis of the computation of ET o To do so, we set the Full ASCE -PM as the standard and evaluate the cost savings and accuracy of alternative ET o equations to produce a final costeffectiveness value for each of the alternative ET o equations on daily, monthly, and annually time steps. Though the Full ASCE-PM equation is the most accurate method, we hypothesize that alternative ET o equations can be cost-effec tive if some of the lessimportant energy and mass transfer terms are omitted and/or net radiation is computed from less-expensive so lar radiation data.

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5 SITE DESCRIPTION Location and Hydrogeological Setting The study site is located on the Fort Mead e Mine in Polk County, Florida (Figure 1). The site is a ~20 year-old clay storage area (CSA) created for the storage of clay-rich waste products of phosphate mining. The CSA is ~6 m above grade and ~75 hectares in size. The CSA is nearly level to undulating with a slight topographic gradient from north to south. The CSA deposits are compri sed of clay and sand from the Bone Valley Member mixed with native groundwater a nd other processing water (Reigner and Winkler, 2001). The top layer (~0.5 m) is a subangular blocky, clay-rich surface layer with abundant desiccation cracks and other macr opores associated with bioturbation such as burrows and root channels. There are several closed-bas in depressions that pond water seasonally. There are no surface water inflows, but there are inte rconnected ditches that discharge through a culvert through the east berm and substantial groundwater discharges to the surrounding surficial aquifer (Murph y et al., In Review).

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Figure 1. Site location at the Ft. Meade mine clay storage area (CSA) in Polk County, FL. 6

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7 Vegetation The predominant vegetation is the invasive Cogon grass ( Imperata cylindrical (L.) Raeuschel). Towards the southern end, and in topographically low areas, the predominant vegetation is the Florida willow ( Salix floridana Chapm.). The seasonal growth patterns of the Cogan grass ranges from lush in the middle to late summer to browning and wilting at the tips during the late winter to middle spring. The meteorological station is surrounded by Cogan grass with an approximate fetch of at least 60 m in all directions and an av erage height of about 1 m. Climate The climate at the study area is subtropical with warm, relatively dry winters and hot, relatively wet summers (Table 1). Su mmer rainfall is due to frequent, local convective thunderstorms, while winter rain fall is due to infrequent cold fronts (Lewelling and Wylie, 1993). Mean ( standa rd deviation) annual temperature is 23.2 o C ( 0.57 o C) (Southeastern Regional Climate Center data for Bartow, Florida for calendar years 1986-2006) (Figure 2a). Mean ( standa rd deviation) annual precipitation is 1375 mm ( 244 mm), with ~58% falling during the f our primary wet-season months of JuneSeptember (Southeastern Regional Climate Cent er data for Bartow, Florida for calendar years 1892-2006) (Figure 2a). Annual temperat ure and precipitation in 2006 for Bartow were 22.0 o C and 952 mm, respectively, while annua l temperature and precipitation for the study area were 21.8 o C and 883 mm, respectively (Figures 2b-c). Conditions were

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8 slightly dryer than normal during the course of this study (Southeas tern Regional Climate Center data for Bartow, Fl orida for water years 2006).

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9 Parameter Mean (Standard Deviation) Daily Value Net Radiation (MJ m -2 ) 10.46 (.90) Solar Radiation (MJ m -2 ) 18.10 (.65) Soil Heat Flux Density (MJ m -2 ) 0.27 (.10) Temperature ( o C) 21.79 (.74) Humidity (%) 70.97 (.96) Wind Speed (m s -1 ) 2.04 (.74) Table 1. Mean daily meteorologi cal values for calendar year 2006.

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15 20 25 30 JAN FEBMARAPRMAYJUNJULAUGSEPOCTNOVDECT (oC)0 50 100 150 200 250Precipitation (mm) Mean Monthly Precipitation Mean Monthly Temperature Figure 2a. Mean monthly temperature and precipitation for Bartow, FL from 1892-2006. 10

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15 20 25 30 JAN FEBMARAPRMAYJUNJULAUGSEPOCTNOVDECT (oC)0 50 100 150 200 250Precipitation (mm) Mean Monthly Precipitation Mean Monthly Temperature Figure 2b. Mean monthly temperature a nd precipitation for Bartow, FL for 2006. 11

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15 20 25 30 JANFEBMARAPRMAYJUNJULAUGSEPOCTNOVDECT (oC)0 50 100 150 200 250Precipitation (mm) Mean Monthly Precipitation Mean Monthly Temperature Figure 2c. Mean monthly temperatur e and precipitation for the CSA for 2006. 12

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13 METHODS Instrumentation and Measurement Instrumentation included a meteorological station on which precipitation, solar radiation, temperature, relati ve humidity, and wind speed and direction were measured; a net radiometer with which net radiation wa s measured; and soil heat flux plates and thermocouples with which soil heat flux dens ity was computed (Table 2). Data was collected hourly and summarized daily fr om October 2005-April 2007. Missing data was replaced by using least-squares regression with data from the study site as the dependent variables and data from the Florida Automated Weather Netw ork Station located ~55 km away in Balm, Florida as independent variables.

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14 Parameter Symbol Campbell Scientific Instrument Net Radiation Rn Kipp & Zonen Net Radiometer (NR-LITE-L11) Soil Heat Flux Density G REBS Soil Heat Flux Plates (HFT3-L50) & Type E Thermocouples (TCAV-L) Solar Radiation Rs Apogee PYR-P Pyranometer (CS300-L11) Wind Speed U Met One Anemometer (014A-L11) Relative Humidity RH Vaisala Temperature/RH Probe (HMP45C-L11) Temperature T Vaisala Temperature/RH Probe (HMP45C-L11) Precipitation Texas Electronics 6 Rain Gauge (TE525-L) Table 2. Meteorological parameters with the associated symbol and instrumentation.

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ET o Equations ET o was computed on daily time steps using five equations: the ASCE-PM equation (Allen et al., 2005), the Priestly-Taylor equation (P riestly and Taylor, 1972), the Radiation/Tmax equation (Abtew, 1996), th e Simple equation (Abtew, 1996), and the Hargreaves equation (Hargreaves, 1 975; Hargreaves and Samani, 1985). ET o from the ASCE-PM equation was computed with five different amounts of measured and computed data, ranging from all data measured to only temperature measured (Allen et al., 2005). The ASCE-PM equation is )34.01( )( 273 900 )(408.02 2U eeU T GR ETas n o where is the slope vapor pressure curve (kPa o C -1 ), is net radiation (MJ m nR -2 day -1 ), is soil heat flux density (MJ m G -2 day -1 ), is the psychrometric constant (kPa o C -1 ), T is mean daily temperature ( o C), is the wind speed at 2 m height (m s 2U -1 ), is mean saturation vapor pressure (kPa), and is actual vapor pressure (kPa). se ae ET o from the Priestly-Taylor equation w ill be calculated using two different amounts of measured and computed data. It will be calculated from measured G, and T and also calculated from solar radiation (estimating ) and T. The PriestlyTaylor equation is nR nR )(26.1 GR ETn o where all terms are as previously defined. 15

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ET o from the Radiation/Tmax equation wa s computed with all data measured (Abtew 1996). The Radiat ion/Tmax equation is max56 1 TR ETs o where is solar radiation (MJ m sR -2 day -1 ), is maximum daily temperature ( maxT o C), and is the latent heat of va porization of water (2.45 MJ kg -1 ). ET o from the Simple equation was comput ed with all data measured (Abtew 1996). The Simple equation is s oR ET 52.0 where all terms are as previously defined. ET o from the Hargreaves equation was computed with all data measured (Hargreaves, 1975; Hargreaves and Samani, 1985). The Hargreaves equation is 5.0 min max min max) )(8.17 2 (0023.0 TT TT R ETa o where is extraterrestri al radiation (MJ m aR -2 day -1 ), min T is minimum daily temperature ( o C), and all other terms are as previously defined. is only a function of latitude. aR ET Analysis Daily averages by month were tabulated against the Full ASCE-PM to depict seasonality error for all ET o equations for 2006. The monthly averages were then compared to the Full ASCE-PM and a percent difference from the Full ASCE-PM was calculated. A linear regression curve was a pplied to each of the reduced sets and compared to the Full ASCE-PM on daily, monthly, and annually time steps. The 16

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Standard Error of Estimate (SEE), which is th e standard deviation of the expected value of the regression curve, was also used to co mpare the reduced sets to the Full ASCE-PM. Effectiveness was calculated as a mean da ily or monthly diffe rence by subtracting the ET o equation to be evaluated by the Full AS CE-PM. Effectiveness for each day or month was then averaged over the entire year. total n nnn X YX ess Effectiven ] || [ where is the Full ASCE-PM ET nX o for day or month is the evaluated ET n nY o equation for day or month and is the total number of da ys (365 days) or months (12 months). n totaln Costs were quoted by Campbell Scien tific for March 2007. Instrumentation, including all mounting and pr otection hardware, for the Full ASCE-PM costs ~$6,850. This price is used as the benchmark for al l subsequent equipment costs and analyses. Labor costs were assumed to be the same fo r each approach as they all require similar installation and maintenance. The cost/effectiveness ratio was computed as PM FASCE Alt PM FASCE Altess Effectiven ess Effectiven Cost Cost ess Effectiven Cost / where the subscript Alt refers to the alternative ET o value and the subscript FASCEPM refers to the Full ASCE-PM ET o value. 17

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18 RESULTS ET o by the Full ASCE-PM Equation Mean (standard deviation) daily ET o for calendar year 2006 was 4.10 mm (.12 mm). Total annual ET o for calendar year 2006 was 1496 mm, which was 169% of total annual precipitation for calendar year 2006 and 109% of the mean a nnual precipitation at Bartow for calendar years 1892-2006 (Figures 2a-c). ET o was strongly seasonal (Figure 3). ET o was lowest in December, when mean (standard deviation) daily ET o was 2.58 mm (0.90 mm), and highest in April, when mean (standard deviation) daily ET o was 5.48 mm (0.47 mm).

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0 1 2 3 4 5 6 7January-06 February-06 Ma r c h -06 A p ri l06 May-06 Jun e -0 6 Jul y-0 6 Aug u st-06 September-06 O ct o b e r06 No v embe r -0 6 De ce mber-0 6ETo (mm) Figure 3. Daily ET o values for 2006 calculated from the Full ASCE-PM. 19

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20 Comparisons on Daily Time Steps Least-squares regressions with the al ternative equations as the dependent variables and the Full ASCE-PM equation as the independent variable indicate that some of the alternative equations ar e better than others at provid ing accurate estimates of daily ET o (Figure 4a-i). Slopes ranged from 0.86 to 1.17, R 2 ranged from 0.61 to 0.96, and SEE ranged from 0.22 to 0.70 mm/d. The most accurate alternative equations were the ASCE-PM ( Rs, U, RH, T ) and the Simple equations. Both had slopes of 1.00, and the ASCE P-M ( Rs, U, RH, T ) equation had the highest R 2 and lowest SEE (0.96 and 0.22 mm/d, respectively), while the Simple equation had the second-highest R 2 and secondlowest SEE (0.87 and 0.40 mm/d, respectively). The least accurate alternative equation was the Hargreaves equation, with a slope of 0.86 and the lowest R 2 and the highest SEE (0.61 and 0.70 mm/d, respectively).

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y = 0.92x + 0.40 R2 = 0.85 SEE = 0.44 mm d-1p < 0.01 0 1 2 3 4 5 6 7 0123456 Full ASCE-PM (mm)ASCE-PM ( Rn, G, T ) (mm) 7 Figure 4a. Daily leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rn, G, T ). 21

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y = 1.00x 0.15 R2 = 0.96 SEE = 0.22 mm d-1p < 0.01 0 1 2 3 4 5 6 7 0123456 Full ASCE-PM (mm)ASCE-PM ( Rs, U, RH, T ) (mm) 7 Figure 4b. Daily least-s quares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs, U, RH, T ). 22

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y = 0.91x + 0.30 R2 = 0.82 SEE = 0.48 mm d-1p < 0.01 0 1 2 3 4 5 6 7 0123456 Full ASCE-PM (mm)ASCE-PM ( Rs, T ) (mm) 7 Figure 4c. Daily leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs, T ). 23

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y = 0.98x + 0.65 R2 = 0.64 SEE = 0.67 mm d-1p < 0.01 0 1 2 3 4 5 6 7 8 0123456 Full ASCE-PM (mm)ASCE-PM (T ) (mm) 7 Figure 4d. Daily least-s quares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (T ). 24

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y = 1.10x 0.82 R2 = 0.84 SEE = 0.45 mm d-1p < 0.01 0 1 2 3 4 5 6 7 0123456 Full ASCE-PM (mm)Priestly-Taylor ( Rn, G, T ) (mm) 7 Figure 4e. Daily leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rn, G, T ). 25

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y = 1.10x 0.99 R2 = 0.79 SEE = 0.52 mm d-1p < 0.01 0 1 2 3 4 5 6 7 0123456 Full ASCE-PM (mm)Priestly-Taylor ( Rs, T ) (mm) 7 Figure 4f. Daily least-squares regression of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rs, T ). 26

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y = 1.17x 1.11 R2 = 0.83 SEE = 0.46 mm d-1p < 0.01 0 1 2 3 4 5 6 7 0123456 Full ASCE-PM (mm)Radiation/Tmax (mm) 7 Figure 4g. Daily least-s quares regression of ET o from the Full ASCE-PM for 2006 calculated by the Radiation/Tmax. 27

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y = 1.00x 0.25 R2 = 0.87 SEE = 0.40 mm d-1p < 0.01 0 1 2 3 4 5 6 7 0123456 Full ASCE-PM (mm)Simple (mm) 7 Figure 4h. Daily least-s quares regression of ET o from the Full ASCE-PM for 2006 calculated by the Simple. 28

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y = 0.86x + 0.48 R2 = 0.61 SEE = 0.70 mm d-1p < 0.01 0 1 2 3 4 5 6 7 0123456 Full ASCE-PM (mm)Hargreaves (mm) 7 Figure 4i. Daily leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the Hargreaves. 29

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30 Comparisons on Monthly Time Steps Least-squares regressions with the al ternative equations as the dependent variables and the Full ASCE-PM equation as the independent variable indicate that some of the alternative equations are better than others at pr oviding accurate estimates of monthly ET o (Figure 5a-i). Slopes ranged from 1.00 to 1.31, R 2 ranged from 0.84 to 0.98, and SEE ranged from 4.19 to 11.80 mm/month. The most accurate alternative equations were the ASCE-PM (R s U, RH, T ) and the Simple equations. Both had slopes of 1.00 and R 2 of 0.98, and the ASCE-PM ( R s U, RH, T ) equation had the lowest SEE (4.19 mm/month), while the Simple equa tion had the second -lowest SEE (4.52 mm/month). The least accurate alternative equation was the Hargreaves equation, with a slope of 1.23 and the lowest R 2 and the highest SEE (0.84 and 11.80 mm/d, respectively).

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y = 1.00x + 2.14 R2 = 0.95 SEE = 6.22 mm month-1p < 0.01 50 80 110 140 170 200 50 80 110 140 170 200 Full ASCE-PM (mm)ASCE-PM (Rn, G, T) (mm) Figure 5a. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rn, G, T ). 31

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y = 1.06x 12.92 R2 = 0.98 SEE = 4.19 mm month-1p < 0.01 50 80 110 140 170 200 50 80 110 140 170 200 Full ASCE-PM (mm)ASCE-PM (Rs, U, RH, T) (mm) Figure 5b. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs, U, RH, T ). 32

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y = 1.02x 4.89 R2 = 0.91 SEE = 8.71 mm month-1p < 0.01 50 80 110 140 170 200 50 80 110 140 170 200 Full ASCE-PM (mm)ASCE-PM (Rs, T) (mm) Figure 5c. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs, T ). 33

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y = 1.30x 19.19 R2 = 0.87 SEE = 10.35 mm month-1p < 0.01 50 80 110 140 170 200 50 80 110 140 170 200 Full ASCE-PM (mm)ASCE-PM (T) (mm) Figure 5d. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (T ). 34

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y = 1.26x 44.81 R2 = 0.92 SEE = 8.05 mm month-1p < 0.01 50 80 110 140 170 200 50 80 110 140 170 200 Full ASCE-PM (mm)Priestly-Taylor (Rn, G, T) (mm) Figure 5e. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rn, G, T ). 35

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y = 1.31x 56.46 R2 = 0.87 SEE = 10.57 mm month-1p < 0.01 50 80 110 140 170 200 50 80 110 140 170 200 Full ASCE-PM (mm)Priestly-Taylor (Rs, T) (mm) Figure 5f. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rs, T ). 36

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y = 1.26x 44.36 R2 = 0.89 SEE = 9.83 mm month-1p < 0.01 50 80 110 140 170 200 50 80 110 140 170 200 Full ASCE-PM (mm)Radiation/Tmax (mm) Figure 5g. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the Radiation/Tmax. 37

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y = 1.00x 7.44 R2 = 0.98 SEE = 4.52 mm month-1p < 0.01 50 80 110 140 170 200 50 80 110 140 170 200 Full ASCE-PM (mm)Simple (mm) Figure 5h. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the Simple. 38

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y = 1.23x 31.32 R2 = 0.84 SEE = 11.80 mm month-1p < 0.01 50 80 110 140 170 200 50 80 110 140 170 200 Full ASCE-PM (mm)Hargreaves (mm) Figure 5i. Monthly leastsquares regression of ET o from the Full ASCE-PM for 2006 calculated by the Hargreaves. 39

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40 Comparisons on an Annual Time Step Comparisons indicate that some of the al ternative equations ar e better than others at providing accurate estimates of annual ET o (Figure 6). Four alternative equations provided annual ET o estimates that were within 5% of the annual ET o estimate provided by the Full ASCE-PM. The most accurate was the ASCE-PM ( Rn, G, T ), with an annual ET o estimate of +1.3% of the annual ET o estimate provided by the Full ASCE-PM. The next most accurate were the ASCE-PM ( Rs, T ), Hargreaves, and ASCE-PM ( Rs, U, RH, T ), with annual ET o estimates of -1.7%, -2.3%, and -4.3% of the annual ET o estimate provided by the Full ASCE-PM, respectively. The least accurate were the ASCE-PM ( T ) and the Priestly-Taylor ( Rs, T ), with annual ET o estimates of +14.2% and -14.2% of the annual ET o estimate provided by the Full ASCE-PM, respectively.

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Figure 6. Annual comparison of the various ET o equations from the Full ASCEPM for 2006. 41

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42 Seasonality Comparisons of monthly ET o indicate that some of th e alternative equations show little or no seasonal deviation from the Full ASCE-PM, while other alternative equations show marked seasonal deviation from the Full ASCE-PM (Figure 7a-i). Monthly ET o from the ASCE-PM ( Rn, G, T ), ASCE-PM ( Rs, U, RH, T ), and ASCE-PM ( Rs, T ) equations were always <10% different than monthly ET o from the Full ASCE-PM. Similarly, monthly ET o from the Simple equation were t ypically <10% and always <20% different than monthly ET o from the Full ASCE-PM. Monthly ET o from the other alternative equations were typi cally >20% different than ET o from the Full ASCE-PM. In these cases, seasonal deviations had a r ecurring trend, with hi gher relative values during the summer months and lower rela tive values during the winter months.

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ASCE-PM ( Rn, G, T ) -50 -40 -30 -20 -10 0 10 20 30 40 50 JanFebMarAprMayJunJulAugSepOctNovDec% difference from Full ASCE-PM Figure 7a. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rn, G, T ). 43

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ASCE-PM ( Rs, U, RH, T ) -50 -40 -30 -20 -10 0 10 20 30 40 50 JanFebMarAprMayJunJulAugSepOctNovDec% difference from Full ASCE-PM Figure 7b. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs, U, RH, T ). 44

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ASCE-PM ( Rs, T ) -50 -40 -30 -20 -10 0 10 20 30 40 50 JanFebMarAprMayJunJulAugSepOctNovDec% difference from Full ASCE-PM Figure 7c. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (Rs, T ). 45

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ASCE-PM (T ) -50 -40 -30 -20 -10 0 10 20 30 40 50 JanFebMarAprMayJunJulAugSepOctNovDec% difference from Full ASCE-PM Figure 7d. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the ASCE-PM (T ). 46

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Priestly-Taylor (Rn, G, T) -50 -40 -30 -20 -10 0 10 20 30 40 50 JanFebMarAprMayJunJulAugSepOctNovDec% difference from Full ASCE-PM Figure 7e. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rn, G, T ). 47

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Priestly-Taylor (Rs, T) -50 -40 -30 -20 -10 0 10 20 30 40 50 JanFebMarAprMayJunJulAugSepOctNovDec% difference from Full ASCE-PM Figure 7f. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the Priestly-Taylor ( Rs, T ). 48

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Radiation/Tmax -50 -40 -30 -20 -10 0 10 20 30 40 50 JanFebMarAprMayJunJulAugSepOctNovDec% difference from Full ASCE-PM Figure 7g. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the Radiation/Tmax. 49

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Simple -50 -40 -30 -20 -10 0 10 20 30 40 50 JanFebMarAprMayJunJulAugSepOctNovDec% difference from Full ASCE-PM Figure 7h. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the Simple. 50

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Hargreaves -50 -40 -30 -20 -10 0 10 20 30 40 50 JanFebMarAprMayJunJulAugSepOctNovDec% difference from Full ASCE-PM Figure 7i. Monthly seasonality of ET o from the Full ASCE-PM for 2006 calculated by the Hargreaves. 51

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52 Cost/Effectiveness Analysis on Daily Time Steps Three alternative equations were more cost/effective when ET o was computed on daily time steps (Table 3; Figure 8a). The mo st cost/effective alternative equations were the ASCE-PM (Rs, U, RH, T ), ASCE-PM ( Rs, T ), and Simple equations with cost/effectiveness values of 11.84, 7.34, and 6.47, respectively. The remaining alternative equations had cost/effectiveness values of 4.23. The least cost/effective alternative equation was the Priestly-Taylor ( Rn, G, T ) equation with a cost/effectiveness value of 1.02. Cost/Effectiveness Analysis on Monthly Time Steps Three alternative equations were more cost/effective when ET o was computed on monthly time steps (Table 3; Figure 8b). Th e most cost/effective alternative equations were the ASCE-PM (Rs, T ), Simple, and ASCE-PM ( Rs, U, RH, T ) equations with cost/effectiveness values of 11.72, 11.08, and 8.57, respectively. The remaining alternative equations had cost/effectiveness values of 5.97. The least cost/effective alternative equation was the Priestly-Taylor ( Rn, G, T ) equation with a cost/effectiveness value of 1.43.

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53 Cost/Effectiveness Analysis on an Annual Time Step Three alternative equations were more cost/effective when ET o was computed on an annual time step (Table 3; Figure 8c). The most cost/effective alternative equations were the ASCE-PM (Rs, T ), Hargreaves, and ASCE-PM ( Rn, G, T ) equations with cost/effectiveness values of 43.32, 33.78, 15.02, respectively. The remaining alternative equations had cost/effectiveness values of 11.72. The least cost/effective alternative equation was the Priestly-Taylor ( Rn, G, T ) equation with a cost/effectiveness value of 1.97.

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54 Equation Parameters Cost Cost Ratio Daily Effectiveness Monthly Effectiveness Annual Effectiveness Daily Cost/Effectiveness Monthly Cost/Effectiveness Annual Cost/Effectiveness ASCE-PM Rn, G, U, RH, T 6870 1.00 1.000 1.000 1.000 N/A N/A N/A ASCE-PM Rn, G, T 5567 0.81 0.905 0.965 0.987 2.00 5.42 15.02 ASCE-PM Rs, U, RH, T 3867 0.56 0.941 0.949 0.958 11.84 8.57 10.30 ASCE-PM Rs, T 2038 0.30 0.897 0.940 0.984 7.34 11.72 43.32 ASCE-PM T 1657 0.24 0.773 0.868 0.858 3.22 5.75 5.33 Priestly-Taylor Rn, G, T 5567 0.81 0.853 0.867 0.904 2.96 1.43 1.97 Priestly-Taylor Rs, T 2038 0.30 0.813 0.821 0.858 1.02 3.93 4.96 Radiation/Tmax Rs, T 2038 0.30 0.833 0.858 0.901 4.21 4.95 7.08 Simple Rs 1848 0.27 0.891 0.934 0.938 6.47 11.08 11.72 Hargreaves T 1657 0.24 0.820 0.873 0.978 4.23 5.97 33.78 Table 3. Cost/effectiveness an alysis for calendar year 2006.

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0.70 0.75 0.80 0.85 0.90 0.95 1.00 01000200030004000500060007000 CostEffectiveness y = 2.2E-5x + 0.85 A SCE-PM ( Rs, T ) Simple ASCE-PM (Rs, U, RH, T) Full ASCE-PM Figure 8a. Cost/effectivene ss plot of all of the ET o equations with the optimum cost/effectiveness line at a daily time step. 55

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0.80 0.85 0.90 0.95 1.00 01000200030004000500060007000 CostEffectiveness y = 1.3E-5x + 0.91 Simple ASCE-PM (Rs, T) ASCE-PM (Rs, U, RH, T) ASCE-PM (Rn, G, T) Full ASCE-PM Figure 8b. Cost/effectiveness plot of all of the ET o equations with the optimum cost/effectiveness line at a monthly time step. 56

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0.80 0.85 0.90 0.95 1.00 01000200030004000500060007000 CostEffectiveness y = 3E-6x + 0.97 Simple ASCE-PM (Rs, T) ASCE-PM (Rs, U, RH, T) ASCE-PM (Rn, G, T) Hargreaves Full ASCE-PM Figure 8c. Cost/effectivene ss plot of all of the ET o equations with the optimum cost/effectiveness line at a yearly time step. 57

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58 DISCUSSION Accuracy There are numerous equations commonly used to provide operational estimates of ET o However, these equations vary in their accuracy in peninsular Florida (Jacobs and Satti, 2001) and across the 48 conterminous stat es (Jensen et al., 1990). On daily and monthly time steps, the ASCE-PM ( Rs, U, RH, T ) and the Simple equations were most accurate. Others were less accurate, with the Hargreaves equation being the least accurate. On an annual time step, the ASCE-PM ( Rn, G, T ), ASCE-PM ( Rs, T ), Hargreaves, and ASCE-PM ( Rs, U, RH, T ) were most accurate. Others were less accurate, with the ASCE-PM ( T ) and the Priestly-Taylor ( Rs, T ) equations being the least accurate. One source of error may be that many equations commonly used to provide operational estimates of ET o were originally calibrated to provide PET from a particular reference crop rather than ET o from the standard reference crop. However, many of the particular reference crops had characteristics similar to the standard reference crop, i.e., they were short, uniform grasses. Theref ore, many equations originally calibrated to compute PET from a particular reference crop (e.g., Hargreaves and Samani, 1982) have more recently been used to compute ET o from the standard reference crop (e.g., Hargreaves and Samani, 1985). The less-accurate alternative equations te nded to show a seas onal deviation from the Full ASCE-PM, with higher relative va lues during the summer months and lower

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59 relative values during the winter months. In peninsular Flor ida, summer temperatures are high, but days are cloudy and humid, while wint er temperatures are moderate, but days are sunny and subhumid. Therefore, alternative equations that use T without satisfactory energy and/or mass-transfer terms may tend to overestimate ET o in the summer and underestimate ET o in the winter. This kind of se asonal deviation was evident in the alternative equations that only require T or Rs and T Conversely, this kind of seasonal deviation was not evident in the S imple equation, which requires only Rs Cost/Effectiveness On daily and monthly time steps, the ASCE-PM (Rs, T ), Simple, and ASCE-PM ( Rs, U, RH, T ) equations were most cost/effective. Others were less cost/effective, with the Priestly-Taylor ( Rn, G, T ) equation being the least cost/e ffective. On an annual time step, the ASCE-PM ( Rs, T ), Hargreaves, and ASCE-PM ( Rn, G, T ) equations were the most cost/effective. Others were less cost/effective, with the Priestly-Taylor ( Rn, G, T ) equation again being the least cost/effective. ET is dominated by energy rather than ma ss transfer (Priestly and Taylor, 1972). Furthermore, Rn (Fritschen, 1967; Alle n et al., 2005) and G (Allen et al., 2005) can be accurately estimated from Rs With Rn and G being the most-expensive terms to measure (~$3,000), the ability of Rs to closely-approximate these terms at a lower cost (~$300) makes alternative equations in which Rn and G are computed from Rs substantially more cost/effective. Furthermore, net radiom eters require yearly calibration and other maintenance due to common errors that ha ve a range of 10% from calibrated and measured values (Llasat and Snyder 1998). Ther efore, the most cost /effective alternative

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60 equations tend to be those in which mass-transfer terms are omitted and Rn and G are computed from less-expensive Rs data. Perhaps the best example is the Simple equation, which only require a coefficient and Rs and which was generally an accurate and cost/effective alternative equation. Howeve r, this study was conducted in peninsular Florida where winds are modera te and humidities are high. Mass-transfer terms may be more important in other environments where winds are high and/or humidities are low. This fact is implicit in the two common form s of the Priestly-Taylor equation, in which the coefficient that replaces the mass-transfer terms is lower for humidities <40% and higher for humidities >40% (Priestly and Taylor, 1972). This cost/effectiveness analysis does not include the ways that the end users value accuracy. In some cases, the need for greate r accuracy may justify the use of a moreaccurate equation regardless of the cost/effectiv eness of the equation. In other cases, the lack of funding may justify the use of a less-accurate equation regardless of the cost/effectiveness of the equati on. In all cases, however, the cost/effectiveness figures can help end users make informed decisions regarding which equa tions will provide the best accuracy given the av ailable funding (Figure 8). To some extent, the cost and effectiveness values in this study are characteristic to the models and/or vendors selected. Alternative equipment sets could be purchased and installed at lower or higher co sts. Similarly, alternative equi pment sets could be more or less accurate. However, a subset of alternative equations were relatively clearly and consistently more accurate and cost/effective across daily, monthly, and annual time steps. Therefore, though the details of the cost/effectiveness analysis might differ, the trends of the cost/effectiveness analysis woul d be unlikely to change if different models and/or vendors were selected.

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61 Obtaining ET from ET o The ET o values computed in this study are comparable to ET o values computed for a variety of land covers in peninsular Florida (Jacobs and Satti, 2001; Sumner and Jacobs, 2005) and to actual evaporation com puted for lakes and estuaries in peninsular Florida (Sacks et al., 1994; Lee and Swan car, 1997; Swancar et al., 2000; Sumner and Belaineh, 2005). Actual evapotranspirati on (ET) can be computed by multiplying ET o by a crop coefficient (K c ). K c are available, though most are for agricultural land covers and vary only on seasonal time scales (e.g., Door enbos and Pruitt, 1977; Allen et al., 2005). K c can be computed using concurrently-co llected lysimeter or eddy-flux data and meteorological data. In this case, K c can be computed by divi ding actual ET computed from the lysimeter or eddy -flux data by ET o computed using the data from the meteorological station. If done on a daily or mo nthly time step, then a curve can be fit to the K c vs. annual water year day data and used to compute a generic daily-or monthlyvarying K c for use in similar environments. Doi ng this on a daily time step, using data from a nearby study (D. Sumner, unpublished da ta), gives an annual actual ET of 1073 mm/year, which is comparable to the actual ET computed for a variety of land covers in peninsular Florida (Bidlake et al., 1996).

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62 CONCLUSION There are numerous equations commonly used to provide operational estimates of ET o The ASCE-PM equation is becoming the sta ndard in the U.S. (Allen et al., 2005). The tendency may be to believe that the mo st accurate and cost/effective alternative equations are those that are the most complex. This is not the case. Rather, the most accurate and cost/effective alternative equations tend to be those in which mass-transfer terms are omitted and Rn and G are computed from less-expensive Rs data. Perhaps the best example is the Simple equation, which only require a coefficient and Rs and which was generally an accurate and cost/effective alternative equation, pa rticularly on daily and monthly time steps.

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63 REFERENCES Abtew, W., 1996. Evapotranspiration Measur ements and Modeling for Three Wetland Systems in South Florida. Wate r Resources Bulletin 32(3):465-473. Allen, R.G., M. Smith, A. Perrier and L.S. Pereira, 1994b. An Update for the Calculation of Reference Evapotranspirati on. ICID Bulletin 43(2):35-92. Allen, R.G., I.A. Walter, R.L. Elliott, T.A. Howell, D. Itenfisu, M.E. Jensen and R.L. Snyder (eds.), 2005. The ASCE Standard ized Reference Evapotranspiration Equation. American Society of Ci vil Engineers, Washington DC. Bidlake, W.R., W.M. Woodham and M.A. L opez, 1996. Evapotranspiration from Areas of Native Vegetation in West-Central Florida. 2430, U.S. Geological Survey Water-Supply Paper 2430. Doorenbos, J. and W.O. Pruitt (Editors), 1977. Guidelines for Prediction of Crop Water Requirements. FAO Irrigation and Drainage Paper No. 24, Rome. Fritschen, L.J. 1967, Net and Solar Radiati on Relations Over Irrigated Field Crops. Agricultural Meteorology 4:55-62. Hargreaves, G.H. and R.G. Allen, 2003. Hi story and Evaluation of Hargreaves Evapotranspiration Equation. Journal of Irrigation and Drainage Engineering 129(1):53-63. Hargreaves, G.H. and Z.A. Samani, 1985. Reference Crop Evapotranspiration from Temperature. Applied Engineer ing in Agriculture 1(2):96-99. Irmak, S. and D.Z. Haman, 2003. Evapotranspirati on: Potential or Reference? Institute of Food and Agricultural Sciences, University of Florida: ABE 343. Irmak, S., A. Irmak, R.G. Allen and J.W. Jones, 2003. Solar and Net Radiation-Based Equations to Estimate Reference Evapotra nspiration in Humid Climates. Journal of Irrigation and Drainage Engineering 129(5):336-347. Jacobs, J.M. and S.R. Satti, 2001. Evaluation of Reference Evapotranspiration Methodologies and AFSIRS Crop Water use Simulations, University of Florida. Jensen, M.E., R.D. Burman and R.G. Allen, 1990. Evapotranspiration and Irrigation Requirements. ASCE Manuals and Repor ts on Engineering Practice, No. 70 360.

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64 Lee, T.M. and A. Swancar, 1997. Influe nce of Evaporation, Ground Water, and Uncertainty in the Hydrologic Budget of Lake Lucerne, a Seepage Lake in Polk County, Florida. U.S. Geological Survey Water-Supply Paper 2439. Monteith, J.L., 1965. Evaporation and Environment. 19th Symposia of the Society for Experimental Biology:205-234. Penman, H.L., 1948. Natural Evaporation from Open Water, Bare Soil, and Grass. Proceedings of the Royal Society of London 193(1032):120-145. Priestly, C.H.B. and R.J. Taylor, 1972. On the Assessment of Surface Heat Flux and Evaporation using Large-Scale Parameters. Monthly Weather Review 100(2):8192. Rosenberry, D.O., D.I. Stannard, T.C. Wint er and M.L. Martinez, 2004. Comparison of 13 Equations for Determining Evapotranspiration from a Prairie Wetland, Cottonwood Lake Area, North Dakot a, USA. Wetlands 24(3):483-497. Sacks, L.A., T.M. Lee and M.J. Radell, 1994. Comparison of Energy-Budget Evaporation Losses from Two Morphometrically Differe nt Florida Seepage Lakes. Journal of Hydrology 156:311. Sumner, D.M. and G. Belaineh, 2005. Evaporation, Precipitation, and Associated Salinity Changes at a Humid, Subtropi cal Estuary. Estuaries 28:844. Sumner, D.M. and J.M. Jacobs, 2005. Utility of Penman-Monteith, Priestly-Taylor, Reference Evapotranspiration, and Pan Ev aporation Methods to Estimate Pasture Evapotranspiration. Journal of Hydrology 308:81-104. Swancar, A., T.M. Lee and T.M. OHare, 2000. Hydrogeologic setting, water budget, and preliminary analysis of ground-water exchange at Lake Starr, a seepage lake in Polk County, Florida. U.S. Geological Survey Water-Resources Investigations Report 00-4030. Ventura, F., D. Spano, P. Duce and R. L. Snyder, 1999. An Evaluation of Common Evapotranspiration Equations. Irrigation Science 18:163-170. Winter, T.C. and D.O. Rosenberry, 1995. Ev aluation of 11 equations for determining evaporation for a small lake in the nort h central United States. Water Resources Research 31(4):983-993.

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65 BIBLIOGRAPHY Abtew, W. and J. Obeysekera, 1995. Lysime ter Study of Evapotranspiration of Cattails and Comparison of Three Estimation Met hods. American Society of Agricultural Engineers 38(1):121-129. Allen, R.G., 1996. Assessing Integr ity of Weather Data for Re ference Evapotranspiration Estimation. Journal of Irrigation and Drainage Engineering 122(2):97-106. Allen, R.G., M. Smith, A. Perrier and L.S. Pereira, 1994a. An Update for the Definition of Reference Evapotranspira tion. ICID Bulletin 43(2):1-34. Burt, C.M., A.J. Mutziger, R.G. Allen and T.A. Allen, 2005. Evaporation Research: Review and Interpretation. Journal of Irrigation and Drainage Engineering 131(1):37-58. Droogers, P. and R.G. Allen, 2002. Estimating Reference Evapotranspiration under Inaccurate Data Conditions. Irriga tion and Drainage Systems 16:33-45. Ewel, K.C. and J.E. Smith, 1992. Evapotrans piration from Florida Pondcypress Swamps. Water Resources Bulletin 28(2):299-304. Fuchs, M., 2003. Evapotranspiration, Referen ce and Potential. Encyclopedia of Water Science:264-266. Garber, A.M. and C.E. Phelps, 1997. Economic Foundations of Cost-Effectiveness Analysis. Journal of Health Economics 16:1-31. Grismer, M.E., M. Orang, R. Snyder and R. Matyac, 2002. Pan Evapotranspiration to Reference Evapotranspiration Conversion Methods. Journal of Irrigation and Drainage Engineeri ng 128(3):180-184. Hargreaves, G.H., 1975. Moisture Availability and Crop Production. Transactions of the ASAE:980-984. Hargreaves, G.H., 1994. Defining and Using Re ference Evapotranspiration. Journal of Irrigation and Drainage Engineering 120(6):1132-1139. Hargreaves, G.H. and Z.A. Samani, 1982. Estimating Potential Evapotranspiration. Journal of the Irrig ation and Drainage Division 108:225-230. Irmak, S., R.G. Allen and E.B. Whitty, 2003. Daily Grass and Alfalfa-Reference Evapotranspiration Estimates and Alfalf a-to-Grass Evapotrans piration Ratios in

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66 Florida. Journal of Irrigation a nd Drainage Engineering 129(5):360-370. Irmak, S., A. Irmak, J.W. Jones, T.A. Howell, J.M. Jacobs, R.G. Allen and G. Hoogenboom, 2003. Predicting Daily Net Radiation Using Minimum Climatological Data. Journal of Irrigation and Drainage Engineering 129(4):256269. Jacobs, J.M., S.L. Mergelsberg, A.F. Lope ra and D.A. Myers, 2002. Evapotranspiration from a Wet Prairie Wetland under Drought Conditions: Paynes Prairie Preserve, Florida, USA. Wetlands 22(2):374-385. Jensen, D.T., G.H. Hargreaves, B. Temesg en and R.G. Allen, 1997. Computation of ET o under Nonideal Conditions. Journal of Irrigation and Drainage Engineering 123(5):394-400. Lu, J., G. Sun, S.G. Steven, G. McNulty and D.M. Amatya, 2005. A Comparison of Six Potential Evapotranspiration Methods for Regional use in the Southeastern United States. JAWRA 41(3):621-633. Monteith, J.L., 1981. Evaporation and Surface Temperature. Quarterly Journal of the Royal Meteorological Society 107(451):1-27. Nachabe, M., N. Shah, M. Ross and J. Vomacka, 2005. Evapotranspiration of Two Vegetated Covers in a Shallow Water Table Environment. Soil Science Society of America 69:492-499. Pereira, A.S. and V. Barbieri, 1995. A Model for the Class A Pan Coefficient. Agricultural and Fore st Meteorology 76:75-82. Pereira, L.S., A. Perrier, R.G. Allen and I. Alves, 1999. Evapotranspiration: Concepts and Future Trends. Journal of Irrigation and Drainage Engineering 125(2):45-51. Sumner, D.M., 2006. Adequacy of Selected Evapotranspiration Approximations for Hydrologic Simulation. JAWRA 42(3):699-711. Trajkovic, S., 2006. Temperature-Based A pproaches for Estimating Reference Evapotranspiration. Journal of Irrigati on and Drainage Engineering 131(4):316323. Xu, C.-Y. and V.P. Singh, 2001. Evaluation a nd Generalization of Temperature-Based Methods for Calculating Evaporatio n. Hydrological Processes 15:305-319.

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67 APPENDICES

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