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Assessing the performance of water bodies in Hillsborough County, Florida using Data Envelopment Analysis (DEA)

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Title:
Assessing the performance of water bodies in Hillsborough County, Florida using Data Envelopment Analysis (DEA)
Physical Description:
Book
Language:
English
Creator:
Fouad, Geoffrey George
Publisher:
University of South Florida
Place of Publication:
Tampa, Fla
Publication Date:

Subjects

Subjects / Keywords:
Benchmark
Efficiency frontier
Geographic Information Systems (GIS)
Lake
Land use
Dissertations, Academic -- Geography -- Masters -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: The purpose of this thesis is to describe the relationship between surface water quality and land use. Water management recommendations will be divulged based upon the interaction of lake water quality and land use. The methodology developed for this research applied Data Envelopment Analysis (DEA), a performance measurement tool, to evaluate lake water quality in relation to surrounding land use. Lake performance ratings were generated by DEA software that assessed multiple variables describing surface water nutrient loads and surrounding land use. Results from this analysis revealed a significant trend between lake water quality and land use within the study area. Lakes located within a two mile radius of more naturally preserved land area typically attained higher performance ratings than lakes located within a two mile radius of less naturally preserved land area. The spatial quantity of naturally preserved land influenced lake nutrient concentrations. Also, lake performance ratings generally declined in two mile radius delineations that contained less naturally preserved land area indicating a direct relationship between natural land area and lake performance.
Thesis:
Thesis (M.S.)--University of South Florida, 2009.
Bibliography:
Includes bibliographical references.
System Details:
Mode of access: World Wide Web.
System Details:
System requirements: World Wide Web browser and PDF reader.
Statement of Responsibility:
by Geoffrey George Fouad.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 134 pages.

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University of South Florida
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aleph - 002028855
oclc - 436459282
usfldc doi - E14-SFE0002824
usfldc handle - e14.2824
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SFS0027141:00001


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ABSTRACT: The purpose of this thesis is to describe the relationship between surface water quality and land use. Water management recommendations will be divulged based upon the interaction of lake water quality and land use. The methodology developed for this research applied Data Envelopment Analysis (DEA), a performance measurement tool, to evaluate lake water quality in relation to surrounding land use. Lake performance ratings were generated by DEA software that assessed multiple variables describing surface water nutrient loads and surrounding land use. Results from this analysis revealed a significant trend between lake water quality and land use within the study area. Lakes located within a two mile radius of more naturally preserved land area typically attained higher performance ratings than lakes located within a two mile radius of less naturally preserved land area. The spatial quantity of naturally preserved land influenced lake nutrient concentrations. Also, lake performance ratings generally declined in two mile radius delineations that contained less naturally preserved land area indicating a direct relationship between natural land area and lake performance.
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Assessing the Performance of Water Bodies in Hillsborough County, Florida Using Data Envelopment Analysis (DEA) by Geoffrey George Fouad A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science Department of Geography College of Arts and Sciences University of South Florida Major Professor: Kamal Alsharif, Ph.D. Hyun Kim, Ph.D. Philip Reeder, Ph.D. Date of Approval: April 3, 2009 Keywords: Benchmark, Efficiency Fr ontier, Geographic Information Systems (GIS), Lake, Land Use Copyright 2009, Geoffrey Fouad

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i Table of Contents 1. List of Tables ................ .................. .................. .................. .................. ...........iii 2. List of Figures ................ .................. .................. .................. ................ ...........iv 3. Abstract .................. ................ .................... ................ .................... ................vi 4. Introduction ................ .................. .................. .................. .................. ..............1 5. Literature Review ..............,... ................ ................ ................ ................ ...........4 5.1 Water Management Application ................ .................. .................. .......... ........4 5.2 Environmental Assessment Application ................ .................... ............ .........5 5.2 Agricultural Application .................. .................. .................. .................. ...........7 5.3 Land Management Application .................. .................. .................. .................9 5.4 Methods Other than DEA ................ ................ ................ ................ .............12 6. Research Design .................. ................ ................ ................ ................ .........15 7. DEA Background Information .................. ................ .................... ................20 7.1 An Introduction to DEA ................ .................. .................. .................. ...........20 7.2 Single Output and Input Production Ratios .................. .................. ..............25 7.3 Production Ratios with Two Inputs .................. .................. ................ ...........27 7.4 Production Ratios with Two Outputs ................ .................. ................ ...........29 7.5 Applying Weights to Variables in DEA ................ ................ ................ ..........32 7.6 Summarizing DEA Production Ratios ................ ................ ................ ..........34 8. Methodology ................ .................. .................. .................. ................ ............39 9. Study Area ................ .................. .................. .................. .................. .............53

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ii 10. Results .................. ................ .................... ................ .................... ...............61 10.1 CCR-I Model Results ……….…………………………………………………64 10.2 BCC-I Model Results ……………………….…………………………………78 10.3 Additive Model Results …………….…………..……………………………….91 10.4 Comparing DEA Model Result s to Trophic State Index .…...…………..….102 11. Discussion ................ .................. .................. .................. .................. .........107 12. Recommendations and Conclusion ................ ................ ................ ........121 13. References Cited .................. .................. .................. .................. ...............131

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iii List of Tables 1. Two Mile Radius Delineation Feature Summary ................ .................. ...........41 2. Summary of Study Variab les ...……………………………………….…............43 3. Lakes Eliminated Due to Lack of Natural Land Use Area ...…………………...51 4. Hillsborough County Land Use Summary …………………………..…….........56 5. Hydrologic Summary of St udy Lakes .…………………………………........…..59 6. Raw Input and Output Variabl e Data ..……………………….………...………..63 7. CCR-I Lake Performance Ratings and Rank ..………………………………….65 8. Input Concentration, ‘Projection’, Di fference, and Percent Difference ..……...73 9. CCR-I ‘Slack’ Measurements ..……………………………………………………76 10. CCR-I Variable Correlation Matrix ….………………………………………….78 11. BCC-I Lake Performance Ra tings and Rank .………………………….……...80 12. BCC-I ‘Slack’ Measurements ………………………………………………….89 13. BCC-I Variable Correlation Matrix ….………………………………………….91 14. Additive Lake Performance Summary ………………………………….……..93 15. Lake Performance Ratings and TSI Measurements ...……………...……..103

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iv List of Figures 1. ‘Efficient Frontier’ Line Exampl e .................. ................ .................... ...............21 2. ‘Efficient Frontier’ Line for Two Inputs and One Output ............ .............. .......28 3. ‘Efficient Frontier’ Line for Two Outputs an d One Input ............ .............. .......30 4. Study Area Map ………….............. .................. .................. .................. ............54 5. Total Chlorophyll Versus CCR-I Lake Perfo rmance Rating .......... ..................67 6. Total Phosphorous Versus CCR-I Lake Perf ormance Rating ........ ................67 7. Total Nitrogen Versus CCR-I Lake Performanc e Rating .............. ..................68 8. Natural Land Use Area Versus CCR-I Lake Pe rformance Rating ... ...............69 9. Natural Land Percentage Versus CCR-I Lake Performance Rating ………….70 10. Total Chlorophyll Versus BCCI Lake Performance Rating ………………….82 11. Total Phosphorous Versus BCC-I Lake Performance Rating …………….….82 12. Total Nitrogen Versus BCC-I Lake Performance Rating …………………….83 13. Natural Land Use Area Versus BCC-I Lake Performance Rating …………..84 14. Natural Land Percentage Versus BCC-I Lake Performance Rating ………..85 15. Total Chlorophyll Versus Additive Lake ‘Stability’ Value …….……………….95 16. Total Phosphorous Versus Additive Lake ‘Stability’ Value …….…………….96 17. Total Nitrogen Versus Additive Lake ‘Stability’ Value …….…………………..96 18. Natural Land Use Area Versus Additi ve Lake ‘Stability’ Value …….………...98 19. Natural Land Percentage Versus Additive Lake ‘Stability’ Value …….……...98 20. CCR-I Performance Rating Versus TSI …………………………...…...……..105

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v 21. BCC-I Performance Rating Versus TSI ……………………...…………...…..106 22. Additive Performance Rating Versus TSI ………………………………...…..106

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vi Assessing the Performance of Water Bodies in Hillsborough County, Florida Using Data Envelopment Analysis (DEA) Geoffrey Fouad ABSTRACT The purpose of this thesis is to describe the relationship between surface water quality and land use. Water management recommendations will be divulged based upon the interaction of lake water quality and land use. The methodology developed for this research applied Data Envelopment Analysis (DEA), a performance measurement tool, to evaluate lake water quality in relation to surrounding land use. Lake performance ratings were generated by DEA software that assessed multiple vari ables describing surface water nutrient loads and surrounding land use. Results fr om this analysis revealed a significant trend between lake water quality and land use within the study area. Lakes located within a two mile radius of more naturally preserved land area typically attained higher performance ratings than lake s located within a two mile radius of less naturally preserved land area. The spatial quantity of nat urally preserved land influenced lake nutrient concentra tions. Also, lake performance ratings generally declined in two mile radius deli neations that contained less naturally preserved land area indicating a direct relationship between natural land area and lake performance.

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1 Introduction The intention of this thesis is to explore existing scientific literature discussing previously attempted environmental and water management applications of Data Envelopment A nalysis (DEA), a performance measurement tool. It is also the intention of this thesis to devise water management recommendations for Hillsborough County using a DEA methodology. This methodology was an attempt to characteri ze the impacts of land use on lake water quality. In doing so, the applied re search provides a means to develop specific water management recommendat ions based on localized data from Hillsborough County, Florida. D EA was implemented as a performance measurement tool to gauge the impact of surrounding land uses. The scientific research for this thesis represents an application of DEA not previously attempted in available liter ature. DEA has not been previously used to assess the relationship between land use and water quality. The applied research exami ned the effects of multiple variables on water quality including total chlorophyll, tota l nitrogen, total phosphorous, and natural land area. These variables were sele cted based upon internet availability and relativity. In subsequent sections, a fu rther description and justification for the selected variables will be provided. DEA was applied as a tool to examine the previously mentioned variables in the form of a cross-se ctional analysis of select

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2 Hillsborough County lakes. In doing so, the applied research identified benchmarks in water quality that resulted in optimum DEA performance measurements. After identifying maxi mum performance benchmarks, the reader is provided with water management reco mmendations based upon recreating or sustaining the optimal conditions co rresponding to the said benchmarks. Water has become an increasingly significant natural resource. Throughout history, water has been the sour ce of human conflict and the root of civilization meltdowns. Currently, water is a strictly managed commodity with monetary and intrinsic value. The value of water has so risen that humans are constantly exploring new and improved methods for managing it (Postel 1997; Feldman 2007; Houck 2002). This effo rt has been constricted by steadily shrinking budgets and man power (Poste l 1997; Feldman 2007). Universally, water management has been further comp licated by steadily declining water quality as a result of an assortment of hum an activities (Reddy and Dev 2006). It has been widely discussed and agreed that the overall quality of water resources in the United States has declined in re cent years due to urbanization (Reddy and Dev 2006; Wescoat and White 2003; Gleick et al. 2006). In light of these challenges, water managers have become more reliant on remote monitoring methods that require less cost and labor (Castelletti and Soncini-Sessa 2007). Remote monitori ng is powered by advancing computer technology that allows users to proce ss large volumes of data. The selected method of processing data can unveil statistical results that sometimes influence managerial decisions. DEA is one such method that has recently been applied to

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3 water management issues for optimizati on purposes (Alsharif et al. 2008; Castelletti and Soncini-Sessa 2007). D EA integrates actually observed data related to environmental quality when a ssessing system performance. This efficiency measurement tool is suppor ted by numerous computer software platforms which have been typically applied to economic and industrial production assessment. Recent scientif ic publications have discussed the application of DEA to natural resource management and more specifically water management concerns (Alsharif et al. 2008; Shafiq and Rehman 2000; Jaenicke and Lengnick 1999; Castelletti and Soncin i-Sessa 2007). This application of DEA represents a relatively new and vast ly unexplored management tool that could possibly become very valuable in the future. DEA is a performance assessment tool that can be and has previously been used to optimize the beneficial aspects of a given natural resour ce (Alsharif et al. 2008; Shafiq and Rehman 2000; Jaenicke and Lengnick 1999; Castelletti and Soncini-Sessa 2007). In doing so, DEA focuses on act ually observed data that potentially impacts the performance of an environmental system.

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4 Literature Review Water Management Application In a study performed by Alsharif et al. (2008), DEA was applied to the performance of water supply systems in the Palestinian territories. The methodology of this study focused on wate r resources in a region experiencing population increases that have contributed to diminished water resources and increasingly negative human impacts (Als harif et al. 2008). The methodology discussed in this paper was an attempt to improve water management strategies that must cope with a limited budget. D EA was used to evaluate the efficiency of individual water supplies. This entails the use of production ratios composed of outputs over inputs (Stolp 1990). The single output included in the DEA performed for this study was total re venue generated from water distribution activities. Input variables for this study focused on investments and losses related to water distribution systems. Water losses, energy, maintenance, and salary of workers associated with Palest inian water distribution systems were all considered by the DEA. Analyses of these ratios yi eld interpretable efficiency measures that can be referred to while managing water supplies. Findings of the study dete rmined DEA to be a highly applicable tool for the management of stressed water supplies (Als harif et al. 2008). By referring to benchmarks known as an ‘efficient frontier’ the study successfully established

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5 the relative efficiencies of individual wa ter supplies. Given the appropriate, timesensitive data, DEA was characterized as a valuable method for managing water resources when confronted with limited m an power and funding (Alsharif et al. 2008). The stability of these water res ources were also successfully assessed (Alsharif et al. 2008). Results of the assessment discovered t hat productivity for water resources within the Gaza Strip were significantly lower than that of neighboring water resources in the West Bank (Alsharif et al 2008). Alsharif et al. (2008) identified water loss as the primary input variable a ffecting water supply efficiencies in the region. The input variable for municipality populations had little bearing on these results (Alsharif et al. 2008). Manager ial policies recommended by the study suggested that water gover ning entities in the Pa lestinian region should concentrate on limiting water losses by making the necessary repairs to water distribution systems (Alsharif et al. 2008). In relation to the content of this thesis, the research conducted by Alsharif et al (2008) is a direct example of how DEA can be applied to a wate r management issue. Environmental Assess ment Application In a study conducted by Jaenicke and Lengnick (1999), the quality of soil was examined in relation to its agricultu ral productivity. The applied research necessary for completing this exami nation employed DEA to evaluate the performance of soils located within U.S. Department of Agriculture experimental fields in Maryland. Soil performance was measured by the crop yields of these

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6 fields. The study determined the quality of soil in an economic context. During the study, crop yields were perceived as an economic product that reflected the quality of soil in which the crop was planted. The methodology for such an undertaking applied DEA to establish efficiency benchmarks representing the best known crop production levels. In simple applications of DEA, productivi ty is determined by production ratios containing single output over a single in put. In this study, a simple DEA application was deemed impossible due to the complexity of the relationship between soil quality and crop yields. App lications requiring multiple inputs and outputs for each production ratio abide by a mathematical method developed by Caves, Christensen, and Diewert (1982). Input variables included in the produc tion ratios for this study were composed of management inputs such as fertilizer application, weather conditions such as precipitation, and soil quality properties such as soil moisture (Jaenicke and Lengnick 1999). Production ratios for this study also included output variables composed of crop produc tion in mass yield and mass yield of crop by-products (Jaenicke and Lengnick 1999). The study performed by Jaenicke and Lengnick (1999) relied upon an Additive, or alternative, form of D EA. After evaluating the nonparametric application of DEA, Jaenicke and Lengn ick (1999) conclude that the methodology used during the study is a solution to creating a universal and practical soil quality index. This c onclusion was supported by the study’s acceptance of economic and quantitative terms for expressing the productive

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7 efficiency of a particular type of soil. T he study demonstrates t hat the quality of an environmental factor can be assess ed based upon quantitat ive figures that represent economic value. Researcher s that participated in this study recommend that future soil quality indices, especially those applied to agricultural systems, should incorporate DEA as a co st-effective tool for examining crop production yields in relation to biologica l, chemical, and physical soil parameters (Jaenicke and Lengnick 1999). In relation to the content of this thesis, the research conducted by Jaenicke and Lengni ck (1999) provides a useful example of how DEA can be applied to environmental assessments. Agricultural Application In a study performed by Shafiq a nd Rehman (2000), the sources of production inefficiencies for cotton producti on in the Punjab province of Pakistan were identified using DEA. Information regarding the actual farmers responsible for a particular cotton field were co llected and used as inputs within the production ratios of the study. This information was collected primarily as quantitative data that expressed such fa ctors as the age of the farmer and the amount of land attended to by the farmer. Other inputs considered during the study performed by Shafiq and Rehman ( 2000) included nitrogen fertilizer use, phosphorous-based fertilizer use, artificial irrigation levels, and hours of field plowing activity. Inputs were also cat egorized even further by using descriptive variables that framed the situation in which the cotton was being produced. Examples of these input categorizations included a classification scheme for available land to grow cotton as well as a classification scheme for precipitation

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8 levels. Similar to Jaenicke and Lengnick (1999), outputs consisted of various quantitative forms of evaluating crop yiel ds. The various quantitative outputs measured crop production by ma ss and monetary profits. Shafiq and Rehman (2000) applied an A dditive DEA model during their study of inefficiencies for cotton production in the Punjab province of Pakistan. This DEA methodology is also frequently re ferred to as a DEA alternative model (Ramanathan 2003). Researchers determi ned that this application of a nonparametric DEA model is an appropriate technique for identifying production inefficiencies and the specific variables contributing to diminished crop yields (Shafiq and Rehman 2000). However, the re searchers pointedly remark that the interpretation of results gathered from th is form of DEA should be developed in a cautious manner (Sha fiq and Rehman 2000). Agricultural management interpretati ons based upon an application of DEA could be misleading if the model param eters do not reflect the actual inputs or outputs of a system. The same w ould be true for environmental management interpretations or any other realm of st udy with DEA applicability. Shafiq and Rehman (2000) acknowledge t he power of which input and output variables are selected for an application of DEA. If cert ain variables are chosen to receive the expected results from a DEA model, the re searcher could quite possibly omit a relevant variable or variables that woul d otherwise completely alter the outcome of the model. Subsequently, interp retations based upon that model would contribute to misguided manage ment practices. Therefor e, the scientific validity of a DEA model is heavily conting ent upon the input and output variables

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9 selected for the analysis. This process is subjective and determined by the given researcher’s logic. The final reco mmendation posed by Shafiq and Rehman (2000) demanding that researchers proceed with caution should be viewed as a universal truth during attempts to develop management strategies through the use of DEA. Land Management Application In a study administered by Rhod es (1986), land management issues confronted by the National Park Service (N PS) were prioritized according to the performance of individual parks. The efficiency with which parks employ their associated natural resources was examin ed during this DEA. The decisionmaking units (DMUs) examined during this study consisted of individual parks managed by the NPS. This allowed Rhodes (1986) to co mpare the efficiency of NPS managerial operations bet ween parks. Previous st udies that assessed the performance of NPS managerial operations were only site specific typically focusing on anywhere from one to th ree parks (Rhodes 1986). The study performed by Rhodes (1986) was unique fr om previous studies because it sought to evaluate the efficiency of NPS operations by comparing numerous parks simultaneously. The overall objective of this study was to determine how well the NPS was fulfilling the agency’s mission statemen t. DEA was considered a suitable production assessment tool for this purpos e because it is capable of evaluating multiple inputs and outputs, performanc e measures produced by DEA are scalar eliminating assumptions t hat typically restrict ot her forms of performance

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10 analysis, and finally, the ‘technical’ and ‘scale efficiency’ components of DEA allow it to provide interpretation based upon the relationship between park size and efficiency (Rhodes 1986). ‘Technical effi ciency’ refers to a system that can improve performance by incr easing outputs proportionately (Cooper et al. 2000). ‘Scale efficiency’ refers to a system that can improv e performance by increasing outputs (or inputs) without cons idering their proportions. At the time of the st udy, the mission statement of the NPS provided a generalized notion regardi ng how the agency should preserve historic and natural sites for public use. Therefore, multiple DEA models were devised during this study that emphasized the various elements discussed by the NPS mission statement. Variable select ion and data collection for each of the DEA models were based upon a collaborative effort between the author of the study, park policy-makers, and available park information stored by the NPS and the Department of the Interior (DOI). These variables were then grouped together by the element of the Park Service’s missi on that the variable describes. For instance, the number of historic build ings, engineering sites, prehistoric structures, and archaeolog ical artifacts were grouped together as output variables that fulfilled the historical pr eservation element of the Park Service’s mission. The alternative grouping of out put variables fulfill ed the educational and natural resource preservation aspects of the Park Service’s mission. This grouping included variable data for number of educational activities, visitors attending educational activities, att endants using trails, recreational hours devoted to the park, and overnight campers. Input variables were also separated

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11 into two different groupings. The num ber of permanent full-time employees, career seasonal employees, and tempor ary employees were categorized together as labor input variables. Fo r variables representing capital and land inputs, the model incl uded data for number of buildings designated for visitor use, park operational buildings, miles of tra ils within the park, and miles of roads within the park. Model results from the study reveal ed that parks attempting to increase visitation at the expense of natural resource management typically achieve maximum efficiency by reducing the st aff members and receive short visits during daylight hours (Rhodes 1986). As expected, NPS properties that exclusively preserve historic monum ents or sites typically perform more efficiently when recreational outputs are minimized along with labor inputs. Exactly five parks included in the study re ceived optimal efficiency ratings for all DEA models ran by Rhodes ( 1986). Upon further inve stigation, the author concluded that these DMUs were act ually examples of parks with labor and equipment deficiencies (Rhodes 1986). This investigation was prompted by the unlikelihood of a park obtai ning optimal efficiency scores for all the various operational goals of the NPS. Overall, Rhodes (1986) acknowledges that DEA is a valid tool for assessing the performance of land management activities. The series of models developed by Rhodes (1986) aluminates the potential for DEA to be used during land management and use studies. This st udy provides a viable example of how DEA can be implemented to assess m anagerial practices and their impacts on

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12 operational efficiency. Re sults from the DEA can then be referred to while adjusting managerial practices for t he purpose of improving operational efficiency. Methods Other than DEA In previously published scientific lit erature, the rela tionship between land use and water quality has been explored usi ng techniques other than DEA. One such study conducted by Griffith et al (2002) examined the interrelationship shared by land cover and water quality usin g remotely sensed indicators known as normalized difference vegetation inde x (NDVI) and vegetation phenological metrics (VPM). This study focus ed on 290 randomly selected stream sites located throughout the U.S. Central Pl ain states of Nebraska, Kansas, and Missouri. These sites were sampled for water quality parameters such as conductivity, turbidity, total phosphorous, nitr ate-nitrite nitrogen, a biotic integrity index, and a habitat integrity index. Wate r quality data collected during the study was then compared to landscape data fo r NDVI and VPM representative of individual sample site watersheds. The study then proceeded to perform statistical testing for significant rela tionships between the water quality data and the remotely sensed landscape data. The methodology developed and perform ed by Griffith et al. (2002) embraced a recent transfer in scope from stream runs to the entire stream catchment basin for studies regarding wate r quality impacts. This shift in scope has become prevalent during recent studies concerning the degradation of water resources (Sidle and Hornbeck 1991; Johnson and Gage 1997; O’Neill et al.

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13 1997; Wiley et al. 1997). Studies adopting this new scope operate with the understanding that water resource condi tions are heavily contingent upon largescale interrelationships that span an ent ire catchment basin. For the study performed by Griffith et al. (2002), a large-scale scope encompassing entire catchment basins was assumed while st atistically analyzing the relationship between remotely sensed vegetation dat a and water quality variables. In most cases studied by Griffith et al. (2002), a statistically significant correlation between the remotely sensed vegetation data and the water quality parameters existed. The relationsh ip between vegetative cover within a catchment basin and water quality condition s was more strongly correlated than the relationship between ov erall land uses within a catchment basin and water quality conditions. Therefore, vegetative cover has more of a bearing on water quality conditions than land use accord ing to the study. This unexpected conclusion was further explained by a significant correlation between the vegetative cover data and the la nd use data. Based on this correlation, the study determined that land use shared a statisti cally significant relationship with the vegetative cover data that was previously correlated to the stream water quality data. Therefore, the land use data prov ides an indirect explanation of the water quality data. The study introduced a vi able methodology for interrelating water quality data to land cover data without the use of DEA. Allan (2004) offered another example of a study t hat did not implement a methodology based on DEA to establish a relationship between land use and aquatic conditions. During this study, t he index of biotic integrity (IBI) was

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14 identified as a water qualit y measure that typically s hared a significant correlation with the land uses of a catchment basin Allan (2004) agreed that freshwater resources have recently been increasingly studied from a largescale perspective that views individual catchment basins as decision-making units. The research conducted by Allan (2004) supported this recent trend and perceives the IBI method as the most effective for eval uating the relationship between water quality conditions and land use. The proce ss of correlating IBI to land use within a catchment basin represents a viable method for investigating water quality degradation at a variety of spatial scales. Therefore, this study has identified a method for devising resource management decisions based on the relationship between water quality and land use.

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15 Research Design The contents of this section will pr esent the problem statement of the thesis along with research questions, hypotheses related to the research questions, research objectives, and just ification for conducting the research. Impacts on freshwater bodies of Hillsborough County will be assessed by analyzing Geographic Information System (GIS) land use layers along with selected variables composed of environm ental contaminant data collected and freely distributed via the Hillsborough County online Water Atlas. In doing so, the applied and previously unperformed research portion of this thesis will attempt to establish a relationship between land use and lake performance in terms of water quality. The applied research for this thesis will answer the following problem statement: Can a notable re lationship between surrounding land uses and lake water quality be established, and if so, what impact does naturally preserved land have on lake water quality? In addressi ng this problem st atement, benchmarks, a term that in the scope of this research describes water quality conditions that optimized a lake’s performanc e, will be identified through the application of DEA. Along with the problem statement, vari ous other research questions will be answered.

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16 These research questions are listed below. 1. After analyzing the various forms of scientifically acceptable data using DEA computer software, does naturally preserved land typically contribute to a water quality benchmark opt imizing lake performance? 2. How can water managers operating within the boundaries of Hillsborough County reproduce the necessary conditions to achieve an optimal water quality benchmark? 3. Short of altering the current l and use surrounding a given lake through land acquisition techniques, how c an localized water managers improve management techniques to achieve an ec ologically optimal water quality benchmark? 4. After performing the necessary anal ysis, will the devised methodology be easily transposable to other study areas? Hypotheses numerically corresponding to the above research questions are provided below. 1. Lakes surrounded by a gr eater proportion of natura lly preserved land will attain higher DEA performance rati ngs than those lakes surrounded by a lesser proportion of natura lly preserved land. 2. Results generated from the DEA will support water management strategies focused on preserving natur al land and rehabilitating impaired natural land.

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17 3. Water management efforts based on BMPs that reduce lake nutrient deposition and artificially simulate t he pollutant filtration function of naturally preserved land wil l also likely be supported by the results of the DEA. 4. The methodology developed for this t hesis will be readily transferable to other study areas that collect and store the required datasets. The project will attempt to reveal t he effects of land use on the overall performance and quality of water bodies within Hillsborough County. The content of this thesis will focus on det ermining the relationship of land use to water quality by applying DEA, a perform ance measurement t ool. As stated previously, DEA is a performance assessment application that has been historically used to evaluate economic and industrial productivity. In recent available literature, DEA has been increasingly applied to performance evaluations concerning agricultural and environmental systems (Alsharif et al. 2008; Shafiq and Rehman 2000; Jaenicke and Lengnick 1999; Malana and Malano 2006). A literature review of the most relevant journals was performed to discover recently published scientific arti cles discussing the results of applying DEA methodologies to environmenta l and agricultural systems. Besides providing an extensive litera ture review of environmental and agricultural DEA applications, the content of this thesis will research and evaluate the applicability of water management techniques that enhance the performance of freshwater bodies in Hillsborough Count y. This evaluation will focus on land use alteration and Best Management Prac tices (BMPs) intended to improve

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18 freshwater quality in lakes. Both of the aforementi oned techniques have recently assumed a role on the forefront of em erging comprehensive water management strategies (Castelletti and Soncini-Sessa 2007; Gleick et al. 2006; Reddy and Dev 2006). The content of this thesis also attempted to reveal instances in which DEA has directly improved water managem ent practices. A thorough literature review based upon this topic as well as a cr itical review of the applied research portion of this thesis revealed t he advantages and disadvantages of applying DEA to environmental perfo rmance assessments. As discussed earlier, the content of this thesis will consist of an applied research component in which DEA will measure the performance of Hillsborough County water bodies in relation to land us e. The research objectives of this applied science element have been listed in numbered format below. The research questions posed previously during this section will be answered by completing the following re search objectives. 1. The applied research porti on of this thesis will first identify the land uses surrounding forty-three lakes within Hi llsborough County through GIS data post-processing techniques and the use of a land use classification scheme developed by The Planning Co mmission of Hillsborough County. 2. Three DEA models, CCR-I, BCC-I, and Additive, will then be implemented to supply a comparative analysis in which the relationship between land use and water quality is examined.

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19 3. Through this analysis, water qualit y benchmarks will be established that identify optimum environmental condition s within a freshwater, inland lake of Hillsborough County. 4. With the water quality benchmarks established, the research will then focus on identifying land use alterations and BMPs that will restore or maintain environmental conditions associated with optimum water quality performance in Hillsborough County lakes. The content of this thesis contri buted research toward a relatively unexplored application of a commonly used performance measurement tool. While DEA has been widely implement ed for economic and industrial performance concerns, it has been generally ignored by those participating in environmental assessments. After a thorough review of the available scientific literature, it was determi ned that DEA has not been prev iously implemented to assess the performance of lakes in relation to land use. It is the goal of this thesis to contribute to the published scient ific literature regar ding environmental applications of DEA. In doing so, the re sults of this thesis discuss and evaluate the applicability of DEA for environmental assessments. The applied research portion of this thesis is supported by an in depth review of scientific literature discussing environmental applic ations of DEA.

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20 DEA Background Information An Introduction to DEA Prior to an in depth discussion of the applied methodology, it will be important for the reader to gain an intr oductory knowledge of DEA. For that purpose, this section will summarize the basic aspects of DEA as discussed by Cooper et al. (2000), Sexton (1986), Ramanathan (2003), and Thanassoulis (2001). The information provided in th is section will assist the reader’s understanding of the applied methodology. According to Cooper et al. (2000), DEA received its name from mathematical terminology that describes a scatter plot depicting an output versus a relevant input. When a line shelters all of the points of a scatt er plot, the line is said to ‘envelop’ the points of the scatter plot. This line is termed the ‘efficient frontier’, which can be most easily def ined as a high performance benchmark. Typically, a collection of performance ratios are analyzed with DEA computer software. After which, the highest leve ls of performance ar e identified by the ‘efficient frontier’. Decision making units identified as efficient will occupy a point along the ‘efficient frontier’ line. The ‘effici ent frontier’ is a concept unique to DEA

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21 that separates it fr om other forms of st atistical analyses (Sexton 1986). ‘Efficient frontier’ lines are typically displayed on ordinary xand y-axis scatter plots. Figure 1 provided below is a rudimentary example of an ‘efficient frontier’ line represented by an xand y-axis scatter pl ot derived from the Charnes, Cooper, and Rhodes DEA model (Cooper et al. 2000). 0 1 2 3 4 012345InputOutput Figure 1. ‘Efficient Fr ontier’ Line Example DEA is a mathematical platform for re viewing performance related ratios. Performance ratios are composed of a si ngle output over a single input such as number of sales over number of employees at a store or the quantity of products generated per person employed at a factory. The concept of a performance ratio consisting of a single output over a singl e input stands alone as the initial idea behind DEA (Thanassoulis 2001). Perfo rmance ratios provide the foundation upon which DEA has been developed. DEA has vaulted itself to the forefront of performance measurement tool s because of its capability to assimilate multiple

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22 inputs and outputs (Ramanathan 2003). As a result, this method has become widely implemented by operat ion managers attempting to maximize productivity (Ramanathan 2003). The modeling c apability of DEA has been strongly substantiated by its ability to incorporat e inputs and outputs in a multivariate fashion (Ramanathan 2003). During its relatively short history beginning in 1978, DEA has typically been applied to issues regarding economic productivity or industrial efficiency (Cooper et al. 2000). In recently emer ging scientific literat ure, DEA has been increasingly applied to performance-based questions related to agricultural productivity, ecosystem services, and land-use decisions (Fraser and Hone 2001; Shafiq and Rehman 2000; Malana and Ma lano 2006; Alsharif et al. 2008; Jaenicke and Lengnick 1999). Previous st udies have referred to DEA methods when attempting to assess the effici ency of water management strategies (Alsharif et al. 2008; Tong and Chen 2002) DEA is a mathematically-based performance assessment application that incorporates production ratios (Thanassoulis 2001). These production ra tios are commonly formatted with an output (or outputs) over an input (or inputs) (Thanassoulis 2001). Performance ratios evaluated by DEA measure the pr oductivity of individual components that compile a multifaceted system. In this s ense, these ratios should be considered ‘partial productivity measures’ (Cooper et al. 2000). Cooper et al. (2000) describes a collection of performance rati os as ‘partial productivity measures’ because this terminology separates DEA from other performance measurement tools that attempt to acc ount for every output and input of a process. DEA is a

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23 ‘partial productivity measure’ because it only attempts to incorporate a select number of inputs and outputs that dictate performance. Therefore, DEA does not measure the performance of an entire system It only measures selected inputs and outputs of a process or system. This concept has made DEA an appealing tool for environmental researchers t hat assess the performance of natural systems (Sexton 1986; Cooper et al. 2000; Thanassoulis 2001). DEA does not incorporate performanc e ratios that assess the total productivity of a system without consider ing the system’s individual components such as employee efficiency or output per agricultural field (Cooper et al. 2000). In this manner, DEA is capable of identifyi ng excesses in individual inputs as well as shortages in specific outputs. By evaluating the indi vidual components of a system, DEA avoids assigning false or inflat ed values to a relatively unimportant performance factor. This is an analytic ally valuable aspect of DEA because a performance assessment can identify s pecific production areas in need of improvement. For example, a produc tion increase might be attributed to employee labor efficiency when in actualit y the individual ratios reflect that increased production was due to an increase in capital. ‘Partial productivity measures’ ha ve frequently encountered complications or limitations because the mathematic al programming for executing these evaluations has not previously been wid ely dispersed (Cooper et al. 2000). Advances in computer programming hav e made it possible to process a wide variety of variables and pl ace quantitative values on how these variables interact (Cooper et al. 2000). The co mputer software current ly performing DEA does not

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24 require the evaluator to assign weight s and functional forms to each performance variable (Cooper et al. 2000). Comput er programming improvements in DEA software have made it easier to addre ss complicated performance-related questions. Computational progress has permitted DEA to be applied to a wider variety of managerial, social, envir onmental, and economic issues. Widely dispersed standardized yet flexible DEA programming frees the evaluator from the burden of creating cust omized software designed for a fixed evaluation and allows the evaluator to concentrate on t he actual application of DEA. The body of literature related to DEA applications has also progressed and expanded in the recent past (Cooper et al. 2000), which simplifies subsequent studies that will apply DEA in a similar manner. Simplifying D EA application to a variety of fields has increased the opportunity for f eedback between the analysts and those who make decisions based upon the results of the analysis (Ramanathan 2003). Increasing the feedback between analysts and those who ultimately make policy decisions has allowed more detail ed and significant performance-based questions to be posed during DEA. Performance improvements as they re late to DEA can be executed with quantitative simplicity by altering either the output (y) or t he input (x). By modifying the output (y) or the input (x), the analyst can adjust underperforming points to a location within the scatter plot al ong the ‘efficient frontier’ line. In this quantitative manner, policy amendments need only address the quantity of outputs or inputs assigned to a specific location. By doing so, underperforming locations can improve to the best know n level of performance efficiency.

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25 From a strictly quantitative perspective the efficiency of a point removed from the ‘efficient front ier’ can be improved by linear movement toward the ‘efficient frontier’ but not surpassing it (Ramanathan 2003). This represents the optimal placement along the ‘efficient fr ontier’ (Ramanathan 2003). However, efficiency improvement could be realiz ed by altering the point’s location anywhere along the appropriate line segment of the ‘efficient fr ontier’ (Cooper et al. 2000). Efficiency improvement can be ex ecuted by altering either the quantity of an input or output (Cooper et al. 2000). When a decision making unit is fully efficient, it is no longer possible to impr ove any input or output without detracting from some other input or output (Cooper et al. 2000). Single Output and Input Production Ratios A simplified explanation of DEA can be accomplished by referring to an analysis composed of only a single performanc e ratio. This ratio places a single output over its associated i nput. When the ration is divi ded, the resulting number ranges from zero to one and expresses the productivity of a particular system component. From this point, single performa nce ratios from various locations are computed and can be expressed graphically with a scatter plot that places the output on the vertical line (y-axis) and t he input on the horizontal line (x-axis). When the origin (0,0) and the point of eac h ratio are connected via a straight line, the slope of that line is compared to the slopes of the other decision making units. These slopes are compared by their rate of increase with more drastic slopes identified as more efficiently perfo rming locations (Cooper et al. 2000). The slopes of these lines are quantitatively measured by the traditional method

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26 for calculating the slope of a line. The li ne connecting the origin (0,0) to the point of an individual ratio with the most drastic slope is known as the “efficient frontier” (Cooper et al. 2000). This lin e touches at least one of the ratio points, while the remaining ratio points are located on or below this line. Data Envelopment Analysis received its name from mathemat ical terminology that describes this phenomenon (Cooper et al. 2000). When a line shelters all of the points of a scatter plot underneath it, the line is said to ‘envelop’ the points of the scatter plot (Cooper et al. 2000). In other performance assessment techni ques, a statistical regression line can be fitted to a scatter plot. This form of statistical analysis splits the plotted data into two separate categories cons isting of inferior and exemplary productivity (Cooper et al. 2000). Poin ts above the regression line are considered exemplary, while points below the regression line are characterized as inferior. Productivity can then be assessed quantitatively by measuring the magnitude of deviation from the fitted regressi on line. Standard deviation is the descriptive statistic typically used to measure the distance of a sampled point from a fitted regression li ne (Mendenhall and Sincich 2003). By incorporating the ‘efficient frontier’ concept, DEA measures the deviation of points from the most productive point (Cooper et al. 2000) This represent s the fundamental difference between regression analysis and DEA. The DEA for this thesis will not incorporate a regression line. It will com pare lake water quality to the ‘efficient frontier’ line representing optimal performance. Regr ession analysis is focused on the central trends of a data set, while DE A avoids the use of a best-fit line and

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27 measures deviation from an actually obs erved line illustrating the best known performance. These two methods of statis tical analysis create two very different perspectives that can greatly influ ence policy decisions for performance improvement. DEA identif ies a line that represent s the most efficient performance of a functional relationsh ip between an output and an input. When making decisions intended to improve system performance, DEA uses an actually observed performance line as a benchmark (Cooper et al. 2000). A policy based upon the results of a D EA will attempt to improve system performance in a more dramatic fashion than a policy based upon the results of an accompanying regression analysis eval uating the same set of data. Production Ratios with Two Inputs Performance ratios can also reflec t productivity of a system component that relies upon two inputs, which within the ratio format would be placed under one output or more practically known as the product of the two inputs. When plotting such a system component, the first input is divided by the only output to form a unitized vertical y-axis, and the se cond input is also divided by the only output to form a unitized horizontal x-axis (Cooper et al. 2000). From a logical perspective, systems that use fewer inputs to generate a single unit of output are considered more efficient. When two inputs are plotted in unison with a normalized output, the ‘efficient frontier’ is segmented into multiple frontiers that illustrate input tradeoffs between the tw o complimentary inputs (Cooper et al. 2000). The segmented line that envelops a data set including two separate inputs is located beneath the ot her points of the scatter plo t. In this instance, the

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28 segmented frontier line r epresents the point at wh ich an input cannot be increased without having a negative im pact on the other input (Ramanathan 2003). By extending a ve rtical line down from the data point possessing the highest vertical value (y-value) and a horizon tal line to the left of the data point with the highest horizontal value (x-val ue), a production possibility set can be established for the data set (Cooper et al. 2000). This area withi n the scatter plot represents all of the possibl e rates of production for t he process being analyzed. An example of the ‘efficient frontier’ li ne for a system with two inputs and a single output is displayed in Figure 2 pr ovided below (Cooper et al. 2000). 0 1 2 3 4 5 0123456789 Input 1 / OutputInput 2 / Output Figure 2. ‘Efficient Frontier’ Li ne for Two Inputs and One Output The performance inefficiencies of poi nts within the production possibility set are then measured using the ‘efficient fr ontier’ as a reference line. This task is completed by calculating two distanc es and dividing those distances (Cooper et al. 2000). The first distance is composed of a line from the origin (0,0) to the

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29 intersecting point along the ‘efficient fr ontier’ line between the origin (0,0) and the point being analyzed. The second distance is simply from the origin (0,0) to the point being analyzed. To measure the per formance inefficiency of a point, the analyst must divide the first distance by the second distance. After this task has been performed, the analyst can also dete rmine which segment of the line should be used to evaluate a point’s inefficiency. The line segment of the ‘efficient frontier’ that is intersected by the line from the origin (0,0 ) to the point being analyzed is the line segment of the ‘efficient frontier’ that should be used when evaluating a point’s inefficiency (Cooper et al. 2000). The two end points of the ‘efficient frontier’ line segment intersect ed by the line emanating from the origin (0,0) are considered the reference data set for the point bei ng analyzed (Cooper et al. 2000). A reference data set can differ from point to point based upon the angle and distance of line segments compos ing the ‘efficient frontier’. Points along the ‘efficient frontier’ can also be considered more representative of the entire data set. This designation is det ermined by the overall distribution of points in relation to the ‘efficient frontier’ line. Points along the ‘efficient frontier’ line segments that are further removed from the majority of t he points within the production possibility set likely possess uni que characteristics that alter its performance from the remai nder of the data set. Production Ratios with Two Outputs Performance ratios can also reflec t productivity of a system component that relies upon two outputs, which within the ratio format would be placed over one input or practically known as the invest ment. Just as a ratio with two inputs,

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30 displaying a performance ratio with two out puts can also be accomplished with a scatter plot that contains a unitized xand y-axes (Cooper et al 2000). The first output is divided by the only input to form the x-axis, while the second output is also divided by the only input to form t he y-axis. Upon plotting the data points, the ‘efficient frontier’ can be establish ed by locating the outermost points and connecting them via straight line segment s. The segmented ‘efficient frontier’ represents the outer boundary of the production possibility set, and the xand yaxes form the innermost range of the producti on possibility set. Therefore, when analyzing a ratio with two outputs, one c an guarantee that the line segments of the ‘efficient frontier’ house the other dat a points of the produc tion possibility set. An example of the ‘efficient frontier’ line for a system with two outputs and a single input is displayed in Figure 3 prov ided below (Cooper et al. 2000). 0 1 2 3 4 5 6 7 8 01234567 Output 1 / Input Output 2 / Input Figure 3. ‘Efficient Frontier’ Li ne for Two Outputs and One Input

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31 Data points within the range from the xand y-axes to the ‘efficient frontier’ are categorized as inefficient. The magnitu de of such a point’s inefficiency can be calculated by referring to the ‘efficient frontier’. A line can be drawn from the plot’s origin (0,0) that intersects both the inefficient data point and one of the ‘efficient frontier’ line segm ents. Where this line inte rsects one of the ‘efficient frontier’ line segments, the ev aluator can assume a point ex ists at this location. Once this point has been established along the ‘efficient frontier’ line segment, the distance from the origin (0 ,0) to the inefficient point is divided by the distance from the origin (0,0) to the point along the ‘efficient frontie r’ (Cooper et al. 2000). This calculation reveals the magnit ude of inadequate production efficiency for any point housed within the ‘efficient frontier’. A division calculation of this nature is commonly known as a ‘radial measure’, which in essence is a ratio composed of two distance measures (Cooper et al 2000). Since the distance from the origin (0,0) to the inefficient point wil l always be shorter than the distance from the origin (0,0) to the ‘efficient fronti er’ line segment, we can assume that the result of dividing these two distances will always provide a number from zero to one. From a managerial perspective, this fi gure reveals information concerning two outputs of a process only when the figur e’s reciprocal is interpreted (Cooper et al. 2000). Therefore, a value of th ree divided by four would be practically interpreted by dividing four over three. This calculation would reveal that the inefficient point would achieve optimal e fficiency within the production possibility set if it were to increase outputs by a value of 1.33. When increasing outputs for

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32 a production ratio with multiple outputs, the increase should not alter the proportions of any of the ratio’s outputs (C ooper et al. 2000). Inefficiencies that can be rectified by increasing outputs propor tionately are referred to as ‘technical inefficiencies’ (Cooper et al. 2000). The term ‘mix inefficiency’ refers to an inefficiency that can be nullified by in creasing the outputs (or inputs) without maintaining proportions (Cooper et al. 2000). Applying Weights to Variables in DEA Production ratios containing multiple inputs and outputs can be assessed with DEA by assigning weights or a quantit ative value represent ing importance to the various inputs and outputs included in the ratio. Variable weights are assigned in the form of a ratio that is intended to reflect the manner in which individual outputs and inputs interact with one another (Ramanathan 2003). In DEA, ratios for a weighted variable only express how outputs and inputs interact on a separate basis. When performing an appl ied analysis of an actual system, values that weight specific inputs and outputs of a production process must be justified through quantitative records (Ramanathan 2003). The process of assigning weights to a variable can cast doubt on the results of a production ratio if the weight for a particular variable cannot be established through the analysis of reliable quantitative observations (Cooper et al. 2000). Another issue that clouds the analysis of production ratios in cluding weighted variables is the level of inefficiency attributable to the a ssigned weights and the level of efficiency actually occurring.

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33 DEA attempts to remove these doubt casting issues by only applying variable weights that have been directly derived from the observational data set being analyzed (Cooper et al. 2000). We ighted variables in DEA can also be chosen based upon maximizing the relative efficiencies of the entities or locations being analyzed (Cooper et al. 2000) In DEA, it is understood that an increase or improvement in an output will not negatively impact its associated input until the decision making unit has ac hieved optimal efficiency (Cooper et al. 2000). When a decision making unit is operatin g at optimal efficiency, it is not possible to augment any input or out put without negatively impacting another input or output (Cooper et al. 2000). The Charnes, Cooper, and Rhodes model (CCR model) of DEA accomplishes this task by selecting variable weights that will ultimately result in the best known production levels (Sexton 1986). Using the CCR model expands the production possibi lity set to include all known levels of production. This model also provides an ‘efficient frontier’ that reflects the best known production efficiencies for a gi ven data set. Improved performance efficiencies are accomplished through linear alterations in the ratio describing outputs over inputs. Inefficiencies associated with entitie s or locations being evaluated with a multiple output and input production ratio can be labeled as a ‘technical inefficiency’, a ‘mix inefficiency’, or a ‘scale inefficiency’ (Cooper et al. 2000). DEA computer programs assi st users by automatically identifying the form of inefficiency taking place and assigning the ap propriate inefficiency values to each variable included in the ratio (Cooper et al. 2000). The benchmark reference

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34 data set that achieves the best known prod uction efficiency is also automatically identified by DEA computer programs (Cooper et al. 2000). Another advantage of DEA computer programs is that they avoid the use of statistical assumptions based upon the trends of an entire populati on (Cooper et al. 2000). Avoiding these assumptions increases the accuracy of the computations performed by the program. DEA computer programs do not require t he relationships between variables to be defined (Cooper et al. 2000) which can often be an arbitrary task that only weakens the results of an analysis A final advantage of DEA is that the variables evaluated to assess perform ance can be expressed in different measurement units. Summarizing DEA Production Ratios Production ratios measure the effici ency of a process or system by dividing the output (or outputs) by the input (or inputs). In cases when multiple inputs and outputs are required to complete a production proce ss, the variables within such a ratio are weighted accord ing to the observed data set. These weights can be derived directly from the observational data set by employing DEA computer program s. In DEA, variable weig hts are not applied uniformly amongst the various outputs and inputs. Variable weights assigned by a DEA computer program reflect the best set of weights that result in the highest benchmark of efficiency. Overall, DEA is consider ed an advantageous method of performance analysis because it is capable of isolating sources of inefficiency and attributing a level of inefficien cy to specified outputs and inputs of a production process. DEA is also a pref erred measure of performance because it

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35 identifies the entities or locations with the most efficient production levels and uses these observations to form a benchmark of highest known production efficiency. This benchmark is then us ed as a reference to compare all other observations that fail to attain the highes t known level of production efficiency. DEA requires that entities or locations being assessed include the same inputs and produced outputs. Observational dat a evaluated by DEA must be only composed of positive values (Sexton 1986). This limitation is also true while assigning variable weights (Sexton 1986). The selection of inputs and outputs for a designated process is determined by the evaluator performing the DEA. Inputs and outputs are commonl y selected at the discret ion of the performance analyst (Cooper et al. 2000). In more advanced forms of DEA, inputs and outputs are further classified as discr etionary and non-discretionary (Cooper et al. 2000). Such a classification system wa s not used during the analytical portion of this thesis. Therefore, discret ionary and non-discretionary designations will not be further defined. Categorical vari ables can also be applied to DEA. Variables of a categorical nature provi de further differentiation between a set of production ratios and assumedly increase the level of real analytical accuracy. Application of DEA to a land cover analysi s of Hillsborough County as it relates to the performance of water bodies will only include physically measurable inputs and an individual output that im pact performance efficiency. At the completion of this thesis, categorical variables were not integrated into the structure of the DEA model because they were not applicable. Due to the design of the DEA model,

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36 categorical variables were not requir ed. The subsections above provided a general description of DEA and background in formation useful for framing DEA in the context of the thesis research, which entails measuring the impacts of land uses on the performance of nearby water bodies. The following paragraph will serve as a summary of the advantages and disadvantages of using DEA performance ratios during the study performed for this thesis. It will also discuss how the methodology developed during this thesis will attempt to overcome the disadvant ages of applying DEA performance ratios to a cross-sectional analysis of la kes in Hillsborough County. The DEA technique is disadvantageous because it is only a partial measure of performance. This aspect of DEA poses a problem because inputs and outputs of a freshwater lake represent an intricat e ecological relationship. It was not possible to include all of these input s and outputs due to the current state of available water quality data on the Hil lsborough County Water Atlas. The process of selecting relevant variable s hinged upon the signi ficance of an input or output as well as data availability. This process requir ed a great deal of research on the Water Atlas database to vi ew the available data for every lake within the political jurisdiction of Hillsborough County. After performing this process, it was readily apparent that the inputs of total chlorophyll, total phosphorous, and total nitrogen as well as t he output of naturally preserved land surface area surrounding a particular lake represent sufficient variables for identifying a lake’s optimum performanc e benchmark. The other significant disadvantage of DEA is that its variabl e selection process can be vulnerable to

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37 scrutiny and should proceed with caution. As discussed during the examination of the study performed by Shafiq and Rehman (2000), any DEA methodology relies upon a variable selection process dependent upon the researcher’s logic. If careless, the DEA user c ould unintentionally skew the results of the model as well as the management recommendations derived from the model’s results. When using DEA, it is import ant to justify the variable selection process with valid arguments for each input and output chosen. In the case of this thesis, the input and output variables were select ed based upon both valid and unbiased arguments. The variables were first selected based upon significance with regards to water quality and the performanc e of a freshwater lake. This was determined by reviewing the available li terature discussing the status of lake water quality in Hillsborough County. The subsequent literature review identified specific substances most threatening to lake water quality in Hillsborough County. Following this first selection par ameter, the variables were then selected based upon data availability on the Hil lsborough County Water Atlas. An advantage of applying DEA performance ratios to a cross-sectional analysis of lakes is that this research is capable of identifying the levels of inputs and outputs that resulted in optimal aquatic conditions. Also, DEA enabled this research to identify the exact quantities at which a specific input or output is most beneficial to the performance of the aquatic ecosystem of a freshwater lake. Furthermore, the performance ratios used by DEA are designed to examine the

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38 most critical inputs and outputs related to an environmental system. Finally, DEA performance ratios supplied this research with the necessary evidence to suggest the most effective water managem ent techniques for the freshwater lakes of Hillsborough County.

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39 Methodology The scientific research of this thesis applied DEA, a performance assessment tool, to the lakes of Hillsbor ough County. Becaus e of the original nature of this research, the methodology wi ll be provided for the first time within this paper. For the applied research of this thesis, the DEA output consisted of data measuring naturally preserved land su rface area within a tw o mile radius of each lake selected for the study. Initia lly, the output variable measured natural land area within sub-basins previously determined by the Southwest Florida Water Management District (SWFWMD). This method for calculating natural land area was eliminated becau se it did not provide enough variability in the output data set. Lakes contained by the same sub-basin recorded the same output values. In many instances, the st udy lakes were located within the same sub-basin reducing the variability of t he output data set. In an attempt to counteract this, it was decided to meas ure natural land area within a two mile radius of study lakes. This effort re turned improved output dat a variability. A distance of two miles was selected because it reflected a size comparable to SWFWMD sub-basins. Also, a two mile radius was determined to be an appropriate size because of the sparse geographic distribution of natural land in Hillsborough County.

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40 Several of the two mile radius delineations extend into neighboring counties surrounding Hills borough County. Areas in wh ich the two mile radius delineations extend beyond the Hillsbor ough County boundary were considered during the natural land cover selection process, however, these areas failed to yield any naturally preserved land. All naturally preserved land within two miles of a study lake was selected for t he DEA regardless of county boundaries. The thesis methodology isolates lakes according to spatially oriented polygons that represent a two mile radi us surrounding each study lake. These two mile radius delineations hav e been automatically assigned feature identification numbers by the ‘Buffer’ tool of ArcMap. Table 1 lists each of the two mile radius delineations included in this study by feature identification numbers and provides the corresponding natura lly preserved surface area. This table also displays which lake is locat ed within each two mile radius delineation feature. The final column of the table displays the natural land use percentage within each two mile radius delineation feature.

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41 Table 1. Two Mile Radius Delineation Feature Summary Two Mile Radius Delineation Feature Identification Number (FID) Surface Area (in acres) Lake within Two Mile Radius Delineation Feature Natural Land Use Percentage within Two Mile Radius Delineation Feature 00 8,650 Garden Lake 0.9402 01 10,277 Brant Lake 3.5855 02 10,485 Lake Hiawatha 0.9815 03 15,115 Lake Thonotosassa 0.6194 04 8,820 Flynn Lake 0.6034 05 10,446 Pretty Lake 2.2794 06 9,681 Hanna Lake 3.9308 07 9,563 Lake Josephine 2.3540 08 9,094 Echo Lake 1.2807 09 15,042 Lake Keystone 1.8600 10 9,301 Lake Armistead 1.9134 11 8,993 Lake Harvey 2.2417 12 9,213 Sunset Lake 0.8827 13 8,859 Cypress Lake 2.7560 14 8,928 Chapman Lake 0.1616 15 8,954 Lake Virginia 2.2515 16 8,602 Burrell Lake 0.6187 17 10,288 Lake Thomas 3.6078 18 9,552 Rock Lake 2.2959 19 9,818 Osceola Lake 0.8119 20 8,847 James Lake 2.7597 21 10,228 Lake Alice 1.7454 22 9,495 Lake Weeks 1.3223 Natural land area is considered an output because of the perceived notable relationship between water qualit y and surrounding land use. Ideally, water quality should directly relate to t he amount of natural land area surrounding a particular lake. In this case, water qua lity is maximized by increasing amounts of natural land area. Data for th e output variable was derived from the intersection of a land use shapefile laye r provided by The Planning Commission

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42 of Hillsborough County, a lake polygon s hapefile layer stored in the Florida Geographic Data Library and Map Server, and polygon shapefiles representing a two mile radius surrounding each of the st udy lakes. GIS tools supplied within the ArcMap software package were used to calculate naturally preserved land surface area positioned within a two mile radius of each study lake. The natural land surface area calculations acquired from ArcMap populated the sample data for the DEA output variable. Inputs consis ted of recorded data for substances in aquatic ecosystems that typically have a negative impact on lake performance. For this particular study, total chlorophy ll, total phosphorous, and total nitrogen were examined as input variables. Thes e substances were selected as input variables because they are the three most significant indicators of impaired water quality performance in Hillsborough County lakes (Poe et al. 2005). After a certain threshold, lakes containing an excess amount of these substances experience a decline in water quality, which negatively impacts overall lake performance (Poe et al. 2005). It is expected that minimizing input concentrations and maximizing the output vari able will result in higher DEA lake performance measurements.

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43 Table 2. Summary of Study Variables Variable Variable Type (Input/Output) Measurement Units Data Source Total Chlorophyll (EPA method 0445.0) Input ug/L Hillsborough County Water Atlas Total Nitrogen (EPA method 0351.2) Input ug/l Hillsborough County Water Atlas Total Phosphorous (EPA method 0365.1) Input ug/L Hillsborough County Water Atlas Naturally Preserved Land Area Output Acreage The Planning Commision of Hillsborough County The measurement unit used to express raw input data was not consistent with the measurement unit us ed to quantify the raw output data. Input data for total chlorophyll, total nitrogen, and total phosphorous was expressed as micrograms per liter, while output data for natural land use area was quantified by acres. This inconsistency in m easurement units is acceptable within the mathematical framework of DEA (Cooper et al. 2000). Measur ement units used to express raw input and output data enter ed into a DEA are not required to be equivalent (Cooper et al. 2000; Ram anathan 2003; Thanassoulis 2001). The ultimate goal of the applied research portion of this thesis is to link land use activity to aquatic conditions in a lake. The chosen methodology will accomplish this goal by relating the concent rations of three critical pollutants to the spatial extent of natur ally preserved land surrounding a lake. By doing so, the research will unveil trends linking surf ace water quality to surrounding land uses. The DEA developed for this thesis c onsisted of input variables that should

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44 be minimized and an output variable which should be maximized to increase lake performance. Input variables assessed by this study consisted of significant pollutants that diminish lake performance as their concentrations increase. The output variable included in this DEA r epresents a positive influence on lake performance that should be maximized. Naturally preserved land area was selected as the output variable becaus e this land use type maximizes water quality (Tong and Chen 2002; Castelletti and Soncini-Sessa 2007; Osborne and Wiley 1988; Lee 2002), which subsequently improves lake performance. In the state of Florida, a naturally preserved land use category has been previously identified by the Florida D epartment of Transportation in a government document entitled Florida Land Use, Cover and Forms Classification System (1999). This classification system was re ferred to while spatially analyzing the land use shapefile provided by The Planning Commission of Hillsborough County. The naturally preserved land us e category was selected as the output variable because it enhances lake performanc e as it is maximized. Multiple studies and texts have corroborated the fact that water quality typically improves with the increase of natural land uses (Xian et al. 2007; Wang 2001; Tong and Chen 2002; Gleick et al. 2006; Castelle tti and Soncini-Sessa 2007; Lenat and Crawford 1994; Stauffer 1991). Output variable data was gather ed through a GIS data processing technique. Naturally preserved land us e area was calculated within a polygon shapefile representing a two mile radius surrounding each of the study lakes. Initially, ArcMap was populated with thr ee shapefiles depicting the land uses,

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45 lakes, and a two mile radius surrounding each of the study lakes. The shapefile depicting lakes was then redefined to onl y include those lakes selected for the study. Then, a tool by the name of ‘Clip ’ was used to select only the land use polygons which fell directly within the shapefile depicting a two mile radius surrounding each of the study lakes. Afte r redefining the land use layer, it was then feasible to select onl y the naturally preserved l and use polygons which are spatially located within a tw o mile radius of a study lake and create a new layer from this selection. Finally, the su rface area of naturally preserved land surrounding each lake was individually ca lculated. This task was accomplished using a tool known as ‘Calculate Geometry ’ located in the attribute table of the most recently generated layer depicting nat urally preserved land use within a two mile radius of a study lake. Data sources that supplied the necessary information for completing this methodology are publicly accessible via t he internet. Quantitative records for substances that impact the water quality of a lake popu lated the input variable data set. Three of the most significant inputs related to water quality in Hillsborough County populated the input variable data set. Total chlorophyll, total phosphorous, and total nitrogen represent th ree of the most significant aquatic pollutants currently being deposited in Hillsborough County freshwater lakes (Poe et al. 2005). The concentrations fo r these water pollutants have been recorded by a variety of partner agencies on a consistent basis for multiple years dependent upon the lake in question. Thes e records were retrieved from the Water Atlas hosted and maintained by the City of Tampa and Hillsborough

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46 County governments (http://www.hillsborough. wateratlas.usf.edu/). The surface area for naturally preserved land uses withi n a two mile radius of each study lake populated the output variable data set. Fo r the purpose of this study, it was determined that naturally preserved land is the mo st significant land use influencing the performance of lakes in Hillsborough County. This determination was made because the natural lands surrounding lakes along with the water quality within these lakes has steadily di minished in recent decades (Poe et al. 2005). From this observation, it appears as though the spatial extent of natural lands surrounding lakes has a direct correlation with lake performance. Therefore, natural land area will be examined by the output va riable of this study. The data set for the input variables consisted of meas urements from 2006 through 2008. Only data collected duri ng the spring and summer months from March to September were included in t he input variable data set. This time frame was established by a survey of the available data in the Water Atlas website. GIS land cover layers for Hillsborough County are available on publicly accessible websites hosted by a variet y of governmental agencies such as Hillsborough County Planni ng Department, the Envi ronmental Protection Commission of Hillsborough County, and S outhwest Florida Water Management District. Certain websites designated as GIS data clearinghouses may also provide pertinent land use layers for Hillsborough County. For this thesis, one specific Hillsborough County land use layer was used. This layer has been developed, disseminated, and updated on a quarterly basis by The Planning Commission of Hillsborough County. After ex amining the attribute table of this

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47 land use data layer, it was determi ned that this shapef ile contained the necessary information to calculate the ar eal extent of naturally preserved land uses within a two mile radius of each st udy lake. The polygon shapefile depicting the lakes of Hillsborough County was re covered from the Florida Geographic Data Library and Map Server, a GIS data cl earinghouse for the state of Florida. And, the polygon shapefile depicting a two mile radius surrounding each of the study lakes was generated using a tool supported by the ArcMap software package known as ‘Buffer’. The data collected from this assortment of websites was entered into two specialized computer programs that execute DEAs These programs are named ‘DEA solver’ and ‘DEAlytics’. ‘DEA solv er’ produced the results for the CCR-I and BCC-I models, while ‘DEAlytics’ produced the results for the Additive model. Three different DEA models were used to process the collected data. The Charnes, Cooper, Rhodes (CCR) model is capable of measuring ‘technical inefficiency’ and ‘mix ineffici ency’ (Cooper et al. 2000). ‘Technical inefficiency’ is eliminated without alte ring the proportions of system inputs and outputs, while ‘mix inefficiency’ is re moved by adjusting the proportion of system inputs and outputs (Cooper et al. 2000). Mult iple versions of the CCR model are used to determine both of these forms of ine fficiency. For this particular analysis, the CCR-Input (CCR-I) model was applied to assess water quality inefficiencies associated with Hillsborough County lake s. The CCR-I model is designed for analyses in which the input variables ar e minimized and the output variables do not require any mathematical augmentati ons. It was determined that the input

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48 oriented version of the CCR model was the most suitable for this analysis because lake water quality optimizati on depends upon the minimization of the selected input variables. The CCR-I model is expressed by the following set of mathematical equations: max = es+ es+ subject to s= xo – X s+ = Y – yo 0, s0, s+ 0 (Cooper et al. 2000), where e is equal to a vector of ones so that es= sand es+ = s+, is equal to the optimal objective value, srepresents input excesses, s+ represents output shortages, xo represents the input vector, yo represents the output level, X and Y are the matrices of the inputs and outputs, represents performance maximization, and represents a measurement known as slack. The BCC model is also capable of measuring both ‘tec hnical’ and ‘mix inefficiency’ (Cooper et al. 2000). Multiple versions of the BCC model have been devised to determine both of these forms of inefficiency. For this particular analysis, the BCC-Input (BCC-I) model was applied to assess water quality inefficiencies associated with Hillsborough C ounty lakes. Just like its other input oriented counterpart, the BCCI model is designed for analyses in which the input variables are minimized and the output va riables are maintained at actually

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49 observed levels. The input oriented vers ion of the BCC model was selected for this analysis because lake water quality opt imization depends significantly upon minimizing input variable concentrations. The BCC-I model is expressed by the following set of mathematical equations: (Alsharif et al. 2008), where xij and yrj are inputs and outputs, respectively, si represents input excesses, sr represents output shortages, zo represents performance optimization, is equal to the optimal objective value, is equal to the sum of input and output deficiencies, and represents the slack measurement. The Additive model is capable of distinguishing between efficient and inefficient DMUs, however, it differs fr om the previously discussed DEA models because it has no means of measuring ineffi ciency (Cooper et al. 2000). Instead, the Additive model specializes in dire ctly identifying input excesses and output deficiencies through a measurement known as a ‘stability value’ (Cooper et al. 2000). These values quantitatively express the level of efficiency or inefficiency achieved by a particular decision making unit. Stability values for inefficient units

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50 are expressed as negative numbers, while st ability values for efficient units are expressed as positive num bers. Increasingly negativ e numbers indicate higher levels of inefficiency, and increasingly pos itive numbers indicate higher levels of efficiency. The Additive model should be applied to performance assessments in which the input variables are minimized and the output variables are maximized. For the performance assessment conducted dur ing this thesis, lake water quality should theoretically be optimized by mi nimizing inputs and maximizing outputs. Therefore, it is suitable to apply the Additive model during this performance assessment of lake water quality in Hills borough County. The Additive model is expressed by the following se t of mathematical equations: min (eTs+ eTs-) subject to Y – s+ = Yj X + s= Xj eT = 1 s+, s0 (Feroz et al. 2001), where X and Y are the matrices of the i nputs and outputs, respectively, s-and s+ are excesses in inputs and insuffici encies in outputs, respectively, e is equal to a vector of ones so that es= sand es+ = s+, and represents the slack measurement. According to the framework of DEA, each lake represents a DecisionMaking Unit, or DMU. In th is study, the DMUs influence the ‘efficient frontier’ line depicting optimum lake water quality condi tions. DMU selection was based on a sampling design that considered geographic lo cation and the availability of water

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51 quality data. Initially, ev ery lake within Hillsborough County was considered a potential DMU. This sample was then dimi nished by the availability of relevant water quality data on the Hillsborough County Water Atlas. Only lakes with water quality data for total chlorophyll, total nitrogen, and total phosphorous concentrations during the spring and su mmer months of 2006 through 2008 were selected as DMUs. Forty-three lakes within Hillsborough Count y satisfied this selection criterion. Finally, this sample was further diminished by the lack of any naturally preserved land use area in twenty of the two m ile radius delineations. Lakes spatially contained by a two mile radius with a recorded natural land use area of zero were excluded from the sample. These lakes were excluded because they would automatically render a performance rating of zero due to the mathematical framework of DEA. After considering all of the above selection criteria, twenty-three lakes were select ed as DMUs for the DEA conducted during this thesis. A list of the twenty lakes e liminated during this selection process has been provided in Table 3. Table 3. Lakes Eliminated Due to Lack of Natural Land Use Area Lake Name Boat Lake Dorset Lake Lipsey, Lake Reinheimer Lake Carroll, Lake Eckles, Lake Magdalene, Lake Round Lake Cedar Lake Halfmoon Lake Mango Lake Saddleback Lake Cooper Lake Hobbs, Lake Noreast Lake Starvation Lake Crenshaw, Lake Leclare, Lake No rth Crystal LakeWimauma, Lake

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52 The final step of the applied research methodology for this thesis was to enter the data into a DEA computer softw are and interpret the statistical results that emerge from the anal ysis. Statistical result s from the DEA computer software were in the form of efficiency ratings for individual lakes. Careful interpretations of these efficiency ratings allowed the researcher to recommend adjustments related to the inputs and out puts of a specific lake. The DEA software selected the lakes with the highest efficiency ratings based upon the data sets for the input and output vari ables. These lakes represented the ‘efficient frontier’. Lakes with the most desirable water quality data were included along the ‘efficient frontier’. The ‘effi cient frontier’ served as an efficiency benchmark for all other lakes not achieving similar levels of performance. Lake inefficiency levels were determined by re ferring to the efficiency benchmark or ‘efficient frontier’. Computer software that specializes in DEA also provided statistical measures that attribute specif ic amounts of inefficiency to individual input and output variables. DEA not only evaluated the total magnitude of inefficiency related to a particular lake, but it also statistically assigned numerical values describing the level of inefficiency pertaining to a particu lar variable. After the DEA computer software has pres ented this information, it was the responsibility of the researc her to properly interpret t he results and formulate the appropriate water management recommendat ions for Hillsborough County lakes.

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53 Study Area As stated previously, the study ar ea consisted of Hillsborough County, Florida. More specifically, the thesis will focus its applied research on twentythree of the freshwater lakes locat ed within the Hillsboro ugh County political boundary. Figure 4 is a map of the study area that depi cts the spatial distribution of lakes selected for the study along wit h their corresponding two mile radius delineations. The distribution of naturally preserved land loca ted within two miles of a study lake is also displayed by the figure provided below.

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54 Map Projection: NAD 1983 UTM Zone 17N Figure 4. Distribution of Study Lakes Two Mile Radii, and Natural Land

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55 The study area for this thesis is a highly urbanized county in west-central Florida with a humid, subtropical clim ate characterized by a pronounced wet season from June to September. Hillsborough County is populated by approximately 1.2 million peopl e according to the 2006 estimate provided by the United States Census Bureau. The study area occupies 1,076 square miles according to the GIS shapefile prov ided by The Planning Commission of Hillsborough County. This corresponds to a population densit y of approximately 1,115 people per square mile. The land use shapefile examined during this thesis was also provided by The Planning Commission of Hillsborough Count y. According to this shapefile, Hillsborough County contains 20 specific land uses consistent with Florida’s Department of Transportation land categorization scheme outlined by Florida Land Use, Cover and Forms Classification System (1999). The land uses included in this shapefile are listed with their corresponding surface area and percent occupying Hillsborough Count y in Table 4 provided below.

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56 Table 4. Hillsborough C ounty Land Use Summary Land Use Category Surface Area (in acres) Percent of Hillsborough County (%) Agricultural 157,079 22.80 Educational 6,011 0.8725 Heavy Commercial 2,481 0.3601 Heavy Industrial 10,466 1.519 Light Commercial 13,756 1.997 Light Industrial 8,143 1.182 Mining 26,007 3.775 Mobile Home Park 5,661 0.8217 Multi-Family 30,273 4.394 Natural 8,787 1.275 Not Classified 50,783 7.371 Public/Institutions 135,182 19.62 Public Communications/Utiliites 4,617 0.6702 Recreational/Open Space 7,675 1.114 Right of Way/Roads 1,425 0.2068 Single Family/Mobile Home 126,641 18.38 Two Family 1,000 0.1451 Unknown 227 0.03295 Vacant 58,783 8.532 Water 33,937 4.926 Historically, the predominant land uses in Hillsborough County were agriculturally related (Poe et al. 2005). However, recent trends in development over the previous two decades have transformed Hillsborough County into a

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57 metropolitan area predominantly containing ur ban, built-up land uses (Poe et al. 2005). It has been widely publicized that fo rmerly agricultural lands have been converted into urbanized or industrial l and uses within Hillsborough County over the past two decades (Poe et al. 2005). The following paragraphs describe the environmental monitoring program and status of the freshwater lakes in the study area. Surface water issues have been highlighted to provide readers with a general under standing of lake conditions in Hillsborough County. Wate r monitoring is a necessary component of any large-scale water management effor t. Currently in the Tampa Bay area, a host of agencies are responsible for moni toring the quality of surface water (Poe et al. 2005). Agencies involved in this e ffort include but are not limited to the Southwest Florida Water Management District (SWFWMD), Hillsborough County Environmental Protection Commission (EPC), and Florida Department of Environmental Protection (Poe et al. 2005). These agencies actively monitor the quality of surface water to assess resource performance and contribute to managerial decisions. According to the Baywide Environment al Monitoring Report (2005), recent monitoring efforts in the Tampa Bay area, sp ecifically in the di strict known as Old Tampa Bay or Hillsborough County, have revealed negative trends in water quality and clarity. Factors associated with this trend toward poorer water quality will be identified during an ongoi ng research project. Fr eshwater tributaries in the Tampa Bay Area are experiencing incr easing levels of hypoxia, sediment contamination, and eutrophicati on. As a result, the diversity and resilience of

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58 benthic communities within negatively impacted tributaries has declined. Contaminants were detected at toxic levels in many freshwater resources. This information has prompted research to identify point and non-point sources related to the elevated levels of specific water contaminants. The Baywide Environmental Monitori ng Report (2005) identifies increased urbanization rates as the cause for the heightened levels of degradation observed in many of the freshwater bodies in the Bay area. Urbanized areas replace agricultural and forested land, which function as a natural filter for aquatic environments (Tong and Chen 2002; Ca stelletti and Soncini-Sessa 2007; Osborne and Wiley 1988; Lee 2002). Theref ore, surface area losses in these land uses have predictably resulted in increasingly impaired water resources located within the Bay area (Poe et al. 2005). The synopsis provided above regarding the status of fres hwater resources in the Tampa Bay area serves as further justification for completing the appli ed research portion of this thesis. The selected study area, Hillsbor ough County, is witnessing rapid declines in surface water quality that can only be remedied wit h rapid assessment techniques that contribute to adaptive m anagement strategies. Data for twenty-three lakes within Hillsborough County was included for the DEA conducted during this thesis. Each of these lakes was composed of freshwater. Areas surrounding these lakes were primarily composed of urbanized uses with a limit ed amount of naturally preserved land. Table 5 provided below contains hydrologic information corresponding to each of the

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59 lakes chosen for this study. This table also contains a column describing the overall condition of each lake in relation to its designated uses. The information for this table was retrieved from the Hillsborough County Water Atlas. Table 5. Hydrologic Summary of Study Lakes Lake Name Surface Area (in acres) Mean Depth (in feet) Max Depth (in feet) Approximate Volume (in gallons) Lake Condition Category Alice 92 9 25 248,817,000 Fully supports designated use Armistead 34 9 28 91,865,734 Fully supports designated use Brant 55 6 16 101,616,511 Fully supports designated use Burrell 22 NA NA NA Fully supports designated use Chapman 42 5 11 7,356,604 Fully supports designated use Cypress 16 12 27 59,445,932 Fully supports designated use Echo 24 9 16 73,643,500 Fully supports designated use Flynn 12 NA NA NA Fully supports designated use Garden 8 6 21 18,937,700 Does not support designated use Hanna 34 5 15 52,854,890 Partially supports designated use

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60 Table 5 (continued). Hydrologic Summary of Study Lakes Harvey 21 10 28 73,083,950 Partially supports designated use Hiawatha 135 11 24 494,966,000 Fully supports designated use James 15 7 15 39,876,500 Fully supports designated use Josephine 50 7 24 111,487,453 Fully supports designated use Keystone 431 11 24 1,509,570,177 Fully supports designated use Osceola 60 6 16 22,649,596 Fully supports designated use Pretty 81 11 27 282,248,369 Fully supports designated use Rock 53 7 21 113,864,497 Partially supports designated use Sunset 33 8 21 93,028,200 Fully supports designated use Thomas 60 13 27 258,565,350 Fully supports designated use Thonotosassa 849 8 18 NA Does not support designated use Virginia 19 7 24 50,487,800 Partially supports designated use Weeks 47 7 6 66,978,494 Does not support designated use

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61 Results The DEA for this thesis examined th ree input variables and a single output variable. Input variables consisted of water quality data re trieved from the Hillsborough County Water Atlas. Total chlorophyll, total nitrogen, and total phosphorous concentrations were designated as inputs during the DEA. These variables quantitatively descr ibed individual lake nutrien t loading, which has been previously documented as the most severe threat to lake water quality in the Tampa Bay area (Poe et al. 2005). The single output variable consisted of acreage measurements for naturally preser ved land use within a two mile radius of each study lake. The output variabl e was selected based upon the previously documented relationship between natural land use area and lake water quality established in the Baywide Environmental Monitoring Report of 2005. Natural land use area was selected as the output variable because surface water quality in the Tampa Bay area has historica lly become degraded during the same time periods in which natural land cover is mo re rapidly removed (Poe et al. 2005). Natural land use area and distribution have been identified as the land coverage variables that most significantly influence the status of lake water quality in the Tampa Bay area (Poe et al. 2005). Natura l land area was selected as the output because it directly reflects the status of la ke water quality. It is typically assumed that when natural land use area increases the quality of lake water improves.

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62 The quantitative figures for this variable we re derived from the spatial intersection of three GIS shapefiles depicting land us e, lakes, and polygons representing a two mile radius surrounding each study lake Surface analysis tools provided by the ArcInfo software package were used to calculate the surface area of naturally preserved land within a two mile radius of each study lake. The raw data for the input and output vari ables is displayed in Table 6. This data was entered into two different computer programs that execute DEAs, ‘DEA Solver’ and ‘DEAlytics’. After enteri ng the raw data into these programs, water quality performance ratings for each study lake were generated. During this analysis, the performance rating is synonymous with the overall water quality for each study lake. Lake performance ratings are numerically expressed with values from zero to one. A performanc e rating of one typically indicates that a lake is operating at optimum water quality conditions, while a performance rating less than one indicates that a lake is oper ating at less than optimum water quality conditions. In some rare instances, a performance rating of one is not indicative of optimum performance. These in stances are revealed through other performance measurements provided by ‘DEA Solver’ and ‘DEAlytics’ such as ‘slack’ and ‘projection’ ratings. In order to be considered an optimally performing DMU, both the ‘slack’ and ‘projection’ m easurements must be equal to zero, and the performance rating must be equal to one.

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63 Table 6. Raw Input and Ou tput Variable Data Lake Name (I) Total Chlorophyll (in ug/L) (I) Total Phosphorous (in ug/L) (I) Total Nitrogen (in ug/L) (O) Natural Land Use Area (in acres) Alice, Lake 2.6 19.0 363.0 178.5218 Armistead, Lake 4.0 17.5 656.7 177.9678 Brant, Lake 12.5 21.7 695.0 368.4807 Burrell Lake 10.0 48.0 906.7 53.2218 Chapman Lake 5.2 23.0 1,004.0 14.4276 Cypress Lake 1.5 7.0 375.0 244.1508 Echo Lake 4.5 16.3 656.7 116.4646 Flynn Lake 13.7 15.7 1,030.0 53.2218 Garden Lake 66.7 48.7 2,013.3 81.3264 Hanna Lake 15.0 44.0 1,496.0 380.5429 Harvey, Lake 38.5 27.3 1,330.0 201.5969 Hiawatha, Lake 14. 0 16.5 615.0 102.9058 James, Lake 5.5 12.5 670.0 244.1508 Josephine Lake 34.7 23.3 965.0 225.1115 Keystone Lake 3.0 10.5 426.7 279.7858 Osceola, Lake 4.0 11.3 696.7 79.7158 Pretty Lake 10.0 14.0 695.0 238.1067 Rock Lake 29.3 33.3 1,176.7 219.3028 Sunset Lake 1.5 11.5 430.0 81.3264 Thomas Lake 42.0 20.3 713.3 371.1753 Thonotosassa, Lake 99.7 204.0 2,356.7 93.6222 Virginia, Lake 32. 0 36.0 1,423.3 201.5969 Weeks, Lake 152.4 264.0 2,699.0 125.5515 The reader may notice that certain pairs of lakes are located within a two square mile radius of the same amount of naturally preserved land. This is a result of the spatial position of several of the lakes chosen for the study. Lakes that were surrounded by the same amount of natural land area were closely located next to each other. Four pairs of lakes were surrounded by the same amount of natural land ar ea. These lakes were bounded by two mile radius delineations that contained the same natur al land area due to comparable spatial

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64 orientations. Cypress Lake and Jame s Lake produced two mile radius delineations that contained the same natural land area at 244.1508 acres. Lake Harvey and Lake Virginia were surrounded by the same amount of natural land area at 201.5969 acres within a two mile ra dius of both lakes. Garden Lake and Sunset Lake were also surrounded by the sa me amount of natural land area at 81.3264 acres. Finally, Burrell Lake and Flynn Lake produced two mile radius delineations that contained the same natur al land area at 53.2218 acres. Each of these pairs of lakes contained the same output variable data. Therefore, these lakes will prove useful in further examin ation focused on isolat ing the influence of the input variables on lake performance. Lakes that share the same output variable data are strictly influenced by t he input variable data. In instances when a lake shares the same output variable data, it is possible to solely examine the impacts of the input variables on lake performance. Within each pair of lakes sharing the same output variable data, it is expected that t he lake containing lower input variable concentrations will perform at a higher level. This subject will be discussed further in subsequent model results sections. CCR-I Model Results Lake performance ratings derived during this analysis describe the relationship between select water qualit y variables and surrounding land use. The CCR-I model returned an average per formance rating of 0.3822 for the entire set of lakes. This value indicate s that the entire set of lakes operated at only 38.22% of optimal performance effici ency. The standard deviation for the entire set of lake performance ratings equaled 0.2968. This value indicates a

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65 relatively wide distribution of performance ra tings for the entire set of lakes. The lake water quality performance ratings derived from the CCR-I model have been provided in Table 7. As expected, t hese ratings increase for lakes surrounded by greater amounts of naturally preserv ed land. Performance ratings also predictably increase for those lakes c ontaining lower conc entrations of the selected input variables. The CCR-I model determined that only two lakes were performing at optimal efficiency. Table 7. CCR-I Lake Performance Ratings and Rank Lake Name Performance Rating Lake Performance Rank Cypress Lake 1.0000 1 Keystone Lake 1.0000 1 Brant, Lake 0.8086 3 Thomas Lake 0.7936 4 Alice, Lake 0.7500 5 James, Lake 0.5600 6 Pretty Lake 0.5253 7 Armistead, Lake 0.4142 8 Hanna Lake 0.3879 9 Josephine Lake 0.3560 10 Sunset Lake 0.3331 11 Rock Lake 0.2842 12 Echo Lake 0.2706 13 Hiawatha, Lake 0.2552 14 Harvey, Lake 0.2323 15 Virginia, Lake 0.2160 16 Osceola, Lake 0.2023 17 Flynn Lake 0.0972 18 Burrell Lake 0.0895 19 Weeks, Lake 0.0709 20 Garden Lake 0.0616 21 Thonotosassa, Lake 0.0606 22 Chapman Lake 0.0220 23

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66 The CCR-I performance ratings generated during this study follow general trends that describe the relationship bet ween lake water quality and land use. General trends in the data are graphically represented by Figures 5, 6, and 7 for total chlorophyll, total phosphorous, and total nitrogen, respectively. These scatter plots represent the strength of relationship between a respective input variable and lake performance. The statistical lines of best-fit are provided for each of these scatter plots. The relationship between each water quality parameter and lake performanc e is depicted by the statis tical lines of best-fit. The best-fit lines support the trend that lakes cont aining lower input variable concentrations typically obtained higher performance ratings. After observing this trend, it can be stated that lake per formance shared an indirect relationship with the input variables. Accordingly, la ke performance optimiz ation is achieved by minimizing inputs. This outcome supports the previously mentioned expectations that input mi nimization would result in optimum lake performance. When viewing these graphs, the reader should keep in mind that the calculated R2 values provided in each scatter plot are only a partial measure of the model’s effectiveness. The R2 values in each scatter plot quantify the strength of relationship between the pl otted water quality parameter and lake performance. The R2 values provided in Figures 5, 6, and 7 should not be considered a measure of how effective the entire model is at predicting lake performance.

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67 Figure 5. Total Chlorophyll Versus CCR-I Lake Performance Rating Figure 6. Total Phosphorous Versus CCR-I Lake Performance Rating

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68 Figure 7. Total Nitrogen Versus CCR-I Lake Performance Rating General trends in the data are graphi cally represented by Figures 8 and 9 for natural land area and natural land per centage, respectively. These scatter plots represent the strength of relati onship between the output variable and lake performance. The statistical lines of bestfit are provided for both output oriented scatter plots. The relationship between natural land and lake performance is depicted by the statistical lines of best-fit. The best-fit lines support the trend that lakes surrounded by more natural land typically received higher performance ratings. As the single output variable increased, lake performance ratings typically improved. After observing th is trend, it can be stated that lake performance shared a direct relationship with the output variable. Accordingly,

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69 lake performance optimization is achieved by maximizing outputs. This outcome supports the previously mentioned expecta tions that output maximization would result in optimum la ke performance. When viewing these graphs, the reader should keep in mind that the calculated R2 values provided in each scatter plot are only a partial measure of the model’s effectiveness. The R2 values in each scatter plot quantify the strength of relationship between natural land and lake performance. The R2 values provided in Figures 8 and 9 should not be considered a measure of how effective the entire model is at predicting lake performance. Figure 8. Natural Land Use Area Vers us CCR-I Lake Performance Rating

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70 Figure 9. Natural Land Percentage Versus CCR-I Lake Performance Rating Each of the lakes included in this st udy were assigned a ranking based on the DEA performance ratings. Two separ ate lakes claimed the number one rank as well as an optimum performance rati ng of one. Cypress Lake as well as Keystone Lake both achieved an optimum performance measurement. Cypress Lake was located within a two mile radius of 244.1508 acres classified as natural land, while Keystone Lake was surrounded by 279.7858 acres of natural land within a two mile radius. Naturally pr eserved land occupied 2.7560% of Cypress Lake’s two mile radius delineation, wh ile Keystone Lake was situated in a two mile radius delineation that contained 1.8600% natural land cover. Input variable concentrations for these two lakes were low relative to the nutrient loads of other inefficiently performing lake s included in the study.

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71 Chapman Lake received the lowest perfo rmance rating amongst the set of lakes. This lake obtained the last ranking because it is located in a two mile radius delineation that only contained 14.4276 acres of nat urally preserved land. Naturally preserved land only occupied 0.1616% of Chapman Lake’s two mile radius boundary. The input variable concent rations for this lake also contributed to its poor performance rank. Each input variable concentration was high relative to the nutrient loads of other lakes include d in the study. In fact, Chapman Lake contained concentrations of total phosphorous and total nitrogen higher than the sampled median. From this observation, it is evident that nutrient concentrations within Chapman Lake hindered its water quality performance. Directly in the middle of the perfo rmance ranks, Rock Lake obtained a rating of 0.2842. This lake was repres entative of the average performance for the entire data set. As previously stat ed, the average perfo rmance rating for the entire set of lakes was equal to 0.3822. The standard deviation for lake performance ratings was equal to 0.2968. Therefore, the performance rating obtained by Rock Lake was representative of the CCR-I model results because it fell within one standard deviati on of the average. Input and output variable data for Rock Lake was also representative of the averages calculated for the entire data set. Rock Lake was located withi n two miles of 219.3028 natural land acreage. On average, the tw o mile radius delineations established for this study contained 179.6641 acres of natural land. The standard deviation for natural land use area data collected during this study was equal to 103.8114 acres. Therefore, the natural land area surrounding Rock Lake was representative of

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72 the entire data set because it fell within one standard deviation of the average. Rock Lake was located in a two mile r adius delineation occupied by 2.2959% natural land use. On av erage, the two mile radius delineations included in this study were occupied by 1.8175% natural land use. The standard deviation for natural land use percent surrounding t he study lakes was equal to 1.0354%. Therefore, it can be stated that the percentage of natural land surrounding Rock Lake was representative of the entire dat a set because it fell within one standard deviation of the average. The total chlorophyll concentration for Rock Lake equaled 29.30 ug/L, while the average concen tration of total chlorophyll for the entire data set was equal to 26.1870 ug/L. Rock Lake contained 33.30 ug/L of total phosphorous, while the average concen tration of total phosphorous for the entire data set was equal to 41.1043 ug/L. Finally, Rock Lake recorded a 1,176.70 ug/L concentration of total nitrogen, which was comparable to the total nitrogen concentration aver age of 1,017.1217 ug/L calculated for the entire data set. Table 8 displays a numeric value generat ed for the input concentrations of each DMU known as a ‘projection’. A DM U’s performance efficiency is improved when input variables are reduced or increas ed according to its ‘projection’. The numeric values provided for a DMU’s ‘proje ction’ can be either greater than or less than observed values. When a ‘project ion’ is less than observed values, the performance efficiency of a DMU will be improved by radially reducing input values. Conversely, when a ‘projection’ is greater than observed values, the performance efficiency of a DMU will be im proved by increasing input values. A

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73 ‘projection’ value is provided for each input variable. The DMU will attain optimal performance if the input variables are adj usted according to the ‘projection’. ‘DEA Solver’ also provided the difference between the ‘projection’ and the actual data recorded for the input variable. T he computed difference value was then converted into a percentage expressing t he percent change in the input variable necessary to achieve optimal performance. Table 8. Input Concentration, ‘Project ion’, Difference, and Percent Difference Concentration (in ug/L) ‘Projection’ Difference Percent Difference Chapman Lake 2.20E-02 Total Chlorophyll (ug/L) 5.2 0.114456 -5.08554 -97.80% Total Phosphorous (ug/L) 23 0.463594 -22.5364 -97.98% Total Nitrogen (ug/L) 1004 22.09875 -981.901 -97.80% Burrell Lake 8.95E-02 Total Chlorophyll (ug/L) 10 0.57067 -9.42933 -94.29% Total Phosphorous (ug/L) 48 1.997345 -46.0027 -95.84% Total Nitrogen (ug/L) 906.7 81.16832 -825.532 -91.05% Flynn Lake 9.72E-02 Total Chlorophyll (ug/L) 13.7 0.326981 -13.373 -97.61% Total Phosphorous (ug/L) 15.7 1.525912 -14.1741 -90.28% Total Nitrogen (ug/L) 1030 81.74528 -948.255 -92.06% Osceola, Lake 0.202258 Total Chlorophyll (ug/L) 4 0.489753 -3.51025 -87.76% Total Phosphorous (ug/L) 11.3 2.285516 -9.01448 -79.77% Total Nitrogen (ug/L) 696.7 122.4384 -574.262 -82.43% Garden Lake 6.16E-02 Total Chlorophyll (ug/L) 66.7 0.845974 -65.854 -98.73% Total Phosphorous (ug/L) 48.7 3.001683 -45.6983 -93.84% Total Nitrogen (ug/L) 2013.3 124.0922 -1889.21 -93.84% Sunset Lake 0.333099 Total Chlorophyll (ug/L) 1.5 0.499649 -1.00035 -66.69% Total Phosphorous (ug/L) 11.5 2.331693 -9.16831 -79.72% Total Nitrogen (ug/L) 430 124.9121 -305.088 -70.95% Thonotosassa, Lake 0.060586 Total Chlorophyll (ug/L) 99.7 1.003863 -98.6961 -98.99% Total Phosphorous (ug/L) 204 3.51352 -200.486 -98.28% Total Nitrogen (ug/L) 2356.7 142.7828 -2213.92 -93.94% Hiawatha, Lake 0.255189 Total Chlorophyll (ug/L) 14 1.103406 -12.8966 -92.12% Total Phosphorous (ug/L) 16.5 3.861922 -12.6381 -76.59% Total Nitrogen (ug/L) 615 156.9411 -458.059 -74.48% Echo Lake 0.270585 Total Chlorophyll (ug/L) 4.5 1.217634 -3.28237 -72.94% Total Phosphorous (ug/L) 16.3 4.310492 -11.9895 -73.56% Total Nitrogen (ug/L) 656.7 177.6934 -479.007 -72.94% Weeks, Lake 7.09E-02 Total Chlorophyll (ug/L) 152.4 1.346225 -151.054 -99.12% Total Phosphorous (ug/L) 264 4.711786 -259.288 -98.22% Total Nitrogen (ug/L) 2699 191.478 -2507.52 -92.91% Armistead, Lake 0.414212 Total Chlorophyll (ug/L) 4 1.656848 -2.34315 -58.58% Total Phosphorous (ug/L) 17.5 6.192533 -11.3075 -64.61%

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74 Table 8 (continued). Input Concentration, ‘Projection’, Difference, and Percent Difference Total Nitrogen (ug/L) 656.7 272.0131 -384.687 -58.58% Alice, Lake 0.750035 Total Chlorophyll (ug/L) 2.6 1.914198 -0.6858 -26.38% Total Phosphorous (ug/L) 19 6.699693 -12.3003 -64.74% Total Nitrogen (ug/L) 363 272.2628 -90.7372 -25.00% Harvey, Lake 0.232295 Total Chlorophyll (ug/L) 38.5 1.528914 -36.9711 -96.03% Total Phosphorous (ug/L) 27.3 6.341656 -20.9583 -76.77% Total Nitrogen (ug/L) 1330 308.9525 -1021.05 -76.77% Virginia, Lake 0.216015 Total Chlorophyll (ug/L) 32 2.16162 -29.8384 -93.24% Total Phosphorous (ug/L) 36 7.565671 -28.4343 -78.98% Total Nitrogen (ug/L) 1423.3 307.4545 -1115.85 -78.40% Rock Lake 0.284234 Total Chlorophyll (ug/L) 29.3 2.351472 -26.9485 -91.97% Total Phosphorous (ug/L) 33.3 8.230151 -25.0698 -75.28% Total Nitrogen (ug/L) 1176.7 334.4577 -842.242 -71.58% Josephine Lake 0.355964 Total Chlorophyll (ug/L) 34.7 2.334056 -32.3659 -93.27% Total Phosphorous (ug/L) 23.3 8.293959 -15.006 -64.40% Total Nitrogen (ug/L) 965 343.5052 -621.495 -64.40% Pretty Lake 0.525283 Total Chlorophyll (ug/L) 10 1.735405 -8.26459 -82.65% Total Phosphorous (ug/L) 14 7.353956 -6.64604 -47.47% Total Nitrogen (ug/L) 695 365.0714 -329.929 -47.47% Cypress Lake 1 Total Chlorophyll (ug/L) 1.5 1.5 0 0.00% Total Phosphorous (ug/L) 7 7 0 0.00% Total Nitrogen (ug/L) 375 375 0 0.00% James, Lake 0.56 Total Chlorophyll (ug/L) 5.5 1.5 -4 -72.73% Total Phosphorous (ug/L) 12.5 7 -5.5 -44.00% Total Nitrogen (ug/L) 670 375 -295 -44.03% Keystone Lake 1 Total Chlorophyll (ug/L) 3 3 0 0.00% Total Phosphorous (ug/L) 10.5 10.5 0 0.00% Total Nitrogen (ug/L) 426.7 426.7 0 0.00% Brant, Lake 0.808587 Total Chlorophyll (ug/L) 12.5 3.95103 -8.54897 -68.39% Total Phosphorous (ug/L) 21.7 13.82861 -7.87139 -36.27% Total Nitrogen (ug/L) 695 561.9682 -133.032 -19.14% Thomas Lake 0.793604 Total Chlorophyll (ug/L) 42 3.979923 -38.0201 -90.52% Total Phosphorous (ug/L) 20.3 13.92973 -6.37027 -31.38% Total Nitrogen (ug/L) 713.3 566.0777 -147.222 -20.64% Hanna Lake 0.387944 Total Chlorophyll (ug/L) 15 4.080367 -10.9196 -72.80% Total Phosphorous (ug/L) 44 14.28128 -29.7187 -67.54% Total Nitrogen (ug/L) 1496 580.3642 -915.636 -61.21% For this particular study, input vari able data belonging to inefficiently performing lakes must be reduced to achi eve optimal water quality conditions. The ‘projection’ values for those lakes t hat did not perform optimally are all less

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75 than the observed input values. Therefor e, the input concentrations must be minimized to achieve optimum lake wate r quality performance. The ‘projection’ values for both lakes that performed at optimum efficiency ar e the same as the observed input values. This observation refl ects that no alterations to the actual input values are necessary to achieve optimum efficiency for those lakes that already received a performance rating of one. Cypress Lake and Keystone Lake both received performance ratings of one, a nd their ‘projection’ values are equal to the observed input values. This indicates that both Cypress Lake and Keystone Lake require no input concentrati on adjustments to function at an optimal level. According to the ‘proje ction’ values, the two lakes performing at optimum efficiency require no further adjustments regarding input variable concentrations. Meanwhile, lakes that performed less than efficiently must reduce input variable concentrations according to ‘projection’ values that were all less than actually observed values. The ‘p rojection’ values computed for this model support input minimization when a ttempting to improve lake water quality performance. The CCR-I model is particularly useful because it generates a measurement known as a ‘slack’. This measurement is provided for the input and output variables of each DMU, or lake in this instance. ‘Slack’ is a scalar measurement that indicates the nece ssary input and output augmentations to produce an optimally performing DMU (C ooper et al. 2000). Input and output variables should be adjusted according to the numeric values provided for the ‘slack’ measurement. In this particula r DEA, the ‘slacks’ measure excesses in

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76 the input variables and shortages in t he single output variable. For this CCR-I model, the ‘slack’ measurem ent provided for the input variables indicate the reductions necessary to obtain optimum la ke water quality performance. ‘Slack’ measurements for the single output variabl e indicate the increases required to obtain optimum lake water quality performanc e. Table 9 provided below displays the ‘slack’ measurements fo r the input and output vari ables of each lake. Table 9. CCR-I ‘Slack’ Measurements Lake Name Rating Excess in Total Chlorophyll (in ug/L) Excess in Total Phosphorous (in ug/L) Excess in Total Nitrogen (in ug/L) Shortage in Natural Land Area (in acres) Chapman Lake 0.0220 0.0000 0.0427 0.0000 0.0000 Burrell Lake 0.0895 0.3245 2.2996 0.0000 0.0000 Flynn Lake 0.0972 1.0045 0.0000 18.3623 0.0000 Osceola, Lake 0.2023 0. 3193 0.0000 18.4748 0.0000 Garden Lake 0.0616 3.2652 0.0000 0.0000 0.0000 Sunset Lake 0.3331 0.0000 1.4989 18.3204 0.0000 Thonotosassa, Lake 0.0606 5.0366 8.8460 0.0000 0.0000 Hiawatha, Lake 0.2552 2.4692 0.3487 0.0000 0.0000 Echo Lake 0.2706 0.0000 0.1000 0.0000 0.0000 Weeks, Lake 0.0709 9.4656 14.0174 0.0000 0.0000 Armistead, Lake 0.4142 0.0000 1.0562 0.0000 0.0000 Alice, Lake 0.7500 0.0359 7.5510 0.0000 0.0000 Harvey, Lake 0.2323 7.4144 0.0000 0.0000 0.0000 Virginia, Lake 0.2160 4.7509 0.2109 0.0000 0.0000 Rock Lake 0.2842 5.9766 1.2348 0.0000 0.0000 Josephine Lake 0.3560 10.0179 0.0000 0.0000 0.0000 Pretty Lake 0.5253 3.5174 0.0000 0.0000 0.0000 Cypress Lake 1.0000 0.0000 0.0000 0.0000 0.0000 James, Lake 0.5600 1.5800 0.0000 0.2000 0.0000 Keystone Lake 1.0000 0.0000 0.0000 0.0000 0.0000 Brant, Lake 0.8086 6.1563 3.7177 0.0000 0.0000 Thomas Lake 0.7936 29.3514 2.1804 0.0000 0.0000 Hanna Lake 0.3879 1.7388 2.7883 0.0000 0.0000

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77 For this particular model, input vari able data belonging to inefficiently performing lakes must be reduced to achi eve optimal water quality conditions. The ‘slack’ measurements for input variables of those lakes t hat did not perform optimally represent reductions. Theref ore, the input concentrations must be minimized to achieve optimum lake water quality performance. ‘Slack’ measurements for the output variable did not vary from zero because the input oriented CCR model was applie d. The ‘slacks’ for the output variable were not considered by the model bec ause it was input oriented. Inefficiently performing lakes we re capable of receiving ‘slack’ measurements equal to zero for individual variables, however, these lakes could not receive ‘slack’ measurements of ze ro for each variable. The ‘slack’ measurement for at least a single variabl e was not equal to zero for those DMUs that did not obtain an optimum perform ance rating of one. These ‘slack’ measurements reflected that efficiently performing lakes such as Cypress and Keystone required no adjustments to achieve optimization. The final component explaining the re sults from the CCR-I model is a correlation matrix. The correlation matrix contains proportions that describe the relationship between variables included in the CCR-I model. These proportions are derived from correlation coeffici ents and are known as coefficients of determination. A coefficient of determi nation is a proportion that reveals the interrelatedness between variables. This numerical value quantifies how much a particular variable is responsible for t he outcome of an accompanying variable. The correlation matrix provides numerica l values for the proportion of a variable

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78 that explains another variable. For this CCR-I model, the proportions of particular interest are thos e that provide descriptions of the relationship between input and output variables. These proportions will quantify the level of interaction between input and output variables. Interp retation of these figures will expose how greatly natural land use area infl uences lake nutrient concentrations. Correlation proportions reveal the strengt h of relationship between natural land use area and nutrient concentrations. Proportions describing input and output interaction will quantify the influence of nat ural land use area in regulating lake nutrient concentrations. The correlati on matrix for the CCR-I model has been provided in Table 10 below. Table 10. CCR-I Variable Correlation Matrix Total Chlorophyll Total Phosphorous Total Nitrogen Natural Land Use Area Total Chlorophyll 1 0.9224 0.9019 0.1188 Total Phosphorous 0.9224 1 0.8507 0.2007 Total Nitrogen 0.9019 0.8507 1 0.1982 Natural Land Use Area 0.1188 0.2007 0.1982 1 BCC-I Model Results Performance ratings computed by the BCC-I model describe the relationship between lake nutrient loads and surrounding land use. The BCC-I model returned an average performance rati ng of 0.5824 for the entire set of lakes. This value indicates that the entire set of lakes oper ated at 58.24% of optimal performance efficiency, which wa s a significant improvement over the

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79 results from the CCR-I model The standard deviation for the entire set of lake performance ratings equaled 0.3069. This value indicates a relatively wide distribution of performance ratings for t he entire set of lakes. Performance ratings from the previously conduc ted CCR-I model had a standard deviation equal to 0.2968, which was similar to t hat of the BCC-I model. Both input oriented models obtained performance rating standard deviations that reflected a wide range of results. The lake wate r quality performance ratings derived from the BCC-I model have been provided in Tabl e 11. As expected, these ratings increase for lakes surrounded by greater am ounts of naturally preserved land. Performance ratings also predictably incr ease for those lakes containing lower concentrations of the sele cted input variables.

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80 Table 11. BCC-I Lake Performance Ratings and Rank Lake Name Performance Rating Lake Performance Rank Alice, Lake 1.0000 1 Brant, Lake 1.0000 1 Cypress Lake 1.0000 1 Hanna Lake 1.0000 1 Keystone Lake 1.0000 1 Thomas Lake 1.0000 1 Sunset Lake 1.0000 7 Osceola, Lake 0.6195 8 Hiawatha, Lake 0.6049 9 Echo Lake 0.5676 10 Armistead, Lake 0.5666 11 James, Lake 0.5600 12 Pretty Lake 0.5388 13 Flynn Lake 0.4459 14 Burrell Lake 0.4003 15 Josephine Lake 0.3865 16 Chapman Lake 0.3720 17 Rock Lake 0.3157 18 Harvey, Lake 0.2814 19 Virginia, Lake 0.2618 20 Garden Lake 0.1853 21 Thonotosassa, Lake 0.1540 22 Weeks, Lake 0.1345 23 The BCC-I performance ratings generat ed during this study follow general trends that describe the relationship bet ween lake water quality and land use. General trends in the data are graphically represented by Figures 10, 11, and 12 for total chlorophyll, total phosphorous, and total nitrogen, respectively. These scatter plots represent the strength of relationship between a respective input variable and lake performance. The statistical lines of best-fit are provided for each of these scatter plots. The relationship between each water quality parameter and lake performanc e is depicted by the statis tical lines of best-fit.

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81 The best-fit lines support the trend that lakes cont aining lower input variable concentrations typically obtained higher performance ratings. After observing this trend, it can be stated that lake per formance shared an indirect relationship with the input variables. Accordingly, la ke performance optimiz ation is achieved by minimizing inputs. This outcome supports the previously mentioned expectations that input mi nimization would result in optimum lake performance. When viewing these graphs, the reader should keep in mind that the calculated R2 values provided in each scatter plot are only a partial measure of the model’s effectiveness. The R2 values in each scatter plot quantify the strength of relationship between the pl otted water quality parameter and lake performance. The R2 values provided in Figures 10, 11, and 12 should not be considered a measure of how effective the entire model is at predicting lake performance.

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82 Figure 10. Total Chlorophyll Versus BCC-I Lake Performance Rating Figure 11. Total Phosphorous Versus BCC-I Lake Performance Rating

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83 Figure 12. Total Nitrogen Versus BCC-I Lake Performance Rating General trends in the data are graphi cally represented by Figures 13 and 14 for natural land area and natural land percentage, respectively. These scatter plots represent the strength of relati onship between the output variable and lake performance. The statistical lines of bestfit are provided for both output oriented scatter plots. The relationship between natural land and lake performance is depicted by the statistical lines of best-fit. The best-fit lines support the trend that lakes surrounded by more natural land typically received higher performance ratings. As the single output variable increased, lake performance ratings typically improved. After observing th is trend, it can be stated that lake performance shared a direct relationship with the output variable. Accordingly,

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84 lake performance optimization is achieved by maximizing outputs. This outcome supports the previously mentioned expecta tions that output maximization would result in optimum la ke performance. When viewing these graphs, the reader should keep in mind that the calculated R2 values provided in each scatter plot are only a partial measure of the model’s effectiveness. The R2 values in each scatter plot quantify the strength of relationship between natural land and lake performance. The R2 values provided in Figures 13 and 14 s hould not be considered a measure of how effective the entire model is at predicting lake performance. Figure 13. Natural Land Use Area Vers us BCC-I Lake Performance Rating

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85 Figure 14. Natural Land Percentage Vers us BCC-I Lake Performance Rating Each of the lakes included in this st udy were assigned a ranking based on the performance ratings. Seven separate lakes claimed a performance rating of one, however, only six were classified as optimally performing. Sunset Lake achieved a performance rating of one, but it failed to obtain ‘slack’ measurements equal to zero for each of the input variabl es. Therefore, the number one rank as well as an optimum performance rating of one was only achieved by the following six lakes: Lake Alice, Lake Brant, Cy press Lake, Hanna Lake, Keystone Lake, and Thomas Lake. 178.5218 acres of natural land were located within a two mile radius from Lake Alice translating into 1.7454% of Lake Alice’s two mile radius delineation. Lake Brant was situated in a two mile radius delineation that contained 368.4807 acres of naturally preser ved land. Naturally preserved land occupied 3.5855% of Lake Brant’s two mile radius delineation. Cypress Lake

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86 was located within a two mile radius of 244.1508 acres classified as natural land. Naturally preserved land occupied 2.7560% of Cypress Lake’s two mile radius delineation. 380.5429 acres of natural land we re located within a two mile radius from Hanna Lake. Hanna Lake was situated in a two mile radius delineation that contained 3.9308% natural land cover. Keystone Lake was surrounded by 279.7858 acres of natural land within a two mile radius. Keystone Lake was situated in a two mile radius delineat ion that contained 1.8600% natural land cover. Finally, Thomas Lake was situated in a two mile radius delineation that contained 371.1753 acres of naturally pres erved land. Natural land occupied 3.6078% of the two mile radius surr ounding Thomas Lake. Input variable concentrations for these lakes were low re lative to the nutrient loads of other inefficiently performing lake s included in the study. Lake Weeks received the lowest performance rating amongst the set of lakes at 0.1345. This lake obtained the last ranking because it is located in a two mile radius delineation wit h only 125.5515 acres of natur ally preserved land. This acreage of naturally preserved land was significantly below the average calculated for the entire data set which was 179.6641. Naturally preserved land only occupied 1.3223% of Lake Week’s tw o mile radius delineation. This percentage of naturally preserved l and was significantly below the average calculated for the entire data set wh ich was 1.8175%. The input variable concentrations for this lake also contri buted to its poor performance rank. Each input variable concentration was high relati ve to the nutrient loads of other lakes included in the study. In fact, Lake Weeks consistently contained the highest

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87 concentrations of total chlorophyll, tota l phosphorous and total nitrogen. From this observation, it is blatantly evident that nutrient concentrations within Lake Weeks hindered its water quality performance. Directly in the middle of the perfo rmance ranks, Lake James obtained a rating of 0.5600. This lake was repres entative of the average performance for the entire data set. As previously stat ed, the average perfo rmance rating for the entire set of lakes was equal to 0.5824. Input and output variable data for Lake James was also representative of the aver ages calculated for the entire data set. Lake James was located within two miles of 244.1508 acres of natural land. On average, the two mile radi us delineations established for this study contained 179.6641 acres of natural land. The standard deviation for natural land use area data collected during this study was equal to 103.8114 acres. Therefore, the natural land area surrounding Lake James wa s representative of the entire data set because it fell within one standard deviati on of the average. Lake James was located in a two mile radius delineation occupied by 2.7597% natural land use. On average, the two mile r adius delineations establis hed in this study were occupied by 1.8175% natural land use. The standard deviation for natural land use percent surrounding the study lakes wa s equal to 1.0354%. Therefore, it can be stated that the percentage of natur al land surrounding Lake James was representative of the entire data set because it fell within one standard deviation of the average. The total chlorophyll concentration for Lake James equaled 5.50 ug/L, while the average concentration of total chlorophyll for the entire data set was equal to 26.1870 ug/L. Lake Ja mes contained 12.50 ug/L of total

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88 phosphorous, while the average concentration of total phosphorous for the entire data set was equal to 41.1043 ug/L. Fina lly, Lake James recorded a 670.00 ug/L concentration of total nitrogen, which wa s somewhat comparable to the total nitrogen concentration average of 1,017. 1217 ug/L calculated for the entire data set. Like the CCR-I model, the BCC-I model is particularly useful because it generates a measurement known as a ‘slack’ This measurement is provided for the input and output variables of each DMU, or lake in this instance. A lake’s performance efficiency is optimized when input and output variables are reduced or increased according to its ‘slack’ (Cooper et al. 2000). Input and output variables should be adjusted according to the numeric values provided for the ‘slack’ measurement. In this particula r DEA, the ‘slacks’ measure excesses in the input variables and shortages in the single output variable. Therefore, input variable ‘slacks’ represent reductions required to accomplish optimum DMU performance, and output variable ‘slacks’ represent increases required to accomplish optimum DMU performance. Table 12 provided below displays the ‘slack’ measurements for the input and output variables of each lake.

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89 Table 12. BCC-I ‘Slack’ Measurements Lake Name Rating Excess in Total Chlorophyll (in ug/L) Excess in Total Phosphorous (in ug/L) Excess in Total Nitrogen (in ug/L) Shortage in Natural Land Area (in acres) Chapman Lake 0.3720 0.2916 0.0000 0.0000 221.2163 Burrell Lake 0.4003 1.4035 0.2169 0.0000 125.2982 Flynn Lake 0.4459 4.6082 0.0000 84.2348 190.9266 Osceola, Lake 0.6195 0.9779 0.0000 56.5835 164.4326 Garden Lake 0.1853 10.6712 0.0000 0.0000 151.7635 Sunset Lake 1.0000 0.0000 4.5000 54.9995 162.8220 Thonotosassa, Lake 0.1540 12.7566 12.4218 0.0000 84.8978 Hiawatha, Lake 0.6049 6.6954 0.0000 0.0000 124.9394 Echo Lake 0.5676 0.8478 0.0000 0.0000 115.3675 Weeks, Lake 0.1345 17.8967 16.5063 0.0000 52.9685 Armistead, Lake 0.5666 0.4991 0.0000 0.0000 50.2358 Alice, Lake 1.0000 0.0000 0.0003 0.0000 0.0000 Harvey, Lake 0.2814 9.2727 0.0000 0.0000 38.8142 Virginia, Lake 0.2618 6.6544 0.0000 0.0000 29.2962 Rock Lake 0.3157 7.4280 0.0000 0.0000 5.6334 Josephine Lake 0.3865 11.7283 0.0000 0.0000 8.0662 Pretty Lake 0.5388 3.8381 0.0000 0.0000 3.0719 Cypress Lake 1.0000 0.0000 0.0000 0.0000 0.0000 James, Lake 0.5600 1.5800 0.0000 0.2000 0.0000 Keystone Lake 1.0000 0.0000 0.0000 0.0000 0.0000 Brant, Lake 1.0000 0.0000 0.0000 0.0000 0.0000 Thomas Lake 1.0000 0.0000 0.0000 0.0000 0.0000 Hanna Lake 1.0000 0.0000 0.0000 0.0000 0.0000 For this particular model, input vari able data belonging to inefficiently performing lakes must be reduced to achi eve optimal water quality conditions. Output variable data belonging to i nefficiently performing lakes must be increased to achieve optimal water quality conditions. Inefficiently performing lakes were capable of receiving ‘slack’ m easurements equal to zero for individual variables, however, these lakes could not receive ‘slack’ measurements of zero for each variable. With the exception of Sunset Lake, ‘slack’ measurements for each variable of those lakes that achi eved optimum performance ratings equaled

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90 zero. These ‘slack’ measurements refl ected that efficiently performing lakes required no adjustments to achieve opt imization. Sunset Lake received a performance rating of one, however, severa l ‘slack’ measurem ents belonging to both these DMUs were not equal to zero and indicated that changes were necessary to achieve optimization. This represents a rare case in which a DMU obtains a performance rating of one, but the ‘slack’ measurements indicate that variable adjustments are still necessary to acquire optimized performance. It should be mentioned that Lake Alice did not obtain a ‘slack’ measurement of zero for each variable. Lake Alice’s ‘slack’ measurement for total phosphorous was equal to 0.0003. It was determined that such a small measurement was negligible when considering the overall performance of Lake Alice. For the purpose of this analysis, Lake Alice was considered an optimally performing DMU, and its negligible non-zero ‘slack ’ measurement for total phosphorous was ignored. Overall, the ‘slack’ meas urements support input minimization and output maximization when attempting to ac hieve optimum lake performance. The final component explaining the re sults from the BCC-I model is a correlation matrix. The correlation matrix contains proportions that describe the relationship between variables included in the BCC-I model. The correlation matrix provides numerical values for t he proportion of a variable that explains another variable. For this BCC-I model, t he proportions of particular interest are those that provide descriptions of the relations hip between input and output variables. These proportions will quantify the level of interaction between input and output variables. Interpretation of these figures will ex pose how greatly

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91 natural land use area influences lake nutrient concentrations. Correlation proportions reveal the str ength of relationship between natural land and nutrient concentrations. Proportions describing input and output interaction will quantify the influence of natural land use area in r egulating lake nutrient concentrations. The correlation matrix for the BCC-I model of this thesis has been provided in Table 13 below. If the reader refers to the correlation matrix provided for the CCR-I model, it will be evident that the pr oportions within this table are equal between the two input oriented models. Table 13. BCC-I Variable Correlation Matrix Total Chlorophyll Total Phosphorous Total Nitrogen Natural Land Use Area Total Chlorophyll 1 0.9224 0.9019 0.1188 Total Phosphorous 0.9224 1 0.8507 0.2007 Total Nitrogen 0.9019 0.8507 1 0.1982 Natural Land Use Area 0.1188 0.2007 0.1982 1 Additive Model Results The Additive model produces performance ratings influenced equally by both input and output variables. These ratings describe the relationship between lake performance and nutrient loads as well as lake performance and natural land use area. Primarily, the performanc e ratings derived fr om the Additive model are intended to describe the relati onship between lake nutrient loads and surrounding land use. The Additive model returned an average performance rating of 0.6333 for the entire set of la kes, which was similar to the average

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92 performance rating obtained during the BCC-I model. This value indicates that the entire set of lakes oper ated at 63.33% of optimal performance efficiency, which was a significant improvement over the results from the CCR-I model but similar to the results obtained during t he BCC-I model. The standard deviation for the entire set of lake performanc e ratings equaled 0.2671. This value indicates a relatively wide distribution of performance ratings for the entire set of lakes. Performance ratings from t he previously conducted CCR-I and BCC-I models had standard deviations equal to 0.2968 and 0.3069, respectively. Performance rating standard deviations ca lculated for each of the models are relatively similar and reflect a wide range of results. The lake water quality performance ratings derived from the A dditive model have been provided in Table 14 along with a column for ‘st ability’ values. The meaning and interpretation of ‘stability’ values will be di scussed further in latter portions of this section. As expected, these rating s increase for lakes surrounded by greater amounts of naturally preserved land. Performance ratings also predictably increase for those lakes containing lower concentrations of t he selected input variables.

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93 Table 14. Additive Lake Performance Summary Lake Name Performance Rating ‘Stability’ Value Lake Performance Rank According to ‘Stability’ Brant, Lake 1.0000 0.1713 1 Cypress Lake 1.0000 0.0851 2 Hanna Lake 1.0000 0.0650 3 Keystone Lake 1.0000 0.0393 4 Thomas Lake 1.0000 0.0273 5 Alice, Lake 1.0000 0.0118 6 Sunset Lake 0.6463 0.0000 7 James, Lake 0.8014 -0.0936 8 Armistead, Lake 0.7009 -0.0955 9 Osceola, Lake 0.6203 -0.0955 10 Echo Lake 0.6377 -0.1146 11 Pretty Lake 0.7345 -0.1293 12 Chapman Lake 0.4910 -0.1413 13 Flynn Lake 0.4955 -0.2117 14 Hiawatha, Lake 0.5748 -0.2311 15 Josephine Lake 0.4991 -0.3091 16 Burrell Lake 0.4462 -0.3246 17 Harvey, Lake 0.4318 -0.4167 18 Rock Lake 0.4713 -0.4851 19 Virginia, Lake 0.4275 -0.5613 20 Garden Lake 0.2803 -0.9820 21 Weeks, Lake 0.1356 -1.4043 22 Thonotosassa, Lake 0.1715 -1.5493 23 Each of the lakes included in this st udy were assigned a ranking based on the ‘stability’ value. The ‘stability’ val ue is a measurement unique to the Additive model. This measurement quantifies DMU efficiency at a finer scale than the traditional DEA performance rating. DMUs that receive a maximum performance rating of one are assigned positive ‘stability ’ values, while inefficiently performing DMUs are assigned negative ‘stability’ values. ‘Stability’ values directly indicate DMU efficiency levels. DMUs with higher levels of efficiency receive greater

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94 ‘stability’ values. The major advantage of ‘s tability’ values is that it allows the analysis to further rank the effici ency of those DMUs with a maximum performance rating of one. The Additive ‘stability’ values gener ated during this study follow general trends that describe the re lationship between lake water quality and land use. General trends in the data are graphically represented by Figures 15, 16, and 17 for total chlorophyll, total phosphorous, and total nitrogen, respectively. These scatter plots represent the strength of relationship between a respective input variable and lake ‘stability’ values. The st atistical lines of bestfit are provided for each of these scatter plots. The relationship between each water quality parameter and lake ‘stability’ values is depicted by the stat istical lines of best-fit. The best-fit lines support the trend that lakes cont aining lower input variable concentrations typically obtained higher ‘sta bility’ values. After observing this trend, it can be stated that lake perform ance shared an indirect relationship with the input variables. Accordingly, lake performance optimization is achieved by minimizing inputs. This outcome supports the previously mentioned expectations that input minimization would resu lt in optimum lake performance. When viewing these graphs, the reader should keep in mind that the calculated R2 values provided in each scatter plot are only a partial measure of the model’s effectiveness. The R2 values in each scatter plot quantify the strength of relationship between the plo tted water quality parameter and lake

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95 ‘stability’ values. The R2 values provided in Figures 15, 16, and 17 should not be considered a measure of how effective the entire model is at predicting lake performance. Figure 15. Total Chlorophyll Versus Additive Lake ‘Stability’ Value

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96 Figure 16. Total Phosphorous Versus Additive Lake ‘Stability’ Value Figure 17. Total Nitrogen Versus Additive Lake ‘Stability’ Value

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97 General trends in the data are graphi cally represented by Figures 18 and 19 for natural land area and natural land per centage, respectively. These scatter plots represent the strength of relati onship between the output variable and lake ‘stability’ values. The statistical lines of best-fit are provided for both output oriented scatter plots. The relationship between natural land and lake ‘stability’ values is depicted by the statistical lines of best-fit. The best-fit lines support the trend that lakes surrounded by more natural land typically received higher ‘stability’ values. As the single output va riable increased, lake ‘stability’ values typically improved. After observing th is trend, it can be stated that lake performance shared a direct relationship with the output variable. Accordingly, lake performance optimization is achieved by maximizing outputs. This outcome supports the previously mentioned expecta tions that output maximization would result in optimum la ke performance. When viewing these graphs, the reader should keep in mind that the calculated R2 values provided in each scatter plot are only a partial measure of the model’s effectiveness. The R2 values in each scatter plot quantify the strength of relationship bet ween natural land and lake ‘stability’ values. The R2 values provided in Figures 18 and 19 s hould not be considered a measure of how effective the entire model is at predicting lake performance.

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98 Figure 18. Natural Land Use Area Versus Additive Lake ‘Stability’ Value Figure 19. Natural Land Percentage Versus Additive Lake ‘Stability’ Value

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99 In the Additive model pe rformed for this thesis, six separate lakes claimed an optimum performance rating of one, wh ich is similar to the BCC-I model. Lake Alice, Lake Brant, Cypress Lake, Hanna Lake, Keystone Lake, and Thomas Lake all achieved an optimum performance rati ng of one. The ‘stability’ values corresponding to each of these lakes allo wed them to be further ranked beyond the performance rating of one. According to the ‘stability’ values, Lake Brant achieved the highest performance efficien cy followed in order by Cypress Lake, Hanna Lake, Keystone Lake, Thomas Lak e, and Lake Alice. Lake Brant received the greatest ‘stability’ value at 0. 1713. Therefore, it can be stated that Lake Brant performed at the highest level of efficiency in the Additive model. Lake Brant was located within a two mile radius that contained 368.4807 acres of naturally preserved land translating into 3.5855% of Lake Brant’s two mile radius delineation. As anticipated, input vari able concentrations for Lake Brant were low relative to the nutrient loads of other lakes included in the study. Lake Thonotosassa received the lowest ‘stability’ value amongst the set of lakes at -1.5493. This lake obtained the last ranking because it is located within a two mile radius of only 93.6222 acres of naturally preserved land. Naturally preserved land only occupied 0.6194% of Lake Thonotosassa’s two mile radius delineation. Lake Thonotosassa’s ‘stab ility’ value was the lowest amongst the entire set of lakes partially due to its i nput variable concentrations. Each input variable concentration was high relative to the nutrient loads of other lakes

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100 included in the study. In fact, Lake Thonotosassa consistently contained the second highest concentration of each type of input variable. Input variable concentrations for Lake Thonotosassa negatively impacted its water quality performance and subsequently reduced it s ‘stability’ value. Directly in the middle of the perform ance ranks, Pretty Lake obtained a rating of 0.7345 and a ‘stability’ value of -0 .1293. This lake was representative of the average performance for the entire dat a set. As previously stated, the average performance rating for the entire set of lakes was equal to 0.6333. Also, the average ‘stability’ value for the entire set of lakes was equal to -0.2933. Input and output variable data for Pretty Lake wa s also representative of the averages calculated for the entire data set. Pre tty Lake was located within a two mile radius containing 238.1067 acres of natural land. On average, the two mile radius delineations established during th is study contained 179.6641 acres of natural land. The standard deviation fo r natural land area was equal to 103.8114 acres. Therefore, t he natural land area surrounding Pretty Lake was representative of the entire data set because it fell within one standard deviation of the average. Pretty Lake was loca ted in a two mile radius delineation occupied by 2.2794% natural land use. On average, the two mile radius delineations established in this study were occupied by 1.8175% natural land use. The standard deviation for natural land use percent surrounding the study lakes was equal to 1.0354%. Therefore, it can be stated that the percentage of natural land surrounding Pretty Lake was representative of the entire data set because it fell within one standard deviation of the average. The total chlorophyll

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101 concentration for Pretty Lake equal ed 10.00 ug/L, wh ile the average concentration of total chlorophyll for the entire data set was equal to 26.1870 ug/L. Pretty Lake contained 14.00 ug/L of total phosphorous, while the average concentration of total phosphorous for t he entire data set was equal to 41.1043 ug/L. Finally, Pretty Lake recorded a 695. 00 ug/L concentration of total nitrogen, which was somewhat comparable to the total nitrogen concentration average of 1,017.1217 ug/L calculated fo r the entire data set. The Additive model is particularl y useful because it generates a measurement known as a ‘stability’ val ue. This measurement pertains to the individual efficiency of a DMU. The ‘stability’ value is a more accurate measurement of efficiency than the tradi tional DEA performance rating. DMU efficiency is directly measured by the ‘stab ility’ value. The ‘stability’ value is a useful measurement because it can be used to further classify the efficiency of individual DMUs beyond their DEA performanc e ratings. For this set of lake data, it was observed that in some instanc es the ‘stability’ value rankings did not directly correspond to the rankings that would have been determined by the DEA performance ratings. For ex ample, simply referring to the traditional performance ratings would have led one to rank Sunset Lake at tenth in overall efficiency, however, the ‘stability’ value unique to t he Additive model ranked Sunset Lake at seventh in overall efficiency. This discrepancy between the traditional DEA performance rating and ‘stability’ value is du e to the mathematical platform of the Additive model. Values for ‘stability’ are derived from a variati on of the equations

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102 used to produce the traditional performanc e ratings. Therefore, discrepancies between the two forms of measurement occur in rare instances. Comparing DEA Model Result s to Trophic State Index According to the Hillsborough County Water Atlas website, the Trophic State Index (TSI) assigns quantitative ratings to individual lakes based on measurements of biological productivity. TSI ratings are derived from data for total chlorophyll, total phosphorous, and to tal nitrogen. Essentially, TSI rates individual lakes according to nutrient loads that contribute to eutrophic conditions. TSI lake ratings are specifically derived from measurements for total phosphorous and chlorophyll-A concentration s along with Secchi depth. The TSI functions as a classification system that evaluates a lake based upon its nutrient loads. TSI measurements specifically focus on nutrient loads while rating the quality of water within individual lakes. The TSI uses a numeric scale from one to one hundred to express the quality of lake water. Lower values along the scale from one to one hundred are equivale nt to lower nutrient loads and environmentally beneficial lake water quality. Higher values along the scale from one to one hundred are equivalent to higher nutrient loads that contribute to environmentally harmful lake water quality. Aquatic conditions in lakes that receive lower TSI measurements are more environmentally beneficial. Higher TSI measurements reflect aquatic conditions that are not beneficial to naturally functioning ecologic systems. Table 15 displays the TSI measurements for each of the twenty-three lakes studied during this thesis. The TSI measurements for each of the study lakes were retriev ed from the Hillsborough County Water Atlas

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103 website. The table below also displa ys study lake performance ratings derived from each of the DEA models applied during the study. Table 15. Lake Performance Ratings and TSI Measurements Lake Name CCR-I Performance Rating BCC-I Performance Rating Additive Performance Rating Trophic State Index (TSI) Alice, Lake* 0.7500 1.0000 1.0000 33 Armistead, Lake 0.4142 0.5666 0.7009 41 Brant, Lake* 0.8086 1.0000 1.0000 53 Burrell Lake 0.0895 0.4003 0.4462 53 Chapman Lake 0.0220 0.3720 0.4910 45 Cypress Lake* 1.0000 1.0000 1.0000 27 Echo Lake 0.2706 0.5676 0.6377 42 Flynn Lake 0.0972 0.4459 0.4955 51 Garden Lake 0.0616 0.1853 0.2803 73 Hanna Lake* 0.3879 1.0000 1.0000 61 Harvey, Lake 0.2323 0.2814 0.4318 63 Hiawatha, Lake 0.2552 0.6049 0.5748 53 James, Lake 0.5600 0.5600 0.8014 40 Josephine Lake 0.3560 0.3865 0.4991 58 Keystone Lake* 1.0000 1.0000 1.0000 35 Osceola, Lake 0.2023 0.6195 0.6203 38 Pretty Lake 0.5253 0.5388 0.7345 58 Rock Lake 0.2842 0.3157 0.4713 60 Sunset Lake 0.3331 1.0000 0.6463 27 Thomas Lake* 0.7936 1.0000 1.0000 51 Thonotosassa, Lake 0.0606 0.1540 0.1715 82 Virginia, Lake 0.2160 0.2618 0.4275 64 Weeks, Lake 0.0709 0.1345 0.1356 85 indicates efficient DMUs accordi ng to both BCC-I and Additive models DEA performance ratings range from ze ro to one. Theoretically, higher ratings along this scale are indicative of environmentally beneficial lake water

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104 quality. Performance ratings closer to zero theoretically signify that a lake contains higher nutrient loads that contribut e to eutrophic conditions. Lakes that obtained performance ratings closer to one should contain lower nutrient loads that fail to establish eutrophic conditi ons. Therefore, higher DEA performance ratings should correspond to lower TS I measurements. DEA performance ratings in this study should share an indi rect relationship with TSI measurements. Lakes that obtained a higher performance rating should have received a lower TSI measurement. The performance ra tings derived from each of the DEA models used during this thesis are com pared to TSI in Figures 20, 21, and 22 displayed below. These scatter plots r epresent the strength of relationship between DEA performance ratings and TSI. T he statistical lines of best-fit along with their associated R2 value are provided for each of these scatter plots. The relationship between DEA performance ratings and TSI is depicted by the statistical lines of best-fit and R2. The best-fit lines supp ort the trend that DEA performance ratings correspond appropriate ly to TSI measurements. After observing this trend, it can be stated t hat DEA lake performance ratings shared an indirect relationship with TSI. DEA performance ratings derived during this thesis correspond appropriately to study lake TSI. Therefore, it can be stated that a majority of the study lakes received performance ratings reflecting actual lake water quality conditions as described by TSI measurements. This statement is appropriate for performance ratings deriv ed from each of the models used during this thesis. Overall, performance ratings derived from each of the DEA

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105 models provide an accurate representation of lake water quality. By comparing DEA performance ratings to TSI measurement s, it was verified that results from each of the models accurately descri be lake water quality conditions. Figure 20. CCR-I Performance Rating Versus TSI

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106 Figure 21. BCC-I Performance Rating Versus TSI Figure 22. Additive Performance Rating Versus TSI

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107 Discussion Input and output variables influenced the performance ratings derived from the DEA. Differences in performanc e ratings for each lake reflect changes in input and output variable data. D EA performance ratings generated during this study fluctuate according to trends in the input and output variable data. Minimizing input data and maximizing the si ngle output variable resulted in higher performance ratings. Therefore, lake wa ter quality was optimized by minimizing total chlorophyll, total phosphorous, and to tal nitrogen, while maximizing natural land area within a two mile radius. This general trend is exposed by Figures 5 through 19 comparing the individual variabl es to each lake’s performance rating. DEA performance ratings reflect lake water quality conditions. Performance ratings provided a numerical scale for quantifying the level of lake water quality optimization. In this ca se, higher performance ratings represented higher levels of lake water quality optimiz ation. The interaction between nutrient loads and natural land uses determi ned the level of lake water quality optimization. Results from the DEA revealed notable trends that describe the relationship between land use and surface water quality of lakes in Hillsborough County. Lakes located within a two mile radius containing higher amounts of natural land area typically received a hi gher performance rating. Figures 8, 9,

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108 13, 14, 18, and 19 graphically support this trend in the relationship between lake water quality performance and natural land use area. An optimum performance rating of one was achieved by only two separate DMUs, Cypress Lake and Keystone Lake, in the CCR-I model. Keystone Lake and Cypress Lake were located in two mile radius delineations containing the fourth and fifth highest amount of natural land area, respectively. This statistic undoubtedly contributed to their optimum performance ratings. An optimum performance rating of one was achieved by seven DMUs, Lake Alic e, Lake Brant, Cypress Lake, Hanna Lake, Keystone Lake, Sunset Lake, and T homas Lake, in the BCC-I model. Upon further scrutiny of t he BCC-I model results, the ‘slack’ measurements indicated that Sunset Lake was not in fact operating at optimum efficiency. Therefore, it should be st ated that only six lakes we re optimized by the BCC-I model. With the exception of Lake Alice, optimally performing lakes were located in advantageous two mile radi us delineations that consis tently contained at least 64.4867 acres above the average fo r the entire data set. In fact, five of the six remaining optimally performing lakes were surrounded by the five highest measurements for natural land area. Hanna Lake, Thomas Lake, Lake Brant, Keystone Lake, and Cypress Lake represent the five optimally performing lakes that were situated within two mile radius delineations of the first, second, third, fourth, and fifth highest amounts of natur al land area, respectively. When focusing attention on these five particular la kes, it became especially evident that natural land uses positively influenced water quality performance ratings. An optimum performance rating of one was obt ained by six DMUs, Lake Alice, Lake

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109 Brant, Cypress Lake, Hanna Lake, Keyst one Lake, and Thomas Lake, in the Additive model. With the exception of Lake Alice, optimally performing lakes were located in advantageous two mile r adius delineations that consistently contained at least 64.4867 acres above the average for the entire data set. The reader may notice that the same six lake s isolated by the Additive model were also specifically identified during t he BCC-I model discussion above. When focusing attention on these si x particular lakes, it bec ame especially evident that natural land uses positively influenced water quality performance ratings. The Additive model further corroborates t hat optimum performance ratings were significantly dependent upon the amount of natural land surrounding a lake. Just as the other two input or iented models have indicated, the Additive model confirms that natural land uses possess a positive influence on lake water quality performance. The trend discussed in the previous paragraph indicates that a designated land cover composed of a greater perc entage of natural us e area will generally contain lakes with lower nutrient load concen trations. Therefor e, nutrient loading within lakes shares an indirect relationshi p with natural land us e area. Each of the DEA models applied in this thesis supported the assumption that natural lands protect lakes from environmentally harmful nutrient loads. Natural lands assimilate soluble pollutants that w ould otherwise be directly deposited into aquatic ecosystems. In this manner, natural lands function as a pollution filtration mechanism for freshwater resources. This concept represents an area of

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110 potential future scientific research. Fu ture studies could focus on determining how spatial distribution and habitat type a ffect the potential for natural land to protect against lake nu trient loading. Lakes containing lower concentrations of total chlorophyll, total nitrogen, and total phosphorous typically received higher performance ratings. This significant trend revealed an indirect re lationship between nutrient loads and lake water quality optimization. Lake wate r quality was optimized when nutrient concentrations were minimized. Lakes with elevated nutrient concentrations typically occurred in two mile radius del ineations containing lower percentages of natural land area. This significant tr end is explained by the nutrient filtration properties of natural land types (R eddy and Dev 2006; Osborne and Wiley 1988; Lenat and Crawford 1994). Natural land ty pes assimilate nutrients that would otherwise be deposited in hydrologically co nnected surface waters such as lakes (Reddy and Dev 2006; Osborne and Wile y 1988; Lenat and Crawford 1994). Results from the individual DEA models established a significant relationship between natural land use and aquatic nutrient contaminants. Typically, nutrient concentrations diminished in those la kes surrounded by a higher percentage of natural land use area. The interaction between nutrient conc entrations and natural land use area was the focus of each DEA model applied during this thesis. Results from the DEA models revealed that natural land use area improves the performance of lakes and diminishes the presence of sol uble nutrients. ‘Pro jection’ figures generated by the CCR-I model indicated that the input variables for each lake

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111 except Cypress Lake and Keyst one Lake required reductions to obtain optimal water quality performance. Non-coin cidentally, Cypress Lake and Keystone Lake were the only lakes to achieve an opt imal water quality performance rating of one. Therefore, the ‘pro jection’ figures for both thes e lakes reflected that no change in the input variables were necessary to accomplish optimal efficiency. With the exception of both Cypre ss Lake and Keystone Lake, each lake included in the study possessed inflated input variable data according to the ‘slack’ measurements returned by both the CCR-I and BCC-I models. Cypress Lake and Keystone Lake were the only DMUs to return all ‘slack’ measurements equal to zero for both input oriented models. The only two lakes to receive all ‘slack’ measurement equal to zero fo r both the CCR-I and BCC-I models were Cypress and Keystone. Also, each DM U except for both Cypress Lake and Keystone Lake was classified as ineffici ent by at least one of the models analyzed during this thesis. Therefore, it can be stated that each lake except for Cypress Lake and Keystone Lake contained excesses in nutrient concentrations that prohibited optimal performance ratings across all three of the DEA models. To achieve optimal performance for these failing lakes, nutrient concentrations would have to be reduced according to the value indicated by the ‘slack’ measurement produced in the CCR-I model. Nutrient load augmentations should obey the ‘slack’ measurements retu rned by the CCR-I model because it produced a more stringent ‘efficient fr ontier’ line than the BCC-I model. Therefore, adjusting nutri ent concentrations according to the ‘slack’ measurements returned by the CCR-I model would improve lake water quality

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112 most drastically. For the most drastic improvement in lake water quality, the CCR-I ‘slack’ measurements should be cons ulted. For a detailed account of ‘slack’ measurements comput ed by both these models, th e reader should refer to the ‘Results’ section of this thesis. The ‘slack’ measurements corresponding to each input as well as output variable can be viewed in Tables 9 and 12. Table 9 provides the ‘slack’ measurements rela ted to the CCR-I model, while Table 12 reveals the ‘slack’ measurements produced by the BCC-I model. Reducing the input variables according to the amount indicated by the ‘slack’ measurement woul d result in each underperforming lake obtaining an optimal performance rating. This augment ation in lake nutrient concentration could be accomplished by preserving natur al buffer areas surrounding lakes as well as increasing the overall acreage of natural land within an entire two mile radius surrounding a lake (Tong and Chen 2002; Castelletti and Soncini-Sessa 2007; Osborne and Wiley 1988; Lee 2002). In this aspect, lake nutrient concentrations are functionally de pendent upon the surrounding land uses (Reddy and Dev 2006; Osborne and Wiley 1988; Allan 2004). As this study and others have revealed, nutrient concentration s share an indirect relationship with the spatial quantity of natural land use surrounding a lake (Reddy and Dev 2006; Griffith et al. 2002; Allan 2004). Nutrient concentrations typically decline in lakes surrounded by greater proporti ons of naturally preserved land (Tong and Chen

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113 2002; Lenat and Crawford 1994; Griffith et al. 2002; Allan 2004). In the DEA model developed for this study, every lake with the exception of two, Cypress Lake and Keystone Lake, contained elevat ed nutrient concentrations that required reductions to achieve opt imal water quality performance. The correlation matrices provided as Tables 10 and 13 contain proportions that quantify the significance of the re lationship between natural land use and lake nutrient concentrations. Table 10 contains the correlation proportions produced during the CCR-I model, while T able 13 contains the correlation proportions produced during the BCC-I model. The values within both tables are identical. The ‘DEAlytics’ software used to compute the Additive model did not produce correlation proportions, however, it can be assumed that the correlation proportions for the Additive model remai ned the same as those in the CCR-I and BCC-I models. Therefore, the following analysis of correlation proportions applies to all three DEA models referred to during this thesis. The correlation proportion representing the relationshi p between natural land use and total phosphorous was equal to 0.2007, or 20.07%. This figure can be interpreted by stating that approximately 20.07% of the variable dat a for total phosphorous can be explained by natural land use area. The correlation proportion representing the relationship between natural land use and total chlorophyll was equal to 0.1188, or 11.88%. This figure can be inte rpreted by stating that approximately 11.88% of the variable data for total chlo rophyll can be explained by natural land use area. Finally, the correlation pr oportion representing the relationship between natural land use and total nitr ogen was equal to 0.1982, or 19.82%.

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114 This value can be interpreted by stat ing that approximat ely 19.82% of the variable data for total nitrogen can be ex plained by natural land use area. The correlation percentages provided in the above paragraph establish a notable relationship between natural land us e and lake nutrient concentrations. While these correlation percentages do not appear impressive initially, further evaluation of the model and its variable data reveals that correlation percentages for the relationship between natural l and use and nutrient concentrations have been limited by various fa ctors. Correlation bet ween natural land use and nutrient concentrations is limited due to the restricted spatial distribution of naturally preserved land in Hillsborough County. If the county contained a more balanced distribution of natural and built-up land uses, the correlation percentages would be capable of more accurately representing the relationship between natural land use and lake nutrient concentrations. Also, the deposition of soluble nutrients into lakes is dict ated by an intricate system of hydrologic exchanges (Lee 2002; Sacks et al. 1998; Sacks 2002). This system is composed of hydrologic sinks and sources that control the movement of soluble nutrients (Lee 2002; Sacks et al. 1998; Sacks 2002). When considering the intricacy of this system and amount of pot ential sinks and sources involved, the correlation percentages provided by the model appear a great deal more significant. Natural land uses as sinks explain anywhere between 11.88% and 20.07% of nutrient deposition in Hillsborough County lakes. Given the multitude of possible sinks and sources in the hy drologic exchange system of soluble

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115 nutrients, the range of correlation percent ages depicting the significance of the relationship between natural land use and lake nutrient loads becomes more impressive than previously perceived at first glance. According to the DEA model, the functioning of nat ural lands as hydrologic sinks influences lake nutrient loads between 11.88% and 20.07% in Hillsborough County. This is a significant figure when cons idering the intricacy of t he system that dictates soluble nutrient deposition into surface water lakes. Completion of this study exposed both disadvantages and advantages associated with applying DEA to accomplis h the research objectives of this thesis. A disadvantage with the DEA dev eloped during this st udy was that the model failed to include a variable repres enting a potential source of nutrient contamination. Within the model devised for this study, the single output variable only represents a potential net sink for nutri ent loads in the form of natural land use area. Unfortunately, this disadv antage could not be addressed because all remaining land uses within Hillsborough Coun ty have been traditionally classified as net nutrient contaminant sources (Tong and Chen 2002; Lenat and Crawford 1994; Osborne and Wiley 1988). Therefore, it would not have been prudent to include the remaining area of each lake ’s two mile radius delineation as a potential nutrient load source. Also, a va riable such as this would not have been compatible with the over all scheme of the model, which sought to generate optimal water quality performance rati ngs by minimizing the inputs and maximizing the outputs. A variable repr esenting a net nutrient source could not have been included as an input because this DEA’s inputs were restricted to

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116 nutrient contaminants. Simply put, the va riable for land uses that act as net nutrient sources could not be classified as an input variable because it is not a type of nutrient contaminant. Conversely, this variable could not be included as an output variable because outputs were maximized when generating optimal performance ratings. In theor y, the variable for land uses that act as net nutrient sources would have to be minimized to improve water quality performance. Therefore, this variable could not be classified as an output. Another disadvantage encountered by the models used during this study was due to the study area in which the m odel was applied. Natural land area has been greatly diminished in the predomi nantly urbanized count y examined by the model. The limited spatial distribution of natural lands in Hillsborough County restricted the model’s applic ability. Numerous lakes within Hillsborough County failed to contain any natural land area wit hin a two mile radius. Due to the mathematical framework of DEA based on production ratios, lakes contained by a two mile radius without any natural lands could not be examined by the model because they failed to fit on the ‘efficient frontier’ line. Performance ratings for lakes within these two mile radius de lineations would have automatically been zero, which would not have accurately represented the lake’s water quality performance. Therefore, lakes within two mile radius delineations that did not contain any natural land could not be incl uded in the model. Essentially, variable data collected for the model had to be positive, non-zero numbers for the purpose of generating relevant performance ratings capable of being interpreted. Due to the lack of natural land use dist ribution in Hillsborough County, certain

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117 lakes located within highly urbanized por tions of the County could not be included in the model. The model devis ed for this study should only be applied to study areas that are known to contain some form of natural land use. This application limitation represents a disadvantage associ ated with the model. An additional disadvantage related to th is application of DEA in assessing the relationship between lake perform ance and land use was that the models failed to examine how much of the nutri ent loads were received from external sources. Lake nutrient loading ca n occur through internal processes independent of external nutrient sources. Therefore, it would be useful to devise a DEA model that distinguishes between in ternal and external nutrient loads. This could be accomplished using a DEA model that incorporates categorical input variables representing internal and external loading. The categorical variables would function to distinguish nut rient loads originating from either an external or internal source. By design ing the model such as this, the DEA would be able to examine the impact on lake wa ter quality from either external or internal nutrient deposits. For the study area of this thesis, it was not possible to make this distinction because there wa s no available data concerning internal and external nutrient loads for each individu al lake examined by the DEA. Given the appropriate internal and external nutri ent load data, it would be possible to devise a DEA that distinguishes between the two types of nutrient deposits. This could be accomplished by creating separate input variables for internally and externally deposited nutr ient concentrations.

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118 The final disadvantage of this DEA application was that the analysis failed to include a spatial component. The spatia l distribution of naturally preserved land was not considered by the DEA cons tructed for this thesis. The DEA applied in this thesis simply evaluated the overall amount of natural land area located within a two mile radius from each study lake. It ignored the spatial distribution of net nutrient si nks within a two mile radius of study lakes. This can be considered a disadvantage because the spat ial distribution of a specific land use has been linked to the quality of freshw ater resources in previous studies (Lee 2002; Griffith et al. 2002). The spat ial distribution of particular land uses likely influence the overall surface water qua lity of a lake (Lee 2002; Griffith et al. 2002). Therefore, it is a disadvantage t hat this DEA application neglected to consider the spatial distribution of nat ural land when attempting to describe the relationship between lake water quality and land use. Certain advantages associated with the model were identified after completing the applied research component of this thesis. The model examined the impact of natural land us e area on lake nutrient loading. The design of the model successfully isolated the variable fo r natural land use area to evaluate its correlation with nutrient contaminant concentrations. Correlation figures produced by the model described the signi ficance of the relationship between natural land use area and lake nutrient l oading. Also, the model could be easily transformed to evaluate the significanc e of other land coverage types that typically function as net sinks for solubl e nutrients. Any land type that should be maximized for the purpose of establishi ng optimal water quality conditions could

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119 be included as an output variable in the model. For instance, the output variable could consist of land use area data for wetland habitats within a two mile radius of each study lake. Model inputs could also be replaced in similar fashion. Any type of aquatic contaminant that should be mini mized for the purpose of establishing optimal water quality conditions could be integrated as an input variable in the model. In theory, this means that t he model could be used to establish the significance of the relationship between any water contaminant and any land type classified as a net sink of soluble mate rials. For instance, the input variables could consist of aquatic contaminant data for arsenic concentrations in a lake. Another advantage of the model was its simplistic design. Data generated by the model was readily interpret ed for the purpose of describing the relationship between natural land use and lake nutrient loading. Variables included in the model were classified as inputs or outputs according to their typically observed impact on lake water qua lity. Aquatic contaminant variables that required minimization to achieve optimal water quality performance were designated as inputs, while the single natural land use variable that required maximization was categorized as an output. This division of variables enabled the model to produce data that specific ally examined the re lationship between water quality and natural land use. T he model generated dat a that directly measured the correlation between natural land use and nutrient loading in Hillsborough County.

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120 The final advantage of the model is t hat it can be readily applied to other study areas. This advantage is contingent upon the land uses examined by the model as well as the spatial distribution of those land uses within the study area. As previously discussed, variable data for the model must be positive or non-zero to produce production ratings capable of being interpreted. Therefore, the model can only be transposed to a study area that contains the particular land use of interest. This contingency is the onl y limitation related to applying the DEA model developed for this thesis to other study areas. The advantage of being able to transpose the model to other st udy areas answers one of the overall research questions addressed by this t hesis (refer to the ‘Research Design’ section of this document). The DEA model completed during this thesis generated data that was interpreted to describe the significance of the relationship between natural land use and lake nutrient concentrations in Hillsborough County. In doing so, the discussion produced by this thesis contributed previously uncovered knowledge regarding the relationship between land use and lake water quality. Overall, the research discovered that a moderately significant positive correlation exists between natural land use area and lake wate r quality performance. Also, it was confirmed that indicators of soluble nut rient pollution such as total chlorophyll, total phosphorous, and total nitrogen detract from the performance of lake water quality. Finally, the research conducted for this thesis rea ffirmed that natural land uses enhance lake water quality (Tong and Chen 2002; Lenat and Crawford 1994; Osborne and Wiley 1988).

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121 Recommendations and Conclusion The research questions listed below we re posed in the ‘Research Design’ section of this thesis. 1. After analyzing the various forms of scientifically acceptable data using DEA computer software, does naturally preserved land typically contribute to a water quality benchmark opt imizing lake performance? 2. How can water managers operating within the boundaries of Hillsborough County reproduce the necessary conditions to achieve an optimal water quality benchmark? 3. Short of altering the current l and use surrounding a given lake through land acquisition techniques, how c an localized water managers improve management techniques to achieve an ec ologically optimal water quality benchmark? 4. After performing the necessary analysi s, will the devised methodology be easily transposable to other study areas? These questions were all directly ans wered during the research conducted for this thesis. After analyzing the sele cted input and output variables with DEA, naturally preserved land was identified as a positive contributor to water quality. The methodology performed during this t hesis indicated that natural land enhances lake water quality and ecologic pe rformance. These findings should

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122 persuade water managers to preserve or rehabilitate natural land whenever feasible. When natural land preservation is not feasible, water managers should implement water quality BMPs as well as effo rts to artificially simulate the nutrient filtration properties of natural land. Finally, it was discovered that the methodology conducted during this thesis would be readily transferable to other study areas given the required data sets. As with any applied research effort, ce rtain hypotheses are identified prior to conducting the analysis. In this case, it was expected that lakes surrounded by a higher proportion of natural land wo uld receive higher DEA performance ratings. This result was expected bec ause it has been previously documented that the surface area of natural l and surrounding a lake shares a direct relationship with the performance of t hat lake (Reddy and Dev 2006; Wescoat and White 2003; Gleick et al. 2006). Meaning, the perform ance of a lake declines as the natural lands surrounding that lake are removed. The DEA performed for this thesis supported the relationship between lake water quality performance and natural land area menti oned in the previous sentence. A significant trend was established by the DEA in which DMUs surrounded by a greater amount of natural land area typically received higher performance ratings. It was also hypothesized t hat results generated from the DEA would support water management strategies focu sed on preserving natural lands and rehabilitating impaired natural lands. This prediction was supported by the DEA model because lakes surrounded by a greater proportion of natural land typically

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123 received higher performance ratings. Therefore, the preservation and rehabilitation of natural land would likely enhance lake water quality performance. Another hypothesis predicted that water management efforts based on BMPs designed to artificially simulate the pollutant filtration function of naturally preserved land would be supported by the re sults of the DEA. This hypothesis was indeed supported by the DEA because natural lands improved lake water quality performance by functioning as a net sink for nutrient loads. In this manner, management efforts proven to simula te the assimilative qualities of natural lands would also function to enhance lake water quality. Assumedly, these water management techniques would pr ovide net sinks for nutrient loading thereby improving the quality of water in nearby lakes. Finally, it was hypothesized that the methodology develop ed for this thesis would be readily transferable to other study areas that collect and stor e the required datasets. After performing the methodology developed for this thesis, it is evident that the model could be readily transposed to any study area containi ng the appropriate datasets. Cities or count ies concerned with lake nutrient loading due to land use could potentially refer to the m odel developed during this thesis. Interpretations of the results from the three DEA models revealed notable trends between natural land use and lake water quality performance. These interpretations contribute information that supports specific water management

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124 actions. In general, water managem ent recommendations based on these interpretations would encourage the pres ervation of natural lands whenever possible and especially surrounding thos e lakes that received lower DEA performance ratings. Lakes that achieved lower performanc e ratings should be the initial focus of any water management recommendations derived from the DEA conducted for this study. Lakes performing at a lower le vel represent situations in which the most improvement to water quality can be accomplished. Conditions should be maintained for those lakes determined to be functioning at an optimum level. However, lakes that did not achieve optimum performance should be subjected to water management actions that reduce nutrient loading and increase the positive impacts from natur ally preserved land. In a highly urbanized setting such as Hillsborough County, the economic motivation to develop residential, commercial, and industrial facilities may oft en create situations in which it is not feasible to preserve natural lands. Natu ral land preservation in the study area of this thesis frequently fails due to the economic pressures of development. Therefore, it may be more prudent to rely upon BMPs that protect water resources from harmf ul pollutants. Results from the DEA suggest that rehab ilitation to restore the assimilative properties of natural land would be an effective water management tactic when attempting to improve lake water quality. In frequent instances when this is not possible, improvements to lake water quality in the study area could also be realized if BMPs were implemented that si mulated the filtration function of natural

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125 lands. After interpreting the results prov ided by the DEA, it was apparent that water managers should attempt to improve t he permeability of land surfaces as a preventive measure to reduce soluble nut rient deposition in Hillsborough County lakes. Land surface permeability is improv ed by removing impenetrable surfaces such as concrete. Exact measures to improve land surface permeability can be accomplished by complying with envir onmentally conscious construction practices. Land surface permeability is improved by any technique that reduces both water run-off and the use of imperm eable concrete materials. Increased natural land area was discovered to impr ove lake water quality performance. The permeability of natural land is typica lly higher than that of built-up land uses (Tong and Chen 2002). This physical property of natural land contributes to its ability to assimilate nutrient loads t hereby protecting fres hwater bodies from eutrophication (Tong and Chen 2002). T herefore, completing the necessary measures to improve land surface permeability within a designated area surrounding a lake would contribute to enhanced water quality and a reduction in soluble nutrient concentrations. Lake water quality improvement is ty pically witnessed on seasonal scales (Castelletti and Soncini-Sessa 2007; R eddy and Dev 2006). When actions are conducted to enhance lake water quality, im provements are typically observable after the passage of a wet season (Cas telletti and Soncini-Sessa 2007; Reddy

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126 and Dev 2006). After an attempt at impr oving lake water quality, the time necessary to witness any positive impacts is highly dependent upon the targeted water resource and the type of management action used to improve the quality of the lake’s water. In the DEA model, lakes that contai ned lower concentrations of soluble nutrients obtained higher performance rati ngs. This would indicate that regulations limiting the dispersal of soluble nutrients would improve the performance of lakes within the study area. Water management efforts to lower nutrient loading would impr ove the water quality performance of area lakes. Efforts to do so might include regulations that mandate a reduction in residential, agricultural, and commercial fertilizer us e. Water managers could also require specific fertilizer techniques or products that typically generate lesser volumes of soluble nutrient run-off. An y fertilizer regulations support ed by the results of this DEA would enforce BMPs that protect fres hwater resources. Results from the model support previously enacted BMPs that have been proven to reduce soluble nutrient deposition in freshwater resources. Such BMPs may include natural buffer areas surrounding surface waters, fertilizer techniques that encourage application only durin g the growing season, and restrictions that prohibit fertilizer application within a designated proximity of an aquatic ecosystem. The literature review and DEA applic ation conducted for this thesis revealed additional research opport unities that would extend scientific understanding of how land use and lake wa ter quality interact. These research

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127 opportunities would focus on determining the significance of the relationship between land use and lake water quality through the application of DEA. Complimentary studies would attempt to determine the significance of the relationship between lake water quality and various built-up land uses through DEA. Also, future research should exam ine the influence of spatial distribution on the relationship between land use and lake water quality. The spatial distribution of particular land uses surr ounding a lake likely influence its water quality (Lee 2002; Griffith et al. 2002). T herefore, future studies should focus on determining the significance of naturally preserved buffer areas on lake water quality. Additionally, studies of this nat ure would also have to examine how builtup areas directly surrounding lakes infl uence water quality. Future studies should apply DEA to itemize the impact from each land use type contained in a study area on lake water quality. This all inclusive model could be developed given the appropriate data. Such a study would assist water managers in identifying specific land uses that negatively or positively impact lake water quality. Potential results from this study would allo w water managers to devise strategies that either negate or enhance t he influence of particular land uses on lake water quality. Future DEA mode ling could incorporate water quality data collected during different time periods The water quality performance of individual lakes could then be compared between the different time periods examined by the DEA. This would a llow water managers to monitor the water quality performance of an individual lake during different time periods. Finally, future applications of DEA in describi ng the relationship between lake water

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128 quality and land use could examine a variet y of other types of input variables such as Total Suspended Solids (TSS), To tal Suspended Volatile Solids (TSVS), and other forms of aquatic contaminants. Incorporating these different types of input variables will broaden the scope of future research concerning the application of DEA in studying the relati onship between surface water quality and land use. Of the three different DEA models applied during this study, the CCR-I model would be the most effective for supporting drastic management efforts to protect or improve lake water quality. According to the CCR-I model, only two lakes achieved optimum performance, whereas, six lakes achieved optimum performance using the other two models. This observa tion alone indicates that the CCR-I model is less lenient than the ot her two models. Therefore, the CCR-I model should be used to support stronger measures aimed at improving lake water quality. In this sense, the CCRI model represents the most effective option for instituting change in water management emphasizin g the improvement of lake conditions. The more stringent rating system of the CCR-I model would encourage preventive water m anagement actions reducing the likelihood of lake impairment. From a water managem ent perspective, the CCR-I model represents the most stringent of the three models that could be used to justify the most protective water quality policies. An original applicati on of a performance assessment methodology was explored during the research conducted for this thesis. The applied research and accompanying literature review for this thesis provided previously unexplored

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129 and overdue dialogue regardi ng the application of DEA to water management concerns. Assessing the status of Hillsborough County lakes proved to be a valuable task in the face of gro wing water demands and intensifying human impacts (Poe et al. 2005). The ultimate obj ective of this thesis was to provide water management recommendations and interpretations based on a DEA assessment, GIS land use layers, and preexi sting scientific literature. While accomplishing this primary research objec tive, it was discovered that DEA has been increasingly applied to natural resour ce performance related questions in a variety of environmental disciplines (Als harif et al. 2008; Fraser and Hone 2001; Jaenicke and Lengnick 1999; Malana and Malano 2006; Rhodes 1986; Shafiq and Rehman 2000). From a review of t he available literature, it became apparent that the application of DEA to environmental concerns is a burgeoning endeavor with vast stores of potentia l research yet to be conducted. The applied research com ponent of this thesis revealed that DEA can be effectively applied to water management i ssues that specif ically address the relationship between land use and lake wa ter quality. The DEA model produced during this thesis serves as a viabl e example of how DEA can be applied to assess the performance of lake water quality in relation to surrounding land uses. This research revealed the potential to generate additional st udies based on DEA modeling techniques that assess the re lationship between land use and lake water quality. Through the applied resear ch portion of this thesis, it was determined that the perfo rmance measurement capabilit ies of DEA provide an effective platform for assessing land use and lake water quality interactions.

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130 Through the use of DEA, notable trends we re identified that described how water quality parameters are impact ed by land use. The relationship between land use and lake water quality was effectively examined by the DEA methodology developed during this thesis.

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131 References Cited Allan, J.D. 2004. Landscapes and Riverscapes: The Influence of Land Use on Stream Ecosystems. Annual Review of Ecology, Evolution and Systematics 35: 257-284. Alsharif, K. 2008. Assessment of the Lake Ecosystem s in Hillsborough County by Using Frontier Estimation Technique Application for Pollution Recovery Fund Assistance. Alsharif, K., E.H. Feroz, A. Klemer, and R. Raab. 2008. Governance of water supply systems in the Palestinian Te rritories: A data envelopment analysis approach to the management of water resources. Journal of Environmental Management 87: 80-94. Castelletti, A. and R. Soncini-Sessa. 2007. Topics on System Analysis and Integrated Water Resources Management Oxford, United Kingdom: Elsevier Ltd. Caves, D.W., L.R. Christensen, and W.E. Diewert. 1982. The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity. Econometrica 50 (6): 1393-1414. Cooper, W.W., L.M. Seif ord, and K. Tone. 2000. Data Envelopment Analysis: A Comprehensive Text wit h Models, Applications, References and DEASolver Software Boston, Massachusetts: Kluwer Academic Publishers. Feldman, D.L. 2007. Water Policy for Sustainable Development Baltimore, Maryland: The John Hopkins University Press. Feroz, E.H., R. Raab, and S. Haag. 2001. An income efficiency model approach to the economic consequences of the OSHA cotton dust regulation. Australian Jour nal of Management 26: 69-89. Florida Department of Transportati on Geographic Mapping Section. 1999. Florida Land Use, Cover, and Forms Classification System Tallahassee, Florida: Florida Department of Transportation.

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133 Poe, A., A.J. Janicki, H. Greening. 2005. Baywide Environmental Monitoring Report, 2002-2005 Tampa, Florida: Tam pa Bay Estuary Program. Postel, S. 1997. Last Oasis: Facing Water Scarcity New York City: W.W. Norton and Company. Ramanathan, R. 2003. An Introduction to Data Envelo pment Analysis: A Tool for Performance Measurement Thousand Oaks, California: Sage Publications. Reddy, V.R. and S.M. Dev. 2006. Managing Water Resources: Policies, Institutions, and Technologies New Delhi, India: Oxford University Press. Rhodes, E.L. 1986. An Exploratory Analysis of Variations in Performance Among U.S. National Parks. In Measuring Efficiency: An Assessment of Data Envelopment Analysis ed. Silkman, R.H., 47-71. San Francisco: JosseyBass. Sacks, L.A. 2002. Estimating Ground-Water Inflow to Lakes in Central Florida Using the Isotope Mass-Balance Approach Tallahassee, Florida: United States Geological Survey. Sacks, L.A., A. Swancar, and T.M. Lee. 1998. Estimating Ground-Water Exchange with Lakes Using Water-Budget and Chemical Mass-Balance Approaches for Ten Lakes in Rid ge Areas of Polk and Highlands Counties, Florida Tallahassee, Florida: Unit ed States Geological Survey. Sexton, T.R. 1986. The Methodology of Data Envelopment Analysis. In Measuring Efficiency: An Assessm ent of Data Envelopment Analysis ed. Silkman, R.H., 7-29. San Francisco: Jossey-Bass. Shafiq, M. and T. Rehman. 2000. The extent of resource use inefficiencies in cotton production in Pakistan’s P unjab: an application of Data Envelopment Analysis. Agricultural Economics 22: 321-330. Sidle, R. and J. Hornbeck. 1991. Cumu lative effects: a broader approach to water quality research. Journal of Soil and Water Conservation 46: 268271. Stauffer, R.E. 1991. Effects of Citrus Agriculture on Ridge Lakes in Central Florida. Water, Air, and Soil Pollution 59: 125-144. Stolp, C. 1990. Strength and weaknesse s of data envelopment analysis: an urban and regional perspective. Computers, Environment, and Urban Systems 14: 103-116.

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134 Thanassoulis, E. 2001. Introduction to the Theory and Application of Data Envelopment Analysis Boston, Massachusetts: Kluwer Academic Publishers. The Planning Commission of Hillsborough Count y. 2008. Available from internet, http://www.theplanningcommission.org/. Tong, S.T.Y. and W. Chen. 2002. Modeling the rela tionship between land use and surface water quality. Journal of Environmental Management 66: 377393. Wang, X. 2001. Integrating water qualit y management and land use planning in a watershed context. Journal of Environmental Management 61: 25-36. Wescoat, J.L. and G.F. White. 2003. Water for life: water management and environmental policy Cambridge, United Kingdom: Cambridge University Press. Wiley, M., S. Kohler, and P. Seelbach. 1997. Reconciling landscape and local views of aquatic communities: less ons from Michigan trout streams. Freshwater Biology 37: 133-148. Xian, G., M. Crane, and J. Su. 2007. An analysis of urban development and its environmental impact on the Tampa Bay watershed. Journal of Environmental Management 85: 965-976.