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A Linear Regression Model for Predicting Stream Response Time in Karst Watersheds Using DEMs

Permanent Link: http://ufdc.ufl.edu/UFE0022120/00001

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Title: A Linear Regression Model for Predicting Stream Response Time in Karst Watersheds Using DEMs
Physical Description: 1 online resource (167 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

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Subjects / Keywords: Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A liner regression model was developed to investigate the effect of karst topography on two common measures of watershed response time: Centroid Lag and Centroid Lag-to-Peak. Hourly precipitation and streamflow data from three different rainfall events were used to obtain time parameters for each watershed. ArcHydro and GIS tools were applied on Digital Elevation Models to delineate 16 watersheds in Southwest Florida Water Management District and to calculate characteristics of each watershed. Six watershed characteristics known to be the most important parameters in rainfall-runoff modeling (area, slope, stream density, basin roughness, compactness ratio, and percentage of impervious area) along with percentage of karst area in each watershed and rainfall duration and rainfall volume were considered to be the independent variables of the linear regression model. Results of the linear regression model indicate that percentage of karst area in a watershed has a positive relationship with Centroid Lag and does not have a significant effect on Centroid Lag-to-Peak. The model shows that karst area creates longer hydrographs but does not change the timing of peaks. Therefore, lower flow rates at the watershed outlet are expected. Results of this study can be used to simulate the effects of karst topography on rainfall-runoff modeling and to improve flood forecasting in ungaged basins.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Hatfield, Kirk.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022120:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022120/00001

Material Information

Title: A Linear Regression Model for Predicting Stream Response Time in Karst Watersheds Using DEMs
Physical Description: 1 online resource (167 p.)
Language: english
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: Civil and Coastal Engineering -- Dissertations, Academic -- UF
Genre: Civil Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A liner regression model was developed to investigate the effect of karst topography on two common measures of watershed response time: Centroid Lag and Centroid Lag-to-Peak. Hourly precipitation and streamflow data from three different rainfall events were used to obtain time parameters for each watershed. ArcHydro and GIS tools were applied on Digital Elevation Models to delineate 16 watersheds in Southwest Florida Water Management District and to calculate characteristics of each watershed. Six watershed characteristics known to be the most important parameters in rainfall-runoff modeling (area, slope, stream density, basin roughness, compactness ratio, and percentage of impervious area) along with percentage of karst area in each watershed and rainfall duration and rainfall volume were considered to be the independent variables of the linear regression model. Results of the linear regression model indicate that percentage of karst area in a watershed has a positive relationship with Centroid Lag and does not have a significant effect on Centroid Lag-to-Peak. The model shows that karst area creates longer hydrographs but does not change the timing of peaks. Therefore, lower flow rates at the watershed outlet are expected. Results of this study can be used to simulate the effects of karst topography on rainfall-runoff modeling and to improve flood forecasting in ungaged basins.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Hatfield, Kirk.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2009-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022120:00001


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A LINEAR REGRESSION MODEL FOR PREDICTING STREAM RESPONSE TIME IN KARST WATERSHEDS USING DEMS By ALI SEDIGHI A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008 1

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2008 Ali Sedighi 2

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To my mother, Parvin 3

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ACKNOWLEDGMENTS I would like to offer my utmo st appreciation to Dr. Kirk Hatfield, my supervisory committee chair, who was much more than an advi sor to me. He played a key role in guiding me with unlimited patience and energy and gave me all the support I could ask for. His experience and guidance have enlightened my education, as well as my life. I would also like to thank my committee members, Dr. Louis H. Motz, Dr. Ma rk Clark, and Dr. Mark Newman, for their valuable encouragement, ideas, and compassion. I am also grateful to all my previous professors at Sharif University of Technology in Tehran, Ira n. I am grateful to my friend, Harald Klammler, for all of his help, support, and gr eat contribution to my work. I also wish to thank all my friends, who have added richness to my life. I am endle ssly grateful to my pare nts, Parvin Bagherzadeh and Abdolvahab Sedighi; and my sister, Vida, for their emotional and financial support. 4

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TABLE OF CONTENTS page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF TABLES ...........................................................................................................................7LIST OF FIGURES .........................................................................................................................8ABSTRACT ...................................................................................................................... .............11CHAPTER 1 INTRODUCTION ................................................................................................................ ..121.1 Importance of Flood Forecasting ......................................................................................121.2 Flood Forecasting in Ungaged Basins ..............................................................................131.3 Watershed Delineation and Stream Network Detection Using DEMs .............................141.4 Flood Processes in Karst Systems ....................................................................................161.5 Research Objectives ..........................................................................................................172 LITERATURE REVIEW .......................................................................................................202.1 Rainfall-Runoff Modeling Using Watershed Characteristics ...........................................202.2 Watershed Delineation and Stream Network Detection ...................................................242.2.1 Single Flow Direction Algorithms .........................................................................302.2.1.1 Deterministic 8 (D8) .....................................................................................302.2.1.2 Random 8 (Rho8) .........................................................................................302.2.2 Multiple Flow Dire ction Algorithms ......................................................................302.2.2.1 Flow Direction 8 (FD8) ................................................................................302.2.2.2 Deterministic infinity (D ) ..........................................................................312.3 Rainfall-Runoff Modeling in Karst Systems ....................................................................322.4 Quantitative Description of Response Hydrographs ........................................................343 METHODOLOGY ................................................................................................................. 383.1 Introduction .......................................................................................................................383.2 Selection of the Study Area and its Karst Feature Formation ..........................................383.3 Precipitation and St reamflow Data ...................................................................................403.3.1 Streamflow data ......................................................................................................403.3.2 Precipitation Data ...................................................................................................423.4 Digital Elevation Model ................................................................................................... 423.5 Delineating and Selecting Watersheds .............................................................................433.5.1 Digital Elevation Model Reconditioning ................................................................433.5.2 Fill Sinks .................................................................................................................443.5.3 Flow Direction ........................................................................................................443.5.4 Flow Accumulation ................................................................................................44 5

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3.5.5 Stream Definition ...................................................................................................453.5.6 Stream Segmentation ..............................................................................................453.5.7 Catchment Grid Delineation ...................................................................................453.5.8 Catchment Polygon Processing ..............................................................................453.5.9 Drainage Line Processing .......................................................................................463.5.10 Adjoint Catchment Processing .............................................................................463.5.11 Batch Watershed Delineation ...............................................................................463.5.12 Watershed Selection .............................................................................................473.6 Watershed Characteristics ................................................................................................4 93.6.1 Area ........................................................................................................................493.6.2 Slope .......................................................................................................................493.6.3 Stream Density .......................................................................................................503.6.4 Watershed Roughness ............................................................................................503.6.5 Basin Shape ............................................................................................................503.6.6 Percentage of Karst Area ........................................................................................513.6.7 Percentage of Impervious Area ..............................................................................513.6.8 Storm Selection and Hydrogr aph/Hyetograph Generation .....................................534 MODEL DEVELOPMENT ....................................................................................................824.1 Regression Analysis ..........................................................................................................824.2 Multiple Regression for Centroid Lag ..............................................................................834.3 Multiple Regression for Centroid Lag-to-Peak ................................................................874.4 Model Evaluation ..............................................................................................................895 DISCUSSION .................................................................................................................. .....1175.1 Introduction .....................................................................................................................1175.2 Discussion of Results ......................................................................................................1175.3 Significance of Research ................................................................................................1205.4 Limitations of the Model ................................................................................................1215.5 Future Research ..............................................................................................................1225.6 Conclusions .....................................................................................................................122APPENDIX A DAILY PRECIPITATION AND DISCHARGE GR APHS FROM USGS WEBSITE .......124B HOURLY PRECIPITATION AN D DISCHARGE GRAPHS .............................................143LIST OF REFERENCES .............................................................................................................159BIOGRAPHICAL SKETCH .......167 6

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LIST OF TABLES Table page 2-1. Definitions of terms used to desc ribe hyetograph and response hydrograph. .......................373-1. List of the 17 watersheds with signi ficantly different ArcHydro and USGS areas ...............743-2. List of the 23 watersheds that approximately match the areas from the USGS website .......754-1. Variables and their corresponding abbrevia tions used in the re gression analysais ...............944-2. Summary of all the values of the independent and dependent variables for 44 observations .......................................................................................................................954-3. Statistical information for Centroid Lag ................................................................................974-4. Correlation between different variables for Centroid Lag .....................................................984-5. ANOVA table for Centroid Lag with all nine variables ........................................................994-6. ANOVA table for Centroid Lag with five variables ...........................................................1024-7. Statistical information for Centroid Lag-to-Peak ................................................................1034-8. Correlation between different va riables of Centoid Lag-to-Peak ........................................1044-9. ANOVA table for Centroid Lag-to-Peak with nine variables before removing observation number 20 .....................................................................................................1054-10. Residuals for predicted Centroid Lag-to -Peak with nine variables before removing observation number 20 .....................................................................................................1064-11. ANOVA table for Centroid Lag-to-Peak with nine variables after removing observation number 20 .....................................................................................................1084-12. ANOVA table for Centroid Lag-to-Peak with seven variables .........................................1114-13. Summary of all the information of 27 observations used for model validation ................1124-14. Statistical information for the predicte d and the observed Centroid Lag and Cetroid Lag-to-Peak ................................................................................................................... ...1134-15. Statistics for comparing the goodness-of-f it for Centroid Lag and Centroid Lag-toPeak models .....................................................................................................................1144-16. Sum of Mean Square Errors of observed versus predicted values for each watershed .....116 7

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LIST OF FIGURES Figure page 1-1. Global trends of wate r-related disasters 1960 .............................................................192-1. Flow direction using the Rho8 algorithm. .............................................................................352-2. Flow distribution among downslope cells using the FD8 algorithm. ....................................352-3. Flow direction defined as steepest dow nward slope on planar tr iangular facets on a block centered grid. ............................................................................................................362-4. Terms used to describe hye tograph and response hydrograph. .............................................363-1. Distributions of the USGS st reamflow stations in Florida ....................................................553-2. Locations of the SWFW MD precipitation stations ...............................................................563-3. Number of reported new sinkhol es in West-Central Florida. ................................................573-4. Map of real-time streamflow compared to hi storical streamflow for the day of the year .....573-5. Precipitation for one of the ga ging stations in the study area ................................................583-6. Discharge for the station of Figure 3-5 ..................................................................................583-7. Locations of the USGS preci pitation stations in Florida .......................................................593-8. The 15 m resolution DEM for the state of Florida ................................................................603-9. Cross section of a stream before and after reconditioning ....................................................613-10. Original 15m resolution DEM for the study area ................................................................623-11. Hydro100 data for the study area ........................................................................................633-12. Digital Elevation Mode l of the study area after reconditioning based on the hydro100 data. ......................................................................................................................... ...........643-13. Digital Elevation Model af ter the Fill Sink process ............................................................653-14. Deterministic 8 (D8) Single Flow Di rection algorithm where flow goes from the center of a cell to only one of the surroundi ng cells that has the lowest elevation ............663-15. Flow direction grid for the study area .................................................................................673-16. Flow accumulation grid creation ........................................................................................ .683-17. Flow accumulation grid for a part of the study area ............................................................68 8

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3-18. Stream definition grid based on the 4.5 km2 contributing area ............................................693-19. Stream segmentation fo r part of the study area ...................................................................693-20. Catchment Grid Delineation for part of th e study area .......................................................703-21. Drainage line for the study area ...........................................................................................713-22. Location of 40 stations a nd the delineated watersheds ........................................................723-23. Available data for a st ation from USGS website .................................................................733-24. Drainage basin boundaries from US GS website (red) and ArcHydro delineated drainage basin boundaries (blue). ......................................................................................733-25. Digital Elevation Model a nd aerial photo showing that D8 algorithm fails to detect stream bifurcation where water is flowing from right to left and divides into two streams. ...................................................................................................................... ........743-26. Example of a hydrograph that is not well reproduced, possibly due to the error in the gaging stations device ........................................................................................................763-27. Final 16 watersheds selected for the study. .........................................................................773-28. Two watersheds in the study area with minimum (1.40) and maximum (2.43) value of the compactness ratio ......................................................................................................... 783-29. Map of the aquifer vulnerabili ty in Florida from FAVA study ...........................................793-30. Karst features in the study area ....................................................................................... .....803-31. Distribution of impervious area in the watersheds of the study area ...................................814-1. Distribution of observed values for Centroid Lag (Histogram, Boxplot, Density Plot, and Normal Plot) .............................................................................................................. ..974-2. Analysis of the regression results for Centroid Lag ............................................................1004-3. Relationship between residuals and variables for Centroid Lag .........................................1004-4. Effect of each variable on the linear re gression model and the change in RMSE after eliminating each variable for Centoid Lag model (X1 to X9 represent variables in this order: Area, Slope, Stream Densit y, Basin Roughness, Compactness Ratio, Karst Area Percentage, Impervious Area Per centage, Rainfall Duration, and Rainfall Volume) ....................................................................................................................... ....1014-5. Distribution of observed values for Centroid Lag-to-Peak (Histogram, Boxplot, Density Plot, and Normplot). Boxplot shows an outlier in the data ..............................................102 9

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4-6. Distribution of observed values for Centroid Lag-to-Peak (Histogram, Boxplot, Density Plot, and Normplot) after eliminating the outlier (observation number 28) ....................1034-7. Analysis of the regression results for Centroid Lag-to-Peak before removing observation number 20 .....................................................................................................1074-8. Analysis of the regression results for Centroid Lag-to-Peak after removing observation number 20 ..................................................................................................................... ...1094-9. Relationship between residuals a nd variables for Centroid Lag-to-Peak ............................1094-10. Effect of each variable on the linear re gression model and the change in RMSE after eliminating each variable for Centoid Lag-to-Peak model (X1 to X9 represent variables in this order: Area, Slope, Stream Density, Basin Roughness, Compactness Ratio, Karst Area Percentage, Impervious Area Percentage, Rainfall Duration, and Rainfall Volume) .............................................................................................................1 104-11. Scatterplot of the predicted and observed values for Centroid Lag ..................................1134-12. Scatterplot of the pr edicted and observed values for Centroid Lag-to-Peak .....................1144-13. Clustered column chart to compare the predicted and observed values for Centroid Lag ...................................................................................................................................1154-14. Clustered column chart to compare the predicted and observed values for Centroid Lag-to-Peak ................................................................................................................... ...115 10

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11 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A LINEAR REGRESSION MODEL FOR PREDICTING STREAM RESPONSE TIME IN KARST WATERSHEDS USING DEMS By Ali Sedighi May 2008 Chair: Kirk Hatfield Major: Civil Engineering A liner regression model was developed to i nvestigate the effect of karst topography on two common measures of watershed response ti me: Centroid Lag and Centroid Lag-to-Peak. Hourly precipitation and streamflow data from three different rainfa ll events were used to obtain time parameters for each watershed. ArcHydro a nd GIS tools were applie d on Digital Elevation Models to delineate 16 watersheds in Southwes t Florida Water Manageme nt District and to calculate characteristics of each watershed. Six watershed characteristics known to be the most important parameters in rainfall-runoff modeling (area, slope, stream density, basin roughness, compactness ratio, and percentage of impervious area) along with percentage of karst area in each watershed and rainfall duration and rainfall volume were considered to be the independent variables of the linear regressi on model. Results of the linear regression model indicate that percentage of karst area in a watershed has a positive relationship with Centroid Lag and does not have a significant effect on Centroid Lag-to -Peak. The model shows that karst area creates longer hydrographs but does not change the timing of peaks. Therefore, lower flow rates at the watershed outlet are expected. Results of this stu dy can be used to simulate the effects of karst topography on rainfall-runoff mode ling and to improve flood for ecasting in ungaged basins.

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CHAPTER 1 INTRODUCTION 1.1 Importance of Flood Forecasting Knowledge of the flow of water and the nation s stream network plays a vital role in flood protection, water supply, pollution control, and environmental management. In 1998, at the request of Congress, the U.S. Geological Survey (USGS) prep ared a report entitled A New Evaluation of the USGS Streamgaging Network, stating that the networks ability to meet longstanding federal goals had declined. The report also stated that new resource management issues and data delivery capabilities have incr eased the demand for streamflow information. New technologies and methodologies are needed to impr ove the reliability of streamflow information and decrease its cost (NRC, 2004). Floods are among the most frequent and cost ly natural disasters in terms of human hardship and economic loss. As much as 90% of the damage related to natural disasters (excluding droughts) is caused by floods and associated mud and debris flows. The nation has a program to reduce flood damage that includes flood warnings and rive r forecasts (Mason and Weigner, 1995). According to the United Stat es Army Corps of Engineers (CORPS) Annual Flood Damage Report of 1998, flooding kills ove r 100 people and causes approximately $4.5 billion in damage annually. Based on the Na tional Weather Service information, flooding remains the number one weather related killer in the United States. Natural disasters caused by floods challenge scientists to forecast the magn itude and timing of peak flood discharges more accurately (Julien et al., 1998). Figure 1-1 shows that water-re lated disasters in particul ar (such as flood, drought and water epidemics), have been increasing in scale and with greater impact than ever before. The regions that suffer the greatest human impacts are usually those where measurement networks 12

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are least developed and undergoing further cutbacks. This is true for many developing countries where lack of hydrometric data, coupled with the effects of climatic and land-use changes, have led to depletion of water resources and ecosy stem degradation (Sivapalan et al. 2003). The National Weather Service (NWS), whic h is part of the National Oceanic and Atmospheric Administration, is widely known as the Federal agency in charge of weather forecasting and warning in the USA. The NWS also is charged by law with the responsibility of issuing river forecasts and fl ood warnings. The National Weather Bureau Organic Act of 1890 (U.S. Code title 15, section 311) ma ndates that the National Weathe r Service is the responsible agent for "the forecasting of weather, the issue of storm warnings, the display of weather, and flood signals for the benefit of agriculture." This has made the NWS focus on continued improvements in accessibility and availabil ity of higher quality and detailed hydrologic information. Advances in technology have increased the capacity to se rve this mission. The NWS uses many sources of data when developing its flood forecasts. The U.S. Geological Survey (USGS) is the principal sour ce of data on river depth and flow. 1.2 Flood Forecasting in Ungaged Basins One of the most difficult problems in hydrol ogy is to predict the runoff behavior of watersheds that have no availabl e precipitation or discharge reco rds. The way these watersheds handle the precipitation a nd how much and how fast water ap pears in the channel as direct runoff, has a direct bearing on the management of water, both as a resource and as a quality perspective. The ability to predic t, even in general terms, the pe rcentage of the precipitation that is discharged from the headwater areas as stormflow would be of inestimable value in environmental resource planning. It would also provide insight into the effects, if any, of land use upon the hydrograph (Woodruff and Hewle tt, 1970). Flood for ecasting in ungaged watersheds contains large uncer tainties, due to the complex processes of basin response, 13

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heterogeneity of watershed characteristics, inadequate representation of the contributory factors that control watershed response, and m easurement errors in gaged watersheds. Despite the uncertainties associated with flood forecasting in ungaged watersheds, it is important to formulate and implement appropria te science programs to make improvements to the overall predictive capability and to make reliable predictions in ungaged basins. New knowledge and new technological advances ar e becoming available to the hydrological community. There is now increased process understanding, more adva nced theories, new measurement technologies such as satellites and environmental tracers, advanced data processing, data archiving, and visualization technologies. These capabilities point to exciting new opportunities for advancing th e science of hydrology that are unimaginable at the present time, and for improved predictions for the be nefit of mankind (Sivap alan et al. 2003). 1.3 Watershed Delineation and Stream Network Detection Using DEMs Watersheds are a fundamental landscape unit for the cycling of water, sediment and dissolved geochemical and biogeochemical constituen ts. As such, they integrate all aspects of the hydrological cycle within a defined area that can be studied, quantified and acted upon. The watershed, thus, is a metaphor for integration of hydrological processes rela ted to surface water, groundwater, evapotranspiration, etc., and the ex plicit coupling of hydrology, geochemistry and ecology. Flood forecasting is predicting flow rates and water levels for periods ahead, using realtime precipitation and streamflow data in rainfall-runoff and streamflow routing models. Depending on the size of the watershed or river basin time periods may vary from a few hours to several days. Several hydrological models are deve loped to accentuate the essential aspects of a system in order to simplify the complexity of the rainfallrunoff in the real world. Predictions of hydrological response require prior knowledge of water sources and pathways within basins and 14

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cannot be performed adequately without first addressing issues related to water quantity and the distribution of flow path ways and residence times (Sivapalan et al. 2003). Stream networks were traditionally obtain ed by land surveying te chniques and utilizing paper maps. This method is time consuming, labor intensive, and prone to errors, due to unavoidable human error and prec ision limitations. The field of catchments delineation and stream network detection was re volutionized in the 20th century by the computer manipulation of spatial arrays of terrain he ights, or digital elevation mode ls (DEMs), which can quantify and portray ground-surface form over large areas (Maune, 2001). The development of geographic information systems (GIS) and DEMs has provided an opportunity to describe the pathways of water movement in a watershed. DEM databases fo r the United States provi de data that allows the extraction of drainage networks from them (Band 1986; O'Callaghan and Mark 1984). Topographic structure, watershed delineations, an d overland flow paths derived from DEMs can be transferred to a vector-bas ed GIS for further analysis. Adequate DEM resolution is of high importance. Local, state, and federal agencies have relied on US Geological Survey 1:24,000 scale topographic maps for information on stream networks for planning, management, and regulatory programs related to streams. Darling et al. (2002) demonstrated the low accuracy of US Geological Survey 1:24,000 scale maps in depicting the presence and location of low order, headwaters streams. Apart from the resolution issue, there are errors in USGS DEMs (Shortridge, 2001). Most of the errors in US Geological Survey DEMs originated in the contour maps from which they were derived and thus cannot be reduced through efforts of the user. Contour maps were never intended to provide elevations of the high density and accuracy increasingly required for terrain modeling. Map accuracy standards vary widely and do not provide a rigorous evaluation. Production standards only 15

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guarantee a statistical le vel of quality; locally, accuracy can be low (Pike, 2002). Contour maps are merely models of varying fi delity of topography, just as DEMs are, in turn, imperfect models of the maps (Ollier, 1967). DEM creation techniques that avoid map contours as the so urce of digital heights can improve quality. Airborne Laser Swath Mappi ng (ALSM) technology (a lso referred to as LIDAR) promises DEMs of fine resolution a nd high accuracy. ALSM enables beach and upland mapping with a spatial resolution of 1 m or be tter, a vertical accur acy of 5 cm, and a horizontal accuracy of 30 cm However, all DEMs are in some respect flawed (Coops, 2000) and considerable attention has to be paid to the errors in the train model itself. Several algorithms have been developed for rapid parameterization of drainage network and subcatchment properties from available DEMs which later can be implemented for subsequent use in hydrologic surf ace runoff models. Most existing DEMs have been interpolated by sampling designs and computer algorithms that add artifacts and other di stortions inherent in the processing (Shortridge, 2001). Therefore, it is important to understand the limitations of each algorithm. 1.4 Flood Processes in Karst Systems Karst terrain is characterized by sinkholes, depressions, caves, and underground drainage, generally underlaid by soluble rocks such as limestone and dolomite. The major obstacles for modeling flood processes in karst areas are a lack of understanding and model representations of the distinctive features and processe s associated with runoff generation ( Liu et. al, 2005). Part of the rainfall infiltrates the surface and rainfall in excess of the infiltration capacity of the surface becomes Hortonian overland flow. The infiltrated wate r flows downhill through porespace in the shallow subsurface as stormflow and also percolates into deeper soil becoming groundwater. When shallow subsurface stormflow reach es saturated soil it returns to the surface 16

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and joins overland flow as runoff (Dunne and Leopold 1978). This runoff reaches the stream network and flows to the outlet of the basin b ecoming a flood if it overtops banks or levees. Karst topography represents a special case where the groundwater can flow through voids and channels in the underlying limestone bedr ock and resurface miles downstream while not appearing on the surface as ove rland flow. This subsurface runoff also responds to rainfall and can be correlated with associated upstream rainfall events. The rate that water infiltrates in karst features is an important fact or and varies in different ar eas. The complex hydrological and hydrogeological structure of karst topography needs to be ta ken into account in the rainfallrunoff models. The focus of this work will be on the effects of karst topography on rainfall-runoff modeling. Six watershed characteris tics that are known to be the most important parameters in rainfall-runoff modeling (area, slope, stream density, basin roughness, compactness ratio, and percentage of impervious area) al ong with percentage of karst area in each watershed and rainfall duration and rainfall volume are considered to be the variables of a linea r regression model. The source of the karst topography coverage for this research is the Florida aquifer Vulnerability Assessment (FAVA) study which is explained more in section 3.6.6. 1.5 Research Objectives This research was conducted in order to take into account the complex structure of karst topography in the rainfall-runoff models. For this purpose, a model was explained in mathematical terms by executing a linear re gression analysis base d on seven watershed characteristics and two rainfall characteristics. ArcHydro and GIS tools were used to delineate 16 watersheds in Southwest Florida Water Management District and to calculate characte ristics of each watershed. Two common measures of watershed response time, Centroid Lag a nd Centroid Lag-to-Peak, are calculated from 17

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hydrograph/hyetograph pairs and are considered to be the dependent variables of two different linear regression models. Hourly pr ecipitation and streamflow data from three different rainfall events were used to obtain time parameters for each watershed. Six watershed characteristics that are known to be the most important parameters in rainfall-runoff modeling (area, slope, stream density, basin roughness, compactness ratio, and pe rcentage of impervi ous area) along with percentage of karst area in each watershed and rainfall duration and rainfall volume are considered to be the independent vari ables of the linear regression model. The main objective of this study is to investig ate how karst systems affect the Centroid Lag and Centroid Lag-to-peak in watersheds. Apart from simulating the effects of karst topography on rainfall-runoff modeling, the resu lts of this study can be used to improve flood forecasting in ungaged basins. Also, this study established an approach by applying GIS into modeling of stream response time and can be used as a refe rence for the process of watershed delineation and stream network detection using remote sensed data, GIS, and ArcHydro tools. 18

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Figure 1-1. Global trends of water-related disasters 19604 ( World Water Development Report, Managing Risks: Securing the Gain of Development, 2006). 19

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CHAPTER 2 LITERATURE REVIEW 2.1 Rainfall-Runoff Modeling Usin g Watershed Characteristics The quantitative analysis of drainage networks and catchme nt shapes is a subject of interest to both geomorphologists and hydrologi sts (Moussa, 2003). Rainfa ll-runoff modeling at the catchment scale involves the analytical a nd/or numerical derivati on of both the dynamical and statistical properties of the discharge at the catchments outlet in terms of the rainfall and other climate, soil, vegetation, and geomorphological properties of the catchment (Sivapalan et al., 2002). Starting with Horton (1945) and Stra hler (1957, 1958, 1964), ba sin physiographic characteristics have been considered important indices of surface processes. These parameters have been used in various studies of geomorphology and surface water hydrology, such as flood characteristics, sediment yield and evolution of basin morphology. More recently, terrain characterization has become an important pa rt in modeling surface processes (Nogami, 1995). Many researchers have investigated the ma nner in which the basin geomorphology enters into our understanding of hydrological processe s on the basin scale (W oodruff and Hewlett, 1970, Magette et al., 1976, Gupta et al., 1986, Gupta and Mesa, 1988, Hughes, 1989, Vandewiele et al., 1991, Boughton and Chiew, 2007). Woodruff and Hewlett (1970) developed a linear regression model to predict the average annual hydrologic response (ratio of annual direct runoff to annual precipitation) in the eas tern US against 15 factors availa ble on 90 selected test basins (2 to 100 square miles) from New York to Alabam a. This study appears to be one of the first to attempt to predict stormflow volumes from basin parameters. The resulting regression coefficients of their study were nonsignificant indicating that the average percentage of a basin's annual precipitation that will b ecome quick flow cannot be predicted from available basin 20

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morphometry and implying that response is co ntrolled mainly by porous mantle factors not measurable on normal data sources. Magette et al (1976) used 16 catchments and were able to derive multiple linear regression equations for six of the model parameters. They used up to six of 15 catchment characteristics and observed mu ltiple regression coefficients of 0.80 to 0.95. Hughes (1989) used 33 catchments within 10 diffe rent regions in South Africa and the United States of America ranging from arid areas to te mperate areas with snow cover during winter for the estimation of parameters in an event based model. He used 13 physical catchment variables and was able to establish linea r relationships between most of the 12 model parameters and combinations of two to five of the 13 catchment characteristics. Vandewiel e et al. (1991) used 24 catchments in Northern Belgium and found high correlations between the three model parameters and the percentage of the permeab le area in the catchment. Boughton and Chiew (2007) performed multiple linear regression analysis to relate average annual runoff to average annual rainfall and potential ev apotranspiration (PET) using da ta from 213 catchments grouped according to location in six of the major Drainage Divisions of Australia. In his study, two-thirds of the estimates of average annual runoff were within 25% of the actual value. The regression approach was criticized in McIntyre et al. (2005). They suggest investigating the catchment de scriptor model parameter re lationship to produce a joint distribution function of the model parameters. Howe ver, this approach re quires a large number of observed catchments. Heuvelmans et al. (2006) investigated the use of neural nets for regionalization. Parajka et al. (2005) used kriging and a similarity based approach to transfer model parameters from one catchment to another. Beven and Kirkby developed TOPMODEL (Beven and Kirkby, 1979) which predicts the dynamics of the contributing areas based on the pattern of the soil topographic index. 21

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TOPMODEL has been applied in many practical hydrological studies such as estimation of flood frequency distribution, by continuous simulati on in ungaged catchments (Blazkova and Beven, 1997, 2002, 2004). Moretti and Montanari (2007) developed AFFDEF model which is a spatially distributed (grid based) model and performs continuous time si mulations of river flows at any time step and at any location in the catchment. AFFDEF was made computationally efficient by using simplified representations of some hydrological processes. In part icular, the subsurface flows are modeled using a simple approach, which does no t distinguish between ne ar surface and deep groundwater fluxes. This approximation might re sult in significant impr ecision in the modeling of the recessing limb of the hydrograph, especially in the case of highly permeable and flat river basins. AFFDEFs main strength is its comput ational efficiency, which allows the model to perform long simulation runs (e.g. thousands of years at hourly time step). Also, AFFDEF may represent an easy model to use and attractive in strument for hydrological applications where long simulation runs of river flows are needed at different locations of the catchment. The Curve Number (CN) Method is an appr oach based on relationships among rainfall, land characteristics, and streamfl ow, which developed from empiri cal investigations on small agricultural watersheds, and appeared in the US Soil C onservation Services National Engineering Handbook in the mid-1960s (Mockus, 1972). It was later extended and adapted for use in urban catchments (USDA-SCS, 1983, 1986). It is likely the most widely applied and accepted rainfall-runoff model in engineering pract ice, due to ease of use, widely available parameter estimation tables, and its incorporation in publicly available software such as TR-20 (USDA-SCS, 1983), TR-55 (USDA-SCS, 1986), HEC-1 (USACE-HEC, 1985), and HEC-1s later incarnation, HEC-HMS (USACE-HEC, 2000) The parameter estimation tables for CN 22

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enable one to easily determine the impacts of la nd-use and soil characteristics on runoff in a detailed and comprehensive fashion which is no t really comparable to any other existing watershed model. Those extensive and practical tables of CN published in USDA (1986) and many hydrology textbooks and handbooks enable e ngineers to evaluate detailed hydrologic impacts of various land-development and BMP strategies (Limbrunner et. al. 2004). Rainfall-runoff models could be transferred to ungaged basins using regression based methods (Abdulla and Lettenmaier, 1997; Kokkonen et al., 2003). However, the transfer of parameters is difficult. Choosing paramete r sets depend on the models and the objective functions used to measure their performa nce (Gupta et al., 1998; Madsen, 2003). Also, parameters are themselves uncertain (Kuczera and Mroczkowski, 1998) and a diverse set of possible parameter values can lead to simila r model performances (Beven and Freer, 2001). Bardossy (2007) performed a calibration of hydrological model parameters for ungaged catchments in the German part of the Rhine Rive r Watershed and concluded that parameter sets are considered as transferable if the corresponding model perf ormance on the donor catchment is good and the regional sta tistics: means and variances of annual discharges estimated from catchment properties and annual climate statis tics for the recipient catchment are well reproduced by the model. As model calibration can lead to non-unique sets of parameters it is difficult to associate the parameters estimated through calibration with the characteristics of the catchment and to transfer them to ungaged locations. In Hundech a and Bardossy (2004), model parameters were regionalized through simultaneous calibration of the same hydrological model on different catchments. This procedure however assumes pa rameters whose dependence can be described 23

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using a priori defined function. Further, only one set of parameters is obtained for the ungaged catchment. 2.2 Watershed Delineation and Stream Network Detection From the time when the methodology of basin analysis was first developed, it has been known for its tediousness and labor intensity. Mo st measurements must be made manually on large to medium scale topographic maps. This shortcoming has seriously limited the potential applications of drainage basi n characteristics in hydrology and geomorphology. Since the mid 1980s, with increasing popularity of geographic information sy stems (GIS) technology and availability of digital elevation models (DE Ms), the potential of us ing DEMs in studies of surface processes has been widely rec ognized (Moore et al., 1992; Wharton, 1994). Stream order was defined by Leopold (1994) as "a measure of the position of a stream in the hierarchy of tributaries." This definition of stream order evolved originally from Horton (1947) and was later modified by Strahler (1957). The Strahlers stream ordering system assigns source streams as first order; a segment downstr eam of the confluence of two (or more) first order streams is a second order stream; the c onfluence of two (or more) second order streams produces a third order stream and so on. When a st ream of a given order r eceives a tributary of lower order, its order does not change. Historically, watershed delineation has been done by visually interpreting and manually marking drainage divides on 1:240000-scale USGS topographic quadrangles and then properties such as link lengths and junction angles were measured (McDonnell, 1996). This process is tedious, time consuming, and inaccurate due to unavoidable human and t echnical errors. Also, the low resolution topographic quadrangles fail in depicting firstand second order streams. 24

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Speight (1968) manually applied the concept of runoff exceeding some minimum threshold to represent a channel network. Th is was performed based on the f act that a stream network is characterized by the dominance of fluvial processes over slope processes. Puecker and Douglas (1975) were among the fi rst to utilize DEMs to identify potential streams. In their approach, they employed th e upward concave and convex area concept in DEMs. Flow network is defined by local surfac e concavity because any part of a topographic surface which is locally concave-upward will yield an area of concentrated surface runoff. Thus, it can be inferred that the concave-upwards areas of the DEM represent channels. To detect these areas, a small window can be moved over the DEM. If there is a concave-upward region within the window, cells with the lowest elevation are assigned to be part of the stream network (Peucker and Douglas 1975). However, one of the most serious shortcomings of this method was that it generated discontinuous network segments and required intensive post processing to connect these segments. For low relief and topogr aphically complex landscapes, this problem can become more apparent and can inhibit the effectiveness of the t echnique (OCallaghan and Mark, 1984). Stream network detection from DEMs has three major steps: filling pits, computing flow direction, and then computing the contributing ar ea draining to each grid cell. Based on Speights flow accumulation approach, OCallaghan a nd Mark (1984) developed the D8 flow accumulation algorithm for automated extraction of drainage network using DEMs. In this approach, channels on a DEM are defined as al l points that accumulated runoff above some threshold. The overland flow accumulation appro ach represents basic hydrologic processes largely responsible for initiating and maintaining stream channels and is capable of generating a 25

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fully connected network. In the flow accumulation da ta set, each cell is as signed a value equal to the number of cells that flow to it (OCallaghan and Mark, 1984). One of the major problems in automatic networ k detection is the pres ence of depressions or sinks in DEMs which create obstacles during the calculation of flow direction. Mark (1984) developed a depression filling proc edure in which depression cells ar e raised to the elevation of the lowest neighboring cell. The resulting elevations are treated as a flat area and then assigned flow direction. This method assumes that depr essions are the result of underestimation of elevation values. Martz and De Jong (1988) assumed all sinks to be real topographic features which represent ponds or reservoirs, wher eas Jenson and Domingue (1988) followed the assumption that sinks are primarily data errors or artifacts. Martz and De Jongs algorithm did not give satisfactory results for relatively lo wer resolution DEMs (Martz and Garbrecht, 1992). Tribe (1991) developed an algorithm that inte grated cells other than the adjacent eight neighbors in evaluating the flow dire ction in flat areas. In this approach, the flow directions are assigned based on an interpolated straight line, thereby implementi ng a flow pattern to drain into the interpolated channel within th e flat area of a DEM. Tribes approach assumes depressions in a DEM are spurious and fills them to genera te flat surface and then assigns them flow directions. Tribes method increases the probl em of channel straightening and produces unrealistic, straight cut stream channel sec tions across high eleva tion areas (Martz and Garbrecht, 1995). The stream channels detected by the OCa llaghan and Mark algorithm matched the manual channels detected from the USGS contours. Th is procedure has been widely used and is implemented in Arc Hydro (Maidment, 2002). In the D8 approach, flow from each cell is 26

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directed into only one of eight possible directions and does not represent a realistic pattern when flow is dispersed on a hillslope (Quinn et al., 1991; Co sta-Cabral and Burges, 1994). Tarboton (1997) established the D multiple flow direction model for the representation of flow within a DEM. Tarbotons approach repr esents flow direction as a vector along the direction of the steepes t downward slope on eight triangular facets center ed at each grid cell (Figure 2.2.1) rather than repres enting flow in one of the eight possible directions from a grid cell to an adjacent or diagonal neighbor (D8). In this approach, an angle between 0 and 2 represents flow direction from each cell and an in finite number or flow directions are possible. Flow from a grid cell is shared between the two down gradient gr id cells closest to the vector flow angle based on angle proportioning. Using the right area threshold is a significant part of the automatic delineation. Tarboton et al. (1991) suggested methods base d on the relationship between sl ope and contributing area, and the constant stream drop prope rty to objectively decide upon a support area threshold. They emphasized that for a channel network to be usef ul, it should be extract ed at a correct length scale or drainage density. The constant drop pr operty is an empirical geomorphological attribute of properly graded drainage ne tworks, which has a physical basi s in terms of geomorphological laws governing drainage networ k evolution (Tarboton et al., 1992). By using the smallest weighted support area that produces networks consistent with this property, we are extracting the highest resolution drainage networ k that is statistically consiste nt with geomorphological laws. A smaller weighted support area thre shold would result for drainage networks where the first order stream drops inconsistent with the rest of the drainage network. When such a network is mapped one observes that streams seem to extend upward in what appears to be smooth hillslopes. A weighted support area larger than required for consistency with th e constant drop law results in a 27

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coarse drainage network that omits drainage paths from what contour examination would indicate to be valley forms where concentrat ed flow occurs (Tarboton, 2003). This procedure brings objectivity to the procedure but is still limited because the drainage density of the network extracted is still spatiall y uniform. Therefore, Tarboton and Ames (2001) suggested identification of local curvature as a method to account for spatially variable drainage density. Recent interest in automated watershed delin eation and stream detection is in improving stream data from more accurate and more de tailed surface topology. Jeffery et al. (1999) obtained different grid spaci ng from contours on the 1:25,000 scale topographical maps and compared digital elevation models of various grid spacings with a ground truth data set, acquired by ground survey. They studied the implications of these differences on key hydrologic statistics. In their study, catchment sizes and stream ne tworks from published DEMs were found to be significantly different than those from the ground truth in most in stances. Furthermore, the width functions and cumulative area relationships dete rmined from the published DEMs were found to fall consistently outside the 90% confidence lim its determined from the ground truth for more than 60% of the relationship, suggesting that these hydrologic properties are poorly estimated from published DEMs (Jeffery et al., 1999). Shiess and Tryall (2003) showed that there ar e inaccuracies when stream locations are determined using USGS 30m resolution DEMs. Within their study area (in the Sate of Washington), stream network fr om USGS DEMs were in some cases shifted by 300 feet and in some places the detected stream was not extending to the major channels. Hancock (2005) examined the effect of di gital elevation model grid resolution on hydrological and geomorphological char acteristics of a catchment ar ea in the Northern Territory, Australia. Examination of the effects of digita l elevation model grid scale demonstrates that 28

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while considerable catchment info rmation can be gained at digita l elevation grids greater than 10 m by 10 m, hillslope and hydrological detail can be lost. Geomorphic descriptors such as the areaslope relationship, cumulative area distribution, width function, and Strahler statistics were shown to be sensitive to digital elevation mode l grid scale. Conseque ntly, caution is needed when deciding on an appropriate grid resolution as well as the interpretation and analysis of catchment properties at grid scales greater than that for optimal hillslope and area aggregation definition (Hancock, 2005). A series of parameters influence the runoff response of a watershed. From an engineering hydrology point of view, a catchment can of ten be described by a hydrograph and if a hydrological model can describe th is hydrograph then a catchment is adequately characterized. From a geomorphological perspectiv e, the description of a catchment (and the ability to compare catchments) is a much deeper question that no t only includes the ability to understand runoff processes (i.e. the hydrograph) but also catchment form (i.e. hillslope length and shape, soil catena) (Hancock, 2003). Flow routing algorithms determine the water pa th from higher elevations in a DEM to the watershed outlet. Each algorithm creates differe nt results for the upsl ope contributing area and catchment area and selecting the right algorithm is of vital importance to the quality of any automated watershed delineation. Several flow routing algorithms have been developed and utilized in numerous GIS softwa re. In general, all of these algorithms are either single flow direction algorithms (water flows along a singl e direction from each cell) or multiple flow direction (water flows to more than one neighboring cell). The four most common algorithms are as follows: 29

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2.2.1 Single Flow Direction Algorithms 2.2.1.1 Deterministic 8 (D8) Flow goes from the center of a cell to only one of the surrounding cells that has the lowest elevation. Flow directions are, therefore, rest ricted to multiples of 45 degrees (OCallaghan & Mark 1984). The D8 algorithm limits flow to one grid cell which is the main reason it oversimplifies the possible flow and as a result, is unable to simulate divergent flows (Holmgren 1994). Also, this method resolves flow directions too coarsely, introducing grid bias (Tarboton 1997). 2.2.1.2 Random 8 (Rho8) This algorithm uses a degree of randomness ba sed on slope weight. Th e flow direction is determined by a random argument that is depend ent on the difference between elevation and the direction of the two adjacent ne ighbor cells as shown in Figur e 2-1 (Fairfield and Leymarie 1991). This algorithm breaks up the parallel flow paths that D8 produces (Wilson and Gallant 2000). However, a different flow network will be produced each time. Plus, upslope and specific catchment areas are deterministic quantities that we should be able to compute in a repeatable way and this algorithm may calcula te unrealistic and inc onsistent flow directions (Wilson et al., 2000 and Tarboton, 1997). 2.2.2 Multiple Flow Direction Algorithms 2.2.2.1 Flow Direction 8 (FD8) Water flows to all adjacent cells with lower elevation based on slope weight as shown in figure 2-2 (Quinn et al. 1991). In this approach, each cell will receive only a fraction of the discharge from neighboring higher el evation cell, and ther efore, the upslope contributing area of the receiving cell is composed of flows from different cells (Costa-Cabral and Burges 1994). This approach introduces substan tial dispersion. Since flow may be proportioned in up to eight 30

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possible directions, eight numbers need to be stored for each pixel (or recalculated each time they are needed), resulting in inefficient data storage (Tarboton, 1997). 2.2.2.2 Deterministic infinity (D ) Flow goes from one cell to two contiguous surrounding cells. The pr ocedure is based on representing flow direction as a single angle taken as the stee pest downward slope on the eight triangular facets centered at each grid point. Upslope area is then calculated by proportioning flow between two downslope pixels according to how close this fl ow direction is to the direct angle to the downslope pixel as shown in Figur e 2-3 (Tarboton 1997). This procedure offers improvements over prior procedures that have re stricted flow to eigh t possible directions (introducing grid bias) or proportioned flow according to slope (introducing unrealistic dispersion). To implement this procedure first consider a single triangular facet (Figure 4). Slope (downward) is represented by the vector (S1, S2) where: 1101)( dees 2212)( dees and ei and di are elevations and distances between pi xels as labeled in Figure 4. The slope direction and magnitude are )(tan12 1ssr 2 1 2 2 2 1sss Algorithm searches for the facet with the largest slope in order. The direction of steepest descent for each cell is th en represented as a continuous quantity between 0 and 2 31

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2.3 Rainfall-Runoff Modeling in Karst Systems In traditional hydrology, streamflow is divided into three major components, the fast (or surface) flow, the interflow, and the baseflow (Barnes, 1939; Ponce, 1989; Fetter, 1994). Surface flow usually occurs when the precipitation rate exceeds the infiltration capacity (Hortonian flow) or when land surface is saturated (Hewlett flow). The interflow is the infiltrated water that moves horizontally in the uns aturated zone and merges into the stream (Fetter, 1994), and the baseflow is the contribution of aquifer to the streamflow. This concept leads to the result that in surface hydrology models of large catchments with shallow aquifers, all three components depend in one way or another on th e size of the geographic catchment s. However, this is not the case of karst hydrology. In karst ba sins part of the water may en ter the earth surface through high permeability channels and voids that feed the karst network and may produce quick and large response of groundwater discharge to rainfall events (Rimmer and Salingar, 2006). Other part may infiltrate through low permeability areas to th e soil, and contribute smaller changes to the groundwater level (Jeannin and Grasso, 1997). Als o, in karst areas, the rainfall-discharge transformation is strongly dependent on the morphol ogy of the basin and the soil cover. If there is no soil, both the surface and in ter flow are practically absent, a nd the total stream discharge is composed of quick and slow flow components of groundwater (Jeannin and Grasso, 1997). In addition, typical for karst regions, large springs may immerge into streams in various locations and contribute large baseflow, which is not related to the size of the geographic surface catchments (Rimmer and Salingar, 2006). Rimmer and Salingar (2006) developed a mode l for both the baseflow and the surface flow components of a karst basin and verified their model by compari ng the calculated surface flow and baseflow with the daily time series of the baseflow separation procedure, and 32

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demonstrated good agreement of both the surface (r2 > 0.6) and baseflow (r2 > 0.77) components of each stream. Several field experiments (e.g. Anderson et al., 1997, Uchida et al., 2002, Freer et al., 2002), showed that runoff is to a large extent supplied by water following subsurface routes to the streams, either through the soil matrix, or within the fractured bedrock. This is typically observed in karst catchments where most of the runoff emerges from springs fed by water following subsurface routes, and surface runoff is small to negligible. Depending on pre-event soil moisture and rainfall intensity, diverse path ways are activated in the shallow subsurface and in the underlying rock formation, resulting in a broad distribution of travel times from the catchment surface to the springs. This extreme vari ability in travel times is caused by hydraulic property variations acting at seve ral continuous and discrete scales as a result of the intertwined arrangement of macro and micros tructural elements. However, this complexity remains largely unknown, because subsurface features are difficult to observe (Majone, 2004). An important appearance of such complexity is the large variability of the hydrographs typically observed at a spring (Baedke and Krot he, 2001). However, inference of travel time statistics from spring hydrographs is full of difficulties; the most critical are the non-linear effects due to soil moisture dynamics and pre-ev ent water contribution du ring storm flow (Labat et al., 2000). Modeling such complexity in karst areas is a challenging task and only a few attempts have been done so far to develop models (Labat et al., 2002), and to my know ledge none investigated how the karst structure influences time para meters of runoff generation. In this study, the complexity associated with karst systems is t ackled by a simplified linear regression model. The model assumes that time parameters of runoff at the watershed ou tlet (Centroid Lag and Centroid 33

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Lag-to-Peak) are function of watershed charac teristics and rainfall dur ation and volume. The main objective of this study is to investigate how karst systems affect the Centroid Lag and Centroid Lag-to-Peak in watersheds. The model developed here can contribute some information to the previous models aiming to explain the karst systems. 2.4 Quantitative Description of Response Hydrographs The terms normally used to analyze and mode l event hydrographs are defined on figure 2-4 and table 2-1. The Centroid Lag is defined as the time between the centroids of input and response and is a theoretically useful value characterizing the response time of a watershed. However, a more commonly used measure of watershed response time is the time between the centroid of input and the peak, called the Centro id Lag-to-Peak. Conceptually, the Centroid Lag is a constant characteristic of a watershed that depend on the time of travel of water to the basin outlet, and hence on basin size, topography, geolo gy, and land use. However, Centroid Lag-toPeak depends on both the watershed characteristic s and the duration and timing of input. There are three scientific and practical motivations for studying stream response to water-input events: water supply, flood prediction and forecasting, and water quality ( Dingman, 2002) The rationale behind selecting Centroid Lag and Centroid Lag-to -Peak is to describe both timing of the peak and hydrograph length quantitatively. Another reas on is to model a time parameter that is a constant characteristic of a watershed and a time parameter that depends on both the watershed characteristics and the duration and timing of in put. In this study, both these parameters are considered to be the dependent variables of two different linear regression models. 34

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S (a) = (100-96)/dx1 = 0.4 S (b) = (100-95)/dx2 = 0.35 S (c) = (100-98)/dx1 = 0.2 P (a) = 0.4/0.95 = 0.42 P (b) = 0.35/0.95 = 0.37 P (c) = 0.2/0.95 = 0.21 Figure 2-1. Flow direction using the Rho8 algorithm (Fairfield and Leymarie 1991). S (a) = (100-96)/dx1 = 0.4 S (b) = (100-95)/dx2 = 0.35 S (c) = (100-98)/dx1 = 0.2 a = 0.4/0.95 = 0.42 b = 0.35/0.95 = 0.37 c = 0.2/0.95 = 0.21 Figure 2-2. Flow distribution among downslope cells using th e FD8 algorithm (Quinn et al., 1995). 35

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Figure 2-3. Flow direction defi ned as steepest downward slope on planar triangular facets on a block centered grid (from Tarboton 1997). Figure 2-4. Terms used to describe hyetograph and response hydrograph (Dingman, 2002) 36

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37 Table 2-1. Definitions of terms used to describe hyetograph and response hydrograph (Dingman, 2002) Time instants Time durations t p 0 = beginning of precipitation Tw = t p e t p 0 = duration of water input t p c = centroid of precipitation Trl = t q 0 t p 0 = response lag t p e = end of precipitation T r = t pk t q 0 = time of rise t q 0 = beginning of hydrograph rise Tl p = t pk t p 0 = lag-to-peak t pk = time of peak discharge Tlc = t q c t p c = centroid lag t q c = centroid of response hydrograph T b = t q e t q 0 = time base t q e = end of response hydrograph Tc = t q e t p e = time of concentration

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CHAPTER 3 METHODOLOGY 3.1 Introduction This chapter covers the process of selecti ng study area, delineating watersheds within the study area, and data acquisition for the selected watersheds. Also, an overview of the model development for forecasting Centroid Lag and Centroid Lag-to-Peak as two important time parameters of hydrographs is presented in th is chapter. The model will be explained in mathematical terms by executing a linear re gression analysis base d on seven watershed characteristics and two rainfall characteristics. 3.2 Selection of the Study Area and its Karst Feature Formation In the modeling approach of this study, a pair of streamflow and pr ecipitation station is required for each watershed. Therefore, the delin eation and selection of watersheds depends on the availability of gaging stati ons. Figure 3-1 shows the location of USGS streamflow stations in Florida. This figure shows that there is a concentr ation of flow gaging sta tions in the south part of the Southwest Florida Water Management District (SWFWMD). Also, SWFMD has enough precipitation stations that record hourly precipitation throughout the district and these stations will be used for the rainfall data in the model (Figure 3-2). Another reason for selecting this area is that the relief is relatively high and theref ore, more detailed streams will be detected. The state of Florida, for the most part, is prone to sinkhole formati on. This is due to the fact that Florida is underlaid by thick carbonate deposits that ar e susceptible to dissolution by circulating groundwater. In rece nt geologic period, the Florid a carbonate platform has been exposed due to the fluctuations in sea level. Duri ng the ice ages, when much of the earths water was frozen in polar ice and gl aciers, sea level along the Flor ida peninsula was 280 to 330 feet lower than the current level. This low sea level exposed the carbonate platforms to karst 38

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processes. The lower sea level stands were accompanied by lower groundwater levels, which accelerated the development of karst (Watts, 1980; Watts and Hansen, 1988). As this ice melted, sea levels and groundwater levels increased, subm erging many of the karst features. This created many of the numerous lakes and ponds of west-central Florida as overburden materials settled into cavities in the unde rlying limestone. The type and thic kness of the overburden material control the type, loca tion, and frequency of sinkhole subsidence in the Southwest Florida Management District. In the s outh part of the SWFWMD, the ove rburden materials are generally thicker and less permeable and consist of cohe sive sediments. Although sinkhole formation is uncommon under these geologic conditions, where si nkholes do occur they are usually large and deep (Tihansky, 1999). Also, in north part of the SWFWMD, hydraulic heads in the in the surficial and intermediate aquifer systems are hi gher that than heads in the Upper Floridan aquifer. This causes downward movement of the groundwater from the surf icial aquifer system, recharging the intermediate aquifer system and the Upper Floridan aquifer which improves the formation of sinkholes by facilitating traveling of unconsolidated sediments into the subterranean cavities. Vertical shafts and sand-filled sinkholes can form high permeability pathways through otherwise effective confining un its (Stewart and Parker, 1992). From Figure 3-3 there appears to be an increasing frequency of sinkholes during the drought years in the 80s, although the statistics may be affected by reporting biases (Tihansky, 1999). Although many new sinkholes develop naturally, in west-central Florida, their increasing frequency corresponds to the accelerated deve lopment of groundwater and land resources. Floridas principal source of freshwater, groundwater, moves into and out of storage in the carbonate aquifers which are some of the most productive in the nation. Development of these ground water resources for municipal, industrial and agricultural water su pplies creates regional 39

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groundwater level declines that play a role in accelerating si nkhole formation (Tihansky, 1999). Limestone dissolution rates (on the order of millimeters per thousand years) are highest in areas where precipitation rates are high. Cavities deve lop in limestone over geologic time and result from chemical and mechanical erosion of material (Ford and Williams, 1989). 3.3 Precipitation and Streamflow Data 3.3.1 Streamflow data The growth and development of the United St ates was dependent on the availability of water resources and increasing ne ed for reliable water supplies quickly led to the need for streamflow data with which to design storage an d distribution facilities. In 1889, the first stream gaging station operated in the United States by the U.S. Geological Survey (USGS) was established on the Rio Grande near Embudo, New Mexico. The establishm ent of this early station was an outgrowth of effort s to train individuals to measure the flow of rivers and streams and to define standard stream-gag ing procedures (Wahl et al., 1995). As part of the U.S. Geological Surveys program for disseminating water data within USGS, to USGS cooperators, and to the gene ral public, the USGS maintains a distributed network of computers and fileservers for th e acquisition, processing, review, and long-term storage of water data. This water data is coll ected at over 1.5 million sites around the country and at some border and territorial s ites (Figure 3-4). This distribute d network of computers is called the National Water Information System (NWIS) Many types of data are stored in NWIS, including comprehensive information for site characteristics, well-construction details, timeseries data for gage height, streamflow, gr ound-water level, precipitation, and physical and chemical properties of water. Additionally, peak flows, chemical analyses for discrete samples of water, sediment, and biological media are accessible within NWIS. 40

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The "Real-time streamflow" map tracks short-te rm changes (over several hours) in rivers and streams. The map depicts streamflow conditions as computed at USGS gaging stations. The colors represent real-time streamflow compared to percentiles of historical da ily streamflow for the day of the year. NWISWeb is the USGS public web interface to much of the data stored and managed within NWIS. The goal of NWISWeb is to prov ide USGS, USGS cooperators, and users from the general public with a geographically seamless a nd easy-to-use interface to most of the USGS water data maintained in NWIS. Data prov ided by NWISWeb are updated from NWIS on a regularly scheduled basis, and real-time data are generally updated upon receipt at local Water Science Centers. NWISWeb provides several out put options including: graphs of real-time streamflow, water levels, and wa ter quality; tabular output in HTML and ASCII tab-delimited files; and summary lists for selected sites that ca n be used as a basis fo r reselection to acquire refined details. NWISWeb provides a framework to obtain data on the basis of category, such as surface water, groundwater, or wa ter quality, and by geographic area. Further refinement is possible by choosing specific site-s election criteria and by defini ng the output desired. NWIS data originates from all 50 states, plus border and territorial sites, and includes data from as early as 1899 to present (2008). Of the over 1.5 million sites with NWIS data, the vast majority are for wells; however, there are thousands of sites with streamflow data, many sites with atmospheric data such as precipitation, and about 10,900 of the sites provide real-time data ( http://waterda ta.usgs.gov/nwis ). The primary source of streamflow data in th e study area is the USGS streamflow gaging station network. NWISWeb is not, however, configur ed to present all NWIS data and users may need to contact local USGS offices to obtain some information. Also, hourly data for more than 41

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30 days must be requested from the USGS tape archives. For this study, hourly streamflow data were requested from the USGS Orlando office for 23 stations. Based on the downloaded daily rainfall-runoff graphs, three different periods we re selected for this study and the hourly data were obtained via email: 1. December 25th 2004 to January 10th 2005 2. January 14th 2005 to February 11th 2005 3. February 3rd 2006 to February 28th 2006 The reason for selecting these time periods is that a single isolated rainfall event is observed within these periods a nd there was no rainfall for several days before and after the storm event. Figure 3-5 shows the precipitation fo r one of the selected gaging stations in the study area and Figure 3-6 shows th e discharge for that station. The isolated storm events and corresponding discharges can be obs erved in these figures. More pr ecipitation-streamflow graphs are available in appendix A. 3.3.2 Precipitation Data The number of USGS precipitation stations in the study area is not enough for this study (Figure 3-7 ). Therefore, SWFWMDs precipitati on stations were used for hourly rainfall data. The Supervisory Control and Data Acquisition (SCADA) system for SW FWMD collects realtime rainfall data, surface and groundwater levels and selected atmospheric readings within 16 counties in Florida (Figure 3-2). 3.4 Digital Elevation Model The Digital Elevation Model fo r this study is the 15m reso lution DEM for the state of Florida that was developed by the Florida Depa rtment of Environmenta l Protection (FDEP) Florida Geological Survey (FGS) for use in the deve lopment of the evidential layers used in the 42

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Florida Aquifer Vulnerability Assessment (F AVA) study. Figure 3-8 shows the 15m resolution DEM for the state of Florida. 3.5 Delineating and Selecting Watersheds The study area was extracted from the original DEM using GIS tools. ArcHydro was used to perform several processes on th e extracted DEM to select the fi nal 16 watersheds in this area. Different DEM manipulations and step s of this process are as follows: 3.5.1 Digital Elevation Model Reconditioning The DEM Reconditioning function modifies Di gital Elevation Models by imposing linear features onto them. This function is an implementation of the AGREE method developed by Ferdi Hellweger at the University of Texas at Austin in 1997 (http://www.ce.utexas.edu/prof/maidment/GISHYDR O/ferdi/research/agree/agree.html). The system adjusts the surface eleva tion of the DEM to be consistent with a vector coverage. The vector coverage can be a stream or ridge line coverage. The vector coverage for DEM reconditioning in this study is the hydrographic features from 1:100,000 USGS maps (hydro100) and was downloaded from SWFWMDs website. The hydro100 data were converted to ArcInfo coverages from the 1:100,000 USGS Digital Line s Graphs (DLG). Figure 3-9 shows the cross section of a stream before and after reconditioning. Figure 3-10 shows the original 15m resoluti on DEM for the study area and Figure 3-11 shows the hydro100 data (stream locations deri ved from the USGS 1:100 topographic maps) for the study area. Figure 3-12 shows the DEM of the study area after reconditioning based on the hydro100 data. The values used for the AGREE parameters depend on the nature of the DEM and the issues that are being resolved. In many cases, a trial and error approa ch is needed before 43

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satisfactory results are obtained. For this study, a stream buffer of 8 ce lls (120m) and smooth drop of 15ft and sharp drop of 3ft were considered. 3.5.2 Fill Sinks This function fills the sinks in a grid. If cells with higher elevation surround a cell, the water is trapped in that cell and cannot flow. Th e Fill Sinks function modifies the elevation value to eliminate these problems. Most of the sinks in the DEM are located on the streams. This means that filling after the original AGREE procedure could wipe out the sm oothed channel upstream of the sink. This can be eliminated by dropping the stream a large dist ance. That way any filling done to remove sinks in the stream remains in the trench of the str eam. Figure 3-13 shows the DEM after the Fill Sink process. 3.5.3 Flow Direction This function computes the flow direction for a given grid. The values in the cells of the flow direction grid indicate the direction of th e steepest descent from that cell. ArcHydro uses Deterministic 8 (D8) Single Flow Direction algor ithm where flow goes from the center of a cell to only one of the surrounding cells that has the lowest elevation. Fl ow directions are, therefore, restricted to multiples of 45 degrees (OCallaghan & Mark 1984) as shown in figure 3-14. This function uses the filled sink DEM to dete rmine the direction for each cell. Figure 3-15 shows the flow direction grid for the study area. 3.5.4 Flow Accumulation This function takes as input a flow direction grid and comput es the flow accumulation grid that contains the accumulated number of cells upstr eam of a cell, for each cell in the input grid (Figure 3-16). Figure 3-17 shows the fl ow accumulation grid for the study area. 44

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3.5.5 Stream Definition The Stream Definition function takes a flow accumulation grid as input and creates a Stream Grid for a user-defined threshold. This th reshold is defined as a number of cells (default 1%). However, any other value of threshold as a drainage area in square kilometers can be selected. For example, the USGS Elevation Derivatives for National Applications (EDNA http://edna.usgs.gov/ ) approach uses a threshold of 5000 30 x 30 m cells (an area of 4.5 km2) for catchment definition. A smaller thre shold will result in a denser st ream network and usually in a greater number of delineated catchments. This fu nction computes a grid which contains a value of "1" for all the cells in the input flow accumulati on grid that have a value greater than the given threshold. All other cells in th e Stream Grid contain no data. Fo r this study, an area of 4.5 km2 was considered which is shown in Figure 3-18. 3.5.6 Stream Segmentation This function creates a grid of stream segments that have a unique identification. Either a segment may be a head segment, or it may be defined as a segment between two segment junctions. All the cells in a particular segment have the same grid code that is specific to that segment (Figure 3-19). 3.5.7 Catchment Grid Delineation This function creates a grid in which each ce ll carries a value (grid code) indicating to which catchment the cell belongs. The value co rresponds to the value carried by the stream segment that drains that area, defined in the stream segment link grid (Figure 3-20). 3.5.8 Catchment Polygon Processing The Catchment Polygon Processing function takes as input a catchment grid and converts it into a catchment polygon feature class. The adj acent cells in the grid that have the same grid 45

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code are combined into a single area, whose boundary is vectorized. The result will be similar to figure 24 with converted raster data to vector format. 3.5.9 Drainage Line Processing The Drainage Line Processing function (Terra in Preprocessing menu) converts the input Stream Link grid into a Drainage Line feature class. Each line in the feature class carries the identifier of the catchment in which it resides (Figure 3-21). One of the tasks performed by this function is the identification of upstream-downstream relationship. In rare cases, this relationshi p cannot be determined automatically based on connectivity and DEM, and the user will be asked to identify whether a segment is an outlet or not. This situation usually occurs when a drainage line segment is very short and the elevation at its beginning and end is the same, thus preventi ng the application from identifying the correct directionality. In such cases, the questionable segment will be highlighted, the application will zoom on it, and an input box will be brought up. Th e input box enables the user to zoom in or out of the segment and specify whether the segment is an outlet (most of the times) or not. This process is repeated for every such segment until the directionality is fully established. 3.5.10 Adjoint Catchment Processing The Adjoint Catchment Processing function generates the aggregated upstream catchments from the "Catchment" feature cl ass. For each catchment that is not a head catchment, a polygon representing the whole upstream area draining to its inlet point is constructed and stored in a feature class that has an "Adjoint Catchment" tag. This feature cla ss is used to speed up the point delineation process. 3.5.11 Batch Watershed Delineation The Arc Hydro tool Batch Point Generation can be used to interactively create the Batch Point feature class. In this study, Batch Point Generation was used on the location of 40 USGS 46

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streamflow stations. Each sta tion will be an outlet point of a watershed in the study area. The Batch Watershed Delineation function was used for each batch point to delineate the watershed in corresponding to each stream flow station. Figure 3-22 shows the location of 40 stations and the delineated watersheds. Some of the watersheds are part of a larger watershed and therefore the total number of watershe ds that can be seen in fi gure 27 is less than 40 polygons. 3.5.12 Watershed Selection As shown in Figure 3-23, USGS provides drai nage area for each station. The contributing area for each station is based on drainage basin boundaries that were in terpreted and digitized from the USGS 1:24,000 quadrangles. These boundaries were validated using on-screen visual inspection of the data at a scale of 1:12,000 and estimated to meet the National Map Accuracy standards, (approximately 13 meters) as of Ap ril 2000. However, new land developments have changed the topology of the region and these boundaries do not accurately follow the high elevations. Figure 3-24 shows the difference be tween the USGS drainage basin boundaries and the more accurate ArcHydro delineated drai nage basin in part of the study area. In some cases, deterministic 8 (D8) Single Flow Direction algorithm that is used in ArcHydro fails to detect stream bifurcati on and this causes delineating basin boundaries inaccurately which is one of the shortcomings of ArcHydro. Figure 3-25 is an example of stream bifurcation and shows that ArcHydro has followed only one of the paths. Also, the fill sink process is one of the necessa ry steps in watershed delineation to create a hydrologically correct train. However, when worki ng with large DEMs, this process fills some sinks that are within larger sinks. This might change the real contributing area for each Batch Point. As explained in 3.2., Development of ground wate r resources for municipal, industrial and agricultural water supplies create s regional ground-water-level decl ines that play a role in 47

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accelerating sinkhole formation. Also, manmade im poundments used to treat or store water, sewage effluent, or runoff can cr eate a significant increase in the load bearing on the supporting geologic materials, causing new si nkholes to form (Tihansky, 1999). The inaccuracies in the USGS drainage basin boundaries along with the ArcHydro shortcomings in watershed delineation and development of the new sinkholes, causes a difference between the watershed area delineated using ArcHydro tools and the contributing area from USGS Website. After delineating 40 wate rsheds, each watersheds area was calculated using ArcHydro tools and was compared with the watershed area obtained from the USGS website and it was realized that the area of some watersheds are significan tly different from the published areas in the USGS website. The ArcHydro areas for most of the selected watersheds are within 15% of the published USGS area for those watersheds. There are two watersheds (watershed ID 29 with 10.31 mi2 and watershed ID 31 with 3.13 m2) that do not satisfy the 15% criterion, but are included in th e model in order to include smal l-size watersheds in the model and to have some watersheds in the model with areas different from the USGS areas. Therefore 23 watersheds were remained for this study. Ta ble 3-1 shows the eleminiated watersheds and Table 3-2 shows the 23 watersheds with deline ated areas close to the USGS published areas. After looking at all 23 USGS stations, it was realized that discharge data are not available for five watersheds that woul d be desirable to sample. Figur e 3-23 shows information for a station that has data from 1962 to 1972 and ther efore cannot be used for this study. Also, two hydrographs are not well reproduced possibly due to the error in the gaging stations (Figure 326). Hence seven of the 23 watersheds were eliminat ed and 16 watersheds were determined to be desirable and remained for the analysis. Figure 327 shows the final 16 watersheds for this study. 48

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3.6 Watershed Characteristics Hydrologists frequently use watershed physic al characteristics as an aid in studying watershed hydrology. The most common characteris tics that affect runof f include area, slope, stream network density, basin roughness, and basin shape (Horton 1945, Strahler 1952, Taylor and Schwarz 1952, Haan and Read 1970, Woodruff et. al, 1970). Arc Hydro tools can be used to delineate watersheds from DEMS and ArcGIS tools will be used in this study to obtain watershed characteristics. Wate rshed characteristics that ease runoff removal produce high peaks and short hydrographs and characteristics that delay runoff removal produce low peaks and long hydrographs. The following watershed characteri stics will be consider ed the morphological characteristics and will be utilized to develop the linear regression model for this study. 3.6.1 Area Watershed area replicates the volume of water that a rainfall event generates. Peak flow volume is known to increase with increasing basin area and time to peak flow decreases with increasing peak flow volume (Taylor and Schwar z 1952). This study looks at the effect of area on time factors of hydrograph. For this purpose, each watersheds area wa s determined after delineation process and using GIS tools. The sma llest watershed is 3.13 mi2 and the largest one is 137.74 mi2. The average area for all 16 watersheds is 54.12 mi2. 3.6.2 Slope The simple relationship between increased ch annel slope and peak discharge has been recognized and demonstrated in previous studies. Slope is an important fa ctor in the momentum of the runoff which reflects flood ma gnitudes. It is expected that slope will have some effect on duration of runoff. Steeper watersheds will have mo re velocity and shorter time to peak. For this study, slope (in feet per mile) was described as relative relief (t he maximum elevation difference 49

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within the watershed) divided by basin parameter. In this study, slope va ries between 1.33 ft/mile and 3.44 ft/mile with an average of 2.35 ft/mile. 3.6.3 Stream Density Stream density is the ratio of the total length of streams within a watershed to the total area of the watershed. The streams that develop in a watershed increase the velocity of runoff by concentrating and moving it quickly to the main channel. Thus, a high value of the stream will cause a rapid storm response (Horton 1945). In this study, the minimum value of the stream density is 0.14 mile/mi2 and the maximum is 0.52 mile/mi2 with the average of 0.44 mile/mi2. 3.6.4 Watershed Roughness Watershed roughness is a product of stream de nsity multiplied by watershed relief (the maximum elevation difference within the watershe d). A smooth channel will cause larger peak values since roughness affects the velocity of overl and flow. This study will look at the effect of the roughness on the time factors of the hydrogra ph. In this study, the minimum, maximum, and average values of watershed roughness are 4.23, 118.58, and 49.34 mile.ft/mi2. 3.6.5 Basin Shape In a circular watershed, the rate of increase in streamflow is faster in comparison to a stretched out watershed. Elongate d basins collect and transmit runoff slowly while circular basins do so quickly (Strahler 1952). After Horton advocated the form factor, other wa ys of expressing the shape of a basin were proposed. In this study, compactness ra tio that was proposed by Miller (1953) as the ratio of the area of a drainage basin to the area of a circle having the same perimeter as a drainage basin, was used to represent the basin shape. The minimum value of the compactness ratio is 1.40 and the maximum value is 2.43 and the average is 1.95 for the 16 watersheds. Figure 3-28 shows these two watersheds. 50

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3.6.6 Percentage of Karst Area Recognizing the ubiquitous vulnerability of Floridas aquifer systems, the Florida Aquifer Vulnerability Assesment (FAVA) was developed to identify areas of relative aquifer vulnerability based on the lo cal hydrogeologic setting. Specifi cally, the FAVA project was designed to provide a detailed distribution of relative vulnerab ility which is based solely on natural properties of Floridas hydrogeology (Arthur et. al, 2005). Figure 3-29 shows the result of the FAVA study. The initial phase of the FAVA project involv ed identifying all spatial data potentially relevant to aquifer vulnerability in Florida and modified closed topographic depression coverage served as the proxy for karst feature density. Ev en though this method of identifying karst may have overestimated the number of karst features many of the false features were eliminated through spatial filtering prior to input into the FAVA models. Als o, the final product of the karst features was matched with more than 2,600 reported sinkholes mainta ined by the Florida Geological Survey (FGS, 2004). GIS tools were used to calculate the percentage of karst area in each watershed. The minimum percentage was 0.05 and the maximum was 6.6 and the average was 1.76 percent of the 16 watersheds area. Figure 3-30 shows the distribution of karst features in the study area. 3.6.7 Percentage of Impervious Area The fraction of rainfall that becomes runo ff depends on the cumulative precipitation, soil cover, and land use. Soil Conservation Serv ice(SCS) Curve Number(CN) model estimates precipitation excess as a func tion of cumulative precipitation, soil cover, land use, and antecedent moisture, using the following equation: (1) SIP IP Pa a e 2)( 51

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Pe = Accumulated precipitation excess at time t (mm) P = Accumulated rainfall depth at time t (mm) Ia = the initial abstraction (initial loss) (mm) S = potential maximum retention (mm) Ia = 0.2S (2) (Empirical relationship of Ia and S) SP SP Pe8.0 )2.0(2 (3) (substitute (2) for (1)) CN CN S 25425400 (4) (for SI Unit) CN= Curve number (30 < CN < 100) The curve number is a hydrologic parameter used to describe the storm water runoff potential for a drainage area. The curve number is a function of land use, soil type, and soil moisture. A feature showing impervious areas wa s used to represent the curve number in each watershed. High values of curve number are a ssociated with high runoff potential and low infiltration rates which are charact eristics of the impervious areas. In this study, areas with curve number of 84 (hard surface roads) and more are considered to be impervious areas (SCS, 1986) and the percentage of the impervious area was calculated for each watershed. Figure 3-31 shows the distribution of impervious area in the watersheds. The percentage of the impervious area changes from zero percent to 23.94% with an average of 6.54%. 52

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3.6.8 Storm Selection and Hydrograph/Hyetograph Generation In addition to the physical features of the watershed, the spatial and temporal characteristics of rainfall also control the sh ape of the runoff hydrograph. The primary source of streamflow data for this study is the USGS streamflow gagi ng station network. Based on the downloaded daily rainfall-runoff gr aphs, three different periods we re selected for this study and the hourly data were obtained from the US GS office in Orlando, Florida via email: 1. December 25th 2004 to January 10th 2005 2. January 14th 2005 to February 11th 2005 3. February 3rd 2006 to February 28th 2006 The reason for selecting these time periods is that after inspecting daily rainfall and streamflow graphs, a single isolated rainfall ev ent is observed within these periods and there was no rainfall for several days before and after the storm event. Also, the number of USGS precipitation stations in the st udy area is not enough for this study (Figure 3-7). Therefore, SWFWMDs precipitation stations were used fo r hourly rainfall data. Also, the necessity of using precipitation data records some distance from the watershed requires using the set of rainfall events that is distributed evenly throughout the study area. For this study, potential rainfall-streamflow gauge pairs were determined from the GIS maps for each watershed. Hydrograph/hyetograph pa irs for each rainfall event were plotted and used to calculate Centroid Lag and Centroid La g-to-Peak for each event. Four of the total 48 graph pairs were unrealistic (pr obably due to the gaging station failure during those periods) and determined to be useless for this st udy. These four graphs are from the 3rd rainfall event (February 3rd 2006 to February 28th 2006) and all together, 44 observations were used for the linear regression analysis. Appendix B show s all the 48 hydrograph/hyetograph pairs. 53

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54 Calculated centroid lag and centroid lag-to-peak values from hydrograph/hyetograph pairs are the dependent variables in the regression analysis. Apar t from the seven watershed characteristics that were discussed before, rainfall duration and rainfall volume for each observation were considered to be the independent values of the model as the characteristics of rainfall.

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Figure 3-1. Distributions of the USGS streamflow stations in Florida 55

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Figure 3-2. Locations of the SWFWMD precipitation stations 56

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Figure 3-3. Number of reporte d new sinkholes in West-Centr al Florida (Tihansky, 1999). Figure 3-4. Map of real-time streamflow compared to historical streamflow for the day of the year 57

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Figure 3-5. Precipitation for one of th e gaging stations in the study area Figure 3-6. Discharge for the station of Figure 3-5 58

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Figure 3-7. Locations of the USGS precipitation stati ons in Florida 59

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Figure 3-8. The 15 m resolution DEM for the state of Florida 60

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Figure 3-9. Cross section of a stream before and after reconditioning 61

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Figure 3-10. Original 15m resolution DEM for the study area (Elevation in ft) 62

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Figure 3-11. Hydro100 data for th e study area (Elevation in ft) 63

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Figure 3-12. Digital Elevation Model of the study area after reconditioning based on the hydro100 data (Elevation in ft) 64

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Figure 3-13. Digital Elevation Model afte r the Fill Sink process (Elevation in ft) 65

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Figure 3-14. Deterministic 8 (D8) Single Flow Direction algorithm where flow goes from the center of a cell to only one of the surroundi ng cells that has the lowest elevation (OCallaghan and Mark, 1994) 66

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Figure 3-15. Flow directi on grid for the study area 67

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Figure 3-16. Flow accumulation grid creation Figure 3-17. Flow accumulation grid for a part of the study area (Elevation in ft) 68

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Figure 3-18. Stream defini tion grid based on the 4.5 km2 contributing area (Elevation in ft) Figure 3-19. Stream segmentation for pa rt of the study area (Elevation in ft) 69

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Figure 3-20. Catchment Grid Delinea tion for part of the study area 70

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Figure 3-21. Drainage line for the study area 71

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Figure 3-22. Location of 40 stations and the delineated watersheds 72

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Figure 3-23. Available data fo r a station from USGS website Figure 3-24. Drainage basin boundaries from USGS website (red) and ArcHydro delineated drainage basin boundaries (blue). 73

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Figure 3-25. Digital Elevation Model and aerial photo showing that D8 algorithm fails to detect stream bifurcation where water is flowing from right to left and divides into two streams. Table 3-1. List of the 17 watersheds with si gnificantly different Ar cHydro and USGS areas Watershed ID USGS area (mi2) ArcHydro area (mi2) ArcHydro area / USGA area 1 89.27 71.95 0.81 2 35.58 3.12 0.09 3 84.67 143.2 1.69 4 58.9 42.45 0.72 5 22.3 12.16 0.55 6 11.88 3.13 0.26 7 22.97 60.11 2.62 10 162.15 200.81 1.24 21 23.84 15.82 0.66 22 na 32.99 #VALUE! 25 149.69 183.53 1.23 27 42.58 34.58 0.81 33 81.25 108.19 1.33 34 20.1 8.34 0.41 36 109.02 129.92 1.19 38 60.43 85.48 1.41 40 8.71 18.35 2.11 Min 8.71 3.12 Max 162.15 200.81 Ave 61.46 67.89 74

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Table 3-2. List of the 23 wate rsheds that approximately match the areas from the USGS website Watershed ID USGS area (mi2) ArcHydro area (mi2) ArcHydro area / USGA area 8 53 60.08 1.13 9 135 144.2 1.07 11 390 420.56 1.08 12 135 137.74 1.02 13 107 105.83 0.99 14 121 123.96 1.02 15 31.4 36.08 1.15 16 21.4 19.7 0.92 17 38.4 37.27 0.97 18 65.3 70.27 1.08 19 25.61 26.28 1.03 20 50.6 50.93 1.01 23 120 121.87 1.02 24 47.2 52.27 1.11 26 17.5 16.34 0.93 28 29.2 28.12 0.96 29 6.1 10.31 1.69 30 6.59 6.93 1.05 31 3.93 3.13 0.80 32 36.5 38.54 1.06 35 38.8 36.54 0.94 37 233 230.82 0.99 39 373 374.39 1.00 Min 3.93 3.13 Max 390 420.56 Ave 90.68 93.57 75

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Precipitation and Discharge for Watershed 9-022944910 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 1415161718192021222324 Time (Day of January 2005)Precipitation (in ) 0 5 10 15 20 25 30 35 40Discharge (cfs) Precipitation (in) Discharge (cfs) TLPC=1.707 Day TLC=5.176 Day Figure 3-26. Example of a hydrograph that is no t well reproduced, possibly due to the error in the gaging stations device 76

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Figure 3-27. Final 16 watershe ds selected for the study. 77

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Figure 3-28. Two watersheds in the study area with minimum (1.40) a nd maximum (2.43) value of the compactness ratio 78

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Figure 3-29. Map of the aquifer vulne rability in Florida from FAVA study ( http://www.dep.state.fl.us/geology/programs/hydrogeology/fava.htm ) 79

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Figure 3-30. Karst features in the study area 80

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Figure 3-31. Distribution of impervious ar ea in the watersheds of the study area 81

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CHAPTER 4 MODEL DEVELOPMENT 4.1 Regression Analysis Regression analysis involves identifying the re lationship between a dependent variable and one or more independent variables. A model of the relationship is hypothe sized, and estimates of the parameter values are used to develop an estimated regression equation. Various tests are then employed to determine if the model is satisfact ory. If the model is deemed satisfactory, the estimated regression equation can be used to pred ict the value of the de pendent variable given values for the independent variables (Lindley, 1987). In simple linear regression, the model used to describe the relations hip between a single dependent variable y and a single independent variable x is y = a0 + a1x + k. a0and a1 are referred to as the model parameters, and k is a probabilisti c error term that account s for the variability in y that cannot be explained by the linear relationship with x. If the error term were not present, the model would be deterministic; in that case, know ledge of the value of x would be sufficient to determine the value of y. The rationale behind the way the regression line is calculated is best seen from the point of view of prediction. A line gives a go od fit to a set of data if the points are close to it. Where the points are not tightly grouped about any line, a line gives a good fit if the poi nts are closer to it than to any other line. For predictive purposes, th is means that the predicted values obtained by using the line should be close to th e values that were actually obser ved, that is, that the residuals should be small. Therefore, when assessing the fit of a line, the vertical di stances of the points to the line are the only distances that matter. In multiple regression, more than one variable is used to predict the dependent value. The general purpose of multiple regression is to l earn more about the relationship between several 82

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independent or predictor variables and a depende nt or criterion variab le. In this study, seven watershed characteristics (are a, slope, stream density, ba sin roughness, compactness ratio, percentage of karst area, and pe rcentage of impervious area) and two rainfall characteristics (duration and volume) are considered to be the independent variables of a multiple linear regression model. Each set of ni ne variables were used separate ly to model Centroid Lag and Centroid Lag-to-Peak as dependent variables. Table 4-1 shows the short terms used in the equations for each parameter. Therefore, the regression equati on for Centroid Lag-to-Peak is: RVRDIAKACRBRSDSLDA RVRDIAKACRBRSDSLDA LPC T 9876543210 ,,,,,,,, Consequently, regression e quation for Centroid Lag is: RVRDIAKACRBRSDSLDA RVRDIAKACRBRSDSLDA LC T 9876543210 ,,,,,,,, RVRDIAKACRBRSDSLDA RVRDIAKACRBRSDSLDA LC T 9876543210 ,,,,,,,, Table 4-2 shows the summary of all the values of the independent a nd dependent variables for 44 observations. 4.2 Multiple Regression for Centroid Lag Table 4-3 shows the basic statistical informa tion for Centroid Lag. In order to use some well-developed theorems concerning hypothesis, it is necessary to make the assumption that the values of the dependent variable are independe ntly distributed as a normal distribution. A rough check would be to note that, for the normal dist ribution, 95% of the values should be within 2 standard deviations of the mean or only about 5% of the values should lie outside the interval -2 to 2 The 44 observed values of Centroid Lag sa tisfy this criterion. Also, the assumption of normality can be checked by the values of skewness and kurtosis. The skewness of a normal distribution is zero and its kurtosis is 3. However, there are no clear cut acceptable values for 83

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these items. The acceptable values, if any, depend on the specific guideline or area that the research is being taken on in. Tabachnick and Fidell (1996) suggest the following tests to validate the values of sk ewness and kurtosis. First we comput e standard error of skewness (SES) which is approximately n 6and is going to be 0.3693 for this case. Now if the absolute value of the skewness is greater than two times SES, we can conclude that data is considerably skewed. Since the absolute value of the skewness, 0.0668, is less than two times SES, 0.7386, we can safely assume the data is not skewed. A similar approximation for the standard error of kurtosis (SEK) is as follows: n SEK 24 which is 0.7385 for our case. If the absolute value of the difference of kurtosis and number 3 is greater than two times SE K, we would say the data has kurtosis problem. The absolute value of the difference of kurtosis and number 3 is equal to 0.6568 which is less than two times SEK, 1.47, suggesting that the data have no kurtosis problem. The normality of the Centroid Lag can be more observed in Figure 4-1 that shows the distribution of Centroid Lag us ing Histogram, Boxplot, density pl ot and Normplot. All of these plots suggest that Centroid Lag is convincingly a normal distribution. To go forward with the multiple linear regr ession modeling, first we do a single linear regression between every two possible pairs of variables. Table 4-4 shows the R2 correlation resulted from the linear regressions. As it can be seen, Centroid Lag has high co rrelation with Area and some moderate correlation with Slope, Stream Density, and Basi n Roughness. Also it can be seen that Basin Roughness and Area are strongly correl ated. But if their effects ar e in opposite directions we cannot eliminate one for the sake of simplicity of the model (Haan, 1977). As it will be seen in a little while, that is exactly the case here. We have nine variables and we would try to remove the 84

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least important ones along the way. First we do an overall multiple linear regression using all the nine variables: RVRDIAKACRBRSDSLDA RVRDIAKACRBRSDSLDA LC T 9876543210 ,,,,,,,, where TLC is the predicted value for Centroid Lag The vector resulted from the regression is shown in table 4-5 and the statistical features of these regression are listed as: R2 = 0: 7872 which means that 79% of th e variation in Centroid Lag is explained by the regression equation, FStat = 13 : 975, MSE is 0.3249 and standard error is 0.57. The value of FStat is used for a test of hypothesis that th e entire regression equation is not explaining a significant amount of the variation. This hypothesis is rejected since it exceeds F0.95, 9, 34=2.170. As it was mentioned previously, and values show, even though Basin Roughness and Area are highly correlated but their effects ar e in the opposite directi on which is due to the different signs of 1 and 4 in table 4.2.3. This means that as the area increases Centroid Lag increases but as basin roughness increas es the Centroid Lag decreases. The upper-left graph of Figure 4-2 shows mode led versus observed values of Centroid Lag. The points are nicely formed around a line and there is not any noticeable sign of nonlinearity due to undermodeling or overmodeling of certain data. The other graphs of Figure 4-3 give us some information about the residual data. We would like these data to be normal, and as it can be seen from the boxplot and the pr obability plot, the residual have a good normal distribution with skewness of 0.0197 and kurtosi s of 2.5667. One of the as sumptions in linear regression is that the errors are independent. This means that there should be no correlation between the errors and observations (Hann, 1977) As the upper-right graph of Figure 4-2 and graphs of the Figure 4-3 show, there is not any correlation between the re siduals and other data. 85

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Multiple regression is used to find a linear model for predicting unobserved values for the dependent variable. The model that is developed does not necessarily have to contain all of the independent variables. Thus, the points of concern are: 1) can a linear model be used and 2) what independent variables should be included (Ha nn, 1977). Therefore, we need to simplify the model in terms of the number of va riables. For this purpose, a test of the hypothesis that some of the independent variables are not significantly cont ributing to explaining th e linear variation in the dependent variable can be made by rearra nging the model so that only the independent variables that are contributing significantly to explaining the linear variation are left. Haan (1977) suggests that all of the variables retained in a re gression should make a significant contribution to the regression unle ss there is an overriding reason (theoretical or intuitive) for retaining a non-significant variab le. Since percentage of karst ar ea has a theoretical significance in this model, we eliminate all the variables with calculated t statistic values less than the t value for percentage of karst area. Therefore, compact ness ratio, slope, rainfall volume, and rainfall duration are eliminated at one time and the re gression shown in Table 4-6 results. Using the stepwise function from MATLAB (eliminating one va riable at a time) gives the same result as shown in Figure 4-4. This means we can reduce the number of predictors to five and the other four variables have no significant effect on the model and the statistical information of the model. Table 4-6 shows the new set of values for the vector resulted from the regression with five variables. In going to the second regression, R2 has been reduced from 0 : 79 to 0.78, MSE has been reduced from 0.3249 to 0.3058, and standa rd error has been reduced from 0.57 to 0.55. The FStat increased to 26.354 which exceeds F0.95, 5, 38=2.463 and it is concluded that the variables compactness ratio, slope, rainfall volume, and rainfall duration are not significant. The resulting prediction model is: 86

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TLC = 0.65 + 0.03 (Area) + 6.21 (Stream Density) 0.04 (Basin Roughness) + 0.07 (Karst Area Percentage) + 0.03 (Impervious Area Percentage) 4.3 Multiple Regression for Centroid Lag-to-Peak The boxplot graph in Figure 4-5 shows that ther e is an outlier in the Centroid Lag-to-Peak data. So we remove the corresponding datum (observation number 28 with TLPC=1.441 days) and then we continue our analys is using the filtered data. Tabl e 4-7 shows the basic statistical information of the new set of data for Centroid Lag-to-Peak. Figure 4-6 shows the distribu tion of Centroid Lag-to-Peak using Histogram, Boxplot, Density Plot, and Normplot after eliminating th e outlier. This figure shows that the data are normally distributed. To go forward with the multiple linear regr ession modeling, first we do a single linear regression between every two possible pairs of variab les as in our previous analysis of Centroid Lag. Table 4-8 shows the R2 correlation resulted from the linear regressions. Centroid Lag-toPeak has a good correlation with the Area, but it does not show any significant correlation with other variables. This suggests that the information about Centro id Lag-to-Peak is distributed among many variables and we expect that the model of Centroid Lag-to-Peak involves more variables than that of Centroid Lag. First we do an overall multiple linear regression using all the nine variables. RVRDIAKACRBRSDSLDA RVRDIAKACRBRSDSLDA LPC T 9876543210 ,,,,,,,, Where TLPC is the predicted value for Centroid Lag-to-Peak. Table 4-9 shows the ANOVA table for Centroid Lag-to-Peak with nine variables and Table 4-10 shows residuals for predicted Centroid Lag-to-Peak values. Similar to the Cent roid Lag, we would like the distribution of the residuals to be normal. However, the Boxplot of the Figure 4-7 for the re siduals at this point 87

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shows an outlier. To continue with our modeli ng, we remove this outlier (observation number 20) from our computations. Now we model the new set of Centroid Lag-to -Peak in terms of all the nine variables. Table 4-11 shows the ANOVA table for Centroid Lag-to-Peak with nine variables after removing the observation number 20. The vector resulted from the regression is shown in Table 4-11 and the statistical features of the regression are listed as: R2 = 0 : 8552, FStat = 21.004, MSE is 0.0176, and standard error is 0.13. As it was mentioned, and values show, even though Basin Roughnessand and Area are highly correlated, but th eir effects are in the opposite directi on which is due to the different signs of 1 and 4 in Table 4-11. The upper-left graph of Figure 4-8 shows mode led versus observed values of Centroid Lag-to-Peak The points are nicely formed around a line and there is not any noticeable sign of nonlinearity due to undermodeling or overmodeling of certain data. The other graphs give us some information about the residual data and confir m that there is no outlier in the residuals after removing the observation number 20. We would like these data to be normal, and as it can be the probability plot, the residual have a good norma l distribution with skewness of -0.0504 and kurtosis of 2.5005. As the upper-right graph of Fi gure 4-8 and graphs of the Figure 4-9 show, there is not a relationship between the residuals and ot her data. This has again another tie with the residuals being independent and possibly having a normal distribution. Now we need to simplify the model in terms of the number of variab les. Similar to the analysis of the Centroid Lag regression model, we use the t-stat and p-value for each coefficient and confirm the process with th e stepwise function from MATLA B which is shown in Figure 410. These numbers show that ka rst area percentage and imperv ious area percentage have no 88

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significant effect on the model a nd we can reduce the number of predictors to seven. Table 4-12 shows the new set of values for the vector resulted from the regression with seven variables. In this regression, R2 has been reduced from 0 : 855 to 0. 846, and MSE and standard error have remained the same. The FStat increased to 26.707 which exceeds F0.95, 7, 34=2.294 and it is concluded that the variables area percentage and impervious area percentage are not significant. The resulting prediction model is: TLPC = 5.01 0.01 (Area) 0.67 (Slope) 1.34 (S tream Density) + 0.02 (Basin Roughness) 1.50 (Compactness Ratio) + 0.40 (Rainfa ll Duration) 0.07 (Rainfall Volume) 4.4 Model Evaluation One of the objectives of mode ling physical processes in the hydrologic science is the prediction of a variable from a set of inputs. Us ually, pairwise comparisons of predicted values with observations determine how well a model f its the observed data (Legates and McCabe, 1999). The 17 watersheds that were eliminated from the initial 40 watersheds (table 3-1) are used to evaluate the linear regression models. After looking at all 17 USGS st ations, it was realized that discharge data are not available for six waters heds during the three periods that were used to develop the models. Also, two hydrographs are not well reproduced, possibly due to the error in the gaging stations. Therefore, eight watersheds were eliminat ed and nine watersheds were determined to be useful for model verification. Th e same time periods that were used to develop the model are applied in the model for evalua tion. Table 4-13 shows th e summary of all the values of the independent variables, along with the predicted and observed Centroid Lag and Cetroid Lag-to-Peak values for the nine watersheds. Table 4-14 shows the statistical information for the predicted and the observed Centroid Lag and Cetroid Lag-to-Peak and figures 4-11 and 4-12 show the scatterplot of the predicted and observed values. The coefficient of determination (R2), for Centroid Lag is 0.40 which indicates 89

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that the model explains 40% of the variability in the observed data. Simila rly, the coefficient of determination for Centroid Lag-to-Peak is 0.53 which indicates a stronger relationship between observed and predicted values compared to Centroid Lag. Cohen (1998) suggests that a co rrelation of 0.5 and above is large, between 0.3 and 0.5 is moderate, and less than 0.3 is small. However, he argues that such criteria are in some ways arbitrary and should not be observe d too strictly. Coefficient of determination has been widely used to evaluate the goodnessof-fit of hydrologic models. Howe ver, since it only evaluates linear relationships between the variables, it is limited in that it standardizes for differences between the observed and pred icted means (Legates and McCabe, 1999). To overcome the limitations of R2, the coefficient of efficiency (E) has b een used to evaluate the performance of hydrologic models. The coefficient of efficiency is defined by Nash and Sutcliffe (1970) as the ratio of mean square error (MSE) to the varian ce in the observed data, subtracted from unity: Coefficient of efficiency can range from minus infinity to 1.0, with higher values indicating better accuracy of the model. An efficiency of 1.0 ( E =1) occurs when there is a perfect match between the modeled and the obser ved data. An efficiency of zero ( E =0) shows that the model predictions are as good as the mean for obs erved values, whereas an efficiency less than zero (< E <0) indicates that the observed mean is a better predictor than the model. Willmott (1981) developed index of agreement to overcome the insensitivity of coefficient of determination to differences in the obser ved and predicted means and variances and its 90

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oversensitivity to outliers. Index of agreement is defined as the ratio between the mean square error and the potential error (PE), multiplied by n and then subtracted from unity: D=1.0n (MSE/PE) In this equation, potential e rror (PE) is defined as: The index of agreement varies from 0.0 to 1.0, with higher valu es indicating better agreement between the predicted and observed values. Coefficient of efficiency is suggested as th e most appropriate relative error or goodness-offit available. However, the index of agreemen t has advantages due to its bound between 0.0 and 1.0 (Legates and McCabe, 1999). Table 4-15 shows statistics for compar ing the goodness-of-fit for Centroid Lag and Centroid Lag-to-Peak models. Assuming an Alpha value of 0.05, d1 = 27 25 1 = 1 and d2 = 25, the critical level of F is 4.24. For Centroid Lag, since Fstat = 16.8 is much higher than 4.24, it is extremely unl ikely that an F value this hi gh occurred by chance. That is, the hypothesis that there is no relationship betw een observed and predicted values for Centroid Lag is rejected. Using Excels FDIST we can obt ain the probability that an F value this high occurred by chance. FDIST (16.8, 1, 25) = 3.84111E04 indicates an extremely small probability and we can conclude that the regression equation is useful in predicting the Centroid Lag. Simillarly, since Fstat value for Centroid Lag-to-Peak (27.8) is much higher than 4.24, it is extremely unlikely that an F value this high occurred by chance (With Alpha = 0.05, the hypothesis that there is no relati onship between observed and predic ted values for Centroid Lagto-Peak to be rejected when F exceeds the cr itical level, 4.24). Using Excels FDIST we can obtain the probability that an F value this high occurred by chance. FDIST (27.8, 1, 25) = 91

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1.8401E-5 which indicates an extremely small probability and we can conclude that the regression equation is useful in predicting the Centroid Lag-to-Peak. The examination of coefficient of determination (R2) and coefficient of efficiency (E) in table 4-15 shows similarities betw een the two coefficients. However, the values for the index of agreement, which are less sensi tive to outliers, show more pr omising relationships between predicted and observed values for both models. Fi gure 4-13 shows the cluste red column chart to compare the values of predicted and observed values for Centroid Lag. A basic inspection of this figure confirms that there is a good correlation be tween two sets of values. However, the model is underestimating the value of Centroid Lag for all three rainfall events in watersheds 2 and 4 and overestimating the value of Centroid Lag for all three rainfall events in watersheds 21 and 25. Table 4-16 shows that the mean square of re siduals are smaller in watersheds 40, 25, 36, and 21 suggesting that the model perf orms well in predicting Centro id Lag in these watersheds. Figure 4-14 shows the clustered column chart to compare the values of predicted and observed values for Centroid Lag-to-Peak. A basic in spection of this figure confirms that there is a good correlation between two sets of values. Ho wever, the model is un derestimating the value of Centroid Lag-to-Peak for all three rainfall ev ents in watershed 27 and overestimating the value of Centroid Lag-to-Peak for all three rainfall events in wate rsheds 34 and 40. Table 4-16 shows that the mean square of residuals are smaller in watersheds 4, 34, 2, and 36 suggesting that the model performs well in predicting Centro id Lag-to-Peak in these watersheds. The regression model for Centroid Lag is not performing well in watershed 2 (SMSR = 3.44) but the predicted values of Centroid Lag-to-P eak in this watershed are relatively close to the observed values (SMSR = 0.07). Table 3-1 sh ows a large difference between the ArcHydro area and the published USGS ar ea for this watershed (3.12 mi2 and 35.58 mi2). It is possible that 92

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93 ArcHydro has not properly delineated the watershed boundary and hence other watershed characteristics are not realistic for this waters hed. However, since Centroid Lag-to-Peak is a function of both the watershed characteristics and the duration and timing of input, the regression model for predicting Centroid Lag-to-Peak performs better for this watershed. The differences in the predicted and observed va lues could be due to the heterogeneity of the karst systems. Also, since the ArcHydro ar eas of watersheds that are used for model validation are different from the published USGS areas, watershed char acteristics could be different from the real condition and hence the predicted values are different from the observed values.

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Table 4-1. Variables and their corresponding abbr eviations used in th e regression analysais Variable Abbreviation Area DA Slope SL Stream Density SD Basin Roughness BR Comp Ratio CR Karst Area Percentage KA Impervious Area Percentage IA Rainfall Duration RD Total Rainfall RV Centroid Lag-to-Peak TLPC Centroid Lag TLC 94

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Table 4-2. Summary of all the va lues of the independent and depe ndent variables for 44 observations Observation Watershed ID Centroid Lag-to-Peak TLPC (Day) Centroid Lag TLC (Day) ArcHydro Area (mi2) Slope Stream Density Basin Roughness Compactnes s Ratio Karst Area Percentage Impervious Area Percentage Rainfall Duration (Day) Total Rainfall (in) 1 8 0.421 4.128 60.0847 2.435391 0.391062 52.65974 2.012231 1.99202409 23.9368956 0.208333 3.14 2 12 1.162 3.892 137.7398 2.524345 0.469369 98.5789097 1.999797 0.43409177 17.3267027 0.208333 0.73 3 13 0.537 5.178 105.8307 1.472472 0.46661 60.9551237 2.432756 1.21907096 2.624755 0.208333 0.73 4 14 0.786 4.500 123.9612 1.747758 0.478529 57.7034767 1.748094 2.3663231 2.76408004 0.166667 1.86 5 15 0.319 2.273 36.08222 1.879856 0.462206 39.9435991 2.158913 1.9100332 1.71912718 0.208333 2.1 6 17 0.075 2.865 37.27258 2.10114 0.519398 57.4123638 2.430809 0.41556463 1.86469523 0.25 1.23 7 20 0.458 2.098 50.92965 2.28716 0.503709 63.2707303 2.170881 0.05044729 3.84522021 0.208333 2.23 8 23 0.753 3.854 121.8691 2.571086 0.504312 118.586915 2.337057 5.33904355 11.6186348 0.25 1.82 9 24 0.613 3.871 52.26641 2.49798 0.416848 49.8488398 1.86798 0.52168296 4.24357415 0.166667 1.97 10 26 0.771 2.791 16.34101 2.845599 0.407215 28.64405 1.725014 0.55566518 2.48667482 0.5 0.67 11 28 0.645 2.924 28.12309 1.954047 0.462253 32.5155346 1.91487 1.5737901 4.65368348 0.208333 3.02 12 29 0.603 2.579 10.31439 2.45492 0.348038 16.4375594 1.689843 2.48363967 1.90705976 0.208333 3.02 13 30 0.282 3.572 6.92758 3.078262 0.409749 18.5286247 1.574433 0.72970119 0 0.125 2.13 14 31 0.395 1.491 3.132598 3.440667 0.140271 4.22865461 1.396478 0.51127657 0.74889868 0.125 3 15 32 1.350 5.052 38.54253 1.333592 0.50349 25.2972493 1.711925 1.39204811 1.54018234 0.166667 1.37 16 35 0.226 3.463 36.53513 2.941062 0.515823 64.7923721 1.993234 6.60303432 23.4293289 0.125 1.58 17 8 0.462 4.190 60.0847 2.435391 0.391062 52.65974 2.012231 1.99202409 23.9368956 0.25 3.03 18 12 1.120 4.517 137.7398 2.524345 0.469369 98.5789097 1.999797 0.43409177 17.3267027 0.875 2.28 19 13 0.728 4.954 105.8307 1.472472 0.46661 60.9551237 2.432756 1.21907096 2.624755 0.791667 2.62 20 14 0.718 5.665 123.9612 1.747758 0.478529 57.7034767 1.748094 2.3663231 2.76408004 0.875 2.15 21 15 0.439 3.223 36.08222 1.879856 0.462206 39.9435991 2.158913 1.9100332 1.71912718 0.208333 1.34 22 17 0.073 3.211 37.27258 2.10114 0.519398 57.4123638 2.430809 0.41556463 1.86469523 0.083333 1.35 23 23 0.982 4.113 121.8691 2.571086 0.504312 118.586915 2.337057 5.33904355 11.6186348 0.916667 2.63 24 24 0.729 3.458 52.26641 2.49798 0.416848 49.8488398 1.86798 0.52168296 4.24357415 0.625 0.39 25 26 0.811 2.135 16.34101 2.845599 0.407215 28.64405 1.725014 0.55566518 2.48667482 0.666667 2.04 26 29 0.614 2.057 10.31439 2.45492 0.348038 16.4375594 1.689843 2.48363967 1.90705976 0.458333 1.49 27 31 0.453 1.388 3.132598 3.440667 0.140271 4.22865461 1.396478 0.51127657 0.74889868 0.416667 0.91 28 32 1.441 4.672 38.54253 1.333592 0.50349 25.2972493 1.711925 1.39204811 1.54018234 0.708333 3.37 29 8 0.491 4.148 60.0847 2.435391 0.391062 52.65974 2.012231 1.99202409 23.9368956 0.458333 1.53 95

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9630 12 1.128 4.363 137.7398 2.524345 0.469369 98.5789097 1.999797 0.43409177 17.3267027 0.208333 0.41 31 13 0.650 4.645 105.8307 1.472472 0.46661 60.9551237 2.432756 1.21907096 2.624755 0.666667 2.58 32 14 0.997 5.686 123.9612 1.747758 0.478529 57.7034767 1.748094 2.3663231 2.76408004 0.583333 2.74 33 15 0.402 2.759 36.08222 1.879856 0.462206 39.9435991 2.158913 1.9100332 1.71912718 0.5 2.62 34 17 0.191 2.786 37.27258 2.10114 0.519398 57.4123638 2.430809 0.41556463 1.86469523 0.666667 2.44 35 20 0.406 2.979 50.92965 2.28716 0.503709 63.2707303 2.170881 0.05044729 3.84522021 0.166667 0.66 36 23 0.873 4.513 121.8691 2.571086 0.504312 118.586915 2.337057 5.33904355 11.6186348 0.583333 3.03 37 24 0.821 3.753 52.26641 2.49798 0.416848 49.8488398 1.86798 0.52168296 4.24357415 0.5 2.57 38 26 0.677 2.781 16.34101 2.845599 0.407215 28.64405 1.725014 0.55566518 2.48667482 0.541667 0.7 39 28 0.502 2.882 28.12309 1.954047 0.462253 32.5155346 1.91487 1.5737901 4.65368348 0.583333 3.27 40 29 0.563 2.388 10.31439 2.45492 0.348038 16.4375594 1.689843 2.48363967 1.90705976 0.208333 3.37 41 30 0.337 4.071 6.92758 3.078262 0.409749 18.5286247 1.574433 0.72970119 0 0.583333 3.27 42 31 0.357 1.436 3.132598 3.440667 0.140271 4.22865461 1.396478 0.51127657 0.74889868 0.5 3.45 43 32 1.172 4.004 38.54253 1.333592 0.50349 25.2972493 1.711925 1.39204811 1.54018234 0.208333 1.84 44 35 0.288 3.628 36.53513 2.941062 0.515823 64.7923721 1.993234 6.60303432 23.4293289 0.375 2.62

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Table 4-3. Statistical info rmation for Centroid Lag Information Value Min 1.3880 Max 5.6860 Mean 3.5213 Median 3.6000 Standard Deviation 1.0987 Skewness -0.0668 Kurtosis 2.3432 Figure 4-1. Distribution of obser ved values for Centroid Lag (H istogram, Boxplot, Density Plot, and Normal Plot) 97

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Table 4-4. Correlation between diffe rent variables for Centroid Lag R2 TLC ArcHydro Area (mi2 ) Slope Stream Density Basin Roughness Comp Ratio Karst Area Percentage Impervious Area Percentage Rainfall Duration (Day) Total Rainfall (in) TLC 1.0000 0.5315 0.3107 0.3250 0.2498 0.0877 0.0475 0.0773 0.0642 0.0000 ArcHydro Area (mi2 ) 0.5315 1.0000 0.1289 0.2223 0.7101 0.2341 0.0492 0.1414 0.0717 0.0183 Slope 0.3107 0.1289 1.0000 0.3820 0.0169 0.1945 0.0032 0.0466 0.0048 0.0000 Stream Density 0.3250 0.2223 0.3820 1.0000 0.3608 0.4459 0.0754 0.0344 0.0041 0.0242 Basin Roughness 0.2498 0.7101 0.0169 0.3608 1.0000 0.4756 0.1650 0.2961 0.0313 0.0294 Comp Ratio 0.0877 0.2341 0.1945 0.4459 0.4756 1.0000 0.0391 0.0527 0.0037 0.0191 Karst Area Percentage 0.0475 0.0492 0.0032 0.0754 0.1650 0.0391 1.0000 0.2303 0.0015 0.0585 Impervious Area Percentage 0.0773 0.1414 0.0466 0.0344 0.2961 0.0527 0.2303 1.0000 0.0038 0.0001 Rainfall Duration (Day) 0.0642 0.0717 0.0048 0.0041 0.0313 0.0037 0.0015 0.0038 1.0000 0.0591 Total Rainfall (in) 0.0000 0.0183 0.0000 0.0242 0.0294 0.0191 0.0585 0.0001 0.0591 1.0000 98

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Table 4-5. ANOVA table for Centroid Lag with all nine variables Regression Statistics Multiple R 0.887234745 R Square 0.787185492 Standard Error 0.570052752 Observations 44 ANOVA Df SS MS F Regression 9 40.86813901 4.540904335 13.97372714 Residual 34 11.04864477 0.32496014 Total 43 51.91678378 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -0.527082345 2.439063912 -0.21610026 0.830200896 -5.483856561 4.429691871 ArcHydro Area (mi2) 0.0323674 0.007501666 4.314695022 0.000130259 0.017122181 0.04761262 Slope 0.215308755 0.423741937 0.508112925 0.614655095 -0.645838465 1.076455974 Stream Density 7.481997065 2.182635274 3.427964879 0.001609096 3.046348538 11.91764559 Basin Roughness -0.0414515 0.015409123 -2.6900622 0.01099277 -0.072766607 -0.010136394 Comp Ratio -0.002501958 0.643130093 -0.003890283 0.996918748 -1.30949955 1.304495635 Karst Area Percentage 0.054394751 0.067631003 0.804287211 0.426819286 -0.083047983 0.191837485 Impervious Area Percentage 0.03191714 0.015539195 2.053976361 0.047731415 0.000337696 0.063496585 Rainfall Duration (Day) 0.320068892 0.410766302 0.779199487 0.441252292 -0.514708666 1.154846449 Total Rainfall (in) 0.057432491 0.111266585 0.516170161 0.609076474 -0.168688414 0.283553396 99

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Figure 4-2. Analysis of the regression results for Centroid Lag Figure 4-3. Relationship be tween residuals and vari ables for Centroid Lag 100

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Figure 4-4. Effect of each variable on the linear regression model and the change in RMSE after eliminating each variable for Centoid Lag mode l (X1 to X9 represent variables in this order: Area, Slope, Str eam Density, Basin Roughness, Compactness Ratio, Karst Area Percentage, Impervious Area Per centage, Rainfall Duration, and Rainfall Volume) 101

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Table 4-6. ANOVA table for Centro id Lag with five variables Regression Statistics Multiple R 0.881005219 R Square 0.776170197 Standard Error 0.552994801 Observations 44 ANOVA df SS MS F Regression 5 40.29626028 8.059252056 26.35437018 Residual 38 11.62052351 0.30580325 Total 43 51.91678378 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 0.649025489 0.421643707 1.539274695 0.132023836 -0.204547564 1.502598541 ArcHydro Area (mi2) 0.030632474 0.003692934 8.294887213 4.69355E-10 0.023156519 0.038108429 Stream Density 6.210463495 1.159706537 5.355202628 4.35714E-06 3.862760369 8.55816662 Basin Roughness -0.037590506 0.006823239 -5.509187712 2.68217E-06 -0.051403432 -0.02377758 Karst Area Percentage 0.07043191 0.059740191 1.178970284 0.245739487 -0.050505783 0.191369602 Impervious Area Percentage 0.031481662 0.014430978 2.181533499 0.035399343 0.002267675 0.060695649 Figure 4-5. Distribution of obser ved values for Centroid Lag-to-Peak (Histogram, Boxplot, Density Plot, and Normplot). Boxplot shows an outlier in the data 102

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Table 4-7. Statistical informa tion for Centroid Lag-to-Peak Information Value Min 0.0730 Max 1.3500 Mean 0.6135 Median 0.6030 Standard Deviation 0.3045 Skewness 0.4465 Kurtosis 2.6764 Figure 4-6. Distribution of obser ved values for Centroid Lag-to-Peak (Histogram, Boxplot, Density Plot, and Normplot) after eliminating the outlier (observation number 28) 103

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Table 4-8. Correlation between different variables of Centoid Lag-to-Peak R2 TLCP ArcHydro Area (mi2 ) Slope Stream Density Basin Roughness Comp Ratio Karst Area Percentage Impervious Area Percentage Rainfall Duration (Day) Total Rainfall (in) TLCP 1.0000 0.2962 0.0737 0.0294 0.1053 0.0204 0.0000 0.0071 0.0629 0.0277 ArcHydro Area (mi2 ) 0.2962 1.0000 0.1526 0.2328 0.7110 0.2311 0.0487 0.1388 0.0821 0.0156 Slope 0.0737 0.1526 1.0000 0.3769 0.0295 0.2453 0.0025 0.0392 0.0003 0.0032 Stream Density 0.0294 0.2328 0.3769 1.0000 0.3893 0.4775 0.0783 0.0396 0.0018 0.0346 Basin Roughness 0.1053 0.7110 0.0295 0.3893 1.0000 0.4690 0.1648 0.2901 0.0432 0.0221 Comp Ratio 0.0204 0.2311 0.2453 0.4775 0.4690 1.0000 0.0383 0.0485 0.0077 0.0133 Karst Area Percentage 0.0000 0.0487 0.0025 0.0783 0.1648 0.0383 1.0000 0.2300 0.0020 0.0648 Impervious Area Percentage 0.0071 0.1388 0.0392 0.0396 0.2901 0.0485 0.2300 1.0000 0.0019 0.0002 Rainfall Duration (Day) 0.0629 0.0821 0.0003 0.0018 0.0432 0.0077 0.0020 0.0019 1.0000 0.0435 Total Rainfall (in) 0.0277 0.0156 0.0032 0.0346 0.0221 0.0133 0.0648 0.0002 0.0435 1.0000 104

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Table 4-9. ANOVA table for Cent roid Lag-to-Peak with nine variables before removing observation number 20 Regression Statistics Multiple R 0.889354157 R Square 0.790950816 Standard Error 0.15707139 Observations 43 ANOVA Df SS MS F Regression 9 3.080414183 0.342268243 13.87307 Residual 33 0.81415691 0.024671422 Total 42 3.894571093 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 5.220884913 0.712618776 7.32633645 2.07E-08 3.771051 6.670719 ArcHydro Area (mi2) -0.006182166 0.002176231 -2.840766949 0.007653 -0.01061 -0.00175 Slope -0.706978619 0.125721253 -5.623381893 2.93E-06 -0.96276 -0.4512 Stream Density -1.648815055 0.604265765 -2.728625632 0.010115 -2.8782 -0.41943 Basin Roughness 0.022587433 0.00441211 5.119417035 1.3E-05 0.013611 0.031564 Comp Ratio -1.521235187 0.190826936 -7.971805343 3.4E-09 -1.90948 -1.13299 Karst Area Percentage -0.03116635 0.018796074 -1.658130829 0.106768 -0.06941 0.007075 Impervious Area Percentage 0.000467988 0.004301267 0.108802449 0.914018 -0.00828 0.009219 Rainfall Duration (Day) 0.28437095 0.116598236 2.438895822 0.020277 0.04715 0.521592 Total Rainfall (in) -0.050234546 0.030923678 -1.62446868 0.113791 -0.11315 0.01268 105

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Table 4-10. Residuals for predic ted Centroid Lag-to-Peak with nine variables before removing observation number 20 Observation Predicted Centroid Lag-to-Peak (Day) Residuals 1 0.46187097 -0.041024595 2 1.012429243 0.149671225 3 0.418095277 0.119005191 4 0.955517014 -0.169169488 5 0.419744174 -0.100994174 6 0.244798717 -0.169934218 7 0.53268361 -0.074350276 8 0.760315769 -0.007568516 9 0.662922111 -0.049706652 10 0.551879507 0.219566702 11 0.585522159 0.059085684 12 0.479348047 0.12359313 13 0.255428477 0.02644558 14 0.378160849 0.016446994 15 1.112694875 0.2371315 16 0.257916337 -0.03172586 17 0.479245655 -0.016950573 18 1.124146424 -0.00367541 19 0.489035228 0.23846794 20 1.142378323 -0.424742664 21 0.45792243 -0.018867703 22 0.191375318 -0.118535812 23 0.909206514 0.073183423 24 0.872629285 -0.144075355 25 0.530453432 0.280412581 26 0.62729964 -0.012855196 27 0.566092673 -0.112795832 28 0.613841327 -0.123056196 29 1.028504298 0.099544502 30 0.455498241 0.194276555 31 1.029798319 -0.032656313 32 0.476563832 -0.07504868 33 0.302502907 -0.111832617 34 0.599703247 -0.193768901 35 0.79432219 0.078436249 36 0.727571605 0.092953689 37 0.562221355 0.11442185 38 0.679602628 -0.177203638 39 0.461765956 0.101336164 40 0.328497685 0.008888331 41 0.46219441 -0.10482726 42 1.100933238 0.071150093 43 0.276765146 0.011348549 106

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Figure 4-7. Analysis of the regression resu lts for Centroid Lag-to-Peak before removing observation number 20 107

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Table 4-11. ANOVA table for Ce ntroid Lag-to-Peak with ni ne variables after removing observation number 20 Regression Statistics Multiple R 0.924784 R Square 0.855226 Standard Error 0.13255 Observations 42 ANOVA Df SS MS F Regression 9 3.321237 0.369026 21.00372 Residual 32 0.562226 0.01757 Total 41 3.883463 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 5.123525 0.601918 8.512 9.99E-10 3.897459 6.349592 ArcHydro Area (mi2) -0.00461 0.001883 -2.4466 0.020097 -0.00844 -0.00077 Slope -0.68449 0.10626 -6.44162 3.04E-07 -0.90093 -0.46804 Stream Density -1.34669 0.516135 -2.60918 0.013686 -2.39802 -0.29535 Basin Roughness 0.020167 0.003778 5.338416 7.42E-06 0.012472 0.027862 Comp Ratio -1.56059 0.161371 -9.67081 5.11E-11 -1.88929 -1.23189 Karst Area Percentage -0.02142 0.016069 -1.33313 0.191902 -0.05415 0.011309 Impervious Area Percentage -0.00035 0.003636 -0.09526 0.924701 -0.00775 0.00706 Rainfall Duration (Day) 0.386398 0.102018 3.787557 0.000634 0.178595 0.594202 Total Rainfall (in) -0.05722 0.026161 -2.18736 0.036137 -0.11051 -0.00394 108

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Figure 4-8. Analysis of the regression resu lts for Centroid Lag-to-Peak after removing observation number 20 Figure 4-9. Relationship betw een residuals and variables for Centroid Lag-to-Peak 109

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Figure 4-10. Effect of each variable on the li near regression model a nd the change in RMSE after eliminating each variable for Centoi d Lag-to-Peak model (X1 to X9 represent variables in this order: Area, Slope, Stream Density, Basin Roughness, Compactness Ratio, Karst Area Percentage, Impervious Area Percentage, Rainfall Duration, and Rainfall Volume) 110

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111 Table 4-12. ANOVA table for Centroid Lag-to-Peak with seven variables Regression Statistics Multiple R 0.919846 R Square 0.846117 Standard Error 0.132576 Observations 42 ANOVA Df SS MS F Regression 7 3.285866 0.469409 26.70682 Residual 34 0.597597 0.017576 Total 41 3.883463 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 5.006341 0.59388 8.429891 7.63E-10 3.799432 6.21325 ArcHydro Area (mi2) -0.00389 0.001804 -2.15397 0.038419 -0.00755 -0.00022 Slope -0.66739 0.103998 -6.41736 2.49E-07 -0.87875 -0.45604 Stream Density -1.33966 0.515924 -2.59662 0.013808 -2.38814 -0.29118 Basin Roughness 0.018279 0.003531 5.177114 1.01E-05 0.011103 0.025454 Comp Ratio -1.50307 0.156212 -9.62196 3.1E-11 -1.82053 -1.18561 Rainfall Duration (Day) 0.402824 0.099344 4.054855 0.000277 0.200934 0.604715 Total Rainfall (in) -0.07147 0.024148 -2.95974 0.005575 -0.12055 -0.0224

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Table 4-13. Summary of all th e information of 27 observations used for model validation Observation Watershed ID ArcHydro Area (mi2 ) Slope Stream Density Basin Roughness Comp Ratio Karst Area Percentage Impervious Area Percentage Rainfall Duration (Day) Total Rainfall (in) Predicted Centroid Lag TLC (Day) Observed Centroid Lag TLC (Day) Predicted Centroid Lagto-Peak TLPC (Day) Observed Centroid Lagto-Peak TLPC (Day) 1 2 3.1187 1.3213 0.0971 1.3584 1.6914 2.4438 5.9777 0.2083 1.32 1.6426 2.537 1.4444 1.794 2 4 42.4473 2.7023 0.3768 45.8433 1.9493 8.0112 29.3770 0.1250 2.11 3.8718 4.879 0.1652 0.118 3 10 200.8081 2.9102 0.4589 171.9337 2.5629 6.7924 6.8890 0.7917 1.73 3.3288 2.288 0.2271 0.149 4 21 15.8182 3.2110 0.3887 33.1607 1.8842 4.4319 1.5403 0.2083 1.03 2.5687 1.629 0.0277 0.434 5 25 183.5317 1.7791 0.4441 84.2865 2.2212 0.9824 6.1915 1.0417 1.65 5.7970 4.674 0.0427 0.203 6 27 34.5842 1.1353 0.5485 27.2582 2.0997 1.4604 0.5968 0.9167 1.49 4.1238 3.076 0.8265 1.073 7 34 8.3432 0.9101 0.4521 9.5051 2.2558 0.0802 4.4366 0.9167 0.87 3.4667 4.229 0.8231 0.443 8 36 129.9236 2.6825 0.5229 144.9848 2.5583 3.1200 2.5428 0.6250 3.01 2.2900 3.415 0.3144 0.817 9 40 18.3546 1.6156 0.3643 14.5049 1.6227 0.8105 0.5065 0.7083 2.43 2.9547 2.237 1.2251 0.556 10 2 3.1187 1.3213 0.0971 1.3584 1.6914 2.4438 5.9777 0.2083 2.16 1.6426 4.407 1.3856 1.612 11 4 42.4473 2.7023 0.3768 45.8433 1.9493 8.0112 29.3770 0.2083 2.44 3.8718 4.893 0.1755 0.319 12 10 200.8081 2.9102 0.4589 171.9337 2.5629 6.7924 6.8890 0.6250 2.27 3.3288 5.327 0.1227 0.736 13 21 15.8182 3.2110 0.3887 33.1607 1.8842 4.4319 1.5403 0.7917 1.98 2.5687 2.253 0.1945 0.698 14 25 183.5317 1.7791 0.4441 84.2865 2.2212 0.9824 6.1915 1.0417 1.73 5.7970 5.254 0.0371 0.167 15 27 34.5842 1.1353 0.5485 27.2582 2.0997 1.4604 0.5968 0.4583 1.85 4.1238 4.977 0.6180 0.909 16 34 8.3432 0.9101 0.4521 9.5051 2.2558 0.0802 4.4366 0.1250 0.94 3.4667 3.591 0.5016 0.389 17 36 129.9236 2.6825 0.5229 144.9848 2.5583 3.1200 2.5428 0.4583 1.46 2.2900 2.198 0.3563 0.267 18 40 18.3546 1.6156 0.3643 14.5049 1.6227 0.8105 0.5065 0.7083 2.34 2.9547 3.282 1.2314 0.905 19 2 3.1187 1.3213 0.0971 1.3584 1.6914 2.4438 5.9777 0.1250 1.87 1.6426 3.013 1.3726 1.210 20 4 42.4473 2.7023 0.3768 45.8433 1.9493 8.0112 29.3770 0.2083 3.11 3.8718 4.221 0.1286 0.402 21 10 200.8081 2.9102 0.4589 171.9337 2.5629 6.7924 6.8890 1.0417 2.83 3.3288 2.498 0.2501 0.178 22 21 15.8182 3.2110 0.3887 33.1607 1.8842 4.4319 1.5403 0.9167 1.22 2.5687 1.744 0.2977 0.174 23 25 183.5317 1.7791 0.4441 84.2865 2.2212 0.9824 6.1915 1.0417 0.82 5.7970 5.715 0.1008 0.561 24 27 34.5842 1.1353 0.5485 27.2582 2.0997 1.4604 0.5968 0.2083 2.45 4.1238 4.742 0.4760 1.210 25 34 8.3432 0.9101 0.4521 9.5051 2.2558 0.0802 4.4366 0.4583 2.08 3.4667 2.165 0.5551 0.383 26 36 129.9236 2.6825 0.5229 144.9848 2.5583 3.1200 2.5428 0.4167 2.63 2.2900 2.864 0.2577 0.384 27 40 18.3546 1.6156 0.3643 14.5049 1.6227 0.8105 0.5065 0.6250 1.82 2.9547 3.498 1.2344 0.756 112

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Table 4-14. Statistical informati on for the predicted and the observed Centroid Lag and Cetroid Lag-to-Peak Information Count 27 27 27 27 Mean 3.3382 3.5410 0.5330 0.6239 Standard Error 0.2234 0.2375 0.0919 0.0865 Median 3.3288 3.4155 0.3144 0.4427 Standard Deviation 1.1608 1.2339 0.4774 0.4496 Sample Variance 1.3474 1.5225 0.2279 0.2021 Kurtosis 0.3725 -1.3328 -0.7791 0.6926 Skewness 0.7143 0.1424 0.8458 1.0941 Range 4.1545 4.0864 1.4168 1.6761 Minimum 1.6426 1.6288 0.0277 0.1184 Maximum 5.7970 5.7152 1.4444 1.7945 y = 0.6739x + 1.2913 R = 0.4019 0 1 2 3 4 5 6 7 01234567Observed Centroid Lag (Day)Predicted Centroid Lag (Day)Observed vs Predicted Centroid Lag Figure 4-11. Scatterp lot of the predicted and observed values for Centroid Lag 113

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y = 0.6834x + 0.2597 R = 0.5266 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 00.250.50.7511.251.51.752Observed Centroid Lag to Peak (Day)Predicted Centroid Lag to Peak (Day)Observed vs Predicted Centroid Lag to Peak Figure 4-12. Scatterplo t of the predicted and observed va lues for Centroid Lag-to-Peak Table 4-15. Statistics for comparing the goodness-o f-fit for Centroid Lag and Centroid Lag-toPeak models Statistics Centroid Lag Centroid Lag-toPeak Coefficient of Determination (R2) 0.401 0.526 Mean Square Error (MSE) 0.87681 0.092143 Fstat 16.8 27.8 Coefficient of Efficiency (E) 0.424 0.544 Index of Agreement (d) 0.821 0.880 114

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0 1 2 3 4 5 6 7 241021252734364024102125273436402410212527343640 123456789101112131415161718192021222324252627Centriod Lag (Day)ObservationObserved and Predicted Centroid Lag Predicted Centroid Lag TLC (Day) Observed Centroid Lag TLC (Day) Figure 4-13. Clustered column chart to compare the predicted and observed values for Centroid Lag 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 241021252734364024102125273436402410212527343640 123456789101112131415161718192021222324252627Centriod Lag to Peak (Day)ObservationObserved and Predicted Centroid Lag to Peak Predicted Centroid Lag to Peak TLPC (Day) Observed Centroid Lag to Peak TLPC (Day) Figure 4-14. Clustered column chart to compare the predicted and observed values for Centroid Lag-to-Peak 115

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116 Table 4-16. Sum of Mean Square Errors of observed versus predicted values for each watershed Watershed ID SMSE for Centroid Lag SMSE for Centroid Lag-to-Peak 2 3.440257 0.066774 4 0.726248 0.032417 10 1.921298 0.129077 21 0.554131 0.144716 25 0.521007 0.084761 27 0.735774 0.228021 34 0.763683 0.062403 36 0.535089 0.092254 40 0.305466 0.261231

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CHAPTER 5 DISCUSSION 5.1 Introduction This research was conducted in order to take into account the complex structure of karst topography in the rainfall-runoff models. For this purpose, a model was explained in mathematical terms by executing a linear re gression analysis base d on seven watershed characteristics and two rainfall characteristics. ArcHydro and GIS tools were used to delineate 16 watersheds in Southwest Florida Water Management District and to calculate characte ristics of each watershed. Two common measures of watershed response time, Centroid Lag a nd Centroid Lag-to-Peak, are calculated from hydrograph/hyetograph pairs and are considered to be the dependent variables of two different linear regression models. Hourly pr ecipitation and streamflow data from three different rainfall events were used to obtain time parameters for each watershed. Six watershed characteristics that are known to be the most important parameters in rainfall-runoff modeling (area, slope, stream density, basin roughness, compactness ratio, and pe rcentage of impervi ous area) along with percentage of karst area in each watershed and rainfall duration and rainfall volume are considered to be the independent vari ables of the linear regression model. 5.2 Discussion of Results Exploratory data analysis of the observed Centroid Lag values showed that the data are normally distributed. An overall multiple linear re gression for Centroid Lag using all the nine variables accounts for 79% of the variation in Centroid Lag, where MSE is 0.32 and standard error is 0.57. However, through analysis of the tstat and Pvalue of the variables in Table 4-5, it was concluded that the variables co mpactness ratio, slope, rainfall vol ume, and rainfall duration are not significant. Table 4-4 shows that there is a correlation betw een compactness ratio and two 117

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other variables that left in the model which could justify its insignificance in this model. The fact that Centroid Lag does not profoundly depend on th e duration and volume of input is in agree with Dingmans (2002) idea that Centroid Lag is a constant characteristic of a watershed that depends on the time of travel of water to the basin outlet, and hence on basin size, topography, geology, and land use. The resul ting prediction model using the remaining five variables is: TLC = 0.65 + 0.03 (Area) + 6.21 (Stream Density) 0.04 (Basin Roughness) + 0.07 (Karst Area Percentage) + 0.03 (Impervious Area Percentage) With the FStat value of 26.354 which exceeds F0.95, 5, 38=2.463, there is strong evidence to reject the null hypothesis that area, stream dens ity, basin roughness, karst area percentage, and impervious area percentage do not have an effect on the Centroid Lag. This model explains 78% of the variation in Centroid Lag, has a standard error of 0.55, and a mean square error of 0.31. The model indicates that Centroid Lag is posi tively correlated with the percentage of karst area, that is, the time between the centroids of input and respons e increases with increasing the percentage of karst area. In karst areas, part of the rainfall infiltrates the surface and rainfall in excess of the infiltration capacity of the surface becomes Hortonian overland flow. The infiltrated water flows downhill through pore spa ce in the shallow subsurface as stormflow and also percolates into deeper soil becoming groundwater. When shallow subsurface stormflow reaches saturated soil, it returns to the surface and joins overland flow as runoff. This runoff reaches the stream network and flows to the outlet of the basin becoming a flood (Dunn and Leopold, 1978). This process explains the findings of the model that presence of karst area in a watershed delays the runoff travel time to th e watershed outlet and produces long hydrographs. Initial data analysis of the observed Centroid Lag-to-Peak values show ed an outlier in the data. After removing the corresponding observati on, the data showed a normal distribution. 118

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The initial correlation matrix showed that Centroid Lag-to-Peak had a good correlation with the area, but it did not s how any significant correlation with other variables. This suggests that the information about Centroid Lag-to-P eak is distributed among many variables and we expect that the model of Centroid Lag-to-Peak involves more variables th an that of Centroid Lag. An overall multiple linear regression for Centro id Lag using all the nine variables accounts for 86% of the variation in Ce ntroid Lag-to-Peak, where MSE is 0.02 and standard error is 0.13. However, through analysis of the tstat and Pvalue of the variables in Table 4-11, it was concluded that the variables karst area per centage and impervious area percen tage have no significant effect on the model. We can therefore reduce the number of predictors to seven. The fact that rainfall duration and rainfall volume are significant parameters of the Centroid Lag-to-Peak confirms Dingmans (2002) idea that Centro id Lag-to-Peak depends on both the watershed characteristics and the duration and timing of input. The resul ting prediction model usin g the remaining seven variables is: TLPC = 5.01 0.01 (Area) 0.67 (Slope) 1.34 (S tream Density) + 0.02 (Basin Roughness) 1.50 (Compactness Ratio) + 0.40 (Rainfa ll Duration) 0.07 (Rainfall Volume) With the FStat of 26.71 which exceeds F0.95, 7, 34=2.294, there is strong evid ence to reject the null hypothesis that area, slope, stream densit y, basin roughness, compactness ratio, rainfall duration, and rainfall volume do not have an e ffect on the Centroid Lag-to-Peak. This model explains 85% of the variation in Centroid Lagto-Peak, has a standard error of 0.13, and a mean square error of 0.02. The model is a good repres entation of Centroid Lag-to-Peak based on its nearly zero MSE and small standard error. 119

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The model indicates that Centoid Lag-to-Peak is negatively correlated with area. This finding is consistent with Taylor and Schwarz (1952) that sugges t peak flow rate is known to increase with increasing basin area and time to p eak flow decreases with increasing peak flow rate. Also, as expected, Centoid Lag-to-Peak is ne gatively correlated with slope since steeper watersheds will have more velocity and shorter time to peak. However, the model indicates that presence of karst area does not have a significant effect on the time between the centroid of input and peak. The fact that karst area creates longer hydroghraphs but does not change the timing of peaks indicates that it affects the magnitude of peaks. Therefore, lower flow rates at the watershed outlet are expected. The results of model evaluation indicate that the predicted values of Centroid Lag have moderate correlation with the observed values and the predicted values of Centroid Lag-to-Peak have large correlation with the observed values. 5.3 Significance of Research The complex hydrological and hydrogeological st ructure of karst topog raphy needs to be taken into account in the rainfa ll-runoff models. Modeling such complexity in karst areas is a challenging task and only a few attempts have been done so far to develop models (Labat et al., 2002), and to my knowledge none of the models inve stigated how the karst structure influences time parameters of runoff generation. In this study, the complexity associated with karst systems is tackled by a simplified linear regression model that combines the effect of karst topography with other watershed characteristics for the qua ntification of their e ffects on hydrographs. This model can contribute valuable information to the previous models aiming to explain the rainfallrunoff process in karst system which consequen tly will provide a good basi s to the planners of the watershed management systems in ka rst-affected areas such as Florida. 120

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Also, unlike similar linear regression models in this study, watershed delineation, stream detection, and extraction of wate rshed characteristics were ex ecuted using DEMs as the main source of data. This study esta blished an approach by applying GIS into modeling of stream response time and can be used as a reference for the process of watershed delineation and stream network detection using remote sens ed data, GIS, and ArcHydro tools. Apart from simulating the effects of ka rst topography on rainfall-runoff modeling, the results of this study can be used to improve flood forecasting in ungaged basins. Such information, along with contaminant concentrations, can consequently be linked to water quality models to estimate contaminant loads in waters hed management plans. DEMs and precipitation data are two main model inputs and both are available from diffe rent sources for virtually any part of the USA. 5.4 Limitations of the Model This model is a simplified representation of actual hydrological conditions. Determining time factors for real watersheds is difficult due to the variability of contributing area, flow rates, and pre-event soil moisture and other seasonal factors. Also, the rate that water infiltrates in karst features is an important factor and varies in different areas. Another limitation is the lack of informati on on the timing and amounts of effective, as opposed to total, water inputs and outputs. The m odel assumes using data of a rainfall event that is distributed evenly throughout the watershed. For this model, this problem is tackled by applying the set of rainfall events that are distributed evenly throughout the study area. However, this assumption is not valid for large areas a nd the model may not be applied for significantly larger watersheds. Since forecasts and predictions of runoff response are very sensitive to climate and topography, the results of this model may not be applied to other geogr aphical regions. For 121

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example, this model was developed based on characteristics of small to moderate-size watersheds in Florida, where snow is absent. Snowfall and snowmelt contribution to runoff will create different conditions that ar e not considered in this model. 5.5 Future Research This research was conducted by applying a lim ited number of storms between the years 2004 and 2006. Similar research can be performed for more severe storms at a recurrence interval of 25-, 50-, 100-, and 500-year. The three storm events selected for this study are during the months of December through February and the seasonal effect could be a co ntributing factor for the model parameters. The model behavior could be observed in different seasons to account fo r pre-event soil moisture and other seasonal factors. Also, the model could be evaluated for watersheds in other geographical regions. 5.6 Conclusions The results of the linear regr ession model described in this research indicate that percentage of karst area in a watershed has a positi ve relationship with Centroid Lag. This is due to the fact that in ka rst areas, flow paths are predominantly in the subsurface and when the shallow subsurface flow reaches saturated soil, it returns to the surface and joins overland flow as runoff. Therefore, longer hydrographs are gene rated in karst affected watersheds. Also, the model indicates that presence of karst area does not have a significant effect on the time between the centroid of input and peak. The fact that karst area create s longer hydrographs but does not change the timing of peaks indicate s that it affects the magnitude of peaks. Therefore, lower flow rates at the watershed outlet are expected. The model developed for predicting Centroid La g explains 78% of the variation and has a standard error of 0.55 and a mean square error of 0.31. Similarly, the model developed for 122

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predicting Centroid Lag-to-Peak explains 85% of the variation and has a standard error of 0.13 and a mean square error of 0.02. The results of model evaluation indicate that the predicted values of Centroid Lag have moderate correlation with the observed values and the predicted values of Centroid Lag-to-Peak have large correlation with the observed values. 123

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APPENDIX A DAILY PRECIPITATION AND DISCHARGE GRAPHS FROM USGS WEBSITE 124

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APPENDIX B HOURLY PRECIPITATION AN D DISCHARGE GRAPHS Precipitation and Discharge for Watershed 8-022942170 0.2 0.4 0.6 0.8 1 1.2 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 10 20 30 40 50 60Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.421 Day TLC=4.128 Day Precipitation and Discharge for Watershed 8-022942170 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 3.04.05.06.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 10 20 30 40 50 60 70 80 90 100Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.462Day TLC=4.190 Day Precipitation and Discharge for Watershed 8-022942170 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 2 4 6 8 10 12 14 16 18 20Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.491 Day TLC=4.148 Day 143

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Precipitation and Discharge for Watershed 12-023010000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 100 200 300 400 500 600Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=1.162 Day TLC=3.892 Day Precipitation and Discharge for Watershed 12-023010000 0.1 0.2 0.3 0.4 0.5 0.6 3.04.05.0 6.07.0 8.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 100 200 300 400 500 600 700 800 900Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=1.120 Day TLC=4.517 Day Precipitation and Discharge for Watershed 12-023010000 0.05 0.1 0.15 0.2 0.25 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 50 100 150 200 250 300Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=1.128 Day TLC=4.363 Day 144

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Precipitation and Discharge for Watershed 13-023013000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 50 100 150 200 250 300Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.537 Day TLC=5.178 Day Precipitation and Discharge for Watershed 13-023013000 0.2 0.4 0.6 0.8 1 1.2 34567891 01 11 21 3 Time (Day of February 2006)Precipitation (in)0 50 100 150 200 250 300Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.728 Day TLC=4.954 Day Precipitation and Discharge for Watershed 13-023013000 0.2 0.4 0.6 0.8 1 1.2 1.4 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 20 40 60 80 100 120 140 160 180Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.650 Day TLC=4.645 Day 145

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Precipitation and Discharge for Watershed 14-022954200 0.2 0.4 0.6 0.8 1 1.2 1.4 1415161718192021222324 Time (Day of January 2005)Precipitation (in)0 50 100 150 200 250 300 350 400Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.786 Day TLC=4.500 Day Precipitation and Discharge for Watershed 14-022954200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 3.04.05.06.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 20 40 60 80 100 120 140 160 180 200Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.718 Day TLC=5.665 Day Precipitation and Discharge for Watershed 14-022954200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 252627282930311234 Time (Day of December 2004Januray 2005)Precipitation (in)0 50 100 150 200 250 300 350 400Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.997 Day TLC=5.686 Day 146

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Precipitation and Discharge for Watershed 15-023001000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 20 40 60 80 100 120 140 160 180Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.319 Day TLC=2.273 Day Precipitation and Discharge for Watershed 15-023001000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 3.04.05.06.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 20 40 60 80 100 120 140Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.439 Day TLC=3.223 Day Precipitation and Discharge for Watershed 15-023001000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 20 40 60 80 100 120Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.402 Day TLC=2.759 Day 147

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Precipitation and Discharge for Watershed 17-023003000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 20 40 60 80 100 120 140 160 180Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.075 Day TLC=2.865 Day Precipitation and Discharge for Watershed 17-023003000 0.2 0.4 0.6 0.8 1 1.2 3 4 5 6 7 8 9 10 11 12 13 Time (Day of February 2006)Precipitation (in)0 50 100 150 200 250Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.073 Day TLC=3.211 Day Precipitation and Discharge for Watershed 17-023003000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 20 40 60 80 100 120 140 160 180 200Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.191 Day TLC=2.786 Day 148

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Precipitation and Discharge for Watershed 20-023000180 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 50 100 150 200 250 300Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.458 Day TLC=2.098 Day Precipitation and Discharge for Watershed 20-023000180 0.2 0.4 0.6 0.8 1 1.2 3.04.05.06.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 20 40 60 80 100 120 140Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.286 Day TLC=2.410 Day Bad Data Precipitation and Discharge for Watershed 20-023000180 0.05 0.1 0.15 0.2 0.25 0.3 0.35 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 50 100 150 200 250Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.406 Day TLC=2.979 Day 149

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Precipitation and Discharge for Watershed 23-022695200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 20 40 60 80 100 120 140Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.753 Day TLC=3.854 Day Precipitation and Discharge for Watershed 23-022695200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 34567891 01 11 21 3 Time (Day of February 2006)Precipitation (in)0 20 40 60 80 100 120 140Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.982 Day TLC=4.113 Day Precipitation and Discharge for Watershed 23-022695200 0.2 0.4 0.6 0.8 1 1.2 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 20 40 60 80 100 120 140 160 180Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.873 Day TLC=4.513 Day 150

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Precipitation and Discharge for Watershed 24-022950130 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 20 40 60 80 100 120Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.613 Day TLC=3.871 Day Precipitation and Discharge for Watershed 24-022950130 0.02 0.04 0.06 0.08 0.1 0.12 3.04.05.06.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 10 20 30 40 50 60 70 80Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.729 Day TLC=3.458 Day Precipitation and Discharge for Watershed 24-022950130 0.2 0.4 0.6 0.8 1 1.2 1.4 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 20 40 60 80 100 120Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.821 Day TLC=3.753 Day 151

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Precipitation and Discharge for Watershed 26-022960570 0.1 0.2 0.3 0.4 0.5 0.6 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 5 10 15 20 25 30Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.771 Day TLC=2.791 Day Precipitation and Discharge for Watershed 26-022960570 0.1 0.2 0.3 0.4 0.5 0.6 0.7 3.04.05.06.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 10 20 30 40 50 60 70Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.811 Day TLC=2.135 Day Precipitation and Discharge for Watershed 26-022960570 0.05 0.1 0.15 0.2 0.25 0.3 0.35 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 10 20 30 40 50 60Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.677 Day TLC=2.781 Day 152

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Precipitation and Discharge for Watershed 28-022984880 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 50 100 150 200 250Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.645 Day TLC=2.924 Day Precipitation and Discharge for Watershed 28-022984880 0.05 0.1 0.15 0.2 0.25 0.3 3.04.05.06.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 5 10 15 20 25 30 35 40Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.899 Day TLC=3.127 Day Bad Data Precipitation and Discharge for Watershed 28-022984880 0.2 0.4 0.6 0.8 1 1.2 1.4 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 20 40 60 80 100 120 140 160 180Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.502 Day TLC=2.882 Day 153

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Precipitation and Discharge for Watershed 29-022984920 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 20 40 60 80 100 120 140Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.603 Day TLC=2.579 Day Precipitation and Discharge for Watershed 29-022984920 0.05 0.1 0.15 0.2 0.25 0.3 3.04.05.06.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 5 10 15 20 25 30 35 40 45 50Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.614 Day TLC=2.057 Day Precipitation and Discharge for Watershed 29-022984920 0.2 0.4 0.6 0.8 1 1.2 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 20 40 60 80 100 120Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.563Day TLC=2.388 Day 154

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Precipitation and Discharge for Watershed 30-022985300 0.2 0.4 0.6 0.8 1 1.2 14 151617 1819 20 21 22 2324 Time (Day of January 2005)Precipitation (in)0 10 20 30 40 50 60 70 80 90 100Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.282 Day TLC=3.572 Day Precipitation and Discharge for Watershed 30-022985300 0.2 0.4 0.6 0.8 1 1.2 3456 Time (Day of February 2006)Precipitation (in)0 0.5 1 1.5 2 2.5 3Discharge (cfs)Precipitation (in) Discharge (cfs) NO DATA Precipitation and Discharge for Watershed 30-022985300 0.2 0.4 0.6 0.8 1 1.2 1.4 2 52 62 72 82 93 03 11234 Time (Day of December 2004Januray 2005)Precipitation (in)0 10 20 30 40 50 60Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.337 Day TLC=4.071 Day 155

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Precipitation and Discharge for Watershed 31-022984950 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 20 40 60 80 100 120Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.395 Day TLC=1.491 Day Precipitation and Discharge for Watershed 31-022984950 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 3.04.05.06.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 10 20 30 40 50 60 70Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.453 Day TLC=1.388 Day Precipitation and Discharge for Watershed 31-022984950 0.2 0.4 0.6 0.8 1 1.2 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 20 40 60 80 100 120 140Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.357 Day TLC=1.436 Day 156

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Precipitation and Discharge for Watershed 32-022994100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 10 20 30 40 50 60 70 80 90Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=1.350 Day TLC=5.052 Day Precipitation and Discharge for Watershed 32-022994100 0.2 0.4 0.6 0.8 1 1.2 1.4 3.04.05.0 6.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 10 20 30 40 50 60Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=1.441 Day TLC=4.672 Day Precipitation and Discharge for Watershed 32-022994100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 10 20 30 40 50 60 70 80Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=1.172 Day TLC=4.004Day 157

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158 Precipitation and Discharge for Watershed 35-022700000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 14 15 16 17 18 19 20 21 22 23 24 Time (Day of January 2005)Precipitation (in)0 5 10 15 20 25 30 35 40 45Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.226 Day TLC=3.463 Day Precipitation and Discharge for Watershed 35-022700000 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 3.04.05.06.07.08.09.010.011.012.013.0 Time (Day of February 2006)Precipitation (in)0 10 20 30 40 50 60Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.134 Day TLC=2.672 Day Bad Data Precipitation and Discharge for Watershed 35-022700000 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 25 26 27 28 29 30 31 1 2 3 4 Time (Day of December 2004Januray 2005)Precipitation (in)0 10 20 30 40 50 60 70Discharge (cfs)Precipitation (in) Discharge (cfs) TLPC=0.288 Day TLC=3.628 Day

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LIST OF REFERENCES Abdulla, F. A. and Lettenmaier, D. P. 1997, Development of regional estimation equations for a macroscale hydrologic mode l, J. Hydrol., 197, 230. Anderson, S.P., Dietrich, W.E., Montgomery, D.R., Torres, R., Conrad, M.E., Loague, K., 1997. Subsurface flow paths in a steep, unchanne led catchment. Water Resour. Res. 33(12), 2637. Arthur, J., Baker, A. E., Cichon, J. R. Wood, A. R. Rudin, A., 2005, Florida Aquifer Vulnerability Assesment (FAVA): Contamination Potential of Floridas Principal Aquifer Systems, Devision of Water Resource Managemnt, Florida Department of Environmental Protection. Baedke, S.J., Krothe, N.C., 2001. Derivation of eff ective hydraulic parameters of a karst aquifer from discharge hydrograph analysis Water Resour. Res. 37(1), 13. Band, L. E. 1986. Topographic partition of waters heds with digital elevation models. Water Resour. Res., 22(1), 15-24. Bandaragoda, C.; Tarboton, D.G.; Woods, R.A. (2004). Applications of TOPNET in the distributed model inte rcomparison project. Journal of Hydrology 298(1) : 178 Bardossy, A., 2007. Calibration of hydrological model parameters for ungauged catchments, Hydrol. Earth Syst. Sci., 11, 703-710, Barnes, B.S., 1939. The structure of discharge recession curves. Trans. Am. Geophys. Union 20, 721. Beven, K. and Freer, J.: Equifinality, data as similation, and data uncertainty estimation in mechanistic modelling of complex environm ental systems using the GLUE methodology, J. Hydrol., 249, 11, 2001. Beven, K.J., Kirkby, M.J., 1979. A physically based, variable contributing area model of basin hydrology. Hydrological Scienc e Bulletin 24 (1), 43e69. Blazkova, S., Beven, K.J., 1997. Flood frequency prediction for data limited catchments in the Czech Republic using a stoc hastic rainfall model and TOP-MODEL. Journal of Hydrology 195, 256e278. Blazkova, S., Beven, K.J., 2002. Flood frequency estimation by continuous simulation for a catchment treated as ungauged (with uncerta inty). Water Resources Research 38 (8), doi:10.1029/2001WR000500. Blazkova, S., Beven, K.J., 2004. Flood frequency estimation by continuous simulation of subcatchment rainfalls and discharges with the aim of improving da m safety assessment in a large basin in the Czech Re public. Journal of Hydrology 292, 153e172. 159

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BIOGRAPHICAL SKETCH Ali Sedighi was born in 1975 in Tehran, Iran. He graduated from Sharif University of Technology with a Bachelor of Scie nce in civil engineering. He en rolled in the graduate school at the University of Florida in fall of 2001 and received his Master of E ngineering degree from Department of Civil and Coastal Engineering in 2003. He continued towards his PhD program under the guidance of his major pr ofessor, Dr. Kirk Hatfield. 167