U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2012–5071

Prepared in cooperation with the Kentucky Division of Water

Phase II Modification of the Water Availability Tool for 

Environmental Resources (WATER) for Kentucky: 

The Sinkhole-Drainage Process, Point-and-Click Basin 

Delineation, and Results of Karst Test-Basin Simulations

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1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

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Daily mean discharge, in millimeters per day

Date

Phase II Modification of the Water 

Availability Tool for Environmental 

Resources (WATER) for Kentucky: 

The Sinkhole-Drainage Process, 

Point-and-Click Basin Delineation, and 

Results of Karst Test-Basin Simulations

By Charles J. Taylor, Tanja N. Williamson, Jeremy K. Newson, Randy L. Ulery, 

Hugh L. Nelson, Jr., and Peter J. Cinotto

Prepared in cooperation with the Kentucky Division of Water 

Scientific Investigations Report 2012–5071

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2012

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Suggested citation:

Taylor, C.J., Williamson, T.N., Newson, J.K., Ulery, R.L., Nelson, H.L., Jr., and Cinotto, P.J., 2012, Phase II modification 

of the Water Availability Tool for Environmental Resources (WATER) for Kentucky: The sinkhole-drainage process, 

point-and-click basin delineation, and results of karst test-basin simulations: U.S. Geological Survey Scientific Investigations Report 2012–5071, 19 p. (plus appendixes)
iii

Contents

Abstract ..........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................2

Previous Work .......................................................................................................................................2

Phase II Modification of WATER .................................................................................................................3

Sinkhole-Drainage Process ...............................................................................................................4

Point-and-Click Basin Delineation.....................................................................................................5

Results of Karst Test-Basin Simulations ....................................................................................................8

Limitations of the SDP-TOPMODEL Approach...............................................................................12

Summary and Conclusions.........................................................................................................................16

References Cited .........................................................................................................................................17

Figures

1. Map showing physiographic regions of Kentucky and locations of karst test 

basins and U.S. Geological Survey streamflow gages used in the study ...........................3

2. Schematic showing major data-processing and computational steps in the 

A, standard (Phase I) TOPMODEL and B, modified (Phase II) sinkhole-drainage 

process (SDP) TOPMODEL approaches ...................................................................................4

3. Screen image of WATER graphical user interface (GUI) showing boundaries 

of simulation basin and sinkhole catchment subbasins .......................................................5

4. Screen-image examples of the information displays provided by the WATER 

graphical user interface (GUI)....................................................................................................6

5. Screen image of the data tree structure for the six principal input-data folders 

used by WATER.............................................................................................................................7

6. Histogram showing bias statistics for karst test basins used in the study.......................10

7. Histogram showing root mean square error (RMSE) statistics for karst test 

basins used in the study ............................................................................................................10

8. Histogram showing correlation statistics for karst test basins used in the study ..........11

9. Histogram showing Nash-Sutcliffe efficiency (Ef) coefficient statistics for karst 

test basins used in the study ....................................................................................................11

10. Boxplots showing statistical distribution for observed and simulated flow-duration 

data for karst test basins 0325300, 03287600, 03289300, and 03292470 ..............................13

11. Boxplots showing satistical distribution for observed and simulated flow-duration 

data for karst test basins 03295890, 03301700, 03307000, and 03310300 ............................14

12. Boxplots showing statistical distribution for observed and simulated flow-duration 

data for karst test basins 03312765, 03313700, 03413200, and 03438000 ............................15

Tables

1. Karst test basins and corresponding U.S. Geologcial Survey streamflow gages 

used for statistical evaluation of the karst-modified (Phase II) WATER-TOPMODEL 

sinkhole-drainage\process .........................................................................................................8
iv

Conversion Factors and Abbreviations

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

meter (m) 3.281 foot (ft)

meter (m) 1.094 yard (yd)

Area

acre 4,047 square meter (m2)

acre 0.4047 hectare (ha)

acre 0.4047 square hectometer (hm2)

acre 0.004047 square kilometer (km2)

square kilometer (km2) 247.1 acre

square kilometer (km2) 0.3861 square mile (mi2)

Flow rate

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s)

millimeter per day (mm/d) 0.039 inch per day (in/d)
v

Abbreviations

DEM – digital elevation model

Ef – Nash-Sutcliffe efficiency 

GIS – geographic information system

GUI – graphical user interface 

HUC – hydrologic unit code

KDOW – Kentucky Division of Water 

KPDES – Kentucky Pollutant Discharge Elimination System 

NEXRAD – Next Generation Weather Radar

NHD – National Hydrography Dataset 

NLCD – National Land Cover Data

Qbase – base-flow coefficient

RMSE – root mean square error

SD – sinkhole drainage 

SDP – sinkhole-drainage process

SSURGO – Soil Survey Geographic Database

STATSGO – State Soil Geographic Database 

SWAT – Soil and Water Assessment Tool

TD – topographically drained 

TWI – Topographic Wetness Index 

USGS – U.S. Geological Survey

WATER – Water Availability Tool for Environmental Resources

Phase II Modification of the Water Availability Tool for 

Environmental Resources (WATER) for Kentucky: 

The Sinkhole-Drainage Process, Point-and-Click Basin 

Delineation, and Results of Karst Test-Basin Simulations 

By Charles J. Taylor, Tanja N. Williamson, Jeremy K. Newson, Randy L. Ulery, Hugh L. Nelson, Jr., and 

Peter J. Cinotto

Abstract 

This report describes Phase II modifications made to 

the Water Availability Tool for Environmental Resources 

(WATER), which applies the process-based TOPMODEL 

approach to simulate or predict stream discharge in surface 

basins in the Commonwealth of Kentucky. The previous 

(Phase I) version of WATER did not provide a means of 

identifying sinkhole catchments or accounting for the effects 

of karst (internal) drainage in a TOPMODEL-simulated basin. 

In the Phase II version of WATER, sinkhole catchments are 

automatically identified and delineated as internally drained 

subbasins, and a modified TOPMODEL approach (called the 

sinkhole drainage process, or SDP-TOPMODEL) is applied 

that calculates mean daily discharges for the basin based on 

summed area-weighted contributions from sinkhole drainage (SD) areas and non-karstic topographically drained (TD) 

areas. Results obtained using the SDP-TOPMODEL approach 

were evaluated for 12 karst test basins located in each of 

the major karst terrains in Kentucky. Visual comparison of 

simulated hydrographs and flow-duration curves, along with 

statistical measures applied to the simulated discharge data 

(bias, correlation, root mean square error, and Nash-Sutcliffe 

efficiency coefficients), indicate that the SDP-TOPMODEL 

approach provides acceptably accurate estimates of discharge 

for most flow conditions and typically provides more accurate 

simulation of stream discharge in karstic basins compared to 

the standard TOPMODEL approach. 

Additional programming modifications made to the Phase 

II version of WATER included implementation of a point-andclick graphical user interface (GUI), which fully automates 

the delineation of simulation-basin boundaries and improves 

the speed of input-data processing. The Phase II version of 

WATER enables the user to select a pour point anywhere on 

a stream reach of interest, and the program will automatically delineate all upstream areas that contribute drainage to 

that point. This capability enables automatic delineation of 

a simulation basin of any size (area) and having any level of 

stream-network complexity. WATER then automatically identifies the presence of sinkholes catchments within the simulation basin boundaries; extracts and compiles the necessary 

climatic, topographic, and basin characteristics datasets; and 

runs the SDP-TOPMODEL approach to estimate daily mean 

discharges (streamflow). 

Introduction

The U.S. Geological Survey (USGS), in cooperation with 

the Kentucky Division of Water (KDOW), began a project 

in 2007 to develop a customized hydrologic-modeling and 

geospatial data-processing tool needed to assist State waterresource regulators with water-budget assessments and other 

water-resource management decisions. For planning purposes, the project was divided into two phases. Phase I of the 

project involved assembling the basic geospatial, climatic, and 

hydrologic-input datasets necessary for hydrologic-response 

modeling and developing the computer code needed to employ 

the TOPMODEL rainfall-runoff approach originally developed by Beven and Kirkby (1979). The outcome of the Phase 

I project was named the Water Availability Tool for Environmental Resources (WATER), and the programming structure, 

input-data requirements, output, and calibration and testing for 

stream basins in the non-karst areas of Kentucky were fully 

described in a previously published report by Williamson and 

others (2009). 

Since its development, the results of trial-run simulations 

using WATER to simulate stream discharges in the non-karst 

areas of Kentucky have been evaluated by the USGS and its 

cooperators to explore the practical uses and limitations of the 

TOPMODEL approach and determine what additional programming modifications are required to improve the accuracy 

of simulations, enhance ease of use, and expand the usefulness 

of WATER as a water-resources management tool. Feedback 

received as a result of these evaluations led to implementation of Phase II of the project, which was undertaken during 

2008–10. 
2 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Purpose and Scope

This report summarizes the modifications made to the 

WATER program during Phase II of its programming development to (1) improve the graphical user interface (GUI) to 

enable fully automated delineation of the simulation basin 

and improve the speed of input-data extraction and hydrologic modeling, and (2) to develop a modified TOPMODEL 

method that better simulates the unique drainage characteristics of karstic watersheds (basins) of Kentucky. Results of 

these programming modifications are evaluated by comparing 

simulated discharge against measured (observed) discharge for 

12 karst test basins located throughout the state. Simulated and 

observed hydrographs and flow-duration curves are presented 

for each test basin, and statistical evaluations of the modeled 

basin discharge are presented and discussed. 

Previous Work

As noted previously, the hydrologic-modeling capability of WATER is built upon the TOPMODEL rainfall-runoff 

approach originally developed by Beven and Kirkby (1979). 

The TOPMODEL approach applies the variable-source-area 

concept to describe how water accumulates in a simulation 

basin and derives estimates of stream discharge from the 

frequency-distribution histogram of Topographic Wetness 

Index (TWI) values computed by the following equation: 

TWI = ln {A/tanβ} (1)

where 

A is upslope contributing area per unit contour 

width (meters) and 

	 β is local slope (degrees) as derived from a 

preprocessed digital elevation model 

(DEM)-based raster dataset (Quinn and 

others, 1997). 

Other critical input parameters used in the TOPMODEL 

approach are obtained using climate data (precipitation and 

temperature), and mean soil properties obtained from the Soil 

Survey Geographic Database (SSURGO; http://soils.usda.

gov/survey/geography/ssurgo/). Wolock and McCabe (1999) 

showed that an accurate precipitation record was the most significant variable required for a successful hydrologic-response 

model, while soil-moisture storage (derived from pedological 

data) was identified as the next most critical variable.

Williamson and others (2009) documented the creation 

of programming code and the input-data files used for applying the TOPMODEL application to simulate streamflow 

characteristics of basins in the non-karst areas of Kentucky. 

Their report provides details about the programming and 

input-data-file structure of the Phase I WATER-TOPMODEL 

code and describes procedures used in the calibration, testing, 

and statistical evaluation of TOPMODEL outputs obtained 

for 20 test basins ranging in area from 16 to 1,565 km2 and 

located throughout the State. Historically, input data for 

the TOPMODEL application have been estimated by using 

soil parameters from a combination of the State Soil Geographic (STATSGO) Database (http://soils.usda.gov/survey/

geography/statsgo/) and manual estimation techniques (Brasington and Richards, 1998; Wolock, 2003) with soil parameters including available water-holding capacity, field capacity, 

porosity, soil thickness, saturated hydraulic conductivity, a 

conductivity multiplier, and a basin-scaling parameter as the 

principal physical-input parameters. However, Williamson and 

Odom (2007) showed that the SSURGO Database provided 

input data at a resolution that was more appropriate for analysis of small upland basins and yielded better results without 

the subjectivity of manual estimation. Using SSURGO data 

and Next Generation Weather Radar (NEXRAD) precipitation data, Williamson and others (2009) demonstrated that the 

WATER-TOPMODEL program developed for use in Kentucky 

was capable of providing acceptable estimates of surface flows 

in non-karst area basins, based on Nash-Sutcliffe efficiencies 

(Ef) ranging from .26 to .72. 

Beyond its application to Kentucky, the TOPMODEL 

application has been used successfully to study a wide variety 

of hydrologic-research topics, including topographic effects 

on water quality (Wolock, 1988; Wolock and others, 1989, 

1990), topographic effects on streamflow (Beven and Wood, 

1983; Beven and others, 1984; Kirkby, 1986), spatial-scale 

effects on hydrologic processes (Sivapalan and others, 1987; 

Wood and others, 1988, 1990; Famiglietti and Wood, 1991; 

Famiglietti, 1992), and the geomorphic evolution of basins 

(Ijjász-Vásquez and others, 1992). TOPMODEL also has been 

used for estimating flood frequency (Beven, 1986a and b), 

effects of climate change on hydrologic processes (Wolock 

and Hornberger, 1991), carbon budgets (Band and others, 

1991), base-flow residence times (Vitvar and others, 2002), 

and ecological-flow factors (Kennen and others, 2008). 

An Internet search of the published scientific literature 

typically will generate a large list of published studies using 

the keywords “karst” and “rainfall-runoff” or “hydrologic 

response” modeling; however, the majority of these studies 

discuss statistical methods or use of groundwater models to 

simulate discharges from karst springs (for example: Dooge, 

1973; Neuman and de Marsily, 1976; Dreiss, 1982, 1989; 

Zhang and others, 1995; Wicks and Hoke, 2000; Scanlon 

and others, 2003). By comparison, there are relatively few 

published studies that address simulation of sinkhole or 

surface-stream drainage in well-developed karst areas. Arikan 

(1988) applied a linked multi-reservoir approach to create a 

numerical model of regional streamflows in a karst area of 

Turkey. Campbell and others (2003) evaluated the results 

and limitations of using conventional geographic information 

system (GIS) flow-accumulation methods to estimate stream 

discharges from a sinkhole-drained valley in northeastern 

Alabama. Spruill and others (2000) applied the Soil and Water 

Assessment Tool (SWAT) numerical model to simulate daily 

streamflows in a small karstic watershed in central Kentucky 

over a 2-year period. Wolfe and others (2004) developed a 
Phase II Modification of WATER 3

hydrologic model using a rainfall-runoff approach to estimate 

the duration of ponding in a karst wetland in middle Tennessee. Salerno and Tartari (2009) investigated the application of 

wavelet analysis to model and evaluate base-flow discharges 

of rivers in karst areas. Field (2010) describes theoretical 

mathematical models that can be used to simulate drainage into and out of flooded sinkholes of various shapes and 

volumes. To the best knowledge of the authors, this report 

documents the first attempt to apply a TOPMODEL-based 

rainfall-runoff approach to the problem of simulating surfacestream discharge in karstic watersheds.

Phase II Modification of WATER

Most hydrologic-modeling techniques, including the 

conventional TOPMODEL approach, rely on use of artificially 

smoothed DEM-input data, which eliminates the presence of 

internally drained “non-contributing areas” prior to applying 

flow-accumulation methods to estimate surface runoff to a 

grid-based stream network, and are therefore unsuitable for 

use in sinkhole-dominated karst terrains (Taylor and Greene, 

2008). By most estimates, approximately 55 to 65 percent of 

Kentucky is characterized by moderately to well-developed 

karst (Paylor and Currens, 2001) whose geographic boundaries correlate broadly to four major physiographic regions: 

the Inner Bluegrass, the Outer Bluegrass, the Eastern Pennyroyal, and the Western Pennyroyal (fig. 1). Within these 

regions, normal (topographically controlled) surface drainage 

is altered to various degrees by sinkholes, sinking streams, 

and subsurface networks of solution conduits (Ray, 2001). 

Where karst features such as sinkholes are extensive and well 

developed, surface streamflows may be partly or completely 

pirated by underground conduits, and surface-stream reaches 

may be scarce and disconnected from one another. Surface 

runoff commonly is diverted underground by way of sinkholes 

and sinking streams, rapidly transported through pipe-like or 

channel-like subsurface conduits, and discharged back to the 

land surface at one or more karst springs, which are tributaries 

or headwaters for base-level surface streams. 

Outer Bluegrass

Purchase

Western coal field

Western Pennyroyal

Eastern coal field

Eastern Pennyroyal

Inner Bluegrass

Knobs

EXPLANATION

Physiographic Regions

USGS streamflow gage

Karst test basins

0 25 50 75 100 MILES

0 25 50 75 100 KILOMETERS

Figure 1. Physiographic regions of Kentucky and locations of karst test basins and U.S. Geological Survey streamflow gages used 

in the study
4 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Sinkhole-Drainage Process 

Conceptually, sinkholes can be treated as internally 

drained subbasins within the boundaries of the simulation 

basin that contribute water to the pour-point of the stream during storm events by way of subsurface stream reaches (conduits). To account for the anticipated differences in hydrologic 

responses between sinkhole drainage (SD) areas and normal 

topographically drained (TD) areas of a basin, a new raster 

input-data file was created to represent the locations and areas 

of sinkhole catchments previously mapped by Taylor and Nelson (2008), and then the TOPMODEL code used by WATER 

was modified so that the presence of sinkholes would generate 

a TWI distribution representative of the collective hydrologic 

response of all internally drained subbasins within the simulation-basin boundaries. This Phase II modification is called the 

sinkhole-drainage process, or SDP-TOPMODEL approach.

Figure 2 shows a schematic diagram which illustrates 

differences in the data-input and computational-processing 

steps between the standard (Phase I) WATER-TOPMODEL 

A. Standard (Phase I) TOPMODEL Approach B. Modified (Phase II) Sinkhole-Drainage Process (SDP) 

 TOPMODEL Approach

Figure 2. Major data-processing and computational steps in the A, standard (Phase I) TOPMODEL and B, modified (Phase II) sinkholedrainage process (SDP) TOPMODEL approaches.
Phase II Modification of WATER 5

and the SDP-TOPMODEL approaches. Three major dataprocessing steps that are incorporated into the SDP-TOPMODEL approach that are not part of the standard (Phase 1) 

approach include: (1) mapped sinkhole and (or) sinking stream 

catchment areas (SD areas) are identified and delineated as 

internally drained subbasins of the larger simulation basin; 

(2) area-normalized discharge is computed separately for the 

normal topographically-drained areas and SD areas; and (3) 

the area-normalized discharges from the two are summed at 

the end of the modeling process to calculate a total discharge 

for the simulation basin. 

As part of the third step, the water-budget accounting 

used in the standard TOPMODEL code was modified so that 

the drainage into SD areas bypasses the base-flow coefficient 

(Qbase) and is computationally added directly to the streamdischarge coefficient at each time step. As indicated on fig. 2, 

no such modification is applied to the computation of drainage from TD areas, so the calculated base-flow contribution 

to the stream is derived entirely from the Qbase values for 

TD areas of the simulation basin. The practical effect of this 

programmed water-budget modification is to increase the 

storm-peak response of simulated hydrographs, thereby better 

simulating the flashy hydrologic behavior typically observed 

for streams in conduit-dominated karst regions in Kentucky. 

Point-and-Click Basin Delineation

The original (Phase I) design for WATER incorporated a 

menu-driven GUI to select and extract pre-processed geospatial data for drainage basins having boundaries fixed at the 

hydrologic unit code (HUC)-12 level and to generate climatic 

data and hydrologic data needed by the TOPMODEL application to estimate streamflows (discharge) at the predefined pour 

point of the basin. During Phase II, the GUI and the programming were restructured to provide enhanced flexibility in 

basin delineation, faster geospatial-input data processing, and 

greater ease of use. 

The Phase II GUI provides the user with the ability to 

select a pour point anywhere on a stream line of interest and 

have the program automatically delineate all upstream areas 

(subbasins) that contribute drainage to that point (fig. 3). The 

main benefit of this programming modification is to allow 

the user the ability to delineate a simulation basin of any size 

(or area) or having any level of stream-network complexity. 

Once the pour point is selected, WATER automatically runs a 

routine to delineate the boundaries of the simulation basin and 

begins to extract and compile the necessary climatic, topographic, and basin-characteristics data (such as soil properties) needed to run the TOPMODEL application, including an 

“on the fly” calculation of the TWI histogram. All these data 

are displayed and may be reviewed and edited if necessary 

Figure 3. Screen image of WATER graphical user interface (GUI) showing boundaries of simulation basin and sinkhole catchment 

subbasins
6 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

by the user through the interactive GUI (fig. 4). No recognition of, or special adjustments for, karst terrain are required 

by the user. As part of the basin-delineation process, WATER 

automatically checks for, and the GUI displays, the presence 

of internally drained catchments, and employs the previously 

described SDP-TOPMODEL approach. 

The input-data file structure used by the revised version 

of the WATER-TOPMODEL application is organized by the 

various folders and subfolders that facilitate data extraction for 

the automated basin-delineation processing and the subsequently used TOPMODEL application (fig. 5). The primary 

input datasets used by WATER are organized into six folders, 

which are summarized here:

1. admin folder: The administration folder contains the 

overall display datasets pertaining to the GUI, such as 

geographic boundaries, highways and roads, and USGS 

streamflow-data files. The folder also contains the simulations.shp file, which is a dataset generated by WATER to 

show the user where simulations have been created.

2. clim folder: The climate folder contains text files currently 

(2011) created by a separate climate-generator model that 

calculates the precipitation and temperature in the simulaFigure 4. Screen-image examples of the information displays provided by the WATER graphical user interface (GUI). 
Phase II Modification of WATER 7

tion basin from multiple climate stations and outputs a 

.txt file using the inverse distance-weighting approach 

coupled with an elevation adjustment at a HUC-12 level, 

as described in Williamson and others (2009). For simulations of hydrologic conditions beginning after January 1, 

2000, NEXRAD is used for precipitation-data input (see 

Williamson and others, 2009, for more detail).

3. geog folder: Currently (2011), this folder contains only 

the mask used to identify any internally drained catchments and is the only dataset located in this folder. The 

TOPMODEL application uses this integer dataset to determine which areas contain sinkholes.

4. hydr folder: This folder contains specific GIS datasets 

used both for display purposes as well as for input-data 

extraction, including

• rsvr – identification of ponds, lakes, and reservoirs 

greater than 10 acres.

• strm – identification of stream and river reaches 

(greater than 3,000 cells in flow-accumulation raster 

file). 

• nhd.mdb – flow lines (feature class representing 

streams) contained in the National Hydrography Dataset (NHD), which are used during the automated basin 

delineation. 

• dischargePermits – a file listing the locations of 

surface-discharge permits reported by the Kentucky 

Pollutant Discharge Elimination System (KPDES) 

database. Under the present (Phase II) version, the 

locations are plotted on the GUI display; however, 

Figure 5. Screen image of the data tree structure for the six 

principal input-data folders used by WATER.

discharge and quantities are not used in basin discharge 

computations because of known or suspected errors 

and uncertainties in these data. 

• lake_area – a point dataset containing identified lakes 

and their associated bank full surface area.

• nhdrsvrgrid – an integer-grid dataset used to calculate 

the upstream contributing area of each lake or manmade reservoir in the delineated basin of interest.

• withdrawalPermits – a file listing the locations of 

surface-discharge permits reported by the KPDES 

database. Under the present (Phase II) version, the 

locations are plotted on the GUI display; however, 

discharge and quantities are not used in basin discharge 

computations because of known or suspected errors 

and uncertainties in these data. It contains a list of all 

water-withdrawal permits and their locations. 

5. topo folder: contains several types of numerically generated topological data, organized at the HUC-6 level, 

including

• felv – 10-m DEM data.

• flwa – flow accumulation used by the WATER basindelineation application. 

• flwd – flow directions used by the WATER basin-delineation application. 

• snet – synthetic stream network used by the WATER 

basin-delineation application to create the simulation 

area of interest.

6. phys folder: contains the TWI grids needed by TOPMODEL organized by HUC-6 code numbers, the 

SSURGO geodatabase that contains soil characteristics 

data, and other ancillary data including

• clipg – State integer grid of 1, identifies Commonwealth of Kentucky State boundaries.

• hu6grid – integer grid identifying the area of the 

HUC-6 basin.

• imp – a dataset containing the percent ground impervious, obtained from National Land Cover Data 

(NLCD).

• imprd - a dataset containing the percent road impervious, obtained by clipping the NLCD layer and clipping 

to the USGS National Map transportation layer.

• obsn – database that contains basin names and locations.

• obsn12 – used to identify the climate directory of the 

simulated basin.

• wbd12 – identifies downstream basins.
8 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Results of Karst Test-Basin Simulations

An evaluation of the SDP-TOPMODEL approach was 

conducted by simulating stream-discharge records obtained 

from continuous measurements collected during 2000–06 

from USGS streamflow gages in 12 karst test basins (fig. 1) 

ranging from 57 to 671 km2 in area, and having internally 

drained areas ranging from less than 2 to about 47 percent of 

the total basin area (table 1). The test basins were selected 

mainly on the basis of three criteria: (1) located wholly within 

one of four major karst physiographic regions in the State; 

(2) having, or having had, a USGS streamflow-gaging station 

measuring flow from a surface catchment (drainage) area completely underlain by karstic carbonate bedrocks; and (3) having a hydrograph period of record encompassing the 2000–06 

period of NEXRAD precipitation data. Where possible, 

preference was given to gaged basins having a known absence 

of flow regulation and location in a non-urban environment. 

Hydrograph plots for each test basin that illustrate 

observed versus simulated mean daily discharges, and residuals (differences between observed and simulated mean daily 

discharge values), are presented in appendix 1. Observed and 

SDP-TOPMODEL simulated hydrographs are plotted using 

log-scale because the range in stream discharge encompasses 

two or more orders of magnitude while residuals are plotted 

using linear-scale. The plots are difficult to characterize generally because the hydrologic responses vary from basin to basin 

and the hydrograph and residual trend lines exhibit considerable temporal variability. Four statistical measures applied in 

previous studies of TOPMODEL simulations conducted elsewhere by Wolock (1993) and Wolock and McCabe (1999), and 

in the Phase I investigation by Williamson and others (2009), 

Table 1. Karst test basins and corresponding U.S. Geologcial Survey streamflow gages used for statistical evaluation of the 

karst-modified (Phase II) WATER-TOPMODEL sinkhole-drainage\process.

[USGS, U.S. Geological Survey; mi2, square mile; <, less than]

Physiographic region 

(Karst terrain)1

USGS

streamflow-gage 

number 

USGS

stream name

Drainage 

area (mi2

)

Percent 

internally 

drained

Available period 

of record 

(year-month-day)

Inner Bluegrass region 03289300 South Elkhorn Creek near 

Midway, Ky.

105 21.2 1987-12-30

2008-11-04

03287600 North Elkhorn Creek 

at Bryan Station Road 

at Montrose, Ky.

21.5 2.2 1997-09-20

2008-11-05

Outer Bluegrass 

region

03252300 Hinkston Creek near 

Carlisle, Ky.

154 <2 1991-10-01

2008-11-05

03295890 Brashears Creek at 

Taylorsville, Ky.

259 <2 1981-07-01

2008-11-05

03292470 Harrods Creek at 

Highway 329, Ky.

70.3 2.2 1999-01-01 

2008-11-05

Eastern Pennyroyal or 

Coal Field region

03413200 Beaver Creek near 

Monticello, Ky.

43.4 4.2 1968-10-01 

2008-11-04

03307000 Russell Creek near 

Columbia, Ky.

173 9 1939-10-01 

2008-11-04

Western Pennyroyal 

region

03310300 Nolin River at 

White Mills, Ky.

240 35.4 1959-10-01

2008-11-04

03313700 West Fork Drakes Creek near 

Franklin, Ky.

91 20.2 1968-06-01

2008-11-05

03301700 Mill Creek near 

Fort Knox, Ky.

38.2 27.9 1998-04-16

2008-11-05

03312765 Beaver Creek at Highway 31 

E near Glasgow, Ky.

49.6 47.4 1999-09-01

2002-09-30

03438000 Little River near 

Cadiz, Ky.

244 36.8 1940-02-06

2008-11-04

1

Paylor and Currens (2001).
Results of Karst Test-Basin Simulations 9

were applied during this study to better evaluate the results of 

the test-basin simulations discussed here. The statistics include

Bias: ( ) x y

n

∑ i i − (2)

Root mean square error (RMSE): ( ) y x

n

∑ i i − 2

(3)

Correlation:

( )( )

( ) ( )

x x y y

x x y y

i i

i i

− −

− −

∑

∑ ∑

2 2 (4)

Nash-Sutcliffe efficiency (Ef): 1− −

−

∑

∑

( )

( )

x x

y x

i

i i

(5)

where 

xi is observed mean discharge at the USGS 

streamflow-gaging station for an individual 

day, 

yi is modeled discharge for an individual day,

x is mean observed discharge for the period of 

record,

y is mean modeled discharge for the period of 

record, and 

n is the number of observations. 

Values of bias and RMSE (also known as standard deviation) 

that are closer to zero indicate a better agreement between 

observed and model-estimated flow values. Correlation and 

Ef values that are closer to 1 indicate better modeled results; 

an Ef = 0 indicates that the model-flow estimates are no more 

accurate than using a mean-flow value, and an Ef <0 indicates 

that the mean-flow value is more accurate than the modeled 

results (Nash and Sutcliffe, 1970; McCuen and others, 2006). 

Histograms that summarize the statistics computed 

from simulated hydrograph data obtained using the standard 

(Phase I) TOPMODEL and SDP-TOPMODEL approaches 

are shown in figures 6–9 for each of the 12 test basins. 

Compared to the other statistics, the bias (fig. 6) exhibited 

the greatest variability among the test basins and between the 

standard TOPMODEL and SPD-TOPMODEL simulations. 

Bias values ranging from −.3 to .3 were obtained for 8 of the 

12 test basins using both the standard TOPMODEL and the 

Figure 6. Bias statistics 

for karst test basins used 

in the study. -0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

03289300 03287600 03252300 03295890 03292470 03413200 03307000 03310300 03313700 03301700 03312765 03438000

Karst test basins

Bias, in units

Standard method

SDP-TOPMODEL

EXPLANATION
10 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

SDP-TOPMODEL approaches. The bias values obtained using 

the SDP-TOPMODEL approach were closer to zero than those 

obtained using the standard TOPMODEL approach in 10 of 

the 12 basins: 

1. 03252300–Hinkston Creek, 

2. 03287600—North Elkhorn Creek, 

3. 03292470—Harrods Creek, 

4. 03295890–Brashears Creek, 

5. 03301700–Mill Creek, 

6. 03307000–Russell Creek, 

7. 03310300–Nolin River, 

8. 03312765–Beaver Creek near Glasgow, 

9. 03313700—West Fork Drakes Creek, and 

10. 03438000–Little River. 

Five basins simulated using the SDP-TOPMODEL approach 

yielded negative bias values, indicating that model output 

under-predicted stream discharge for these basins, probably 

because of local variability in basin characteristics that are not 

adequately accounted for in the simulations. 

Relatively more consistency in the range of values was 

obtained for the RMSE and Correlation statistics (figs. 7 and 

8, respectively) for both the SDP-TOPMODEL and standard 

TOPMODEL simulations. RMSE values varied slightly from 

basin to basin, but values < 2 were obtained in 8 of 12 basins 

using both the standard TOPMODEL and SDP-TOPMODEL 

approaches (fig. 7). Among these, RSME was slightly closer to 

zero in 6 of 12 basins using the SDP-TOPMODEL approach: 

1. 03289300–South Elkhorn Creek, 

2. 03295890–Brashears Creek, 

3. 03307000–Russell Creek, 

4. 03312765—Beaver Creek near Glasgow, 

5. 03313700—West Fork Drakes Creek, and 

6. 03438000—Little River. 

Correlation values (fig. 8) were consistently high and > .7 

using both the standard and SDP-TOPMODEL approaches for 

11 of the 12 test basins. Of these, values closer to one were 

obtained using the SDP-TOPMODEL approach in 7 of 12 

basins: 

1. 03287600—North Elkhorn Creek, 

2. 03295890—Brashears Creek, 

3. 03301700—Mill Creek, 

4. 03307000—Russell Creek, 

5. 03312765—Beaver Creek near Glasgow, 

6. 03413200—Beaver Creek near Monticello, and 

7. 03438000—Little River. 

In addition, the Correlation value of the SDP-TOPMODEL 

simulation for 03292470—Harrods Creek exceeded the .7 

threshold and the value obtained for the standard TOPMODEL 

simulation of this basin.
Results of Karst Test-Basin Simulations 11

Standard method

SDP-TOPMODEL

EXPLANATION

0

1

2

3

4

5

6

Karst test basins

Root mean square error (RMSE)

03287600 03252300 03295890 03292470 03413200 03307000 03310300 03313700 03301700 03312765 03438000

Figure 7. Root mean square error (RMSE) statistics for karst test basins used in the study.

Standard method

SDP-TOPMODEL

EXPLANATION

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

03289300 03287600 03252300 03295890 03292470 03413200 03307000 03310300 03313700 03301700 03312765 03438000

Karst test basins

Correlation

Figure 8. Correlation statistics for karst test basins used in the study.
12 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Ef values (fig. 9) exceeded .4 in 9 of 12 basins using 

either the standard TOPMODEL or SDP-TOPMODEL 

approaches, and were > .6 in 5 of 12 basins using both 

simulation techniques. Of the later, Ef values obtained for 

the SDP-TOPMODEL simulations were closer to one in 4 

of the 5 basins, and overall, Ef values obtained for the SDPTOPMODEL approach were > .6 for 10 of 12 test basins: 

8. 1) 03252300–Hinkston Creek, 

9. 2) 03287600—North Elkhorn Creek, 

10. 3) 03289300—South Elkhorn Creek, 

11. 4) 03295890–Brashears Creek, 

12. 5) 03301700–Mill Creek, 

13. 6) 03307000–Russell Creek, 

14. 7) 03312765–Beaver Creek near Glasgow, 

15. 8) 03313700—West Fork Drakes Creek, 

16. 9) 03413200—Beaver Creek near Monticello, and 

17. 10) 03438000–Little River.

Ef values obtained using the SDP-TOPMODEL 

approach were lowest (<.5) for test basins 03292470–

Harrods Creek, and 03310300–Nolin River (fig. 9). These 

test basins were used with reservations because of physical 

hydrologic characteristics that were anticipated to be 

problematic to modeling. For example, the basin for the 

Harrods Creek streamflow gage includes several developing 

suburban residential areas, and its hydrology is believed to 

be significantly affected by on-going land disturbance and 

changes in the percentage of pervious-to-impervious landsurface areas. The basin delineated for the streamflow gage on 

Nolin River (at White Mills, Kentucky) is located less than a 

few hundred feet from a large karst spring whose discharge, 

measured at approximately .2 m3/s at base flow (Ray and Blair, 

2005), is partly diverted to a public water supplier, and is 

partly recharged by a subsurface meander cutoff conduit that 

diverts water from the river by way of several known upstream 

swallow holes (Mull and others, 1988). Nevertheless, these 

two basins were included in the evaluation in order to bolster 

the total number of karst test basins in the study and to expand 

the range of percent area of sinkhole drainage in the Western 

Pennyroyal and Outer Bluegrass karst terrains.

Comparison of flow-duration curves for observed 

discharges and SDP-TOPMODEL simulated discharges 

(appendix 2) were visually evaluated to assess the relative 

accuracy of the SDP-TOPMODEL outputs over different 

flow regimes. The flow-duration curves are constructed 

by calculating the exceedance probability of the modeled 

daily flow values. The data points are arranged according to 

magnitude in a range of classes, and the percent of the time 

each class exceeds the total is computed; a curve then can be 

drawn through the points. The techniques used by the USGS 

are described by Searcy (1959). In general, peak flows (0–30 

percent exceedance) appear to be most accurately simulated 

for the test basins, based on the relative visual match of the 

two curves. Results among the various basins vary somewhat 

in the moderate flow range (30–70 percent) and although there 

is a perceived tendency for the SDP-TOPMODEL simulated 

curves to slightly overestimate discharges in most basins, 

the overall results, based on the apparent relative differences 

between the two curves for each basin, fall within a generally 

acceptable range. Note that all hydrographs presented here 

Standard method

SDP-TOPMODEL

EXPLANATION

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

03289300 03287600 03252300 03295890 03292470 03413200 03307000 03310300 03313700 03301700 03312765 03438000

Karst test basins

Nash-Sutcliffe Ef

Figure 9. Nash-Sutcliffe efficiency (Ef) coefficient statistics for karst test basins used in the study. 
Results of Karst Test-Basin Simulations 13

are plotted at logarithmic scale, thereby visually exaggerating 

apparent differences (on the y-axis) between the simulated 

hydrographs at discharges less than 1 mm/d. Greater apparent 

uncertainties, and a more consistent tendency for modeled 

discharge to overestimate actual observed discharges, are 

apparent in the low-moderate to low-flow range (70 percent 

and greater probability of flow exceedance). 

A more quantitative evaluation of the attributes of SDPTOPMODEL simulated flow-duration curves is accomplished 

using boxplots (figs. 10, 11, and 12) in the manner described 

by Helsel and Hirsch (2002) that illustrate the median values 

(center point of the boxplot), the variation or interquartile 

range (the boxplot height), skewness (relative size of the 

two halves of the boxplot), and the presence or absence of 

extreme or outlier values (lower and upper “detached” values). 

Comparison of paired observed and modeled boxplots for each 

test basin illustrates that the hydrographs simulated using the 

SDP-TOPMODEL approach generally exhibit a slightly high 

overall bias compared to observed data. The bias is observed 

by comparing the relative positions of the 75th-percentile 

discharge, median discharge, and 25th-percentile discharge 

between each respective observed and modeled dataset. The 

bias is more pronounced for low-flow conditions (with respect 

for the graphical exaggeration resulting from the logarithmic 

plot), as it also appears to be on the flow-duration curves. 

However, overlap of the interquartile range (variability) and 

similarity of quartile skew indicate that overall model response 

generally falls within an acceptable range for most hydrologic 

applications, as also indicated by the Ef values, described 

previously.

2412 2412 2412 2412 2412 2412 2412 2412

1,000

100

10

1

0.1

Discharge, in millimeters per day

0.01

0.001

0.0001

sim. 

03292470

obs. 

03292470

sim. 

03289300

obs. 

03289300

sim. 

03287600

obs. 

03287600

sim. 

03252300

obs. 

03252300

Figure 10. Statistical distribution for observed and simulated flow-duration data for karst test basins 0325300, 03287600, 03289300, 

and 03292470 [Explanation: obs.—observed discharge data; sim.— simulated discharge data]. 
14 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

2412 2412 2412 2412 2412 2412 2412 2412

100

10

1

0.1

Discharge, in millimeters per day

0.01

0.001

0.0001

0

sim. 

03310300

obs. 

03310300

sim. 

03307000

obs. 

03307000

sim. 

03301700

obs. 

03301700

sim. 

03295890

obs. 

03295890

Figure 11. Satistical distribution for observed and simulated flow-duration data for karst test basins 03295890, 03301700, 03307000, and 

03310300 [Explanation: obs.—observed discharge data; sim.— simulated discharge data]. 
Results of Karst Test-Basin Simulations 15

1004 1004 1735 1735 2412 2412 2412 2412

100

10

1

0.1

Discharge, in millimeters per day

0.01

0.001

sim. 

03438000

obs. 

03438000

sim. 

03413200

obs. 

03413200

sim. 

03313700

obs. 

03313700

sim. 

03312765

obs. 

03312765

Figure 12. Statistical distribution for observed and simulated flow-duration data for karst test basins 03312765, 03313700, 03413200, 

and 03438000. 
16 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Limitations of the SDP-TOPMODEL Approach

Presently (2011), all basin or watershed boundaries 

are automatically delineated by the WATER program using 

topographic-data derived 10-m DEM datasets. Manual editing 

of these boundaries is not available as an option. Once the 

user-selected pour point is established, WATER automatically 

runs a basin-delineation routine to determine the topographic 

boundaries of the catchment area upstream of the pour point 

and begins to extract and compile the necessary climatic, 

topographic, and basin characteristics input data needed for 

the hydrologic modeling application. As part of this process, 

WATER automatically checks for the presence of sinkholes 

or sinking-stream catchments within the boundaries of 

the simulation basin and automatically employs the SDPTOPMODEL approach if any such karst features are present. 

The working assumption used in the present version 

of WATER for the SDP-TOPMODEL approach is that 

topographic-drainage divides automatically derived using 

the point-and-click GUI are accurate and represent the actual 

contributing area to a stream. However, in each of the karst 

terrains of Kentucky, water-tracer tests have demonstrated 

that subsurface solution conduits typically extend beneath 

local topographic-drainage divides, resulting in subsurface 

transfers of water into, or out of, many topographically defined 

drainage basins. As a consequence, in many karst areas the 

actual size of the contributing area of a stream may be larger 

or smaller than the area indicated by the topographic-basin 

boundaries of the stream (Ray, 2001). The user is advised to 

consult the series of 15-minute karst atlas maps published 

for Kentucky (Currens and Ray, 1999) to assess the accuracy 

of the delineated basin boundaries and to identify possible 

locations where sinkhole-dominated surface drainage may be 

misattributed to a particular basin because of the effects of 

subsurface-conduit piracy. However, at present, no capabilities 

exist within the WATER GUI to enable manual editing of 

basin boundaries to correct for misattributed sinkhole drainage 

areas. The addition of this capability may be the subject of 

future WATER programming revisions. It also should be noted 

that water-tracer test results and karst-mapping data may not 

be available for specific basins in many areas of Kentucky. 

As described previously, visual inspection and boxplot 

statistical analysis of simulated flow-duration curves 

(appendix 2) indicates that simulations obtained using the 

SDP-TOPMODEL approach are most accurate at peak 

flows (0–30 percent flow duration), acceptable at most 

moderate flows (30–70 percent), and are acceptable but 

with comparatively less overall accuracy at low flows (>70 

percent). Therefore, simulation of low-flow stream conditions 

should be anticipated as having the greatest chances of 

potential uncertainty or error. This may be a consequence 

of several factors, including the inability of the present 

TOPMODEL code to incorporate seasonal variability in 

evapotranspiration and soil-water storage owing to changes in 

vegetation growth, and longer-term storage and discharge of 

subsurface water in the epikarst zone. In well-developed karst 

watersheds, the lack of a water-budget component capable 

of accounting for storage in solutional conduits below the 

water table also may contribute to greater potential errors 

in low-flow simulations. Subsurface routing of flow from 

individual sinkholes and sinking streams through conduits is 

likely to be a major factor controlling the timing and volume 

of water discharged to streams in karst areas; however, these 

cannot be incorporated into karst-basin simulations because 

TOPMODEL is not a true distributed-deterministic model. 

Future work is needed to incorporate flow routing into 

TOPMODEL and to further modify water-budget calculations 

to improve the ability of WATER to simulate recessional 

hydrograph periods and low-flow conditions in both karst and 

non-karst watersheds. Currently (2011), the user is advised 

to anticipate greater potential errors and uncertainties when 

applying WATER to address water-management issues 

involving low-flow conditions. 

An additional consideration when using the SDPTOPMODEL approach in well-developed karst areas is 

this: no karstic basins having SD areas >50 percent of the 

total basin area were tested during this study because of the 

lack of suitable streamflow data. It is therefore unknown 

how the standard or SDP-TOPMODEL approaches perform 

in karstic basins largely dominated by internal drainage. 

It also should be emphasized that neither the standard nor 

SDP-TOPMODEL approaches include water-budget terms 

specifically for groundwater recharge and storage, or a routing 

or computational method that is capable of representing 

rapid flow through subsurface conduits. Therefore, the 

SDP-TOPMODEL approach is intended for the simulation 

of discharge from karst springs and should be used with 

caution in karstic basins characterized by extensive sinkhole 

development, multiple sinking or disappearing stream reaches, 

and discharge to multiple karst springs.

The standard and SDP-TOPMODEL approaches 

currently (2011) available in WATER are calibrated only for 

use in surface basins in Kentucky. With the exception of test 

basin 03313700—West Fork Drakes Creek, stream basins that 

cross the State line between Kentucky and Tennessee cannot 

be simulated using the Phase II version of WATER. 

Summary and Conclusions

Modifications made to the Water Availability Tool 

for Environmental Resources (WATER)-TOPMODEL 

programming code during this project (Phase II) enable 

sinkholes and sinking-stream catchments to be physically 

simulated as hydrologic features in karstic basins of Kentucky. 

The practical effect of this programming modification—called 
References Cited 17

the sinkhole-drainage process or SDP-TOPMODEL 

approach—enables WATER to more realistically simulate 

the internal drainage and flashy hydrologic responses that 

are characteristic of karstic watersheds in the State. The 

accuracy of stream-discharge estimates obtained using the 

SDP-TOPMODEL approach was evaluated using streamflow 

data collected during 2000–06 from 12 test basins located 

throughout each of Kentucky’s four karst terrains: Inner 

Bluegrass, Outer Bluegrass, Eastern Pennyroyal, and Western 

Pennyroyal. 

Visual and statistically based evaluations of simulated 

hydrographs and flow-duration curves indicate that most 

karstic basins in Kentucky can be modeled to an acceptable 

level of accuracy using either the standard (Phase I) 

TOPMODEL or the SDP-TOPMODEL approaches. However, 

the SDP-TOPMODEL approach physically incorporates 

contributions from digitally mapped, internally drained 

catchments in the simulation-basin model. Nash-Sutcliffe 

efficiency values, as well as bias, RMSE, and Correlation 

statistics indicate that relatively more accurate simulations 

typically can be expected using the SDP-TOPMODEL 

approach as compared to the standard TOPMODEL approach. 

Simulated flow-duration curves and boxplots of SDPTOPMODEL estimated discharge data indicate that peak flows 

are most accurately simulated using the SDP-TOPMODEL 

approach, and that moderate- to low-flow ranges, though 

typically overestimated, are simulated with acceptable 

accuracy. Stream-discharge estimates in the mid-moderate to 

low-flow ranges were statistically acceptable, though slightly 

overestimated by SDP-TOPMODEL approach, and subject to 

greater potential uncertainties and errors.

The additional modifications made to WATER during 

this Phase II project included implementation of an improved 

point-and-click graphical user interface (GUI), which fully 

automates the delineation of simulation-basin boundaries and 

WATER input-data processing. The current (2011) version 

of WATER (Phase II) provides the user with the ability to 

select a pour point anywhere on a stream line of interest, 

and the program automatically delineates all upstream areas 

that contribute drainage to that point. Once the pour point is 

selected, WATER automatically delineates the boundaries of 

the simulation basin and extracts and compiles the necessary 

geospatial-input datasets needed to simulate the hydrologic 

response of the basin using the TOPMODEL application. 

WATER automatically checks for and identifies the presence 

of sinkholes or sinking-stream catchments within the 

boundaries of the simulation basin and automatically employs 

the sinkhole-drainage process if any such karst features are 

present. No special knowledge of local karst topographic or 

hydrologic characteristics or special geospatial data-processing 

actions are required by the user to simulate the hydrology of 

basins located in karst areas of Kentucky. 

References Cited 

Arikan, Alparslan, 1988, MODALP—A deterministic rainfallrunoff model for large karstic areas: Hydrological Sciences 

Journal, v. 33, no. 4, p. 401–414.

Band, L.E., Peterson, D.L., Running, S.W., Coughlan, J.C., 

Lammers, Richard, Dungan, Jennifer, and Nemani, R.R., 

1991, Forest ecosystem processes at the watershed scale—

Basis for distributed simulation: Ecological Modelling, 

v. 56, p. 171–196.

Beven, K.J., 1986a, Runoff production and flood frequency in 

catchments of order n—An alternative approach, in Gupta, 

V.K., Rodriguez-Iturbe, I., and Wood, E.F., eds., Scale 

problems in hydrology: Dordrecht, The Netherlands, 

D. Reidel Publishing Company, p. 107–131.

Beven, K.J., 1986b, Hillslope runoff processes and flood 

frequency characteristics, in Abrahams, A.D., ed., Hillslope 

processes: London, Allen and Unwin, p. 187–202.

Beven, K.J., and Kirkby, M.J., 1979, A physically based, 

variable contributing area model of basin hydrology: 

Hydrological Sciences Bulletin, v. 24, no. 1, p. 43–69.

Beven, K.J., Kirkby, M.J., Schofield, N., and Tagg, A.F., 1984, 

Testing a physically-based flood forecasting model 

(TOPMODEL) for three U.K. catchments: Journal of 

Hydrology, v. 69, nos. 1–4, p. 119–143.

Beven, K.J., and Wood, E.F., 1983, Catchment geomorphology 

and the dynamics of runoff contributing areas: Journal of 

Hydrology, v. 65, nos. 1–3, p. 139–158.

Brasington, James, and Richards, Keith, 1998, Interactions 

between model predictions, parameters and DTM scales 

for TOPMODEL: Computers & Geosciences, v. 24, no. 4, 

p. 299–314.

Campbell, W.C., Lumsdon-West, M., and Davies, S., 2003, 

Geographic information system (GIS) support for karst 

hydrology, in Beck, B.F., ed., Sinkholes and the engineering and environmental impacts of karst, Proceedings of the 

Ninth Multidisciplinary Conference, September 6–10, 2003, 

Huntsville, Ala.: American Society of Civil Engineers, 

Geotechnical Special Publication no. 122, p. 429–438.

Currens, J.C., and Ray, J.A, 1999, Karst atlas for Kentucky, 

in Beck, B.F., Pettit, A.J., and Herring, J.G., eds., 

Hydrogeology and engineering geology of sinkholes and 

karst—1999, Proceedings of the 7th Multidisciplinary 

Conference on Sinkholes and the Engineering and Environmental Impacts of Karst, April 10–14, 1999, HarrisburgHershey, Pa.: Rotterdam, A.A. Balkema, p. 85–90.
18 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Dooge, J.C.I., 1973, Linear theory of hydrologic systems: 

U.S. Department of Agriculture Technical Bulletin 1468, 

327 p.

Dreiss, S.J., 1982, Linear kernels for karst aquifers: Water 

Resources Research, v. 18, no. 4, p. 865–876.

Dreiss, S.J., 1989, Regional scale transport in a karst aquifer, 2—Linear systems and time moment analysis: Water 

Resources Research, v. 25, no. 1, p. 126–134. 

Famiglietti, J.S., 1992, Aggregation and scaling of spatiallyvariable hydrological processes—Local, catchment-scale 

and macroscale models of water and energy balance: Princeton, N.J., Princeton University, Ph.D. dissertation, 207 p.

Famiglietti, J.S., and Wood, E.F., 1991, Evapotranspiration 

and runoff from large land areas—Land surface hydrology for atmospheric general circulation models: Surveys of 

Geophysics, v. 12, nos. 1–3, p. 179–204.

Field, M.S., 2010, Simulating drainage from a flooded sinkhole: Acta Carsologica, v. 39, no. 2, p. 361–378.

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in 

water resources: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 4, chap. A3, 510 p., 

available at http://water.usgs.gov/pubs/twri/twri4a3/.

Ijjász-Vásquez, E.J., Bras, R.L., and Moglen, G.E., 1992, 

Sensitivity of a basin evolution model to the nature of 

runoff production and to initial conditions: Water Resources 

Research, v. 28, no 10, p. 2733–2741.

Kennen, J.G., Kauffman, L.J., Ayers, M.A., Wolock, D.M., 

and Colarullo, S.J., 2008, Use of an integrated flow model 

to estimate ecologically relevant hydrologic characteristics 

at stream biomonitoring sites: Ecological Modelling, 

v. 211, p. 57–76.

Kirkby, M.J., 1986, A runoff simulation model based on 

hillslope topography, in Gupta, V.K., Rodriguez-Iturbe, I., 

and Wood, E.F., eds., Scale problems in hydrology—Runoff 

generation and response: Dordrecht, The Netherlands, 

D. Reidel Publishing Company, p. 39–56.

McCuen, R.H., Knight, Zachary, and Cutter, A.G., 2006, 

Evaluation of the Nash-Sutcliffe efficiency index: Journal 

of Hydrologic Engineering, v. 11, no. 6, p. 597–602.

Mull, D.S., Smoot, J.L., and Liebermann, T.D., 1988, Dye 

tracing techniques used to determine ground-water flow in 

a carbonate aquifer system near Elizabethtown, Kentucky: 

U.S. Geological Survey Water-Resources Investigations 

Report 87–4174, 95 p. 

Nash, J.E., and Sutcliffe, J.V., 1970, River flow forecasting 

through conceptual models, Part 1—A discussion of principles: Journal of Hydrology, v. 10, no. 3, p. 282–290.

Neuman, S.P., and de Marsily, G., 1976, Identification of 

linear systems response by parametric programming: 

Water Resources Research, v. 12, no. 2, p. 253–262.

Paylor, R.L., and Currens, J.C., 2001, Karst occurrence in 

Kentucky: Kentucky Geological Survey, Ser. 12, Map and 

Chart 33, scale 1:1,000,000.

Quinn, P.F., Beven, K.J., and Lamb, R., 1997, The ln(a/tanβ) 

index—How to calculate it and how to use it within the 

TOPMODEL framework, in Beven, K.J., ed., Distributed 

hydrological modeling—Applications of the TOPMODEL 

concept: Chichester, England, Wiley, p. 31–52. 

Ray, J., 2001, Spatial interpretation of karst drainage basins, 

in Beck, B.F., and Herring, J.G., eds., Geotechnical and 

environmental applications of karst geology and hydrology, 

Proceedings of the Eighth Multidisciplinary Conference on 

Sinkholes and the Environmental and Engineering Impacts 

of Karst, April 1–4, 2001, Louisville, Ky.: Lisse, Balkema 

Publishers, p. 235–244.

Ray, J., and Blair, R.J., 2005, Large perennial springs of 

Kentucky—Their identification, base flow, catchment, and 

classification, in Beck, B.F., ed., Proceedings of the 10th 

Multidisciplinary Conference on Sinkholes and the 

Environmental and Engineering Impacts of Karst, 

September 24–28, 2005, San Antonio, Tex.: American 

Society of Civil Engineers Geotechnical Special Publication 

No. 144, p. 410–422.

Salerno, F., and Tartari, G., 2009, A coupled approach of 

surface hydrological modeling and wavelet analysis for 

understanding the baseflow components of river discharge 

in karst environments: Journal of Hydrology, v. 376, 

p. 295–306. 

Scanlon, B.R., Mace, R.E., Barrett, M.E, and Smith, B., 2003, 

Can we simulate regional groundwater flow using equivalent porous media models? Case study, Barton Springs 

Edwards aquifer, USA: Journal of Hydrology, v. 276, 

p. 137–158.

Searcy, J.K., 1959, Flow-duration curves—Manual of hydrology—Part 2, Low-flow techniques: U.S. Geological Survey 

Water-Supply Paper 1542–A, 33 p.

Sivapalan, Murugesu, Beven, K.J., and Wood, E.F., 1987, 

On hydrologic similarity, 2—A scaled model of storm 

runoff production: Water Resources Research, v. 23, no. 12, 

p. 2266–2278.
References Cited 19

Spruill, C.A., Workman, S.R., and Taraba, J.L., 2000, Simulation of daily and monthly stream discharge from small 

watersheds using the SWAT model: Transactions of the 

American Society of Agricultural and Biological Engineers, 

v. 43, no. 6, p. 1431–1439.

Taylor, C.J., and Greene, E.A., 2008, Hydrogeologic characterization and methods used in the investigation of karst 

hydrology, in Rosenberry, D.O., and LaBaugh, J.W., eds., 

Field techniques for estimating water fluxes between 

surface water and ground water: U.S. Geological Survey 

Techniques and Methods 4–D2, chap. 3, p. 71–114. 

Taylor, C.J., and Nelson, H.L., Jr., 2008, A compilation of 

provisional karst geospatial data for the Interior Low 

Plateaus physiographic region, central United States: 

U.S. Geological Survey Data Series 339, 26 p.

Vitvar, T., Burns, D.A., Lawrence, G.B., McDonnel, J.J., and 

Wolock, D.M., 2002, Estimation of baseflow residence 

times in watersheds from the runoff hydrograph recession—Method and application in the Neversink watershed, 

Catskill Mountains, New York: Hydrological Processes, 

v. 16, no. 9, p. 1871–1877.

Wicks, C.M., and Hoke, J.A., 2000, Prediction of the quantity 

and quality of Maramec Spring water: Ground Water, v. 38, 

no. 2, p. 218–225.

Williamson, T.N., and Odom, K.R., 2007, Implications of 

SSURGO versus STATSGO data for modeling daily streamflow in Kentucky [abs.]: A century of integrating crops, 

soils & environment, 2007 International Annual Meetings, 

November 4–8, 2007, New Orleans, La.: ASA–CSSA–

SSSA, accessed March 1, 2011, at http://acs.confex.com/

crops/2007am/techprogram/P32289.HTM. 

Williamson, T.N., Odom, K.R., Newson, J.K., Downs, A.C., 

Nelson, H.L., Jr., Cinotto, P.J., and Ayers, M.A., 2009, 

The Water Availability Tool for Environmental Resources 

(WATER)—A water-budget modeling approach for managing water-supply resources in Kentucky—Phase I—Data 

processing, model development, and application to nonkarst areas: U.S. Geological Survey Scientific Investigations 

Report 2009–5248, 34 p.

Wolfe, W.J., Evans, J.P., McCarthy, Sarah, Gain, W.S., and 

Bryan, B.A., 2004, Tree-regeneration and mortality patterns 

and hydrologic change in a forested karst wetland—Sinking 

Pond, Arnold Air Force Base, Tennessee: U.S. Geological 

Survey Water-Resources Investigations Report 03–4217, 

53 p.

Wolock, D.M., 1988, Topographic and soil hydraulic control 

of flow paths and soil contact time—Effects on surface 

water acidification: Charlottesville, Va., University of 

Virginia, Ph.D. dissertation, 188 p.

Wolock, D.M., 1993, Simulating the variable-source-area 

concept of streamflow generation with the watershed model 

TOPMODEL: U.S. Geological Survey Water-Resources 

Investigations Report 93–4124, 33 p.

Wolock, D.M., 2003, Infiltration-excess overland flow 

estimated by TOPMODEL for the conterminous 

United States: U.S. Geological Survey Open-File Report 

03–310, accessed [September 2008], at 

http://water.usgs.gov/lookup/getspatial?ieof48. 

Wolock, D.M., and Hornberger, G.M., 1991, Hydrological 

effects of changes in atmospheric carbon dioxide levels: 

Journal of Forecasting, v. 10, p. 105–116. 

Wolock, D.M., Hornberger, G.M., Beven, K.J., and Campbell, 

W.G., 1989, The relationship of catchment topography and 

soil hydraulic characteristics to lake alkalinity in the northeastern United States: Water Resources Research, v. 25, 

no. 5, p. 829–837.

Wolock, D.M., Hornberger, G.M., and Musgrove, T.J., 1990, 

Topographic effects on flow path and surface water chemistry of the Llyn Brianne catchments in Wales: Journal of 

Hydrology, v. 115, nos. 1–4, p. 243–259.

Wolock, D.M., and McCabe, G.J., Jr., 1999, Explaining spatial 

variability in mean annual runoff in the conterminous 

United States: Climate Research, v. 11, no. 2, p. 149–159.

Wood, E.F., Sivapalan, Murugesu, and Beven, K.J., 1990, 

Similarity and scale in catchment storm response: Reviews 

of Geophysics, v. 28, no. 1, p. 1–18.

Wood, E.F., Sivapalan, Murugesu, Beven, K.J., and Band, 

L.E., 1988, Effects of spatial variability and scale with 

implications to hydrologic modeling: Journal of Hydrology, 

v. 102, nos. 1–4, p. 29–47.

Zhang, Y.K., Bai, E.W., Rowden, R., and Liu, H., 1995, Simulation of spring discharge from a limestone aquifer in Iowa, 

USA: Hydrogeology Journal, v. 4, no. 4, p. 41–54.

Appendixes

Appendix 1. Hydrographs showing observed versus simulated

discharge and residuals for the 12 karst test basins used in the study.

Figures

1–1. Test basin 03252300......................................................................................................................22

1–2. Test basin 03287600......................................................................................................................23

1–3. Test basin 03289300 ......................................................................................................................24

1–4. Test basin 03292470).....................................................................................................................25

1–5. Test basin 03298900 ......................................................................................................................26

1–6. Test basin 03301700 ......................................................................................................................27

1–7. Test basin 03307000 ......................................................................................................................28

1–8. Test basin 03310300 ......................................................................................................................29

1–9. Test basin 03312765 ......................................................................................................................30

1–10. Test basin 03313700 ......................................................................................................................31

1–11. Test basin 03413200 ......................................................................................................................32

1–12. Test basin 03438000 ......................................................................................................................33

Appendix 2. Flow-duration curves showing simulated versus observed

discharge for the 12 karst test basins used in the study.

Figures

2–1. Test basin 03252300 ......................................................................................................................34

2–2. Test basin 03287600 ......................................................................................................................35

2–3. Test basin 03289300 ......................................................................................................................36

2–4. Test basin 03292470 ......................................................................................................................37

2–5. Test basin 03298900 ......................................................................................................................38

2–6. Test basin 03301700 ......................................................................................................................39

2–7. Test basin 03307000 ......................................................................................................................40

2–8. Test basin 03310300 ......................................................................................................................41

2–9. Test basin 03312765 ......................................................................................................................42

2–10. Test basin 03313700 ......................................................................................................................43

2–11. Test basin 03413200 ......................................................................................................................44

2–12. Test basin 03438000 ......................................................................................................................45
22 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 1–1. Observed versus simulated discharge and residuals for test basin 03252300.

-20

0

20

40

60

80

100

0.01

0.1

1

10

100

1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

Residuals, in millimeters per day

Daily mean discharge, in millimeters per day

Date

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals

Appendix 1. Hydrographs showing observed versus simulated discharge and

residuals for the 12 karst test basins used in the study.
Appendix 1 23

Figure 1–2. Observed versus simulated discharge and residuals for test basin 03289300.

-20

0

20

40

60

80

100

0.0001

0.001

0.01

0.1

1

10

100

1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

Residuals, in millimeters per day

Daily mean discharge, in millimeters per day

Date

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
24 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 1–3. Observed versus simulated discharge and residuals for test basins 03289300.

1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

Residuals, in millimeters per day

Daily mean discharge, in millimeters per day

Date

-20

0

20

40

60

80

100

0.01

0.1

1

10

100

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
Appendix 1 25

Figure 1–4. Observed versus simulated discharge and residuals for test basin 03292470.

1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

Residuals, in millimeters per day

Daily mean discharge, in millimeters per day

Date

-20

0

20

40

60

80

100

0.00001

0.0001

0.001

0.01

0.1

1

10

100

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
26 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 1–5. Observed versus simulated discharge and residuals for test basin 03295890.

1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

Residuals, in millimeters per day

Daily mean discharge, in millimeters per day

Date

-20

0

20

40

60

80

100

0.00001

0.0001

0.001

0.01

0.1

1

10

100

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
Appendix 1 27

Figure 1–6. Observed versus simulated discharge and residuals for test basin 03301700.

1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

Residuals, in millimeters per day

Daily mean discharge, in millimeters per day

Date

-20

0

20

40

60

80

100

0.01

0.1

1

10

100

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
28 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 1–7. Observed versus simulated discharge and residuals for test basin 03307000.

1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

Residuals, in millimeters per day

Daily mean discharge, in millimeters per day

Date

-20

0

20

40

60

80

100

0.01

0.1

1

10

100

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
Appendix 1 29

Figure 1–8. Observed versus simulated discharge and residuals for test basin 03310300.

1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

Daily mean discharge, in millimeters per day

Residuals, in millimeters per day

Date

-20

0

20

40

60

80

100

0.01

0.1

1

10

100

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
30 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 1–9. Observed versus simulated discharge and residuals for test basin 03312765.

Residuals, in millimeters per day

Daily mean discharge, in millimeters per day

Date

-20

0

20

40

60

80

100

0.01

0.1

1

10

100

4/9/00 10/26/00 5/14/01 11/30/01 6/18/02 1/4/03

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
Appendix 1 31

Figure 1–10. Observed versus simulated discharge and residuals for test basin 03313700.

Residuals, in millimeters per day

Daily mean discharge, in millimeters per day

Date

-20

0

20

40

60

80

100

0.00001

0.0001

0.001

0.01

0.1

1

10

100

4/9/00 2/3/01 11/30/01 9/26/02 7/23/03 5/18/04 3/14/05

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
32 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 1–11. Observed versus simulated discharge and residuals for test basin 03433200.

-20

0

20

40

60

80

100

0.0001

0.001

0.01

0.1

1

10

100

1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

Date

Daily mean discharge, in millimeters per day

Residuals, in millimeters per day

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
Appendix 1 33

Figure 1–12. Observed versus simulated discharge and residuals for test basin 03438000.

Date

Residuals, in millimeters per day

Daily mean discharge, in millimeters per day

-20

0

20

40

60

80

100

0.01

0.1

1

10

100

1/0/00 5/14/01 9/26/02 2/8/04 6/22/05 11/4/06

EXPLANATION

Discharge

Sinkhole-drainage process 

(SDP)-TOPMODEL discharge

Residuals
34 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 2–1. Flow-duration curves showing simulated versus observed discharge for test basin 03252300.

0.01

0.1

1

10

100

0 20 40 60 80 100 120

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION

Appendix 2. Flow-duration curves showing simulated versus observed

discharge for the 12 karst test basins used in the study.
Appendix 2 35

Figure 2–2. Flow-duration curves showing simulated versus observed discharge for test basin 03287600. Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

0.0001

0.001

0.01

0.1

1

10

100

0 20 40 60 80 100 120

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION
36 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 2–3. Flow-duration curves showing simulated versus observed discharge for test basin 03289300.

0.01

0.1

1

10

100

0 20 40 60 80 100 120

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent
Appendix 2 37

0.001

0.01

0.1

1

10

100

0 20 40 60 80 100 120

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION

Figure 2-4. Flow-duration curves showing simulated versus observed discharge for test basin 03292470–
38 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 2–5. Flow-duration curves showing simulated versus observed discharge for test basin 03295890.

0 20 40 60 80 100 120

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

0

0.0001

0.0010

0.0100

0.1000

1

10

100

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION
Appendix 2 39

0 20 40 60 80 100 120

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

0.01

0.1

1

10

100

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION

Figure 2–6. Flow-duration curves showing simulated versus observed discharge for test basin 03301700.
40 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 2–7. Flow-duration curves showing simulated versus observed discharge for test basin 03310300.

0 20 40 60 80 100 120

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

0.01

0.1

1

10

100

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION
Appendix 2 41

Figure 2–8. Flow-duration curves showing simulated versus observed discharge for test basin 03310300.

0 20 40 60 80 100 120

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

0.01

0.1

1

10

100

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION
42 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 2–9. Flow-duration curves showing simulated versus observed discharge for test basin 03312765.

0 20 40 60 80 100 120

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

0.01

0.1

1

10

100

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION
Appendix 2 43

Figure 2–10. Flow-duration curves showing simulated versus observed discharge for test basin 03313700.

0 20 40 60 80 100 120

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

0.01

0.1

10

1

100

0.001

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION
44 Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky

Figure 2–11. Flow-duration curves showing simulated versus observed discharge for test basin 03413200.

0 20 40 60 80 100 120

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

0.01

0.1

10

1

100

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION
Appendix 2 45

Figure 2–12. Flow-duration curves showing simulated versus observed discharge for test basin 03438000.

0 20 40 60 80 100 120

Daily mean discharge, in millimeters per day

Probability that a given flow will be exceeded, in percent

0.01

0.1

10

1

100

Sinkhole-drainage process (SDP)- TOPMODEL

discharge

Discharge

EXPLANATION


Taylor and others—Phase II Modification of the Water Availability Tool for Environmental Resources (WATER) for Kentucky—Scientific Investigations Report 2012–5071