Prepared in cooperation with the Kentucky Division of Water

Construction of Estimated Flow- and LoadDuration Curves for Kentucky Using the 

Water Availability Tool for Environmental 

Resources (WATER)

Scientific Investigations Report 2012–5168

U.S. Department of the Interior

U.S. Geological Survey

Construction of Estimated Flow- and LoadDuration Curves for Kentucky Using the 

Water Availability Tool for Environmental 

Resources (WATER)

By Michael D. Unthank, Jeremy K. Newson, Tanja N. Williamson, and 

Hugh L. Nelson

Prepared in cooperation with the Kentucky Division of Water

Scientific Investigations Report 2012–5168

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:

Unthank, M.D., Newson, J.K., Williamson, T.N., and Nelson, H.L., 2012, Construction of estimated flow- and loadduration curves for Kentucky using the Water Availability Tool for Environmental Resources (WATER): U.S. Geological 

Survey Scientific Investigations Report 2012–5168, 14 p., at http://pubs.usgs.gov/sir/2012/5168/.
iii

Contents

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

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

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

Previous Studies ...................................................................................................................................2

Model Description .........................................................................................................................................2

Model Calibration and Verification .............................................................................................................3

Construction of Estimated Flow-Duration Curves Using WATER...........................................................6

Identifying and Delineating the Contributing Watershed...............................................................6

Compiling the Watershed Data...........................................................................................................6

Running TOPMODEL and Plotting the Flow-Duration Curve .......................................................11

Construction of Estimated Load-Duration Curves Using WATER ........................................................11

Summary........................................................................................................................................................14

References Cited..........................................................................................................................................14

Figures

1. Map showing physiographic regions, selected watersheds and streamflow-gaging 

stations used for Water Availability Tool for Environmental Resources (WATER) 

model calibration, and watersheds and streamflow-gaging stations used for model 

verification in Kentucky ...............................................................................................................4

2. Flow- and load-duration flow chart for the WATER application...........................................7

3. Screen shot of main interactive window of the WATER application ...................................8

4. Screen shot of selecting and identifying a simulation/watershed catchment point on 

the main interactive window of the WATER application........................................................8

5. Screen shot of delineated watershed of the WATER application ........................................9

6. Example of data required for the hydrologic model of the WATER application. 

A, simulation information. B, basin characteristics. C, topographic wetness index. 

D, available climatic data. .........................................................................................................10

7. Example of output from the hydrologic model of the WATER application. 

A, hydrograph. B, log-normal hydrograph. C, annual water budget. D, flow duration....11

8. Example of flow-duration curve tool for the U.S. Geological Survey WATER 

application ...................................................................................................................................13

Tables

1. Ten U.S. Geological Survey (USGS) streamflow-gaging stations used in the USGS 

WATER simulations for model verification in Kentucky .........................................................5

2. Criteria and associated default value and units provided by the USGS WATER 

application ...................................................................................................................................12

3. Hypothetical water quality Escherichia coli (E. coli) concentrations used as input 

for the load-duration curve of the USGS WATER application.............................................13
iv

Conversion Factors, Datum, and Abbreviations

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.61 kilometer (km)

Area

square mile (mi2) 2.59 kilometer (km2)

Volume

cubic foot (ft3) 0.02832 cubic meter (m3)

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

inch per day (in/d) 25.4 millimeter per day (mm/d)

SI to Inch/Pound

Multiply By To obtain

Length

meter (m) 3.281 foot (ft)

kilometer (km) 0.6214 mile (mi)

Area

square kilometer (km2) 0.3861 square mile (mi2)

Volume

cubic meter (m3) 35.31 cubic foot (ft3)

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)

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Concentrations of chemical constituents in water are expressed in milligrams per liter (mg/L).

pH of water is expressed in standard units.

Concentrations of Escherichia coli (E. coli) and fecal coliform bacteria in water are expressed in 

colonies per 100 milliliters (col/100 mL) or colony forming units per 100 milliliters.
v

Abbreviations

ADAPS Automated Data-Processing System

DEM digital elevation model

Ef Nash-Sutcliffe Efficiency

GUI graphical user interface

KDOW Kentucky Division of Water

NEXRAD Next Generation Radar

NWIS National Water Information System

NWS National Weather Service

SDP sinkhole-drainage process

TMDL total maximum daily load

TOPMODEL TOPographically Based Hydrological MODEL

TWI topographic wetness index

USGS U.S. Geological Survey

WATER Water Availability Tool for Environmental Resources

Construction of Estimated Flow- and Load-Duration 

Curves for Kentucky Using the Water Availability Tool for 

Environmental Resources (WATER)

By Michael D. Unthank, Jeremy K. Newson, Tanja N. Williamson, and Hugh L. Nelson

Abstract

Flow- and load-duration curves were constructed from 

the model outputs of the U.S. Geological Survey’s Water 

Availability Tool for Environmental Resources (WATER) 

application for streams in Kentucky. The WATER application 

was designed to access multiple geospatial datasets to generate 

more than 60 years of statistically based streamflow data for 

Kentucky. The WATER application enables a user to graphically select a site on a stream and generate an estimated hydrograph and flow-duration curve for the watershed upstream 

of that point. The flow-duration curves are constructed by 

calculating the exceedance probability of the modeled daily 

streamflows. User-defined water-quality criteria and (or) 

sampling results can be loaded into the WATER application to 

construct load-duration curves that are based on the modeled 

streamflow results. 

Estimates of flow and streamflow statistics were derived 

from TOPographically Based Hydrological MODEL (TOPMODEL) simulations in the WATER application. A modified 

TOPMODEL code, SDP-TOPMODEL (Sinkhole Drainage 

Process-TOPMODEL) was used to simulate daily mean 

discharges over the period of record for 5 karst and 5 nonkarst watersheds in Kentucky in order to verify the calibrated 

model. A statistical evaluation of the model’s verification 

simulations show that calibration criteria, established by 

previous WATER application reports, were met thus insuring 

the model’s ability to provide acceptably accurate estimates of 

discharge at gaged and ungaged sites throughout Kentucky.

Flow-duration curves are constructed in the WATER 

application by calculating the exceedence probability of the 

modeled daily flow values. The flow-duration intervals are 

expressed as a percentage, with zero corresponding to the 

highest stream discharge in the streamflow record. Load-duration curves are constructed by applying the loading equation 

(Load = Flow*Water-quality criterion) at each flow interval.

Introduction

The Commonwealth of Kentucky is required by the 

U.S. Environmental Protection Agency, under the authority 

of Section 303(d) of the Clean Water Act of 1972, to develop 

total maximum daily loads (TMDLs) for its waters that do 

not or are not expected to meet applicable water-quality 

standards with technology-based controls only. A TMDL is an 

estimate of the maximum pollutant load (material transported 

during a specified time period) that a receiving water body 

can accept without exceeding water-quality standards (U.S. 

Environmental Protection Agency, 1991). 

TMDL development relies on accurate estimates of 

discharge and various streamflow statistics in the given 

stream. Streamflow statistics that support water-management 

decisions and TMDL development are easily calculated for 

locations where long-term, continuous-record gages have 

been in operation. However, at ungaged locations, statistics 

for TMDL development and water-management decisions are 

less accurate when estimated from other gaged locations that 

are hydrologically similar but are located on a different stream 

reach. This latter procedure often is complicated by differences 

between watershed characteristics of gaged and ungaged 

locations such as geology, drainage area, land use, and many 

other variables that not only differ from region to region, 

but can drastically change from stream to stream. Without 

a thorough knowledge of watershed characteristics and an 

adequate number of long-term, continuous-record streamflowgaging stations, it is difficult to accurately estimate streamflow 

at ungaged sites. For this reason, the U.S. Geological Survey’s 

Water Availability Tool for Environmental Resources 

(WATER) application was developed in cooperation with the 

Kentucky Division of Water (KDOW) to provide a consistent 

and statistically based method of estimating streamflow in 

ungaged watersheds.

A flow-duration curve is one method that can be used to 

assess whether or not the TMDL criterion of a stream is being 

exceeded. Use of the flow-duration curve with appropriate 

water-quality data yields a contaminant load, which is 

based on the magnitude of the streamflow and also projects 
2 Construction of Estimated Flow- and Load-Duration Curves for Kentucky Using the WATER

the expected annual duration of that load. Flow-duration 

curves for continuous-record streamflow-gaging stations 

can be generated using the U.S. Geological Survey (USGS) 

automated data-processing system (ADAPS), a component of 

the National Water Information System (NWIS). A method for 

estimating the flow-duration curves of ungaged sites is needed. 

Although the WATER application was initially designed 

for water-budget assessment of individual watersheds, 

outputs from its TOPographically Based Hydrological 

MODEL (TOPMODEL) simulations can easily be used for 

the construction of flow- and load-duration curves used to 

prepare TMDL estimates.

Purpose and Scope

This report describes the construction of estimated flowand load-duration curves for areas in Kentucky with limited or 

no long-term monitoring data. The estimated flow- and loadduration curves can provide a mechanism to evaluate streamflow on ungaged streams for many uses including assessing 

water-availability, determining sustained flow requirements, 

and developing TMDLs.

This study was done in cooperation with the KDOW, in 

part to provide water-resource managers, planners, and regulators with reliable and accurate streamflow statistics at ungaged 

sites throughout Kentucky. The specific study objectives were 

to

1. Test and, if necessary, refine the ability of the TOPMODEL simulations in the WATER application to generate an estimated flow-duration curve for representative 

user-selected streamflow sites in Kentucky; and

2. Combine available water-quality data with the estimated 

flow-duration curve to calculate estimated load-duration 

curves of the selected streamflow sites.

The TOPMODEL application was tested and calibrated 

using streamflow records from 24 long-term, continuousrecord, streamflow-gaging stations in Kentucky by comparing 

simulated flows with observed flows (Williamson and others, 

2009, and Taylor and others, 2012); additional verification of 

the model was comprised of flow comparisons for the period 

of record for selected calibration watersheds. Hypothetical water-quality data supplied by the KDOW were used to 

construct an example of a load-duration curve for an ungaged 

streamflow site.

Previous Studies

TOPMODEL is a physically based watershed model that 

simulates hydrologic fluxes of water (infiltration-excess overland flow, saturation overland flow, infiltration, exfiltration, 

subsurface flow, and evapotranspiration) through a watershed (Beven and others, 1994). This hydrologic forecasting 

model can be used to predict watershed response using only 

measured and estimated parameters without optimization. In 

Beven and Kirkby (1979), the authors provide a model code 

capable of predicting the streamflow in ungaged watersheds, 

incorporating information derived directly from the watershed 

itself without resorting to regional statistical generalizations of 

model parameters.

Within the WATER application, Williamson and others 

(2009) incorporated a version of the TOPMODEL code into 

a Java-based graphical user interface (GUI). The WATER 

application and embedded TOPMODEL code accessed an 

extensive database of watershed characteristics and other 

pertinent background data to provide comprehensive estimates 

and presentations of the watershed processes, including water 

budgets, streamflows, and slope processes in watersheds of 

varying size for non-karst topographic regions in Kentucky. 

The WATER application was built upon a physically based 

hydrologic model, which simulates the variable-source-area 

concept of streamflow and is an extension of the TOPMODEL 

code described in Wolock (1993). Through proper application, 

the user is provided with a consistent and defensible method 

of estimating streamflow and water availability in ungaged 

watersheds throughout Kentucky.

This study extends the previous studies by Williamson 

and others (2009) and Taylor and others (2012) by incorporating water-quality data with the WATER-generated flow-duration curves to calculate load-duration curves for gaged and 

ungaged streamflow sites in Kentucky.

Model Description

Flow-duration curves have been used for many years by 

hydrologists, engineers, and water-use planners. The flowduration curve is a cumulative frequency curve that indicates 

the percentage of time that a particular streamflow has been 

equaled or exceeded. Streamflow data in the curve are not 

in chronological order. The flow-duration curve applies 

only to the period of record for which the streamflow data 

were collected. 

Flow-duration curves can be prepared for daily, weekly, 

monthly, or other frequencies of discharge measurements. The 

streamflow duration data are arranged according to their magnitude in a range of classes, and the percentage of the time that 

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

drawn through the data. The techniques used by the USGS for 

drawing flow-duration curves are described by Searcy (1959).

To develop flow-duration curves for ungaged stream sites 

that do not have measured discharge values, streamflows can 

be estimated through a modeling approach. The TOPMODEL 

computer program simulates the movement of water through 

a watershed from the time it enters the watershed as precipitation to the time it exits the watershed as streamflow. Using a 

time series of precipitation and temperature data, TOPMODEL 

predicts streamflow, estimates overland and subsurface flow, 

and estimates the depth to the water table. Model components simulate the variable-source-area concept of streamflow 

generation (Wolock, 1993), snow accumulation and melt, 
Model Calibration and Verification 3

evapotranspiration, streamflow generation from impervious 

areas, and channel routing of flow from delivery to the stream 

through to the watershed outlet. For a complete discussion 

on the development and operation of TOPMODEL, including theoretical background, model equations, and methods to 

determine parameter values, refer to Wolock (1993).

WATER was developed to provide a consistent and 

statistically based method of estimating streamflow and water 

availability in ungaged watersheds in Kentucky. The tool 

provides hydrographs, flow-duration curves, and a separation 

of flow components that can be used to assist in making watermanagement decisions. The WATER application relies mainly 

on topographic, pedogenic, and anthropogenic water-use data 

and requires no additional input from the user.

The WATER application uses the TOPMODEL code 

described in Wolock (1993) to simulate the variable-sourcearea concept of streamflow. Critical source data include 

a historical record of daily temperature and precipitation, 

digital elevation models (DEMs) of watershed topography, 

the Natural Resources Conservation Service Soil Survey 

Geographic Database (U.S. Department of Agriculture, 

2007), and historical records of water discharges and 

withdrawals. Most of the required input data for a model 

run are contained in the watershed-characteristics database 

of the WATER application; some input parameters require 

additional preprocessing by statistical sampling of spatial data 

layers. The TOPMODEL portion of the WATER application 

also requires a histogram of the topographic wetness index 

(TWI). The TWI is used to describe how water accumulates 

in the watershed based on a DEM (Quinn and others, 1997). 

Current (2011) output types from the WATER application 

include hydrographs, flow-duration curves, annual and 

monthly water budgets, climatic histories, and load-duration 

curves. For a complete listing and description of the modelinput parameters, data-processing routines, and model 

documentation, refer to Williamson and others (2009).

Model Calibration and Verification

The calibration of a model is the procedure used to 

reduce the difference between simulated results and observed 

data by reasonable adjustment of input parameters of the 

model until an acceptable range of differences is achieved. In 

Williamson and others (2009), twelve non-karst watersheds 

(fig. 1) were used to statistically evaluate and calibrate the 

model using daily mean streamflow values for the period 

of December 31, 2000 to August 8, 2006. A range of values 

for each of the input parameters of rooting depth, hydraulic 

conductivity, and scaling factor were tested along with 

variations in model methodology and precipitation records 

from two different datasets: USGS/National Weather Service 

(NWS) cooperative gaging-station network and Next 

Generation Radar (NEXRAD) (NEXRAD data are available 

at http://www.roc.noaa.gov/WSR88D/). The NEXRAD data 

provided a superior match of simulated and observed daily 

mean streamflows and, consequently, were utilized for all 

calibration efforts. The best fit for model calibration was 

determined using four statistics that commonly are used in 

hydrologic-modeling studies: bias, root mean square error, 

correlation, and Nash-Sutcliffe Efficiency (Ef) (Wolock and 

McCabe, 1999; Martin and others, 2000). Williamson and 

others (2009) demonstrated that the WATER-TOPMODEL 

program developed for use in Kentucky was capable of 

providing acceptable estimates of surface flows for a 2,047-

day period of record in non-karst area basins based on NashSutcliffe efficiencies ranging from 0.26 to 0.72 (Taylor and 

others, 2012). A list of the 12 non-karst calibration watersheds, 

results of the model-calibration runs, and the final values of 

the parameters for the non-karst calibration watersheds are 

presented in this report. 

As previously reported, the TOPMODEL code in the 

WATER application was modified so that sinkholes and 

sinking-stream catchments in karst areas could be identified 

and physically represented as hydrologic components of the 

surface-drainage network. Taylor and others (2012) described 

this sinkhole-drainage process (SDP), documented the 

modifications to the TOPMODEL code (SDP-TOPMODEL), 

and evaluated the model’s performance for 12 karst test 

watersheds (fig. 1). Similar to the calibration process presented 

by Williamson and others (2009), visual comparisons of 

simulated hydrographs with statistical measures (bias, root 

mean square error, correlation, and Nash-Sutcliffe efficiency) 

applied to the simulated discharge data indicated that the SDP 

approach provided acceptably accurate estimates of discharge 

for most flow conditions and typically provided more accurate 

simulation of stream discharge in karstic watersheds compared 

to the standard TOPMODEL approach for the calibration 

period of December 31, 2000 to August 8, 2006 (Taylor and 

others, 2012). 

Additional simulations using the SDP-TOPMODEL code 

were run on a subset of the calibration watersheds to verify the 

results of the calibrated model. Flow simulations were run for 

5 non-karst and 5 karst calibration watersheds for their respective period of records using daily mean discharges. Summary statistics (bias, root mean square error, correlation, and 

Nash-Sutcliffe efficiency) were calculated for each verification 

simulation with the results compared to the summary statistics 

from the calibration runs. Table 1 presents the results for the 

model verification.

In general, the results of the verification simulations 

prove that the input parameters for the SDP-TOPMODEL 

code used for model calibration provide a satisfactory fit for 

each of the tested watersheds over the longer period of record 

for daily mean discharges. Using the calibration criteria established in Williamson and others (2009), the Nash-Sutcliffe 

efficiencies range from 0.40 to 0.80 for the verification simulations, somewhat better than the calibration range of 0.26 to 

0.72. The successful verification of the model code establishes 

greater confidence in the model calibration and its ability to 

accurately simulate streamflow conditions for flow-duration 

curve development.
EXPLANATION

Figure 1. Physiographic regions, selected watersheds and streamflow-gaging stations used for Water Availability Tool for Environmental Resources 

model calibration, and watersheds and streamflow-gaging stations used for model verification in Kentucky.
Table 1. Ten U.S. Geological Survey (USGS) streamflow-gaging stations used in the USGS Water Availability Tool for Environmental Resources (WATE

verification in Kentucky.[km2, square kilometer; Min, minimum; Max, maximum; mm/d, millimeter per day; Obs, observed; Sim, simulated; RMSE, root mean square error; Ef, Nash-Sutcliffe efficiency; 

Station 

number Station name

Karst (K) 

or Nonkarst 

(NK)

Watershed 

area 

(km2)

Period of record

Number of 

observations

Min flow 

(mm/d)

Max flow 

(mm/d) Bias RMSE 

Obs Sim Obs Sim Cal Ver Cal Ver 

0321000 Johns Creek near 

Meta, Ky.

NK 146 04/01/1948–03/31/1975 9,861 0 0.08 50 52 0.28 0.33 3.32 1.94 

03280700 Cutshin Creek at 

Wooten, Ky.

NK 158 04/01/1958–03/31/1989 11,323 0 0.15 76 64 0.15 0.08 2.85 2.26 

03282500 Red River near 

Hazel Green, Ky.

NK 171 04/01/1954–03/31/1971 6,209 0 0.14 43 34 0.19 0.2 1.51 1.36 

03611260 Massac Creek near 

Paducah, Ky.

NK 27 04/01/1972–03/31/1993 7,670 0.01 0.07 161 91 0.11 0.69 1.99 4.56 

03611800 Bayou Creek near 

Heath, Ky.

NK 17 04/01/1994–03/31/2006 4,383 0.003 0.01 102 84 0.1 0.47 1.81 3.16 

03307000 Russell Creek near 

Columbia, Ky.

K 448 04/01/1948–03/31/1980 11,688 0.002 0.05 136 80 -0.01 -0.03 1.53 1.85 

03312765 Beaver Creek at 

Highway 31E near Glasgow, Ky.

K 128 04/01/1992–03/31/2002 3,652 0.03 0.12 56 44 0.33 -0.09 1.49 2.42 

03313700 West Fork Drakes 

Creek near Franklin, Ky.

K 236 04/01/1969–03/31/1979 3,652 0.02 0.18 133 70 0.23 0.05 2.4 2.92 

03413200 Beaver Creek near 

Monticello, Ky.

K 112 04/01/1969–03/31/1995 6,939 0.02 0.06 91 56 0.36 0.08 2.45 2.45 

03438000 Little River near 

Cadiz, Ky.

K 632 04/01/1948–03/31/1962 5,113 0.03 0.1 44 44 0.19 0.2 1.51 1.36 
6 Construction of Estimated Flow- and Load-Duration Curves for Kentucky Using the WATER

Construction of Estimated FlowDuration Curves Using WATER

The flow-duration curve is a cumulative frequency curve 

that indicates the percentage of time that a particular streamflow has been equaled or exceeded. This section describes and 

demonstrates the underlying concepts and construction of an 

estimated flow-duration curve using the WATER application. 

The WATER application is designed to access multiple geospatial datasets to generate approximately 60 years of statistically based streamflow data for user-selected sites throughout 

Kentucky. In general, the WATER-application user graphically selects a site on a stream and the application processes 

the underlying data sets to generate streamflow and a flowduration curve for the selected site (fig. 2). The construction of 

flow-duration curves is performed in three steps: first, identifying and delineating the contributing watershed area; second, 

loading the appropriate data; and third, running the model and 

plotting the resulting flow-duration curve. 

Identifying and Delineating the Contributing 

Watershed

A contributing watershed for a selected site is identified 

and delineated by the user while interacting with the main 

window of the WATER application (fig. 3). The purpose of 

the main window is to provide the user with basic geographic 

functionality to locate and select the area of interest and create 

a simulation point that will become the outlet of the created 

watershed. The main window is subdivided into three sections:

1. The table of contents section, which allows the user to 

toggle geospatial layers on and off; 

2. The overview section, which provides the user with a 

general location map; and

3. The map section, where the user can use the supplied 

interactive tools (located above the main interactive section) to zoom in or out, or pan to a desired stream section. 

Additional tools are provided to assist the user during the 

identification and delineation of the simulation point.

When the user has identified a simulation point where 

a flow-duration curve is to be developed, the user must set 

the simulation point (the “pour point” where surface water 

discharges from the modeled watershed) by zooming in close 

enough for the “Pour Point” button to become enabled. Once 

enabled, the user can click the pour point button (located 

above the main map section) and select a location on the 

stream to set the point. When the simulation point is set, 

the WATER application plots and presents the user with the 

selected point location and queries the user to identify the 

name of the simulation point and a description of the simulation (fig. 4). These descriptions are optional and default values 

(coordinates of the point) may be used. When accepted, the 

simulation point is set and a local simulation data folder is created in the background, storing the user’s name, the simulation 

point’s spatial location, and additional spatial data required 

during the delineation and data processing steps. Once the 

simulation point is set, the delineation process is enabled and 

can be initiated by selecting the enabled “Delineate” button, 

located above the map section (figs. 4 and 5). The delineation 

process may take a few minutes, depending on the watershed 

size, as the WATER application is accessing and creating 

spatial datasets that represent the local landscape and how the 

water will flow toward the simulation point. When complete, 

the watershed is stored to the local simulation data folder 

created during the previous step, and the watershed is visually 

displayed so the user can review it prior to loading the data for 

the study area.

Compiling the Watershed Data

The watershed data are compiled by selecting the “Load 

Data” button, located on the simulation window (fig. 5). 

The “Load Data” button initiates the process to identify the 

required data parameters to execute the model, and then those 

parameters are extracted or calculated from the stored spatial 

geodatasets. The WATER application compiles the data for the 

TOPMODEL program by using the delineated watershed as a 

template and seamlessly opening the required spatial geodatasets, such as the 2001 National Land Cover Database (Homer 

and others, 2004), for estimating the average impervious 

land and road cover, and the Soil Survey Geographic Database (U.S. Department of Agriculture, 2007), for estimating 

numerous hydrologic soil values and TOPMODEL- associated 

values within the watershed. For a complete list of datasets, 

refer to Williamson and others (2009). Additional modeling 

parameters, such as latitude, are spatially calculated directly 

from the watershed. When the WATER application has completed the data-loading process, model-specific data (fig. 6) 

will be shown in the window through a series of tab-based 

displays. These tabs include:

1. Simulation information—this is the main tab showing the 

delineated watershed and user-defined site descriptors;

2. Basin characteristics—this tab shows basin characteristics that are the mean value of spatial data extracted or 

calculated from datasets for the delineated watershed; 

these data can be edited by selecting the ‘Edit Simulation’ 

button;

3. Topographic wetness index—this tab shows the distribution of the TWI; the TWI represents how water accumulates in the basin (Williamson and others, 2009); and

4. Available climatic data—this tab shows temperature and 

precipitation data. 
Construction of Estimated Flow-Duration Curves Using WATER 7

Hydrologic 

model

Selected waterquality target Exceedance

Calculate load

Figure 2. Flow- and load-duration flow chart for the Water Availability Tool for Environmental Resources (WATER) application.
8 Construction of Estimated Flow- and Load-Duration Curves for Kentucky Using the WATER

Main map section

Table of contents 

section

Overview section

Zoom, pan, and

measure tools 

Pour point and 

delineation tools

(dark until they

become active)

Figure 3. Main interactive window of the Water Availability Tool for Environmental Resources (WATER) application.

Simulation window

Pour point and 

delineation buttons 

(white-colored font 

indicates the tool is 

active)

Figure 4. Selecting and identifying a simulation/watershed catchment point on the main interactive window of the 

Water Availability Tool for Environmental Resources (WATER) application.
Construction of Estimated Flow-Duration Curves Using WATER 9

Load data button

Figure 5. Delineated watershed of the Water Availability Tool for Environmental Resources (WATER) application.
10 Construction of Estimated Flow- and Load-Duration Curves for Kentucky Using the WATER

A B

C D

Figure 6. Example of data required for the hydrologic model of the Water Availability Tool for Environmental Resources 

(WATER) application. A, simulation information. B, basin characteristics. C, topographic wetness index. D, available 

climatic data.
Construction of Estimated Load-Duration Curves Using WATER 11

Running TOPMODEL and Plotting the FlowDuration Curve

TOPMODEL is initiated by selecting the “Run” button, 

located at the top of the simulation window. Selecting this 

option allows the WATER application to import the data into 

TOPMODEL and, consequently, run the model for each precipitation and temperature value. When completed, the results 

of the model run are stored in the form of a text file in the 

previously created directory structure and displayed in graphical form on an additional tab (fig. 7). Flow- and load-duration 

curves are obtained in WATER by selecting the “Duration” 

submenu under the “Views” button. 

Flow-duration curves are constructed in the WATER 

application by calculating the exceedance probability of the 

modeled, daily flow values. The flow-duration intervals are 

expressed as a percentage, with zero corresponding to the 

highest stream discharge in the record.

Construction of Estimated LoadDuration Curves Using WATER

Flow duration curves serve as the foundation for development of load-duration curves. A load-duration curve is 

developed by multiplying streamflow with a numeric waterquality target or criterion and a conversion factor for the 

water-quality constituent of concern. Using the load-duration 

curve approach, the frequency and magnitude of water-quality 

standard exceedances, allowable loadings, and size of load 

reductions are easily presented (U.S. Environmental Protection Agency, 2007).

An underlying premise of the load duration curve 

is correlation of water-quality impairments to flow 

conditions. Load-duration curves characterize water-quality 

concentrations (or water-quality data) at different flow 

regimes. The WATER application provides a method to 

A B

C D

Figure 7. Example of output from the hydrologic model of the Water Availability Tool for Environmental Resources 

(WATER) application. A, hydrograph. B, log-normal hydrograph. C, annual water budget. D, flow duration.
12 Construction of Estimated Flow- and Load-Duration Curves for Kentucky Using the WATER

visually display the relationship between streamflow and 

loading capacity. The WATER application constructs the loadduration curve by applying the loading equation (equation 1) 

at each flow interval:

Load = Flow * T * C (1)

where

Load is the load of the applicable water-quality 

constituent,

Flow is the estimated daily streamflow provided by 

the model (in cubic feet per second),

T is the selected water-quality criterion (see 

table 2), and

C is a multiplication factor to ensure unit 

consistency.

The load-duration curve tool in the WATER application 

(fig. 8) is grouped into five flow zones (used as general indicators of hydrologic conditions): high, moist, midrange, dry, and 

low flows. Corresponding default flow-regime intervals are set 

at 0–5, 5–12, 12–38, 38–82, and 82–100 percent, respectively. 

The user may redefine these intervals. Additional interactive 

functionality within the WATER application provides the 

user with methods to select the desired water-quality target, 

define the applicable flow regime, and enter user-supplied 

water-quality data. The user may enter water-quality data 

with qualifiers, and select a sample date (flow will be taken 

from model-derived estimates for that specific day) or enter 

a measured, instantaneous flow (in cubic feet per second). 

Water-quality data are loaded into the WATER application by 

a simple copy-and-paste method that utilizes the clipboard 

of the user’s operating system. The user-supplied data must 

be formatted in two columns that contain either sample date 

and water-quality concentration or measured streamflow and 

water-quality concentration, and the data must be transferred 

from an outside application (i.e. Microsoft Excel or a text file) 

into the WATER application by selecting the “Paste Data” 

button. Data are displayed in gridded view and are plotted on 

the load-duration curve for a graphical display. Water-quality 

data are plotted on the load-duration curve by determining the 

exceedance interval of the measured or estimated flow associated with that particular sample. For example, given a list of 

hypothetical water quality E. coli concentrations (table 3) with 

corresponding water quality target, criteria, and units set to 

“Pathogens (E. coli), 240.0, Col/100 mL.” respectively would 

result with a load-duration curve as shown in figure 8.

Table 2. Criteria and associated default value and units provided by the U.S. Geological Survey Water Availability Tool for 

Environmental Resources (WATER) application.

[mg/L, milligrams per liter; E. coli, Escherichia coli; mL, milliliter; ft3/s, cubic foot per second]

Criterion Default value Provided units

Chloride 600 mg/L (default unit)

Dissolved oxygen 5.0 mg/L (default unit)

pH (H+ Ions) 6.0 Standard (default unit)

Pathogens (E. coli) 240 Colonies/100 mL (default unit); billion colonies/100 mL; colony forming units/100 mL; 

billion colony forming units/100 mL

Pathogens (fecal coliform) 240 Colonies/100 mL (default unit); billion colonies/100 mL; colony forming units/100 mL; 

billion colony forming units/100 mL

Nitrate 10 mg/L as N (default unit)

Total phosphorus .1 mg/L as P (default unit)

Total dissolved solids 250 mg/L (default unit)

Total suspended solids 250 mg/L (default unit)

Sulfate 250 mg/L (default unit)

Flow 1 ft3/s (default unit)
Construction of Estimated Load-Duration Curves Using WATER 13

Figure 8. Example of flow-duration curve tool for the U.S. Geological Survey Water Availability Tool for Environmental 

Resources (WATER) application.

Table 3. Hypothetical water quality Escherichia (E. coli) 

concentrations used as input for the load-duration curve of the 

U.S. Geological Survey Water Availability Tool for Environmental 

Resources (WATER) application.

[col/100 mL, colonies per 100 milliliters]

Sample date Sample E. coli concentration

(col/100 mL)

7/26/2002 199,020

7/25/2003 18,786

3/17/2004 163,680

7/28/2004 85,746

8/16/2004 127,782

9/18/2004 48,360

4/14/2006 151,776

7/25/2006 669,600

8/1/2006 151,776

9/24/2006 34,596
14 Construction of Estimated Flow- and Load-Duration Curves for Kentucky Using the WATER

Summary

The Water Availability Tool for Environmental Resources 

(WATER) application was developed, in part, to provide a 

consistent and statistically based method of estimating streamflow and water availability in ungaged basins in Kentucky. 

The application provides hydrographs, flow- and load-duration 

curves, and a separation of flow components that can be used 

to make water-resource management decisions including 

TMDLs for streams. The WATER application uses the TOPographically Based Hydrological MODEL (TOPMODEL) code 

to simulate the movement of water through a watershed from 

the time it enters the watershed as precipitation to the time 

it exits the watershed as streamflow. Model outputs from the 

TOPMODEL simulations can then be used to construct flowand load-duration curves for ungaged streams.

A modified TOPMODEL code, SDP-TOPMODEL, was 

used within the WATER application to simulate daily mean 

discharges over the period of record for a select number of 

karst and non-karst watersheds in Kentucky in order to verify 

the calibrated model. A statistical evaluation of the model’s 

verification simulations show that calibration criteria established by previous model reports were met thus insuring the 

model’s ability to provide acceptably accurate estimates of 

discharge at gaged and ungaged sites throughout Kentucky.

Flow-duration curves are constructed in the WATER 

application by calculating the exceedance probability of the 

modeled daily flow values. The flow-duration intervals are 

expressed as a percentage, with zero corresponding to the 

highest stream discharge in the streamflow record. Load-duration curves are constructed by applying the loading equation 

(Load = Flow * Water-quality criterion) at each flow interval.

References Cited

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variable contributing area model of basin hydrology: 

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Beven, K., Quinn, P., Romanowski, R., Freer, J., Fisher, J., 

and Lamb, R., 1994, TOPMODEL and GRIDATB (2d ed.): 

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Unthank and others—Construction of Estimated Flow- and Load-Duration Curves for Kentucky Using WATER—Scientific Investigations Report 2012–5168