Prepared in cooperation with the U.S. Environmental Protection Agency,

National Exposure Research Laboratory

Simulation of Streamflow in the McTier Creek

Watershed, South Carolina

Scientific Investigations Report 2010–520

National Water-Quality Assessment Program

U.S. Department of the Interior

U.S. Geological Survey
Cover art: Photographs of McTier Creek upstream from the 

streamgage near Monetta at the Secondary Road 25 crossing, 

Aiken County, South Carolina, August 17, 2007 (Toby D. Feaster). 

Map image from report appendix figure 1–1.
Simulation of Streamflow in the McTier Creek 

Watershed, South Carolina

By Toby D. Feaster, Heather E. Golden, Kenneth R. Odom, Mark A. Lowery, 

Paul A. Conrads, and Paul M. Bradley

National Water-Quality Assessment Program

Prepared in cooperation with the U.S. Environmental Protection Agency, 

National Exposure Research Laboratory

Scientific Investigations Report 2010–5202

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: 2010

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Suggested citation:

Feaster, T.D., Golden, H.E., Odom, K.R., Lowery, M.A., Conrads, P.A., and Bradley, P.M., 2010, Simulation of streamflow 

in the McTier Creek watershed, South Carolina: U.S. Geological Survey Scientific Investigations Report 2010–5202, 

61 p. 
iii

Foreword

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information that helps to enhance and protect the overall quality of life and that facilitates 

effective management of water, biological, energy, and mineral resources (http://www.usgs.

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and wildlife. Population growth and increasing demands for water make the availability of that 

water, measured in terms of quantity and quality, even more essential to the long-term sustainability of our communities and ecosystems.

The USGS implemented the National Water-Quality Assessment (NAWQA) Program in 1991 

to support national, regional, State, and local information needs and decisions related to 

water-quality management and policy (http://water.usgs.gov/nawqa). The NAWQA Program 

is designed to answer: What is the quality of our Nation’s streams and groundwater? How are 

conditions changing over time? How do natural features and human activities affect the quality 

of streams and groundwater, and where are those effects most pronounced? By combining 

information on water chemistry, physical characteristics, stream habitat, and aquatic life, the 

NAWQA Program aims to provide science-based insights for current and emerging water issues 

and priorities. From 1991 to 2001, the NAWQA Program completed interdisciplinary assessments and established a baseline understanding of water-quality conditions in 51 of the Nation’s 

river basins and aquifers, referred to as Study Units (http://water.usgs.gov/nawqa/studies/

study_units.html).

National and regional assessments are ongoing in the second decade (2001–2012) of the 

NAWQA Program as 42 of the 51 Study Units are selectively reassessed. These assessments 

extend the findings in the Study Units by determining water-quality status and trends at sites 

that have been consistently monitored for more than a decade, and filling critical gaps in 

characterizing the quality of surface water and groundwater. For example, increased emphasis 

has been placed on assessing the quality of source water and finished water associated with 

many of the Nation’s largest community water systems. During the second decade, NAWQA is 

addressing five national priority topics that build an understanding of how natural features and 

human activities affect water quality, and establish links between sources of contaminants, 

the transport of those contaminants through the hydrologic system, and the potential effects

of contaminants on humans and aquatic ecosystems. Included are studies on the fate of 

agricultural chemicals, effects of urbanization on stream ecosystems, bioaccumulation of 

mercury in stream ecosystems, effects of nutrient enrichment on aquatic ecosystems, and 

transport of contaminants to public-supply wells. In addition, national syntheses of information 

on pesticides, volatile organic compounds (VOCs), nutrients, trace elements, and aquatic ecology 

are continuing. 

The USGS aims to disseminate credible, timely, and relevant science information to address 

practical and effective water-resource management and strategies that protect and restore 

water quality. We hope this NAWQA publication will provide you with insights and information 

to meet your needs, and will foster increased citizen awareness and involvement in the protection and restoration of our Nation’s waters. 
The USGS recognizes that a national assessment by a single program cannot address all 

water-resource issues of interest. External coordination at all levels is critical for cost-effective 

management, regulation, and conservation of our Nation’s water resources. The NAWQA Program, 

therefore, depends on advice and information from other agencies—Federal, State, regional, 

interstate, Tribal, and local—as well as nongovernmental organizations, industry, academia, and 

other stakeholder groups. Your assistance and suggestions are greatly appreciated.

 William H. Werkheiser

USGS Associate Director for Water

iv
v

Acknowledgments

The authors gratefully acknowledge the support and guidance provided by Leon Kauffman and 

Dave Wolock of the U.S. Geological Survey. The version of the TOPMODEL used in this study was 

based on a version originally documented by Dave Wolock (1993) and later modified by Leon Kauffman (Kennen and others, 2008). Both scientists graciously took time to answer questions by e-mail 

and telephone concerning the application of TOPMODEL and proper interpretations of results. Their 

previous work and guidance for the current application of TOPMODEL added significantly to this 

investigation. 

The U.S. Environmental Protection Agency, through its Office of Research and Development, 

partially funded the research described in this report through Interagency Agreement DW14922794.

vii

Contents

Foreword ........................................................................................................................................................iii

Acknowledgments.........................................................................................................................................v

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

Introduction.....................................................................................................................................................2

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

Previous Studies ...................................................................................................................................3

Description of the McTier Creek Watershed ...................................................................................3

Surficial Geology..........................................................................................................................6

Climate...........................................................................................................................................6

Streamflow....................................................................................................................................8

TOPMODEL Streamflow Concepts............................................................................................................11

Topographic Wetness Index .............................................................................................................11

TOPMODEL Water Balance ..............................................................................................................12

GBMM Streamflow Concepts....................................................................................................................13

Methods of Study.........................................................................................................................................14

Data Collection....................................................................................................................................14

Meteorological Parameters.....................................................................................................14

Watershed Characteristics ......................................................................................................17

Streamflow..................................................................................................................................19

Topographic Wetness Index ....................................................................................................19

GBMM Curve-Number Estimates ...........................................................................................20

Calibration of TOPMODEL and GBMM............................................................................................20

Simulation of the Streamflow for TOPMODEL and GBMM...................................................................21

Simulations for Monetta for the Calibration Period ......................................................................21

Simulations at New Holland for the Confirmation Period ............................................................28

Goodness-of-Fit Statistics for TOPMODEL and GBMM ........................................................................29

Goodness-of-Fit Statistics at Monetta for the Calibration Period Simulations ........................29

Goodness-of-Fit Statistics at Monetta for the Concurrent Period Simulations .......................30

Goodness-of-Fit Statistics at New Holland for Confirmation Period Simulations ...................32

Flow-Duration Curves, Single-Mass Curves, and Residuals................................................................32

Flow-Duration Curves.........................................................................................................................32

Single-Mass Curves ...........................................................................................................................34

Residuals..............................................................................................................................................36

Residuals and Simulated Flow..........................................................................................................38

Residuals (Temporal)..........................................................................................................................40

Watershed Model Uncertainties and Limitations...................................................................................42

Watershed Model Uses ..............................................................................................................................43

Mapping Saturated Areas.................................................................................................................43

Modeling Hydrology in Subwatersheds..........................................................................................43

Loadings from TOPMODEL Flow Components...............................................................................47

Estimating Water, Sediment, and Mercury Balances with GBMM............................................50

Identifying Spatially Explicit Mercury Source Areas in Watersheds.........................................50

Summary........................................................................................................................................................51

References Cited..........................................................................................................................................51
Appendix 1.....................................................................................................................................................56

Model Components in TOPMODEL ..................................................................................................56

Precipitation................................................................................................................................56

Evapotranspiration ....................................................................................................................56

Impervious-Area Runoff ...........................................................................................................56

Pervious-Area Runoff................................................................................................................56

Saturation Overland Flow.........................................................................................................57

Subsurface Flow ........................................................................................................................59

Infiltration-Excess Overland Flow...........................................................................................59

Lake Storage...............................................................................................................................60

Open-Water Bodies...................................................................................................................60

Appendix 2.....................................................................................................................................................60

Model Components of GBMM: Hydrology Module.......................................................................60

Precipitation................................................................................................................................60

Evapotranspiration ....................................................................................................................60

Impervious-Area Runoff ...........................................................................................................61

Pervious-Area Runoff................................................................................................................61

Lake Storage...............................................................................................................................61

Figures

1. Map showing location of the McTier Creek study area, Aiken County, South Carolina...4

2. Map showing McTier Creek watershed land cover, Aiken County, South Carolina..........5

3. Photograph showing McTier Creek near the upper part of the watershed displaying 

characteristics similar to streams in the Piedmont Physiographic Province in 

South Carolina...............................................................................................................................6

4. Photograph showing cross section of hillside displaying soil characteristics similar 

to those of the Coastal Plain Physiographic Province in South Carolina............................6

5–10. Graphs showing—

5. Mean of total monthly rainfall for Aiken, South Carolina, 1948–2008..........................7

6. Cumulative annual rainfall for Aiken, South Carolina, 1948–2008................................7

7. Average monthly mean streamflow at USGS streamflow-gaging station 02172300, 

McTier Creek near Monetta, South Carolina, 1995–1997 and 2001–2008...................8

8. Average monthly mean streamflow at South Fork Edisto River near Denmark, 

South Carolina, 1931–1971 and 1980–2008.......................................................................9

9. Average monthly mean streamflow at McTier Creek near Monetta and South 

Fork Edisto River near Denmark, South Carolina, for the concurrent period of 

record at both stations........................................................................................................9

10. Minimum, average, and maximum monthly mean flow per square mile 

at McTier Creek near Monetta and South Fork Edisto River near Denmark, 

South Carolina....................................................................................................................10

11. Diagram defining selected water-source variables from TOPMODEL..............................12

12. Map showing meteorological stations in the vicinity of McTier Creek watershed, 

South Carolina, considered for use in this investigation .....................................................15

13–30. Graphs showing—

13. Single-mass curve reviews of the National Weather Service precipitation data..16

viii
ix

14. Single-mass curve reviews of the National Weather Service precipitation data 

along with a weighted curve computed using inverse distance weighting............16

15. Single-mass curve reviews of the National Weather Service minimum air 

temperature data ...............................................................................................................17

16. Comparison of inverse weighted minimum temperatures with and without the 

Johnston 4SW station data..............................................................................................18

17. TOPMODEL simulated and observed daily mean flows at McTier Creek near 

Monetta for the calibration period, along with observed precipitation data ..........22

18. GBMM simulated and observed daily mean flows at McTier Creek near 

Monetta for the calibration period, along with observed precipitation data ..........23

19. Simulated and observed daily mean flows at McTier Creek near Monetta for 

the calibration period, shown by calendar year...........................................................24

20. Simulated and observed daily mean flows at McTier Creek near New Holland 

for the confirmation period ..............................................................................................29

21. Simulated and observed daily mean flows for McTier Creek near Monetta for 

the concurrent period .......................................................................................................31

22. Flow-duration curves of simulated and observed daily mean flow at Monetta 

for the calibration period, Monetta for the concurrent period, and New Holland 

for the confirmation period ..............................................................................................33

23. Single-mass curves of simulated and observed daily mean flow at Monetta for 

the calibration period, Monetta for the concurrent period, and New Holland for 

the confirmation period ....................................................................................................35

24. Scatter plots of observed and TOPMODEL simulated daily mean flow at 

McTier Creek near Monetta for the calibration period, McTier Creek near 

Monetta for the concurrent period, and McTier Creek near New Holland for 

the confirmation period ....................................................................................................36

25. Scatter plots of observed and GBMM simulated daily mean flow at 

McTier Creek near Monetta for the calibration period, McTier Creek near 

Monetta for the concurrent period, and McTier Creek near New Holland for 

the confirmation period ....................................................................................................37

26. Residuals and TOPMODEL simulated daily mean flow at McTier Creek near 

Monetta for the calibration period, McTier Creek near Monetta for the 

concurrent period, and McTier Creek near New Holland for the 

confirmation period ...........................................................................................................38

27. Residuals and GBMM simulated daily mean flow at McTier Creek near Monetta 

for the calibration period, McTier Creek near Monetta for the concurrent period, 

and McTier Creek near New Holland for the confirmation period............................39

28. Residuals of simulated (TOPMODEL) and observed daily mean flow at 

McTier Creek near Monetta for the calibration period, McTier Creek near 

Monetta for the concurrent period, and McTier Creek near New Holland for 

the confirmation period ....................................................................................................40

29. Residuals of simulated (GBMM) and observed daily mean flow at McTier Creek 

near Monetta for the calibration period, McTier Creek near Monetta for the 

concurrent period, and McTier Creek near New Holland for the 

confirmation period ...........................................................................................................41

30. Simulated (TOPMODEL) daily mean flow and saturated area at McTier Creek 

near New Holland for the confirmation period.............................................................43

31. Maps showing saturated areas from TOPMODEL simulations in the McTier Creek 

watershed under low-flow conditions on August 8, 2007, and high-flow conditions 

on April 11, 2009 ..........................................................................................................................44
32. Map showing McTier Creek subwatersheds, Aiken County, South Carolina...................46

33–36. Graphs showing—

33. Simulated daily mean flow for the concurrent period at McTier Creek near 

Monetta and the sum of the simulated daily mean flow for subwatersheds 

MA01 to MA06....................................................................................................................47

34. Simulated daily mean flow for the confirmation period at McTier Creek near 

New Holland and the sum of the simulated daily mean flow for subwatersheds 

MA01 to MA12....................................................................................................................48

35. Simulated daily mean flow for the concurrent period at McTier Creek near 

Monetta and the sum of the simulated daily mean flow for subwatersheds 

MA01 to MA06, and the confirmation period at McTier Creek near New Holland 

and the sum of simulated daily mean flow for subwatersheds MA01 to MA12......49

36. TOPMODEL flow components from simulation at McTier Creek near 

New Holland for the confirmation period......................................................................50

1–1. Map showing topographic wetness indices for the McTier Creek watershed in 

South Carolina.............................................................................................................................58

1–2. Graph showing relative frequency distribution of topographic wetness indices 

values for McTier Creek watershed in South Carolina ........................................................59

Tables

1. U.S. Geological Survey streamflow-gaging stations, reference names, 

and periods of record...................................................................................................................8

2. Meteorological stations in the vicinity of the McTier Creek watershed, 

South Carolina, considered for use in this investigation .....................................................15

3. Watershed characteristics for use with the topography based hydrological model .....18

4. Watershed and grid cell characteristics for use with the grid based mercury model...19

5. Station number and name, period of record used in the model calibration and 

confirmation simulations, and model simulation period reference name for the 

McTier Creek watershed, South Carolina ..............................................................................20

6. Parameter values used for the TOPMODEL calibration for McTier Creek near 

Monetta for the calibration period...........................................................................................22

7. Parameter values used for GBMM calibration for McTier Creek near Monetta 

for the calibration period...........................................................................................................22

8. Parameter values used for the TOPMODEL calibration for McTier Creek near 

New Holland, South Carolina....................................................................................................28

9. Goodness-of-fit statistics at McTier Creek near Monetta for the calibration period .....30

10. Goodness-of-fit statistics for McTier Creek near Monetta for the concurrent period...31

11. TOPMODEL and GBMM calibration statistics at McTier Creek near New Holland 

for the confirmation period .......................................................................................................32

x
Conversion Factors

SI to Inch/Pound

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

hectare (ha) 2.471 acre

square kilometer (km2) 247.1 acre

square kilometer (km2) 0.3861 square mile (mi2)

Volume

cubic meter (m3) 35.31 cubic foot (ft3)

Flow rate

meter per second (m/s) 3.281 foot per second (ft/s) 

cubic meter per day (m3/d) 35.31 cubic foot per day (ft3/d) 

Hydraulic conductivity

meter per day (m/d) 3.281 foot per day (ft/d) 

Hydraulic gradient

meter per kilometer (m/km) 5.27983 foot per mile (ft/mi) 

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 0.004047 square kilometer (km2)

square mile (mi2) 2.590 square 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)

cubic foot per second per square mile

[(ft3/s)/mi2]

0.01093 cubic meter per second per square 

kilometer [(m3/s)/km2]

inch per hour (in/h) 0.0254 meter per hour (m/h)

Hydraulic conductivity

foot per day (ft/d) 0.3048 meter per day (m/d)

Hydraulic gradient

foot per mile (ft/mi) 0.1786 meter per kilometer (m/km)

xi
Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F = (1.8 × °C) + 32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C = (°F – 32) / 1.8

Horizontal coordinate information is referenced to the North American Datum of 1927 or 1983 

(NAD 27 or NAD 83, respectively).

Vertical coordinate information is referenced to the North American Datum of 1988 (NAVD 88) or 

National Geodetic Vertical Datum of 1929 (NGVD 29).

Elevation, as used in this report, refers to distance above the vertical datum.

xii
Acronyms and Abbreviations Used in the Report

BASINS Better Assessment Science Integrating Point and Non-Point Sources

Calibration period model simulations at Monetta for February 7, 2001, to September 30, 2009

Concurrent period model simulations at Monetta for June 13, 2007, to September 30, 2009

Confirmation period model simulations at New Holland for June 13, 2007, to September 30, 2009

DDS dynamically dimensioned search

DEM digital elevation model

DOC dissolved organic carbon

E Nash-Sutcliffe coefficient of model-fit efficiency index

ET evapotranspiration

GBMM grid-based mercury model

GIS geographic information system

Hg mercury

HSPF Hydrologic Simulation Program–Fortran

ISC total impervious surface cover

MA01–MA12 model assessment points

MAE mean absolute error

MeHg methylmercury

Monetta Station 02172300, McTier Creek near Monetta, SC

New Holland Station 02172305, McTier Creek near New Holland, SC 

NHD National Hydrography Dataset

NLCD National Land-Cover Dataset

NRCS Natural Resources Conservation Service

NWS National Weather Service

PEST parameter estimation program

PET potential evapotranspiration

ppt precipitation

qb subsurface flow

qimp impervious flow

qinf infiltration-excess overland flow

qof overland saturation flow

qpred total in-stream flow

qret return flow

qsrip flow from open-water bodies (lakes, ponds, precipitation directly into the channel)

r Pearson’s correlation coefficient

RMSE root mean square error

SC South Carolina

SCS Soil Conservation Service

SCS-CN Soil Conservation Service curve number

South Fork Edisto Station 02172300, South Fork Edisto River near Denmark, SC

SSURGO Soil Survey Geographic Database

SWAT Soil and Water Assessment Tool

TOPMODEL topography-based hydrological model

TR-55 Technical Release 55

TWI topographic wetness index

USDA U.S. Department of Agriculture

USEPA U.S. Environmental Protection Agency

USGS U.S. Geological Survey

WASP Water-Quality Analysis Simulation Program

WATER Water Availability Tool for Environmental Resources

xiii

Abstract

The McTier Creek watershed is located in the Sand Hills 

ecoregion of South Carolina and is a small catchment within 

the Edisto River Basin. Two watershed hydrology models 

were applied to the McTier Creek watershed as part of a 

larger scientific investigation to expand the understanding 

of relations among hydrologic, geochemical, and ecological 

processes that affect fish-tissue mercury concentrations within 

the Edisto River Basin. The two models are the topographybased hydrological model (TOPMODEL) and the grid-based 

mercury model (GBMM). TOPMODEL uses the variablesource area concept for simulating streamflow, and GBMM 

uses a spatially explicit modified curve-number approach 

for simulating streamflow. The hydrologic output from 

TOPMODEL can be used explicitly to simulate the transport 

of mercury in separate applications, whereas the hydrology 

output from GBMM is used implicitly in the simulation of 

mercury fate and transport in GBMM. The modeling efforts 

were a collaboration between the U.S. Geological Survey and 

the U.S. Environmental Protection Agency, National Exposure 

Research Laboratory. 

Calibrations of TOPMODEL and GBMM were done 

independently while using the same meteorological data and 

the same period of record of observed data. Two U.S. Geological Survey streamflow-gaging stations were available for 

comparison of observed daily mean flow with simulated daily 

mean flow—station 02172300, McTier Creek near Monetta, 

South Carolina, and station 02172305, McTier Creek near 

New Holland, South Carolina. The period of record at the 

Monetta gage covers a broad range of hydrologic conditions, 

including a drought and a significant wet period. Calibrating 

the models under these extreme conditions along with the 

normal flow conditions included in the record enhances the 

robustness of the two models. 

Several quantitative assessments of the goodness of fit 

between model simulations and the observed daily mean flows 

were done. These included the Nash-Sutcliffe coefficient of 

model-fit efficiency index, Pearson’s correlation coefficient, 

the root mean square error, the bias, and the mean absolute 

error. In addition, a number of graphical tools were used to 

assess how well the models captured the characteristics of the 

observed data at the Monetta and New Holland streamflowgaging stations. The graphical tools included temporal plots 

of simulated and observed daily mean flows, flow-duration 

curves, single-mass curves, and various residual plots. The 

results indicated that TOPMODEL and GBMM generally 

produced simulations that reasonably capture the quantity, 

variability, and timing of the observed streamflow. For the 

periods modeled, the total volume of simulated daily mean 

flows as compared to the total volume of the observed daily 

mean flow from TOPMODEL was within 1 to 5 percent, and 

the total volume from GBMM was within 1 to 10 percent. A 

noticeable characteristic of the simulated hydrographs from 

both models is the complexity of balancing groundwater recession and flow at the streamgage when flows peak and recede 

rapidly. However, GBMM results indicate that groundwater 

recession, which affects the receding limb of the hydrograph, 

was more difficult to estimate with the spatially explicit curve 

number approach. Although the purpose of this report is not 

to directly compare both models, given the characteristics of 

the McTier Creek watershed and the fact that GBMM uses the 

spatially explicit curve number approach as compared to the 

variable-source-area concept in TOPMODEL, GBMM was 

able to capture the flow characteristics reasonably well.

Simulation of Streamflow in the McTier Creek Watershed, 

South Carolina

By Toby D. Feaster, Heather E. Golden, Kenneth R. Odom, Mark A. Lowery, Paul A. Conrads, 

and Paul M. Bradley
2 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Introduction

An important part of the USGS mission is to provide 

scientific information for the effective water-resources 

management of the Nation. To assess the quantity and quality 

of the Nation’s surface water, the USGS collects hydrologic 

and water-quality data from rivers, lakes, and estuaries by 

using standardized methods and maintains the data from these 

stations in a national database. In 2007, the USGS developed 

a science strategy (U.S. Geological Survey, 2007a) outlining 

the major natural science issues facing the Nation in the next 

decade. The hydrologic study of McTier Creek, along with 

a concurrent mercury (Hg) study in the watershed, directly 

addresses the strategic goals of understanding ecosystems 

and predicting ecosystem change as well as providing the 

Nation with information needed to meet the challenges of 

the 21st century. 

In South Carolina, levels of mercury concentrations in 

fish tissue that may be harmful have resulted in consumption 

advisories for several river basins within the Coastal Plain 

Physiographic Province, including the Edisto River Basin 

(South Carolina Department of Health and Environmental 

Control, 2006). Understanding the fundamental hydrologic, 

geochemical, and ecologic processes that affect the levels of 

fish-tissue mercury concentrations within the Edisto River 

Basin is an environmental priority. 

The risk of mercury in the Edisto River Basin aquatic 

environment, including the risk to human health, is inextricably linked to hydrology. Water provides habitat for aquatic 

biota, limits oxygen supply in saturated soil/sediment, 

and contributes to the onset of iron- and sulfate-reducing 

conditions, which support microbial production of toxic 

alkyl-mercury species (Compeau and Bartha, 1985; Benoit 

and others, 2003; Fleming and others, 2006). Methylmercury 

(MeHg), in particular, is neurotoxic (Clarkson and others, 

2003) and readily accumulated in aquatic food webs (Bloom, 

1992; Hall and others, 1997; Brumbaugh and others, 2001). 

Methylmercury is the primary form of mercury in fish (Bloom, 

1992). Wetlands are recognized source areas for environmental 

methylmercury (St. Louis and others, 1994; Grigal, 2002; 

Hall and others, 2008; Rypel and others, 2008; Brigham and 

others, 2009).

Thus, a fundamental control on mercury bioaccumulation 

in the Edisto River Basin is the transport of methylmercury

from the site and matrix of production in the wetlands to the 

base of the stream aquatic food web (Bradley and others, 

2009; Chasar and others, 2009). A recent study (P.M. Bradley, 

U.S. Geological Survey, unpub. data, 2010) demonstrated 

that the characteristically coarse-grained sediments of the 

Coastal Plain in South Carolina favor efficient exchange of 

water between streams and shallow groundwater systems in 

this physiographic province. This efficient exchange of water 

promotes transport of methylmercury from riparian wetland 

source areas to the stream aquatic habitat and, consequently, 

creates an inherent vulnerability to mercury bioaccumulation 

in Coastal Plain streams. Stream systems, such as the Edisto 

River, are particularly vulnerable to mercury bioaccumulation 

because they are entirely or largely within this Coastal Plain 

region and, consequently, are primarily subject to a groundwater flood mechanism that transports methylmercury to the 

stream channel aquatic habitat.

In light of the critical role of hydrology as a driver of 

methylmercury concentrations within the stream aquatic 

habitats of the Edisto River Basin, numerical tools that 

reliably simulate the direction, timing, and quantity of water 

transport can contribute substantially to an understanding of 

the temporal and spatial variability of methylmercury bioavailability in the stream aquatic habitat. This report documents 

the application of two distinct approaches to modeling the 

hydrology of the surface and shallow subsurface flow system 

in McTier Creek, which is a small headwater watershed within 

the Edisto River Basin of South Carolina. 

Purpose and Scope

The purpose of this report is to present analyses and 

simulations of the hydrology of the McTier Creek watershed. 

The study area is from the headwater of McTier Creek to the 

New Holland gage and the surficial aquifer above the confining bedrock. As part of the analysis, two watershed hydrology 

models—the topography-based hydrological model 

(TOPMODEL) and the grid-based mercury model (GBMM)—

were applied to the McTier Creek watershed. TOPMODEL 

uses the variable-source-area concept for simulating 

streamflow, and GBMM uses a spatially explicit modified 

curve-number approach for simulating streamflow. Hydrologic 

output from both models is used to better understand the 

spatial and temporal variability relation of mercury and 

hydrology. The hydrologic output from TOPMODEL can be 

used explicitly to simulate the transport of mercury in separate 

applications, whereas the hydrologic output from GBMM is 

used implicitly in the simulation of mercury fate and transport 

in GBMM. The applications of the models were a collaborative effort between the U.S. Geological Survey (USGS) and 

the U.S. Environmental Protection Agency, National Exposure 

Research Laboratory. 

This report does not compare the two hydrologic 

models but rather provides documentation of the application 

of the two models. Although the two models use the same 

datasets for calibration, no attempt was made to use the same 

calibration techniques as would be required for a hydrologic 

model comparison. 

USGS streamflow data are measured and reported in 

English units; consequently, most of the data presented in this 

report are provided using English units. However, because the 

TOPMODEL used in this investigation includes both English 

and International System of Units (SI) and GBMM uses SI 

units, the report includes both systems of measurement. 
Introduction 3

Previous Studies

TOPMODEL is a physically based watershed model 

that simulates the variable-source-area concept of streamflow 

generation (Wolock, 1993). The model was first described by 

Beven and Kirkby (1979) and has continually evolved along 

with the understanding of how precipitation moves over and 

through watersheds and ultimately contributes to streamflow. 

By design, the modeling concepts in TOPMODEL have been 

kept simple to preserve a flexible model structure that can be 

tailored based on the researcher’s perceptions of the behavior 

of a particular watershed (Singh, 1995). As a result, numerous 

versions of TOPMODEL exist. Beven (1997) documents a 

variety of versions and applications of TOPMODEL.

The version of TOPMODEL used in this investigation 

was documented by Kennen and others (2008) and has most 

recently been incorporated into the Water Availability Tool for 

Environmental Resources (WATER) as part of an investigation 

to model ungaged streams in Kentucky (Williamson and others, 2009). In the investigation by Kennen and others (2008), 

TOPMODEL was part of an integrated hydroecological model 

that provided a comprehensive set of hydrologic variables 

representing major components of the flow regimes at 856 

aquatic-invertebrate monitoring sites in New Jersey. Kennen 

and others (2008) noted that the TOPMODEL code used in 

their study had been modified from an earlier version used in 

an investigation by Wolock (1993). The purpose of the Wolock 

(1993) report was to describe the theoretical background of 

TOPMODEL, the model equations, the methods used to determine parameter values, and the FORTRAN computer code. 

The introduction to the Wolock (1993) report also provides an 

extensive list of papers and reports for which TOPMODEL 

has been used to study a variety of research areas.

Wolock (1993) stated that the version of TOPMODEL 

described in his report was derived from the version 

documented by Hornberger and others (1985), with extensive 

modifications. Hornberger and others (1985) modified the version of TOPMODEL documented by Beven and Wood (1983) 

and applied it to a small forested catchment in Shenandoah 

National Park, VA. 

With respect to assessing water chemistry in a catchment, Hornberger and others (1994) applied TOPMODEL 

(Beven and Kirkby, 1979) to the Snake River catchment 

near Montezuma, CO. The model was used to examine 

hydrological mechanisms for the purpose of explaining the 

observed variability of dissolved organic carbon (DOC) in the 

Snake River. Conceptually, the DOC model represented a soil 

reservoir in which DOC accumulated during low-flow periods 

and was flushed out by infiltrating snowmelt water. The work 

of Hornberger and others (1994) represented one of the first 

attempts to quantitatively describe the hydrological controls 

on DOC dynamics in a headwater stream.

GBMM is a recently developed, spatially explicit, 

watershed-scale model that computes daily mass balances for 

hydrology, sediment, and mercury within each geographic 

information system (GIS) raster grid cell (Dai and others, 

2005; Tetra Tech, 2006). The model has been validated in 

several catchments in the southeastern United States with 

strong reproduction of daily and monthly hydrographs and 

is currently being added to the Better Assessment Science 

Integrating Point and Non-Point Sources (BASINS) modeling 

framework (U.S. Environmental Protection Agency, 2009: 

Tim Wool, U.S. Environmental Protection Agency, Region IV, 

oral commun., 2009). A recent application of GBMM focuses 

on the hydrological component of watershed mercury fate 

and transport in the Haw River and Deep River watersheds, 

located in the upper Cape Fear River Basin in North Carolina 

(Golden and others, 2010). The authors assessed whether 

precipitation implemented within a regional air-quality model 

links efficiently with the standard precipitation sources used 

to calibrate watershed models (for example, rain-gage data) 

so that GBMM-simulated runoff and, subsequently, biogeochemical flux estimates are not substantially offset. Based on 

this study, GBMM currently is being implemented to evaluate 

the response of mercury fluxes, as well as nitrate fluxes, to 

diverse land-cover change in the Haw River watershed. Nitrate 

fluxes are estimated using a simple nitrate flux model linked to 

GBMM (H.E. Golden, U.S. Environmental Protection Agency, 

oral commun., 2010). 

Description of the McTier Creek Watershed

Headwaters typically are defined as the upper reaches of 

a basin or watershed and, thus, contain smaller streams and 

tributaries to larger water bodies. McTier Creek is a small 

headwater stream located in the Edisto River Basin and is a 

tributary to the South Fork Edisto River (fig. 1). The entire 

McTier Creek watershed encompasses about 38 square miles 

(mi2), is designated by the 12-digit hydrologic unit code 

030502040102, and lies completely in the county of Aiken, 

SC (Eidson and others, 2005). The study area encompasses 

about 31 mi2 of the watershed, and land-cover categories are 

as follows: 50 percent forest, 20 percent grassland/herbaceous, 

16 percent agriculture, 8 percent wetland, 5 percent developed, 

and about 1 percent open water (Homer and others, 2004; 

fig. 2). 

McTier Creek lies within the inland part of the Coastal 

Plain Physiographic Province known as the Sand Hills 

(Griffith and others, 2002; fig. 1). Some studies integrate the 

Sand Hills within a broader area referred to as the inner or 

upper Coastal Plain (Bloxham, 1976; Marshall, 1993; Bennett 

and Patton, 2008). The McTier Creek watershed begins near 

the Fall Line (fig. 1), which is the name given to the boundary 

between the Piedmont and Coastal Plain Physiographic 

Provinces. In general, this boundary is characterized by a 

series of rapids or falls where the streams cascade off the more 

resistant rocks of the Piedmont into the deeper valleys worn in 

the softer sandy sediments of the Coastal Plain (Cooke, 1936). 

Commonly, the headwaters of watersheds located just below 

the Fall Line transition from characteristics similar to Piedmont streams in the headwaters to Coastal Plain characteristics 
4 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Figure 1. Location of the McTier Creek study area, Aiken County, South Carolina.

02172305

8136’ 8132’

3352’

33

48’

3344’

Watershed

boundary

Fall Line

SOUTH

Atlantic

Ocean

GEORGIA

McTier Creek

watershed

Blue Ridge

Piedmont

Lower

Coastal Plain

Sand Hills

Fall

Line

Upper

Coastal Plain

NORTH CAROLINA

CAROLINA

Base from National Hydrography Dataset and digital line graphs, 1:100,000

ESRI data and maps, 2006

Albers equal area projection; central meridian-96 00 00; datum NAD 83

South

McTier

Creek

Gully

Creek

Fork Edisto

River

20

SALUDA

AIKEN

02172300

0 0.5 1 2 KILOMETERS

0 0.5 1 2 MILES

Figure 1. 
Introduction 5

Figure 2. McTier Creek watershed land cover, Aiken County, South Carolina.

Base from national hydrography dataset and digital line graphs, 1:100,000

ESRI data and maps, 2006

Albers equal area projection; central meridiean - 96 00 00; datum NAD83

Figure 1. 

02172300

02172305

02172305

EXPLANATION

0 1 2 MILES

0 1 2 KILOMETERS

Gully

McTier

Creek

Creek

Open water

Developed

Forest

Grassland/herbaceous

Agriculture

Wetland

McTier Creek watershed boundary

USGS streamgage and gage number

SC Edisto

River

basin

Atlantic

Ocean

McTier Creek

watershed

GA

NC

8138’

3350’

33

48’

3346’

33

44’

8136’ 81

34’ 8132’

Land-cover data from 2001

National Land-Cover Dataset (Homer and others, 2004)

Albers projection, NAD 83 datum,

Central meridian -96 00 00

Figure 2. 

SALUDA

AIKEN
6 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

downstream. In the upper part of the McTier Creek watershed, 

the channel is characterized by rock outcrops, a characteristic 

of many Piedmont streams (fig. 3). The hillside cross section 

in figure 4 illustrates the transition to Coastal Plain characteristics. The survey rod shown in figure 4 is extended approximately 20 feet to illustrate the depth of the sand deposits in the 

area of the Sand Hills, which is only located about 0.2 mile 

(mi) from the location shown in figure 3. 

Surficial Geology

The surficial geology of the McTier Creek watershed 

is described by Horton and Dicken (2001) and Nystrom and 

others (1986). The oldest rocks that underlie the study area are 

Cambrian-age migmatitic paragneiss and schist of the Kiokee 

belt (Horton and Dicken, 2001). Unconsolidated sands and 

clays of Cretaceous age nonconformably overlie the Kiokee 

belt rocks (Nystrom and others, 1986). Unconformably overlying the Cretaeous-age sediments are sand and clays of the 

Eocene-age Huber Formation and Barnwell Group (Nystrom 

and others, 1986). The informally named Upland unit, consisting of clayey sand and gravel, occurs in the highest elevations 

of the study area.

Climate

The climate of the McTier Creek watershed is characterized by typical subtropical humid conditions. Based on 

climate data for Aiken, SC, for the period from 1945 to 2008, 

the average annual mean air temperature was 64 degrees 

Fahrenheit (°F) (South Carolina Department of Natural 

Resources, 2009). The average annual temperatures ranged 

from a minimum of 53 °F to a maximum of 80 °F. The highest 

maximum temperature of 109 °F occurred on August 22, 1983. 

The lowest minimum temperature of 4 °F was recorded on 

January 9 and 10, 1970, and again on December 26, 1985.

Annual average rainfall in Aiken County is 47 inches. 

Based on the precipitation summary from 1893 to 2008, the 

driest year occurred in 1933 when 21 inches of rainfall was 

recorded (South Carolina Department of Natural Resources, 

2009). The wettest year occurred in 1964 when 71 inches of 

rainfall was recorded. The highest daily rainfall occurred on 

April 16, 1969, when 9.68 inches of rainfall was recorded. 

Although a rare occurrence in the Sand Hills, the highest 

daily snowfall of 15 inches was recorded in Aiken County on 

February 10, 1973. 

Total monthly precipitation data obtained from the 

National Weather Service Aiken 5SE station for the period 

from 1948 to 2008 indicate that typically March, June, July, 

and August have the highest total precipitation and October 

and November have the lowest (fig. 5). Additionally, the 

cumulative annual rainfall data as depicted in the single-mass 

curve (fig. 6) show no significant change in the slope of the 

cumulative curve, indicating no long-term change in the 

rainfall patterns at this station. 

Figure 3. McTier Creek near the upper part of the watershed 

displaying characteristics similar to streams in the Piedmont 

Physiographic Province in South Carolina.

Figure 4. Cross section of hillside displaying soil characteristics 

similar to those of the Coastal Plain Physiographic Province in 

South Carolina. Note that this location is only about 0.2 mile from 

the location shown in figure 3.

Figure 3. 

Figure 4. 
Introduction 7

Figure 5. Mean of total monthly rainfall for Aiken, South Carolina, 1948–2008.

Figure 6. Cumulative annual rainfall for Aiken, South Carolina, 1948–2008. (Line breaks 

indicate missing data.)

6

5

4

3

2

1

0

J F M A M J J A S O N D

MEAN OF TOTAL MONTHLY RAINFALL, IN INCHES

Figure 5. 

CUMULATIVE ANNUAL RAINFALL, IN INCHES

Figure 6. 

3,000

2,500

2,000

1,500

1,000

500

0

1940 1950 1960 1970 1980 1990 2000 2010 2020
8 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Streamflow

The average of the monthly mean streamflow data in 

McTier Creek, as recorded at USGS streamflow-gaging 

station 02172300, McTier Creek near Monetta, SC, for the 

period October 1995 to September 1997 and March 2001 to 

September 2008, shows a seasonal variation that is common 

for natural streams in South Carolina (fig. 7). (Hereafter, 

streamflow-gaging stations discussed in this report will be 

referred to by the reference name listed in table 1.) The 1argest 

average monthly mean streamflow occurs in winter or early 

spring, and the lowest average monthly mean streamflow 

occurs in late summer or early fall. The observation that summer months have the highest monthly rainfall totals while the 

streamflow records show a continuous recession of monthly 

streamflow throughout the summer is explained by the fact 

that the highest evapotranspiration rates for a given year occur 

during the growing season.

To assess the streamflow record at Monetta in the context 

of a longer flow period, a comparison was made with the 

South Fork Edisto station. Streamflow data from South Fork 

Edisto, which has record available from September 1931 to 

August 1971 and from October 1980 to September 2008, were 

analyzed in a similar manner as data from the Monetta station. 

The average monthly mean flow data (fig. 8) show a pattern 

similar to that for Monetta (fig. 7).

To more directly compare streamflow data from the two 

stations, the data were normalized by drainage area, which 

allows for comparison of streamflow in units of cubic feet per 

second per square mile. For the concurrent periods of record, 

the average monthly mean flow per square mile is higher at 

Monetta than at South Fork Edisto (fig. 9).

It is interesting to note that the flow per unit area is 

smaller for South Fork Edisto than for Monetta. Exploration 

of the reason for this is beyond the scope of this investigation. 

Possibilities include differences in watershed sizes or differences in amounts of precipitation for the two watersheds. 

Also, average evapotranspiration may be higher in the South 

Fork Edisto Basin because of variations in the land cover 

(Homer and others, 2004). Additionally, the South Fork Edisto 

could be losing water to an aquifer that discharges outside of 

the basin.

In order to put the monthly mean streamflow per unit area 

at McTier Creek into a longer historical context, additional 

comparisons of the minimum, average, and maximum monthly 

mean flow per square mile for the concurrent period of record 

at Monetta and South Fork Edisto were made along with 

the same characteristics for the complete period of record at 

South Fork Edisto (fig. 10A, B, C). The minimum monthly 

mean flow per square mile at the two stations are quite similar, 

indicating similarity in the groundwater sources feeding these 

systems during periods of low flow. The minimum monthly 

Table 1. U.S. Geological Survey streamflow-gaging stations, reference names, and periods of record.

Station 

number Station name Reference name used in this report Period of record

02172300 McTier Creek near Monetta, SC Monetta October 1995–September 1997;

February 2001–September 2009

02172305 McTier Creek near New Holland, SC New Holland June 2007–September 2009

02173000 South Fork Edisto River near Denmark, SC South Fork Edisto September 1931–August 1971;

October 1980–September 2008

Figure 7. Average monthly mean streamflow at USGS streamflow-gaging station 

02172300, McTier Creek near Monetta, South Carolina, 1995–1997 and 2001–2008. AVERAGE MONTHLY MEAN FLOW, IN CUBIC FEET PER SECOND

Figure 7. 

30

25

20

15

10

5

0

J F M A M J J A S O N D
Introduction 9

Figure 8. Average monthly mean streamflow at South Fork Edisto River near Denmark, 

South Carolina, 1931–1971 and 1980–2008.

Figure 9. Average monthly mean streamflow at McTier Creek near Monetta and 

South Fork Edisto River near Denmark, South Carolina, for the concurrent period of 

record (October 1995–September 1997 and March 2001–September 2008) at both stations. AVERAGE MONTHLY MEAN FLOW, IN CUBIC FEET PER SECOND

Figure 8. 

1,200

1,000

800

600

400

200

0

J F M A M J J A S O N D

AVERAGE MONTHLY MEAN FLOW, 

IN CUBIC FEET PER SECOND

PER SQUARE MILE

Figure 9. 

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

Monetta

South Fork Edisto River

J F M A M J J A S O N D
10 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Figure 10. (A) minimum, (B) average, and (C) maximum monthly mean flow per square mile at McTier Creek near Monetta 

(October 1995–-September 1997 and March 2001–September 2008) and South Fork Edisto River near Denmark 

(September 1931–August 1971 and October 1980–September 2008), South Carolina.

2.0

1.5

1.0

0.5

0

JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC.

MINIMUM

MONTHLY MEAN FLOW,

IN CUBIC FEET PER SECOND

PER SQUARE MILE

AVERAGE

MONTHLY MEAN FLOW,

IN CUBIC FEET PER SECOND

PER SQUARE MILE

MAXIMUM

MONTHLY MEAN FLOW,

IN CUBIC FEET PER SECOND

PER SQUARE MILE

Monetta

South Fork Edisto (period of record)

South Fork Edisto (concurrent)

Monetta

South Fork Edisto (period of record)

South Fork Edisto (concurrent)

Monetta

South Fork Edisto (period of record)

South Fork Edisto (concurrent)

A.

2.0

1.5

1.0

0.5

0

B.

5.0

4.0

3.0

2.0

1.0

0

C.

Figure 10. 
TOPMODEL Streamflow Concepts 11

mean flows per square mile at South Fork Edisto for the 

complete period of record (about 70 years) and for the period 

of record that is concurrent with Monetta (about 11 years) 

are the same (fig. 10A). Consequently, this indicates that the 

period of record at Monetta captures the lowest flow periods 

that have occurred in at least 70 years. Figure 10C shows a 

significant difference in the maximum monthly mean flow per 

square mile between the complete record at South Fork Edisto 

and the period that is concurrent with Monetta for nearly 

all months except July, implying that the short record 

at Monetta is biased toward lower flow conditions. Hypotheses 

concerning the differences in average monthly mean flow 

were discussed earlier; however, as figure 10B indicates for 

South Fork Edisto, it is reasonable to assume that the longer 

term average monthly mean flows at Monetta will increase 

over time. 

TOPMODEL Streamflow Concepts

TOPMODEL (a topography-based hydrological 

model) is a physically based watershed model that simulates 

streamflow based on the variable-source-area concept of 

streamflow generation. It is a semi-distributed model that 

groups hydrologically similar portions of a watershed based 

on a topographic index. In the variable-source-area concept, 

saturation land-surface areas are sources of streamflow during 

precipitation events in several ways. Saturation overland 

flow (also called Dunne overland flow) is generated if the 

subsurface hydraulic characteristics are not transmissive and 

if slopes are gentle and convergent (Dunne and Black, 1970; 

Wolock, 1993). Saturation overland flow can arise from direct 

precipitation on the saturated land-surface areas or from 

return flow of subsurface water to the surface in the saturated 

areas. Subsurface stormflow is generated if the near-surface 

soil zone is very transmissive (large saturated hydraulic 

conductivity) and if gravitational gradients (slopes) are steep. 

Whipkey (1965) defined subsurface stormflow as underground 

stormflow that reaches the stream channel without entering the 

groundwater storage zone. 

Topographic Wetness Index

The original conceptualization of TOPMODEL was 

based on three basic assumptions (Singh, 1995; Beven, 1997).

1. The dynamics of the saturated zone can be approximated by successive steady-state representations.

2. The hydraulic gradient of the saturated zone can be 

approximated by the local surface topographic slope, 

tan β. 

3. The distribution of downslope transmissivity, T, with 

depth is an exponential function of storage deficit or 

depth to the water table:

/ , S m T T eo− =

where 

	 To is the lateral (horizontal) transmissivity when 

the soil is just saturated (dimensions of 

length squared per time),

	 e	 is the exponential function approximately 

equal to 2.718281828,

	 S is a local storage deficit below saturation 

(dimensions of length), and 

	 m	 is a model parameter controlling the rate of 

decline of transmissivity in the soil profile 

(dimensions of length).

These assumptions lead to relations between watershed 

storage (or storage deficit) and local levels of the water table 

(or storage deficit due to drainage) in which the main factor is 

the topographic wetness index (TWI), defined as

TWI ln( / tan ), = a 

where a is the upslope contributing area per unit contour 

length, and tan β is the local slope. High values of the TWI 

indicate areas with large contributing areas and relatively flat 

slopes, which typically occur at the base of hillslopes and 

near the stream (large a value and small tan β value). These 

areas tend to correspond with locations where groundwater 

discharge would be expected to occur. Low TWI values tend 

to be found at the tops of hills where there is relatively little 

upslope contributing area, and slopes are steep (small a value 

and large tan β value). These areas generally correspond with 

groundwater recharge areas (Hornberger and others, 1998). 

Inamdar (2009) defined high TWI values as those being in 

the range of 9 to 16 and low TWI values as those being in the 

range of 2 to 5.

The TWI is used to derive the areas of saturation or 

variable-source areas. The variable-source-area concept states 

that streamflow during precipitation events is generated on 

saturated surface areas called “source areas,” which occur in 

places where the water table rises to the land surface (Wolock, 

1993). The rise in the water table occurs because of infiltration of precipitation into the soil and down to the saturated 

subsurface zone and the subsequent downslope movement of 

water in the saturated subsurface zone. Saturated land-surface 

areas commonly develop near existing stream channels and 

expand as more water enters the subsurface through infiltration 

and moves downslope as saturated subsurface flow. 

(1)

(2)
12 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

TOPMODEL Water Balance

TOPMODEL is a process-oriented watershed hydrology 

model that systematically accounts for water as it enters the 

watershed as precipitation until it leaves the watershed through 

evapotranspiration, by direct withdrawal, or as streamflow. 

TOPMODEL can simulate snow accumulation and melt, and 

routing of flow from delivery to the stream to the watershed 

outlet; however, the snow-related and routing algorithms were 

not used in this study because of the characteristics of the 

McTier Creek watershed.

In the water balance, rain on a given day is used first 

to satisfy the potential evapotranspiration for the day. The 

remainder moves overland to a stream if the rain falls on 

impervious surface that is connected to a stream (qimp), soil 

that is already saturated (qof), or soil through which the water 

cannot infiltrate rapidly enough (qinf) (fig. 11). Precipitation 

that falls on a surface-water body is added to the streamflow 

(qsrip). The remaining water infiltrates into the upper soil 

zone. Any water stored in the saturated subsurface zone is 

assumed to move downslope toward the stream channel and 

enters the stream as return flow (qret) in saturated areas and 

(or) subsurface flow (qb) at the streambanks. The portion of 

the subsurface water that drains into the stream depends on 

the volume in storage and the values of the TOPMODEL 

input parameters. 

Figure 11. Definition of selected water-source variables from TOPMODEL (modified from Wolock, 1993).

Precipitation (ppt)

Water table

Figure 11.

Open-water

bodies (qsrip)

Impervious flow (qimp)

Infiltration-excess

overland flow (qinf)

Evapotranspiration (pet)

Total flow in stream (qpred)

Land surface

Stream

Potential regions for

overland saturation flow (qof)

and return flow (qret)

Subsurface flow (qb)

(includes traditional base

flow and subsurface

storm flow)
GBMM Streamflow Concepts 13

GBMM Streamflow Concepts

The GBMM computes daily mass balances for hydrology, 

sediment, and mercury within each GIS raster grid cell (Dai 

and others, 2005; Tetra Tech, 2006). In the hydrology module, 

GBMM has three hydrological layers: the unsaturated zone, 

shallow groundwater, and deep groundwater. Runoff generation occurs by overland flow and base flow (groundwater 

flow). In this study, GBMM implements a simple daily water 

balance per 10-meter (m) grid cell on pervious surfaces to 

compute available soil water in the unsaturated zone (Sw, in 

centimeters) when levels are greater than or equal to wilting 

point using the equation

, w wo tot o c S S P R ET P = + − − −

where 

	 Swo is the initial water in the unsaturated zone 

(in centimeters), 

Ptot is the total available water inputs at the 

soil surface (rainfall + snowmelt, 

in centimeters), 

Ro is the surface runoff (in centimeters), 

ET is actual evapotranspiration (in centimeters), 

and 

Pc is soil percolation from the unsaturated 

to saturated groundwater zones 

(in centimeters). 

Runoff is computed using a modified Soil Conservation Service (SCS) curve-number approach (SCS-CN) for each grid 

cell, now called the Natural Resources Conservation Service 

(NRCS) curve-number method, which is similar to the Soil 

and Water Assessment Tool (SWAT), a widely used model 

for estimating runoff and nutrient loading from watersheds 

(Neitsch and others, 2005). The SCS-CN also is sometimes 

referred to as the TR-55 curve number, where TR is an abbreviation for a NRCS Technical Release document (U.S. Department of Agriculture, 1986). The modified SCS-CN method 

varies the curve-number calculations daily based on 5-day 

antecedent moisture conditions. Kim and Lee (2008) provide 

a detailed explanation of the modified SCS-CN methods, and 

further details can be found in appendix 2.

GBMM computes a simple daily shallow groundwater 

balance for inclusion in the total streamflow output as

, G G P G S w wo c o p = + − −

where 

Gw is the shallow groundwater at the end of each 

time step (in centimeters), 

Gwo is the shallow groundwater at the beginning 

of each time step (in centimeters),

Go is shallow groundwater outflow 

(in centimeters per day), and 

Sp is seepage to a deep aquifer (in centimeters 

per day). 

Shallow groundwater outflow is computed as

, G g G o r w = ∗

where gr is the groundwater recession coefficient (per day), 

and Gw is shallow groundwater storage (in centimeters). 

The groundwater recession coefficient can be derived from 

observed streamflow during the recession of the hydrograph 

using the formula

( 2 ) ( 1 )

2 1

ln ln , rF F

g t t

− = −

where 

F2 is streamflow at t

2 (in cubic meters per day), 

F1 is streamflow at t

1 (in cubic meters per day), 

t

2 is the time for streamflow F2

 (per day), and 

t

1 is the time for streamflow at F1

 (per day). 

Groundwater seepage to a deep aquifer (Sp, in centimeters per 

day) is computed using the following simple equation:

, p r w S s G = ∗

where sr is the groundwater seepage coefficient (per day).

(3)

(4)

(5)

(6)

(7)
14 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Flow travel time, both overland and in-stream, is computed from each grid cell to the designated watershed outlet 

using calculations derived from the NRCS (U.S. Department 

of Agriculture, 1986). Total flow travel time from each grid 

cell to the watershed outlet (Ttot, in hours) is

, T T T tot ov ch = +

where Tov is the overland flow travel time (in hours), and Tch is 

the within-channel flow travel time (in hours). Overland flow 

travel time (Tov) is calculated using the formula

( )

0.8

0.5 0.4

2

0.0289 , ovn L

T

P S

∗ ∗ = ∗

where 

n is Manning’s roughness coefficient, 

L is flow length (in meters), 

P2 is the 2-year, 24-hour rainfall (in centimeters) 

computed regionally across the United 

States, and 

S is the slope of the land surface (in meters 

per meter). 

The within-channel flow travel time (Tch) is computed as

, 3600 ch

L T

V = ∗

where V is the flow velocity (in meters per second). Velocity in 

the stream channel is calculated using Manning’s equation:

2 1

3 2 1 V R S , n

= ∗

where R is the hydraulic radius of the channel (in meters). 

Stream dimensions (for example, hydraulic radius and 

channel cross-sectional area, depth, and width) are computed 

using regional regression equations (Dai and others, 2005). 

Flow routing for both overland and within the stream channel 

flow is dependent on a base digital elevation map, which is 

used for computing flow direction and length, in addition to 

creating daily overland travel time zones (water that is routed 

through travel time zones from which water is accumulated 

and transferred). A grid for Manning’s roughness coefficient 

is computed for each 2001 Multi-Resolution Land Chacterization, National Land-Cover Database (NLCD; Homer and 

others, 2004) land-cover type within the study watershed, 

and the average of the coefficients for each grid cell along a 

flow path is used for calculating surface and in-stream flow 

travel times. 

Methods of Study

The following sections of the report document the data 

needed to develop the TOPMODEL and GBMM, the compilation and review of the data, and the calibration procedures for 

the models. In addition, the goodness-of-fit statistics used to 

assess the simulated and measured data are described.

Data Collection

Watershed simulations and calibration of TOPMODEL 

and GBMM require the following types of data: (1) meteorological parameters (precipitation and air temperature) and 

(2) watershed characteristics. Streamflow data are not required 

for the model calibration but are used to assess how well the 

simulations capture the characteristics of the measured data. In 

addition to these, TOPMODEL uses the topographic wetness 

indices to estimate runoff, and GBMM implements a curve 

number (see Pervious-Area Runoff and Impervious-Area 

Runoff sections in appendix 2) based on soil type and land 

cover for each 10-m grid cell. For both models, measured 

streamflow also is needed to assess the model performance. 

The following sections of the report document the collection, 

assembly, and analyses of these various model inputs. 

Meteorological Parameters

The meteorological parameters required for the watershed 

modeling are daily precipitation and average daily temperature. An assessment of National Weather Service (NWS) 

meteorological stations near the McTier Creek watershed was 

made to determine data available for use in the model simulations. Stations chosen for inclusion in the study were based 

on period of available record and location from the centroid 

of the McTier Creek watershed. Based on those criteria, five 

NWS stations were chosen (table 2; fig. 12). In addition, two 

USGS rainfall gages in or near the watershed were available 

for assessment; however, due to the limited amount of record 

at the USGS rainfall gages and differences in collection and 

reporting methods, only the NWS rainfall data were used in 

the model calibration.

The meteorological data were reviewed and compared 

using single-mass curves, which present a cumulative plot 

of data over time and represent the volume of the parameter 

being reviewed (fig. 13). For precipitation data, a significant 

change in the slope of the single-mass curve would indicate 

a change in the hydrologic regime or a systematic problem 

with the recording device. For the NWS precipitation data, the 

single-mass curves seemed reasonable because all stations had 

similar slopes and shapes. It should be noted that if a station 

had missing record, the cumulative value computed up to the 

point when the data became missing was used as the starting 

point once the data began to be collected again. Thus, for 

significant periods of missing record, this approach causes 

(8)

(9)

(10)

(11)
Methods of Study 15

Table 2. Meteorological stations in the vicinity of the McTier Creek watershed, South Carolina, considered for use 

in this investigation.

[°, degrees;  ́, minutes; NWS, National Weather Service; USGS, U.S. Geological Survey]

Meteorological station Latitude 

(north)

Longitude 

(west)

Parameters 

available Agency Number Name

380074 Aiken 5SE 33°30 ́ 81°42 ́ rainfall, temperature NWS

380506 Batesburg 33°54 ́ 81°32 ́ rainfall NWS

382712 Edgefield 3 NNE 33°50 ́ 81°55 ́ rainfall NWS

384607 Johnston 4 SW 33°47 ́ 81°51 ́ rainfall, temperature NWS

386775 Pelion 4 NW 33°43 ́ 81°16 ́ rainfall, temperature NWS

387631 Saluda 34°00 ́ 81°46 ́ rainfall, temperature NWS

02172300 a McTier Creek near Monetta, SC 34°45 ́ 81°66 ́ rainfall USGS

335358081331900 a USGS Raingage at Batesburg Fire 

Department at Batesburg, SC

33°54 ́ 81°33 ́ rainfall USGS

a

 USGS raingages were not used in the model calibration because of limited data and differences in collection and reporting methods 

compared to the NWS stations. 

Figure 12. Meteorological stations in the vicinity of McTier Creek watershed, South Carolina, 

considered for use in this investigation. Distance units are in miles.

!

!

!

!

!

!

!

!

Saluda

Batesburg

Aiken 5SE

Pelion 4NW

Johnston 4SW

Edgefield 3NNE

McTier Creek

near Monetta, SC

USGS Raingage at

Batesburg Fire Dept.

at Batesburg, SC

20.36

19.17

18.85

18.22

14.68

9.02

8.59

1.9

Gage 02172305

basin boundary

RICHLAND

NEWBERRY

EDGEFIELD

SALUDA

LEXINGTON

AIKEN

BARNWELL 

ORANGEBURG

ESRI Data and Maps, 2006, 1:50,000

0 3 6 12 MILES

0 3 6 12 KILOMETERS

8145’

34

3345’

33

30’

81

30’ 8115’

Figure 12. 
16 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

the curve to deviate from curves at stations with no break in 

data collection. The slope would, however, still be useful for 

comparison with slopes for the other stations. In figure 13, this 

effect is illustrated with data missing from April 2003 through 

July 2003 for the Aiken 5SE station. Thus, the Aiken 5SE 

curve appears lower than the other curves beginning about 

August 2003, mainly due to the 4 months of missing record. 

The slope of the Aiken 5SE curve is still similar to those of the 

other stations.

The precipitation data were weighted using inverse 

distance weighting based on the distance from each NWS station to the centroid of the McTier Creek watershed (Shepard, 

1968). Single-mass curves of the weighted data along with 

the single-mass curves for the individual stations also were 

reviewed. When plotted with the individual curves shown 

in figure 13, the weighted curve appears to be a reasonable 

representation (fig. 14).

Figure 13. Single-mass curve reviews of the National Weather Service precipitation data.

Figure 14. Single-mass curve reviews of the National Weather Service precipitation data along with a weighted 

curve computed using inverse distance weighting.

Saluda

Edgefield

Batesburg

Aiken

Johnston

Pelion

450

400

350

300

250

200

150

100

50

0

JULY 24,

1998

JULY 6,

2009

DEC. 6,

1999

APRIL 19,

2001

SEPT. 1,

2002

JAN. 14,

2004

MAY 28,

2005

OCT. 10,

2006

FEB. 22,

2008

CUMULATIVE PRECIPITATION, IN INCHES

Figure 13. 

Saluda

Edgefield

Batesburg

Aiken

Johnston

Pelion

Weighted

450

400

350

300

250

200

150

100

50

0

JULY 24,

1998

JULY 6,

2009

DEC. 6,

1999

APRIL 19,

2001

SEPT. 1,

2002

JAN. 14,

2004

MAY 28,

2005

OCT. 10,

2006

FEB. 22,

2008

CUMULATIVE PRECIPITATION, IN INCHES

Figure 14. 
Methods of Study 17

2

1

2

1

, 1

n i

i i k n

i i

Z

d Z

d

=

=

=

∑

∑

where

Zk is the meteorological value at the centroid of 

McTier Creek watershed,

Zi is the meteorological value at the NWS 

station, and

di is the distance from the centroid of the 

watershed to the NWS station (in miles).

Similar analyses were made of the maximum and 

minimum air temperature data that were available at four 

of the six NWS stations listed in table 2. Average daily air 

temperatures were computed from that data and compared 

using single-mass curves. From those comparisons, it was 

noted that the minimum air temperatures for the Johnston 4SW 

gage tended to differ from those for the other three stations 

(fig. 15). To further check the quality of the Johnston 4SW 

minimum data, the inverse weighted minimum temperature 

was computed with and without the data from the Johnston 

4SW gage. As can be seen in figure 16, when the Johnston 

4SW gage was not included in the weighting, the inverse 

weighted minimum temperatures were higher, as indicated 

by a larger number of the data points plotting above the 

one-to-one line. Because of the uncertainty in these values, the 

Johnston 4SW station was not included in the final weighting 

of the average temperatures. For the final weighted average 

temperature, the average temperature for the three remaining 

stations was computed from the minimum and maximum air 

temperature and then weighted using inverse distance weighting to get a final set of average temperature data that was used 

in TOPMODEL and GBMM. 

Watershed Characteristics

Along with the precipitation and air temperature data, 

other TOPMODEL and GBMM inputs included watershed 

characteristics describing the topographic features, soils 

characteristics, and watershed latitude. A 1:24,000-scale 

digital raster graphics coverage was used to delineate the 

watershed boundaries. Water-body features were determined 

using a 1:24,000-scale National Hydrography Dataset (NHD) 

and 2006 digital orthophoto quarter quadrangles. Impervious 

surface was determined from a 30-m impervious grid from the 

2001 NLCD.

Soils characteristics were determined from the Soil 

Survey Geographic (SSURGO) Database (Natural Resources 

Conservation Service, 2008). After pre-processing of the 

SSURGO data (Michael E. Wieczorek, U.S. Geological 

Survey, written commun., December 2008), the watershed 

model soil parameters were computed in ArcGIS® using the 

zonal statistics tool. Both vertical and horizontal data were 

weighted to determine average watershed values. The names, 

units of measure, and data sources for the measured watershed 

characteristics used in TOPMODEL are listed in table 3, and 

those used as inputs to GBMM are listed in table 4. 

Figure 15. Single-mass curve reviews of the National Weather Service minimum air temperature data.

Saluda

Aiken

Johnston

Pelion

160,000

140,000

120,000

100,000

80,000

60,000

40,000

20,000

0

JULY 24,

1998

JULY 6,

2009

DEC. 6,

1999

APRIL 19,

2001

SEPT. 1,

2002

JAN. 14,

2004

MAY 28,

2005

OCT. 10,

2006

FEB. 22,

2008

CUMULATIVE MINIMUM TEMPERATURE, IN DEGREES FAHRENHEIT

Figure 15. 

(12)
18 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Figure 16. Comparison of inverse weighted minimum temperatures with and without the Johnston 4SW 

station data.

Table 3. Watershed characteristics for use with the topography based hydrological model.

[SSURGO, Soil Survey Geographic Database]

Watershed characteristic Unit Data source

total area square kilometer 1:24,000 digital raster graphics (http://topomaps.usgs.gov/drg/)

lake area square kilometer 1:24,000-scale National Hydrography Dataset (http://nhd.usgs.gov/)

stream area square kilometer 1:24,000-scale National Hydrography Dataset

saturated conductivity inches per hour SSURGO (http://www.soils.usda.gov/survey/geography/ssurgo/)

soil depth inches SSURGO (calibration)

field capacity unitless SSURGO

water holding capacity unitless SSURGO

porosity unitless SSURGO

percent impervious percent National Land-Cover Dataset 2001 (http://www.mrlc.gov/nlcd.php)

percent road impervious percent National Land-Cover Dataset 2001 and National Map transportation 

layer (http://nationalmap.gov/)

latitude decimal degrees 1:24,000 digital raster graphics

uplake area square kilometer 1:24,000 digital raster graphics, 1:24,000-scale National Hydrography 

Dataset, and 2006 digital orthophoto quadrangles (http://eros.usgs.

gov/products/aerial/doq.php)

effective impervious decimal percent Calibration

percent macropore decimal percent Calibration

scaling parameter (m) inches Calibration

depth of root zone meter Calibration

impervious runoff constant unitless Kennen and others (2008)

TR-55 curve number unitless Kennen and others (2008)

lake delay unitless Calibration

90

80

70

60

50

40

30

20

10

0

IN

0 10 20 30 40 50 60 70 80 90 VERSE WEIGHTED 

MINIMU

M TEMPERATURE WITHOUT THE JOHNSTON STATION

INVERSE WEIGHTED MINIMUM TEMPERATURE WITH THE JOHNSTON STATION

Figure 16. 
Methods of Study 19

Streamflow

Streamflow data included in this investigation were 

collected at the Monetta, New Holland, and South Fork Edisto 

stations (table 1). The South Fork Edisto data were not used 

in the model calibration but were used to assess the McTier 

Creek streamflow data in the context of a longer flow period. 

As previously discussed, the Monetta station has a historical 

record from October 1995 to September 1997. Streamflow 

data at Monetta used in this analysis were collected from February 2001 to September 2009. New Holland was established 

specifically for this study with streamflow data collection 

beginning in June 2007 and continuing through September 2009. Streamflow data at these stations were continuously 

collected at 15-minute intervals using techniques described 

by Rantz and others (1982). The process involves measuring 

water level (or stage) on a continuous basis. A series of 

streamflow measurements throughout a range of stages are 

measured and then used to develop a stage-streamflow relation 

also known as a rating curve. The rating curve is then used 

to determine streamflow from measured stage. Once the 

stage-streamflow rating is developed, periodic measurements 

are made on a regular basis to verify the stage-streamflow 

relation, and as necessary, adjustments (or shifts) to the 

stage record are applied to account for deviations from the 

stage-streamflow relation.

Topographic Wetness Index

TOPMODEL is based on the idea that the topography of 

a watershed exerts a dominant control on flow moving through 

upland basins (Beven and Kirkby, 1979). The topographic 

wetness index (TWI) combines local upslope contributing 

area and slope, and quantifies the topographical control on 

hydrological processes. For this investigation, the TWI was 

computed using ArcGIS in conjunction with a 10-m-resolution 

digital elevation model (DEM) and a 1:24,000-scale National 

Hydrography Dataset of stream features or flowlines.

Table 4. Watershed and grid cell characteristics for use with the grid based mercury model.

[m, meter; cm, centimeter; SSURGO, Soil Survey Geographic Database; cm/m, centimeter per meter; g/cm3, gram per cubic centimeter; 

Ksat, saturated conductivity; μm/s, micrometer per second] 

Watershed characteristic Unit Data source

stream properties and connections unitless National Hydrography Datset (ftp://nhdftp.usgs.gov/FOD_Data/)

land-cover type (per grid cell) unitless National Land-Cover Dataset 2001 (30-meter resolution) 

(http://www.mrlc.gov/nlcd.php)

elevation m National Elevation Dataset (http://seamless.usgs.gov/)

hydrologic soil group (per grid cell) unitless SSURGO (http://www.soils.usda.gov/survey/geography/ssurgo/)

curve numbers (per grid cell) unitless Calibration

break points for curve number modifications cm Calibration

crop management factor (per grid cell) unitless SSURGO

land-use practice factor (per grid cell) unitless SSURGO

vegetation evapotranspiration coefficient 

(growing season; per grid cell)

unitless SSURGO

vegetation evapotranspiration coefficient 

(non-growing season; per grid cell)

unitless SSURGO

available water capacity (per grid cell) cm/m SSURGO

bulk density (per grid cell) g/cm3 SSURGO

Ksat (permeability; per grid cell) μm/s SSURGO

depth to bedrock m Estimated from SSURGO

percent clay (per grid cell) percent SSURGO

unsaturated soil depth m Calibration

initial shallow groundwater cm/m Calibration

groundwater seepage coefficient per day Calibration

groundwater recession coefficient per day Calibration

channel width and depth m Calculated within model from Rosgen (1996) for Eastern 

United States

Manning’s roughness coefficient for channel unitless Bedient and Huber (1992)
20 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

The NHD streams were first converted to a grid by 

overlaying 10-m by 10-m grid cells on the NHD flowlines 

and designating as stream cells any grid cell containing a 

portion of an NHD flowline. Stream cells were then assigned 

a value of 0, and all other cells were assigned a value of 1 to 

distinguish water features from land features. To ensure that 

known streams were accurately represented in the DEM, the 

stream grid described above was used to “burn” the streams 

into the DEM by forcing the stream cells onto the DEM, 

thereby ensuring downstream flow once the cells’ elevations 

are taken into account.

Any sinks in the DEM were then “filled” to ensure 

all land-surface cells sloped toward the streams. Sinks are 

non-stream grid cells (or groups of cells) with a lower elevation than the eight surrounding cells and are usually the result 

of erroneous data. The elevations of sinks were artificially 

raised using the Map Algebra tool in ArcGIS, which utilizes 

elevations of surrounding cells to determine the correct outfall 

or pour point within a group of cells.

The flow-direction grid, which indicates the direction 

of flow from each grid cell into adjacent cells, was then 

created from the “filled” DEM and used to derive the flowaccumulation grid, whose cell values indicate the number of 

upstream cells flowing into, or contributing to, downstream 

cells. Using a predetermined threshold value with the 

flow-accumulation grid, wetted grid cells, assumed to be 

headwaters in the more upslope areas of the watershed, 

were established.

The slope grid, which identifies the steepest downhill 

slope for a location on a surface, was created from the 

original DEM. All zero values in the slope grid were set to 

0.01 because the TWI computation includes the slope in the 

denominator and, therefore, cannot have a value of zero.

Finally, the TWI was calculated by using the Map 

Algebra tool in ArcGIS to determine the natural log of the 

local upslope contributing area (flow-accumulation grid) 

divided by the local slope (tangent of the slope grid).

GBMM Curve-Number Estimates

GBMM implements numerous steps to prepare raster 

grids for estimating curve number runoff from each grid cell 

within the McTier Creek watershed. This is an automated 

process in the GBMM pre-processing module, which includes 

(1) burning the streams into the 10-m DEM, (2) filling 

sinks within the DEM, (3) creating a flow-direction grid, 

(4) developing a flow-accumulation grid, and (5) overlaying 

a 2001 NLCD raster grid with a raster grid of hydrologic soil 

group data from the SSURGO database. Steps 1–4 are similar 

to those implemented for TOPMODEL (see Topographic Wetness Index section). The final raster grid from step 5 includes 

unique land-cover/hydrologic soil group combinations for 

each grid cell. This raster is then linked to a table containing 

curve number values for each unique land-cover/hydrologic 

soil group combination. Based on each cell’s curve number, 

runoff is routed daily using the flow accumulation grid 

developed in step 4 and equation 8. The equations for base 

curve-number modifications during wet periods, dry periods, 

the growing season, and non-growing season for each grid cell 

are in appendix 2. 

Calibration of TOPMODEL and GBMM

Calibrations of TOPMODEL and GBMM were 

conducted independently using the same precipitation data, 

temperature data, and period of record. In the McTier Creek 

watershed, two USGS streamflow gages were available for 

comparison of observed daily mean flows with simulated 

daily mean flows: (1) Monetta and (2) New Holland (table 1). 

Initial calibration of model parameters for TOPMODEL and 

GBMM was done for Monetta using measured or estimated 

watershed characteristics as defined in tables 3 and 4. The 

continuous period of record from 2001 to 2009 at Monetta 

covers a full range of hydrologic conditions, including (1) a 

significant dry period in 2001–2002, which appears to be the 

driest period in about 70 years, based on comparisons with the 

long-term record at South Fork Edisto, and (2) a significantly 

wet period that occurred in 2003 (National Oceanic and 

Atmospheric Administration, 2008). The short period of 

record from October 1995 to September 1997 at Monetta is 

more representative of normal flow conditions and is similar to 

the 2004–2005 period. Consequently, only the February 2001 

to September 2009 period was included in the model calibrations. To simplify references to the periods of record used in 

the calibration process, those periods will be referred to by the 

reference names listed in table 5. 

For TOPMODEL, the parameter estimation program 

PEST was used to assist in calibrating the model parameters 

for which measured values were not available (Doherty, 2005). 

PEST is a nonlinear parameter estimator that adjusts model 

parameters until the fit between model estimates and field 

observations are optimized using a weighted least squares 

Table 5. Station number and name, period of record used in the model calibration and confirmation 

simulations, and model simulation period reference name for the McTier Creek watershed, South Carolina.

Station 

number Station name Period of record used in model simulation

Model simulation period 

reference name

02172300 McTier Creek near Monetta, SC Feb. 7, 2001–Sept. 30, 2009 Calibration period

02172300 McTier Creek near Monetta, SC June 13, 2007–Sept. 30, 2009 Concurrent period

02172305 McTier Creek near New Holland, SC June 13, 2007–Sept. 30, 2009 Confirmation period
Simulation of the Streamflow for TOPMODEL and GBMM 21

scheme. For the McTier Creek TOPMODEL, the differences 

in estimated and observed daily mean flows were optimized.

Parameter adjustments for GBMM model calibration 

were conducted using an automated parameter optimization 

method (OSTRICH; Matott, 2005) with a global dynamically 

dimensioned search (DDS) algorithm (Tolson and Shoemaker, 

2007) and a weighted sum of squared errors objective function. Subsequent trial-and-error parameter-fitting and calibration exercises were conducted to cross-check and complete 

this exercise due to the length of calibration model runs. The 

trial-and-error fitting also included minor modifications to the 

curve number table input for each unique land cover–soils 

combination, which could not be adjusted during the autocalibration exercise. 

The goodness-of-fit statistics used to assess subsequent 

trial-and-error parameter fitting and to explore different 

aspects of simulation errors for the two models were (1) the 

Nash-Sutcliffe coefficient of model-fit efficiency index (Nash 

and Sutcliffe, 1970), (2) Pearson’s correlation coefficient 

(r), (3) the root mean square error (RMSE), (4) the bias, 

and (5) the mean absolute error (MAE). The Nash-Sutcliffe 

coefficient of model-fit efficiency, E, is calculated as 

2 2

1 1

2

1

( ) ( )

,

( )

N N

i i i

i i

N

i

i

Qo Qo Qo Qs

E

Qo Qo

= =

=

− − −

=

−

∑ ∑

∑

where

Qoi is the observed flow for time step i,

Qo is the mean observed flow for the 

simulation period,

Qsi is the simulated flow for time step i, and

N is the number of time steps in the 

simulation period.

Pearson’s correlation coefficient, r, is calculated as

1

1

2

2 2

1 1

( )( )

.

( ) ( )

N

i i

i

N N

i i

i i

Qo Qo Qs Qs

r

Qo Qo Qs Qs

=

= =

− −

=

  − −    

∑

∑ ∑

where Qs is the mean simulated flow for the simulation period, 

and other variables are as previously defined.

The RMSE is calculated as

2 ( ) . Qs Qo i i RMSE

N

− = ∑

The bias is calculated as

1 .

N

i i

i

Qs Qo

bias

N

=

−

=

∑

The MAE is calculated as

1

| |

.

N

i i

i

Qs Qo

MAE

N

=

−

=

∑

In addition to the goodness-of-fit statistics, plots of 

simulated and observed daily mean flows were prepared. 

Flow-duration curves of simulated and observed daily mean 

flows were plotted along with various residual plots. These 

graphs were reviewed to determine potential bias during 

specific time periods and (or) specific flow regimes.

Simulation of the Streamflow for 

TOPMODEL and GBMM

TOPMODEL and GBMM were calibrated based on 

comparison of observed daily mean flows at Monetta for 

the calibration period (table 5). The calibration parameters 

were then applied at New Holland to simulate daily mean 

flows for the confirmation period. In order to better assess 

the application of the calibrated parameters at Monetta to the 

model simulations at New Holland, additional statistical and 

graphical assessments were made at Monetta for the concurrent period.

Simulations for Monetta for the 

Calibration Period

The measured and calibrated input parameters for simulations for Monetta for the calibration period are listed in table 6 

for TOPMODEL and in table 7 for GBMM. For GBMM, 

parameters requiring grid cell-specific values (such as those 

based on soil and (or) land-cover types) and those calculated 

within the model but listed in table 4 are not listed in table 7.

Plots of the observed and simulated daily mean flows at 

Monetta show that both models perform relatively well with 

respect to capturing the timing and variability of the flows 

(figs. 17, 18). Observed and simulated daily mean flow data 

for TOPMODEL and GBMM are shown in more detail in 

figure 19. While simulated flows in some years match the 

observed data well (for example, years 2006–2009), other 

years exhibit a slightly weaker relation (for example, years 

2003–2004) in matching peaks and temporal patterns between 

simulated and observed flows. A noticeable characteristic of 

(13)

(14)

(15)

(16)

(17)
22 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Table 6. Parameter values used for the TOPMODEL 

calibration for McTier Creek near Monetta for the 

calibration period.

[*, indicates adjustment during calibration; calibration period is 

Feb. 7, 2001–Sept. 30, 2009]

Model parameter Value

Total area (square kilometers) 40.46

Lake area (square kilometers) 0.63

Stream area (square kilometers) 0.47

Saturated conductivity (inches per hour) 6.57

Soil depth (inches) 74.0*

Field capacity (unitless) 0.18

Water holding capacity (unitless) 0.094

Porosity (unitless) 0.39

Percent impervious 1.5*

Percent road impervious 1.0*

Latitude 33.754

Effective impervious (decimal percent) 0.8*

Conductivity multiplier 2.9*

Percent macropore (decimal percent) 0.5*

Scaling parameter (m) 47.0*

Depth of root zone (meters) 1.9*

Impervious runoff constant 0.10

TR-55 curve number 98

Uplake area (square kilometers) 34.0

Lake delay (unitless) 1.2*

Table 7. Parameter values used for GBMM calibration for 

McTier Creek near Monetta for the calibration period.

[*, indicates adjustment during calibration; calibration period is 

Feb. 7, 2001–Sept. 30, 2009]

Model parameter Value

Break point for curve number: dry, growing season 

(centimeters)

4.56

Break point for curve number: wet, growing season 

(centimeters)

15.00

Break point for curve number: dry, non-growing 

season (centimeters)

1.07

Break point for curve number: wet, non-growing 

season (centimeters)

12.17

Depth to bedrock (meters) 1.8

Unsaturated soil depth (meters) 0.095*

Initial shallow groundwater (centimeters per meter) 10.67*

Groundwater seepage coefficient (per day) 0.026*

Groundwater recession coefficient (per day) 0.017*

Manning’s roughness coefficient for channel 0.045

Figure 17. TOPMODEL simulated and observed daily mean flows at McTier Creek near Monetta for the calibration period 

(Feb. 7, 2001–Sept. 30, 2009), along with observed precipitation data.

0

1

2

3

4

5

6

7

8

9

10

250

200

150

100

50

0

TOTAL DAILY PRECIPITATION, IN INCHES

DAILY MEAN FLOW, IN CUBIC FEET PER SECOND

JAN.

MAY

SEPT.

2001

JAN.

MAY

SEPT.

2002

JAN.

MAY

SEPT.

2003

JAN.

MAY

SEPT.

2004

JAN.

MAY

SEPT.

2005

JAN.

MAY

SEPT.

2006

JAN.

MAY

SEPT.

2007

JAN.

MAY

SEPT.

2008

JAN.

MAY

SEPT.

2009

Observed

TOPMODEL simulated

Precipitation

Figure 17. 
Simulation of the Streamflow for TOPMODEL and GBMM 23

some of the GBMM-simulated hydrographs is the complexity of balancing groundwater recession and flow at the 

streamgage when flows peak and recede rapidly. This also 

is the case for certain periods for the TOPMODEL results. 

However, GBMM results suggest that groundwater recession, 

which affects the receding limb of the hydrograph, was more 

difficult to estimate with the spatially explicit curve-number 

approach (fig. 18). For example, for the 2003 spring and 

summer simulation, if the GBMM groundwater recession 

coefficient is increased above the calibrated value of 0.017, 

GBMM overpredicts peak flows. In TOPMODEL, hydrograph 

Figure 18. GBMM simulated and observed daily mean flows at McTier Creek near Monetta for the calibration period 

(Feb. 7, 2001–Sept. 30, 2009), along with observed precipitation data.

recession is related to soils, controlled by the assumption of 

exponential decay of hydraulic conductivity with soil depth. 

The calibration parameters associated with the groundwater 

recession in TOPMODEL seem appropriate for the majority of 

the flow conditions during the calibration period. To balance 

peak runoff and recession rates, however, excessively wet 

years such as 2003 seem to present a challenge for both a 

curve-number based model and a variable-source-area based 

model such as TOPMODEL. Conversely, both GBMM and 

TOPMODEL tend to perform well during periods when flow 

is more evenly distributed during most of the year. 

0

1

2

3

4

5

6

7

8

9

10

250

200

150

100

50

0

TOTAL DAILY PRECIPITATION, IN INCHES

DAILY MEAN FLOW, IN CUBIC FEET PER SECOND

JAN.

MAY

SEPT.

2001

JAN.

MAY

SEPT.

2002

JAN.

MAY

SEPT.

2003

JAN.

MAY

SEPT.

2004

JAN.

MAY

SEPT.

2005

JAN.

MAY

SEPT.

2006

JAN.

MAY

SEPT.

2007

JAN.

MAY

SEPT.

2008

JAN.

MAY

SEPT.

2009

Observed

GBMM simulated

Precipitation

Figure 18. 
24 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Figure 19. Simulated and observed daily mean flows at McTier Creek near Monetta for the calibration period 

(Feb. 7, 2001–Sept. 30, 2009), shown by calendar year.

240

220

200

180

160

140

120

100

80

60

40

20

0

DAILY MEAN FLO

W, IN CUBIC FEET PER SECOND

Observed

TOPMODEL

GBMM

JAN. FEB. MAR. APR. MAY JUNE

2002

JULY AUG. SEPT. OCT. NOV. DEC.

JAN. FEB. MAR. APR. MAY JUNE

2001

JULY AUG. SEPT. OCT. NOV. DEC.

A. Calendar year 2001

240

220

200

180

160

140

120

100

80

60

40

20

0

Observed

TOPMODEL

GBMM

B. Calendar year 2002

Figure 19A,B. 
Simulation of the Streamflow for TOPMODEL and GBMM 25

Figure 19. Simulated and observed daily mean flows at McTier Creek near Monetta for the calibration period 

(Feb. 7, 2001–Sept. 30, 2009), shown by calendar year.—Continued

240

220

200

180

160

140

120

100

80

60

40

20

0

DAILY MEAN FLO

W, IN CUBIC FEET PER SECOND

Observed

TOPMODEL

GBMM

JAN. FEB. MAR. APR. MAY JUNE

2004

JULY AUG. SEPT. OCT. NOV. DEC.

JAN. FEB. MAR. APR. MAY JUNE

2003

JULY AUG. SEPT. OCT. NOV. DEC.

C. Calendar year 2003

240

220

200

180

160

140

120

100

80

60

40

20

0

Observed

TOPMODEL

GBMM

D. Calendar year 2004

Figure 19C,D. 
26 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Figure 19. Simulated and observed daily mean flows at McTier Creek near Monetta for the calibration period 

(Feb. 7, 2001–Sept. 30, 2009), shown by calendar year.—Continued

240

220

200

180

160

140

120

100

80

60

40

20

0

DAILY MEAN FLO

W, IN CUBIC FEET PER SECOND

Observed

TOPMODEL

GBMM

JAN. FEB. MAR. APR. MAY JUNE

2006

JULY AUG. SEPT. OCT. NOV. DEC.

JAN. FEB. MAR. APR. MAY JUNE

2005

JULY AUG. SEPT. OCT. NOV. DEC.

E. Calendar year 2005

240

220

200

180

160

140

120

100

80

60

40

20

0

Observed

TOPMODEL

GBMM

F. Calendar year 2006

Figure 19E,F. 
Simulation of the Streamflow for TOPMODEL and GBMM 27

Figure 19. Simulated and observed daily mean flows at McTier Creek near Monetta for the calibration period 

(Feb. 7, 2001–Sept. 30, 2009), shown by calendar year.—Continued

240

220

200

180

160

140

120

100

80

60

40

20

0

DAILY MEAN FLO

W, IN CUBIC FEET PER SECOND

Observed

TOPMODEL

GBMM

JAN. FEB. MAR. APR. MAY JUNE

2008

JULY AUG. SEPT. OCT. NOV. DEC.

JAN. FEB. MAR. APR. MAY JUNE

2007

JULY AUG. SEPT. OCT. NOV. DEC.

G. Calendar year 2007

240

220

200

180

160

140

120

100

80

60

40

20

0

Observed

TOPMODEL

GBMM

H. Calendar year 2008

Figure 19G,H. 
28 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Simulations at New Holland for the 

Confirmation Period

The New Holland streamgage is located at the downstream reach of the study area and represents an approximate 

doubling of the watershed area as compared to Monetta. As 

shown in table 5, the period of record available for model 

simulations was June 13, 2007, to September 30, 2009 (confirmation period). For both TOPMODEL and GBMM, the initial 

calibrated input parameters were set at the same levels as those 

determined during calibration at Monetta. For TOPMODEL, 

to get an improved fit at New Holland, the m value and percent 

macropore were slightly modified (47 to 46 and 0.5 to 0.4, 

respectively; table 8). These minor adjustments seem reasonable given the increase in watershed area between Monetta 

and New Holland. The TOPMODEL soils parameters for 

the New Holland watershed are almost the same as those for 

Monetta (tables 6, 8). Those parameters are average values for 

the entire watershed. Because the parameters remained fairly 

constant with those obtained at Monetta, even though the 

watershed area increased by almost 100 percent, commonality 

in the soils characteristics in the upper and lower watersheds 

of McTier Creek is indicated.

A plot of the observed and simulated daily mean flows 

at New Holland shows that both models perform reasonably 

well with respect to capturing the timing and variability of 

the flows (fig. 20). However, periods of underestimation and 

overestimation of flows are notable for both models. Also, 

issues relating to hydrograph recession that were discussed 

previously for the Monetta simulations are present.

Figure 19. Simulated and observed daily mean flows at McTier Creek near Monetta for the calibration period 

(Feb. 7, 2001–Sept. 30, 2009), shown by calendar year.—Continued

Table 8. Parameter values used for the TOPMODEL 

calibration for McTier Creek near New Holland, 

South Carolina.

[*, indicates adjustment during calibration]

Model parameter Value

Total area (square kilometers) 79.41

Lake area (square kilometers) 1.22

Stream area (square kilometers) 0.91

Saturated conductivity (inches per hour) 7.17

Soil depth (inches) 74.2*

Field capacity (unitless) 0.18

Water holding capacity (unitless) 0.09

Porosity (unitless) 0.39

Percent impervious 1.3*

Percent road impervious 0.9*

Latitude 33.718

Effective impervious (decimal percent) 0.8*

Conductivity multiplier 2.9*

Percent macropore (decimal percent) 0.5*

Scaling parameter (m) 45.0*

Depth of root zone (meters) 1.9*

Impervious runoff constant 0.10

TR-55 curve number 98

Uplake area (square kilometers) 59.0

Lake delay (unitless) 1.2*

240

220

200

180

160

140

120

100

80

60

40

20

0

DAILY MEAN FLO

W, IN CUBIC FEET PER SECOND

Observed

TOPMODEL

GBMM

JAN. FEB. MAR. APR. MAY JUNE

2009

JULY AUG. SEPT. OCT. NOV. DEC.

I. Calendar year 2009

Figure 19I. 
Goodness-of-Fit Statistics for TOPMODEL and GBMM 29

Goodness-of-Fit Statistics for 

TOPMODEL and GBMM

As previously stated, the goodness-of-fit statistics used 

to assess the TOPMODEL and GBMM simulations with 

respect to how well they match the observed daily mean flows 

were (1) the Nash-Sutcliffe coefficient of model-fit efficiency 

index (E) (Nash and Sutcliffe, 1970), (2) Pearson’s correlation 

coefficient (r), (3) the RMSE, (4) the bias, and (5) the MAE. 

The following sections provide details on these statistics for 

the two models relative to the simulation periods discussed 

earlier for the simulations at Monetta and New Holland.

Goodness-of-Fit Statistics at Monetta for the 

Calibration Period Simulations

The goodness-of-fit statistics between the simulated 

and observed daily mean flows at Monetta for the calibration 

period are listed in table 9. For TOPMODEL and GBMM, the 

mean and median simulated flows at Monetta are similar to the 

observed values suggesting that overall the models do a good 

job of matching the observed flows, with TOPMODEL doing 

a slightly better job with respect to the mean. The correlation 

coefficients also are relatively high, which further confirms a 

good fit between the simulated and observed flows. However, 

comparisons of the maximum and minimum flows indicate 

that TOPMODEL tended to perform somewhat better at the 

extremes. The standard deviation of the observed flows, which 

is a measure of the average spread of the data, is similar 

to that of the simulated flows; this also indicates that the 

models are capturing the variability of the daily mean flows, 

with TOPMODEL being slightly closer to the observed data 

than GBMM.

The bias is the mean of the residuals between the 

observed and simulated data. The bias indicates whether the 

model is, on average, over- or underpredicting the value being 

assessed. The bias for TOPMODEL was 0.23 cubic foot per 

second (ft3/s), which indicates that on average, the model was 

slightly overpredicting the daily mean flows. For GBMM, 

the negative bias of –1.13 ft3/s suggests a greater tendency to 

underpredict daily mean flows. The negative bias is potentially 

related to the application of the curve-number runoff approach 

in GBMM. The bias may be further explained by minor offsets 

in and interactions between calibrated parameters that could 

influence low-flow simulations, such as low seepage rates to 

the groundwater, rapid groundwater recession coefficients, and 

a deeper than average unsaturated soil zone. However, because 

(1) model input parameters fall within a realistic range of 

values for the watershed and (2) GBMM requires a lumped 

watershed value for these particular input parameters, the 

Figure 20. Simulated and observed daily mean flows at McTier Creek near New Holland for the confirmation period 

(June 13, 2007–Sept. 30, 2009).

0

1

2

3

4

5

6

7

8

9

10

240

220

200

180

160

140

120

100

80

60

40

20

0

TOTAL DAILY PRECIPITATION, IN INCHES

DAILY MEAN FLOW, IN CUBIC FEET PER SECOND

JUNE

JULY

AUG.

SEPT.

OCT.

NOV.

DEC.

JULY

AUG.

SEPT.

JAN.

FEB.

MAR.

APR.

MAY

OCT.

NOV.

DEC.

JUNE

JULY

AUG.

SEPT.

JAN.

FEB.

MAR.

APR.

MAY

OCT.

JUNE

2007 2008 2009

Observed

TOPMODEL 

GBMM

Precipitation

Figure 20. 
30 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

influence each parameter might exert on model bias potentially 

reflects the spatial variability of these watershed characteristics rather than poor calibration or measurements.

While the bias is a useful statistic, it does not provide any 

indication of the absolute differences between the observed 

and simulated data. That is, a bias of zero only indicates that 

the model is equally over- and underpredicting but provides no 

information on the magnitude of the over- or underpredictions. 

One approach to assessing such differences is by computing 

the variance, which is the average square of the residuals 

(Norman and Streiner, 1997). However, because the variance 

is not in the units of the original data, it is difficult to interpret. 

Consequently, the square root of the variance is taken and 

provides the RMSE, which is in the units of the original data. 

The RMSE represents the mean of the absolute distance 

between the observed and simulated values. A lower RMSE 

indicates a better fit between the observed and simulated data. 

For the calibration period at Monetta, the TOPMODEL and 

GBMM RMSE were 10.4 ft3/s and 9.04 ft3/s, respectively. 

Although lower RMSE indicates a better fit between the 

observed and simulated data, the difference between GBMM 

and TOPMODEL simulations was considered to be minimal. 

Janssen and Heuberger (1993) noted that one weakness 

of the RMSE is that it is sensitive to outliers because the 

differences between observed and simulated data are squared. 

The MAE is less sensitive to outliers. The MAE is similar 

to the bias except that it is the mean of the absolute value of 

the residuals as opposed to the mean of the actual residuals. 

Thus, the MAE provides the average of the magnitude of 

the residuals. In general, the RMSE can be expected to be 

greater than or equal to MAE for the range of most values. 

The degree to which the RMSE exceeds the MAE provides 

an indication of the extent to which outliers exist in the data 

(Legates and McCabe, 1999). For the calibration period, the 

MAEs for TOPMODEL and GBMM were 5.34 and 6.87 ft3/s, 

respectively. For TOPMODEL and GBMM, the differences 

between the RMSE and MAE were 5.06 and 2.17 ft3/s, 

respectively. Thus, although the standard deviation and 

range of values are larger in the GBMM model runs, 

GBMM simulations appear to have fewer outliers than 

TOPMODEL simulations. 

The Nash-Sutcliffe efficiencies (E) for the calibration 

period for TOPMODEL and GBMM were 0.47 and 0.38, 

respectively. An E value of 1.0 would indicate a perfect fit 

between the modeled and simulated data, and a value of zero 

or less would indicate that using the mean of the observed data 

would be a better predictor than the model (Krause and others, 

2005). Because the E value is computed using the squared 

differences of the observed and simulated data, under- or 

overpredictions of the higher flow values tend to carry more 

weight. As a result, the wet period in 2003 would be assumed 

to have a substantial effect on the E value, which would be 

true of the RMSE as well. Krause and others (2005) noted that 

one disadvantage of the E value is that the differences between 

the simulated and observed data are squared. Therefore, 

substantial over- or underpredictions of high-flow values can 

have a considerable effect on the E value, whereas differences 

in the lower values have less influence. Consequently, the 

overall E value for the wet period in 2003 could be lower due 

to the large difference between simulated and observed flows. 

To reduce the problem of the square differences and, thus, the 

sensitivity to the extreme values, the E value can be computed 

using the natural logarithms of the observed and simulated 

data. For example, the TOPMODEL E value for the calibration 

period when computed using natural logarithms resulted in an 

E value of 0.68, which is a 36 percent improvement over the 

E value computed with the wet period included. 

Goodness-of-Fit Statistics at Monetta for the 

Concurrent Period Simulations

The New Holland streamgage is located at the outlet 

of the study area. As discussed earlier, the streamgage was 

installed at that location to collect flow data during the 

mercury investigation and, thus, data are only available for the 

period from June 13, 2007, to September 30, 2009 (concurrent 

period). Therefore, in order to compare the New Holland 

model simulations with the Monetta simulations, the following 

goodness-of-fit statistics are provided for the Monetta simulation period that is concurrent with the New Holland simulation 

period. Plots of the simulated and observed data were previously shown in figure 19G–I, and a plot of the simulation at 

Monetta for the concurrent period also is shown in figure 21.

The goodness-of-fit statistics for the TOPMODEL show 

that for the concurrent period at Monetta, the mean, median, 

and minimum simulated daily mean flows are similar to those 

computed from the observed data (table 10). The standard 

deviation of the simulated data is slightly lower than that of 

the observed data but still indicates that the model reasonably 

captures the dynamics and variability of the daily mean flows. 

Table 9. Goodness-of-fit statistics at McTier Creek near Monetta 

for the calibration period.

[ft3/s, cubic foot per second; RMSE, root mean square error; MAE, mean absolute error; r, Pearson’s correlation coefficient; E, Nash-Sutcliffe coefficient of 

model-fit efficiency calibration period is Feb. 7, 2001–Sept. 30, 2009]

Observed Simulated 

(TOPMODEL)

Simulated 

(GBMM)

Maximum (ft3/s) 173 140 235

Mean (ft3/s) 14.0 14.2 12.9

Median (ft3/s) 11.0 10.5 10.6

Minimum (ft3/s) 1.40 1.11 0.11

Standard deviation (ft3/s) 14.3 13.6 12.1

Bias (ft3/s) 0.23 –1.13

RMSE (ft3/s) 10.4 9.04

MAE (ft3/s) 5.34 6.87

r 0.72 0.67

E 0.47 0.38
Goodness-of-Fit Statistics for TOPMODEL and GBMM 31

Pearson’s correlation coefficient, r, also indicates a good 

correlation between the observed and simulated daily mean 

flows. The E coefficient is improved with the longer period 

model from 2001 to 2009 as are the RMSE and MAE. For this 

period, the difference between the RMSE and MAE was the 

same for both models (3.4 ft3/s). 

As was the case for TOPMODEL, the r and E statistics 

for GBMM are higher for this shorter period (2007–2009), 

suggesting a good fit with the streamgage data. This is 

expected because (1) the 2007–2009 period was less hydrologically variable than the previous simulation period, which 

included the diverse precipitation years of 2001–2003, and 

(2) the sample size (N) is lower for the shorter period. Though 

the observed and GBMM-simulated maximum and mean 

daily flows are similar, the minimum daily flows simulated 

by GBMM are lower than the observed data, which further 

supports previous discussions of GBMM’s tendency toward 

underestimating flows in this watershed during low-flow 

periods. Overall, the goodness-of-fitness statistics indicate 

that both models generally provide a good representation of 

the streamflow in McTier Creek for the concurrent period.

Figure 21. Simulated and observed daily mean flows for McTier Creek near Monetta for the concurrent period 

(June 13, 2007–Sept. 30, 2009).

Table 10. Goodness-of-fit statistics for McTier Creek near 

Monetta for the concurrent period (June 13, 2007–Sept. 30, 2009).

[ft3/s, cubic foot per second; RMSE, root mean square error; MAE, mean 

absolute error; r, Pearson’s correlation coefficient; E, Nash-Sutcliffe coefficient 

of model-fit efficiency]

Observed Simulated 

(TOPMODEL)

Simulated 

(GBMM)

Maximum (ft3/s) 123 67 122

Mean (ft3/s) 10.4 10.7 11.1

Median (ft3/s) 7.5 7.3 10.0

Minimum (ft3/s) 1.8 2.0 0.62

Standard deviation (ft3/s) 12.0 9.0 9.5

Bias (ft3/s) 0.27 0.75

RMSE (ft3/s) 7.6 8.4

MAE (ft3/s) 4.2 5.0

r 0.78 0.72

E 0.61 0.51

0

1

2

3

4

5

6

7

8

9

10

140

120

100

80

60

40

20

0

TOTAL DAILY PRECIPITATION, IN INCHES

DAILY MEAN FLOW, IN CUBIC FEET PER SECOND

JUNE

JULY

AUG.

SEPT.

OCT.

NOV.

DEC.

JULY

AUG.

SEPT.

JAN.

FEB.

MAR.

APR.

MAY

OCT.

NOV.

DEC.

JUNE

JULY

AUG.

SEPT.

JAN.

FEB.

MAR.

APR.

MAY

OCT.

JUNE

2007 2008 2009

Observed

TOPMODEL 

GBMM

Precipitation

Figure 21. 
32 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Goodness-of-Fit Statistics at New Holland for 

Confirmation Period Simulations

The efficiency and correlation coefficients (E and r, 

respectively) for the confirmation period simulations at New 

Holland (table 11) are similar to those for the concurrent 

period at Monetta (table 10). In addition, the mean of the 

simulations for both models is almost equal to that of the 

measured data. As at Monetta, GBMM undersimulated 

the minimum flow. For the maximum flow at Monetta, the 

GBMM estimate was close to the observed maximum flow, 

but at New Holland, the GBMM maximum flow was well 

above the observed maximum flow. For TOPMODEL, the 

minimum flow at New Holland is about twice the observed 

minimum flow; at Monetta, the minimum simulated flow 

from TOPMODEL and the observed minimum flow at the 

streamgage were almost equal. Although the bias at New Holland is smaller than that at Monetta for both models, the MAE 

is larger, suggesting an overall average larger deviation from 

the observed data than was the case at Monetta. As was true 

for the concurrent period at Monetta, the differences between 

the RMSE and the MAE for TOPMODEL and GBMM were 

about equal (4.5 and 4.8 ft3/s, respectively). The standard 

deviation for both models again suggests that the variability of 

the simulated flows is similar to the observed flow. 

Flow-Duration Curves, Single-Mass 

Curves, and Residuals

Along with temporal plots of simulated and observed 

daily mean flows for the TOPMODEL and GBMM models, 

several other graphical tools were used to assess how well 

the models capture the characteristics of the observed data at 

the Monetta and New Holland gages. Those graphical tools 

include flow-duration and single-mass curves along with 

various plots of model residuals, which are the differences 

between the observed and simulated values. These graphical 

tools are discussed in this section, and plots are presented for 

the various simulation periods previously discussed.

Flow-Duration Curves

The flow-duration curve is a cumulative frequency curve 

that shows the percentage of time during which specified flows 

were equaled or exceeded for the given period of analysis 

(Searcy, 1959). The flow-duration curves at Monetta for the 

calibration period are shown in figure 22A. In general, the 

flow-duration characteristics of the simulated flows from 

TOPMODEL and GBMM match those of the observed flows 

reasonably well. However, GBMM tends to underestimate 

flows that are equaled or exceeded approximately 2–5 percent 

of the time (high flows) and 95–100 percent of the time 

(lower flows). Underestimating simulated flows may reflect 

the overall capacity of the curve-number runoff method to 

capture saturation excess overland flow response, which 

could be a significant contributor during peak runoff periods 

(Schneiderman and others, 2007). The curve-number method 

is biased toward infiltration-excess overland flow because the 

infiltration capacity of soils is one of the two main factors 

determining curve-number runoff (Garen and Moore, 2005; 

Walter and Shaw, 2005). Saturation-excess overland flow is 

particularly important in the McTier Creek watershed, which 

has abundant riparian wetland areas that are more likely to 

respond rapidly to a soil saturation surplus. 

The flow-duration curves for TOPMODEL and GBMM 

at the Monetta gage for the concurrent period tend to match 

the observed curve reasonably well with TOPMODEL, 

providing an overall slightly better fit (fig. 22B). As with the 

longer period shown in figure 22A, GBMM deviates from the 

observed curve for the lowest flows (those exceeded 95 to 

100 percent of the time). This again likely reflects the complex 

calibration balance between seasonal curve number thresholds 

and groundwater recession rates. GBMM flow rates are lower 

than observed base-flow rates for the fall of 2007 and winter 

of 2009, which were both relatively dry precipitation periods 

in the watershed (fig. 21).

Table 11. TOPMODEL and GBMM calibration statistics at 

McTier Creek near New Holland for the confirmation period 

(June 13, 2007–Sept. 30, 2009).

[ft3/s, cubic foot per second; RMSE, root mean square error; MAE, mean 

absolute error; r, Pearson’s correlation coefficient; E, Nash-Sutcliffe coefficient of model-fit efficiency]

Observed Simulated 

(TOPMODEL)

Simulated 

(GBMM)

Maximum (ft3/s) 163 130 234

Mean (ft3/s) 21.8 21.6 21.6

Median (ft3/s) 17.0 14.9 19.5

Minimum (ft3/s) 2.6 5.0 1.2

Standard deviation (ft3/s) 19.9 17.1 18.2

Bias (ft3/s) 0.15 0.22

RMSE (ft3/s) 11.7 13.8

MAE (ft3/s) 7.2 9.0

r 0.80 0.73

E 0.64 0.49
Flow-Duration Curves, Single-Mass Curves, and Residuals 33

Figure 22. Flow-duration curves of simulated and observed daily mean flow at (A) Monetta for the calibration period, 

(B) Monetta for the concurrent period, and (C) New Holland for the confirmation period.

1,000

100

10

1

0.1

DAILY MEAN FLO

W, IN CUBIC FEET PER SECOND

Observed

TOPMODEL

GBMM

A. Station 02172300, McTier Creek near Monetta, SC (Feb. 7, 2001–Sept. 30, 2009)

Observed

TOPMODEL

GBMM

Observed

TOPMODEL

GBMM

B. Station 02172300, McTier Creek near Monetta, SC (June 13, 2007–Sept. 30, 2009)

0 10 20 30 40 50 60 70 80 90 100

C. Station 02172305, McTier Creek near New Holland, SC (June 13, 2007–Sept. 30, 2009)

Figure 22. 

1,000

100

10

1

1,000

100

10

1

0.1

0.1

PERCENTAGE OF TIME INDICATED FLOW WAS EQUALED OR EXCEEDED
34 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

The flow-duration curves for TOPMODEL and GBMM 

at the New Holland gage for the confirmation period show that 

the flow-duration curve characteristics of simulated flows are 

similar to those of the observed daily mean flows (fig. 22C). 

For the flows that are equaled or exceeded about 90 or more 

percent of the time (the lowest flows), the duration curves 

for the simulated flows for both models continue to have 

shapes similar to those for the observed flows but diverge 

with TOPMODEL duration values being higher than observed 

values and GBMM duration values being lower than observed 

values. This is consistent with the flow-duration curves at 

Monetta (fig. 22B). 

Single-Mass Curves

Figure 23A shows a single-mass curve that presents the 

cumulative daily mean flows and represents the cumulative 

volume of daily mean flow for the calibration period. Both 

TOPMODEL and GBMM show a good fit with the observed 

curve through the winter of 2003. However, after 2003, 

GBMM begins to underpredict the cumulative volume, and 

TOPMODEL begins to overpredict the cumulative volume. 

The significant change in the slopes of the single-mass curves 

indicates changes in the hydrologic regime. From figure 19C, 

it can be seen that the abrupt change in the slope of the mass 

curve for the measured data was due to the significantly wet 

period that occurred in the spring of 2003. In addition, the 

difference in the magnitude of the cumulative volume from 

TOPMODEL and the cumulative volume of the observed 

flows is likely related to the slower rates of hydrograph 

recession for the TOPMODEL simulations during the wet 

period as compared to those of the observed hydrographs 

and of the GBMM simulations. For the total period analyzed, 

however, the difference between the simulated and measured 

total volume for TOPMODEL was about 5 percent (fig. 23A) 

and was slightly less than 10 percent for GBMM. It is worth 

noting that the USGS considers the accuracy of a streamflow 

record to be “good” if about 95 percent of the daily flows are 

within 10 percent of the true flow (Novak, 1985). As a point 

of comparison, Donigian and others (1984) present general 

guidelines for characterizing calibrations for the Hydrologic 

Simulation Program–Fortran (HSPF) watershed model. For 

annual and monthly volumes, HSPF model calibration is 

considered very good when the error is less than 10 percent, 

good when the error is 10 to 15 percent, and fair when the 

error is 15 to 25 percent (Ockerman, 2005).

For the concurrent period at Monetta, the single-mass 

curves for TOPMODEL and GBMM have shapes similar to 

that of the observed data, and GBMM volumes tend to more 

closely track those of the observed data than the TOPMODEL 

values do throughout the simulation period (fig. 23B). 

The deviation of the TOPMODEL curve is likely due to 

its underestimation of several large peak-flow events that 

occurred during the concurrent period (fig. 21). Nonetheless, 

for the total simulation period, the differences in the total 

volume of the TOPMODEL and GBMM simulations with 

respect to the total observed volume only were about 3 percent 

and 7 percent, respectively.

The single-mass curves for the confirmation period 

at New Holland are shown in figure 23C. The curves are 

consistent with those for the concurrent period at Monetta. The 

shapes of the single-mass curves for TOPMODEL and GBMM 

cumulative flows are similar to that for the observed data, and 

the GBMM data more closely follow the observed data than 

do the TOPMODEL data throughout much of the simulation 

period. However, the total volumes for the simulation period 

for both models are within about 1 percent of the total volume 

of the observed daily mean flow at New Holland. 
Flow-Duration Curves, Single-Mass Curves, and Residuals 35

Figure 23. Single-mass curves of 

simulated and observed daily mean 

flow at (A) Monetta for the calibration 

period, (B) Monetta for the concurrent 

period, and (C) New Holland for the 

confirmation period.

50,000

45,000

40,000

35,000

30,000

25,000

20,000

15,000

10,000

5,000

0

CUMULATIVE DAILY MEAN FLOW, IN CUBIC FEET PER SECOND

JAN.

MAY

AUG.

DEC.

APR.

AUG.

DEC.

APR.

AUG.

DEC.

APR.

AUG.

DEC.

APR.

AUG.

DEC.

APR.

AUG.

DEC.

MAR.

JULY

NOV.

MAR.

JULY

NOV.

MAR.

JULY

NOV.

2001 2002 2003 2004 2005 2006 2007 2008 2009

10,000

9,000

8,000

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Figure 23. 

Observed

TOPMODEL

GBMM

A. Station 02172300, McTier Creek near Monetta, SC (Feb. 7, 2001–Sept. 30, 2009)

Observed

TOPMODEL

GBMM

B. Station 02172300, McTier Creek near Monetta, SC (June 13, 2007–Sept. 30, 2009)

Observed

TOPMODEL

GBMM

C. Station 02172305, McTier Creek near New Holland, SC (June 13, 2007–Sept. 30, 2009)

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2007 2008 2009
36 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Residuals 

For the Monetta site, scatter plots of simulated and 

observed daily mean flows for the calibration period for 

TOPMODEL and GBMM are shown in figures 24A and 

25A, respectively. For the TOPMODEL simulated flows, no 

significant bias exists as shown by the values being evenly 

spread about the one-to-one line (line of agreement); however, 

some bias exists at the extremes. For GBMM simulated flows, 

the flows also are evenly distributed about the one-to-one 

line with some bias at the extremes. As discussed earlier, the 

residuals also reflect the issue of the GBMM recession rates. 

The scatter plots of TOPMODEL and GBMM simulations at Monetta for the concurrent period show that the 

Figure 24. Scatter plots of observed and TOPMODEL simulated daily mean flow at (A) McTier Creek near Monetta for the calibration 

period, (B) McTier Creek near Monetta for the concurrent period, and (C) McTier Creek near New Holland for the confirmation period.

1,000

100

10

1

0.1

A. Station 02172300, McTier Creek near Monetta, SC (Feb. 7, 2001–Sept. 30, 2009)

B. Station 02172300, McTier Creek near Monetta, SC (June 13, 2007–Sept. 30, 2009)

0.1 1 10 100 1,000

C. Station 02172305, McTier Creek near New Holland, SC (June 13, 2007–Sept. 30, 2009)

Figure 24. 

1,000

100

10

1

1,000

100

10

1

0.1

0.1

OBSERVED DAILY MEAN FLOW, IN CUBIC FEET PER SECOND

TOPMODEL SIMULATED DAILY MEAN FLOW, IN CUBIC FEET PER SECOND
Flow-Duration Curves, Single-Mass Curves, and Residuals 37

Figure 25. Scatter plots of observed and GBMM simulated daily mean flow at (A) McTier Creek near Monetta for the calibration 

period, (B) McTier Creek near Monetta for the concurrent period, and (C) McTier Creek near New Holland for the confirmation period.

majority of modeled flow values are scattered about the 

one-to-one line, indicating no consistent bias (figs. 24B, 25B). 

Some bias at the flow extremes, however, does exist. 

The scatter plots for the New Holland simulations for 

the confirmation period are presented in figures 24C and 

25C, respectively. Overall, the results are similar to those for 

Monetta with the majority of flow values being well spread 

about the one-to-one line with some bias at the extremes. In 

addition, the GBMM issue relating to recession rates for the 

lower flows is evident.

1,000

100

10

1

0.1

A. Station 02172300, McTier Creek near Monetta, SC (Feb. 7, 2001–Sept. 30, 2009)

B. Station 02172300, McTier Creek near Monetta, SC (June 13, 2007–Sept. 30, 2009)

0.1 1 10 100 1,000

C. Station 02172305, McTier Creek near New Holland, SC (June 13, 2007–Sept. 30, 2009)

Figure 25. 

1,000

100

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1

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1

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0.1

OBSERVED DAILY MEAN FLOW, IN CUBIC FEET PER SECOND

GBMM SIMULATED DAILY MEAN FLOW, IN CUBIC FEET PER SECOND
38 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Residuals and Simulated Flow

For the calibration period, the TOPMODEL residuals 

are in good agreement for the majority of the data points. 

TOPMODEL residuals begin to develop a heteroscedastic 

relation as the flows increase, which indicates a non-constant 

variance (Helsel and Hirsch, 1995; fig. 26A). About 80 percent 

of the simulated flows are about 20 ft3/s or less (fig. 22A). 

Consequently, much of the heteroscedasticity is probably 

related to the high residuals from the wet period in 2003 and 

peak flows for which TOPMODEL tended to underpredict. 

Although not quite as pronounced, a similar pattern is evident 

for the concurrent and confirmation periods at both Monetta 

and New Holland, respectively (fig. 26B, C). For GBMM, a 

Figure 26. Residuals and TOPMODEL simulated daily mean flow at (A) McTier Creek near Monetta for the calibration period, 

(B) McTier Creek near Monetta for the concurrent period, and (C) McTier Creek near New Holland for the confirmation period.

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A. Station 02172300, McTier Creek near Monetta, SC (Feb. 7, 2001–Sept. 30, 2009)

B. Station 02172300, McTier Creek near Monetta, SC (June 13, 2007–Sept. 30, 2009)

0.1 1 10 100 1,000

C. Station 02172305, McTier Creek near New Holland, SC (June 13, 2007–Sept. 30, 2009)

Figure 26. 

RESIDUALS (SIMULATED MINUS OBSERVED), IN CUBIC FEET PER SECOND

TOPMODEL SIMULATED DAILY MEAN FLOW, IN CUBIC FEET PER SECOND
Flow-Duration Curves, Single-Mass Curves, and Residuals 39

Figure 27. Residuals and GBMM simulated daily mean flow at (A) McTier Creek near Monetta for the calibration period, 

(B) McTier Creek near Monetta for the concurrent period, and (C) McTier Creek near New Holland for the confirmation period.

relatively consistent pattern in the residuals is evident up to 

a mean daily flow of approximately 10 ft3/s, with the exception of the systematic underprediction below about 1 ft3

/s 

(fig. 27A). Above 10 ft3/s, the mean daily flows become more 

variable as indicated by the heteroscedastic shape as was noted 

for TOPMODEL. Similar to the TOPMODEL results, approximately 80 percent of the simulated mean daily flows from the 

2001 to 2009 period are below approximately 20 ft3/s. Thus, 

the wet 2003 period likely exerts an influence on GBMM 

results as well. The GBMM residuals for the concurrent and 

confirmation periods at Monetta and New Holland, respectively, show similar patterns, with the New Holland residuals 

showing more variability (fig. 27B, C).

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A. Station 02172300, McTier Creek near Monetta, SC (Feb. 7, 2001–Sept. 30, 2009)

B. Station 02172300, McTier Creek near Monetta, SC (June 13, 2007–Sept. 30, 2009)

0.1 1 10 100 1,000

C. Station 02172305, McTier Creek near New Holland, SC (June 13, 2007–Sept. 30, 2009)

Figure 27. 

RESIDUALS (SIMULATED MINUS OBSERVED), IN CUBIC FEET PER SECOND

GBMM SIMULATED DAILY MEAN FLOW, IN CUBIC FEET PER SECOND
40 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Residuals (Temporal)

Finally, temporal plots of residuals are shown in 

figures 28 and 29 for TOPMODEL and GBMM, respectively. 

Although there appears to be some seasonal pattern to the 

TOPMODEL residuals, such as residual values being negative 

in the fall, those patterns are not always consistent (no significant cluster of negative residuals in the fall of 2002, 2006, 

or 2008). The plot of simulated and observed flows by year 

(fig. 20) shows that during low flows, which typically occur in 

the fall, the model accuracy is low. As previously discussed, 

the TOPMODEL assumption that the water table parallels the 

Figure 28. Residuals of simulated (TOPMODEL) and observed daily mean flow at (A) McTier Creek 

near Monetta for the calibration period, (B) McTier Creek near Monetta for the concurrent period, 

and (C) McTier Creek near New Holland for the confirmation period.

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A. Station 02172300, McTier Creek near Monetta, SC (Feb. 7, 2001–Sept. 30, 2009)

B. Station 02172300, McTier Creek near Monetta, SC (June 13, 2007–Sept. 30, 2009)

C. Station 02172305, McTier Creek near New Holland, SC (June 13, 2007–Sept. 30, 2009)

Figure 28. 

RESIDUALS (TOPMODEL SIMULATED MINUS OBSERVED), IN CUBIC FEET PER SECOND

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2006 2010
Flow-Duration Curves, Single-Mass Curves, and Residuals 41

Figure 29. Residuals of simulated (GBMM) and observed daily mean flow at (A) McTier Creek near Monetta for the calibration period, 

(B) McTier Creek near Monetta for the concurrent period, and (C) McTier Creek near New Holland for the confirmation period.

topography is questionable during the lowest flow periods. 

The cluster of positive residuals in the spring of 2003 indicates 

an extended period of overprediction by TOPMODEL for 

the calibration period. For the concurrent and confirmation 

periods, respectively, the temporal plots of TOPMODEL 

residuals have similar patterns at Monetta and New Holland 

with the majority of the residuals being relatively close to zero 

and with the model underpredicting in the fall of 2007 and 

overpredicting in the spring of 2009 (fig. 28B, C). Again, it 

is worth noting that fall tends to be the time of the year when 

the lowest streamflow occurs, and spring tends to be when 

the highest streamflow occurs. This pattern suggests that the 

extremes present the most challenge for TOPMODEL, even 

though the model did well throughout the entire year for 2008. 

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A. Station 02172300, McTier Creek near Monetta, SC (Feb. 7, 2001–Sept. 30, 2009)

B. Station 02172300, McTier Creek near Monetta, SC (June 13, 2007–Sept. 30, 2009)

C. Station 02172305, McTier Creek near New Holland, SC (June 13, 2007–Sept. 30, 2009)

Figure 29. 

RESIDUALS (GBMM SIMULATED MINUS OBSERVED), IN CUBIC FEET PER SECOND

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2006 2010
42 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

A temporal plot of the GBMM residuals at Monetta also 

suggests some seasonal patterns in model errors (fig. 29A). For 

example, for most years during the calibration period, GBMM 

overpredicts slightly during the summer but underpredicts in 

the winter, though the pattern in the over- and underpredictions tends to vary. During the summer months, rainfall often 

occurs in sporadic events. Because the duration of these events 

is brief, the uplands may remain hydrologically disconnected 

from the stream. Thus, even though event-based antecedent 

precipitation rates produce rapid runoff using GBMM’s curvenumber methodology, observed watershed runoff may not 

respond as quickly as the curve-number approach suggests, 

and slight overpredictions occur for summer. Additionally, a 

cluster of positive residuals reflects GBMM’s overprediction 

during the wet spring and early summer of 2003, similar to 

TOPMODEL results (fig. 29A).

For the concurrent and confirmation periods at Monetta 

and New Holland, respectively, the GBMM residuals indicate 

some seasonality, but no strong, consistent pattern occurs, 

which is similar to the TOPMODEL residuals (fig. 29B, C). 

Underpredictions in the fall of 2007 and the winter of 2009 

are most evident, with the most noticeable overpredictions 

occurring in the fall of 2008 and late summer of 2009. As with 

TOPMODEL, slightly more variability is noticeable at New 

Holland, which has a drainage area that is about twice the size 

of the drainage area at Monetta.

Watershed Model Uncertainties 

and Limitations

All watershed models employ mathematical descriptions 

based on simplifying assumptions about the processes that 

underlie complex natural systems (Beven, 2002). The 

extent to which these simplifications deviate from the hydrologic reality is a fundamental source of uncertainty in such 

models (Ockerman, 2005). The mathematical structures of 

TOPMODEL and GBMM differ substantially, each capturing 

the actual hydrologic character of the McTier Creek watershed 

to varying degrees. Runoff simulations in TOPMODEL 

involve a semi-distributed approach using the variable-sourcearea concept where saturation excess overland flow and subsurface flow are the dominant runoff generating mechanisms. 

Further, runoff response is based on the general assumption 

that the water table mirrors the watershed’s topography and 

that hydraulic conductivity decreases exponentially with 

depth. In comparison, GBMM’s runoff methodology involves 

a spatially explicit modified curve-number approach based 

on soil infiltration capacity and land cover, which assumes 

that infiltration excess overland flow is the dominant runoffgenerating process in the watershed. While output from both 

models fit the daily hydrograph relatively well, neither model 

captures the full complexity of hydrologic processes in the 

watershed. In addition to such systematic errors, limitations in 

the input data needed for the model are another source of error.

TOPMODEL and GBMM simulations are driven by time 

series of precipitation and air temperature. As a result, model 

accuracy is dependent on the accuracy of these data. The 

precipitation and air temperature data for this investigation 

were obtained from the NWS meteorological data network at 

stations located in the vicinity of the McTier Creek watershed. 

To improve the areal coverage of the data, inverse-distance 

weighting techniques were used to generate a better representation of the “average” meteorological conditions in the 

watershed. Variations in average daily temperatures at the various NWS stations around McTier Creek tend to be relatively 

minor. However, rainfall can vary greatly over small distances; 

thus, the assumption of spatially uniform rainfall is unrealistic, 

especially during summer months when convective storms can 

produce spatially variable amounts of rainfall. For the McTier 

Creek watershed specifically, these events could produce 

large precipitation amounts that may not even be captured 

in the TOPMODEL input data. During an investigation in 

Mecklenburg County, NC, from July 1995 through June 1997, 

precipitation data were collected at 46 sites (Robinson and 

others, 1998). The results of that investigation showed that the 

distribution of annual rainfall in parts of Mecklenburg County 

ranged from 35 to 50 inches. With respect to particular events, 

the distribution of recurrence intervals for a 24-hour rainfall 

duration in the city of Charlotte for the storm of August 26–27, 

1995, based on 24 rainfall-gaging stations, ranged from less 

than 2 years to more than 100 years (Hershfield, 1961; Hazell 

and Bales, 1997). Consequently, there will always be some 

level of uncertainty in rainfall-runoff models that assume 

uniform rainfall over the watershed.

In addition to the meteorological data, TOPMODEL and 

GBMM inputs include soils parameters and other watershed 

characteristics. The McTier Creek watershed tends to have 

similar soils characteristics; therefore, average values probably 

represent most parts of the watershed well. Nonetheless, some 

amount of uncertainty is introduced into the model simulations 

from both the uncertainty in the soil measurements used to 

develop the SSURGO coverages and the process of using 

a single, average value to represent the entire watershed 

being modeled. In addition, watershed characteristics, such 

as watershed area, stream area, and imperviousness, are 

computed from available GIS coverages. Certainly the use of 

GIS techniques has increased the accuracy of these watershed 

characteristics, but some level of uncertainty in those measurements still remains and will be part of the uncertainty in the 

model simulations.

Another area of uncertainty is related to the accuracy 

of the observed streamflow data. For USGS streamflow 

records, accuracy depends primarily on the stability of the 

stage-streamflow relation, and the frequency and reliability 

of stage and streamflow measurements (Novak, 1985). Four 

accuracy classifications are used to rate station records. A 

rating of “excellent” indicates that about 95 percent of the 

daily mean flows are within 5 percent of the true flow; “good” 

ratings are within 10 percent; “fair” are within 15 percent; and 

“poor” means that daily flows have less than “fair” accuracy. 
Watershed Model Uses 43

For the most recent period of record collected at Monetta, the 

records for water years 2001, 2002, 2003, 2005, 2006, and 

2008 were rated as fair (Cooney and others, 2002; Cooney and 

others, 2003; U.S. Geological Survey, 2004, 2006, 2009). For 

water years 2004 and 2007, the records were rated as good 

(U.S. Geological Survey, 2005, 2008).

Watershed Model Uses

The purpose of using the watershed models previously 

described is to provide a framework for a better understanding 

of the spatial and temporal variability of the relation between 

hydrology and mercury in the McTier Creek watershed. A few 

examples of potential ways in which the models can be used 

are provided below.

Mapping Saturated Areas

One of the outputs from TOPMODEL is the percentage 

of the watershed predicted to be saturated for each modeled 

time step. This information along with the topographic wetness indices can be used to map the saturated areas throughout 

the watershed, providing a depiction of the hydrologic 

conditions that may trigger connections between the riparian 

wetlands and the channel and where these connections are 

occurring. Information on the timing and magnitude of these 

connections may provide insight into potential mobilization of 

mercury from the wetlands to the receiving streams. 

The relation between the simulated daily mean flow 

and fraction of saturated area at New Holland during the 

confirmation period is shown in figure 30. From that period, 

the total saturated areas for a low-flow condition (7.0 ft3/s on 

Aug. 8, 2007) and high-flow condition (130 ft3/s on Apr. 11, 

2009) are shown in figure 31. Although the percentage of the 

watershed shown to be saturated at any one time during this 

simulation period was relatively small, the increase in amount 

of area saturated from the low-flow to high-flow condition 

was approximately 350 percent. With respect to delivery of 

constituents that can affect the water quality of the stream, 

such an increase may be substantial. Thus, the use of the 

saturated area and other flow components from TOPMODEL 

can provide additional insight to the relation between the 

hydrology and the water quality in the watershed.

Modeling Hydrology in Subwatersheds

TOPMODEL can be used for modeling the hydrology 

of ungaged watersheds. Such an application on a larger-scale 

basis than the McTier Creek watershed was recently documented by Williamson and others (2009) for a project in which 

Figure 30. Simulated (TOPMODEL) daily mean flow and saturated area at McTier Creek near New Holland 

for the confirmation period.

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TOPMODEL 

Saturated area

Figure 30. 
44 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Figure 31A. Saturated areas from TOPMODEL simulations in the McTier Creek watershed under low-flow conditions on 

August 8, 2007.

SALUDA

LEXINGTON

AIKEN

EXPLANATION

Land-surface elevation, in feet

600 to 650

570 to 600

540 to 570

510 to 540

480 to 510

450 to 480

420 to 450

360 to 420

317 to 360

Saturation

8136’

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81

33’

0 0.5 1 2 KILOMETERS

0 0.5 1 2 MILES

Base from National Hydrography Dataset, 1:100,000

ESRI Data and Maps, 2006

Albers equal area projection; central meridian -96 00 00; NAD 83 datum

Figure 31A. 
Watershed Model Uses 45

Figure 31B. Saturated areas from TOPMODEL simulations in the McTier Creek watershed under high-flow conditions on 

April 11, 2009.

SALUDA

LEXINGTON

AIKEN

EXPLANATION

Land-surface elevation, in feet

600 to 650

570 to 600

540 to 570

510 to 540

480 to 510

450 to 480

420 to 450

360 to 420

317 to 360

Saturation

8136’

33

51’

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48’

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45’

81

33’

0 0.5 1 2 KILOMETERS

0 0.5 1 2 MILES

Base from National Hydrography Dataset, 1:100,000

ESRI Data and Maps, 2006

Albers equal area projection; central meridian -96 00 00; NAD 83 datum

Figure 31B. 
46 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

TOPMODEL is being used in Kentucky to assist with managing the State’s water-supply resources. Calibration of the 

model was done at a limited number of gaged locations, and 

then the calibrated parameters were used along with measured 

soils and watershed characteristics to model the hydrology in 

ungaged watersheds with similar characteristics. 

For McTier Creek, a similar approach was applied. 

The McTier Creek watershed was subdivided into 

12 subwatersheds (fig. 32). The calibrated parameters from 

Monetta and New Holland were then used along with the 

measured soils and watershed characteristics from the subwatersheds to simulate flows for the concurrent and confirmation periods, respectively. Consequently, the subwatersheds’ 

models are separate, individual TOPMODEL applications. The 

topographic wetness indices were computed for each subwatershed. The same temperature and precipitation data used 

Figure 32. McTier Creek subwatersheds, Aiken County, South Carolina.

SALUDA

LEXINGTON

AIKEN 

EXPLANATION

Subwatershed descriptors

 

8136’

33

51’

33

48’

33

45’

81

33’

0 0.5 1 2 KILOMETERS

0 0.5 1 2 MILES

Base from National Hydrography Dataset, 1:100,000

ESRI Data and Maps, 2006

Albers equal area projection; central meridian -96 00 00; NAD 83 datum

Figure 32. 

MA10

MA11

MA09

MA08

MA04

MA02

MA07

MA05

MA03

MA01

MA06

MA12

MA12
Watershed Model Uses 47

for the models at Monetta and New Holland were used for the 

subwatershed models. The simulated streamflow values for 

subwatersheds MA01 to MA06 were summed and compared 

to the streamflow values at Monetta, and the streamflow 

values for subwatersheds MA01 to MA12 were summed and 

compared to the simulated streamflow values at New Holland 

(figs. 33, 34, respectively). Figure 35 shows the simulated 

flows for the Monetta and New Holland gages plotted with the 

summation of the simulated subwatershed flows along the line 

of agreement. The sum of the simulated daily mean flow values from the subwatersheds matches the simulated flow values 

for the gages very well. The total volume of the subwatersheds 

as compared to the total volume at Monetta and New Holland 

was within about 1 and 3 percent, respectively. Modeling 

of the subwatersheds allows for assessment of mercury in 

various parts of the McTier Creek watershed. In addition, the 

subwatershed flows can be used as hydrology inputs for other 

models such as the U.S. Environmental Protection Agency 

Water-Quality Analysis Simulation Program (WASP) model, 

which can be used for a more comprehensive modeling of the 

mercury mechanisms in the watershed. 

Loadings from TOPMODEL Flow Components

Another benefit of TOPMODEL simulations is the 

assessment of constituent loadings from various flow paths 

in the McTier Creek watershed. As discussed in appendix 1, 

Figure 33. Simulated daily mean flow for the concurrent period at McTier Creek near Monetta and the sum of the 

simulated daily mean flow for subwatersheds MA01 to MA06.

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DAILY MEAN FLO

W

AT STATION 02172300, IN CUBIC FEET PER SECOND

Monetta

Sum of subbasins MA01–MA06

Figure 33. 

MAY AUG.

2007

NOV. AUG.

2008

FEB. MAY NOV. FEB. AUG.

2009

MAY NOV.
48 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Figure 34. Simulated daily mean flow for the confirmation period at McTier Creek near New Holland and the sum of the 

simulated daily mean flow for subwatersheds MA01 to MA12.

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

DAILY MEAN FLO

W

AT STATION 02172305, IN CUBIC FEET PER SECOND

New Holland

Sum of subbasins MA01–MA12

Figure 34. 

MAY AUG.

2007

NOV. AUG.

2008

FEB. MAY NOV. FEB. AUG.

2009

MAY NOV.
Watershed Model Uses 49

Figure 35. Simulated daily mean flow for (A) the concurrent period at McTier Creek near Monetta and the sum of the 

simulated daily mean flow for subwatersheds MA01 to MA06, and (B) the confirmation period at McTier Creek near New 

Holland and the sum of simulated daily mean flow for subwatersheds MA01 to MA12.

1,000

100

10

1

SIMULATED DAILY MEAN FLOW, IN CUBIC FEET PER SECOND

Figure 35. 

1,000

100

10

1

1 10 100 1,000

SUM OF SIMULATED DAILY MEAN FLOW FOR SUBBASINS MA01–MA12, IN CUBIC FEET PER SECOND

1 10 100 1,000

SUM OF SIMULATED DAILY MEAN FLOW FOR SUBBASINS MA01–MA06, IN CUBIC FEET PER SECOND

A. Station 02172300, McTier Creek near Monetta, SC (June 13, 2007–Sept. 30, 2009)

B. Station 02172305, McTier Creek near New Holland, SC (June 13, 2007–Sept. 30, 2009)
50 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

TOPMODEL output provides flow estimates from various 

surface and subsurface pathways (fig. 11). Those pathways 

include total in-stream flow, return flow, subsurface flow, 

overland saturation flow, infiltration-excess overland flow, 

impervious flow, and flow from water bodies (such as lakes 

and ponds). An example of the TOPMODEL estimates of 

these flow components is shown in the time-series plot in 

figure 36. Those assorted flows and constituent concentrations 

measured at various locations in the watershed can be used to 

assess constituent loadings as measured in the channel to help 

provide insight into how those total loads are being delivered 

to the stream. Initial assessments can be made using relatively 

conservative constituents and evaluated from a simple 

conservative mixing approach or other mixing approaches 

(Hornberger and others, 1994; Boyer and others, 1996). 

Estimating Water, Sediment, and Mercury 

Balances with GBMM

GBMM is one of the first models designed to simulate 

spatially explicit watershed mercury processing and fluxes 

from watersheds to surface-water systems. Therefore, aside 

from its ability to predict streamflow at assessment points 

along a stream network, an important feature of GBMM is 

its capacity to estimate daily mass balances for water, sediment, and mercury within each ArcGIS grid cell in a study 

watershed. This mass balance simulation feature was recently 

applied to assess GBMM’s long-term water balance response 

to inputs of diverse spatially explicit precipitation datasets 

when the model was previously calibrated using rain-gage data 

(Golden and others, 2010). 

Identifying Spatially Explicit Mercury Source 

Areas in Watersheds

Another feature of GBMM is its capacity to calculate the 

amount of mercury derived from each land-cover type in a 

watershed. Such spatially explicit characterization of mercury 

source areas is particularly useful in studies assessing the 

effects of land cover or climate change on water, sediment, 

and mercury fluxes. A current research application of GBMM 

focuses on estimating the response of mercury and nitrogen 

fluxes to land-cover changes in a Piedmont watershed in 

North Carolina. Initial model estimates from the basic case 

scenario (for example, current land cover) fall within the range 

of measured mercury concentrations at the stream gage, and 

land-cover change scenarios yield distinct changes in mercury 

fluxes (H.E. Golden, U.S. Environmental Protection Agency, 

oral commun., April 27, 2010). For example, when pasture 

land is converted to a suburbanized landscape, mercury loading to the watershed outlet increases due to increased flows 

and particulate transport from new impervious surfaces.

Figure 36. TOPMODEL flow components from simulation at McTier Creek near New Holland for the confirmation period.

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

SI

MULATED FLOW, IN CUBIC FEET PER SECOND

JUNE

JULY

AUG.

SEPT.

OCT.

NOV.

DEC.

JULY

AUG.

SEPT.

JAN.

FEB.

MAR.

APR.

MAY

OCT.

NOV.

DEC.

JUNE

JULY

AUG.

SEPT.

JAN.

FEB.

MAR.

APR.

MAY

OCT.

JUNE

2007 2008

EXPLANATION

2009

Total (qpred)

Return (qret)

Subsurface (qb)

Overland (qof)

Infiltration excess (qinf)

Impervious (qimp)

Water bodies (qsrip)
References Cited 51

Summary

As part of a larger scientific investigation to expand the 

understanding of linkages between hydrologic, geochemical, 

and ecological processes that drive fish-tissue mercury 

concentrations within the Edisto River Basin, two watershed 

hydrology models—the topography-based hydrological model 

(TOPMODEL) and the grid-based mercury model (GBMM)—

were calibrated and applied to the McTier Creek watershed. 

McTier Creek is a small headwater stream located in the 

Edisto River Basin and is a tributary to the South Fork Edisto 

River. The models were a collaborative effort between the 

U.S. Geological Survey (USGS) and the U.S. Environmental 

Protection Agency, National Exposure Research Laboratory. 

TOPMODEL and GBMM were calibrated independently 

but used the same meteorological data and the same period 

of record of observed data. Although the two models used 

the same datasets for calibration, no attempt was made to 

use the same calibration techniques that would be required 

if hydrologic model comparison was the goal of this study. 

Two USGS streamflow-gaging stations were available for 

comparison of observed daily mean flow with simulated daily 

mean flow: (1) 02172300, McTier Creek near Monetta, SC, 

and (2) 02172305, McTier Creek near New Holland, SC. The 

Monetta gage has historic record covering the period from 

February 2001 to September 2009. The New Holland gage, 

which is located at the outlet of the study reach, was established specifically for this investigation and has streamflow 

record available from June 2007 to September 2009. 

To assess the streamflow record at Monetta in the context 

of a longer flow period, comparisons of average monthly mean 

flows at Monetta were made with a long-term streamflowgaging station on the South Fork Edisto River. The data 

indicated that the yield of the average monthly mean flow 

for Monetta is similar to that of the South Fork Edisto River. 

Minimum monthly mean flows at South Fork Edisto for the 

complete period of record (about 70 years) were compared 

with those for the period of record that is concurrent with 

Monetta (2001 to 2009). The results showed that the 8-year 

period of record at Monetta captures the lowest flow period in 

about 70 years. In addition, the spring of 2003 tended to be a 

significantly wet period for the period of record at Monetta. 

Along with several years of more normal flows, the period 

of record available for model calibration at Monetta should 

provide for model calibrations that are rather robust with 

respect to encompassing a wide range of flow conditions.

A number of quantitative assessments (goodness-of-fit 

statistics) providing insight into how well the model simulations matched the observed daily mean flows were used in this 

investigation. The assessments included the Nash-Sutcliffe 

coefficient of model-fit efficiency index, Pearson’s correlation 

coefficient, the root mean square error, the bias, and the mean 

absolute error. Simulation periods for Monetta included 

February 2001 to September 2009 (calibration period) and 

a period that was concurrent with New Holland, which was 

June 2007 to September 2009 (concurrent period). The period 

simulated at New Holland (June 2007 to September 2009) 

was referred to in the text as the confirmation period. For 

the calibration period, TOPMODEL and GBMM tended to 

capture the variability and timing of the observed flows quite 

well. Although not very different, the goodness-of-fit statistics 

indicate that TOPMODEL tended to perform slightly better 

with a bias of 0.23 cubic foot per second (ft3/s), a root mean 

square error of 10.4 ft3/s, a mean absolute error of 5.34 ft3/s, a 

correlation coefficient of 0.72, and a Nash-Sutcliffe efficiency 

coefficient of 0.47 as compared to the corresponding values 

for GBMM of –1.13 ft3/s, 9.04 ft3/s, 6.87 ft3/s, 0.67, and 0.38, 

respectively. Both models tended to perform best under normal 

flow conditions and tended to perform worse during extreme 

conditions and with situations involving the complexity of 

balancing groundwater recession and streamflow when flows 

peak and recede rapidly. Simulated and observed flow data 

indicated that GBMM tended to underpredict flows during 

periods of sustained low flows. This is likely due to the issue 

of having to calibrate with a single groundwater recession 

coefficient that is applied to flows throughout a wide range of 

hydrologic conditions.

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56 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Appendix 1

Model Components in TOPMODEL

The version of TOPMODEL used in this investigation 

was documented by Kennen and others (2008), and much of 

the information included in this appendix comes from that 

paper. For a more detailed discussion of the mathematical 

underpinnings of TOPMODEL, see Beven and Kirkby (1979), 

Beven (1997), Hornberger and others (1998), Wolock (1993), 

or Beven (2001).

TOPMODEL is a process-oriented watershed hydrology 

model that systematically accounts for water from the time 

that it enters the watershed as precipitation until it leaves the 

watershed through evapotranspiration, by direct withdrawal, 

or as streamflow. TOPMODEL simulates snow accumulation 

and melt, evapotranspiration, streamflow derived from water 

that moves overland into the stream and water that moves 

through the subsurface into the stream, and routing of flow 

from delivery to the stream to the watershed outlet. Because 

of the characteristics of the McTier Creek watershed, the snow 

related and routing algorithms were not utilized in this study.

In the water balance, rain on a given day is used first 

to satisfy the potential evapotranspiration for the day. The 

remainder moves overland to a stream if the rain falls on 

impervious surface that is connected to a stream (qimp), soil 

that is already saturated (qof), or soil through which the water 

cannot infiltrate rapidly enough (qinf) (fig. 11). Precipitation 

that falls on a surface-water body is added to the streamflow 

(qsrip). The remaining water infiltrates the upper soil zone. 

Any water stored in the saturated subsurface zone is assumed 

to move downslope toward the stream channel and enters the 

stream as return flow (qret) in saturated areas and (or) subsurface flow (qb) at the streambanks. The portion of the subsurface water that drains into the stream depends on the volume 

in storage and the values of the TOPMODEL parameters. The 

major paths that water follows in the version of TOPMODEL 

used in this investigation are shown in figure 11 along with the 

abbreviation names, shown in the parentheses, as provided in 

the program’s output file. 

Precipitation

Precipitation is the main forcing function in 

TOPMODEL. For this study, spatial estimates of precipitation and temperature for the McTier Creek watershed were 

determined by inverse-distance weighting using data obtained 

from nearby National Weather Service stations (table 2; 

fig. 12). More robust methods are available, which take into 

account such factors as elevation (Hay, 1998). However, 

given the size of the McTier Creek watershed and the Coastal 

Plain environment as opposed to a more mountainous setting, 

it was concluded that the inverse-distance weighting procedure 

was sufficient. 

Evapotranspiration

Evapotranspiration is a function of the potential rate (the 

rate that would occur if unlimited water were available) and 

the actual amount of water that is available in the soil. Potential evapotranspiration is calculated using the Hamon formula 

(Hamon, 1961), the maximum possible clear-sky duration 

of sunshine, the mass density of water in air as a function of 

air temperature, and an empirical relation, which includes an 

empirical constant. Duration of sunshine is estimated from 

watershed latitude by calculating the solar declination and the 

sunset-hour angle (Keith and Kreider, 1978). Any precipitation 

not exceeding the potential evapotranspiration rate for a given 

day is assumed to be part of the actual evapotranspiration. 

If precipitation is insufficient to meet the potential evapotranspiration, then evapotranspiration depletes water from 

the root zone of the soil (as described by Beven and others, 

1995) until it is exhausted. The maximum root-zone water 

storage is estimated as a function of the root-zone depth and 

the available water capacity of the soil. For the McTier Creek 

watershed, the root zone was assumed to be 1.9 meters (m) 

thick based on information from Crow (2005) and calibration 

parameterization assessments using PEST (Doherty, 2005).

Impervious-Area Runoff

Impervious-area runoff is calculated as a function 

(effective portion) of the total impervious surface cover (ISC) 

in a watershed using the TR-55 curve-number method (Natural 

Resources Conservation Service, 1986). The value of ISC is 

treated as a starting point for the calculation of imperviousarea runoff because not all impervious areas of a watershed are 

effective in generating direct runoff. After evapotranspiration 

is removed from the daily rainfall, impervious-area runoff is 

computed for the effective ISC by assuming an initial runoff 

curve number for paved surfaces of 98. The runoff curve 

number is then adjusted (higher for wetter conditions, lower 

for drier conditions) on the basis of the 5-day antecedent 

rainfall. Wet antecedent conditions (5-day antecedent rainfall 

greater than 2.81 centimeters (cm) for the non-growing season 

or greater than 5.63 cm for the growing season) yield a curve 

number of 99.1, and dry conditions (5-day antecedent rainfall 

less than 1.28 cm for the non-growing season or less than 

3.58 cm for the growing season) yield a curve number as low 

as 95.3. Runoff is computed and assumed to enter the stream 

channel directly. Any water remaining (precipitation minus 

evapotranspiration and runoff) is distributed uniformly to the 

water budget that governs the pervious-area runoff components of the watershed.

Pervious-Area Runoff

In TOPMODEL, the major processes considered are 

subsurface flow, saturation overland flow (also known as 

Dunne overland flow (Dunne and Black, 1970)), return flow, 
Appendix 1 57

infiltration excess overland flow (also known as Horton 

overland flow (Horton, 1933)), and precipitation/evapotranspiration over water. The starting point for deriving expressions 

to compute subsurface flow, saturation overland flow, and 

return flow is the continuity equation, applied at a location 

in the watershed, and Darcy’s Law (Beven, 1984). If steadystate conditions with a spatially uniform recharge rate to the 

water table are assumed, continuity holds that the outflow 

from a location is equal to the inflow to that location minus 

the change in storage. Flow is a function of the surface area 

upslope from that location, the transmissivity of the saturated 

thickness, the hydraulic gradient, and the distance traversed by 

subsurface flow at the location.

As noted previously in equation 1, the transmissivity of 

the saturated thickness at a point is computed by assuming 

that saturated hydraulic conductivity decreases exponentially 

with depth (measured positively in the downward direction) as 

a function of a parameter, f, that controls the rate of decrease 

(Beven, 1984; Elsenbeer and others, 1992). A TOPMODEL 

convention is to use a scaling (or decay) parameter, m, to 

account for the vertical distribution of hydraulic conductivity 

over the soil column based on f and the drainable soil porosity. 

The value of m is given as

m = − (porosity field capacity) . ÷ f

The parameter, m, in equation 1–1 is arguably the single most 

important variable in determining the fit of the generated 

hydrograph to a measured hydrograph. Beven (2001) states 

that a physical interpretation of the decay parameter m is that it 

controls the effective depth or active storage of the catchment 

soil profile. A larger value of m effectively increases the active 

storage of the soil profile, whereas a small value generates a 

shallow effective soil with pronounced transmissivity decay.

The topographic wetness index (TWI; eq. 2) is based 

on the concept that topography defines the three-dimensional 

configuration of the gravitational effects on soil-moisture 

drainage (Wolock, 1993). A geographic information system 

(GIS) is used to compute the TWI from the digital topography 

(digital elevation model). The TWI is defined as the natural 

log of the contributing area draining to a point divided by the 

local slope at that point. As infiltrated water moves downslope 

in the subsurface, it collects in the topographically flatter 

areas where hillslope drainage converges. The gradient of 

downslope areas combined with the transmissivity of the soil 

profile at a location (soil hydraulic conductivity times soil 

depth) determines the ability of subsurface water to move 

farther downslope. The mean of these soil properties and the 

distribution of the TWI are the basis for the distribution of soil 

moisture (Kirkby and Chorley, 1967; Dunne and others, 1975; 

Beven, 1978; Burt and Butcher, 1985) and the generation of 

runoff from pervious areas. Figure 1–1 shows a graphical 

representation of the TWI distributions for the McTier Creek 

watershed. The dark areas on the TWI figure have the largest 

values and, therefore, are the most likely to become saturated.

TOPMODEL equations are expressed in terms of the 

saturation deficit for the entire watershed (average saturation 

deficit). The saturation deficit is conceptually and mathematically equivalent to the depth to the water table multiplied 

by the readily drained soil porosity. The saturation deficit at 

any location is determined by the average saturation deficit 

and the difference between the mean TWI and the value of 

the TWI at the location. Large values of the index indicate 

the locations within a watershed most likely to be saturated 

and produce overland flow and return flow. These locations 

are topographically convergent and have gentle slopes and 

low transmissivity; that is, they drain a large portion of the 

upslope area of the watershed and have limited capacity to 

conduct water downslope from the drained area. The scaling 

parameter, m, affects the range of variability in the saturation 

deficit over the watershed given the distribution of the TWI. 

For McTier Creek, the watershed was divided into 30 classes 

of TWI for the purpose of determining the values of saturation 

overland flow and return flow (fig. 1–2). Each class represents 

a range of TWI values for a percentage of the watershed. The 

range of TWI values in each class is narrow enough that the 

watershed area represented is assumed to act similarly in terms 

of hydrological response. The TWI classes are determined by 

subtracting the lowest TWI value in the watershed from the 

highest TWI value and then evenly dividing into the number 

of desired classes. TWI values for the entire watershed are 

then placed into their respective class. The average for each 

class is simply the sum of all TWI values divided by the 

number of TWI values stored in that class. The saturation 

deficit is calculated for each class of TWI. Any location in the 

watershed where the saturation deficit is less than or equal to 

zero is saturated and has the potential to produce saturation 

overland flow; any location where the saturation deficit is 

less than zero produces return flow. For TWI classes with a 

saturation deficit that is less than zero, saturation overland 

flow is equal to the difference between precipitation and 

evapotranspiration multiplied by the area represented by 

the TWI class, and return flow is the absolute value of the 

saturation deficit multiplied by the area represented by the 

TWI class. For TWI classes with a positive saturation deficit, 

the values of saturation overland flow and return flow are zero. 

The values of saturation overland flow and return flow for 

the entire watershed are computed by summing the values for 

each of the TWI classes.

Saturation Overland Flow

Saturation overland flow is generated from precipitation 

falling directly on saturated soil areas that are common where 

the water table rises to the land surface. The rise in the water 

table that creates saturated areas occurs because of infiltration 

of precipitation into the soil and (or) soil-water movement and 

accumulation downslope. Saturated areas commonly develop 

near existing stream channels and expand as rainfall increases 

during a storm; they are predicted by the TWI. TOPMODEL 

(1–1)
58 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

Figure 1–1. Topographic wetness indices for the McTier Creek watershed in South Carolina.

EXPLANATION

Topographic wetness index

1 to 4

4 to 5

5 to 6

6 to 7

7 to 8

8 to 9

9 to 12

12 to 15

15 to 21

SALUDA

LEXINGTON

AIKEN 

8136’

33

51’

33

48’

33

45’

81

33’

0 0.5 1 2 KILOMETERS

0 0.5 1 2 MILES

Base from National Hydrography Dataset, 1:100,000

ESRI Data and Maps, 2006

Albers equal area projection; central meridian -96 00 00; NAD 83 datum

Figure A1-2. 
Appendix 1 59

computes the amount of saturation overland flow by multiplying the amount of precipitation adjusted for evapotranspiration 

by the area of the watershed that is represented by classes of 

the TWI that have a saturation deficit that is less than or equal 

to zero.

Subsurface Flow

Return flow (Dunne and Black, 1970), one type of 

subsurface flow, is generated from downslope drainage of 

subsurface water and its subsequent emergence in saturated 

areas. The water table rises by vertical drainage of water from 

above or lateral drainage of water from other parts of the 

watershed. Where the contributions of water are sufficiently 

large, the water table rises to the land surface, the area 

becomes saturated, and return flow is produced. TOPMODEL 

computes the volume of return flow for each TWI class that 

has a negative saturation deficit by multiplying the absolute 

value of the saturation deficit by the area represented by the 

TWI class. A negative saturation deficit represents water above 

the land surface. 

Subsurface stormflow (Hewlett and Hibbert, 1967), 

another type of subsurface flow, is generated if the nearsurface soil zone is very transmissive (large saturated 

hydraulic conductivity) and hillslopes are steep. Where these 

two factors are present, this rapid subsurface flow occurs when 

infiltration rates are greater than precipitation rates, such as in 

well-vegetated areas. Dunne and Leopold (1978) also noted 

that runoff is produced from subsurface stormflow when a 

rainstorm causes the water table to rise near the stream while 

remaining relatively stationary under the higher part of the 

hillside. This rise near the stream causes an increase in the 

slope of the water table in that area and, according to Darcy’s 

Law, should result in an increase in the subsurface flow. In the 

computer code for the version of TOPMODEL used in this 

study, subsurface flow is the generic term used for the state 

variable qb. Some researches use the term base flow for low 

values of qb, while others use the term subsurface stormflow 

for high values of qb (D.M. Wolock, U.S. Geological Survey, 

written commun., June 2009). TOPMODEL does not conceptually split the subsurface stormflow and more traditional 

base flow (L.J. Kauffman, U.S. Geological Survey, written 

commun., March 2009). In addition, conceptually differentiating between return flow and subsurface stormflow also can 

be difficult; however, together, they are a major component 

of streamflow. In TOPMODEL, they are calculated by two 

separate but related algorithms.

Infiltration-Excess Overland Flow

Infiltration-excess overland flow is generated by 

overland flow that is produced when precipitation rates 

exceed infiltration rates. This type of overland flow typically 

occurs during periods of high rainfall intensity in areas of 

low soil permeability or in disturbed, compacted, or poorly 

vegetated areas. Infiltration-excess overland flow is computed 

using the Green-Ampt equation (Green and Ampt, 1911) as 

implemented by Beven (1984). Rather than use only the mean 

Figure 1–2. Relative frequency distribution of topographic wetness indices values for McTier Creek watershed 

in South Carolina.

30

25

20

15

10

5

0

1.71 2.82 3.92 5.02 6.13 7.25 8.37 9.51 10.65 11.77 12.89 14.00 15.15 16.17

RELATIVE FREQUENCY, IN PERCENTAGE OF

WATERSHED AREA

Ln(a/tanβ) VALUE, IN Ln(METERS)

Appendix 1-1.
60 Simulation of Streamflow in the McTier Creek Watershed, South Carolina

soil permeability in the calculation of the infiltration excess, 

calculations are based on the mean soil permeability and an 

expected variance of the log of soil permeability.

Lake Storage

The McTier Creek watershed has a number of small lakes 

or ponds (fig. 1). Lake or pond storage can dampen and delay 

surface runoff in some watersheds. To account for the lakestorage effects or delays in runoff, the portion of watershed 

area upstream from any lakes was determined. A decay 

function was then applied to a fraction of the runoff equivalent 

to the lake-affected fraction of the watershed. The remaining 

runoff was treated as previously described. In the version of 

TOPMODEL being used in this investigation, lake storage is 

represented by the variable dsrip. A positive dsrip indicates 

water being stored in the lakes, and a negative dsrip indicates 

water being released from the lakes (L.J. Kauffman, U.S. Geological Survey, written commun., September 2, 2009). 

Open-Water Bodies

In TOPMODEL, precipitation falling directly on openwater bodies, such as lakes, ponds, and the stream-channel 

water surface, also are considered in the water budget. For the 

open-water bodies, evapotranspiration is always satisfied, and 

any precipitation generates streamflow. With respect to the 

output from the version of TOPMODEL used in this investigation, the variable qsrip represents streamflow directly from 

open-water bodies (fig. 36; L.J. Kauffman, U.S. Geological 

Survey, written commun., September 2, 2009). When precipitation is greater than the potential evapotranspiration (PET), 

qsrip is positive and increases the total predicted streamflow. 

On days when PET is greater than the precipitation, qsrip

is negative and represents evaporation directly from the 

open-water bodies. The evaporation represented by negative 

qsrip is accounted for by being proportionally taken from qb

(subsurface flow) and qret (return flow).

Appendix 2

Model Components of GBMM: Hydrology Module

The main components of GBMM’s hydrology module 

are similar to those of the TOPMODEL simulations and 

follow from the GBMM Streamflow Concepts section of the 

report. This appendix discusses the main model components in 

greater detail.

Precipitation

Precipitation is the primary forcing function for GBMM’s 

hydrology module. The best possible estimates of rainfall and 

temperature, which influence evapotranspiration calculations, 

within the watershed are required. Precipitation inputs to 

GBMM are the same as those used for TOPMODEL, which 

follow an inverse-distance weighting scheme using data 

obtained from nearby NWS stations (see Data Collection 

section of the report).

Evapotranspiration

Potential evapotranspiration is estimated using the 

Hamon formula (Hamon, 1961). This calculation is used 

along with a vegetation cover factor for each land-cover 

type during growing and non-growing seasons to calculate 

actual evapotranspiration. 

where 

	 ET is the actual evapotranspiration 

(in centimeters), 

PET is the Hamon-derived potential 

evapotranspiration (in centimeters), 

VCF is the vegetation cover factor (derived from 

Soil and Water Assessment Tool (SWAT) 

land-cover coefficients for both the 

growing and non-growing seasons), and 

WP is the soil water content at wilting point 

(in centimeters). 

Wilting point is calculated using Neitsch and others, (2005):

0.4 , WP mc BD d = ∗ ∗ ∗ unsat

where mc is the percentage of clay content in the soil layer, 

BD is the bulk density of the soil (in grams per cubic centimeters), and dunsat is the unsaturated soil depth (in meters). If, however, the soil water content is in excess of the field capacity 

water content for each time step, percolation to groundwater 

(Pc, in centimeters per day) is estimated, using the formula

( ) , P S c w excess =

where Sw(excess) is drainage excess water in the unsaturated zone 

calculated by

( ) 0 , w excess w tot S S P R ET FC = + − − −

where FC is water content in the soil at field capacity (in centimeters), which is found with the following equation:

min * , ( ), (2–1) ET PET VCF S P R WP = w tot o + − −

(2–2)

(2–3)

(2–4)
Appendix 2 61

( ), FC WP AWC d = + ∗ unsat

where AWC is the available water capacity in unsaturated soil 

(in centimeters per meter).

Impervious-Area Runoff

For impervious surfaces, modified curve-number algorithms are used, and ranges of impervious land cover for urban 

areas can be found in Neitsch and others (2005). Calculations 

for curve-number runoff are found in the Pervious-Area 

Runoff section of this appendix. Impervious urban land cover 

is categorized into two groups: (1) grid cells hydrologically 

connected to the watershed’s surface and subsurface drainage area and (2) grid cells not hydrologically connected to 

the drainage area. Separate curve-number calculations are 

implemented on impervious land cover depending on this 

categorization. A curve number of 98 is used for all impervious surfaces directly connected to the drainage area; however, 

for disconnected portions of impervious grids, modified 

equations are used:

[ ]

[ ] 2 * 1 98 * 1

for ( 0.30),

tot dcon

con

tot

CN imp imp CN

imp

imp

− + = −

>

where 

CN is the composite curve number, 

CN2 is the pervious curve number, 

imptot is the fraction of the grid area that is 

impervious (both directly connected 

and disconnected),

impcon is the fraction of the grid area that is 

impervious and hydraulically connected to 

the drainage system, and 

impdcon is the fraction of the grid area that is 

impervious but not hydraulically connected 

to the drainage system.

Pervious-Area Runoff

For pervious surfaces, surface runoff in GBMM is estimated using the modified SCS-CN method. A curve-number 

estimate is calculated for each 30-m grid cell using 

the formula:

2540 25.4, DS CN = −

where Ds is the detention storage (in centimeters), and CN is 

the curve number. Curve numbers for the standard average 

moisture conditions are estimated by way of select vegetation and soil combinations (Haith and others, 1992) but are 

modified based upon antecedent moisture condition. Vegetation characteristics are derived from the NLCD 2001 LandCover Data (Homer and others, 2004), and soil data include 

the hydrologic soil group from the Soil Survey Geographic 

(SSURGO) Data Base (Natural Resources Conservation Service, 2008). 

Curve-number modifications for dry (CN1) and wet (CN3) 

conditions are

2

1

2

 and

(2.334 0.01334* )

CN CN

CN = −

2

3

2

. (0.4036 0.0059* )

CN CN

CN = +

The curve number used for each day is a linear function 

of the 5-day antecedent moisture:

1

5 ,

5

( ),

t

d tot n

n t

A P

−

= −

= ∑

where A5d is the 5-day antecedent moisture (in centimeters), 

and Ptot is the total available input water at the surface (for 

example, rainfall + snowmelt, in centimeters). The value of 

A5d determines the thresholds above and below which CN3 

or CN1 will be implemented, respectively. These values vary 

depending on whether the simulation time step occurs during 

the growing season or the dormant season. Therefore, the four 

critical values of A5d, (growing and non-growing season and 

threshold values for CN3 and CN1) can be adjusted during the 

hydrologic calibration process. Runoff from the curve number 

is then routed as described in the GBMM Streamflow Concepts section of this report.

Lake Storage

Lake storage and water flux can be an important 

component to the hydrologic balance in many watersheds. The 

current version of GBMM maintains a place holder for lake, 

wetland, and pond water balances; however, these balances 

currently cannot be simulated in GBMM.

(2–5)

[ ]

2 * 1 98 * 

2 2 1

for ( 0.30) or

dcon dcon

tot

con

tot

imp imp CN imp

CN

imp

imp

    − + +         = −

≤

(2–6)

(2–7)

(2–8)

(2–9)

(2–10)

(2–11)

Manuscript approved on September 22, 2010

Prepared by:

USGS Enterprise Publishing Network

Raleigh Publishing Service Center

3916 Sunset Ridge Road

Raleigh, NC 27607

For additional information regarding this publication, contact:

USGS South Carolina Water Science Center

720 Gracern Road, Suite 129

Columbia, SC 29210–7651

phone: 803–750–6100

http://sc.water.usgs.gov/
Feaster and others—Simulation of Streamflow in the McTier Creek Watershed, South Carolina—Scientific Investigations Report 2010–5202