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

National Exposure Research Laboratory

Data Visualization, Time-Series Analysis, and Mass-Balance 

Modeling of Hydrologic and Water-Quality Data for the 

McTier Creek Watershed, South Carolina, 2007–2009

National Water-Quality Assessment Program

Open-File Report 2011–1209

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 (photographs by Toby D. Feaster, USGS). Screen capture of a TOPMODEL 

worksheet from the report.
Data Visualization, Time-Series Analysis, and 

Mass-Balance Modeling of Hydrologic and Water-Quality 

Data for the McTier Creek Watershed, 

South Carolina, 2007–2009

By Stephen T. Benedict, Paul A. Conrads, Toby D. Feaster, Celeste A. Journey, Heather E. Golden, 

Christopher D. Knightes, Gary M. Davis, and Paul M. Bradley

National Water-Quality Assessment Program

Open-File Report 2011–1209

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

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

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Benedict, S.T., Conrads, P.A., Feaster, T.D., Journey, C.A., Golden, H.E., Knightes, C.D., Davis, G.M., and Bradley, P.M., 

2012, Data visualization, time-series analysis, and mass-balance modeling of hydrologic and water-quality data for 

the McTier Creek watershed, South Carolina, 2007–2009: U.S. Geological Survey Open-File Report 2011–1209, 21 p. 
iii

Contents

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

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

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

Description of Study Area ...................................................................................................................2

Measured and Modeled Data Used in the McTier Creek Data Viewer................................................4

Measured Water-Quality Data............................................................................................................4

Measured Hydrologic Data.................................................................................................................4

Model Output Data................................................................................................................................4

TOPMODEL....................................................................................................................................4

TOPLOAD and TOPLOAD-H........................................................................................................8

Load Estimator (LOADEST).........................................................................................................8

Grid-Based Mercury Model (GBMM) ......................................................................................8

Visualizing Ecosystems for Land Management Assessment (VELMA) ..............................9

Features of the McTier Creek Data Viewer ..............................................................................................9

Time-Series and Scatter Plots of Selected Hydrologic and Water-Quality Data.....................10

Comparison Plots of Selected Model Simulations........................................................................10

Summary........................................................................................................................................................15

Selected References...................................................................................................................................16

Appendix........................................................................................................................................................18

Mass-Balance Model.........................................................................................................................18

TOPLOAD Model .................................................................................................................................19

TOPLOAD-H Model.............................................................................................................................20

Figures

 1. Map showing location of the McTier Creek watershed study area in Aiken 

County, South Carolina ...........................................................................................................3

 2. Diagram defining selected water-source variables from TOPMODEL................................6

 3. Screen capture from the McTier Creek Data Viewer showing “Title

Sheet” worksheet .................................................................................................................12

 4. Screen capture from the TOPMODEL worksheet showing dropdown menu 

of selected constituent to be shown with the measured flow data. ............................12

 5. Screen capture from the TOPMODEL worksheet showing selected constituent 

concentration with the TOPMODEL simulated flow components.................................13

 6. Screen capture from the scatter plot worksheet showing scatter plots of 

the selected constituent and various measured flow and simulated 

flow components...................................................................................................................13

 7. Screen capture from the model comparison worksheet showing the measured 

and simulated flows from TOPMODEL, GBMM, and VELMA along with the 

selected constituent by season..........................................................................................14

 8. Screen capture from the model comparison worksheet showing the measured 

and simulated loads from TOPLOAD-H, LOADEST, GBMM, and VELMA.....................14

 A1. Screen capture from the TOPLOAD worksheet showing input table for 

manually assigning concentrations to the TOPMODEL flow components..................19

 A2. Schematic showing the partitioning of the ground-water flow component .................20
iv

Tables

 1. Measured in-stream hydrologic and water-quality data included in the McTier 

Creek Data Viewer collected from the New Holland streamflow-gaging station, 

June 2007 to August 2009................................................................................................................5

 2. Simulated hydrologic time-series data included in the McTier Creek Data 

Viewer for the New Holland streamflow-gaging station...........................................................7

 3. Simulated time-series water-quality loads included in the McTier Creek Data 

Viewer for the New Holland streamflow-gaging station...........................................................7

 4. Description of selected worksheets and applications included in the McTier 

Creek Data Viewer..........................................................................................................................11
v

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

mile (mi) 1.609 kilometer (km)

square mile (mi2

) 2.590 square kilometer (km2)

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

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

or National Geodetic Vertical Datum of 1929 (NGVD 29).
vi

Acronyms and Variables Used in this Report

DEM Digital elevation map

GBMM Grid-Based Mercury Model

GIS Geographic information system

LOADEST LOAD ESTimator model

NAWQA National Water-Quality Assessment Program

NRCS-CN National Resource Conservation Service curve number

TOPMODEL TOPography-based hydrological MODEL

TOPLOAD Water-quality load model developed from TOPMODEL

TOPLOAD-H Water-quality load model developed from TOPMODEL with Hornberger’s ground-water partitioning algorithm

USGS U.S. Geological Survey

VELMA Visualizing Ecosystems for Land Management Assessment model

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)
Data Visualization, Time-Series Analysis, and Mass-Balance 

Modeling of Hydrologic and Water-Quality Data for the 

McTier Creek Watershed, South Carolina, 2007–2009

By Stephen T. Benedict,1 Paul A. Conrads,1 Toby D. Feaster1 Celeste A. Journey,1 Heather E. Golden,2

Christopher D. Knightes,3

 Gary M. Davis,3 and Paul M. Bradley1

1

U.S. Geological Survey.

2

U.S. Environmental Protection Agency, Office of Research and 

Development, Ecological Exposure Research Division, Cincinnati, Ohio.

3

U.S. Environmental Protection Agency, Office of Research and 

Development, Ecosystems Research Division, Athens, Georgia.

Abstract

The McTier Creek watershed is located in the headwaters 

of the Edisto River Basin, which is in the Coastal Plain region 

of South Carolina. The Edisto ecosystem has some of the 

highest recorded fish-tissue mercury concentrations in the

United States. In an effort to advance the understanding of 

the fate and transport of mercury in stream ecosystems, the 

U.S. Geological Survey, as part of its National Water-Quality 

Assessment Program, initiated a field investigation of mercury

in the McTier Creek watershed in 2006. The initial efforts of 

the investigation included the collection of extensive hydrologic and water-quality field data, along with the development

of several hydrologic and water-quality models. This series of 

measured and modeled data forms the primary source of information for this investigation to assess the fate and transport of 

mercury within the McTier Creek watershed.

The visualization of data is an important tool for understanding the trends and influencing variables of an ecosystem.

One of the initial efforts for evaluating the hydrology and 

water quality in the McTier Creek watershed was the development of a digital spreadsheet for systematically visualizing 

and interrogating selected hydrologic, water-quality, and 

model data. This report briefly describes the development and

application of the McTier Creek Data Viewer. The extensive

database incorporated into the data viewer also provides a 

means for analysis and the development of analytical tools that 

may provide insights into the water quality within the McTier 

Creek watershed. One such application was the development 

of a simple water-quality load model that utilized a massbalance equation in conjunction with the topography-based 

hydrological model (TOPMODEL) developed to simulate 

flow in the McTier Creek watershed. Several variations of

this simple load model were developed and are presented in 

the report.

Introduction

The bioaccumulation of mercury in the food chain of 

stream ecosystems is a public health concern in many parts 

of the United States (Mergler and others, 2007; Swain and 

others, 2007) and is one of the leading causes for impairment of the Nation’s water bodies (U.S. Environmental 

Protection Agency, 2008). Inorganic mercury is typically 

delivered to stream ecosystems through atmospheric deposition (Grigal, 2002). Under reducing conditions, inorganic 

mercury can be converted to methylmercury, which is highly 

toxic and biomagnifies at the top of the food chain (Wiener

and others, 2003). An understanding of the fate and transport 

of methylmercury in stream ecosystems is critical. The U.S. 

Geological Survey (USGS) through its National Water-Quality 

Assessment (NAWQA) Program has been conducting field

investigations of mercury with the goal of advancing the 

knowledge and ultimately developing tools to assist water 

officials in managing and mitigating the adverse effects of

mercury in stream ecosystems.

The McTier Creek watershed is located in the headwaters 

of the Edisto River Basin in Aiken County, South Carolina. 

The Edisto River has some of the highest recorded fish-tissue

mercury concentrations in the United States (Scudder and 

others, 2009). To better understand why these high concentrations exist, the USGS collected hydrologic and water-quality

data in the McTier Creek watershed including continuous 

streamflow at several streamflow-gaging stations and numerous discrete samples for 48 water-quality constituents over a 

30-month period (Bradley and others, 2010; 2011). 

In addition to the field data, several hydrologic and

water-quality models were developed for the McTier Creek 

watershed. These models include the following:

•	 GBMM—Grid-Based Mercury Model (Dai and others, 

2005; Feaster and others, 2010);

•	 VELMA—Visualizing Ecosystems for Land Management Assessment (A. Abdelnour, Georgia Institute of 

Technology, written commun., 2011; G. Davis and 

C. Knightes, U.S. Environmental Protection Agency, 

written commun., 2011; H. Golden, U.S. Environmental Protection Agency, written commun., 2011);
2 Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed

•	 LOADEST—LOAD ESTimator model (Runkel and 

others, 2004; C. Journey, U.S. Geological Survey, written commun., 2010); and

•	 TOPMODEL—TOPography-based hydrological 

MODEL (Wolock, 1993; Feaster and others, 2010).

These models provide tools to evaluate the hydrology and 

the fate and transport of mercury and other water-quality constituents within the McTier Creek watershed. The hydrologic 

and water-quality field data, as well as the modeled flow data,

for the watershed collectively comprise an extensive resource

for understanding the chemical, biological, and hydrologic 

characteristics that influence the methylation, transport, and

bioaccumulation of mercury in stream ecosystems.

As with any research endeavor, the visualization of data 

can be an important tool for evaluation of the hydrologic and 

water-quality trends and influencing variables of an ecosystem. Therefore, the McTier Creek Data Viewer was developed 

to integrate the various measured hydrologic and water-quality 

data and simulated model data. The McTier Creek Data 

Viewer provides a spreadsheet application so researchers can 

quickly visualize and interrogate the data and model output for 

the McTier Creek watershed and also provides a foundation 

for the development of analysis tools that may give insight 

into the quality of water in the McTier Creek watershed. One 

such application was the development of a simple waterquality load model that utilized a mass-balance equation in 

conjunction with the hydrologic simulations from the McTier 

Creek TOPMODEL (Feaster and others, 2010). Several 

variations of this load model were developed. One variation, 

called TOPLOAD, used the unadjusted TOPMODEL hydrologic data. A second variation, called TOPLOAD-H, modified

the subsurface hydrologic components with a ground-water 

partitioning algorithm presented in Hornberger and others 

(1994), hence the “H” in TOPLOAD-H. A detailed comparison of TOPLOAD and TOPLOAD-H with the other waterquality models developed in the McTier Creek investigation 

can be found in Golden and others (2012).

Purpose and Scope

The purposes of this report are to briefly describe the

(1) measured and modeled hydrologic and water-quality data 

used in the development of the McTier Creek Data Viewer; 

(2) development and application of the data viewer used to 

visualize trends in measured and modeled hydrologic and 

water-quality data associated with the McTier Creek watershed investigation of mercury; and (3) development of the 

TOPLOAD and TOPLOAD-H water-quality load models for 

the McTier Creek watershed based on a mass-balance equation in conjunction with the hydrologic simulations from the 

TOPMODEL. Plots of load computations for TOPLOAD, 

TOPLOAD-H, LOADEST, GBMM, and VELMA were developed in the data viewer, and selected results are presented in 

this report.

An important role of the USGS mission is to provide 

scientific information for the effective management of the

Nation’s water resources. The techniques presented in this 

report demonstrate how valuable information can be extracted

from disparate databases of continuous time-series data, 

non-periodic discrete data, and model simulation output into 

a user-friendly spreadsheet application to meet the needs of 

researchers. The techniques are readily applicable to other systems for evaluation of historical data and simulation models. 

Description of Study Area

McTier Creek is a small headwaters 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 mi2

 in Aiken County, South Carolina, and is 

designated by the 12-digit hydrologic unit code 030502040102 

(Eidson and others, 2005). The study area is primarily rural, 

with land-cover categories that include 50 percent forest, 

20 percent grassland/herbaceous, 16 percent agriculture, 8 percent wetland, 5 percent developed, and about 1 percent open 

water (National Land Coverage Data 2001; Homer and 

others, 2004).

The McTier Creek watershed lies within the inland part 

of the Coastal Plain Physiographic Province, known as the 

Sand Hills (fig. 1), in South Carolina (Vigil and others, 2000;

Griffith and others, 2002). 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 marks the transition from the Piedmont to the upper Coastal Plain (Cooke, 1936). The McTier 

Creek watershed displays transitional characteristics in which 

the upper part of the watershed has Piedmont characteristics 

with steep gradients and rock outcrops, transitioning to a lower 

gradient stream with riparian floodplains characteristic of the

Coastal Plain. 

The surficial geology of the McTier Creek watershed is

dominated by an outcrop of the highly permeable sediments of 

the Tertiary sand aquifer that covers much of the southwestern 

part of the upper Coastal Plain in South Carolina. The Tertiary 

sand aquifer within this region is noted for high ground-water 

recharge rates, steep ground-water potentiometric gradients, 

and substantial ground-water contributions to total streamflow

(Aucott and Speiran, 1985). The prominent contribution of 

ground water to the hydrology of the McTier Creek watershed 

is considered an important factor in the fate and transport of 

mercury within the system (Bradley and others, 2010). There 

are two USGS streamflow-gaging stations located in the

McTier Creek watershed: station 02172300, McTier Creek 

near Monetta, South Carolina, and station 02172305, McTier 

Creek near New Holland, South Carolina (fig. 1). Hereafter,

these stations will be referred to as Monetta and New Holland, respectively. Data from these streamflow-gaging stations

provide a valuable resource for understanding the hydrology 

of the McTier Creek watershed.
Introduction 3

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’; datum NAD 83

South

McTier

Creek

Gully

Creek

Fork Edisto

River

20

SALUDA

AIKEN

02172300

0 1 2 KILOMETERS 0.5

0 0.5 1 2 MILES

02172305

USGS streamflow-gaging station

 and number

EXPLANATION

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

[USGS, U.S. Geological Survey]
4 Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed

Measured and Modeled Data Used in 

the McTier Creek Data Viewer

An extensive set of measured and modeled data was

collected to investigate the fate and transport of mercury and 

other water-quality constituents within the McTier Creek 

watershed. Selected data were compiled into the McTier Creek 

Data Viewer including water-quality and hydrologic field measurements and model data from TOPMODEL, TOPLOAD, 

TOPLOAD-H, LOADEST, GBMM, and VELMA. A brief 

description of the selected data is provided in this section. The 

data compiled in the McTier Creek Data Viewer are a subset 

of the larger database for the McTier Creek watershed, which 

can be accessed at http://pubs.usgs.gov/sir/2012/5173/ (Journey and others, 2012).

Measured Water-Quality Data

Sampling of water quality was conducted at the McTier 

Creek watershed from June 2007 to August 2009. Measurements were made for in-stream bimonthly samples, in-stream 

time-series samples over selected hydrographs, and watershed synoptic samples to define the spatial variation of water

quality within the surface water, ground water, and riparian 

wetlands. The in-stream bimonthly and time-series samplings 

included 45 samples collected primarily at the USGS New 

Holland streamflow-gaging station (fig. 1). The synoptic

samplings included 42 samples collected at selected locations 

throughout the watershed (Bradley and others, 2011). All samples were collected and analyzed according to USGS protocols 

(Brigham and others, 2009). Collected water-quality data 

included about 450 discrete measurements of 48 constituents. 

The in-stream water-quality data were the primary data used in 

the McTier Creek Data Viewer to assess the relation between 

hydrologic factors and selected water-quality measurements. 

Measured Hydrologic Data

Streamflow data were collected from the Monetta and

New Holland streamflow-gaging stations (fig. 1). Monetta had

a period of record from October 1995 to September 1997 and 

from February 2001 to September 2009. New Holland was 

established specifically for the McTier Creek watershed study

with a period of record from June 2007 to September 2009. 

Streamflow data at both gaging stations were continuously

collected at 15-minute intervals using standard techniques 

(Rantz and others, 1982). Streamflow data collected from

June 2007 to August 2009 are the primary hydrologic data in 

the data viewer, particularly from New Holland—the primary 

in-stream water-quality sampling station. The measured waterquality and hydrologic data in the McTier Creek Data Viewer 

are listed in table 1.

Model Output Data

Computerized process-based models can be useful tools 

to gain insight into complex ecosystem processes. The McTier

Creek watershed investigation developed several hydrologic 

and (or) water-quality models, including TOPMODEL, TOPLOAD, TOPLOAD-H, LOADEST, GBMM, and VELMA. 

There are specific uses and limitations associated with each

model; together the models are useful for testing various 

hypotheses regarding the McTier Creek watershed. The 

worksheet “ReleaseNotes” in the McTier Creek Data Viewer 

provides references on the model configuration being used in

the data viewer. The models, simulation period, and the hydrologic and water-quality model outputs are listed in tables 2 

and 3, respectively. Brief descriptions of each model are 

described herein.

TOPMODEL

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 semidistributed 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 stormwater flow is generated if the nearsurface soil zone is very transmissive (large saturated hydraulic conductivity) and if gravitational gradients (slopes) are 

steep. Whipkey (1965) defined subsurface stormwater flow as

underground stormwater flow that reaches the stream channel

without entering the ground-water storage zone. 

TOPMODEL is a process-based watershed hydrology 

model that systematically accounts for water as it enters the 

watershed as precipitation (ppt) until it leaves the watershed 

through evapotranspiration (pet), by direct withdrawal, or as 

streamflow (qpred) (fig. 2). In the water balance, precipitation on a given day is used first to satisfy the potential evapotranspiration for the day. The remainder moves overland to a 

stream if the precipitation falls on an 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). 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 stream 
Table 1. Measured in-stream hydrologic and water-quality data included in the McTier Creek Data Viewer collected from 

the New Holland streamflow-gaging station, June 2007 to August 2009.

 Constituent Units

 Time-Series Hydrologic Data

Streamflow cubic feet per second

 Discrete In-Stream Water-Quality Data

Air temperature Degrees Celsius

Water temperature Degrees Celsius

Field pH Standard units

Field specific conductance Microsiemens per centimeter

Laboratory specific conductance Microsiemens per centimeter

Laboratory alkalinity Milligrams per liter as calcium carbonate

Dissolved ammonia Milligrams per liter

Dissolved calcium Milligrams per liter

Dissolved chloride Milligrams per liter

Dissolved iron Micrograms per liter

Dissolved magnesium Milligrams per liter

Dissolved nitrate plus nitrite Milligrams per liter

Dissolved nitrite Milligrams per liter

Dissolved organic carbon Milligrams per liter

Dissolved orthophosphate Milligrams per liter

Dissolved oxygen concentration Milligrams per liter

Dissolved potassium Milligrams per liter

Dissolved silica Milligrams per liter

Dissolved sodium Milligrams per liter

Dissolved sulfate Milligrams per liter

Total nitrogen Milligrams per liter

Total phosphorus Milligrams per liter

Suspended inorganic carbon Milligrams per liter

Suspended organic carbon Milligrams per liter

Suspended sediment Milligrams per liter

Suspended sediment finer than 63 microns Percent

Suspended total carbon Milligrams per liter

Suspended total nitrogen Milligrams per liter

Filtered methylmercury Nanograms per liter

Filtered total mercury Nanograms per liter

Particulate methylmercury Nanograms per liter

Particulate total mercury Nanograms per liter

Total mercury (filtered plus particulate total mercury) Nanograms per liter

Hydrophilic acid to specific ultraviolet absorbance ratio Fraction

Hydrophilic acids Percent

Hydrophobic organic acid to specific ultraviolet absorbance ratio Fraction

Hydrophobic organic acids Percent

Measured and Modeled Data Used in the McTier Creek Data Viewer 5
Table 1. Measured in-stream hydrologic and water-quality data included in the McTier Creek Data Viewer collected from 

the New Holland streamflow-gaging station, June 2007 to August 2009.—Continued

 Constituent Units

 Discrete In-Stream Water-Quality Data—Continued

Transphillic acid to specific ultraviolet absorbance ratio Fraction

Transphillic acids Percent

Ash-free phytoplankton biomass Milligrams per liter

Chlorophyll a Micrograms per liter

Pheophytin a Micrograms per liter

Phytoplankton biomass as ash weight Milligrams per liter

Phytoplankton biomass as dry weight Milligrams per liter

Computed ultraviolet absorbance at 254 nanometers Per centimeter (corrected for iron concentration)

Specific ultraviolet absorbance Milligrams per liter DOC per meter

Ultraviolet absorbance at 254 nanometers Per centimeter

Ultraviolet absorbance at 365 nanometers Per centimeter

6 Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed

Precipitation (ppt) Evapotranspiration (pet)

Land surface

Infiltration-excess

overland flow (qinf)

Water table

Subsurface flow (qb)

(Includes traditional base 

flow and subsurface

storm flow.)

Potential regions for 

overland saturation flow (qof)

and return flow (qret)

Stream

Total flow in stream (qpred)

Open-water 

bodies (qsrip)

Impervious flow (qimp)

Figure 2. Definition of selected water-source variables from TOPMODEL (modified from Wolock, 1993).
Measured and Modeled Data Used in the McTier Creek Data Viewer 7

Table 2. Simulated hydrologic time-series data included in 

the McTier Creek Data Viewer for the New Holland streamflowgaging station.

[TOPMODEL, Topography-Based Hydrological Model; GBMM, Grid-Based 

Mercury Model; VELMA, Visualizing Ecosystems for Land Management 

Assessment Model]

Variable Variable definition Units

Selected TOPMODEL Output

(Wolock, 1993; Feaster and others, 2010)

Simulation Period: February 7, 2001 through September 30, 2009

acsat Percent of the area predicted to 

be saturated Percent

aversz Average (over all wetness index

bins) storage in the root zone Millimeters per day

avesuz

Average (over all wetness index

bins) storage in the unsaturated zoneMillimeters per day

pet Potential evapotranspiration Millimeters per day

pettot Actual evapotranspiration Millimeters per day

ppt Precipitation Millimeters per day

qb Base flow Millimeters per day

qimp Flow from impervious areas Millimeters per day

qinf Infiltration excess Millimeters per day

qof Overland flow Millimeters per day

qpred Total predicted flow at basin outlet Millimeters per day

qret Return flow Millimeters per day

qrip Flow from open-water bodies Millimeters per day

quz Flow in unsaturated zone Millimeters per day

S Average saturation deficit Millimeters per day

Selected GBMM Output 

(Dai and others, 2005; Feaster and others, 2010)

Simulation Period: June 13, 2007 through September 30, 2009

Evap Evapotranspiration for the day Centimeters per day

Gout Groundwater outflow, base flow Centimeters per day

Gwat Groundwater storage Centimeters per day

Perc Percolation to the shallow 

ground water

Centimeters per day

Ptot Total precipitation (rain + snowmelt) for the day

Centimeters per day

Roff Surface runoff for the day Centimeters per day

Swat Soil water storage Centimeters per day

Seep Seepage to the deep 

ground water

Centimeters per day

Total flow Total predicted flow at basin outlet Centimeters per day

Selected VELMA Output

(A. Abdelnour, Georgia Institute of Technology, 

written commun., 2011; 

G. Davis and C. Knightes, U.S. Environmental Protection Agency, 

written commun,, 2011)

Simulation Period: June 13, 2007 through September 30, 2009

Discharge Total predicted flow at basin outlet Cubic feet per 

second per day

Table 3. Simulated time-series water-quality loads included in 

the McTier Creek Data Viewer for the New Holland streamflowgaging station.

[TOPLOAD, Water-quality load model developed from TOPMODEL; TOPLOAD-H, Water-quality load model developed from TOPMODEL with Hornberger’s (Hornberger and others, 1994) groundwater partitioning algorithm; 

GBMM, Grid-Based Mercury Model; VELMA, Visualizing Ecosystems for 

Land Management Assessment Model; LOADEST, LOAD ESTimator model]

Constituent Units

TOPLOAD and TOPLOAD-H

(see appendix)

Simulation period: June 13, 2007 through September 30, 2009

Dissolved calcium Kilograms per day

Dissolved chloride Kilograms per day

Dissolved sulfate Kilograms per day

Filtered total mercury Milligrams per day

Dissolved sodium Kilograms per day

Dissolved organic carbon Kilograms per day

Total mercury (filtered

plus particulate total 

mercury)

Milligrams per day

GBMM

(Dai and others, 2005; Feaster and others, 2010)

Simulation period: June 13, 2007 through September 30, 2009

Total mercury Milligrams per day

Total suspended solids Kilograms per day

VELMA

(A. Abdelnour, Georgia Institute of Technology, 

written commun., 2011

G. Davis and C. Knightes, U.S. Environmental

Protection Agency, written commun, 2011)

Simulation period: June 13, 2007 through September 30, 2009

Total mercury Milligrams per day

Dissolved organic carbon Kilograms per day

Dissolved inorganic 

nitrogen Kilograms per day

Dissolved organic nitrogen Kilograms per day

LOADEST

(Runkel and others, 2004)

Simulation period: October 1, 2004 through September 30, 2009

Filtered methylmercury Milligrams per day

Filtered total mercury Milligrams per day

Particulate total mercury Milligrams per day

Particulate methylmercury Milligrams per day

Total mercury (filtered

plus particulate total 

mercury)

Milligrams per day

Dissolved organic carbon Kilograms per day

Suspended sediment Kilograms per day

Particulate organic carbon Kilograms per day

Dissolved chloride Kilograms per day

Dissolved sulfate Kilograms per day
8 Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed

banks. 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.

TOPLOAD and TOPLOAD-H

The version of TOPMODEL applied to the McTier Creek 

investigations (Feaster and others, 2010) does not include a 

mass-balance algorithm for evaluating water-quality loads. 

However, such an algorithm can be applied externally to the

surface and subsurface flows simulated by the TOPMODEL

leading to a load model that can assess the mass fluxes for

a given water-quality constituent. The development of a 

water-quality load model by the application of a mass-balance 

algorithm to the TOPMODEL output is simple and allows 

flexibility for testing variations in the underlying algorithm.

As previously mentioned, several variations of the load model 

were developed for this study. One variation, TOPLOAD, used 

the unadjusted TOPMODEL hydrologic flow components.

A second variation, TOPLOAD-H, modified the subsurface

hydrologic components of TOPMODEL using the groundwater partitioning algorithm presented in Hornberger and others 

(1994). The synoptic water-quality data in conjunction with 

the in-stream data were used to assign concentrations to various surface and subsurface flow components in the development of the TOPLOAD and TOPLOAD-H models. A brief 

description of the development of these simple load models is 

presented in the appendix. The TOPLOAD and TOPLOAD-H

load models were applied to selected water-quality constituents (table 3) in the McTier Creek watershed, and the results 

were incorporated into the data viewer.

Load Estimator (LOADEST)

Loads for selected water-quality constituents (table 3) 

were computed using the S-LOADEST (Lorenz and others, 

2011) plug-in for TIBCO Spotfire S+ 8.1® software (TIBCO

Spotfire Co., Palo Alto, Calif.). S-LOADEST is derived from

LOADEST, a FORTRAN program that has been used extensively for estimating constituent loads in streams and rivers 

(Runkel and others, 2004). S-LOADEST allows the user to 

estimate annual, monthly, and seasonal constituent loads using 

a regression (rating curve) approach (Cohn, 2005). The regression model computes daily loads based on relations between 

constituent load and explanatory variables that are functions

of streamflow and time. The time component can be represented as increasing and decreasing trends over time and as 

seasonal changes. 

Instantaneous constituent loads are computed by the following equation:

 LHg = CHg * Qi * Cl, , (1)

where 

LHg is the mercury species (or other constituent 

of interest) load at the time of sampling, 

in milligrams per day, 

CHg is the concentration of the mercury species 

(or other constituent of interest), in 

nanograms per liter; 

Qi 	 is the instantaneous streamflow at the time of

sampling, in cubic feet per second; and 

Cl is a unit conversion factor (2.447).

Yields are computed as:

 YHg = (LHg/DA) * Cy , (2)

where

YHg is the mercury species (or other constituent 

of interest) yield, in micrograms per 

hectare per day; 

LHg is the mercury species (or other constituent 

of interest) load at the time of sampling 

in milligrams per day; 

DA is the upstream watershed drainage area, in 

hectares; and

Cy is a unit conversion factor (1,000).

The LOADEST program contains nine predefined regression models that can be used to estimate loads that account for 

the different possible combinations of explanatory variables of

streamflow and time. The load equation (model 6) used in this

study is as follows:

L = βo + β1LnQ+β2LnQ2 + β3 sine(2πT) + β4 cosine(2πT), (3)

where 

L is the natural logarithm (log) of the estimated 

load, in milligrams per day; 

	 βn 	 are the estimated coefficients for each

variable; 

Q 	 is the log of the daily mean streamflow, in

cubic feet per second;

	 π 	 is pi (3.14); and

T is the centered time in decimal years. 

For the constituent of interest, the formulated regression 

model was used to estimate loads over a selected time interval 

(estimation period), October 2004 to September 2009. 

Grid-Based Mercury Model (GBMM)

The Grid-Based Mercury Model (GBMM) was designed 

to simulate the daily fluxes and mass balances of water,

sediment, and mercury at watershed outlets using a spatially 

explicit, process-based, model structure. The model has three

main modules that compute daily mass balances of hydrology, 

sediment, and mercury within each geographic information 
Features of the McTier Creek Data Viewer 9

system (GIS) raster grid cell. Daily fluxes of water, sediment,

and mercury from each grid cell are routed through the watershed tributary networks to assessment points along stream 

channels. 

 The GBMM performs a simple water balance and 

estimates a modified National Resource Conservation Service

curve number (NRCS-CN) for each grid cell on a daily basis. 

The mass balance of mercury at the watershed outlet is simulated using the equation:

 

, (4)

L = Lp for pervious surfaces (5)

 L = Lf + Ld for forested areas (6)

 Vs =Ac * zd (7)

where 

Cs is the concentration of mercury in watershed 

soils, in micrograms per cubic meter;

 L is the mercury deposition load, in micrograms 

per day; 

Vs is the watershed soil volume, in cubic meters;

Kr is the reduction rate constant, in per day, 

where reduced mercury is assumed to 

immediately volatilize and is considered a 

loss from the watershed;

Kl is the leaching loss constant, in per day; 

Kro is the runoff loss constant, in per day;

Ke is the erosion loss constant, in per day; 

Lp is the mercury deposition load on pervious 

land, in micrograms per day; 

Lf is the mercury deposition load on forest land, 

in micrograms per day; 

Ld is the litter decomposition mercury load on 

forestland, in micrograms per day; 

Ac is the grid area, in square meters; and

zd 	 is the watershed soil mixing depth, in meters.

The current version of GBMM is structured to partition 

total mercury between its solid and aqueous forms in the soil 

system. Therefore, by calibrating the partition coefficient in

the model (i.e., the ratio of the equilibrium concentration in 

the soil particle to the concentration in soil water), GBMMsimulated total mercury dynamics are largely associated with 

particulate production and movement from soils to surface 

waters. GBMM has been applied and validated in multiple settings in the southeastern United States, including the Piedmont 

Physiographic Province (Golden and others, 2010) and Coastal 

Plain Physiographic Province (Dai and others, 2005; Feaster 

and others, 2010). (Note: The GBMM loads were converted to 

units shown in table 3 for comparison with other models.)

Visualizing Ecosystems for Land Management 

Assessment (VELMA)

The Visualizing Ecosystems for Land Management 

Assessment (VELMA) model is a spatially distributed ecohydrological model that simulates soil water infiltration and

redistribution, evapotranspiration, surface and subsurface 

runoff, carbon and nitrogen cycling in plants and soils, and 

the transport of dissolved organic carbon, dissolved inorganic 

nitrogen, and dissolved organic nitrogen from the terrestrial 

landscape to streams (A. Abdelnour, Georgia Institute of 

Technology, written commun., 2011). Recently, dissolved 

organic carbon driven mercury components were added to 

the existing VELMA framework (G. Davis and C. Knightes,

U.S. Environmental Protection Agency, written commun., 

2011). The VELMA uses a distributed soil column framework to simulate the lateral and vertical movement of water, 

heat, and nutrients within the soil. The modeling domain of 

VELMA is a 3-dimensional matrix covering the topographical

surface (x-y) and four soil layers (z). The soil column model

consists of three coupled submodels:

Hydrological model—This model simulates vertical and 

lateral movement of water within the soil, and losses of water 

from the soil and vegetation to the atmosphere;

Soil temperature model—This model simulates daily 

ground soil layer temperatures from surface air temperature 

and snow depth; and

Biogeochemistry model—This model simulates carbon, 

nitrogen, and mercury dynamics.

The soil column model is then placed within a catchment 

framework to create a spatially distributed model applicable 

to watersheds and landscapes. Adjacent soil columns interact 

with each other through the downslope lateral transport of 

water. Surface and subsurface lateral flow are routed using

a multiple flow direction method. A digital elevation map

(DEM) is used to determine flow direction and compute the

flow contribution area. Required input data include air temperature, precipitation, soil texture, soil depth, and DEM.

Features of the McTier Creek 

Data Viewer 

The abundant hydrologic and water-quality data associated with the McTier Creek watershed mercury investigation 

necessitates the integration of the datasets into a visualization 

tool for understanding the trends and influencing variables

of the stream ecosystem. Therefore, one of the initial efforts 

for evaluating trends in the McTier Creek watershed was the 

development of a tool, or data viewer, for systematically visualizing combinations of selected hydrologic, water-quality, and 

model data. The McTier Creek Data Viewer was developed by 

organizing selected data into a Microsoft Excel® spreadsheet 

with applications that provide a means for developing various 

plots for visualizing trends. Worksheets and applications that 

 = – (Kr + Kl + Kro + Ke ) * Cs

dCs

 

 dt

 L

Vs
10 Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed

comprise the McTier Creek Data Viewer are listed in table 4. 

A screen capture of the “Title Sheet” worksheet in the 

McTier Creek Data Viewer Microsoft Excel® application is 

shown in figure 3.

While a broad array of plots potentially could be developed with the data viewer, primary attention was given to 

developing graphs to display (1) time-series plots and scatter 

plots of selected hydrologic and water-quality data, (2) seasonal trends associated with selected water-quality constituents, and (3) comparison plots of selected model simulations. 

Brief descriptions of these data viewer functions are described 

in this section.

Time-Series and Scatter Plots of Selected 

Hydrologic and Water-Quality Data

Hydrology is an important determinant of ecosystem 

water quality (Bradley and others, 2010). The various hydrologic components (surface and subsurface flow) deliver waterquality constituents of varying concentrations to a stream 

and determine the in-stream water quality and ultimately the 

water-quality loads of the ecosystem. In order to understand 

the relation between in-stream water quality and the surface 

and subsurface hydrology, time-series plots and scatter plots 

of selected in-stream water-quality constituents in relation to 

measured and modeled flow components were developed in

the McTier Creek Data Viewer. The in-stream water-quality 

measurements concurrent with streamflow measurements

occur at the New Holland streamflow-gaging station from June

2007 to August 2009. Therefore, the plots in the data viewer 

were limited to modeled and measured data associated with 

this gaging station and time period. 

The time-series plots display selected water-quality 

values associated with the 45 discrete in-stream measurements overlain on time-series plots of measured or modeled 

continuous daily average flows. The scatter plots display the

same water-quality constituents, but with respect to the daily 

average flow at the time of the water-quality measurements.

The daily average flows in the time-series and scatter plots

can reflect measured data at the New Holland streamflowgaging station or simulated flows from VELMA, GBMM, and

TOPMODEL. There are 48 water-quality constituents associated with the discrete in-stream water-quality measurements 

at New Holland. A dropdown menu was incorporated into 

the data viewer so that the trends for a selected water-quality 

constituent, with respect to the hydrologic components, could 

be displayed one parameter at a time in the time-series and 

scatter plots. Time-series plots of the relation for total mercury 

to measured flows and to TOPMODEL simulated flows at

New Holland are shown in figures 4 and 5, respectively. The

time-series plots are helpful in displaying the antecedent and 

current flow conditions associated with selected water-quality

measurements and can give insights to hydrologic conditions 

that promote the observed water-quality trends.

Chemical, biological, and hydrologic processes within an 

ecosystem can display seasonal trends. Therefore, the waterquality data for the time-series plots and scatter plots were 

grouped by the dormant and growing seasons. The growing season data are identified by solid green circles and the

dormant (or non-growing) season data are identified by solid

light blue circles (figs. 4–7). The scatter plots display waterquality trends associated with concurrent flow conditions

(measured and modeled) and can help indicate if the waterquality constituent of interest displays a trend associated with 

flow. In particular, the scatter plots identify influences from

surface and subsurface flow components, indicating potential

sources for the water-quality constituent of interest. Examples

of scatter plots in figure 6 show the relation of total mercury to

measured and simulated flows at the New Holland streamflowgaging station.

Comparison Plots of Selected Model 

Simulations

For the McTier Creek watershed mercury investigation, 

six hydrologic and (or) water-quality models were developed including TOPMODEL, TOPLOAD, TOPLOAD-H, 

LOADEST, GBMM, and VELMA. To assist in evaluating 

the performance of these models, time-series plots, similar to 

figures 4 and 5, were developed in the data viewer to show the

simulated flows and water-quality loads of the models with

respect to each other as well as to the measured data (figs. 7

and 8). Time-series plots of the simulated streamflows (total

flow) at New Holland as determined by the TOPMODEL,

GBMM, and VELMA models are shown in figure 7. The measured flow at this streamflow-gaging station also is included in

the plot. As evidenced, the patterns indicate that each model is 

capturing the general trends of flow at New Holland.

Evaluating the performance of the models for simulating 

the hydrology of the McTier Creek watershed provides insight 

on the performance of the models for simulating loads into 

the stream ecosystem. The “Load” spreadsheet allows users to 

visualize the measured and simulated loads from TOPLOAD, 

TOPLOAD-H, LOADEST, GBMM, and VELMA. A timeseries plot of the simulated mass flux (or load) for total mercury as determined by the TOPLOAD-H, LOADEST, GBMM, 

and VELMA models is shown in figure 8. The field estimated

load associated with the water-quality measurement also is 

included in the plot.
Table 4. Description of selected worksheets and applications included in the McTier Creek Data Viewer.

[TOPMODEL, Topography-based hydrological model; TOPLOAD, Water-quality load model developed from TOPMODEL; 

TOPLOAD-H, Water-quality load model developed from TOPMODEL with Hornberger’s ground-water partitioning algorithm; 

GBMM, Grid-Based Mercury Model; VELMA, Visualizing Ecosystems for Land Management Assessment Model; LOADEST, 

LOAD ESTimator model]

Worksheet Name Description

Title Sheet Title sheet for data viewer.

ReleaseNotes

References and selected information associated with hydrologic and 

water-quality models used in the data viewer and a description of 

each worksheet in the data viewer.

Chart (Hydrology)

Time-series plot comparing simulated flows from TOPMODEL,

GBMM, and VELMA with measured flows, along with concentration of selected water-quality constituent by season. (Note: Dropdown menus allow the user to select the model flow components

and water-quality constituent of interest for display.)

QW Scatter Plots

Scatter plots for measured water-quality constituents with respect to 

selected simulated and measured flows. (Note: A dropdown menu

allows the user to select the water-quality constituent of interest 

for display.)

Chart (Load)

Time-series plot comparing selected simulated water-quality loads 

from TOPLOAD, TOPLOAD-H, LOADEST, GBMM, and VELMA along with measured loads. (Note: Dropdown menus allow 

the user to select the load model components and water-quality 

constituent of interest for display.)

Plot Data Selected hydrology, water-quality, and load data are stored on this 

worksheet and used to generate selected plots in the data viewer.

Hydrology Data

Simulated time-series hydrologic output data from TOPMODEL, 

GBMM, and VELMA and measured flow associated with streamflow-gaging station 02172305, McTier Creek near New Holland,

South Carolina.

QW Data

Water-quality data for 48 water-quality constituents associated with 

45 discrete measurements collected at streamflow-gaging station

02172305, McTier Creek near New Holland, South Carolina.

Load Data

Simulated water-quality load data for selected water-quality constituents from TOPLOAD, TOPLOAD-H, LOADEST, GBMM, and 

VELMA along with measured loads.

Chart (TOPLOAD)

Time-series plot of simulated loads for TOPLOAD along with 

measured discrete loads for a selected water-quality constituent. 

(Note: An input table allows assignment of water-quality concentrations for the TOPLOAD computations.)

TOPLOAD Contains TOPMODEL hydrology data and algorithms used to compute loads for TOPLOAD.

Chart (TOPLOAD-H)

Time-series plot of simulated loads for TOPLOAD-H along with 

measured discrete loads for a selected water-quality constituent. 

(Note: An input table allows assignment of water-quality concentrations for the TOPLOAD-H computations.)

TOPLOAD-H Contains TOPMODEL and Hornberger flow component data and

algorithms used to compute loads for TOPLOAD-H.

Selection Tables Provides information used to drive selected dropdown menus and 

automated data retrieval in the data viewer.

Define Flow Parameters Provides an illustration defining the surface- and subsurface-flow

components associated with TOPMODEL.

Features of the McTier Creek Data Viewer 11
12 Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed

Figure 3. Screen capture from the McTier Creek Data Viewer showing “Title Sheet” worksheet.

Figure 4. Screen capture from the TOPMODEL worksheet showing dropdown menu of selected constituent to be shown with the 

measured flow data.
Features of the McTier Creek Data Viewer 13

Figure 5. Screen capture from the TOPMODEL worksheet showing selected constituent concentration with the TOPMODEL 

simulated flow components.

Figure 6. Screen capture from the scatter plot worksheet showing scatter plots of the selected constituent and various measured 

flow and simulated flow components.
14 Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed

Figure 7. Screen capture from the model comparison worksheet showing the measured and simulated flows from 

TOPMODEL, GBMM, and VELMA along with the selected constituent by season.

Figure 8. Screen capture from the model comparison worksheet showing the measured and simulated loads from TOPLOAD-H, 

LOADEST, GBMM, and VELMA.
Summary 15

Summary

The U.S. Geological Survey, as part of its National 

Water-Quality Assessment Program, has been conducting 

research regarding the fate and transport of mercury in stream 

ecosystems. Part of this national research program includes a 

field investigation of mercury in the McTier Creek watershed

in Aiken County, South Carolina. McTier Creek is a small 

stream ecosystem in the headwaters of the Edisto River Basin, 

which is noted for having some of the highest recorded fishtissue mercury concentrations in the United States. A primary 

focus of this investigation was the collection of field data and

the development of hydrologic and water-quality models. 

These efforts yielded an extensive quantity of data including

continuous streamflow records, numerous discrete waterquality measurements, and simulated data from six hydrologic

and (or) water-quality models. These data provide a valuable resource for investigating the chemical, biological, and 

hydrologic characteristics that influence the fate and transport

of mercury in stream ecosystems.

Because of the large quantity of data associated with the 

McTier Creek watershed investigation, a tool to quickly and 

easily visualize the measured and simulated hydrologic and 

water-quality data was considered an important resource for 

investigating the trends and influencing variables of the stream

ecosystem. Therefore, one of the initial efforts for evaluating 

trends in the McTier Creek watershed was the development 

of a data viewer consisting of a set of digital spreadsheets for 

systematically visualizing selected hydrologic, water-quality, 

and model data. The general description of the data viewer 

provided in the report gives an overview of how such a tool 

can be developed and demonstrates through sample plots some 

benefits that can be derived from the data viewer with regard

to visualizing trends associated with the McTier Creek watershed mercury investigation. 

The extensive database incorporated into the data viewer

can provide a foundation for the development of other analysis 

tools. One example of utilizing the data viewer in this manner

was the development of the TOPLOAD and TOPLOAD-H 

models. These models utilize a mass-balance equation in 

conjunction with the hydrologic simulations from the McTier 

Creek TOPMODEL (data included in the data viewer) to 

develop simple water-quality load models. The overview for 

the development of these models in the appendix provides a

general approach for how other analysis tools and (or) models 

might be developed with the data viewer. 
16 Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed

Selected References

Aucott, W.R., and Speiran, G.K., 1985, Ground-water flow in

the Coastal Plain aquifers of South Carolina: Ground Water, 

v. 23, p. 736–745.

Bennett, D.G., and Patton, J.C., eds., 2008, A geography of the 

Carolinas: Boone, North Carolina, Parkway Publishers, 

266 p.

Bloxham, W.M., 1976, Low-flow characteristics of streams in

the Inner Coastal Plain of South Carolina: South Carolina 

Water Resources Commission Report No. 5, 41 p.

Bradley, P.M., Burns, D.A., Riva-Murray, Karen, Brigham, 

M.E., Button, D., Chasar, L.C., Marvin-DiPasquale, M., 

Lowery, M.A., and Journey, C.A., 2011, Spatial and seasonal variability of dissolved methylmercury in two stream 

basins in the eastern United States: Environmental Science 

and Technology, v. 46, no. 6, p. 2048–2055, doi: 10.1021/

es103923j.

Bradley, P.M., Chapelle, F.H., and Journey, C.A., 2009, 

Comparison of methylmercury production and accumulation in sediments of the Congaree and Edisto River Basins, 

South Carolina, 2004–06: U.S. Geological Survey Scientific

Investigations Report 2009–5021, 9 p.

Bradley, P.M., Journey, C.A., Chapelle, F.H., Lowery, M.A., 

and Conrads, P.A., 2010, Flood hydrology and methylmercury availability in Coastal Plain rivers. Environmental 

Science and Technology, v. 44 no. 24, p. 9285–9290.

Brigham, M.E., Krabbenhoft, D.P., and Hamilton, P.A., 2003, 

Mercury in stream ecosystems—New studies initiated by 

the U.S. Geological Survey: U.S. Geological Fact Sheet 

016–03, 4 p.

Brigham, M.E., Wentz, D.A., Aiken, G.R., and Krabbenhoft, 

D.P., 2009, Mercury cycling in stream ecosystems, 1, Water 

column chemistry and transport: Environmental Science and 

Technology, v. 43, no. 8, p. 2720–2725.

Chasar, L.C., Scudder, B.C., Stewart, A.R., Bell, A.H., and 

Aiken, G.R., 2009, Mercury cycling in stream ecosystems, 

3, Trophic dynamics and methylmercury bioaccumulation: 

Environmental Science and Technology, v. 43, no. 8, 

p. 2733–2739.

 Cohn, T.A., 2005, Estimating contaminant loads in rivers— 

An application of adjusted maximum likelihood to type 1

censored data: Water Resources Research, v. 41, W07003, 

doi:10.1029/2004WR003833. 

Cohn, T.A., Caulder, D.L., Gilroy, E.J., Zynjuk, L.D., and 

Summers, R.M., 1992, The validity of a simple statistical 

model for estimating fluvial constituent loads—An empirical study involving nutrient loads entering Chesapeake Bay: 

Water Resources Research, v. 28, no. 9, p. 2353–2363.

Cooke, C.W., 1936, Geology of the Coastal Plain of South 

Carolina: U.S. Geological Survey Bulletin 867, 196 p.

Dai, T., Ambrose, R.B., Alvi, K., Wool, T., Manguerra, H., 

Choski, M., Yang, H., and Kraemer, S., 2005, Characterizing spatial and temporal dynamics—Development of a 

grid-based watershed mercury loading model, in Moglen, 

G.E., (ed.), Managing watersheds for human and natural 

impacts—Engineering, ecological, and economic challenges, Williamsburg, Virginia, July 19–22, 2005: Reston,

Virginia, American Society of Civil Engineers.

DeWild, J.F., Olson, M.L., and Olund, S.D., 2001, Determination of methyl mercury by aqueous phase ethylation, followed by gas chromatographic separation with cold vapor 

atomic fluorescence detection: U.S. Geological Survey

Open-File Report 01–445, 14 p.

Dunne, T., and Black, R.D., 1970, Partial area contributions 

to storm runoff in a small New England watershed: Water 

Resources Research, v. 6, p. 1296–1311.

Eidson, J.P., Lacy, C.M., Nance, Luke, Hansen, W.F., Lowery, 

M.A., and Hurley, N.M., Jr., 2005, Development of a 10- 

and 12-digit hydrologic unit code numbering system for 

South Carolina, 2005: U.S. Department of Agriculture, 

Natural Resources Conservation Service, 38 p., 1 pl. 

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.

Golden, H.E., and Knightes, C.D., 2011, Simulated watershed 

mercury and nitrate flux responses to multiple land cover

conversion scenarios—Environmental Toxicology and

Chemistry, v. 30, no. 4, p. 773–786.

Golden, H.E., Knightes, C.D., Cooter, E.J., Dennis, R.L., Gilliam, R.C., and Foley, K.M., 2010, Linking air quality and 

watershed models for environmental assessments: Analysis 

of the effects of model-specific precipitation estimates on

calculated water flux—Environmental Modeling & Software, v. 25, no. 12, p. 1722–1737.

Golden, H.E., Knightes, C.D., Conrads, P.A., Davis, G.M., 

Feaster, T.D., Journey, C.A., Benedict, S.T., Brigham, M.E., 

and Bradley, P.M., 2012, Characterizing mercury concentrations and fluxes in a Coastal Plain watershed: Insights

from dynamic modeling and data, Journal of Geophysical 

Research, 117, 17 pp., doi:10.1029/2011JG001806.

Griffith, G.E., Omernik, J.M., Comstock, J.A., Schafale, M.P.,

McNab, W.H., Lenat, D.R., MacPherson, T.F., Glover, J.B., 

and Shelburne, V.B., 2002, Ecoregions of North Carolina 

and South Carolina—U.S. Geological Survey color poster 

with map, scale 1:1,500,000.
Selected References 17

Grigal, D.F., 2002, Inputs and outputs of mercury from terrestrial watersheds: A review: Environmental Reviews, 

no. 10, p. 1–39.

Helsel, D.R., 2005, Nondetects and data analysis—Statistics 

for censored environmental data: New Jersey, WileyInterscience, 250 p. 

Helsel, D.R., and Hirsch, R.M., 1992, Statistical methods in 

water sources: U.S. Geological Survey Techniques of Water 

Resources Investigations, book 4, chap., A3, 512 p.

Homer, C., Huang, C., Yang, L., Wylie, B.K., and Coan, M., 

2004, Development of a 2001 National Landcover Database 

for the United States: Photogrammetric Engineering and 

Remote Sensing, v. 70, p. 829–840.

Hornberger, G.M., Bencala, K.E., and McKnight, D.M., 1994, 

Hydrological controls on dissolved organic carbon during 

snowmelt in the Snake River near Montezuma, Colorado: 

Biogeochemistry, v. 25, p. 147–165.

Hornberger, G.M., Raffensperger, J.P., Wiberg, P.L., and 

Eshleman, K.N., 1998, Elements of physical hydrology: 

Baltimore, Maryland, The John Hopkins University Press.

Journey, C.A., Burns, D.A., Riva-Murray, K., Brigham, M.E., 

Button, D., Feaster, T.D., Petkewich, M.D., and Bradley, 

P.M., 2012, Fluvial transport of mercury, organic carbon, 

suspended sediment, and selected major ions in contrasting 

stream basins in South Carolina and New York, October 

2004 to September 2009: U.S. Geological Survey Scientific

Investigations Report 2012–5173, 125 p.

Krabbenhoft, D.P., Wiener, J.G., Brumbaugh, W.G., Olson, 

M.L., DeWild, J.F., and Sabin, T.J., 1999, A national pilot 

study of mercury contamination of aquatic ecosystems 

along multiple gradients; in Morganwalp, D.W., and 

Buxton, H.T., eds., U.S. Geological Survey Toxic Substances Hydrology Program—Proceedings of the Technical 

Meeting, Volume 2 of 3—Contamination of hydrologic 

systems and related ecosystems, March 8–12, 1999,

Charleston, South Carolina: U.S. Geological Survey WaterResources Investigations Report 99–4018B, p. 147–160.

Lewis, M.E., and Brigham, M.E., 2004, National field manual

for the collection of water-quality data, section 5.6.4.B, 

Low-level mercury: U.S. Geological Survey Techniques of 

Water-Resources Investigations Report, book 9, chap. A5. 

Lorenz, D.L., and others, 2011, USGS library for S-PLUS for 

Windows—Release 4.0: U.S. Geological Survey Open-File 

Report 2011–1130.

Marshall, W.D., ed., 1993, Assessing change in the Edisto 

River Basin—An ecological characterization: South Carolina Water Resources Commission Report No. 177, 149 p.

Mergler, D., Anderson, H.A., Chan L.H.M., Mahaffey, K.R., 

Murray, M., Sakamoto, M., and Stern, A.H., 2007, Methylmercury exposure and health effects in humans—A worldwide concern: Ambio, v. 36, no. 1, p. 3–11.

National Land Coverage Data (NLCD), 2001, Multi-resolution 

land characteristics consortium (MRLC): Accessed at http://

www.epa.gov/mrlc/nlcd-2001.html.

Rantz, S.E., and others, 1982, Measurement and computation 

of streamflow: U.S. Geological Survey Water-Supply Paper

2175, v. 2, 631 p.

Robson, A., Beven, K., and Neal, C., 1992, Towards identifying sources of subsurface flow—A comparison of components identified by a physically based runoff model and

those determined by chemical mixing techniques: Hydrologic Processes, v. 6, p. 199–214.

Runkel, R.L., Crawford, C.G., and Cohn, T.A., 2004, Load 

estimator (LOADEST)—A FORTRAN program for estimating constituent loads in streams and rivers: U.S. Geological Survey Techniques and Methods, book 4, 

chap. A5, 69 p.

Scudder, B.C., Chasar, L.C., Wentz, D.A., Bauch, N.J., 

Brigham, M.E., Moran, P.W., and Krabbenhoft, D.P., 2009, 

Mercury in fish, bed sediment, and water from streams

across the United States, 1998–2005: U.S. Geological Survey Scientific Investigations Report 2009–5109, 74 p.

Swain, E.B., Jakus, P.M., Rice, G., Lupi, F., Maxson, P.A.,

Pacyna, J.M., Penn, A., Spiegel, S.J., and Veiga, M.M., 

2007, Socioeconomic consequences of mercury use and 

pollution: Ambio, v. 36, no. 1, p. 45–61.

U.S. Environmental Protection Agency, 2008, Biennial national listing of fish advisories: Report EPA823-F-09-007, 7 p.

Vigil, J.F., Pike, R.J., and Howell, D.G., 2000, A tapestry of 

time and terrain: U.S. Geological Survey Geologic Investigations Series 2720. 

Whipkey, R.Z., 1965, Subsurface stormflow from forested

slopes: Hydrological Sciences Bulletin, v. 10, p. 74–85.

Wiener, J.G., Krabbenhoft, D.P., Heinz, G.H., and 

Scheuhammer, A.M., Ecotoxicology of mercury, Chapter

16; in Hoffman, D.J., Rattner, B.A., Burton, G.A., Jr., and 

Cairns, J., Jr., Handbook of ecotoxicology (2nd ed.): Boca

Raton, Florida, CRC Press.

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

concept of streamflow generation with the watershed model

TOPMODEL: U.S. Geological Survey Water-Resources 

Investigations Report 93–4124, 33 p.
18 Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed

Appendix

Mass-Balance Model

The surface and subsurface flow components of an

ecosystem that combine to form the total in-stream flow will

typically have their own unique water-quality properties. The 

water quality of these flow components is partially a function

of the path that each component takes to reach the stream, 

with surface flows having their water-quality characteristics

influenced by the flow path along the land surface and subsurface flows having their characteristics influenced by the flow

path through the soil matrix. Studies by Hornberger and others

(1994; 1998) and Robson and others (1992) indicate that the 

land surface can function as a storage reservoir for waterquality constituents delivered through atmospheric deposition 

and natural processes, whereas the subsurface soil matrix can

function as a storage reservoir for selected constituents that 

are leached into the soils through infiltration. Because of the

long retention times often associated with subsurface flows,

it is possible that the deeper subsurface flow components can

have relatively high water-quality concentrations for selected 

constituents. Together the surface and subsurface mass flux

(or load) combines to form the water-quality characteristics of 

the streamflow. Therefore, in order to evaluate and understand

the in-stream water quality of an ecosystem, it is important to 

assess the various surface and subsurface flow components

and their respective water-quality characteristics. 

To define the surface and subsurface flow components

of a watershed, one must primarily rely on hydrologic models 

and accept the limitations associated with those models. For 

this particular application to the McTier Creek watershed, the 

TOPMODEL (Wolock, 1993; Feaster and others, 2010) was 

used to accomplish this task. Although other models could 

be used, an objective of the investigation was to evaluate 

the potential use of the hydrologic model TOPMODEL as a 

water-quality load model. To define the water-quality characteristics (or more specifically, the concentration of selected

constituents) associated with each flow component, one must

rely on limited field measurements and judgment to estimate

these values. A review of the water-quality field data collected

in the McTier Creek watershed was utilized for this purpose. 

Although each watershed will have unique considerations in 

the assignment of constituent concentrations associated with 

the various surface and subsurface flow components, the studies by Hornberger and others (1994; 1998) and Robson and 

others (1992) provide practical insights on how this assignment can be accomplished. Having defined the surface and

subsurface flow components and their respective concentrations for selected water-quality constituents, these data can 

be combined to develop a mass-balance model based on the 

principle of the conservation of mass. 

A general mass-balance equation for a given waterquality constituent in a stream ecosystem can be expressed as,

dM

dt = KQsubCsub + KQsurfCsurf – KQstrCstr + ∑ s + ∑ r

 

, (A1)

where

 is rate of change of mass for the water-quality 

constituent within the stream ecosystem, in 

milligrams per day;

K is unit conversion coefficient equal to 2.447;

Qsub is flow associated with subsurface flow, in

cubic feet per second;

Csub is concentration of the water-quality 

constituent associated with subsurface 

flow, in nanograms per liter;

Qsurf is flow associated with surface flow, in cubic

feet per second;

Csurf is concentration of the water-quality 

constituent associated with surface flow, in

nanograms per liter;

Qstr is flow associated with the total in-stream

flow, in cubic feet per second;

Cstr is concentration of the water-quality 

constituent associated with the total instream flow, in nanograms per liter;

s is rate at which the mass of the water-quality 

constituent is being added to the stream 

ecosystem, in milligrams per day; and

r is rate at which the mass of the water-quality 

constituent is being removed from the 

stream ecosystem, in milligrams per day.

It should be noted that units for concentration can vary 

with water-quality constituent requiring an adjustment to the 

unit conversion coefficient, K, in order to maintain equation 

units. This applies to all equations listed in the appendix.

If steady-state conditions for the rate of change of mass 

within the ecosystem are assumed, equation A1 simplifies to

the following:

dM

 dt

QstrCstr = QsubCsub + Qsurf Csurf , (A2)

Equation A2 is a simple but useful tool that can be 

applied in various ways to investigate the separation of 

hydrograph flow components, identify potential sources for

a given water-quality constituent, and develop water-quality 

load models. For many field investigations, the variables on

the left side of equation A2 can be defined with standard field

measurement techniques. The variables on the right side of the 

equation are more challenging to define. To define the surface and subsurface flow components in equation A2, hydrologic models, such as the TOPMODEL, must be used. With 
Appendix 19

definition of these flow components, the water-quality concentrations associated with the surface and subsurface flows can

then be evaluated, and insights regarding water-quality sources 

within the ecosystem can be gained. If the constituent concentrations on the right side of the equation can be approximated

through a combination of field measurements and judgment,

then it is possible to approximate the surface and subsurface

hydrographs that form the in-stream flow, giving insights into

the hydrology of the ecosystem. Additionally, if all of the 

variables on the right side of equation A2 can be defined, the

water-quality constituent load can be estimated and the equation becomes a simple load model. The studies by Hornberger 

and others (1994; 1998) and Robson and others (1992) provide 

practical insights on how varying forms of equation A2 can 

be applied to field conditions for assessing the hydrology and

water quality of an ecosystem.

TOPLOAD Model

One objective of the current (2011) McTier Creek 

investigation is to utilize the mass-balance equation (eq. A2) 

in combination with the TOPMODEL hydrologic simulation 

to develop a load model for selected water-quality constituents in the McTier Creek watershed. To apply equation A2 

to the TOPMODEL flow components, the equation must be

expanded to include additional terms for the surface (qinf, 

qimp, qsrip, qof) and subsurface (qb, qret) flow components in

the model, as shown in equation A3 (see “TOPMODEL” section in report for definition of flow components):

 , (A3)

QstrCstr = QqbCqb + QqretCqret + Qqinf Cqinf

 + QqimpCqimp + QqsripCqsrip + Qqof Cqof

where

Qqb is subsurface base flow from TOPMODEL,

in cubic feet per second;

Cqb is water-quality constituent concentration 

for subsurface base flow, in nanograms

per liter;

Qqret is subsurface return flow from TOPMODEL,

in cubic feet per second;

Cqret is water-quality constituent concentration for 

subsurface return flow, in nanograms per

liter;

Qqinf is surface infiltration-excess overland flow

from TOPMODEL, in cubic feet per 

second;

Cqinf is water-quality constituent concentration for 

surface infiltration-excess overland flow, in

nanograms per liter;

Qqimp is surface impervious flow from

TOPMODEL, in cubic feet per second;

Cqimp is water-quality constituent concentration 

for surface impervious flow, in nanograms

per liter;

Qqsrip is surface open-water body flow from

TOPMODEL, in cubic feet per second

Cqsrip is water-quality constituent concentration 

for surface open-water body flow, in

nanograms per liter;

Qqof is surface overland saturation flow from

TOPMODEL, in cubic feet per second; and

Cqof is water-quality constituent concentration 

for surface overland saturation flow, in

nanograms per liter.

Figure A1. Screen capture from the TOPLOAD worksheet showing input table for manually assigning concentrations to the 

TOPMODEL flow components.
20 Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed

If the hydrologic and water-quality components on the 

right side of equation A3 are estimated with TOPMODEL and 

water-quality field measurements, respectively, and applied to

equation A3, then the result (left side of equation A3) represents the predicted load for a given constituent. In this application, equation A3 becomes a simple model for evaluating loads 

and will be called the TOPLOAD model.

To apply equation A3, the time-series output data for 

TOPMODEL must be imported into a spreadsheet and the 

flow components organized into a tabular format. Because the

McTier Creek Data Viewer (see description in “Features of the 

McTier Creek Data Viewer” section in report) already contained the TOPMODEL output data, it was used as the initial 

spreadsheet for developing the load model. Concentrations 

for the constituent of interest must then be assigned to each 

flow component and tabulated in the spreadsheet. TOPLOAD

provides two methods for assigning water-quality concentrations to each flow component. One method allows the user to

manually assign these values on the worksheet (fig. A1) that

contains the time-series plot of the simulated loads, so that the 

effect of the assigned concentration can be readily observed. 

The other method automates the process through an algorithm 

that utilizes the Excel Solver to determine the assigned waterquality concentrations that minimize the root mean square 

error between predicted and observed loads. For the initial 

application of the TOPLOAD model to McTier Creek watershed, it was assumed that the concentrations for a given flow

component would be constant. The validity of this assumption 

probably varies with water-quality constituent and flow component and will likely need further investigation. However, 

for initial applications of TOPLOAD to the McTier Creek 

watershed, the assumption is not an unreasonable approach as 

shown by the work of Hornberger and others (1994; 1998) and 

Robson and others (1992). Using standard spreadsheet applications, the loads for each flow component on the right side of

equation A3 were computed and then summed to predict the 

total load, as represented by the left side of the equation. This 

computation is applied to each time-series step (1 day) for the 

TOPMODEL output that extends during the period from June

2007 through August 2009. 

In order to evaluate the performance of the TOPLOAD 

model, the hydrologic and water-quality field measurements

collected at the New Holland streamflow-gaging station were

used to estimate the measured loads. Using the 45 discrete 

in-stream water-quality measurements in conjunction with the 

average daily streamflow collected at New Holland, the average daily field loads associated with the day of the measurements can be computed and compared with the TOPLOAD 

model. A time-series plot of the TOPLOAD load estimates 

along with the field measured loads for total mercury are

shown in figure A1.

TOPLOAD-H Model

Hornberger and others (1994) presented a mass-balance 

conceptual model consisting of three flow components including overland (or surface) flow and a lower and upper soil flow

component. The conceptual model assumes that the breakpoint 

between the upper and lower soil zones is approximately the

perennial water table (fig. A2). As water rises into the upper

soil zone, that portion of the subsurface flow will acquire

water-quality characteristics different from those of the lower 

soil zone. This conceptual model is presented in equation A4 

and is similar in form to equation A2.

Flowupper

Soil zone Water efflux

Flowlower

Zupper

Zlower

Figure A2. Schematic showing the partitioning 

of the ground-water flow component (from 

Hornberger and others, 1994).

QstrCstr = QoverCover + QlowerClower + QupperCupper , (A4)

where

Qover is flow associated with overland (or surface)

flow, in cubic feet per second;

Cover is concentration of water-quality constituent 

associated with overland (or surface) flow,

in nanograms per liter;

Qlower is the flow associated with a lower soil zone,

in cubic feet per second;

Clower is concentration of water-quality constituent 

associated with a lower soil zone, in 

nanograms per liter;

Qupper is flow associated with an upper soil zone, in

cubic feet per second; and

Cupper is concentration of water-quality constituent 

associated with an upper soil zone, in 

nanograms per liter.
Appendix 21

To estimate Qlower and Qupper at a given time, Hornberger 

and others (1994) suggest the following equation:

Qupper = Qsub(nzupper – S) / (nztotal – S) , (A5)

where

Qsub is flow associated with subsurface flow and

is equal to the sum of Qupper and Qlower , 

in cubic feet per second. (Note: In the 

development of this model it was assumed 

that Qqret is equal to Qsub. This assumption 

allows the TOPMODEL flow component,

Qqb, to function as a third lower flow zone);

n is soil porosity;

zupper is depth of the upper soil zone, in millimeters;

ztotal is depth of the total soil zone and equal to the 

sum of the upper and lower soil zone, in 

millimeters;

S is saturation deficit, which is the amount of

water required to cause the water table to 

rise to the ground surface, in millimeters 

(Note: If S is greater than nzupper, then Qupper

is set to zero).

Using selected input and output data from TOPMODEL 

(Wolock, 1993; Feaster and others, 2010), Qsub, S, ztotal, and 

n can be defined for application to equation A5 leading to an

estimate of Qupper and Qlower. Assuming that Qqret will be the 

primary source of flow for the Hornberger upper and lower

soil zones, Qupper and Qlower can then be substituted for Qqret in 

equation A3 to obtain the following equation:

 

QstrCstr = QqbCqb + QupperCupper + QlowerClower + QqinfCqinf

+ QqimpCqimp + QqsripCqsrip + QqofCqof

,(A6)

where

Cupper is water-quality constituent concentration for 

	 	 the upper soil flow, in nanograms per liter; 	 	

 and 

Clower is water-quality constituent concentration for 

	 	 the lower soil flow, in nanograms per liter.

Using the TOPMODEL data from the McTier Creek 

Data Viewer and a similar approach for the development of 

TOPLOAD, equation A6 was applied to the TOPMODEL data 

to develop another simple model for evaluating loads. This 

model is called the TOPLOAD-H model.
For additional information regarding this 

publication, contact:

Director

USGS South Carolina Water Science Center

Stephenson Center, Suite 129

720 Gracern Road

Columbia, SC 29210-7651

(803) 750-6181

email: dc_sc@usgs.gov

Or visit the USGS South Carolina Water 

Science Center Web site at:

 http://sc.water.usgs.gov

Prepared by:

USGS Science Publishing Network

Raleigh Publishing Service Center

3916 Sunset Ridge Road

Raleigh, NC 27607

Benedict and others—Data Visualization, Time-Series Analysis, and Mass-Balance Modeling for the McTier Creek Watershed—Open-File Report 2011–1209