TOPMODEL Simulations of Streamflow and 

Depth to Water Table in Fishing Brook 

Watershed, New York, 2007–09

National Water-Quality Assessment Program

Scientific Investigations Report 2011–5190

U.S. Department of the Interior

U.S. Geological Survey
Cover. Front cover: Inlet to Pickwacket Pond, taken 10/08/2009. Back cover: Sixmile Brook in Sixmile Wetland (with depth-to-water-table 

piezometers taken from site SS04, looking west towards sites SS05, MA08, and MA09), taken 05/19/2009. Both are in the Fishing Brook 

Watershed, near Long Lake, New York. Overlay image: Map of topographic wetness index.
National Water-Quality Assessment Program 

TOPMODEL Simulations of Streamflow 

and Depth to Water Table in Fishing Brook 

Watershed, New York, 2007–09

By Elizabeth A. Nystrom and Douglas A. Burns 

Scientific Investigations Report 2011–5190

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: 2011

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Suggested citation:

Nystrom, E.A., and Burns, D.A., 2011, TOPMODEL simulations of streamflow and depth to water table in Fishing 

Brook Watershed, New York, 2007–09: U.S. Geological Survey Scientific Investigations Report 2011–5190, 54 p. 

at http://pubs.usgs.gov/sir/2011/5190/.
iii

Foreword

The U.S. Geological Survey (USGS) is committed to providing the Nation with reliable scientific 

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.

gov/). Information on the Nation’s water resources is critical to ensuring long-term availability 

of water that is safe for drinking and recreation and is suitable for industry, irrigation, and fish 

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).

In the second decade of the Program (2001–2012), a major focus is on regional assessments 

of water-quality conditions and trends. These regional assessments are based on major river 

basins and principal aquifers, which encompass larger regions of the country than the Study 

Units. Regional assessments extend the findings in the Study Units by filling critical gaps in 

characterizing the quality of surface water and groundwater, and by determining water-quality 

status and trends at sites that have been consistently monitored for more than a decade. In 

addition, the regional assessments continue to build an understanding of how natural features 

and human activities affect water quality. Many of the regional assessments employ modeling 

and other scientific tools, developed on the basis of data collected at individual sites, to 

help extend knowledge of water quality to unmonitored, yet comparable areas within the 

regions. The models thereby enhance the value of our existing data and our understanding 

of the hydrologic system. In addition, the models are useful in evaluating various resourcemanagement scenarios and in predicting how our actions, such as reducing or managing 

nonpoint and point sources of contamination, land conversion, and altering flow and (or) 

pumping regimes, are likely to affect water conditions within a region.

Other activities planned during the second decade include continuing national syntheses 

of information on pesticides, volatile organic compounds (VOCs), nutrients, trace elements, 

and aquatic ecology; and continuing national topical studies on the fate of agricultural 

chemicals, effects of urbanization on stream ecosystems, bioaccumulation of mercury in 

stream ecosystems, effects of nutrient enrichment on stream ecosystems, and transport of 

contaminants to public-supply wells.
iv

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
v

Acknowledgments

The authors wish to thank the staff at the Adirondack Ecological Center of the State University 

of New York, College of Environmental Science and Forestry (SUNY–ESF) for providing access 

to facilities and equipment at the Huntington Wildlife Forest. Special acknowledgment goes 

to Myron Mitchell from SUNY–ESF for access to meteorological and flow data from the 

Arbutus Lake Watershed. The authors would like to thank Finch, Pruyn & Co. and The Nature 

Conservancy for providing access to the Fishing Brook Watershed.
This page has been left blank intentionally.
vii

Contents

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

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

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

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

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

Description of the Fishing Brook Watershed...................................................................................2

TOPMODEL .....................................................................................................................................................5

Topographic Wetness Index and Saturation Deficit.......................................................................5

TOPMODEL Streamflow-Generation Concepts ...............................................................................5

Previous Studies ...................................................................................................................................7

Specific TOPMODEL Version ..............................................................................................................7

Observed Data................................................................................................................................................8

Input Data for Model Processing.......................................................................................................8

Meteorological Data ...................................................................................................................8

Precipitation ........................................................................................................................8

Temperature.........................................................................................................................8

Topographic Wetness Index ......................................................................................................9

Model Parameters.......................................................................................................................9

Watershed Characteristics ..............................................................................................9

Calibration Parameters....................................................................................................10

Unused Model Parameters .............................................................................................11

Observed Streamflow and Depth to Water Table for Model Evaluation ...................................11

Streamflow..................................................................................................................................11

Depth to Water Table ................................................................................................................12

TOPMODEL Calibration...............................................................................................................................13

Snowmelt Calibration.........................................................................................................................14

Results of Snowmelt Calibration .............................................................................................14

Runoff and Depth-to-Water-Table Calibration ...............................................................................19

Runoff Objective Function ........................................................................................................19

Depth-to-Water-Table Objective Functions...........................................................................20

Absolute Depth to Water Table ......................................................................................20

Relative Depth-to-Water-Table Fluctuations................................................................20

Combined Multiple-Objective Function..................................................................................20

Generalized Sensitivity Analysis ......................................................................................................21

TOPMODEL-Simulation Results.................................................................................................................22

Runoff ..................................................................................................................................................28

Prediction-Interval Uncertainty Analysis ..............................................................................34

Depth to Water Table .........................................................................................................................34

Prediction-Interval Uncertainty Analysis ..............................................................................42

Application of Calibration to Subwatersheds ................................................................................48

Summary .......................................................................................................................................................52

References Cited..........................................................................................................................................52
viii

Figures

1. Map showing location and principal hydrologic features of the Fishing Brook study

area, New York..............................................................................................................................3

2. Map showing topography of the Fishing Brook study area, New York, and

subwatersheds, model-assessment points, and synoptic sites ...........................................4

3. Map showing topographic wetness index and wetland areas in the Fishing Brook

study area, New York ...................................................................................................................6

4. Graph showing relative frequency distribution of the topographic wetness index for

the Fishing Brook study area, New York ..................................................................................9

5. Graph showing monthly mean runoff at U.S. Geological Survey streamgages

01312000, Hudson River near Newcomb, New York, and 0131199050, Fishing Brook

at County Line Flow near Newcomb, New York ....................................................................11

6. Photograph showing Sixmile Wetland with depth-to-water-table piezometers, May

2009. Photograph taken from site SS04, looking west towards sites SS05, MA08,

and MA09 .....................................................................................................................................12

7. Graph showing observed depth to water table at Sixmile Wetland, Fishing Brook

study area, New York, May and August 2009.........................................................................13

8. Graph showing observed depth-to-water-table fluctuations at Sixmile Wetland,

Fishing Brook study area, New York, April–August 2009 .....................................................13

9. Graphs showing snowmelt calibration A, raw precipitation and temperature, 

B, equivalent liquid precipitation and simulated snow water-equivalent depth, 

and C, simulated and observed runoff for Fishing Brook at County Line Flow near

Newcomb, New York, water year 2007 ...................................................................................16

10. Graphs showing snowmelt calibration A, raw precipitation and temperature, 

B, equivalent liquid precipitation and simulated snow water-equivalent depth, 

and C, simulated and observed runoff for Fishing Brook at County Line Flow near

Newcomb, New York, water year 2008 ...................................................................................17

11. Graphs showing snowmelt calibration A, raw precipitation and temperature, 

B, equivalent liquid precipitation and simulated snow water-equivalent depth, 

and C, simulated and observed runoff for Fishing Brook at County Line Flow near

Newcomb, New York, water year 2009 ...................................................................................18

12. Graphs showing Nash-Sutcliffe efficiency of runoff for snowmelt

calibration-parameter space for A, water year (WY) 2007, B, WY 2008, and 

C, WY 2009...................................................................................................................................19

13. Graphs showing generalized sensitivity analysis cumulative-probability

distributions for TOPMODEL calibration parameters with Kolmogorov–Smirnov d

statistic value ..............................................................................................................................21

14. Dotty plots of combined multiple-objective function and component-objective

functions.......................................................................................................................................22

15. Graphs showing simulated runoff and watershed-average saturation deficit,

best run for the modeling period and prediction intervals, Fishing Brook at County

Line Flow near Newcomb, New York, water year 2007........................................................23

16. Graphs showing simulated runoff and watershed-average saturation deficit,

best run for the modeling period and prediction intervals, Fishing Brook at County

Line Flow near Newcomb, New York, water year 2008........................................................24

17. Graphs showing simulated runoff and watershed-average saturation deficit,

best run for the modeling period and prediction intervals, Fishing Brook at County

Line Flow near Newcomb, New York, water year 2009........................................................25
ix

18. Boxplots of calibration-parameter values, by prediction-interval

class..............................................................................................................................................27

19. Graph showing simulated runoff, observed runoff, and equivalent liquid

precipitation for Fishing Brook at County Line Flow near Newcomb, New York, 

best run for the modeling period..............................................................................................29

20. Graphs showing simulated runoff, observed runoff, residuals, and equivalent 

liquid precipitation for Fishing Brook at County Line Flow near Newcomb, 

New York, best run for the modeling period for A, water year (WY) 2007, 

B, WY 2008, and C, WY 2009......................................................................................................30

21. Scatter plot of observed runoff and simulated runoff for Fishing Brook at County

Line Flow near Newcomb, New York, best run for the modeling period...........................31

22. Scatter plot of simulated runoff and residuals for Fishing Brook at County Line 

Flow near Newcomb, New York, best run for the modeling period ...................................31

23. Graph showing flow-duration curves of observed and simulated runoff for 

Fishing Brook at County Line Flow near Newcomb, New York, best run for the 

modeling period ..........................................................................................................................32

24. Graphs showing A, Cumulative simulated and observed runoff, and B, cumulative

difference, simulated and observed runoff, for Fishing Brook at County Line Flow

near Newcomb, New York, best run and range for all model runs for the modeling

period............................................................................................................................................33

25. Boxplots of simulated runoff for A, low flow (September 5, 2007), B, moderate flow

(May 5, 2009), and C, high flow (April 24, 2007) example days, Fishing Brook at

County Line Flow near Newcomb, New York, by prediction-interval class......................35

26. Diagram showing width of runoff prediction intervals for the modeling period 

for Fishing Brook at County Line Flow near Newcomb, New York, by predictioninterval class ...............................................................................................................................36

27. Graphs showing simulated depth to water table at Sixmile Wetland, Fishing Brook

study area, New York, best run for the modeling period and prediction intervals for

A, water year (WY) 2007, B, WY 2008, and C, WY 2009.........................................................37

28. Graph showing simulated and observed depth to water table at Sixmile Wetland,

Fishing Brook study area, New York, best run for the modeling period and

prediction intervals, April–August 2009 ..................................................................................38

29. Graph showing simulated and observed relative depth-to-water-table fluctuations

at Sixmile Wetland, Fishing Brook study area, New York, best run for the modeling

period and prediction intervals, April–August 2009..............................................................39

30. Scatter plot of observed and simulated depth above average at Sixmile Wetland,

Fishing Brook study area, New York, April–August 2009, best run for the 

modeling period ..........................................................................................................................40

31. Graph showing simulated saturation deficit and depth to water table, Fishing 

Brook study area average, Sixmile Wetland, and example upland area, best run 

for the modeling period..............................................................................................................41

32. Graph showing simulated saturated area, as percent of Fishing Brook study area,

New York, best run for the modeling period...........................................................................42

33. Map showing simulated saturated areas, showing minimum and maximum

saturation of Fishing Brook study area, New York, best run for the modeling period ....43

34. Boxplots of simulated watershed-average saturation deficit for A, low flow

(September 5, 2007), B, moderate flow (May 5, 2009), and C, high flow 

(April 24, 2007) example days, Fishing Brook study area, New York, by predictioninterval class ...............................................................................................................................44
x

Tables

1. TOPMODEL calibration parameters, watershed characteristics, and data sources

for the Fishing Brook study area, New York...........................................................................10

2. Snowmelt calibration-parameter ranges and fixed values.................................................15

3. Snowmelt calibration parameter and objective values, by water year ............................15

4. TOPMODEL parameter-calibration ranges ............................................................................19

5. Calibrated-model parameter values, best run, and prediction-interval classes .............26

6. Objective-function values for selected model runs and ranges ........................................28

7. Descriptive statistics for simulated runoff, best run, and all model runs during the

model period for Fishing Brook at County Line Flow near Newcomb, New York ............29

8. Descriptive statistics for observed and simulated daily mean runoff and best run

during the model period for Fishing Brook at County Line Flow near Newcomb,

New York ......................................................................................................................................32

9. Runoff prediction-interval widths, by class, for Fishing Brook at County Line Flow

near Newcomb, New York ........................................................................................................34

10. Descriptive statistics for simulated saturation deficit and depth to water table for

the best run during the model period for Fishing Brook study area average, Sixmile

Wetland, and example upland area.........................................................................................36

11. Simulated depth-to-water-table goodness-of-fit statistics for the best run and all

model runs ...................................................................................................................................40

12. Saturation-deficit prediction-interval widths, by prediction-interval class .....................44

13. Depth to water table in Sixmile Wetland prediction-interval widths, by

prediction-interval class............................................................................................................47

14. Subwatershed characteristics for the Fishing Brook study area ......................................48

15. Streamflow measurements at synoptic survey sites for the Fishing Brook study

area, New York, 2007–09............................................................................................................51

35. Diagram showing width of simulated watershed-average saturation deficit

prediction intervals for the modeling period, Fishing Brook study area, New York, 

by prediction-interval class ......................................................................................................45

36. Boxplots of simulated depth to water table at Sixmile Wetland, Fishing Brook study

area, New York, for A, low flow (September 5, 2007), B, moderate flow (May 5,

2009), and C, high flow (April 24, 2007) example days, by prediction-interval class........46

37. Diagram showing width of simulated depth-to-water-table prediction intervals 

for the modeling period, Fishing Brook study area, New York, by predictioninterval class ...............................................................................................................................47

38. Graphs showing simulated runoff for selected subwatersheds, Fishing Brook study 

area, New York, for A, water year (WY) 2007, B, WY 2008, and C, WY 2009 .....................49

39. Graphs showing simulated saturation deficit and watershed-average depth to water 

table for selected subwatersheds for A, water year (WY) 2007, B, WY 2008, and 

C, WY 2009....................................................................................................................................50

40. Scatter plot of simulated runoff and observed runoff for selected subwatersheds, 

Fishing Brook study area, New York........................................................................................51
xi

Conversion Factors and Datum

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square kilometer (km2

) 247.1 acre

square kilometer (km2) 0.3861 square mile (mi2

)

Flow rate

millimeter per day (mm/d) 0.03937 inch per day (in/d)

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

°F=(1.8×°C)+32

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88)

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

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

Water year: The 12-month period from October 1 through September 30. The water year is 

designated by the calendar year in which it ends.
xii

Acronyms and Abbreviations

CASTNET Clean Air Status and Trends Network

cdf cumulative-distribution function 

DEM digital elevation model

DOC dissolved organic carbon

E Nash-Sutcliffe coefficient of model-fit efficiency

E(ln) Nash-Sutcliffe coefficient evaluated for the natural logarithm of a quantity 

ESRI Environmental Systems Resource Institute

GBMM grid-based mercury model

GLUE Generalized Likelihood Uncertainty Estimate

Hg mercury

KSD Kolmogorov–Smirnov d

MA01–MA13 model-assessment points 01 to 13

MAE mean absolute error

NADP National Atmospheric Deposition Program

NADP–NTN National Atmospheric Deposition Program–National Trends Network

NAWQA National Water-Quality Assessment Program

NED National Elevation Dataset

NHD National Hydrography Dataset

r Pearson’s correlation coefficient

RMSE root mean squared error

S saturation deficit

SS01–07 synoptic sites 01 to 07

SSURGO Soil Survey Geographic Database

SUNY–ESF State University of New York College of Environmental Science and Forestry

TWI topographic wetness index

USGS U.S. Geological Survey

WATER Water Availability Tool for Environmental Resources

WY water year
TOPMODEL Simulations of Streamflow and Depth 

to Water Table in Fishing Brook Watershed, 

New York, 2007–09

By Elizabeth A. Nystrom and Douglas A. Burns 

Abstract

TOPMODEL, a physically based, variable-source area 

rainfall-runoff model, was used to simulate streamflow and 

depth to water table for the period January 2007–September 

2009 in the 65.6 square kilometers of Fishing Brook 

Watershed in northern New York. The Fishing Brook 

Watershed is located in the headwaters of the Hudson River 

and is predominantly forested with a humid, cool continental 

climate. The motivation for applying this model at Fishing 

Brook was to provide a simulation that would be effective 

later at this site in modeling the interaction of hydrologic 

processes with mercury dynamics.

TOPMODEL uses a topographic wetness index computed 

from surface-elevation data to simulate streamflow and 

subsurface-saturation state, represented by the saturation 

deficit. Depth to water table was computed from simulated 

saturation-deficit values using computed soil properties. In 

the Fishing Brook Watershed, TOPMODEL was calibrated 

to the natural logarithm of streamflow at the study area 

outlet and depth to water table at Sixmile Wetland using a 

combined multiple-objective function. Runoff and depth 

to water table responded differently to some of the model 

parameters, and the combined multiple-objective function 

balanced the goodness-of-fit of the model realizations with 

respect to these parameters. Results show that TOPMODEL 

reasonably simulated runoff and depth to water table during 

the study period. The simulated runoff had a Nash-Sutcliffe 

efficiency of 0.738, but the model underpredicted total runoff 

by 14 percent. Depth to water table computed from simulated 

saturation-deficit values matched observed water-table depth 

moderately well; the root mean squared error of absolute depth 

to water table was 91 millimeters (mm), compared to the mean 

observed depth to water table of 205 mm. The correlation 

coefficient for temporal depth-to-water-table fluctuations 

was 0.624. The variability of the TOPMODEL simulations 

was assessed using prediction intervals grouped using 

the combined multiple-objective function. The calibrated 

TOPMODEL results for the entire study area were applied to 

several subwatersheds within the study area using computed 

hydrogeomorphic properties of the subwatersheds.

Introduction

Mercury (Hg) is a potent neurotoxin that originates as 

emissions largely from human activities such as coal-fueled 

power generation and to a lesser extent from natural sources 

such as volcanism (Selin, 2009). These Hg emissions are 

transported by and later deposited from the atmosphere at 

local, regional, and global scales where many hydrological, 

geochemical, and biological processes affect the movement 

and accumulation of Hg in biota that can include humans 

through fish consumption. Identifying and modeling the 

processes that control Hg cycling in the environment is an 

important research goal and presents a formidable multidisciplinary challenge. One key element in this challenge is 

identifying and modeling the role of hydrological processes 

in transporting Hg from soils, where large stores representing 

decades of Hg deposition are present (Munthe and others, 

2007), to the aquatic environment, where bioaccumulation and 

food web dynamics can result in Hg levels in freshwater fish 

that are considered unsafe for human consumption. Elevated 

levels of Hg in fish are a widespread problem, with fishconsumption advisories issued by all 50 States in the United 

States (U.S. Environmental Protection Agency, 2009).

The U.S. Geological Survey (USGS) National WaterQuality Assessment Program (NAWQA) includes studies to 

better understand the processes that control the cycling of 

Hg as it affects rivers and streams in the U.S. An objective 

of the current (2011) NAWQA Hg study, of which this report 

represents a component, is testing and developing models 

that will lead to improved understanding of how watershed 

hydrological processes are linked to Hg bioaccumulation. 

Factors such as hydrological flow paths, watershed 

geomorphology, the permeability of soils, and many others 

may affect processes such as transport and methylation, which 

greatly influence Hg bioaccumulation. Past Hg-modeling 

approaches focused explicitly on biogeochemical and physical 

processes within lakes (Driscoll and others, 1995) and 

sometimes with inclusion of a simple watershed-loading factor 

(Knightes and Ambrose, 2007). Other Hg-modeling studies 

have linked the terrestrial environment with surface waters by 

applying simple catchment-transfer factors (Knightes, 2008) 
2 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

with some capable of moving Hg among vegetation, soils, 

groundwater, and the stream or lake (Chen and others, 2008; 

Chen and Herr, 2010). Despite an often detailed representation 

of the biogeochemical and physical processes that control Hg 

transformations in many of these models, most do not consider 

spatial representations of catchment hydrology, which may 

greatly affect Hg dynamics and transport such as a distinction 

between riparian and upland areas (Chen and others, 2008; 

Knightes, 2008).

A goal of the current (2011) NAWQA study is to develop 

improved modeling approaches that link hydrological 

processes to Hg transport in riverine settings. TOPMODEL, 

a semi-distributed, variable-source, physically based rainfallrunoff model was selected as an appropriate model for 

application in this case because the model is believed to 

provide a good representation of hydrologic-flow sources 

to streams (Hornberger and others, 1994), and Hg mobility 

has been shown to be strongly linked with these surface- and 

shallow subsurface-flow processes (Krabbenhoft and others, 

1995; Schelker and others, 2011). In particular, the ability 

of TOPMODEL to simulate the depth of the water table on 

a daily basis as a function of the topographic wetness index 

(TWI) (a computed value that describes the likelihood of 

saturation, described later in text) provides a potentially 

attractive approach to simulate Hg transport from shallow flow 

paths as a function of catchment geomorphological variation. 

In this study, TOPMODEL was applied at the 

Fishing Brook Watershed, a headwater of the Upper 

Hudson River Basin in New York State, for the period 

January 2007–September 2009. TOPMODEL was calibrated 

to observed runoff and depth to water table in the Fishing 

Brook Watershed using a Monte Carlo calibration evaluated 

with a combined multiple-objective function. Calibration 

results for the watershed also were used to simulate runoff 

and depth to water table for subwatersheds within the study 

area. The results of this model are intended for use as input to 

several additional Hg-modeling efforts as part of the NAWQA 

Program Hg study. Model-generated simulations of daily 

streamflow, water-table depth, and water fluxes from various 

flow-generation processes are anticipated to prove useful in 

these Hg-modeling applications, which are currently (2011) 

in process.

Purpose and Scope

The purpose of this report is to document the methods 

and results of a hydrologic-model application to the Fishing 

Brook Watershed, N.Y. The semi-distributed hydrologic 

model, TOPMODEL, was used to simulate streamflow 

and watershed-average saturation deficit on a daily basis 

for Fishing Brook Watershed and subwatersheds during 

2007–09. Data used for model input and evaluation included 

locally observed hydrologic and meteorologic data and 

remotely sensed digital elevation model (DEM) and soils 

data. TOPMODEL parameters were calibrated to observed 

streamflow and depth to water table using a multipleobjective Monte-Carlo optimization. A simplified predictioninterval uncertainty analysis was performed to assess the 

uncertainty and variability in the model results. Results from 

the Fishing Brook Watershed were applied to simulations in 

subwatersheds, which were compared to available discretestreamflow measurements. 

The TOPMODEL code used in this modeling effort 

contains a combination of English and metric units. For 

consistency within this report, all values used were converted 

to metric units.

Description of the Fishing Brook Watershed

Fishing Brook is a tributary of the Hudson River near 

its headwaters in New York (fig. 1). The study area, which 

covers 65.6 km2

, is defined as the portion of the Fishing Brook 

Watershed above USGS streamgage 0131199050, Fishing 

Brook at County Line Flow near Newcomb, N.Y. (fig. 1). 

The study area is located in Hamilton and Essex Counties 

in northern New York State and has a humid continental 

climate with cool summers. The mean yearly temperature is 

4.4oC, and the study area receives an average of 1,080 mm 

of precipitation per year (National Climatic Data Center, 

2002). Precipitation is distributed fairly evenly throughout 

the year, without specific wet or dry seasons, but much of the 

precipitation for December–March is snowfall, and as a result, 

streamflow in the study area shows significant seasonal trends, 

with the greatest flows usually observed during the spring 

snowmelt. Elevations in the study area range from 502 m at 

the outlet of the study area to 1,083 m; the highest elevations 

in the study area (over 1,000 m) are at the northern and 

southern ends of the basin (fig. 2).

The Fishing Brook study area is located in the Eastern 

Forest–Boreal Transition Ecoregion and is mostly (87 percent) 

forested with a mix of deciduous and evergreen forest; the 

remainder of land cover in the basin includes wetlands 

(9 percent), open water (3 percent), and developed land 

(1 percent) (Homer and others, 2004). Only one major paved 

road exists in the basin—route 28N (fig. 1)—and less than 

1 percent of the basin area consists of impervious surfaces. 

Very few structures exist in the watershed and there is little, 

if any, year-round human habitation. Surficial geology in the 

watershed reflects the effects of the Wisconsin glaciation; most 

of the watershed is covered in a thin layer of poorly sorted 

glacial till, with outwash and alluvial deposits of better-sorted 

material present in the valleys and low-lying areas of the 

watershed (Cadwell, 1991). The bedrock in the study area is 

mainly composed of granitic gneiss (Fisher and others, 1970).

The main tributary to Fishing Brook in the study area 

is Sixmile Brook; other tributaries in the basin generally are 

unnamed. Hydraulically well-connected riparian wetlands are 

present along streams throughout the basin, and the watershed 

contains a large wetland complex—the County Line Flow 

Swamp Megawetland (LaPoint and others, 2004)—a 2.8 km2
Introduction 3

Base from National Hydrography Dataset, 2008, 1:24,000

Universal Transverse Mercator projection

Zone 18

Lakes from New York State Adirondack Park Agency, 

Adirondack Park Freshwater Wetlands, 2000, 1:24,000

Hudson River Basin

0 2 4 MILES

0 2 4 KILOMETERS

ESSEX COUNTY

HAMILTON COUNTY

FRANKLIN COUNTY

Hudson River

near Newcomb

Watershed

Hudson River

NY20/HWF187

01312000

74°20' 74°10' 74°00'

44°05'

44°00'

43°55'

28N

Watershed boundary

Basin boundary

0131199050

0 1 2 MILES

0 1 2 KILOMETERS

74°22' 74°20' 74°18' 74°16'

44°00'

43°58'

43°56'

Pickwacket

Pond

County

Line

Flow

Fishing

Brook

Flow

Fishing

Brook

Fishing 

Sixmile

Brook

Brook

Fishing Brook

Watershed

Sixmile Brook

28N

0131199050

EXPLANATION

0131199050

National Atmospheric 

Deposition Program 

site NY20 and Clean Air

Status and Trends Network

site HWF187 

Fishing Brook

(County Line Flow)

near Newcomb

Hudson River near Newcomb

NY20/

HWF187

01312000

Fishing Brook study area

Hudson River Basin

Hudson River near 

Newcomb Watershed

CANADA

NEW

HAMPSHIRE

VERMONT

NEW YORK

PENNSYLVANIA CONNECTICUT

MASSACHUSETTS

ESSEX COUNTY

ESSEX COUNTY

HAMILTON COUNTY

Figure 1. Location and principal hydrologic features of the Fishing Brook study area, New York.
4 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Base from National Elevation Dataset, 2009,

1/3 arc-second, Universal Transverse Mercator

projection, Zone 18

Hydrology from U.S. Geological Survey,

National Hydrography Dataset, 2008, 1:24,000

Lakes from New York State Adirondack Park Agency,

Adirondack Park Freshwater Wetlands, 2000, 1:24,000

SS01

SS03

SS05

SS06

SS04

SS02

SS07 MA11

MA10

MA09

MA08

MA07

MA04

MA03

MA01

MA13

MA12

MA06

MA05

MA02

450 to 500

>500 to 550

>550 to 600

>600 to 650

>650 to 700

>700 to 750

>750 to 800

>800 to 850

>850 to 900

>900 to 950

>950 to 1,000

>1,000 to 1,050

>1,050 to 1,100

>1,100 to 1,150

Elevation, in meters

EXPLANATION

SS01

MA01 Model-assessment point 

Watershed boundary

Subwatershed boundary

Synoptic site

HAMILTON COUNTY

ESSEX COUNTY

0 1 2 MILES

0 1 2 KILOMETERS

74°22' 74°20' 74°18' 74°16'

44°00'

43°58'

43°56'

Figure 2. Topography of the Fishing Brook study area, New York, and subwatersheds, model-assessment points, and 

synoptic sites.
TOPMODEL 5

riparian wetland consisting of scrub-shrub vegetation, 

coniferous forested swamp, and emergent marsh, of which 

Sixmile Wetland (approximately 1 km2

) is a part (fig. 3). 

Major surface-water impoundments in the watershed include 

County Line Flow, 0.4 km2

 surface area; Pickwacket Pond, 

0.8 km2

; and Fishing Brook Flow, 0.2 km2 (fig. 1). 

TOPMODEL 

TOPMODEL, first proposed by Beven and Kirkby 

(1979), is a physically based, semi-distributed, variable-source 

area rainfall-runoff model, and is based on the TWI proposed 

by Kirkby (1975). Three main assumptions underlie most 

formulations of TOPMODEL (Beven and others, 1995):

1. The hydraulic gradient of the water table can be 

approximated by the land-surface slope.

2. Dynamic conditions can be adequately represented by a 

steady-state approximation.

3. The saturated hydraulic conductivity decreases 

exponentially with depth.

TOPMODEL is expected to be best applied in watersheds 

where these assumptions hold, for example, humid watersheds 

with shallow soils, which are likely to have topographic 

controls on water-table depth (Beven and others, 1995). 

TOPMODEL groups areas of hydrological similarity using 

a topographically based wetness index and simulates runoff 

generation from several sources based on calculated watershed 

storage and storage deficits.

Topographic Wetness Index and 

Saturation Deficit

The TWI represents the local subsurface hydraulic 

conditions by combining the local hydraulic gradient 

(approximated by the local surface slope) and the volume of 

water draining through a point (proportionate to the upslope 

contributing area). The TWI is defined as

(1)

where 

TWI is the topographic wetness index, in 

ln(meters);

ln is the natural logarithm;

α is the upslope contributing area per unit 

contour length, in meters, and

tan β is the local slope.

and is typically calculated on a spatially distributed basis using 

DEMs. High values of the TWI indicate locations that have 

large contributing areas and low slopes and that are likely 

to be saturated; areas with high TWI values often are found 

along streams, in areas of groundwater discharge, and wetlands (fig. 3) (Wolock and Price, 1994). Low values of TWI 

indicate areas unlikely to be saturated, with small contributing 

areas and high slopes; areas with low TWI values typically 

are found at the top of hillslopes and in areas of groundwater 

recharge. In many versions of TOPMODEL (including the 

version used in this investigation), the TWI is used to group 

hydrologically similar areas in the watershed; calculations 

then are performed in a semi-distributed manner on the groups 

rather than on a fully distributed basis.

In TOPMODEL, the vertical profile of hydraulic 

conductivity is assumed to follow an exponential decay of the 

form:

 (2)

where

Kz is the hydraulic conductivity at depth z, in 

millimeters per hour;

K0 is the hydraulic conductivity at the surface, in 

millimeters per hour;

m is a scaling parameter, in millimeters;

ndrain is the readily drained soil porosity; and, 

z is the depth from the surface, in millimeters.

A steady-state approximation of conservation of mass 

(continuity) and Darcy’s law is applied using the TWI and the 

exponential conductivity profile to calculate subsurface flow 

and storage.

TOPMODEL equations generally are defined in terms 

of the saturation deficit, a measure related to depth to the 

saturated zone; the saturation deficit is equal to the depth to 

water table multiplied by the readily drained soil porosity. The 

saturation deficit at a specific location is related to, and can be 

calculated from, the watershed-average saturation deficit:

Sx= S + m(Λ-TWIx ) (3)

where

Sx is the local saturation deficit, in millimeters;

S is the watershed-average saturation deficit, in 

millimeters;

m is a scaling parameter, in millimeters; 

Λ is the watershed average topographic wetness 

index, in ln(meters); and

TWIx is the local topographic wetness index, in 

ln(meters).

TOPMODEL Streamflow-Generation Concepts

The main forcing mechanism for streamflow generation 

in TOPMODEL is precipitation, and an accurate precipitation 

record is required as input to TOPMODEL for accurate runoff 

prediction (Beven, 2001). TOPMODEL uses variable-source 

area runoff-generation mechanisms to model streamflow, 

including base flow, return flow, runoff generated from 

K K e z 0

ndrain

m z

= –

TWI = 



 



 ln

tan

α

β
6 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Base from National Elevation Dataset, 2009, 1/3 arc-second

Universal Transverse Mercator projection

Zone 18

Wetlands from New York State Adirondack Park Agency, Adirondack Park Freshwater Wetlands, 2000, 1:24,000

Topographic wetness index

EXPLANATION

2 to 4

>4 to 5

>5 to 6

>6 to 7

>7 to 8

>8 to 9

>9 to 10

>10 to 12

>12 to 30

Wetland boundary

Watershed boundary

Sixmile Wetland HAMILTON COUNTY

ESSEX COUNTY

ESSEX COUNTY

0 1 2 MILES

0 1 2 KILOMETERS

74°22' 74°20' 74°18' 74°16'

44°00'

43°58'

43°56'

Figure 3. Topographic wetness index and wetland areas in the Fishing Brook study area, New York.
TOPMODEL 7

precipitation on saturated areas, and direct precipitation 

on open water. TOPMODEL uses two main conceptual 

subsurface stores of water: an unsaturated zone and a 

saturated zone; runoff is generated only from the saturated 

zone. The location of the interface between the two zones 

corresponds to the saturation deficit and controls the types and 

amounts of flow generated by the model.

Potential evapotranspiration is calculated using the 

Hamon method (Hamon, 1961). Precipitation that falls is 

first used to satisfy potential evapotranspiration, and then 

infiltrates into the unsaturated zone and may drain to the 

saturated zone; a macropore-flow term allows a percentage 

of precipitation to infiltrate directly to the saturated zone. 

Evapotranspiration, when not satisfied from precipitation, is 

taken from the root zone at a rate proportional to the root-zone 

storage (Beven and others, 1995). Precipitation that falls on 

open water areas (including lakes and streams) immediately 

becomes streamflow. To account for attenuation in lakes, an 

exponential decay function is applied to the portion of flow in 

the watershed that drains through lakes.

Water from the saturated zone drains to streams as base 

flow based on the steady-state application of continuity and 

Darcy’s law. The saturation deficit is calculated for each TWI 

value; when the saturation deficit is less than zero for a given 

TWI, the saturated zone reaches the land surface, and the 

portion of flow in the saturated zone equivalently “above” 

the land surface becomes return flow. If precipitation falls 

on areas with a saturation deficit equal to or less than zero, 

the precipitation becomes saturation overland flow. Runoff 

generated by infiltration excess occurs when the precipitation 

intensity exceeds the infiltration capacity. 

Previous Studies

TOPMODEL is more a conceptual framework for 

simulating hydrological processes than a single, defined 

model, and can be modified to meet different goals (Beven, 

1997). While most applications have calibrated TOPMODEL 

and evaluated its goodness-of-fit to streamflow data, others 

have explored how well the model can simulate distributed 

water-table levels and their variation in time (Moore and 

Thompson, 1996; Seibert and others, 1997; Blazkova and 

others, 2002). TOPMODEL predictions of water-table levels 

are of specific interest in the current (2011) study because of 

the role of shallow groundwater flow in transporting Hg to 

nearby streams and because saturated, organic-rich surface 

soils are known to be important in the geochemical cycling 

of mercury.

Several investigations have applied TOPMODEL to 

simulate stream-water quality through flow-path partitioning 

driven by model output, the development of surrogate indexes, 

or by linking with a biogeochemical model (Wolock and 

others, 1989; Robson and others, 1992; Band and others, 

1993; Hornberger and others, 1994; Page and others, 2007). 

Of particular interest in the current study are previous 

attempts to use TOPMODEL to simulate dissolved organic 

carbon (DOC) concentrations in stream water as described by 

Hornberger and others (1994) and Boyer and others (1996). In 

these studies, the depth of the water table derived from daily 

saturation-deficit predictions combined with porosity were 

used to simulate the higher DOC concentrations observed in 

a Rocky Mountain river during snowmelt than during base 

flow. The response was modeled as a flushing process of 

DOC from shallow soils where the saturation deficit was used 

to quantitatively partition flow into shallow- and deep-flow 

compartments. The approach described above is potentially 

useful in the NAWQA Hg study because the transport of Hg 

from soils to streams is strongly controlled by and associated 

with the transport of DOC.

Specific TOPMODEL Version

The specific version of TOPMODEL used in this 

investigation is adapted from the FORTRAN code used in 

the Water Availability Tool for Environmental Resources 

(WATER), documented by Williamson and others (2009) and 

Kennen and others (2008). This version was derived from 

the original Beven and Kirkby (1979) version by Hornberger 

and others (1985) and adapted by Wolock (1993). A parallel 

investigation to this study, Feaster and others (2010), applied 

TOPMODEL in a South Carolina Coastal Plain watershed, 

and also includes an application of the grid-based mercury 

model (GBMM). Schelker and others (2011) also applied this 

version of TOPMODEL in the Fishing Brook Watershed for 

the period January 1, 2006, to June 16, 2008, in conjunction 

with water-quality sampling and observation of saturated 

areas for prediction of stream-water Hg concentrations. The 

version of TOPMODEL used in this study and in Schelker 

and others (2011) differs in two ways from that in Feaster 

and others (2010): in the current study, flow generation from 

impervious surfaces is not used (impervious surfaces cover 

less than 1 percent of the study area), and an internal snow 

accumulation and melt routine was activated. 

Snow accumulation and melt routines in the model 

operate on a simple degree-day basis, computing the 

equivalent water depth of the snowpack using a cutoff 

temperature, which is compared to the daily mean air 

temperature. When the daily mean temperature is less than the 

cutoff temperature, any precipitation that falls is added to a 

water-equivalent snowpack. When the daily mean temperature 

is greater than the cutoff temperature, melting or partial 

melting of the accumulated snowpack occurs. The maximum 

melt for any day is limited by the available snowpack-water 

equivalent. Routines are included in the model for melt owing 

to temperature alone and melt owing to the combined effects 

of temperature and rain. Snowmelt owing to temperature 

alone is calculated using an air-temperature index method 

(equation 4). This temperature-index method is best suited for 

use in heavily forested areas (greater than 80 percent forested; 

87 percent of the study area is forested) where the effects of 
8 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

wind and shortwave radiation are not significant factors in 

snowmelt (U.S. Army Corps of Engineers, 1998).

Mt=Cm (Tmean – Tcut ) (4)

where

Mt is the amount of melt, in millimeters per day;

Cm is a melt-rate coefficient, in millimeters per 

degrees Celsius per day;

Tmean is the daily mean air temperature, in degrees 

Celsius; and

Tcut is a cutoff or base temperature, in degrees 

Celsius.

The melt-rate coefficient (equation 4) is related to the 

density of the snowpack; it varies with geographic location 

and can change over time (Gray and Prowse, 1992). Typical 

values are 1.8 to 3.7 mm per degree Celsius per day for 

forested watersheds with higher values in less forested areas 

or windy conditions (U.S. Army Corps of Engineers, 1998). 

The melt-rate coefficient and base-temperature values both are 

specified as model-input parameters and can be calibrated in 

TOPMODEL.

Daily melt owing to rain on snow incorporates a simple 

energy-budget approach:

Mr = (33.833+0.0126P) (Tmean – Tcut ) + 1.27 (5)

where Mr is the amount of melt, in millimeters per day;

P is the daily precipitation, in millimeters per 

day;

Tmean is the daily mean air temperature, in degrees 

Celsius; and

Tcut is a cutoff or base temperature, in degrees 

Celsius.

The energy-budget approach is practicable for use in the 

case of rain on snow because it can be assumed that the air is 

water-saturated and that cloud cover minimizes the effects of 

solar radiation (U.S. Army Corps of Engineers, 1998).

Observed Data

Data observed in the Fishing Brook Watershed were 

used as input to TOPMODEL and to evaluate model 

simulations. Many sources of data were available in Fishing 

Brook Watershed and the surrounding area, including locally 

observed data and remotely sensed data. 

Input Data for Model Processing

To model streamflow, TOPMODEL uses three main 

input sets including (1) a time series of meteorological data, 

(2) the TWI distribution, and (3) model parameters, including 

watershed characteristics and calibration parameters. 

Meteorological Data

Meteorological data required to run TOPMODEL 

include precipitation and temperature; daily total precipitation 

and daily average temperatures were used. Several sources 

of meteorological data are available near the study area, 

including collocated National Atmospheric Deposition 

Program (NADP) and Clean Air Status and Trends Network 

(CASTNET) sites, 3.8 km from the outlet of the study 

area (fig. 1). The NADP and CASTNET sites are located 

in a clearing that is at approximately the same elevation as 

the outlet of the study area (approximately 500 m) and is 

located slightly downstream of the study area in the Fishing 

Brook Watershed.

Precipitation

Daily total precipitation amounts used in the model 

were from the National Atmospheric Deposition Program–

National Trends Network (NADP–NTN) site NY20 (National 

Atmospheric Deposition Program, 2009; data available 

at http://nadp.sws.uiuc.edu/), at which precipitation was 

measured using a Belfort weighing bucket and recorded on 

a daily basis. Daily data were recorded from midnight to 

midnight, eastern daylight time. Other time-series data that 

were recorded at more frequent intervals, such as temperature 

and streamflow, were averaged on a daily basis to match the 

recording period of the precipitation data. Data were quality 

assured by the NADP–NTN (quality-assurance plans available 

at http://nadp.sws.uiuc.edu/lib/qaPlans.aspx). Precipitation 

amounts recorded as “trace” by NADP–NTN were included 

in the model as 0.005 inch (0.13 mm), or half of the minimum 

recordable amount of the instrument. Data that were missing 

or screened as invalid by the NADP–NTN were replaced by a 

secondary precipitation record collected by CASTNET, which 

was recorded at 1-hour intervals and summed to a daily time 

step (Clean Air Status and Trends Network, 2010). For the 

period January 25, 2005, to September 30, 2009, 933 days of 

valid precipitation data from NADP–NTN were used in the 

model; the remaining 47 days of record were filled in with the 

secondary CASTNET record.

Temperature

Daily average temperature for use in the model was 

calculated from hourly values recorded at Huntington Wildlife 

Forest, CASTNET site HWF187 (Clean Air Status and 

Trends Network, 2010, data available at http://java.epa.gov/

castnet/epa_jsp/prepackageddata.jsp). Ambient temperature 

was measured at 9 m above ground surface using a platinum 

resistance-temperature device. Hourly temperature values 

were quality assured by CASTNET, screened before use 

based on the resulting data-quality indicator, and averaged to 

compute daily values. If more than two hourly values were 

missing from the record or were quality assured as invalid, 

data for that day were replaced with data from a secondary 

record. For the period January 25, 2005, to September 30, 
Observed Data 9

2009, 961 days of valid temperature data from CASTNET 

were used in the model. The secondary record of temperature 

data was recorded daily by the State University of New York 

College of Environmental Science and Forestry (SUNY–ESF) 

at a site collocated with the CASTNET site and was used 

for the remaining 19 days (Myron J. Mitchell., SUNY–ESF, 

unpub. data, 2010, information available at http://www.esf.

edu/hss/huntington_forest_research_overview.htm).

Topographic Wetness Index

TWI distributions were computed from the National 

Elevation Dataset (NED) 1/3 arc-second dataset (Gesch and 

others, 2002, data available at http://seamless.usgs.gov/). The 

horizontal resolution of the NED 1/3 arc-second dataset is 

approximately 10 m. The NED raster data were processed in 

Environmental Systems Resource Institute (ESRI) ARCGIS 

using Spatial Analyst tools and the Raster Calculator. Sinks, 

or cells in the DEM that are lower than all surrounding cells, 

were filled to the level of the lowest surrounding cell to ensure 

that the resulting derived hydrology network was continuous. 

Downslope-flow directions were determined from the filled 

DEM as the direction from a cell to its steepest downslope 

neighboring cell. Specific accumulated area for each cell, α

(equation 1), was computed from the flow-direction raster; the 

number of accumulated cells was computed, which then was 

multiplied by the area per cell and divided by the cell width, 

in meters. Cell slopes, tanβ (equation 1), were calculated from 

the percent slope calculated by the Spatial Analyst Surface 

Slope function. Cells with a slope value of zero were replaced 

with a small value (0.01) because a value of zero would cause 

the computed TWI value to equal infinity. The TWI value for 

each cell (fig. 3) then was computed as the natural log of the 

specific accumulated area divided by the slope ratio using 

the Raster Calculator. The TWI was clipped to the watershed 

shapefile and exported as a text file for processing into 

frequency distributions. The relative frequency distributions of 

TWI were computed using 30 equal-width bins (fig. 4).

Model Parameters

In addition to TWI, TOPMODEL uses several model 

parameters that reflect the hydrology, soils, and location of 

the study area (table 1). The values of each of these model 

parameters can be calibrated or set as fixed values based on 

available information; in this application, fixed values were 

used for model parameters based on spatial data such as 

soils and elevation, and parameters based on non-measured 

values were calibrated. Model parameters that were set 

based on available data are referred to herein as watershed 

characteristics; the remaining parameters are referred to as 

calibration parameters.

Watershed Characteristics 

Watershed characteristics used in TOPMODEL include 

areas of the watershed, lakes, and streams; the drainage area 

upstream of lakes; the latitude of the watershed; and soil 

properties (table 1). Watershed boundaries were digitally 

delineated from 1:24,000 scale digital contours, with 

modifications based on field observations in select areas 

with low slope drainage divides. Lake areas were calculated 

0 5 10 15 20 25 30

0

0.05

0.1

0.15

0.2

0.25

Relative frequency, fraction of watershed area

Topographic wetness index, in natural logarithm of meters

Figure 4. Relative frequency distribution of the topographic wetness index for the Fishing Brook study area, New York.
10 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Table 1. TOPMODEL calibration parameters, watershed characteristics, and data sources for the Fishing Brook study area, 

New York.

[APA Freshwater Wetlands (New York State Adirondack Park Agency, 2000); NHD, National Hydrography Dataset (U.S. Geological Survey, 2008); 

SSURGO, Soil survey geographic database (Natural Resources Conservation Service, 2009); NED, National Elevation Dataset (Gesch and others, 2002); 

--, calibrated value]

Model parameter Units Data source

Watershed 

characteristic value, 

Fishing Brook 

study area

Total area square kilometers 1:24,000 digital data 65.64

Lake area square kilometers 1:24,000 APA Freshwater Wetlands 1.74

Stream area square kilometers 1:24,000 NHD .34

Saturated hydraulic conductivity millimeters per hour SSURGO 48.3

Soil depth meters SSURGO 1.50

Field capacity decimal percent SSURGO .24

Water-holding capacity decimal percent SSURGO .18

Porosity decimal percent SSURGO .38

Uplake area decimal percent NED 1/3 arc-second 1.00

Latitude decimal degrees 1:24,000 digital data 43.973

Cut temp (Tcut) degrees Celsius Calibrated --

Snow factor (Cm) millimeters per degree Celsius per day Calibrated --

Scaling parameter (m) millimeters Calibrated --

Conductivity multiplier fractional multiplier Calibrated --

Percent macropore flow decimal percent Calibrated --

Depth of root zone meters Calibrated --

Lake delay days-1 Calibrated --

from the open water class of the 1:24,000 Adirondack Park 

Freshwater Wetlands shapefile (New York State Adirondack 

Park Agency, 2000). The drainage area upstream of lakes was 

calculated using basins delineated at the outlets of each of the 

three largest open water bodies in the study area—Pickwacket 

Pond, County Line Flow, and Fishing Brook Flow (fig. 1). 

Stream area was calculated using the 1:24,000 National 

Hydrography Dataset (NHD) (U.S. Geological Survey, 2008), 

assuming an average stream width of 5 m.

Soil properties, including saturated hydraulic 

conductivity, soil depth, field capacity, water-holding capacity, 

and porosity, were computed from the Soil Survey Geographic 

(SSURGO) Database (National Resources Conservation 

Service, 2009, data available at http://soildatamart.nrcs.usda.

gov/). SSURGO tabular data for each map unit were extracted 

by soil component and horizon and weighted for depth and 

area. Rock outcrops and open water were excluded from the 

soil-property calculations. 

Calibration Parameters

Some model-parameter values could not be set using 

available data because measurements or values were not 

available, and these parameters were therefore calibrated; 

they included snowmelt model parameters, the scaling factor

(m), the conductivity multiplier (conmult), percent macropore 

flow (pmac), root zone depth (zroot), and lake delay factor 

(rip_decay). Snowmelt model parameters, Tcut and Cm, control 

the threshold between snow accumulation and melt and the 

rate of snowmelt per degree above that threshold. The scaling 

parameter, m, is one of the most important TOPMODEL 

parameters (Beven and others, 1995); it controls the rate of 

decrease of the vertical profile of hydraulic conductivity and 

has important effects on the slope of the recession curve. The 

conductivity multiplier represents the comparative difference 

between the mean and maximum hydraulic conductivity of 

the soil. The percent macropore flow parameter represents the 

portion of flow that is routed directly to the saturated zone 

from the surface, bypassing the unsaturated zone; this value is 

difficult to determine from field observations. The lake delay 

parameter controls the relative magnitude and duration of flow 

attenuation through lakes. The depth of root zone parameter 

controls the depth of the zone in which water is available 

to satisfy potential evapotranspiration; no measurements of 

representative root zone depth were available in the study area.
Observed Data 11

Unused Model Parameters

Several model parameters are included in the FORTRAN 

code as documented by Feaster and others (2010), Williamson 

and others (2009), and Kennen and others (2008) that were 

not used in this application of TOPMODEL. Unused model 

parameters mainly described human impacts on the watershed, 

including impervious area-runoff controls (impervious area 

covers less than 1 percent of the study area) and groundwater 

and surface-water withdrawals from and discharges to the 

watershed. An additional channel-routing parameter described 

in Schelker and others (2011) is included in the input file 

for this version of TOPMODEL, but is implemented in a 

separate section of the WATER toolbox and is not used in the 

TOPMODEL code.

Observed Streamflow and Depth to Water Table 

for Model Evaluation

Streamflow and depth to water table measured in the 

study area were used to assess TOPMODEL predictions of 

streamflow and saturation deficit.

Streamflow

Streamflow in the study area was gaged at the outlet of 

County Line Flow, USGS streamgage 0131199050 (fig. 1), 

from January 25, 2007, through early 2010 using a standard 

stage-discharge rating (U.S. Geological Survey, 2011). 

Streamflow data were collected at 15-minute intervals and 

summed to match the daily time period of the NADP daily 

precipitation data. For comparability among watersheds 

and subwatersheds in this area and others, streamflow (with 

units of volume per unit time) will be discussed throughout 

this report in terms of runoff, which is equal to streamflow 

normalized by the drainage area, and has units of length per 

unit of time. 

Runoff in the study area shows significant seasonal 

patterns (fig. 5). At the Hudson River near Newcomb 

(station 01312000, fig. 1), a nearby USGS streamgage with 

a long period of record, the long-term median of monthly 

mean runoff values (fig. 5) varies from a minimum of 

0.72 mm/d in February to a maximum of 5.74 mm/d in April 

(U.S. Geological Survey, 2010). Measured runoff for Fishing 

Brook during the modeling period showed seasonal trends 

Monthly mean runoff, in millimeters per day

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

0

2

4

6

8

10

12

90th percentile

75th

50th (median)

25th

10th

EXPLANATION

Station 01312000—October 1925 to 

September 2009; 69 observations in 

February to September and 68 

observations in October to January

Station 0131199050—February 2007 

to September 2009

Station 01312000—February 2007 to 

September 2009

Monthly mean runoff

Month

Figure 5. Monthly mean runoff at U.S. Geological Survey streamgages 01312000, Hudson River near Newcomb, New York, and 

0131199050, Fishing Brook at County Line Flow near Newcomb, New York.
12 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

similar to those observed at the Hudson River near Newcomb 

during the same time period (fig. 5). The median daily runoff 

for the Fishing Brook study area during the modeling period 

was 1.27 mm/d; the minimum daily runoff was 0.077 mm/d, 

occurring on September 5, 2007; and the maximum daily 

runoff was 23.5 mm/d, occurring on April 24, 2007. 

Depth to Water Table

Depth to water table was measured in Sixmile Wetland 

(fig. 6) during April–September 2009 using 3.8-cm diameter 

piezometers. Thirty-seven piezometers were installed between 

USGS stations 0131199021 and 0131199022 (SS05 and SS04, 

respectively, fig. 2) in two main north/south transects across 

the eastern end of the wetland, with two smaller additional 

groups of piezometers installed close to Sixmile Brook. 

The piezometers were installed and developed during fall 

2008 and had a 30.5 cm slotted section that typically was 

installed approximately 50 to 80 cm below ground surface. 

Two types of water-level measurements were made using the 

piezometers: absolute depth to water table and a time series 

of relative depth-to-water-table fluctuations. The two types 

of depth-to-water-table measurements were used to address 

two components of depth-to-water-table predictions from 

TOPMODEL: depth-to-water-table measurements were used 

to better approximate the quantitative saturation deficit in the 

study area, and the water-table fluctuations were used to assess 

the ability of the model to reproduce water-table fluctuations 

over time in the study area.

Depth to water table was measured using electric 

tapes in 27 of the wells at least once. Three groups of depth 

to water measurements were made (fig. 7): on May 5 

and 6 (24 piezometers measured, median depth to water 

232 mm), May 19 and 20 (24 piezometers measured, 

median depth to water 104 mm), and August 13, 2009 

(20 piezometers measured, median depth to water 279 mm). 

Twenty piezometers were measured during all three sets of 

measurements, one piezometer was measured twice, and six 

piezometers were measured once.

Figure 6. Sixmile Wetland with depth-to-water-table piezometers, May 2009. Photograph taken from site SS04, looking west 

towards sites SS05, MA08, and MA09.
TOPMODEL Calibration 13

-200

200

400

600

800

0

24

20

24

Depth to water table, in millimeters

May 5 to 6 May 19 to 20 August 13

24 Number of 

observations

90th percentile

75th

50th (median)

25th

10th

EXPLANATION

2009

Observation date

Figure 7. Observed depth to water table at Sixmile Wetland, 

Fishing Brook study area, New York, May and August 2009.

Water-table fluctuations were logged in seven 

piezometers from April 23 to September 25, 2009, using 

non-vented submersible pressure transducers at 15-minute 

intervals. Measured pressure data were converted to water 

depth above transducer by subtracting barometric pressure 

and using water density calculated from temperature data 

logged by the pressure transducers. The 15-minute data were 

averaged to a daily time step for use with TOPMODEL results. 

Depth-to-water-table data collected after August 27, 2009, 

were not used in the TOPMODEL calibrations because of a 

backwater effect created in the wetland by the construction of 

a beaver dam at the outlet of Sixmile Wetland. Slug tests were 

conducted on July 30 and 31, 2009; data from these two days 

were excluded from the depth-to-water-table calculations.

Depth-to-water-table time series are compared among 

wells and to TOPMODEL output by subtracting the average 

depth of water from each time series (fig. 8). The median of 

the range recorded in each piezometer over time was 41.5 mm, 

or 3.7 times the median of the daily range among piezometers.

TOPMODEL Calibration

TOPMODEL was used to simulate runoff on a daily 

time step for the Fishing Brook Watershed during the period 

January 25, 2007–September 30, 2009. The period October 1, 

2005–January 24, 2007, was used to condition (or initialize) 

the model. Calibration of TOPMODEL was accomplished 

Figure 8. Observed depth-to-water-table fluctuations at Sixmile Wetland, Fishing Brook study area, New York, 

April–August 2009.

Range

Median

EXPLANATION

2009

Observation date

April 23 May 23 June 23 July 23 August 23

Depth above average, in millimeters

-300

-200

-100

0

100

200

300

400
14 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

in two steps: first, snowmelt parameters were calibrated 

to runoff; second, these snowmelt parameters were held at 

fixed values as the remaining parameters were calibrated to 

runoff and depth to water table using a combined multipleobjective function. A non-directed Monte-Carlo optimization, 

using parameter values randomly selected from uniform 

distributions, was used for both calibration steps. Sensitivity 

analyses and a simplified prediction-interval uncertainty 

analysis were used to evaluate the results. 

Model output is evaluated by comparison to measured 

runoff and depth to water table using several goodness-of-fit 

statistics including (1) the Nash-Sutcliffe model efficiency 

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

coefficient (r), (3) the root mean squared error (RMSE), 

(4) the bias, and (5) the mean absolute error (MAE). The 

definitions for the goodness-of-fit statistics are expressed 

below in terms of runoff; depth to water table also can be 

substituted where appropriate. 

The Nash-Sutcliffe coefficient of model-fit efficiency, 

E, is defined as

E

where 

N is the number of time steps in the simulation 

period,

Qoi is the observed runoff for time step i,

Qo is the mean observed runoff for the simulation 

period, and 

Qsi is the simulated runoff for time step i.

The Nash-Sutcliffe coefficient of model-fit efficiency, E, 

can emphasize the effect of outliers and large flows (McCuen 

and others, 2006); to balance the emphasis on low flows, the 

Nash-Sutcliffe model efficiency of the natural log of runoff 

also is used to evaluate model output.

Pearson’s correlation coefficient, r, is defined as

(7) r

Qo Qo Qs Qs

Qo Qo

i

N

i i

i

N

i i

N

=

− 



 



 − 



 





− 



 





=

= =

∑

∑ ∑

1

1

2

1 Qs Qs i − 



 





2

where

Qs is the mean observed runoff for the simulation 

period.

The RMSE is defined as

(8)

The bias is defined as

(9) bias Qs Qo

N

i

N

i i = ( ) − ∑ =1

RMSE Qs Qo

N

i

N

i i = ( ) − ∑ =1

2

The MAE is defined as

MAE Qs Qo

N

i

N

i i = − ∑ =1

Snowmelt Calibration

Values of the TOPMODEL parameters that affect snow 

accumulation and melt, TCut

 and Cm, can change over time 

with the condition of the snowpack and melting mechanism 

(Gray and Prowse, 1992). Changing snow density, albedo, 

and internal snowpack energy, as well as varying atmospheric 

conditions and solar radiation can all affect Cm, the meltrate coefficient. Conditions preceding snowmelt events are 

likely to vary from year to year. Snowmelt parameters were 

therefore calibrated by individual water year (WY) separately 

from the main TOPMODEL parameters, allowing them to 

adjust to different melt conditions occurring in the watershed. 

TOPMODEL was run in 10,000 Monte-Carlo simulations 

for each WY; snowmelt parameters were assigned randomly 

from a uniform distribution within a specified range of values, 

and the remaining TOPMODEL parameters were set to fixed 

values (table 2). A 1-year period beginning October 1 of 

the previous WY was used to condition the model for each 

snowmelt calibration. In WY 2007, the conditioning period 

was effectively longer because runoff data were not available 

until January 25, 2007, and model output was therefore not 

evaluated for 116 days of WY 2007. From the 10,000 MonteCarlo runs for each WY, optimum snowmelt-parameter values 

were chosen using the Nash-Sutcliffe efficiency of runoff. 

The results of the individual WY snowmelt calibrations were 

applied to the observed rainfall record and then combined 

to generate a continuous equivalent liquid-precipitation 

record. In the equivalent liquid-precipitation record, the time 

of occurrence of precipitation was shifted during periods 

of modeled snowfall and snowmelt; precipitation that was 

modeled as falling snow was shifted to occur as input to 

TOPMODEL during a later modeled snowmelt period. A timeseries record of the equivalent water depth of the snowpack 

also was developed. The equivalent liquid-precipitation 

record then was used in the calibration of the remaining 

TOPMODEL parameters.

Results of Snowmelt Calibration

The results of the snowmelt calibration generally show 

good agreement with observed snowmelt-runoff events 

(figs. 9–11 and table 3). The maximum simulated snowpackwater-equivalent values for each winter during 2007–09 were 

153, 246, and 116 mm, respectively. Runoff in the calibration 

portion of WY 2007 (fig. 9) was dominated by a single spring 

snowmelt-runoff event, which was followed by a relatively 

dry period. The peak runoff for the event was matched well 

by the calibration results, but total volume of runoff for the 

event was underpredicted. Runoff in WY 2008 (fig. 10) was 
TOPMODEL Calibration 15

Table 2. Snowmelt calibration-parameter ranges and fixed values.

Model parameter Units Value or calibration range

Cut temp (Tcut) degrees Celsius −2.22 to 1.67

Snow factor (Cm) millimeters per degree Celsius per day .457 to 4.57

Scaling parameter (m) millimeters 15

Conductivity multiplier multiplier 3

Percent macropore flow decimal percent .2

Depth of root zone meters 1

Lake delay unitless 1

similarly dominated by the spring snowmelt-runoff event, 

but an additional mid-winter snowmelt event and several 

smaller non-snowmelt runoff events also occurred. Calibration 

results reproduce the form of the mid-winter event and the 

double-peaked form of the spring event well; however, a 

peak preceding the main spring snowmelt-runoff event was 

simulated, but not observed, and the magnitude of the spring 

event peaks was overpredicted. The smaller spring snowmeltrunoff peak in WY 2009 was more comparable to nonsnowmelt runoff events (fig. 11) than those in WYs 2007 and 

2008. The magnitude of a mid-winter snowmelt-runoff event 

in WY 2009 was underpredicted, and a snowmelt-runoff event 

in March 2009 was overpredicted. An observed runoff event at 

the end of April 2009 was not predicted by the simulation. 

The Nash-Sutcliffe efficiency of the snowmelt calibration 

was highest for WY 2007 (0.775), which had the shortest 

calibration period and most distinct snowmelt-runoff event, 

and lowest for WY 2009 (0.357), which had the least 

distinct snowmelt-runoff event (table 3). Nash-Sutcliffe 

efficiencies for WYs 2008 and 2009 also may have been 

affected by the occurrence of mid-winter snowmelt-runoff 

events, while in WY 2007, the snowmelt parameters were 

effectively calibrated to a single snowmelt-runoff event. 

In WYs 2008 and 2009, the snowmelt calibration included 

multiple snowmelt events, which may have been preceded 

by different snowpack conditions or caused by different 

snowmelt mechanisms. Calibration runs with the highest 

Nash-Sutcliffe model efficiencies were found in different 

areas of the snowmelt calibration-parameter space in each 

WY (table 3 and fig. 12). Figure 12 is a representation of the 

response surface for each snowmelt calibration, showing the 

Nash-Sutcliffe efficiency value for each combination of two 

parameters used. The calibrated value of Tcut for WY 2007 

was almost 1oC greater than for WYs 2008 or 2009, and the 

calibrated value of the melt-rate coefficient, Cm, varied from 

0.55 mm per degree Celsius per day in WY 2009 to 1.55 mm 

per degree Celsius per day in 2008. A discontinuity occurs in 

the Tcut parameter space for the WY 2007 calibration at around 

freezing (fig. 12). The main snowmelt event for that year was 

preceded by 3 days of essentially equal average temperature 

(fig. 9), just below 0oC; Tcut values even slightly below this 

temperature cause the snowmelt to occur too early, resulting 

in a sudden decrease in efficiency. Optimum Tcut and Cm values 

are not identified as clearly for the WY 2009 calibration as for 

WY 2007 or WY 2008; this may be because of a calibration 

conflict between a mid-winter snowmelt-runoff event (fig. 10) 

and a spring snowmelt-runoff event as a result of differences 

in snowpack conditions or snowmelt mechanisms (two bands 

of maxima occur in the Nash-Sutcliffe efficiency parameter 

space corresponding to the snowmelt events) or because of the 

relatively small magnitude of the main snowmelt event. 

Table 3. Snowmelt calibration parameter and objective values, by water year.

[Water year, the 12-month period from October 1 through September 30. The water year is designated by the calendar year in which it ends; Tcut, cutoff 

temperature; Cm, melt-rate coefficient; mm, millimeter; E, Nash-Sutcliffe coefficient of model-fit efficiency; E(ln), Nash-Sutcliffe coefficient evaluated for the 

natural logarithm of a quantity; r, Pearson’s correlation coefficient; RMSE, root mean squared error; MAE, mean absolute error]

Water year

Tcut, 

degrees 

Celsius

Cm, mm 

per degree 

Celsius, per 

day

Time steps 

in 

evaluation

E E(ln) r

RMSE, 

mm 

per day

Bias, 

mm

MAE, 

mm

2007 0.3069 1.0054 249 0.775 0.553 0.901 1.30 −0.520 0.694

2008 −.5883 1.5538 366 .637 .414 .834 1.56 −.210 1.02

2009 −.6890 .5484 365 .357 .629 .647 1.47 −.467 1.12
16 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Raw precipitation

Air temperature

Tcut—Snowmelt cutoff temperature

Equivalent liquid precipitation

Simulated snow depth

Observed runoff

Simulated runoff—Snowmelt calibration 

2006 2007

Water year 2007

EXPLANATION

0

10

20

30

40

50

60

70

80

Precipitation, in millimeters

−20

−15

−10

−5

0

5

10

15

20

Temperature, in degrees Celsius 

0

10

20

30

40

50

60

70

80 0

50

100

150

200

250

300

350

400

Water equivalent, in millimeters

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

0

5

10

15

20

25

Runoff, in millimeters per day

A. Raw precipitation and temperature

C. Simulated and observed runoff

B. Equivalent liquid precipitation and simulated snow water-equivalent depth

Figure 9. Snowmelt calibration A, raw precipitation and temperature, B, equivalent liquid precipitation and simulated 

snow water-equivalent depth, and C, simulated and observed runoff for Fishing Brook at County Line Flow near Newcomb, 

New York, water year 2007.
TOPMODEL Calibration 17

Water year 2008

A. Raw precipitation and temperature

C. Simulated and observed runoff

B. Equivalent liquid precipitation and simulated snow water-equivalent depth

0

10

20

30

40

50

60

70

80

Precipitation, in millimeters

−20

−15

−10

−5

0

5

10

15

20

Temperature, in degrees Celsius 

0

10

20

30

40

50

60

70

80 0

50

100

150

200

250

300

350

400

Water equivalent, in millimeters

0

5

10

15

20

25

Runoff, in millimeters per day

Raw precipitation

Air temperature

Tcut—Snowmelt cutoff temperature

Equivalent liquid precipitation

Simulated snow depth

Observed runoff

Simulated runoff—Snowmelt calibration 

EXPLANATION

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

2007 2008

Figure 10. Snowmelt calibration A, raw precipitation and temperature, B, equivalent liquid precipitation and simulated 

snow water-equivalent depth, and C, simulated and observed runoff for Fishing Brook at County Line Flow near Newcomb, 

New York, water year 2008.
18 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Water year 2009

B. Equivalent liquid precipitation and simulated snow water-equivalent depth

Tcut—Snowmelt cutoff temperature

A. Raw precipitation and temperature

C. Simulated and observed runoff

0

10

20

30

40

50

60

70

80

Precipitation, in millimeters

-20

-15

-10

-5

0

5

10

15

20

Temperature, in degrees Celsius 

0

10

20

30

40

50

60

70

80 0

50

100

150

200

250

300

350

400

Water equivalent, in millimeters

0

5

10

15

20

25

Runoff, in millimeters per day

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

2008 2009

Raw precipitation

Air temperature

Simulated snow depth

Observed runoff

Simulated runoff—Snowmelt calibration 

EXPLANATION

Equivalent liquid precipitation

Figure 11. Snowmelt calibration A, raw precipitation and temperature, B, equivalent liquid precipitation and 

simulated snow water-equivalent depth, and C, simulated and observed runoff for Fishing Brook at County Line 

Flow near Newcomb, New York, water year 2009.
TOPMODEL Calibration 19

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Cm, in millimeters per degree Celsius per day

−2 −1 0 1

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0.5

1

1.5

2

2.5

3

3.5

4

4.5

A. Water year 2007

B. Water year 2008

C. Water year 2009

TCUT , in degrees Celsius

[Tcut, snowmelt cutoff temperature;

Cm , snowmelt rate coefficient]

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 Nash-Sutcliffe 

 efficiency (E)

EXPLANATION

Figure 12. Nash-Sutcliffe efficiency of runoff for 

snowmelt calibration-parameter space for A, water 

year (WY) 2007, B, WY 2008, and C, WY 2009.

Runoff and Depth-to-Water-Table Calibration

Using the equivalent liquid-precipitation record generated 

by the snowmelt calibration, TOPMODEL was calibrated 

to observed runoff and depth to water table using 100,000 

Monte-Carlo model runs evaluated with a combined multipleobjective function. The combined multiple-objective function 

contained terms representing the evaluation of goodness-of-fit 

of runoff and depth to water table. TOPMODEL parameters 

were assigned randomly from a uniform distribution within 

a range of values (table 4). Parameter ranges were based 

on values from previous studies and initial, experimental 

model runs.

Table 4. TOPMODEL parameter-calibration ranges.

Model parameter Units Calibration range

Scaling parameter (m) millimeters 11–40

Conductivity multiplier multiplier 1.05–100

Percent macropore flow decimal percent .01–.6

Depth of root zone meters .2–1.5

Lake delay unitless 1–3

Runoff Objective Function

The goodness-of-fit of simulated runoff was evaluated by comparison to observed runoff at USGS streamgage 

0131199050 using the Nash-Sutcliffe efficiency of the natural 

logarithm of runoff. The Nash-Sutcliffe efficiency can range 

from negative infinity to 1; where the computed value of the 

Nash-Sutcliffe efficiency was negative (E values less than zero 

indicate that the average observed value would be a better 

predictor than the simulated values), the value of the runoff 

objective function was set to zero:

 (11) Obj E Q

ln Qo ln Qs

Q

i i i

N

= ( ) ( ) [ ] = − ( ) ( ) − ( ) ∑ = maximum m ln , aximum

l

0 1

2

1

n ln

,

Qo Qo i i

N

( ) ( ) − ( )



















 ∑ =

2

1

0

where 

ObjQ is the runoff objective function, and

ln[Q] is the natural logarithm of runoff.

The logarithm of runoff was used to balance the 

emphasis on the range of flows for the main calibration. The 

untransformed runoff was used in the snowmelt calibration 

because the larger flows were of most interest for accurate 

calibration of snowmelt events, but accurate reproduction 

of the full range of flows was considered important in the 

main calibration. 
20 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Depth-to-Water-Table Objective Functions

The saturation deficit predicted by TOPMODEL was 

incorporated into the calibration by conversion to a measure 

of local depth to water table and comparison to observed 

values from depth-to-water-table measurements made in 

Sixmile Wetland (fig. 3). Depth to water table was computed 

first by converting the basin-average saturation deficit, S, to a 

local saturation deficit, Sx

, using equation 3, which offsets the 

saturation deficit by a factor related to model parameter m and 

the difference between the watershed-average TWI and the 

local TWI. The TWI in Sixmile Wetland near the observation 

locations was approximately 11.04 ln(m); the watershed 

average TWI for the study area was 6.86 ln(m). A local depth 

to water table then was computed:

 (12)

where

zx is the local depth to water table, in 

millimeters;

Sx is the local saturation deficit, in millimeters; 

and

ndrain is the readily drained soil porosity.

The modeled depth to water table was compared to 

two components of observed values: (1) absolute depth to 

water table and (2) relative depth-to-water-table fluctuations. 

While depth-to-water-table measurements were available in 

only one location in the study area, providing limited spatial 

information, their use provides a reference point within the 

study area to constrain simulated saturation-deficit values. 

Additionally, because the location of the groundwater 

measurements is in a wetland area where methylation and 

transport of Hg to the stream is believed to be important, this 

location is believed to be especially valuable when using 

TOPMODEL output calibrated to depth to water table to 

develop approaches for modeling Hg, a goal of the overall 

NAWQA Hg study.

Absolute Depth to Water Table

The simulated absolute depth to water table was 

compared to the tape-down measurements. The measurements 

were made in three groups: May 5 and 6; May 19 and 20, 

and August 13, 2009. For purposes of evaluation, values 

from consecutive days were combined; the median observed 

depth to water table for a group was compared to the mean 

of the simulated depth to water table for the group (a 1- or 

2-day period). The combined depth-to-water-table value was 

evaluated by normalizing the RMSE and subtracting from one. 

Similar to E, this value can range from negative infinity to 1; 

where this value was negative, the objective function was set 

to zero:

 

 (13)

where

ObjDTW TD is the absolute depth-to-water-table 

objective function, 

RMSE(DTW TD) is the root mean squared error of the 

combined observed and simulated 

absolute depth to water table, and 

DTW TDo is the mean of the combined observed 

depth to water table.

Relative Depth-to-Water-Table Fluctuations

The relative depth-to-water-table fluctuations was 

evaluated using the Pearson correlation coefficient (r) of the 

observed and simulated depth to water table for the period 

of observed depth to water table described previously in 

this report. This approach tests the ability of the model to 

simulate the variation of depth to water table over time 

without constraining it to an absolute value; Seibert and 

McDonnell (2002) applied this method to depth to water 

table in the calibration of a three-box conceptual model to 

runoff, depth to water table, and additional fuzzy measures, 

including measures of new water and reservoir volume. The 

simulated and observed depth to water table for the period 

of the piezometer measurements was converted to a depthabove-average water table. The correlation of the daily time 

series of water levels in each of the seven piezometers with the 

simulated depth to water table was computed, and the relative 

depth-to-water-table fluctuation objective function was 

computed as the mean of the seven correlation coefficients:

 (14)

where 

ObjDTW TS is the relative depth-to-water-table objective 

function,

rj is Pearson’s correlation coefficient for 

piezometer j, and

M is the number of piezometers.

The correlation coefficient can range from −1 to 1; in this 

case, all simulated values were positively correlated with the 

observed values.

Combined Multiple-Objective Function

The three objective functions (runoff, absolute depth 

to water table, and relative groundwater table level) were 

combined into a single objective function using a weighted 

geometric mean. Runoff was weighted equally to depth to 

water table; within the depth to water table, the absolute depth 

to water table was weighted equally to relative depth to water 

table, as follows:

z S

n x

x

drain

=

Obj r

M DTW TS

j

M

j

 = ∑ =1

Obj

RMSE DTW TD

DTW TD DTW TD

o

= − ( ) 













 maximum 1 0
TOPMODEL Calibration 21

Objcomb = ObjQ

1⁄2

*ObjDTW TD

1⁄4

*ObjDTW TS

1⁄4 (15)

where 

Objcomb is the weighted combined multiple-objective 

function.

The combined-objective function then will have a value 

between zero and 1.

Generalized Sensitivity Analysis

A generalized sensitivity analysis, following the form 

proposed in Spear and Hornberger (1980) and Hornberger and 

Spear (1981), was performed on the set of 100,000 maincalibration runs. The cumulative-distribution function (cdf) 

for each of the five model-calibration parameters (fig. 13) was 

compared for ‘behavioral’ runs (the highest 10 percent for 

the combined-objective function) and ‘nonbehavioral’ runs 

(the lowest 90 percent for the combined-objective function). 

If the model (or objective function evaluating the model) is 

sensitive to a calibration parameter, the cdf for the behavioral 

runs will be different from the cdf for the nonbehavioral runs. 

The Kolmogorov–Smirnov d (KSD) statistic was used as a 

simple measure to quantify the difference among distributions 

(Spear and Hornberger, 1980); higher values of KSD 

represent larger differences among cdfs. The results of the 

sensitivity analysis showed that the most sensitive parameter 

is the scaling parameter m (KSD 0.69). The parameter 

conductivity multiplier conmult showed moderate sensitivity 

(KSD 0.32); the root zone depth zroot and lake delay factor 

rip_decay showed some sensitivity (KSD 0.18 and 0.13, 

respectively). The percent macropore flow parameter showed 

little sensitivity (KSD 0.01). The results of the generalized 

sensitivity analysis should be considered somewhat subjective, 

as they depend on the objective function used and the cutoff 

between behavioral and non-behavioral runs; co-dependence 

of multiple parameters sometimes can be exhibited as a lack 

of sensitivity. 

Dotty plots of the model-calibration parameters versus 

the combined multiple-objective function and each of the 

component-objective functions (fig. 14) reveal different 

patterns of interaction among model parameters and each of 

the component-objective functions. Dotty plots represent a 

method to collapse the multi-dimensional parameter space into 

single parameter dimensions; each point in the plot represents 

one model run and shows the value of one parameter versus 

a measure of the model outcome. While dotty plots cannot 

show the complex interactions between multiple parameters, 

they can help illustrate the response of the model. Some of 

the objective measures are not sensitive to certain individual 

model parameters; for example, ObjQ shows little, if any, 

response to the conductivity multiplier parameter, and 

ObjDTW TD shows little response to the lake delay factor, with 

values reaching the maximum and minimum of the objective 

across the range of the model-parameter value. These model 

parameters do, however, affect other objective functions, with 

maximum values of the objective function being attained by 

specific ranges of the model parameter. While ObjQ shows 

little response to the conductivity-multiplier parameter, higher 

values of ObjDTW TD occur for higher values of this parameter. 

The parameter that shows the most specific effect of all of the 

50 100

0

0.2

0.4

0.6

0.8

1

Conductivity multiplier

KSD=0.32

Fraction

0.2 0.4 0.6

Percent macropore flow

KSD=0.01

20 30 40

Scaling factor (m)

KSD=0.69

0.5 1 1.5

Root zone depth

KSD=0.18

1 2 3

Lake decay factor

KSD=0.13

Objcomb bottom 90 percent

Objcomb top 10 percent

EXPLANATION

[KSD, Kolmogorov-Smirnov d statistic;

Objcomb, combined multiple-objective function]

Value

Figure 13. Generalized sensitivity analysis cumulative-probability distributions for TOPMODEL calibration parameters 

with Kolmogorov–Smirnov d statistic value.
22 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

EXPLANATION

0

0.2

0.4

0.6

0.8

1

Objcomb ObjQ ObjDTW TD

20 40 60 80 100

ObjDTW TS 

Conductivity multiplier Percent macropore flow

20 30 40

Scaling factor (m)

1

Root zone depth

1 2 3

Lake decay factor

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

0.2 0.60.4 0.5 1.5 1.5 2.5

ObjDTW TS

ObjDTW TD

Objcomb

ObjQ

Combined multiple-objective function

Runoff objective function

Absolute depth-to-water-table objective function

Relative time series depth-to-water-table objective function

Figure 14. Dotty plots of combined multiple-objective function and component-objective functions.

objective functions—the scaling factor m—shows a slightly 

different response shape in each of the component-objective 

functions; the shape of the multiple-objective function scatter 

plot balances these component objectives when combined.

TOPMODEL-Simulation Results

The runoff and saturation deficits simulated 

by TOPMODEL are shown in figures 15–17. In the 

following sections, the results are described qualitatively, 

graphically, and statistically. Two main aspects of the 

results of TOPMODEL simulations are discussed: 

(1) the single TOPMODEL run with the highest value of the 

combined-objective function, referred to hereafter as the ‘best 

run,’ is compared to observed values, and (2) the variability 

within the set of model runs and the uncertainty of the model 

predictions is assessed using prediction intervals.

A prediction interval, as used in this study, is a group of 

simulated values for a defined class of Monte-Carlo model 

runs. In this case, the classes are defined based on percentiles 

of the combined-objective function. Because the model 

output is highly dependent on the selection of calibrationparameter ranges and objective function(s), formal statistical 

probabilities are not assigned, as in Bayesian uncertainty 

analysis or more formal applications of the Generalized 

Likelihood Uncertainty Estimate (GLUE) as described in 

Beven and Binley (1992). The prediction-interval classes are 
TOPMODEL-Simulation Results 23

All model runs

Objcomb > 0

Objcomb top 1 percent

Observed

Simulated, best run

Runoff, in millimeters per day

0

5

10

15

20

25

Saturation deficit, in millimeters

0

50

100

150

200

250

300

350

400

A. Runoff

B. Saturation deficit

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

2006 2007

Water year 2007

EXPLANATION

[Objcomb , Combined multiple objective function]

Figrue 15. Simulated runoff and watershed-average saturation deficit, best run for the modeling period and prediction 

intervals, Fishing Brook at County Line Flow near Newcomb, New York, water year 2007.
24 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

All model runs

Objcomb > 0

Objcomb top 1 percent

Observed

Simulated, best run

EXPLANATION

[Objcomb , Combined multiple-objective function]

Runoff, in millimeters per day

0

5

10

15

20

25

Saturation deficit, in millimeters

A. Runoff

B. Saturation deficit 0

50

100

150

200

250

300

350

400

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

2007 2008

Water year 2008

Figrue 16. Simulated runoff and watershed-average saturation deficit, best run for the modeling period and prediction 

intervals, Fishing Brook at County Line Flow near Newcomb, New York, water year 2008.
TOPMODEL-Simulation Results 25

Depth-to-water-table time series start and end dates

Depth-to-water-table tape down measurement dates

All model runs

Objcomb > 0

Objcomb top 1 percent

Observed

Simulated, best run

EXPLANATION

Runoff, in millimeters per day

0

5

10

15

20

25

Saturation deficit, in millimeters

A. Runoff

B. Saturation deficit 0

50

100

150

200

250

300

350

400

Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

2008 2009 Water year 2009

[Objcomb , Combined multiple-objective function]

Figrue 17. Simulated runoff and watershed-average saturation deficit, best run for the modeling period and prediction 

intervals, Fishing Brook at County Line Flow near Newcomb, New York, water year 2009.
26 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

defined starting with the best run; followed by those runs with 

the highest 0.1 percent of combined-objective values (referred 

to as ‘Objcomb top 0.1 percent’), the highest 1 percent of runs 

(‘Objcomb top 1 percent’), and the highest 10 percent of runs 

(‘Objcomb top 10 percent’); then all 64,746 runs with combined 

objective greater than zero (‘Objcomb > 0’); and finally, the full 

range of 100,000 model runs (‘all runs’). Simulated values 

within each group are compared; variability of model output 

also is described by the width of the prediction interval, 

or the difference between the maximum and minimum 

simulated values within a group at a time step. Predictioninterval widths (figs. 15–17) for three of the classes, as shown 

by shaded areas, vary over time with the general basinsaturation condition. 

The calibrated model-parameter values are listed in 

table 5 and are shown in figure 18 by prediction-interval class. 

The specificity of the calibration parameters generally reflects 

the results of the sensitivity analysis; the most sensitive 

parameters have smaller ranges and standard deviations in the 

highest interval classes compared to their overall distribution. 

For example, the ratio of the standard deviation of parameter 

values for the 1 percent class as compared to that of all runs 

is 0.17 for the scaling parameter m, and 0.91 for percent 

macropore flow (table 5). 

The maximum value of the combined multipleobjective function achieved in the 100,000 model runs 

was 0.678 (table 6). Component objective-function values 

corresponding to the model run with the highest combinedobjective values were in the 89th percentile or higher of their 

individual objective-function value ranges. The maximum 

values of each of the component-objective functions also 

are shown in table 6, along with the values of the other 

component-objective functions for that model run; they 

illustrate the specificity of each of the objective functions, 

and that calibration of TOPMODEL to runoff alone will 

not necessarily produce accurate predictions of depth to 

water table.

Table 5. Calibrated-model parameter values, best run, and prediction-interval classes.

[Obj , weighted combined multiple objective function; %, percent; >, greater than] comb

Conductivity 

multiplier

Percent 

macropore 

flow 

Scaling 

parameter m, 

millimeters

Depth of 

root zone, 

meters

Lake delay, 

days-1

Calibration range

Value, best run

1.05 to 100

99.117

0.01 to 0.6

0.509

11 to 40

16.904

0.2 to 1.5

0.921

1 to 3

2.315

Objcomb top 0.1% 92.917 .512 16.821 .886 2.410

Objcomb top 1% 87.308 .403 17.105 .878 2.384

Median

Objcomb top 10% 72.296 .302 18.097 .836 2.175

Obj > 0 comb 49.496 .313 20.385 .840 2.005

All runs 50.461 .305 25.483 .851 2.003

Objcomb top 0.1% 4.809 .100 .957 .079 .375

Objcomb top 1% 11.029 .154 1.429 .119 .430

ation

Objcomb top 10% 20.874 .170 2.178 .261 .516

devi

Obj > 0 comb 28.495 .172 5.473 .374 .576

rd 

All runs 28.457 .170 8.364 .376 .576

Standa

Ratio, Objcomb top .17 .59 .11 .21 .65

0.1% to all runs

Ratio, Objcomb top 1% .39 .91 .17 .32 .75

to all runs
TOPMODEL-Simulation Results 27

Conductivity multiplier

20

40

60

80

100

Percent macropore flow

0.1

0.2

0.3

0.4

0.5

0.6

Scaling parameter (

m), in millimeters

1.0

1.5

2.0

2.5

3.0

Lake delay, in days-1

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Depth of root zone, in meters

15

20

25

30

35

40

All runs

Objcomb > 0

Objcomb top 10 percent

Objcomb top 1 percent

Objcomb top 0.1 percent

Best run

90th percentile

75th

50th (median)

25th

10th

A. Conductivity multiplier

D. Depth of root zone E. Lake delay

B. Percent macropore flow C. Scaling factor

EXPLANATION

[Objcomb , Combined multiple-objective function]

Figure 18. Boxplots of calibration-parameter values, by prediction-interval class.
28 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Table 6. Objective-function values for selected model runs and ranges.

, weighted combined multiple objective function; ObjQ, runoff objective function; ObjDTW TD [Obj , absolute depth-to-water-table objective function; comb

Obj , relative time series depth-to-water-table objective function] DTW TS

Model run Objective value or percentile

Objcomb Obj Obj Q DTW TD ObjDTW TS

Best run (maximum Objcomb) 0.678 0.782 0.554 0.624

Best run (maximum Objcomb) -- 99 96 89

component objective percentile

Maximum ObjQ .580 .795 .285 .626

Maximum ObjDTW TD .586 .542 .715 .560

Maximum ObjDTW TS .581 .652 .404 .666

Minimum, all runs .000 .000 .000 .494

Median, all runs .443 .574 .279 .540

Maximum, all runs .678 .795 .715 .666

Runoff

Plots of the simulated runoff for the best run show 

that the model captures the general shape and trends of the 

observed runoff fairly well (fig. 19); the Nash-Sutcliffe 

efficiency of runoff is 0.738, and 0.782 for the natural log of 

runoff (table 7). The residuals of the simulated and observed 

runoff for the best run are shown by WY in figure 20. The 

model generally underpredicts the peak value of runoff 

events (seen as negative residual peaks in fig. 20); the relative 

magnitude of this error generally is greater for small to 

moderate events, similar to TOPMODEL simulations for 

the same Fishing Brook Watershed as shown in Schelker 

and others (2011). A scatter plot of simulated and observed 

daily runoff (fig. 21) shows that flows generally fall along 

the 1:1 line of correspondence, with a Pearson correlation 

coefficient of 0.868 (table 7); however, at low flows, residuals 

tend to be positive (overestimation by the model, plotting 

above the 1:1 line), and at mid to high flows, residuals tend 

to be negative (underestimation by the model, plotting below 

the 1:1 line). The largest residuals, both positive and negative, 

occur at the higher simulated flows; residuals are small for low 

flows (fig. 22). These overpredictions and underpredictions 

also are apparent in the basic statistics describing runoff 

(table 8) and in the flow-duration curves for the modeling 

period (fig. 23). 

Overall, the model underpredicts the total volume 

of runoff by approximately 14 percent (fig. 24), with an 

average bias of −0.287 mm/d (table 7). Total simulated 

evapotranspiration for the modeling period was 1,463 mm, 

or 46 percent of total precipitation. Murdoch and others 

(1987), by comparison, observed evapotranspiration rates of 

approximately 40 percent in two watersheds approximately 

50 km from the Fishing Brook study area. 

Most of the 100,000 Monte-Carlo model runs 

underpredicted total runoff (the range of simulated cumulative 

runoff as shown by the shaded area in fig. 24); interestingly, 

the model run with the highest combined multiple-objective 

function is close to the minimum simulated cumulative 

runoff (or largest underprediction) for all of the model 

runs. The majority (89 percent) of the total underprediction 

for the best run occurred during three events (dark blue 

in fig. 24) comprising 20 percent of the modeling period: 

during snowmelt 2007, the mid-winter melt events during 

October–December 2007, and a post-snowmelt event in 

2009. These three events contained negative residuals that 

were not balanced by the occurrence of any significant 

positive residuals, unlike many other events. The average 

underprediction during these events was 1.25 mm/d, compared 

to 0.04 mm/d during the remainder of the modeling period; 

without these three events, total model underprediction is 

approximately 1.5 percent. These three underprediction events 

could represent an artifact of the separate snowmelt calibration 

or of the objective function used.
TOPMODEL-Simulation Results 29

Equivalent liquid precipitation

Observed

Simulated, best run

EXPLANATION

0

50

100

150

200

250

Equivalent liquid precipitation, in millimeters per day

0

5

10

15

20

25

Runoff, in millimeters per day

Jan. Apr. July

2007 2008 2009

Oct. Jan. Apr. July Oct. Jan. Apr. July Oct. 

Month and year

Figure 19. Simulated runoff, observed runoff, and equivalent liquid precipitation for Fishing Brook at County Line Flow 

near Newcomb, New York, best run for the modeling period.

Table 7. Descriptive statistics for simulated runoff, best run, and all model runs during the model period for Fishing Brook at County 

Line Flow near Newcomb, New York.

[E, Nash-Sutcliffe coefficient of model-fit efficiency; E(ln), Nash-Sutcliffe coefficient evaluated for the natural logarithm of a quantity; r, Pearson’s correlation 

coefficient; RMSE, root mean squared error; mm/d, millimeter per day; MAE, mean absolute error]

E E(ln) r RMSE, mm/d Bias, mm/d MAE, mm/d

Best run 0.738 0.782 0.868 1.224 −0.287 0.696

Minimum, all runs .349 −.135 .648 1.149 −.323 .683

Median, all runs .616 .574 .803 1.483 −.226 .855

Maximum, all runs .769 .795 .886 1.931 .045 1.154
30 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Equivalent liquid precipitation

Observed runoff

Simulated runoff, best run

Residual, best run

0

25

50

75

−10

−5

0

5

10

15

20

25

0

25

50

75

−10

−5

0

5

10

15

20

25

Runoff, in millimeters per day

0

25

50

75

Equivalent liquid precipitation, in millimeters per day

−10

−5

0

5

10

15

20

25 A. Water year 2007

C. Water year 2009

B. Water year 2008

EXPLANATION

Month and year

Oct. Nov. Dec.

2006 2007

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Oct. Nov. Dec.

2007 2008

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Oct. Nov. Dec.

2008 2009

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Figure 20. Simulated runoff, observed runoff, residuals, and equivalent liquid precipitation for Fishing Brook at 

County Line Flow near Newcomb, New York, best run for the modeling period for A, water year (WY) 2007, B, WY 2008, 

and C, WY 2009.
TOPMODEL-Simulation Results 31

10-2 10-1 100 101 102 10-2

10-1

100

101

102

Observed runoff, in millimeters per day

Simulated runoff, in millimeters per day

Figure 21. Scatter plot of observed runoff and simulated runoff for Fishing Brook at County Line 

Flow near Newcomb, New York, best run for the modeling period. The blue line represents a 1:1 

correspondence of simulated and observed runoff.

10-1 100 101 102 -8

-6

-4

-2

0

2

4

6

Simulated runoff, in millimeters per day

Residual runoff, in millimeters per day

Figure 22. Scatter plot of simulated runoff and residuals for Fishing Brook at County Line Flow near Newcomb, New 

York, best run for the modeling period.
32 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Table 8. Descriptive statistics for observed and simulated daily mean runoff and best run during the model period for Fishing Brook at 

County Line Flow near Newcomb, New York.

Observed runoff, Simulated runoff, best run, Residual runoff, best run,

millimeters per day millimeters per day millimeters per day

Minimum 0.078 0.129 −7.37

Median 1.27 1.17 −.031

Mean 2.08 1.78 −.287

Maximum 23.3 16.8 4.29

Standard deviation 2.39 2.02 1.19

Sum, 1/25/2007 to 9/30/2009 2,043 1,761 −282

Observed runoff

Simulated runoff

EXPLANATION

0 10 20 30 40 50 60 70 80 90 100

10-2

10-1

100

101

102

Runoff, in millimeters per day

Percentage of time runoff was equaled or exceeded

Figure 23. Flow-duration curves of observed and simulated runoff for Fishing Brook at County Line Flow near Newcomb, 

New York, best run for the modeling period.
TOPMODEL-Simulation Results 33

Range, all model runs

Observed

Simulated, best run

Difference, best and observed

Underprediction event

EXPLANATION

Month and year

Total runoff, in millimeters

0

500

1,000

1,500

2,000

2,500

−300

−200

−100

0

100

Total residual, in millimeters

A. Cumulative runoff

B. Cumulative difference, simulated and observed runoff

Jan. Apr. July

2007 2008 2009

Oct. Jan. Apr. July Oct. Jan. Apr. July Oct. 

Figure 24. A, Cumulative simulated and observed runoff, and B, cumulative difference, simulated and observed runoff, 

for Fishing Brook at County Line Flow near Newcomb, New York, best run and range for all model runs for the modeling 

period.
34 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Prediction-Interval Uncertainty Analysis

The forms of the runoff-prediction intervals generally 

are similar to that of the best model run (figs. 15–17).The best 

run as determined by the combined-objective function tended 

to underpredict or “miss” many of the small or moderate, 

non-snowmelt rainfall-runoff events; comparing the timing of 

the peaks in the prediction intervals to those of the observed 

runoff reveals a slight timing offset in many of the summer 

and fall events. Timing offsets can cause significant decreases 

in the Nash-Sutcliffe efficiency (McCuen and others, 2006); 

therefore, the combined-objective function was probably 

insensitive to these runoff events, as the simulated-runoff 

peak occurred during a different time step than the observedrunoff peak. 

The median width of the prediction intervals for the 

five classes varied from 0.292 to 1.36 mm/d (table 9). The 

median width of the prediction intervals was smaller than the 

median simulated runoff for the top three classes of prediction 

intervals (table 9). The range of simulated-runoff values 

generally was much larger for larger runoff (for example 

fig. 25C). Correspondingly, the width of each of the prediction 

intervals varied with time; prediction-interval widths were 

5 mm/d or less for almost all time steps and classes (fig. 26); 

the maximum range in predicted values over all model 

runs was 27.3 mm/d, which is approximately equal to the 

maximum observed runoff during the modeling period. 

Depth to Water Table

Simulated watershed-average saturation deficits for the 

best run ranged from 26.7 to 161 mm, with a median value of 

99.3 mm and a range of 134 mm during the modeling period 

(table 10 and figs. 15–17). The median depth to water table 

calculated using the watershed-average readily drained soil 

porosity is 715 mm for the entire watershed (table 10), with a 

range of about 1 m during the modeling period (fig. 27). 

Plots of observed and simulated depth to water table 

(fig. 28) and relative depth-to-water-table fluctuations (fig. 29) 

show that depth to water table computed from TOPMODEL 

predicted-saturation deficits fall within the range of observed 

values. The observed depth to water table follows a generally 

increasing, or drying, trend over the period of observations; 

a corresponding overall decrease in runoff also was observed 

during this period. Both plots show that the slope of 

TOPMODEL-simulated depth to water table was greater than 

the observed depth to water table; the model “dries out” more 

rapidly than indicated by observations. 

Goodness-of-fit statistics for absolute depth to water 

table (left side of table 11) show the RMSE and MAE for the 

model run with the highest combined-objective value were 

approximately 90 mm; in comparison, the average observed 

depth to water table was 205 mm. The median depth-to-watertable bias of all model runs (table 11) was positive (drier 

than observed), while the best run as chosen by the combined 

objective had a negative depth-to-water-table bias (wetter 

than observed).

The relative depth-to-water-table fluctuation component 

objective—the average Pearson correlation coefficient—

ranged from 0.494 to 0.666 (right side of table 11); this range 

was narrower than for other component-objective values 

(table 6). A scatter plot of all observed depth-above-average 

time series and the simulated depth-above-average time series 

(fig. 30) has a correlation of 0.59 and generally falls around a 

1:1 line.

Saturation deficits and depth to water table calculated 

for specific TWIs and mapped back to locations in the 

watershed are offset from the watershed average by a constant 

proportional to the TWI. The median depth to water table at 

Sixmile Wetland for the best run was 206 mm (table 10) and 

ranged from −316 to 647 mm (fig. 31); for an example upland 

area with a TWI of 5, the median depth to water table was 

939 mm. The saturation deficit computed for Sixmile Wetland, 

the location where depth to water table was observed, is 

Table 9. Runoff prediction-interval widths, by class, for Fishing Brook at County Line Flow near Newcomb, New York.

[mm/d, millimeter per day; Objcomb, weighted combined multiple-objective function; %, percent; >, greater than]

Minimum width of 

prediction interval, 

mm/d

Median width of 

prediction interval, 

mm/d

Maximum width of 

prediction interval, 

mm/d

Ratio, median width 

to best run median 

simulated runoff, 

(1.17 mm/d)

Ratio, median width 

to best run simulatedrunoff range, 

(16.7 mm/d)

Objcomb top 0.1% 0.071 0.292 7.178 0.249 0.017

Objcomb top 1% .132 .469 10.4 .400 .028

Objcomb top 10% .191 .771 16.9 .658 .046

Obj > 0 comb .375 1.26 26.0 1.07 .075

All runs .436 1.36 27.3 1.16 .082
TOPMODEL-Simulation Results 35

0

1

2

5

10

15

20

25

Simulated runoff, in millimeters

A.

Low flow

September 5, 2007

C.

High flow

April 24, 2007

B.

Moderate flow

May 5, 2009

EXPLANATION

[Objcomb , Combined multiple-objective function]

All runs

Objcomb > 0

Objcomb top 10 percent

Objcomb top 1 percent

Objcomb top 0.1 percent

Best run

90th percentile

75th

50th (median)

25th

10th

95th percentile

5th percentile

Figure 25. Boxplots of simulated runoff for A, low flow (September 5, 2007), B, moderate flow (May 5, 2009), 

and C, high flow (April 24, 2007) example days, Fishing Brook at County Line Flow near Newcomb, New York, by 

prediction-interval class.
36 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

All runs

Obj

comb > 0

Obj

comb top 10 percent

Obj

comb top 1 percent

Obj

comb top 0.1 percent

EXPLANATION

90th percentile

75th

50th (median)

25th

10th

Outlier

Outlier

[Objcomb , Combined multiple-objective function]

Width of prediction interval for simulated runoff, 

in millimeters per day 

0

1

2

3

10

20

30

Figure 26. Width of runoff prediction intervals for the modeling period for Fishing 

Brook at County Line Flow near Newcomb, New York, by prediction-interval class.

Table 10. Descriptive statistics for simulated saturation deficit and depth to water table for the best run during the model period for 

Fishing Brook study area average, Sixmile Wetland, and example upland area.

[Study-area average topographic wetness index (TWI) is 6.86; Sixmile Wetland TWI is 11.04, and example upland area TWI is 5.00. The location of Sixmile 

Wetland is shown in figure 3]

Simulated saturation deficit, millimeters Simulated depth to water table, millimeters

Fishing Brook Sixmile Example study area wetland upland area averageFishing Brook Sixmile Example study area wetland upland area average

Minimum, best run 26.7 −44.0 58.2 192 −316 419

Median, best run 99.3 28.7 131 715 206 941

Mean, best run 99.0 28.4 131 712 204 939

Maximum, best run 161 89.9 192 1,155 647 1,382

Range, best run 134 134 134 963 963 963

Standard deviation, 26.7 26.7 26.7 192 192 192

best run
TOPMODEL-Simulation Results 37

All model runs

Objcomb > 0

Objcomb top 1 percent

Best run

90th percentile

75th

50th (median)

25th

10th

EXPLANATION

Observed depth to water table Simulated depth to water table

Month and year

[Objcomb , Combined multiple-objective function]

−500

0

500

1,000

1,500

Depth to water table, in millimeters

−500

0

500

1,000

1,500

−500

0

500

1,000

1,500

A. Water year 2007

C. Water year 2009

B. Water year 2008

Oct. Nov. Dec.

2006 2007

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Oct. Nov. Dec.

2007 2008

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Oct. Nov. Dec.

2008 2009

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Figure 27. Simulated depth to water table at Sixmile Wetland, Fishing Brook study area, New York, best run for the 

modeling period and prediction intervals for A, water year (WY) 2007, B, WY 2008, and C, WY 2009.
38 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

All model runs

Objcomb > 0

Objcomb top 1 percent

Best run

90th percentile

75th

50th (median)

25th

10th

Observed depth to water table Simulated depth to water table

EXPLANATION

Date

[Objcomb , Combined multiple-objective function]

2009

May 1 June 1 July 1 August 1 August 27

Depth to water table, in millimeters

−200

0

200

400

600

800

1,000

1,200

1,400

Figure 28. Simulated and observed depth to water table at Sixmile Wetland, Fishing Brook study area, New York, 

best run for the modeling period and prediction intervals, April–August 2009.
TOPMODEL-Simulation Results 39

All model runs

Objcomb > 0

Objcomb top 1 percent

Observed

Simulated, best run

2009

May 1 June 1 July 1 August 1 August 27

EXPLANATION

Date

[Objcomb , Combined multiple-objective function]

0

Depth above average, in millimeters

−400

−300

−200

−100

100

200

300

400

500

Figure 29. Simulated and observed relative depth-to-water-table fluctuations at Sixmile Wetland, Fishing Brook study 

area, New York, best run for the modeling period and prediction intervals, April–August 2009.
40 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Table 11. Simulated depth-to-water-table goodness-of-fit statistics for the best run and all model runs.

[RMSE, root mean squared error; MAE, mean absolute error; r, Pearson’s correlation coefficient; ObjDTW TS, relative time series 

depth-to-water-table objective function]

Absolute depth to water table Relative fluctuations

RMSE, millimeters Bias, millimeters MAE, millimeters r

(Obj ) DTW TS

Best run 91.261 −44.422 86.934 0.624

Minimum, all runs 58.393 −199.533 5.167 .494

Median, all runs 147.615 63.116 123.177 .540

Maximum, all runs 482.305 444.366 444.366 .666

−300 −200 −100 0 100 200 300 400

−300

−200

−100

0

100

200

300

400

Observed depth above average, in millimeters

Simulated depth above average, in millimeters

Figure 30. Scatter plot of observed and simulated depth above 

average at Sixmile Wetland, Fishing Brook study area, New 

York, April–August 2009, best run for the modeling period. The 

blue line represents a 1:1 correspondence of simulated and 

observed runoff.
TOPMODEL-Simulation Results 41

Fishing Brook study area average, TWI = 6.86

Sixmile Wetland, TWI = 11.04

Example upland area, TWI = 5.00

EXPLANATION

[TWI, topgraphic wetness index]

Month and year

−100

−50

0

50

100

150

200

Saturation deficit, in millimeters

−500

0

500

1,000

Depth to water table, in millimeters

Jan. Apr. July

2007 2008 2009

Oct. Jan. Apr. July Oct. Jan. Apr. July Oct. 

Figure 31. Simulated saturation deficit and depth to water table, Fishing Brook study area average, Sixmile Wetland, 

and example upland area, best run for the modeling period.
42 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

smaller than the watershed-average saturation deficit, and the 

minimum simulated-saturation deficit for Sixmile Wetland 

is negative (table 10 and fig. 27), indicating the occurrence 

of surface saturation during the modeling period. Surface 

saturation was expected to occur at this location and was 

observed in the field during the modeling period (Schelker and 

others, 2011). Conversely, the saturation deficit predicted for 

an example upland area is greater than the watershed-average 

saturation deficit, and saturation does not occur.

TOPMODEL-simulated saturated areas in the basin 

ranged from 0.5 percent of basin area (not including 

permanently saturated areas, such as lakes and ponds) on 

September 5, 2007, to approximately 20 percent (inclusive of 

permanently saturated areas) on April 24, 2007 (fig. 32). As 

expected from the mathematical framework of TOPMODEL, 

the simulated saturated-area time series follows a similar 

form to that of the simulated basin-average saturation deficit. 

A map of the range of predicted saturated areas (fig. 33), 

generated using the TWI distribution for the study area, 

shows that during low-flow conditions (high saturation 

deficit), mainly riparian areas and stream cells are predicted 

to be saturated. During high-flow (low saturation deficit) 

conditions, the mapped saturated areas extend throughout 

wetlands and farther upstream in the watershed, likely along 

ephemeral-stream channels. Schelker and others (2011) 

predicted a range of 6 to 12 percent saturation for the period 

January 2007–June 2008, including 5 percent of the basin 

considered permanently saturated, consisting mainly of open 

water and adjacent areas. The minimum saturated areas 

reported in this report agree well with those reported by 

Schelker and others (2011) when permanently saturated areas 

are taken into account. The maximum saturated areas reported 

in this report are greater than those reported by Schelker 

and others (2011); this may reflect differences in computed 

watershed characteristics or calibrated parameter values.

Prediction-Interval Uncertainty Analysis

The prediction intervals for simulated-saturation deficit 

(figs. 15–17) and depth to water table (fig. 27), like those for 

runoff, generally follow the form of the model run with the 

highest combined-objective function. The range of predicted 

saturation-deficit values is directly related to the magnitude 

of the deficit (fig. 34), but is more consistent among flow and 

saturation conditions than runoff. The prediction intervals 

(table 12 and fig. 35) are more distinct between classes, 

with less overlap than those for runoff and less skewness in 

their variation over time. The ratio of the median prediction 

interval to the median saturation deficit is similar for most 

classes, but the ratio of the median prediction interval to 

the range of saturation deficit values is much larger than 

for runoff (table 12). As one moves from all model runs to 

ranges of model runs with progressively better fits to the 

combined-objective function (fig. 34), the median and range 

of saturation-deficit values moves towards lower-saturation 

deficits (wetter conditions). 

The variability of simulated depth to water table for 

a single time step (fig. 36) and the prediction intervals for 

depth to water table (fig. 37) are similar to those for the 

saturation deficit. The median prediction-interval width for 

the top 0.1 percent of model runs was approximately 80 mm 

(table 13); this is equal to about 10 percent of the median 

prediction-interval width for all model runs. An interesting 

artifact of the relative-depth-to-water-table computations 

is that the variability of simulated depth above average 

(fig. 29) is much less than that for absolute depth to water 

table (fig. 28). The process of removing the average from the 

fluctuations removed much of the spread seen in the absolute 

depth-to-water simulations, indicating that most simulations 

follow a similar form with a simple offset in the mean value.

Simulated saturated area, in percent

0

0.05

0.1

0.15

0.2

0.25

Jan. Apr. July

2007 2008 2009

Oct. Jan. Apr. July Oct. Jan. Apr. July Oct. 

Month and year

Figure 32. Simulated saturated area, as percent of Fishing Brook study area, New York, best run for the modeling period.
TOPMODEL-Simulation Results 43

EXPLANATION

Minimum—0.5 percent of watershed, 9/5/2007

Maximum—19.8 percent of watershed, 4/24/2007

Simulated saturated areas

Watershed boundary

Base from National Elevation Dataset, 2009, 1/3 arc-second

Universal Transverse Mercator projection

Zone 18

HAMILTON COUNTY

ESSEX COUNTY

0 1 2 MILES

0 1 2 KILOMETERS

74°22' 74°20' 74°18' 74°16'

44°00'

43°58'

43°56'

Figure 33. Simulated saturated areas, showing minimum and maximum saturation of Fishing Brook study area, New 

York, best run for the modeling period.
44 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

All runs

Objcomb > 0

Objcomb top 10 percent

Objcomb top 1 percent

Objcomb top 0.1 percent

Best run

EXPLANATION

[Objcomb , Combined multiple-objective function]

90th percentile

75th

50th (median)

25th

10th

95th percentile

5th percentile

0

100

200

300

400

Simulated saturation deficit, in millimeters

A.

Low flow

September 5, 2007

B.

Moderate flow

May 5, 2009

C.

High flow

April 24, 2007

Figure 34. Boxplots of simulated watershed-average saturation deficit for A, low flow (September 5, 2007), 

B, moderate flow (May 5, 2009), and C, high flow (April 24, 2007) example days, Fishing Brook study area, New York, 

by prediction-interval class.

Table 12. Saturation-deficit prediction-interval widths, by prediction-interval class.

[mm, millimeter; S, saturation deficit; Objcomb, weighted combined multiple-objective function; %, percent, >, greater than]

Minimum width of Median width of Maximum width of Ratio, median width Ratio, median width 

prediction interval, prediction interval, prediction interval, to best run median S to best run S range 

mm mm mm (99.3 mm) (134 mm)

Objcomb top 0.1% 8.50 28.6 49.9 0.288 0.214

Objcomb top 1% 15.9 5.80 95.3 .511 .379

Objcomb top 10% 26.0 78.0 142 .785 .582

Obj > 0 comb 69.5 162 253 1.63 1.21

All runs 127 238 352 2.39 1.77
TOPMODEL-Simulation Results 45

All runs

Objcomb > 0

Objcomb top 10 percent

Objcomb top 1 percent

Objcomb top 0.1 percent

EXPLANATION

90th percentile

75th

50th (median)

25th

10th

Outlier

Outlier

[Objcomb , Combined multiple objective function]

0

100

200

300

400

Width of prediction interval for 

simulated saturation deficit, in millimeters 

Figure 35. Width of simulated watershed-average saturation deficit 

prediction intervals for the modeling period, Fishing Brook study area, 

New York, by prediction-interval class.
46 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

All runs

Objcomb > 0

Objcomb top 10 percent

Objcomb top 1 percent

Objcomb top 0.1 percent

Best run

90th percentile

75th

50th (median)

25th

10th

95th percentile

5th percentile

EXPLANATION

[Objcomb , Combined multiple objective function]

Simulated depth to water table, in millimeters

-500

0

500

1,000

1,500 A.

Low flow

September 5, 2007

B.

Moderate flow

May 5, 2009

C.

High flow

April 24, 2007

Figure 36. Boxplots of simulated depth to water table at Sixmile Wetland, Fishing Brook study area, New York, for 

A, low flow (September 5, 2007), B, moderate flow (May 5, 2009), and C, high flow (April 24, 2007) example days, by 

prediction-interval class.
TOPMODEL-Simulation Results 47

All runs

Objcomb > 0

Objcomb top 10 percent

Objcomb top 1 percent

Objcomb top 0.1 percent

EXPLANATION

90th percentile

75th

50th (median)

25th

10th

Outlier

Outlier

[Objcomb , Combined multiple objective function]

Width of prediction interval for simulated depth to water table,

 in millimeters

0

200

400

600

800

1,000

1,200

1,400

1,600

1,800

Figure 37. Width of simulated depth-to-water-table prediction 

intervals for the modeling period, Fishing Brook study area, New York, 

by prediction-interval class.

Table 13. Depth to water table in Sixmile Wetland prediction-interval widths, by prediction-interval class.

[mm, millimeter; DTW, depth to water; SMW, Sixmile Wetland; Objcomb, weighted combined multiple-objective function; %, percent; >, greater than]

Minimum width of 

prediction interval, 

Median width of 

prediction interval, 

Maximum width of 

prediction interval, 

Ratio, median width 

to median simulated 

DTW, SMW 

Ratio, median width 

to simulated 

DTW range mm mm mm (206 mm) (963 mm)

Objcomb top 0.1% 10.9 80.6 277 0.393 0.099

Objcomb top 1% 31.6 141 525 .684 .175

Objcomb top 10% 77.0 236 753 1.15 .288

Obj > 0 comb 119.4 552 1,248 2.68 .574

All runs 211.9 845 1,663 4.10 .870
48 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Application of Calibration to Subwatersheds

For use of the TOPMODEL simulations in other 

modeling and water-quality applications, the results of the 

calibration were applied to several subwatersheds within the 

study area (fig. 2). Subwatersheds were defined for modelassessment points (MAxx) for input into Hg models, and at 

additional synoptic sites (SSxx) where samples for Hg analysis 

were collected; the entire study area is designated MA06. 

To produce a simulated time series of runoff and saturation 

deficit for each subwatershed, watershed characteristics 

(table 14) and the TWI distribution were calculated for each 

subwatershed; model parameter values from the overall 

study area model run with the highest combined-objective 

value (table 5) then were applied to TOPMODEL for each 

subwatershed. 

Subwatersheds ranged in area from 0.96 km2

 (MA13) to 

60.60 km2

 (MA05). Many of the subwatersheds were nested; 

for example, subwatershed MA03 contained subwatersheds 

MA01 and MA02 (fig. 2). The watershed-average TWI varied 

from 5.95 ln(m) for MA13 (table 14), a small, steep watershed 

with almost no wetlands (figs. 2 and 3); to 7.37 ln(m) for 

MA09, a watershed that contains large portions of the 

Sixmile Wetland (figs. 2 and 3). TOPMODEL results for the 

subwatersheds are illustrated by these two basins to show the 

range in simulated values among the subwatersheds.

Simulated runoff for the subwatersheds is similar to 

that for the whole study area (fig. 38); responses to rainfall 

events are initially higher in subwatershed MA13 (the smaller, 

steeper basin), whereas the recession curve typically is more 

sustained in subwatershed MA09 (the larger, flatter basin with 

more wetlands). The simulated-saturation deficits for the two 

subwatersheds also are similar to those for the whole study 

area (fig. 39); although, surprisingly, the watershed-average 

saturation deficit for subwatershed MA13 is slightly less than 

that of subwatershed MA09. The computed watershed-average 

depth to water table shows the same patterns as the simulatedsaturation deficits. 

Table 14. Subwatershed characteristics for the Fishing Brook study area.

[TWI, topographic wetness index; ln m, natural logarithm (meters); model-assessment points are shown in figure 2; MA06 is the main study area]

Watershed Total area 

(square kilometers)

Lake area

(square kilometers)

Stream area

(square kilometers)

Uplake area

(decimal percent)

Watershed average 

TWI 

(ln m)

MA01

MA02

MA03

MA04

MA05

MA06

MA07

MA08

MA09

MA10

MA11

MA12

MA13

SS01

SS02

SS03

SS04

SS05

SS06

SS07

20.69

27.06

3.04

49.98

60.60

65.64

4.73

7.33

9.68

19.10

2.31

8.43

.96

15.85

4.57

24.99

17.74

17.04

6.88

1.31

0.11

.31

.32

.46

1.33

1.75

.07

.08

.02

.12

.01

.87

.00

.08

.02

.11

.11

.10

.08

.00

0.12

.15

.16

.29

.33

.34

.03

.05

.07

.13

.01

.03

.01

.08

.04

.14

.12

.11

.04

.01

0.00

.99

.89

.54

.52

1.00

.00

.00

.00

.00

.00

.57

.00

.00

.00

.00

.00

.00

.00

.00

6.54

6.63

6.67

6.84

6.87

6.86

6.37

6.63

7.37

7.09

6.30

6.93

5.95

6.45

6.94

6.57

7.07

7.05

6.58

5.99
TOPMODEL-Simulation Results 49

MA06

MA09

MA13

EXPLANATION

Month and year

0

5

10

15

20

25

30

Runoff, in millimeters

0

5

10

15

20

25

30

0

5

10

15

20

25

30 A. Water year 2007

C. Water year 2009

B. Water year 2008

Oct. Nov. Dec.

2007 2008

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Oct. Nov. Dec.

2008 2009

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Oct. Nov. Dec.

2006 2007

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Figure 38. Simulated runoff for selected subwatersheds, Fishing Brook study area, New York, for A, water year 

(WY) 2007, B, WY 2008, and C, WY 2009.
50 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

MA06

MA09

MA13

EXPLANATION

0

50

100

150

200

0

200

400

600

800

1,000

1,200

1,400

Saturation deficit, in millimeters

0

50

100

150

200

0

200

400

600

800

1,000

1,200

1,400

Depth to water table, in millimeters

0

50

100

150

200

0

200

400

600

800

1,000

1,200

1,400

A. Water year 2007

C. Water year 2009

B. Water year 2008

Oct. Nov. Dec.

2006 2007

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Oct. Nov. Dec.

2007 2008

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Oct. Nov. Dec.

2008 2009

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. 

Month and year

Figure 39. Simulated saturation deficit and watershed-average depth to water table for selected subwatersheds for 

A, water year (WY) 2007, B, WY 2008, and C, WY 2009.
TOPMODEL-Simulation Results 51

In addition to the continuous record of streamflow 

available at the outlet of the study area, streamflow 

measurements were made at selected sites throughout the 

basin (table 15 and fig. 2) several times during the modeling 

period as part of synoptic surveys of the concentrations of 

Hg species. For some sites, on some occasions more than one 

measurement was made during a day; these measurements 

were averaged for analysis. After screening for multiple 

measurements, there were 66 measurements made at 11 sites 

(table 15); runoff measured at these sites ranged from 0.02 to 

21 mm/d. A scatter plot shows some correlation of observed 

runoff and simulated runoff (fig. 40). Some individual 

measurements show better agreement with the subwatershed 

simulated runoff (overall Pearson correlation coefficient 

0.654) than with the simulated runoff for the entire study 

area (correlation coefficient 0.653), but comparison to gaged 

runoff at the study-area outlet yields the best correlation 

coefficient (0.708).

Table 15. Streamflow measurements at synoptic survey sites for the Fishing Brook study area, New York, 2007–09.

[Model-assessment points are shown in figure 2]

Station 

identification 

number

Modelassessment 

point

Station name

Number of 

measurements 

available

01311990 MA02 Fishing Brook at 28N near Long Lake NY 7

0131199040 MA05 Fishing Brook Above County Line Flow near Long Lake NY 6

0131199035 MA12 Pickwacket Pond Outlet at mouth near Long Lake NY 6

0131199045 MA13 Unnamed Tributary to County Line Flow near Long Lake NY 7

01311985 SS01 Fishing Brook near Windfall Mountain near Long Lake NY 3

0131199010 SS02 Sixmile Brook at 28N near Long Lake NY 7

01311989 SS03 Fishing Brook near Long Lake NY 3

0131199022 SS04 Sixmile Brook near Long Lake NY 12

0131199021 SS05 Sixmile Brook below Sixmile Brook Tributary near Long Lake NY 6

0131199020 SS06 Sixmile Brook Tributary near Long Lake NY 5

0131199029 SS07 Pickwacket Pond Inlet near Long Lake NY 4

MA02

MA05

MA12

MA13

SS01

SS02

SS03

SS04

SS05

SS06

SS07

EXPLANATION

Sites

Measured subwatershed runoff, in millimeters per day

Simulated subwatershed runoff, in millimeters per day

10 -2 10 -1 10 0 101

-1 10

100

101

Figure 40. Scatter plot of simulated runoff and 

observed runoff for selected subwatersheds, 

Fishing Brook study area, New York.
52 TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09

Summary 

TOPMODEL, a physically based, variable-source area 

rainfall-runoff model, was applied for the period January 

2007–September 2009 to model streamflow and depth to water 

table in the medium-sized (65.6 square kilometers) Fishing 

Brook Watershed, which is located in northern New York. The 

study area is mainly forested, with substantial wetland area 

and little impervious surface. This application of TOPMODEL 

is part of a larger U.S. Geological Survey National WaterQuality Assessment Program study of mercury (Hg) cycling; 

model-hydrology results will be linked (in the future) with 

models to simulate Hg in the study watershed. 

A Monte-Carlo calibration with a combined multipleobjective function was applied to calibrate runoff at the study 

area outlet and depth to water table at Sixmile Wetland. 

The combined multiple-objective function included terms 

representing the Nash-Sutcliffe efficiency of the natural log of 

runoff at the study area outlet, the root mean squared error of 

the absolute depth to water table in Sixmile Wetland, and the 

Pearson correlation coefficient (r) of the relative fluctuations 

of depth to water table in Sixmile Wetland. Runoff was 

weighted equally with depth to water table in the combined 

multiple-objective function. Snowmelt parameters were 

calibrated separately from main model parameters to allow for 

variability in snowmelt-parameter values on a yearly basis; 

snowmelt calibration was evaluated using the Nash-Sutcliffe 

efficiency of the runoff at the study area outlet. 

The single “best” run as selected from 100,000 

TOPMODEL runs by the combined multiple-objective 

function was compared to observed runoff and depth to water 

table. The simulated runoff generally matched observed runoff 

well, with an overall Nash-Sutcliffe efficiency of 0.738, but 

the model underpredicted total runoff by 14 percent. Depth 

to water table computed from simulated saturation-deficit 

values matched observed water table depth moderately well. 

The root mean squared error of absolute depth to water table 

was 91 millimeters (mm); comparatively, the mean depth 

to water table on three observation dates was 205 mm. The 

Pearson correlation coefficient (r) for the depth-to-water-table 

fluctuations was 0.624. 

The variability of the TOPMODEL predictions as a 

function of model parameters was assessed using a simplified 

prediction-interval uncertainty assessment. Prediction intervals 

for runoff and saturation deficit generally followed the form 

of the model run with the highest combined objective value, 

but some deviation from this form was observed, especially 

in the time series of runoff. The width of prediction intervals 

compared to range over time was greater for the simulated 

saturation deficit than for runoff; the variability of predictioninterval widths over time (and with basin-average saturation 

condition) was greater for runoff than for saturation deficit.

The calibrated TOPMODEL results for the entire 

study area were applied to several subwatersheds within the 

study area using computed properties of the subwatersheds. 

Simulated runoff in subwatersheds varies as would be 

expected based on subwatershed characteristics, but a 

comparison of observed instantaneous runoff at subwatersheds 

shows better agreement with observed runoff for the overall 

study area than with simulated runoff.

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Nystrom and Burns—TOPMODEL Simulations of Streamflow and Depth to Water Table in Fishing Brook Watershed, New York, 2007–09—Scientific Investigations Report 2011–5190