Summary of Hydrologic Modeling for the Delaware River 

Basin Using the Water Availability Tool for Environmental 

Resources (WATER)

Chenango

Schoharie

Greene

Ulster

Orange

Sullivan

Delaware

Broome

Susquehanna

Wayne

Pike

Luzerne Monroe

Carbon Northampton

Berks

Chester

Lancaster

Lehigh

Lebanon

Schuylkill

Kent

Sussex

Atlantic Cecil

Cape

May

Salem

Cumberland

New

Castle

Burlington Ocean

Montgomery

Gloucester Delaware

Camden

Philadelphia

Lackawanna

Morris

Sussex

Warren

Bucks

Monmouth

Hunterdon

Mercer

42 °0 '0 "N

41 °0 '0 "N

40 °0 '0 "N

New development, in acres

2060

Temperature change factor, in degrees Celsius (°C)

0.8

1.0

1.2

1.4

0 1 2 3 4 5

●

Potential evapotranspiration change factor (proportional)

1.0

1.2

1.4

●

1.0

1.2

1.4

●

1.0

1.2

1.4

CanESM2

NCARCCSM4

GISSE2-H

GFDLESM2G

Scientific Investigations Report 2015–5143

U.S. Department of the Interior

U.S. Geological Survey
Cover: Left image shows forecasted development for 2060 in the Delaware River Basin (from figure 6B). 

Right image shows range of forecasted annual change in temperature and potential evapotranspiration for 2030 and 2060, (from figure 7B).
Summary of Hydrologic Modeling for 

the Delaware River Basin Using the 

Water Availability Tool for Environmental 

Resources (WATER)

By Tanja N. Williamson, Jeremiah G. Lant, Peter R. Claggett, Elizabeth A. Nystrom, 

Paul C.D. Milly, Hugh L. Nelson, Scott A. Hoffman, Susan J. Colarullo, and 

Jeffrey M. Fischer

Scientific Investigations Report 2015–5143

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2015

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

resources, natural hazards, and the environment—visit http://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod/.

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Williamson, T.N., Lant, J.G., Claggett, P.R., Nystrom, E.A., Milly, P.C.D., Nelson, H.L., Hoffman, S.A., Colarullo, S.J., 

and Fischer, J.M., 2015, Summary of hydrologic modeling for the Delaware River Basin using the Water Availability 

Tool for Environmental Resources (WATER): U.S. Geological Survey Scientific Investigations Report 2015–5143, 68 p., 

http://dx.doi.org/10.3133/sir20155143.

ISSN 2328-0328 (online)
iii

Preface

Development of the Water Availability Tool for Environmental Resources (WATER) for the 

Delaware River Basin (DRB) was done as part of a U.S. Geological Survey National Water 

Census Focus Area Study. The DRB Focus Area Study is part of implementation of the U.S. 

Department of Interior’s Secure Water Act to Sustain and Manage America’s Resources for 

Tomorrow (WaterSMART). WATER–DRB addresses multiple aspects of this WaterSMART work 

by providing a foundation on which to better understand streamflow, water use, and ecological 

water needs under current conditions and those associated with forecasted climate change and 

population expansion. This report documents data used to develop and inform the model, those 

hydrologic and hydroclimatic models encapsulated within WATER–DRB, and how this decision 

support system has been integrated with general circulation models and urbanization forecasts 

to provide resource managers with a way to objectively and consistently investigate water 

management strategies.
iv

Acknowledgments

Development of the Water Availability Tool for Environmental Resources (WATER) for the 

Delaware River Basin (DRB) has benefitted from interaction with a large group of stakeholders 

who helped U.S. Geological Survey (USGS) identify critical questions in the basin. Among those 

stakeholders are the Delaware River Basin Commission and the five states included in the DRB.

The WATER decision support system (DSS) was developed in parallel with other DRB efforts. 

The Water-Census team was welcoming in helping to incorporate the needs of the WATER DSS 

into their data preparation and output, and they enabled the seasonal approach incorporated 

in the DSS. In addition, Natural Resources Conservation Service soil scientists in Pennsylvania 

(Yuri Plowden) and New Jersey (Richard Shaw and Edwin Muñiz) were integral to our obtaining 

an updated set of soils data while the newer Soil Survey Geographic dataset was still being processed. Kenneth Clark of the U.S. Department of Agriculture (USDA) Forest Service graciously 

helped us access evapotranspiration data from the New Jersey pineland sites, and Mathieu 

Gerbush, assistant State climatologist, helped us access data from the New Jersey Mesonet 

of climate sites. Finally, Amy Shallcross and Hernán Quinodoz, from the Delaware River Basin 

Commission, patiently helped us access and incorporate the subbasins needed to integrate 

WATER output with their Planning Support Tool format. Several universities have shown interest 

in incorporating WATER into future research, including Drexel University, The Pennsylvania State 

University, and the State University of New York, where Theodore Endreny and Yong Seuk Kwon 

provided a test of the DSS during its developmental stages
v

Contents

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

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

Purpose and Scope ..............................................................................................................................3

Focus Area and Overall Approach of WATER..................................................................................3

Uses and Objectives of WATER..........................................................................................................3

Framework of the WATER Decision Support System .....................................................................4

Relation of Delaware River Basin WATER to Previous Studies ....................................................6

Data Sources and Processing of Data for WATER...................................................................................6

Data That Inform the Models..............................................................................................................9

Topography ...................................................................................................................................9

Climate Data..................................................................................................................................9

Land Cover..................................................................................................................................10

Soils Data ....................................................................................................................................10

Linking Topographic and Soil Data for Hydrologic Models ................................................10

Data Used for Validating Simulations..............................................................................................11

Historical Streamflow and Optimization-Validation Basins................................................11

Hydroclimatic Variables............................................................................................................18

Data That Enable Scenario Testing..................................................................................................18

Water-Use Data Provided in WATER Application Utilities..................................................18

Land-Cover Projection and Urbanization Forecasts Used to Replace the National 

Land Cover Database 2011 for Future Time Periods...............................................19

General Circulation Models and Projections of Future Climate ........................................24

Evaluating Uncertainty for Scenario Testing...........................................................................................29

Model Development, Statistical Evaluation, and Validation of Hydroclimatic Components 

of WATER .........................................................................................................................................29

Hydroclimatic Water-Budget Components.....................................................................................29

Accumulation and Melting of Snow .......................................................................................29

Evapotranspiration ....................................................................................................................35

Optimization of Remaining Hydrologic Parameters and Differentiation of Hydrologic 

Response Units......................................................................................................................35

Incorporation of Water-Use Data.....................................................................................................36

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using 

WATER..............................................................................................................................................36

Goodness-of-Fit Statistics.................................................................................................................36

Evaluation of Daily Streamflow ........................................................................................................37

Estimating Uncertainty for Daily Streamflow Simulations by Using the Normalized 

Root Mean Squared Error....................................................................................................58

Evaluation of Daily Streamflow Distribution by Using the Flow-Duration Curve .....................58

Evaluation of Mean Monthly Streamflow Simulations by Using Normalized 

Root Mean Squared Error....................................................................................................58

Summary .......................................................................................................................................................64

References Cited..........................................................................................................................................64
vi

Figures

1. Map showing the Delaware River Basin, including parts of Delaware, 

New Jersey, New York, and Pennsylvania, as well as a small part of Maryland..............2

2. Schematic diagram of how the Water Availability Tool for Environmental 

Resources samples geospatial data and feeds it to the two hydrologic models. 

The basin is apportioned into three hydrologic response units ...........................................5

3. Map showing parts of the Delaware River system for which streamflow information 

from the Water Availability Tool for Environmental Resources should be used 

cautiously because of stream regulation and tidal influences.............................................8

4. Map showing U.S. Geological Survey streamgages and other monitoring 

sites used for model optimization and statistical evaluation of the Water 

Availability Tool for Environmental Resources streamflow simulation and 

hydroclimatic variables for the Delaware River Basin.........................................................17

5. Map showing water-use locations in the Delaware River Basin.......................................20

6. Maps showing land-cover data for the Delaware River Basin provided with the 

Water Availability Tool for Environmental Resources ..........................................................22

7. Maps and graphs showing summary of general circulation models ................................25

8. Graphs showing example of how the monthly change factor is A, calculated and 

B, applied in order to incorporate general circulation model data....................................28

9. Graph showing comparison of Water Availability Tool for Environmental Resourcesderived daily basin averages of snow water equivalent for four northern validation 

basins to point observations from National Weather Service observations in the 

Delaware River Basin ................................................................................................................30

10. Graph showing a north-south transect of maximum daily temperature for three 

basins with U.S. Geological Survey gages.............................................................................31

11. Graphs showing comparison of observed and Water Availability Tool for 

Environmental Resources-derived A, potential evapotranspiration and B, actual 

evapotranspiration at a range of sites in the Delaware River Basin, each of which 

primarily consists of one of the three hydrologic response units—forested, 

agricultural, or developed .........................................................................................................32

12. Graph showing water-budget components from Water Availability Tool for 

Environmental Resources simulations for homogeneous basins in the Delaware 

River Basin...................................................................................................................................33

13. Graphs showing statistical evaluation of actual evapotranspiration from the Water 

Availability Tool for Environmental Resources. A, Comparison of WATER-derived 

actual evapotranspiration at 21 sites in the Delaware River Basin to areal estimates 

from the Simplified Surface Energy Balance model.............................................................34

14. Maps showing statistical evaluation of hydrologic simulations for 48 basins in the 

Delaware River Basin. For each statistic, green indicates better performance .............38

15. Graphs showing goodness-of-fit statistics for 48 basins in the Delaware River 

Basin as a function of individual streamflow percentiles: A, normalized root mean 

squared error, B, root mean squared error / standard deviation, C, Spearman 

rank correlation coefficient, and D, bias ................................................................................39

16. Graphs showing goodness-of-fit streamflow-percentile statistics grouped as a 

function of basin area and percentage of forested area.....................................................43
vii

17. Graph showing normalized root mean squared error as a function of percentage 

of forested area. Forested-area categories are 0–25 percent, >25–50 percent, 

>50–75 percent, and >75–100 percent.....................................................................................44

18. Graph showing root mean squared error/standard deviation as a function 

of percentage of forested area ................................................................................................45

19. Graph showing normalized root mean squared error as a function of basin area .........46

20. Graph showing root mean squared error/standard deviation as a function 

of basin area................................................................................................................................47

21. Graphs showing comparison of four goodness-of-fit statistics for 48 optimization 

basins and 9 test basins ............................................................................................................48

 22. Graphs showing observed and simulated streamflow for October 1, 2009, through 

September 30, 2010, with and without water use, together with cumulative streamflow for the 2001–10 period in A, a forested basin and B, an agricultural basin..............49

23. Graphs showing examples of observed and simulated streamflow for 

A, a forested basin and B, an agricultural basin with four different uncertainty 

ranges: ±1 normalized root mean squared error from individual sites (RMSEn), 

±2 RMSEn, ±1 normalized root mean squared error averaged from all sites 

(RMSEn57), and ±2 RMSEn57.......................................................................................................51

24. Graphs showing examples from A, a forested basin and B, an agricultural basin 

of observed and simulated streamflow with site-specific uncertainty ranges from 

normalized root mean squared error and for individual streamflow components...........53

 25. Graphs showing the proportion of days, over the period of record for all 57 statistical 

evaluation sites in the Delaware River Basin, on which observed streamflow is not 

bounded by the confidence interval based on the average normalized root 

mean squared error for all sites...............................................................................................56

26. Boxplot showing the percentage of error for each streamflow percentile in the 

flow-duration curve; median error is notated on the graph................................................57

 27. Graphs showing examples from A, a forested basin and B, an agricultural basin of 

observed and simulated mean-monthly streamflow with uncertainty ranges from 

normalized root mean squared error averaged from all sites in the Delaware River 

Basin with 108-month records..................................................................................................59

28. Graphs showing the proportion of period of record during which the mean monthly 

observed streamflow is not bounded by the confidence interval based on the 

normalized root mean squared error over the period of record for all 45 validation 

sites in the Delaware River Basin with an observation period of 108 months. 

Fourteen sites have less than 90 percent of the streamflows bounded by +2/-1 

RMSEn45-mon ..................................................................................................................................60

29. Graph showing root mean squared error for mean monthly streamflow 

normalized for the period of record for all 57 sites in the Delaware River Basin 

and for the 45 sites with a 9-year period of record...............................................................61

 30. Graph showing observed and simulated mean-monthly streamflow normals for 

2001–10 time period for 57 sites in the Delaware River Basin ............................................62

31. Graph showing proportion of mean monthly-flow normals not bounded by 

simulated discharge if using either the month-specific or averaged normalized 

root mean squared error of the normalized mean-monthly streamflow 

for all 57 sites in the Delaware River Basin............................................................................63
viii

Tables

1. Data sources and citations for the Delaware River Basin Water Availability Tool 

for Environmental Resources .....................................................................................................4

2. Parameters optimized for regional hydrologic simulations with the Water 

Availability Tool for Environmental Resources ........................................................................7

3. Fifty-eight USGS streamgage sites in the Delaware River Basin used for model 

optimization and statistical evaluation of simulations of the Water Availability Tool 

for Environmental Resources ...................................................................................................12

4. Sources of point observations used to optimize hydroclimatic components of 

water budget in the Delaware River Basin ............................................................................18

5. Water-use categories ................................................................................................................19

6. Data Sources for the Chesapeake Bay Land Change Mode....................................................21

7. General circulation models provided as part of the WATER database .............................27

8. Representative concentration pathways—data are provided for RCPs 4.5 and 8.5.......27

9. Number of days of observed streamflow not bounded by normalized root mean 

squared error -based confidence intervals over the period of record at two sites 

in the Delaware River Basin, including the site-specific RMSEn, the average 

RMSEn from 57 sites, and the site-specific RMSEn for the observed streamflow 

percentile .......................................................................................................................................5

10. Results of Wilcoxon signed-rank test comparing the error for each streamflow 

percentile from the flow-duration curve for all 57 sites in the Delaware River Basin. 

Values shown are p-values from paired tests .......................................................................58

11. Number of months of observed mean monthly streamflow not bounded by the 

confidence interval based on the mean normalized root mean squared error over 

the period of record for all 45 validation sites in the Delaware River Basin with an 

observation period of 108 months, for Beaver Kill, New York, and Tulpehocken 

Creek, Pennsylvania, sites in the Delaware River Basin .....................................................61
ix

Conversion Factors

[International System of Units to Inch/Pound]

Multiply By To obtain

Length

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

cubic meter per second (m3

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

cubic meter per second (m3

/s) 22.83 million gallons per day (Mgal/d) 

millimeter per year (mm/yr) 0.03937 inch per year (in/yr) 

Radiative forcing

watt per square meter (W/m2) 0.3170 British thermal unit per hour 

per square foot

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

°F = (1.8 × °C) + 32.

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

°C = (°F – 32) / 1.8.

Datum

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.

Supplemental Information

1 micrometer (μm) is 10-6 meter.

Carbon dioxide concentrations are given in parts per million (ppm).
x

Abbreviations

AET actual evapotranspiration

awc available water-holding capacity

CBLCM Chesapeake Bay Land Change Model

CMIP5 Coupled Model Intercomparison Project Phase 5

conmult conductivity multiplier

δ change factor or delta

DEM digital elevation model

DRB Delaware River Basin

DSS decision support system

Ef Nash-Sutcliffe efficiency

EPA U.S. Environmental Protection Agency

ET evapotranspiration

fc field capacity

FDC flow-duration curve

GCM general circulation model

gSSURGO gridded Soil Survey Geographic dataset

GUI graphical user interface

HRU hydrologic response unit

HUC–12 12-digit hydrologic unit code

ICLUS EPA Integrated Climate and Land Use Scenarios

Ksat saturated hydraulic conductivity

m scaling parameter

NED National Elevation Dataset

NLCD National Land Cover Database

NRCS Natural Resources Conservation Service

NWIS National Water Information System

NWS National Weather Service

PET potential evapotranspiration

PST Planning Support Tool 

rho Spearman rank correlation coefficient
xi

RMSEn normalized root mean squared error

RMSEn57 average RMSEn for daily streamflow at 57 sites used for statistical evaluation 

 of WATER

RMSEn45-mon average RMSEn for mean monthly streamflow at 45 sites that had a 9-year 

 period of record for statistical evaluation

RMSEn57mon-PORnorm average RMSEn for mean monthly streamflow at 57 sites normalized over the 

 period of record for each site

RSR ratio of the root mean squared error to the standard deviation of the observed 

 record

SpCf spatial coefficient

SSEB Simplified Surface Energy Balance

SSURGO Soil Survey Geographic dataset

TR–55 USDA Technical Release 55 (an urban hydrology model)

TWI topographic wetness index

USACE U.S. Army Corps of Engineers

USDA U.S. Department of Agriculture

USGS U.S. Geological Survey

WATER Water Availability Tool for Environmental Resources

WaterSMART Secure Water Act to Sustain and Manage America’s Resources for Tomorrow

Summary of Hydrologic Modeling for the Delaware River 

Basin Using the Water Availability Tool for Environmental 

Resources (WATER)

By Tanja N. Williamson, Jeremiah G. Lant, Peter R. Claggett, Elizabeth A. Nystrom, Paul C.D. Milly, 

Hugh L. Nelson, Scott A. Hoffman, Susan J. Colarullo, and Jeffrey M. Fischer

Abstract

The Water Availability Tool for Environmental Resources 

(WATER) is a decision support system for the nontidal part 

of the Delaware River Basin that provides a consistent and 

objective method of simulating streamflow under historical, forecasted, and managed conditions. In order to quantify 

the uncertainty associated with these simulations, however, 

streamflow and the associated hydroclimatic variables of 

potential evapotranspiration, actual evapotranspiration, and 

snow accumulation and snowmelt must be simulated and 

compared to long-term, daily observations from sites. This 

report details model development and optimization, statistical evaluation of simulations for 57 basins ranging from 2 to 

930 km2

 and 11.0 to 99.5 percent forested cover, and how this 

statistical evaluation of daily streamflow relates to simulating 

environmental changes and management decisions that are 

best examined at monthly time steps normalized over multiple 

decades. The decision support system provides a database of 

historical spatial and climatic data for simulating streamflow 

for 2001–11, in addition to land-cover and general circulation model forecasts that focus on 2030 and 2060. WATER 

integrates geospatial sampling of landscape characteristics, 

including topographic and soil properties, with a regionally 

calibrated hillslope-hydrology model, an impervious-surface 

model, and hydroclimatic models that were parameterized 

by using three hydrologic response units: forested, agricultural, and developed land cover. This integration enables 

the regional hydrologic modeling approach used in WATER 

without requiring site-specific optimization or those stationary 

conditions inferred when using a statistical model.

Introduction

The Water Availability Tool for Environmental Resources 

(WATER) was constructed for the Delaware River Basin 

(DRB; fig. 1) to provide a decision support system (DSS) that 

could be used by regulators, managers, and other interested 

parties. The DRB WATER DSS (hereafter called WATER) 

employs a process-based hydrologic model that was implemented with a spatial dataset that catalogues the spatial 

variability in topography, climate, soil properties, and anthropogenic features that affect water movement in this five-state 

area (fig. 1).

WATER was developed and implemented by using historical data; however, the ultimate goal was to provide a DSS 

that could simulate streamflow under a range of forecasted 

climatic and land-use scenarios. Initial work in the DRB 

focused on modeling of minimally impacted streams that were 

upstream of the reservoir system that provides public-supply 

water for the basin as well as New York City, New York. 

Streamflow was simulated for the period 2001–11, using the 

National Land Cover Database (NLCD), data from the Soil 

Survey Geographic (SSURGO) database, Daymet precipitation and temperature data, and water-use data provided by 

the U.S. Geological Survey (USGS) National Water Census 

program; sources and details of these data are provided in 

the section “Framework of the WATER Decision Support 

System.” Because WATER was designed to use a standard 

set of data sources that are available for the entire study area, 

temperature-indexed equations were used to simulate snowpack and potential evapotranspiration (PET). To provide for 

reservoir management planning, streamflow simulations can 

be completed for inflow points to the reservoirs and formatted 

in the output required by the Delaware River Basin Commission’s DRB-Planning Support Tool (PST; DRBC [2015]), 

formerly the DRB-OASIS model (Hydrologics, 2002). 

WATER also interacts with a scenario-building tool 

(WATER Application Utilities) that provides a range of general circulation model (also known as global circulation model 

or global climate model; GCM) datasets that use the changefactor (delta [δ]) approach to synthesize a climate record for 

future conditions. This approach quantifies the difference for 

each GCM between historical and forecasted conditions for 

hydroclimatic variables; this difference is then applied to those 

historical data provided with WATER in order to create a new 

hydroclimatic record for the desired time period. The scenario 

builder also incorporates water-use data and reformats the 

simulated flow record into the desired output structure.
Lake 

Wallenpaupack

Cannonsville 

Reservoir

Pepacton 

Reservoir

Neversink

Reservoir

ATLANTIC 

OCEAN

Wilmington

Trenton

Philadelphia

New York

NEW YORK

CONNECTICUT

MASSACHUSETTS

PENNSYLVANIA

MARYLAND

DC DELAWARE

NEW JERSEY

020401

020402

39°0'

40°30'

42°0'

73°30'

75°0'

75°0'

76°30'

42°0'

40°30'

39°0'

Open water

Impervious surface

Delaware River Basin

Hydrologic Unit Code 6 Basins

020401—Upper

020402—Lower

States within basin

States outside basin

EXPLANATION

0 10 20 30 40 MILES

0 10 20 30 40 KILOMETERS

Figure 1. The Delaware River Basin (DRB), including parts of Delaware, New Jersey, New York, and 

Pennsylvania, as well as a small part of Maryland. Also shown are major population centers and upper-basin reservoirs.

2 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)
Introduction 3

Purpose and Scope

This report focuses on the aggregation and sampling of 

geospatial data, the hydrologic model approach, and the ability 

of WATER to simulate streamflow for historical conditions in 

the DRB. The uncertainty of historical simulations can be used 

to understand the uncertainty related to streamflow simulation for forecasted conditions and scenario testing. However, 

although uncertainty associated with scenario testing is discussed in this report, results from scenario testing are intended 

to be discussed in separate publications.

Focus Area and Overall Approach of WATER

The DRB encompasses 35,075 square kilometers (km2; 

13,539 square miles [mi2]) and includes parts of Delaware, 

Maryland, New Jersey, New York, and Pennsylvania, including the population centers of Wilmington, Delaware, Philadelphia, Pennsylvania, and Trenton, New Jersey, and a total population in 2010 of approximately 8.2 million people (fig. 1). 

In addition, the basin supplies drinking water to New York 

City, N.Y. (essentially doubling the effective population), via 

an interbasin transfer that is supplied by a series of reservoirs 

in the northern part of the DRB. This interbasin transfer is 

managed in accordance with the 1954 Supreme Court decree 

that specifies a minimum flow requirement of 1,750 cubic 

feet per second (ft3/s) at Montague, NJ (U.S. Supreme Court, 

1954, 1982). A 1983 agreement later established a minimum 

flow requirement of 3,000 ft3/s at Trenton, NJ (DRBC, 2013).

Because the DRB reservoir system is strictly managed on a 

daily basis, evaluation of WATER and the associated hydroclimatic variables focused on basins upstream of this reservoir 

system.

Uses and Objectives of WATER

WATER was developed for users with the range of 

hydrologic understanding, geographic interest, and management responsibility included in the DRB stakeholder group. 

Potential users include but are not limited to the following:

• university researchers focused on small subbasins 

where a historical streamflow record is not available;

• local water-resource managers tasked with determining 

the effect of new water-use permits;

• conservation managers working to establish streamflow-restoration goals;

• regional planners who need an objective and informed 

method for assessing expansion of developed areas in 

the coming decades; and

• those needing local or regional quantifications related 

to forecasted climate, including snowpack, growing season and presence of plant-available water for 

evapotranspiration (ET), and seasonal streamflow 

changes.

Consequently, the explanation of the hydrologic modeling approach, data sources, and uncertainty (or error) of 

streamflow simulations are presented at multiple time steps 

and with different organizational approaches (for example, 

streamflow simulations can be compared as a function of land 

cover or organized by streamflow percentiles). Depending on 

the question being asked, WATER output should be used differently and with a different approach to uncertainty, as in the 

following examples:

• Those simulating historical streamflow can use 

WATER output in its original form as daily streamflow 

because the original precipitation and temperature data 

were reported at a daily time step.

• Those asking questions involving forecasted climate 

(GCMs) are strongly discouraged from examining the 

daily WATER output. Instead, these users should focus 

on aggregated streamflow metrics, for example the 

flow-duration curve (FDC) or monthly averages across 

the entire period of record, because climate data are 

adjusted according to a forecasted, long-term, monthly 

change in climatic conditions.

The objectives of this report were to:

1. detail the spatial layers used by WATER to delineate 

basins and inform the hydrologic models;

2. document the incorporation of a 2010 snapshot of water 

use for the DRB;

3. explain how GCM data were processed and incorporated 

and how WATER simulates potential evapotranspiration 

(PET) and actual evapotranspiration (AET) for 2030 and 

2060 target conditions;

4. document the development and incorporation of landcover projections used to characterize 2030 and 2060 

target conditions;

5. compare hydroclimatic observations that affect the water 

budget of the landscape (snow accumulation and snowmelt, PET, and AET) to those simulated by WATER;

6. quantify the uncertainty in daily streamflow simulations 

for the 2001–10 time period and how this uncertainty 

varies with land cover, basin size, and flow regime;

7. quantify the uncertainty in aggregated simulation results, 

including FDCs and monthly flow normals; and

8. explain how uncertainty in streamflow simulations can 

be incorporated into scenario testing.
4 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Framework of the WATER Decision Support 

System

WATER integrates geospatial sampling of landscape 

characteristics with a hillslope-hydrology model and an impervious-surface model in order to simulate water movement to 

streams in the DRB. The hillslope-hydrology model underlying WATER, TOPMODEL (Beven and Kirkby, 1979), is a 

rainfall-runoff model that is based on a water-budget approach 

and simulates hillslope water movement as a function of 

topographically defined landscape positions. TOPMODEL is 

process based and simulates the variable-source-area concept 

of streamflow generation from pervious areas (in other words, 

areas where precipitation infiltrates into the soil) by combining these topographic landscape positions with basin soil 

characteristics (Wolock, 1993). TOPMODEL assumes three 

conditions:

•	 steady-state recharge to the groundwater,

•	 a hydraulic gradient of the water table that approximates that of the surface slope, and

•	 soil-water movement that decreases exponentially with 

depth.

WATER combines streamflow simulation from TOPMODEL for pervious areas with an estimation of runoff 

from impervious surfaces derived by using the curve number approach described in U.S. Department of Agriculture 

(USDA) Technical Release 55 (TR–55; USDA, 1986). To 

inform these models and differentiate pervious from impervious areas, WATER geospatially samples climatic, land-cover, 

topographic, and soils data for the basin of interest (table 1 

and fig. 2; details of different DSS processes are discussed 

in the sections "Data Sources and Processing of Data for 

WATER" and "Model Development, Statistical Evaluation, 

and Validation of Hydroclimatic Components of WATER"). 

The hydrologic models are driven by a daily precipitation and 

temperature record, and WATER provides mean daily streamflow. Hydroclimatic variables, including PET and snow accumulation and snowmelt, are simulated within DRB WATER 

through the use of temperature-indexed equations (Hamon, 

1963; U. S. Army Corps of Engineers [USACE], 1998); AET 

is calculated by TOPMODEL on a daily time step on the basis 

of a combination of PET and soil-water storage. Disposition 

of precipitation as infiltration, overland flow, and soil-water 

storage and movement are simulated by TOPMODEL as a 

function of soil characteristics, including soil thickness, poresize distribution, and saturated hydraulic conductivity (Ksat). 

Any remaining precipitation infiltrates into the soil, and the 

soil-water storage is then equilibrated with the rest of the soil 

thickness before gravity drainage delivers water to either a 

downslope landscape position or to streamflow. This streamflow is then combined with runoff generated from impervious surfaces in the basin (TR–55). Soil-water storage is then 

averaged for the entire basin as a mass balance (equation 2). 

Simulated streamflow generated from forested, agricultural, 

and developed areas are then added to obtain daily streamflow.

WATER is a DSS that is based on a regional modeling approach, meaning that the model works with the same 

parameterization in all areas of the basin. WATER is able to 

model areas with specificity because it uses geospatial data 

layers that catalog differences in land use, soil conditions, and 

topography on a cell size less than or equal to (≤) 30 meters 

(m), with no site-specific optimization (Williamson and others, 

2009, 2013); instead, parameters were optimized as a function of land cover. By using this regional approach, with 

no site-specific optimization, this process-based simulation of streamflow and the water budget can be used to 

examine management scenarios that involve forecasted 

climate change, expansion of urban and suburban areas, 

and restoration goals of minimally impacted flow environments. In contrast, statistical models cannot be used to model 

nonstationary conditions like those associated with land-cover 

and climate change (Farmer and others, 2015).

Table 1. Data sources and citations for the Delaware River Basin Water Availability Tool for Environmental Resources.

[WATER, Water Availability Tool for Environmental Resources; SSURGO, Soil Survey Geographic; NRCS, Natural Resources Conservation Service; 

DEM, digital elevation model; TWI, topographic wetness index; HRU, hydrologic response unit]

Data source Contribution to WATER

Daymet (Thornton and others, 2012)

http://daymet.ornl.gov/index.html

Daily temperature and precipitation data for 1980–2011

National Elevation Dataset (Gesch and others, 2002)

http://ned.usgs.gov/

Elevation data (as DEM) used for basin delineation and 

TWI calculations

2011 National Land Cover Database (Jin and others, 2013)

http://www.mrlc.gov/

HRUs and impervious area

Soil Survey Geographic (SSURGO) database 

(SSURGO; NRCS, 2014)

http://datagateway.nrcs.usda.gov/

Hydrologic soil characteristics and TOPMODEL specific parameters
Soil propeties

from SSURGO

specific to HRU

New basin delineated or basin from imported shapefile

Sample NLCD for HRUs

Topographic

Wetness

Index

Histogram

specific

to HRU

Aggregate climate data

 from 3736 DEM-derived polygons

Proportion of 

precipitation on

impervious area

TR-55

Actual ET from

root zone

If precipitation > 

potential ET?

Infiltration

Yes

No

Daily

streamflow 

from

HRU

Drainage

 to next 

TWI bin

Next

Day

Forested

Agricultural

Developed

Summed

as daily

streamflow

for basin

IF 

temperature <0,

build snowpack; ELSE 

melt snowpack

Delay proportion

of flow upstream

of water body

Retain DailyTimestep

Rooting Zone 

soil storage

Equilibration

with subsoil

Gravity drainage 

by TWI bin 

1 to n-1 | n

Convert to 

HourlyTimestep

Saturation Deficit:

mass

balance over

TWI bins

Proportion of daily 

precipitation on pervious area

EXPLANATION

Basin-wide

Done within HRU

Data sampling

TOPMODEL process

Introduction 5

Figure 2. How the Water Availability Tool for Environmental Resources samples geospatial data and feeds it to the two hydrologic 

models (TOPMODEL and the U.S. Department of Agriculture urban hydrology model [TR–55]). The basin is apportioned into three 

hydrologic response units (HRUs). Daily precipitation is sampled from Daymet and proportionally distributed between pervious and 

impervious areas. Potential evapotranspiration (PET) is estimated from Hamon (1963). Actual evapotranspiration (AET) is removed from 

soil-water storage in the root zone (table 2), and the remainder infiltrates into the soil. The soil-water storage is then equilibrated with 

the rest of the soil thickness before gravity drainage delivers water either to the next topographic-wetness-index (TWI) bin (bins 1 

to n–1; n=30) or to streamflow. Soil-water storage for the entire basin is then averaged using a mass balance (equation 2). Simulated 

streamflow generated from three separate HRUs is then summed to obtain daily streamflow. DEM, digital elevation model; 

ET, evapotranspiration; NLCD, National Land Cover Database; SSURGO, Soil Survey Geographic database; >, greater than; <, less than.
6 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

The WATER developed for the DRB includes the entire 

basin. For some areas, streamflow simulations derived with 

WATER should be used cautiously. For example, WATER 

provides no method of simulating the influence of tides on 

streamflow that would be expected in stream reaches south 

of Trenton, N.J., along the Delaware River, and in tributaries 

along Delaware Bay (fig. 3). In addition, WATER does not 

take into account the daily controlled releases from dams and 

reservoirs in the basin, so it will not accurately simulate flows 

on large rivers affected by these releases. These rivers include, 

in particular, the entire length of the main-stem Delaware 

River, but also parts of the Neversink, Lackawaxen, Mongaup, 

Lehigh, Schuylkill Rivers and Brandywine Creek, as well 

as other locations (fig. 3). In anticipation of this constraint, 

WATER was designed to output data at river locations (nodes) 

known to be inflow points for the DRB-PST (DRBC, 2015) 

and is compatible with this reservoir operation support tool. If 

WATER is used to simulate streamflow for areas that include 

reservoirs, they will be treated as areas with any other water 

bodies. Consequently, users should be familiar enough with 

their area of interest to understand whether streamflow is controlled by reservoir management.

Relation of Delaware River Basin WATER to 

Previous Studies

WATER is built upon a physically based hydrologic 

model that simulates the variable-source-area concept of 

streamflow and is an extension of the TOPMODEL code 

described in Wolock (1993). The TOPMODEL code was originally developed by Beven and Kirkby (1979); however, many 

researchers have extensively modified the code, and numerous versions of TOPMODEL now exist in several programming languages (e.g. Robson and others, 1992; Romanowicz, 

1997; Metcalfe and others, 2014). TOPMODEL has been used 

to study a variety of hydrologic research topics, including 

topographic effects on water quality (Wolock, 1988; Wolock 

and others, 1990; Wolock and McCabe, 1999), topographic 

effects on streamflow (Beven and Wood, 1983; Beven and others, 1984; Kirkby, 1986), spatial-scale effects on hydrologic 

processes (Sivapalan and others, 1987; Beven and others, 

1988; Wood and others, 1988; Sivapalan and others, 1990; 

Wood and others, 1990; Famiglietti and Wood, 1991; Famiglietti, 1992), and the geomorphic evolution of basins (IjjászVásquez and others, 1992). TOPMODEL has also been used 

for estimating regional-scale variability in hydrologic properties in the United States (Wolock, 2003), flood frequency 

(Beven, 1986a, b), effects of climate change on hydrologic 

processes (Wolock and Hornberger, 1991), soil-water storage 

(Williamson and others, 2014), carbon budgets (Band and 

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

2002), and ecological-flow factors (Kennen and others, 2008). 

Finally, TOPMODEL has been used to reveal interactions 

among variables in model-parameter calibration (Hornberger 

and others, 1985; Wolock, 1988; Wolock and McCabe, 1995; 

Williamson and others, 2013), including how input data must 

change with a change in digital-data resolution (Brasington 

and Richards, 1998).

WATER for the DRB builds on previous hydrologic 

modeling in New Jersey (Kennen and others, 2008) and is an 

updated version of the DSS developed in Kentucky (Williamson and others, 2009, 2013). New functionality in WATER for 

the DRB includes estimates of snow accumulation and melting as well as implementation of a hydrologic response unit 

(HRU) approach that is based on three general land-cover categories: forested, agricultural, and developed areas. This HRU 

refinement enabled multiple aspects of the WATER approach 

by differentiating the interaction among the topography, soil 

characteristics, and hydroclimatic variables critical to TOPMODEL and how it simulates the water-budget and hillslope 

processes among the HRUs. Consequently, data sources and 

parameterization discussed in the following section are unique 

to WATER for the DRB.

Data Sources and Processing of Data 

for WATER

WATER is provided with a database of model inputs for 

the 2001–11 period because this is the temporal overlap of the 

many data layers required to inform the model. Limitations 

leading to the selection of this time period are the intersection 

of the historical climate record (1980–2011), the generation 

of land-cover data (2011), and the water-use snapshot (2010). 

Other data (for example, topography and soil data) are not 

time sensitive. Each of these data sources is encapsulated 

within WATER to provide all of those data required to simulate streamflow and water availability. Unless otherwise stated, 

all geospatial data are at a 10-m resolution in the North American Datum of 1983 Albers Equal Area Projection using the 

Geodetic Reference System 1980 spheroid. All geoprocessing 

was done with ArcMap 10.0 (https://www.arcgis.com). Output 

of the hydrologic simulations is provided on daily (WATER.

txt), monthly (WATERMonth.txt), and annual (WATERAnnual.txt) time steps and can be imported by the user into a 

spreadsheet or statistical program for analysis.

As described in the section “Framework of the WATER 

Decision Support System,” WATER uses a hydrologic modeling approach that depends on the accompanying spatial layers 

of topography, soil properties, and climatic data to simulate 

precipitation disposition throughout the DRB (fig. 2). HRUs 

are delineated by intersecting an individual basin (either delineated by WATER or provided by the user) with the land cover 

in order to separate forested, agricultural, and developed areas; 

each HRU may include multiple, discontinuous areas with 

similar land cover. WATER then calculates an arithmetic mean 

for each spatial layer for each HRU; currently, this process 

uses the Spatial Analyst extension in ArcGIS 10.0. To optimize 

the incorporation of these geospatial data with the hydrologic 

modeling, a subset of ten parameters (table 2) that control the 
Data Sources and Processing of Data for WATER 7

Table 2. Parameters optimized for regional hydrologic simulations with the Water Availability Tool for Environmental Resources. These 

parameters control the soil-plant-water interactions and how they differ among hydrologic response units. These parameters also equip 

the model for scenario testing in terms of both land-cover and climate forecasts.

[Color coding is included to highlight the parameters related to TOPMODEL (white), interaction with water bodies (grey), impervious-surface runoff (blue), 

snow accumulation (purple), and evapotranspiration (green). AET, actual evapotranspiration; ET, evapotranspiration; >, greater than; km2, square kilometers; 

NLCD, National Land Cover Database; TR–55, U.S. Department of Agriculture Technical Release 55; USDA, U.S. Department of Agriculture; 

mm/d/°C, millimeters per day per degree Celsius; USACE, U.S. Army Corps of Engineers; PET, potential evapotranspiration; HRU, hydrologic response unit]

Parameter Parameter alias Application and unit Hydrologic response unit

Forested Agricultural Developed

Spatial coefficient spatialcoeff Used to calculate scaling parameter (m) 

for TOPMODEL

0.4 0.3 0.25

Topographic 

adjustment

wiadjustment Adjusts topographic-wetness-index values 

in histogram for TOPMODEL

1 1 0.5

Rooting depth factor rootdepthfactor Proportion of soil thickness used for ET in 

TOPMODEL

0.75 0.25 0.75

Travel through 

macropores

percentmacropore Proportion of precipitation that bypasses ET 

soil thickness in TOPMODEL

0.15 0.15 0.2

Water-body delay lakedelay days—proportional increase in days that water 

is delayed if upstream of a water body; 

water bodies >10 acre (0.04 km2

) 

15 1.5 1.5

Effective impervious effimpervious Multiplied by NLCD value to change total 

impervious surface for study area

0.7 1 1

Impervious runoff 

delay

imperviousrunoff Proportion of precipitation delayed to next day 

from impervious surface and TR–55 calculations

0.1 0.5 0.1

Impervious curve 

number

imperviouscurve TR–55 parameter that characterized type of 

impervious surface (USDA, 1986)

90 90 100

Snowmelt coefficient snowcoeff mm/d/°C above 0 (USACE, 1998) for snowmelt 2 2 4

Rain-on-snowmelt 

coefficient

rainonsnowcoeff mm/d/°C above 0 (USACE, 1998) for snowmelt 3 4 6

Exponent for 

seasonal AET etexponent

Exponent

calculated maximum storagesoil

storagesoil PETAET 













 = ×

0.5 

(growth)

5 

(dormant)

Growing season 

trigger

growtemp °C—transitions to/from growing season 

exponent for AET calculation 15
Schuylkill

Lehigh

Upper 

Delaware

Lower

Delaware

Cohansey-Maurice

Lackawaxen

BroadkillSmyrna

East Branch

Delaware

Brandywine- Christina

Delaware 

Bay

CrosswicksNeshaminy

Middle 

DelawareMusconetcong

Middle 

DelawareMongaupBrodhead

EXPLANATION

Delaware River Basin

Approximate extent of 

tidal influence

Reservoirs

Surface water

Downstream of large 

reservoir—Regulated

Reservoir storage alters 

streamflow

Lehigh Hydrologic Unit 

Code 8 Basin

NEW 

YORK

PENNSYLVANIA

MARYLAND

NEW 

JERSEY

DELAWARE

0 10 20 30 40 MILES

0 10 20 30 40 KILOMETERS

42°

76° 75° 74° 73°

41°

40°

39°

42°

41°

40°

39°

77° 76° 75°

8 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 3. Parts of the Delaware River system for which streamflow information from the 

Water Availability Tool for Environmental Resources should be used cautiously because of stream 

regulation and tidal influences.
Data Sources and Processing of Data for WATER 9

interaction of topography and vegetation with precipitation 

disposition was regionally optimized for the individual DRB 

HRUs (forested, agricultural, and developed land cover) to 

create the best fit for streamflow observations in basins with 

relatively homogeneous land cover. This regional approach 

to HRU optimization followed Williamson and others (2009) 

and incorporated parameter exploration (Doherty, 2008); this 

approach was used instead of site-specific optimization to 

identify a single set of HRU parameters that work throughout 

the DRB. An additional four parameters were optimized for 

simulation of snowmelt and accumulation as well as ET.

Data sources can be separated into those that inform the 

hydrologic models, those used for optimization and statistical validation of WATER simulations, and those that enable 

scenario testing. Data that inform the hydrologic models and 

those that enable scenario testing are included in the WATER 

database and WATER Application Utilities. The optimization and statistical validation discussed in the section “Model 

Development, Statistical Evaluation, and Validation of Hydroclimatic Components of WATER” provides a reference for 

understanding the potential error and uncertainty associated 

with hydrologic simulation (1) where no observations exist 

and (2) for forecasted or proposed scenarios in basin management or environmental change.

Data That Inform the Models

Data required for the hydrologic models (TOPMODEL 

and TR–55) to run include daily precipitation and temperature 

as well as basin characteristics that quantify topography and 

the potential to store water in the soil. In addition, parameters 

that describe how these basin characteristics interact and how 

water moves through the soil to the stream are derived with 

these same data.

Topography

Topographic data are from the 10-m resolution National 

Elevation Dataset (NED; Gesch and others, 2002). These data 

are used for three purposes: (1) basin delineation, (2) development of a digital elevation model (DEM)-derived stream 

network, and (3) development of the topographic wetness 

index (TWI). Because WATER was developed to analyze 

basins from physiographically diverse terranes, hydrologic 

parameters such as stream-channel width and the drainage 

area required to initiate channelized streamflow had to be uniformly defined. To estimate stream-cell area, the stream network raster was developed by applying the following criteria:

1. Streams were defined as 1 cell wide for the entire network.

2. Streams were initiated after accumulating a total of 

0.3 km2 (3,000 10-m cells) upstream area by using the 

Arc Hydro Flow Accumulation tool (with a single-flowdirection algorithm; https://www.arcgis.com).

These two flow-accumulation criteria area were established to include first-order, perennial, channelized drainages 

while excluding small, ephemeral, hillslope systems.

Basins are delineated within WATER by using a combination of flow-direction and flow-accumulation rasters, 

combined with 3,736 predelineated, DEM-derived polygons 

that range in size from 0.0001 to 132.4 km2, with a mean area 

of 9.4 km2 and median of 7.6 km2. These predelineated basins 

were produced by using Arc Hydro (https://www.arcgis.com) 

and make the basin delineation process faster by providing a 

sequenced network of basins that can be aggregated into the 

site-specific basin delineation. Although the USGS National 

Hydrography Dataset (http://nhd.usgs.gov; U.S. Geological 

Survey and others, 2009) is used to help orient the user in 

the WATER graphical user interface (GUI), WATER uses the 

DEM-derived stream network to delineate basins and calculate 

stream area. The result is that WATER can be used to delineate 

a new basin from a pour-point (basin outlet) that is anywhere 

on the DEM-derived stream network.

The TWI raster used by TOPMODEL (discussed below) 

was developed from these same flow-direction and flow-accumulation rasters. Because TWI values along stream channels 

do not reflect hillslope processes (Quinn and others, 1997), 

these high values were removed. This prevents cells with high 

TWI values from altering the TWI distribution for a given 

basin while still maintaining a representative riparian zone to 

serve as a variable source area for streamflow.

Climate Data

The Daymet historical climate record was originally at a 

resolution of 1 km2 (Thornton and others, 2012), and a geospatial mean was sampled by using the 3,736 DEM-derived polygons and processed by the USGS Geo Data Portal (http://cida.

usgs.gov/gdp/). These Daymet data were geospatially sampled 

and supplied as part of the database in order to provide a long 

period of record with a minimum of processing time, and 

they include a historical record from January 1, 1980, through 

December 11, 2011. These data include maximum daily 

temperature and total daily precipitation. Total daily precipitation is randomly distributed during each day by WATER 

using a set seed, or starting point, so that the randomization is 

the same every time the model is run—this insures reproducibility of results and comparability of results among historical and forecasted conditions. This randomization distributes 

the daily total of precipitation to individual hours in the day; 

TOPMODEL functions on an hourly time step on days with 

precipitation. WATER uses maximum daily temperature to 

estimate daily PET (Hamon, 1963), and the accumulation and 

melt of snow (USACE, 1998), by using temperature-indexed 

equations; this is discussed in “Hydroclimatic Water-Budget 

Components” in more detail. Precipitation and temperature 

data are stored in the WATER database as text files for those 

3,736 DEM-derived polygons.
10 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Land Cover

The land-cover raster in the WATER database is NLCD 

2011 (Jin and others, 2013), although initial development of 

WATER proceeded with NLCD 2006 until more recent data 

were published. The NLCD 2011 dataset has a 30-m resolution 

and is used for two purposes: (1) delineation of the forested, 

agricultural, and developed HRUs and (2) calculation of basin 

averages of impervious area.

These HRUs are a simplification of land cover into three 

categories: forested (deciduous, evergreen, mixed, shrubland, 

and wetland areas; NLCD classes 41–43, 51–52, and 90–95), 

agricultural (pasture and cropland; NLCD classes 81 and 

82), and developed (all remaining categories; NLCD classes 

21–24, 31, and 71). The DSS initially classifies open water 

(NLCD class 10) as developed because it does not match 

either the forested or agricultural land-cover categories, but 

the DSS later reassigns it as water.

The proportion of impervious surface area in the basin is 

estimated from a combination of the 2011 NLCD and a road 

layer (10-m resolution 2010 NAVTEQ; Homeland Security 

Infrastructure Program [2012]). WATER allocates a proportion of precipitation to the TR–55 impervious flow model on 

the basis of the proportion of impervious surface in the basin. 

The remaining precipitation is distributed for the pervious 

portion of the basin as a function of hillslope hydrology by 

TOPMODEL.

Soils Data

Representative values of soil parameters were aggregated 

from the SSURGO database by using a series of queries in 

Microsoft Access; these parameters include Ksat, soil thickness, 

field capacity (fc), total porosity, and available water-holding 

capacity (awc). Similarly to the case with NLCD, development of WATER originally proceeded with data downloaded 

in 2012 (Natural Resources Conservation Service [Soil Survey 

Staff [NRCS], 2012]), but the newer SSURGO (Soil Survey 

Staff [NRCS], 2014) product was used to replace these 2012 

data during the validation process, and are provided in the 

WATER database; this was done to incorporate recent correlations among counties on the basis of discussion with NRCS. 

Soil-property data were upscaled from soil-layer data (corresponding to one or more horizons) to component-weighted 

means (corresponding to one or more soil series) for each 

soil-mapping unit after Williamson and others (2014) and were 

joined to spatial data by using the unique identifiers of soilmapping-unit polygons. These polygons, attributed with individual soil parameters, were then converted to a 10-m raster to 

match that of the DEM and used for geospatial statistics.

For compilation of this database, soil thickness was 

defined as the sum of the soil layers for which the representative Ksat reported in the SSURGO database was greater than 

(>) 1 micrometer per second (μm/s)—approximately the conductivity of a silty sand (Dingman, 2002). This is equivalent 

to choosing all soil layers for which Ksat is “moderately high 

or higher” as defined by the Natural Resources Conservation 

Service (Soil Survey Staff [NRCS], 1993). The elimination 

of layers with Ksat ≤1 μm/s is based on previous work that 

showed that these subsoil layers are not involved in the daily 

hydrologic processes simulated by TOPMODEL (Williamson and others, 2009). Consequently, the first query run on 

SSURGO data eliminated all soil layers that did not meet this 

criterion. The remaining soil layers were used to determine the 

soil thickness. Other soil properties, including fc, total porosity, and awc were upscaled by using the same soil layers.

Linking Topographic and Soil Data for Hydrologic 

Models

In addition to the soil properties listed above, two other 

hydrologic properties—the conductivity multiplier (conmult) 

and the scaling parameter—were calculated for each mapping 

unit. The conmult estimates the relative change in Ksat with 

depth:

conmult = Ksat-high

Ksat-low , (1) 

where

Ksat-high is maximum Ksat value for the soil map unit 

and

Ksat-low is minimum Ksat value for the soil map unit for 

which the representative Ksat is >1μm/s in 

the SSURGO database.

A smaller conmult indicates less change in Ksat with depth. 

Within the WATER database, the minimum conmult is 2, 

indicating that the Ksat at the surface is twice that at the base 

of the soil. TOPMODEL incorporates this vertical change in 

Ksat movement to simulate soil-water movement through the 

hillslope. 

The scaling parameter (m) incorporates the conmult

and is used by TOPMODEL to estimate spatial variability in 

saturation deficit across the landscape by linking the mean 

saturation deficit, or unfilled pore space in the soil, with the 

local difference in the topography (after Beven, 1984):

 , (2)

where

Sx is local saturation deficit in a grid cell 

(10-m cells);

S S x x = + ( ) SpCf m× − ( ) TWI TWI

S is mean saturation deficit in basin;

m is scaling parameter;

SpCf is HRU-specific spatial coefficient determined 

during model optimization; 

TWI is mean topographic wetness index in basin 

(discussed below); and

TWIx is local topographic wetness index in grid 

cell;
Data Sources and Processing of Data for WATER 11

with , (3) m porosity field capacity

f ≡ −

. (4)

Optimization for the individual HRUs, following the approach 

of Williamson and others (2009) and incorporating parameter exploration (Doherty, 2008), showed that streamflow 

simulation improved when the m directly calculated from 

the SSURGO database was multiplied by the HRU-specific 

spatial coefficient (SpCf; table 2) to empirically fit the relation 

between soil-water deficit and topography, given the resolution 

of those spatial data and the three different land-cover types. 

The scaling parameter (m) acts directly on the deficit calculation (equation 2). The magnitude of this parameter is critical 

to how much water is retained in the soil pores during dry 

periods and to the resultant hydrograph response in terms of 

flood peaks. A larger m results in an exaggeration of the topography (quantified by the TWI), resulting in more downslope 

movement of soil water and smaller peak flows in the stream. 

To optimize discharge estimates, some TOPMODEL-based 

research has estimated the conmult and m parameters without always maintaining the numerical link indicated by the 

equations (for example Band and others, 1993; Pellenq and 

others, 2003); this type of parameterization is not feasible 

without site-specific optimization, so it is not done for the 

regional approach used by WATER. Brasington and Richards 

(1998) showed that the magnitude of m is related to the spatial 

resolution of the input data and that, when DEM rasters on 

the order of 20 m are used, a laboratory-determined Ksat and 

correspondingly small m value produced the most accurate 

results. Use of this HRU-specific spatial coefficient (SpCf) 

allows the regional modeling approach to proceed by informing the model with spatially detailed soils data. At the same 

time, this spatial coefficient makes use of an optimization that 

has shown that the relation between the soil and topography 

differs for the different HRUs.

TOPMODEL uses a numerical characterization of landscape position called the topographic wetness index (TWI) to 

simulate streamflow and hillslope hydrology:

and ln conmult f soil thickness =

 

ln

tan

A TWI

β

  =     , (5)

where

A is upslope contributing area per unit contour 

width (meters) and

β is local slope (degrees) of individual cells 

(that is, in the 10-m DEM resolution).

In general, lower TWI values indicate drier positions on the 

landscape (such as drainage divides and steep slopes); higher 

TWI values indicate wetter landscape positions (such as 

riparian areas). However, because the TWI incorporates both 

local slope and upslope area, it is possible for the TWI value 

to either decrease or increase from one cell to another in a 

downslope direction. Therefore, instead of basing computations on the TWI value of individual cells in a basin, TOPMODEL classifies the cells into a histogram (WATER uses a 

30-bin histogram), and each bin of cells from the histogram, 

a quantitative representation of landscape position, is dealt 

with as a group on the basis of the mean TWI value of that 

bin; this mean TWI value is adjusted for developed areas by 

using the topographic adjustment parameter to decrease the 

topographic gradient and account for localized water retention 

(table 2). All of the cells from each bin are treated the same 

way for all future calculations; the TWI value for each bin for 

an individual basin is a constant and is used to calculate the 

changes in the local saturation deficit (equation 2 and fig. 2) 

on the principle that cells with a similar TWI value will have 

a similar hydrologic response (Beven and Kirkby, 1979). It is 

the integration of this approach to topography with a spatially 

detailed description of soil properties that enables the regional 

hydrologic modeling approach used in WATER without requiring site-specific optimization.

Data Used for Validating Simulations

Although a primary intention of WATER is to provide the 

ability to estimate streamflow at ungaged locations, the model 

development, optimization, and statistical evaluation documented in this report would be impossible without long-term 

streamflow monitoring sites. Statistical evaluation of model 

performance is an important part of developing WATER for 

a large region like the DRB—this involves comparison of 

WATER simulations to observations from long-term streamflow gages and other types of hydroclimatic monitoring. This 

statistical evaluation, in turn, allows the user to have confidence in WATER simulations and incorporate these results 

into the decision-making process.

Historical Streamflow and OptimizationValidation Basins

Observed mean daily streamflow (National Water 

Information System [NWIS] parameter code 00060; http://

waterdata.usgs.gov/nwis) was first used to optimize hydrologic parameters (table 2) and then used to statistically 

evaluate mean daily streamflow simulated by WATER and 

to validate model output after development was completed. 

USGS streamgage sites were selected on the basis of the 

availability of streamflow data for 3 to 10 years during the 

2001–10 time period. An additional selection criterion was 

that gaged streams be unaffected by reservoir releases or flow 

regulation. WATER parameters (table 2), most of which are 

HRU-specific, were optimized by using observations from 

21 streamgage sites in the DRB (table 3 and fig. 4), each of 

which consisted primarily of a single HRU (either forested 

[>75 percent], agricultural [>60 percent], or developed [>70 

percent] land cover); one of these sites, USGS site 01466500, 
12 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Table 3. Fifty-eight USGS streamgage sites in the Delaware River Basin used for model optimization and statistical evaluation 

of simulations of the Water Availability Tool for Environmental Resources (WATER). Those 21 basins with relatively homogeneous 

land cover, consisting primarily of a single hydrologic response unit (HRU), were used for optimization of select WATER parameters 

(table 2); mixed land-cover basins were used to statistically evaluate select WATER parameters and to optimize incorporation of 

water-use data; nine basins were set aside for final testing of model performance. Basins were only included if the streamgage 

period of record overlapped with the climatic and land-cover datasets used by WATER. Only complete water years (October through 

September of the following year) were included. Locations are shown in figure 4.—Continued

[Optimization and statistical evaluation use numbers, with percentages based on NLCD 2006: a, greater than (>) 60 percent agricultural; d, >70 percent 

developed; f, >75 percent forested; m, mixed land cover; t, test basin. USGS, U.S. Geological Survey; ID, identification number; mi2, square miles; 

km2, square kilometers; %, percent; NJ, New Jersey; NY, New York; PA, Pennsylvania; U.S. United States; DE, Delaware; PET, potential evapotranspiration; 

AET, actual evapotranspiration]

USGS site ID and name

Drainage area Hydrologic response unit (%) Optimization 

and

validation 

use 

Period of 

record

(water years)

Begin End

Complete 

(mi2

) (km2) Forested Agricultural Developed years

01411500 Maurice River at 

Norma NJ

111.3 288.3 48.5 23.6 27.9 m 1933 2010 9

01413500 East Branch 

Delaware River 

at Margaretville 

NY

163.2 422.9 87.6 8.2 4.2 f 1937 2010 9

01414500 Mill Brook near 

Dunraven NY

25.1 65.1 93.8 3.9 2.3 f 1937 2010 9

01415000 Tremper Kill near 

Andes NY

33.1 85.7 79.0 17.3 3.7 f 1937 2010 9

01420500 Beaver Kill at 

Cooks Falls NY

242.4 628.0 93.2 2.4 4.4 f 1914 2010 9

01421618 Town Brook 

southeast of 

Hobart NY

14.3 37.0 64.9 32.4 2.7 t 1999 2010 9

01421900 West Branch 

Delaware River 

upstream from 

Delhi NY

134.4 348.2 64.0 31.0 5 t 1937 2010 9

01422389 Coulter Brook 

near Bovina 

Center NY

0.8 2.0 99.5 0.0 0.5 f 1999 2010 7

01422500 Little Delaware 

River near 

Delhi NY

49.8 129.1 75.4 19.5 5.1 f 1938 2010 9

01422738 Wolf Creek at 

Mundale NY

0.6 1.6 69.2 26.5 4.3 m 2000 2010 7

was only used for estimating a monthly water budget for ET 

optimization because it is a swamp, so it does not meet the 

underlying requirements for using TOPMODEL. An additional 

28 streamgage sites with a mix of land cover were then used 

for validation of optimized model parameters and refinement 

of how water-use data were incorporated (discussed in “WaterUse Data Provided in WATER Application Utilities”). Finally, 

nine streamgage sites were tested after all model development 

had been completed. This brings the total to 57 sites that were 

used to statistically evaluate hydrologic simulations. In the 

remainder of the report, the terms “site” and “basin” are used 

interchangeably because WATER samples basin properties and 

simulates streamflow generated within a basin that delineates 

the total area upstream of a site along a stream.
Data Sources and Processing of Data for WATER 13

Table 3. Fifty-eight USGS streamgage sites in the Delaware River Basin used for model optimization and statistical evaluation of 

simulations of the Water Availability Tool for Environmental Resources (WATER). Those 21 basins with relatively homogeneous land 

cover, consisting primarily of a single hydrologic response unit (HRU), were used for optimization of select WATER parameters (table 

2); mixed land-cover basins were used to statistically evaluate select WATER parameters and to optimize incorporation of water-use 

data; nine basins were set aside for final testing of model performance. Basins were only included if the streamgage period of record 

overlapped with the climatic and land-cover datasets used by WATER. Only complete water years (October through September of the 

following year) were included. Locations are shown in figure 4.—Continued

[Optimization and statistical evaluation use numbers, with percentages based on NLCD 2006: a, greater than (>) 60 percent agricultural; d, >70 percent developed; f, >75 percent forested; m, mixed land cover; t, test basin. USGS, U.S. Geological Survey; ID, identification number; mi2

, square miles; km2, square 

kilometers; %, percent; NJ, New Jersey; NY, New York; PA, Pennsylvania; U.S. United States; DE, Delaware; PET, potential evapotranspiration; 

AET, actual evapotranspiration]

USGS site ID and name

Drainage area Hydrologic response unit (%) Optimization 

and

validation 

use 

Period of 

record

(water years)

Begin End

Complete 

(mi2

) (km2) Forested Agricultural Developed years

01422747 East Brook east of 

Walton NY

24.7 63.9 63.9 31.3 4.8 m 2000 2010 9

01423000 West Branch 

Delaware River 

at Walton NY

331.9 859.9 67.2 27.1 5.7 m 1951 2010 9

01424108 Sherruck Brook 

Tributary near 

Trout Creek NY

1.3 3.3 97.7 0.0 2.3 m 1999 2007 6

01428750 West Branch 

Lackawaxen 

River near 

Aldenville PA

40.6 105.1 60.8 31.0 8.2 t 1987 2010 9

01435000 Neversink River 

near Claryville 

NY

66.7 172.7 98.9 0.2 0.9 f 1938 2010 9

01439500 Bush Kill at Shoemakers PA117.2 303.7 89.7 0.0 10.3 f 1909 2010 9

01440000 Flat Brook near 

Flatbrookville 

NJ

65.1 168.5 89.3 6.2 4.5 f 1924 2011 9

01440400 Brodhead Creek 

near Analomink 

PA

67.5 174.8 90.2 1.0 8.8 f 1958 2010 9

01442500 Brodhead Creek at 

Minisink Hills 

PA

260.6 675.0 74.5 4.0 21.5 f 1951 2010 9

01443500 Paulins Kill at 

Blairstown NJ

126.1 326.7 59.4 23.9 16.7 m 1922 2011 9

01445000 Pequest River at 

Huntsville NJ

31.0 80.2 66.0 17.2 16.8 m 1940 2011 8

01445500 Pequest River at 

Pequest NJ

106.1 274.9 60.5 26.1 13.4 m 1922 2011 9

01446000 Beaver Brook near 

Belvidere NJ

36.6 94.9 52.8 37.0 10.2 m 1923 2011 7

01447500 Lehigh River at 

Stoddartsville 

PA

91.8 237.7 88.2 0.3 11.5 t 1944 2010 9
14 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Table 3. Fifty-eight USGS streamgage sites in the Delaware River Basin used for model optimization and statistical evaluation of 

simulations of the Water Availability Tool for Environmental Resources (WATER). Those 21 basins with relatively homogeneous land 

cover, consisting primarily of a single hydrologic response unit (HRU), were used for optimization of select WATER parameters (table 

2); mixed land-cover basins were used to statistically evaluate select WATER parameters and to optimize incorporation of water-use 

data; nine basins were set aside for final testing of model performance. Basins were only included if the streamgage period of record 

overlapped with the climatic and land-cover datasets used by WATER. Only complete water years (October through September of the 

following year) were included. Locations are shown in figure 4.—Continued

[Optimization and statistical evaluation use numbers, with percentages based on NLCD 2006: a, greater than (>) 60 percent agricultural; d, >70 percent developed; f, >75 percent forested; m, mixed land cover; t, test basin. USGS, U.S. Geological Survey; ID, identification number; mi2

, square miles; km2, square 

kilometers; %, percent; NJ, New Jersey; NY, New York; PA, Pennsylvania; U.S. United States; DE, Delaware; PET, potential evapotranspiration; 

AET, actual evapotranspiration]

USGS site ID and name

Drainage area Hydrologic response unit (%) Optimization 

and

validation 

use 

Period of 

record

(water years)

Begin End

Complete 

(mi2

) (km2) Forested Agricultural Developed years

01449360 Pohopoco Creek 

at Kresgeville 

PA

49.8 129.0 56.4 19.9 23.7 t 1967 2010 9

01450500 Aquashicola 

Creek at 

Palmerton PA

76.6 198.4 69.6 19.8 10.6 m 1940 2010 9

01451500 Little Lehigh 

Creek near 

Allentown PA

81.9 212.2 24.9 38.7 36.4 m 1946 2010 9

01451800 Jordan Creek near 

Schnecksville 

PA

53.0 137.3 29.7 59.4 10.9 m 1967 2010 9

01452000 Jordan Creek at 

Allentown PA

76.2 197.5 29.7 53.1 17.2 m 1945 2010 9

01452500 Monocacy Creek 

at Bethlehem 

PA

43.3 112.1 9.0 54.9 36.1 m 1949 2010 9

01464500 Crosswicks Creek 

at Extonville NJ

80.7 209.2 48.8 26.2 25 t 1938 2010 9

01464907 Little Neshaminy 

Creek at Valley 

Road near 

Neshaminy PA

27.0 70.1 21.3 12.0 66.7 t 2000 2010 9

01465798 Poquessing Creek 

at Grant Avenue 

at Philadelphia 

PA

21.4 55.4 13.4 4.9 81.7 d 1966 2010 9

014665001 McDonalds 

Branch in 

Byrne State 

Forest NJ

2.3 6.1 92.6 0.0 7.4 f 1954 2010 9

01467048 Pennypack Creek 

at Lower 

Rhawn Street 

Bridge, 

Philadelphia PA

49.8 129.1 20.1 1.9 78 d 1966 2010 9
Data Sources and Processing of Data for WATER 15

Table 3. Fifty-eight USGS streamgage sites in the Delaware River Basin used for model optimization and statistical evaluation of 

simulations of the Water Availability Tool for Environmental Resources (WATER). Those 21 basins with relatively homogeneous land 

cover, consisting primarily of a single hydrologic response unit (HRU), were used for optimization of select WATER parameters (table 

2); mixed land-cover basins were used to statistically evaluate select WATER parameters and to optimize incorporation of water-use 

data; nine basins were set aside for final testing of model performance. Basins were only included if the streamgage period of record 

overlapped with the climatic and land-cover datasets used by WATER. Only complete water years (October through September of the 

following year) were included. Locations are shown in figure 4.—Continued

[Optimization and statistical evaluation use numbers, with percentages based on NLCD 2006: a, greater than (>) 60 percent agricultural; d, >70 percent developed; f, >75 percent forested; m, mixed land cover; t, test basin. USGS, U.S. Geological Survey; ID, identification number; mi2

, square miles; km2, square 

kilometers; %, percent; NJ, New Jersey; NY, New York; PA, Pennsylvania; U.S. United States; DE, Delaware; PET, potential evapotranspiration; 

AET, actual evapotranspiration]

USGS site ID and name

Drainage area Hydrologic response unit (%) Optimization 

and

validation 

use 

Period of 

record

(water years)

Begin End

Complete 

(mi2

) (km2) Forested Agricultural Developed years

01467086 Tacony Creek at 

County Line, 

Philadelphia PA 

16.2 42.0 13.2 0.3 86.5 d 1966 2010 5

01467150 Cooper River at 

Haddonfield NJ

17.1 44.3 25.9 0.8 73.3 d 1964 2010 9

01468500 Schuylkill River at 

Landingville PA

137.1 355.3 74.8 4.0 21.2 m 1948 2010 9

01470500 Schuylkill River at 

Berne PA

358.3 928.2 71.1 12.5 16.4 m 1948 2008 9

01470779 Tulpehocken 

Creek near 

Bernville PA

70.4 182.5 11.0 71.9 17.1 a 1976 2008 9

01471980 Manatawny Creek 

near Pottstown 

PA

85.5 221.5 43.6 36.5 19.9 m 1975 2004 3

01472157 French Creek near 

Phoenixville PA

59.0 153.0 51.3 29.7 19 m 1969 2008 9

01472198 Perkiomen Creek 

at East 

Greenville PA

37.7 97.5 42.6 31.3 26.1 m 1982 2008 9

01472199 West Branch 

Perkiomen 

Creek at 

Hillegass PA

23.1 59.8 44.9 32.8 22.3 m 1982 2008 9

01475530 Cobbs Creek at 

U.S. Highway 1 

at Philadelphia 

PA

4.8 12.4 11.9 0.1 88 d 1965 2008 6

01475850 Crum Creek 

near Newtown 

Square PA

15.8 41.0 39.3 24.3 36.4 m 1982 2008 9

01477120 Raccoon Creek 

near 

Swedesboro NJ

26.0 67.3 29.6 49.0 21.4 m 1967 2010 9

01477800 Shellpot Creek at 

Wilmington DE

7.3 19.0 18.9 0.1 81 d 1945 2010 9
16 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Table 3. Fifty-eight USGS streamgage sites in the Delaware River Basin used for model optimization and statistical evaluation of 

simulations of the Water Availability Tool for Environmental Resources (WATER). Those 21 basins with relatively homogeneous land 

cover, consisting primarily of a single hydrologic response unit (HRU), were used for optimization of select WATER parameters (table 

2); mixed land-cover basins were used to statistically evaluate select WATER parameters and to optimize incorporation of water-use 

data; nine basins were set aside for final testing of model performance. Basins were only included if the streamgage period of record 

overlapped with the climatic and land-cover datasets used by WATER. Only complete water years (October through September of the 

following year) were included. Locations are shown in figure 4.—Continued

[Optimization and statistical evaluation use numbers, with percentages based on NLCD 2006: a, greater than (>) 60 percent agricultural; d, >70 percent developed; f, >75 percent forested; m, mixed land cover; t, test basin. USGS, U.S. Geological Survey; ID, identification number; mi2

, square miles; km2, square 

kilometers; %, percent; NJ, New Jersey; NY, New York; PA, Pennsylvania; U.S. United States; DE, Delaware; PET, potential evapotranspiration; 

AET, actual evapotranspiration]

USGS site ID and name

Drainage area Hydrologic response unit (%) Optimization 

and

validation 

use 

Period of 

record

(water years)

Begin End

Complete 

(mi2

) (km2) Forested Agricultural Developed years

01478000 Christina River at 

Coochs Bridge 

DE

20.9 54.0 27.3 25.0 47.7 t 1943 2010 9

01479000 White Clay Creek 

near Newark DE

89.1 230.8 29.4 32.7 37.9 m 1932 2010 9

01480000 Red Clay Creek at 

Wooddale DE

47.3 122.6 33.6 33.3 33.1 m 1943 2010 9

01480300 West Branch 

Brandywine 

Creek near 

Honey Brook PA

18.5 47.8 23.9 59.9 16.2 m 1961 2008 9

01480675 Marsh Creek near 

Glenmoore PA

8.5 22.1 44.9 37.3 17.8 m 1967 2008 9

01482500 Salem River at 

Woodstown NJ

14.6 37.8 18.2 70.1 11.7 a 1940 2010 8

01484000 Murderkill River 

near Felton DE

12.5 32.5 34.7 57.5 7.8 m 1932 2009 1

01484050 Pratt Branch near 

Felton DE

3.1 8.1 12.6 64.4 23 a 1905 2009 1

01484100 Beaverdam Branch 

at Houston DE

3.5 9.1 37.4 58.3 4.3 t 1958 2010 9

01484270 Beaverdam Creek 

near Milton DE

6.9 17.9 34.7 54.4 10.9 m 1966 2005 3

1

This basin was used only for statistical evaluation of PET and AET because of its proximity to three Ameriflux sites (Clark and others, 2012).
Schuylkill

Lehigh

Upper Delaware

Lower Delaware

Cohansey-Maurice

Lackawaxen

BroadkillSmyrna

East 

Branch Delaware

BrandywineChristina

Delaware 

Bay

CrosswicksNeshaminy

Middle 

DelawareMusconetcong

Middle 

DelawareMongaupBrodhead

74° 73°

75°

75°

76°

76°

77°

42°

42°

41°

41°

40°

40°

39°

39°

EXPLANATION

National Weather Service 

snow

New Jersey Mesonet 

Evapotranspiration

US Forest Service—

Ameriflux 

Evapotranspiration

Basins labeled with 

USGS Site ID

Forested Basins

(>75 percent)

Agricultural Basins

(>60 percent)

Developed Basins 

(>70 percent)

Mixed Validation Basins

Test Basins

Hydrologic Unit 

Code 8 Basin

Open water

100 20 30 40 MILES

0 10 20 30 40 KILOMETERS

Lehigh

01484270

01480300

01479000

01478000

01484100

01421614

01428000

01484000

01484050

01475850

01477120

01482500

01477800

01470779

01467086

01480675

01472157

01467150

01475530

01480000

01411500

01452500

01450500

01440400

01443500

01442500

01451500

01464500

Cream Ridge

Cedar Bridge

Fort Dix

Silas 

Little

Experimental 

Forest

Upper Deerfield

Woodbine

ESHN6

NKGN6

SPDN6

HMTN6

Pequest

01468500

01428750

01426000

01419500

01421900

01422500

01422389 01424108

01422738

01422747

01421618

01435000

01420000

01472198

01472199 01471980

01451800

01467048

01465798

01464907

01446000

01440000

01447500

01449360

01439500

01470500

01445000

01415000

01420500

01423000

01413500

01445500

01452000

Data Sources and Processing of Data for WATER 17

Figure 4. U.S. Geological Survey (USGS) streamgages and other monitoring sites used for model optimization and statistical evaluation 

of the Water Availability Tool for Environmental Resources (WATER) streamflow simulation and hydroclimatic variables for the Delaware 

River Basin. Details for each site are in tables 3 and 4. Basin color coincides with the optimization and statistical-evaluation use indicted 

in table 3. ID, identification number; %, percent.
18 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Hydroclimatic Variables

To optimize the simulation of snow accumulation and 

snowmelt as well as both potential evapotranspiration (PET) 

and actual evapotranspiration (AET), simulated values were 

compared to observed values for basins with relatively homogeneous forest cover. For each of these hydroclimatic components of the water budget, the observed values were mostly 

point data, most of which were near (less than [<] 10 kilometers [km] away), but not within, the basins that had coincident 

streamflow observations (table 4 and fig. 4). Additionally, 

observations of snowpack thickness were available for only 

four sites in the DRB and were recorded monthly and (or) 

weekly during winter. In contrast, the daily WATER-simulations of snow accumulation and melting and PET are based on 

a maximum daily temperature that is an areal average for the 

entire basin. Consequently, no statistical analysis of these data 

is presented, and validation of these data is limited to a visual 

analysis.

Data That Enable Scenario Testing

Those process-based hydrologic models (TOPMODEL 

and TR–55) incorporated within WATER simulate how precipitation is transferred to streamflow. However, in much of the 

basin, water-resource management alters this relation. Incorporation of water-use data improves the ability of WATER to 

simulate streamflow in areas where streamflow withdrawals 

and returns significantly affect mean daily streamflow. The 

regional, process-based approach encapsulated by WATER 

also provides a DSS that can simulate streamflow under a 

range of forecasted climatic and land-use scenarios; it is estimated that maximum daily temperature will increase approximately 5.5 degrees Celsius (°C) and that precipitation will 

increase by 10 percent by 2100 (Frumhoff and others, 2007).

Water-Use Data Provided in WATER Application 

Utilities

Water-use data were acquired from the USGS National 

Water Census effort in the DRB (Hutson and others, in press). 

Data included in the model are seasonal totals for surfacewater and groundwater use. Data are from 2010 except for 

New Jersey and Pennsylvania, for which multiyear data 

were available and the median values were used. Seasons are 

defined as January–March, April–June, July–September, and 

October–December; these breakdowns enable comparison 

to both calendar and water years (October to September). 

Water-use data are provided as million gallons per day for 12 

categories (table 5) that can be differentiated as

•	 12 groundwater and 12 surface water sources, or

•	 17 withdrawal, 5 return, and 2 transfer types, or

•	 19 point-specific and 5 areally-averaged classes.

Surface-water-use and groundwater-use data are in 

separate datasets for each category; withdrawals and return 

flows are also provided separately. However, the DSS applies 

a single, daily water-use total. Point data are included for 

over 6,000 sites (fig. 5) but do not include water use from 

Maryland (21 km2

 of the 35,075 km2 DRB total). Areally 

averaged categories include irrigation, livestock, and domestic 

self-supply; for these categories, county-wide estimates were 

integrated with land-use and population data to provide a better spatial understanding of where this water use interacts with 

the hydrologic system. The reader is referred to Hutson and 

others (in press) for a detailed explanation of these water-use 

categories and their distribution in the basin.

Table 4. Sources of point observations used to optimize hydroclimatic components of water budget in the Delaware River Basin. 

Locations are shown in figure 4.

Hydroclimatic variable Source Site Period of record

Evapotranspiration Ameriflux (Clark and others, 2012) Cedar Bridge, Fort Dix, and Silas Little, 

New Jersey

2006–8

Evapotranspiration Office of the New Jersey State 

Climatologist at Rutgers 

University (Mathieu Gerbush, 

written commun., April 25, 2013)

Cream Ridge, Pequest, Upper Deerfield, 

and Woodbine, N.J.

2009–11

Snow accumulation 

and snowmelt

National Weather Service (2012) ESHN6, HMTN6, NKGN6, SPDN6 2003–11
Data Sources and Processing of Data for WATER 19

To protect the privileged information associated with 

these water-use data, point data were originally aggregated 

to 12-digit hydrologic unit code (HUC–12) basins for use in 

WATER. However, during optimization of WATER using the 

28 mixed land-cover basins, it became apparent that data were 

distributed too generally for accurate streamflow simulation, 

so data were reaggregated to the 3,736 DEM-derived polygons; this is the spatial unit with which these water-use data 

are provided in the WATER database.

Water-use data are applied with the WATER Application 

Utilities that are provided with WATER. These utilities allow 

the user to increase, decrease, or remove individual water-use 

categories by using a factor approach. The water-use factor ranges from zero (no water use) and, for example, if the 

factor is set to 1, the data provided by the USGS National 

Water Census (Hutson and others, in press) are used without 

adjustment. A sum of seasonal water use is applied on a daily 

time step after the natural streamflow has been simulated for 

the entire period so that the user can compare the natural and 

water-use-affected records (two separate variables in WATER.

txt output); no distinction is made between groundwater and 

surface-water sources. However, when considering water-use 

effects, users should remember that a seasonal median of the 

daily volume of water use is being used and that no daily or 

annual variability of water use is available.

Land-Cover Projection and Urbanization 

Forecasts Used to Replace the National Land 

Cover Database 2011 for Future Time Periods

To provide a land-cover snapshot that is contemporaneous with the 25-year climate records provided with WATER 

(centered on 2030 and 2060), two forecasted land-cover 

datasets are provided with WATER in addition to the 2011 

NLCD (fig. 6). These forecasts were developed by using 

a stochastic (a random probability distribution) simulation 

model to forecast urbanization in large watersheds. The model 

was originally developed by the USGS for the Chesapeake 

Bay watershed and hence is called the Chesapeake Bay 

Land Change Model (CBLCM; table 6; Claggett and others 

[2014]). The CBLCM was parameterized and applied to the 

DRB to forecast urbanization from 2010 to 2060 in decadal 

increments. The CBLCM stochastically simulates the spatial 

location and extent of residential and commercial development; for the DRB, this simulation was run over 101 iterations 

for each time interval. The model is driven by exogenous 

projections of population produced by using the U.S. Environmental Protection Agency’s Integrated Climate and Land 

Use Scenarios (ICLUS) model (ICLUS; U.S. Environmental 

Protection Agency, 2009). Historical population and employment data were analyzed for the period 1990–2010 to develop 

county-level trends in the ratio of population to employment. 

These trends were extrapolated to 2060 and multiplied by the 

population projections to estimate future employment.

Table 5. Water-use categories.

Water-use category

Type of water use

Surface water or 

groundwater

Withdrawal or 

return

Point data or 

areal average

Aquaculture Both Withdrawal Point

Commercial Both Withdrawal Point

Domestic self-supply Groundwater Withdrawal Areally averaged

Industrial Both Both Point

Irrigation Both Both Both

Livestock Groundwater Withdrawal Both

Mining Both Withdrawal Point

Remediation Groundwater Withdrawal Point

Thermoelectric Both Withdrawal Point

Public water supply Both Both Point

Sewage treatment Surface water Return Point

Interbasin transfer Surface water Both Point
73°

42°

75° 74°

41°

40°

39°

77° 76° 75°

39°

40°

41°

42°

0 10 20 30 40 MILES

0 10 20 30 40 KILOMETERS

Surficial Geology

Carbonate

Clastic

Coal

Diabase

Metamorphic

Unconsolidated

Water-use location

Removed from database

EXPLANATION

20 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 5. Water-use locations in the Delaware 

River Basin (DRB). Median, seasonal values of 

water use were provided as part of the DRB 

water-use effort (Hutson and others, in press) 

and are incorporated in the WATER Application 

Utilities. Surficial geology was used to isolate 

regions where streamflow simulation was less 

accurate after water use was incorporated. 

Consequently, groundwater withdrawals and 

returns were removed from the unconsolidated 

Coastal Plain as well as the carbonate region in 

the central part of the basin.
Data Sources and Processing of Data for WATER 21

To spatially simulate development, a probability surface 

raster was created by relating observed changes in developed 

land cover (as captured by NLCD 2001 and 2011) with proximity to urban areas, proximity to recent growth in housing, 

and topographic slope (using NED; Gesch and others, 2002). 

The probability surface informed the likelihood of future 

growth at a given location. The sizes of simulated patches of 

residential and commercial development were informed by 

the cumulative frequency distribution of historical patches of 

developed land cover. The shapes of simulated patches were 

based on proximity to roads. In the model, growth occurs 

preferentially near roads, resulting in elongated patch shapes 

along roads and circular shapes far from roads. For each future 

decade, from 2020–60, the CBLCM was applied in a Monte 

Carlo simulation routine to produce 101 iterations of residential and commercial development mosaicked with the 2011 

NLCD.

For each iteration, attribute data associated with individual patches of development were summarized over all iterations and all decades by HUC–12 (USGS and others, 2009). 

Data reported by HUC–12 included statistics on the mean, 

median, maximum, and minimum acres of commercial and 

residential development, forest and farmland acres converted 

to development, total employment, total population, total 

households, and median residential lot size. For all HUC–12s, 

the raster iterations representing the median amount of total 

development (commercial plus residential) were extracted and 

mosaicked together to spatially represent the median amount 

of future development in 2030 and 2060 throughout the DRB 

(fig. 6). The forecasted areas of commercial and residential 

growth in all 505 iteration rasters (five decadal snapshots for 

each of 101 iterations), in addition to the composite 2030 

and 2060 median-condition rasters, were then translated into 

development intensities and impervious-surface values consistent with the 2011 NLCD and informed by the underlying 

housing densities.

Table 6. Data Sources for the Chesapeake Bay Land Change Model.

[The Chesapeake Bay Land Change Model (CBLCM) (Claggett and others, 2014). EPA, U.S. Environmental Protection Agency; USGS, U.S. Geological Survey; USDA, U.S. Department of Agriculture; NRCS, Natural Resources Conservation Service; GAP, Gap Analysis Program; NJDEP, New Jersey Department 

of Environmental Protection; Delaware OMB, Delaware Office of Management and Budget]

Data source Contribution to CBLCM

2000 and 2010 U.S. Decennial Census of Population and Housing

(U.S. Census Bureau, 2012)

Decadal housing and population values 

2010 NAVTEQ Streets (Homeland Security Infrastructure 

Program, 2012), supplied through license agreement with 

the U.S. Environmental Protection Agency.

Production of asymmetric housing maps and refinement of 

urban land cover

Longitudinal Employer-Household Dynamics database

(U.S. Census Bureau, 2013)

Estimates of total employment by census block

Integrated Climate and Land Use Scenarios v1.3.2 

Population Forecasts (2005–2100) (US EPA, 2009)

Population projections 

2010 Census TIGER/Line files (U.S. Census Bureau, 2011) Census county and block boundaries, 

National Watershed Boundary Database 

(USGS and others, 2009)

Summary units for reporting data; Delaware River Basin 

boundary

2001 and 2011 National Land Cover Database 

(Jin and others, 2013)

Patterns of growth and urban patch size distributions

National Elevation Dataset (Gesch and others, 2002) Derive slope (percent) as a constraint on areas suitable for 

development

Protected Areas Database, v1.3 (USGS GAP, 2012) Constrains areas suitable for development

2007 New Jersey land-use dataset (NJDEP, 2007) Refines areas suitable for growth; refines estimates of housing 

and employment densities

2007 Delaware land-use dataset (Delaware OMB, 2007) Refines areas suitable for growth; refines estimates of housing 

and employment densities
2011 2030 2060

77° 76° 75° 77° 76° 75° 77° 76° 75°

76°

42°41°40°

39

75° 74° 75° 74° 75° 74°

42°

41°

40°

39

38

0 10 20 30 40 MILES

0 10 20 30 40 KILOMETERS

EXPLANATION Open Water

Developed, Open spaceDeveloped, Low IntensityDeveloped, Medium IntensityDeveloped, High Intensity

Barren Land (Rock/Sand/Clay)Deciduous ForestEvergreen ForestMixed ForestShrub/Scrub

Grassland/HerbaceousPasture/HayCultivated CropsWoody WetlandsEmergent Herbaceous Wetlands

Hydrologic Unit Code Basins

HUC-12 BasinsHUC-6 Basins

—020401 and 

020402

National Land Cover Database classes

020401

020402

020401 020401

020402 020402

A

22 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER) Figure 6. Land-cover data for the Delaware River Basin provided with the Water Availability Tool for Environmental Resources. 

A, Land-cover rasters for 2011 (National Land 

Cover Database; Fry and others, 2011), 2030, and 2060. The latter two are aggregations of Hydrologic Unit Code 12 (HUC–12) basins from the median of 101 Chesapeake Bay Land Change Model iterations. 

B, Forecasted development in each of 426 HUC–12 basins according to the median iterations of 101 simulations for 2030 and 2060.
Chenango

Schoharie

Greene

Ulster

Orange

Sullivan

Delaware

Broome

Susquehanna

Wayne

Pike

Luzerne Monroe

Carbon

Northampton

Berks

Chester

Lancaster

Lehigh

Lebanon

Schuylkill

Kent

Sussex

Atlantic Cecil

CapeMay

Salem

Cumberland

New

Castle

Burlington Ocean

Montgomery

Gloucester

Camden Delaware

Philadelphia

Lackawanna

Morris

Sussex

Warren

Bucks

Monmouth

Hunterdon

Mercer

Chenango

Schoharie

Greene

Ulster

Orange

Sullivan

Delaware

Broome

Susquehanna

Wayne

Pike

Luzerne Monroe

Carbon Northampton

Berks

Chester

Lancaster

Lehigh

Lebanon

Schuylkill

Kent

Sussex

Atlantic Cecil

Cape

May

Salem

Cumberland

New

Castle

Burlington Ocean

Montgomery

Gloucester Delaware

Camden

Philadelphia

Lackawanna

Morris

Sussex

Warren

Bucks

Monmouth

Hunterdon

Mercer

42°

76° 75° 74°

77° 76° 75° 77° 76° 75°

76° 75° 74°

41°

40°

39°

42°

41°

40°

39°

Source: Esri, DigitalGlobe, GeoEye, i-cubed,USDA, USGS, AEX, 

Getmapping, Aerogrid, IGN, IGP, swisstopo, and the GIS User Community

42 °0 '0 "N

41 °0 '0 "N

40 °0 '0 "N

EXPLANATION

New development, in acres

4–50

51–100

101–200

201–400

401–800

801–1,600

1,600–3,200

3,201–4,201

No growth

HUC 12 Watershed 

Basin boundary

County boundary Kent

B

0

0 30 60 MILES

2030 30 60 KILOMETERS 2060

Data Sources and Processing of Data for WATER 23

Figure 6. Land-cover data for the Delaware River Basin provided with the Water Availability Tool for Environmental Resources. 

A, Land-cover rasters for 2011 (National Land Cover Database; Fry and others, 2011), 2030, and 2060. The latter two are aggregations 

of Hydrologic Unit Code 12 (HUC–12) basins from the median of 101 Chesapeake Bay Land Change Model iterations. B, Forecasted 

development in each of 426 HUC–12 basins according to the median iterations of 101 simulations for 2030 and 2060.—Continued
24 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

General Circulation Models and Projections of 

Future Climate

A selection of general circulation models (GCMs) is provided with the WATER Application Utilities that characterize a 

range of how forecasted changes in precipitation, temperature, 

and available energy (surface net radiation minus ground heat 

flux) may alter streamflow and water availability in the DRB. 

These changes can be assessed in terms of the following:

•	 snow accumulation and timing of snowmelt;

•	 evapotranspiration (both potential and actual), frostfree days, and growing-season days in the year; and

•	 aggregated effects on seasonal streamflow variability.

GCM data are provided for two target time periods; these 

data forecast 25-year monthly normals (means) centered on 

2030 and 2060. Change factors were derived for each of four 

Coupled Model Intercomparison Project Phase 5 (CMIP5; 

Taylor and others, 2011) GCM datasets (fig. 7 and table 7; 

Taylor and others, 2011) and two representative concentration 

pathways (RCPs) that forecast different amounts of change in 

the chemical composition of the atmosphere (representative 

concentration pathways 4.5 and 8.5; table 8). Change factors 

for the four GCMs and two RCP scenarios provide for consideration of how differences among individual climate models 

affect forecasts of streamflow; some researchers have found 

that these differences create an uncertainty that is larger than 

that associated with hydrologic modeling (for example Teng 

and others, 2011); consequently, this suite of GCMs provides a 

means of incorporating this range of forecasted conditions. All 

of these GCMs should be included in scenario testing and the 

overall trend among all models considered when results are 

interpreted.

These CMIP5 data are at a spatial resolution ranging 

from approximately 105-km to 310-km tile spacings; Daymet 

data were geospatially sampled by using the 3,736 DEMderived polygons, which averaged 9.4 km2

 in size. To keep 

the spatial resolution provided by the initial Daymet historical 

climate record, monthly change factors, or deltas (δ), between 

the current and target time period were calculated for precipitation and temperature and are applied to the original climate 

record by the WATER Application Utilities (figs. 7B and 8).

A 25-year period was selected for the historical dataset 

provided with each CMIP5 model (1981–2005) and for the 

2030 (2018–42), and the 2060 (2048–72) targets. Monthlynormal δ were calculated for precipitation (a multiplicative 

factor) and daily maximum temperature (an additive factor) 

by using the 25-year periods to estimate a monthly-normal δ 

between the historical and target time periods provided with 

each model and scenario combination; WATER then simulates 

snowpack on a daily time step by using the adjusted Daymet 

daily values of precipitation and temperature (fig. 8).

Previous researchers (for example Milly and Dunne, 

2010) have noted a likely overestimation of PET when calculated by using a temperature-indexed approach and daily temperatures indicated by future climate projections. This concern 

is relevant to a Hamon (1963)-derived estimation of PET, such 

as that incorporated in WATER, because the equation used 

to estimate PET is based on a historical, empirical relation 

between temperature and energy availability that cannot be 

assumed to hold under anthropogenic climate change. For this 

reason, the forecasted PET in WATER can be calculated from 

a multiplicative δ factor based on a radiation-based PET (in 

energy units; Priestley and Taylor, 1972):

PET =∝ R G n

∆

∆ + ( ) − γ , (6)

where

α is 1.26 and is calibration constant (Priestley 

and Taylor, 1972);

Δ is slope of the saturation vapor pressure 

temperature curve—a function of 

temperature;

γ is psychrometric constant and is related to air 

pressure;

Rn is net radiation; and

G is heat flux density to the ground.

To implement this approach, a monthly-normalized δ was 

calculated for the available energy term (Rn–G) by using the 

ratio of the historical sum to the forecasted sum of the sensible 

heat flux and latent heat flux. This ratio was used as the change 

factor and was applied to the PET values calculated from the 

Daymet temperature record by using Hamon (1963):

PET PET FC = ∂ Hh PETptFC * , (7)

where

PETFC is the daily PET value for forecasted 

conditions;

PETHh is daily PET calculated using the Hamon 

(1963) method and the Daymet maximum 

daily temperature for the 1985–2005 time 

period; and

δPETpfFC is the monthly, 25-year normalized δ 

for Priestley-Taylor-derived PET for 

the forecasted condition relative to the 

historical condition for that GCM.
A

NCAR_

CCSM4_72

NCAR_

CCSM4_62

NCAR_

CCSM4_52

NCAR_

CCSM4_42

NCAR_

CCSM4_32

NCAR_

CCSM4_22

NCAR_

CCSM4_73*

NCAR_

CCSM4_74

NCAR_

CCSM4_64*

NCAR_

CCSM4_54

NCAR_

CCSM4_44*

NCAR_

CCSM4_34

NCAR_

CCSM4_24 NCAR_

CCSM4_23

GFDL-ESM2G_41

GFDL-ESM2G_42

GFDL-ESM2G_31

GFDL-ESM2G_32

GFDL-ESM2G_21

GFDL-ESM2G_22

GISS-E2-H_21

GISS-E2-H_31

GISS-E2-H_41

GISS-E2-H_42

GISS-E2-H_32

GISS-E2-H_22

CanESM2_31

CanESM2_32

CanESM2_22 CanESM2_21

CanESM2_11

CanESM2_12

77.5o

75o

72.5o 

71.7o

74.5o

77.3o 

38o

40o

39.1o

41.9o

42o

77.5o

75o

72.5o 

38.4o 

40.5o 

42.5o 

42.4o 

76.9o 

41.5o

38.6o

39.6o

74.4o 

0 40 80 120 160 MILES

0 40 80 120 160 KILOMETERS

EXPLANATION

Tile boundary for 

global circulation 

models labeled 

with model and 

tile number

NCAR_

CCSM4_62

Evaluating Uncertainty for Scenario Testing 25

Figure 7. Summary of general circulation models (GCMs). A, Four GCM tile extents provided with the Water Availability Tool for 

Environmental Resources (WATER). All were accessed through the Coupled Model Intercomparison Project Phase 5 data portal 

(http://cmip-pcmdi.llnl.gov/cmip5/data_portal.html). Tile size differs among these GCMs (table 7). Those tiles in the NCAR_CCSM4 model 

marked with asterisks have been replaced, because of the small areas they cover, with data from the adjacent tile (63 or 43). 

B, Forecasted change factors (δs) for two time periods (2030 and 2060) and two scenarios (representative concentration pathways [RCP] 

4.5 and 8.5) for four GCMs. Note that precipitation and potential evapotranspiration (PET) δs are both multiplicative and are shown with 

the same scale; a value of one indicates no change. Precipitation and PET are shown as a function of the forecasted change in the 

maximum daily temperature; this δ is additive and a value of zero indicates no change.
B

Temperature change factor, in degrees Celsius (°C)

0.8

1.0

1.2

1.4

0 1 2 3 4 5

●

Temperature change factor, in degrees Celsius (°C)

0.8

1.0

1.2

1.4

0 1 2 3 4 5

●

Precipitation change factor (proportional)

Potential evapotranspiration change factor (proportional)

1.0

1.2

1.4

● 1.0

1.2

1.4

●

1.0

1.2

1.4

●

1.0

1.2

1.4

●

1.0

1.2

1.4

1.0

1.2

1.4

●

South

Central

North

CanESM2

NCARCCSM4

GISSE2-H

GFDLESM2G

2030 RCP 4.5

EXPLANATION

2030 RCP 8.5

2060 RCP 4.5

2060 RCP 8.5

26 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 7. Summary of general circulation models (GCMs). A, Four GCM tile extents provided with the Water Availability Tool for 

Environmental Resources (WATER). All were accessed through the Coupled Model Intercomparison Project Phase 5 data portal 

(http://cmip-pcmdi.llnl.gov/cmip5/data_portal.html). Tile size differs among these GCMs (table 7). Those tiles in the NCAR_CCSM4 model 

marked with asterisks have been replaced, because of the small areas they cover, with data from the adjacent tile (63 or 43). 

B, Forecasted change factors (δs) for two time periods (2030 and 2060) and two scenarios (representative concentration pathways [RCP]

4.5 and 8.5) for four GCMs. Note that precipitation and potential evapotranspiration (PET) δs are both multiplicative and are shown with 

the same scale; a value of one indicates no change. Precipitation and PET are shown as a function of the forecasted change in the 

maximum daily temperature; this δ is additive and a value of zero indicates no change.—Continued
Evaluating Uncertainty for Scenario Testing 27

Table 7. General circulation models provided as part of the WATER database. The differences among models are detailed by 

Forster and others (2013).

Source Abbreviation General 

circulation model

Tile size 

(kilometers) Documentation

National Oceanic and Atmospheric Administration—

Geophysical Fluid Dynamics Laboratory

GFDL_NOAA ESM2G 200 Dunne and others 

(2012)

National Aeronautics and Space Administration—

Goddard Institute for Space Studies

GISS E2-H 220 Nazarenko and others 

(2015)

National Center for Atmospheric Research—

Community Climate System Model

NCAR_CCSM4 CCSM4 105 Gent and others 

(2011)

Canadian Centre for Climate Modelling and Analysis CanESM2 CGCM4 310 von Salzen and others 

(2013)

Table 8. Representative concentration pathways (RCP; summarized from van Vuuren and others, 2011)—

data are provided for RCPs 4.5 and 8.5 (bolded). For comparison, the January 2015 global mean 

CO2

 concentration was 400.14 parts per million (ppm), up from 397.42 ppm in January 2014 

(Earth System Research Laboratory, 2015; verified March 25, 2015).

[RCP, representative concentration pathway; W/m2, watts per square meter; ppm, parts per million]

Representative 

concentration 

pathway

Radiative forcing

Approximate 

carbon dioxide 

concentration

RCP 8.5 Rising radiative forcing to 8.5 W/m2

 by 2100 1,370 ppm CO2

RCP 6 Stabilization at 6 W/m2 after 2100 850 ppm CO2

RCP 4.5 Stabilization at 4.5 W/m2

 at 2100 650 ppm CO2

RCP 2.6 Peak at about 3 W/m2 before 2100 and then decline 

to 2.6 W/m2

 by 2100

490 ppm CO2
Daily precipitation, in millimeters

0

5

10

15

20

25

30

35

40

25-year Average of monthly sum of precipitation, in millimeters

0

20

40

60

80

100

120

140

Jan. Feb. Mar. Apr. May JulyJune

Month

Aug. Sept. Oct. Nov. Dec.

July

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

Difference in JULY average precipitation from 

GCM record for historic and future time period

138 mm

115 mm

= 1.2 future

historic=

Historic GCM monthly 

precipitation total for 

1981–2005

Forecasted GCM monthly 

precipitation total for 

25-year period

2030 used 2018–2042

2060 used 2048–2072 

EXPLANATION

EXPLANATION

Daily precipitation from 

Daymet historic record

Adjusted precipitation using 

monthly change factor 

July change factor (1.2 in example) 

is applied to daily precipitation for 

each day in July for entire record. 

A

B

28 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 8. Example of how the monthly change factor (δ) is A, calculated and B, applied in order 

to incorporate general circulation model (GCM) data. The change factor is multiplicative for both 

precipitation and potential evapotranspiration. For temperature, the change factor is a difference 

instead of a ratio. mm, millimeter.
Model Development, Statistical Evaluation, and Validation of Hydroclimatic Components of WATER 29

Evaluating Uncertainty for Scenario 

Testing

Statistical evaluation, validation, and uncertainty of 

WATER simulations are discussed in subsequent sections in 

terms of daily, mean monthly, and normalized mean monthly 

(that is, mean monthly averaged over the 25-year simulation 

period) streamflow simulations. These different time steps 

account for the difference in temporal resolution as one navigates from

•	 the historical record of daily precipitation to

•	 incorporation of seasonal median of water use to

•	 application of the monthly-normal δ used for forecasted 

climate to the historical climate record.

It is important to note, however, that only one land-cover dataset is provided for each target time period. These land-cover 

datasets are specific to 2011, 2030, and 2060. The simulations 

do not include the potential changes in land cover associated 

with the climate record. Instead, the 25-year climate record 

centered on each target year is used to understand the potential range of streamflow associated with this time period. It 

also follows that streamflow for the historical record will not 

incorporate land-cover and water-use changes between 1980 

and 2010. Also, because the temperature-, precipitation-, and 

PET-δ factors are each based on a 25-year monthly normal, a 

similar time step should be used to identify significant changes 

in streamflow associated with these forecasted changes in climate. For example, mean monthly streamflow rather than daily 

streamflow should be assessed, and significant differences in 

mean mean-monthly streamflow for the period of record (that 

is, 25-year normals of mean monthly streamflow) are the best 

indicator of potential changes in streamflow and water availability due to forecasted climate change.

Model Development, Statistical 

Evaluation, and Validation of 

Hydroclimatic Components of WATER

Optimization and validation of different components of 

WATER proceeded concurrently and as data became available. Development and optimization of WATER used streamflow observations that extended from 2001–11. This time 

period was selected because it is at the intersection of those 

data available from NLCD (2006 and 2011; Fry and others, 

2011) and the Daymet historical record of precipitation and 

temperature (Thornton and others, 2012). Although daily 

streamflow values simulated for the period before 2001 are 

expected to have more error because of changes in land and 

water use, WATER does provide a streamflow record extending from 1981–2011 because this longer record is critical in 

the consideration of aggregated streamflow metrics (monthly 

streamflow normals and flow-duration curves [FDCs]) that are 

of interest when incorporating land-cover and climate change 

forecasts. Streamflow was optimized and validated using the 

period 2001–10, including nine complete water years.

Hydroclimatic Water-Budget Components

The hillslope-hydrology model underlying WATER, 

TOPMODEL, is based on a water-budget approach. Independent aspects of the water budget, including PET and 

snow accumulation and snowmelt, are temperature indexed 

according to the daily precipitation and temperature provided 

by Daymet (Thornton and others, 2012). Daily precipitation 

amounts are randomly distributed within WATER as hourly 

precipitation amounts, with the model shifting to an hourly 

time step on days with precipitation. In its current configuration as a desktop DSS, WATER uses the same temperature 

time series for simulating both PET and snow to minimize 

processing time. As the following section explains, WATER 

uses the maximum daily temperature for both.

Accumulation and Melting of Snow

The maximum daily temperature (Tmax; Thornton and others, 2012) is used by the model to simulate when precipitation 

occurs as rainfall as opposed to snowfall. Any simulated snowfall accumulates to create a snowpack that is melted using 

the temperature-indexed method of the USACE (1998); total 

snowmelt can not exceed standing snowpack. Each HRU uses 

a separate combination of snowmelt and rain-on-snowmelt 

coefficients (table 2) that apply the potential melt (Ms) to the 

standing snowpack:

M C s m = − ( ) T C° max 0 . (8)

Simulation of snow accumulation and melt was evaluated 

with data from four National Weather Service (NWS) National 

Operational Hydrologic Remote Sensing Center stations 

(table 4; NWS, 2012). Daymet was also considered for evaluation of snowpack simulation; however, the transition between 

individual calendar years creates a bias after January 1 (Thornton and others, 2012). Consequently, only point data that are 

reported weekly or monthly were available for this comparison 

(figs. 4 and 9), and a direct, statistical comparison between 

observed and simulated values cannot be made. WATER 

converts precipitation from rain to snow (1 mm precipitation 

= 10 mm snow) when the temperature (averaged for the entire 

basin) is <0 °C; these basin-average values are reported in the 

WATER.txt file as snowpack (millimeters of snow) but are 

handled by the water budget as snow-water equivalent (millimeters of water). On the basis of comparison to the available 

observations, it was determined that the maximum daily temperature (Tmax) was necessary in order to accurately model the 

accumulation and melt of snow. When the mean daily temperature was used, too much snow accumulated and the snowpack 
0

50

300250200150100

Dec. May Nov. May Nov. May Nov. May Nov. May Nov. May Nov. May Nov. May

Snow-Water Equivalent, in millimeters

2004 2005 2006 2007 2008 2009 2010 2011

EXPLANATION

Observed—NWS Site–

Elevation, in meters

NKGN6–957SPDN6–718ESHN6–670HMTN6–579

WATER Simulation—USGS Site ID–

Elevation, in meters

01422389—78101413500—66701415000—61001422500—56001422500 simulated with T

mean

simulated using Tmax

30 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER) Figure 9. Comparison of Water Availability Tool for Environmental Resources (WATER)-derived daily basin averages of snow water equivalent for four northern validation basins to point observations from National Weather Service (NWS) observations in the Delaware River Basin. Locations are shown in figure 4; NWS sites are located along basin boundaries (topographic divides). Elevations for NWS sites and mean basin elevation are shown for comparison. Additional details about U.S. Geological Survey (USGS) and NWS sites are shown in tables 3 and 4, respectively. WATER simulations use maximum daily temperature to simulate the accumulation and melt of snow. Elevations are in meters 

(m) above the North American Vertical Datum of 1988.
-5

0

5

10

15

20

25

30

Jan. Feb. Mar. Apr. May June

Month

July Aug. Sept. Oct. Nov. Dec.

Average maximum daily temperature, in degrees celcius

1415000

1440400

1466500

South

North

EXPLANATION

USGS Site ID

Model Development, Statistical Evaluation, and Validation of Hydroclimatic Components of WATER 31

Figure 10. A north-south transect of maximum daily temperature for three basins with U.S. Geological Survey (USGS) gages. Basins 

are representative of the forested hydrologic response unit (more than 75 percent forested). A value of 15 degrees Celsius (°C)

transitions the evapotranspiration protocol from dormancy to growing conditions. Sites are shown in figure 4.
Mean daily potential evapotranspiration, in millimeters

0

1

2

3

4

5

6

7

8

9

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

Mean Daily Actual Evapotranspiration, in millimeters

0

1

2

3

4

5

6

7

8

9

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

EXPLANATION

PET 

AET

PET

AET

PET

AET

PET

AET

PET 

AET

PET 

AET

Woodbine

Upper Deerfield

Creamridge

Pequest

New Jersey Mesonet Point Measurement

Potential evapotranspiration

01466500

01482500

01467150

Simplified Surface Energy Balance Model 

Basin Average Actual evapotranspiration

A

B

Ameriflux Point measurement 

Potential and Actual evapotranspiration

Cedar Bridge, NJ

Fort Dix, NJ

Silas Little, NJ

Basin average simulated by WATER

01466500 McDonalds Branch in Byrne 

State Forest, NJ

01482500 Salem R at Woodstown, 

NJ

01467150 Cooper R at Haddonfield, 

NJ

32 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 11. Comparison of observed and Water 

Availability Tool for Environmental Resources (WATER)-

derived A, potential evapotranspiration (PET) and B, 

actual evapotranspiration (AET) at a range of sites in the 

Delaware River Basin, each of which primarily consists 

of one of the three hydrologic response units—forested, 

agricultural, or developed (table 3). Sites are shown in 

figure 4. U.S. Geological Survey (USGS) basins were 

selected for proximity to both Ameriflux and Mesonet 

sites (table 4) as well as minimization of the latitudinal 

difference. PET simulated within WATER by using the 

basin-average maximum daily temperature is bracketed 

by observations at the Ameriflux and New Jersey 

Mesonet sites. AET, which is controlled by basin-average 

soil-water availability within WATER, is higher during fall 

and winter relative to observations at Ameriflux sites and 

estimates from the Simplified Surface Energy Balance 

(SSEB) model (Senay and others, 2013). The PET at the 

forested USGS site (01466500) is lowest, but this site 

experiences the highest AET as simulated by both WATER 

and the SSEB. Also, both WATER and SSEB indicate that 

AET is lowest in the developed basin (01467150).
0

500

1000

1500

2000

01413500

0141450001415000

014205000142238901422500

014350000143950001440000

0144040001442500014665000146579801467048

0146708601467150

0147553001477800014707790148250001484050

Mean Water Budget Contribution (mm/year)

Forested Developed Agricultural

USGS Site ID

Observed

Precipitation

Streamflow

WATER simulation

Actual evapotranspiration

Streamflow

Model Development, Statistical Evaluation, and Validation of Hydroclimatic Components of WATER 33

Figure 12. Water-budget components from Water Availability Tool for Environmental Resources simulations 

for homogeneous basins in the Delaware River Basin. Each is an annual sum normalized for the 9-year period of 

record from October 2001 through September 2010. The actual evapotranspiration portion of the water budget was 

used to help optimize the simulation of observed streamflow. Streamflow was normalized for basin area; both the 

observed and simulated values are shown. All water-budget components are in millimeters.
0

100

200

300

400

500

600

700

800

900

01413500

01414500

01415000

0142050001422389

0142250001435000

0143950001440000

0144040001442500

01466500

014657980146704801467086014671500147553001477800

01470779

0148250001484050

Actual Evapotranspiration, in millimeters per year

Forested Developed Agricultural

USGS Site ID

450

500

550

600

650

700

750

800

850

SSEB AET, in millimeters per year

450 500 550 600 650 700 750 800 850

WATER AET, in millimeters per year

A 

 Agricultural

 Developed

 Forested

B 

WATER simulated

Simplified Surface Energy Balance model

EXPLANATION

34 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 13. Statistical evaluation of actual evapotranspiration from the Water Availability Tool for Environmental Resources (WATER). 

A, Comparison of WATER-derived actual evapotranspiration (AET) at 21 sites in the Delaware River Basin to areal estimates from 

the Simplified Surface Energy Balance (SSEB) model (Senay and others, 2013). Sites are shown in figure 4. B, Scatterplot of observed 

versus simulated AET basin averages. WATER consistently estimates higher AET than SSEB does. However, a Spearman rank 

correlation test shows these two different estimates are significantly correlated (p-value = 0.0007), indicating that the relative AET is 

similar among the sites.
Model Development, Statistical Evaluation, and Validation of Hydroclimatic Components of WATER 35

did not melt until late spring (fig. 9); this is in contrast to the 

normal melt period historically occurring by April. The melt 

coefficients (table 2) create an environment in which snowmelt 

is slowest in forested areas and most rapid in developed areas. 

This is logical given the protection provided by the forest 

canopy as well as the acceleration and management of melt 

that would be expected on the pavement and exposed land of 

urban areas (through salt application and snow removal).

Evapotranspiration

Potential evapotranspiration (PET) was simulated in 

WATER by using a temperature-indexed approach (Hamon, 

1963), which combines daily temperature with estimates of 

day length and solar radiation that are based on latitude. The 

Tmax was used as the daily temperature, and the evapotranspiration (ET) exponents (table 2) were used to control the relation 

between the daily PET and the soil-water storage calculated on 

the basis of the daily mean saturation deficit (S in equation 2). 

Because the model was designed to examine the potential 

effects of forecasted changes in climate, including increases in 

winter temperatures by as much as 6.5 °C (12 °Fahrenheit [F]; 

Frumhoff and others, 2007), instead of triggering the growing 

season by a calendar date, a temperature of 15 °C (60 °F) was 

selected to trigger the transition from dormancy to growing 

conditions and back. During the early season, before plant ET 

accelerates, only direct evaporation from the soil is expected 

to be underway. This growth-temperature threshold is applied 

on a daily time step—the beginning and end of the growing 

season may be punctuated by periods of decreased ET. For 

the historical time period (2001–11), this generally resulted 

in growing conditions and aggressive ET from approximately 

May through October and as early as April in the southern part 

of the basin (figs. 10 and 11). Comparison to observations at 

a combination of forested Ameriflux sites and mixed land-use 

Mesonet sites (table 4) shows that PET simulated in WATER 

is bounded by these observations. 

WATER calculates actual evapotranspiration (AET) on a 

daily time step; the calculation is based on soil-water availability in the soil thickness that is accessible to roots, and it 

uses parameters that were optimized to differentiate dormancy 

from growing conditions (table 2). For each group of homogeneous land-cover basins, AET was used as a means of empirically optimizing streamflow as part of the overall water budget 

for each basin (fig. 12). As a consequence of these ET and soil 

parameters, more water is accessed for AET in the forested 

areas (table 2 and figs. 11–13), relative to agricultural and 

developed areas, because of a combination of the following:

• the smaller percentage of water that bypasses the rootzone as a function of macroporosity,

• the larger proportion of the soil that is accessible to 

roots, and

• the effect of the larger m, which slows movement of 

soil-water downslope towards the stream.

AET estimates from WATER are consistently higher than 

point observations from the Ameriflux sites (fig. 11B), each 

of which is from the top of the forest canopy. AET was also 

compared to estimates from the Simplified Surface Energy 

Balance (SSEB) model (Senay and others, 2013), which 

was geospatially sampled for each of the 21 homogeneous 

land-cover basins in the DRB by using the USGS Geo Data 

Portal. WATER consistently estimates a significantly higher 

AET than that from the SSEB (paired Wilcoxon signed-rank 

test, p-value <0.0001; figs. 11 and 13A); however a Spearman 

rank correlation test shows these estimates are significantly 

correlated (rho=0.6974; p-value = 0.0006), indicating that the 

relative AET is similar among the sites regardless of which 

model is used (fig. 13B). Most of this excess AET is in the fall 

and winter months; the spring AET estimates from WATER 

are bounded by observations from the Ameriflux sites and 

SSEB simulations. The range of AET estimates in the WATER 

simulations differs from the range of estimates in the SSEB 

simulations, with more similarity among land-cover types in 

the WATER estimates than the SSEB estimates. This may be 

related to the difference in spatial resolution. WATER simulations use 10-m resolution topography combined with temperature averaged for 3,736 DEM-derived basins that average 9.4 

km2

. In contrast, SSEB uses topographic and satellite data at a 

resolution of 1 km2 (Senay and others, 2013).

Optimization of Remaining Hydrologic 

Parameters and Differentiation of Hydrologic 

Response Units

After optimization of individual hydroclimatic variables, 

including PET and snow accumulation and snowmelt, the 

remaining parameters that link topography, soils, and land 

cover were evaluated (first eight parameters in table 2). Each 

of these was optimized by using 21 relatively homogeneous 

basins (table 3), and the resultant combination was validated 

by using those 28 basins with mixed land cover—no additional changes were made on the basis of statistical evaluation 

of those mixed land-cover basins. Each of these parameters 

would be expected to vary among the HRUs because of a 

combination of differences in preservation of natural soil properties, natural and managed plant communities, anthropogenic 

infrastructure, and connectivity of impervious surface. For 

example, the importance of individual parameters for hydrologic simulation of forested areas follows:

• The relatively large spatial coefficient (SpCf; 0.4) 

preserves the topographic gradient characterized by the 

TWI and enables storage of soil water in the landscape 

that provides base flow.

• The topographic adjustment (1) focuses on the natural 

topography instead of the anthropogenic infrastructure.
36 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

• The proportion of the soil available to plant roots 

(0.75) reflects the perennial vegetation and permanent, 

deep roots that characterize the forest environment.

• The percentage of precipitation (15 percent) that is 

routed through macropores by the model is similar to 

natural estimates and does not assume tile- or stormdrains that might cause water to bypass the root zone 

and AET.

• The long water-body delay (15 days) reflects the size of 

the water-bodies and resultant storage.

• The effective-impervious multiplier (0.7) decreases the 

percentage of impervious area estimated from NLCD 

for forested areas, where impervious areas are likely 

discontinuous, in order to simulate how much of the 

water falling on impervious areas can run onto pervious areas and infiltrate the soil instead of being routed 

by the model directly to the stream.

• The impervious runoff delay (0.1) is relatively low, 

causing the majority of the precipitation that falls on 

impervious areas to be delivered to the stream that day 

instead of delaying the runoff in retention basins that 

might be present in more developed areas.

• The impervious curve number (90) is lower than that 

used in developed areas and causes the TR–55 model 

(USDA, 1986) to generate relatively less runoff for the 

same amount of impervious area in developed areas.

Incorporation of Water-Use Data

Water-use data were originally aggregated to a HUC–12 

basin in order for this study to stay aligned with the rest of 

the water-use reporting for the USGS Water Census Focus 

Area Studies. However, optimization of the incorporation of 

these water-use data, by using the 21 homogeneous basins 

that were used to optimize the rest of the modeling approach 

(“f,” “a,” and “d” in table 3) plus 28 additional basins of 

mixed land-cover (“m” in table 3), indicated that the aggregation of data to a HUC–12 basin caused excessive error in the 

streamflow simulations. Use of the original point locations 

improved model performance. However, there were still areas 

of poor performance, where summer and fall withdrawals 

were far in excess of streamflow, in the unconsolidated sediments of the Coastal Plain as well as the carbonate regions 

(fig. 5). Residents in these areas of the DRB are dependent on 

groundwater from deep aquifers (Hutson and others, in press). 

Surficial geology (fig. 5) was used to isolate these regions, 

and groundwater withdrawals and returns in the Coastal Plain 

and carbonate regions were removed from the point database 

because each of these areas includes groundwater withdrawals from deep aquifers that are a combination of confined and 

unconfined aquifers (in the Coastal Plain) or fracture systems 

(in the carbonate regions) that are not in equilibrium with the 

daily hydrology simulated by TOPMODEL. Point data were 

then reaggregated to those 3,736 DEM-derived polygons; this 

protects the individual locations by placing them in areas >0.1 

km2

; these basins have a mean area of 9.4 km2 and a maximum 

area of 132.4 km2.

Statistical Evaluation, Validation, and 

Uncertainty of Streamflow Simulated 

by Using WATER

A total of 57 basins were used for statistical evaluation 

of hydrologic simulation by the WATER DSS (table 3). As 

discussed previously, 21 of these basins, used for optimization 

of model parameters (table 2), were relatively homogeneous 

in land cover that corresponded to the HRUs used by WATER; 

one basin was excluded from streamflow validation because it 

drains a hardwood swamp with a surface water-groundwater 

interaction that is not captured by this TOPMODEL approach 

(USGS site 01466500, McDonalds Branch in Lebanon State 

Forest, N.J.; Mast and Turk [1999]). The remaining 37 basins 

were mixed in land cover. Twenty-eight of these mixed basins 

were used to validate model parameters and to optimize the 

incorporation of water-use data. Nine mixed basins were set 

aside and used as test basins for final validation that WATER 

would perform similarly in areas not used to optimize the 

hydrologic models or datasets. The WATER output discussed 

in this section uses streamflow estimates that have been 

adjusted by seasonal water-use-median totals for specific point 

locations (discussed in “Incorporation of Water-Use Data”); 

these are streamflow estimates from WATER to which wateruse data were applied with WATER Application Utilities.

Goodness-of-Fit Statistics

A series of goodness-of-fit statistics were run on observed 

versus simulated streamflow by using the USGS EflowStats 

R-statistics package (Thompson and Archfield, 2014) to evaluate overall model performance as well as the ability of the 

model to distinguish individual streamflow components associated with high-streamflow, midrange, and low-streamflow 

conditions. A combination of statistics for evaluating overall 

model performance is presented; each statistic evaluated a 

comparison of daily streamflow for the period of October 2001 

through September 2010 (3,287 days; 12 sites had 366–2,922 

days; table 3); these statistics were run with only complete 

water years. Groups were compared through paired, Wilcoxon 

signed-rank tests, and the comparisons are two sided unless 

otherwise noted. Statements of significance indicate a p-value 

<0.05. The goodness-of-fit statistics used included those 

described as follows:
Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 37

• The Nash-Sutcliffe efficiency (Ef) statistic ranges from 

negative infinity to 1 (Nash and Sutcliffe, 1970):

 

∑

∑ −

− −= 2

2

)(

)( 1

xx

xy E

i

ii

f

. (9)

A value of 1 indicates that the simulation perfectly 

matches those observed data for each day of the 

comparison. A value of zero indicates that the simulation provides no more information than a mean annual 

streamflow value. Each of the Ef values reported was 

calculated by using the natural log (ln) of the daily 

streamflow (observed [xi] and simulated [yi]) to better 

represent all parts of the hydrograph and not concentrate on the largest streamflow events.

• The normalized root mean squared error (RMSEn) 

calculates the error as a multiple of the daily observed 

streamflow value:

 RMSEn y x x

n

i i i = ∑( ) − / )2

. (10)

The RMSEn provides an estimation of uncertainty for 

the simulations that can be transitioned to simulations 

at ungaged sites and those involving scenario testing; 

this statistic is essentially a proportional error relative 

to daily streamflow. This same statistic also is used to 

estimate uncertainty for aggregated streamflow. 

• The ratio of the root mean squared error to the standard 

deviation of the observed streamflow (RSR) calculates 

the error as a proportion of variability in observed 

streamflow:

 . (11)

RSR

y x

n

x x

n

i

=

( ) ( ) −

( ) − ( )

∑

∑

1 1

2

2

The RSR helps to identify those sites and seasons during which observed streamflow variability caused by 

anthropogenic controls (such as water use) or weather 

patterns (such as snowmelt) may affect the ability to 

simulate streamflow because of water storage or redistribution that is not represented in those datasets used 

by WATER.

•	 The Spearman rank correlation coefficient (rho) incorporates ranks (R) of daily observed and simulated 

streamflow within the entire record:

 rho

Rx Ry n n

n n

i i

=

( ) −  +



 





( ) −

∑ 1

2

1 12

2

2 /

. (12)

This statistic quantifies the ability of the simulation to 

accurately separate individual streamflow components 

in terms of how individual days rank among the entire 

streamflow record.

•	 The bias (B) calculates error as a percentage of the 

daily streamflow value:

 

∑

∑ − =

i

ii

x

xy B )( *100 . (13)

The bias helps to identify whether the model consistently overestimates or underestimates streamflow for 

individual sites or time periods. A positive bias indicates that WATER overestimates streamflow.

Evaluation of Daily Streamflow

This group of goodness-of-fit statistics shows how 

WATER performs throughout the DRB (fig. 14). Fifty-three of 

57 basins have an Ef between 0.39 and 0.83. Normalized root 

mean squared error ranges from 0.32 to 3.11, and RSR ranges 

from 0.45 to 1.64. Bias ranges from -26.7 to 27.4 percent, 

with 35 of 57 basins between ±10 percent. The Spearman rank 

correlation coefficient ranges from 0.69 to 0.92 (not shown in 

figure 14).

Three basins in particular have poor performance relative 

to the other validation basins. Two of these (01451500—Little 

Lehigh Creek at Allentown, Pa.; and 01452500—Monocacy 

Creek near Bethlehem, Pa.) are populated regions in the 

carbonate area of the DRB, where groundwater use makes 

it difficult to simulate streamflow (fig. 5). A third basin 

(01484270—Beaverdam Creek near Milton, Del.) is in the 

Coastal Plain region and may be influenced by high tides 

(fig. 3). The RMSEn of several basins in the midlatitudes of 

the DRB, including basins where the land cover is relatively 

equally split among the three HRUs, ranges from 0.76 to 0.90; 

daily water use may be more difficult to characterize from 

seasonal estimates for the mixed land-cover environment than 

for basins with primarily one HRU. The RMSEns of several 

basins in the northern part of the DRB shows relatively high 

values; however, comparison to the observed variability (RSR) 

suggests that there is a high variability in daily streamflow 

for these basins. For each basin, a 3-day moving average 

of streamflow significantly improved model performance 

(p<0.01); this 3-day average accounts for the random distribution of precipitation events, the potential for a precipitation 

event to span more than 1 day, and the variable snow-water 

equivalent among and within events. There is no apparent 

spatial pattern in the bias.

For an understanding of the accuracy of hydrologic 

simulations for different streamflow conditions, streamflows 

were divided into six percentiles (≤10 percent, >10–25 percent, >25–50 percent, >50–75 percent, >75–90 percent, and 

>90 percent) and compared to overall model performance 

(fig. 15). The RMSEn (fig. 15A) indicates no significant difference in model performance for streamflows larger than 

the 25th percentile, and the average value is less than 1 for 

these streamflows. The RMSEn is significantly larger for the 
01480675 01487086

01422500

01413500

01414500

01435000

01422747

01424108

01451800 01468500

01479000

01480300

01470779

01411500

01467150

01482500

01477120 01480000

01471980

01470500 01451500

01440400

01440000

01445000

01443500

01439500

01442500

01450500

01475850

01475530

01465798

01472199

01472198

01467048

01472157

01452000

01446000

01452500

01420500

01423000

01415000

01484000

01484270

01484050

01445500

Schuylkill

CrosswicksNeshaminy

Lackawaxen

Upper

East Branch

Delaware

Delaware

Middle 

DelawareMongaupBrodhead

Lower 

Delaware

BrandywineChristina

BroadkillSmyrna

CohanseyMaurice

Delaware Bay

Lehigh

Middle DelawareMusconetcong

01480000

76° 75° 76° 75° 76° 75°

42°41°40°39°

42°41°39°38°

74° 75° 74° 75° 74° 75° 74° 75°

–1.14 to 0.000.01 to 0.250.26 to 0.500.51 to 0.750.76 to 0.83

0 to 0.500.51 to 0.750.76 to 1.001.01 to 1.501.51 to 2.75

0.45 to 0.500.51 to 0.750.76 to 0.900.91 to 1.001.01 to 1.64

–26.7 to –15.0–14.9 to –2.0–1.9 to 2.02.1 to 15.015.1 to 27.2

 Normalized root mean squared error Nash-Sutcliffe Efficiency (Ef

)

 Basin boundaries

Subbasin numbers

EXPLANATION

Root mean squared error / 

standard deviation (RSR)

 Bias, in percent

01484270

0 30 60 MILES

0 30 60 KILOMETERS

38 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER) Figure 14. Statistical evaluation of hydrologic simulations for 48 basins in the Delaware River Basin. For each statistic, green indicates better performance. The first three of these statistics are unitless. The Nash-Sutcliffe efficiency (

E) was evaluated by using the natural log of the daily streamflow value. The Nash-Sutcliffe efficiency has a range of 

f

negative infinity to 1; a value of 1 indicates that the simulation perfectly matches those observed data for each day of the comparison. The normalized root mean squared error (RMSEn) describes error as a proportion of observed daily streamflow. The ratio of the root mean squared error (RMSE) to the standard deviation of observed streamflow (RSR) describes error in terms of variability of observed streamflow. Bias is reported as a percent (%); a positive bias indicates an overestimation by the Water Availability Tool for Environmental Resources simulation.
0 10 25 50 75 90 100

Normalized root mean squared error

All

Streamflows

876543210

Percent of streamflow record exceeded

z

z

z z

y

y

w

014115000141350001414500014150000142050001422389

014225000142273801422747014230000142410801435000

014395000144000001440400014425000144350001445000

014455000144600001450500014515000145180001452000

014525000146579801467048014670860146715001468500

014705000147077901471980014721570147219801472199

014755300147585001477120014778000147900001480000

014803000148067501482500014840000148405001484270

Average for all sites

EXPLANATION

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 39 Figure 15. Goodness-of-fit statistics for 48 basins in the Delaware River Basin as a function of individual streamflow percentiles: 

A, normalized root mean squared error, 

B, root 

mean squared error / standard deviation (RSR), 

C, Spearman rank correlation coefficient, and 

D, Bias. The values for the entire streamflow record are shown all the way to the 

right. Those largest streamflows are shown to the left such that, for example, points between 90 and 100 include those that exceed 90 percent (%) of the observed streamflow record. Letters indicate statistically different groupings (p-value <0.05) among streamflow components according to two-sided, paired Wilcoxon signed-ranked tests. Streamflow percentiles labeled with different letters significantly differ from each other. Groups labeled with multiple letters are not different from other groups with the same letter. For example, those streamflow percentiles noted with a 

w are significantly different from those labeled with a 

y, but neither group significantly differs from those labeled as yw.

A
0 10 25 50 75 90 100 All

Streamflows

86420

201816141210

Root mean squared error / standard deviation (RSR)

Percent of streamflow record exceeded

z

yw

yw

yw

y

w

v

Averagefor all sites

EXPLANATION

014115000141350001414500014150000142050001422389

01422500

0142273801422747014230000142410801435000

014395000144000001440400014425000144350001445000

014455000144600001450500014515000145180001452000

014525000146579801467048014670860146715001468500

014705000147077901471980014721570147219801472199

014755300147585001477120014778000147900001480000

014803000148067501482500014840000148405001484270

40 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER) Figure 15. Goodness-of-fit statistics for 48 basins in the Delaware River Basin as a function of individual streamflow percentiles: 

A, normalized root mean squared error, 

B, root 

mean squared error / standard deviation (RSR), 

C, Spearman rank correlation coefficient, and 

D, Bias. The values for the entire streamflow record are shown all the way to the 

right. Those largest streamflows are shown to the left such that, for example, points between 90 and 100 include those that exceed 90 percent (%) of the observed streamflow record. Letters indicate statistically different groupings (p-value <0.05) among streamflow components according to two-sided, paired Wilcoxon signed-ranked tests. Streamflow percentiles labeled with different letters significantly differ from each other. Groups labeled with multiple letters are not different from other groups with the same letter. For example, those streamflow percentiles noted with a 

w are significantly different from those labeled with a 

y, but neither group significantly differs from those labeled as yw.—

B

Continued
C

0 10 25 50 75 90 100 All 

Streamflows

-0.2

0

0.80.60.4

0.2

1

Percent of streamflow record exceeded

Spearman rank correlation coefficient

z

y

w

w

w

w

v

Averagefor all sites

EXPLANATION

014115000141350001414500014150000142050001422389

014225000142273801422747014230000142410801435000

014395000144000001440400014425000144350001445000

014455000144600001450500014515000145180001452000

014525000146579801467048014670860146715001468500

01475530 01470500

0147077901471980014721570147219801472199

0147585001477120014778000147900001480000

014803000148067501482500014840000148405001484270

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 41 Figure 15. Goodness-of-fit statistics for 48 basins in the Delaware River Basin as a function of individual streamflow percentiles: 

A, normalized root mean squared error, 

B, root 

mean squared error / standard deviation (RSR), 

C, Spearman rank correlation coefficient, and 

D, Bias. The values for the entire streamflow record are shown all the way to the 

right. Those largest streamflows are shown to the left such that, for example, points between 90 and 100 include those that exceed 90 percent (%) of the observed streamflow record. Letters indicate statistically different groupings (p-value <0.05) among streamflow components according to two-sided, paired Wilcoxon signed-ranked tests. Streamflow percentiles labeled with different letters significantly differ from each other. Groups labeled with multiple letters are not different from other groups with the same letter. For example, those streamflow percentiles noted with a 

w are significantly different from those labeled with a 

y, but neither group significantly differs from those labeled as yw.—

Continued
D

0 10 25 50 75 90 100

-100

-50

0

50

150100

Bias, in percent

Percent of streamflow record exceeded

All

Streamflows

z

y

y

w

v

u

t

014115000141350001414500014150000142050001422389

014225000142273801422747014230000142410801435000

014395000144000001440400014425000144350001445000

014455000144600001450500014515000145180001452000

014525000146579801467048014670860146715001468500

014705000147077901471980014721570147219801472199

014755300147585001477120014778000147900001480000

014803000148067501482500014840000148405001484270

Averagefor all sites

EXPLANATION

42 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER) Figure 15. Goodness-of-fit statistics for 48 basins in the Delaware River Basin as a function of individual streamflow percentiles: 

A, normalized root mean squared error, 

B, root 

mean squared error / standard deviation (RSR), 

C, Spearman rank correlation coefficient, and 

D, Bias. The values for the entire streamflow record are shown all the way to the 

right. Those largest streamflows are shown to the left such that, for example, points between 90 and 100 include those that exceed 90 percent (%) of the observed streamflow record. Letters indicate statistically different groupings (p-value <0.05) among streamflow components according to two-sided, paired Wilcoxon signed-ranked tests. Streamflow percentiles labeled with different letters significantly differ from each other. Groups labeled with multiple letters are not different from other groups with the same letter. For example, those streamflow percentiles noted with a 

w are significantly different from those labeled with a 

y, but neither group significantly differs from those labeled as yw.—

Continued
0

0.5

1

1.5

2

2.5

3

3.5

0 20 40 60 80 100

Normalized

Forested area, in percentt

 root mean square error

Normalized root mean square error

0

0.5

1

1.5

2

2.5

3

3.5

0 200 400 600 800 1,000

Basin area, in square kilometers

0

1

2

3

4

5

6

7

8

9

10

0 200 400 600 800 1,000

Basin area, in square kilometers

0

0.1

0.2

0.3

0.4

0.5

0.6

0 200 400 600 800 1,000

Basin area, in square kilometers

Basin area, in square kilometers

Spearman rank coefficientSpearman rank coefficient

0

0.1

0.2

0.3

0.4

0.5

0.6

0 20 40 60 80 100

Forested area, in percent

-40

-20

0

20

40

60

80

100

0 200 400 600 800 1,000

Bias, in percent

-60 -60

-40

-20

0

20

40

60

80

0 20 40 60 80 100

Bias, in percent

Forested area, in percent

0

1

2

3

4

5

6

7

8

9

10

Root mean squared error /

0 20 40 60 80 100

 standard deviation (RSR)

Root mean squared error /

 standard deviation (RSR)

Forested area, in percent

EXPLANATION

≥ 90 percent

> 75–90 percent

> 50–75 percent

> 25–50 percent

> 10–25 percent

< 10 percent

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 43

Figure 16. Goodness-of-fit streamflow-percentile statistics grouped as a function of basin area and 

percentage of forested area. Forested-area categories are 0–25 percent (%), >25–50 percent, >50–75 

percent, and >75–100 percent. Basin-area categories are 0–25 square kilometers (km2

), >25–50 km2, 

>50–100 km2

, >100–250 km2, >250–500 km2, and >500–928 km2; points are shown at basin average for the 

range. For each statistic, the overall mean for all 48 sites is shown at 0 percent forested area on left. 

>, greater than; <, less than.
smallest streamflows (<25th percentile). However, when the 

root mean squared error is normalized by the natural variability for each basin (RSR; fig. 15B), there is no significant 

difference among those streamflows smaller than the 90th 

percentile. This suggests that the larger error in streamflow 

simulation, as indicated by the RMSEn, is a function of 

day-to-day variability in observed streamflow that might be 

caused, for example, by temporal distribution of precipitation 

events or actual water use during summer and fall. The RSR 

also shows that for the largest streamflows (90–100th percentiles), on average the root mean squared error is equal to the 

standard deviation of observed streamflow for this streamflow 

percentile (RSR=0.98) and is similar to that for all streamflows (RSR=0.73).

The Spearman rank correlation coefficient (fig. 15C) 

shows that within individual streamflow percentiles, the 

simulations are less accurate when the entire flow record is 

considered; there is no significant difference in performance 

for streamflows <75th percentile. However, the notably higher 

value for all streamflows (rho=0.84) indicates that the model 

successfully differentiates individual daily streamflow in 

terms of where these rank in the entire streamflow record. The 

evaluation of bias (fig. 15D) shows the most difference among 

the streamflow percentiles. Overall, the largest streamflows 

show a positive bias (30 percent), indicating that these largest 

streamflows are overestimated; this is likely a function of how 

precipitation is randomly distributed within WATER, making 

it difficult to accurately simulate the timing of peak streamflow. The average bias for the entire streamflow record in all 

basins is -1.14 percent, and streamflows from the 90th–25th 

percentile have a bias of approximately -7 percent and a similar distribution of positive and negative bias among individual 

basins. The two smallest streamflow percentiles (>25-10th 

and <10th) also show a similar spread of positive and negative bias, but with a more negative average bias (-13 and -25 

percent, respectively). In both cases, the absolute percent 

All basins n = 48

0–25 percent n = 11

>25–50 percent n = 14

>50–75 percent n = 12

>75–100 percent n = 11 

EXPLANATION

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

Flows, by month

0

2

4

6

8

Normalized root mean squared error

44 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 17. Normalized root mean squared error (RMSEn) as a function of percentage of forested area. Forestedarea categories are 0–25 percent, >25–50 percent, >50–75 percent, and >75–100 percent. Note that U.S. Geological 

Survey site 01422389 has zero-streamflow days in September and October, so no RMSEn is reported for those months 

or as annual value and only five forested sites are shown for these time periods.
0

2

4

Root mean squared error / standard deviation (RSR)

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

Flows, by month

All basins n = 48

0–25 percent n = 11

>25–50 percent n = 14

>50–75 percent n = 12

>75–100 percent n = 11 

EXPLANATION

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 45

Figure 18. Root mean squared error/standard deviation (RSR) as a function of percentage of forested area. Forested-area 

categories are 0–25 percent, >25–50 percent, >50–75 percent, and >75–100 percent.
0

2

4

6

8

Normalized root mean squared error

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

Flows, by month

All basins n = 48

0–25 square kilometers 

(km2

)

 n = 8

>25–50 km2 n = 6

>50–100 km2 n = 9

>100–250 km2 n = 15

>250–500 km2 n = 6

>500–928 km2

 n = 4

EXPLANATION

46 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 19. Normalized root mean squared error (RMSEn) as a function of basin area. Area categories are 

0–25 square kilometers (km2

), >25–50 km2, >50–100 km2, >100–250 km2, >250–500 km2, and >500–928 km2. Note that 

U.S. Geological Survey site 01422389 has zero-streamflow days in September and October, so no RMSEn is reported 

for those months or as an annual value and only five forested sites are shown for these time periods.
0

2

4

Root mean squared error / standard deviation (RSR)

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

Flows, by month

All basins n = 48

0–25 square kilometers 

(km2

)

 n = 8

>25–50 km2

 n = 6

>50–100 km2

 n = 9

>100–250 km2

 n = 15

>250–500 km n = 6

>500–928 km2

 n = 4

EXPLANATION

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 47

Figure 20. Root mean squared error/standard deviation (RSR) as a function of basin area. Area categories are 

0–25 square kilometers (km2

), >25–50 km2, >50–100 km2, >100–250 km2, >250–500 km2, and >500–928 km2.
48 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

bias is significantly larger for the smallest streamflows than 

for the 25–50th streamflow component (p-value = 0.018 and 

p-value <0.001, respectively); the difficulty in simulating these 

small streamflows is compounded by the day-to-day deviation 

of the seasonal water-use estimate from the actual daily value.

Individual streamflow percentiles were also assessed 

in order to understand if there was a relation of streamflow 

to land-cover distribution (0–25 percent, >25–50 percent, 

>50–75 percent, >75–100 percent) or basin size (0–25 km2, 

>25–50 km2, >50–100 km2, >100–250 km2, >250–500 km2, 

and >500 km2) (fig. 16); each of the four goodness-of-fit 

statistics was averaged for sequential ranges of basin area and 

percentage of forested area. The RMSEn, RSR, and Spearman 

rho all show similar trends for each of the streamflow percentiles when evaluated as a function of basin area and percentage 

of forested area. The largest streamflows (≥90th percentile) 

are the general exception to this and exhibit different bias and 

RSR relative to the other streamflow percentiles. For example, 

the RSR for the largest streamflows is lower than that for 

the other streamflow percentiles; this is true in terms of both 

forested area and basin size. This is further evidence that bias 

in the largest streamflows is a function of how precipitation 

is distributed in the model as opposed to other aspects of the 

model, because this error is consistent regardless of location 

within the DRB, basin size, or land-cover distribution. Similarly, those basins smaller than 25 km2

 have the largest RSR 

and lowest Spearman rho for streamflows <90th percentile; an 

accurate and precise precipitation distribution, beyond what 

is available in WATER, is critical in these small basins, where 

Optimization Test Optimization Test Optimization Test Optimization Test

Simulated sites

−1.5

−1.0

−0.5

 0.0

 0.5

 1.0

Nash-Sutcliffe Efficiency (

Ef 

)

48 9

0

0.5

1.0

Spearman rank correlation

48 9

0

1

2

3

Normalized root mean squared error (proportion of flow)

48 9

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Root mean squared error / standard deviation (RSR)

48 9

Figure 21. Comparison of four goodness-of-fit statistics for 48 optimization basins and 9 test basins. Note that for each statistic, the 

nine test basins perform comparably to those basins use for optimization.
A

1

10

100

1,000

10,000 1 Oct.

15 Oct.

29 Oct.

12 Nov.

26 Nov.

10 Dec.

24 Dec.

7 Jan.

21 Jan.

4 Feb.

18 Feb.

4 Mar.

18 Mar.

1 Apr.

15 Apr.

29 Apr.

13 May

27 May

10 June

24 June

8 July

22 July

5 Aug.

19 Aug.

2 Sept.

16 Sept.

30 Sept.

2010

Streamflow, in cubic feet per second

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

Oct.

2001

Oct.

2002

Oct.

2003

Oct.

2004

Oct.

2005

Year

Oct.

2006

Oct.

2007

Oct.

2008

Oct.

2009

Oct.

2010

Cumulative streamflow, in millimeters

10

100

1,000

10,000

100,000

10 100 1,000 10,000 100,000

Simulated, in cubic feet per second

Observed, in cubic feet per second

Simulated natural streamflow

Adjusted for water use

1:1

EXPLANATION

01420500 Beaver Kill at Cooks Falls, NY Ef (ln) = 0.75 RMSEn = 0.57

RSR = 0.69 Bias = –6.4%

Spearman rho = 0.88

Observed

EXPLANATION

Simulated natural streamflow

Adjusted for water use

Observed

EXPLANATION

Simulated natural streamflow

Adjusted for water use

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 49

Figure 22. Observed and simulated streamflow for October 1, 2009, through September 30, 2010, with and without water use, together 

with cumulative streamflow for the 2001–10 period in A, a forested basin (01420500 Beaver Kill at Cooks Falls, NY) and B, an agricultural 

basin (01470779 Tulpehocken Creek near Bernville, PA). Note that for the forested basin, there is little change when water use is 

applied. All plots are at the same scale. Site-specific statistics have also been included. Ef

(ln), Nash-Sutcliffe efficiency of the natural 

log of streamflow; RMSEn, normalized root mean squared error; RSR, ratio of the root mean squared error to the standard deviation of 

observed streamflow.
B

1

10

100

1,000

10,000

2010

Streamflow, in cubic feet per second

01470779 Tulpehocken Creek near Bernville, PA Ef (ln) = 0.40 RMSEn = 0.61

RSR = 0.73 Bias = –3.6%

Spearman rho = 0.87

15 Oct.

29 Oct.

12 Nov.

26 Nov.

10 Dec.

24 Dec.

7 Jan.

21 Jan.

4 Feb.

18 Feb.

4 Mar.

18 Mar.

1 Apr.

15 Apr.

29 Apr.

13 May

27 May

10 June

24 June

8 July

22 July

5 Aug.

19 Aug.

2 Sept.

16 Sept.

30 Sept.

1 Oct.

1,000

2,000

3,000

4,000

5,000

6,000

Cumulative streamflow, in millimeters

0

Year

Oct.

2001

Oct.

2002

Oct.

2003

Oct.

2004

Oct.

2005

Oct.

2006

Oct.

2007

Oct.

2008

Oct.

2009

Oct.

2010

10

1

100

1,000

10,000

Simulated, in cubic feet per second

1 10 100 1,000 10,000

Observed, in cubic feet per second

Observed

EXPLANATION

Simulated natural streamflow

Adjusted for water use

Observed

EXPLANATION

Simulated natural streamflow

Adjusted for water use

EXPLANATION

Simulated natural streamflow

Adjusted for water use

1:1

50 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 22. Observed and simulated streamflow for October 1, 

2009, through September 30, 2010, with and without water use, 

together with cumulative streamflow for the 2001–10 period in A, 

a forested basin (01420500 Beaver Kill at Cooks Falls, NY) and B, 

an agricultural basin (01470779 Tulpehocken Creek near Bernville, 

PA). Note that for the forested basin, there is little change when 

water use is applied. All plots are at the same scale. Site-specific 

statistics have also been included. Ef (ln), Nash-Sutcliffe efficiency 

of the natural log of streamflow; RMSEn, normalized root mean 

squared error; RSR, ratio of the root mean squared error to the 

standard deviation of observed streamflow.—Continued
Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 51

response to individual events can be rapid and directly reflects 

the magnitude and duration of precipitation as well as local 

soil-water storage capacity; in contrast, spatial and temporal 

differences in precipitation and soil-water storage are masked 

by channel storage and tributary integration that occurs in 

larger basins (Dingman, 2002). Finally, those basins with the 

smallest percentage of forested area, where the variability in 

daily water use combines with localized snowpack management, have a relatively large RSR for streamflows <90th 

percentile.

To further understand the variability in streamflow 

simulation, the RMSEn and RSR were examined as a function 

of both percentage of forested area and basin size by using 

monthly streamflow distributions (figs. 17–20). The highest 

monthly RMSEn (fig. 17) is in September for 01422738—

Wolf Creek at Mundale, N.Y., the smallest basin evaluated 

(1.6 km2); this is one of the two months for which a nearby 

basin (01422389–Coulter Brook near Bovina, N.Y. [2.0 km2]) 

has zero-streamflow days. In general, RMSEn is higher in 

the warmer and drier months (July–October) when individual 

plant species, beyond the specification of the forested HRU, 

can increase their rooting depth in response to soil-water stress 

and access deeper soil layers not used during the rest of the 

growing season. Those basins with >75-percent-forested area 

also have higher RMSEn in January relative to the February–June period—most of these basins are in the northern 

part of the DRB, where simulation of daily snow accumulation and snowmelt processes are likely compounding model 

error. The RSR of these same basins is larger in October and 

June, a month later in the spring than for those basins with 

25–50-percent-forested area (fig. 18). This may be related to 

the transition into and out of the aggressive ET period of the 

year, which starts later in the northern part of the DRB, where 

those basins with >75-percent-forested area are concentrated 

(fig. 4). The highest monthly RSR is in August for USGS site 

01484000—Murderkill River near Felton, Del.; this site is at 

the fringe of the tidally influenced area, where the low streamflows may be impacted by high tides (fig. 3).

A

1

10

100

1,000

10,000 1 Oct.

15 Oct.

29 Oct.

12 Nov.

26 Nov.

10 Dec.

24 Dec.

7 Jan.

21 Jan.

4 Feb.

18 Feb.

4 Mar.

18 Mar.

1 Apr.

15 Apr.

29 Apr.

13 May

27 May

10 June

24 June

8 July

22 July

5 Aug.

19 Aug.

2 Sept.

16 Sept.

30 Sept.

2010

01420500 Beaver Kill at Cooks Falls, NY

Observed

EXPLANATION

Simulated

Estimates of uncertainty

1 RMSEn

2 RMSEn

1 RMSEn57

2 RMSEn57

Streamflow, in cubic feet per second

Figure 23. Examples of observed and simulated streamflow for A, a forested basin and B, an agricultural basin with four different 

uncertainty ranges: ±1 normalized root mean squared error from individual sites (RMSEn), ±2 RMSEn, ±1 normalized root mean 

squared error averaged from all sites (RMSEn57), and ±2 RMSEn57.
B

1

10

100

1,000

10,000

1 Oct.

15 Oct.

29 Oct.

12 Nov.

26 Nov.

10 Dec.

24 Dec.

7 Jan.

21 Jan.

4 Feb.

18 Feb.

4 Mar.

18 Mar.

1 Apr.

15 Apr.

29 Apr.

13 May

27 May

10 June

24 June

8 July

22 July

5 Aug.

19 Aug.

2 Sept.

16 Sept.

30 Sept.

2010

Streamflow, in cubic feet per second

01470779 Tulpehocken Creek near Bernville, PA 

Observed

EXPLANATION

Simulated

Estimates of uncertainty

1 RMSEn

2 RMSEn

1 RMSEn57

2 RMSEn57

52 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 23. Examples of observed and simulated streamflow for A, a forested basin and B, an agricultural basin with four different 

uncertainty ranges: ±1 normalized root mean squared error from individual sites (RMSEn), ±2 RMSEn, ±1 normalized root mean 

squared error averaged from all sites (RMSEn57), and ±2 RMSEn57.—Continued
A

1

10

100

1,000

10,000 1 Oct.

15 Oct.

29 Oct.

12 Nov.

26 Nov.

10 Dec.

24 Dec.

7 Jan.

21 Jan.

4 Feb.

18 Feb.

4 Mar.

18 Mar.

1 Apr.

15 Apr.

29 Apr.

13 May

27 May

10 June

24 June

8 July

22 July

5 Aug.

19 Aug.

2 Sept.

16 Sept.

30 Sept.

2010

Streamflow, in cubic feet per second

01420500 Beaver Kill at Cooks Falls, NY

Percent

0–10

>10–25

>25–50

>50–75

>75–90

>90–100

Flow, in cubic 

feet per second

 112

 212

 406

 742

 1,360

 4,890

RMSEn 

 0.95

 0.65

 0.54

 0.44

 0.40

 0.53

Observed

EXPLANATION

Simulated

Estimates of uncertainty

1 RMSEn

2 RMSEn

1 RMSEn-percentile

2 RMSEn-percentile

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 53

Figure 24. Examples from A, a forested basin (01420500 Beaver Kill at Cooks Falls, NY) and B, an agricultural basin (01470779 

Tulpehocken Creek near Bernville, PA) of observed and simulated streamflow with site-specific uncertainty ranges from normalized root 

mean squared error (±1 RMSEn and ±2 RMSEn from figure 23) and for individual streamflow components (±1 RMSEn-percentile and ±2 

RMSEn-percentile, values shown as inset). Note that axis has been shifted for agricultural basin B but that the range shown includes 

the same orders of magnitude.
B

0

2

20

200

2,000 Streamflow, in cubic feet per second 1 Oct.

15 Oct.

29 Oct.

12 Nov.

26 Nov.

10 Dec.

24 Dec.

7 Jan.

21 Jan.

4 Feb.

18 Feb.

4 Mar.

18 Mar.

1 Apr.

15 Apr.

29 Apr.

13 May

27 May

10 June

24 June

8 July

22 July

5 Aug.

19 Aug.

2 Sept.

16 Sept.

30 Sept.

2010

Percent

0–10

>10–25

>25–50

>50–75

>75–90

>90–100

Flow, in cubic 

feet per second

 38

 62

 94

 141

 208

 504

RMSEn 

 0.39

 0.94

 0.52

 0.63

 0.49

 0.51

01470779 Tulpehocken Creek near Bernville, PA 

Observed

EXPLANATION

Simulated

1 RMSEn

2 RMSEn

1 RMSEn-percentile

2 RMSEn-percentile

Estimates of uncertainty

54 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 24. Examples from A, a forested basin (01420500 Beaver Kill at Cooks Falls, NY) and B, an agricultural basin (01470779 

Tulpehocken Creek near Bernville, PA) of observed and simulated streamflow with site-specific uncertainty ranges from normalized root 

mean squared error (±1 RMSEn and ±2 RMSEn from figure 23) and for individual streamflow components (±1 RMSEn-percentile and ±2 

RMSEn-percentile, values shown as inset). Note that axis has been shifted for agricultural basin B but that the range shown includes 

the same orders of magnitude.—Continued
Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 55

Table 9. Number of days of observed streamflow not bounded by normalized root mean squared error 

(RMSEn)-based confidence intervals over the period of record at two sites in the Delaware River Basin, 

including the site-specific RMSEn, the average RMSEn from 57 sites, and the site-specific RMSEn for the 

observed streamflow percentile.

[n=3,287 days. USGS, U.S. Geological Survey; ID, identification number; RMSEn, normalized root mean squared error; %, percent]

USGS

site ID

Observed streamflow not bounded by 

confidence interval, in days

+1 RMSEn -1 RMSEn +2 RMSEn -2 RMSEn

Site specific

01420500 345 (10%) 108 (3.3%) 163 (5.0%) 0 (0%)

01470779 1165(35%) 39 (1.2%) 219 (6.7%) 0 (0%)

Average for all sites (n=57)

01420500 207 (6.3%) 0 (0%) 74 (2.3%) 0 (0%)

01470779 618 (19%) 1 (0.03%) 42 (1.3%) 0 (0%)

By observed streamflow percentile

01420500 414 (12.6%) 147 (4.5%) 208 (6.3%) 0 (0%)

01470779 1165 (35.4%) 39 (1.2%) 219 (6.7%) 0 (0%)
−1 RMSEn57 +1 RMSEn57 +2 RMSEn57

Uncertainty Bound

0.0

0.5

1.0

Proportion of observations not bounded by average uncertainty for all 57 sites

EXPLANATION

 Forested (n = 11)

 Agricultural (n = 3)

 Developed (n = 6)

 Test basin (n = 9)

 Mixed basin (n = 28)

 75th percentile

 25th percentile

 Median

EXPLANATION

Maximum value

Minimum value

−1 RMSEn57 +1 RMSEn57 +2 RMSEn57

Uncertainty Bound

0.0

0.5

1.0

56 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 25. The proportion of days, over the period of record for all 57 statistical evaluation sites in the Delaware River Basin, on which

observed streamflow is not bounded by the confidence interval based on the average normalized root mean squared error (RMSEn57) for 

all sites. Only Monocacy Creek near Bethlehem, Pennsylvania, has less than 90 percent of the streamflows bounded by +2/-1 RMSEn. 

Data are shown both as individual points, with basin types differentiated, and as a boxplot for all 57 observations.
When these same statistics are considered as a function 

of basin area (figs. 19 and 20), the error in the smallest basins 

appears to follow a seasonal trend, with higher error optimization in winter and summer relative to spring and fall. These 

small basins include those with 11.9–99.5-percent-forested 

area, so this error is not interpreted to be a function of land 

use. Again, this higher error is likely a function of the random 

distribution of precipitation by the model, which is unlikely to 

perfectly mimic actual events; this precipitation distribution 

is especially important in smaller basins where response to 

individual events can be rapid (Dingman, 2002). The seasonal 

trend in error becomes less apparent as basin size increases.

Nine basins, ranging in size from 2 to 348 km2, were used 

to test model performance for basins not included in any part 

of the optimization process (figs. 4 and 21). For each statistic, 

these test basins performed comparably to those 48 basins 

used for optimization of WATER parameters and incorporation 

of water-use data. When these nine sites are incorporated, the 

mean RMSEn for all sites increases from 0.875 to 0.939, and 

the median changes from 0.614 to 0.762; the mean RMSEn for 

the nine test basins is 1.27, and the median is 1.04.

Two basins will be used as examples to further illustrate 

model performance; one is predominantly forested (fig. 22A), 

and the other is predominantly agricultural (fig. 22B). Over the 

9-year period evaluated, there was an average underestimation 

of cumulative streamflow of 62.3 millimeters per year (mm/yr; 

49.1 mm/yr without water use) in the forested basin. The agricultural basin had an average underestimation of 20.8 mm/yr 

(36.0 mm/yr without water use).

90 75 50 25 10

Flow exceedance, in percent

−100

 0

 100

 200

 300

 400

 Error, in percent

Largest flows Smallest flows

4.9 7.2

-4.6 -7.6

2.7

Absolute error, in percent

Maximum value

Minimum value

Extreme outlier

Outliers

75th percentile

Median

25th percentile

EXPLANATION

Median 

Mean 

 9.99

18.76

11.83

18.56

16.36

18.76 

25.91

29.46

29.38

54.66

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 57

Figure 26. The percentage of error for each streamflow percentile (n=57 sites) in the flow-duration curve; 

median error is notated on the graph. Median and mean values of absolute error for each percentile are 

summarized at bottom. All data are shown. 
58 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Estimating Uncertainty for Daily Streamflow 

Simulations by Using the Normalized Root Mean 

Squared Error

The RMSEn provides an estimation of uncertainty for the 

simulations that can be transitioned to simulations at ungaged 

sites and those involving scenario testing; this statistic is 

essentially a proportional error of daily streamflow simulation. 

For each of the 57 sites, the site-specific RMSEn was applied 

to the simulated discharge and compared to uncertainty 

bounds by using the mean RMSEn (an average of the RMSEn 

for all 57 sites; RMSEn57) as well as the site-specific RMSEn 

for each streamflow percentile as indicated by the observed 

streamflow. For the two basins shown (figs. 23 and 24), on the 

basis of the site-specific RMSEn, >90 percent of the streamflows are bounded by the addition of 2 RMSEn and subtraction of 1 RMSEn (+2/-1 RMSEn; fig. 23); this is also true for 

the mean RMSEn57 (0.939; n=57) and for the RMSEn specific 

to the observed streamflow percentile for each site (fig. 24 and 

table 9). When all 57 sites are considered (fig. 25) by using 

the mean RMSEn57, only Monocacy Creek near Bethlehem, 

Pa., has <90 percent of the streamflows bounded by +2/-1 

RMSEn57; the remaining 56 sites have >93 percent of the 

individual days bounded by +2/-1 RMSEn57, and 53 of these 

have >95 percent of days bounded by +2/-1 RMSEn57. Note 

that this error is not a function of land cover as is shown by 

the distribution of the different land-cover groupings (table 3) 

in the plot.

Evaluation of Daily Streamflow Distribution by 

Using the Flow-Duration Curve

As was discussed in a comparison of hydrologic flow 

models for the southeast U.S. (Farmer and others, 2015), the 

daily flow-duration curve (FDC) is a representation of the distribution of daily streamflow at a given site. The FDC is used 

to understand the average streamflows and extreme events in 

a basin for the period of record by quantifying, for example, 

the streamflow value that exceeds 90 percent of the streamflow 

record (percentile = 0.9). Five streamflow percentiles (0.1, 

0.25, 0.5, 0.75, 0.9) were evaluated for each of the 57 evaluated sites by using the RMSEn and bias statistics used for 

daily streamflow. When this cumulative distribution function 

is compared for each site (n=5 streamflow percentiles), there 

is a median RMSEn of 0.44 for all sites. When the streamflow 

percentiles are evaluated independently (n=57 sites; fig. 26 

and table 10), there are significant differences in percentage of 

error (100 × [sim–obs]/obs) among the streamflow percentiles, 

with absolute error decreasing as the magnitude of streamflow 

increases. This is consistent with the statistical evaluation of 

daily streamflow, which indicates that the smallest streamflows 

have the largest proportion of error; however these smallest 

streamflows also have the largest observed variability (fig. 15). 

Together, this statistical evaluation of daily streamflow and 

the aggregated streamflow percentiles indicates that although 

there is a difference in the ability to differentiate among the 

individual streamflow percentiles, the higher observed variability during low-streamflow conditions, relative to those that 

exceed the smallest 25 percent of streamflows, suggests that 

uncertainty is similar for the entire streamflow record.

Evaluation of Mean Monthly Streamflow 

Simulations by Using Normalized Root Mean 

Squared Error

The WATER DSS was developed to provide a modeling 

environment that could be used to evaluate land-cover, climate, and water-use-allocation scenarios. For scenario testing, 

each of these variables is altered on a monthly, seasonal, and 

(or) decadal time step. Consequently, it is recommended that 

the change associated with scenarios be evaluated at a monthly 

time step that is normalized for the 25-year climatic record.

Evaluation of mean monthly streamflow simulations 

focused on the RMSEn, a statistic that quantifies error as a 

percentage of the streamflow value so can be most easily 

transferred to streamflow simulation at ungaged sites; site 

period of record ranged from 12 to 108 months for 57 sites. 

Two sites, Beaver Kill at Cooks Falls, N.Y., and Tulpehocken 

Creek near Bernville, Pa., were used to illustrate the difference 

in observed and simulated mean monthly streamflows over the 

2001–10 time period (fig. 27). The RMSEn for mean monthly 

streamflows ranged from 0.226–6.253 for all 57 sites, with 

a mean of 1.15 and a median of 0.526. However, when only 

those 45 sites with a full 108 months (9 years) were included 

(table 1), the maximum was 1.61, the mean was 0.527, and 

the median was 0.400. This mean RMSEn for (0.527, n=45) 

Table 10. Results of Wilcoxon signed-rank test comparing the 

error for each streamflow percentile from the flow-duration curve 

for all 57 sites in the Delaware River Basin. Values shown are 

p-values from paired tests. Significant differences are indicated 

by asterisks (*). For example, there is no significant difference 

(p-value = 0.263) between error in simulation of the lowest 10 

percent of streamflows and the error in simulation of the highest 

10 percent of streamflows (90th percentile). Data are shown in 

figure 26.

[%, percent, <, less than; —, not applicable]

p-values Streamflow percentile

25% 50% 75% 90%

Streamflow

percentile

10% <0.001* 0.001* 0.201 0.263

25% — 0.505 0.029* 0.066

50% — — <0.001* 0.008*

75% — — — 0.703
Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr.

Mean monthly flow, in cubic feet per second

B

0

100

200

300

400

500

600

700

800

2002 2003 2004 2005 2006 2007 2008 2009 2010

01470779 Tulpehocken Creek near Bernville, Pennsylvania EXPLANATION

Observed flow

Simulated flow

Uncertainty estimates

1 RMSEn45-mon

2 RMSEn45-mon

EXPLANATION

Observed flow

Simulated flow

Uncertainty estimates

1 RMSEn45-mon

2 RMSEn45-mon

01420500 Beaver Kill at Cooks Falls, New York 

0

500

1,000

1,500

2,000

2,500

3,000

3,500

4,000

Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr. Oct. Apr.

2002 2003 2004 2005 2006 2007 2008 2009 2010

Mean monthly flow, in cubic feet per second

A

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 59

Figure 27. Examples from A, a forested basin (01420500 Beaver Kill at Cooks Falls, NY) and B, an agricultural basin (01470779 

Tulpehocken Creek near Bernville, PA) of observed and simulated mean-monthly streamflow with uncertainty ranges from normalized 

root mean squared error (RMSEn) averaged from all sites in the Delaware River Basin with 108-month (9-year) records 

(RMSEn45-mon = 0.527).
−1 RMSEn45-mon +1 RMSEn45-mon +2 RMSEn45-mon

Uncertainty bound

0

0.5

1.0

Proportion of mean-monthly flow observations not bounded by average uncertainty from 45 sites

−1 RMSEn45-mon +1 RMSEn45-mon +2 RMSEn45-mon

Uncertainty bound

0

0.5

1.0

Maximum value

3rd quartile

Median

1st quartile

Minimum value

Forested (n=11)

Agricultural (n=3)

Developed (n=6)

Test basin (n=9)

Mixed basin (n=28)

EXPLANATION EXPLANATION

60 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 28. The proportion of period of record during which the mean monthly observed streamflow is not bounded 

by the confidence interval based on the normalized root mean squared error (RMSEn) over the period of record for all 

45 validation sites in the Delaware River Basin with an observation period of 108 months (RMSEn45-mon=0.527). Fourteen 

sites have less than 90 percent of the streamflows bounded by +2/-1 RMSEn45-mon. Data are shown both as individual 

points, with basin types differentiated, and as a boxplot for all 57 observations.
Table 11. Number of months of observed mean monthly streamflow not bounded by the 

confidence interval based on the mean normalized root mean squared error (RMSEn) over 

the period of record for all 45 validation sites in the Delaware River Basin with an observation 

period of 108 months (RMSEn45-mon=0.527), for Beaver Kill, New York, and Tulpehocken Creek, 

Pennsylvania, sites in the Delaware River Basin.

[USGS, U.S. Geological Survey; ID, identification number; RMSEn, normalized root mean squared error; 

%, percent]

USGS site ID Months not bounded by confidence interval, as total (and percentage)

+1 RMSEn -1 RMSEn +2 RMSEn -2 RMSEn

01420500 9 (8.3%) 1 (0.9%) 4 (3.70%) 0 (0%)

01470779 27 (25.0%) 1 (0.9%) 2 (1.85%) 0 (0%)

0

0.1

0.2

0.3

0.4

0.5

0.6

Jan. Feb. Mar. Apr. May June

Month

July Aug. Sept. Oct. Nov. Dec.

Normalized root mean squared error (proportion of flow)

All Sites

9-year period of record

Mean 0.3255 (0.2147)

EXPLANATION

Median 0.2795 (0.2248)

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 61

Figure 29. Root mean squared error (RMSEn) for mean monthly streamflow normalized for the period of record for all 57 sites 

in the Delaware River Basin and for the 45 sites with a 9-year period of record (in parentheses).
Jan. Feb. Mar.* Apr. May June* July Aug. Sept. Oct.* Nov. Dec.

Normalized mean monthly streamflow, in cubic feet per second

1x10-1

1x100

1x101

1x102

1x103

1x104 Forested (n=11)

Agricultural (n=3)

Developed (n=6)

Test basin (n=9)

Mixed basin (n=28)

Observed

Simulated

EXPLANATION

62 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

Figure 30. Observed and simulated mean-monthly streamflow normals for 2001–10 time period for 57 sites in the 

Delaware River Basin. Asterisk (*) indicates that observed and simulated monthly normals significantly differ for 

those 45 sites with a full 108-month period of record.
0

0.5

1.0

Proportion of mean mean-monthly streamflow observations not bounded by average uncertainty

−2 RMSEn −1 RMSEn +1 RMSEn +2 RMSEn

Uncertainty bounds

RMSEn specific to month

RMSEn57mon-PORnorm (0.3255)

EXPLANATION

Statistical Evaluation, Validation, and Uncertainty of Streamflow Simulated by Using WATER 63

Figure 31. Proportion of mean monthly-streamflow normals (n=12 months) not bounded by simulated 

discharge if using either the month-specific (shown in figure 29) or averaged nomralized root mean 

squared error (RMSEn) of the normalized mean-monthly streamflow (RMSEn57mon-PORnorm) for all 57 sites 

in the Delaware River Basin.
64 Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)

was used to estimate uncertainty for mean monthly streamflow 

simulations (RMSEn45-mon)

. Similarly to the daily simulations, 

a confidence interval of +2/-1 RMSEn45-mon bounds >95 percent of the streamflows for the two example sites (fig. 28 and 

table 11). When these uncertainty bounds are applied to all 57 

validation sites, two sites have >10 percent of mean monthly 

streamflows not bounded by +2 RMSEn45-mon, and 12 sites 

have >10 percent of mean monthly streamflows that are not 

bounded by -1 RMSEn45-mon. Monocacy Creek near Bethlehem, Pa., is the most poorly estimated, with 24 of 108 months 

not included in the +2 RMSEn45-mon/-1 RMSEn45-mon uncertainty 

bounds. Again, it should be noted that this uncertainty is not 

a function of land-cover; this is critical if scenario testing will 

incorporate land-cover forecasts.

When the mean monthly streamflow is normalized for 

the period of record, with a single mean for each month for 

each site, error is generally highest during the late summer 

and fall (fig. 29), although this seasonal difference is smaller 

when only those sites with a full 9-year period of record are 

included. When the observed and simulated mean streamflow 

for each month are compared for all 57 sites, only March, 

June, and October significantly differ (fig. 30). When the 

mean monthly streamflow normalized for the period of 

record is bounded by using the mean RMSEn uncertainty 

(RMSEn57mon-PORnorm=0.3255), a +2/-2 RMSEn57mon-PORnorm is 

needed to bound >90 percent of the monthly streamflow estimates (fig. 31). Depending on the question being asked, one 

could use the RMSEn normalized for each month (fig. 31); 

however, there is little difference between this and using the 

overall mean.

Evaluating the mean monthly streamflow over the 

period of record used for validation is analogous to evaluating mean monthly streamflows by using monthly normals 

when implementing scenario testing for land-cover, climate, 

or water-use changes. Consequently, applying an uncertainty 

of +2/-2 RMSEn57mon-PORnorm (0.3255 × mean monthly streamflow) is recommended for quantifying expected streamflow 

magnitudes.

Summary 

The Water Availability Tool for Environmental Resources 

(WATER) decision support system (DSS) was developed to 

provide the Delaware River Basin community an ability to 

investigate the potential effects of different management decisions, forecasted changes in climate, and land-cover change. 

Although the WATER DSS can be used for the entire Delaware River Basin, there are some streams, including those 

downstream of regulated reservoirs and those within the tidal 

zone, where simulations should only be used for general information. WATER provides consistent simulation of hydrologic 

conditions, including high and low streamflows, for basins 

with ranges of size, land cover, and location within the Delaware River Basin. Individual hydroclimatic components of the 

water budget are also effectively simulated. Consequently, this 

process-based, regionally calibrated DSS can be used to investigate the sustainability and resiliency of water-resources as a 

result of forecasted environmental and management scenarios. 

Scenario testing can be accomplished because the WATER 

DSS provides for potential changes in both the natural and 

the anthropogenic environment by independently incorporating land-cover, climate, and landscape (topography and soils) 

characteristics. 

Ultimately, it is the responsibility of the user to interpret 

results. However, some precautions and suggestions for use of 

the WATER DSS follow:

1. An uncertainty range of +2/-1 normalized root mean 

squared error averaged from all sites (RMSEn57; 0.939) 

is recommended for daily streamflow simulations.

2. For those scenarios involving general circulation model 

(GCM) data and land-cover change, mean monthly 

streamflows, not mean daily streamflows, should be the 

finest unit considered because GCM data are applied 

by using a monthly normal and land-cover simulations 

were derived at a decadal time step. Normalized mean 

monthly streamflow (in other words, streamflow averaged for each month for the 25-year climate record) 

should be used with the normalized root mean squared 

error that has been normalized for the period of record 

for all 57 sites (RMSEn57mon-PORnorm; 0.3255) to quantify 

the forecasted range of streamflow and water availability 

for a given scenario.

3. All scenarios should be compared to simulation of 

the same site by using the historical conditions (2011 

National Land Cover Database and 2010 water use) 

provided with the DSS. This is similar to the approach 

illustrated with the determination of the GCM change 

factor calculations. Multiple GCMs and representative concentration pathways should be incorporated in 

scenario testing, and the overall trend in streamflow and 

other hydroclimatic variables among multiple GCM 

simulations should be used to plan for forecasted change.

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Williamson and others—Summary of Hydrologic Modeling for the Delaware River Basin Using the Water Availability Tool for Environmental Resources (WATER)—Scientific Investigations Report 2015–5143

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20155143