Open-File Report 2010-1014

U.S. Department of the Interior

U.S. Geological Survey

In Cooperation with the Delaware River Basin Commission

Simulation of Runoff and Reservoir Inflow for Use in a 

Flood-Analysis Model for the Delaware River, 

Pennsylvania, New Jersey, and New York, 2004-2006
In Cooperation with the Delaware River Basin Commission

Simulation of Runoff and Reservoir Inflow for Use in a 

Flood-Analysis Model for the Delaware River, 

Pennsylvania, New Jersey, and New York, 2004-2006

By Daniel J. Goode, Edward H. Koerkle, Scott A. Hoffman, R. Steve Regan, Lauren E. Hay, and Steven L. Markstrom

Open-File Report 2010-1014

U.S. Department of the Interior

U.S. Geological Survey
ii

U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

For product and ordering information:

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Suggested citation:

Goode, D.J., Koerkle, E.H., Hoffman, S.A., Regan, R.S., Hay, L.E., and Markstrom, S.L., 2010, Simulation of runoff 

and reservoir inflow for use in a flood-analysis model for the Delaware River, Pennsylvania, New Jersey, and New 

York, 2004-2006: U.S. Geological Survey Open-File Report 2010-1014, 68 p.

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endorsement by the U.S. Government.

Although this report is in the public domain, permission must be secured from the individual 

copyright owners to reproduce any copyrighted material contained within this report.
iii

Preface

This report describes a model, comprised of software and data files, for hydrologic simulation of 

the main-stem subbasin of the Delaware River. The performance of this model has been tested on several 

different computer systems and configurations. Future use, however, might reveal errors that were not 

detected in the test simulations. Users are requested to send notification of any errors found in this report 

or the model to:

Director

USGS Pennsylvania Water Science Center

215 Limekiln Road

New Cumberland, Pennsylvania 17070

dc_pa@usgs.gov

The latest version of the model and this report can be obtained using the Internet address below (accessed 

January 2010):

http://pa.water.usgs.gov/drbfam
iv

Contents

Preface .......................................................................................................................................................................... iii

Contents ........................................................................................................................................................................iv

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

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

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

Previous Studies ........................................................................................................................................................ 5

Description of Study Area .......................................................................................................................................... 5

Precipitation-Runoff Modeling System........................................................................................................................... 6

PRMS Modules .......................................................................................................................................................... 7

Model Documentation and Previous Applications .....................................................................................................10

Hourly Simulation Mode............................................................................................................................................10

Snowmelt ..................................................................................................................................................................10

Output for Reservoir Model.......................................................................................................................................10

Use of Measured Reservoir Discharge .....................................................................................................................11

User Interface ...........................................................................................................................................................11

Model Development......................................................................................................................................................12

Elevation Data and Watershed Discretization ...........................................................................................................12

Watershed Characteristics Data ...............................................................................................................................14

Climate Data .............................................................................................................................................................24

Climate Station Data .............................................................................................................................................24

Estimation of Hourly Temperature Using Daily Station Data .................................................................................29

Precipitation Estimated from Radar Data ..............................................................................................................30

Model Application .........................................................................................................................................................32

Calibration and Testing .............................................................................................................................................32

Limitations.................................................................................................................................................................50

Suggestions for Model Application............................................................................................................................50

Summary ......................................................................................................................................................................53

Acknowledgments ........................................................................................................................................................54

References Cited..........................................................................................................................................................55

Appendix – Documentation of PRMS Modules Modified for This Study .......................................................................61
v

Figures

1. Location of the Delaware River main-stem subbasin and selected reservoirs, Pennsylvania, New Jersey, and 

New York.......................................................................................................................................................... 3

2. Location of hydrologic response units and simulated stream reaches for the Delaware River main-stem 

subbasin, Pennsylvania, New Jersey, and New York..................................................................................... 13

3. Land-cover data for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York, 

2001 . ............................................................................................................................................................. 21

4. Impervious-surface data for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New 

York, 2001 . .................................................................................................................................................... 22

5. Mean percent impervious values for model hydrologic response units for the Delaware River main-stem 

subbasin, Pennsylvania, New Jersey, and New York..................................................................................... 23

6. Locations of selected National Oceanic and Atmospheric Administration meteorological stations in the 

Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.......................................... 27

7. National Weather Service Multi-sensor Precipitation Estimate hourly data for 9 a.m. Eastern Standard Time 

on September 18, 2004, used for model data for the Delaware River main-stem subbasin, Pennsylvania, New 

Jersey, and New York..................................................................................................................................... 30

8. Model hourly precipitation for 9 a.m. Eastern Standard Time on September 18, 2004, for Hydrologic 

Response Units for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York..... 31

9. Location of selected streamgages in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, 

and New York. ............................................................................................................................................... 34

10. Simulated and observed streamflow, September 13 to 26, 2004, at selected U.S. Geological Survey 

streamgages in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York. 

Streamflow at these locations is not regulated by reservoirs simulated in HEC-ResSim................................ 41

11. Simulated and observed streamflow, September 13 to 26, 2004, at selected U.S. Geological Survey 

streamgages below reservoirs in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and 

New York. Simulated streamflow is from HEC-ResSim reservoir and routing model using runoff and reservoir 

inflow from the PRMS model ......................................................................................................................... 43

12. Simulated and observed streamflow, March 26 to April 8, 2005, at selected U.S. Geological Survey 

streamgages in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York. 

Streamflow at these locations is not regulated by reservoirs simulated in HEC-ResSim................................ 44

13. Simulated and observed streamflow, March 26 to April 8, 2005, at selected U.S. Geological Survey 

streamgages below reservoirs in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and 

New York. Simulated streamflow is from HEC-ResSim reservoir and routing model using runoff and reservoir 

inflow from the PRMS model ......................................................................................................................... 46

14. Simulated and observed streamflow, June 22 to July 5, 2006, at selected U.S. Geological Survey 

streamgages in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York. 

Streamflow at these locations is not regulated by reservoirs simulated in HEC-ResSim................................ 47

15. Simulated and observed streamflow, June 22 to July 5, 2006, at selected U.S. Geological Survey 

streamgages below reservoirs in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and 

New York. Simulated streamflows are from HEC-ResSim reservoir and routing model using runoff and 

reservoir inflow from the PRMS model .......................................................................................................... 49

16. Simulated soil-moisture saturation at noon on A) March 26, 2005, and B) June 23, 2006, for model hydrologic 

response units for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York....... 51

17. Simulated maximum runoff rate during June 22 to July 5, 2006, to model stream segments for the Delaware 

River main-stem subbasin, Pennsylvania, New Jersey, and New York.......................................................... 52
vi

Tables

1. Selected reservoirs in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York... 4

2. Precipitation-Runoff Modeling System modules used for the Delaware River main-stem subbasin, 

Pennsylvania, New Jersey, and New York. ...................................................................................................... 8

Source of parameter values for selected model hydrologic response unit distributed parameters for the 

Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York ......................................... 15

Selected whole-model nondistributed parameters estimated by calibration and ranges of values for the 

Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York ......................................... 18

5. Selected climate stations in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New 

York. .............................................................................................................................................................. 25

6. Solar-radiation stations used for model data for the Delaware River main-stem subbasin, Pennsylvania, New 

Jersey, and New York..................................................................................................................................... 28

7. Streamgages selected for use in model calibration for the Delaware River main-stem subbasin, Pennsylvania, 

New Jersey, and New York. ........................................................................................................................... 33

8. Parameters calibrated in each step of the calibration process – daily mode. ................................................. 36

9. Parameters calibrated in each step of the calibration process – storm mode................................................. 37

10. Observed and simulated mean and standard deviation of hourly streamflow, in cubic feet per second, for 

streamgages used for model calibration for the Delaware River main-stem subbasin, Pennsylvania, New 

Jersey, and New York. .................................................................................................................................. 39
vii

Conversion Factors, Datum, and Acronyms

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 4,047 square meter (m2)

acre 0.4047 hectare (ha)

square foot (ft2) 0.09290 square meter (m2)

square inch (in2) 6.452 square centimeter (cm2)

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

gallon (gal) 3.785 liter (L) 

gallon (gal) 0.003785 cubic meter (m3) 

million gallons (Mgal) 3,785 cubic meter (m3)

cubic foot (ft3) 0.02832 cubic meter (m3) 

Flow rate

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

cubic foot per second per square mile 

[(ft3/s)/mi2]

0.01093 cubic meter per second per 

square kilometer [(m3/s)/km2]

gallon per minute (gal/min) 0.06309 liter per second (L/s)

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3/s)

inch per hour (in/h) 0 .0254 meter per hour (m/h)

Pressure

atmosphere, standard (atm) 101.3 kilopascal (kPa)

bar 100 kilopascal (kPa) 

inch of mercury at 60oF (in Hg) 3.377 kilopascal (kPa) 

pound per square inch (lb/in2) 6.895 kilopascal (kPa) 

Density

pound per cubic foot (lb/ft3) 16.02 kilogram per cubic meter 

(kg/m3)

pound per cubic foot (lb/ft3) 0.01602 gram per cubic centimeter 

(g/cm3)
viii

Acronyms used in this report

COOP Cooperative Climate Station

DEM digital elevation model

DRBC Delaware River Basin Commission

EST Eastern Standard Time

GIS geographic information system

GMT Greenwich Mean Time

HEC Hydrologic Engineering Center

HEC-DSS USACE HEC Data Storage System

HEC-ResSim USACE HEC Reservoir System Simulation program

HRU hydrologic response unit

MARFC Middle Atlantic River Forecast Center

MMS Modular Modeling System

MPE Multisensor Precipitation Estimate

NCDC National Climatic Data Center

NED National Elevation Dataset

NOAA National Oceanic and Atmospheric Administration

NRCC Northeast Regional Climate Center

NRMSE normalized root mean square error

NWS NOAA’s National Weather Service

NYCDEP New York City Department of Environmental Protection

OUI Object User Interface

PRMS Precipitation-Runoff Modeling System

STATSGO State Soils Geographic Database

USACE U.S. Army Corps of Engineers

USGS U.S. Geological Survey
1

Simulation of Runoff and Reservoir Inflow for Use in a 

Flood-Analysis Model for the Delaware River,

Pennsylvania, New Jersey, and New York, 2004-2006

By Daniel J. Goode, Edward H. Koerkle, Scott A. Hoffman, R. Steve Regan, Lauren E. Hay, and Steven L. 

Markstrom

Abstract

A model was developed to simulate inflow to reservoirs and watershed runoff to streams during 

three high-flow events between September 2004 and June 2006 for the main-stem subbasin of the 

Delaware River draining to Trenton, N.J. The model software is a modified version of the U.S. 

Geological Survey (USGS) Precipitation-Runoff Modeling System (PRMS), a modular, physically

based, distributed-parameter modeling system developed to evaluate the impacts of various 

combinations of precipitation, climate, and land use on surface-water runoff and general basin 

hydrology. The PRMS model simulates time periods associated with main-stem flooding that occurred 

in September 2004, April 2005, and June 2006 and uses both daily and hourly time steps. Output from 

the PRMS model was formatted for use as inflows to a separately documented reservoir and riverrouting model, the HEC-ResSim model, developed by the U.S. Army Corps of Engineers Hydrologic 

Engineering Center to evaluate flooding. The models were integrated through a graphical user interface. 

The study area is the 6,780 square-mile watershed of the Delaware River in the states of 

Pennsylvania, New Jersey, and New York that drains to Trenton, N.J. A geospatial database was created 

for use with a geographic information system to assist model discretization, determine land-surface 

characterization, and estimate model parameters. The USGS National Elevation Dataset at 100-meter 

resolution, a Digital Elevation Model (DEM), was used for model discretization into streams and 

hydrologic response units. In addition, geospatial processing was used to estimate initial model 

parameters from the DEM and other data layers, including land use. The model discretization represents 

the study area using 869 hydrologic response units and 452 stream segments. The model climate data 

for point stations were obtained from multiple sources. These sources included daily data for 22 

National Weather Service (NWS) Cooperative Climate Station network stations, hourly data for 15 

stations from the National Climatic Data Center, hourly data for 1 station from the NWS Middle 

Atlantic River Forecast Center records, and daily and hourly data for 7 stations operated by the New 

York City Department of Environmental Protection. The NWS Multisensor Precipitation Estimate data

set for 2001-2007 was used for computing daily precipitation for the model and for computing hourly 

precipitation for storm simulation periods. 

Calibration of the PRMS model included regression and optimization algorithms, as well as 

manual adjustments of model parameters. The general goal of the calibration procedure was to minimize 

the difference between discharge measured at USGS streamgages and the corresponding discharge 

simulated by the model. Daily streamflow data from 35 USGS streamgages were used in model 

calibration. The streamflow data represent areas draining from 20.2 to 6,780 square miles.
2

The PRMS model simulates reservoir inflow and watershed runoff for use as input into HECResSim for the purpose of evaluating and comparing the effects of different watershed conditions on 

main-stem flooding in the Delaware River watershed draining to Trenton, N.J. The PRMS model is 

useful as a planning tool to simulate the effects of land-use changes and different antecedent conditions 

on local runoff and reservoir inflow and, as input to the HEC-ResSim model, on flood flows in the main 

stem of the Delaware River.

Introduction

Major flooding occurred in the Delaware River Basin in September 2004, April 2005, and June 

2006. To evaluate the impact of reservoir levels and other factors on flooding, the Delaware River Basin 

Commission (DRBC), U.S. Geological Survey (USGS), U.S. Army Corps of Engineers (USACE)

Hydrologic Engineering Center (HEC), and National Oceanic and Atmospheric Administration 

(NOAA) National Weather Service (NWS) developed a Delaware River Flood-Analysis Model. The 

Flood-Analysis Model has two components, a rainfall-runoff watershed model, the PRMS model, and a 

reservoir operation and streamflow-routing model, the HEC-ResSim model. 

Purpose and Scope

This report describes the rainfall-runoff watershed model component of the Flood-Analysis 

Model for the Delaware River above Trenton, N.J. The rainfall-runoff model software is a modified 

version of the USGS Precipitation-Runoff Modeling System (PRMS) (Leavesley and others, 1983; 

Leavesley and Stannard, 1995; Leavesley and others, 2005; Markstrom and others, 2008). This rainfallrunoff model simulates overland flow, groundwater flow, and streamflow to be used as inputs of 

reservoir inflows for 13 reservoirs (table 1, fig. 1), local inflows, and unregulated tributary flows for use 

in a reservoir and river routing model, the HEC-ResSim model, for the comparative analyses of 

different watershed conditions on main stem flows. The HEC-ResSim component of the Flood-Analysis 

Model is documented in a separate report. The PRMS model may be used as a planning tool to evaluate 

the effects of watershed conditions on runoff and, in combination with HEC-ResSim, on flows in large 

rivers and the main stem of the Delaware River above Trenton, N.J. during floods. The PRMS model 

was not developed as a forecasting tool for realtime prediction of flooding.

This report describes the software, data sources, construction, and calibration of the rainfallrunoff model of the Delaware River Basin draining to Trenton, N.J. The model simulates time periods 

associated with main-stem flooding that occurred in September 2004, April 2005, and June 2006. 
3

 

Figure 1. Location of the Delaware River main-stem subbasin and selected reservoirs, Pennsylvania, New 

Jersey, and New York.
Table 1. Selected reservoirs in the Delaware River mainstem subbasin, Pennsylvania, New Jersey, and New York (data from 

Delaware River Basin Commission).

[FA, flow augmentation; FL, flood-loss reduction; P, hydroelectric power generation; WS, water supply; WSA, water supply primarily for flow augmentation]

Reservoir Purpose Storage

(million gallons)

Location

(stream, county, state)

Cannonsville WS, FA 96,726 West Branch Delaware River, Delaware, N.Y.

Pepacton WS, FA 143,701 East Branch Delaware River, Delaware, N.Y.

Neversink WS, FA 35,466 Neversink River, Sullivan, N.Y.

Mongaup System: Rio, Swinging Bridge, Toronto P 15,314 Mongaup River, Sullivan, N.Y.

Lake Wallenpaupack P 29,813 Wallenpaupack Creek, Wayne, Pa.

Prompton FL 6,614 West Branch Lackawaxen River, Wayne, Pa.

Jadwin FL 7,983 Dyberry Creek, Wayne, Pa.

Francis E. Walter FL 35,190 Lehigh River, Luzerne and Carbon, Pa.

Beltzville WSA

FL

12,978

8,797

Pohopoco Creek, Carbon, Pa.

Merrill Creek WSA 15,640 Merrill Creek, Hunterdon, N.J.

Nockamixon WS1 11,990 Tohickon Creek, Bucks, Pa.

1

 Used for flow augmentation during drought emergencies.

4
5

Previous Studies

A number of previous studies provide background information on the Delaware River and its 

watershed. Delaware River Basin Commission (2008a) summarizes the status of the watershed as of 

2008, including flooding and water-supply issues. Ayers and others (1994) describe potential effects of 

climate change on water resources in the basin. Fischer and others (2004) assess the water quality in the 

basin. Sloto and Buxton (2005) compute water budgets for a small subbasin of the Delaware River 

where development is occurring apace. Paulachok and others (2000) describe hydrologic conditions 

during drought in 1998-1999. Previously, Hirsch (1981) analyzed the probabilistic impact of reservoir 

operations on water-resource availability during drought.

Recent flooding in the Delaware River Basin is described in several studies. Brooks (2005) 

describes the flood of September 18-19, 2004, in the upper Delaware River Basin. Effects of the flood 

of April 2005 are described by Suro and Firda (2006) for the Neversink River Basin and by Reed and 

Protz (2007) for the main-stem Delaware River. Suro and others (2009) describe the flooding of June 

26-29 in parts of the Delaware River Basin and other basins in New York. Online summaries of 

flooding during June 2006 are provided by the Delaware River Basin Commission (2008b) and the U.S. 

Geological Survey (2008b). 

The magnitude and recurrence of floods have been evaluated by many previous authors and 

updated as the period of record has been extended. Schopp and Firda (2008) evaluate flood frequency 

and magnitude for the main-stem Delaware River to Trenton, N.J., updating the statistical model of 

flood recurrence using data from the three recent flood events. Roland and Stuckey (2007) present 

flood-frequency models for selected smaller streams in the basin. 

Rainfall-runoff and streamflow models have previously been developed for the study area. 

Flippo and Madden (1994) calibrated a streamflow-routing model for the Delaware River, with an 

emphasis on low-flow simulations. Chepiga and others (2004) developed a statistically based model of 

long-term runoff and water quality for the basin. Middle Atlantic River Forecast Center (MARFC)

(2006, 2007) simulated the impact of reservoir-void changes on downstream flood levels using the 

NWS flood-forecast model for the Delaware River, a model used operationally for flood forecasting. 

Rainfall-runoff and streamflow models have also been developed for smaller watersheds within 

the study area. Tolson and Shoemaker (2007) developed, calibrated, and validated a model of daily 

streamflow into Cannonsville Reservoir on the West Branch Delaware River. Kalin and Hantush (2006) 

compared the use of radar and rainfall data for modeling daily and monthly flows for the Pocono Creek 

watershed in Monroe County, Pa.

A daily reservoir model for the Delaware River above Trenton, OASIS (HydroLogics, Inc., 

2002), has been developed to simulate reservoir releases and downstream flows. Quinodoz (2006) 

describes the use of OASIS to support basin management and planning. Bovee and others (2007) used 

OASIS to develop a model for evaluation of fish habitat in stream reaches in the upper part of the basin, 

including a model of stream temperature.

Description of Study Area

The study area is the watershed of the Delaware River in the states of Pennsylvania, New Jersey, 

and New York that drains to Trenton, N.J. (fig. 1). The watershed is delineated on the basis of the area 

draining to the USGS streamgage on the Delaware River at Trenton, N.J. (USGS 01463500). This is the 

most downstream streamgage on the main stem that is not normally affected by tides. The watershed 

area above the Trenton streamgage is 6,780 mi2. The river length from the confluence of the West 

Branch Delaware River and the East Branch Delaware River at Hancock, N.Y., to Trenton, N.J., is 
6

approximately 200 mi. Watershed characteristics are briefly summarized in this report; additional 

detailed descriptions are provided by previous investigators, including Schopp and Firda (2008), Ayers 

and others (1994), Parker and others (1964), Fischer (1999), and Fischer and others (2004).

The Delaware River Basin has a temperate climate; seasonal and average yearly variations 

generally reflect variations in topography (Jenner and Lins, 1991). Average yearly temperature ranges 

from about 45°F in the north to 56°F in the south. Winter (December – February) monthly average 

temperature is slightly above freezing in the south and about 25°F in the north. The summer (June –

August) average ranges from almost 80°F in the south to 70°F in the north. 

Average annual precipitation ranges from 50 in. in the north to 42 in. in the south and is 

typically distributed evenly throughout the year (Jenner and Lins, 1991). The number of days with 

precipitation generally increases from the southern to the northern part of the basin, whereas the average 

intensity of precipitation for days when precipitation falls generally decreases from the southern to the 

northern part. Variation in mean annual precipitation within the basin is primarily related to elevation 

changes; higher precipitation amounts are related to higher elevations (Ayers and others, 1994).

Soils, vegetation, and topography differ considerably in the basin (Parker and others, 1964). The 

basin lies in four physiographic provinces (Parker and others, 1964). In the southern part of the study 

area, the topography varies from the rolling hills of the Piedmont Physiographic Province to a series of 

parallel ridges, oriented northeast-southwest, in the New England Physiographic Province. These two

provinces are characterized by relatively thin, clayey-loam soils, and streams respond quickly to rainfall. 

About one-third of the southern part of the study area is forested, primarily with hardwoods.

In the northern part of the study area, the Appalachian Plateaus and Valley and Ridge 

Physiographic Provinces are characterized by mountainous topography. Hillslopes are steep and covered 

by well-drained soils. Streamflow response to rainfall is delayed compared to the southern part of the 

study area. The northern part is the only part of the basin where snow accumulation is substantial in 

most years and the only part that once was glaciated. The northern part has numerous lakes and is 

mostly forested in hardwoods.

The Delaware River Basin is a vital water resource for the Nation. The daily average water use 

in the basin is about 4 billion gallons, more than one-half of which is for power generation. Public 

supply, industrial supply, and irrigation account for about 25, 15, and 1 percent, respectively, of the total 

water use. The Delaware River supplies large quantities of water to two of the largest metropolitan areas

in the Nation—New York City and Philadelphia (Fischer and others, 2004). Approximately 620 Mgal/d 

is exported from the basin to New York City, and another 100 Mgal/d is exported to northeastern New 

Jersey. The water-management system in the basin includes many surface reservoirs used for multiple 

purposes, including water supply, flow augmentation, and flood mitigation (table 1). Many of these 

reservoirs are also used to enhance fish and wildlife habitat and increase recreational opportunities 

(Delaware River Basin Commission, 2008a). 

Precipitation-Runoff Modeling System

The USGS PRMS (Leavesley and others, 1983; Leavesley and Stannard, 1995) software is a 

modular, physically based, distributed-parameter modeling system developed to evaluate the impacts of 

climate, topography, geology and land use on surface-water runoff and general basin hydrology. In 

PRMS, each component of the hydrologic system is simulated with known physical laws or empirical 

relations formulated on the basis of measurable watershed characteristics. The distributed-parameter and 

watershed-partitioning features of PRMS are designed to account for the spatial variation in watershed 

characteristics. The watershed is delineated into a series of contiguous spatial units, called hydrologic 

response units (HRUs), where the slope, land use, soil, geology, and precipitation distribution are 
7

similar. HRUs produce and receive flow to and from each other, to the atmosphere, and to the drainage 

network consisting of stream segments and lakes. Each HRU is considered homogeneous as to 

hydrologic response and is instantaneously and fully mixed. Areally weighted averages are computed 

for each characteristic that varies spatially within an individual HRU (Markstrom and others, 2008).

PRMS Modules

PRMS simulates a watershed as an interconnected series of reservoirs that represent a volume of 

finite capacity within each HRU. These reservoirs include water in the canopy, impervious area, 

snowpack, pervious portion of the soil zone—up to field capacity of the soil to rooting depth (capillary 

reservoir), pervious and impervious portions of the soil zone—between field capacity and total soil 

saturation (gravity reservoir), and water stored below the rooting zone—used to simulate groundwater

flow (groundwater reservoir). The gravity reservoir can be split into two reservoirs to simulate a 

relatively faster interflow response (preferential flow) to a precipitation or snowmelt event that is due to 

the presence of macropores within the soil zone. PRMS simulates groundwater flow and storage as a 

combined, finite-volume series of three reservoirs—the capillary, gravity, and preferential-flow 

reservoirs. Flow to and from each reservoir is in the form of evaporation from the canopy and 

impervious areas, sublimation from the snowpack, evapotranspiration from the capillary reservoir, 

interflow and recharge from the gravity reservoir, and groundwater flow from the groundwater

reservoir. Overland runoff is simulated on the basis of the antecedent conditions of the impervious, 

capillary, and gravity reservoirs. A cascading-flow procedure is used in PRMS (Markstrom and others, 

2008) to simulate overland flow, interflow, and groundwater discharge in a cascading pattern between 

HRUs and then to the drainage network. PRMS simulates flow in the stream-channel network as the 

sum of inflows to each stream segment without routing when using a time step of 1 day. For hourly 

simulation, an implicit kinematic wave algorithm is used for streamflow routing.

The PRMS architecture consists of various user-selected modules that represent the different 

components of the hydrologic system and that simulate the processes associated with them. On the basis 

of the issues being investigated, data availability, and appropriateness of an algorithm to a particular 

watershed, modelers can customize PRMS by selecting the most appropriate modules for a given

application. The modules selected for this study are listed in table 2 in computation order. New modules 

were added to PRMS for this study to 1) read preprocessed precipitation and air-temperature data by 

HRU, 2) generate specially formatted output for use as input to the HEC-ResSim model, and 3) simulate 

hourly snowpack processes using the NWS SNOW-17 model.

The PRMS modules, the HEC Data Storage System (HEC-DSS) library, and Modular Modeling 

System (MMS) utilities are compiled and linked to generate the model software used for rainfall-runoff 

simulation. PRMS modules are a group of subroutines that simulate a particular hydrologic or datahandling process. The HEC-DSS library and MMS utilities are not described in detail here. The HECDSS library (U.S. Army Corps of Engineers, Hydrologic Engineering Center, 2006) consists of a set of 

routines that enable retrieval and storage of input and results. The MMS utilities (Leavesley and others, 

1996, 2005) are similar to the HEC-DSS library in that they provide routines to read input and write 

output from a model simulation. In addition, the MMS utilities provide the means to access results from 

modules to be input to other modules. PRMS uses the internal data structure of MMS to make input data 

and model states and fluxes available between PRMS modeling components. 
Table 2. Precipitation-Runoff Modeling System (PRMS) modules used for the Delaware River main-stem subbasin, Pennsylvania, 

New Jersey, and New York.—Continued

[HRU, hydrologic response unit; GWR, groundwater reservoir]

PRMS model

module

PRMS 

module ID Description Reference

basin_prms 1 Computes shared watershed-wide physical parameters used by 

other modules and provides consistency checks of various input 

parameters

Markstrom and others, 2008

cascade_prms 2 Computes the routing order of cascading flow between HRUs and 

GWRs and performs consistency checks of the cascading parameters.

Markstrom and others, 2008

obs_prms 3 Reads and makes available observed precipitation, temperature, and 

solar-radiation data from specified measurement stations

Markstrom and others, 2008

climate_hru_prms 4 Reads and makes available NEXRAD precipitation data and temperature data preprocessed by HRUAppendix

ddsolrad_hru_prms 5 Distributes solar radiation to each HRU and estimates missing 

solar-radiation data using a maximum temperature per degree-day 

relation

Markstrom and others, 2008

potet_jh_prms 6 Determines whether current time period is one of active transpiration 

and computes the potential evapotranspiration using the JensenHaise formulation (Jensen and others, 1969)

Markstrom and others, 2008

intcp_prms 7 Computes volume of intercepted precipitation, evaporation from 

intercepted precipitation, and throughfall that reaches the soil or 

snowpack

Markstrom and others, 2008

snowcomp_prms 8 Initiates development of a snowpack and simulates snow accumulation and depletion processes using an energy-budget approach for 

daily time steps

Markstrom and others, 2008

srunoff_smidx_casc 9 Computes Hortonian surface runoff and soil infiltration for each 

HRU using a non-linear variable-source-area method and partitions precipitation and snowmelt to the pervious and impervious 

portions of each HRU allowing for cascading flow and computed 

evaporation from imperious portions of each HRU for 24-hour 

time steps

Markstrom and others, 2008

grnampt_infil_prms 10 Computes soil infiltration for each HRU using a Green and Ampt 

method and partitions precipitation and snowmelt to the pervious 

and impervious portions of each HRU allowing for cascading flow 

and computed evaporation from imperious portions of each HRU 

for sub-daily time steps

U.S. Geological Survey, 1992a

krout_ofpl_prms 11 Computes Hortonian surface runoff for each HRU using a modified 

kinematic routing method for each HRU allowing for cascading 

flow for sub-daily time steps

U.S. Geological Survey, 1992c

soilzone_prms 12 Computes inflows to and outflows from soil zone of each HRU and 

includes inflows from soil infiltration and upslope HRUs, and 

outflows as evapotranspiration and recharge and interflow and 

Dunnian surface runoff to down-slope HRUs and the drainage 

network

Markstrom and others, 2008

gwflow_casc_prms 13 Sums inflow to groundwater reservoirs and computes outflow to the 

drainage network allowing for cascading flow

Markstrom and others, 2008

krout_chan_prms 14 Routes flow in the drainage network using various Kinematic routing schemes for sub-daily time stepsU.S. Geological Survey, 1992b

strmflow_prms 15 Computes streamflow as the sum of overland runoff, interflow, and 

groundwater flow for daily time steps

Markstrom and others, 2008

8
Table 2. Precipitation-Runoff Modeling System (PRMS) modules used for the Delaware River main-stem subbasin, Pennsylvania, 

New Jersey, and New York.—Continued

[HRU, hydrologic response unit; GWR, groundwater reservoir]

PRMS model

module

PRMS 

module ID Description Reference

subbasin_prms 16 Computes streamflow as the sum of overland runoff, interflow, and 

groundwater flow for subbasins within a watershed

U.S. Geological Survey, 2007b

local_flow_drbc 17 Sums and outputs of overland runoff, interflow, and groundwater 

flow to hard-coded points (reservoirs and stream/river segments) 

within the Trenton basin to an HEC DSS file for use as input to 

HEC-ResSim. Also accumulates and outputs flows below nonmodeled reservoirs for use in calibration.

Apppendix

hru_sum_prms 18 Computes daily, monthly, yearly, and total flow summaries of volumes and flows for each HRUMarkstrom and others, 2008

basin_sum_prms 19 Sums values for daily, monthly, yearly, and total flow summaries of 

volumes and flows for all HRUs

Markstrom and others, 2008

snow17_st 20 Computes snow accumulation and ablation for storm mode Appendix

9
10

Model Documentation and Previous Applications

Documentation for the modeling system is available in the PRMS manual (Leavesley and others, 

1983) and the GSFLOW manual (Markstrom and others, 2008). GSFLOW is a coupled groundwater 

and surface-water flow model that uses PRMS for watershed computations. The GSFLOW manual 

provides the most up-to-date description for the majority of the simulation processes used in the PRMS 

model used in this study. PRMS and the parameterization methods used here have been used in 

numerous other applications, including the effects of urbanization on the spatial distribution of 

groundwater recharge (Vaccaro, 1992; Steuer and Hunt, 2001); water-resources management and 

forecasting (Fulp and others, 1995; Wilby and others, 1999; Berris and others, 2001; Mastin and 

Vaccaro, 2002; Hay and others, 2002; Hay and Clark, 2003; Clark and Hay, 2004; Yeung, 2005);

simulation of sediment production for semi-arid watersheds (Rankl, 1987); heat and water transfer for 

seasonally frozen soils (Emerson, 1991); use of radar data to specify rainfall input for flood simulation 

(Yates and others, 2000); streamflow and wetland storage (Vining, 2002); and flow-frequency 

characteristics (Olson, 2002).

Hourly Simulation Mode

PRMS was used with a daily time step for simulation of antecedent conditions (daily mode) and 

automatically switched to an hourly time step for simulation of storms (storm mode). This approach is 

computationally efficient for the relatively slow changes that occur under normal conditions between 

storms and provides sufficient detail and flood-wave simulation during storms. 

Flow routing in streams during storm mode is simulated through a kinematic wave approach 

(Leavesley and Stannard, 1995; Yates and others, 2000). Runoff components are cascaded from HRU to 

HRU in the downstream direction, until the runoff enters a stream channel or lake. Channel flow is 

accumulated and kinematically routed to downstream junctions and through the drainage network. The 

implicit finite-difference option was used for the kinematic-wave flow routing, and the module 

parameters were identified by calibration. 

Snowmelt

PRMS uses a daily energy-balance model to compute melt and runoff from snow for daily time 

steps (Leavesley and others, 1983). For storm mode, PRMS was modified to use the SNOW-17

algorithm from the River Forecast System of NOAA’s NWS (Anderson, 2006). This model is 

computationally efficient and uses hourly input data available for the study area, specifically

precipitation and air temperature. This model incorporates the diurnal variation of radiation and other 

processes that control snowmelt through an approximate model that is based on air temperature. The 

basis of the SNOW-17 algorithm and its parameters are described in detail by Anderson (2006). 

Additional information about SNOW-17 algorithms is provided in the appendix.

Output for Reservoir Model

PRMS was modified for this study to prepare data needed for simulation of reservoirs and 

streamflow routing downstream of reservoirs in the watershed. The USACE HEC has developed a 

general-purpose reservoir-simulation model, HEC-ResSim (U.S. Army Corps of Engineers, Hydrologic 

Engineering Center, 2007), and has developed a reservoir model for the Delaware River. Hourly runoff 

to reservoirs and local runoff to streams downstream of modeled reservoirs are computed by PRMS and 

used as input for HEC-ResSim. HEC-ResSim computes discharge from reservoirs and routes this flow, 

accumulating local runoff and tributary inflow downstream from modeled reservoirs. 
11

The output data provided from PRMS for use in HEC-ResSim are the time series of streamflow 

and local runoff into reservoirs and local runoff and tributary inflow for streams below modeled 

reservoirs. These PRMS output data are written to a HEC-DSS formatted file (trenton.dss). The HECDSS file format is a standard binary format developed by the HEC for storage of water-resources timeseries data and is used for input for HEC-ResSim. The HEC-DSSVue program (U.S. Army Corps of 

Engineers, Hydrologic Engineering Center, 2006) is available for viewing and working with data stored 

in HEC-DSS files. Incremental flows, which do not include flows simulated at headwater streamgages, 

are also provided in the DSS file for optional use with the HEC-ResSim model for simulations in which 

observed flows at the headwater streamgages can be used instead of simulated flows at those stations. 

Additional information about the modifications for preparing HEC-ResSim data is provided in the 

appendix. 

Use of Measured Reservoir Discharge

Reservoirs in the watershed are not simulated with PRMS, because those computations are 

conducted in the HEC-ResSim component of the Flood-Analysis Model. However, calibration of PRMS 

for local flows downstream of the reservoirs is based on comparison between simulated and measured 

streamflow, which includes the contributions of discharges from reservoirs. PRMS was modified to use 

measured reservoir discharges as the upstream inflow for simulation of downstream flows. Thus, the 

simulated flow at downstream streamgages is a combination of the measured discharge from the 

reservoir, routed to the streamgage, and local flows. This procedure allowed calibration of the model 

parameters that control the local flows downstream of the reservoirs. 

The local flows from PRMS are used as input for HEC-ResSim. However, HEC-ResSim 

simulates the reservoirs and produces reservoir outflows as an output of the simulation on the basis of

input data controlling the operations of the reservoirs. Thus, the use of measured reservoir outflows in 

the PRMS model calibration does not affect the simulated outflow from reservoirs in HEC-ResSim. 

Additional manual calibration of PRMS used simulated downstream flows from the HEC-ResSim 

model to improve the flow volume match. 

User Interface

User interaction with the Flood-Analysis Model is through a graphical user interface developed 

using the Object-User Interface (OUI) (Markstrom and Koczot, 2008). This interface allows the user to 

view PRMS input, to run the model components, and to view model output using a map-based scheme. 

The OUI software is integrated with two open-source, public-domain software packages, GeoTools 

(http://www.geotools.org/) sponsored by the Open Source Geospatial Foundation and National 

Aeronautics and Space Administration (NASA) World-wind (http://worldwind.arc.nasa.gov/java/), for 

geospatial processing and visualization, respectively.

The Flood-Analysis Model user interface is written using OUI and allows the user to change 

physical and simulation control parameters, including specifying input files and the time period for 

simulation, and to select output written to files and graphs. A brief guide to the user interface for the 

Flood-Analysis Model is provided online at http://pa.water.usgs.gov/drbfam. More detailed instructions 

on the functionality and customization of OUI are provided by Markstrom and Koczot (2008). 
12

Model Development

The PRMS model consists of the software, described in the previous section, and data input 

required for rainfall-runoff simulation. This section describes the procedures used to prepare input for, 

or parameterize, PRMS. 

A geospatial database was created for use with a geographic information system (GIS) to assist 

model discretization, to determine land-surface characterization, and to estimate PRMS model 

parameters. The combination of the GIS database and standard spatial processing techniques, similar to 

previously modeled watersheds (Battaglin and others, 1993; Jeton, 2000; Jeton and others, 1996), 

allowed the spatial variations of basin characteristics to be documented and objectively analyzed. All 

data sets in the database are in the same Cartesian coordinate system: Universal Transverse Mercator 

(UTM), zone 18 with NAD 83 as the horizontal control datum.

Elevation Data and Watershed Discretization

Topography, or altitude change on the land surface, is a primary factor in the distribution and 

rates of surface runoff. Hence, a primary input for PRMS is a digital elevation model (DEM) of the 

study area. For this study, the USGS National Elevation Dataset (NED) (U.S. Geological Survey, 

2007a) at 100-m resolution was used for the Delaware River Basin draining to Trenton, N.J. The DEM 

was pre-processed to specify locally low elevations at known stream locations in order to improve the 

match between known stream locations and those generated by automatic processing of the DEM. 

A PRMS model uses the concept of partitioning a watershed into spatial units on the basis of 

watershed characteristics such as elevation, slope, aspect, vegetation type, soil type, land use, and 

precipitation distribution. Initially, the watershed is delineated into stream segments with a minimum 

flow accumulation as determined by a GIS analysis. The DEM was processed using automated 

techniques suggested by the GIS Weasel (Viger and Leavesley, 2007) to create flow-direction and flowaccumulation raster data sets that produced an artificial stream raster on the basis of a selected 

maximum number of contributing cells that totaled approximately 15 mi2. This stream raster was 

manually edited to include selected elevation breaks in the DEM using analytical hillshading as a guide. 

These stream segments were then edited to represent the points at which runoff can be calibrated, at 

selected USGS streamgage locations. The stream network was also split by the outline of the 13 

simulated reservoirs and where very long stream segments might produce instability in computing 

streamflow using the implicit, finite-difference kinematic routing scheme used for sub-daily stream 

routing. 

An iterative procedure was used to discretize the watershed into HRUs and link those HRUs to a 

computational stream network. HRUs were initially generated using the DEM for the study area. The 

edited stream raster was then used to delineate the initial stream-segment contributing areas, or oneplane HRUs. The separate contributing surface areas to the left and right bank of each stream segment, 

two-plane HRUs, are required for storm-mode streamflow routing. These two-plane HRUs were created 

by using the stream raster and the DEM to determine the longest flow path to split the one-plane HRU 

into left- and right-bank drainages. After two-plane HRUs were converted from raster-format data into 

vector-format data, a spatial-join process was used to combine the reservoir polygons with the twoplane HRUs. A map of the reservoirs was overlain on the original HRUs, and simulated reservoirs were 

treated as a special type of HRU, a lake HRU. Manual editing was done as the final step to remove 

small-area HRUs or merge them into an adjacent, hydrologically similar HRU. The PRMS model of the 

Delaware above Trenton is composed of 869 HRUs and 452 stream segments (fig. 2). 
13

 

Figure 2. Location of hydrologic response units and simulated stream reaches for the Delaware River main-stem

subbasin, Pennsylvania, New Jersey, and New York.
14

The GIS Weasel also determined HRU-specific indices describing connectivity of HRUs with 

the stream network. The HRU responses were grouped by stream segments specific to each subbasin, 

and flow was routed through the stream-segment units in a downstream order, enabling output from the 

model to provide estimates of flow at any stream segment.

Watershed Characteristics Data

PRMS model parameters related to watershed properties controlling runoff were assigned to the 

discretized model, HRUs and streams, by processing available GIS coverages of soils, elevation, 

geology, land use, and other characteristics. These initial parameters were subsequently adjusted, in 

some cases, during model calibration. The parameterization methods used include those documented by 

Viger and Leavesley (2007), Battaglin and others (1993), Jeton (2000), and Koczot and others (2005). 

Additional selected parameterization methods recently developed for modeling runoff in Connecticut 

were also used (D.M. Bjerklie, U.S. Geological Survey, written commun., May 11, 2009). 

Digital spatial data were collected for the study in raster format (a gridded data structure made of 

rows and columns) and vector format (discrete coordinates that can be used as points or connected to 

create lines and polygons). The digital data included elevation, generalized geology, land cover, and 

soils. The sources for the spatial data included the USGS NED for elevation (U.S. Geological Survey, 

2007a) where slope and aspect calculations were derived using GIS software ArcGIS version 9.2; state 

geology data from New Jersey (New Jersey Department of Environmental Protection, 1996), New York 

(New York State Museum/New York Geological Survey, 1999), and Pennsylvania (Pennsylvania 

Department of Conservation and Natural Resources, 2001); land cover and impervious surface data 

from the 2001 National Land Cover Database (Multi-Resolution Land Characteristics Consortium, 

2001); and soils data originally from the State Soil Geographic (STATSGO) Database (Soil Survey 

Staff, 1994; Natural Resources Conservation Service, 2006) and further processed with value-added soil 

characteristics (Miller and White, 1998). Selected reclassification tables (Viger and Leavesley, 2007) 

were used with land-cover data to assist in refining the HRU characteristics. The sources of values for 

selected distributed PRMS model parameters are described in table 3, along with ranges of values used. 

Nondistributed parameters that apply to the entire model are described in table 4. 
Table 3. Source of parameter values for selected model hydrologic response unit (HRU) distributed parameters for the Delaware 

River main-stem subbasin, Pennsylvania, New Jersey, and New York (modified from Jeton, 2000; Koczot and others, 2005).—Continued

[CAL, parameters that (a) cannot be estimated from available data and are adjusted during calibration or (b) have initial estimates from measured or published 

data that were adjusted during calibration; DEF, parameters that are considered constant, as provided by Leavesley and others (1983); LIT, obtained from the 

literature as estimated or empirical estimates (Black, 1996, table 4-1, p. 93); GIS, computed in geographic information system from digital coverages; COM, 

computed from climatological data or other measured data]

Model parameter Description of model parameter Range of values Source of 

values

PRMS

module ID1

carea_max Maximum area contributing to surface runoff 

(decimal percent)

0.036–0.796 CAL 9

chan_alpha Kinematic routing parameter “a” for each channel 

segment

0.076–0.693 CAL 14

chan_cmp Kinematic routing parameter “m” for each channel segment1.67 DEF 14

chan_rough Roughness parameter for each channel segment 0.05 LIT 14

cov_type Vegetation cover type (developed-water-open, 

grasses-shrubs, mixed forest, coniferous forest)

Developed-water-open, 

grasses-shrubs, mixed forest, coniferous forest

GIS 7, 8,12

covden_sum Vegetation cover density for summer (decimal 

percent)

0–1.0 GIS 7, 8, 12, 18

covden_win Vegetation cover density for winter (decimal 

percent)

0–0.723 GIS 7, 8, 12, 18

drnpar Drainage factor for redistribution of saturate 

moisture storage to soil recharge as a function 

of hydraulic conductivity (inches/hour)

0.6 CAL 10

fastcoef_lin Linear coefficient in downslope routing equation 

for preferential-flow storage (day-1)

0.0048–0.1061 COM 12

fastcoef_sq Non-linear coefficient in downslope routing equation for preferential-flow storage0.80 DEF 12

ground_melt Daily rate of snowmelt at the snowpack-ground 

interface (millimeters per day)

0 DEF 8

gwflow_coef Groundwater routing coefficient to obtain the 

groundwater flow contribution to streamflow 

(day-1)

0.01–0.05 CAL 13

gwsink_coef Groundwater sink coefficient to compute the 

seepage from each reservoir to a groundwater 

sink (day-1)

0 DEF 13

gwstor_init Storage in each groundwater reservoir at the 

beginning of the simulation (inches)

0.208–4.407 CAL 13

hru_deplcrv Index number for snowpack depletion curve 1 DEF 8

hru_percent_imperv Portion of HRU area that is impervious (decimal 

percent)

0–0.43 GIS 1, 8, 18

imperv_stor_max Maximum impervious retention storage for the 

HRU (inches)

0.135–2.83 GIS 9, 10

jh_coef_hru Air-temperature coefficient used in the Jensen 

and Haise (1963) potential-evapotranspiration 

computations for each HRU

16.2–18.7 COM 6

kpar Hydraulic conductivity of the transmission zone 

(inches per hour)

1.53–5.00 CAL 10

melt_base Base temperature used in calculation of snowmelt 

during periods of no rain (degree Celsius)

0 DEF 8

15
Table 3. Source of parameter values for selected model hydrologic response unit (HRU) distributed parameters for the Delaware 

River main-stem subbasin, Pennsylvania, New Jersey, and New York (modified from Jeton, 2000; Koczot and others, 2005).—Continued

[CAL, parameters that (a) cannot be estimated from available data and are adjusted during calibration or (b) have initial estimates from measured or published 

data that were adjusted during calibration; DEF, parameters that are considered constant, as provided by Leavesley and others (1983); LIT, obtained from the 

literature as estimated or empirical estimates (Black, 1996, table 4-1, p. 93); GIS, computed in geographic information system from digital coverages; COM, 

computed from climatological data or other measured data]

Model parameter Description of model parameter Range of values Source of 

values

PRMS

module ID1

mf_max Annual maximum factor in snowmelt cycle 

(millimeters per degree Celsius per day )

0.50–7.94 CAL 8

mf_min Annual minimum factor in snowmelt cycle 

(millimeters per degree Celsius per day)

0.13–3.99 CAL 8

negmf_max Maximum negative snowmelt factor 

(millimeters per degree Celsius per day)

0.6 DEF 8

ofp_alpha Kinematic routing parameter “a” for overland 

flow plane

0.003 DEF 11

ofp_cmp Kinematic routing parameter “m” for overland 

flow plane

1.67 DEF 11

ofp_impv_alpha Kinematic routing parameter “a” for impervious 

overland flow

2.0 DEF 11

ofp_impv_cmp Kinematic routing parameter “m” for impervious 

overland flow

1.67 DEF 11

ofp_rough Roughness parameter for overland flow plane 0.005 DEF 11

ofp_thresh Minimum depth of flow to continue overland flow 

routing (inches)

0.00001 CAL 11

pref_flow_den Preferential-flow pore density (decimal percent) 0–0.127 GIS 12

psp Product of moisture deficit and capillary drive for 

soil recharge equal to field capacity (inches)

5.208–24.997 CAL 10

rad_trncf Transmission coefficient for short-wave radiation 

through the winter canopy (decimal percent)

0.196–0.935 COM 8

rain_sub_adj Monthly adjustment to rainfall by subbasin 0.6–3.0 CAL 4

rgf Ratio of psp at field capacity to psp at wilting 

point

9.5 DEF 10

sat_threshold Soil saturation threshold (inches) 3.00–8.86 COM 12

sat_threshold_adj Adjustment factor for total soil saturation capacity 1.25 DEF 12

slowcoef_lin Linear gravity-flow reservoir routing coefficient 

(day-1)

0.00031–0.00697 COM 12

slowcoef_sq Non-linear gravity-flow reservoir routing coefficient0.1 DEF 12

smidx_coef Coefficient in the nonlinear contributing area 

algorithm computing surface runoff (decimal 

fraction)

0.0001–0.8473 CAL 9

smidx_exp Exponent in nonlinear contributing area algorithm 

computing surface runoff (inch-1)

0.205–0.787 CAL 9

snarea_thresh Maximum snow water equivalent below which 

the snow-covered area depletion curve is applied (inches)

0.075–7.490 COM 8

snow_intcp Snow interception storage capacity for the major 

vegetation type on an HRU (inches)

0.00047–0.06673 GIS 7

snow_sub_adj Monthly adjustment to snowfall by subbasin 1.0–2.875 CAL 4

16
Table 3. Source of parameter values for selected model hydrologic response unit (HRU) distributed parameters for the Delaware 

River main-stem subbasin, Pennsylvania, New Jersey, and New York (modified from Jeton, 2000; Koczot and others, 2005).—Continued

[CAL, parameters that (a) cannot be estimated from available data and are adjusted during calibration or (b) have initial estimates from measured or published 

data that were adjusted during calibration; DEF, parameters that are considered constant, as provided by Leavesley and others (1983); LIT, obtained from the 

literature as estimated or empirical estimates (Black, 1996, table 4-1, p. 93); GIS, computed in geographic information system from digital coverages; COM, 

computed from climatological data or other measured data]

Model parameter Description of model parameter Range of values Source of 

values

PRMS

module ID1

snowinfil_max Maximum infiltration rate for snowmelt 

(inches per day)

2.727–3.943 CAL 9

soil2gw_max Amount of soil water excess for an HRU that is 

routed directly to the associated groundwater 

reservoir each day (inches)

0.00002–0.35233 CAL 12

soil_moist_adj Adjustment factor for soil_moist_max parameter 1.0 DEF 12

soil_moist_init Initial value of available water in soil profile 

(inches)

0.076–1.30 GIS 12

soil_moist_max Maximum available water-holding capacity of 

soil profile (inches)

0.00024–19.993 CAL 9, 12

soil_rechr_init Initial value for available water in the soil recharge zone (inches) (upper soil zone)1.0 DEF 12

soil_rechr_max Maximum value for available water in the soil 

recharge zone (inches)

0.00008–19.0275 CAL 12

soil_type HRU soil type (sand, loam, or clay) Sand or loam GIS 12

srain_intcp Summer interception storage capacity for the 

major vegetation type on an HRU (inches)

0.00073–0.05 GIS 7

ss2gw_rate Coefficient to route water from subsurface reservoirs to groundwater reservoirs (day-1)

0.08521–0.12322 COM 12

ssrmax_coef Coefficient to route water from subsurface reservoirs to groundwater reservoirs (inches)1.0 DEF 12

ssstor_init Initial storage in each subsurface reservoir 

(inches)

0 DEF 12

transp_beg Month to begin summing maximum temperature 

for each HRU; when sum is greater than or 

equal to TRANSP_TMAX transpiration begins

April–May LIT 6

transp_end Month to stop transpiration November LIT 6

transp_tmax Temperature index to determine the specific date 

of the start of the transpiration period (degrees)

0–1,000 COM 6

wind_adjust Rate of snowmelt due to wind effects (millimeters 

per millibar per day)

0.0344–0.9956 CAL 8

wpcoef_a Wetted perimeter coefficient “a” 0 DEF 14

wpcoef_b Wetted perimeter coefficient “b” 0 DEF 14

wrain_intcp Winter rain interception storage capacity for the 

major vegetation type on an HRU (inches)

0.0005–0.0357 GIS 7

1

PRMS modules are listed on table 2.

17
Table 4. Selected whole-model nondistributed parameters estimated by calibration and ranges of values for the Delaware River 

main-stem subbasin, Pennsylvania, New Jersey, and New York (modified from Jeton, 2000; Koczot and others, 2005).—Continued

[DEF, parameters that are considered constant, as provided by Leavesley and others (1983); LIT, obtained from the literature as estimated or empirical estimates (Black, 1996, table 4-1, p. 93); CAL, parameters that (a) cannot be estimated from available data and are adjusted during calibration or (b) have initial 

estimates from measured or published data that were adjusted during calibration; ET, evapotranspiration; HRU, hydrologic response unit]

Model

parameter Description of model parameter Range of values Source of values

PRMS 

module ID1

albset_rna Proportion of rain in a rain-snow event above which the snow albedo is 

not reset; snowpack accumulation stage (decimal percent)

0.8 DEF 8

albset_rnm Proportion of rain in a rain-snow event above which the snow albedo is 

not reset; snowpack melt stage (decimal percent)

0.6 DEF 8

albset_sna Minimum snowfall, in water equivalent, needed to reset snow albedo during the snowpack accumulation stage (inches)0.05 DEF 8

albset_snm Minimum snowfall, in water equivalent, needed to reset snow albedo during the snowpack melt stage (inches)0.2 DEF 8

cecn_coef Monthly convection condensation coefficient 

(calories per degree Celsius above 0 degrees Celsius)

5.0 DEF 8

chan_chi Finite difference weighting factor for each channel segment (decimal 

percent)

0.6 DEF 14

chan_theta Finite-difference spatial weighting factor for each channel segment (decimal percent)0.5 DEF 14

dday_intcp Monthly intercept in degree-day relation when estimating potential solar 

radiation (degree-days)

(-45)–(-6) LIT 5

dday_slope Monthly slope in degree-day relation when estimating potential solar 

radiation (degree-days per degree)

0.31–0.65 LIT 5

den_init Initial density of new-fallen snow (grams per cubic centimeter) 0.1 DEF 8

den_max Average maximum density of snowpack (grams per cubic centimeter) 0.6 DEF 8

emis_noppt Average emissivity of air on days without precipitation 0.757 DEF 8

freeh2o_cap Free-water holding capacity of snowpack 0.05 DEF 8

ground_melt Daily rate of snow melt at the snowpack_ground interface 

(millimeters per day)

0 DEF 8

jh_coef Monthly air-temperature coefficient used in the Jensen and Haise (1963) 

potential-evapotranspiration computations.

0.0038–0.0068 LIT 6

melt_base Base temperature used in calculation of snowmelt during periods of no 

rain (degree Celsius)

0 DEF 8

melt_look Julian date to start looking for spring snowmelt 30 CAL 8

melt_force Julian date to force snowpack to spring snowmelt 60 CAL 8

mf_curve Monthly snowmelt curve factor 0.5 DEF 8

ofp_chi Finite difference weighting factor for overland flow routing 0.6 DEF 11

ofp_theta Finite-difference spatial weighting factor for overland flow routing 0.5 DEF 11

potet_sublim Proportion of potential ET sublimated from snow surface 0.75 CAL 7, 8

potet_sublim_st Proportion of potential ET sublimated from snow surface in storm mode 0.75 DEF 8

ppt_rad_adj Solar radiation reduced if precipitation exceeds this value (inches) 0.02 DEF 5

radadj_intcp Intercept in temperature-solar radiation relation (degree-day) 1 DEF 5

radadj_slope Slope in temperature-solar radiation relation (degree-day per degree) 0 DEF 5

radj_sppt Adjustment factor for computed summer solar radiation when precipitation is greater than ppt_rad_adj0.44 DEF 5

radj_wppt Adjustment factor for computed winter solar radiation when precipitation 

is greater than ppt_rad_adj

0.5 DEF 5

18
Table 4. Selected whole-model nondistributed parameters estimated by calibration and ranges of values for the Delaware River 

main-stem subbasin, Pennsylvania, New Jersey, and New York (modified from Jeton, 2000; Koczot and others, 2005).—Continued

[DEF, parameters that are considered constant, as provided by Leavesley and others (1983); LIT, obtained from the literature as estimated or empirical estimates (Black, 1996, table 4-1, p. 93); CAL, parameters that (a) cannot be estimated from available data and are adjusted during calibration or (b) have initial 

estimates from measured or published data that were adjusted during calibration; ET, evapotranspiration; HRU, hydrologic response unit]

Model

parameter Description of model parameter Range of values Source of values

PRMS 

module ID1

radmax Maximum portion of potential solar radiation that reaches ground after 

atmospheric interferences (haze, dust, smog, etc.) (decimal percent)

0.8 DEF 5

rain_min Minimum rainfall rate triggering rain-on-snow melt estimates 

(millimeters per hour)

0.25 DEF 8

settle_constant Snowpack settlement time constant 0.1 DEF 8

snarea_curve Snow area depletion curves values 0.05–1.0 CAL 8

sntemp_thresh Threshold snowfall rate above which the temperature index of snowpack 

is reset to temperature of new snowfall (millimeters per hour)

1.5 DEF 8

tmax_allrain Precipitation all rain if maximum HRU temperature is equal to or greater 

than this monthly value (degrees)

44 CAL 5

tmax_allsnow Precipitation all snow if maximum HRU temperature is equal to or less 

than this value (degrees)

32 DEF 8

tmax_index Index temperature used to determine precipitation adjustments to solar 

radiation (degrees)

30–70 CAL 5

tstorm_mo Months when convective storms are prevalent May–Sept LIT 8

1

PRMS modules are listed on table 2.

19
20

The PRMS parameter hru_percent_imperv, the HRU impervious surface as a decimal percent of 

the total HRU area, is determined using GIS processing of the land cover and impervious area data sets. 

The land cover and impervious surface for the study area are shown in figures 3 and 4, and the resultant 

hru_percent_imperv values assigned to each HRU are shown in figure 5. The HRU value of the 

parameter is the average percent impervious for each of the land-cover rasters that fall within the HRU 

polygon, scaled by a factor to account for isolated impervious areas that drain to pervious areas, and do 

not directly contribute to rapid runoff. The scale factor yields an effective impervious surface area that 

is less than the actual area, with a smaller reduction for ―urban‖ HRUs where the actual impervious area 

is larger than 10 percent. The scale factor formulae were determined by analysis of storm runoff in 

Connecticut by Bjerklie and others (D.M. Bjerklie, U.S. Geological Survey, written commun., 2008)

and from previous studies (Alley and Veenhuis, 1983; Sutherland, 1995, 2005). The land-cover data set 

was used for verification, adjusting impervious area where the land cover is not developed, and was 

used for estimation of other parameters, such as those controlling evapotranspiration. Similar procedures 

were used for determining initial values of other model parameters from raster data sets. 

The PRMS model includes storm-mode simulation and, hence, includes cascading of runoff 

from HRU to HRU, eventually to stream segments and lakes, and flow routing in stream segments. 

Markstrom and others (2008, p. 33-34) describe the model parameters controlling cascading, which 

were identified through calibration for this study. 
21

 

Figure 3. Land-cover data for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New 

York, 2001 (data from Multi-Resolution Land Characteristics Consortium, 2001).
22

 

Figure 4. Impervious-surface data for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and 

New York, 2001 (data from Multi-Resolution Land Characteristics Consortium, 2001).
23

 

Figure 5. Mean percent impervious values for model hydrologic response units (HRUs) for the Delaware River 

main-stem subbasin, Pennsylvania, New Jersey, and New York.
24

Climate Data

Climate time-series data – precipitation, air temperature, and solar radiation – are primary input 

data for PRMS. PRMS operates in two modes, daily and storm, using climate time-series data with time 

steps of 1 day and 1 hour, respectively. The model operates using a daily time step (daily mode) for 

periods before and after the storm events and switching to an hourly time step during storm periods

(storm mode). Daily-mode data consisted of total daily precipitation, minimum daily air temperature, 

maximum daily air temperature, and total daily solar radiation. Storm-mode data consisted of total 

hourly precipitation and total hourly solar radiation. Units of measurement used in the model are inches 

for precipitation, degrees Fahrenheit for temperature, and Langleys for solar radiation.

Climate Station Data

Climate data for point stations were obtained from multiple sources. These sources included 

daily data for 22 NWS Cooperative Climate Station (COOP) network stations, hourly data for 15 

stations from the National Climatic Data Center (NCDC), hourly data for 1 station from MARFC

records, and daily and hourly data for 7 stations operated by the New York City Department of 

Environmental Protection (NYCDEP) (fig. 6, table 5). Daily data were retrieved for the period January 

1980 through December 2007. Not all data covered the complete period. Hourly data were retrieved for 

three storm periods: September 13, 2004, through September 27, 2004; March 24, 2005, through April 

14, 2005; and June 19, 2006, through July 9, 2006. Because the availability of hourly climate data is 

limited both in areal coverage and location, not all hourly data were collocated with daily data stations 

and six daily stations had no corresponding hourly stations. Thirteen hourly stations were at varying 

distances from their associated daily station. 

Daily precipitation and temperature data originated from the COOP network and NYCDEP 

meteorological stations. The COOP data were retrieved with Downsizer (Ward-Garrison & others, 

2009; U.S. Geological Survey, 2008a), an automated program that performs quality-assurance/qualitycontrol (QA/QC) checks and formats the data suitable for input directly to PRMS. The NYCDEP daily 

data were limited to at most the period 1994 through 2006. Automated and manual QA/QC were 

performed by NYCDEP up to the end of calendar year 2005. Data for 2006 did not undergo an agency 

QA/QC check and should be considered provisional (Glenn Horton, New York City Department of 

Environmental Protection, written commun., 2007). 

Hourly precipitation and temperature data originated from NCDC quality-controlled local 

climate data (National Climatic Data Center, 2007) and NYCDEP meteorological stations. No 

additional QA/QC was performed on NCDC hourly data. Additional QA/QC for NYCDEP hourly data 

consisted of completion of missing time-series entries, parsing for missing or phantom precipitation by 

comparison to adjacent stations, and visual comparison with radar traces plotted against station locations 

in a GIS environment using the Java NEXRAD viewer (National Climatic Data Center, 2008).
Table 5. Selected climate stations in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.—Continued

[COOP, National Weather Service Cooperative Climate Network; DP, Daily precipitation; DT, Daily temperature; NYCDEP, New York City Department of 

Environmental Protection; HP, Hourly precipitation; HT, Hourly temperature; MARFC, Middle Atlantic River Forecast Center; NCDC, National Climate Data 

Center]

Station name State Source Source

designation

Station

altitude

(feet)

Type

Flemington 5 NNW N.J. COOP 283029 260 DP, DT

Hightstown 2 W N.J. COOP 283951 100 DP, DT

Little Falls N.J. COOP 284887 150 DP, DT

Moorestown N.J. COOP 285728 45 DP, DT

Sussex 2 NE N.J. COOP 288644 649 DP, DT

Binghamton WSO Airport N.Y. COOP 300687 1,600 DP, DT

Delhi 2 SE N.Y. COOP 302036 1,440 DP, DT

Deposit N.Y. COOP 302060 1,000 DP, DT

Lansing Manor N.Y. COOP 304575 1,100 DP, DT

Liberty 1 NE N.Y. COOP 304731 1,549 DP, DT

Slide Mountain N.Y. COOP 307799 2,650 DP, DT

Walden 1 ESE N.Y. COOP 308906 380 DP, DT

Walton 2 N.Y. COOP 308932 1,480 DP, DT

Allentown AP Pa. COOP 360106 390 DP, DT

Blue Marsh Lake Pa. COOP 360785 350 DP, DT

Graterford 1 E Pa. COOP 363437 240 DP, DT

Neshaminy Falls Pa. COOP 366194 60 DP, DT

Palm 3 SE Pa. COOP 366681 300 DP, DT

Pleasant Mount 1 W Pa. COOP 367029 1,799 DP, DT

Reading 4 NNW Pa. COOP 367322 360 DP, DT

Tobyhanna Pocono Mountain A Pa. COOP 368893 1,916 DP, DT

Wilkes Barre WSO Airport Pa. COOP 369705 930 DP, DT

Cannonsville Dam near Stilesville N.Y. NYCDEP DCM074 1,169 DP, DT, HP, HT

Tymeson Farm on Dunk Hill Road near Walton N.Y. NYCDEP DCM076 2,091 DP, DT, HP, HT

Eklund Farm on Bruce Hill Road near Stamford N.Y. NYCDEP DCM077 2,242 DP, DT, HP, HT

Big Bend Club on Hunter Road near Claryville N.Y. NYCDEP DNM147 2,200 DP, DT, HP, HT

Pepacton Dam near Downsville N.Y. NYCDEP DPM110 1,200 DP, DT, HP, HT

Hillriegel Farm on Millbrook near Margaretville N.Y. NYCDEP DPM111 2,199 DP, DT, HP, HT

Triple View Farm on Sally’s Alley near Vega N.Y. NYCDEP DPM112 2,248 DP, DT, HP, HT

Pleasant Mount GOES Pa. MARFC PLXP1 1,810 HP

Somerset County Airport N.J. NCDC SMQ 100 HP, HT

Trenton-Mercer County Airport N.J. NCDC TTN 213 HP, HT

Caldwell-Essex County Airport N.J. NCDC CDW 174 HP, HT

South Jersey Regional Airport N.J. NCDC VAY 53 HP, HT

Sussex County Airport N.J. NCDC FWN 421 HP, HT

Binghamton Link Field Airport N.Y. NCDC BGM 1,637 HP, HT

Monticello-Sullivan County Airport N.Y. NCDC MSV 1,403 HP, HT

Montgomery-Orange County Airport N.J. NCDC MGJ 365 HP, HT

Allentown-Bethlehem Airport Pa. NCDC ABE 384 HP, HT

25
Table 5. Selected climate stations in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.—Continued

[COOP, National Weather Service Cooperative Climate Network; DP, Daily precipitation; DT, Daily temperature; NYCDEP, New York City Department of 

Environmental Protection; HP, Hourly precipitation; HT, Hourly temperature; MARFC, Middle Atlantic River Forecast Center; NCDC, National Climate Data 

Center]

Station name State Source Source

designation

Station

altitude

(feet)

Type

Pottstown-Limerick Airport Pa. NCDC PTW 309 HP, HT

Northeast Philadelphia Airport Pa. NCDC PNE 119 HP, HT

Doylestown Airport Pa. NCDC DYL 385 HP, HT

Reading-Spatz Field Pa. NCDC RDG 353 HP, HT

Mount Pocono Airport Pa. NCDC MPO 1,894 HP, HT

Wilkes Barre Airport Pa. NCDC AVP 962 HP, HT

26
27

 

Figure 6. Locations of selected National Oceanic and Atmospheric Administration meteorological stations in the 

Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York. 
Table 6. Solar-radiation stations used for model data for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and 

New York.

[NSRDB, National Renewable Energy Laboratory National Solar Radiation Database; NRCC, Northeast Regional Climate Center; NYCDEP, New York City 

Department of Environmental Protection]

Station name State Source1 Source

designation

Station

altitude

(feet)

Philadelphia International Airport Pa. NSRDB; NRCC 724080; KPHL 28

Belmar-Farmingdale Airport N.J. NSRDB; NRCC 724084; BLM 159

Northeast Philadelphia Airport Pa. NSRDB; NRCC 724085; PNE 119

Willow Grove Naval Air Station Pa. NSRDB 724086 362

Caldwell-Essex County Airport N.J. NSRDB; NRCC 724094; CDW 174

Trenton-Mercer County Airport N.J. NSRDB; NRCC 724095; TTN 213

McGuire Air Force Base N.J. NSRDB; NRCC 724096; WRI 133

Montgomery-Orange County Airport N.J. NSRDB; NRCC 725015; MGJ 365

Doylestown Airport Pa. NSRDB; NRCC 725113; DYL 385

Wilkes Barre Airport Pa. NSRDB; NRCC 725130; AVP 962

Monticello-Sullivan County Airport N.Y. NSRDB; NRCC 725145; MSV 1,403

Binghamton Link Field Airport N.Y. NSRDB; NRCC 725150; BGM 1,637

Allentown-Bethlehem Airport Pa. NSRDB; NRCC 725170; ABE 384

Albany County Airport N.Y. NSRDB 725180 292

Mount Pocono Airport Pa. NSRDB; NRCC 725434; MPO 1,916

Cannonsville Dam near Stilesville N.Y. NYCDEP DCM074 1,169

Tymeson Farm on Dunk Hill Road near Walton N.Y. NYCDEP DCM076 2,091

Eklund Farm on Bruce Hill Road near Stamford N.Y. NYCDEP DCM077 2,242

Big Bend Club on Hunter Road near Claryville N.Y. NYCDEP DNM147 2,200

Pepacton Dam near Downsville N.Y. NYCDEP DPM110 1,200

Hillriegel Farm on Millbrook near Margaretville N.Y. NYCDEP DPM111 2,199

Triple View Farm on Sally’s Alley near Vega N.Y. NYCDEP DPM112 2,248

1

 Data transitions from NSRDB to NRCC on 1/1/2006.

28
29

Solar-radiation data for 15 airports and 7 NYCDEP locations (table 6) were obtained from the 

National Renewable Energy Laboratory National Solar Radiation Database (NSRDB), the Northeast 

Regional Climate Center (NRCC), and the NYCDEP. Data for 1980 through 2005 consisted of hourly 

METSTAT modeled and measured values of global horizontal radiation published by the NSRDB for 

the airport locations (National Renewable Energy Laboratory, 1992, 2007). Daily solar-radiation data 

for this period were generated by aggregation of hourly data. For 2006 through 2007, solar-radiation 

data at 13 airport sites consisted of hourly and daily estimates of total (global) horizontal radiation 

produced by the NRCC on the basis of a modified Meyers and Dale model (DeGaetano and others, 

1993). If data were not available for an hour, available data from a nearby location were substituted. A 

considerable amount of data was missing for Monticello (MSV). Nearby Stewart Field was the backup 

station, and its data were used extensively in the Monticello files (Keith Eggleston, Northeast Regional 

Climate Center, written commun., 2008). No additional QA/QC was performed on NSRDB and NRCC 

solar-radiation data. The NYCDEP hourly solar-radiation data consisted of measured values collected at 

seven locations and covered 1994 through 2006. QA/QC for NYCDEP hourly solar-radiation data 

consisted of parsing for gross radiation errors on the basis of adjacent stations, time of observation 

errors, duplicate values, and non-zero values during night periods. NYCDEP solar data consisted of 

hourly data aggregated to total daily. 

Review of the temperature and precipitation data quality and initial model-calibration efforts 

indicated that these hourly station data could not be used in the model-calibration procedures. In 

particular, available calibration tools for the model were not compatible with different locations for 

daily and hourly gages. New procedures were developed to estimate the hourly temperature from daily 

minimum and maximum temperature and to estimate hourly and daily precipitation from NWS hourly 

radar data.

Estimation of Hourly Temperature Using Daily Station Data

New procedures were developed to estimate the hourly temperature from daily minimum and 

maximum temperature. Daily maximum and minimum temperature were produced for each HRU using 

PRMS in daily mode, and the xyz distribution technique documented by Hay and others (2000), Hay and 

Clark (2003), and Hay and others (2002). The daily values were used with a modeled hourly 

temperature variation to produce hourly values of temperature for each HRU.

The method of Erbs and others (1983) was used to estimate the hourly temperature at daily 

station locations from daily minimum and maximum values. This method was compared against other 

air-temperature models by Bilbao and others (2002) and shown to perform well and can be adapted to 

work at daily timescale. For each simulation day in storm mode, the hourly temperature for a HRU, 

T(ihr), was computed from the daily maximum temperature (tmax) and minimum temperature (tmin) for 

the HRU:

T(ihr) = tavg + ( A * ( 0.4632 * cos( x - 3.805 ) + 0.0984 * cos( 2x - 0.360 ) (1)

 + 0.0168 * cos( 3x - 0.822 ) + 0.0138 * cos( 4x – 3.513 ) ) )

where tavg = (tmax-tmin)/2

A = (tmax-tmin)

x = (2.0*3.14159265) * (ihr-1)/24

ihr = index of hour of the day, from 1 to 24
30

Precipitation Estimated from Radar Data

The NWS Multisensor Precipitation Estimate (MPE) data set was used for precipitation input 

during daily and storm simulations with PRMS and was provided for this study by NOAA’s NWS 

MARFC (Joseph Ostrowski, NWS Middle Atlantic River Forecast Center, written commun., 2008). The 

MPE is a 4-km resolution gridded data set that is based on NEXRAD radar precipitation measurements. 

The original NEXRAD values are adjusted by NWS to improve the accuracy and reduce bias using 

land-based gage measurements. National Weather Service, Hydrology Laboratory (2009) provides 

background information and technical details on the MPE data sets. The hourly totals MPE data set used 

for this study covers the Delaware River Basin for 2001-2007. An example of the MPE data for 9 a.m.

Eastern Standard Time (EST) on September 18, 2004, is shown in figure 7.

The MPE data sets were preprocessed to reduce computations during PRMS simulations. The 

MPE was provided as a XMRG formatted data set of hourly totals. This was converted to two text file 

format data sets for subsequent simulation: (1) a data set of hourly precipitation by HRU, and (2) a data

set of daily precipitation by HRU. These text files are much smaller than the original gridded data set, 

have times converted from GMT to EST, and incorporate mapping of the MPE grid values to the HRUs 

using a simple area-weighted average. For example, figure 8 shows the model precipitation by HRU for 

9 a.m. EST on September 18, 2004. Hourly totals were summed for the daily data set. 

 

Figure 7. National Weather Service Multi-sensor Precipitation Estimate (MPE) hourly data for 9 a.m. Eastern 

Standard Time on September 18, 2004, used for model data for the Delaware River main-stem subbasin, 

Pennsylvania, New Jersey, and New York.
31

 

Figure 8. Model hourly precipitation for 9 a.m. Eastern Standard Time on September 18, 2004, for Hydrologic 

Response Units (HRUs) for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New 

York.
32

Model Application 

Calibration and Testing 

Calibration of PRMS included regression and optimization algorithms, as well as manual 

adjustments. The general goal of the calibration procedure was to minimize the difference between 

streamflow (discharge) measured at USGS streamgages and the corresponding discharge simulated by 

PRMS. 

The normalized root mean square error (NRMSE) is an objective function that measures the 

overall difference between the simulated and observed streamflows. For the daily values, NRMSEd is 

defined as 

⎛ 1/ 2 ndays

∑( ) ⎞ ⎜ MSD − SIM 2

n n ⎟

NRMSEd = ⎜ n=1 ⎟ ⎜ ndays (2) ⎟ n − ⎜ ∑( ) MSD MN 2

⎟ ⎝ n=1 ⎠

where n is the day index; ndays is the total number of days; and MSD, SIM, and MN are the observed, 

simulated, and mean observed daily flow. The mean observed daily flow, MN, is computed for the days 

of the simulation period only. If NRMSE = 0, then the simulated flows are identical to the observed 

flows. A value of NRMSE = 1 indicates that the sum of squared differences between the observed and 

simulated flows is the same as the sum of squared differences between the observed flows and the mean 

observed flow. 

For the hourly values, NRMSEh is defined as 

⎛

⎜ ( ) ⎞

1/ 2 nhours

∑ MSHm − SIMH 2

m ⎟

NRMSE = ⎜ m=1 ⎟

h ⎜ nhours (3)

MSH − ⎜ ∑( )2 ⎟ m MNH ⎟ ⎝ m=1 ⎠

where m is the hour index; nhours is the total number of hours; and MSH, SIMH, and MNH are the 

observed, simulated, and mean observed hourly flow. The mean observed hourly flow, MNH, is 

computed for the hours of the storm-mode simulation only. 

Daily and hourly streamflow data from 42 USGS streamgages (table 7 and fig. 9) were acquired 

for use in model calibration. Simulated streamflow was compared to data from 35 streamgages at 

corresponding locations, and streamflow data from the other 7 streamgages were used as reservoir 

discharge for calibration at downstream locations. The streamflow data represent areas draining from 

20.2 to 6,780 mi2

. Streamflow data were collected by the USGS using techniques described by Rantz 

and others (1982). Continuous streamflow data were retrieved from the National Water Information 

System (NWIS) (Hoopes, 2004; Sauer, 2002). The hourly calibration simulations included three time 

periods before, during, and after high-flow events: September 13 to 27, 2004; March 24 to April 14, 

2005; and June 19 to July 9, 2006. 
Table 7. Streamgages selected for use in model calibration for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, 

and New York.

[Use codes: C, calibration; R, reservoir discharge; NRMSEd and NRMSEh, normalized root mean square error, daily and hourly respectively]

Drainage U.S. Geological Model daily Model hourly area Survey station Station name Use fit statistic fit statistic (square number NRMSE miles) d NRMSEh

01413500 East Branch Delaware River at Margaretville, N.Y. 163 C 1.26 0.43

01414000 Platte Kill at Dunraven, N.Y. 34.9 C .83 .45

01414500 Mill Brook near Dunraven, N.Y. 25.2 C .98 .70

01415000 Tremper Kill near Andes, N.Y. 33.2 C 1.03 .60

01417000 East Branch Delaware River at Downsville, N.Y. 372 R

01417500 East Branch Delaware River at Harvard, N.Y. 458 C .16 .32

01420500 Beaver Kill at Cooks Falls, N.Y. 241 C 1.01 .45

01421000 East Branch Delaware River at Fishs Eddy, N.Y.

1 784 C .54 .25

01423000 West Branch Delaware River at Walton, N.Y. 332 C .60 .25

0142400103 Trout Creek near Trout Creek, N.Y. 20.2 C .67 .49

01425000 West Branch Delaware River at Stilesville, N.Y. 456 R

01426000 Oquaga Creek at Deposit, N.Y. 67.6 C .74 .45

01426500 West Branch Delaware River at Hale Eddy, N.Y. 595 C .19 .21

01427510 Delaware River at Callicoon, N.Y. 1,820 C .45 .20

01428500 Delaware River above Lackawaxen River near Barryville, N.Y. 2,020 C .50 .23

01428750 West Branch Lackawaxen River near Aldenville, Pa. 40.6 C .87 .46

01429000 West Branch Lackawaxen River at Prompton, Pa. 59.7 R

01429500 Dyberry Creek near Honesdale, Pa. 64.6 R

01431500 Lackawaxen River at Hawley, Pa. 290 C .60 .37

01432900 Mongaup River at Mongaup Valley, N.Y. 76.6 C .74 .28

01434000 Delaware River at Port Jervis, N.Y. 3,070 C .64 .22

01435000 Neversink River near Claryville, N.Y. 66.6 C 1.39 .57

01436000 Neversink River at Neversink, N.Y. 92.6 R

01436690 Neversink River at Bridgeville, N.Y. 171 C .52 .42

01437500 Neversink River at Godeffroy, N.Y. 307 C .59 .39

01438500 Delaware River at Montague, N.J. 3,480 C .64 .23

01439500 Bush Kill at Shoemakers, Pa. 117 C .78 .36

01440000 Flat Brook near Flatbrookville, N.J. 64 C .55 .42

01442500 Brodhead Creek at Minisink Hills, Pa. 259 C .83 .35

01443500 Paulins Kill at Blairstown, N.J. 126 C .72 .45

01446500 Delaware River at Belvidere, N.J. 4,535 C .72 .21

01447500 Lehigh River at Stoddartsville, Pa. 91.7 C .67 .33

01447720 Tobyhanna Creek near Blakeslee, Pa. 118 C .56 .26

01447800 Lehigh River below Francis E Walter Res near White Haven, Pa. 290 R

01449000 Lehigh River at Lehighton, Pa. 591 C .34 .48

01449360 Pohopoco Creek at Kresgeville, Pa. 49.9 C .50 .26

01449800 Pohopoco Creek below Beltzville Dam near Parryville, Pa. 96.4 R

01450500 Aquashicola Creek at Palmerton, Pa. 76.7 C .86 .45

01451000 Lehigh River at Walnutport, Pa. 889 C .40 .34

01452000 Jordan Creek at Allentown, Pa. 75.8 C .54 .47

01453000 Lehigh River at Bethlehem, Pa. 1,279 C 0.49 .27

01463500 Delaware River at Trenton, N.J. 6,780 C 0.79 .27

1

 Includes record from discontinued gage 01420980.

33
34

 

Figure 9. Location of selected streamgages in the Delaware River main-stem subbasin, Pennsylvania, New 

Jersey, and New York. (Streamgages are listed in table 7.)
35

Automatic calibration methods were used for the PRMS model, first in daily mode, and then in 

storm mode. The automatic calibration is performed using LUCA (Hay and Umemoto, 2007; Hay and 

others, 2006), an automatic calibration tool that adjusts model parameters to reduce the difference 

between simulated and measured daily streamflow. LUCA is based on the Shuffled Complex Evolution

(Duan and others, 1993) global search algorithm that assures that intermediate and final states of the 

model are simulated consistently with measured values (Hay and Umemoto, 2007). Subbasins of the 

model were delineated above USGS streamgages, and the parameters of HRUs above each station are 

adjusted separately during LUCA calibration. 

Headwater subbasins of the model were calibrated first (fig. 9). Calibration of model parameters 

for subbasins below the headwaters could then be calibrated, using the headwater flows from those 

calibrated subbasins. Thus, the calibration procedure started in the headwaters and then moved down 

through the watershed. Parameters for ungaged subbasins were assigned using values from the closest 

gaged subbasin. 

Because the PRMS model is designed to provide runoff and inflows for a HEC-ResSim floodanalysis reservoir-simulation model, the reservoirs simulated in that model are not explicitly included in 

the PRMS model. This required a modified procedure for calibration of PRMS local inflows 

downstream of the reservoirs. For daily calibration of these downstream subbasins, the measured daily 

outflow from the reservoir was used as an inflow to the subbasin. In this way, the measured streamflow 

further downstream could be used as a calibration target for local flows below the reservoir in the 

PRMS model. Calibration changed the parameters controlling local inflows downstream of the 

reservoir, but the discharge from the reservoir was not adjusted. For the hourly calibration, additional 

manual calibration was conducted by using the HEC-ResSim model to simulate flow through the 

reservoirs, and to compute streamflow downstream of the reservoirs. Thus, the daily calibration uses 

only PRMS results and observed reservoir outflows, while hourly calibration results use both PRMS and 

HEC-ResSim for simulation of flows at streamgage locations below the reservoirs. Streamflow at 

headwater streamgages, which is not regulated by the reservoirs, is fully simulated by PRMS alone, for 

both daily and hourly simulations. 

The PRMS model was calibrated in a three-step process: automatic calibration in daily mode, 

automatic calibration in storm mode, and manual calibration of storm volumes for main-stem gage 

locations. The first step was calibration of the parameters shown in table 8 using the model in daily 

mode. Two objective functions were used for the daily mode calibration, the absolute difference 

between the observed and simulated total volume of discharge, and the NRMSEd of the daily flows. The 

first objective function was used to determine precipitation adjustment factors, separately for rain and 

snow, by month, so that the total volume of water applied to the basin as precipitation is consistent with 

the total discharge measured at the subbasin streamgage. 

The second objective function for the daily-mode calibration is a measure of the overall match 

between the simulated and observed daily hydrograph. Parameters adjusted on the basis of this measure 

of model fit are generally related to the partitioning of water between relatively slow and fast subsurface 

runoff reservoirs. The groundwater reservoir has a more delayed release of water than the soil-moisture 

reservoir. Daily calibration is chosen for these parameters because the timescale of release from both 

subsurface reservoirs is on the order of days, not hours. A single adjustment of each parameter was used 

for the HRUs within each subbasin. 

The second step of the automatic calibration using LUCA was storm-mode (hourly) calibration 

of the parameters listed in table 9. This method was useful in improving the simulation in headwater 

basins. Parameters for ungaged basins in the model were set at values calibrated from the nearest 

subbasin. 
Table 8. Parameters calibrated in each step of the calibration process, with the model in daily mode.

[Dimensions: nmths, number of months = 12; nsub, number of subbasins = 145; nhru, number of hydrologic response units (HRUs) = 869; PRMS, Precipitation Runoff Modeling System]

Calibration

data set

Objective

function

PRMS parameters 

used to calibrate 

model state

Dimensions Range Parameter

description Comments

Volume of storm 

period

Absolute Differencerain_sub_adj nmths x nsub 0–3 Adjustment factor 

for precipitation on rain 

days

Calibrate as a 

mean value. 

Combine 

calibrated 

values from 

each subbasin 

into a final parameter value. 

Interpolate to 

uncalibrated 

subbasins

snow_sub_adj nmths x nsub 0–3 Adjustment factor 

for precipitation on snow 

days

Daily Values 

during storm 

periods

NRMSEd gwflow_coef nhru Based on observed Groundwater 

routing coefficient

Calibrate as a 

mean value. 

Combine 

calibrated 

values from 

each subbasin 

into a final parameter value. 

Interpolate to 

uncalibrated 

subbasins 

HRUs

gwstor_init nhru Based on observed Storage in each 

GW reservoir 

at beginning 

of run

smidx_coef nhru 0.0001–1 Coefficient in 

non-linear 

surface runoff 

contributing 

area algorithm

smidx_exp nhru 0.2–0.8 Exponent in onlinear surface 

runoff contribution area 

algorithm

soil_moist_max nhru 0–20 Maximum 

available 

water holding 

capacity of soil 

profile

soil_rechr_max nhru 0–20 Maximum available water 

holding capacity for soil 

recharge zone

soil2gw_max nhru 0.0001–0.5 Maximum rate 

of soil water 

excess moving 

to groundwater

36
Table 9. Parameters calibrated in each step of the calibration process, with the model in storm mode.

Calibration

data set

Objective

function

PRMS parameters 

used to calibrate 

model state

Dimensions Range Parameter

description Comments

Values during 

storm periods

NRMSEh kpar nhru 0–5 Hydraulic conductivity of the transmission zone

Calibrate as a 

mean value. 

Combine calibrated values 

from each 

subbasin into a 

final parameter 

value.

psp nhru 0.1–25 Moisture deficit times 

capillary drive

mf_max nhru 0.5–8 Maximum melt factor

mf_min nhru 0.1–4 Minimum melt factor

wind_adjust nhru 0.02–1 Rate of melt due to 

wind effects

37
38

An iterative manual calibration procedure was also used for downstream subbasins and ungaged 

subbasins. Simulated local inflows computed by PRMS were used with the HEC-ResSim reservoir 

simulation and flow-routing model component to compute main-stem flows at streamgage locations. On 

the basis of the comparison between simulated and observed flows at a streamgage, the precipitation 

adjustment factors for the subbasin providing local inflow above the streamgage were calibrated. 

Subbasin precipitation adjustment factors were calibrated in this manner proceeding downstream in the 

basin. This method improved the match between simulated and observed flow volumes but did not 

substantially affect the shape of simulated hydrographs.

The PRMS model was judged to be adequately calibrated for the generation of reservoir inflows, 

local inflows and unregulated tributary flows for input into the HEC-ResSim model to assess the effects 

of watershed characteristics on flooding in regulated tributaries and the main-stem Delaware River. The 

NRMSEh measure of model fit for hourly simulation periods is generally lower than the NRMSEd

measure for daily simulation periods, indicating that the model is generally more accurate for the hourly 

simulation periods (table 7). This reflects the focus of the sequential model calibration effort on the 

hourly simulation of the time periods before, during, and after the three high-flow events. The simulated 

streamflow is generally more accurate for larger rivers and locations downstream of reservoirs, and less 

accurate for headwater or unregulated streams. This reflects the design of the model, by HRU and 

stream discretization, to provide a tool for managing streamflow in the large rivers in the study area, and 

to evaluate the effects of operations of the reservoirs. The observed and simulated mean and standard 

deviations of hourly streamflow further illustrate the model performance (table 10). In general, the 

simulated mean flows are larger than the observed mean flow, which may reflect the effect of manual 

adjustments to precipitation MPE data. These manual adjustments were made to visually improve the 

overall match between the simulated and observed storm volumes and may reflect a bias towards 

matching the high flows. 

Simulated and observed hydrographs at streamgage locations also demonstrate the model’s 

ability to reproduce streamflows that were observed during the flood event (figs. 10-15). Simulated 

hydrographs are smoother than observed hydrographs, suggesting that the model, using a 1-hour time 

step, does not capture all the temporal variability during the watershed hydrologic processes controlling 

streamflow. During calibration procedures, backwater effects on the stage at the Minisink Hills 

streamgage were identified, and the corresponding discharge data were removed from the observed 

record (fig. 10, for example). Overall, the visual match between observed and simulated hydrographs is 

better at streamgages on main rivers below reservoirs than at headwater and unregulated locations. 

These results are consistent with the model fit statistics.

The input data files for the calibrated PRMS model are available online at 

http://pa.water.usgs.gov/drbfam. This website also provides links to the software used in the model, the 

documentation, and other information related to the Flood-Analysis Model.
Table 10. Observed and simulated mean and standard deviation of hourly streamflow, in cubic feet per second, for streamgages used for 

model calibration for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.

[Calibration periods: September 2004: September 13, 1:00 am to September 28, 12:00 am; April 2005: March 24, 1:00 am to April 15, 12:00 am; June 2006: June 

19, 1:00 am to July 10, 12:00 am]

U.S. Geological 

Survey station 

number

Station name

Mean hourly streamflow (cubic feet per second)

September 2004 April 2005 June 2006

Observed Simulated Observed Simulated Observed Simulated

01413500 East Branch Delaware River at Margaretville, 

N.Y.

1,050 1,720 1,540 1,900 1,250 1,790

01414000 Platte Kill at Dunraven, N.Y. 240 350 370 450 220 270

01414500 Mill Brook near Dunraven, N.Y. 140 250 210 260 120 200

01415000 Tremper Kill near Andes, N.Y. 190 290 270 360 200 300

01417500 East Branch Delaware River at Harvard, N.Y. 2,960 3,730 3,180 3,500 3,580 4,690

01420500 Beaver Kill at Cooks Falls, N.Y. 2,540 3,130 3,420 3,500 2,460 3,230

01421000 East Branch Delaware River at Fishs Eddy, N.Y.

1 6,340 7,830 5,810 6,230 7,750 9,120

01423000 West Branch Delaware River at Walton, N.Y. 2,040 2,290 2,920 3,140 2,920 3,040

0142400103 Trout Creek near Trout Creek, N.Y. 180 250 170 220 210 280

01426000 Oquaga Creek at Deposit, N.Y. 510 750 910 860 780 1,000

01426500 West Branch Delaware River at Hale Eddy, N.Y. 3,960 4,530 5,260 5,710 5,550 6,310

01427510 Delaware River at Callicoon, N.Y. 14,200 17,310 18,390 19,210 19,170 21,490

01428500 Delaware River above Lackawaxen River near 

Barryville, N.Y.

16,080 19,030 20,520 21,330 13,690 17,140

01428750 West Branch Lackawaxen River near Aldenville, 

Pa.

260 310 620 580 900 800

01431500 Lackawaxen River at Hawley, Pa. 2,270 2,680 3,840 4,210 4,130 4,800

01432900 Mongaup River at Mongaup Valley, N.Y. 540 650 830 890 430 460

01434000 Delaware River at Port Jervis, N.Y. 22,950 27,030 30,520 31,650 27,390 32,400

01435000 Neversink River near Claryville, N.Y. 470 760 870 910 620 800

01436690 Neversink River at Bridgeville, N.Y. 820 1,050 2,040 2,390 1,120 1,690

01437500 Neversink River at Godeffroy, N.Y. 1,360 1,790 3,490 3,710 1,120 1,900

01438500 Delaware River at Montague, N.J. 26,220 30,080 35,690 37,260 30,010 35,120

01439500 Bush Kill at Shoemakers, Pa. 1,040 1,010 1,200 1,100 870 800

01440000 Flat Brook near Flatbrookville, N.J. 350 440 500 490 530 360

01442500 Brodhead Creek at Minisink Hills, Pa. 1,840 2,010 2,520 2,450 2,260 2,260

01443500 Paulins Kill at Blairstown, N.J. 660 740 930 920 490 480

01446500 Delaware River at Belvidere, N.J. 34,410 39,090 48,420 47,920 37,540 42,610

01447500 Lehigh River at Stoddartsville, Pa. 880 1,010 920 960 950 1,070

01447720 Tobyhanna Creek near Blakeslee, Pa. 1,240 1,410 1,370 1,320 1,340 1,350

01449000 Lehigh River at Lehighton, Pa. 4,400 5,890 5,990 5,630 5,910 6,500

01449360 Pohopoco Creek at Kresgeville, Pa. 360 360 440 410 340 310

01450500 Aquashicola Creek at Palmerton, Pa. 730 960 680 760 540 710

01451000 Lehigh River at Walnutport, Pa. 6,980 8,570 8,880 8,390 8,840 9,530

01452000 Jordan Creek at Allentown, Pa. 550 700 710 810 410 500

01453000 Lehigh River at Bethlehem, Pa. 8,680 10,750 11,690 10,720 10,470 11,090

01463500 Delaware River at Trenton, N.J. 45,990 58,000 62,560 66,800 49,910 61,600

1

 Includes record from discontinued gage 01420980.

39
Table 10. Observed and simulated mean and standard deviation of hourly streamflow, in cubic feet per second, for streamflow-gaging 

stations used for model calibration for the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.—Continued

[Calibration periods: September 2004: September 13, 1:00 am to September 28, 12:00 am; April 2005: March 24, 1:00 am to April 15, 12:00 am; June 2006: June 

19, 1:00 am to July 10, 12:00 am]

U.S. Geological 

Survey station 

number

Standard deviation of hourly streamflow (cubic feet per second)

September 2004 April 2005 June 2006

Observed Simulated Observed Simulated Observed Simulated

01413500 2,040 2,300 2,050 2,250 1,800 2,020

01414000 470 510 450 480 350 400

01414500 400 350 300 320 180 210

01415000 470 430 340 410 370 500

01417500 4,620 4,370 4,420 4,290 5,360 6,040

01420500 6,460 5,130 6,490 4,950 6,200 5,320

01421000 10,680 10,170 8,260 8,300 13,870 12,880

01423000 3,390 3,200 3,400 3,530 5,530 5,300

0142400103 390 410 250 270 480 540

01426000 1,240 1,160 930 980 2,240 1,880

01426500 4,150 4,550 5,140 5,220 8,860 9,820

01427510 22,260 20,750 21,520 21,450 31,740 31,570

01428500 24,680 22,750 23,740 23,420 21,570 23,340

01428750 520 430 1,260 890 1,740 1,490

01431500 3,710 3,350 4,180 4,010 6,400 6,230

01432900 940 960 1,140 1,220 680 710

01434000 32,570 29,960 33,030 31,360 41,790 43,120

01435000 880 980 1,780 1,130 1,220 970

01436690 1,400 1,220 3,730 3,240 2,000 1,690

01437500 1,530 1,530 4,920 4,560 2,000 2,070

01438500 37,170 32,170 41,180 37,570 47,010 45,790

01439500 1,210 1,240 1,140 1,330 1,050 1,250

01440000 660 560 530 520 400 420

01442500 2,740 3,190 3,270 3,820 4,730 4,440

01443500 880 910 750 990 480 450

01446500 43,770 37,070 50,170 44,880 54,120 53,900

01447500 1,750 1,780 1,150 1,290 1,850 2,080

01447720 2,190 2,170 1,990 1,970 2,490 2,080

01449000 3,690 4,540 3,360 3,700 5,720 5,600

01449360 420 450 390 470 400 450

01450500 1,270 1,350 750 830 760 740

01451000 6,610 6,920 5,500 5,380 8,980 8,590

01452000 1,230 1,210 1,020 880 670 720

01453000 9,700 9,540 7,610 7,420 10,450 10,510

01463500 51,090 49,250 54,650 53,980 61,820 66,780

40
41

 

Figure 10. Simulated and observed streamflow, September 13 to 26, 2004, at selected U.S. Geological Survey 

streamgages in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.

Streamflow at these locations is not regulated by reservoirs simulated in HEC-ResSim.
42

 

Figure 10. Simulated and observed streamflow, September 13 to 26, 2004, at selected U.S. Geological Survey 

streamgages in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.

Streamflow at these locations is not regulated by reservoirs simulated in HEC-ResSim. –Continued

Observed data affected by backwater removed from Minisink Hills record. 
43

 

Figure 11. Simulated and observed streamflow, September 13 to 26, 2004, at selected U.S. Geological Survey 

streamgages below reservoirs in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New 

York. Simulated streamflow is from HEC-ResSim reservoir and routing model using runoff and reservoir inflow 

from the PRMS model (Joan Klipsch, U.S. Army Corps of Engineers, written commun., May 4, 2009)
44

 

Figure 12. Simulated and observed streamflow, March 26 to April 8, 2005, at selected U.S. Geological Survey 

streamgages in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.

Streamflow at these locations is not regulated by reservoirs simulated in HEC-ResSim.
45

 

Figure 12. Simulated and observed streamflow, March 26 to April 8, 2005, at selected U.S. Geological Survey 

streamgages in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York. Streamflow 

at these locations is not regulated by reservoirs simulated in HEC-ResSim. –Continued

Observed data affected by backwater removed from Minisink Hills record.
46

 

Figure 13. Simulated and observed streamflow, March 26 to April 8, 2005, at selected U.S. Geological Survey 

streamgages below reservoirs in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New 

York. Simulated streamflow is from HEC-ResSim reservoir and routing model using runoff and reservoir inflow 

from the PRMS model (Joan Klipsch, U.S. Army Corps of Engineers, written commun., May 4, 2009)
47

 

Figure 14. Simulated and observed streamflow, June 22 to July 5, 2006, at selected U.S. Geological Survey 

streamgages in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.

Streamflow at these locations is not regulated by reservoirs simulated in HEC-ResSim.
48

 

Figure 14. Simulated and observed streamflow, June 22 to July 5, 2006, at selected U.S. Geological Survey 

streamgages in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.

Streamflow at these locations is not regulated by reservoirs simulated in HEC-ResSim.–Continued

Observed data affected by backwater removed from Minisink Hills record.
49

 

Figure 15. Simulated and observed streamflow, June 22 to July 5, 2006, at selected U.S. Geological Survey 

streamgages below reservoirs in the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New 

York. Simulated streamflows are from HEC-ResSim reservoir and routing model using runoff and reservoir 

inflow from the PRMS model (Joan Klipsch, U.S. Army Corps of Engineers, written commun., May 4, 2009)
50

Limitations

The PRMS model of the Delaware River subbasin draining to Trenton, N.J., simulates runoff to 

reservoirs and local runoff for input into the HEC-ResSim model to compare the effects of different 

watershed conditions on flows in large rivers within the study area during flooding. The model is 

limited, however, by the following: spatial resolution, data gaps, model simplifications, errors in 

precipitation and temperature input data, errors in streamflow calibration data, and the focus of 

calibration on peak flows.

The large model area caused some computational difficulties during discretization and GIS 

processing. These difficulties limited the minimum size of HRUs and the resolution of the DEM used. 

Precipitation in the study area is correlated with elevation; higher precipitation amounts are related to 

higher elevations. Furthermore, the change in elevation, or slope, is a primary factor in runoff 

characteristics. Hence, discretization with smaller HRUs and more accurate elevations and slopes may 

improve the simulation results, especially in headwater streams. 

Several data gaps exist that affect model accuracy. Stages at the Minisink Hills streamgage are 

affected by backwater during high-flow events and, hence, cannot be used to estimate discharge in the 

tributary during these periods. A few other streamgages were inoperative during peak flows because the 

streamgage equipment was inundated. Substantial portions of the streamflow into many of the major 

reservoirs in the study area are not measured. Some streamgages, especially on the main-stem Delaware 

River, are operated as stage-only streamgages, and the associated rating curve to convert stage into 

discharge is less accurate than at fully maintained streamgages. In addition, missing data and artifacts

were identified in climate data, including MPE precipitation.

This model is judged adequate for providing reservoir inflows, local inflows and unregulated 

tributary flows for input into the HEC-ResSim model to assess the impacts of watershed conditions on 

flows in the regulated tributaries and main stem of the Delaware River during high-flow events. Other 

uses of the model may require additional development or calibration. The model calibration focused on 

time periods before, during, and after the three extreme high-flow events; the model will be less 

accurate for simulations during other conditions.

Suggestions for Model Application

Suggested use of the PRMS model is to provide runoff and streamflow information throughout 

the study area for use in a reservoir-operation model, HEC-ResSim, documented separately. The FloodAnalysis Model, integrating the PRMS and HEC-ResSim models, was developed to be used to evaluate 

the impacts of both basin hydrology and reservoir operations on downstream flood discharges during 

the three high-flow events and was developed as a planning tool. Simulation results with existing or 

historic conditions can be compared to simulation results using alternative conditions, to evaluate the 

impact of those alternative conditions on downstream flows in large rivers. In this approach, the model 

errors common to both simulation results have minimal impact on the relative differences between the 

simulations. This model was not developed as a forecasting tool for realtime prediction of floods on the 

Delaware River.

The PRMS model provides simulated hydrologic conditions throughout the watershed, as 

discretized by the model HRUs. An example of the output from the PRMS model is the soil moisture in 

the watershed, which acts as a reservoir to store and release water (fig. 16). The model also computes 

incremental runoff for simulated stream segments (fig. 17). These variables change hourly during the 

storm-mode simulation. Many other model variables can be examined through the model output files 

and the user interface provided. 
51

 

Figure 16. Simulated soil-moisture saturation at noon on A) March 26, 2005, and B) June 23, 2006, for model hydrologic response units (HRUs) for 

the Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.
52

 

Figure 17. Simulated maximum runoff rate during June 22 to July 5, 2006, to model stream segments for the 

Delaware River main-stem subbasin, Pennsylvania, New Jersey, and New York.
53

The Flood-Analysis Model may be useful as a planning tool to evaluate the effects of watershed 

conditions on flood discharges on large rivers in the Delaware River main-stem subbasin. The model 

can be used to predict streamflow under different past climate conditions, provided those are reasonably 

close to the climate of the calibration events. Model results using different past climate records can help 

understand the watershed response to different storm events. However, the calibration described in this 

report focuses on runoff during three flood events. Applications for non-flood events, or for flood events 

having different conditions than the three events considered here, may require additional calibration.

As a planning tool, the model may also be useful for simulation of the change in high flows for 

cases with different watershed parameters. To assist with land-use planning, for example, an alternative 

model could be developed with PRMS model parameters that could be adjusted to account for 

hypothetical changes in land use. The high flows simulated using such an alternative model could be 

compared to the calibrated model results, and the differences caused in the model by the changes in 

land-use parameters could be used to inform land-use planning decisions. However, the alternative or 

adjusted parameters needed to represent the land-use changes in this example would need to be 

determined by an expert user, using procedures beyond those developed for this study. The validity of 

such an application would rest on the validity of the user-specified parameters. In addition, the 

simulated hydrologic conditions in such an alternative case may extend beyond the conditions used here 

for model calibration, introducing additional error in the simulation results. 

An appropriate use of the model for planning purposes would be to compare model results to 

model results, as input to make decisions about alternative management of the watershed. For example, 

an analysis of the effect of land-use change on streamflow would compare the results of model 

simulations for two different cases of land-use conditions. It would not be appropriate to conduct such 

an analysis by comparing simulated streamflow, with hypothetical land use, to measured streamflow,

because such a comparison would include errors in the simulated streamflow that are present only in the 

model results. By comparing model results to model results, the impact of the unavoidable model errors 

on the differences is minimized. This use is similar to the use of the daily flow model OASIS to inform 

the decision-making process by DRBC (Quinodoz, 2006).

Summary

To evaluate the impact of reservoir levels and other factors on flooding, the DRBC, USGS, 

HEC, and NWS developed a Flood-Analysis Model for the Delaware River. The primary components of 

the model are a rainfall-runoff component (the PRMS model) and a reservoir and streamflow routing 

component (the HEC-ResSim model). This report describes the rainfall-runoff model component, which 

uses a modified version of the PRMS software. PRMS is a modular, physically based, distributedparameter modeling system developed to evaluate the impacts of various combinations of precipitation, 

climate, and land use on surface-water runoff and general basin hydrology. The PRMS model simulates 

time periods associated with main-stem flooding that occurred in September 2004, April 2005, and June 

2006. 

The study area was the 6,780-mi2 watershed of the Delaware River in the states of Pennsylvania, 

New Jersey, and New York that drains to Trenton, N.J. A geospatial database was created for use with a 

GIS to assist model discretization, determine land-surface characterization, and estimate model 

parameters. The USGS NED at 100-m resolution was used for model discretization into 452 stream 

segments and 869 HRUs. In addition, geospatial processing was used to estimate initial model 

parameters from the DEM and other data layers, including land use. Climate data for point stations were 

obtained from multiple sources. These sources included daily data for 22 NWS Coop network stations, 

hourly data for 15 stations from the NCDC, hourly data for 1 station from the NWS Middle Atlantic 
54

River Forecast Center records, and daily and hourly data for 7 stations operated by the NYCDEP. The 

NWS radar-based Multisensor Precipitation Estimate data set was used to compute daily precipitation in 

the study area for 2001-2007 and to compute hourly precipitation for storm periods. 

Calibration of the PRMS model was performed using the LUCA model calibration tool, as well 

as manual adjustments. The general goal of the calibration procedure was to minimize the difference 

between streamflow measured at USGS streamgages and the corresponding streamflow simulated by the 

model. Daily streamflow data from 42 USGS streamgages were acquired for use in model calibration. 

The streamflow data represented areas draining from 20.2 to 6,780 mi2. The model was judged to be 

adequately calibrated for generation of reservoir inflows, local inflows and unregulated tributary flows 

for input into the HEC-ResSim model to assess the effects of watershed characteristics on regulated 

tributary and main stem Delaware River flows during floods. Model uncertainty is lower for streamflow 

on major rivers below reservoirs, and higher for smaller unregulated streams.

The PRMS model simulates runoff and reservoir inflows for input into the HEC-ResSim model 

to assess the impacts of watershed conditions on flows in the regulated tributaries and main stem of the 

Delaware River watershed draining to Trenton, N.J. during high flow events. Suggested application of 

the PRMS model is as a planning tool, in conjunction with the reservoir-simulation component, the 

HEC-ResSim model, of the Flood-Analysis Model. Differences in simulation results for different model 

input may be useful in evaluating alternative management of the land and water resources of the basin. 

Accuracy of the model is limited by the following: spatial resolution, data gaps, model simplifications, 

errors in precipitation and temperature input data, errors in streamflow calibration data, and the focus of 

calibration on peak flows.

Acknowledgments

This work was part of a collaborative project with the Delaware River Basin Commission, the 

U.S. Army Corps of Engineers, Hydrologic Engineering Center, and NOAAs National Weather Service, 

Middle Atlantic River Forecast Center. The authors gratefully acknowledge contributing individuals 

from these agencies, including Amy L. Shallcross, Hernan Quinodoz and Richard Fromuth of DRBC; 

Joan Klipsch and Marilyn Hurst of HEC; and Joseph Ostrowski of MARFC. Contributions of data used 

for model development by the following individuals are also gratefully acknowledged: Karen Reavy of 

DRBC; and Glenn Horton of New York City Department of Environmental Protection. The authors 

gratefully acknowledge the following USGS staff contributing to this work: R. Edward Hickman and 

Donald E. Rice for compilation of streamflow and map information; Roland Viger for assistance and 

guidance for model parameterization and discretization; and David M. Bjerklie for assistance and 

guidance for model parameterization. 
55

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61

Appendix – Documentation of PRMS Modules Modified for This Study

There are three modules that were created or modified for this study. These modules are documented 

herein.
62

Module climate_hru_prms.f

NAME

climate_hru_prms.f

SPECIAL FEATURES

This is a new module. 

MODULE PROCESS (TYPE)

Climate

DEFINITION

Reads input precipitation and temperature variables from the designated data files.

KEYWORDS

CREATION DATE

January 2009

PARAMETERS DECLARED

 Tmax_allsnow – Monthly maximum air temperature at which precipitation is all snow for the HRU.

 Hru_subbasin – Index of subbasin number for each HRU.

 Hru_area – Area of each HRU.

 Tmax_allrain – Monthly minimum air temperature at an HRU that results in all precipitation during a day 

being rain

 Rain_sub_adj – Monthly factor as a decimal fraction used to adjust rain values, by subbasin.

 Snow_sub_adj – Monthly factor as a decimal fraction used to adjust snow values, by subbasin.

VARIABLES DECLARED

 Basin_temp – Basin area-weighted temperature for time step < 24.

 Basin_tmax – Basin area-weighted daily maximum temperature.

 Basin_tmin – Basin area-weighted daily minimum temperature.

 Solrad_tmax – Basin daily maximum temperature for use with solrad.

 Solrad_tmin – Basin daily minimum temperature for use with solrad.

 Tmaxf – HRU adjusted daily maximum temperature, degrees F.

 Tminf – HRU adjusted daily minimum temperature, degrees F.

 Tavgf – HRU adjusted daily average temperature, degrees F.

 Tmaxc – HRU adjusted daily maximum temperature, degrees C.

 Tminc – HRU adjusted daily minimum temperature, degrees C.

 Tavgc – HRU adjusted daily average temperature, degrees C.

 Tempf – HRU adjusted temperature for time step < 24, degrees F.

 Tempc – HRU adjusted temperature for time step < 24, degrees C.

 Tmax – Observed daily maximum temperature at each measurement station, in degrees Fahrenheit.
63

 Tmin – Observed daily minimum temperature at each measurement station, in degrees Fahrenheit.

 Newsnow – New snow on HRU (0=no; 1=yes).

 Pptmix – Precipitation mixture (0=no; 1=yes).

 Basin_ppt – Area weighted adjusted average precipitation for basin, in inches.

 Basin_obs_ppt – Area weighted measured average precipitation for basin, in inches.

 Basin_rain – Area weighted adjusted average rain for basin, in inches.

 Basin_snow – Area weighted adjusted average snow for basin, in inches.

 Hru_ppt – Adjusted precipitation on each HRU, in inches.

 Hru_rain – Computed rain on each HRU, in inches.

 Hru_snow – Computed snow on each HRU, in inches.

 Prmx – Proportion of rain in a mixed event, in inches.

EXTERNAL VARIABLES USED

 Route_on – Simulate flow routing (0=no; 1=yes).

 Newday – Time step is first time step for a day (0=no; 1=yes).

 Active_hrus – Number of active HRUs.

 Hru_route_order – Routing order of HRUs.

 Basin_area_inv – Inverse of total basin area as sum of HRU areas, in acres-1.

DESCRIPTION

This module reads daily and hourly precipitation and temperature data by HRU and makes that 

data available to other modules. Input data file names are hardcoded in the module.

REFERENCES

none

DEVELOPER NAME AND ADDRESS

R. Steve Regan

U.S. Geological Survey

Box 25046, MS 412

Denver Federal Center

Lakewood, CO 80225
64

Module local_flow_drbc.f

NAME

local_flow_drbc.f

SPECIAL FEATURES

This is a new module. 

MODULE PROCESS (TYPE)

Output

DEFINITION

Accumulates and outputs flows for calibration and use by other models. 

KEYWORDS

CREATION DATE

January 2009

PARAMETERS DECLARED

 Hru_area – Area of each HRU.

 Dss_output_file – Name of DSS output file.

 Csv_output_file – Name of comma-delimited output file.

VARIABLES DECLARED

 Locs – Output identifiers for DSS output.

 Loc_flows – Accumulated flows for DSS output.

 Strm_flows – Storm mode flows for calibration output.

 Ifltab – File identifier for DSS file.

 Nowtime – Time formatted for DSS file.

 Jul_day – Julian day.

 Ierr – Error flag for DSS output process.

 Nsegment – Number of output segments for DSS file.

 Cpath – Path identifier for DSS output.

 Ca-f – Identifiers (DSS ―part‖) A through F for DSS output.

EXTERNAL VARIABLES USED

 Route_on – Simulate flow routing (0=no; 1=yes).

 Sub_cfs – Subbasin flow (cfs).

 Sub_inq – Instantaneous subbasin flow (cfs).

 Hru_ppt – Precipitation on HRU (inch).

 Runoff – Observed gage flow (cfs)
65

 Q_chan – Flow at outlet of channel (cfs).

 Qinlat_chan_ts – Time step lateral inflow to channel (cfs).

 Q_chan_timestep – Time step flow at outlet of channel (cfs).

 Qin_instant – Instantaneous flow at inlet of channel (cfs).

 Contrib_area_chan – Channel contributing drainage area (acres).

 Hortonian_lakes – Hortonian runoff to lake HRU (cfs).

 Strm_seg_in – Index of stream segments that flow to current segment.

 Lakein_sz – Soil zone runoff to lake HRU (cfs).

 Lakein_gw – Groundwater runoff to lake HRU (cfs).

DESCRIPTION

This module accumulates flows for calibration and use by other models. Calibration values use 

observed reservoir outflows instead of simulated reservoir outflows because reservoirs are not simulated 

in the present model. Reservoir inflows, local runoff, and tributary flows are output to a HEC-DSS 

format file for use in a separate reservoir simulation and downstream flow routing model using HECResSim. Flow accumulations, output identifiers, and file names are hardcoded in the module.

REFERENCES

U.S. Army Corps of Engineers, Hydrologic Engineering Center, 2006, HEC-DSSVue, HEC Data 

storage system visual utility engine, User’s manual version 1.2 revised [online]: accessed December 

3, 2008, at http://www.hec.usace.army.mil/software/hec-dss/documents/CompleteManual.pdf.

U.S. Army Corps of Engineers, Hydrologic Engineering Center, 2007, HEC-ResSim Reservoir 

simulation system, User’s manual version 3.0 [online]: accessed December 3, 2008, at 

http://www.hec.usace.army.mil/software/hec-ressim/documentation/HECResSim_30_UsersManual.pdf.

DEVELOPER NAME AND ADDRESS

R. Steve Regan

U.S. Geological Survey

Box 25046, MS 412

Denver Federal Center

Lakewood, CO 80225
66

Module snow17_st.f

NAME

snow17_st.f

SPECIAL FEATURES

This is a port of the existing SNOW-17 algorithm to PRMS. No changes were made to the algorithm or 

existing code. 

MODULE PROCESS (TYPE)

Snow

DEFINITION

Snow accumulation and ablation model.

KEYWORDS

CREATION DATE

January 2009

PARAMETERS DECLARED

 SCF – The multiplying factor which adjusts precipitation that is determined to be in the form of snow. SCF 

primarily accounts for gage catch deficiencies, but also implicitly includes the net effect of vapor transfer (sublimation and 

condensation, including from intercepted and blowing snow) and transfers across areal divides.

 MFMAX – Maximum melt factor during non-rain periods – assumed to occur on June 21st (mm•°C-1• 6 hr-1).

 MFMIN – Minimum melt factor during non-rain periods – assumed to occur on December 21st (mm•°C-1• 6 hr-1).

 UADJ – The average wind function during rain-on-snow periods (mm•mb-1). UADJ is only a major parameter 

when there are fairly frequent rain-on-snow events with relatively warm temperatures.

 SI – The mean areal water equivalent above which there is always 100 percent areal snow cover (mm). SI is not a 

major parameter when the model is applied at a point location or when significant bare ground appears soon after melt begins 

no matter the magnitude of the snow cover.

 Area Depletion Curve – Curve that defines the areal extent of the snow cover as a function of how much 

of the original snow cover remains after significant bare ground shows up. The areal depletion curve also implicitly accounts 

for the reduction in the mean areal melt rate that occurs as less of the area is covered by snow. Generally not needed for a 

point location.

 NMF – Maximum negative melt factor (mm•°C-1•6 hr-1). The negative melt factor has the same seasonal variation 

as the non-rain melt factor, thus the maximum value is assumed to occur on June 21st.

 TIPM – Antecedent temperature index parameter (real – range is 0.01 to 1.0). Controls how much weight is put on 

temperatures from previous time intervals when computing ATI. The smaller the value of TIPM, the more previous time 

intervals are weighted.

 PXTEMP – The temperature that separates rain from snow (°C). If the air temperature is less than or equal to 

PXTEMP, the precipitation is assumed to be in the form of snow. The PXTEMP parameter, as defined for SNOW-17, is not 

used if a rain-snow elevation time series is used to determine the form of precipitation.

 MBASE – Base temperature for snowmelt computations during non-rain periods (°C). Typically a value of 0°C is 

used.
67

 PLWHC – Percent liquid water holding capacity (decimal fraction). Indicates the maximum amount of liquid water, 

as a fraction of the ice portion of the snow, that can be held against gravity drainage (maximum allowed value is 0.4).

 DAYGM – Constant daily amount of melt which takes place at the snow-soil interface whenever there is a snow 

cover (mm•day-1).

VARIABLES DECLARED

 WE – Water equivalent of ice portion of snow cover (mm).

 NEGHS – Heat deficit (mm).

 LIQW – Liquid water held by the snow (mm).

 TINDEX – Antecedent temperature index (°C).

 ACCMAX – Maximum amount of water equivalent that existed during accumulation period (mm).

 SB – Water equivalent when new snowfall first occurs on a partly bare area (mm).

 SBAESC – Areal cover when new snowfall occurs on a partly bare area (decimal fraction).

 SBWS – Water equivalent where the areal cover drops below 100% when melt occurs after new snowfall takes 

place on a partially bare area (mm).

 STORGE – Lagged excess liquid water in storage (mm).

 AEADJ – Areal index value computed for use in depletion curve computations after an adjustment to the areal 

extent of snow cover (mm).

 EXLAG(7) – Average hourly lagged excess water for each precipitation time interval (mm).

 SNDPT – Snow depth (cm).

 SNTMP – Snow cover temperature (°C).

EXTERNAL VARIABLES USED

DESCRIPTION

This module does hourly snow accumulation and ablation. 

REFERENCES

Anderson, E.A., 2006, Snow accumulation and ablation model – SNOW-17—Chap. II.2 of NOAA’s 

NWS River Forecast System User Manual [online]: accessed November 18, 2008, at 

http://www.weather.gov/oh/hrl//nwsrfs/users_manual/part2/_pdf/22snow17.pdf.

DEVELOPER NAME AND ADDRESS

R. Steve Regan

U.S. Geological Survey

Box 25046, MS 412

Denver Federal Center

Lakewood, CO 80225
68

For more information concerning this publication contact:

Director

USGS Pennsylvania Water Science Center

215 Limekiln Road

New Cumberland, Pennsylvania 17070

dc_pa@usgs.gov

The latest version of the model and this report can be obtained using the Internet address:

http://pa.water.usgs.gov/drbfam

Published in the Eastern Region, New Cumberland, Pa.

Manuscript approved for publication, January 22, 2010

Edited by Kim L. Otto
Goode and others—Simulation of Runoff and Reservoir Inflow for Use in a Flood-Analysis Model for the Delaware River, 2004-2006—Open-File Report 2010-1014