Appendix Part 2. 139

Appendix Part 2. Precipitation-Runoff Model 

Development and Calibration

Figures

A2–1. Diagram showing simplified schematic representation of the Hydrologic Simulation 

Program-FORTRAN (HSPF) inflows and outflows to a stream..........................................144

A2–2. Bar graphs showing percentages of the Hydrologic Simulation Program-FORTRAN 

(HSPF) model hydrologic response unit (HRU) area contributing to the continuous 

streamflow-gaging stations in the Pawcatuck River Basin, southwestern Rhode Island 

and southeastern Connecticut...............................................................................................148

A2–3. Map showing hydrologically effective impervious area represented in the Hydrologic 

Simulation Program-FORTRAN (HSPF) model of the Pawcatuck River Basin, southwestern Rhode Island and southeastern Connecticut.......................................................150

A2–4. Map showing reaches and subbasin boundaries defined for the Hydrologic Simulation 

Program-FORTRAN (HSPF) model of the Pawcatuck River Basin, southwestern 

Rhode Island and southeastern Connecticut.......................................................................152

A2–5. Graph showing sinusoidal function used to optimize the Lower Zone Evapotranspiration (LZET) parameter in the Hydrologic Simulation Program-FORTRAN (HSPF) of the 

Pawcatuck River Basin, southwestern Rhode Island and southeastern Connecticut.157

A2–6. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Queen River at Exeter, R.I...................162

A2–7. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Queen River at Liberty, R.I..................163

A2–8. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Usquepaug River near 

Usquepaug, R.I. ........................................................................................................................164

A2–9. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Chipuxet River at West 

Kingston, R.I...............................................................................................................................165

A2–10. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Chickasheen Brook at West 

Kingston, R.I. .............................................................................................................................166

A2–11. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Pawcatuck River at Kenyon, R.I........167

A2–12. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Beaver River near Usquepaug, R.I. ..168

A2–13. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Beaver River near Shannock, R.I......169
140 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

A2–14. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Pawcatuck River at Wood River 

Junction, R.I...............................................................................................................................170

A2–15. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Meadow Brook near Carolina, R.I. ...171

A2–16. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Wood River near Arcadia, R.I............172

A2–17. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Wood River at Hope Valley, R.I..........173

A2–18. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow 

duration curves, January 1, 2000, to September 30, 2004, Pawcatuck River at 

Burdickville, R.I. ........................................................................................................................174

A2–19. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow 

duration curves, January 1, 2000, to September 30, 2004, Pendleton Hill Brook near 

Clark Falls, Conn........................................................................................................................175

A2–20. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curve, January 1, 2000, to September 30, 2004, Ashaway River at Ashaway, R.I. .........176

A2–21. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Shunock River near North 

Stonington, Conn.......................................................................................................................177

A2–22. Graphs showing observed and simulated (A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 2004, Pawcatuck River at Westerly, R.I. ....178

A2–23. Scatterplot showing relation of monthly precipitation variability measured as the 

percent difference between the climate station used for the model calibration (FBWR) 

and the average of 5 climatic stations in or near the basin to the percent difference 

between observed and simulated monthly mean streamflow at 17 continuous-record 

streamflow-gaging stations in the Pawcatuck River Basin, southwestern Rhode Island 

and southeastern Connecticut, January 2000 through September 2004.........................179

A2–24. Bar graphs showing composite sensitivity of selected Hydrologic Simulation ProgramFORTRAN (HSPF) variables determined by parameter estimation (PEST) for selected 

model variables and stations, Pawcatuck River Basin, southwestern Rhode Island and 

southeastern Connecticut.......................................................................................................184

A2–25. Diagrams showing relative influence of selected Hydrologic Simulation ProgramFORTRAN (HSPF) model variables on minimizing the objective function measured by 

normalized eigenvectors for three parameter estimation (PEST) runs for (A) CASE 5, 

(B) CASE 6, and (C) CASE 8 at selected stations in the Pawcatuck River Basin, 

southwestern Rhode Island and southeastern Connecticut.............................................185

A2–26. Bar graphs showing average annual water budget for January 2000 through 

December 2003 by component in (A) inches per acre and (B) inches over the entire 

basin from each hydrologic response unit (HRU) simulated with the Hydrologic Simulation Program-FORTRAN (HSPF) of the Pawcatuck River Basin, southwestern Rhode 

Island and southeastern Connecticut...................................................................................187
Appendix Part 2. 141

A2–27. Bar graphs showing water budget for a wet month, March 2001, by component in 

(A) inches per acre and (B) inches over the entire basin from each hydrologic 

response unit (HRU) simulated with the Hydrologic Simulation Program-FORTRAN 

(HSPF) of the Pawcatuck River Basin, southwestern Rhode Island and 

southeastern Connecticut.......................................................................................................188

A2–28. Bar graphs showing water budget for a dry month, August 2002, by component in 

(A) inches per acre and (B) inches over the entire basin from each hydrologic 

response unit (HRU) simulated with the Hydrologic Simulation Program-FORTRAN 

(HSPF), Pawcatuck River Basin, southwestern Rhode Island and southeastern 

Connecticut................................................................................................................................189

A2–29. Bar graphs showing summary of water budgets in inches over the entire basin for 

(A) average annual 2000–03, (B) wet month (March 2001), and (C) dry month 

(August 2002) by component simulated with the Hydrologic Simulation ProgramFORTRAN (HSPF) of the Pawcatuck River Basin, southwestern Rhode Island and 

southeastern Connecticut.......................................................................................................190
142 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Tables

A2–1. Organization and description of Data Set Numbers (DSNs) in the Watershed Data 

Management (WDM) database developed for the Hydrologic Simulation ProgramFORTRAN (HSPF) model of the Pawcatuck River Basin, southeastern Rhode Island 

and southwestern Connecticut..............................................................................................146

A2–2. Constituent attribute (IDCONS) values used in the Watershed Data Management 

(WDM) system for the Hydrologic Simulation Program-FORTRAN (HSPF) model of 

the Pawcatuck River Basin, southeastern Rhode Island and southwestern 

Connecticut................................................................................................................................147

A2–3. Estimated effective impervious area as a percentage of developed land-use categories used in the development of the Hydrologic Simulation Program-FORTRAN (HSPF) 

model of the Pawcatuck River Basin, southeastern Rhode Island and southwestern 

Connecticut................................................................................................................................149

A2–4. Stream reaches (RCHRES) in the Hydrological Simulation Program-FORTRAN (HSPF) 

model of the Pawcatuck River Basin, southwestern Rhode Island and southeastern 

Connecticut................................................................................................................................153

A2–5. Starting and optimized variable values and their 95-percent confidence range 

calculated by PEST in order of ranked influence in the optimization of the Hydrologic 

Simulation Program-FORTRAN (HSPF) model of the Pawcatuck Basin Pawcatuck River 

Basin, southeastern Rhode Island and southwestern Connecticut.................................158

A2–6. Summary of model-fit statistics for daily mean discharge, January 2000 through 

September 2004, simulated by the Hydrologic Simulation Program-FORTRAN (HSPF) 

and observed at 17 continuous-record streamflow-gaging stations, Pawcatuck River 

Basin, southwestern Rhode Island and southeastern Connecticut.................................160

A2–7. Summary of model-fit statistics for monthly mean discharge, January 2000 through 

September 2004, simulated by the Hydrologic Simulation Program-FORTRAN (HSPF) 

and observed at 17 continuous record streamflow-gaging stations, Pawcatuck River 

Basin, southwestern Rhode Island and southeastern Connecticut.................................161

A2–8. Summary of model-fit statistics for daily mean discharge, January 2000 through 

September 2004, simulated by the Hydrologic Simulation Program-FORTRAN (HSPF) 

and estimated for 34 partial-record streamflow-gaging stations, Pawcatuck River 

Basin, southwestern Rhode Island and southeastern Connecticut.................................180

A2–9. Summary of model-fit statistics for monthly mean discharge, January 2000 through 

September 2004, simulated by the Hydrologic Simulation Program-FORTRAN (HSPF) 

and estimated at 34 partial-record streamflow-gaging stations, Pawcatuck River 

Basin, southwestern Rhode Island and southeastern Connecticut.................................181
Functional Description of Hydrologic Simulation Program-FORTRAN (HSPF) 143

Precipitation-Runoff Model

The effects of water withdrawals and land-use change on 

streamflow in the Pawcatuck River Basin were simulated with 

the Hydrological Simulation Program-FORTRAN (Bicknell 

and others, 2000), hereafter referred to as HSPF. The HSPF 

model was chosen because its capabilities make it an appropriate management tool for the continuous simulation of hydrology and complex water-withdrawal patterns in the basin, and 

the model has been a successful management tool for similar 

basins with similar water issues in New England (Zarriello 

and Ries, 2000; Zarriello and Bent, 2004). The computer code 

for HSPF and its companion programs are public domain and 

freely available. In general terms, the model was developed 

by (1) compiling, collecting, and processing needed data; 

(2) creating a model structure that represents the basin; (3) 

calibrating the model; and (4) evaluating its performance. The 

calibrated model was then used to simulate alternative withdrawals and land-use change in the basin. 

Functional Description of Hydrologic Simulation 

Program-FORTRAN (HSPF)

HSPF is a mathematical model designed to simulate the 

hydrology and movement of contaminants in a basin, but only 

the hydrologic simulation capability was developed and used 

in this study. Runoff from a basin is quantified by the continuous simulation of the hydrologic response to climatic and 

human stresses on the basis of the principle of conservation of 

water mass—that is, inflow equals outflow plus or minus any 

change in storage. In HSPF, a basin is represented by a collection of hydrologically similar areas referred to as hydrologic 

response units (HRUs) that drain to a network of stream or 

lake segments (RCHRESs). For each HRU and RCHRES, 

the model computes a water budget (inflows, outflows, and 

changes in storage) for each time step. A complete description 

of the processes involved in computing water budgets and the 

required input model variables are given in the “HSPF User’s 

Manual” (Bicknell and others, 2000).

HRUs reflect areas of similar land use, soil, subsurface 

geology, and other factors deemed important in producing 

a similar hydrologic response to precipitation and potential 

evapotransipiration. HRUs are divided into pervious-area land 

elements (PERLNDs) and impervious-area land elements 

(IMPLNDs). Within these elements are zones that define storages and processes between zones. PERLNDs and IMPLNDs 

have zones that retain precipitation at the surface as interception storage or snowpack storage. All water that is not evaporated from the surface produces runoff from IMPLNDs, but 

PERLNDs allow precipitation to infiltrate into the subsurface, 

where storages and processes are represented by upper, lower, 

and groundwater zones. Processes that control the rate of infiltration and change in subsurface storage make simulation of 

PERLNDs considerably more complex than the water-budget 

calculations for IMPLNDs. Surface runoff from PERLNDs 

and IMPLNDs and subsurface discharge from PERLNDs are 

typically directed into reaches (RCHRESs); however, water 

can be directed elsewhere if desired.

RCHRESs are model elements that represent a length 

of stream channel or reservoir. The downstream end of each 

RCHRES is referred to as a node. Nodes are typically placed 

to define channel segments with similar physical properties, 

such as reach segments with similar slope and width, stream 

junctions, lakes and reservoirs, and locations of data-collection 

sites. Nodes can be placed at other locations where estimates 

of streamflow are desired, such as upstream and downstream 

from municipal well fields, water diversions, or points of 

contaminant discharge. The storage-discharge properties of a 

RCHRES used to route water by the kinematic-wave method 

are specified in the FTABLE of the model input. 

The SCHEMATIC block, the NETWORK block, or 

both are used to represent the physical layout of the basin. 

The area of each IMPLND and PERLND that drains to a 

RCHRES is defined in this section of the model to formulate 

subbasins. The SCHEMATIC or NETWORK blocks are also 

used to define the linkage of one RCHRES to another. The 

MASSLINK associated with a SCHEMATIC block or the 

specifications of the NETWORK block control the linkage 

of flow components between model elements. Typically, this 

linkage involves routing (1) surface runoff from PERLNDs 

and IMPLNDs, (2) interflow and baseflow from PERLNDs to 

reaches, and (3) streamflow from reach to reach. 

The inflows to and outflows from a stream reach are 

illustrated in figure A2–1. Surface runoff can discharge to a 

reach from impervious surfaces (SURI) and pervious surfaces 

(SURO). Infiltrated water can discharge to the reach through 

the subsurface as interflow (IFWO)—a fast-responding shallow subsurface flow, or from active groundwater (AGWO)—a 

slow-responding baseflow component, or, optionally, exit from 

an HRU as deep groundwater flow that discharges outside 

of the basin. Inflow to a reach can also come from upstream 

reaches (IVOL), direct precipitation, and other user-specified 

sources such as treated wastewater. Typically, one or two 

Appendix Part 2. Precipitation-Runoff Model Development and 

Calibration

By Phillip J. Zarriello
144 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

outflow exits (or gates) were designated for each reach in this 

study as illustrated in figure A2–1 (a reach can have up to five 

exits). When two outflow gates are specified (OVOL 1), the 

volume time series of water withdrawals (OUTDGT 1) for 

each reach is read from the EXT SOURCES block (external 

sources). Specifying the first outflow gate for water withdrawals requires that the specified withdrawals are satisfied 

before water is routed through successive outflow gates. In the 

Pawcatuck River Basin model, water was routed downstream 

through the second outflow gate (OVOL 2) in reaches with 

withdrawals. In reaches with no withdrawals, a single outflow 

gate was generally specified.

HSPF requires two primary input files for its operation, the User Control Input (uci) file and the Watershed Data 

Management (WDM) file. The uci file directs the modelprocess algorithms and sets user-specified input variables. The 

WDM file is a binary file that efficiently stores large amounts 

of data. The three primary model elements—PERLNDs, 

IMPLNDs, and RCHRESs—are organized by blocks in the 

uci file. Within each block are modules and submodules that 

define model variables that control the movement of water and 

changes in storage between zones. Some modules are mandatory for simulations and others are optional. For example, 

the PERLND block requires PWATER modules to simulate 

hydrology, but the SNOW module is optional for simulating 

snowpack buildup and melt. A number of other blocks are 

required for administrative functions, such as controlling the 

operational sequence of the program, directing the model to 

external sources, controlling the output of time-series data, and 

defining the linkage between model elements. Other blocks 

are available for data manipulation, displaying and reporting 

model results, and other optional model features. 

RCHRES

SURI

Evaporation

Precipitation

Inflow from

upstream 

reach 

(IVOL) Other 

inflow

Outflow to 

downstream 

reach (OVOL2)

Outflow to pumped well 

or stream withdrawal 

(OVOL1)

Pumped

well

SURO

IFWO

AGWO

Evapotranspiration

EXPLANATION

Precipitation

SURI–Surface runoff from impervious areas

SURO–Surface runoff from pervious areas

IFWO–Interflow (subsurface flow that responds 

rapidly to precipitation)

AGWO–Active groundwater flow (base flow)

RCHRES–Stream reach or reservoir segment

 

IVOL–Inflow volume

 

OVOLx–Outflow volume through individual exits (x). 

Reach can have up to five exits.

 

Figure A2–1. Simplified schematic representation of the Hydrologic Simulation Program-FORTRAN (HSPF) inflows 

and outflows to a stream.
Impervious Areas (IMPLNDs) 145

Database

The WDM file stores time-series data required for simulations or generated by the HSPF model. Precipitation and 

evapotranspiration are required time series; air temperature, 

dew-point temperature, solar radiation, and wind speed are 

required if snowpack buildup and melt are simulated. These 

data are typically entered into the WDM database by use of the 

software IOWDM (Lumb and others, 1990) or WDMUtil. The 

EXT SOURCES block (external sources) of the uci file reads 

data from the WDM file and model-generated time series are 

passed to the WDM file through the EXT TARGETS block 

(external targets) of the uci file. Output time series can be 

generated for any component in the simulation process defined 

in the “Time Series Catalog” section of the user’s manual (for 

example, the active groundwater outflow from a PERLND—

AGWO can be output directly), but streamflow time series 

are typically the primary output. Time-series data in WDM 

can be accessed, displayed, transformed, and plotted by use of 

ANNIE (Flynn and others, 1995), GenScn (Kittle and others, 

1998), or WDMUtil software.

Dataset numbers (DSNs) and attribute information must 

exist in the WDM file to pass time-series data between the 

WDM file and the model. The WDM file is organized by 

DSNs and relational attribute information. The organization 

of the WDM file developed for the Pawcatuck River Basin is 

summarized in table A2–1. Attributes describe the data type, 

time step, location, and other important features of the data. 

The data type is defined by the constituent attribute IDCONS, 

which are defined for the Pawcatuck Basin in table A2–2.

Irrigation withdrawals for long-term simulations (1960–

2004) were simplified by creating two WDM data sets; DSN 

1003 reflects the pattern of daily irrigation on turf farms, 

and DSN 1002 reflects the pattern of daily irrigation on golf 

courses. For days in which the logistic-regression equation 

predicted irrigation, these distribution patterns were expressed 

as hourly irrigation rates defined in cubic feet per second per 

acre. On days of no irrigation, hourly values were set equal to 

zero. For each reach with irrigation withdrawals, hourly withdrawals were read into the HSPF model by multiplying the 

irrigated area applicable to that reach, in acres, by the irrigation rate per acre. Irrigation withdrawals were assumed to be 

lost to evapotranspiration.

Representation of the Basin

The physical and spatial representation of the basin in the 

model is defined by the combination of HRUs (PERLNDs and 

IMPLNDs), their contributing area to a reach, and the linkage 

of one reach to another. The process of defining HRUs, their 

linkage to reaches, and the linkage of reaches to each other 

often is referred to as the schematization or discretization of 

a basin. A geographic information system (GIS) was used to 

aid in this process. Basin and subbasin boundaries in the study 

area were obtained from available USGS, RIGIS, and MAGIC 

sources or digitized from 1:24,000-scale USGS topographic 

maps when necessary. Other digital data layers used in the 

discretization process included surficial geology, land use, 

hydrography, wetlands, and soils. The spatial data were simplified and grouped to obtain categories that were considered 

important to the basin hydrology. The surficial-geology data 

layer was simplified from seven types of material into two 

types on the basis of permeability and storage characteristics; 

(1) sand and gravel and (2) till. The land-use data layer was 

combined with the wetland data layer and then simplified from 

56 to 10 categories; (1) forest, (2) open (3) irrigated crop, (4) 

turf farm, (5) golf course, (6) forested wetland, (7) nonforested 

wetland, (8) low-density residential, (9) moderate- to highdensity residential, and (10) commercial-industrial-transportation (fig. 2–9). Preliminary calibration results indicated that an 

additional HRU type was needed to better define the hydrologic response in the western part of the basin. This HRU was 

defined on the basis of two soil categories (1) those classified 

as bedrock outcrops or rocky soils on steep slopes, and (2) all 

other soils. 

Development of Hydrologic Response Units 

(HRUs)

HRUs were obtained by combining the simplified landuse, surficial geology and soils data layers, which resulted in 

40 unique combinations of land use, surficial-geology types, 

and soils. Unique HRUs with areas less than about 1 percent 

of the basin area were grouped into the HRU with the most 

similar characteristics. For example, open space in commercial 

and industrial areas which accounted for about 1 percent of the 

basin area, was combined with the open space in high-density 

residential areas. From the 40 possible combinations of HRU 

types, 17 pervious-area (PERLNDs) and 2 impervious-area 

(IMPLNDs) HRUs were established for the Pawcatuck Basin 

(fig. A2–2). The area of each HRU for each subbasin was 

computed with a GIS macro program that intersects the HRU 

types with the subbasin boundaries.

Impervious Areas (IMPLNDs)

Impervious areas that drain directly to streams (hydrologically effective impervious areas) are simulated as impervious areas (IMPLNDs). Impervious areas that drain to pervious areas (hydrologically ineffective impervious areas) are 

incorporated into the PERLNDs representing developed areas. 

Initial estimates of effective impervious area were determined 

as a percentage of the area for various developed land-use 

classes (table A2–3) as assigned in the 1995 land-use cover. 

The land-use classes in table A2–3 are more detailed than the 

land-use classes used to develop the model HRUs as indicated 

in fig. A2–2. These percentages of effective impervious area 

by land-use type are similar to the values used in the Usquepaug-Queen Basin HSPF model (Zarriello and Bent, 2004) 

and appear to be representative of the overall responsiveness 
146 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Table A2–1. Organization and description of Data Set Numbers (DSNs) in the Watershed Data Management 

(WDM) database developed for the Hydrologic Simulation Program-FORTRAN (HSPF) model of the 

Pawcatuck River Basin, southeastern Rhode Island and southwestern Connecticut.

DSN Purpose

Model input

20–90 Measured or computed climate data.

101–179 Measured or estimated streamflow data.

307–380 Combined estimated 2000–04 total withdrawals from a reach (current conditions).

407–465 Combined estimated total withdrawals from a reach (1960–04) when selected withdrawals are 

converted from surface-water to groundwater sources.

1021–1203 Measured (1999–04) individual surface-water withdrawals or calculated streamflow depletion 

from groundwater withdrawals, where

1xx1–1xx3 xx, identifies the reach number, and

102x–120x x, identifies individual withdrawal points.

2021–2801 Long-term (1960–04) estimated and measured surface-water withdrawals or calculated 

streamflow depletion from groundwater withdrawals, where

2xx1–2xx3 xx, identifies the reach number, and

201x–280x x, identifies individual withdrawal points.

3321–3803 Measured (1999–04) pump rates from individual groundwater withdrawals, where

3xx1–3xx3 xx, identifies the reach number, and

332x–380x x, identifies individual withdrawal points.

4071–4432 Calculated (1960–04) streamflow depletion rates for irrigation withdrawals converted from 

surface-water to groundwater sources, where

4xx1–4xx2 xx, identifies the reach number, and

407x–443x x, identifies individual withdrawal points.

1002 Hourly (1960–04) golf-course irrigation rate determined from logistic regression.

1003 Hourly (1960–04) turf-farm irrigation rate determined from logistic regression.

Model output

201–284 Simulated streamflow by reach (base scenario).

5001–5219 Simulated flow components by hydrologic response unit (HRU), where

5xx1–5xx9 xx, identifies the reach, and

500x–5210x x, identifies individual flow component.

6x01–6x84 Scenario simulation results, where

6x01–6x84 x, identifies a unique scenario, and

60xx–67xx xx, identifies the reach number.
Pervious Areas (PERLNDs) 147

of the hydrograph to precipitation and water budgets. Two 

IMPLND types were used in the model: (1) commercialindustrial-transportation, and (2) residential. Hydrologically, 

these two IMPLNDs are similar, but they were given unique 

HRUs for possible future water-quality applications. 

About 10 percent of the basin is classified as developed 

(areas classified as residential, commercial, industrial, 

and transportation), but the effective impervious area was 

estimated to be about 1.6 percent of the basin area. Subbasin 

impervious area, as a percentage of the total subbasin area has 

a median value of 0.7 percent and ranged from 0 to 12 percent 

of subbasin areas. The highest concentrations of impervious 

area are found in the lower part of the Pawcatuck Basin in the 

City of Westerly. In several subbasins along the U.S. Interstate 

95 corridor, about 5 percent of the basin area is effective 

impervious area. The distribution of effective impervious area 

is shown in figure A2–3. 

Pervious Areas (PERLNDs)

Nonirrigated pervious areas (PERLNDs) in the basin 

are represented by five HRUs overlying sand and gravel and 

five HRUs of similar land use overlying till (fig. A2–2). For 

each of these ten HRUs, six represent open space in developed areas (PERLNDs 1, 2, 3, 11, 12, and 13), two represent 

open space in undeveloped areas (PERLNDs 4 and 14), and 

two represent forested areas (PERLNDs 5 and 15). PERLND 

16 was created to represent areas where soils were classified 

as rock outcrop or very rocky soils with steep slopes. Other 

PERLNDs represent the three irrigated HRUs—golf courses, 

turf farms, and agriculture (PERLNDs 6, 7, and 8, respectively); open water, which represents small surface-water 

features not associated with a river reach (PERLND 17); and 

the two wetland HRUs—nonforested and forested (PERLNDs 

18 and 19, respectively). Open water and wetland PERLNDs 

were not differentiated by underlying surficial material.

Open space in undeveloped areas (PERLNDs 4 and 14) 

compose about 9.7 percent of the total basin area and is about 

evenly divided between areas overlying sand and gravel and 

till (averages are 5.2 and 4.4 percent, respectively). Open 

space in developed areas compose about 8.1 percent of the 

total basin area. Open space associated with development 

represents the combined area of green space between buildings and the adjacent impervious area that contributes runoff 

to the pervious area. The additional runoff from impervious 

areas causes these areas to respond more rapidly to precipitation than similar undisturbed HRUs; therefore, infiltration and 

soil-water storage were decreased relative to undeveloped 

open space for similar types of surficial geology. 

The dominant HRU in the Pawcatuck River Basin 

(fig. A2–2) is forest. Collectively, forested areas overlying 

sand and gravel, till, and forested wetlands (PERLNDs 5, 15, 

and 19, respectively) compose about 63 percent of the basin 

area. Forested areas mostly overlie till (PERLND 15), which 

composes about 36 percent of the total basin area, but also 

include substantial areas overlying sand and gravel 

(16 percent) and forested wetlands (11 percent). Forest 

overlying till compose as much as 68 percent of the area 

in headwater subbasins; this HRU is less common in the 

subbasins along the lower reaches of the mainstem (as little 

as 1 percent of the subbasin area). Forest overlying sand and 

gravel composes as much as 50 percent of the area in valley 

subbasins and generally little, if any, area in the headwater 

subbasins. Forested wetlands compose between 3.5 and 

37 percent of subbasin areas and are generally more common 

in valley subbasins then in headwater subbasins. 

Table A2–2. Constituent attribute (IDCONS) values used in the 

Watershed Data Management (WDM) system for the Hydrologic 

Simulation Program-FORTRAN (HSPF) model of the Pawcatuck 

River Basin, southeastern Rhode Island and southwestern 

Connecticut. 

[ft3/s, cubic feet per second; °C, degrees Celsius; °F, degrees Fahrenheit; 

mi/hr, miles per hour; mi/d, miles per day]

IDCONS Purpose 

(units)

FLOW Measured or simulated streamflow (ft3/s)

Climate data

AIRT Measured air temperature (°C or °F)

DEWP Measured dew-point temperature (°C or °F)

WIND Measured wind speed (mi/hr)

TWND Computed total wind movement (mi/hr or mi/d)

PREC Measured precipitation (inch)

PET Computed potential evapotranspiration (inch)

SOLR Measured solar radiation (Langley)

Water-use data

ExDemand Total water withdrawal from reach (ft3/s)

SWDL Reported surface-water withdrawal (ft3/s)

STRMDEPL

Calculated streamflow depletion from a pumped 

well (ft3/s)

PUMP Reported groundwater withdrawal (ft3/s)

WSPD Water-supply demand (ft3/s)

Flow or storage components from PERLNDs and IMPLNDs

PERO Total runoff (inch)

SURO Surface runoff (inch)

IFWO Interflow (inch)

AGWO Active groundwater flow (inch)

UZSN Upper-zone storage (inch)

LZSN Lower-zone storage (inch)

AGWET Active groundwater evapotranspiration (inch)
148 Appendix Part 2. Precipitation-Runoff Model Development and Calibration Overlying sand and gravel Overlying till Effective impervious area Overlying sand and gravel Overlying till Effective impervious area Overlying sand and gravel Overlying till Effective impervious area Overlying sand and gravel Overlying till Effective impervious area

1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 19 21 20

Queen River at Exeter, RI (QRPB)Queen River at Liberty, RI (QRLY)Usquepaug River near Usquepaug, RI (USQU)Chickasheen Brook at West Kingston, RI (CBLL)

1 2 3 4 5 6 7 8 11 12 13 14 15 16 17 18 19 21 20

Chipuxet River at West Kingston, RI (CRWK)Beaver River near Usquepaug, RI (BRUS)Beaver River near Shannock, RI (BRSH)Meadow Brook near Carolina, RI (MBCA)

Wood River near Arcadia, RI (WRAR)Wood River at Hope Valley, RI (WRHV)Pendleton Hill Brook near Clark Falls, CT (PHBK)Ashaway River at Ashaway, CT (ASHA)Shunock River at North Stonington, CT (SRNS)

High density

Open

Forest

Golf

Turf Irrigated Agriculture

Open

Forest

Steep, Rocky

Water

Non-Forested

Forested

Residential

Commercial

Commercial

Low density

Residential

High density

Low density

Residential

Commercial

Wetlands

High density

Open

Forest

Golf

Turf Irrigated Agriculture

Open

Forest

Steep, Rocky

Water

Non-Forested

Forested

Residential

Commercial

Commercial

Low density

Residential

High density

Low density

Residential

Commercial

Wetlands

HYDROLOGIC RESPONSE UNIT (HUR) NUMBER

TYPE OF HYDROLOGIC RESPONSE UNIT (HRU)

Pawcatuck River at Kenyon, RI (PRBC)Pawcatuck River at Wood River Junction, RI (PRWR)Pawcatuck River at Burdickville, RI (PRBV)Pawcatuck River at Westerly, RI (PRWS)

0

70605040302010

PERCENTAGE OF SUBBASIN AREA

0

70605040302010

Figure A2–2. Percentages of the Hydrologic Simulation Program-FORTRAN (HSPF) model hydrologic response unit (HRU) area contributing to the continuous streamflow-gaging stations in the Pawcatuck River Basin, southwestern Rhode Island and southeastern Connecticut. (Site locations shown in figure A2–4 and described in table A2–4).)
Pervious Areas (PERLNDs) 149

Three HRUs were established for areas that receive 

irrigation (fig. A2–2)—golf courses (PERLND 6), turf farms 

(PERLND 7), and irrigated agriculture (PERLND 8). The 

1995 digital land cover indicates 1,161 acres in the basin 

are classified as golf courses; however, field investigations 

indicated that about 29 percent (74 acres) of the 258 acres in 

the Queen-Usquepaug subbasin classified as golf course was 

not irrigated. Areas of golf courses that were not irrigated 

were reclassified as open space overlying sand and gravel 

(PERLND 4). Although the underlying surficial material is 

not defined for the irrigated HRUs, about 80 percent of areas 

classified as golf course and nearly all the area classified 

as turf farm or other irrigated agriculture are underlain by 

sand and gravel. For this reason, these HRUs were assigned 

similar model-variable values as the HRU representing open 

space overlying sand and gravel. Collectively, irrigated HRUs 

represent about 2.4 percent of the total basin area, which is 

unevenly distributed; irrigated areas can compose as much as 

20 percent of a subbasin area, but most subbasins contain little 

or no irrigated area. 

Two HRUs were established to represent wetland 

areas (fig. A2–2)—nonforested wetland (PERLND 18) and 

forested wetland (PERLND 19). Collectively, nonforested and 

forested wetlands compose about 14 percent of the Pawcatuck 

River Basin. As a percentage of the subbasin area, the total 

wetland area range from 4.0 to 40 percent; nonforested 

wetland area range from 3.5 to 37 percent, and forested 

wetland area range from 0 to 24 percent. The wetland HRUs 

were not distinguished by their underlying surficial material 

because this was considered secondary to the soil properties 

and evaporation potential of wetlands. About 68 percent of 

nonforested and forested wetlands overlie sand and gravel 

deposits, however. Area classified as open water composes 

about 2.8 percent of the Pawcatuck River Basin and range 

from 0 to 18 percent of the subbasin area.

An alternative model of the Pawcatuck River Basin was 

developed in which additional wetlands and open water were 

simulated as virtual RCHRESs. Virtual RCHRES allowed 

more evaporation than their corresponding HRUs because 

evapotranspiration was not limited to the available moisture 

supply from direct precipitation. To maintain a consistent 

model area, the area of the virtual RCHRESs was set equal to 

the area of wetlands and open water. The area of the virtual 

RCHRES was defined in its corresponding FTABLE over 

which direct precipitation and evaporation were applied. 

Table A2–3. Estimated effective impervious area as a percentage of developed land-use categories used in the development 

of the Hydrologic Simulation Program-FORTRAN (HSPF) model of the Pawcatuck River Basin, southeastern Rhode Island and 

southwestern Connecticut.

[>, greater than]

Land-use classification Total area

(acres)

Percent 

impervious1

Effective impervious area

Total

(acres)

Percent of total 

basin area

High-density residential lot size 0.125 or less 1,391 20 278 0.14

Medium- to high-density residential lot size >0.125 to 0.25 acre 2,262 15 339 0.18

Low- to medium-density residential lot size >0.25 to 1 acre 10,077 5 504 0.26

Low-density residential lot size >1 acre 2,535 2 51 0.03

Light urban and transportation facilities 136 10 14 0.01

Commercial, industrial, and transportation 2,402 80 1,922 0.99

Total 18,803 132 3,108 1.61

1 Percent of total area estimated as effective imperious area.
150 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

1

Worden

Pond

Watchaug

Chapman Pond

Pond

Yawgoo

Pond

71°52'30” 71°45' 71°37'30” 71°30’

41°37'30”

41°30'

41°22'30”

Basin boundary

State boundary

Town boundary

County boundary

EXPLANATION

80

20

15

10

5

2

0 1 2 3 4 5 MILES

0 1 2 3 4 5 KILOMETERS

Percent hydrologically effective 

impervious area

0

Base from U.S. Geological Survey, 1995, 1:24,000

North American Datum of 1983

Rhode Island state plane projection

WINDHAM CO.

NEW LONDON CO.

GREENWICH CO.

WASHINGTON CO.

RHODE ISLAND

CONNECTICUT

Hopkinton

Voluntown

Sterling

West Greenwich

Richmond

South

Kingstown

North

Kingstown

Charlestown

Westerly

North Stonington

Exeter

Voluntown

Figure A2–3. Hydrologically effective impervious area represented in the Hydrologic Simulation Program-FORTRAN (HSPF) model 

of the Pawcatuck River Basin, southwestern Rhode Island and southeastern Connecticut.
Stream Reaches (RCHRES) 151

Stream Reaches (RCHRES)

The Pawcatuck River Basin was segmented into 70 

stream reaches (fig. A2–4; table A2–4). The reach segmentation was based on hydrologic characteristics and the availability of streamflow information. In general, RCHRES are 

numbered in downstream order; however, the number jumps 

to the next nearest increment of 10 for a new major subbasin. 

For example, RCHRESs 1 through 20 define the UsquepaugQueen subbasin as was done previously by Zarriello and Bent 

(2004); then the numbering jumps to RCHRESs 31 through 37 

to define the Chipuxet and Chickasheen subbasins. RCHRESs 

41 through 43 define the Beaver River subbasin, RCHRESs 

51 through 66 defines the Wood River subbasin, RCHRESs 73 

through 77 define the Ashaway River subbasin, and RCHRESs 

81 through 83 define the Shunock River subbasin. The Pawcatuck River is defined by RCHRES 37, 46, 50, 69, 71, 72, 80, 

and ends at RCHRES 84, the mouth of the river. 

The linkage of reaches in the SCHEMATIC block to one 

another, in most cases, is easily identified in figure A2–4. For 

example, RCHRES 1 flows into RCHRES 2, which flows into 

RCHRES 3. Linkages between some tributaries and the main 

stem are less obvious where the confluence does not coincide 

with a reach junction (node). In general, flow in a reach is 

routed into the closest node to provide the most realistic flow. 

If streamflow is monitored at the downstream end of a reach, 

but a major tributary flows into the reach just above that gage, 

this scheme would not include the flow from the tributary 

because its discharge is not accounted for by the model until 

the end of the next RCHRES. In this situation, the COPY feature of HSPF was used to account for all flow at the streamflow-gaging stations prior to writing simulation results to the 

WDM file. COPY operations were used to combine flows 

in RCHRESs 9 and 10; RCHRESs 34 and 374; RCHRESs 

53, 54, and 55; RCHRESs 50, 65, and 66; RCHRESs 59 and 

62; and RCHRESs 80 and 83 prior to outputting simulated 

flows. Output from these COPY operations correspond to 

streamflow-gaging stations at Queen River at Liberty (QRLY, 

01117370), Pawcatuck River at Kenyon (PRBC, 01117430), 

Wood River near Arcadia (WRAR, 011178000); Pawcatuck 

River at Burdickville (PRBV, 01118010), Wood River at Hope 

Valley (WRHV, 01118000), and Pawcatuck River at Westerly 

(PRWS, 01118500). The italicized numbers in the column 

labeled “Upstream RCHRES number” in table A2–4 identify 

RCHRES that are directed to the next downstream RCHRES 

in the model, but are included in the flows output at that station through the COPY operation. 

Reaches typically have one or two exit gates depending 

on the presence of withdrawals from the reach. In reaches that 

do not have simulated withdrawals, water is generally routed 

to the next downstream reach though a single exit gate. In the 

Pawcatuck River Basin HSPF model, 24 of the 70 reaches 

have only one outflow gate. In reaches with specified withdrawals, the first exit gate is used to satisfy the withdrawal 

demand and the second exit gate was used to route water to the 

next downstream reach. In the Pawcatuck River Basin HSPF 

model, 45 reaches have two outflow gates. Exceptions to this 

rule apply to subbasins where the groundwater divide does 

not coincide with the surface-water divide. This condition 

is known to occur in two subbasins in the Pawcatuck River 

Basin—the upper Queens Fort Brook (RCHRES 7) and the 

upper Meadow Brook (RCHRES 47). Diversions through exit 

gates in these subbasins were treated differently. 

The upper Queens Fort Brook reach (RCHRES 7) is 

specialized to account for subsurface discharge from this 

subbasin that is reported to drain to the Hunt-AnnequatucketPettaquamscutt (HAP) Basin (Dickerman and others, 1997; 

Barlow and Dickerman, 2001). In this subbasin, all active 

groundwater outflow, and 80 percent of interflow, is directed 

out of the subbasin as described by Zarriello and Bent (2004). 

These flow components are not routed to other areas in the 

model and, therefore lost from the system.

In the upper Meadow Brook subbasin (RCHRES 47), 

the water-table gradient reported by Allen and others (1966) 

indicates that groundwater in the sand and gravel deposits 

in the center of RCHRES 47 flows south-southeast toward 

the Pawcatuck River at RCHRES 46 (fig. A2–4). Initial 

simulations indicated that low flows were oversimulated 

in RCHRES 47 compared to the measured flows (MBCA, 

01117600), which supports the possibility of groundwater flow 

toward RCHRES 46. To simulate groundwater diversion to 

RCHRES 46, a third outflow gate was added to RCHRES 47. 

The first exit gate is used for water withdrawals in RCHRES 

47, the second exit gate diverts water to RCHRES 46, and 

the third exit gate routes water downstream to RCHRES 48. 

The groundwater diversion specified by the second exit gate 

is controlled by a second discharge column in the RCHRES 

47 FTABLE. Discharges from the second exit gate were 

determined by minimizing the difference between measured 

and simulated flows in the reach and are specified as a 

constant 2.0 ft3/s except at the lowest storage-to-discharge 

values, which are slightly less. 

Alternatively, a percentage of the PERLND active 

groundwater flow component (AGWO) can be diverted from 

RCHRES 47 to RCHRES 46 (similar to the diversion of 

groundwater in the upper Queens Fort Brook subbasin). The 

diversion fluctuates and can be a large percentage of the total 

flow to the RCHRES at times. Specifying a diversion through 

a RCHRES exit gate is controlled by the values specified in 

the FTABLE. The fixed-rate diversion specified by the second 

exit gate in RCHRES 47 appears to represent the diversion 

of groundwater from the basin better than the variable rate 

diversion. In principle, a fixed-rate diversion better 

represents a relatively constant or uniform transmissivity 

and head gradient. 

Subbasins in which the stream channel is largely dominated by open water are simulated with direct precipitation 

and evaporation to the RCHRES. These include RCHRES 34 

(Worden Pond), RCHRES 35 (Yawgoo and Barber Ponds), 

RCHRES 62 (Locustville Pond) and RCHRES 68 (Watchaug 

Pond). The area of these ponds is not included in the HRU 

area for water (PERLND 17) in the corresponding 

SCHEMATIC BLOCK for these subbasins. 
152 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Worden

Pond

Watchaug

Chapman Pond

Pond

Yawgoo

Pond

Barber

Pond

I

*

*

WOOD1

PAWC1

PAWC6

FLAT1

PAWC5

SHUN1

CHIP1

PAWC3

WYAS1

WOOD3

GREE1

PARR1

CHIP3

BREA1

MOSC1

TOMA1

CANO1

PAWC8

PASQ1

WOOD4

BEAV1

PAWC2

POQU1

ASHA1

ROAR1

KELL1

CEDA1

MEAD1

FISH2

FISH1

LOCK1

SHUN2

WOOD2

BEAV2

ASSE1 PAWC4

PEND1

WOOD5

CHIP2

CHIC1

BRUS1

PAWC7

QUFB1

PAWC9

BRUS2

QUEN7

GLEN1

QUEN1

BEAV3

PARM1

PERR1

MEAD2

QUEN5

COON1

GLAD1 CHIC2

TANE1

WOOD6

LWPD1

QUEN6

QUEN3

TRIB1

FISH3

SHER1

QUFB2

QUEN2

PEEP1

QUEN4

LOCK2

RAKE1

0

4 1

7 5 2

31

17

6

3

8

9

10

11

32

35

33

37

14

18

16

15

20

19

13

34

36

42

41

47

44

46

45

43

58

55

54

52

56

53

57

61

60

62

64

78

63

70 48

59

49

50

65

68

67

69

66

51

73

74

75

76

77

81

82

83

79

84 71

80 72

71°52'30” 71°45' 71°37'30” 71°30’

41°37'30”

41°30'

41°22'30”

Basin boundary

State boundary

0 1 2 3 4 5 MILES

0 1 2 3 4 5 KILOMETERS

Subbasin boundary

Continuous streamflow-gaging station

Partial-record streamflow-gaging station

Stream-reach number (RCHRES)

Subbasin-identification name (IDLOCN)

50

PAWC4

EXPLANATION

Base from U.S. Geological Survey, 1995, 1:24,000

North American Datum of 1983

Rhode Island state plane projection

CONNECTICUT

RHODE ISLAND

Figure A2–4. Reaches and subbasin boundaries defined for the Hydrologic Simulation Program-FORTRAN (HSPF) model of 

the Pawcatuck River Basin, southwestern Rhode Island and southeastern Connecticut. (Names of reaches associated with the 

model-reach number and name are given in table A2–4).
Stream Reaches (RCHRES) 153

Table A2–4. Stream reaches (RCHRES) in the Hydrological Simulation Program-FORTRAN (HSPF) model of the Pawcatuck River 

Basin, southwestern Rhode Island and southeastern Connecticut.

[Site locations shown in figure A2–4; USGS stations described in table 1–3; no(s)., number(s); IDLOCN, identification attribute in the Watershed Data Management (WDM) database; mi2

, square miles; --, not applicable; upsteam reach numbers in bold-italics contribute flow to the streamflow-gaging station only, 

not the model reach]

Stream 

reach no. 

(RCHRES)

Subbasin 

IDLOCN Stream name

IDLOCN of streamflowgaging station

(p indicates 

partial record)

Direct 

drainage area

(mi2)

Total 

drainage area

(mi2)

Upstream 

reach nos.

(RCHRES)

USGS 

station no.

1 QUEN1 Queen River (QECC-p) 2.77 2.77 -- 01117354

2 QUEN2 Queen River (QRPB) 0.87 3.64 1 011173545

3 QUEN3 Queen River (QREX-p) 1.27 4.91 2 01117355

4 FISH1 Fisherville Brook 3.94 3.94 -- --

5 FISH2 Fisherville Brook (FBEX-p) 4.02 7.97 4 01117360

6 FISH3 Fisherville Brook 0.91 8.87 5 --

7 QUFB1 Queens Fort Brook 3.19 3.19 -- --

8 QUFB2 Queens Fort Brook (QFBK-p) 0.99 4.18 7 01117367

9 QUEN4 Queen River (QRLY) 0.63 19.3 3,6,8,10 01117370

10 PEEP1 Peeper Pond Brook 0.74 0.74 -- --

11 TRIB1 Unnamed tributary (UTLY-p) 0.95 0.95 -- 01117375

13 QUEN5 Queen River 2.33 22.6 9,11 --

14 LOCK1 Locke Brook (LBLY-p) 4.47 4.47 -- 01117380

15 LOCK2 Locke Brook 0.45 4.92 14 --

16 RAKE1 Rake Factory Brook (RFBK-p) 0.26 0.26 -- 01117385

17 SHER1 Sherman Brook (SBGR-p) 1.06 1.06 -- 01117400

18 GLEN1 Glen Rock Brook (GRGR-p) 2.80 2.80 -- 01117390

19 QUEN6 Queen River (URUS) 1.36 33.0 13,15,16,17,18 01117410

20 QUEN7 Usquepaug River (USQU) 2.96 35.4 19 01117420

31 CHIP1 Chipuxet River (CRWK-p) 6.35 6.35 -- 01117336

32 CHIP2 Chipuxet River (CRWK) 3.33 9.69 31 01117350

33 CHIP3 Chipuxet River 5.77 15.4 32 --

34 PAWC1 Pawcatuck/Chipuxet 

River 

10.4 25.8 33 --

35 CHIC1 Chickasheen Brook (CBLL-p) 3.34 3.34 -- 01117421

36 CHIC2 Chickasheen Brook (CBLL) 1.56 4.89 35 01117424

37 PAWC2 Pawcatuck River (PRBC) 5.91 72.0 20,34,36 01117430

41 BEAV1 Beaver River (BRWY-p) 5.42 5.42 -- 01117465

42 BEAV2 Beaver River (BRUS) 3.97 9.39 41 01117468

43 BEAV3 Beaver River (BRSH) 2.36 11.8 42 01117471

44 PASQ1 Pasquiset Brook (PBWY-p) 6.05 6.05 -- 01117450

45 TANE1 Taney Brook (TBCA-p) 1.61 1.61 -- 01117480

46 PAWC3 Pawcatuck River (PRWR) 7.62 99.1 37,43,44,45 01117500

47 MEAD1 Meadow Brook (MBCA) 4.95 4.95 -- 01117600

48 MEAD2 Meadow Brook 2.41 7.36 47 --
154 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Table A2–4. Stream reaches (RCHRES) in the Hydrological Simulation Program-FORTRAN (HSPF) model of the Pawcatuck River Basin, 

southwestern Rhode Island and southeastern Connecticut.—Continued

[Site locations shown in figure A2–4; USGS stations described in table 1–3; no(s)., number(s); IDLOCN, identification attribute in the Watershed Data Management (WDM) database; mi2

, square miles; --, not applicable; upsteam reach numbers in bold-italics contribute flow to the streamflow-gaging station only, not 

the model reach]

Stream 

reach no. 

(RCHRES)

Subbasin 

IDLOCN Stream name

IDLOCN of streamflowgaging station

(p indicates 

partial record)

Direct 

drainage area

(mi2)

Total 

drainage area

(mi2)

Upstream 

reach nos.

(RCHRES)

USGS 

station no.

49 CEDA1 Cedar Swamp Brook (CSBK-p) 4.82 4.82 -- 01117700

50 PAWC4 Pawcatuck River (PRBV) 4.32 205 46,48,49,65,66 01118010

51 WOOD1 Wood River (WREH-p) 11.1 11.1 -- 01117720

52 KELL1 Kelly Brook (KBEH-p) 4.41 4.41 -- 01117740

53 WOOD2 Wood River (WRAR) 4.79 34.9 51,52,54,55 01117800

54 FLAT1 Flat River (FRAR-p) 8.23 8.23 -- 01117760

55 BREA1 Breakheart Brook (BBAR-p) 6.41 6.41 -- 01117780

56 PARR1 Parris Brook (PBAR-p) 6.54 6.54 -- 01117840

57 WOOD3 Wood River 7.60 46.5 53,56,58 --

58 ROAR1 Roaring Brook (RBAR-p) 5.07 5.07 -- 01117860

59 WOOD4 Wood River (WRHV) 6.43 71.5 57,58,62 01118000

60 BRUS1 Brushy Brook (BBHV-p) 3.66 3.66 -- 01117900

61 MOSC1 Moscow Brook (MBHV-p) 6.91 6.91 -- 01117950

62 BRUS2 Brushy Brook 2.93 13.5 60,61 --

63 WOOD5 Wood River (WRHV) 4.50 76.0 59 --

64 CANO1 Canonchet Brook (CBHV-p) 6.59 6.59 -- 01118006

65 WOOD6 Wood River (WRAL-p) 1.77 86.4 63,64,66 01118009

66 COON1 Coon Hill tributary (CHAL-p) 2.05 2.05 -- 01118008

67 PERR1 Perry Healy Brook (PHBB-p) 2.37 2.37 -- 01118022

68 POQU1 Poquiant Brook 5.38 7.75 67 --

69 PAW5 Pawcatuck River 8.62 221 50,68 --

70 TOMA1 Tomaquag Brook (TBBF-p) 6.68 6.68 -- 01118055

71 PAWC6 Pawcatuck River 10.3 238 69,70 --

72 PAWC7 Pawcatuck River 3.87 242 71 --

73 GREE1 Green Fall River (GRLG-p) 6.74 6.74 -- 01118255

74 PEND1 Pendleton Hill Brook (PHBK) 4.00 4.00 -- 01118300

75 WYAS1 Wyassup Brook (WBCF-p) 7.44 7.44 -- 01118340

76 GLAD1 Glade Brook (GBLG-p) 1.85 1.85 -- 01118352

77 ASHA1 Ashaway River (ARAS) 4.96 27.5 73,74,75,76,78 01118360

78 PARM1 Paramenter Brook (PBHK-p) 2.50 2.50 -- 01118355

79 LWPD1 Lewis Pond Outlet (LPPH-p) 1.59 1.59 -- 01118365

80 PAWC8 Pawcatuck River (PRWS) 6.48 294 72,77,79,83 01118500

81 SHUN1 Shunock River (SRPH-p) 7.80 7.80 -- 01118373

82 ASSE1 Assekonk Brook (ABNS-p) 3.89 3.89 -- 01118375

83 SHUN2 Shunock River (SRNS) 4.62 16.3 81,82 01118400

84 PAWC9 Pawcatuck River (PRWS) 8.39 302 80 --
Automated Parameter Estimation (PEST) 155

Hydraulic Characteristics (FTABLES)

Stage-storage-discharge characteristics (FTABLES) were 

developed for the outflow gate used to route water from each 

of the 84 reaches. The FTABLE characterizes the hydraulic 

properties of the reach by defining the relation between depth, 

storage, and discharge. This relation is usually defined by the 

hydraulic properties at the downstream end of the reach, but 

the discharge-volume relation is a function of the properties of 

the entire reach. 

The channel-geometry analysis program (CGAP) by 

Regan and Schaffranek (1985) was used to define the relations among depth, surface area, and volume. A supplemental 

program, GENFTBL, reads the channel-geometry output 

from CGAP to calculate the stage-storage-discharge relation 

by solving Manning’s equation for open-channel flow. CGAP 

requires data on the cross-section channel geometry; these data 

were obtained from discharge-measurement notes for each of 

the continuous and partial-record streamflow-gaging stations, 

and from USGS 1:24,000-scale digital topographic maps. 

A minimum of three cross-sections were used to define the 

storage-discharge relations for each reach. GENFTBL requires 

Manning’s roughness coefficients for each cross section; these 

coefficients were estimated from field observations and guidelines by Coon (1998) and Arcement and Schneider (1989). 

Model Calibration

The HSPF model was calibrated by comparing simulated and measured streamflows at numerous locations in the 

basin for the period January 1, 2000, to September 30, 2004. 

Streamflow is simulated by using an hourly time step and data 

collected at the FBWR climate station. Variables were initially 

assigned values similar to those used for comparable HRUs 

in the Usquepaug-Queen River Basin HSPF model (Zarriello 

and Bent, 2004). An iterative process then was used to adjust 

these values to minimize the difference between simulated and 

observed flows. Discharges measured at 17 continuous record 

streamflow-gaging stations (fig. A2–4; table A2–4) provided 

the main model-calibration points. In addition to these sites, 

34 partial-record stations were used to evaluate the model fit. 

Hence, the model performance reflects a wide range of basin 

characteristics and sizes. 

The model was calibrated in accordance with guidelines 

by Donigian and others (1984) and Lumb and others (1994). 

Calibration generally entailed adjusting the variable values to 

fit the model output to total and seasonal water budgets; then 

values were further adjusted to improve the model fit for daily 

flows while maintaining the total and seasonal water budgets. 

The model was calibrated by first adjusting variable values as 

a group for PERLNDs overlying sand and gravel, till, and wetlands. Once reasonable simulation results were obtained, further adjustments were made to variable values for PERLNDs 

representing different land-use types within each of these 

groups. Storm runoff and snowmelt were not given detailed 

consideration because the primary purpose of the model is to 

simulate the effects of withdrawals during low-flow periods. 

Snow rarely remains on the ground for appreciable periods; 

thus, the snow-buildup and melt processes were included 

primarily to adjust precipitation data (by a factor of 1.30) to 

compensate for inefficiencies in precipitation-gage measurements during periods of snow. 

The model fit was examined by visual inspection of the 

simulated and observed hydrographs, flow-duration curves, 

and scatterplots, and by mathematical summary statistics 

provided by the GenScn utility “compare two time series”. 

Two of the primary statistics used to evaluate the model fit 

were the coefficient of determination (R2) and the model-fit 

efficiency (also referred to as the Nash-Sutcliffe coefficient 

and herein abbreviated as MFE), both of which provide a measure of the variation in the simulated value explained by the 

observed value. The MFE is sensitive to differences between 

the observed and simulated means and variances providing a 

more rigorous evaluation of the fit quality than the R2, which 

measures the differences between mean values only (Legates 

and McCabe, 1999). In cases where the observed values and 

model residuals are normally distributed, the value of R2 and 

MFE should be equal (Duncker and Melching, 1998). 

Automated Parameter Estimation (PEST)

Once a reasonable empirical fit was obtained, the modelindependent parameter estimation (PEST) program (Doherty, 

2004) was used to refine selected parameter values and to 

evaluate correlated parameter sensitivities. PEST is designed 

to search for parameter values that minimize a user-defined 

objective function. An objective function is typically defined 

as the sum of the squared differences between simulated and 

observed values that, when minimized generally, improve the 

overall performance of the model. To accomplish this, PEST 

has three principal components that (1) define the parameters and the excitation (change) of those parameters used in 

the estimation process, (2) define the observed data that are 

measured against simulated values in the computation of the 

objective function, and (3) perform a nonlinear search by a 

Gauss-Marquardt-Levenberg algorithm to find the optimal 

parameter values being tested. Surface-water utility programs 

developed by Doherty (2003) facilitate input requirements for 

PEST, perform parameter transformations, and provide data 

management and filters for reading and writing data in PEST. 

Many of these utilities are designed specifically to facilitate 

the use of PEST with HSPF. 

The surface-water utility TSPROC was used to build 

PEST control files and to process time-series data for use 

in the optimization process. The control file specifies (1) 

variable values that regulate the nonlinear-search algorithm, 

(2) information on the HSPF parameters to be optimized, 

and (3) the observation data, groups, and weights. One 

of the main functions of the PEST control variables is to 

direct the magnitude and direction of parameter change 
156 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

by searching through a Jacobian matrix that PEST creates 

to define the change in the objective function relative to 

the change (excitation) of a parameter value (derivatives). 

PEST therefore requires at least one model run for each 

excitation of each parameter being optimized (two parameterobservation pairs), but the search algorithm often resorts to 

two model runs to define derivatives by the method of “central 

differences” according to criteria supplied in the control 

file (three parameter-observation pairs). The three-pointderivatives calculation improves the optimization performance 

particularly as parameter values move closer to their optimum 

value. PEST then uses this information to upgrade the 

direction and magnitude of the parameter-change vector for 

the next excitation iteration. PEST also has the ability to 

temporarily hold insensitive parameters at their current value 

to determine a suitable update for other parameters. PEST 

stops when further parameter excitations fail to produce 

further improvements in the objective function. 

When PEST is run the number of model runs can 

be potentially large. Because of this, and because many 

HSPF parameters are correlated, HSPF parameters were 

parsimoniously selected for optimization on the basis of 

their influence in the model-calibration process observed in 

previously developed HSPF models and in the calibration of 

the Pawcatuck HSPF model. Initial PEST runs included the 

optimization of infiltration (INFILT), active groundwaterrecession constant (AGWRC) and its modifier for nonexponential decay (KVARY), lower-zone nominal storage 

(LZSN), upper-zone nominal storage (UZSN), active 

groundwater evapotranspiration (AGWET), and lower-zone 

evapotranspiration index (LZET). UZSN was later removed 

from optimization because it was found to be insensitive. 

In addition, parameter estimation was restricted to the two 

dominant HRUs in the Pawcatuck River Basin, forested areas 

overlying sand and gravel (PERLND 5) and forested areas 

overlying till (PERLND 15). 

The objective function (explained below) was computed 

at four locations representing different parts of the Pawcatuck 

River Basin-Usquepaug River near Usquepaug (USQU, 

01117420), Beaver River near Usquepaug (BRUS, 01117468), 

Pawcatuck River at Wood River Junction (PRWR, 01117500), 

and Wood River at Hope Valley (WRHV, 01118000). A 

subsequent PEST run was made with these parameters for 

soils classified as steep and rocky or bedrock (PERLND 16) 

using an objective function determined at three locations 

where this HRU is prevalent—Pendleton Hill Brook near 

Clarks Falls (PHBK, 01118300), Ashaway River at Ashaway 

(ARAS, 01118360), and Shunock River near North Stonington 

(SRNS 01118400).

The role of PEST is to minimize the objective function, 

which is the sum of the square difference between simulated 

and observed values. The values used to compute the objective 

function can be defined in many different ways or combination of ways. The success of PEST is often affected by how 

well the objective function responds to parameter excitations 

that is facilitated by the surface-water utilities developed for 

PEST (Doherty, 2003). Initial PEST runs were made by minimizing an objective function that included weighted hourly 

time-series values, total monthly runoff volumes, and flows at 

various flow-duration intervals. Observations were weighted 

so that these three components at each of the observation sites 

had about equal influence in the computation of the objective 

function. The hourly time-series data also were weighted so 

that the influence of the observations decreased as the discharge increased. 

Early in the formulation of the optimization problem, 

it was found that the hourly time-series data in the objective 

function produced erratic and often poor results. These results 

were believed to be caused by differences between the timing 

of simulated and observed hourly values that can be affected 

by a number of factors unrelated to the HSPF parameters 

being optimized. These factors include spatial precipitation 

distribution, RCHRES storage-discharge relation, and the 

land-surface roughness and flow-plane length. Thus, when 

PEST was tasked with optimizing HSPF parameters that 

have little effect on the timing of flow, the search algorithm 

performed poorly, often selecting parameter values at the outer 

allowed limit or parameters insensitive in the optimization, 

or both. The time-series component of the objective function 

was subsequently computed with daily mean flows, which 

improved PEST performance because it minimized problems 

associated with the short-term differences in the timing of 

flow. Therefore, all subsequent PEST runs were made with 

an objective function computed from daily mean flows, total 

monthly runoff volumes, and flows at various flow durations 

weighted in the same manner as previously described.

PEST requires information about the parameters used in 

the optimization process. This includes identification of the 

parameters, initial values and allowed limits, relations to other 

parameters, and mathematical transformations in the excitation process. Initial parameter values were set to the manually 

calibrated values. In subsequent parameter-estimation runs, 

the optimal parameter values determined previously were used 

as initial values or fixed when optimizing other parameters. 

All parameters were set to switch to a three-point derivative 

calculation as needed for a more precise computation of the 

Jacobian matrix. 

Par2par, an auxiliary program included in the PEST 

Surface-Water Utilities, provides an unlimited ability to 

transform parameter values for parameter estimation. The 

transformed parameters are used by PEST, but are transformed 

back to allowable parameter values for use by HSPF. Par2par 

made changes in the AGWRC and IRC parameter values 

relatively linear with respect to changes in the model output 

compared to the response of the non-transformed parameters 

values. Monthly LZET parameter (MON–LZET) values were 

calculated by a sinusoidal function and two estimated parameters in par2par as indicated in figure A2–5. No transformations 

were made for excitations of INFILT, KVARY, AGWET, and 

UZSN. Excitations of LZSN were log-transformed to improve 

the derivative linearity. For the same reason, AGWRC, 
Automated Parameter Estimation (PEST) 157

IRC, and LZET parameter values were excited by use of the 

customized parameter transformation utility par2par.

The optimization process also was improved by separating baseflow from non-baseflow by using the PEST digital 

filter surface-water utility. Baseflow separation was performed 

by using a single parameter filter with an recession coefficient 

(alpha value) of 0.95. Filtering simulated and observed values 

prior to the computation of the objective function allows the 

optimization to be targeted to different flow components and 

the parameters that affect those components. 

HSPF parameters LZSN, INFILT, AGWRC, KVARY, 

AGWET, and LZET, which are associated with the simulation 

of baseflow, were optimized with baseflow estimated from 

observed and simulated data at USQU, BRSH, PRWR, and 

WRHV. In a subsequent PEST run, the nonbaseflow runoff 

was used to optimize upper-zone storage (UZSN), interflow 

inflow (INTFW), and interflow recession (IRC) at the same 

four locations in the basin. These HSPF parameters are 

associated with the simulation of interflow and surface runoff. 

The final model calibration was the outcome of the last 

four PEST optimization runs, herein referred to as CASE 5 

through CASE 8. CASEs 5, 6, and 8 were used to perturb 

variables LZSN, INFILT, KVARY, AGWRC, AGWET, 

UZSN, and MON–LZETP. CASEs 5 and 8 perturbed these 

variables for HRUs representing forested areas overlying 

sand and gravel (PERLND 5) and forested areas overlying 

till (PERLND 15), which are the dominant HRU types in 

the basin (about 16 and 36 percent of the entire basin area, 

respectively). Variable values specific to an HRU were 

assigned unique identifiers in PEST and are denoted here 

by the variable abbreviation followed by the HRU number 

it is associated with. For example, INFILT in forested areas 

overlying till (PERLND 15) is identified as INFILT-15. 

For CASE 5, the objective function was calculated for 

the entire flow hydrograph at USQU, BRSH, PRWR, WRHV, 

whereas CASE 8 limited the objective-function calculation to 

baseflow at the same sites plus PHBK. For CASE 6, the same 

variables were perturbed for the HRU representing steeprocky soils (PERLND 16), and the objective function was 

computed at PHBK, ARAS, and SRNS in the northwestern 

part of the basin where this HRU is most dominant (24, 24, 

and 19 percent the total subbasin areas, respectively). CASE 7 

perturbed the interflow (INTFW) and interflow-recessionrate (IRC) variables for HRUs representing forested areas 

overlying sand and gravel (PERLND 5) and till (PERLND 

15), but limited the objective-function computation to nonbaseflow runoff (surface runoff and interflow) at the same 

sites used in CASE 8. Key variable values at the start of the 

optimization process (obtained from manual calibration), their 

optimized values, and their confidence limits are summarized 

in table A2–5. Additional information on model-variable optimization is presented in the sensitivity section of this chapter.

0

0.2

0.4

0.6

0.8

1.0

1 2 3 4 5 6 7 8 9 10 11 12

Upper limit

Lower limit 

Optimized value

Initial values 

INDEX TO LOWER ZONE EVAPOTRANSPIRATION

MONTH

Figure A2–5. Sinusoidal function used to optimize the Lower Zone Evapotranspiration (LZET) parameter in the 

Hydrologic Simulation Program-FORTRAN (HSPF) of the Pawcatuck River Basin, southwestern Rhode Island and 

southeastern Connecticut.
158 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Table A2–5. Starting and optimized variable values and their 95-percent confidence 

range calculated by PEST in order of ranked influence in the optimization of the 

Hydrologic Simulation Program-FORTRAN (HSPF) model of the Pawcatuck Basin 

Pawcatuck River Basin, southeastern Rhode Island and southwestern Connecticut. 

(Sites shown in figure A2–4 and described in table A2–4)

[ND, not determined; No., number]

Adjusted model variable1 Starting 

value

Optimized 

value

95-percent confidence limits

Lower Upper

CASE 5—Forest over sand and gravel (5) and over till (15)

INFILT–15 0.200 0.117 0.107 0.127

AGWET–15 .300 .291 .244 .338

LZET .380 .380 .357 .403

AGWRCTRANS–15 211 192 165 223

(transformed) (.995) (.995) (.994) (.996) 

KVARY–5 .268 .209 .141 .278

AGWET–5 .300 .162 .090 .235

KVARY–15 .791 .800 .705 .895

AGWRCTRANS–5 189 140 108 182

(transformed) (.995) (.993) (.991) (.995)

LZSN–15 5.74 4.65 3.96 5.46

INFILT–5 .428 .400 .253 .547

UZSN–15 .150 .900 .743 1.06

LZSN–5 11.6 7.24 5.03 10.4

UZSN–5 .200 .437 .143 1.02

CASE 6—Steep-rocky soil (16)

INFILT–16 0.020 0.063 0.046 0.079

UZSN–16 .090 .900 .483 1.32

AGWET–16 .020 .300 .012 .588

LZET–16 .220 .380 .166 .594

AGWRCTRANS–16 3.0 59.6 7.7 460

(transformed) (.750) (.983) (.885) (.998)

LZSN–16 3.70 3.82 2.74 5.32

KVARY–16 .610 .800 -1.37 2.97

CASE 7—Non-baseflow

INTFW–5 3.22 ND ND ND

INTFW–15 1.92 2.70 ND ND

INTFW–16 1.72 1.90 ND ND

IRC–5 .850 .950 ND ND

IRC–15 .750 .701 ND ND

IRC–16 .600 .500 ND ND

CASE 8—Baseflow

AGWET–15 0.300 0.300 0.279 .321

INFILT–15 .193 .179 0.173 .184

LZET .380 .380 0.369 .391

AGWRCTRANS–15 213 142 120 167

(transformed) (.995) (.993) (.992) (.994)

KVARY–5 .286 .200 .132 .268

AGWRCTRANS–5 188 83.8 68.5 103

(transformed) (.995) (.988) (.986) (.990)

AGWET–5 .300 .300 .265 .335

KVARY–15 .801 .800 .644 .956

LZSN–15 6.16 8.85 8.17 9.58

LZSN–5 11.3 7.23 5.65 9.24

INFILT–5 .402 .449 .307 .592 1

 Number following the dash indicates the number of the Hydrologic Response Unit (HRU) 

for which the variable was perturbed.

CASE 5

Sites: USQU, BRSH, PRWR, WRHV

RCHRES: 20, 43, 46, 59

Objective function

Start: 487

End: 414

Percent change: -15

No. observations: 7080

No. parameters: 13

No. model runs: 237

CASE 6

Sites: PHBK, ARAS, SRNS

RCHRES: 74, 77, 83

Objective function

Start: 4624

End: 2805

Percent change: -39

No. observations: 5310

No. parameters: 7

No. model runs: 204

CASE 7

Sites: USQU, BRSH, PRWR, WRHV, PHBK

RCHRES: 20, 43, 46, 59, 74

Objective function

Start: 3.96E+11

End: 3.78E+11

Percent change: -5

No. observations: 8520

No. parameters: 6

No. model runs: 109

CASE 8

Sites: USQU, BRSH, PRWR, WRHV, PHBK

RCHRES: 20, 43, 46, 59, 74

Objective function

Start: 3099

End: 1506

Percent change: -51

No. observations: 7080

No. parameters: 11

No. model runs: 174
Model Fit 159

Model Fit

In general, flows simulated by the calibrated model 

matched the observed flows over a wide range of conditions 

and subbasin characteristics within an acceptable range of 

error. The median R2 value for the simulated and observed 

daily mean flows for the 17 continuous streamflow-gaging 

stations is 0.81 and ranged between 0.66 and 0.87; the median 

MFE is 0.79 and ranged between 0.59 and 0.86 (table A2–6). 

Simulated and observed monthly mean flows for the 17 

continuous streamflow-gaging stations has a median R2 of 

0.93 and ranged between 0.86 and 0.95; the MFE is 0.90 and 

ranged between 0.80 and 0.94 (table A2–7). These and other 

calibration statistics for each continuous streamflow-gaging 

station are summarized in tables A2–6 and A2–7.

Statistical measures do not adequately describe all 

aspects of a model fit; visual inspection of the hydrographs, 

flow-duration curves, and scatterplots of simulated and 

observed discharges provide additional information to assess 

model performance. Observed and simulated flow hydrographs, scatterplots, and flow-duration curves are shown for 

the 17 continuous streamflow-gaging stations in figures A2–6 

through A2–22. These graphs generally indicate a close match 

between simulated and observed flows over about five orders 

of magnitude. 

Differences between the mean observed and simulated 

flows, as indicated by the percent error, is generally largest for 

stations at which flows were estimated for part of the calibration period. These stations include Chickasheen Brook at West 

Kingston (CBLL, RCHRES 36; fig. A2–10), Pawcatuck River 

at Kenyon (PRBC, RCHRES 37; fig. A2–11), Beaver River 

near Shannock (BRSH, RCHRES 43; fig. A2–13), Meadow 

Brook near Carolina (MBCA, RCHRES 47; fig. A2–15), 

Pawcatuck River at Burdickville (PRBV, RCHRES 50; 

fig. A2–18), Ashaway River at Ashaway (ARAS, RCHRES 

77; fig. A2–20), and Shunock River near North Stonington 

(SRSN, RCHRES 83; fig. A2–21). Continuous flow monitoring at these sites began in the late summer and early fall of 

2002; thus, daily mean flows had to be estimated for about the 

first half of the calibration period. When model-fit statistics 

were computed for these stations from the period of actual 

record (October 1, 2002, through September 30, 2004), the 

percent error between the mean simulated and observed discharge generally decreased by about half; however, the overall 

R2 and MFE values did not change appreciably.

Another source of model error can result from inaccurate 

withdrawal information, particularly in small headwater 

subbasins during periods of low flow when withdrawals 

can compose a large percentage of the total flow. Under 

this condition, error in measured or estimated withdrawals 

can translate into large model errors. Inaccurate withdrawal 

information is believed to have contributed to the model 

error (particularly at low flows) for the Queen River at Exeter 

(QRPB, RCHRES 2; fig. A2–6), Chipuxet River at West 

Kingston (CRWK, RCHRES 32; fig. A2–9), Chickasheen 

Brook at West Kingston (CBLL, RCHRES 36; fig. A2–10), 

Beaver River near Usquepaug (BRUS, RCHRES 42; 

fig. A2–12), Beaver River near Shannock (BRSH, RCHRES 

43; fig. A2–13), and Meadow Brook near Carolina (MBCA, 

RCHRES 47; fig. A2–15). 

Regulation of in-stream ponds (for example, the placement or removal of flash boards) also affects the relation 

between simulated and observed flows because these types 

of operations are not explicitly simulated. Sudden changes 

in observed flow, such as those in the late summers of 2001 

through 2004 in the Chipuxet River at West Kingston 

(CRWK, RCHRES 32; fig. A2–9), could have been caused 

by this type of alteration. These unexplained changes in 

observed flow could also reflect unknown or inaccurate 

withdrawal information. 

Precipitation spatial variability and measurement error 

can affect simulation results. The Pawcatuck River Basin 

model was calibrated with precipitation data from the FBWR 

station (fig. 1–1). The precipitation measured at this station is 

uniformly distributed across the entire 303-mi2 basin. Often, 

the largest model error, as measured by the percent difference 

between the observed and simulated monthly mean flow, is 

associated with the largest variation in total monthly precipitation (fig. A2–23). Precipitation variation was measured by the 

deviation in the monthly precipitation at the FBWR station 

from the monthly mean precipitation measured at PROVID, 

URI, FBWR, NIC, and WESTERLY stations (fig. 1–1) as a 

percentage of the monthly precipitation at FBWR.

Large precipitation variability, as indicated by the shaded 

area on figure A2–23, can be an appreciable source of model 

error, although the error is not always large. Generally, the 

largest model error was during low flows months when the 

absolute differences between simulated and observed flows 

are small, but the percent differences can be large. The largest 

model error associated with small precipitation variation (near 

the zero line on the y axis; fig. A2–23) mostly correspond to 

small subbasins in the western part of the Pawcatuck River 

Basin when precipitation differences at FBWR and Westerly 

(the westernmost precipitation gage; fig. 1–1) were greatest. 

Other months with relatively large model error were most 

common during periods of low flow and in reaches where 

upstream withdrawals account for a large percentage of the 

total flow; this error could reflect uncertainty in the withdrawal information. 

At several locations, particularly at stations below 

extensive wetlands, the mean simulated flow is appreciably 

greater than the mean observed flow. For example, at 

Pawcatuck River at Kenyon, R.I. (PRBC, RCHRES 37), the 

subbasin with the largest wetland, the simulated mean flow is 

about 10 percent greater than the observed mean flow. This 

difference is attributed to the evapotranspiration (ET) losses 

from wetlands simulated as PERLNDs; wetland PERLNDs 

are believed to undersimulate ET losses because the available 

moisture supply is limited to precipitation held in storage, 

which caps the potential ET loss. ET loss from a natural 

wetland in Wisconsin was shown to exceed potential evapotranspiration (PET) during the height of the growing season 
160 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Table A2–6. Summary of model-fit statistics for daily mean discharge, January 2000 through September 2004, simulated by the 

Hydrologic Simulation Program-FORTRAN (HSPF) and observed at 17 continuous-record streamflow-gaging stations, Pawcatuck River 

Basin, southwestern Rhode Island and southeastern Connecticut.

[Site locations shown in figure A2–4; see table A2–4 for reach names; No, number; RCHRES, model reach; IDLOCN, attribute name for reaches and gages; 

ft3/s, cubic feet per second; RMS, Root mean square. Shaded cells indicate stations for which part of the flow record was estimated]

RCHRES Gage 

IDLOCN

Daily discharge 

(ft3/s) Correlation 

coefficient

Coefficient of 

determination 

(R2)

Mean error 

(ft3/s)

Percent 

mean 

error

RMS 

error 

(ft3/s)

Model fit 

efficiency 

No. (MFE) IDLOCN Observed Simulated

2 QUEN2 QRPB 7.43 7.67 0.91 0.83 -0.24 -3.19 3.4 0.79

9 QUEN4 QRLY 36.1 34.9 0.91 0.82 1.14 3.17 15.1 0.74

20 QUEN7 USQU 71.9 70.9 0.92 0.85 0.99 1.37 24.8 0.82

32 CHIP2 CRWK 21.5 20.3 0.84 0.71 1.18 5.49 9.59 0.64

36 CHIC2 CBLL 8.76 10.4 0.90 0.80 -1.67 -19.1 3.96 0.73

37 PAWC2 PRBC 131 144 0.93 0.86 -12.7 -9.72 44.3 0.82

42 BEAV2 BRUS 20.0 19.6 0.93 0.86 0.40 2.00 6.41 0.85

43 BEAV3 BRSH 23.2 24.7 0.93 0.87 -1.55 -6.68 7.59 0.86

46 PAWC3 PRWR 197 203 0.92 0.85 -5.75 -2.92 59.0 0.84

47 MEAD1 MBCA 9.75 8.89 0.82 0.68 0.86 8.80 5.96 0.64

53 WOOD2 WRAR 68.5 74.4 0.84 0.71 -5.85 -8.54 36.3 0.71

59 WOOD4 WRHV 150 159 0.90 0.81 -9.38 -6.26 63.7 0.80

50 PAWC4 PRBV 401 430 0.92 0.84 -28.5 -7.11 138 0.84

74 PEND1 PHBK 8.42 8.68 0.81 0.66 -0.27 -3.17 6.12 0.59

77 ASHA1 ARAS 53.5 60.9 0.82 0.67 -7.39 -13.8 39.2 0.63

83 SHUN2 SRNS 32.5 36.1 0.85 0.73 -3.56 -11.0 18.6 0.69

80 PAWC8 PRWS 568 620 0.90 0.81 -51.8 -9.11 225 0.80

Median 36.1 36.1 0.90 0.81 -6.26 0.79

Standard deviation 0.04 0.07 7.24 0.09

Minimum 0.81 0.66 1.37 0.59

Maximum 0.93 0.87 -19.1 0.86

(Lott and Hunt, 2001); this finding underscores the problem of 

insufficient simulated ET loss from wetlands. To circumvent 

this limitation of inadequate moisture supply to wetlands, it 

was hypothesized in the Ipswich River Basin HSPF model 

(Zarriello and Ries, 2000) that the moisture supply to wetlands 

is from lateral inflows from surrounding upgradient areas 

in addition to direct precipitation. Simulating this additional moisture supply required treating wetlands as virtual 

RCHRESs with atmospheric gains and losses plus inflows 

from adjacent PERLNDs and IMPLNDs. Virtual RCHRES 

FTABLE characteristics are determined by setting the area 

equal to the corresponding area of wetlands in the subbasin, estimating storage from area and depth, and empirically 

adjusting flow to fit simulated flows to observed flows. 

The virtual RCHRES concept was evaluated in the upper 

Pawcatuck River Basin by converting the wetland areas in 

RCHRESs 34 and 37 to virtual RCHRESs (134 and 137, 

respectively). The subbasins corresponding to RCHRES 34 

and 37 include some of the most expansive area of wetland in 

the Pawcatuck River Basin (about 30 and 40 percent of their 

total subbasin areas, respectively). The additional ET loss 

from wetlands treated as virtual RCHRESs in these subbasins 

decreased the difference between the mean simulated and 

observed flows by about half at Pawcatuck River at Kenyon, 

R.I. (PRBC, RCHRES 37), and resulted in slight improvements of other model-fit statistics. Constructing the model 

with virtual RCHRES in other areas would likely improve 

model performance; however, this was not pursued because 

it was expected to create problems in coupling of HSPF with 

MODFLOW that was anticipated to come later in the project. 

Hence, the HSPF model variables were optimized without 

inclusion of virtual RCHRES for the simulation of wetlands.
Model Fit 161

Table A2–7. Summary of model-fit statistics for monthly mean discharge, January 2000 through September 2004, simulated by the 

Hydrologic Simulation Program-FORTRAN (HSPF) and observed at 17 continuous record streamflow-gaging stations, Pawcatuck River 

Basin, southwestern Rhode Island and southeastern Connecticut.

[Site locations shown in figure A2–4; see table A2–4 for reach names; No., number; RCHRES, model reach; IDLOCN, attribute name for reaches and gages; 

ft3/s, cubic feet per second; RMS, Root mean square. Shaded cells indicate stations for which part of the flow record was estimated]

RCHRES Gage 

IDLOCN

Mean discharge 

(ft3/s) Correlation 

coefficient

Coefficient of 

determination 

(R2)

Mean error 

(ft3/s)

Percent 

mean 

error

RMS 

error 

(ft3/s)

Model fit 

efficiency 

(MFE) No. IDLOCN Observed Simulated

2 QUEN2 QRPB 7.44 7.68 0.97 0.94 -0.24 -3.26 1.40 0.93

9 QUEN4 QRLY 36.1 35.0 0.96 0.92 1.13 3.12 7.98 0.86

20 QUEN7 USQU 72.0 71.0 0.97 0.95 0.94 1.31 11.6 0.93

32 CHIP2 CRWK 21.5 20.4 0.94 0.89 1.18 5.49 4.95 0.81

36 CHIC2 CBLL 8.76 10.44 0.96 0.92 -1.67 -19.1 2.41 0.82

37 PAWC2 PRBC 131 144 0.97 0.94 -12.8 -9.76 25.8 0.90

42 BEAV2 BRUS 20.0 19.7 0.97 0.95 0.38 1.91 3.09 0.94

43 BEAV3 BRSH 23.2 24.8 0.98 0.95 -1.57 -6.75 3.72 0.94

46 PAWC3 PRWR 197 203 0.97 0.93 -5.82 -2.95 34.0 0.91

47 MEAD1 MBCA 9.76 8.90 0.96 0.93 0.86 8.79 2.70 0.81

53 WOOD2 WRAR 68.6 74.5 0.94 0.87 -5.88 -8.57 17.0 0.86

59 WOOD4 WRHV 150 160 0.96 0.93 -9.46 -6.30 28.4 0.91

50 PAWC4 PRBV 402 430 0.97 0.94 -28.6 -7.13 69.7 0.92

74 PEND1 PHBK 8.44 8.70 0.93 0.86 -0.26 -3.10 2.45 0.81

77 ASHA1 ARAS 53.6 61.0 0.94 0.88 -7.39 -13.8 15.9 0.83

83 SHUN2 SRNS 32.6 36.1 0.94 0.88 -3.56 -10.9 9.49 0.80

80 PAWC8 PRWS 569 621 0.96 0.93 -51.9 -9.12 115 0.90

Median 36.1 36.1 0.96 0.93 -6.30 0.90

Standard deviation 0.01 0.03 7.23 0.05

Minimum 0.93 0.86 1.31 0.80

Maximum 0.98 0.95 -19.1 0.94
162 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1

0.1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

B 

10

100

1

0.1

0.1

C 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

10

20

30

40

0 10 20 30 40

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

0.1

Observed

values were 

estimated 

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW

Figure A2–6. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, to 

September 30, 2004, Queen River at Exeter, 

R.I. (QRPB, RCHRES 2, 011173545). Months 

on x-axis are February, April, June, August, 

October, and December for years shown. 

(Site location shown in figure A2–4 and 

described in table A2–4.)
Model Fit 163

Figure A2–7. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, 

to September 30, 2004, Queen River at 

Liberty, R.I. (QRLY, RCHRES 4, 01117370). 

Months on x-axis are February, April, 

June, August, October, and December 

for years shown. (Site location shown in 

figure A2–4 and described in table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1,000

1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100 1,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

1

B C SIMULATED DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
164 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1,000

1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100 1,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

1

B C SIMULATED DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW

Figure A2–8. Observed and simulated 

(A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow 

scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 

2004, Usquepaug River near Usquepaug, 

R.I. (USQU, RCHRES 20, 01117420). Months 

on x-axis are February, April, June, August, 

October, and December for years shown. 

(Site location shown in figure A2–4 and 

described in table A2–4.)
Model Fit 165

Figure A2–9. Observed and simulated 

(A) daily mean hydrograph, (B) daily mean 

flow scatterplot, (C) monthly mean flow 

scatterplot, and (D) daily mean flow duration 

curves, January 1, 2000, to September 30, 

2004, Chipuxet River at West Kingston, R.I. 

(CRWK, RCHRES 32, 01117350). Months on 

x-axis are February, April, June, August, 

October, and December for years shown. 

(Site location shown in figure A2–4 and 

described in table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1,000

1

0.1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100 1,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

B 

10

100

1,000

1

0.1

0.1

C 

SIMULATED DISCHRAGE,

IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

10

20

30

40

50

60

70

80

0 10 20 30 40 50 60 70 80

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

0.1

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
166 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Figure A2–10. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, to 

September 30, 2004, Chickasheen Brook 

at West Kingston, R.I. (CBLL, RCHRES 

36, 01117424). Months on x-axis are 

February, April, June, August, October, and 

December for years shown. (Site location 

shown in figure A2–4 and described in 

table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1

0.1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

B 

10

1

0.1

0.1

100

C 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

10

20

30

40

0 10 20 30 40

Observed

Simulated

1

100

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

0.1

Observed values were estimated 

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
Model Fit 167

Figure A2–11. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, to 

September 30, 2004, Pawcatuck River at 

Kenyon, R.I. (PRBC, RCHRES 37, 01117430). 

Months on x-axis are February, April, June, 

August, October, and December for years 

shown. (Site location shown in figure A2–4 

and described in table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1,000

10,000

1

B 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

10 100 1,000 10,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

10,000

1

1

C 

0

100

200

300

400

500

0 100 200 300 400 500

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

Observed

Simulated

10

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A

1

10,000

Observed values were estimated 

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
168 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Figure A2–12. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, 

to September 30, 2004, Beaver River 

near Usquepaug, R.I. (BRUS, RCHRES 

42, 01117468). Months on x-axis are 

February, April, June, August, October, and 

December for years shown. (Site location 

shown in figure A2–4 and described in 

table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1,000

1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100 1,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

1

B C SIMULATED DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

10

20

30

40

50

60

0 10 20 30 40 50 60

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
Model Fit 169

Figure A2–13. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, 

to September 30, 2004, Beaver River 

near Shannock, R.I. (BRSH, RCHRES 

43, 01117471). Months on x-axis are 

February, April, June, August, October, and 

December for years shown. (Site location 

shown in figure A2–4 and described in 

table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1,000

1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100 1,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

1

B C SIMULATED DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

10

20

30

40

50

60

0 10 20 30 40 50 60

Observed values were estimated

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
170 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Figure A2–14. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, to 

September 30, 2004, Pawcatuck River at 

Wood River Junction, R.I. (PRWR, RCHRES 

46, 01117500). Months on x-axis are 

February, April, June, August, October, and 

December for years shown. (Site location 

shown in figure A2–4 and described in 

table A2–4.)

Observed

Simulated

10

100

1,000

10,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

Observed

Simulated

D 

10

100

1,000

10,000

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

C 

0

100

200

300

400

500

600

0 100 200 300 400 500 600

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

B 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

10 100 1,000 10,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

10,000

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
Model Fit 171

Figure A2–15. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, 

to September 30, 2004, Meadow Brook 

near Carolina, R.I. (MBCA, RCHRES 47, 

01117600). Months on x-axis are February, 

April, June, August, October, and 

December for years shown. (Site location 

shown in figure A2–4 and described in 

table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1,000

1

0.1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100 1,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

1

B 

0.1

C 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

10

20

30

40

0 10 20 30 40

Observed values were estimated

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

0.1

0.1

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
172 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Figure A2–16. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, 

to September 30, 2004, Wood River near 

Arcadia, R.I. (WRAR, RCHRES 53, 01117800). 

Months on x-axis are February, April, June, 

August, October, and December for years 

shown. (Site location shown in figure A2–4 

and described in table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1,000

1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100 1,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

1

B C SIMULATED DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

50

100

150

200

0 50 100 150 200

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
Model Fit 173

Figure A2–17. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, to 

September 30, 2004, Wood River at Hope 

Valley, R.I. (WRHV, RCHRES 59, 01118000). 

Months on x-axis are February, April, June, 

August, October, and December for years 

shown. (Site location shown in figure A2–4 

and described in table A2–4.)

Observed

Simulated

D 

10

100

1,000

10,000

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

C 

0

100

200

300

400

500

0 100 200 300 400 500

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

B 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

10 100 1,000 10,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

10,000

Observed

Simulated

10

100

1,000

10,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
174 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Figure A2–18. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, 

to September 30, 2004, Pawcatuck River 

at Burdickville, R.I. (PRBV, RCHRES 50, 

01118010). Months on x-axis are February, 

April, June, August, October, and 

December for years shown. (Site location 

shown in figure A2–4 and described in 

table A2–4.)

Observed

Simulated

D 

10

100

1,000

10,000

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

C 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

200

400

600

800

1,000

1,200

1,400

0 200 400 600 800 1,000 1,200 1,400

B 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

10 100 1,000 10,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

10,000

Observed

Simulated

10

100

1,000

10,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

Observed values were estimated

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
Model Fit 175

Figure A2–19. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, to 

September 30, 2004, Pendleton Hill Brook 

near Clark Falls, Conn. (PHBK, RCHRES 

74, 01118300). Months on x-axis are 

February, April, June, August, October, and 

December for years shown. (Site location 

shown in figure A2–4 and described in 

table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

0.1

1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100 1,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

1

B 

0.1

0.1

C 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

10

20

30

40

0 10 20 30 40

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

0.1

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
176 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Figure A2–20. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly 

mean flow scatterplot, and (D) daily 

mean flow duration curve, January 1, 

2000, to September 30, 2004, Ashaway 

River at Ashaway, R.I. (ARAS, RCHRES 

77, 01118360). Months on x-axis are 

February, April, June, August, October, and 

December for years shown. (Site location 

shown in figure A2–4 and described in 

table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1,000

1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100 1,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

1

B C SIMULATED DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

50

100

150

200

0 50 100 150 200

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

Observed values were estimated

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
Model Fit 177

Figure A2–21. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly mean 

flow scatterplot, and (D) daily mean 

flow duration curves, January 1, 2000, to 

September 30, 2004, Shunock River near 

North Stonington, Conn. (SRNS, RCHRES 

83, 01118400). Months on x-axis are 

February, April, June, August, October, and 

December for years shown. (Site location 

shown in figure A2–4 and described in 

table A2–4.)

Observed

Simulated

D 

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

10

100

1,000

1

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

1 10 100 1,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

1

B C SIMULATED DISCHARGE, IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120 140

Observed

Simulated

1

100

1,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A 

10

Observed values were estimated

DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
178 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Figure A2–22. Observed and simulated 

(A) daily mean hydrograph, (B) daily 

mean flow scatterplot, (C) monthly 

mean flow scatterplot, and (D) daily 

mean flow duration curves, January 1, 

2000, to September 30, 2004, Pawcatuck 

River at Westerly, R.I. (PRWS, RCHRES 

80, 01118500). Months on x-axis are 

February, April, June, August, October, and 

December for years shown. (Site location 

shown in figure A2–4 and described in 

table A2–4.)

Observed

Simulated

D 

10

100

1,000

10,000

PERCENTAGE OF TIME DISCHARGE WAS EQUALED OR EXCEEDED

DISCHARGE, IN CUBIC FEET PER SECOND

0.5 2 5 10 20 50 70 90 95 98 99.5

C 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

0

400

800

1,200

1,600

2,000

0 400 800 1,200 1,600 2,000

B 

SIMULATED DISCHARGE,

IN CUBIC FEET PER SECOND

10 100 1,000 10,000

OBSERVED DISCHARGE, IN CUBIC FEET PER SECOND

10

100

1,000

10,000

Observed

Simulated

10

100

1,000

10,000

DISCHARGE, IN CUBIC FEET PER SECOND

F A J A O D

2000

F A J A O D

2001

F A J A O D

2002

F A J A O D

2003

F A J A

2004

A DAILY MEAN HYDROGRAPH

DAILY MEAN FLOW

DAILY MEAN FLOW DURATION

MONTHLY MEAN FLOW
Tributary Streams 179

Tributary Streams

Thirty-four partial-record stations established in tributary 

streams for the purpose of the study were also used to evaluate 

the model performance. Continuous flow records were estimated for these stations as previously described. The partialrecord stations were not used directly in the calibration of the 

model, but they did provide an independent confirmation of 

the model performance. 

Simulated and observed daily mean flows for the 34 

partial-record streamflow-gaging stations have an average 

R2 of 0.77 (ranged between 0.53 and 0.84) and an average 

MFE of 0.67 (ranged between -2.36 and 0.82). Simulated and 

observed monthly mean flows at the partial-record stations 

have an average R2 of 0.91 (ranged between 0.80 and 0.94) 

and an average MFE of 0.79 (ranged between -1.12 and 

0.91). These and other calibration statistics for partial-record 

streamflow-gaging stations are summarized in tables A2–8 

and A2–9. 

In general, the model-fit statistics computed for the 

partial-record stations are comparable to the statistics 

computed for the continuous-record stations with the 

exception of some low MFE values. The MFE is more 

sensitive to differences between the observed and simulated 

flows; thus, the greater the uncertainty in the estimated 

discharges at the partial-record station, the greater the 

likelihood that the MFE value is affected. Five partial-record 

stations—Queens Fort Brook (QUFB-p; RCHRES 8), Rake 

Factory Brook (RFBK-p; RCHRES 16), Chickasheen Brook 

(CBLL-p; RCHRES 35), upper Wood River (WREH-p; 

RCHRES 51), and Assekonk Brook (ABNS-p; RCHRES 

82)—account for the largest source of error in the overall 

MFE. If these five sites are discarded from the overall fit 

statistics, the MFE is better than the MFE value obtained for 

the continuous-record streamflow-gaging stations. 

The upper Queens Fort Brook subbasin (QUFB-p; 

RCHRES 8), has the poorest MFE of any partial-record 

station. The poor t MFE at this station is attributed to the 

-400

-300

-200

-100

0

100

200

-100 0 100 200 300 400 500

DEVIATION IN MONTHLY PRECIPITATION AT FBWR FROM 

REGIONAL AVERAGE MONTHLY PRECIPITATION AS 

PERCENTAGE OF PRECIPITATION AT FBWR

PERCENT DIFFERENCE BETWEEN OBSERVED AND SIMULATED MONTHLY 

MEAN STREAMFLOW

Streamflowgaging stations

Shaded area indicates 

months during which 

precipitation variability 

could be an appreciable 

cause of model error 

QRPB

QRLY

USQU

CRWK

CBLL

PRBC

MBCA

PRWR

BRUS

BRSH

WRAR

WRHV

PRBV

PRBK

PHBK

ARAS

SRNS

PRWS

Figure A2–23. Relation of monthly precipitation variability measured as the percent difference between the climate station 

used for the model calibration (FBWR) and the average of 5 climatic stations in or near the basin to the percent difference 

between observed and simulated monthly mean streamflow at 17 continuous-record streamflow-gaging stations in the 

Pawcatuck River Basin, southwestern Rhode Island and southeastern Connecticut, January 2000 through September 2004 

(Surface-water site locations shown in figure A2–4 and described in table A2–4). Climatological sites shown in figure 1–1 and 

described in table 1–1.)
180 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Table A2–8. Summary of model-fit statistics for daily mean discharge, January 2000 through September 2004, simulated by the 

Hydrologic Simulation Program-FORTRAN (HSPF) and estimated for 34 partial-record streamflow-gaging stations, Pawcatuck River 

Basin, southwestern Rhode Island and southeastern Connecticut.

[Site locations shown in figure A2–4; see table A2–4 for reach names; RCHRES, model reach; IDLOCN, attribute name for reaches and gages; No., number; 

ft3/s, cubic feet per second; RMS, root mean square]

RCHRES Gage 

IDLOCN

Mean discharge

(ft3/s) Correlation 

coefficient

Coefficient of 

determination

Mean 

error 

(ft3/s)

Percent 

mean 

error

RMS error 

(ft3/s)

Model fit 

efficiency No. IDLOCN Observed Simulated

1 QUEN1 QECC-p 5.14 5.80 0.89 0.79 -0.65 -12.7 2.89 0.77

5 FISH2 FBEX-p 14.9 16.9 0.92 0.84 -2.06 -13.8 6.18 0.82

8 QUFB2 QUFB-p 2.18 2.71 0.78 0.61 -0.53 -24.2 4.66 -2.36

11 TRIB1 QRTR-p 1.28 2.00 0.90 0.81 -0.73 -56.9 1.04 0.62

14 LOCK1 QRDR-p 8.30 9.56 0.91 0.83 -1.26 -15.2 4.39 0.77

16 RAKE1 RFBK-p 0.23 0.64 0.79 0.62 -0.41 -178 0.60 0.08

17 SHER1 SBGR-p 2.05 2.31 0.86 0.74 -0.26 -12.6 1.31 0.72

18 GLEN1 GRGR-p 4.30 5.96 0.91 0.83 -1.66 -38.7 3.23 0.70

31 CHIP1 CRWK-p 12.8 14.6 0.89 0.80 -1.74 -13.5 5.92 0.67

35 CHIC1 CBLL-p 7.30 6.97 0.88 0.78 0.33 4.51 5.02 0.18

41 BEAV1 BRWR-p 13.5 11.5 0.91 0.82 2.09 15.4 5.21 0.75

44 PASQ1 PBWY-p 8.98 12.71 0.88 0.77 -3.74 -41.6 6.03 0.54

45 TANE1 TBCA-p 2.98 3.50 0.84 0.70 -0.52 -17.3 2.04 0.67

49 CEDA1 CSBK-p 8.21 10.29 0.86 0.74 -2.08 -25.4 5.51 0.67

51 WOOD1 WREH-p 26.8 24.1 0.84 0.70 2.65 9.89 22.3 0.11

52 KELL1 KBEH-p 9.67 9.35 0.89 0.79 0.32 3.31 4.20 0.67

54 FLAT1 FRAR-p 14.4 17.5 0.88 0.77 -3.08 -21.4 9.27 0.69

55 BREA1 BBAR-p 12.2 13.5 0.89 0.80 -1.38 -11.4 6.33 0.77

56 PARR1 PBAR-p 11.5 14.1 0.86 0.74 -2.60 -22.6 7.89 0.68

58 ROAR1 RBAR-p 10.1 10.9 0.89 0.79 -0.83 -8.23 4.59 0.79

60 BRUS1 BBHV-p 7.02 8.04 0.88 0.77 -1.02 -14.6 4.30 0.75

61 MOSC1 MBHV-p 12.7 15.1 0.85 0.73 -2.45 -19.4 9.47 0.68

64 CANO1 CBHV-p 12.0 15.0 0.85 0.72 -3.00 -25.0 9.35 0.67

65 WOOD6 WRAL-p 172 192 0.91 0.82 -19.7 -11.5 74.4 0.81

66 COON1 CHAL-p 3.04 4.35 0.91 0.84 -1.31 -43.2 2.25 0.66

67 PERR1 PHBB-p 4.35 3.64 0.90 0.81 0.71 16.4 1.88 0.77

70 TOMA1 TBBF-p 10.7 12.5 0.91 0.83 -1.80 -16.8 4.83 0.80

73 GREE1 GRLG-p 13.5 15.1 0.73 0.53 -1.67 -12.4 14.7 0.51

75 WYAS1 WBCF-p 22.3 25.1 0.83 0.69 -2.77 -12.4 15.8 0.65

76 GLAD1 GBLG-p 3.20 3.99 0.87 0.75 -0.79 -24.8 2.37 0.72

78 PARM1 PBHK-p 4.06 5.39 0.85 0.73 -1.33 -32.9 3.66 0.54

79 LWPD1 LPPH-p 2.73 3.52 0.87 0.76 -0.79 -28.8 1.51 0.67

81 SHUN1 SRPH-p 13.7 17.3 0.84 0.71 -3.55 -25.9 10.1 0.66

82 ASSE1 ABNS-p 10.1 8.54 0.80 0.64 1.56 15.5 13.9 -1.96
Tributary Streams 181

Table A2–9. Summary of model-fit statistics for monthly mean discharge, January 2000 through September 2004, simulated by the 

Hydrologic Simulation Program-FORTRAN (HSPF) and estimated at 34 partial-record streamflow-gaging stations, Pawcatuck River 

Basin, southwestern Rhode Island and southeastern Connecticut.

[Site locations shown in figure A2–4; see table A2–4 for reach names; RCHRES, model reach; IDLOCN, attribute name for reaches and gages; No., number; 

ft3/s, cubic feet per second; RMS, root mean square]

RCHRES Gage 

IDLOCN

Mean discharge

(ft3/s) Correlation 

coefficient

Coefficient of 

determination

Mean 

error 

(ft3/s)

Percent 

mean 

error

RMS error 

(ft3/s)

Model fit 

efficiency No. IDLOCN Observed Simulated

1 QUEN1 QECC-p 5.15 5.81 0.96 0.92 -0.66 -12.8 1.36 0.89

5 FISH2 FBEX-p 14.9 17.0 0.97 0.94 -2.07 -13.9 3.35 0.90

8 QUFB2 QUFB-p 2.18 2.71 0.90 0.80 -0.53 -24.3 2.10 -1.12

11 TRIB1 QRTR-p 1.28 2.01 0.97 0.93 -0.73 -56.8 0.80 0.57

14 LOCK1 QRDR-p 8.30 9.57 0.96 0.92 -1.27 -15.3 2.58 0.85

16 RAKE1 RFBK-p 0.23 0.64 0.91 0.84 -0.41 -178 0.45 -0.76

17 SHER1 SBGR-p 2.06 2.32 0.95 0.90 -0.26 -12.6 0.55 0.88

18 GLEN1 GRGR-p 4.30 5.97 0.96 0.93 -1.67 -38.8 2.25 0.71

31 CHIP1 CRWK-p 12.9 14.6 0.96 0.92 -1.74 -13.5 3.60 0.75

35 CHIC1 CBLL-p 7.30 6.98 0.96 0.92 0.33 4.48 2.72 0.57

41 BEAV1 BRWR-p 13.56 11.48 0.96 0.92 2.08 15.4 3.24 0.82

44 PASQ1 PBWY-p 8.99 12.73 0.96 0.92 -3.74 -41.6 4.27 0.56

45 TANE1 TBCA-p 2.98 3.50 0.96 0.91 -0.52 -17.4 0.89 0.83

49 CEDA1 CSBK-p 8.22 10.31 0.96 0.92 -2.09 -25.4 2.93 0.76

51 WOOD1 WREH-p 26.8 24.2 0.94 0.89 2.66 9.92 12.0 0.28

52 KELL1 KBEH-p 9.68 9.36 0.95 0.91 0.32 3.32 2.56 0.73

54 FLAT1 FRAR-p 14.4 17.5 0.95 0.91 -3.10 -21.5 4.96 0.80

55 BREA1 BBAR-p 12.2 13.6 0.96 0.91 -1.39 -11.5 3.26 0.88

56 PARR1 PBAR-p 11.6 14.2 0.95 0.91 -2.61 -22.6 3.92 0.84

58 ROAR1 RBAR-p 10.1 10.9 0.96 0.92 -0.84 -8.29 2.26 0.91

60 BRUS1 BBHV-p 7.03 8.05 0.94 0.89 -1.02 -14.6 2.07 0.85

61 MOSC1 MBHV-p 12.7 15.1 0.94 0.89 -2.46 -19.4 4.65 0.80

64 CANO1 CBHV-p 12.0 15.0 0.93 0.86 -3.01 -25.0 4.69 0.75

65 WOOD6 WRAL-p 172 192 0.96 0.93 -19.8 -11.5 36.7 0.90

66 COON1 CHAL-p 3.04 4.36 0.97 0.94 -1.32 -43.3 1.67 0.65

67 PERR1 PHBB-p 3.64 4.36 0.97 0.94 -0.72 -19.7 1.01 0.87

70 TOMA1 TBBF-p 10.7 12.5 0.96 0.93 -1.81 -16.8 2.75 0.88

73 GREE1 GRLG-p 13.5 15.2 0.92 0.84 -1.67 -12.3 4.90 0.77

75 WYAS1 WBCF-p 22.3 25.1 0.94 0.89 -2.78 -12.4 7.14 0.80

76 GLAD1 GBLG-p 3.20 4.00 0.95 0.90 -0.79 -24.8 1.20 0.82

78 PARM1 PBHK-p 4.07 5.40 0.95 0.91 -1.34 -32.9 1.81 0.76

79 LWPD1 LPPH-p 2.73 3.52 0.95 0.91 -0.79 -28.8 0.95 0.72

81 SHUN1 SRPH-p 13.7 17.3 0.94 0.89 -3.56 -25.9 5.27 0.74

82 ASSE1 ABNS-p 10.1 8.6 0.94 0.88 1.56 15.5 6.27 -0.32
182 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

complex subsurface-drainage pattern that differs from its 

surface drainage pattern and likely changes seasonally as the 

water table responds to recharge. An expanded explanation 

of the upper Queens Fort Brook drainage issue is given in 

Zarriello and Bent (2004). During most periods in this study 

and in a study previously reported by Kliever (1995), the 

upper Queens Fort Brook rarely flowed. Thus, the water 

table is likely below the streambed most of the time, and 

groundwater discharges to the Hunt and Annaquatucket River 

Basins or flows sublaterally down the Queens Fort Brook 

valley, or both. Similarly, groundwater in the upper part of 

the lower Queens Fort Brook subbasin (RCHRES 8) may 

discharge to the Chipuxet River subbasin (RCHRES 31) if the 

water-table configuration varies with recharge. As previously 

described, none of the active-groundwater flow (AGWO) and 

only 20 percent of the interflow (IFWO) in upper Queens 

Fort Brook (RCHRES 7) were routed downstream. This 

routing method provided satisfactory results without the added 

complexity of seasonally varied loss. Seasonal varied loss, 

which was simulated through the special action feature in the 

Usquepaug-Queen HSPF model (Zarriello and Bent, 2004), 

provided a better model fit at RCHRES 8. 

The large errors between simulated and estimated flow at 

partial-record stations can be attributed to several factors. One 

is the quality of the estimated flow record. Estimated flows 

at Rake Factory Brook (RFBK-p) have a large uncertainty 

because there is no comparable index station for extrapolating 

the partial-record information for a drainage area of this size 

(0.26 mi2). Estimation of the continuous flow at Chickasheen 

Brook (CBLL-p) is affected by few measurements and poor 

correlation to index stations; this results in potentially large 

error in estimated flows. In the upper Wood River (WREH-p) 

and Assekonk Brook (ABNS-p), partial-record stations that 

were among those with the lowest MFE, there was no apparent 

reason the poor model performance. What is known however, 

is the basin characteristics at these stations are similar to those 

at Pendleton Hill Brook, which was among the continuousrecord stations with the poorest model fit. Thus, the modelvariable values may inadequately represent the hydrology in 

these basins, but it may also be a factor in the estimation of a 

continuous record at the partial-record stations.

Groundwater Underflow

Another potential source of model error, for both continuous- and partial-record stations, is groundwater underflow that 

bypasses flow measured or estimated at the streamflow-gaging 

station. In the HSPF model structure of the Pawcatuck River 

Basin, with the exception of upper Queens Fort Brook and 

the upper Meadow Brook subbasins (previously described in 

the model representation of stream reaches), precipitation that 

enters active-groundwater eventually discharges to the stream 

within its subbasin. Thus, if there’s a significant downgradient 

subsurface-flow component in the stream valley, the model 

could oversimulate flow relative to the measured flow. This 

discrepancy is typically significant in small basins during 

low-flow periods when the groundwater underflow is proportionally large relative to the flow in the stream. Groundwater 

underflow that bypasses a streamflow-gaging station typically 

discharges to the stream downgradient of the station, and the 

calculated model error can be attributed to the simulated flow 

path where groundwater discharges to the stream. The model 

fit during these conditions may appear poor, but in actuality 

may better reflect the total flow exiting the basin than that 

measured at the streamflow-gaging station and should be considered in the evaluation of the model performance. 

Sensitivity Analysis

Sensitivity analysis measures the response of the modelsimulated discharge to changes in variable values representing 

the basin. Thus, for the model structure under consideration, 

the most influential variables are identified, and the range of 

feasible values is indicated by perturbing model variables. 

This type of sensitivity analysis is typically an iterative process whereby the value of a given variable is perturbed while 

all other variable values are held constant, and the response of 

the model is measured as a change in the model-fit statistics. 

In the Usquepaug-Queen HSPF model-sensitivity analysis 

(Zarriello and Bent, 2004) 10 selected PERLND variables 

were perturbed and the response was measured by four modelfit metrics (relative bias, the relative standard error, the MFE, 

and the index of agreement). The variable values were uniformly changed (as a percent change from their initial values) 

across all PERLNDs and included INFILT, LZSN, KVARY, 

AGWRC, AGWET, MON–LZETP, monthly interception storage (MON–INTERCEP), monthly nominal upper-zone storage 

(MON–UZSN), monthly interflow (MON–INTERFLW), and 

monthly interflow-recession rate (MON–IRC). 

The results of the Usquepaug-Queen HSPF modelsensitivity analysis are believed to apply to the Pawcatuck 

HSPF model because the models are similar in structure 

and range of variable values. The Usquepaug-Queen HSPF 

model-sensitivity analysis indicated that changes in AGWRC 

and MON–IRC generally resulted in the largest changes of all 

measures of the model fit. Decreases in INFILT and MON–

INTERFLW also resulted in large changes in the relative 

standard error and index of agreement for hourly discharge 

values. Increases in INFILT and MON–INTERFLW indicated 

a slightly better model fit for hourly discharge, but resulted in 

a slightly worse model fit for total monthly runoff. Changes 

in LZSN and MON–LZETP resulted in changes in the model 

bias relative to most other variables tested, but did not result 

in corresponding changes in the other fit statistics relative to 

the other variables tested. For the other variables tested, the 

model-fit statistics were relatively insensitive to changes in the 

calibrated (base) values. 

This type of analysis provides information about variable values as independent entities, but the approach is not 

sufficient for identifying variables that interact with each 
Sensitivity Analysis 183

other (Wagener and others, 2003). The application of PEST 

in the model calibration facilitated a more complex evaluation of model-variable interactions and their influence on the 

model performance. The results are more difficult to describe, 

however, because PEST was used parsimoniously for selected 

variables as previously described. Thus, the interaction of 

variables and their influence on model performance can only 

be compared for variables common to a PEST optimization 

run. In PEST, sensitivity is measured by the response of the 

objective function to a change in a model variable. 

The composite variable-sensitivity matrix computed by 

PEST in CASE 5 (fig. A2–24) indicates that infiltration on 

forested areas overlying till (INFILT–15) was about two or 

more times more sensitive than the other variables evaluated, 

including infiltration on forested areas over sand and gravel 

(INFILT–5), which was one of the least sensitive variables. 

Although INFILT, in general, was found to be a sensitive 

variable in the Usquepaug-Queen HSPF model (Zarriello and 

Bent, 2004), PEST indicates that its importance in the model 

calibration is largely influenced by the dominance of PERLND 

15 in the basin. The importance of INFILT–15 is also underscored by its weak correlation with the other influential 

variables, most notably monthly lower zone evapotranspiration (LZET) expressed in PEST as a sinusoidal wave function 

for both forested areas overlying till and overlying sand and 

gravel, active groundwater evapotranspiration on forested 

areas overlying till (AGWET–15), the transformed active 

groundwater recession variable on forested areas overlying till 

(AGWRCTRANS–15), and the adjustment variable for active 

groundwater recession on forested areas overlying sand and 

gravel (KVARY–5). 

Eigenvector matrix and eigenvalues calculated by PEST 

provide a measure of the information content that is obtained 

during the optimization process. The combination of the paired 

eigenvector matrix and eigenvalues reflects the interaction 

between variables (correlation matrix and covariance matrix) 

not revealed in the composite sensitivity values; the larger 

the vector value, the less that variable is correlated with other 

variables. Normalizing the eigenvectors by dividing by the 

eigenvalues reveals the most influential model variables, 

which are easily identified by the ranking of values from 

highest to lowest (fig. A2–25). In other words, the normalized 

eigenvectors indicate how much of the model performance 

can be explained by the variable variance. For CASE 5, 

INFILT–15 was clearly the most influential of the variables 

tested, followed by AGWET–15 and LZET. Variables 

AGWRCTRANS–15, KVARY–5, AGWET–5, KVARY–15, 

and AGWRCTRANS–5 have less influence and have about 

equal weight in the optimization process. The other variables 

evaluated (LZSN–15, INFILT–5, UZSN–15, LZSN–5, and 

UZSN–5) have little influence on the model optimization 

because they are relatively insensitive, correlated with other 

variables, or both (fig. A2–25). 

The most influential variables in the optimization process 

are the least correlated with other variables and have the least 

variance. These variables also exhibit the tightest confidence 

bands around their optimized value. For example, the 

95-percent confidence interval for INFILT–15 was 

±0.010 in/hr around an optimized value of 0.117 in/hr. 

Fortuitously, variables such as LZSN–5 and UZSN–5, whose 

95-percent confidence intervals varied widely, were least 

influential in the optimization process. Thus, although these 

variables have a high degree of uncertainty, their uncertainty 

is offset by their lack of influence in the model calibration. 

The optimized variable values and their confidence limits are 

provided in table A2–5; PEST was unable to calculate upper 

and lower confidence limits for CASE 7 because the variables 

were insensitive, correlated, or both. 

The optimization of variables controlling flow from 

forested areas overlying steep-rocky soil (CASE 6) indicate that infiltration (INFILT–16) was about six times more 

sensitive than the other variables evaluated (fig. A2–24). The 

normalized eigenvector matrix (fig. A2–25) also indicates that 

INFILT–16 dominated the optimization process and the other 

variables had little effect on the model calibration.

Optimization of the variables that control the amount of 

surface runoff, upper zone storage, interflow (INTFW), and 

the recession coefficient for interflow (IRC) for the nonbaseflow runoff component (CASE 7) from forested areas 

overlying sand and gravel, till, or steep-rocky soil produced 

uncertain results and produce a correlation or covariance 

matrix. This is because the variables were insensitive, highly 

correlated, or both and PEST was unable to invert the variable 

derivatives (Jacobian matrix). Confidence limits could not 

be determined for the same reasons. Another possible reason 

why PEST was unable to invert the Jacobian matrix could be 

that 66 percent of the non-baseflow values were equal to zero; 

thus, a majority of the matrix values would produce no change 

in the objective function. The composite sensitivities indicate 

that IRC from forested areas overlying till (IRC–15) is about 

three times more sensitive than IRCs for the other two HRUs 

tested and that INTFW is insensitive (fig. A2–24). INTFW 

from forested areas overlying sand and gravel (INTFW–5) was 

insensitive in the model calibration; this is probably because 

rapid infiltration in this HRU provides little opportunity for 

precipitation to discharge through surface runoff and interflow.

Optimization of the variables that control baseflow 

(CASE 8) from forested areas overlying sand and gravel, 

till, or steep-rocky soil indicate that variable sensitivities 

(fig. A2–24) and influence on model performance (fig. A2–25) 

was more evenly divided among the variables examined than 

in the other optimization runs. This more equitable distribution of variable sensitivity partly results from the insensitivity 

of the upper-zone soil storage over till (UZSN–15) and was 

dropped from the optimization analysis. 

PEST and its utilities for use in HSPF provide a broad 

range of possibilities with respect to the types and depth of 

analysis that can be undertaken. This analysis shows the dominance of infiltration, evaporation loss from active groundwater 

and lower-zone storage, and the active groundwater-recession 

variables in the model for forested areas overlying till, the 

predominant HRU in the basin. 
184 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

0

0.004

0.008

0.012

0.016

0

0.005

0.010

0.015

0.020

0.025

0.030

0

20

40

60

80

100

120

140

0

0.005

0.010

0.015

0.020

0.025

0.030

CASE 8 — PERLNDs 5 and 15 for

baseflow at USQU, BRSH, PRWR, WRHV,

and PHBK 

CASE 7 — PERLNDs 5, 15, and 16 for

non-baseflow at USQU, BRSH, PRWR,

WRHV, and PHBK 

CASE 6 — PERLND 16 at PHBK,

ARAS, and SRNS

CASE 5 — PERLNDs 5 and 15 at

USQU, BRSH, PRWR, and WRHV

INFILT-15

AGWET-15

AGWRCTRANS-15

KVARY-5

INFILT-5

LZET

AGWET-5

AGWRCTRANS-5

KVARY-15

UZSN-5

LZSN-15

UZSN-15

LZSN-5

INFILT-16 LZET-16 AGWRC- AGWET-16 KVARY-16

TRANS-16

LZSN-16 UZSN-16

INFILT-15

AGWET-15

AGWRCTRANS-15

KVARY-5

INFILT-5

LZET

AGWET-5

AGWRCTRANS-5

KVARY-15

UZSN-5

IRC-15

LZSN-15

IRC-5 IRC-16 INTFW-16 INTFW-15 INTFW-5

DIMENSIONLESS SCALED COMPOSITE SENSITIVITY 

EXPLANATION

INFILT-x–Infiltration

AGWRCTRANS-x–Transformed active 

groundwater-recession factor

KVARY-x–Non-linear adjustment 

factor for active groundwater 

recession

AGWET-x–Active groundwater 

evapotranspiration

LZSN-x–Lower soil-zone storage

LZET-x–Lower soil-zone 

evapotranspiration

UZSN-x–Upper soil-zone storage

-x–Denotes the Hydrologic Response 

Unit (HRU) associated with the 

variable; if unspecified the variable 

applies to all HRUs used in the 

analysis:

 5–Forests over till

 15–Forest over sand and gravel

 16–Steep-rocky soil 

Stations used in optimization:

USQU–Usquepaug River near 

Usquepaug, Rhode Island

BRSH–Beaver River near Shannock, 

Rhode Island

PRWR–Pawcatuck River at Wood 

River Junction, Rhode Island

WRHV–Wood River at Hope Valley, 

Rhode Island

PHBK–Pendleton Hill Brook near Clark 

Falls, Connecticut

ARAS–Ashaway River at Ashaway, RI

SRNS–Shunock River near North 

Stonington, Connecticut

A

B

D

C

Figure A2–24. Composite sensitivity of selected Hydrologic Simulation Program-FORTRAN (HSPF) variables determined by 

parameter estimation (PEST) for selected model variables and stations, Pawcatuck River Basin, southwestern Rhode Island 

and southeastern Connecticut. (Site locations shown in figure A2–4 and described in table A2–4.)
Sensitivity Analysis 185

VECTOR

3 2

4 6

8

10

1

11

9

7 5

N

O

R

M

AL ZI ED E GI EN

VEC

T

O

RS x104

C 

LZET

AGWRCTRANS-15

KVARY-15

LZSN-15

AGWET-5

AGWRCTRANS-5

KVARY-5

INFILT-5

LZSN-5

AGWET-15

INFILT-15

0

2

4

6

8

10

12

14

16

18

20

Forest overlying till (5) and 

sand & gravel (15) for 

non-baseflow at USQU, BRSH, 

PRWR, WRHV, and PHBK

EXPLANATION

INFILT-x–Infiltration

AGWRCTRANS-x–Transformed 

active groundwater recession 

factor

KVARY-x–Non-linear adjustment 

factor for active groundwater 

recession

AGWET-x–Active groundwater 

evapotranspiration

LZSN-x–Lower zone storage

LZET-x–Lower zone evapotranspiration

UZSN-x–Upper soil-zone storage

-x–Denotes the Hydrologic 

Response Unit (HRU) associated 

with the variable; if unspecified 

the variable applies to all HRUs 

used in the analysis:

 5–Forests over till

 15–Forest over sand and gravel

 16–Steep rocky soil 

VECTOR–is the n dimensions in 

parameter space that the vector 

is moved in during the 

optimization process

Stations used in optimization:

USQU–Usquepaug River near 

Usquepaug, Rhode Island

BRSH–Beaver River near 

Shannock, Rhode Island

PRWR–Pawcatuck River at Wood 

River Junction, Rhode Island

WRHV–Wood River at Hope 

Valley, Rhode Island

PHBK–Pendleton Hill Brook near 

Clark Falls, Connecticut

ARAS–Ashaway River at 

Ashaway, Rhode Isalnd

SRNS–Shunock River near North 

Stonington, Connecticut

Forest overlying till (5) and 

sand & gravel (15) at USQU, 

BRSH, PRWR, and WRHV 

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

0

Steep rocky soil (16) at 

PHBK, ARAS, and SRNS

VECTOR

3

2

4

6

1

7

5 UZSN-16

LZET

AGWRCTRANS-16

INFILT-16

AGWET-16

KVARY-16

LZSN-16

N

O

R

M

AL ZI ED E GI EN

VEC

T

O

RS x104

B 

A 

VECTOR

LZET

UZSN-15

AGWRCTRANS-15

UZSN-5

KVARY-15

LZSN-15

AGWET-5

AGWRCTRANS-5

KVARY-5

INFILT-5

LZSN-5

0

5

10

15

20

25

30

INFILT-15

AGWET-15

N

O

R

M

AL ZI ED E GI EN

VEC

T

O

RS x104

3 2 4

6

8

10

1

11

9

7

5

12 13

CASE 5 

CASE 6

CASE 8

Figure A2–25. Relative influence of selected Hydrologic Simulation Program-FORTRAN (HSPF) model variables on minimizing the 

objective function measured by normalized eigenvectors for three parameter estimation (PEST) runs for (A) CASE 5, (B) CASE 6, and 

(C) CASE 8 at selected stations in the Pawcatuck River Basin, southwestern Rhode Island and southeastern Connecticut. (Site locations 

shown in figure A2–4 and described in table A2–4.)
186 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Simulated Hydrologic Budgets and Flow 

Components

Model-variable values assigned to HRUs control water 

movement through the hydrologic system, loss to evapotranspiration, and the resulting amount and rate of water discharged 

to streams. Hydrologic budgets computed for flow components 

by the model illustrate the hydrologic-response characteristics 

of different HRUs and the influence of various HRUs in the 

Pawcatuck River Basin. Hydrologic budgets were examined 

for the average of the annual budgets from January 1, 2000, 

through December 31, 2003, a wet month (March 2001), and a 

dry month (August 2002). 

Average annual hydrologic budgets are similar for HRUs 

with similar surficial materials—sand and gravel, till, steeprocky soils, and wetlands (fig. A2–26A). Discharge per unit 

area by component to streams from PERLNDs overlying sand 

and gravel averaged about 98 percent from active groundwater 

flow (AGWO), about 2 percent from interflow (IFWO), and a 

negligible amount from surface runoff (SURO). Discharge to 

streams from PERLNDs overlying till averaged about 

71 percent from AGWO, about 28 percent from IFWO, and 

about 1 percent from SURO. Discharge components to streams 

from steep-rocky PERLNDs and wetland PERLNDs were 

more equally distributed among flow components than discharge from HRUs overlying till or sand and gravel. Discharge 

to streams per unit area from steep-rocky HRUs was least of 

any HRU from AGWO (about 22 percent) and greatest from 

SURO (about 38 percent); discharge from IFWO was about 

the same as discharge from SURO. Discharge to streams from 

wetlands was about 43 percent from AGWO, about 39 percent 

from IFWO, and about 18 percent from SURO. All discharge 

to streams from IMPLNDs is from SURO. 

The simulated annual discharge to streams over the 

2000–03 period was 29.3 in., about 50 percent of which was 

from forested HRUs mostly from AGWO (fig. A2–26B). 

Discharge to streams from forested HRUs was predominantly 

from areas overlying till (about 9.9 in.) with about half as 

much from forested areas overlying sand and gravel (about 

4.5 in.). Forested HRUs account for about 59 percent (11.2 in.) 

of the total annual average evapotranspiration losses from the 

basin (19.0 in.). Wetlands HRUs account for about 16 percent 

(3.0 in.) of the total annual average evapotranspiration losses 

from the basin. 

Discharge to streams per unit area during a wet month 

(March 2001) (fig. A2–27A) was generally proportional to 

the annual average flow component discharge during the 

calibration period (fig. A2–26A). Discharge to streams from 

PERLNDs overlying sand and gravel averaged about 

89 percent from AGWO, about 11 percent from IFWO, and 

a negligible amount from SURO. Discharge to streams from 

PERLNDs overlying till averaged about 46 percent from 

AGWO, 50 percent from IFWO, and less than 4 percent 

from SURO. Discharge to streams from steep-rocky HRUs 

averaged about 13 percent from AGWO, 27 percent from 

IFWO, and less than 60 percent from SURO. Discharge to 

streams from wetland PERLNDs (forested and nonforested) 

was about evenly distributed between AGWO, IFWO, and 

SURO (29, 36, and 35 percent, respectively). All discharge to 

streams from IMPLNDs is from SURO.

During March 2001, the water supply (12.7 in.), mostly 

from precipitation, was mainly divided between discharge to 

streams (7.5 in.) and inflow to storage (about 4.9 in.), most 

of which entered into active groundwater storage; a small 

amount of the moisture supply was lost to evapotranspiration 

(about 0.4 in.). About 38 percent of water discharged to 

streams during March 2001 was from forest PERLNDs 

overlying till (fig. A2–27B); this PERLND contributed about 

an equal amount of discharge from AGWO and IFWO. Forests 

overlying sand and gravel contributed only about 8 percent of 

discharge to streams because much of the available moisture 

went into active groundwater storage during this month.

Discharge to streams per unit area during a dry month 

(August 2002) (fig. A2–28A) was markedly different from 

the average annual and wet-month water budgets (figs. 

A2–26A and A2–27A, respectively). Nearly all the discharge 

to streams was from AGWO during this month and mostly 

from PERLNDs overlying sand and gravel. Evapotranspiration 

losses from storage typically exceeded discharge to streams in 

most HRUs, especially in forested HRUs. Forested PERLNDs 

have greater losses to evapotranspiration per unit area relative 

to other PERLNDs because these areas are simulated as having larger losses from lower-zone storage (LZET) and activegroundwater (AGWET) by deep-rooted vegetation. Water 

lost to evapotranspiration from forested PERLNDs were the 

dominant part of the basin water budget during August 2002 

(fig. A2–28B).

Contrasts in the distribution and magnitude of the 

simulated outflow components to streams and losses to 

evapotranspiration for the annual average, a wet month, and a 

dry month are apparent when summarized for the entire basin 

(fig. A2–29). For the annual average water budget, about 59 

percent (29.3 in.) of the moisture supply (mostly precipitation) 

to the basin (about 49.5 in.) was discharged to streams and 

about 38 percent (19.0 in.) was lost to evapotranspiration 

(fig. A2–29A). The remaining 1.2 in. went into storage; hence, 

the discharge to streams and evapotranspiration is slightly 

lower than precipitation. 

The average annual discharge to streams (fig. A2–29A) 

was composed of about 9 percent (2.8 in.) SURO and about 

91 percent (27.1 in.) subsurface discharge as IFWO (6.2 in.) 

and AGWO (20.9 in.). During March 2001, the moisture 

supply that did not go into storage was mostly discharged to 

streams and a small amount was lost to evapotranspiration 

(fig. A2–29B). Discharge to streams during March 2001 was 

composed of about 20 percent SURO (1.5 in.), 34 percent 

IFWO (2.6 in.), and 46 percent AGWO (3.5 in.). During 

August 2002, water loss to evapotranspiration was about 6 

times greater than the discharge to streams (fig. A2–29C) and 

nearly twice the moisture supply to the basin. Nearly all the 

discharge to streams during this period was from AGWO. 
Simulated Hydrologic Budgets and Flow Components 187

Overlying sand 

and gravel

Overlying till

Effective

impervious area

A WATER BUDGET PER UNIT AREA

JANUARY 2000–DECEMBER 2003

BASIN WATER BUDGET

-30

-20

-10

0

10

20

30

40

50

INCHES PER ACRE -10

-8

-6

-4

-2

0

2

4

6

8

10

12

Overlying sand 

and gravel

Overlying till

Effective

impervious area

INCHES OVER BASIN

AGWET–Active groundwater

LZET–Lower zone

UZET–Upper zone

AGWO–Active groundwater CEPE–Interception 

IFWO–Interflow 

SURO–Surface runoff

Outflow to streams from: Evapotranspiration losses from:

EXPLANATION

Outflow to

streams

Losses to

evapotranspiration

Outflow to

streams

Losses to

evapotranspiration

Open space in low- to moderate- density residential

Open space

Forest

Non-forested wetland

Forested wetland

Golf course

Turf farm

Irrigated agriculture

Residential

Open space in commercial/industrial

Commercial/industrial/transportation

Open space

Forest

Water

Steep-rocky soils

Open space in highdensity residential

Open space in low- to moderate- density residential

Open space in commercial/industrial

Open space in highdensity residential

B 

HYDROLOGIC RESPONSE UNIT

Figure A2–26. Average annual water budget for January 2000 through December 2003 by component in (A) inches 

per acre and (B) inches over the entire basin from each hydrologic response unit (HRU) simulated with the Hydrologic 

Simulation Program-FORTRAN (HSPF) of the Pawcatuck River Basin, southwestern Rhode Island and southeastern 

Connecticut.
188 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

INCHES PER ACRE -2

0

2

4

6

8

10

12

14

A 

Overlying sand 

and gravel

Overlying till

Overlying sand 

and gravel

Overlying till

Effective

impervious area

INCHES OVER BASIN -0.5

0

0.5

1.0

1.5

2.0

2.5

3.0

B 

AGWET–Active groundwater

LZET–Lower zone

UZET–Upper zone

CEPE–Interception 

AGWO–Active groundwater 

IFWO–Interflow 

SURO–Surface runoff

Evapotranspiration 

losses from:

Outflow to streams from:

EXPLANATION

Outflow to

streams

Losses to

evapotranspiration

Outflow to

streams

Losses to

evapotranspiration

HYDROLOGIC RESPONSE UNIT

Open space in low- to moderate- density residential

Open space

Forest

Non-forested wetland

Forested wetland

Golf course

Turf farm

Irrigated agriculture

Residential

Open space in commercial/industrial

Commercial/industrial/transportation

Open space

Forest

Water

Steep-rocky soils

Open space in highdensity residential

Open space in low- to moderate- density residential

Open space in commercial/industrial

Open space in highdensity residential

WET MONTH–MARCH 2001

WATER BUDGET PER UNIT AREA

BASIN WATER BUDGET

Figure A2–27. Water budget for a wet month, March 2001, by component in (A) inches per acre and (B) inches over 

the entire basin from each hydrologic response unit (HRU) simulated with the Hydrologic Simulation Program-FORTRAN 

(HSPF) of the Pawcatuck River Basin, southwestern Rhode Island and southeastern Connecticut.
Simulated Hydrologic Budgets and Flow Components 189

Figure A2–28. Water budget for a dry month, August 2002, by component in (A) inches per acre and (B) inches over 

the entire basin from each hydrologic response unit (HRU) simulated with the Hydrologic Simulation Program-FORTRAN 

(HSPF), Pawcatuck River Basin, southwestern Rhode Island and southeastern Connecticut.

INCHES PER ACRE

A 

Overlying sand 

and gravel

Overlying till

Effective

impervious area

-5

-4

-3

-2

-1

0

1

2

3

Overlying sand 

and gravel

Overlying till

Effective

impervious area

INCHES OVER BASIN -1.0

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

AGWET–Active groundwater

LZET–Lower zone

UZET–Upper zone

CEPE–Interception 

AGWO–Active groundwater 

IFWO–Interflow 

SURO–Surface runoff

Evapotranspiration 

losses from:

Outflow to streams from:

EXPLANATION

Outflow to

streams

Losses to

evapotranspiration

Outflow to

streams

Losses to

evapotranspiration

B 

HYDROLOGIC RESPONSE UNIT

Open space in low- to moderate- density residential

Open space

Forest

Non-forested wetland

Forested wetland

Golf course

Turf farm

Irrigated agriculture

Residential

Open space in commercial/industrial

Commercial/industrial/transportation

Open space

Forest

Water

Steep-rocky soils

Open space in highdensity residential

Open space in low- to moderate- density residential

Open space in commercial/industrial

Open space in highdensity residential

DRY MONTH–AUGUST 2002

BASIN WATER BUDGET 

WATER BUDGET PER UNIT AREA
190 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Model Uncertainty and Limitations

Numerical simulation models are, at best, approximations of hydrologic systems because of the necessity to 

simplify the complex processes and physical characteristics of 

a basin. Despite these limitations, models can be useful tools 

to evaluate the hydrologic responses of a basin, provided that 

the model structure and variable values adequately reflect 

the hydrologic responses of the system to the stresses evaluated. Model uncertainty is associated with input data and the 

possibility of alternative model structures and variable values 

that can produce equally acceptable results. The adequacy of 

the available data to distinguish between alternative models 

(model structures and variable values), and the realization that 

alternative structures and variable values can only be rejected 

as acceptable models is a condition that has been described as 

equifinality (Beven, 1993; Beven and Binley, 1992). 

The HSPF model of the Pawcatuck River Basin was 

well calibrated to flow records representing a wide range of 

conditions at 17 continuous-record stations and 34 partialrecord stations distributed throughout the basin to a period 

that spanned about four and half years. The calibration of key 

model variables and the use of the PEST program to evaluate uncertainties in the variables values provided confidence 

in the results as being representative of the hydrology of the 

basin. Yet, despite robust calibration, there are several factors 

to consider in the use of the model and the interpretation of 

model results. 

Extrapolation of a point measurement to define spatially 

varied precipitation and potential evapotranspiration over 

the basin adds uncertainty to the identification of the best-fit 

variable values. For example, total monthly precipitation can 

vary widely as indicated by the deviation of total monthly 

precipitation at the FBWR station (climate data used for the 

model calibration) from the total average monthly precipitation at the five climate stations in and around the Pawcatuck 

River Basin (fig. 2–23). Total monthly precipitation at FBWR 

differed from the combined average precipitation in the region 

by as much as 400 percent; these differences can be more 

pronounced during storms periods. Differences in precipitation over the basin, which are not incorporated into the model, 

result in differences between simulated and observed flows. 

Although spatially varied climate data can be represented in 

the model, this modification was not considered necessary 

because the Pawcatuck River Basin does not have distinctly 

different climatic regions that affect the simulation of withdrawals or land use change. 

Systematic differences between data from stations at 

FBWR and PROVID could bias simulated flows, however. 

Data from the PROVID station, which is about 15 mi northeast of the basin, was used to simulate the response of the 

basin to long-term climatic conditions of the region. From 

December 1, 1999, through December 30, 2004, total precipitation was 11 percent lower and total potential evapotranspiration was 8 percent greater at the PROVID than at the FBWR 

station. Total monthly precipitation was less about one-third 

Figure A2–29. Summary of water 

budgets in inches over the entire basin 

for (A) average annual 2000–03, (B) wet 

month (March 2001), and (C) dry month 

(August 2002) by component simulated 

with the Hydrologic Simulation ProgramFORTRAN (HSPF) of the Pawcatuck River 

Basin, southwestern Rhode Island and 

southeastern Connecticut.

A 

-30

-20

-10

0

10

20

30

40

Average

annual

C 

-3

-2

-1

0

1

Dry

month

B 

-1

0

1

2

3

4

5

6

7

8

9

Wet

month

AGWET–Active groundwater

LZET–Lower zone

UZET–Upper zone

CEPE–Interception 

AGWO–Active groundwater 

IFWO–Interflow 

SURO–Surface runoff

Evapotranspiration 

losses from:

Outflow to streams from:

EXPLANATION

Outflow to

streams

Losses to

evapotranspiration

INCHES
References Cited 191

of the time, and total monthly potential evapotranspiration 

was greater about 16 percent of the time at FBWR than at 

PROVID. Although the differences in total monthly precipitation and evapotranspiration varied between these two stations, 

the differences were more consistent during the winter months 

than at other times of year. These differences illustrate the 

inherent uncertainties of applying a point measurement to 

represent spatially varied data, regional differences in climate, 

systematic measurement bias, or a combination of these factors. Although measures were taken to adjust the PROVID 

data to better match the FBWR data, the differences in the 

data collected at these two stations underscore that simulations 

made with the PROVID data may not reproduce the observed 

day-to-day streamflow in the basin.

Water-use information is another area of data uncertainty. 

Known major water withdrawals were subtracted directly 

from simulated streamflow. Once withdrawals were accounted 

for, the model variable values were adjusted to calibrate the 

basin’s response to precipitation and evapotranspiration. Thus, 

variable values could have been skewed during the calibration process to compensate for inaccuracies or unknown 

water withdrawals. Withdrawals for irrigation can vary widely 

because they depend on climate, plant type and root depth, soil 

characteristics, and management practices. Although irrigation 

was measured to the extent allowed, withdrawals for several 

known irrigation uses could only be estimated. In addition, 

long-term irrigation was estimated from a logistic-regression 

equation developed from irrigation patterns observed during 

2000–04. These irrigation patterns and rates may not be representative of past or future irrigation withdrawals, however. 

The model calibration reflects the combined effects of 

various HRUs (PERLNDs and IMPLNDs) and RCHRESs. 

Hydrologic judgment was used to represent the responses of 

different PERLNDs and IMPLNDs. Although a good fit was 

obtained between simulated and observed flows over a wide 

range of conditions, information was not available to explicitly calibrate individual HRUs. Thus, simulation results from 

ungaged areas or from scenarios that change one type of HRU 

to another (such as buildout simulations) have a high degree of 

uncertainty and, therefore, should be viewed as evidence of a 

relative change instead of an absolute change. Stage, storage, 

and discharge characteristics of RCHRESs (including wetlands) were determined from measured channel geometry to 

the extent possible, but many factors, such as channel roughness and changes in channel geometry along a river reach, 

could not be measured. The stage, storage, and, discharge 

characteristics of a reach affect the simulated flow and the 

stream stage. 

The Pawcatuck River Basin HSPF model was conceptualized and calibrated to evaluate the effects of withdrawals on 

streamflow. Many water-resource-management questions can 

be evaluated by model simulations, but the model may not be 

appropriate for some analyses. Thus, consideration should be 

given to the model uncertainties and limitations to ensure that 

the simulation results do not lead to inaccurate conclusions.

References Cited

Allen, W.B., Hahn, G.W., and Brackley, R.A., 1966, 

Availability of groundwater, upper Pawcatuck River Basin, 

Rhode Island: U.S. Geological Survey Water-Supply Paper 

1821, 66 p., 3 pls. 

Arcement, G.J., Jr., and Schneider, V.R., 1989, Guide for 

selecting Manning’s roughness coefficients for natural 

channels and flood plains: U.S. Geological Survey WaterSupply Paper 2339, 38 p.

Barlow, P.M., and Dickerman, D.C., 2001, Numericalsimulation and conjunctive-management models of the 

Hunt-Annaquatucket-Pettaquamscutt stream-aquifer system, 

Rhode Island: U.S. Geological Survey Professional Paper 

1636, 88 p.

Beven, K.J., 1993, Prophecy, reality, and uncertainty in 

distributed hydrologic modeling: Advances in Water 

Resources, v. 6, p. 253–254.

Beven, K.J., and Binley, A.M., 1992, The future of distributed 

models—Model calibration and predictive uncertainty: 

Hydrological Processes, v. 6, p. 279–298.

Bicknell, B.R., Imhoff, J.C., Kittle, J.L., Jr., Jobes, T.H., 

and Donigian, A.S., Jr., 2000, Hydrological Simulation 

Program-Fortran user’s manual for release 12: Mountain 

View, Calif., AQUA TERRA Consultants, variously paged. 

Coon, W.F., 1998, Estimation of roughness coefficients 

for natural stream channels with vegetated banks: U.S. 

Geological Survey Water-Supply Paper 2441, 133 p.

Dickerman, D.C., Kliever, J.D., and Stone, J.R., 1997, 

Hydrogeology, water quality, and simulation of groundwater-development alternatives in the Usquepaug-Queen 

ground-water reservoir, southern Rhode Island: 

U.S. Geological Survey Water-Resources Investigations 

Report 97–4126, 48 p.

Doherty, John, 2003, PEST surface water utilities: Watermark 

Numerical Computing, University of Idaho, unpublished 

report, variously paged.

Doherty, John, 2004, PEST—Model-independent parameter 

estimation, 5th ed.: Watermark Numerical Computing, 

unpublished report, variously paged.

Donigian, A.S., Imhoff, J.C., Bricknell, B.R., and Kittle, J.L., 

Jr., 1984, Application guide for Hydrologic Simulation 

Program-Fortran (HSPF): Athens, Ga., U.S. Environmental 

Protection Agency-600/3-84-065, Environmental Research 

Laboratory, 177 p.
192 Appendix Part 2. Precipitation-Runoff Model Development and Calibration

Duncker, J.J., and Melching C.S., 1998, Regional rainfallrunoff relations for simulations of streamflow for 

watersheds in DuPage County, Illinois: U.S. Geological 

Survey Water-Resources Investigations Report 98–4035, 

80 p.

Flynn, K.M., Hummel, P.R., Lumb, A.M., and Kittle, J.L. Jr., 

1995, User’s manual for ANNIE, version 2, a computer 

program for interactive hydrologic data management: 

U.S. Geological Survey Water-Resources Investigations 

Report 95–4085, 211 p.

Kittle, J.L., Jr., Lumb, A.M., Hummel, P.R., Duda, P.A., 

and Gray, M.H., 1998, A tool for the analysis of model 

simulation scenarios for watersheds (GenScn): 

U.S. Geological Survey Water-Resources Investigations 

Report 98–4134, 152 p.

Kliever, J.D., 1995, Hydrologic data for the Usquepaug-Queen 

River Basin, Rhode Island: U.S. Geological Survey OpenFile Report 95–305, 68 p.

Legates, D.R., and McCabe, G.J., Jr., 1999, Evaluating 

the use of “goodness-of-fit” measures in hydrologic and 

hydroclimatic model validation: Water Resources Research, 

v. 35, no. 1, p. 233–241.

Lott, R.B., and Hunt, R.J., 2001, Estimating evapotranspiration 

in natural and constructed wetlands: Wetlands, v. 21, no. 4, 

p. 614–628.

Lumb, A.M., Kittle, J.L., Jr., and Flynn, K.M., 1990, Users 

manual for ANNIE, a computer program for interactive 

hydrologic analyses and data management: U.S. Geological 

Survey Water-Resources Investigations Report 89–4080, 

236 p.

Lumb, A.M., McCammon, R.B., and Kittle, J.L., Jr., 1994, 

User’s manual for an expert system (HSPEXP) for 

calibration of the Hydrological Simulation Program-Fortran: 

U.S. Geological Survey Water-Resources Investigations 

Report 94–4168, 102 p.

Regan, R.S., and Schaffranek, R.W., 1985, A computer 

program for analyzing channel geometry: U.S. Geological 

Survey Water-Resources Investigations Report 85–4335, 

40 p.

Wagener, Thorsten, Wheater, H.S., and Gupta, H.V., 2003, 

Identification and evaluation of watershed models, in

Duan, Q., Gupta, H.V., Sorooshian, S., Rousseau, A.N., 

Turcotte, R., Calibration of Watershed Models, Water 

Science and Applications: Washington, D.C., American 

Geophysical Union, p. 29–47.

Zarriello, P.J., and Bent, G.C., 2004, A precipitation-runoff 

model for the analysis of the effects of water withdrawals 

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