Loads, West Fork Trinity River,

Fort Worth, Texas, 1997

Water-Resources Investigations Report 01–4253

U.S. Department of the Interior

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

U.S. Geological Survey

Computed and Estimated Pollutant

Loads, West Fork Trinity River,

Fort Worth, Texas, 1997

By Paul W. McKee and Harry C. McWreath

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 01–4253

In cooperation with the Trinity River Authority

Austin, Texas

2001
ii

U.S. DEPARTMENT OF THE INTERIOR

Gale A. Norton, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

Any use of trade, product, or firm names is for

descriptive purposes only and does not imply

endorsement by the U.S. Government.

For additional information write to

District Chief

U.S. Geological Survey

8027 Exchange Dr.

Austin, TX 78754–4733

E-mail: dc_tx@usgs.gov

Copies of this report can be purchased from

U.S. Geological Survey

Branch of Information Services

Box 25286

Denver, CO 80225–0286

E-mail: infoservices@usgs.gov
CONTENTS iii

CONTENTS

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

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

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

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

Previous Studies ....................................................................................................................................................... 2

Acknowledgments .................................................................................................................................................... 4

Methods of Computing and Estimating Pollutant Loads ..................................................................................................... 5

Computing Loads ..................................................................................................................................................... 5

Estimating Loads With Deterministic Model ........................................................................................................... 6

Estimating Loads With Statistical Model ................................................................................................................. 6

Computed and Estimated Pollutant Loads ........................................................................................................................... 9

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

References Cited .................................................................................................................................................................. 15

FIGURES

1. Map showing location of study area and monitoring sites in the Dallas-Fort Worth metropolitan area .............. 3

2. Map showing land-use categories in the study area ............................................................................................. 4

3. Hydrographs showing accumulated rainfall and discharge at streamflow-gaging station 08048543

for storms of October 23–24 and December 7–8, 1997 ....................................................................................... 5

4–6. Graphs showing:

4. Comparison of use of point rainfall and areal-averaged rainfall, deterministic model—differences

between estimated and computed pollutant loads for 12 properties and constituents for two storms

(October 23–24 and December 7–8, 1997) ................................................................................................ 12

5. Comparison of use of point rainfall and areal-averaged rainfall, statistical model—differences

between estimated and computed pollutant loads for 12 properties and constituents for two storms

(October 23–24 and December 7–8, 1997) ................................................................................................ 13

6. Comparison of results of deterministic model and statistical model, both using areal-averaged

rainfall—mean absolute differences between estimated and computed pollutant loads for 12

properties and constituents for two storms (October 23–24 and December 7–8, 1997) ........................... 14

TABLES

1. Land-use characteristics ....................................................................................................................................... 2

2. Median event-mean concentrations by land-use category .................................................................................... 7

3. Regression equation coefficients for estimating pollutant loads for residential, commercial, industrial,

and nonurban land uses ........................................................................................................................................ 8

4. Regression equation coefficients for estimating pollutant loads for highway land use ....................................... 9

5. Computed and estimated pollutant loads for 12 selected properties and constituents ......................................... 10

Abbreviations

BCF, bias-correction factor

DA, total contributing drainage area

DFW, Dallas-Fort Worth

EMC, event-mean concentration

ft

3/s, cubic foot per second

GIS, Geographic Information System

IA, impervious area

LUC, commercial land use

LUI, industrial land use

LUN, nonurban land use

LUR, residential land use

mi, mile

NEXRAD, NEXt Generation Weather RADar

NPDES, National Pollutant Discharge Elimination System

R2 adj., adjusted coefficient of determination

SE, standard estimate of error

TRN, total storm rainfall

USGS, U.S. Geological Survey

WMM, Watershed Management Model
Abstract 1

Computed and Estimated Pollutant 

Loads, West Fork Trinity River, 

Fort Worth, Texas, 1997

By Paul W. McKee and Harry C. McWreath

Abstract

In 1998 the U.S. Geological Survey, in cooperation with the Trinity River Authority, did a study 

to estimate storm-runoff pollutant loads using two 

models—a deterministic model and a statistical 

model; the estimated loads were compared to loads 

computed from measured data for a large (118,000 

acres) basin in the Dallas-Fort Worth, Texas, metropolitan area. Loads were computed and estimated 

for 12 properties and constituents in runoff from 

two 1997 storms at streamflow-gaging station 

08048543 West Fork Trinity River at Beach Street 

in Fort Worth. Each model uses rainfall as a 

primary variable to estimate pollutant load. In 

addition to using point rainfall at the Beach Street 

station to estimate pollutant loads, areal-averaged 

rainfall for the basin was computed to obtain a 

more representative estimate of rainfall over the 

basin. Loads estimated by the models for the two 

storms, using both point and areal-averaged rainfall, generally did not compare closely to computed 

loads for the 12 water-quality properties and constituents. Both models overestimated loads more 

frequently than they underestimated loads. The 

models tended to yield similar estimates for the 

same property or constituent. In general, arealaveraged rainfall data yielded better estimates of 

loads than point rainfall data for both models. Neither the deterministic model nor the statistical 

model (both using areal-averaged rainfall) was 

consistently better at estimating loads. Several factors could account for the inability of the models to 

estimate loads closer to computed loads. Chief 

among them is the fact that neither model was 

designed for the specific application of this study.

INTRODUCTION

In 1987, the U.S. Congress amended the Clean 

Water Act (Federal Water Pollution Control Act 

Amendments of 1972 and 1977) to require the U.S. 

Environmental Protection Agency to establish phased 

National Pollutant Discharge Elimination System 

(NPDES) regulations for various nonpoint-source discharges including discharges from municipal urban 

areas. The Clean Water Act amendments stipulate that 

all municipalities with populations greater than 100,000 

and with municipal storm-sewer systems separate from 

sewage systems should acquire discharge permits 

according to regulations outlined for NPDES (U.S. 

Environmental Protection Agency, 1992). Part of these 

regulations require municipalities not only to characterize the quantity and quality of storm runoff with 

monitoring and sampling programs but also to estimate 

pollutant concentrations and annual pollutant loads 

from unmonitored watersheds (U.S. Environmental 

Protection Agency, 1990).

Two models (described later in this report) have 

been developed to estimate pollutant loads in storm runoff from urban basins in the Dallas-Fort Worth (DFW) 

metropolitan area, Texas. A deterministic model, the 

Watershed Management Model (WMM), estimates a 

total basin pollutant load by multiplying an event-mean 

concentration (EMC) by estimated runoff for each type 

of land use and then summing the loads for each land 

use (Rouge River National Wet Weather Demonstration 

Project, 1998). A statistical model, developed by the 

U.S. Geological Survey (USGS), uses multi-variable 

regression equations to estimate pollutant loads in storm 

runoff. The deterministic and the statistical models had 

not been tested to determine whether either could produce accurate estimates of pollutant loads in storm runoff for large basins (greater than 160 acres) within the 

DFW metropolitan area. 
2 Computed and Estimated Pollutant Loads, West Fork Trinity River, Fort Worth, Texas, 1997 

In 1998, the USGS did an investigation, in cooperation with the Trinity River Authority, to estimate 

storm-runoff pollutant loads with each of the two models and to compare the estimated loads to computed 

loads. The ability to reliably estimate pollutant loads in 

storm runoff from selected watersheds in the Trinity 

River Basin could aid the Trinity River Authority in 

evaluating suitable best management practices for 

reducing loads.

Purpose and Scope

This report documents the derivation of estimated 

storm-runoff pollutant loads from the two models and 

compares the estimated loads with loads computed from 

measured data at USGS streamflow-gaging station 

08048543 West Fork Trinity River at Beach Street, 

Fort Worth. The properties and constituents for which 

loads were computed are biochemical oxygen demand, 

chemical oxygen demand, suspended solids, dissolved 

solids, total nitrogen, total ammonia plus organic nitrogen (also known as total Kjeldahl nitrogen), total phosphorus, dissolved phosphorus, total recoverable copper, 

total recoverable lead, total recoverable zinc, and total 

diazinon. 

Rainfall, streamflow, and water-quality data for 

this study were available from three storms—October 

23–24, December 7–8, and December 20–21, 1997—

for which samples were collected as a part of a previous 

study. However, data from the December 20–21 storm 

were not used because the computed volume of runoff 

associated with the sampled storm-hydrograph peak 

was small (less than 20 percent of the volumes of the 

two other storms). The sampled peak was believed to 

represent local runoff originating near the gaging station 

rather than runoff from the entire basin. Because the 

models estimate loads assumed to be from the entire 

basin, computed loads from a fraction of the basin (near 

the gaging station) would not be comparable.

Description of Study Area

The study area (about 118,000 acres) is located in 

north-central Texas in southwestern Tarrant County and 

eastern Parker County (fig. 1). Fort Worth is the largest 

city in the study area. The study area is coincident with 

the intervening drainage area of the West Fork Trinity 

River between the Beach Street station and Lake Worth 

and Benbrook Lake. The West Fork Trinity River is one 

of three major tributaries to the main stem Trinity River. 

The mean annual discharge (1977–98) at the Beach 

Street station is 630 ft3

/s (U.S. Geological Survey, 

1999).

Tarrant and Parker Counties are in the Cross Timbers and Grand Prairies physiographic regions within 

the southern extension of the Interior Lowlands 

(Ramos, 1997). Six classifications of land use—residential, commercial, industrial, highway, nonurban, and 

water—were defined and delineated in the study area 

(fig. 2) using a geographic information system (GIS). 

Nonurban land use represents the largest part (47.3 percent) of the basin, and highway land use represents the 

smallest part (4.2 percent) (table 1). The impervious 

fraction of area estimated for each land-use category 

ranges from 0.1 for nonurban to 0.9 for highway.

Previous Studies

Driver and Tasker (1990) describe techniques for 

estimating storm-runoff loads, volumes, and selected 

water-quality property and constituent concentrations 

on the basis of regional data collected in urban watersheds throughout the United States. The regression 

model approach (Driver and Tasker, 1990) used a 

national database developed in the late 1970s as part 

of the Nationwide Urban Runoff Program for three 

major types of land use: residential, commercial, and 

industrial. Baldys and others (1998) used similar techniques on a local scale to estimate stormwater pollutant 

loads in the DFW metropolitan area for four land-use 

categories: residential, commercial, industrial, and nonurban. The data used by Baldys and others (1998) were 

collected by the USGS at 26 sites during 1992–93 as 

part of the DFW municipal NPDES storm-runoff 

characterization study (Baldys and others, 1997). 

Table 1. Land-use characteristics 

Land-use

category

Drainage

area

(acres)

Percent

of total

drainage

area

Estimated

impervious 

fraction

Residential 39,000 33.1 0.5

Commercial 12,800 10.8 .7

Industrial 5,400 4.6 .8

Highway 5,000 4.2 .9

Nonurban 55,800 47.3 .1

All 118,000
INTRODUCTION 3Figure 1. Location of study area and monitoring sites in the Dallas-Fort Worth metropolitan area.

West

Fork

Trinity

River

Elm

Fork Trinity

R.

Trinity

Riv

Village Creek

Mountain

 Creek

White

Rock Creek

Little

Marys

Creek

Marine Creek

EAGLE MOUNTAIN LAKE

LAKE  WORTH

BENBROOK LAKE

GRAPEVINE LAKE

MOUNTAIN CREEK LAKE

JOE POOL LAKE

South

Fork

Trinity River

ARLINGTON LAKE

FORT WORTH

ARLINGTON

PLANO

DALLAS

GRAND  PRAIRIE

IRVING

0806

08055690

08048543

08049950

08048920

Meacham Airport

Love Field

08049860

08049950

08048543

08061515

Study area—Intervening drainage areaof West Fork Trinity River below LakeWorth and Benbrook Lake

Boundary of Dallas-Fort Worthmetropolitan area

Land-use category associated with monitoringsite—Number is U.S. Geological Survey station number

EXPLANATION

Mixed

Highway

Nonurban

I–35W

I–35W

I–30

I–820

State

377

State

199

I–820

State 121

I–30

I–820

State

121

I–635

I–35E

US 183

I–20 Loop 12

I–35E

Loop

12

I–30

I–20

US 75

US 75

0 4 8 12 16 MILES

97o15'

97o30'

32o52'30"

32o37'30"

97o

96o45'

Digital base from U.S. Geological SurveyScale 1:250,000 quadranglesAlbers equal-area projection based onstandard parallels 45.5 and 29.5 degrees

TARRANT COUNTY

PARKER COUNTY

DALLAS COUNTY

DENTON COUNTY
4 Computed and Estimated Pollutant Loads, West Fork Trinity River, Fort Worth, Texas, 1997 

These data were used to characterize stormwater quality 

and to compute loads of 12 selected water-quality 

properties and constituents in storm runoff. The data 

were collected from storm-sewer outfalls that had drainage areas of less than 160 acres and predominantly single land-use categories of residential, commercial, or 

industrial, with minimal nonurban land use.

Acknowledgments

The authors thank the North Central Texas 

Council of Governments for their cooperation and assistance in the completion of this report. Their assistance 

with pollutant load estimation using the WMM, GIS 

land-use mapping and statistics, and average rainfall 

computations for the study area using National Weather 

Little

Marys

Creek

South

Fork

Trinity

River

Marine

Creek

West

Fork

Trinity River

Sycamore Creek

FORT WORTH

FORT WORTH

I–30

I–820

I–820

I–30

I–820

I–35W

0 2 4 6 MILES

97o25'

32o50' 97o

20'

97o

30'

97o

35'

32o

45'

32o

40'

PARKER COUNTY

TARRANT COUNTY

Industrial

Commercial

Residential

Nonurban

EXPLANATION

Highway

Water

U.S. Geological Survey streamflow-gaging station and number

Modified from North Central 

Texas Council of Governments,

unpublished map, 1999

Land-use category

08048543

08048543

Figure 2. Land-use categories in the study area.
METHODS OF COMPUTING AND ESTIMATING POLLUTANT LOADS 5

Service doppler radar data (NEXt Generation Weather 

RADar [NEXRAD]) were invaluable.

METHODS OF COMPUTING AND 

ESTIMATING POLLUTANT LOADS

Computing Loads

Pollutant loads for two storms were computed 

from measured flow-weighted concentrations and 

storm-runoff volume at the Beach Street streamflowgaging station (fig. 3). Concentrations of the 12 properties and constituents were determined analytically from 

a composited sample representing equal volumes of 

storm runoff. An EMC was determined for each property or constituent from the flow-weighted composite 

sample collected during a storm. The storm-runoff 

volume was computed using an established rating curve 

that relates recorded stage to measured discharge. 

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

0

DISCHARGE, IN CUBIC FEET PER SECOND

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

ACCUMULATED RAINFALL, IN INCHES

Storm of October 23–24, 1997

2400

0200

0400

0600

0800

1000

1200

1400

16001800

2000

2200

2400

0200

0400

0600

0800

1000

1200

1400

16001800

2000

2200

2400

TIME, IN HOURS

1.2

1.0

0.8

0.6

0.4

0.2

0

ACCUMULATED RAINFALL, IN INCHES

3,000

2,500

2,000

1,500

1,000

500

0

DISCHARGE, IN CUBIC FEET PER SECOND

1200

1400

16001800

2000

22002400

0200

0400

0600

0800

1000

1200

1400

16001800

2000

2200

2400

TIME, IN HOURS

Storm of December 7–8, 1997

Accumulated rainfall

Discharge

Composite sample

Simulated

 recession

EXPLANATION

Figure 3. Hydrographs showing accumulated rainfall and discharge at streamflow-gaging station 08048543 for 

storms of October 23–24 and December 7–8, 1997.
6 Computed and Estimated Pollutant Loads, West Fork Trinity River, Fort Worth, Texas, 1997 

A load for an individual storm is computed by the 

equation: 

, (1)

where 

= pollutant load (in pounds) for storm i;

= event-mean concentration of property or 

constituent (in milligrams per liter or 

micrograms per liter) for storm i;

= runoff volume (in cubic feet) for storm i; 

and

= conversion factor (6.2382-5 if constituent is 

in milligrams per liter or 6.2382-8 if 

constituent is in micrograms per liter).

Base-flow loads at the West Fork Trinity River at 

Beach Street station were considered negligible on the 

basis of the magnitude of difference between base-flow 

and storm-runoff volumes and associated pollutant concentrations. In addition, base flow was not enough to 

dilute storm-runoff concentrations. Therefore, no 

adjustment was made to the total storm load for loads 

produced during base-flow conditions. 

Estimating Loads With Deterministic Model

The WMM, originally developed by Camp 

Dresser & McKee, Inc. (Rouge River National Wet 

Weather Demonstration Project, 1998), is a simple 

deterministic model that simulates the generation and 

fate of pollutant loads from a variety of pollutant 

sources in a basin. The model estimates annual or seasonal pollutant loads carried in storm runoff on the basis 

of associated EMCs, land use, impervious fraction, and 

rainfall. 

The model estimates runoff volumes from storm 

rainfall and runoff coefficients for the pervious and 

impervious areas in each land-use category. For this 

report, a runoff coefficient of 0.90 was used for impervious areas and 0.20 for pervious areas. These coefficients designate 90 percent of the rainfall as runoff from 

the impervious fraction of each land-use area and 20 

percent of the rainfall as runoff from the pervious fraction of each land-use area. The equation for runoff volume for any land use (L) is 

, (2)

where 

= runoff volume for land use (in cubic feet);

= pervious area runoff coefficient;

= impervious area runoff coefficient;

= impervious fraction of land-use area 

(table 1);

= storm rainfall (in inches);

= area of land use (in acres); and

= conversion factor (3,630).

The total storm runoff from the basin is the sum of the 

runoff volumes for all land uses.

For the deterministic model, an equation similar 

to equation 1 is used to estimate the pollutant load for 

each land use by multiplying the runoff volume for each 

land use (RVL) by the corresponding EMC for each land 

use:

, (3)

where 

 = pollutant load for each land use,

 = EMC for each land use, and

 and are the same as defined for equation 2.

For this study, the median EMCs reported by 

Baldys and others (1998), which characterized storm 

runoff throughout the DFW metropolitan area during 

1992–93, were used for residential, commercial, and 

industrial land uses (table 2). Median EMCs were used 

rather than means because medians are less influenced 

by outliers in the data. EMCs for highway land use 

(table 2) were computed using data collected during 28 

storms sampled during 1993–94 at four highway stormrunoff monitoring sites (USGS stations 08048920, 

08049860, 08049950, and 08055690) located throughout the DFW metropolitan area (fig. 1). EMCs for 

nonurban land use (table 2) were computed from one 

nonurban storm-runoff monitoring site (USGS station 

08061515) in Plano (fig. 1), northeast of Dallas. These 

EMCs reflect concentrations in runoff from six storms 

sampled during 1998–99.

Estimating Loads With Statistical Model

The statistical model was developed by the USGS 

from a 1992–93 study (Baldys and others, 1998) using 

multiple regression analysis and local storm-runoff 

quality data representing three major (in terms of area) 

urban land-use categories (residential, commercial, and 

industrial) and one minor category (nonurban). The 

local regression equations developed were used to estimate pollutant loads produced by individual storms for 

each of the 12 selected properties and constituents. The 

storm-runoff quality data used to develop the regression 

LOADi EMCi RVi = × × CF

LOADi

EMCi

RVi

CF

RVL Cp Ci Cp ( ) – IMPL [ ] + × I AL = × × ×CF

RVL

Cp

Ci

IMPL

I

AL

CF

LOADL EMCL RVL = × × CF

LOADL

EMCL

RVL CF
METHODS OF COMPUTING AND ESTIMATING POLLUTANT LOADS 7

model were collected at 26 small (less than 160 acres) 

gaged basins throughout the DFW metropolitan area. 

These gaged basins have a median size of 51.4 acres.

Seven explanatory variables were used in the 

multiple regression analysis. The regression equation 

for the load produced by an individual storm was developed using a logarithmic transformation (log base-10) 

of the response and explanatory variables and then 

detransformed to become

, (4)

where 

= ;

b0–b7 = regression coefficients;

TRN = total storm rainfall (in inches);

DA = total contributing drainage area (in square 

miles);

IA = impervious area, as a percentage of DA;

LUI = industrial land use, as a percentage of DA;

LUC = commercial land use, as a percentage of DA;

LUR = residential land use, as a percentage of DA;

LUN = nonurban land use, as a percentage of DA; 

and

BCF = bias correction factor.

Unity (+1) is added to the impervious-area and landuse percentages to avoid the (undefined) logarithm of 

zero. The BCF is included to obtain an unbiased estimate of the mean response (load), which is systematically underestimated during detransformation of the 

regression equation (Miller, 1984) and is defined by

, (5)

where 

SE = standard error of estimate (in log units) of 

the regression equation.

The regression equation coefficients developed 

by Baldys and others (1998) for estimating loads of the 

12 selected properties and constituents for residential, 

commercial, industrial, and nonurban land uses are 

listed in table 3. For a more detailed explanation of the 

multiple regression analysis method, see Baldys and 

others (1998) and Driver and Tasker (1990).

LOAD b′

0 ( ) TRN

b1 ( ) DAb2 ( ) IA 1 +b3 = × × ×

( ) LUI 1 +

b4 ( ) LUC 1 +b5 × ×

( ) LUR 1 +

b6 ( ) LUN 1 +b7

× × × BCF

b′

0 10

b0

BCF 10 1.151 SE2 ( ) ( ) =

Table 2. Median event-mean concentrations by land-use category 

[EMC, event-mean concentration; mg/L, milligrams per liter; μg/L, micrograms per liter; --, no measured data above 

analytical detection limit] 

1

 Baldys and others, 1998, table 14.

Property or 

constituent

Residential

(11 sites)1

Commercial

(6 sites)1

Industrial

(9 sites)1 Highway(4 sites)

Nonurban

(1 site)

No. of

samples

Median

EMC

No. of

samples

Median

EMC

No. of

samples

Median

EMC

No. of

samples

Median

EMC

No. of

samples

Median

EMC

Biochemical oxygen demand, mg/L 72 7.3 38 6.6 61 7.5 28 6.5 6 3.7

Chemical oxygen demand, mg/L 76 70 42 56 59 67 28 59 3 26

Suspended solids, mg/L 69 78 35 52 60 104 27 90 6 236

Dissolved solids, mg/L 70 58 37 50 60 69 27 184 6 146

Total nitrogen, mg/L 77 1.7 42 1.2 63 1.4 28 2.0 6 2.5

Total ammonia plus organic 

nitrogen, mg/L

77 1.1 42 .80 63 .80 28 1.2 6 1.3

Total phosphorus, mg/L 77 .33 42 .14 63 .21 28 .21 6 .52

Dissolved phosphorus, mg/L 77 .21 42 .06 63 .09 28 .11 4 .28

Total recoverable copper, μg/L 74 8.0 38 8.0 61 12 28 11 6 7.0

Total recoverable lead, μg/L 74 13 40 30 61 29 28 11 6 6.0

Total recoverable zinc, μg/L 75 60 40 80 59 130 28 60 6 20

Total diazinon, μg/L 76 .55 40 .10 62 .05 28 -- 5 .0050
8 Computed and Estimated Pollutant Loads, West Fork Trinity River, Fort Worth, Texas, 1997 

Table 3. Regression equation coefficients for estimating pollutant loads for residential, commercial, industrial, and 

nonurban land uses1

[LOAD, storm-runoff load of property or constituent, in pounds; , intercept in regression model; b1, coefficient for variable 

TRN (total storm rainfall); b2, coefficient for variable DA (drainage area); b3, coefficient for variable IA (impervious area); 

b4, coefficient for variable LUI (industrial land use); b5, coefficient for variable LUC (commercial land use); b6, coefficient 

for variable LUR (residential land use); b7, coefficient for variable LUN (nonurban land use); BCF, bias correction factor; 

--, variable not included; SE, standard error of regression equation; R2 adj., adjusted coefficient of determination, in percent. 

Equation form is: 

.] 

1

 Baldys and others, 1998, table 17.

Property or constituent

Biochemical oxygen demand 9.01 0.879 0.725 0.656 0.104 0.085

Chemical oxygen demand 10.2 .711 .593 .961 .176 .123

Suspended solids 5.85 .889 .544 .913 .463 .170

Dissolved solids 104 .764 .745 .568 .131 .124

Total nitrogen 1.14 .838 .597 .725 .072 .056

Total ammonia plus organic nitrogen .666 .878 .544 .716 .045 .037

Total phosphorus .955 .932 .475 -- .286 .176

Dissolved phosphorus .546 1.05 .477 -- .281 .121

Total recoverable copper .0023 .894 .623 .996 .138 .057

Total recoverable lead .00000086 1.21 .500 2.55 .371 .210

Total recoverable zinc .00020 .905 .520 1.85 .363 .198

Total diazinon .0013 1.47 .305 -- -- --

Property or constituent BCF SE R2 adj.

Biochemical oxygen demand -- -- 1.11 48.7 64.0

Chemical oxygen demand 0.130 -- 1.16 58.5 53.6

Suspended solids .328 -- 1.52 115 42.0

Dissolved solids -- -- 1.13 52.3 59.2

Total nitrogen .052 -- 1.15 57.1 49.9

Total ammonia plus organic nitrogen .077 -- 1.18 63.0 45.0

Total phosphorus .272 -- 1.20 66.2 51.5

Dissolved phosphorus .333 -- 1.25 75.7 52.7

Total recoverable copper .012 -- 1.24 72.8 49.2

Total recoverable lead .274 0.265 1.41 99.5 58.8

Total recoverable zinc .201 .266 1.20 65.8 65.3

Total diazinon .374 -- 2.32 210 40.6

b′

0

LOAD b′

0 ( ) TRN

b1 ( ) DAb2 ( ) IA 1 +b3 ( ) LUI 1 +b4

× ( ) LUC 1 +

b5 × ( ) LUR 1 +b6 × ( ) LUN 1 +b7 = × × × × × BCF

b′

0 b1 b2 b3 b4 b5

b6 b7
COMPUTED AND ESTIMATED POLLUTANT LOADS 9

The highway land-use category was not 

addressed by Baldys and others (1998) during development of the regression model. For this study, loads from 

areas categorized as highway land use were computed 

from flow-weighted EMCs (table 2) and runoff volumes 

from seven sampled storms in each of four gaged basins. 

These data were used to develop a regression equation 

for highway land use, which was needed to complete the 

statistical model for estimation of pollutant loads for the 

entire study area. 

Stepwise regression with the explanatory variables TRN and DA was used to develop equations for 

highway land use for each property and constituent. 

An explanatory variable was retained if it was significant at the 5-percent level (p = 0.05); two constituents 

for which exceptions were made were dissolved solids 

and total recoverable zinc, with p-values of 0.19 and 

0.065, respectively, for DA. The SE and the adjusted 

coefficient of determination (R2

 adj.) also were used to 

evaluate the use of a specific explanatory variable by 

indicating how well the regression equations fit the 

measured data; maximizing R2 adj. and minimizing SE 

resulted in a better fit. The form of the regression equation relating the response and explanatory variables is

. (6)

The regression equation coefficients for estimating loads of the 12 selected properties and constituents 

for highway land use are listed in table 4. SE ranges 

from 40 to 113 percent, and R2 adj. ranges from 27 

to 74 percent. Estimated loads for each property and 

constituent from the statistical model were thus 

obtained by adding the loads obtained from equations 4 

and 6.

COMPUTED AND ESTIMATED 

POLLUTANT LOADS

Pollutant loads for each property and constituent 

(table 5) were computed for each of the two storms on 

the basis of measured EMCs and computed runoff volumes. Accumulated point rainfall and runoff at the 

Beach Street station for the two storms are shown by 

the hydrographs in figure 3. The October 23–24 storm 

LOAD b′

0 ( ) TRN

b1 ( ) DAb2 = × × × BCF

Table 4. Regression equation coefficients for estimating pollutant loads for highway land use

[LOAD, storm-runoff load of property or constituent, in pounds; , intercept in regression model; b1, coefficient for variable 

TRN (total storm rainfall); b2, coefficient for variable DA (drainage area); BCF, bias correction factor; SE, standard error of 

regression equation; R2

 adj., adjusted coefficient of determination, in percent; --, variable not included. Equation form is:

]. 

1 No measured data higher than analytical detection limit.

Property or constituent BCF SE R2 adj.

No. of

storms

Biochemical oxygen demand 22.7 0.861 0.205 1.08 40 60 28

Chemical oxygen demand 286 .781 .381 1.31 85 34 28

Suspended solids 871 1.157 .507 1.28 80 31 27

Dissolved solids 2,004 .254 .760 1.11 48 74 27

Total nitrogen 8.24 .896 .245 1.09 42 61 28

Total ammonia plus organic nitrogen 6.54 .891 .323 1.14 54 54 28

Total phosphorus .642 1.395 -- 1.22 70 52 28

Dissolved phosphorus .376 1.383 -- 1.26 76 45 21

Total recoverable copper .0175 .771 -- 1.18 63 27 28

Total recoverable lead .167 1.197 .508 1.51 113 42 28

Total recoverable zinc .368 .613 .423 1.35 91 29 28

Total diazinon1 -- -- -- -- -- -- --

b′

0

LOAD b′

0 ( ) TRN

b1 ( ) DAb2 = × × × BCF

b′

0 b1 b2
1

0ComputedandEstimatedPollutantLoads,WestForkTrinityRiver,FortWorth,Texas,1997

Table 5. Computed and estimated pollutant loads for 12 selected properties and constituents 

1 

.

Property or constituent Storm date Computed load (pounds)

Deterministic model Statistic

Point rainfall Areal-averaged rainfall Point rainfall 

Estimated

load

(pounds)

Difference1

between 

estimated 

and computed loads 

(percent)

Estimated

load

(pounds)

Difference1

between 

estimated 

and computed loads 

(percent)

Estimated

load

(pounds)

Difference1

between 

estimated 

and computed loads 

(percent)

Biochemical oxygen demand 10/23–24/1997 61,700 110,000 78 77,200 25 79,100 28 

12/07–08/1997 28,300 87,200 208 58,700 107 65,200 130 

Chemical oxygen demand 10/23–24/1997 266,000 970,000 264 690,000 159 731,000 175 

12/07–08/1997 119,000 770,000 548 520,000 338 625,000 426 

Suspended solids 10/23–24/1997 1,900,000 2,100,000 11 1,500,000 -21 2,050,000 8 

12/07–08/1997 1,340,000 1,700,000 27 1,100,000 -18 1,690,000 26 

Dissolved solids 10/23–24/1997 1,010,000 1,600,000 58 1,100,000 9 713,000 -30 

12/07–08/1997 1,000,000 1,300,000 30 870,000 -13 602,000 -40 

Total nitrogen 10/23–24/1997 8,140 627 -92 444 -95 7,210 -11 

12/07–08/1997 3,550 502 -86 338 -90 5,870 65 

Total ammonia plus organic 10/23–24/1997 5,810 19,000 227 13,500 132 12,800 121 

nitrogen 12/07–08/1997 6,220 15,200 144 10,200 64 10,600 70 

Total phosphorus 10/23–24/1997 1,820 5,810 219 4,120 127 7,210 296 

12/07–08/1997 1,440 4,650 224 3,130 118 5,870 308 

Dissolved phosphorus 10/23–24/1997 318 3,290 934 2,330 633 4,770 1,400 

12/07–08/1997 272 2,640 871 1,770 553 3,780 1,300 

Total recoverable copper 10/23–24/1997 97 112 15 79 -19 104 6 

12/07–08/1997 57 90 59 60 6 85 50 

Total recoverable lead 10/23–24/1997 292 271 -7 192 -34 285 -3 

12/07–08/1997 113 217 92 146 29 218 93 

Total recoverable zinc 10/23–24/1997 390 1,030 164 730 87 2,850 630 

12/07–08/1997 283 825 192 555 96 2,330 723 

Total diazinon 10/23–24/1997 .65 .05 -92 .04 -94 19.9 3,000 

12/07–08/1997 .37 .04 -89 .03 -92 14.4 3,810 

Difference estimated computed – computed = ----------------------------------------------------------- × 100
COMPUTED AND ESTIMATED POLLUTANT LOADS 11

produced a single-peak hydrograph in which the entire 

increase and recession of runoff was sampled (fig. 3). 

The December 7–8 storm produced two runoff peaks 

separated by more than 12 hours, with the first peak 

receding by about 75 percent before the second peak 

(fig. 3). Only the runoff volume represented by the first 

peak was sampled; a simulated 95-percent recession 

was used to compute the sampled runoff volume. The 

second peak likely resulted from rainfall in an ungaged 

part of the basin.

Each of the models uses rainfall as a primary 

variable to estimate pollutant load. In addition to using 

measured point rainfall at the Beach Street station to 

estimate pollutant loads, areal-averaged rainfall for the 

basin was computed to obtain a more representative 

estimate of rainfall over the entire basin. Areal-averaged 

rainfall was computed using NEXRAD data that consist 

of estimated hourly rainfall in 2.5-by-2.5-mi cells 

throughout the basin. The NEXRAD data were calibrated using control points where point rainfall was 

measured accurately. Estimated hourly rainfall for all 

2.5-by-2.5-mi cells in the basin was averaged to provide 

a basin-wide hourly rainfall; the hourly averages then 

were summed for the duration of the storm to estimate 

total rainfall (Scott Rae, North Central Texas Council of 

Governments, oral commun., 1999). Areal-averaged 

rainfall was 29 percent smaller for the October 23–24 

storm and 33 percent smaller for the December 7–8 

storm than each corresponding point rainfall: 

Pollutant loads were estimated with the deterministic model and the statistical model using both point 

and areal-averaged rainfall for both storms (table 5). 

The ability of each model to estimate loads was evaluated by graphically comparing percent differences 

between estimated loads and computed loads (estimated 

load minus computed load divided by computed load, 

times 100) for the October 23–24 and December 7–8 

storms (figs. 4–5). Loads estimated by the models for 

the two storms (using either point or areal-averaged 

rainfall) generally did not compare closely to computed 

loads for the 12 water-quality properties and constituents (figs. 4–5). Both models overestimated loads more 

frequently than they underestimated loads. The models 

tended to yield similar estimates for the same property 

or constituent—the differences for properties and 

constituents from the deterministic model (fig. 4) are 

similar to those for corresponding properties and constituents from the statistical model (fig. 5), except for 

nitrogen, zinc, and diazinon. 

For the deterministic model using point rainfall, 

estimated loads were closest to computed loads for suspended solids (mean difference for the two storms 19 

percent) (fig. 4). For the deterministic model using 

areal-averaged rainfall, estimated loads were closest to 

computed loads for dissolved solids (mean [absolute] 

difference for the two storms 11 percent)—and nearly 

as close for total recoverable copper (mean [absolute] 

difference for the two storms 13 percent). The deterministic model using both types of rainfall was least accurate in estimating dissolved phosphorus loads. 

For the statistical model using point rainfall, 

estimated loads were closest to computed loads for 

suspended solids (mean difference for the two storms 17 

percent) (fig. 5); using areal-averaged rainfall, estimated loads were closest to computed loads for total 

recoverable copper (mean [absolute] difference for the 

two storms 14 percent) and nearly as close for suspended solids (mean [absolute] difference for the two 

storms 18 percent) (fig. 5). The statistical model was 

least accurate in estimating total diazinon loads and 

also, like the deterministic model, relatively inaccurate 

in estimating dissolved phosphorus loads.

With one exception, areal-averaged rainfall data 

yielded better estimates of loads than point rainfall data 

for both models. The exception is dissolved solids loads 

from the statistical model—point rainfall data yielded 

estimated loads closer to computed loads for both 

storms.

Neither the deterministic model nor the statistical 

model (both using areal-averaged rainfall) was consistently better at estimating loads (fig. 6). The deterministic model yielded loads closer to computed loads than 

the statistical model for 7 of the 12 properties and 

constituents, and the statistical model yielded loads 

closer to computed loads than the deterministic model 

for 5 properties and constituents. The median difference 

between estimated and computed loads for the deterministic model (92 percent) was about twice that for 

the statistical model (45 percent) (both using arealaveraged rainfall); but the largest differences (mean differences for both storms of 840 and 1,830 percent for 

dissolved phosphorus and total diazinon, respectively) 

were associated with the statistical model.

Storm

date

Duration

(hours)

Point

rainfall

(inches)

Areal-averaged

rainfall

(inches)

October 23–24 26 1.41 1.0

December 7–8 36 1.13 .76
12 Computed and Estimated Pollutant Loads, West Fork Trinity River, Fort Worth, Texas, 1997 

Several factors could account for the inability 

of the models to estimate loads closer to computed 

loads. The ability of the deterministic model to accurately estimate loads depends to a large extent on 

calibrated runoff coefficients and on EMCs. The lack 

of available storm data precluded optimum calibration 

of the runoff coefficients. Any inaccuracies in runoff 

coefficients and EMCs cause proportional inaccuracies 

in estimated loads. The deterministic model originally 

was developed to estimate annual or seasonal pollutant 

DIFFERENCE, IN PERCENT

-100

 0

100

200

300

400

500

600

700

800

900

1,000

-200

BIOCHEMICAL OXYGEN

 DEMAND

CHEMICAL OXYGEN

 DEMAND

SUSPENDED SOLIDS

DISSOLVED SOLIDS

TOTAL NITROGEN

TOTAL AMMONIA PLUS

 ORGANIC NITROGEN

TOTAL PHOSPHORUS

DISSOLVED PHOSPHORUS

TOTAL RECOVERABLE

 COPPER

TOTAL DIAZINON

TOTAL RECOVERABLE

 ZINC

TOTAL RECOVERABLE

 LEAD

PROPERTY OR CONSTITUENT

Percent difference using point rainfall

Percent difference using areal-averaged rainfall

Note: Line joins like data points for October and 

December 1997 storms.

Figure 4. Comparison of use of point rainfall and areal-averaged rainfall, deterministic model—differences 

between estimated and computed pollutant loads for 12 properties and constituents for two storms (October 23–24 

and December 7–8, 1997).
COMPUTED AND ESTIMATED POLLUTANT LOADS 13

~~

~~

~~

~~

~~ ~~

~~

~~

~~ ~~

3,900

-200

-100

 0

100

200

300

400

500

600

700

800

900

1,000

1,100

1,200

1,300

1,400

1,500

1,600

1,700

1,900

2,000

2,900

3,800

3,000

DIFFERENCE, IN PERCENT

BIOCHEMICAL OXYGEN

 DEMAND

CHEMICAL OXYGEN

 DEMAND

SUSPENDED SOLIDS

DISSOLVED SOLIDS

TOTAL NITROGEN

TOTAL AMMONIA PLUS

 ORGANIC NITROGEN

TOTAL PHOSPHORUS

DISSOLVED PHOSPHORUS

TOTAL RECOVERABLE

 COPPER

TOTAL DIAZINON

TOTAL RECOVERABLE

 ZINC

TOTAL RECOVERABLE

 LEAD

PROPERTY OR CONSTITUENT

Percent difference using point rainfall

Percent difference using areal-averaged rainfall

Note: Line joins like data points for October and 

December 1997 storms.

Figure 5. Comparison of use of point rainfall and areal-averaged rainfall, statistical model—differences between 

estimated and computed pollutant loads for 12 properties and constituents for two storms (October 23–24 and 

December 7–8, 1997).
14 Computed and Estimated Pollutant Loads, West Fork Trinity River, Fort Worth, Texas, 1997 

loads, not individual storm loads. The statistical 

model was developed from data for small (less than 

160 acres) urban basins with little influence from 

nonurban land use. The study area (basin) in this 

application is 118,000 acres, of which nearly one-half 

is nonurban (table 1). Aside from these sources of 

inaccuracy, data from two storms are insufficient to 

thoroughly evaluate the ability of the two models to 

adequately estimate loads; but given these sources of 

inaccuracy, the potential for the two models to yield 

estimated loads close to computed loads probably is 

low. 

MEAN ABSOLUTE DIFFERENCE, IN PERCENT

 0

100

200

300

400

500

600

700

800

900

1,800

1,900

2,000

BIOCHEMICAL OXYGEN

 DEMAND

CHEMICAL OXYGEN

 DEMAND

SUSPENDED SOLIDS

DISSOLVED SOLIDS

TOTAL NITROGEN

TOTAL AMMONIA PLUS

 ORGANIC NITROGEN

TOTAL PHOSPHORUS

DISSOLVED PHOSPHORUS

TOTAL RECOVERABLE

 COPPER

TOTAL DIAZINON

TOTAL RECOVERABLE

 ZINC

TOTAL RECOVERABLE

 LEAD

PROPERTY OR CONSTITUENT

Deterministic model

Statistical model

~~ ~~ ~~

Figure 6. Comparison of results of deterministic model and statistical model, both using areal-averaged rainfall—

mean absolute differences between estimated and computed pollutant loads for 12 properties and constituents for 

two storms (October 23–24 and December 7–8, 1997).
SUMMARY 15

SUMMARY 

In 1998 the USGS, in cooperation with the Trinity 

River Authority, did a study to estimate storm-runoff 

pollutant loads using two models—a deterministic 

model and a statistical model; the estimated loads were 

compared to loads computed from measured data for 

a large (118,000 acres) basin in the DFW metropolitan 

area. Loads were computed and estimated for 12 

selected properties and constituents: biochemical oxygen demand, chemical oxygen demand, suspended 

solids, dissolved solids, total nitrogen, total ammonia 

plus organic nitrogen, total phosphorus, dissolved phosphorus, total recoverable copper, total recoverable lead, 

total recoverable zinc, and total diazinon. The deterministic model, developed by Camp Dresser & McKee, 

Inc., estimates pollutant loads using storm-runoff 

estimates on the basis of rainfall, impervious fraction, 

and EMC data for each land-use category. The statistical 

model, developed by the USGS, uses multiple regression analysis of local storm-runoff data to estimate 

pollutant loads. The data from which computed and 

estimated loads were obtained were collected from two 

1997 storms at USGS streamflow-gaging station 

08048543 West Fork Trinity River at Beach Street in 

Fort Worth. 

Each model uses rainfall as a primary variable to 

estimate pollutant load. In addition to using measured 

point rainfall at the Beach Street station to estimate 

pollutant loads, areal-averaged rainfall for the basin was 

computed to obtain a more representative estimate of 

rainfall over the entire basin. Pollutant loads were estimated using the deterministic model and the statistical 

model on the basis of both point and areal-averaged 

rainfall for both storms. The ability of each model to 

estimate loads was evaluated by graphically comparing 

percent differences between estimated loads and computed loads for the two storms. 

Loads estimated by the models for the two 

storms, using both point and areal-averaged rainfall, 

generally did not compare closely to computed loads for 

the 12 water-quality properties and constituents. Both 

models overestimated loads more frequently than they 

underestimated loads. The models tended to yield similar estimates for the same property or constituent. In 

general, areal-averaged rainfall data yielded better estimates of loads than point rainfall data for both models.

Neither the deterministic model nor the statistical 

model (both using areal-averaged rainfall) was consistently better at estimating loads. The deterministic 

model resulted in estimated loads that were closer to 

computed loads than the statistical model for seven 

properties and constituents; and the statistical model 

resulted in estimated loads that were closer to computed 

loads than the deterministic model for five properties 

and constituents. 

The ability of the deterministic model to accurately estimate loads depends to a large extent on calibrated runoff coefficients and on EMCs. The lack of 

available storm data precluded optimum calibration of 

the runoff coefficients. The deterministic model originally was developed to estimate annual or seasonal pollutant loads, not individual storm loads. The statistical 

model was developed from data for small (less than 160 

acres) urban basins with little influence from nonurban 

land use. The study area (basin) in this application is 

118,000 acres, of which nearly one-half is nonurban. 

Aside from these sources of inaccuracy, data from two 

storms are insufficient to thoroughly evaluate the ability 

of the two models to adequately estimate loads; but 

given these sources of inaccuracy, the potential for the 

two models to yield estimated loads close to computed 

loads probably is low. 

REFERENCES CITED 

Baldys, Stanley, III, Raines, T.H., Mansfield, B.L., and 

Sandlin, J.T., 1997, Hydrologic data for urban stormwater studies in the Dallas-Fort Worth area, Texas, 

1992–94: U.S. Geological Survey Open-File Report 

96–482, 256 p.

______1998, Urban stormwater quality, event-mean 

concentrations, and estimates of stormwater pollutant 

loads, Dallas-Fort Worth area, Texas, 1992–93: U.S. 

Geological Survey Water-Resources Investigations 

Report 98–4158, 51 p. 

Driver, N.E., and Tasker, G.D., 1990, Techniques for 

estimation of storm-runoff loads, volumes, and selected 

constituent concentrations in urban watersheds in the 

United States: U.S. Geological Survey Water-Supply 

Paper 2363, 44 p. 

Miller, D.H., 1984, Reducing transformation bias in curve fitting: The American Statistician, v. 38, no. 2, p. 124–126.

Ramos, M.G., ed., 1997, 1998–1999 Texas almanac: The 

Dallas Morning News, Inc., 672 p.

Rouge River National Wet Weather Demonstration Project, 

1998, Technical Memorandum RPO–NPS–TM27.01—

User’s manual—Watershed Management Model 
16 Computed and Estimated Pollutant Loads, West Fork Trinity River, Fort Worth, Texas, 1997 

version 4.0: Accessed July 22, 1999, at URL 

http://www.waynecounty.com/rougeriver/

proddata/wmm.html

U.S. Environmental Protection Agency, 1990, National 

Pollutant Discharge Elimination System permit application regulations for stormwater discharges—Final rule: 

U.S. Federal Register, v. 55, no. 222, p. 47,989–48,091.

______1992, National Pollutant Discharge Elimination 

System storm water sampling guidance document: 

U.S. Environmental Protection Agency, 121 p.

U.S. Geological Survey, 1999, Water resources data for 

Texas, water year 1998, v. 1: U.S. Geological Survey 

Water-Data Report TX–98–1, 530 p.