U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with the

Virginia Department of Environmental Quality

Effects of Storm-Sampling Frequency on Estimation 

of Water-Quality Loads and Trends in Two 

Tributaries to Chesapeake Bay in Virginia

Water-Resources Investigations Report 01-4136
U.S. Department of the Interior

U.S. Geological Survey

Effects of Storm-Sampling Frequency on Estimation 

of Water-Quality Loads and Trends in Two 

Tributaries to Chesapeake Bay in Virginia

By Lori A. Sprague

Water-Resources Investigations Report 01-4136

Prepared in cooperation with the

Virginia Department of Environmental Quality

Richmond, Virginia

2001
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

The use of trade or product names in this report is for identification 

purposes only and does not constitute endorsement by the 

U.S. Geological Survey.

For additional information write to: Copies of this report can be purchased from:

District Chief U.S. Geological Survey

U.S. Geological Survey Branch of Information Services

1730 East Parham Road Box 25286, Federal Center

Richmond, VA 23228 Denver, CO 80225-0286
Abstract ................................................................................................................................................................................ 1

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

Purpose and Scope ..................................................................................................................................................... 4

Description of Study Area .......................................................................................................................................... 4

Acknowledgments ...................................................................................................................................................... 5

Methods of Study ................................................................................................................................................................. 5

Data Collection ........................................................................................................................................................... 5

Load Estimation .......................................................................................................................................................... 6

Experimental Design .................................................................................................................................................. 6

Streamflow Partitioning ................................................................................................................................... 7

Data-Set Construction ...................................................................................................................................... 7

James River Load Estimates ................................................................................................................................................. 7

Ten-Year Loads .......................................................................................................................................................... 8

Total Suspended Solids .................................................................................................................................... 8

Total Phosphorus .............................................................................................................................................. 13

Total Nitrogen ................................................................................................................................................... 13

Dissolved Nitrite-plus-Nitrate .......................................................................................................................... 16

Dissolved Orthophosphorus ............................................................................................................................. 16

Five-Year Loads ......................................................................................................................................................... 16

Total Suspended Solids .................................................................................................................................... 16

Total Phosphorus ..............................................................................................................................................

page 24

Total Nitrogen ...................................................................................................................................................

page 24

Dissolved Nitrite-plus-Nitrate ..........................................................................................................................

page 24

Dissolved Orthophosphorus ............................................................................................................................. 20

Comparison of Ten-Year and Five-Year Loads .......................................................................................................... 20

Rappahannock River Load Estimates ................................................................................................................................... 20

Ten-Year Loads .......................................................................................................................................................... 20

Total Suspended Solids .................................................................................................................................... 21

Total Phosphorus .............................................................................................................................................. 21

Total Nitrogen ................................................................................................................................................... 21

Dissolved Nitrite-plus-Nitrate .......................................................................................................................... 24

Dissolved Orthophosphorus ............................................................................................................................. 24

Five-Year Loads ......................................................................................................................................................... 24

Total Suspended Solids .................................................................................................................................... 26

Total Phosphorus .............................................................................................................................................. 26

Total Nitrogen ................................................................................................................................................... 26

Dissolved Nitrite-plus-Nitrate .......................................................................................................................... 26

Dissolved Orthophosphorus ............................................................................................................................. 26

Comparison of Ten-Year and Five-Year Loads .......................................................................................................... 26

Trend Estimates .................................................................................................................................................................... 28

Summary and Conclusions ................................................................................................................................................... 30

References Cited .................................................................................................................................................................. 36

Appendix .............................................................................................................................................................................. 37

CONTENTS
FIGURES

1. Map showing drainage area and location of two monitoring stations in the Chesapeake Bay Watershed .............. 3

2-14. Graphs showing:

2. Percentage of total daily streamflow as baseflow for the period of record at the monitoring stations ............. 8

3. Water-quality samples and daily mean discharge at James River monitoring station for 

each storm data set, 1990 through 1995 (A) and 1995 through 1999 (B) ........................................................ 9

4. Water-quality samples and daily mean discharge at Rappahannock River monitoring station 

for each storm data set, 1990 through 1995 (A) and 1995 through 1999 (B) ................................................... 11

5. Annual total streamflow at the James River monitoring station, 1990 through 1999 ...................................... 13

6. Annual loads of selected constituents at the James River monitoring station, 1990 

through 1999 ..................................................................................................................................................... 14

7. Standard error of prediction of selected constituent loads at the James River monitoring 

station, 1990 through 1999 ............................................................................................................................... 15

8. Annual loads of selected constituents at the James River monitoring station, 1995 through 1999 .................. 17

9. Standard error of prediction of selected constituent loads at the James River monitoring 

station, 1995 through 1999 ............................................................................................................................... 19

10. Annual total streamflow at the Rappahannock River monitoring station, 1990 through 1999 ........................ 21

11. Annual loads of selected constituents at the Rappahannock River monitoring station, 1990 

through 1999 ..................................................................................................................................................... 22

12. Standard error of prediction of selected constituent loads at the Rappahannock River 

monitoring station, 1990 through 1999 ............................................................................................................ 23

13. Annual loads of selected constituents at the Rappahannock River monitoring station, 

1995 through 1999 ............................................................................................................................................ 25

14. Standard error of prediction of selected constituent loads at the Rappahannock River 

monitoring station, 1995 through 1999 ............................................................................................................ 27

TABLES

1. Land area and land use upstream from the monitoring stations ............................................................................. 4

2. Trends in flow-adjusted concentrations of selected constituents at the James River monitoring 

station for each of the storm data sets, 1990 through 1999 ..................................................................................... 29

3. Trends in flow-adjusted concentrations of selected constituents at the James River monitoring 

station for each of the storm data sets, 1995 through 1999 ..................................................................................... 31

4. Trends in flow-adjusted concentrations of selected constituents at the Rappahannock River 

monitoring station for each of the storm data sets, 1990 through 1999 ................................................................... 32

5. Trends in flow-adjusted concentrations of selected constituents at the Rappahannock River 

monitoring station for each of the storm data sets, 1995 through 1999 ................................................................... 33

APPENDIX

1. Number of storm-flow days in the streamflow record, number of days on which a water-quality 

sample was collected, and number of storm-flow samples at the James and Rappahannock River 

monitoring stations for each data set ....................................................................................................................... 38
CONVERSION FACTORS AND WATER-QUALITY UNITS

Water-Quality Units: Chemical concentration is reported in milligrams per liter (mg/L) or micrograms per liter (μg/L). Milligrams per 

liter is a unit expressing the concentration of chemical constituents in solution as weight (milligrams) of solute per unit volume (liter) of 

water. One thousand micrograms per liter is equivalent to one milligram per liter. For concentrations less than 7,000 mg/L, the

numerical value is the same as for concentrations in parts per million.

Multiply By To obtain

Area

acre 4,047 square meter

acre 0.4047 hectare

mile 1.609 kilometer

square mile (mi2) 259.0 hectare

square mile (mi2) 2.590 square kilometer

Flow

foot per second (ft/s) 0.3048 meter per second

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

Mass

pound (lb) 0.4536 kilogram

pound per acre (lb/acre) 1.121 kilogram per hectare
Abstract 7

ABSTRACT

Annual loads and flow-adjusted 

concentration trends were estimated by use of 

water-quality and streamflow data collected from 

1990 through 1999 at monitoring stations on two 

tributaries to Chesapeake Bay in Virginia—James 

River at Cartersville, Va., and Rappahannock 

River near Fredericksburg, Va. The effects of 

storm-sampling frequency on the accuracy and 

precision of load and trend estimates were 

determined by use of data sets containing 0, 20, 

40, 60, 80, and 100 percent of all storm samples 

collected in these two basins of different size, 

relief, and land use. Data sets included a range of 

dissolved and particulate constituents for the 10-

year period from 1990 to 1999 and the 5-year 

period from 1995 to 1999.

Loads of dissolved constituents were 

estimated with greater accuracy and precision with 

fewer storm samples than loads of particulate 

constituents in both basins and for both time 

periods. All constituent loads were estimated with 

greater precision with fewer storm samples in the 

James River than in the Rappahannock River for 

both periods. The high relief and smaller drainage 

area of the Rappahannock River Basin caused 

quicker and more variable stream response than in 

the James River Basin, which led to less precise 

load estimates of all constituents, regardless of 

how many storm samples were included. For the 

James River, the magnitudes of the load estimates 

in the 5-year period were close to the estimates 

from the same years for the 10-year period for the 

dissolved constituents, but were smaller for the 

particulate constituents. Load estimates were more 

variable for the Rappahannock River than for the 

James River during the shorter period. In both 

basins, all estimates in the 5-year period had 

higher prediction errors than those in the 10-year 

period. Overall, loads of dissolved constituents 

were estimated with greater accuracy and 

precision with fewer storm samples than loads of 

particulate constituents; loads of all constituents 

were estimated with greater accuracy and 

precision over the longer time period; and load 

estimates of all constituents were more precise and 

required fewer storm samples in the larger and less 

flashy James River Basin than in the Rappahannock River Basin.

As with load estimates, estimates of flowadjusted concentration trends were sensitive to the 

length of the monitoring period and the size of the 

basin; however, trend estimates generally were 

less sensitive than load estimates to the number of 

storm samples in the data set. Trends in flowadjusted concentrations were estimated reasonably 

well with fewer storm samples for both dissolved 

and particulate constituents in the James River for 

the 10-year period, with the exception of total 

suspended solids. Data sets containing more storm 

samples were needed to obtain reasonable trend 

estimates for the 5-year period in this river. For the 

10-year period in the Rappahannock River, more 

storm samples were necessary than in the James 

River to obtain reasonable estimates of trends for 

all constituents. No significant trends were 

observed for the 5-year period in this river, so the 

effect of storm-sampling frequency could not be 

determined. Because of the small number of 

significant trends throughout these data sets, it was 

not possible to determine whether fewer storm 

samples were required for estimating trends of 

dissolved constituents than particulate 

constituents. The results indicate that more storm 

Effects of Storm-Sampling Frequency on Estimation of 

Water-Quality Loads and Trends in Two Tributaries to 

Chesapeake Bay in Virginia

By Lori A. Sprague
8 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

samples were necessary for accurate estimation of 

trends during the shorter time period and in the 

smaller and flashier Rappahannock River Basin.

INTRODUCTION

Chesapeake Bay, the largest estuary in the 

United States, drains approximately 65,000 mi2 of Virginia, West Virginia, Maryland, Delaware, Pennsylvania, New York, and the District of Columbia (fig. 1). 

The estuary extends nearly 200 mi from the mouth of 

the Susquehanna River in Maryland to the Atlantic 

Ocean along the southeastern coast of Virginia. From 

1970 to 2000, the population in the Chesapeake Bay 

Watershed grew from a little more than 14 million to an 

estimated 15.5 million; by 2020, an estimated 18 million people will live in the watershed (U.S. Environmental Protection Agency, 1999). Population growth 

has led to substantial agricultural and urban development in the region, which has adversely affected the 

water quality of the Bay.

Excess nutrients and sediments enter the Bay and 

its tributaries from nonpoint sources such as urban and 

agricultural runoff and atmospheric deposition, and 

from point sources such as wastewater treatment plants. 

Elevated sediment concentrations and algal blooms 

caused by excess nutrients can deprive deep waters of 

sunlight needed to support the submerged aquatic vegetation that serves as a food supply and habitat for fish, 

shellfish, and other aquatic organisms. Subsequent 

decay of algae depletes the water of dissolved oxygen, 

further compromising the health of living resources in 

the Bay.

In 1987, the District of Columbia and the States 

of Virginia, Maryland, and Pennsylvania signed the 

Chesapeake Bay Agreement, a commitment to reduce 

controllable nutrient loads entering Chesapeake Bay 

(U.S. Environmental Protection Agency, 1988). In 

order to assess the effectiveness of nutrient and sediment reduction strategies, the U.S. Geological Survey 

(USGS) began the River Input Monitoring (RIM) Program in Virginia in 1988 in cooperation with the Virginia Department of Environmental Quality (VDEQ) 

and in Maryland in 1984 in cooperation with the Maryland Department of Natural Resources (MDNR) and 

the Metropolitan Washington Council of Governments 

(MWCOG). The purpose of the RIM Program is to 

monitor the water quality of the nine major tributaries 

that drain to Chesapeake Bay and to quantify loads and 

long-term trends in nutrient and sediment concentrations entering the Bay from these tributaries.

Water-quality monitoring conducted as part of 

the RIM Program is designed so that samples are 

obtained during a full range of hydrologic conditions, 

as in-stream concentrations are influenced by streamflow. For example, where point sources are the dominant nutrient source to a stream, dilution from an 

increase in streamflow decreases in-stream concentrations. In contrast, where nonpoint sources are the dominant nutrient source, increased streamflow from storm 

runoff generally increases in-stream concentrations. Instream concentrations of particulate constituents derived primarily from surface runoff typically increase 

in response to storm events, whereas concentrations of 

dissolved constituents often decrease. Therefore, it is 

necessary to sample during both high-flow (elevated 

flow during and after storm events) and base-flow 

(background low flow between storm events) conditions to accurately monitor water quality in the tributaries to Chesapeake Bay.

Water-quality samples for the RIM Program in 

Virginia are obtained twice a month during base-flow 

conditions and periodically during high-flow conditions. VDEQ, which monitors additional sites in the 

Chesapeake Bay Watershed, collects water-quality 

samples once a month on pre-scheduled dates. This 

fixed-interval sampling typically results in the collection of samples during base-flow conditions; storm 

events are not targeted for additional sampling. To estimate loads and flow-adjusted concentration trends at 

all of the monitoring sites, the ESTIMATOR program 

is used to fit a log-linear regression model with explanatory variables of discharge, season, and time to the 

observed data (Cohn and others, 1992). Estimated daily 

concentrations from the model are used with daily 

mean discharges to calculate daily load estimates, 

which then are summed to provide monthly and annual 

load estimates.

In a previous study in which the regression 

model was used with data from large river basins in the 

Great Lakes region, fixed-interval sampling led to 

underestimates of the true total phosphorus load during 

a 2- to 3-year period (Preston and others, 1992). The 

addition of 12 high-flow samples per year reduced the 

bias and error of the estimates, particularly in the relatively small and rapidly responding basins. The effects 

of additional storm sampling on load and trend estimation in the Chesapeake Bay Watershed, where addi-
Introduction 9

DELAWARE

BAY

VIRGINIA

WEST VIRGINIA

NEW YORK

PENNSYLVANIA

EXPLANATION

77o

43o 

75o

41o 

79o

39o

ATLANTIC

OCEAN

40o

80o 

45o

75o 

Washington, D.C.

D.C.

JAMES RIVER BASIN

RAPPAHANNOCK RIVER BASIN 

BASIN BOUNDARY

Chesapeake Bay

Watershed

VIRGINIA

WEST

VIRGINIA

PENNSYLVANIA

NEW YORK

DELAWARE MARYLAND

Susquehanna

River

Potomac

Potomac

River

Rappahannock

River

R

River

River

R

R

River

Pamunkey

James

James

Choptank

River

York

R

CHESAPEAKE

Base from U.S. Geological Survey Albers Equal-Area Conic projection

State lines from 1:100,000 TIGER files, 1990

Hydrography from USEPA River Reach Files Version 1 at 1:500,000, 1982

Watershed boundaries from 1:250,000 USGS Hydrologic Units, 1994

0 40 KILOMETERS

0 20 40 MILES

20

MONITORING STATION

MARYLAND

Rappahannock

R

Mattaponi

Patuxent

River

Appomattox

FALL

LINE

Cartersville

Norfolk

Baltimore

Annapolis

Harrisburg

Williamsport

Scranton

Fredericksburg

Richmond

Figure 1. Drainage area and location of two monitoring stations in the Chesapeake Bay Watershed.
10 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

tional constituents are monitored and where the data 

sets typically cover a longer period, have not been 

examined thoroughly.

Purpose and Scope

The purpose of this report is to determine the 

effects of storm-sampling frequency on (1) load and 

trend estimation in two basins of different size, relief, 

and land use in the Chesapeake Bay Watershed by 

comparing estimates from model simulations in which 

input data sets contained 0, 20, 40, 60, 80, and 100 percent of all storm samples; (2) load and trend estimation 

during two monitoring periods of different durations by 

comparing model estimates covering the 10-year 

period from 1990 to 1999 and the 5-year period from 

1995 to 1999; and (3) estimation of a range of dissolved and particulate constituent loads and trends, 

including total nitrogen, dissolved nitrite-plus-nitrate 

(as N), dissolved orthophosphorus (as P), total phosphorus, and total suspended solids. Water-quality and 

streamflow data from 1990 through 1999 from two Virginia RIM stations—James River at Cartersville, Va. 

(02035000) and Rappahannock River near Fredericksburg, Va. (01668000)—were used in these analyses.

Description of Study Area

Together, the James and Rappahannock River 

Basins comprise more than 50 percent of the Chesapeake Bay drainage area in Virginia, and about 20 percent of the total Chesapeake Bay drainage area (fig. 1). 

Both RIM stations are located near the Fall Line, the 

boundary between the Piedmont and the Coastal Plain 

Physiographic Provinces and the point farthest downstream unaffected by tides. Each station is co-located 

with an active USGS stream-gaging station.

The James River Basin, at 10,200 mi2, is the 

third largest tributary basin in the Chesapeake Bay 

Watershed. The James River originates in the Appalachian Mountains near the Virginia-West Virginia border, flows through the Valley and Ridge, the Blue 

Ridge, the Piedmont, and the Coastal Plain Physiographic Provinces, and joins Chesapeake Bay near the 

city of Norfolk in southeastern Virginia. The monitoring station is in Cartersville, Va., about 40 mi upstream 

from the Fall Line. This location was selected because 

a long-term discharge record is available; no major 

streams enter the river between Cartersville and the 

Fall Line. The monitoring station receives drainage 

from about 60 percent of the James River Basin.

Land use upstream from the monitoring station is 

dominated by forest (80 percent) and agriculture 

(16 percent) (table 1). The agricultural areas are concentrated in the western part of the basin in Rockbridge, Botetourt, and Nelson Counties (Battaglin and 

Goolsby, 1994). Of the nine rivers monitored as part of 

the RIM Program, the James River contributes about 12 

percent of the streamflow, 5 percent of the total nitrogen load, and 20 percent of the total phosphorus load to 

Chesapeake Bay, making it the third largest source of 

streamflow and nutrients to the Bay, after the Susquehanna and Potomac Rivers (Belval and Sprague, 1999).

The Rappahannock River Basin, at 2,800 mi2, is 

the fourth largest tributary basin in the Chesapeake Bay 

Watershed. The Rappahannock River originates near 

the eastern edge of the Blue Ridge Physiographic 

Province and extends eastward through the Piedmont 

and Coastal Plain Physiographic Provinces. The 

monitoring station is located at the Fall Line just 

upstream from Fredericksburg, Va., where it receives 

drainage from about 57 percent of the Rappahannock 

River Basin. Upstream from the monitoring station, the 

basin’s relief and steep slopes cause the river to 

respond rapidly to storm events.

USGS 

station 

number

Station name

Upstream 

land-surface 

area (mi2)

Land use (percent)

Urban Agricultural Forested Other

02035000 James River at Cartersville, Va. 6,260 1 16 80 3

01668000 Rappahannock River near Fredericksburg, Va. 1,600 1 36 61 2

Table 1. Land area and land use upstream from the monitoring stations

[USGS, U.S. Geological Survey; mi2, square mile; land-use data from Vogelmann and others, 1998; land use expressed as a percentage of 

total land-surface area upstream from each monitoring station; other land use includes barren/transitional and water] 
Methods of Study 11

Land use upstream from the monitoring station is 

dominated by forest (61 percent) and agriculture 

(36 percent). The Rappahannock River Basin contains 

the highest percentage of agricultural land above the 

Fall Line of the five major tributary basins in Virginia. 

The agricultural areas are generally located in the central part of the basin, in Fauquier, Culpeper, Madison, 

and Orange Counties (Battaglin and Goolsby, 1994). 

Of the nine rivers monitored in the RIM Program, the 

Rappahannock River contributes about 3 percent of the 

streamflow, 2 percent of the total nitrogen load, and 8 

percent of the total phosphorus load delivered annually 

from the nontidal part of the Chesapeake Bay Watershed (Belval and Sprague, 1999).

Because of the smaller area, greater relief, and 

smaller percentage of forested land in the Rappahannock River Basin, the stream response to storm events 

is “flashy” relative to that of the James River Basin—

stream levels rise and recede more quickly during and 

immediately after storm events in the Rappahannock 

River Basin. Corresponding stream discharge values 

can change rapidly during the course of a day, and the 

difference between the instantaneous discharge at the 

time of sampling and the daily mean discharge can be 

large. Because concentration values typically vary in 

response to streamflow, the difference between the 

instantaneous in-stream concentration at the time of 

sampling and the daily mean concentration also can be 

large. These factors may influence load estimation, 

because daily mean streamflow and concentration 

values are represented in the load regression model.

Acknowledgments

The RIM Program is supported in Virginia 

through a cooperative agreement between VDEQ and 

USGS. The water-quality and streamflow data used in 

this report were collected by many USGS and VDEQ 

personnel. Dave Eckhardt and Joel Blomquist of the 

USGS and Rick Hoffman of VDEQ reviewed this 

report and provided many helpful comments. 

METHODS OF STUDY

The methods used to collect water-quality data 

and to estimate loads and trends are discussed below. In 

addition, the experimental design for determining the 

effects of storm-sampling frequency on load and trend 

estimation is described.

Data Collection

Water-quality samples used in this study were 

collected from 1990 through 1999. Base-flow samples 

were collected twice a month—once by USGS personnel and once by VDEQ personnel at the James River 

monitoring station, and twice by USGS personnel at 

the Rappahannock River monitoring station. Samples 

were collected at the two monitoring stations by use of 

the equal-discharge increment (EDI) method, in which 

multiple samples from the centroids of equal-discharge 

increments across the river channel are composited 

(Wilde and others, 1999). The channels of both rivers 

are stable at the sampling locations, and the discharge 

ratings changed little each year. Samples were collected by USGS personnel with a depth-integrated sampler when streamflow velocities exceeded 1.5 ft/s; 

water enters this sampler at the same velocity as the 

stream at each depth and the intake comes as close to 

the stream bottom as possible without disturbing the 

bottom sediment. A weighted bottle was used at lower 

velocities at which depth-integrated samplers are not 

effective. All samples collected by VDEQ personnel at 

the James River monitoring station were obtained with 

a weighted bottle; if the stream velocity at the time of 

sampling exceeded 1.5 ft/s, the data were not used in 

this study.

In addition to the bimonthly base-flow samples, 

30 to 40 high-flow samples per year were collected by 

USGS personnel at each site at the beginning of the 

study period. High-flow samples were defined as those 

collected above a gage height reached in each river 

about 40 times per year. During periods of extreme low 

flow, the sampling criteria were modified slightly to 

obtain the target number of high-flow samples. After 3 

years, the number of storm samples was reduced to 

approximately 20 per year. Emphasis was placed on 

sampling throughout a range of rising, peak, and falling 

gage heights to avoid bias in concentrations. As a result 

of this sampling design, about half of the samples collected represented high-flow conditions.

Water samples collected for determination of 

nutrient and total suspended solids concentrations were 

analyzed at the Virginia Division of Consolidated Laboratory Services (VDCLS) in Richmond, Va. Qualityassurance samples were analyzed at VDCLS and the 

USGS National Water-Quality Laboratory in Denver, 

Colo. Quality-assurance procedures for the Virginia 

RIM Program are described in detail in Belval and 

others (1995) and Bell and others (1996).
12 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

Load Estimation

Annual constituent loads at each station were 

estimated with the observed concentration and streamflow data as input to the ESTIMATOR model, a sevenparameter log-linear regression model that uses time, 

flow, and season terms to predict daily concentrations 

(Cohn and others, 1992). The model incorporates a 

minimum variance unbiased estimator to correct for 

log-transformation bias and an adjusted maximum likelihood estimator to assign concentration values to data 

below the detection limit (Cohn, 1988). The regression 

equation used is as follows: 

where

ln[] = the natural logarithm function,

C = the constituent concentration (in mg/L),

Q = the mean daily discharge (in ft3/s),

T = time (in years),

sin = the sine function,

cos = the cosine function,

π = 3.14169,

β = model coefficients,

ε = model error, and

 ~

Q and ~T = centering variables.

β0 through β6 are the coefficients of the regression model that were computed from the observed concentration data. The model error (ε) is assumed to be 

independent and normally distributed with a mean of 

zero and constant variance. Centering variables simplify the numerical work and have no effect on the load 

estimates, so that the regression coefficients are statistically independent. This equation results in a predicted 

daily concentration. The predicted daily concentration 

values were multiplied by measured daily mean discharge values to estimate daily load values, which were 

summed to obtain annual load estimates.

Annual load estimates were compared on the 

basis of variance and bias. The standard error of prediction (SEP) is a measure of the variance, or precision, of 

the load estimate. All SEP values in this report were 

normalized to the total load estimate to facilitate comparisons among constituents, time periods, and basins, 

and are presented as percent SEP. The bias, or difference between the estimated load and the “true” load, is 

a measure of the accuracy of the load estimate. Because 

the true load cannot be determined without a continuous record of discharge and concentration, it was 

assumed that load estimates were converging toward 

the true load value as more storm samples were 

included. For the purposes of this study, convergence 

occurred when the median of the percent difference 

between the annual loads estimated with one storm 

data set and the annual loads estimated with the next 

highest storm data set was less than 5 percent. This 

generalized estimate of convergence is constrained by 

the fact that only six scenarios were tested.

The overall trend in flow-adjusted concentration 

was calculated by use of the beta coefficient of the 

linear time parameter (β3) from the regression model. 

The trends are inherently flow-adjusted because the 

model separates variability in concentration due to 

variability in flow from that due to variability in time. 

The average percent change in flow-adjusted concentration over the time period was calculated as:

% ∆ C = 100{eβ3∆t - 1} 

where

% ∆ C = percent change in flow-adjusted concenration,

e = anti-log of the natural log,

β3 = coefficient of the linear time parameter,

 and

∆t = the period of time over which the 

regression model is calibrated.

The confidence interval of the trend was calculated by use of the standard deviation of β3.

Experimental Design

In order to determine the effect of the number of 

storm samples in a data set on load and trend estimation, subsets of storm samples were chosen randomly 

and removed from the full data sets of the James River 

and Rappahannock River RIM stations. Loads and 

trends were then estimated for each new, smaller data 

set.

ln C β0 β1ln Q Q ̃ ⁄ β2 ln Q Q ̃   ⁄   2

T T ̃ – β4 β5 2πT β6 sin + cos 2πT + ε

+ +

+ ++

=

(1)

(2)
James River Load Estimates 13

Streamflow Partitioning

The sampling design of the RIM Program is to 

obtain samples during a full range of flow conditions. 

The decision to sample a high-flow event is based in 

large part on regional precipitation amounts and gageheight fluctuations. To obtain a more rigorous designation of storm samples for this study, water-quality samples were classified as either “storm” or “base” on the 

basis of streamflow partitioning. The program PART 

was used to estimate daily base flow for the period of 

record from daily streamflow values (Rutledge, 1998). 

The method sets base flow equal to streamflow on days 

when surface runoff can be considered negligible 

(based on a requirement of antecedent recession) and 

linearly interpolates base-flow values on other days.

“Storm” samples were designated as those collected on days when base flow made up less than 60 

percent of the total streamflow. Other studies that have 

described a similar storm-flow designation technique 

covered a wide range of threshold values. For example, 

in a study of base-flow and storm-flow yields in Kentucky, samples were not classified as base flow on days 

when base flow made up less than 90 percent of the 

total streamflow (Evaldi and Moore, 1994). In another 

study examining episodic acidification of streams in 

Virginia, samples were classified as storm flow on days 

when base flow made up less than 25 percent of the 

total streamflow (Eshleman and others, 1995). The 60-

percent threshold chosen for this study is intermediate 

between these two values and covers the interquartile 

range of streamflow at the James and Rappahannock 

River monitoring stations (fig. 2).

 Both the streamflow partitioning and the stormsample designation procedures used in this study are 

arbitrary and have limitations. They do provide, however, a more consistent and quantitative classification 

of streamflow conditions at the time of sampling.

Data-Set Construction

After base- and storm-flow samples had been 

designated, data sets with 0, 20, 40, 60, 80, and 100 

percent storm samples (“storm data sets”) were created 

for each station, for the 10-year period from 1990 

through 1999 and for the 5-year period from 1995 

through 1999. All base-flow samples were retained in 

each data set, and storm samples were selected randomly with replacement for removal from each data 

set. The 100-percent data sets were the full data sets, 

including all base and storm samples. The 0-percent 

data sets included only base-flow samples; all storm 

samples were removed. The 80-percent data sets were 

created by removing 20 percent of the storm samples 

from each full data set; individual storm samples were 

selected randomly for removal. The 60-, 40-, and 20-

percent data sets were created in a similar fashion. 

Appendix 1 lists the total number of storm-flow days in 

the daily streamflow record for each station during the 

5- and 10-year periods and the number of storm-flow 

days in each data set on which a water-quality sample 

was collected. Figures 3 and 4 show all of the streamflow and water-quality sampling records for the James 

and Rappahannock Rivers, respectively.

The 0-, 20-, 40-, 60-, 80-, or 100-percent data-set 

designation refers to the percentage of the total number 

of storm samples in the full RIM data set that was left 

in the new data set—it does not represent the percentage of storms in the new data set. For example, the full 

Rappahannock River RIM data set (the designated 100-

percent data set in this report) had 385 total samples 

from 1990 through 1999; 163 of those samples, or 42 

percent, were storm samples. The 80-percent data set 

included 80 percent, or 130, of the 163 storm samples 

and all of the base-flow samples, resulting in a new 

data set with 37 percent storm samples (Appendix 1, 

figs. 3 and 4).

The number of storm events that corresponds to 

the 0-, 20-, 40-, 60-, 80-, or 100-percent designation 

differs depending on the station and time period. For 

example, for the period from 1990 through 1999, the 

60-percent data set for the James River station contained 43 percent storm samples, whereas the 60-

percent data set for the Rappahannock River station 

contained 31 percent storm samples.

JAMES RIVER LOAD ESTIMATES

A wide range of hydrologic conditions occurred 

in the James River during the period from 1990 through 

1999, making it an ideal period for examining the 

effects of storm-sampling frequency on load and trend 

estimation. The annual total streamflow from 1990 

through 1999 at the James River monitoring station, 

along with the long-term mean-annual streamflow for 

the period of record (1899-1999), is shown in figure 5. 

Streamflow in 1990, 1993, 1994, 1996, and 1998 was 

above the long-term mean; in 1996, Hurricane Fran 

contributed to the highest annual total flow in the mon-
14 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

JAMES

RIVER STATION

RAPPAHANNOCK

RIVER STATION

0

20

40

60

80

100

PERCENTAGE OF TOTAL DAILY 

STREAMFLOW AS BASE FLOW

75th percentile

25th percentile

Data value less than or equal to

1.5 times the interquartile range

outside the quartile

Outlier data value greater than 1.5

times the interquartile range

outside the quartile

Median

EXPLANATION

itoring period. Streamflow in 1997 and 1999 was below 

the long-term mean; 1999 was a drought year and had 

the lowest annual total flow in the monitoring period.

Ten-Year Loads

Annual loads for the 10-year period from 1990 

through 1999 were estimated for a range of dissolved 

and particulate constituents—total suspended solids, 

total phosphorus, total nitrogen, dissolved nitrite-plusnitrate, and dissolved orthophosphorus—with all storm 

data sets for the James River monitoring station (fig. 6). 

(The “dissolved” and “particulate” classification used 

throughout this report refers to the primary phase in 

which these constituents are found during both baseand storm-flow conditions.)

Total Suspended Solids

Load estimates for total suspended solids varied 

among the storm data sets; they varied most during 

1993, 1996, and 1998 and least during 1997 and 1999 

(fig. 6). During all years, the data set without storm 

samples (the 0-percent data set) led to underestimates 

of total suspended solids loads relative to the data sets 

with storm samples. The 20-percent data set overestimated the loads relative to the higher percentage data 

sets during high-flow years, but during low-flow years 

the estimates were closer to those of the higher percentage data sets. The SEPs were highest with the lower 

percentage data sets, particularly the 0-percent data set 

(fig. 7). The relatively poor predictions in the lower 

percentage data sets were likely a result of the lack of a 

sufficient number of high concentration values in the 

input data set to constrain the model estimates at high 

Figure 2. Percentage of total daily streamflow as base flow for the period of record 

at the monitoring stations.
James River Load Estimates 15

160,000

120,000

0

40,000

80,000

160,000

120,000

0

40,000

80,000

160,000

120,000

0

40,000

80,000

1990

1991

1992

1993

1994

1995

1996

1997

19981999

1990

1991

1992

1993

1994

1995

1996

1997

19981999

DISCHARGE, IN CUBIC FEET PER SECOND

DAILY MEAN DISCHARGE

INSTANTANEOUS DISCHARGE AT 

TIME OF WATER-QUALITY SAMPLE

PERCENTAGE OF STORM SAMPLES

IN THE DATA SET

EXPLANATION

(A)

100-percent data set

(54)

60-percent data set

(43)

80-percent data set

(50)

40-percent data set

(33)

20-percent data set

(20)

0-percent data set

(0)

(43)

Figure 3. Water-quality samples and daily mean discharge at James River monitoring station for each storm data 

set, 1990 through 1995 (A) and 1995 through 1999 (B).
16 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

160,000

120,000

0

40,000

80,000

160,000

120,000

0

40,000

80,000

160,000

120,000

0

40,000

80,000

DISCHARGE, IN CUBIC FEET PER SECOND

1995 1996 1997 1998 1999 1995 1996 1997 1998 1999

100-percent data set

(53)

60-percent data set

(42)

80-percent data set

(50)

40-percent data set

(33)

20-percent data set

(19)

0-percent data set

(0)

(B)

DAILY MEAN DISCHARGE

INSTANTANEOUS DISCHARGE AT 

TIME OF WATER-QUALITY SAMPLE

PERCENTAGE OF STORM SAMPLES

IN THE DATA SET

EXPLANATION

(19)

Figure 3. Water-quality samples and daily mean discharge at James River monitoring station for each storm data 

set, 1990 through 1995 (A) and 1995 through 1999 (B)—Continued.
James River Load Estimates 17

60,000

45,000

0

15,000

30,000

60,000

45,000

0

15,000

30,000

60,000

45,000

0

15,000

30,000

DISCHARGE, IN CUBIC FEET PER SECOND

(A)

1990

1991

1992

1993

1994

1995

1996

1997

19981999

1990

1991

1992

1993

1994

1995

1996

1997

19981999

100-percent data set

(42)

60-percent data set

(31)

80-percent data set

(37)

40-percent data set

(23)

20-percent data set

(13)

0-percent data set

(0)

DAILY MEAN DISCHARGE

INSTANTANEOUS DISCHARGE AT 

TIME OF WATER-QUALITY SAMPLE

PERCENTAGE OF STORM SAMPLES

IN THE DATA SET

EXPLANATION

(13)

Figure 4. Water-quality samples and daily mean discharge at Rappahannock River monitoring station for each 

storm data set, 1990 through 1995 (A) and 1995 through 1999 (B).
18 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

60,000

45,000

0

15,000

30,000

60,000

45,000

0

15,000

30,000

60,000

45,000

0

15,000

30,000

DISCHARGE, IN CUBIC FEET PER SECOND

1995 1996 1997 1998 1999 1995 1996 1997 1998 1999

100-percent data set

(43)

60-percent data set

(31)

80-percent data set

(37)

40-percent data set

(23)

20-percent data set

(13)

0-percent data set

(0)

(B)

DAILY MEAN DISCHARGE

INSTANTANEOUS DISCHARGE AT 

TIME OF WATER-QUALITY SAMPLE

PERCENTAGE OF STORM SAMPLES

IN THE DATA SET

EXPLANATION

(13)

Figure 4. Water-quality samples and daily mean discharge at Rappahannock River monitoring station for each 

storm data set, 1990 through 1995 (A) and 1995 through 1999 (B)—Continued.
James River Load Estimates 19

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

4,500,000

2,000,000

2,500,000

3,000,000

3,500,000

4,000,000

0

500,000

1,000,000

1,500,000

DISCHARGE, IN CUBIC 

FEET PER SECOND

ANNUAL TOTAL STREAMFLOW

LONG-TERM (1899-1999) MEAN ANNUAL

TOTAL STREAMFLOW

EXPLANATION

flows. Additional variability in load estimates among 

all data sets resulted from the high variability in the 

laboratory measurement of total suspended solids 

(Gray and others, 2000). As more storm samples were 

included beyond the 20-percent data set, load estimates 

varied less. Load estimates converged with the 80-percent data set, and no substantial reduction in SEPs 

occurred as more storm samples were added. As a 

result, data sets with at least 50 percent storm samples 

(the 80- and 100-percent data sets, fig. 3a) led to the 

most accurate and precise estimates of total suspended 

solids loads. 

Total Phosphorus

As with estimates of total suspended solids 

loads, total phosphorus load estimates varied most 

during 1996 and least during 1997 and 1999 (fig. 6). 

The data set without storm samples led to underestimates of loads relative to the data sets with storm samples during all years. During high-flow years, the 20-

percent data set led to overestimates of total phosphorus loads relative to the higher percentage data sets; 

during the low-flow years, these load estimates were 

closer to those of the higher percentage data sets. As 

more storms were included beyond the 0- and 20-percent data set, load estimates varied less. The SEPs generally were highest with the 0- and 20-percent data sets 

(fig. 7), probably as a result of the lack of high-flow, 

high-concentration values in the input data set. Because 

load estimates converged with the 40-percent data set, 

and no substantial decrease in SEPs consistently 

occurred as more storm samples were included, data 

sets with at least 33 percent storm samples led to the 

most accurate and precise estimates of total phosphorus 

loads (fig. 3a).

Total Nitrogen

Estimates of total nitrogen loads varied less than 

those of total phosphorus and total suspended solids 

loads (fig. 6). Differences in load estimates as more 

storms were included generally were smaller than those 

of total suspended solids and total phosphorus loads, 

likely because less of the total nitrogen loading occurs 

in response to storm events. The data set without storm 

samples led to underestimates of total nitrogen loads 

relative to the data sets with storm samples owing to 

the predominance of low-flow, low-concentration 

values in the data set. The SEPs with the 0-percent data 

set were as much as twice those of the other storm data 

sets (fig. 7). Because load estimates converged with the 

20-percent data set, and no substantial decrease in 

SEPs consistently occurred as more storm samples 

Figure 5. Annual total streamflow at the James River monitoring station, 1990 through 1999.
20 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

0

4.5x109

4.0x109

ANNUAL LOAD, IN KILOGRAMS PER YEAR

0

1.6x107

1.4x1071.2x1071.0x1070.8x1070.6x107

0.4x107

0

3.5x106

3.0x1062.5x1062.0x1061.5x1061.0x1060.5x106

0 perce

20 perce40 perce60 perce80 perce

100 perce

STORM DATA 

EXPLANAT

Standard eof predictio

Total suspended solids

0

1.4x107

1.2x1071.0x1070.8x1070.6x1070.4x1070.2x107

0

6.0x105

5.0x1054.0x1053.0x1052.0x1051.0x105

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

1990 1991 1992 1993 1994 199

Dissolved nitrite-plus-nitrateDissolved orthophosphorus

Total nitrogen

Total phosphorus

3.5x109

3.0x1092.5x1092.0x1091.5x1091.0x1090.5x109

0.2x107

Figure 6. Annual loads of selected constituents at the James River monitoring station, 1990 through 1999.
James River Load Estimates 21 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

0

102030

40

506070

05

10

15

20

25

30

0

1990 1991 1992 1993 1994 199

5

10

15

20

25

30

35

0 percent

20 percent40 percent60 percent80 percent

100 percent

STORM DATA SET

EXPLANATION

STANDARD ERROR OF PREDICTION, IN PERCENT

Total suspended solids Dissolved nitrite-plus-nitrate

Dissolved orthophosphorus

Total nitrogen

Total phosphorus

All standard errors of pnormalized to the total 

70

80

90

100

60

5040

30

20

10

0

35

30

25

2015

10

5

0

40

Figure 7. Standard error of prediction of selected constituent loads at the James River monitoring station, 1990 throug
22 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

were included, data sets with at least 20 percent storm 

samples led to the most accurate and precise estimates 

of total nitrogen loads (fig. 3a).

Dissolved Nitrite-plus-Nitrate

Dissolved nitrite-plus-nitrate load estimates 

varied the least of all the constituents considered as 

more storms were included (fig. 6). The data set without storm samples led to overestimates of these loads 

relative to the data sets with storm samples, but the relative magnitude of the difference was much smaller 

than with total suspended solids, total phosphorus, or 

total nitrogen. The SEPs with the 0-percent data set 

were nearly twice those with other storm data sets 

(fig. 7). This may be a result of the substantial groundwater input of nitrate to the James River; from 1985 to 

1998 at the monitoring station, an average of 21 percent of the total nitrogen load in the river came from 

ground-water inputs of nitrate (Sprague and others, 

2000). The under-representation of lower concentrations arising from dilution effects at high flows may 

have led to model predictions of higher concentrations 

at higher flows. Because load estimates converged with 

the 20-percent data set, and no substantial decrease in 

SEPs occurred as more storm samples were included, 

data sets with at least 20 percent storm samples led to 

the most accurate and precise estimates of dissolved 

nitrite-plus-nitrate loads (fig. 3a).

Dissolved Orthophosphorus

The data set without storm samples led to underestimates of dissolved orthophosphorus loads relative 

to the data sets with storm samples owing to the predominance of low-flow, low-concentration values in 

the input data set. Additionally, the SEPs with the 0-

percent data set were nearly double those with the 

higher percentage data sets (fig. 7). No substantial 

decrease in SEPs consistently occurred beyond the 20-

percent data set. Load estimates for dissolved orthophosphorus converged with the 40-percent data set, but 

continued to increase as the number of storm samples 

increased. This increase could be due in part to the desorption of orthophosphorus from particulate material 

that reaches the stream during storm events (Heathwaite and others, 2000). Because load estimates converged with the 40-percent data set, data sets with at 

least 33 percent storm samples led to the most accurate 

and precise estimates of dissolved orthophosphorus 

loads (fig. 3a).

These results show that data sets having little or 

no storm data resulted in variable and less precise load 

estimates for the constituents associated with particulate material, total suspended solids and total phosphorus, particularly in high-flow years when surface runoff 

of particulate material increased. In contrast, data sets 

with a small number of storm samples provided relatively accurate and precise load estimates of the dissolved constituents orthophosphorus and nitrite-plusnitrate. The percentage of total samples as storm samples required for accurate and precise load estimation 

for the 10-year period in the James River ranged from 

50 percent for total suspended solids to 20 percent for 

dissolved nitrite-plus-nitrate.

Five-Year Loads

Annual loads for the 5-year period from 1995 

through 1999 were estimated (fig. 8) and compared to 

those for the 10-year time period to determine whether 

the amount of storm sampling necessary for accurate 

and precise load estimation differed on the basis of the 

length of the data set.

Total Suspended Solids

As with the 10-year load estimates, the data set 

without storm samples led to underestimates of total 

suspended solids loads relative to the data sets with 

storm samples in the 5-year period (fig. 8). The difference between the 0-percent data set and the higher percentage data sets was greatest in 1996, the year with the 

highest total flow. The SEPs for the 0-percent data set 

were as much as three times as high as those of the 

higher percentage data sets, with the largest difference 

occurring in 1996 (fig. 9). The relatively poor predictions with the lower percentage data sets were likely a 

result of the lack of high concentration values in the 

input data set and the variability associated with the 

laboratory measurement of total suspended solids. 

Because load estimates converged with the 60-percent 

data set, and no substantial decrease in SEPs occurred 

as more storm samples were included, data sets with at 

least 42 storm samples led to the most accurate and 

precise estimates of total suspended solids loads 

(fig. 3b).
James River Load Estimates 23 1995 1996 1997 1998 1999

1995 1996 1997 

0

4.5x109

4.0x1093.5x1093.0x1092.5x1092.0x1091.5x1091.0x1090.5x109

0

0

1.4x107

1.0x1070.6x1070.2x1070.4x1070.8x1071.2x107

6.0x105

4.0x1052.0x1051.0x1053.0x1055.0x105

0

1.6x107

1.2x1070.8x1070.6x1070.4x1070.2x1071.0x1071.4x107

0

3.5x106

3.0x1062.5x1062.0x1061.5x1060.5x1061.0x106

ANNUAL LOAD, IN KILOGRAMS PER YEAR

0 perce

20 perce40 perce60 perce80 perce

100 perce

STORM DAT

EXPLANA

Standard eof predictio

Total suspended solids D

Dissolved orthophosphorus

Total nitrogenTotal phosphorus

Figure 8. Annual loads of selected constituents at the James River monitoring station, 1995 through 1999.
24 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

During the 10-year period, more storm samples 

were necessary for the convergence of total suspended 

solids load estimates, but SEPs were lower across all 

storm data sets. Additionally, the magnitudes of total 

suspended solids load estimates in the 5-year period 

were generally lower than those in the same years 

during the 10-year period. Differences in magnitudes 

were greatest in 1996, the highest flow year, and were 

smallest in 1997 and 1999, the lowest flow years. 

Increasing the number of storm events beyond the 60-

percent data set in the 5-year time period did not appear 

to close the gap in magnitude between the 5- and 10-

year load estimates.

Total Phosphorus

As in the 10-year period, the data set without 

storm samples led to underestimates of the total phosphorus loads relative to the data sets with storm samples in the 5-year period (fig. 8). The greatest 

difference in load estimation between the 0-percent 

data set and the higher percentage data sets occurred in 

1996. The SEPs for the 0-percent data set were more 

than twice those for the higher percentage data sets in 

some years; the difference was largest in 1996 (fig. 9). 

As in the longer time period, the poor predictions with 

the 0-percent data set probably resulted from the lack 

of high concentration values in the input data set. 

Because load estimates for total phosphorus converged 

with the 40-percent data set in the 5-year period as they 

did in the 10-year period, and no substantial decrease in 

SEPs consistently occurred as more storm samples 

were included, data sets with at least 33 percent storm 

samples led to the most accurate and precise estimates 

of total phosphorus loads (fig. 3b). 

The magnitudes of the total phosphorus load 

estimates in the 5-year period were generally lower 

than those in the same years during the 10-year period 

for all storm data sets, particularly in 1996. In addition, 

the SEPs in the 5-year period were slightly higher than 

those in the 10-year period, particularly with the 0-percent data set. Increasing the percentage of storm samples beyond the 40-percent data set in the 5-year time 

period did not close the gap in magnitudes between the 

5- and 10-year load estimates.

Total Nitrogen

The data set without storm samples resulted in 

load estimates of total nitrogen that were closer in magnitude to those for the data sets with storm samples in 

the 5-year period than in the 10-year period under all 

flow conditions (fig. 8). The SEPs for the 0-percent 

data set, however, were as much as three times as high 

as those for the other storm data sets in the 5-year 

period (fig. 9). Because load estimates for total nitrogen in the 5-year period converged with the 40-percent 

data set, and no substantial decrease in SEPs occurred 

as more storm samples were included, data sets with at 

least 33 percent storm samples led to the most accurate 

and precise estimates of total nitrogen loads (fig. 3b).

Despite the slightly greater variability in load 

estimates for the 10-year period, these estimates converged with fewer storm samples and SEPs were lower 

across all storm data sets relative to the 5-year period. 

The magnitudes of the total nitrogen load estimates in 

the 5-year period were generally close to those in the 

same years during the 10-year period for all storm data 

sets, though they were slightly lower during high-flow 

years.

Dissolved Nitrite-plus-Nitrate

The data set without storm samples led to much 

greater overestimates of dissolved nitrite-plus-nitrate 

loads relative to data sets with storm samples in the 5-

year period than in the 10-year period (fig. 8). The 

SEPs for the 0-percent data set in the 5-year period 

were as much as six times as high as those for the 

higher percentage data sets (fig. 9). This may be a 

result of the lack of high-flow, low-concentration data 

in the input data set. As in the 10-year period, load estimates in the 5-year period converged with the 20-percent data set, and no substantial decrease in SEPs 

occurred as more storm samples were included (fig. 9). 

Therefore, data sets with at least 19 percent storm samples led to the most accurate and precise estimates of 

dissolved nitrite-plus-nitrate loads (fig. 3b). With the 

exception of the 0-percent data set, the magnitudes of 

the load estimates in the 5- and 10-year periods were 

similar for all storm data sets. Of the five constituents 

considered, dissolved nitrite-plus-nitrate loads were the 

most similar between the two time periods under all 

hydrologic conditions.
James River Load Estimates 25 0 percent 20 percent 40 percent 60 percent 80 percent 100 percent

STORM DATA SET

EXPLANATION

STANDARD ERROR OF PREDICTION, IN PERCENT

100

302040

50

60

70

80

90

10

0

70

60

50

40

30

20

10

0

30

25

20

1510

5

0

35

30

25

20

15

10

5

0

40

35

3025

20

15

10

5

0

All standard errors of normalized to the tota

Total suspended solids 

Total nitrogen

Total phosphorus

1995 1996 1997 1998 1999

1995 1996 1997 

Figure 9. Standard error of prediction of selected constituent loads at the James River monitoring station, 1995 through 
26 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

Dissolved Orthophosphorus

The data set without storm samples appeared to 

result in load estimates of dissolved orthophosphorus 

that were closer in magnitude to those for the data sets 

with storm samples in the 5-year period than in the 10-

year period (fig. 8). The SEPs for the 0-percent data 

set, however, were as much as four times as high as 

those for the higher percentage data sets in the 5-year 

period, whereas in the 10-year period, the SEPs for the 

0-percent data set were only as much as twice as high 

(figs. 7 and 9). Because load estimates for dissolved 

orthophosphorus converged with the 0-percent data set 

in the 5-year period, and no substantial decrease in the 

SEPs consistently occurred beyond the 20-percent data 

set, data sets with at least 19 percent storm samples led 

to the most accurate and precise estimates of dissolved 

orthophosphorus loads (fig. 3b). Even with the convergence, the magnitudes of the load estimates in the 5-

year period differed from those in the same years 

during the 10-year period, though they were not consistently lower or higher.

Comparison of Ten-Year and Five-Year 

Loads

These results indicate that load estimates for the 

constituents associated with particulate material in the 

5-year period were generally lower than those in the 

same years in the 10-year period for all storm data sets. 

Differences in magnitude were greatest in 1996, the 

highest flow year, and were smallest in 1997 and 1999, 

the lowest flow years. In addition, the SEPs in the 5-

year period were higher than those in the same years in 

the 10-year period, particularly with the 0-percent data 

sets and in the higher flow years. Thus, loads of particulate constituents were estimated more accurately and 

precisely in the longer time period, when a greater 

number of moderate-flow samples was included in the 

data set (figs. 3a, b).

In contrast, load estimates for the dissolved constituents in the 5-year period generally were closer to 

those in the same years in the 10-year period for all 

storm data sets, regardless of the annual flow conditions. This result indicates that the model better predicted loads of dissolved constituents than particulateassociated constituents during the shorter period. The 

inclusion of a greater number of high- and moderateflow samples in the overall 10-year data set was not as 

important with the dissolved constituents, as much of 

their loading occurs during lower flow conditions. Consequently, 5 years of data led to load estimates that 

were similar in magnitude to those obtained from 10 

years of data, though they were less precise in the 

shorter period.

The percentage of total samples as storm samples required for convergence of the load estimates in 

the 10-year period in the James River ranged from 50 

percent for total suspended solids to 20 percent for dissolved nitrite-plus-nitrate. In the 5-year period, the 

range was from 42 percent for total suspended solids to 

19 percent for dissolved nitrite-plus-nitrate and dissolved orthophosphorus. Though fewer storm samples 

were necessary for accurate load estimates during the 

shorter time period, these estimates were less precise 

for all constituents, regardless of the number of storm 

samples included.

RAPPAHANNOCK RIVER LOAD 

ESTIMATES

The 1,600-mi2 area that drains to the Rappahannock River monitoring station is approximately onefourth the size of the area that drains to the James River 

monitoring station. The smaller basin size, in addition 

to the greater relief and smaller percentage of forested 

area, causes the Rappahannock River to respond more 

rapidly to storm events than the James River. The 

annual total streamflow from 1990 through 1999, along 

with the long-term mean annual total for the period of 

record (1907-1999), is shown in figure 10. Streamflow 

in 1993, 1994, 1996, and 1998 was above the long-term 

mean—the highest annual total flow in the monitoring 

period occurred in 1996. Streamflow in 1991, 1997, 

and 1999 was below the long-term mean—the lowest 

annual total flow in the monitoring period occurred in 

1999.

Ten-Year Loads

Annual loads for the 10-year period from 1990 

through 1999 were estimated for total suspended solids, total phosphorus, total nitrogen, dissolved nitriteplus-nitrate, and dissolved orthophosphorus with all 

storm data sets for the Rappahannock River monitoring 

station (fig. 11). These load estimates were compared 

to the 10-year load estimates for the James River Basin 
Rappahannock River Load Estimates 27

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

DISCHARGE, IN CUBIC 

FEET PER SECOND

ANNUAL TOTAL STREAMFLOW

LONG-TERM (1907-1999) MEAN ANNUAL

TOTAL STREAMFLOW

EXPLANATION

to assess the effects of storm-sampling frequency on 

load estimation in basins with different drainage areas 

and basin characteristics.

Total Suspended Solids

Load estimates for total suspended solids were 

highly variable (fig. 11). The quick response of the 

Rappahannock River makes it difficult to collect a 

storm sample that represents the daily mean concentration used in the model. In addition to the environmental 

variability, there is high variability in the laboratory 

measurement of total suspended solids (Gray and 

others, 2000). The regression model diagnostics indicate that the model for total suspended solids did not 

adhere to the underlying assumptions and therefore was 

not valid for the 0-, 20-, 40-, and 60-percent data sets—

plots of residuals against the predicted values indicated 

heteroscedasticity and probability plots of the residuals 

were not normally distributed. The homoscedasticity 

and normality assumptions were met with the 80- and 

100-percent data sets, but the SEPs were still high 

(fig. 12). Because only the 80- and 100-percent data 

sets adhered to the model assumptions, data sets with at 

least 37 percent storm samples (fig. 4a) were required 

to estimate total suspended solids loads in the Rappahannock River, though even these estimates had large 

prediction errors.

Total Phosphorus

The 0- and 20-percent data sets underestimated 

total phosphorus loads relative to the higher percentage 

data sets, particularly during high-flow years (fig. 11). 

The relatively poor predictions were likely a result of 

the under-representation of high-flow, high-concentration values in the input data set. The SEPs were variable among all storm data sets, and the model fit was 

not consistently better as more storm samples were 

included (fig. 12). This may be a consequence of the 

difficulty of collecting storm samples representing the 

daily mean concentration. Because load estimates converged with the 60-percent data set, and the SEPs did 

not consistently decrease with the inclusion of more 

storm samples, data sets with at least 31 percent storm 

samples led to the most accurate and precise estimates 

of total phosphorus loads (fig. 4a).

Total Nitrogen

Estimates of total nitrogen loads varied less 

across storm data sets than those of total phosphorus 

and total suspended solids loads (fig. 11), likely 

because less of the total nitrogen loading occurs in 

response to storm events. During high-flow years, the 

0-percent data set just slightly overestimated total 

nitrogen loads relative to the higher percentage data 

sets; during the low-flow years, load estimates were 

Figure 10. Annual total streamflow at the Rappahannock River monitoring station, 1990 through 1999.
28 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

0

8.0x109

4.0x1092.0x1096.0x109

10.0x109

0

1.6x105

1.2x1050.4x1050.2x1050.6x105

0.8x105

1.0x1051.4x105

0

2.5x106

1.5x1060.5x1061.0x1062.0x106

0

6.0x106

4.0x1061.0x1062.0x1063.0x1065.0x106

0

3.0x106

2.0x1060.5x1061.0x1061.5x1062.5x106

ANNUAL LOAD, IN KILOGRAMS PER YEAR

0 perc

20 perc40 perc60 perc80 perc

100 perc

STORM DA

EXPLANA

Standard of predict

Total suspended solids Dissolved nitrite-plus-nitrate

Dissolved orthophosphorus

Total nitrogen

Total phosphorus

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

1990 1991 1992 1993 1994 19

Figure 11. Annual loads of selected constituents at the Rappahannock River monitoring station, 1990 through 1999.
Rappahannock River Load Estimates 29 0 percent 20 percent 40 percent 60 percent 80 percent 100 percent STORM DATA SET EXPLANATION

STANDARD ERROR OF PREDICTION, IN PERCENT

100120

80

60

40

20

0

40

35

30

25

20

15

10

50

40

35

30

25

20

15

10

50

30

25

20

15

10

5

0

50

40

30

2010

0

Total suspended solids Dissolved nitrite-plus-nitrate

Dissolved orthophosphorus

Total nitrogen

Total phosphorus

All standard errors of normalized to the tota

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

1990 1991 1992 1993 1994 19

Figure 12. Standard error of prediction of selected constituent loads at the Rappahannock River monitoring station, 19
30 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

closer to those of the higher percentage data sets. The 

SEPs were as much as twice as high with the 0-percent 

data set as with any other storm data set (fig. 12). 

Because load estimates converged with the 40-percent 

data set, and no substantial decrease in SEPs consistently occurred as more storm samples were included, 

data sets with at least 23 percent storm samples led to 

the most accurate and precise estimates of total nitrogen loads (fig. 4a).

Dissolved Nitrite-plus-Nitrate

The 0-percent data set did not lead consistently 

to under- or overestimates of dissolved nitrite-plusnitrate loads relative to the higher percentage data sets 

(fig. 11), though the SEPs were always higher (fig. 12). 

The inclusion of more high-flow, low-concentration 

values led to continually decreasing load estimates as 

more storms were included in the data set. This 

decrease was greater than in the James River, in part 

because ground-water inputs of nitrate are higher (26 

percent) at the Rappahannock River monitoring station 

(Sprague and others, 2000). Despite the continuing 

decrease, load estimates converged with the 20-percent 

data set, and no substantial decrease in SEPs occurred 

as more storm samples were included. Therefore, data 

sets with at least 13 percent storm samples led to the 

most accurate and precise estimates of dissolved 

nitrite-plus-nitrate loads (fig. 4a).

Dissolved Orthophosphorus

Estimates of dissolved orthophosphorus loads 

varied the least of all the constituents considered 

among storm data sets in the Rappahannock River 

(fig. 11). The data set without storm samples led to 

load estimates that were similar to those for the data 

sets with storm samples, though the SEPs were as 

much as twice as high (fig. 12). No substantial decrease 

in SEPs occurred for data sets containing more storm 

samples than the 20-percent data set. Load estimates 

for dissolved orthophosphorus converged with the 0-

percent data set, but because the SEPs were much 

higher with the 0-percent data set, more precise load 

estimates were obtained with the 20-percent and higher 

data sets. Therefore, data sets with at least 13 percent 

storm samples led to the most accurate and precise estimates of dissolved orthophosphorus loads (fig. 4a).

These results show that data sets with little or no 

storm data resulted in variable and less precise load 

estimates for the constituents associated with particulate material than for the dissolved constituents in the 

Rappahannock River, particularly in high-flow years. 

In contrast, data sets with a relatively small number of 

storm samples provided more precise load estimates of 

the dissolved constituents orthophosphorus and nitriteplus-nitrate. The percentage of total samples as storm 

samples required for reasonably accurate and precise 

load estimation for the 10-year period in the Rappahannock River ranged from 37 percent for total suspended 

solids to 13 percent for dissolved nitrite-plus-nitrate 

and dissolved orthophosphorus.

In general, fewer storm samples were necessary 

for accurate load estimation in the Rappahannock River 

than in the James River, but the estimates were less precise than those in the James River for all storm data 

sets. More storm samples were required just to meet the 

model assumptions for total suspended solids, in large 

part because the stream response in the Rappahannock 

River Basin is quicker and more variable than in the 

James River Basin. The quicker and more variable 

streams response also led to less precise load estimates, 

regardless of how many storm samples were included. 

Additionally, the difference in load estimates as more 

storms were included was slightly greater in the Rappahannock River, indicating that the influence of stormsampling frequency on load estimation was greater in 

this smaller and flashier basin.

Five-Year Loads

Annual loads for the 5-year period from 1995 

through 1999 were estimated for a range of particulate 

and dissolved constituents with all Rappahannock 

River storm data sets (fig. 13). The 5-year load estimates were compared to those for the 10-year period to 

determine whether the amount of storm sampling necessary for accurate and precise load estimation in this 

basin differed on the basis of the length of the data set. 

These load estimates also were compared to the 5-year 

load estimates for the James River to assess the effects 

of storm-sampling frequency on load estimation for a 

shorter time period in basins with different drainage 

areas and basin characteristics.
Rappahannock River Load Estimates 31 0 perce

20 perce40 perce60 perce80 perce

100 perce

STORM DAT

EXPLANA

Standard eof predictio

6.0x1064.0x1062.0x1061.0x1063.0x1065.0x106

0

3.0x106

2.0x1061.0x106

0.5x106

1.5x1062.5x106

0

1.6x105

1.2x1050.8x1050.4x1050.2x1050.6x1051.0x1051.4x105

0

1.0x1010

2.5x1061.5x1060.5x1061.0x1062.0x106

0

0.8x109

0.4x109

0.2x109

0.6x109

0

ANNUAL LOAD, IN KILOGRAMS PER YEAR

Total suspended solids 

Total nitrogenTotal phosphorus

1995 1996 1997 1998 1999

1995 1996 1997 

Figure 13. Annual loads of selected constituents at the Rappahannock River monitoring station, 1995 through 1999.
32 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

Total Suspended Solids

Load estimates for total suspended solids were 

highly variable (fig. 13). The model diagnostics indicate that, as with the 10-year model, the 5-year model 

for total suspended solids did not adhere to the assumptions of normality and homoscedasticity of the residuals for the 0-, 20-, 40-, and 60-percent data sets. The 

assumptions were met with the 80- and 100-percent 

data sets, but the SEPs were still very high (fig. 14). 

Because load estimates converged with the 80-percent 

data, and no substantial decrease in SEPs occurred as 

more storm samples were included, data sets with at 

least 37 percent storm samples led to the most accurate 

and precise estimates of total suspended solids loads 

(fig. 4b). It is difficult to compare the magnitudes of the 

estimates between the 5- and 10-year data sets because 

load estimates were poor for both time periods, even 

with 100 percent of the storm samples included.

Total Phosphorus

As in the 10-year period, the 0-percent data set in 

the 5-year period led to underestimates of total phosphorus loads relative to higher percentage data sets, 

particularly during high-flow years (fig. 13). The estimates with the other storm data sets in the 5-year 

period, unlike those in the 10-year period, were variable and did not converge. The SEPs for the 5-year 

period did not decrease consistently as more storms 

were included, indicating that even with 100 percent of 

the storm samples included, the number of high-flow 

samples was insufficient to produce a good model fit 

(fig. 14). In contrast, load estimates converged at a reasonable value in the 10-year period. The behavior of 

total phosphorus in this basin is therefore better characterized in the longer time period, for which a greater 

number of moderate-flow samples is included in the 

data set.

Total Nitrogen

Estimates of total nitrogen loads with the 0-percent data set were similar in magnitude to those with 

the higher percentage data sets (fig. 13); however, SEPs 

were as much as twice as high with the 0-percent data 

set (fig. 14). Because estimates of total nitrogen loads 

in the 5-year period converged with the 20-percent data 

set, and no substantial decrease in SEPs occurred as 

more storm samples were included, data sets with at 

least 13 percent storm samples led to the most accurate 

and precise estimates of total nitrogen loads (fig. 4b). 

The magnitudes of the total nitrogen load estimates in 

the 5-year period were generally similar to those in the 

same years during the 10-year period for all storm data 

sets, though SEPs were higher.

Dissolved Nitrite-plus-Nitrate

The 0-percent data set led to estimates of dissolved nitrite-plus-nitrate loads that were not consistently under- or overestimated relative to the higher 

percentage data sets (fig. 13). The SEPs were always 

higher, particularly during high-flow years (fig. 14). 

Load estimates in the 5-year period were similar to 

those in the 10-year period and converged with the 20-

percent data set; no substantial decrease in SEPs 

occurred as more storm samples were included. Therefore, data sets with at least 13 percent storm samples 

led to the most accurate and precise estimates of dissolved nitrite-plus-nitrate loads (fig. 4b). The magnitudes of the load estimates in the 5- and 10-year 

periods were similar for all storm data sets, though 

there were slight differences in high-flow years.

Dissolved Orthophosphorus

The load estimates for dissolved orthophosphorus were slightly more variable among storm data sets 

for the 5-year period than among those for the 10-year 

period (fig. 13). For the 5-year period, the 0-percent 

data set slightly overestimated loads of dissolved orthophosphorus relative to those for the higher percentage 

data sets, and the SEPs were nearly three times as high 

during some years (fig. 14). Because load estimates for 

dissolved orthophosphorus converged with the 40-percent data set in the 5-year period, and no substantial 

decrease in the SEPs consistently occurred as more 

storms were included, data sets with at least 23 percent 

storm samples led to the most accurate and precise estimates of dissolved orthophosphorus loads (fig. 4b). 

After the load estimates converged, their magnitudes in 

the 5-year period were similar to those in the same 

years in the 10-year period.

Comparison of Ten-Year and Five-Year 

Loads

These results indicate that the length of the data 

set had a greater effect on the load estimation of particulate constituents than dissolved constituents in the 
Rappahannock River Load Estimates 33

30

10

5

0

15

20

25

25

20

15

10

5

0

40

3530

10

5

0

15

20

25

40

35

30

0

2040

60

80

100

5040

3020

10

0

120

Total suspended solids Dissolved nitrite-plus-nitrate

Dissolved orthophosphorus

Total nitrogen

Total phosphorus

0 percent

20 percent40 percent60 percent80 percent

100 percent

STORM DATA SET

EXPLANATION

STANDARD ERROR OF PREDICTION, IN PERCENT

All standard errors of normalized to the tota

1995 1996 1997 1998 1999

1995 1996 1997 

Figure 14. Standard error of prediction of selected constituent loads at the Rappahannock River monitoring station, 1
34 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

Rappahannock River. Loads of particulate constituents 

were estimated more precisely with data from the 

longer time period when a greater number of moderateflow samples was included in the data set (fig. 3). Both 

total phosphorus and total suspended solids loads were 

poorly estimated for the 5-year period, but total phosphorus loads were estimated reasonably well for the 

10-year period. The SEPs for the 5-year period were 

higher than those in the same years for the 10-year 

period, particularly with the 0-percent data sets and in 

the higher flow years. In contrast, dissolved constituent 

loads in the Rappahannock River were estimated reasonably well with data sets that included a small 

number of storm samples during both the 10- and 5-

year periods, though the SEPs were higher during the 

shorter period. The percentage of storm samples 

required for reasonably accurate and precise load estimation during a 5-year period in the Rappahannock 

River ranged from 37 percent for total suspended solids 

to 13 percent for total nitrogen and dissolved nitriteplus-nitrate. Reasonable load estimates for total phosphorus could not be obtained even with the inclusion of 

100 percent of the storm samples collected in this 

study.

For the 5-year period in the James River, 

whereas estimates of some constituent loads converged 

with a higher percentage of storm samples, all estimates had lower SEPs than in the Rappahannock River. 

In addition, as observed for the 10-year period, the difference in load estimates as more storm samples were 

included was slightly greater in the Rappahannock 

River, indicating that the influence of storm events on 

load estimation is greater in the Rappahannock River 

Basin for both time periods. The James River responds 

more slowly and consistently to storm events than does 

the Rappahannock River. As a result, loads in this basin 

can be estimated with greater accuracy and precision 

over shorter time periods and often with fewer storm 

samples.

Several changes in load estimates as more storm 

samples were included could not be explained. The 

method of storm data set construction used in this study 

may have led to results that were particularly sensitive 

to the nature of the single, random subset of data, and 

differences in load estimates may have resulted in part 

from differences between the individual distribution of 

sample populations in each storm data set. More 

detailed analyses for some constituents, perhaps by use 

of Monte Carlo simulations, would provide additional 

insight into the differences in load estimates as stormsampling frequency increases.

Additionally, both of the basins examined in this 

study are relatively large, and the conclusions drawn in 

this study likely do not apply to smaller basins. In 

smaller basins, the response of streamflow and instream concentration values to storm events would be 

quicker than in either the James or the Rappahannock 

River Basins. Storm sampling in smaller basins can 

lead to positively biased and less precise load estimates 

because measured concentrations during storm events 

are often higher than the daily mean concentrations 

employed in the regression model (Robertson and 

Roerish, 1999). 

TREND ESTIMATES

Trends in flow-adjusted concentrations of total 

suspended solids, total phosphorus, total nitrogen, dissolved nitrite-plus-nitrate, and dissolved orthophosphorus were estimated with storm data sets covering both 

time periods at the James River and Rappahannock 

River RIM stations. The 5-year trend estimates were 

compared to those from the 10-year period to determine whether the amount of storm sampling necessary 

for reasonable trend estimates differed on the basis of 

the length of the data set. The James River trend estimates also were compared to the Rappahannock River 

trend estimates to assess the effects of storm-sampling 

frequency in basins with different sizes and characteristics.

For the 10-year period in the James River, the 

estimates of flow-adjusted concentration trends (eq. 2) 

were similar in magnitude and significance with all 

storm data sets for all constituents except total suspended solids (table 2). The 95-percent confidence 

intervals for the trend magnitudes decreased slightly as 

more storm samples were included, indicating that the 

model better estimated the “true” trends with the inclusion of a greater number of storm samples. Trend estimates for total suspended solids were significant with 

the 60-percent and higher data sets, and magnitudes 

were similar for the 80- and 100-percent data sets. A 

Type I error occurred with the 0-percent data set—at a 

significance level of 0.05, the null hypothesis that the 

β3 coefficient (eq. 1) did not differ from zero was inappropriately rejected. This error was suggested by the 

acceptance of the null hypothesis with the 20- and 40-
Trend Estimates 35

Data set Lower 

magnitude

Mean 

magnitude

Upper 

magnitude p-value

Total suspended solids

100% -43 -26 -4 .0216

80% -44 -26 -3 .0281

60% -52 -35 -12 .0037

40% -44 -23 +6 .1014

20% -48 -26 +5 .0794

0% -54 -34 -4 .0222

Total phosphorus

100% -55 -45 -33 <.0001

80% -54 -44 -31 <.0001

60% -55 -45 -32 <.0001

40% -53 -42 -29 <.0001

20% -49 -35 -18 .0003

0% -51 -37 -20 .0002

Total nitrogen

100% -32 -22 -11 .0003

80% -33 -22 -10 .0007

60% -30 -19 -7 .0028

40% -32 -20 -7 .0038

20% -34 -21 -5 .0106

0% -40 -26 -10 .0030

Dissolved nitrite-plus-nitrate

100% -52 -43 -31 <.0001

80% -55 -45 -33 <.0001

60% -47 -36 -22 <.0001

40% -55 -43 -28 <.0001

20% -60 -47 -31 <.0001

0% -62 -48 -28 .0001

Dissolved orthophosphorus

100% -53 -42 -29 <.0001

80% -52 -41 -27 <.0001

60% -50 -38 -22 <.0001

40% -55 -42 -26 <.0001

20% -55 -41 -24 .0001

0% -57 -41 -20 .0006

Table 2. Trends in flow-adjusted concentrations of selected constituents at the 

James River monitoring station for each of the storm data sets, 1990 through 

1999

[Trends expressed as percent change. The lower and upper magnitudes represent the 95-percent 

confidence interval of the trend. Trends that were significant with p-value less than or equal to 

0.05 are shown in bold type. <, less than]
36 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

percent data sets. The results indicate that over a 10-

year period at the James River monitoring station, 

trends in flow-adjusted concentrations can be estimated 

reasonably well with a small number of storm samples 

for both dissolved and particulate constituents, with the 

exception of total suspended solids.

For the 5-year period in the James River, the 

trend estimates were not significant for total suspended 

solids or total nitrogen with all storm data sets 

(table 3). The trend estimates were strongly significant 

for dissolved orthophosphorus with all storm data sets, 

though the confidence intervals decreased as more 

storm samples were added. Owing to the predominance 

of point-source inputs of dissolved orthophosphorus, 

much of the decrease likely occurred within the lower 

flow samples included in all data sets. The downward 

trends in flow-adjusted concentrations of total phosphorus and dissolved nitrite-plus-nitrate were smaller 

in magnitude and were significant with only the 60-percent and higher data sets. Trend estimates for these two 

constituents were similar in significance and magnitude 

with the 60-, 80-, and 100-percent data sets, but the pvalues decreased slightly as more storm samples were 

included. These results indicate that reasonable trend 

estimates for the 5-year period in the James River were 

obtained for both dissolved and particulate constituents 

with data sets in which at least 42 percent of the samples were storm samples (fig. 3b). More storm samples 

are required at this monitoring station for trend estimation for the 5-year period than for the 10-year period. 

Because no significant trends were observed in several 

of the constituents for the 5-year period, there was no 

clear evidence that dissolved-constituent trends were 

better estimated with fewer storm samples than particulate-constituent trends.

More storm samples were necessary for trend 

estimation in the Rappahannock River than in the 

James River for the 10-year period. The p-values for 

trends in dissolved nitrite-plus-nitrate in the Rappahannock River decreased steadily as the number of storm 

samples increased; the trend estimate was significant 

only when 100 percent of the storm samples were 

included (table 4). Trends in dissolved orthophosphorus were significant with the 0-, 20-, and 40-percent 

data sets, but were not significant with the data sets 

containing more storm samples. It is possible that the 

increases in contributions from nonpoint sources at 

higher flows offset decreases in contributions from 

point sources and, as a result, a false overall trend in 

orthophosphorus was detected when the higher flow 

samples were not included. Trends in total phosphorus 

were significant and the magnitudes were similar for 

the 40-percent and higher data sets. Trends in total suspended solids and total nitrogen were not significant 

with all data sets (with the exception of an apparent 

Type I error in the total suspended solids trend with the 

40-percent data set). There was no clear evidence that 

trends in dissolved constituents were better estimated 

with fewer storm samples than trends in constituents 

associated with particulate material. To predict particulate- and dissolved-constituent trends for the 10-year 

period in the Rappahannock River, it was necessary to 

include 100 percent of the possible storm samples in 

this study, or 42 percent of the samples in the data sets 

as storm samples (fig. 4a).

For the 5-year period in the Rappahannock 

River, trends were not significant for any constituents 

except dissolved orthophosphorus (table 5). Downward 

trends in flow-adjusted concentrations of dissolved 

orthophosphorus were large and were detected with all 

storm data sets. There was no consistent decrease in 

p-values for the other constituents as more storm samples were included, and it appears that including more 

storm samples would not lead to better trend estimates. 

It is likely that the true trends during this period were 

not significant. Therefore, the amount of storm sampling necessary for reliable trend estimation for both 

dissolved and particulate constituents in this basin for 

the 5-year period could not be determined. 

SUMMARY AND CONCLUSIONS

Annual loads and flow-adjusted concentration 

trends were estimated from water-quality and streamflow data collected from 1990 through 1999 at monitoring stations on two tributaries to the Chesapeake 

Bay in Virginia—James River at Cartersville, Va., and 

Rappahannock River near Fredericksburg, Va. The 

effects of storm-sampling frequency on load and trend 

estimates in these two basins of different size, relief, 

and land use were determined by use of input data sets 

that included 0, 20, 40, 60, 80, and 100 percent of all 

available storm samples; all available base-flow samples were used in each data set. Loads and trends were 

estimated for total suspended solids, total phosphorus, 

total nitrogen, dissolved nitrite-plus-nitrate, and dissolved orthophosphorus in order to determine the 

effects of storm-sampling frequency on estimation of 

dissolved and particulate constituent loads and trends. 
Summary and Conclusions 37

Data set Lower 

magnitude

Mean 

magnitude

Upper 

magnitude p-value

Total suspended solids

100% -44 -13 +36 .5341

80% -43 -8 +49 .7196

60% -51 -16 +44 .5106

40% -48 -8 +63 .7597

20% -54 -21 +37 .3745

0% -59 -21 +53 .4438

Total phosphorus

100% -52 -34 -9 .0103

80% -54 -35 -9 .0111

60% -53 -32 -2 .0369

40% -43 -18 +17 .2569

20% -55 -37 -11 .0070

0% -50 -25 +11 .1361

Total nitrogen

100% -31 -11 +14 .3569

80% -33 -13 +14 .3043

60% -38 -16 +13 .2332

40% -22 +3 +36 .8038

20% -36 -16 +9 .1792

0% -44 -21 +10 .1439

Dissolved nitrite-plus-nitrate

100% -58 -40 -12 .0078

80% -61 -41 -10 .0128

60% -65 -44 -9 .0163

40% -47 -16 +32 .4272

20% -57 -28 +20 .1894

0% -59 -21 +52 .4594

Dissolved orthophosphorus

100% -81 -74 -64 <.0001

80% -80 -72 -61 <.0001

60% -82 -74 -64 <.0001

40% -79 -70 -57 <.0001

20% -79 -70 -55 <.0001

0% -79 -68 -50 <.0001

Table 3. Trends in flow-adjusted concentrations of selected 

constituents at the James River monitoring station for each of the storm 

data sets, 1995 through 1999

[Trends expressed as percent change. The lower and upper magnitudes represent the 95-

percent confidence interval of the trend. Trends that were significant with p-value less 

than or equal to 0.05 are shown in bold type. <, less than]
38 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

Data set Lower 

magnitude

Mean 

magnitude

Upper 

magnitude p-value

Total suspended solids

100% -42 -12 +34 .5380

80% -40 -7 +43 .7220

60% -48 -19 +28 .3592

40% -47 -15 +37 .4787

20% -49 -19 +29 .3593

0% -53 -24 +22 .2350

Total phosphorus

100% -45 -29 -9 .0063

80% -40 -23 -2 .0291

60% -45 -29 -8 .0081

40% -44 -27 -7 .0111

20% -38 -21 +1 .0528

0% -37 -21 0 .0445

Total nitrogen

100% -26 -13 +1 .0605

80% -24 -11 +4 .1584

60% -26 -12 +3 .1188

40% -28 -14 +2 .0746

20% -26 -12 +5 .1457

0% -26 -11 +8 .2497

Dissolved nitrite-plus-nitrate

100% -44 -26 -1 .0391

80% -44 -25 +2 .0667

60% -43 -20 +11 .1792

40% -43 -19 +16 .2559

20% -40 -11 +33 .5759

0% -41 -8 +44 .7225

Dissolved orthophosphorus

100% -32 -15 +6 .1310

80% -34 -18 +2 .0661

60% -36 -19 +4 .0859

40% -39 -23 -1 .0382

20% -45 -30 -10 .0049

0% -47 -31 -9 .0078

Table 4. Trends in flow-adjusted concentrations of selected constituents at 

the Rappahannock River monitoring station for each of the storm data sets, 

1990 through 1999

Trends expressed as percent change. The lower and upper magnitudes represent the 95-percent 

confidence interval of the trend. Trends that were significant with p-value less than or equal to 

0.05 are shown in bold type]
Summary and Conclusions 39

Data set Lower 

magnitude

Mean 

magnitude

Upper 

magnitude p-value

Total suspended solids

100% -3 +90 +275 .0561

80% -4 +96 +302 .0590

60% -32 +42 +199 .3316

40% -3 +106 +338 .0469

20% -17 +65 +225 .1306

0% -26 +39 +159 .2933

Total phosphorus

100% -21 +12 +58 .5188

80% -15 +21 +72 .2752

60% -28 +2 +45 .8929

40% -4 +36 +92 .0793

20% -4 +33 +83 .0773

0% -13 +16 +54 .3108

Total nitrogen

100% -11 +15 +50 .2688

80% -13 +15 +51 .3117

60% -17 +11 +48 .4709

40% -7 +25 +68 .1242

20% -11 +18 +57 .2462

0% -15 +17 +63 .3203

Dissolved nitrite-plus-nitrate

100% -45 -11 +45 .6316

80% -48 -12 +50 .6349

60% -50 -10 +61 .7195

40% -53 -11 +68 .7085

20% -43 +11 +117 .7474

0% -44 +21 +163 .6116

Dissolved orthophosphorus

100% -63 -49 -31 <.0001

80% -63 -49 -29 .0001

60% -65 -50 -29 .0001

40% -68 -53 -33 .0001

20% -60 -41 -14 .0060

0% -65 -47 -21 .0018

Table 5. Trends in flow-adjusted concentrations of selected constituents at 

the Rappahannock River monitoring station for each of the storm data sets, 

1995 through 1999

[Trends expressed as percent change. The lower and upper magnitudes represent the 

95-percent confidence interval of the trend. Trends that were significant with p-value 

less than or equal to 0.05 are shown in bold type. <, less than]
40 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

Estimates of loads and trends for the 10-year period 

from 1990 to 1999 were compared to those for the 5-

year period from 1995 to 1999 to determine whether 

the length of the data set had an effect on the frequency 

of storm sampling required to obtain accurate load and 

trend estimates.

For the 10-year period in the James River, the 

percentage of storm samples required for accurate and 

precise load estimation ranged from 50 percent for total 

suspended solids to 20 percent for dissolved nitriteplus-nitrate. For the 5-year period, the percentage of 

total samples as storm samples required for convergence of the load estimates ranged from 42 percent for 

total suspended solids to 19 percent for dissolved 

nitrite-plus-nitrate and dissolved orthophosphorus. The 

magnitudes of the load estimates in the 5-year period 

were close to those for the same years in the 10-year 

period for the dissolved constituents, but were lower 

for the particulate constituents. Additionally, all estimates in the 5-year period had higher prediction errors 

than those in the 10-year period. Therefore, the model 

better predicted loads of dissolved constituents than 

loads of particulate constituents with fewer storm samples for both time periods in the James River, though 

all constituent loads were better predicted for the 

longer time period.

For the 10-year period in the Rappahannock 

River, the percentage of storm samples required for 

reasonably accurate and precise load estimation ranged 

from 37 percent for total suspended solids to 13 percent 

for dissolved nitrite-plus-nitrate and dissolved orthophosphorus. For the 5-year period, a similar percentage 

of storm samples provided reasonable estimates of dissolved constituent loads and total suspended solids 

loads, but the prediction errors were much higher than 

for the 10-year period. Load estimates for total phosphorus never converged when data from the 5-year 

period were used, and the prediction errors did not 

decrease consistently as more storms were included, 

indicating that even when 100 percent of the available 

storm samples were included, the number of high-flow 

values was insufficient to accurately estimate total 

phosphorus loads during the shorter period. The load 

estimates for the 5-year period were not consistently 

higher or lower than those for the same years in the 10-

year period for any constituent. As with the James 

River, all estimates had higher prediction errors for the 

5-year period than for the 10-year period. Therefore, 

the model better predicted loads of dissolved constituents than particulate constituents with fewer storm 

samples for both periods, though, as observed in the 

James River, all constituent loads were better predicted 

in the longer time period.

Loads of dissolved and particulate constituents 

were estimated with fewer storm samples and were 

slightly more accurate and precise in the James River 

than in the Rappahannock River during both periods. 

The high relief and smaller drainage area of the Rappahannock River Basin cause quicker and more variable 

stream response than in the James River Basin, which 

led to less precise load estimates, regardless of how 

many storm samples were included. In addition, the 

difference in load estimates as more storms were 

included was slightly greater in the Rappahannock 

River during both periods, indicating that the influence 

of storm events on load estimation is greater in this 

smaller and flashier basin. Overall, the results of this 

study indicate that loads in the larger and less flashy 

James River Basin can be estimated with greater accuracy and precision over shorter time periods and 

usually with fewer storm samples than in the Rappahannock River Basin.

Trends in flow-adjusted concentrations were 

estimated reasonably well with few storm samples for 

both dissolved and particulate constituents in the James 

River for the 10-year period, with the exception of total 

suspended solids. Data sets having more storm samples—at least 42 percent of the total number of samples—were needed to obtain reliable trend estimates 

for the 5-year period. For the 10-year period in the 

Rappahannock River, at least 42 percent storm samples 

was necessary for reasonable estimates of trends in 

both dissolved and particulate constituents. No significant trends were observed for the 5-year period, so the 

minimum number of storm samples for trend estimation could not be determined. Because of the small 

number of significant trends throughout these data sets, 

it was not possible to determine whether dissolved constituent trends were better estimated with fewer storm 

samples than particulate constituent trends. The results 

do indicate that, as with load estimation, more storm 

samples were necessary for trend estimation during 

shorter time periods and in the smaller and flashier 

Rappahannock River Basin. Both load and trend estimates were sensitive to the length of the monitoring 

period and the size of the basin; however, load estimates were more sensitive to the number of storm samples in the data set than were trend estimates.
Summary and Conclusions 41

The best overall monitoring strategy for accurate 

and precise load and trend estimation of particulate and 

dissolved constituents in the James and Rappahannock 

River Basins was found to consist of 50 percent baseflow samples and 50 percent storm samples. If total 

suspended solids—a constituent that has large associated measurement errors—were not considered, however, a minimum of 33 percent storm samples would be 

sufficient.

The results of this study indicate that the optimal 

sampling design of monitoring programs in large river 

basins will differ depending on the basin size and 

hydrologic response, the length of the monitoring program, and the constituents of interest. Flashier basins 

will require collection of a greater number of storm 

samples, particularly if particulate constituents are 

monitored, though lengthening the monitoring period 

may reduce the amount of storm sampling required. 

Many monitoring programs begin as short-term efforts, 

however, making it impractical to initially design a 

sampling strategy that will be optimal over long periods. If the monitoring period is extended after several 

years of relatively high-intensity storm sampling, a significant reduction in storm-sampling frequency may 

bias trend estimates in the long term. The potential for 

this bias should be investigated prior to making substantial changes to a monitoring program.
42 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

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APPENDIX
44 Effects of Storm-Sampling Frequency on Estimation of Water-Quality Loads and Trends 

Data set Number of 

samples

Number of 

storm-flow 

samples

Percent 

storm-flow 

samples

James River, 1990-99

Streamflow Record (days) 3,652 729 20

1100% 407 221 54

80% 355 177 50

60% 312 133 43

40% 266 88 33

20% 225 44 20

0% 182 0 0

James River, 1995-99

Streamflow Record (days) 1,826 344 19

1100% 178 94 53

80% 151 75 50

60% 134 56 42

40% 116 38 33

20% 98 19 19

0% 80 0 0

Rappahannock River, 1990-99

Streamflow Record (days) 3,652 752 21

1100% 385 163 42

80% 352 130 37

60% 320 98 31

40% 287 65 23

20% 255 33 13

0% 222 0 0

Rappahannock River, 1995-99

Streamflow Record (days) 1,826 384 21

1100% 182 78 43

80% 166 62 37

60% 152 47 31

40% 135 31 23

20% 120 16 13

0% 104 0 0

Appendix 1. Number of storm-flow days in the streamflow record, 

number of days on which a water-quality sample was collected, and 

number of storm-flow samples at the James and Rappahannock 

River monitoring stations for each data set

1 100% data set is the full data set with all base-flow and storm-flow samples included.