Prepared in cooperation with the City of Champaign, Illinois, the City of Urbana, Illinois, 

and the University of Illinois at Urbana-Champaign

Using Observed Postconstruction Peak Discharges 

to Evaluate a Hydrologic and Hydraulic Design Model, 

Boneyard Creek, Champaign and Urbana, Illinois

Scientific Investigations Report 2011–5176

U.S. Department of the Interior

U.S. Geological Survey
Cover. Photograph at the top shows Boneyard Creek flowing through campus of the University of Illinois at Urbana-Champaign during 

the storm event of June 26, 2007 (photograph by Anthony Spencer, USGS Illinois Water Science Center). Photograph at lower right shows 

Boneyard Creek emerging from underneath a flow restrictor at Wright Street in Champaign, Illinois, during the storm event of June 26, 2007 

(photograph by Anthony Spencer, USGS Illinois Water Science Center). Photograph at lower left shows an acoustic Doppler current profiler 

on a moving boat upstream from the Parshall flume at USGS streamgage 03337000 (Boneyard Creek at Urbana, Ill.) on December 3, 2003 

(photograph by Kevin K. Johnson, USGS Illinois Water Science Center).
Using Observed Postconstruction Peak Discharges to 

Evaluate a Hydrologic and Hydraulic Design Model, 

Boneyard Creek, Champaign and Urbana, Illinois

By Thomas M. Over, David T. Soong, and Robert R. Holmes, Jr.

Prepared in cooperation with the City of Champaign, Illinois, the City of Urbana, Illinois, 

and the University of Illinois at Urbana-Champaign

Scientific Investigations Report 2011–5176

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Over, T.M., Soong, D.T., and Holmes, Jr., R.R., 2011, Using observed postconstruction peak discharges to evaluate a 

hydrologic and hydraulic design model, Boneyard Creek, Champaign and Urbana, Illinois: U.S. Geological Survey Scientific Investigations Report 2011–5176, 37 p.
iii

Contents

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

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

Technical Approach .............................................................................................................................3

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

Methodology...................................................................................................................................................5

Modeling With the Stormwater Management Model ....................................................................5

Sources and Processing of Data .......................................................................................................6

Precipitation Data........................................................................................................................6

Stream-Discharge and Stage Data...........................................................................................8

Events Selected for Analysis ..............................................................................................................8

Discharge-Uncertainty Analysis ......................................................................................................12

Uncertainty of the Observed Peak Discharge on Boneyard Creek at Lincoln Avenue....................13

Rating-Curve Regression...................................................................................................................13

Measurement Error Computation ....................................................................................................16

Discharge-Computation Uncertainty...............................................................................................17

Comparison of Simulated and Observed Peak Discharges and Stages.............................................23

Discharge at Lincoln Avenue............................................................................................................23

Stage at Lincoln Avenue and Stage and Discharge at Supplementary Streamgages............27

Summary........................................................................................................................................................36

Acknowledgments.......................................................................................................................................36

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

Figures

1. Map showing Boneyard Creek watershed in Champaign-Urbana, Ill., and 

locations of flood-control improvements, U.S. Geological Survey (USGS) 

rain gages and streamgages ......................................................................................................2

2. Map showing example of Thiessen polygons covering subbasins in the 

Boneyard Creek Stormwater Management Model (SWMM)...............................................7

3. Graph showing stage-discharge ratings used for USGS streamgage 03337100 

(Boneyard Creek at Lincoln Avenue, Urbana, Ill.), water years 2002 through 2009...........9

4. Graph showing computation of alternative estimates of peak discharge 

for the June 26, 2007, high-flow event at USGS streamgage 03337100 

(Boneyard Creek at Lincoln Avenue, Urbana, Ill.) .................................................................11

5. Graph showing stage-discharge rating-curve regression for USGS streamgage 

03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.) using measurements 

obtained between June 2003 and September 2009 when the depth of flow was 

greater than 5 feet (gage height greater than 12 feet). A, Scatterplot of data and 

fitted line. B, Residuals as a function of time.........................................................................14
iv

6. Graph showing stage-discharge rating-curve regression for USGS streamgage 

station 03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.) using 

measurements obtained during water years 2005 through 2009 when the 

depth of flow was greater than 1 foot (gage height greater than 8 feet). A, Scatterplot of data and fitted line. B, Residuals as a function of time..........................15

7. Graph showing components of uncertainty of computed discharge as a 

function of discharge for USGS streamgage 03337100 (Boneyard Creek at 

Lincoln Avenue, Urbana, Ill.), using measurements obtained from June 2003 

through September 2009 when the depth of flow was greater than 5 feet. A, Measurement error of 5 percent. B, Measurement error of 7.5 percent .....................20

8. Graph showing uncertainty of computed discharge expressed as a standard 

deviation at USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, 

Urbana, Ill.), using measurements obtained from June 2003 through September 

2009 when the depth of flow was greater than 5 feet ..........................................................21

9. Graph showing approximate 95-percent confidence interval of instantaneous 

discharge uncertainty at USGS streamgage station 03337100 (Boneyard Creek 

at Lincoln Avenue, Urbana, Ill.), using measurements obtained from June 2003 

through September 2009 when the depth of flow was greater than 5 feet.......................21

10. Graph showing peak discharges from SWMM4 simulations and observed 

values with estimated 95-percent confidence intervals for USGS streamgage 

03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.), for storm events 

analyzed during this study.........................................................................................................25

11. Graph showing peak stages from SWMM4 simulations and observed values 

at USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.) 

for storm events analyzed during this study ..........................................................................28

12. Graph showing peak discharges from SWMM4 simulations and observed values 

at USGS streamgage 03337000 (Boneyard Creek at Urbana, Ill.) on the campus 

of the University of Illinois at Urbana-Champaign for storm events analyzed 

during this study..........................................................................................................................30

13. Graph showing peak stages from SWMM4 simulations and observed values 

at USGS gaging station 03337000 (Boneyard Creek at Urbana, Ill.) on the 

campus of the University of Illinois at Urbana-Champaign, for storm events 

analyzed for this study ...............................................................................................................32

14. Graph showing peak stages from SWMM4 simulations and observed values 

at USGS streamgage 03337250 (Boneyard Creek at Race Street, Urbana, Ill.) 

for storm events analyzed during this study ..........................................................................34
v

Tables

1. Selected stormwater improvements in the Boneyard Creek watershed in 

Champaign-Urbana, Ill. ................................................................................................................3

2. Storm-event periods simulated by using the RUNOFF module of the Stormwater 

Management Model (SWMM) on Boneyard Creek in Champaign-Urbana, Ill., 

for this study ..................................................................................................................................6

3. Precipitation depths and resulting stages of flow at USGS streamgage 03337100 

(Boneyard Creek at Lincoln Avenue, Urbana, Ill.) for storm events analyzed 

during this study............................................................................................................................9

4. Observed peak discharges at USGS streamgage 03337100 (Boneyard Creek 

at Lincoln Avenue, Urbana, Ill.) for storm events analyzed during this study ..................10

5. Observed peak discharges and stages at selected streamgages on 

Boneyard Creek, Urbana, Ill., for storm events analyzed during this study......................11

6. Results of discharge measurement uncertainty analysis on selected 

measurements at USGS streamgage 03337100 (Boneyard Creek at 

Lincoln Avenue, Urbana, Ill.).....................................................................................................16

7. Instantaneous-discharge-computation uncertainty components for a 

discharge of 700 cubic feet per second for USGS streamgage 03337100 

(Boneyard Creek at Lincoln Avenue, Urbana, Ill.) .................................................................18

8. Observed peak discharges and their 95-percent confidence intervals, 

assuming a measurement error of 5 percent, at USGS streamgage 03337100 

(Boneyard Creek at Lincoln Avenue, Urbana, Ill.) for storm events analyzed 

during this study..........................................................................................................................22

9. Comparison of simulated and observed peak discharges at USGS streamgage 

03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.) for storm events 

analyzed during this study.........................................................................................................24

10. Simulated peak discharges and differences between simulated and 

observed peak discharges at USGS streamgage 03337100 (Boneyard Creek 

at Lincoln Avenue, Urbana, Ill.) for storm events analyzed during this study ..................26

11. Comparison of simulated and observed peak stages at USGS streamgage 

03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.) for storm events 

analyzed during this study.........................................................................................................29

12. Comparison of simulated and observed peak discharges at USGS 

streamgage 03337000 (Boneyard Creek at Urbana, Ill.) on the campus of 

the University of Illinois at Urbana-Champaign for storm events analyzed 

during this study..........................................................................................................................31

13. Comparison of simulated and observed peak stages at USGS streamgage 

03337000 (Boneyard Creek at Urbana, Ill.) on the campus of the University 

of Illinois at Urbana-Champaign for storm events analyzed during this study.................33

14. Comparison of simulated and observed peak stages at USGS streamgage 

03337250 (Boneyard Creek at Race Street, Urbana, Ill.) for storm events 

analyzed during this study.........................................................................................................35
vi

Conversion Factors and Vertical Datum

Multiply By To obtain

Length

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 0.4047 hectare (ha)

acre 0.004047 square kilometer (km2)

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

acre-foot (acre-ft) 1,233 cubic meter (m3)

Flow rate

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

mile per hour (mi/h) 1.609 kilometer per hour (km/h) 

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 29).
Using Observed Postconstruction Peak Discharges 

to Evaluate a Hydrologic and Hydraulic Design Model, 

Boneyard Creek, Champaign and Urbana, Illinois

By Thomas M. Over, David T. Soong, and Robert R. Holmes, Jr.

Abstract

Boneyard Creek—which drains an urbanized watershed 

in the cities of Champaign and Urbana, Illinois, including part 

of the University of Illinois at Urbana-Champaign (UIUC) 

campus—has historically been prone to flooding. Using the 

Stormwater Management Model (SWMM), a hydrologic and 

hydraulic model of Boneyard Creek was developed for the 

design of the projects making up the first phase of a long-term 

plan for flood control on Boneyard Creek, and the construction 

of the projects was completed in May 2003. The U.S. Geological Survey, in cooperation with the Cities of Champaign 

and Urbana and UIUC, installed and operated stream and rain 

gages in order to obtain data for evaluation of the designmodel simulations. In this study, design-model simulations 

were evaluated by using observed postconstruction precipitation and peak-discharge data.

Between May 2003 and September 2008, five high-flow 

events on Boneyard Creek satisfied the study criterion. The 

five events were simulated with the design model by using 

observed precipitation. The simulations were run with two different values of the parameter controlling the soil moisture at 

the beginning of the storms and two different ways of spatially 

distributing the precipitation, making a total of four simulation 

scenarios. The simulated and observed peak discharges and 

stages were compared at gaged locations along the Creek. The 

discharge at one of these locations was deemed to be critical 

for evaluating the design model. The uncertainty of the measured peak discharge was also estimated at the critical location 

with a method based on linear regression of the stage and discharge relation, an estimate of the uncertainty of the acoustic 

Doppler velocity meter measurements, and the uncertainty of 

the stage measurements.

For four of the five events, the simulated peak discharges 

lie within the 95-percent confidence interval of the observed 

peak discharges at the critical location; the fifth is just outside 

the upper end of this interval. For two of the four simulation 

scenarios, the simulation results for one event at the critical location were numerically unstable in the vicinity of the 

discharge peak. For the remaining scenarios, the simulated 

peak discharges over the five events at the critical location 

differ from the observed peak discharges (simulated minus 

observed) by an average of 7.7 and −1.5 percent, respectively. 

The simulated peak discharges over the four events for which 

all scenarios have numerically stable results at the critical 

location differs from the observed peak discharges (simulated minus observed) by an average of −6.8, 4.0, −5.4, and 

1.5 percent, for the four scenarios, respectively. Overall, the 

discharge peaks simulated for this study at the critical location are approximately balanced between overprediction and 

underprediction and do not indicate significant model bias or 

inaccuracy. Additional comparisons were made by using peak 

stages at the critical location and two additional sites and using 

peak discharges at one additional site. These comparisons 

showed the same pattern of differences between observed and 

simulated values across events but varying biases depending 

on streamgage and measurement type (discharge or stage). 

Altogether, the results from this study show no clear evidence 

that the design model is significantly inaccurate or biased and, 

therefore, no clear evidence that the modeled flood-control 

projects in Champaign and on the University of Illinois 

campus have increased flood stages or discharges downstream 

in Urbana.

Introduction

Boneyard Creek (fig. 1) drains an urbanized watershed of 

approximately 7.45 mi2 that flows, in upstream-to-downstream 

order, through the city of Champaign, Ill., the campus of the 

University of Illinois at Urbana-Champaign (UIUC), and the 

city of Urbana, Ill. Recurrent and increasing flooding problems 

along Boneyard Creek resulted from the land-cover change 

and storm sewerage associated with the urbanization (Wilson, 

1978; Berns, Clancy and Associates, 1998; Chaille and Yen, 

2000). To remedy these problems, several flood-control projects were constructed over the past several decades (table 1). 

These projects began in the late 1950s and early 1960s with 

the construction of the Northwest Diversion Structure, which 

diverts the upper 1.12 mi2

 of drainage directly to the Saline 
88°16' 88°15' 88°14' 88°13' 8

40°07' 40°06' 0 

0 0.5 

WATERSHED BOUNDARY

Champaign City 

Boundary

Urbana City 

Boundary

Healey Streetdetentionbasin

Dorner Drivedetentionbasin 

Eureka-Elmdetention basin

Oak-Ashdetentionbasin

Boneyard Creek

SW Branch

West Fork

Campustowninlinestorage

University of Illinoischannel improvements

Neil Street

Neil Street

University Avenue

Springfield Avenue

Green Street

Wright Street

Bradley Avenue

Cunningham Avenue

Vine Street Florida Avenue Kirby Avenue

Lincoln Avenue

Prospect Avenue

Fourth Street

First Street

University of Illinois

Base from U.S. Census Bureau, U.S. Department of Commerce TIGER Line Files, 2006 Second Edition, Illinois, Champaign County.

o o o Albers Equal-Area Conic projection, central meridian -89 , standard parallels 33 and 45 .

Race Street

Urbana Mrain gage(station 4

Healey Street rain gage(station 400610088152501) Campus

streamgage and rain gage(station 03337000)

Lincoln Avenuestreamgage(station 03337100)

Race Streetstreamgage(station 033372

EXPLANATION

Northwest 

diversion 

structure

U.S. Geological Survey (USGS) rain gageUSGS streamgageColocated USGS streamgage and rain gage

Figure 1.

Figure 1. Boneyard Creek watershed in Champaign-Urbana, Ill., and locations of flood-control improvements, U.S. Geological Survey (USGS) rain ga
Introduction 3

Branch (fig. 1), and the deepening and widening of the channel in Urbana. In 1980s and 1990s, two detention basins were 

built in Champaign (Oak-Ash and Eureka-Elm) and one on the 

UIUC campus (Dorner Drive).

In the 1990s, an additional set of flood-control projects 

comprising Phase I of five planned phases of further Boneyard Creek improvement projects by the City of Champaign 

were designed. As part of the design process, simulations of 

the Stormwater Management Model (SWMM) were used to 

test the behavior of the system with the designed changes in 

place. These projects, consisting of channel improvements and 

detention facilities (including work by UIUC) and constructed 

between 1998 and May 2003, were designed to address 

flooding problems in Champaign and on the UIUC campus 

while not increasing flooding downstream in Urbana (Berns, 

Clancy and Associates, 1998). Nevertheless, when originally 

proposed, the projects met with public controversy, and the 

City of Urbana commissioned reviews of the design and the 

associated modeling (Rust Environment & Infrastructure, 

1997, 1998). 

As an extension of this review of the projects, the 

U.S. Geological Survey, in cooperation with the Cities of 

Champaign and Urbana and with UIUC, installed and operated 

rain gages and streamgages to evaluate the design model after 

construction. The study began in 2000 with the installation 

of supplementary rain, stage, and streamgages. In 2008, after 

five peak discharges at the Lincoln Avenue streamgage were 

determined to exceed the qualifying magnitude of 696 ft3/s 

(the estimated 0.20-probability annual maximum flood; Jeff 

Smith, City of Champaign, written commun., 1999), the 

evaluation of design model simulations began. This part of the 

study included the use of existing precipitation and streamgage 

data in addition to data from the supplementary study gages. 

The uncertainties inherent in the observation of precipitation 

and streamflow data and the effect of the antecedent moisture 

condition of the watershed and its uncertainty were considered 

in the study design.

Technical Approach

In order to evaluate the accuracy of the design model 

predictions of the effects of the Phase I flood-control projects, 

postconstruction observed events were simulated for this study 

by using the design model, as modified to represent the asbuilt conditions. Other approaches for evaluating the impact of 

the flood-control projects were considered but were determined to be infeasible. An empirical approach for evaluating 

the effects of the flood-control projects would require data that 

would have to have been obtained before construction. For 

example, if similar storms before and after the Phase I projects 

were to be compared, adequate precipitation data during both 

pre- and post-project periods would be needed to characterize the rainfall events as well as streamflow at the location(s) 

of interest. The similar-storms approach would also require 

subjective judgments of “similarity” between events because 

of the complex structure of precipitation and antecedent soil 

moisture in space and time. A flood-frequency approach would 

require only streamflow data, but those data would need to be 

available at the relevant location(s) and for a sufficient period 

with stationary watershed conditions in both the pre- and postproject periods to make the analysis valid.

On Boneyard Creek, streamflow data have been collected by the USGS since 1948 at a streamgage downstream 

from Wright Street on the UIUC campus (station 03337000, 

labeled as the Campus streamgage in fig. 1), but precipitation 

data during this period are spatially and temporally insufficient 

because only one recording rain gage was available, and it is 

Table 1. Selected stormwater improvements in the Boneyard Creek watershed in Champaign-Urbana, Ill.

[mi2, square miles; acre-ft, acre-feet; ft, feet]

Year Description

1960 Northwest Diversion Structure completed. Diverts upper 1.12 mi2 of the watershed directly into the Saline Branch.

1963–64 Boneyard Creek main channel is deepened in Urbana by 4–5 feet from Lincoln Avenue downstream to Race Street, 

leaving a drop a Lincoln Avenue. Channel cross section is changed to a rectangular section with sheet-piling walls and 

concrete bottom.

1980–97 Three stormwater detention facilities constructed in the Boneyard Creek watershed: Oak-Ash (59 acre-ft), Eureka-Elm 

(14.6 acre-ft), and Dorner Drive (12 acre-ft). 

1998–May 2003 Phase I of Champaign’s Boneyard Improvement Plan is constructed. Champaign constructs 114 acre-ft detention basin 

at Healey Street and buries and enlarges approximately 2,700 ft of the Boneyard Creek through Campustown (ending 

at Wright Street), providing an additional 20 acre-ft of detention storage and estimated 25- to 100-year flood protection. A flow restrictor is installed at Wright Street to offset the additional flow capacity provided by the Campustown 

improvements not offset by Healey detention. UIUC lowers and widens 2,600 ft of the channel through its campus 

(Wright Street to Lincoln Avenue), eliminating the drop at Lincoln Avenue.

September 2008 Construction begins on Phase II of Champaign’s long-range Boneyard Improvement Plan.
4 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

southwest of the watershed boundary. Because the storms that 

typically induce the highest peak flows for Boneyard Creek 

are summer convective thunderstorms, one rain gage outside 

the basin is inadequate to represent the spatially heterogeneous rainfall that accompanies convective thunderstorms in 

the Midwestern United States. Furthermore, the ideal location for the streamgage on which to base an evaluation would 

be at Lincoln Avenue in Urbana, about 2,000 ft downstream 

from the Campus streamgage, because that location is at 

the downstream end of the part of the watershed where the 

Phase I flood-control projects were constructed. In addition, 

as is evident from table 1, the Boneyard Creek watershed has 

had numerous hydrologic alterations throughout its history, 

so it fails to have the stationary watershed conditions that 

are needed for a valid comparison by the flood-frequency 

approach.

Because adequate preproject hydrologic data do not 

exist in the study area to implement an empirical approach to 

project evaluation by preproject and postproject comparison, 

it was necessary to use an alternative approach. The approach 

described herein is based on evaluating the model used to 

design the projects. The design and permitting of the Boneyard 

flood-control projects were predicated on the assumption of 

the accuracy of Stormwater Management Model (SWMM) 

results used in the design process to estimate peak discharges 

for a given set of (design storm) rainfall inputs. This assumption can be validated if the accuracy of SWMM model can 

be demonstrated in simulating storm events in the real-world 

conditions represented in the model; that is, the conditions of 

the post-project period. This approach requires precipitation 

and streamflow data to be collected during only the post-project period, and it requires these data only for several events of 

appropriate magnitude, rather than for a long series of stationary conditions as in the flood-frequency approach; furthermore, it does not rely on evaluations of storms subjectively 

defined as “similar.”

The magnitude of qualifying events for the study 

(696 ft3/s), the estimated 0.20 probability annual maximum 

flood at station 03337000, was selected at a relatively low 

value because this implies that it was likely to be exceeded at 

least a few times in a reasonable period of time (the observation period for the study was set to end after three qualifying 

events or 10 years, whichever came first) and because higher, 

out-of-bank flows would make the discharge measurements 

much more challenging. The selected magnitude turned out 

to have been well chosen, because the first qualifying event 

occurred in July 2003, just two months after the Phase I projects were completed, followed by a second in June 2007 and 

then three in 2008, with the last occurring just as construction 

of the next phase of flood-control projects was about to begin, 

which would significantly change the conditions in the Creek 

and invalidate further comparisons. The relatively high probability of the floods that are analyzed in this study however also 

leaves some uncertainty regarding how the model and observations would compare for higher, less probable flood events. 

Purpose and Scope

The results of the Boneyard Creek design simulation 

model evaluation study by the USGS, in cooperation with the 

Cities of Champaign and Urbana and the UIUC, are reported 

herein. An estimated uncertainty of the peak discharges at the 

critical location was determined and is presented as a 95-percent confidence interval, along with the design model simulation results. The uncertainty introduced by rain gages sampling 

a spatially variable rainfall field is addressed approximately 

through comparing separate simulations with spatially uniform 

and spatially variable precipitation inputs to the model. Atgage uncertainty in precipitation measurement is not explicitly 

addressed; instead, a multiple-event sample is simulated to 

control for the errors in representing highly variable rainfall 

field with a necessarily limited number of rain gages. The 

antecedent moisture condition of the watershed was estimated by beginning the simulation during the event prior 

to the event of interest; simulations using two values of the 

parameter controlling the recovery of soil infiltration capacity 

during the dry period between the events were done to assess 

the sensitivity of the model results to the uncertainty of the 

moisture condition. The design simulation model is considered 

to be accurate or conservative if the simulated peaks of the 

observed flow events are within or greater than the 95-percent 

confidence intervals of the observed peak discharges. Results 

of comparisons between simulated and observed stages at the 

critical location and between simulated and observed discharge and stage at additional streamgages along the Creek 

also are presented.
Methodology 5

Methodology

The basic methodology of this study consists of modeling the response of flows in Boneyard Creek to observed 

precipitation events by means of the model used to design the 

1998–2003 Boneyard Creek improvements and comparing 

the modeled and observed peak discharges and stages at the 

USGS streamgage on Boneyard Creek at Lincoln Avenue in 

Urbana (taking into account the uncertainty in the computation 

of the observed discharge) and at supplementary streamgages 

on the UIUC campus and at Race Street in Urbana. This section describes the use of the design model in this study, the 

precipitation and streamflow data and their processing, and 

the method used to estimate the uncertainty in the observed 

peak discharges. 

Modeling With the Stormwater Management 

Model (SWMM)

As described in Berns, Clancy and Associates (1998), 

the model development for the design of the Phase I Boneyard Creek flood-control improvements was completed by 

Camp Dresser & McKee, Inc. (CDM), by using the SWMM4 

model with design-storm precipitation with annual exceedance probabilities down to 1 percent (the 100-year flood) 

based on the methods and data given in Illinois State Water 

Survey Bulletin 70, Circular 172, and Circular 173 (Huff and 

Angel, 1989a,b; Huff, 1990). The version of SWMM4 used 

was an in-house CDM version called CDMSWMM that did 

not include the final design of the UIUC channel (Pat Lach, 

CDM, written commun., May 7, 2004). After the final design 

and construction of the UIUC channel, CDM staff updated 

the geometry of the model to include the as-built properties of 

the channel, updated the input file to make it compatible with 

SWMM4.4H (which was by then the official public version 

of SWMM and which included many of the features added by 

CDM to CDMSWMM), and provided the model to the USGS. 

This as-built SWMM4.4H model was taken as the design 

model to be evaluated in this study. In 2005, EPA released a 

complete rewrite of SWMM as SWMM5, but the cooperators 

and the USGS agreed that there was a strong likelihood that a 

SWMM5 version of the model would be substantially different from the SWMM4 design model and therefore would be 

inconsistent with the objective of the study. 

The SWMM4 model system contains seven individual 

modules (James and others, 2003); this study makes use of 

the modules for precipitation analysis (RAIN module), runoff 

generation (RUNOFF module), and extended transport analysis (EXTRAN module). The RAIN module formats rainfall 

data for use as input to the RUNOFF module. The RUNOFF 

module simulates the generation and hydrologic routing of 

runoff, including all the basic hydrologic processes: precipitation, snow accumulation and melting, evaporation, infiltration, 

groundwater/surface-water interaction, and hydrologic routing 

of runoff overland and through pipes. The model system also 

includes a water-quality component to simulate the transport 

of constituents of interest in the runoff. Because flood events 

on Boneyard Creek generally result from summer thunderstorms and base flow in the creek is small and therefore does 

not contribute significantly to flood flows, groundwater and 

snow are not simulated in the Boneyard SWMM model. Water 

quality is likewise not addressed in this model. 

Infiltration in the SWMM RUNOFF module as implemented for the Boneyard model is simulated by the Horton 

infiltration equation. The associated parameters depend on 

land use, soil type, and the antecedent moisture condition 

of the soil; determination of the associated parameters is 

described in Berns, Clancy and Associates (1998). All RUNOFF parameter values were maintained as found in the final 

SWMM4.4H model except the following, which were changed 

to enable use of the model for simulating observed events 

rather than in a design-storm mode: (1) evaporation parameters were modified to reflect the month in which each observed 

event occurred, and (2) the parameter REGEN [dimensionless], defined as the ratio of the exponential decay rate [T-1] at 

which soil infiltration capacity is regenerated to the exponential decay rate [T-1] at which soil infiltration capacity decays 

during infiltration, was modified. The REGEN parameter is 

irrelevant for simulating design storms and had been given the 

default value of 0.01; this value appeared to perhaps allow for 

the infiltration capacity to regenerate too quickly given the soil 

characteristics in the Boneyard watershed (following the guidance in James and others, 2003). Therefore results from using 

REGEN values of 0.01 and 0.001 are presented in this report.

The other change in the use of the RUNOFF module 

between the design-storm mode and the observed-event mode 

used in this study is in the setting of the antecedent moisture 

condition for the soil, which affects the initial value of the 

infiltration capacity in the Horton infiltration equation. In the 

design model, this condition was taken as type II or “average.” 

For observed events simulated here, the intent is to match 

conditions as they actually were at the beginning of the storm. 

Rather than changing the Horton parameters as determined 

by CDM for the design model, in this study the antecedent 

moisture condition was simulated by means of a continuous 

simulation approach: the RUNOFF modeling was initialized 

at average conditions at the beginning of the rain event prior 

to each peak event of interest (usually a few days earlier; 

see table 2). During this prior event and the intervening dry 

period, the infiltration capacity decayed and then was regenerated (at a rate depending on the value of REGEN as discussed 

above) so that in this way it was adjusted to the approximate 

conditions that actually led up to the peak event of interest.

Using the discharges simulated by the RUNOFF module 

as input, the EXTRAN module simulates the one-dimensional 

gradually varied unsteady flow of water based on the conservation of mass and momentum through a network of 

links (pipes and open channels) connected by nodes (usually 

manholes) and other system components including weirs, 

pumps, orifices, storage basins, and outfall structures. The 

basic differential equations are then solved in finite-difference 
6 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Table 2. Storm-event periods simulated by using the RUNOFF module of the Stormwater Management Model 

(SWMM) on Boneyard Creek in Champaign-Urbana, Ill., for this study.

Date of peak discharge

(month/day/year)

Begin date of storm-event simulation 

(month/day/year)

End date of storm-event simulation 

(month/day/year)

07/09/2003 07/08/2003a 07/11/2003

06/26/2007 06/21/2007 06/28/2007

06/03/2008 05/30/2008 06/05/2008

07/08/2008 07/02/2008 07/09/2008

09/14/2008 09/11/2008 09/16/2008

a

This event included three smaller storms in the 24 hours prior to the storm causing the event peak, so beginning the simulation 

period just the day before the peak event was deemed sufficient to set the antecedent moisture condition for the peak event.

form. Three numerical solution schemes are available in 

SWMM4: these are called “explicit” (parameter ISOL = 0), 

“enhanced explicit” (ISOL = 1), and “iterative” (ISOL = 2). 

The EXTRAN model provided by CDM used the explicit 

method with a timestep (parameter DELT) of 0.1 second. The 

EXTRAN runs required considerable computer time (on the 

order of an hour on a desktop PC running Windows XP) and 

encountered occasional problems with numerical stability in 

the simulation of the selected observed events; therefore, other 

values of ISOL and DELT were tested. However, the values 

of ISOL and DELT from the original model were found to 

have the best stability and were used for all the results shown 

in this report. All other EXTRAN geometric and numerical 

parameters were maintained as in the final SWMM4.4H model 

provided by CDM.

Sources and Processing of Data

Precipitation Data

Precipitation data available to this study include continuous records at 5-minute intervals at three tipping-bucket 

rain gages operated by the USGS as part of this study and a 

variable number of daily nonrecording rain gages operated 

by volunteers in the Boneyard Precipitation Network (BYN) 

(http://www.isws.illinois.edu/atmos/boneyard/). The USGSoperated rain gages used are those at Healey Street (USGS 

station 400641088152501), at the Campus streamgage 

(USGS station 03337000), and at Urbana Middle School 

(USGS station 400610088122201). Their data were obtained 

from the internal USGS ADAPS database. Until the incorporation of the BYN into the Community Cooperative Rain, 

Hail, and Snow (CoCoRAHS) network in November 2008, 

the BYN used wedge-shaped gages that were usually read 

at 7:00 a.m. local standard time (Westcott and others, 2008). 

Despite the differences in the recording intervals, the two 

sources complement each other to provide better spatial coverage of precipitation for the Boneyard Creek watershed. 

Because the runoff events being evaluated in this study 

are caused by short-duration, high-intensity summer convective rainfall events—which generally last, at most, a few 

hours—and the highest flows correspond to the heaviest rainfall intensity—which usually occurred within a period of 1–

2 hours—the precipitation inputs used in the simulations were 

at a 5-minute interval corresponding to the measurements at 

the USGS rain gages. Disaggregating the daily data from the 

BYN stations to the 5-minute time interval was accomplished 

by following the temporal distribution of the nearest USGS 

rain gage but preserving the daily total depth of each gage. 

Assigning precipitation time series to subbasins to represent 

spatial distribution of a rainstorm was achieved by using the 

Thiessen (1911) polygon approach (fig. 2). The USGS rain 

gage at Urbana Middle School was generally found to record 

anomalously low depths, so it was not used for distributing 

precipitation spatially; however, its time pattern was used 

for disaggregation. 

The spatial distribution of precipitation obtained by 

applying the Thiessen polygon method was used in both 

spatially uniform and spatially variable modes. In the spatially 

uniform mode, the fraction of the basin lying inside each 

polygon was used as a weight to obtain a spatial average value 

for each time step that was applied uniformly to the entire 

simulated watershed. In the spatially variable mode, at each 

time step, each subbasin was assigned the precipitation depth 

in the polygon in which it lies so that the precipitation was 

spatially variable. The spatially uniform mode corresponds to 

the spatial structure of the design storms used for simulating 

the system during the design phase, whereas the spatially variable mode should provide a more realistic representation of 

the actual storm event.

The scope of this study does not include a direct assessment of precipitation-measurement uncertainty or its effects; 

however, one particular phenomenon that can lead to a 

significant negative bias during thunderstorms or other windy 

periods—wind-induced gage catch deficiency—was examined. Wind data from the Automated Surface Observing System (ASOS) at Willard Airport in Champaign were obtained 
0 

0 0.5 

88°16' 88°15' 88°14' 88°13' 8

40°07'40°06'

Base from U.S. Census Bureau, U.S. Department of Commerce TIGER Line Files, 2006 Second Edition, Illinois, Champaign County.

o o o Albers Equal-Area Conic projection, central meridian -89 , standard parallels 33 and 45 .

Sub-basin boundaries from Berns, Clancy and Associates, P.C., Urbana, Illinois.

E

U.S. GBoneBoneSubbStorm Thies

CP-9

WILL

NEW 

(CP-12)

CP-17

Healey Street(station 400610088152501) Campus (station 03337000)

Figure 2. Figure 2. Example of Thiessen polygons covering subbasins in the Boneyard Creek Stormwater Management Model (SWMM). The group of subbas

polygon is shown by using a distinct color.
8 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

from Weather Underground (http://www.wunderground.com/) 

during the qualifying storm events to characterize the possible 

gage catch deficiency. These data show that all five of the 

events were associated with elevated wind speeds, with typical wind speeds of 10–20 mi/h and gusts to at least 30 mi/h. 

For reference, the approximate expected undercatch for an 

unshielded gage is about 10 percent at 10 mi/h and 20 percent at 20 mi/h (Larson and Peck, 1974). However, because 

no gage catch deficiency correction was made to the design 

storms in Bulletin 70 (Huff and Angel, 1989a; Jim Angel, 

Illinois State Water Survey, written commun., 2010) and 

because the wind measurement at Willard Airport is in an 

open field at a 10-m height whereas the rain gages used in this 

study are usually in more sheltered conditions at a much lower 

height, it was concluded that (a) it is unclear if correction of 

the precipitation data for wind-induced gage catch deficiency 

is appropriate and (b) choosing the appropriate magnitude of 

such a correction would be difficult. Therefore, no such correction was made.

Stream-Discharge and Stage Data

In accordance with the study design, the discharge data 

from the streamgage on Boneyard Creek at Lincoln Avenue 

(USGS station 03337100) were the primary data used to 

evaluate the performance of design model. Some further 

details regarding this streamgage are warranted because of 

the importance of the peaks recorded there for this study. 

The streamgage began operation on December 11, 2001. The 

relevant equipment installed consisted of a continuous pressure sensor (for computing stage), a two-path acoustic velocity 

meter (AVM), and a crest-stage gage. On May 5, 2003, the 

temporary cofferdam upstream from the gage was removed at 

the end of the Boneyard Creek Phase I improvements project. 

On September 23, 2004, an uplooking acoustic Doppler velocity meter (ADVM) was installed on the bottom of the channel 

along with a 6- by 6-in. angle iron to provide low-flow control. 

The AVM proved to be unreliable partly because its measurement paths were submerged only intermittently, and it was 

removed on November 9, 2005. 

Acoustic technology designed to measure velocity was 

installed at this site because of the intermittent backwater 

affecting the stage-discharge relation caused by the 54-in. 

storm sewer that drains into Boneyard Creek under the 

Lincoln Avenue bridge just downstream from the gage. The 

ADVM did not successfully record the peak flows of interest, 

so discharge computations at the gage throughout its period 

of operation have been by means of stage-discharge ratings 

(SDRs), which are constructed by fitting a smooth curve to 

field-measured discharges and their corresponding stages 

(gage heights) (fig. 3). SDR 1 was based on the 24 measurements made in the first water year1

 of operation (ending 

September 30, 2002), with discharges ranging from 2.05 to 

1

“Water year” in USGS reports dealing with surface-water supply is 

the 12-month period October 1 through September 30. The water year is 

designated by the calendar year in which it ends and which includes 9 of the 

12 months. Thus, the year ending September 30, 2008, is called “water year 

2008.”

271 ft3/s (fig. 3). Discharges continued to be computed by 

using SDR 1 until December 28, 2005, when the lower part 

of the rating was revised, creating SDR 2 (fig. 3), as a result 

of new measurements showing the effect of the angle iron 

installed in 2004. SDR 2 was used to compute discharges 

until October 17, 2007, when SDR 3, which adjusted the high 

end of the rating, went into effect (fig. 3). SDR 3 was used 

throughout water year 2008. After three high peak flows in 

summer 2008, SDR 4 was established and went into effect on 

May 13, 2009; SDR 4 is nearly identical to SDR 3 except for 

being extended to higher flows and stages (fig. 3). 

Supplemental data from two additional streamgages on 

Boneyard Creek were also collected for use in this study: 

Boneyard Creek at Urbana (the Campus streamgage, USGS 

station 03337000) and Boneyard Creek at Race Street (USGS 

station 03337250). The Campus streamgage is about 2,000 ft 

upstream from Lincoln Avenue at a pedestrian bridge on the 

campus of the UIUC (fig. 1) and is a source of both stage and 

discharge data, the latter computed from a stage-discharge 

rating in the same general manner as for the gage at Lincoln 

Avenue. As mentioned, this gage has been in operation since 

1948 except for brief outages for maintenance or moving and 

reinstallation. The gage was in its present location for the 

duration of this study. The Race Street streamgage is a stageonly gage about 3,500 ft downstream from the Lincoln Avenue 

streamgage (fig. 1). 

Events Selected for Analysis

Between May 2003, when the Phase I flood-control 

improvements were completed, and September 2008, when 

construction of the Phase II improvements began, five events 

officially exceeded the 696-ft3/s threshold at Lincoln Avenue. Information regarding these events is given in table 3, 

including the date and time, the gage height and corresponding elevation, and the estimated depth of precipitation that 

occurred over the watershed during three periods prior to the 

peak discharge. The peak discharges themselves are listed in 

table 4. The first precipitation period presented in table 3 was 

selected as the 2 hours before the peak because all the high 

flow events were preceded by significant precipitation events 

of 1–2 hours’ duration. The additional two precipitation periods of 24 hours’ duration were selected to give an indication 

of antecedent soil-moisture conditions before the precipitation 

event causing the high flow.

Table 4 lists the official observed peak discharges (where 

an official peak is defined as the published annual maximum 

peak discharge or the value that would have been published 

as the annual maximum peak if it had been the largest) and 

some alternative values for observed peak discharge that are 

obtained depending on two factors: (1) the SDR used and 

(2) the application of shifts. Because the streamgage on Boneyard Creek at Lincoln Avenue is relatively new, ratings have 
Methodology 9

been recomputed regularly as additional discharge measurements have been made. Because SDR 4 is the newest rating 

and no channel modifications affecting the high flow stagedischarge relation have been made over the period considered 

in this study, adjusting the peak discharges to the values they 

would have by using SDR 4 constitutes the best available 

information. Therefore, SDR 4 peak discharges are used as the 

basis for comparison in this report. It can be seen from table 4

that switching from SDRs 1 and 2 to SDR 4 has an appreciable 

effect on the first two events; however, for the last three events 

(which occurred in 2008 and whose discharges were computed 

by using SDR 3), the effect of switching to SDR 4 is quite 

small. The issue of shifts is addressed next.

0

200

400

600

800

1,000

1,200

5 7 9 11 13 15 17 19 21

Gage height, in feet

Rated discharge, in cubic feet per second

Stage-discharge rating 1

ating 2

ating 3

ating 4

Stage-discharge r

Stage-discharge r

Stage-discharge r

Figure 3.

EXPLANATION

Figure 3. Stage-discharge ratings used for USGS streamgage 03337100 (Boneyard Creek at Lincoln 

Avenue, Urbana, Ill.), water years 2002 through 2009.

Ill.) for storm events analyzed during this study.

 [in., inches; ft, feet; NGVD 29, National Geodetic Vertical Datum of 1929]

Table 3. Precipitation depths and resulting stages of flow at USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, Urbana, 

Occurrence of observed 

peak discharge

Stage of observed 

peak discharge

Depth of storm precipitationa

(in.)

Date

(month/day/year)

Time

(hour/minutes)

Gage height

(ft)

Elevation

(ft, NGVD 29)

2 hours prior to 

peak discharge

2–26 hours prior to 

peak discharge

26–50 hours prior 

to peak discharge

07/09/2003 17:55 17.00 711.00 2.54 2.83 0.00

06/26/2007 10:34 14.63 708.63 1.35 0.02 0.00

06/03/2008 05:14 16.80 710.80 1.45 0.39 0.00

07/08/2008 17:54 16.29 710.29 2.13 0.00 1.39

09/14/2008 09:56 17.26 711.26 2.15 1.20 0.22

a

Precipitation depths appearing in this table are watershed-average values obtained by using the Thiessen polygon method.
10 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Only one of the qualifying events, on June 26, 2007, 

required application of a shift in the computation of its official 

peak discharge (table 4). Shifts are adjustments to ratings to 

account for temporary changes in the elevation of the hydraulic control at a streamgage, such as would be caused by the 

accumulation of debris on the control during a flood. For the 

Boneyard Creek at Lincoln Avenue streamgage, shifts have 

been applied usually to account for the effects of the 54-in. 

storm drain that discharges into the creek just downstream 

from the gage. Because the flow from this storm drain is 

unmeasured, its effects are observed only when a discharge 

measurement is made. For this event, the peak stage occurred 

at 10:34 a.m., and a measurement was made between 10:47 

and 10:55 a.m. To make the measurement (discharge of 

653 ft3/s at a gage height of 13.83 ft) lie on the rating curve 

that was then in use (SDR 2), the stage had to be increased 

(shifted) by 1.28 ft (fig. 4). The same shift was applied for 

the official discharge computation because the peak stage had 

occurred so recently, raising the computed discharge from 

the SDR 2 value at a gage height of 14.63 of 616 ft3/s to the 

official value of 714 ft3/s. If no shift had been applied, the 

value at the time of the peak stage (616 ft3/s) would have been 

less than the measured value when the stage was only 13.83 ft. 

Applying the newest rating, SDR 4, the peak discharge at 

the observed stage without application of a shift would be 

652 ft3/s, about the same as the discharge measured 15 minutes 

later when the stage was 0.80 ft lower.

The peak discharge for the June 26, 2007 event computed without a shift would be correct only if the measured 

discharge were erroneously high or the drop in stage was the 

result of the reduction in flow from the storm drain under the 

bridge rather than a reduction in discharge in the creek. Both 

conditions are possible. Measurement uncertainty is addressed 

later in this report. Regarding the effect of the storm-drain discharge, a positive shift is anomalous in this situation because 

adjusting for the backwater caused by the discharge would 

require a negative shift, not a positive one. Indeed, the 2007 

station analysis (an internal USGS document discussing the 

year’s measurements at a streamgage) notes that “the measurement probably indicates a temporary condition of increased 

fall due to lack of inflow downstream.” The question remains 

whether the magnitude of this increased fall was as large at the 

time of the peak as at the time of the measurement. According 

to the notes from this measurement, eight transect measurements were made with an acoustic Doppler current profiler 

(ADCP), with a mean discharge of 653 ft3

/s and a standard 

deviation of 46.7 ft3/s between 10:47 and 10:55. The gage 

height fell from 14.14 to 13.55 ft from 10:46 to 10:56, but the 

transect discharges do not show a significant trend, indicating 

that at least part of the decrease in stage between the peak and 

the measurement is unrelated to a decrease in discharge and 

suggesting that at least part of the shift is unnecessary and the 

official discharge may be overestimated. On the basis of this 

analysis, the peak discharge using SDR 4 without a shift being 

applied (table 4, last column, 652 ft3/s) is used as the basis for 

the comparison of the simulated peak discharge with the confidence interval of the observed peak discharge for this event.

The complete set of observed peak discharge and stage 

observations for the three streamgages and five events used in 

this study is presented in table 5. Comparison of these values 

confirms that discharge is increasing and stage is decreasing in the downstream direction, as expected. Comparisons 

with the corresponding simulated values are presented in the 

“Comparison of Simulated and Observed Peak Discharges and 

Stages” section.

Table 4. Observed peak discharges at USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.) for storm events 

analyzed during this study. 

[ft, feet; ft3/s, cubic feet per second; SDR, stage-discharge rating; — , not applicable]

Event date 

(month / day / year)

Peak gage height 

(ft)

Officiala

 peak 

discharge 

(ft3

/s)

Identification 

number of SDR used 

to compute official 

peak discharge

Shift applied to 

official peak 

discharge 

(ft) stage

Peak discharge 

using official SDR 

but no shift 

(ft3

/s)

Peak discharge 

using SDR 4 

and no shift 

(ft3

/s)

07/09/2003

06/26/2007

17.00

14.63

797

714

1

2

0.00

1.28

— 

616

856

652

06/03/2008 16.80 837 3 0.00 — 842

07/08/2008

09/14/2008

16.29

17.26

793

877

3

3

0.00

0.00

— 

— 

793

878

a

The official peak discharge is defined as the published annual maximum peak discharge, or the value that would have been published as the annual maximum 

peak, if it had been the largest that water year. 
Methodology 11

Figure 4.

400

450

500

550

600

650

700

750

800

850

900

13 13.5 14 14.5 15 15.5 16 16.5 17

Gage height, in feet

Rated discharge, in cubic feet per second

Stage-discharge rating 1

Stage-discharge rating 2

Stage-discharge rating 3

Stage-discharge rating 4

Peak discharge - 1.28 foot shift - rating 2

Peak discharge - No shift - rating 2

Peak discharge - rating 4

Measured discharge

1.28 ft

1.28 ft

13.83

14.63

15.11

15.91

714

653

652

616

EXPLANATION

Figure 4. Computation of alternative estimates of peak discharge for the June 26, 2007, high-flow event at USGS streamgage 

03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.).

Table 5. Observed peak discharges and stages at selected streamgages on Boneyard Creek, Urbana, Ill., 

for storm events analyzed during this study. 

[ft, feet; ft3/s, cubic feet per second; NGVD 29, National Geodetic Vertical Datum of 1929]

Peak discharge (ft3/s) Peak stage (ft, NGVD 29)

Event date 

(month/day/year)

Lincoln Avenue Campus gage gage (station 03337000) (station 03337100)Lincoln Avenue Campus gage Race Street gage gage (station 03337000) (station 03337250) (station 03337100)

07/09/2003 780 856 712.59 711.00 705.68

06/26/2007 571 652 710.76 708.63 703.41

06/03/2008 727 842 712.13 710.80 705.06

07/08/2008 686 793 711.78 710.29 705.26

09/14/2008 812 878 712.85 711.26 705.30
12 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Discharge-Uncertainty Analysis

A modification of the method proposed by Dymond and 

Christian (1982) was selected for estimating the observed 

discharge uncertainty at Lincoln Avenue. The quantity to be 

computed is σ2

Q , the variance of an instantaneous discharge 

value computed by using a stage-discharge rating. The original 

method of Dymond and Christian was developed to apply 

under the following conditions: (1) discharges are estimated 

by using a stage-discharge rating curve that can be approximated with the power-law functional form Q = a′(h – h0 )b′, 

where Q is discharge, h is stage, h0 is stage when discharge is 

zero (assumed known), and a′ and b′ are parameters to be estimated by using ordinary least-squares (OLS) regression after 

taking logs of both sides of the rating curve; and (2) ratingcurve shifts are random and not persistent between events. 

The method considers uncertainty (or “error”) resulting from 

three main sources: (1) error in the measurement of stage, 

(2) error resulting from “ignoring all physical parameters other 

than [stage],” which will be termed “model error” herein, and 

(3) error in the rating curve.

Strictly speaking, the presence of stage-measurement 

error in an OLS framework is not statistically valid, because 

the effect of measurement error on the x-axis of a regression 

requires a generalized form of least-squares regression, an 

“errors-in-variables model” (Brent Troutman, U.S. Geological Survey, written commun., 2010; Draper and Smith, 1981; 

Fuller, 1987). Draper and Smith (1981, p. 122–125) and Fuller 

(1987, p. 1–5), however, show that the effect of such errors 

is proportional to the ratio between the x-axis variable’s error 

and its range. In the present case, the stage-measurement error 

is about 0.04 ft while the range of stages being considered is 

3–7 ft, implying a very small effect, so the uncertainty computation in the OLS framework as presented by Dymond and 

Christian (1982) is retained as an approximation.

In the present application, the following modification of 

the Dymond and Christian (1982) method is made: because 

the rating curve is well approximated by a straight line, that 

is, Q = a′(h – h0 )b′ with b′ = 1, the rating-curve regression 

employs the functional form Q = a + bh. With this modification, the uncertainty estimation method can be expressed as

σ 2

Q = σ 2QΔh

 + σ 2

θ

 + σ 2

mr (1)

where σ 2

QΔh

 is the discharge uncertainty resulting from stagemeasurement uncertainty, σ 2

θ

 is model error variance, and σ 2

mr is 

rating-curve error variance.

The computation of each term in equation 1 will now be 

discussed. The discharge uncertainty resulting from stagemeasurement uncertainty is given by

σ 2

QΔh

 = b2σ 2

Δh (2)

where b is, as before, the slope of the rating curve and σ 2

Δh is 

the variance of the stage-measurement error Δh. An examination of the gage-height corrections given in the station 

analyses for Boneyard Creek at Lincoln Avenue shows that a 

good estimate, SΔh

, of the stage-measurement error (σΔh) would 

be 0.04 ft, giving a stage-measurement error variance estimate 

S2

Δh of 0.042

 = 0.0016 ft2. 

The model error variance σ 2

θ is computed as

σ σ θ ε σ σ 2 2 2 2 = −  − 0  

 max , Q Q ∆h m ∆ (3)

where σ 2

ε

 is the variance of the error term (ε) of the regression 

equation and ΔQm is the discharge-measurement error; that is, 

the uncertainty in the measured discharges used to construct 

the rating curve. The maximum function max [] is used in 

equation 3 to prevent the value of the model error variance 

σ 2

θ from becoming negative when the sum of the dischargemeasurement error variance σ 2

ΔQm and the stage-measurement 

error contribution σ 2

QΔh exceeds the regression error variance 

σ 2

ε

. If this does occur, it also suggests some problem because it 

would imply that there is no model error. Most likely in such a 

case, the discharge-measurement error will have been overestimated, assuming stage-measurement error contribution is 

small.

The regression error term σ 2

ε

 is estimated by the squared 

standard error S2

ε of the regression,

σε ε

2 2 2

1

1

2 ≈ = − ( ) − =

S ∑ n y ŷ i i

i

n

where yi, i = 1, 2, . . . , n are the observed y values (the measured discharges) and ŷi

 are y values predicted by the regression equation; that is, ŷi = a + bxi , where xi

 are the observed 

stages (that is, xi = hi). 

The other component, rating-curve error σ 2

mr, is estimated 

by using the standard result for the uncertainty of the estimation of the mean value of Y given a certain value, X0

, of X in 

OLS regression (see, for example, Draper and Smith, 1981, 

equations 1.4.9–1.4.10):

σ (5) mr mr ε

i

i

n S S

n

X X

X X

2 2 2 0

2

2

1

1 ≈ = + ( ) −

( ) −























 =

∑

Combining the model error and rating-curve error terms 

(equations 1 and 3) gives the uncertainty of a given value of 

discharge σ 2

Q estimated from the stage-discharge rating as

σ

To help in interpretation of this result, notice that if 

S2

ε > S 2ΔQm +S 2QΔh 

, the maximum function may be removed and 

equation 6 may be written as

S S (7)

n

X X

X X

S Q

i

i

n Qm

2 2 0

2

2

1

2 1 1

= + + ( ) −

( ) −

























−

=

∑ ε ∆
Uncertainty of the Observed Peak Discharge on Boneyard Creek at Lincoln Avenue 13

Note that the first term is the uncertainty of an individual (as 

opposed to the mean) predicted value at X0 in OLS regression for the usual case in which the error term in prediction 

is the same as in the observations (in other words, there is no 

measurement error) (Draper and Smith, 1981, equation 1.4.11; 

Helsel and Hirsch, 2002, p. 241). Because the discharge-measurement error will not be present in the predicted value, its 

variance estimate S2

ΔQm is subtracted. 

Uncertainty of the Observed Peak 

Discharge on Boneyard Creek at 

Lincoln Avenue

The discharge uncertainty methodology described above 

relies on three computations: an estimate of the effect of 

stage-measurement error, a rating-curve regression and an 

estimation of measurement uncertainty. The results of these 

computations and their combination to obtain the uncertainty 

of the overall observed peak discharge are described in this 

section. Because the discharges at Lincoln Avenue are of 

primary importance for the evaluation of the design model, the 

uncertainty of the observed peak discharge are computed for 

that streamgage only.

Rating-Curve Regression

Two factors were considered in deciding which measurements to use in computing the rating curves that in turn were 

used to compute discharge-estimation uncertainty. One is that 

the higher discharges are of interest. The other is that two 

modifications were made to the channel near the gage during its period of record: (a) the cofferdam upstream from the 

gage was removed with the completion of the UIUC channel 

improvements in May 2003, and (b) a new channel control 

was installed in September 23, 2004 (a 6- by 6-in. angle iron 

bolted to the channel bottom). The latter modification would 

imply that only measurements after that date should be considered; however, for higher discharges, the installation of the 

angle iron may have little effect because the hydraulic control 

is downstream from it (Kevin K. Johnson, U.S. Geological 

Survey, oral commun., 2010). Linear rating-curve regressions 

for two different groups of measurements were used to compute discharge-estimation uncertainty and are presented here. 

The choice of these groups of measurements was based on the 

timing of the two channel modifications and the objective of 

rating high flows.

The first group consists of measurements between June 

2003 and September 2009 that were made when the depth 

at the gage was greater than 5 ft (equivalent to gage heights 

greater than 12 ft). It comprises 23 values from events 

between June 11, 2003, and May 13, 2009, and discharges 

between 378 and 704 ft3/s. For this range of dates and depths, 

it is assumed that the low-flow channel control installed in 

September 2004 has little effect for such relatively high flows. 

For this group of measurements, the slope of the rating curve, 

b, is about 80.5 (ft3/s)/ft, and the regression standard error, 

Sε, is about 62 ft3/s (fig. 5A). The residuals around this rating curve as a function of time are shown in figure 5B. The 

residuals plot shows a few cases where multiple measurements 

were made during the same event. The wide range of residuals during the same event suggests a looped rating curve; that 

is, a curve for which the relation between stage and discharge 

is not unique. Although some sediment moves through this 

channel, the presence of a concrete channel bottom means that 

the looping is not the result of scouring and filling but instead 

results from hydraulic effects, including the backwater effect 

from discharge of the large storm drain into the creek under 

the Lincoln Avenue bridge. 

The other rating-curve regression considered here 

consists of measurements from water years 2005 through 

2009 (that is, October 1, 2004 through September 30, 2009) 

when the depth at the gage was greater than 1 ft (equivalent 

to gage heights greater than 8 ft). This group of measurements comprises 29 values from events between October 

18, 2004, and May 13, 2009, and discharges between 57.6 

and 704 ft3/s. Because this range of dates includes only the 

period after the installation of the channel control in September 2004, a greater range of depths is included. According to 

this group of measurements, the slope of the rating curve, b, 

is about 86.7 (ft3/s)/ft, and the regression standard error, Sε, 

is about 56 ft3/s (fig. 6A). This regression also shows what is 

only suggested in figure 5: reduced scatter at the midrange 

of flows, approximately 250 to 400 ft3/s. The cause of this 

phenomenon is not clear, but one important implication is that 

the somewhat smaller value of Sε obtained for this rating-curve 

regression may not be not as characteristic of the higher flows 

as the result from the regression shown previously in figure 

5. Because of this concern about the characterization of the 

uncertainty of the higher flows that are of primary interest 

in this study, the final results of the study use the first rating 

curve, shown in figure 5.

The residuals around the second rating curve as a function of time are shown in figure 6B. This plot, like figure 5B, 

shows a few times when multiple measurements were made 

during the same event (in fact, it includes the measurements 

shown in figure 5 over their common period but adds some 

additional measurements, especially during summer 2008).
14 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Figure 5.

A

B

300

350

400

450

500

550

600

650

700

750

12 12.5 13 13.5 14 14.5 15

Stage, in feet

Measured discharge, in cubic feet per second

-150

-100

-50

0

50

100

150

9/16/023/18/039/17/033/18/049/17/043/19/059/18/053/20/069/19/063/21/079/20/073/21/089/20/083/22/099/21/09

Date

Rating curve residuals, in cubic feet per second

Discharge measurement

Rating curve

EXPLANATION

Figure 5. Stage-discharge rating-curve regression for USGS streamgage 03337100 (Boneyard Creek at 

Lincoln Avenue, Urbana, Ill.) using measurements obtained between June 2003 and September 2009 when the 

depth of flow was greater than 5 feet (gage height greater than 12 feet). A, Scatterplot of data and fitted line. 

B, Residuals as a function of time. The parameters obtained are the slope, b = 80.49 cubic feet per second per 

foot, and the regression standard error, Sε

 = 62.2 cubic feet per second.
Uncertainty of the Observed Peak Discharge on Boneyard Creek at Lincoln Avenue 15

A

B

Stage, in feet

Measured dishcarge, in cubic feet per second

-150

-100

-50

0

50

100

150

Date

Rating curve residuals, in cubic feet per second

Figure 6.

3/18/049/17/04

3/19/059/18/05

3/20/069/19/06

3/21/079/20/07

3/21/089/20/08

3/22/099/21/09

0

100

200

300

400

500

600

700

800

8 10 12 14 16

Rating curve

Discharge measurement

EXPLANATION

Figure 6. Stage-discharge rating-curve regression for USGS streamgage station 03337100 (Boneyard Creek 

at Lincoln Avenue, Urbana, Ill.) using measurements obtained during water years 2005 through 2009 when the 

depth of flow was greater than 1 foot (gage height greater than 8 feet). A, Scatterplot of data and fitted line. 

B, Residuals as a function of time. The parameters obtained are the slope, b = 86.68 cubic feet per second per 

foot, and regression standard error, Sε

 = 56.3 cubic feet per second.
16 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Measurement Error Computation

The discharge measurements in the Boneyard Creek at 

Lincoln Avenue rating curve for high flows were generally 

obtained by using a Rio Grande broadband ADCP manufactured by Teledyne RD Instruments (RDI). Estimates of 

the measurement error for four ADCP measurements were 

computed by Luke Fitzgerald of the Office of Surface Water 

(OSW) of the USGS, under the supervision of Kevin Oberg, 

also of OSW, using a spreadsheet provided by Randy Marsden 

of RDI (written commun., 2004, 2005, 2007, 2008, 2009). 

The results of these computations are given in table 6, which 

show values of 2.7 to 3 percent for three of the measurements, including the largest two discharges, and a somewhat 

larger value of 3.65 percent for the measurement with the 

least discharge, most shallow flow depth, and smallest fraction of directly measured discharge. (The remainder—the 

flow in the boundary regions at the top and bottom of the 

water column and along the sides of the channel—cannot be 

measured directly with the ADCP but instead is estimated by 

extrapolation from the measured values next to these areas). 

This measurement also had a significant percentage of invalid 

depth cells2

, which are those depth cells in the measured 

area for which the instrument could not resolve meaningful 

information.

The uncertainty values given in table 6 for these selected 

measurements on Boneyard Creek may be compared with 

the values appearing in general tables, for example, table 

13.3 of Herschy (1999), which gives 5 percent as the “attainable” (minimum) uncertainty in discharge measurement 

at the 95-percent level, which is equivalent to a standard 

deviation of 2.5 percent. These values also may be compared 

with ADCP uncertainty estimates based on comparison with 

reference measurements (current-meter measurements, rated 

2

 A depth cell is a subdivision of the reflected ADCP signal, corresponding 

to a position in the vertical of the measured transect. 

discharges, or rated discharges adjusted by using currentmeter measurements), such as are given in Morlock (1996) 

and Oberg and Mueller (2007). In Morlock’s study (1996), 

31 ADCP measurements made with an early model of an RDI 

ADCP at 12 sites were compared. At 10 of the 12 sites, the 

magnitudes of all the differences were less than 5 percent. 

At the two remaining sites, the magnitudes of the differences were approximately 7 percent when compared with 

rated discharges, but these became 5.1 percent or less when 

the rated discharges were adjusted by using current-meter 

measurements made concurrently with the ADCP measurements, with a standard deviation of 2.7 percent. (This standard 

deviation value is not from Morlock (1996) but was computed 

for this study). Only one site used in Morlock’s study (1996) 

had a reference discharge less than 2,000 ft3/s; at that site, the 

reference discharge was 768 ft3/s, and the ADCP measurements were 758 and 745 ft3

/s, yielding differences of −1.3 and 

−3.0 percent.

In Oberg and Mueller (2007), results from laboratory 

(tow-tank) and field measurements made with several different ADCP models are given. Here we concentrate on the 61 

field measurements at 16 sites Oberg and Mueller obtained by 

using the RDI Rio Grande in Water Mode 12, for which the 

reference discharges ranged from 69.6 to 6,850 ft3/s. These 

measurements were made with the same instrument model 

and water mode as used in the Boneyard Creek measurements 

listed in table 6. For these measurements, differences between 

the ADCP and reference discharges ranged from −15.9 to 

8.7 percent, with a mean of −0.14 percent (not statistically 

different from zero). The standard deviation of the percent differences was 5.8, more than double the values from Herschy 

(1999) and Morlock (1996).In Oberg and Mueller (2007), 

results from laboratory (tow-tank) and field measurements 

made with several different ADCP models are given. Here we 

Table 6. Results of discharge measurement uncertainty analysis on selected measurements at USGS streamgage 03337100 

(Boneyard Creek at Lincoln Avenue, Urbana, Ill.).

[ft3/s, cubic feet per second; %, percent]

Date of 

measurement

Measurement 

number

Measured 

discharge 

(ft3

/s)

Flow depth 

(feet), for stage 

of zero flow: 

7.00 feet

Fraction of 

directly measured 

discharge 

(%)

Fraction of 

invalid depth 

cells 

(%)

Error standard 

deviation 

(%)

Error standard 

deviation 

(ft3

/s)

June 3, 2008 106 234 3.50 32 0 2.70 6.3

July 12, 2008

September 14, 2008

May 13, 2009

108

113

117

170

704

628

2.15

7.64

6.59

22

37

49

43

4

0

3.65

2.75

2.93

6.2

19.4

18.4
Uncertainty of the Observed Peak Discharge on Boneyard Creek at Lincoln Avenue 17

concentrate on the 61 field measurements at 16 sites Oberg 

and Mueller obtained by using the RDI Rio Grande in Water 

Mode 12, for which the reference discharges ranged from 69.6 

to 6,850 ft3/s. These measurements were made with the same 

instrument model and water mode as used in the Boneyard 

Creek measurements listed in table 6. For these measurements, 

differences between the ADCP and reference discharges 

ranged from −15.9 to 8.7 percent, with a mean of −0.14 

percent (not statistically different from zero). The standard 

deviation of the percent differences was 5.8, more than double 

the values from Herschy (1999) and Morlock (1996).

In interpreting the results of such comparisons between 

ADCP and reference discharges as are given in both Morlock 

(1996) and Oberg and Mueller (2007), it should be kept in 

mind that the reference discharges also are subject to error, so 

the stated percent differences are likely to be larger on average 

than what would result from comparison to the true value. A 

quantitative estimate of this effect can be obtained by assuming that the observed value is the difference between two 

uncorrelated random variables, say, X1 and X2, with a common 

variance σ 2

X . Then the variance σ 2Y of the difference Y = X1

 – X2 

is σ 2

Y= 2σ 2X , and the standard deviation is σY = √ ̅

2σ X , suggesting a standard deviation inflation factor of √ ̅

2. Applying this 

model to the Water Mode 12 RDI Rio Grande measurements 

from Oberg and Mueller (2007), the error standard deviation resulting from ADCP errors alone would be 5.8/√ ̅

2 = 4.1 

percent. If the errors were positively correlated, the inflation 

factor would be larger, whereas if they were negatively correlated, it would be smaller. 

Summarizing the results from these previous studies 

of ADCP error, Herschy (1999) indicated that under ideal 

conditions the ADCP error standard deviation might be 

2.5 percent, and the field study by Morlock (1996) attained 

a similar result (2.7 percent) without adjustment for a variance inflation factor, whereas the larger study of Oberg and 

Mueller (2007) indicated an error standard deviation without 

variance inflation adjustment of 5.8 percent and 4.1 percent 

after adjustment with a roughly estimated variance inflation 

factor of √ ̅

2. Given the large fraction of the unmeasured area 

when using an ADCP in a small stream such as Boneyard 

Creek, matching the minimum ADCP error seems unlikely 

(Kevin Oberg, U.S. Geological Survey, oral commun., 2010). 

Therefore, to include both the increase in percent error for 

smaller discharges and the possibility that the values in table 6

are too small, the estimates of computed discharge uncertainty 

are obtained using a minimum value of 2.5 percent and larger 

assumed values of 5 and 7.5 percent. 

Discharge-Computation Uncertainty

The results of applying the methodology for estimation 

of discharge-computation uncertainty presented previously, 

as adapted from Dymond and Christian (1982), are presented 

in table 7. These results were obtained with the rating-curve 

regressions shown in figures 5 and 6 at a discharge of 700 ft3/s. 

These results show, first of all, that the effect of stage-measurement uncertainty is indeed small, at about 3.2–3.5 ft3

/s, 

compared to the other terms, which are on the order of tens of 

cubic feet per second. The next two columns give the uncertainties arising from the rating-curve regression alone: the 

regression standard error, Sε, and the rating-curve uncertainty, 

Smr, at the stage corresponding to the given discharge. The 

remaining columns depend on the measurement uncertainty, 

for which the three values 2.5, 5, and 7.5 percent were used. 

Using these measurement errors allows computation of the 

model error, Sθ (by using equation 3), given in the next column 

and then the overall instantaneous discharge computation 

uncertainty, SQ (by using equation 6), given in the next-to-last 

column. Because the model error is positive, the instantaneous-discharge-computation uncertainty is equivalently also 

given by equation 7. Nevertheless, the model-error component 

of discharge-computation error decreases with measurement 

error, as equation 6 shows. Finally, the last column gives 

95-percent confidence intervals for the instantaneous-discharge-computation uncertainty estimated as Q ± 2SQ. These 

intervals range from 62 to almost 150 ft3/s and imply (with 

95-percent certainty) that when the instantaneous discharge at 

the Boneyard Creek at Lincoln Avenue gage is computed as 

700 ft3/s, it lies within a minimum range of 638 to 762 ft3/s if 

the measurement uncertainty is 7.5 percent and the appropriate 

rating-curve regression to use is for water years 2005–9 and 

a flow depth greater than 1 ft (bottom row). Table 7 further 

shows that a computed discharge of 700 ft3/s lies within a 

maximum range of 552 to 848 ft3/s if the measurement uncertainty is 2.5 percent and the appropriate regression to use is for 

June 2003 through September 2009 and a flow depth greater 

than 5 ft (top row).
Table 7. Instantaneous-discharge-computation uncertainty components for a discharge of 700 cubic feet per second for USGS streamgage 0333710Lincoln Avenue, Urbana, Ill.). [WY, water year; ft3/s, cubic feet per second; %, percent] Rating-curve regression conditions Discharge- computation error from stage measurement error, SQΔh (ft3/s) Regression error, Sε (ft3/s) Rating-curve uncertainty, Smr (ft3/s) Discharge- measurement error, SΔQm (ft3/s) Model error, Sθ (ft3/s) Discharge- computation error, SQ (ft3/s) Discharge

computation e

as a fraction 

discharge, S 

(%) 

Discharge measurement error = 2.5 percent WY 2002–2009, depth >5 ft (Figure 5) WY 2005–09, depth >1 ft (Figure 6) 3.22 3.47 62.2 56.3 43.5 23.6 17.5 17.5 59.6 53.4 73.9 58.5 10.6 8.4 

Discharge measurement error = 5 percent WY 2002–2009, depth >5 ft (Figure 5) WY 2005–09, depth >1 ft (Figure 6) 3.22 3.47 62.2 56.3 43.5 23.6 35.0 35.0 51.3 44.0 67.4 50.0 9.6 7.1 

Discharge measurement error = 7.5 percent WY 2002–2009, depth >5 ft (Figure 5) WY 2005–09, depth >1 ft (Figure 6) 3.22 3.47 62.2 56.3 43.5 23.6 52.5 52.5 33.2 20.1 54.8 31.2 7.8 4.5 
Uncertainty of the Observed Peak Discharge on Boneyard Creek at Lincoln Avenue 19

The components of the uncertainty as a function of 

discharge for measurement uncertainties of 5 and 7.5 percent 

based on the rating curve regression computed from depths 

greater than 5 ft are presented in figure 7. This figure shows 

two important features: (a) the regression-based rating-curve 

error has a minimum at about 500 ft3/s (this occurs at the 

discharge corresponding to the average stage, as can be seen 

in equation 5), which leads to a minimum in the computed 

discharge error, and (b) the model error decreases with discharge when the measurement error is a constant percentage 

of the discharge, as it must, according to equation 3; here, for 

a measurement uncertainty of 7.5 percent, the condition where 

the measurement error variance σ 2

ΔQm

 exceeds the regression error variance σ 2

ε such that the model error variance is 

taken as zero (see equation 3) occurs for discharges greater 

than about 820 ft3/s, suggesting the measurement error has 

been overestimated, at least in this range of discharge (or the 

regression error is heteroscedastic). Given this anomalous 

behavior, assuming a 5-percent measurement error seems 

preferable. Although a 5-percent measurement error could be 

an underestimate, at the same time, because of the influence 

of the backwater caused by the discharge of the storm drain 

under the Lincoln Avenue bridge, the model error is not likely 

to be zero even if the true rating is linear. A complete resolution of this issue would require not only an improved method 

of estimating the ADCP measurement error but also more 

measurements at the streamgage to refine the structure of the 

rating-curve residuals, both of which are outside the scope of 

this study. As a result, the final results presented in this report 

reflect a compromise assumption that the measurement error is 

5 percent. 

Discharge-computation-uncertainty results for discharges 

from 300 to 900 ft3/s given in figures 8 and 9 illustrate the 

sensitivity of the discharge uncertainty to the discharge value. 

Figure 8 indicates that the uncertainty of the computed discharge, SQ, is 80 ft3

/s at a discharge of 300 ft3/s and decreases 

to a minimum about 60 ft3/s at a discharge of about 510 ft3/s 

for measurement errors of 2.5 and 5 percent, whereas the 

minimum occurs at about 590 ft3/s and has a value of about 

48 ft3/s for measurement error of 7.5 percent (final results in 

this report assume a measurement error of 5 percent; results 

for measurement errors of 2.5 and 7.5 percent are given for 

the purpose of illustration). The existence of minimums in 

the discharge-uncertainty result arises from the rating-curve 

uncertainty, Smr, which increases away from 511.5 ft3/s, the 

average of the data used in the regression, and the differences 

in the locations of the minimums results from differences in 

the shapes of the model error variance term (fig. 7). After the 

minimum, the discharge uncertainty increases again, reaching 

values of 80–100 ft3/s at a discharge of 900 ft3/s. The computed discharge uncertainty is only weakly dependent on the 

measurement error for the values of 2.5 and 5 percent, with a 

slightly smaller value for the larger measurement error, as the 

results in table 7 already showed, whereas a larger decrease is 

evident for a measurement error of 7.5 percent. In figure 9, the 

discharge-computation uncertainty is shown as an estimated 

95-percent confidence band (computed as Q ± 2SQ , where the 

SQ values are as shown in figure 8 for a measurement error of 

5 percent). The observed peak discharges and their 95-percent 

confidence intervals using the values from figure 9 are given 

in numerical form in table 8.
20 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Figure 7.

0

20

40

60

80

100

120

140

160

Computed discharge, in cubic feet per second

Computed discharge error, 

in cubic feet per second

0

20

40

60

80

100

120

140

300 400 500 600 700 800 900

Computed discharge error, 

in cubic feet per second

A : Measurement error of 5% 

B : Measurement error of 7.5% 

Computed discharge error

Model error

Rating curve error

Regression standard error

Discharge computation error from stage measurement error

EXPLANATION

Figure 7. Components of uncertainty of computed discharge as a function of discharge 

for USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.), using 

measurements obtained from June 2003 through September 2009 when the depth of flow 

was greater than 5 feet. A, Measurement error of 5 percent. B, Measurement error of 

7.5 percent. Measurements included in the rating-curve regression range from 378 to 

704 cubic feet per second.
Uncertainty of the Observed Peak Discharge on Boneyard Creek at Lincoln Avenue 21

Figure 8.

0

20

40

60

80

100

120

140

160

300 400 500 600 700 800 900

Computed instantaneous discharge, in cubic feet per second

Uncertainty in computed instantaneous 

discharge, in cubic feet per second

Measurement error: 2.5%

Measurement error: 5%

Measurement error: 7.5%

EXPLANATION

Figure 8. Uncertainty of computed discharge expressed as a standard deviation at 

USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.), using 

measurements obtained from June 2003 through September 2009 when the depth of flow 

was greater than 5 feet. Curves reflect varied assumptions on measurement uncertainty. 

Measurements included in the rating-curve regression range from 378 to 704 cubic feet 

per second.

Figure 9.

300 400 500 600 700 800 900

Computed instantaneous discharge, in cubic feet per second

0

200

400

600

800

1,000

1,200

1,400

Instantaneous discharge, in cubic feet per second

Lower limit of 95% confidence interval

Upper limit of 95% confidence interval

Computed instantaneous discharge

EXPLANATION

Figure 9. Approximate 95-percent confidence interval of instantaneous discharge 

uncertainty at USGS streamgage station 03337100 (Boneyard Creek at Lincoln Avenue, 

Urbana, Ill.), using measurements obtained from June 2003 through September 2009 

when the depth of flow was greater than 5 feet. Assumed measurement error is 

5 percent. Measurements included in the rating-curve regression range from 378 to 

704 cubic feet per second.
22 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Table 8. Observed peak discharges and their 95-percent confidence intervals, assuming a 

measurement error of 5 percent, at USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, 

Urbana, Ill.) for storm events analyzed during this study.

[Q, observed peak discharge; SQ, discharge uncertainty expressed as a standard deviation; ft3/s, cubic feet per second; 

%, percent]

Date of event

(month/day/year)

Observed peak 

discharge, Q

(ft3/s)

2SQ

(ft3/s)

Upper limit of 

95% confidence 

interval, Q+ 2SQ

(ft3/s)

Lower limit of 

95% confidence 

interval, Q – 2SQ

(ft3/s)

Official peak dischargesa

7/9/2003 797 160 957 637

6/26/2007 714 138 852 576

6/3/2008 837 172 1,009 665

7/8/2008 793 159 952 634

9/14/2008 877 186 1,063 691

Average of all five events 804 163

Average of last four events 805 164

Peak discharges computed with stage-discharge rating 4, no shifts

7/9/2003 856 179 1,035 677

6/26/2007 652 125 777 527

6/3/2008 842 174 1,016 668

7/8/2008 793 159 952 634

9/14/2008 878 186 1,064 692

Average of all five events 804 165

Average of last four events 791 161

a

The official peak discharge is defined as the published annual maximum peak discharge, or the value that would 

have been published as the annual maximum peak, if it had been the largest that water year.
Comparison of Simulated and Observed Peak Discharges and Stages 23

Comparison of Simulated and Observed 

Peak Discharges and Stages

The observed peak discharges at the primary comparison 

streamgage at Lincoln Avenue and their uncertainties can now 

be compared with the simulated peak discharges obtained 

from the four SWMM simulation scenarios. Supplementary 

comparisons of peak stage at Lincoln Avenue, stage and 

discharge at the Campus streamgage, and stage at Race Street 

also are presented. 

Discharge at Lincoln Avenue

The peak discharges obtained from the as-built 

SWMM4.4H design model at Lincoln Avenue for the four 

simulation scenarios, along with the observed peak discharges 

and measures of the simulation error, are given in table 9. The 

simulated peak discharges with spatially variable precipitation for the first event are quite high as a result of numerical 

instability in the EXTRAN part of the SWMM model and 

should be ignored. Several alternative values of the EXTRAN 

parameters controlling the chosen numerical algorithm were 

tried, but none were successful in removing this instability. 

For spatially uniform precipitation, however, it was possible to 

successfully simulate this event. Overall, a comparison of the 

simulated peak discharges obtained by using spatially uniform 

precipitation to those obtained by using spatially variable 

precipitation show no discernible pattern and have similar 

averages. The effect of using REGEN = 0.001 as compared 

to the REGEN = 0.01 to create the antecedent soil moisture 

conditions for the event generating the peak is more consistent: the peak obtained using REGEN = 0.001, and therefore 

higher antecedent soil moisture, is always higher compared 

to REGEN = 0.01. The value of REGEN is also important to 

the comparison of simulated to observed peak discharges: for 

REGEN = 0.001 and spatially uniform precipitation, three of 

five simulated peaks exceed the observed peak and the average error is positive; for REGEN = 0.01, three of five simulated peaks are less than the observed and the average error 

is negative.

The numerical values of the observed peak discharges 

and their 95-percent confidence intervals are given in tables 

8 and 10, respectively. The observed and the simulated peak 

discharges based on SDR 4 are plotted together in figure 10. 

When comparing the simulated and observed peak discharges, 

one must be mindful that modeling uncertainties may not be 

completely accounted for in the approach taken in this study. 

These uncertainties include precipitation measurement errors 

(both at-gage and the spatial variability of the precipitation) 

and the antecedent moisture condition of the soil. Figure 

10 shows that all of the simulated peak discharge values lie 

within or very near the 95-percent confidence intervals of the 

observed peak discharges. For one event, on July 9, 2003, 

simulated discharges are near the upper limit of the 95-percent 

confidence interval of the observed value; for one other event, 

on June 3, 2008, the simulations are near the lower limit of the 

95-percent confidence interval of the observed value. For two 

events, on June 26, 2007, and July 8, 2008, simulated values 

are distributed around the center of the of the 95-percent confidence intervals of the observed value, though the simulated 

discharges for June 26, 2007, are lower and those for July 

8, 2008, are higher. For the remaining event, on September 

14, 2008, the simulations are in the upper half of the 95-percent confidence interval of the observed value. Therefore, it 

appears that, overall, the model is simulating the peak discharges at Lincoln Avenue usually within the 95-percent confidence intervals and with differences that are approximately 

balanced between overprediction and underprediction. 

The overall bias of the simulated peak discharges is 

quantified in table 10. The results for spatially uniform 

precipitation, for which all five events could be simulated, 

show a positive average bias of 63 ft3/s of the simulations 

compared to either the official or SDR 4-derived observations 

where REGEN = 0.001 (therefore, somewhat wetter antecedent moisture conditions) and a small positive bias of 1–2 ft3

/s 

where REGEN = 0.01 (the default and design model value). 

When considering just the last four events that could be 

simulated for spatially variable precipitation, the bias remains 

positive for REGEN = 0.001 in the case of the SDR 4-based 

observed values but becomes negative for REGEN = 0.01. 

This change is not surprising because the July 9, 2003, event 

has the largest positive simulation bias among all the events. 

Considering all the events, however, the average simulation 

bias is small to significantly positive. Combining the uncertainty and bias results, the five events studied here provide no 

clear evidence that the Boneyard Creek SWMM design model 

peak discharges at Lincoln Avenue are significantly inaccurate 

or biased. 
Table 9. Comparison of simulated and observed peak discharges at USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, Urbanalyzed during this study. [ft3/s, cubic feet per seco N/A, not applicable] Event date (month/day/year) 7/9/2003 nd; REGEN, Stormwat Observed peak discharge (stage- discharge rating 4, no shifts) (ft3/s) 856 er Management Model (SWMM) parameter controlling rate at which infiltration capacity is regenerated during inte

Simulated peak discharge Spatially uniform precipitation Spatially variable p

REGEN = 0.01 REGEN = 0.001 REGEN = 0.01 

Discharge Percent Discharge Percent Discharge Percent 

(ft3/s) errora (ft3/s) errora (ft3/s) errora 

1,024 19.6 1,049 22.5 1,431b N/A 

6/26/2007 652 531 −18.6 616 −5.5 633 −2.9 

6/3/2008 842 701 −16.7 722 −14.3 703 −16.5 

7/8/2008 793 746 −5.9 917 15.6 716 −9.7 

9/14/2008 877 1,001 14.1 1,055 20.3 943 7.5 

Average of all five events 804 801 −1.49 872 7.74 N/A N/A 

Average of last four events aPercent error is defin bPeak-discharge value 791 ed as 100×(Qsim−Qobs)/Qobs occurs during period o 745 , where Qsim is f significant mode −6.8 the simulated peak d l instability. 828 ischarge and Qobs 4.0 is the observed pea 749 k discharge. −5.4 
Comparison of Simulated and Observed Peak Discharges and Stages 25

Table 10. Simulated peak discharges and differences between simulated and observed peak discharges at 

USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.) for storm events analyzed during 

this study.

[REGEN, Stormwater Management Model (SWMM) RUNOFF module parameter controlling the rate at which soil infiltration capacity is regenerated between storm events; Qsim, simulated peak discharge; Qobs–off, official observed peak discharge; Qobs–r4, observed 

peak discharge computed with stage-discharge rating 4 and no shifts; ft3/s, cubic feet per second; N/A, not available]

Date of event

(month/day/year)

REGEN = 0.001 REGEN = 0.01

Qsim

(ft3/s)

Qsim – Qobs–off

(ft3/s)

Qsim – Qobs–r4

(ft3/s)

Qsim

(ft3/s)

Qsim – Qobs–off

(ft3/s)

Qsim – Qobs–r4

(ft3/s)

Spatially uniform precipitation

7/9/2003 1,024 227 168 1,049 252 193

6/26/2007 616 −98 −36 531 −183 −121

6/3/2008 722 −115 −120 701 −136 −141

7/8/2008 917 124 124 746 −47 −47

9/14/2008 1,055 178 177 1,001 124 123

Average of all 5 events 867 63.2 62.6 806 2.0 1.4

Average of last 4 events 828 22.3 36.3 745 −60.5 −46.5

Spatially variable precipitation

7/9/2003 N/A N/A N/A N/A N/A N/A

6/26/2007 700 −14 48 633 −81 −19

6/3/2008 721 −116 −121 703 −134 −139

7/8/2008 786 −7 −7 716 −77 −77

9/14/2008 1,000 123 122 943 66 65

Average of all 5 events N/A N/A N/A N/A N/A N/A

Average of last 4 events 802 −3.5 10.5 749 −56.5 −42.5
26 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Figure 10. 

400

500

600

700

800

900

1,000

1,100

7/9/2003 6/26/2007 6/3/2008 7/8/2008 9/14/2008

Date of high-flow event

Discharge, in cubic feet per second

Observed with 95% confidence interval

REGEN = 0.01, Spatially uniform precipitation

REGEN = 0.01, Spatially varying precipitation

REGEN = 0.001, Spatially uniform precipitation

REGEN = 0.001, Spatially varying precipitation

EXPLANATION

Figure 10. Peak discharges from SWMM4 simulations and observed values with estimated 95-percent 

confidence intervals for USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.), 

for storm events analyzed during this study. Observed discharges were computed from stage-discharge 

rating 4, with no shifts. For the event on July 9, 2003, only discharge values resulting from stable simulations 

are shown.
Comparison of Simulated and Observed Peak Discharges and Stages 27

Stage at Lincoln Avenue and Stage and 

Discharge at Supplementary Streamgages

Not surprisingly, but reassuringly, the pattern of peak 

stages from the four SWMM simulation scenarios relative to 

the observed peak stage at Lincoln Avenue (fig. 11) is similar to the peak-discharge comparison at the same location 

(fig. 10), though quantitatively, the errors are shifted in the 

positive direction (table 11); that is, the simulated peak stages 

are usually somewhat higher than the observed. This correspondence between peak discharge and stage comparisons is 

reassuring because it indicates approximate agreement in the 

observed and modeled stage-discharge relations, at least for 

peak values. 

At the Campus streamgage, simulated peak discharge 

(fig. 12 and table 12) and stage (fig. 13 and table 13) both 

tend to be low compared to the observations; like at Lincoln 

Avenue, however, the stage differences (simulated minus 

observed) are more positive than the discharge differences. 

The reason for the apparent negative bias in the simulated 

peaks at the Campus streamgage is not immediately clear. 

One possibility is that although both the Lincoln Avenue and 

Campus streamgages are recently constructed, the rating curve 

for Lincoln Avenue is based on many more high-flow measurements than that for the Campus streamgage because of the 

emphasis on measurements at Lincoln Avenue as a result of 

this study. 

Only stage comparisons are available at the Race Street 

streamgage. The distribution pattern of the simulated stages 

around the observations is similar to that at the other gages 

(fig. 14 and table 14). Here, like at Lincoln Avenue (table 11

and fig. 11) but unlike at the Campus streamgage (figs. 12

and 13), the simulated stages tend to be somewhat high 

relative to the observed stages, though not by as much as at 

Lincoln Avenue. 

The common pattern of distribution of simulated values 

relative to the observations across the different streamgages 

(the July 9, 2003, simulated peak stages and discharges 

being generally high relative to the observations, the June 

26, 2007, and June 3, 2008, simulations being low, and the 

September 14, 2008, simulations being again high) bears 

further comment. This pattern could have resulted from either 

a hydrologic cause (errors in the precipitation measurements 

or antecedent moisture values in the model) or a hydraulic 

cause (errors in the SWMM model results for the particular 

flows in the Boneyard pipe and channel system for that event). 

Observed-flow computation error seems unlikely to explain 

this common pattern because the pattern is seen across three 

different streamgages. The tendency for simulations at the 

different gages to be generally higher or lower relative to 

observations at other gages could, however, result at least 

partly from errors in observed-flow computation (for example, 

uncertainty in the rating curves in the case of peak discharges), 

in addition to SWMM model error. 
28 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Figure 11.

7/9/2003 6/26/2007 6/3/2008 7/8/2008 9/14/2008

Date of high-flow event

Observed

REGEN = 0.01, Spatially uniform precipitation

REGEN = 0.01, Spatially varying precipitation

REGEN = 0.001, Spatially uniform precipitation

REGEN = 0.001, Spatially varying precipitation

EXPLANATION

707

708

709

710

711

712

713

714

Elevation, in feet above NGVD 29

Figure 11. Peak stages from SWMM4 simulations and observed values at USGS streamgage 03337100 

(Boneyard Creek at Lincoln Avenue, Urbana, Ill.) for storm events analyzed during this study. For the 

July 9, 2003, event, only values resulting from stable simulations are shown.
Table 11. Comparison of simulated and observed peak stages at USGS streamgage 03337100 (Boneyard Creek at Lincoln Avenue, Urbana, Ill.) for stothis study.[ft, feet; NGVD 29, National Geodetic Vertical Datum of 1929; REGEN, Stormwater Management Model (SWMM) parameter controlling rate at which infiltration capacity is reperiods; N/A, not applicable]

Observed peak stage Simulated peak stage (ft, NGVD 29)

Spatially uniform precipitation Spatially variable 

Elevation

Event date Gage height (datum: REGEN = 0.01 REGEN = 0.001 REGEN = 0.01 

(month/day/year) (ft) 694.00 ft, 

NGVD 29) Elevation Error Elevation Error Elevation Error 

(ft) (ft) (ft) (ft) (ft) (ft) 

7/9/2003 17.00 711.00 712.96 1.96 712.99 1.99 713.85a N/A 

6/26/2007 14.63 708.63 707.56 −1.07 708.50 −0.13 708.54 −0.09 6/3/2008 16.80 710.80 710.25 −0.55 711.31 0.51 710.43 −0.37 7/8/2008 16.29 710.29 711.65 1.36 712.33 2.04 711.40 1.11 9/14/2008 17.26 711.26 712.72 1.46 712.97 1.71 712.62 1.36 Average of all five 16.40 710.40 711.03 0.63 711.62 1.22 N/A N/A 

events

Average of last four 16.25 710.25 710.55 0.30 711.28 1.03 710.75 0.50 

events

aPeak-stage value occurs during period of significant model instability.
30 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Figure 12.

7/9/2003 6/26/2007 6/3/2008 7/8/2008 9/14/2008

Date of high-flow event

Observed

REGEN = 0.01, Spatially uniform precipitation

REGEN = 0.01, Spatially varying precipitation

REGEN = 0.001, Spatially uniform precipitation

REGEN = 0.001, Spatially varying precipitation

EXPLANATION

300

400

500

600

700

800

900

Discharge, in cubic feet per second

Figure 12. Peak discharges from SWMM4 simulations and observed values at USGS streamgage 

03337000 (Boneyard Creek at Urbana, Ill.) on the campus of the University of Illinois at Urbana-Champaign 

for storm events analyzed during this study. For the July 9, 2003, June 26, 2007, and June 3, 2008 events, 

only values resulting from stable simulations are shown.
Table 12. Comparison of simulated and observed peak discharges at USGS streamgage 03337000 (Boneyard Creek at Urbana, Ill.) on thof Illinois at Urbana-Champaign for storm events analyzed during this study.[ft3/s, cubic feet per sec

N/A, not applicable]

Event date

(month/day/year)

7/9/2003

ond; REGEN, Stormw

Observed peak 

discharge

(stage-discharge 

rating 20, 

no shifts)

(ft3/s)

780

ater Management Model (SWMM) parameter controlling rate at which infiltration capacity is regenerated during in

Simulated peak discharge

Spatially uniform precipitation Spatially variable 

REGEN = 0.01 REGEN = 0.001 REGEN = 0.01 

Discharge Percent Discharge Percent Discharge Percent 

(ft3/s) errora (ft3/s) errora (ft3/s) errora 

785 0.6 802 2.8 853b N/A 

6/26/2007 571 455b N/A 595b N/A 469 −17.9 6/3/2008 727 588 −19.1 587 −19.3 566b N/A 

7/8/2008 686 615 −10.3 648 −5.5 574 −16.3 

9/14/2008 812 770 −5.2 797 −1.8 697 −14.2 

Average of all five 

events

715 690 −8.50 709 −6.0 N/A N/A 

Average of last four 

events

aPercent error is definbPeak-discharge valu

699

ed as 100×(Qsim−Qobs)/Qobs

e occurs during period

658

, where Qsim i

 of significant mo

−11.5

s the simulated peak

del instability.

677

 discharge and Qobs

−8.9

 is the observed p

580

eak discharge.

−16.1 
32 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Figure 13.

7/9/2003 6/26/2007 6/3/2008 7/8/2008 9/14/2008

Date of high-flow event

Observed

REGEN = 0.01, Spatially uniform precipitation

REGEN = 0.01, Spatially varying precipitation

REGEN = 0.001, Spatially uniform precipitation

REGEN = 0.001, Spatially varying precipitation

EXPLANATION

707

708

709

710

711

712

713

714

715

Elevation, in feet above NGVD 29

Figure 13. Peak stages from SWMM4 simulations and observed values at USGS gaging station 03337000 

(Boneyard Creek at Urbana, Ill.) on the campus of the University of Illinois at Urbana-Champaign, for 

storm events analyzed for this study.
Table 13. Comparison of simulated and observed peak stages at USGS streamgage 03337000 (Boneyard Creek at Urbana, Ill.) on the campus of the UUrbana-Champaign for storm events analyzed during this study.[ft, feet; NGVD 29, National Geodetic Vertical Datum of 1929; REGEN, Stormwater Management Model (SWMM) parameter controlling rate at which infiltration capacity is rperiods; N/A, not applicable]

Observed peak stage Simulated peak stage (ft, NGVD 29)

Spatially uniform precipitation Spatially variable p

Event date Elevation

(month/day/year) Gage height (datum: REGEN = 0.01 REGEN = 0.001 REGEN = 0.01 

(ft) 694.00 ft, 

NGVD 29) Elevation Error Elevation Error Elevation Error 

(ft) (ft) (ft) (ft) (ft) (ft) 

7/9/2003 18.59 712.59 713.51 0.92 713.57 0.98 713.73 1.14 6/26/2007 16.76 710.76 708.90 −1.86 709.78 −0.98 709.40 −1.36 6/3/2008 18.13 712.13 710.86 −1.27 711.71 −0.42 710.97 −1.16 7/8/2008 17.78 711.78 712.06 0.28 712.69 0.91 711.70 −0.08 9/14/2008 18.85 712.85 713.35 0.50 713.53 0.68 713.11 0.26 Average of all five 18.02 712.02 711.74 −0.29 712.26 0.23 711.78 −0.24 

events

Average of last four 17.88 711.88 711.29 −0.59 711.93 0.05 711.30 −0.58 

events
34 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Figure 14.

7/9/2003 6/26/2007 6/3/2008 7/8/2008 9/14/2008

Date of high-flow event

Observed 

REGEN = 0.01, Spatially uniform precipitation

REGEN = 0.01, Spatially varying precipitation

REGEN = 0.001, Spatially uniform precipitation

REGEN = 0.001, Spatially varying precipitation

EXPLANATION

Elevation, in feet above NGVD 29

700

701

702

703

704

705

706

707

708

709

710

Figure 14. Peak stages from SWMM4 simulations and observed values at USGS streamgage 03337250 

(Boneyard Creek at Race Street, Urbana, Ill.) for storm events analyzed during this study. For the July 9, 2003, 

and September 14, 2008, events, only values resulting from stable simulations are shown.
Table 14. Comparison of simulated and observed peak stages at USGS streamgage 03337250 (Boneyard Creek at Race Street, Urbana, Ill.) for storm this study.[ft, feet; NGVD 29, National Geodetic Vertical Datum of 1929; REGEN, Stormwater Management Model (SWMM) parameter controlling rate at which infiltration capacity is rperiods; N/A, not applicable]

Observed peak stage Simulated peak stage (ft, NGVD 29)

Spatially uniform precipitation Spatially variable p

Event date Elevation Gage height REGEN = 0.01 REGEN = 0.001 REGEN = 0.01 

(month/day/year) (datum: 694.00 (ft) ft, NGVD 29) Elevation Error Elevation Error Elevation Error 

(ft) (ft) (ft) (ft) (ft) (ft) 

7/9/2003 11.68 705.68 706.38 0.70 706.91a N/A 706.57 0.89 

6/26/2007 9.41 703.41 703.04 −0.37 704.27 0.86 703.41 0.00 6/3/2008 11.06 705.06 704.43 −0.63 705.14 0.08 704.24 −0.82 7/8/2008 11.26 705.26 705.24 −0.02 705.98 0.72 705.06 −0.20 9/14/2008 11.30 705.30 706.48 1.18 706.37 1.07 706.42 1.12 

Average first four 10.85 704.85 704.77 −0.08 N/A N/A 704.82 −0.03 

events

Average of last four 10.76 704.76 704.80 0.04 705.44 0.68 704.78 0.03 

events

aPeak-stage value occurs during period of significant model instability.
36 Using Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek

Summary

The design model for a set of flood-control projects 

was evaluated by comparing simulated peak flows for events 

observed after construction of the projects to the observed 

peak flows five high-flow events between May 2003 and September 2008 on Boneyard Creek in Champaign-Urbana, Ill., 

using the as-built version of the SWMM model used to design 

the projects. Results from four different simulation scenarios 

were obtained by using two values of a parameter that controls 

the antecedent moisture condition, in combination with either 

spatially uniform or spatially variable versions of the precipitation fields, which were developed from rain-gage data 

distributed by means of Thiessen polygons. At the primary 

evaluation location, all of the simulated peak discharge values 

lie within or very near the 95-percent confidence intervals of 

the observed peak discharges, and overall, the simulation bias 

is approximately balanced between overprediction and underprediction. Supplementary comparisons of simulated stage at 

the primary location and other stage and discharge at nearby 

gages were also made; these showed the same pattern of differences between observed and simulated values across events 

but varying biases depending on streamgage and measurement 

type (discharge or stage). Results from this study show no 

clear evidence that design model is significantly inaccurate 

or biased and, therefore, no clear evidence that the modeled 

flood-control projects in Champaign and on the University 

of Illinois campus have increased flood stages or discharges 

downstream in Urbana. 

Acknowledgments

The authors thank several USGS colleagues for assistance with this study: Crystal Prater, for processing of the 

input and output data and carrying out the SWMM model 

runs; David Anning, for discussions of discharge uncertainty 

computations; Kevin Oberg, for insights into streamflow-measurement technologies and their uncertainties; Kevin Johnson, 

Jim Duncker, Patrick Miller, and many others for scrambling 

to measure Boneyard Creek’s “flash floods” without regard to 

time of day and heavy precipitation; and Kevin Johnson and 

Marv Harris, for explanations of the Boneyard Creek streamflow-record computations.

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sing Observed Postconstruction Peak Discharges to Evaluate a Hydrologic and Hydraulic Design Model, Boneyard Creek—Scientific Investigations Report 2011–5176