Prepared in cooperation with the North Carolina Department of Transportation

Simulation of Water-Surface Elevations and Velocity 

Distributions at the U.S. Highway 13 Bridge over the 

Tar River at Greenville, North Carolina, Using Oneand Two-Dimensional Steady-State Hydraulic Models

Scientific Investigations Report 2007–5263
Cover. Three-dimensional rendering of the Tar River bathymetry through the U.S. Highway 13 bridge near Greenville, 

North Carolina, overlain with a simulated two-dimensional velocity field output from the Finite Element Surface-Water 

Modeling System (FESWMS).
Simulation of Water-Surface Elevations and 

Velocity Distributions at the U.S. Highway 13 

Bridge over the Tar River at Greenville, North 

Carolina, Using One- and Two-Dimensional 

Steady-State Hydraulic Models

By Chad R. Wagner

Prepared in cooperation with the North Carolina Department of Transportation

Scientific Investigations Report 2007–5263

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2007

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

reproduce any copyrighted materials contained within this report.

Suggested citation:

Wagner, C.R., 2007, Simulation of water-surface elevations and velocity distributions at the U.S. Highway 13 bridge 

over the Tar River at Greenville, North Carolina, using one- and two-dimensional steady-state hydraulic models: U.S. 

Geological Survey Scientific Investigations Report 2007–5263, 33 p. (only online at http://pubs.water.usgs.gov/

sir2007-5263/)
iii

Contents

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

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

Background............................................................................................................................................2

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

Study Site and Data..............................................................................................................................3

Methods...........................................................................................................................................................4

Data Collection......................................................................................................................................4

Bathymetry and Topography......................................................................................................5

Water-Surface Elevations ..........................................................................................................5

Velocity and Discharge...............................................................................................................5

Scour Observations.....................................................................................................................6

Modeling.................................................................................................................................................6

Two-Dimensional Model.............................................................................................................6

Computational Grid.............................................................................................................7

Boundary Conditions..........................................................................................................8

One-Dimensional Model.............................................................................................................8

Model Development ...........................................................................................................8

Boundary Conditions..........................................................................................................9

Simulation of Water-Surface Elevations and Velocity Distributions.....................................................9

Model Calibration..................................................................................................................................9

Water-Surface Elevations ........................................................................................................10

Flow Continuity...........................................................................................................................10

Two-Dimensional Model Velocity Distribution......................................................................12

Effects of Debris.........................................................................................................................12

Model Uncertainty..............................................................................................................................12

Topographic Data.......................................................................................................................12

Hydraulic Parameters ...............................................................................................................14

Model Calibration Data.............................................................................................................14

Debris. .........................................................................................................................................14

Overbank Flow and Debris .......................................................................................................14

Model Scenarios for Existing Bridge and Pre-Roadway Conditions .........................................14

Flood-Frequency Calculations.................................................................................................14

Boundary Conditions.................................................................................................................15

Model Scenario Results ...........................................................................................................15

Water-Surface Elevations ...............................................................................................15

Two-Dimensional Model Flow Fields.............................................................................17

Comparisons of One-Dimensional and Two-Dimensional Modeling Results to Field Data.............17

Water-Surface Elevations .................................................................................................................17

Velocity Distributions .........................................................................................................................19

Scour Estimates ..................................................................................................................................19

Suggestions for Selecting Appropriate Modeling Approach......................................................25

Summary........................................................................................................................................................27

References Cited..........................................................................................................................................28
iv

Appendix—Difference maps of simulated velocity magnitudes for the existing and preroadway model scenarios for U.S.-13 over the Tar River at Greenville, North Carolina....29

Figures

1. Aerial view of the study area on the Tar River at Greenville, North Carolina, 2003 ............ 3

2. Photographs of debris accumulation (A) upstream from U.S.-13 and (B) between the 

parallel bridges of U.S.-13 over the Tar River at Greenville, North Carolina, on 

June 20, 2006 ................................................................................................................................ 4

3. Finite element grid configuration through the U.S.-13 bridge over the Tar River at 

Greenville, North Carolina.......................................................................................................... 7

4. Measured and simulated velocity distributions through the U.S.-13 bridge over the 

Tar River at Greenville, North Carolina, for high-flow conditions associated with 

Hurricane Charley, August 2004, and (B) Tropical Storm Alberto, June 2006.................. 13

5. Modeled water-surface elevations for existing bridge and pre-roadway scenarios 

for (A) 50- and 10-year floods and (B) 500- and 100-year floods for the Tar River at 

Greenville, North Carolina, study area....................................................................................16

6. Modeled water-surface elevations for high-flow conditions associated with 

(A) Hurricane Charley in August 2004 and (B) Tropical Storm Alberto in June 2006.......18

7. Measured and simulated velocity distributions through the U.S.-13 bridge over the 

Tar River at Greenville, North Carolina, for high-flow conditions associated with 

(A) Hurricane Charley, August 2004, and (B) Tropical Storm Alberto, June 2006 ........... 20

8. Measured and simulated velocity vectors at the upstream side of the U.S.-13 bridge 

over the Tar River at Greenville, North Carolina, for high-flow conditions associated 

with Hurricane Charley, August 2004 ......................................................................................22

9. Measured and simulated velocity vectors at the upstream side of the U.S.-13 bridge 

over the Tar River at Greenville, North Carolina, for high-flow conditions associated 

with Tropical Storm Alberto, June 2006 ................................................................................. 23

Tables

1. Summary of field data collection in the study reach at the U.S. Geological Survey 

streamgaging station on the Tar River at Greenville, North Carolina ..................................5

2. Summary of water-surface elevation calibration for the Tar River at Greenville 

study reach ..................................................................................................................................10

3. Summary of continuity checks for the modeled reach of the Tar River at Greenville, 

North Carolina .............................................................................................................................11

4. Flood-frequency estimates for U.S. Geological Survey streamgaging station 

02084000 (Tar River at Greenville, North Carolina)............................................................... 15

5. Modeled water-surface elevations at the approach section of U.S.-13 bridge 

over the Tar River at Greenville, North Carolina, for the existing bridge and 

pre-roadway scenarios .............................................................................................................17

6. One- and two-dimensional model simulated maximum velocities for the main 

channel and overflow U.S.-13 bridges over the Tar River at Greenville, 

North Carolina .............................................................................................................................21

7. One- and two-dimensional model simulated approach velocities for the piers 

supporting the U.S.-13 bridge over the Tar River at Greenville, North Carolina ..............21
v

8. Pier-scour estimates for the U.S.-13 bridge over the Tar River at Greenville, 

North Carolina, using modeled hydraulic data for high-flow conditions 

associated with Hurricane Charley, August 2004..................................................................24

9. Pier-scour estimates for the U.S.-13 bridge over the Tar River at Greenville, 

North Carolina, using modeled hydraulic data for high-flow conditions 

associated with Tropical Storm Alberto, June 2006 .............................................................24

10. Abutment-scour estimates for the U.S.-13 bridge over the Tar River at Greenville, 

North Carolina, using hydraulic data from two high-flow events.......................................25

11. Definitions of potentially relevant bridge-site characteristics for the development 

of modeling guidelines at bridges, including site characteristics for the U.S.-13 

bridge over the Tar River at Greenville, North Carolina .......................................................26

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square foot (ft2) 0.09290 square meter (m2

)

square mile (mi2) 2.590 square kilometer (km2) 

Flow rate

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

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

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Elevation, as used in this report, refers to distance above the vertical datum.

Abstract

The use of one-dimensional hydraulic models currently 

is the standard method for estimating velocity fields through 

a bridge opening for scour computations and habitat assessment. Flood-flow contraction through bridge openings, 

however, is hydrodynamically two dimensional and often 

three dimensional. Although there is awareness of the utility 

of two-dimensional models to predict the complex hydraulic 

conditions at bridge structures, little guidance is available 

to indicate whether a one- or two-dimensional model will 

accurately estimate the hydraulic conditions at a bridge site. 

The U.S. Geological Survey, in cooperation with the 

North Carolina Department of Transportation, initiated a 

study in 2004 to compare one- and two-dimensional model 

results with field measurements at complex riverine and 

tidal bridges in North Carolina to evaluate the ability of each 

model to represent field conditions. The field data consisted of 

discharge and depth-averaged velocity profiles measured with 

an acoustic Doppler current profiler and surveyed watersurface profiles for two high-flow conditions. For the initial 

study site (U.S. Highway 13 over the Tar River at Greenville, 

North Carolina), the water-surface elevations and velocity 

distributions simulated by the one- and two-dimensional 

models showed appreciable disparity in the highly sinuous 

reach upstream from the U.S. Highway 13 bridge. Based on 

the available data from U.S. Geological Survey streamgaging 

stations and acoustic Doppler current profiler velocity data, 

the two-dimensional model more accurately simulated the 

water-surface elevations and the velocity distributions in the 

study reach, and contracted-flow magnitudes and direction 

through the bridge opening. 

To further compare the results of the one- and twodimensional models, estimated hydraulic parameters (flow 

depths, velocities, attack angles, blocked flow width) for 

measured high-flow conditions were used to predict scour 

depths at the U.S. Highway 13 bridge by using established 

methods. Comparisons of pier-scour estimates from both 

models indicated that the scour estimates from the twodimensional model were as much as twice the depth of the 

estimates from the one-dimensional model. These results can 

be attributed to higher approach velocities and the appreciable 

flow angles at the piers simulated by the two-dimensional 

model and verified in the field. 

Computed flood-frequency estimates of the 10-, 50-, 

100-, and 500-year return-period floods on the Tar River at 

Greenville were also simulated with both the one- and twodimensional models. The simulated water-surface profiles and 

velocity fields of the various return-period floods were used 

to compare the modeling approaches and provide information 

on what return-period discharges would result in road overtopping and(or) pressure flow. This information is essential in 

the design of new and replacement structures.

The ability to accurately simulate water-surface 

elevations and velocity magnitudes and distributions at 

bridge crossings is essential in assuring that bridge plans 

balance public safety with the most cost-effective design. By 

compiling pertinent bridge-site characteristics and relating 

them to the results of several model-comparison studies, the 

framework for developing guidelines for selecting the most 

appropriate model for a given bridge site can be accomplished.

Introduction

The use of one-dimensional hydraulic models currently 

is the standard method for estimating velocity fields through 

a bridge opening for scour computations and habitat assessments. Flood-flow contraction through bridge openings, 

however, is hydrodynamically two dimensional and often 

three dimensional. One of the most important factors in using 

numerical models to simulate flow contraction at bridges is 

the ability of the model to accurately represent the velocity 

distribution laterally across the stream and floodplain. 

There is a growing emphasis on development and use 

of two-dimensional numerical models that produce more 

Simulation of Water-Surface Elevations and Velocity 

Distributions at the U.S. Highway 13 Bridge over the 

Tar River at Greenville, North Carolina, Using Oneand Two-Dimensional Steady-State Hydraulic Models

By Chad R. Wagner
2 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

detailed and accurate analyses of river systems and bridge 

crossings. Until recently, the use of two-dimensional models 

required extensive field surveys and significant increases 

in personnel and computer resources compared with 

traditional one-dimensional approaches. With high-resolution 

topographic data becoming more readily available, the advent 

of graphical user interfaces for two-dimensional modeling 

software, and continued improvements in computer hardware, 

significant advances have been made in the ability to apply 

two-dimensional models to solve practical problems. Although 

there is awareness of the utility of two-dimensional models to 

predict the complex hydraulic conditions at bridge structures, 

little guidance is available to indicate whether a one- or 

two-dimensional model will accurately estimate the hydraulic 

conditions at a bridge site. Criteria also are needed for 

simulating hydraulics through bridges for evaluating alternative designs of single or multiple bridge openings in relation 

to overall structural cost, scour, backwater, and flood hazard 

mapping.

The U.S. Geological Survey (USGS), in cooperation with 

the North Carolina Department of Transportation (NCDOT), 

initiated a study in 2004 to compare one- and two-dimensional 

model results with field measurements at complex riverine and 

tidal bridges in North Carolina to evaluate the ability of each 

model to represent field conditions. The results of these model 

comparisons will provide an initial basis for development of 

modeling guidelines that will ensure cost-effective hydraulic 

analysis at bridges in other parts of the country. 

Background

The NCDOT Hydraulics Unit is responsible for providing 

preliminary designs for bridges, culverts, and other drainage 

features throughout the State, as well as providing information 

on wetlands, permit requirements, and water quality. During 

the design stage, the Hydraulics Unit develops detailed design 

recommendations for hydraulic structures, including bridges, 

box culverts, pipes, ditches, channels, stream relocations, 

and storm drainage systems. The Unit also is responsible for 

providing field data and hydraulic design recommendations to 

the NCDOT Bridge Maintenance Unit for the ongoing bridge 

replacement program. 

In order to provide hydraulic design recommendations 

for the construction of new bridges and(or) embankments, the 

NCDOT uses numerical models to simulate bridge hydraulics 

for various flow conditions. One-dimensional step-backwater 

models, such as the Hydraulic Engineering Center-River 

Analysis System (HEC-RAS; U.S. Army Corps of Engineers, 

2003) and Water-Surface Profile Computations (WSPRO; 

Shearman, 1990), are used almost exclusively by NCDOT to 

simulate the hydraulics for bridge design regardless of the site 

conditions. Many bridges, however, have site-specific characteristics that produce lateral and(or) vertical variability in the 

velocity distribution that cannot accurately be represented with 

a one-dimensional step-backwater model. 

Site characteristics that can produce hydraulic complexities at a bridge include upstream channel alignment (meanders), geomorphic setting of the river valley, and floodplain 

alignment relative to the channel and hydraulic structures 

(levees, dikes). For example, flow distributions at flood stages 

can significantly be altered when flows leave a channel and 

enter a floodplain at a channel bend. When the channel bend 

is just upstream from a bridge, concentrated channel flows 

can be directed to a section of a bridge opening that would 

not typically experience this magnitude of flow if the channel 

were straight. Under these conditions, the flow fields are 

inherently two dimensional and cannot be accurately represented with a one-dimensional model. Guidance for selecting 

the appropriate model to simulate bridge hydraulics would 

improve the ability to accurately simulate velocity magnitudes 

and distributions at bridge crossings, which is essential in 

assuring that bridge plans balance public safety with the most 

cost-effective design.

Purpose and Scope

The purpose of this report is to describe the development 

of one- and two-dimensional models to simulate hydraulic 

conditions at a complex riverine bridge site and to compare 

the modeling results to field data as a means of evaluating 

the capability of each model to accurately simulate field 

conditions. The results of this and other similar studies will 

build the knowledge base from which modeling guidelines 

can be developed. Such modeling guidelines can be valuable 

in directing engineers in the selection of the most appropriate 

modeling approach when new bridges are being designed. 

The selected study site was the U.S. Highway 13 

(U.S.-13) bridge over the Tar River at Greenville, North 

Carolina, and the study reach extended approximately 

2.9 miles upstream and 1 mile downstream from the U.S.-13 

bridge. Detailed bathymetry data were collected and merged 

with light detection and ranging (LiDAR) topographic data for 

model development and velocity. Discharge and water-surface 

elevations were collected in the study reach during two 

high-flow events for model calibration and comparison. The 

two models used in the study are HEC-RAS (U.S. Army Corps 

of Engineers, 2003) to simulate one-dimensional hydraulics 

and the Finite Element Surface-Water Modeling System 

(FESWMS; Froehlich, 2002) to simulate two-dimensional, 

vertically averaged hydraulics. Scour estimates also were 

compared by using the scour prediction equations from 

Hydraulic Engineering Circular-18 (HEC-18; Richardson and 

Davis, 2001) and input parameters derived from the HEC-RAS 

and FESWMS models. This information will help provide a 

basis for ongoing development of modeling guidelines that 

will ensure cost-effective hydraulic analysis.
Introduction 3

Study Site and Data

The U.S.-13 bridge over the Tar River at Greenville, 

North Carolina, was selected for study because of (1) its 

abutment slope stability problems, which stem from a highly 

skewed channel configuration directly upstream from the 

bridge (fig. 1), and (2) plans by the NCDOT for a replacement 

bridge, for which model results would be a valuable design 

tool. The U.S.-13 bridge is skewed approximately 60 degrees 

to the direction of flow in the Tar River. The U.S.-13 bridge 

over the Tar River spans 540 feet (ft), has an average roadway 

elevation of approximately 27 ft (North American Vertical 

Datum of 1988 (NAVD 88)), and has a low-steel elevation of 

approximately 24.5 ft, which induces pressure-flow conditions 

at the structure for the 500-year recurrence-interval flow 

(hereafter referred to as 500-year flood) that is estimated to be 

73,000 cubic feet per second (ft3/s). 

There are two overflow bridges associated with U.S.-13 

in the study area, both located on the left floodplain (fig. 1). 

Overflow bridge number 730057 begins approximately 

760 ft to the northeast of the U.S.-13 bridge over the Tar 

River, has an average roadway elevation of approximately 

24.5 ft and a low-steel elevation of approximately 20.5 ft, 

and spans approximately 255 ft. Overflow bridge number 

730070 begins approximately 2,560 ft to the northeast of the 

U.S.-13 bridge over the Tar River, has an average roadway 

elevation of approximately 24.5 ft and a low-steel elevation of 

approximately 21.5 ft, and spans approximately 125 ft. The 

low point (21.5 ft above NAVD 88) on U.S.-13 in the study 

reach is located approximately 2,000 ft northeast of overflow 

bridge 730070. 

Two high-flow hydrographic surveys were conducted 

in the study reach to collect discharge data, cross-sectional 

Figure 1. Aerial view of the study area on the Tar River at Greenville, North Carolina, 2003. [ADCP, acoustic Doppler current profiler]

Tar

River

Overflow bridge

730070

Overflow bridge

730057

U.S. 13

bridge

U.S. Highway 13

Downstream model

boundary

Green Street

bridges

USGS streamgaging

station 02084000

USGS streamgaging

station 02083893

Upstream model

boundary

0 0.25 0.50 0.75 1 MILE

0 0.25 0.50 0.75 1 KILOMETER

3539’

3538’

3537’

7725’ 7724’ 7723’

Figure 1. Aerial view of the study area on the Tar River at Greenville, North Carolina, 2003 Acoustic Doppler Current

 Profiler.

1

2

3

4

5 6

7

8

ADCP cross section 2 and number

LOCATION OF STUDY AREA IN NORTH CAROLINA
4 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

velocity profiles (fig. 1 inset), and water-surface elevation 

data concurrently for model calibration and to provide a 

basis for model comparisons. The first measured high-flow 

condition was caused by precipitation associated with Hurricane Charley in August 2004 and the second was caused by 

precipitation from Tropical Storm Alberto in June 2006. The 

survey in 2004 was made approximately 18 hours prior to 

the storm’s peak flow at Greenville, North Carolina, and the 

survey in 2006 captured the storm’s peak flow. The measured 

discharges during the 2004 and 2006 surveys were 11,500 ft3/s 

and 21,000 ft3

/s, respectively, both of which are less than 

the estimated 10-year return-period flow. Large floating 

debris rafts between pile bent 2 and 5 were observed during 

both high-flow hydrographic surveys (fig. 2). The general 

location of the debris accumulation was consistent for both 

high-flow surveys; however, the spatial extent of the debris 

varied. The debris raft extended from the upstream face to the 

downstream face of the parallel bridges during the Tropical 

Storm Alberto (21,000 ft3

/s) condition but was more restricted 

to the upstream bridge face during the Hurricane Charley 

(11,500 ft3/s) condition. It was evident from the field measurements that the debris had a major effect on flow through the 

bridge; therefore, the general debris configurations observed 

in the field were incorporated into the models. Methods and 

specific information regarding the data collection and how the 

data were used to develop, calibrate, and compare the models 

are discussed in the Methods section.

Methods 

The availability of reliable bathymetric and topographic 

information is key to the development of reliable hydraulic 

models. The bathymetric and topographic data that were collected and processed for the model development are described 

in this section. Field data-collection techniques used to collect 

model calibration and comparison data (water-surface profiles, 

velocity distribution, and discharge) are also described. 

Comparisons of the one- and two-dimensional modeling 

results to the field data provided the basis for evaluating the 

differences between the two models and the implications of 

the differences. The model comparisons also provide valuable 

information for the development of guidelines for applying 

two-dimensional models at bridge sites.

Data Collection

Channel bathymetry data were collected from a moving 

boat by using a 200-kilohertz (kHz) single-beam echo sounder 

and differentially corrected global positioning system (DGPS). 

The data were collected over a 2-day period in December 

2004. The echo sounder is specified by the manufacturer to 

have an accuracy of 1 centimeter (cm) at one standard deviation. The DGPS unit is specified by the manufacturer to be 

accurate to 3.3 ft at two standard deviations; tests and prior use 

of this unit indicate that typically about 80 percent of the data 

are within 3.3 ft of the true location. Water-surface elevations, 

discharge, and detailed water velocities were measured at 

two different high-flow conditions (11,500 and 21,000 ft3

/s). 

The 11,500 ft3

/s flow condition was measured on August 19, 

2004, and was a result of rainfall produced by the passage of 

Hurricane Charley over eastern North Carolina. The water 

surface measured at USGS streamgaging station 02084000 

(located at the downstream boundary of the modeled reach) 

during the survey on August 19, 2004, was 10.7 ft (NAVD 88), 

which is 1.3 ft above the Tar River flood stage at Greenville, 

North Carolina (table 1). The 21,000 ft3

/s flow condition was 

measured on June 20, 2006, and was a result of rainfall from 

the remnants of Tropical Storm Alberto passing over North 

Carolina. The water surface measured at USGS streamgaging 

station 02084000 during the survey on June 20, 2006, was 

Figure 2. Debris accumulation (A) upstream from U.S.-13 and 

(B) between the parallel bridges of U.S.-13 over the Tar River at 

Greenville, North Carolina, on June 20, 2006.

A.

B.

Figure 2. Debris accumulation (A) upstream from U.S. 13 and (B) between the parallel bridges of

 U.S. 13 over the Tar River near Greenville, North Carolina, on June 20, 2006.

Flow direction
Methods 5

14.7 ft (NAVD 88), which is 5.3 ft above the Tar River flood 

stage at Greenville, North Carolina (table 1). Water-surface 

elevations for both flow conditions were measured at three 

locations on the Tar River, two of which are located within 

the study reach and the other located 1 mile upstream from 

the study reach. Detailed water-velocity measurements and 

channel-bathymetry data were collected at eight cross sections 

during each of the hydraulic surveys (fig. 1 inset).

Bathymetry and Topography

Bathymetry data were collected along cross sections 

spaced approximately one channel width apart (200 ft) 

throughout the study area. The raw bathymetry data were 

collected and processed to filter out (1) problems related to the 

echo sounder processing a multiple-return acoustic signal in 

shallow water (which causes the measured depth to be twice 

the actual depth), (2) GPS problems, and (3) redundant areas 

along the banks caused by failure to properly end data collection at various cross sections. Analog printouts of the bottom 

profiles were produced as part of the data-collection process 

and used as a quality-assurance measure because multiplereturn errors can easily be identified in the analog printouts. 

The processed bathymetry data (including edge of water 

points) were exported into a text file that included geographic 

coordinates and a corresponding depth for 182,449 surveyed 

data points on 118 cross sections. The water depths were then 

subtracted from the water-surface elevation to establish an 

elevation for the streambed. The water-surface profile through 

the surveyed reach was established using tapedowns from a 

reference mark on the U.S.-13 bridge and measured water 

levels at USGS streamgaging stations 02083893 and 02084000 

located approximately 1 mile upstream and at the downstream 

extent of the study reach, respectively (fig. 1). An average 

water-surface slope for the survey period (December 2–3, 

2004) was computed and used to adjust the water surface from 

which the streambed elevations were computed throughout the 

reach. 

Development of the model required accurate land-surface 

elevation data. In January 2001, contractors for the North 

Carolina Floodplain Mapping Program (FMP) used LiDAR 

systems to acquire elevation data along with the horizontal 

position of each elevation data point 

for the Tar River basin. Raw LiDAR 

data subsequently were processed to 

remove returns from objects, such as 

trees, buildings, and other structures. 

The initial data set, known as the bare 

earth mass points data, is distributed by 

the FMP free of charge through their 

Floodplain Mapping Information System (FMIS; http://www.ncfloodmaps.

com). The root mean square error of the 

LiDAR data for all of the counties in 

the Tar River basin is less than 20 cm 

(7.9 inches), which is the vertical 

accuracy required by the FPM for acceptance of LiDAR data 

measured in coastal plain counties of North Carolina. LiDAR 

data for the floodplains in the study area were available from 

the FMP. Bare earth mass point data received from the FMP 

were a collection of irregularly spaced points. These data 

were reprocessed into a digital elevation model (DEM) with 

regularly spaced, 10-ft by 10-ft cells. An analysis was done 

by the USGS in North Carolina to determine the resolution 

for which to reprocess the bare earth LiDAR data that best 

balanced topographic accuracy and efficiency of use. For 

the coastal plain of North Carolina, a 10-ft by 10-ft grid was 

determined to be the best resolution. The DEM was created by 

first generating a triangulated irregular network (TIN). A TIN 

maintains the exact horizontal and vertical positions of the 

source data at the vertices of each triangle in the TIN, which 

maintains the integrity of the original data. A representation 

of major streams (known as breaklines) provided by the FMP 

was used to guide the interpolation along the edges of the 

triangles. The processed LiDAR data (10-ft by 10-ft grid) for 

the floodplain and overbank topography consisted of more 

than 2.5 million data points. The 10-ft by 10-ft overbank and 

floodplain DEM was merged with the bathymetry data using 

routines provided in the Surface-Water Modeling System 

(SMS), version 9.0 (Brigham Young University, 2005), 

modeling interface to develop a comprehensive topographic 

map for the model reach.

Water-Surface Elevations

Water-surface elevations in the study reach were 

determined from USGS streamgaging stations 02083893 and 

02084000 on the Tar River and by tapedown from a surveyed 

reference mark on the downstream guardrail of the U.S.-13 

bridge (fig. 1). USGS streamgaging station 02084000 (Tar 

River at Greenville) was used as the downstream boundary for 

all modeling efforts. 

Velocity and Discharge

Water-velocity and discharge data were collected from 

a moving boat. The horizontal position of the boat was 

Table 1. Summary of field data collection in the study reach at the U.S. Geological 

Survey streamgaging station on the Tar River at Greenville, North Carolina.

[USGS, U.S. Geological Survey; NAVD 88, North American Vertical Datum of 1988; ft, feet; ft/ft, foot 

per foot; ft3/s, cubic feet per second]

Measurement 

date

Water-surface 

elevation at 

USGS streamgaging 

station 02084000 

(ft above NAVD 88)

Distance 

above 

flood stage 

(ft)

Water-surface 

slope in study 

reach 

(ft/ft)

Range in measured 

discharge 

(ft3

/s)

8/19/04 10.7 1.3 0.00017 11,300 – 11,600

6/20/06 14.7 5.3 0.00015 20,900 – 21,700
6 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

measured by use of a DGPS receiver. The DGPS system 

received its differential corrections from a local U.S. Coast 

Guard beacon.

Advances in velocity-measurement technology allow 

three-dimensional velocities to be measured from a moving 

boat by using an acoustic Doppler current profiler (ADCP) 

(Oberg and Mueller, 1994; Mueller, 1996; Oberg and others, 

2005). All velocities were measured with an ADCP. Threedimensional velocities were measured from approximately 

3.5 ft beneath the water surface to within 6 percent of the 

depth to the bottom. Depths ranged from 11.5 to 29 ft for 

the August 19, 2004, survey and from 18 to 31.5 ft for the 

June 20, 2006, survey. Established methods were used to 

estimate the discharge in the unmeasured top and bottom 

portions of the profile (Simpson and Oltmann, 1991). Depthaveraged velocities were computed from the three-dimensional 

field data at each cross section; these discrete depth-averaged 

velocities were computed as an average of the measured 

velocity, so no velocities were computed in the unmeasured 

portions of the water column. Two cross-sectional measurements were made in succession at each of the eight velocity 

profile sections for quality assurance.

Discharge was also measured by the ADCP for each 

velocity profile section; however, these measurements were 

not representative of the total discharge because dense floodplain vegetation limited data collection by the ADCP to only 

the main channel. A separate total discharge measurement was 

collected during the surveys at a contracted bridge opening 

for the Highway 264 bypass (located approximately 2.5 miles 

downstream from the study reach) through which all of the Tar 

River flow passed. In order to compensate for unsteadiness in 

flow during the surveys, discharge and water-surface elevation 

measurements made at the beginning and end of the velocity 

data collection were averaged to produce a time-averaged flow 

rate and water-surface profile that were representative of the 

survey period (table 1).

Scour Observations

Debris accumulation, high velocities, and shallow depths 

limited the ability to collect velocity and depth data from a 

moving boat directly adjacent to the abutments and piers. For 

the two high-flow hydrographic surveys, however, comparison 

of the measured cross sections upstream and downstream 

from U.S.-13 showed that the deepest section of the channel is 

located directly upstream from the right abutment. The actual 

streambed elevation directly upstream from the right abutment 

differed by less than 0.25 ft for the two high-flow surveys, 

which is within the error of the instrument and data-collection 

method in turbulent conditions. The streambed upstream 

from the U.S.-13 bridge near the right abutment was 4 to 

5 ft deeper than the streambed directly downstream from the 

right abutment. The depths associated with the June 20, 2006, 

flood measurements were deep enough to collect data within 

approximately 25 ft of the left abutment, and the streambed 

at this location was about 1.25 ft deeper than the adjacent 

streambed. Data near the left abutment were not collected during the August 19, 2004, flood measurements because water 

depths were too shallow to collect ADCP data. The streambed 

downstream from the U.S.-13 bridge on the left side of the 

main channel (the area between piers 5 and 8, numbered from 

right to left looking downstream; fig. 3) was 5 to 6 ft deeper 

than the streambed upstream from the bridge, which indicates 

a combination of contraction and pier scour through the 

bridge. The streambed elevations through the bridge opening 

showed no change between the two high-flow measurements.

Modeling

A two-dimensional and one-dimensional model of 

the study reach were developed separately using the field 

data described previously, 2-ft pixel black and white aerial 

photography, and bridge plans from the NCDOT. The domain 

for both models was identical for all simulated conditions. 

The modeled reach is 4 miles long, with floodplain widths 

that vary from 5,400 to 1,050 ft for the surveyed high-flow 

conditions. The lateral extent of the modeled reach coincides 

with the approximate peak water-surface elevation (30 ft above 

NAVD 88 at U.S.-13) measured following Hurricane Floyd 

in 1999, which was estimated to be a 500-year flood. Depths 

represented by the models ranged from 0.01 to 39.25 ft.

Two-Dimensional Model

The two-dimensional, vertically averaged Finite Element 

Surface-Water Modeling System (FESWMS), version 3.0, was 

implemented by the USGS for the selected bridge site over 

the Tar River. FESWMS is currently supported by the Federal 

Highway Administration (FHWA) and has been described as 

being “designed specifically to analyze flow at bridge crossings where natural processes and fabricated structures have 

created complicated hydraulic conditions that are difficult to 

evaluate using conventional methods” (Froehlich, 2002). An 

earlier version of the model was successfully used to simulate 

bridge hydraulics and help compare predicted scour with measured scour at the U.S. Highway 70 bridge over Bear Creek 

near Mays Store, North Carolina, during Hurricane Floyd in 

1999 (Wagner and others, 2005). Previous research has shown 

that the simulation of pressure flow at bridges is problematic 

in FESWMS, version 3.0 (Zevenbergen and others, 2002). 

Even for relatively simple cases, such as low discharges and 

flow velocities, numerical instability causes the model to 

diverge when the water surface reaches the bottom of a bridge 

deck. Similar problems were encountered during this study, 

which limited the accuracy of the hydraulics in the study reach 

for conditions that induced pressure flow. Increased roughness 

coefficients of 0.55–0.65 were used in an attempt to simulate 

the energy losses associated with pressure flow at the main 

channel and overflow bridges of U.S.-13.
Methods 7

Figure 3. Finite element grid configuration through the U.S.-13 bridge over the Tar River at Greenville, North Carolina.

Computational Grid

The finite-element mesh for the two-dimensional model 

consisted of 27,450 to 28,160 active grid cells (elements) 

ranging in size from 378,900 square feet (ft2

) on the floodplains to 235 ft2

 in the main channel upstream and downstream 

from U.S.-13 and 7 ft2

 in the main channel through the U.S.-13 

bridge opening. The resolution of the grid was refined in the 

area surrounding the U.S.-13 bridge to improve simulation 

of small-scale hydraulic complexities caused by the structure 

(fig. 3). 

Each element within the computational mesh was 

assigned a material type, which is associated with a unique 

set of hydraulic characteristics (Manning’s n, eddy viscosity, 

marsh porosity, pressure-flow potential) that directly influences how water moves through an element. Aerial photography was used to assign material types to elements based on 

similar land-use characteristics (forest, residential, wetland, 

industrial). The actual hydraulic characteristics associated 

with each material type were initially assigned on the basis of 

published guidance and engineering judgment, then slightly 

adjusted during the calibration process. The final Manning’s n

roughness values ranged from 0.038 in the main channel to 

0.14 on the floodplains, and base eddy viscosity values ranged 

from 9 pound-second per square foot (lb-sec/ft2

) for the main 

channel and overbanks to 15 lb-sec/ft2

 for all other material 

types. Eddy viscosity was allowed to vary from cell to cell 

according to the bed shear velocity, depth, and the horizontal 

dimensions of the cell using equation 1.

3537’02”

3537’11”

7723’32” 7723’18”

Pier 10

Pier 11

Pier 8 Pier 9

Pier 6 Pier 7

Pier 4 Pier 5

Pier 2

Pier 1

Pier 3

0 100 200 300 400 500 FEET

0 20 40 60 80 100 METERS

Figure 3. Finite element grid configuration through the US 13 bridge over the Tar River at Greenville, North Carolina.

Disabled elements

representing piers

Finite element grid cells
8 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

where:

vt = depth-averaged kinematic eddy viscosity;

vt 0 = base kinematic eddy viscosity;

c

μ1

, c

μ2 = dimensionless coefficients;

H = water depth;

μ* = bed shear velocity;

 = determinant of the jacobian matrix of element coordinate transformations, which provides point-wise 

measures of element area;

 = partial differential of depth-averaged velocity in the x direction; 

and

 = partial differential of depth-averaged velocity in the y direction.

boundary coincided with the USGS streamgaging station 

02084000 (Tar River at Greenville), and the water-surface 

elevation was determined from water-level data collected at 

USGS streamgaging station 02084000.

One-Dimensional Model

The one-dimensional, step-backwater model HEC-RAS 

was used for hydraulic modeling at the study site (U.S. Army 

Corps of Engineers, 2003). (Version 3.1.2, released in April 

2004, was used for this application.) HEC-RAS is widely used 

for simulating steady-flow water-surface profiles in stream 

reaches and for one-dimensional hydraulic analysis at bridge 

crossings. The one-dimensional energy equation is solved 

within HEC-RAS for determination of water-surface profiles. 

The momentum equation can be included in the solution for 

situations in which the water-surface profile changes markedly 

with distance, such as at hydraulic jumps, bridges and culverts, 

and stream junctions. The effects of obstructions, such as 

bridges, culverts, weirs, and structures in the floodplain, are 

included in the hydraulic computations (U.S. Army Corps 

of Engineers, 2003). Unsteady flow simulations also can be 

performed using HEC-RAS.

Model Development

The development of the HEC-RAS model relied 

entirely on the data sets used to develop the two-dimensional 

FESWMS model. Cross sections were extracted directly 

from the two-dimensional model’s topographic data sets and 

imported to the HEC-RAS geometric data editor. Surveyed 

geometry and LiDAR data were used to incorporate the 

roadway and bridges associated with U.S.-13 and Green 

Street into the one-dimensional model by using the bridge 

design module within HEC-RAS. Manning’s n values that 

(1)

The dimensionless coefficients, cμ1

 and cμ2, were assigned to 

be 0.3 and 0.1, respectively, for the channel and overbank elements and 0.9 and 0.5, respectively, for all other elements.

To correctly simulate bridge hydraulics, the roadways in 

the study area had to be positioned accurately in the model. 

A geo-referenced digital map of the roadway alignments 

and pier locations was unavailable and had to be developed 

in AutoCad using existing NCDOT bridge plans and aerial 

photography. The spatial orientation of the U.S.-13 and 

Green Street roadways and associated piers in the model was 

established using the developed map. The elements through 

the bridge section were sized to correspond with the footprint 

of the bridge piles (1.67 ft diameter). The 144 individual piles 

supporting the U.S.-13 bridge were modeled with no-slip 

conditions as disabled elements, which designate an element 

as a barrier to flow. Disabled elements and increased Manning’s roughness values were used to simulate the floating 

debris accumulated through the U.S.-13 bridge opening. The 

elements directly in front of piers 2–5 (numbered from right 

to left, looking downstream; fig. 3) were disabled to represent 

the heavy debris that was accumulated against the piers. To 

simulate the observed floating debris, the elements through the 

bridge opening between piers 2–5 were assigned Manning’s 

n values that varied by depth. The top 2.5 to 3.5 ft of water 

in these areas was assigned a Manning’s n value that ranged 

from 0.075 to 0.20, whereas the remaining area of the water 

column below a depth of 3.5 ft was assigned a roughness value 

of 0.045.

Boundary Conditions

Measured steady-state discharges of 11,500 and 

21,000 ft3/s were used as the upstream boundary condition 

for the model, and the inflow distribution across the upstream 

boundary was based on depth. The downstream model 

2 2 2

01 2

1

2 , t t

U V UV

x y yx

v v c Hc J P P

G G GG

G G GG P
 §· § · § ·  ̈  ̧  ̈ ̧  ̈  ̧ © 1 ©1 © 1

     

J

U

x

G

G

V

y

G

G
Simulation of Water-Surface Elevations and Velocity Distributions 9

were associated with the calibrated two-dimensional model 

were also transferred into HEC-RAS. The HEC-RAS model 

was calibrated using the two hydraulic conditions that were 

measured in the field and used in the FESWMS model. 

The U.S.-13 bridge was modeled as one bridge in 

HEC-RAS with multiple openings (one main channel and 

two relief openings). The areas between the bridge openings 

were modeled as ineffective flow areas. Ineffective flow areas 

were also assigned in the bridge opening and contraction 

and expansion cross sections. A 1:1 contraction ratio (for 

example, if the model cross section is 10 ft upstream from the 

bridge, the effective flow area is 10 ft wider than the bridge 

opening on either bank) was used to assign the ineffective 

flow areas upstream from the bridge, and a 2:1 expansion ratio 

was applied downstream from the bridge. These ratios were 

applied using guidance from the HEC-RAS hydraulic 

reference manual (U.S. Army Corps of Engineers, 2003). 

Contraction and expansion coefficients (0.3 and 0.5, respectively) were elevated at the approach and exit sections and 

through the bridge opening relative to the coefficients in the 

other cross sections in the model (0.1 and 0.3, respectively).

Modeled flow conditions with water-surface elevations 

that were below the low chord of the U.S.-13 bridge were 

computed using the momentum, energy equation (standard 

step), and WSPRO bridge modeling routines. The routine 

that computed the highest energy loss through the bridge was 

used for the final solution. HEC-RAS also has the ability to 

compute flows that come into contact with the maximum 

low-chord elevation of the bridge by either the energy equation 

or by using separate equations for pressure and(or) weir flow. 

The energy-based method performs all computations as though 

they are open channel flow; however, the area obstructed by 

bridge piers, abutments, and bridge deck are subtracted from 

the flow area, and additional wetted perimeter is added. For 

the pressure and weir-flow method, pressure flow is computed 

using a sluice gate type of equation when only the upstream 

side of the bridge is in contact with the water, and the standard 

full-flowing orifice equation is used when both the upstream 

and downstream sides of the bridge are submerged. Flow over 

the bridge and(or) roadway is calculated using the standard 

weir equation. When the weir becomes highly submerged, 

HEC-RAS will automatically switch to calculating the 

upstream water surface by the energy equation instead of 

using the pressure and weir-flow equations. The criteria for 

when the model switches to the energy equation is based on 

percentage submergence of the bridge (submergence is defined 

as the depth of water above the minimum weir elevation on 

the downstream side of the bridge divided by the height of 

the energy gradeline above the minimum weir elevation on 

the upstream side) (U.S. Army Corps of Engineers, 2003). 

The default submergence criterion (95 percent) was used for 

the study. The energy equation solution was used to compute 

the energy loss through the U.S.-13 bridge for all simulated 

flow conditions, including flows that overtopped the roadway 

because the water-surface elevations of those overtopping 

conditions fully submerged the roadway/weir. 

HEC-RAS allows the user to specify up to 45 locations 

in each cross section for which the program will compute 

flow distribution output. At each cross section where a 

flow distribution is specified, HEC-RAS will compute the 

flow, area, wetted perimeter, percentage of conveyance, and 

average velocity for each of the user-defined slices, referred 

to hereafter as conveyance tubes. Velocity distributions were 

extracted from the one-dimensional model and compared to 

two-dimensional model results and field data using the mean 

velocity output from 45 conveyance tubes distributed on cross 

sections that coincided with locations of field measurements.

Boundary Conditions

The same steady-state discharges used in the twodimensional model (11,500 and 21,000 ft3

/s) were used in the 

one-dimensional model. These discharges were used as the 

upstream-boundary condition for the model. The downstream 

head-boundary condition was determined from water-level 

data collected at USGS streamgaging station 02084000, and 

the downstream model extent coincided with the location of 

USGS streamgaging station 02084000.

Simulation of Water-Surface 

Elevations and Velocity Distributions

Water-surface elevations and velocity distributions of 

both models were compared to measured field data to evaluate 

the ability of each model to represent field conditions. A 

summary of the calibration process and model comparisons is 

presented.

Model Calibration

The two-dimensional model was initially calibrated to 

water-surface slope by using published roughness values and 

uniform eddy viscosity values, and not accounting for the 

accumulated debris through the bridge. Although measured 

and simulated water-surface slopes agreed for the August 19, 

2004, (11,500 ft3/s) conditions, there was disagreement 

between the measured and simulated velocity distributions. 

This is a noteworthy finding and demonstrates the values of 

site-specific velocity data for model calibration and testing. 

The roughness values and eddy viscosity terms were adjusted, 

and the mesh configuration through the U.S.-13 bridge was 

refined and incorporated the floating debris (as described 

previously) until the modeled water-surface elevations 

and velocities for the steady flow of 11,500 ft3

/s matched 

those measured in the field. The steady-flow condition 

of 21,000 ft3/s was then simulated without changing the 

computational mesh or model parameters, and the simulated 

water-surface elevations and velocities were compared with 

those observed in the field. Minor adjustments were made 

to some material types and hydraulic parameters (mainly for 
10 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

those elements representing the floating debris accumulated 

through the bridge) such that model results displayed good 

agreement with field data for both flow conditions. Calibration 

results are presented in the following sections.

The Manning’s n values used for the FESWMS model 

were also used initially to calibrate the HEC-RAS model to 

the measured water-surface elevation for both steady-flow 

conditions. Manning’s n values in the main channel were 

increased slightly for the one-dimensional model to better 

match the measured water-surface elevation. The distribution 

of mean velocities in the conveyance tubes extracted from the 

one-dimensional model output were insensitive to reasonable 

changes (based on published values and engineering judgment) in Manning’s n values and cross-sectional contraction 

and expansion coefficients; therefore, no adjustments could 

be made to the one-dimensional model during the calibration 

process to improve agreement between simulated and measured velocity distributions. 

Water-Surface Elevations

Although water-surface elevations were measured at three 

locations during each high-flow survey, the location of the two 

USGS streamgaging stations precluded them from being used 

to compare measured and simulated water-surface elevations. 

USGS streamgaging station 02083893 was useful in establishing the measured water-surface slope in the study reach; 

however, it is located approximately 1 mile upstream from the 

upstream model boundary and, therefore, cannot be compared 

directly to simulated results. Water-surface elevation data from 

USGS streamgaging station 02084000 are used as the downstream model boundary condition and hence does not provide 

a measure of model performance. Thus, the only location in 

which measured and simulated water-surface elevations were 

able to be compared was at the U.S.-13 bridge. A comparison 

of the simulated and measured water-surface elevations at the 

downstream side of the U.S.-13 bridge over the Tar River for 

the one- and two-dimensional hydraulic models is presented in 

table 2. 

Flow Continuity

Flow continuity was checked throughout the models 

to assure that (1) mass was being conserved within the 

two-dimensional model and (2) flow was being accurately 

distributed through the main channel and overflow bridges of 

U.S.-13 for both models. The two-dimensional model conserved mass throughout the domain for both flow conditions 

and provided better agreement with measured flow through the 

U.S.-13 main channel bridge than the one-dimensional model 

(table 3). Discharges for cross sections 4–7 in table 3 represent 

main channel flow only; vegetation and shallow depths 

prevented data collection on the floodplains. A tolerance of 

+/–3 percent in mass conservation discrepancy is typically 

acceptable for most hydraulic models (Donnell and others, 

2005).

Table 2. Summary of water-surface elevation calibration for the Tar River at Greenville study reach.

[Values are in feet above North American Vertical Datum of 1988. 1D, one dimensional; 2D, two dimensional]

Location

Hurricane Charley, 

August 2004

Tropical Storm Alberto, 

June 2006

Measured 

water-surface 

elevation 

1D model 

watersurface 

elevation 

2D model 

watersurface 

elevation 

Measured 

water-surface 

elevation 

1D model 

watersurface 

elevation 

2D model 

watersurface 

elevation 

Downstream side of U.S.-13 bridge 11.80 11.47 11.67 15.96 15.40 15.70

Measured event Water-surface elevation at the downstream side of U.S.-13 bridge

Measured 1D model 2D model

Hurricane Charley (8/19/04) 11.80 11.47 11.67

Tropical Storm Alberto (6/20/06) 15.96 15.40 15.70
Simulation of Water-Surface Elevations and Velocity Distributions 11

Table 3. Summary of continuity checks for the modeled reach of the Tar River at Greenville, North Carolina.[Values are in cubic feet per second. Cross section #, cross section numbers are referenced to the inset of figure 1]

Location

Hurricane Charley, 

August 2004

Tropical Storm Alberto, 

June 2006

Measured 

discharge

One-dimensional 

model discharge

Two-dimensional 

model discharge

Measured 

discharge

One-dimensional 

model discharge

Two-dimensional 

model discharge

Upstream model boundary 11,500 11,500 11,500 21,000 21,000 21,000

Cross section # 4 7,800 6,950 6,400 7,360 10,050 6,600

Cross section # 5 (upstream side of 

U.S.-13 bridge) 8,650 10,380 8,660 12,300 18,100 13,000

Cross section # 6 (downstream side of 

U.S.-13 bridge) 9,800 10,230 9,000 12,700 18,270 13,400

Cross section # 7 5,900 7,050 5,000 10,970 10,700 10,560

Downstream model boundary 11,500 11,500 11,500 21,000 21,000 21,000
12 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

Two-Dimensional Model Velocity Distribution

The two-dimensional model calibration process consisted 

of comparing measured and simulated cross-sectional velocity 

profiles at the four cross sections located adjacent to the 

U.S.-13 bridge (lines 4–7 in fig. 1 inset). The cross section 

along the downstream face of the bridge (line 6) is most 

indicative of the hydraulics through the bridge opening; therefore, the calibration process focused on matching the field data 

at that location. The simulated velocity distribution for line 6 

displayed good agreement with field measurements for both 

flow conditions as illustrated by figure 4. The largest discrepancy between the simulated and measured velocity distribution 

exists near the right bank in an area influenced by heavy 

debris accumulation. The debris constricts the cross-sectional 

area of the channel in that region and, therefore, increases 

the flow velocity. The complex hydrodynamics induced by 

the debris accumulation are three dimensional in nature and 

cannot accurately be represented by a two-dimensional, 

vertically averaged hydraulic model. A three-dimensional 

model would provide a more representative simulation of the 

hydraulics through the U.S.-13 bridge opening for conditions 

in which accumulated debris is present. Despite the limitations 

of the two-dimensional model regarding simulation of the 

three-dimensional hydraulics around the accumulated debris, 

the shape of the field- and modeled-velocity distributions 

were similar, whereas the cross-sectional median difference 

between measured and simulated velocity magnitudes ranged 

from 0.40 to 0.69 feet per second (ft/s).

Effects of Debris

Debris accumulation was determined to have an 

appreciable effect on the velocity distributions through the 

U.S.-13 bridge. Large floating debris rafts between piers 

2 and 5 were observed during both hydrographic surveys 

(fig. 2). The general location of the debris accumulation 

was the same for both surveys, but the spatial extent of the 

debris varied. The debris raft extended from the upstream 

face to the downstream face of the parallel bridges during 

the June 20, 2006 (21,000 ft3/s), condition but was more 

restricted to the upstream bridge face during the August 19, 

2004 (11,500 ft3/s), condition. The two-dimensional model 

calibration process initially did not take into account the debris 

accumulation at U.S.-13, but comparisons of modeled and 

measured velocity distributions made it evident that the debris 

had a major effect on flow through the bridge. Therefore, 

the general debris configurations observed in the field were 

incorporated into the two-dimensional model by disabling 

elements and increasing roughness values through the bridge, 

as previously described. As a result, measured and simulated 

velocities were more consistent with measured data (fig. 4). 

Debris was incorporated into the one-dimensional model by 

specifying a floating debris height and width for piers 2–5 

in the pier data editor within the HEC-RAS graphical user 

interface that was consistent with the debris configuration used 

in the two-dimensional model. 

The NCDOT current (2007) designation of debris 

potential at bridges is “high, moderate, or low” based on 

field observations and interviews with bridge maintenance 

personnel. The field observations during this study indicate 

that debris potential is moderate to high at the U.S.-13 bridge, 

which was shown to appreciably affect the velocity magnitudes and lateral distribution through the bridge. 

Model Uncertainty

Hydraulic models require three types of data: (1) topographic data for the hydraulic model computational grid; 

(2) effective friction values (Manning’s n) and eddy viscosity 

terms for each computational segment (one-dimensional 

model) or element (two-dimensional model); and (3) model 

validation data of some type (Bates and others, 2004). Uncertainties exist in each of these data types (Bales and others, 

2006). More specific factors that introduce uncertainty into 

the Tar River at Greenville model are the debris configuration 

through the U.S.-13 bridge and potentially reduced floodplain 

storage from accumulated debris from past floods and passage 

of tropical systems (hurricanes and tropical storms).

Topographic Data

Bathymetric data were collected for the model along 

cross sections spaced less than one channel width apart 

and with point spacing less than 0.25 ft. Despite the dense 

bathymetric data, uncertainty is introduced during the creation 

of a continuous bathymetric map of the channel from crosssectional data. Surveyed bathymetric data do not fall on 

perfectly straight cross sections because of inconsistencies in 

the boat course across the river. Internal triangulation routines 

by the FESWMS interface software package Surface-Water 

Modeling System (SMS), version 9.0 (Brigham Young 

University, 2005), did not properly interpolate the collected 

bathymetry data (Wagner and Mueller, 2001). Instead, a 

uniform grid of the raw bathymetry data was developed 

using the channel template routine included in the MultiDimensional Surface-water Modeling System (MD-SWMS) 

interface developed by the USGS (McDonald and others, in 

press). The bathymetric data used to build the computational 

mesh are an interpolated representation of the raw data, which 

introduces model uncertainty, especially in the areas between 

measured cross sections and the region between the last 

measured bathymetric point and the bank point.

Uncertainty also exists in merging the bathymetric data 

with the LiDAR data. For many overbank areas within the 

model domain, the bathymetric data overlapped the LiDAR 

data. In these cases, visual inspection and orthophotography 

were used to determine which data to preserve. The interpretation of these overlapping regions introduced additional 

geometric uncertainty.
Simulation of Water-Surface Elevations and Velocity Distributions 13

Figure 4. Measured and simulated velocity distributions through the U.S.-13 bridge over the Tar River at Greenville, North 

Carolina, for high-flow conditions associated with Hurricane Charley, August 2004, and (B) Tropical Storm Alberto, June 2006.

DISTANCE FROM LEFT BANK, IN FEET

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

DEPTH-AVERAGED VELOCITY, IN FEET PER SECOND

Field data

Two-dimensional

model (with debris)

Two-dimensional

model (no debris)

0 50 100 150 200 250 300 350

DISTANCE FROM LEFT BANK, IN FEET

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360

Field data

Pier 7 Pier 6 

Pier 5 Pier 4 Pier 3 Pier 2 

Pier 8 Pier 7 

Pier 6 Pier 5 Pier 4 Pier 3 Pier 2 

Figure 4. Measured and simulated velocity distributions through the U.S. 13 bridge over the Tar River

 at Greenville, North Carolina, for high-flow conditions associated with (A) Hurricane Charley and

 (B) Tropical Storm Alberto, June 2006.

A.

B.

Two-dimensional

model (no debris)

Two-dimensional

model (with debris)
14 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

Hydraulic Parameters

Friction values (Manning’s n) and eddy viscosity values 

were assigned to the model on the basis of engineering 

judgment and in accordance with published literature. Digital 

orthophotography from 2003 was used to assign the hydraulic 

parameters to the elements (two-dimensional model) and cross 

sections (one-dimensional model) according to various land 

uses, such as residential, forest, wetland, and industrial. The 

orthophotography does not provide the resolution that windshield surveys and photographs can offer for estimating the 

hydraulic characteristics of each particular land use and, thus, 

can limit the accuracy of approximating model parameters. 

Model Calibration Data

The Tar River through the study reach was out of its 

banks for both high-flow calibration surveys. There are no 

contracted sections within the model domain in which to 

measure a total discharge with a manned boat; therefore, the 

survey crew had to go downstream approximately 2.5 miles 

to a fully contracted opening (U.S. Highway 264 Bypass) to 

measure the total discharge. There are no major tributaries to 

the Tar River between the model’s upstream boundary and the 

location of the discharge measurement. However, depending 

on where on the flood hydrograph the discharge measurements 

were indicated to be made, water may be moving into or out of 

storage between the model’s inflow boundary and the measurement location. Velocity profiles collected with the ADCP 

included random noise associated with the measurement of the 

Doppler shift off moving particles in the water column. 

Debris

Debris accumulation at the U.S.-13 bridge was observed 

by USGS personnel during the study to occur at high flows 

in excess of at least the estimated 1.5-year recurrence interval 

flow and had an appreciable effect on velocity distributions. 

Although debris was noted during both field surveys, 

photographs of the debris during the 11,500 ft3

/s event were 

not taken. The actual debris configuration and depth below 

the water surface incorporated into the models required some 

estimation from survey crew field notes and bridge inspection 

reports from 2003. 

Although the general location of the debris accumulation 

was similar between the two surveyed events, the extent and 

quantity of debris were different. Thus, there is uncertainty 

associated with modeling conditions that have not been 

surveyed because of the natural variability in debris supply 

and configuration for various flows.

There is also uncertainty associated with the technique 

used to model the debris in the two-dimensional model. The 

use of disabled elements (creates a barrier to flow in the 

model) to represent debris accumulated directly upstream 

from the piers may not be realistic because flow can convey 

through and under the floating woody debris. The true depth 

of floating debris was unknown; therefore, there is uncertainty 

associated with the procedure of assigning roughness values 

by depth to simulate the debris through the bridge. 

Overbank Flow and Debris

The flooding and wind damage throughout the Tar River 

basin as a result of Hurricanes Fran and Floyd in the late 

1990s left large accumulations of debris on the floodplains of 

the Tar River and the main channels of most tributaries in the 

basin. Stage-discharge ratings at many USGS streamgaging 

stations in the Tar River basin underwent shifts as a result 

of the debris accumulation from Hurricanes Fran and Floyd. 

Following Hurricane Floyd in 1999 through 2002 and from 

mid-2004 through early 2006, much of eastern North Carolina 

was experiencing below-average precipitation or drought 

conditions, which reduced the opportunity for the removal of 

accumulated debris by high-flow events. The accumulated 

debris on the floodplains in the model reach may have affected 

the model calibration process by increasing roughness 

values above published values and decreasing the storage 

volume in the floodplains, which would reduce the natural 

tendency of flow to leave the channel and spread out across 

the floodplain. Comparisons of simulated and measured main 

channel discharge upstream and downstream from U.S.-13 

show that the measured flow is higher for both surveyed 

conditions, which is consistent with increased roughness and 

reduced storage volume in the floodplains. Roughness values 

on the floodplains were increased above published values in 

the models, but the potential reduction in floodplain storage 

volume as a result of accumulated debris was not accounted 

for in the modeling process. 

Model Scenarios for Existing Bridge and 

Pre-Roadway Conditions

Computed flood-frequency estimates of the 10-, 50-, 

100-, and 500-year return-period floods on the Tar River 

at Greenville were simulated with both the one- and twodimensional models. The simulated water-surface profiles and 

velocity fields were used to compare the modeling approaches 

and provide information on what return-period discharges 

would result in road overtopping and(or) pressure flow, which 

is essential in the design of new and replacement structures. 

A pre-roadway construction scenario (excluded the U.S.-13 

bridge and roadway) was simulated with both models for 

the 10-, 50-, 100-, and 500-year return-period floods and 

compared to simulations of the existing bridge conditions. 

Flood-Frequency Calculations

Flood-frequency estimates for the 10-, 50-, 100-, and 

500-year discharges were taken from the Flood Insurance 
Simulation of Water-Surface Elevations and Velocity Distributions 15

Study Report for Pitt County, North Carolina, submitted to 

the Federal Emergency Management Agency (FEMA) in 

2002 (Federal Emergency Management Agency, 2002). The 

published flood-frequency discharges for the Tar River in Pitt 

County did not directly coincide with USGS streamgaging 

station 02084000 (drainage area 2,660 square miles), but discharges were provided for locations upstream and downstream 

from the study reach (drainage areas of 2,521 and 2,757 square 

miles, respectively). The 10-, 50-, 100-, and 500-year returnperiod flows in the study reach (at USGS streamgaging station 

02084000) were estimated by interpolating the locations 

of FEMA-published flood-frequency discharges using the 

drainage area ratio correction shown in equation 2 (table 4).

where:

QG = x-year discharge on Tar River at 

Greenville, 

Q222 = published x-year discharge on Tar River at 

State Route (SR) 222,

x-year = specific flood-frequency return period 

(10, 50, 100, 500),

DAG = drainage area for Tar River at Greenville 

(2,660 square miles),

DA222 = published drainage area for Tar River at 

SR 222 (2,521 square miles), and

CRP = coefficient from published (Pope and 

others, 2001) flood-frequency equations 

for x-year discharge in the Coastal Plain 

hydrologic area.

Boundary Conditions

The flood-frequency discharges computed for USGS 

streamgaging station 02084000 were applied as the upstream 

boundary conditions for the 10-, 50-, 100-, and 500-year 

modeled scenarios. The water-surface elevations for the 

downstream boundary conditions were determined from the 

stage-discharge rating curve at USGS streamgaging station 

02084000. 

Model Scenario Results

The results of the one- and two-dimensional models 

of the study area for existing and pre-roadway conditions 

were summarized to (1) provide information on the effect of 

U.S.-13 on hydraulics in the study area; (2) determine what 

return-period discharges would result in road overtopping 

and(or) pressure flow; and (3) compare the results of the oneand two-dimensional models. 

Water-Surface Elevations

There was generally good agreement between the 

water-surface elevations simulated by the one- and twodimensional models downstream from the U.S.-13 bridge 

(fig. 5). However, appreciable disparity occurred between 

the one- and two-dimensional models in simulating watersurface elevations upstream from the U.S.-13 bridge. The 

water-surface elevations at the approach section of the U.S.-13 

bridge for all modeled scenarios are summarized in table 5. 

The model results for the 500-year flood showed that aside 

from the U.S.-13 bridge, most of the U.S.-13 roadway in the 

study area is overtopped and that pressure flow occurs at the 

U.S.-13 bridge. For the 100-year return-period flow (hereafter 

referred to as the 100-year flood), the models did not indicate 

pressure flow at the U.S.-13 bridge, and roadway overtopping 

was confined to a region beginning approximately 2,000 ft 

northeast of the overflow bridge 730070 and extended to the 

model boundary on the left floodplain. The two-dimensional 

simulated water-surface elevation for the 100-year flood at 

the U.S.-13 upstream bridge face varied from 23.5 to 23.9 ft, 

which provides approximately 1.0 to 0.6 ft of freeboard below 

the low-steel elevation. Neither model indicated any road 

overtopping or pressure flow for the 50- and 10-year returnperiod discharges.

(2)

Table 4. Flood-frequency estimates for 

U.S. Geological Survey streamgaging 

station 02084000 (Tar River at Greenville, 

North Carolina).

[ft3/s, cubic feet per second]

Return period Estimated discharge 

(ft3

/s)

500-year 73,000

100-year 52,000

50-year 44,000

10-year 29,000

CRP Q Q (DA DA ) G 222 G 222 =
16 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

Figure 5. Modeled water-surface elevations for existing bridge and pre-roadway scenarios for (A) 50- and 10-year floods 

and (B) 500- and 100-year floods for the Tar River at Greenville, North Carolina, study area.

Figure 5. Modeled water-surface elevations for existing bridge and pre-roadway scenarios for (A) 50- and 10-year

 floods and (B) 500- and 100-year floods for the Tar River at Greenville, North Carolina, study area.

WATER-SURFACE ELEVATION, IN FEET ABOVE NAVD 88

2D model with U.S.-13 bridge,

10-year flood

2D model without U.S.-13 bridge,

10-year flood

1D model with U.S.-13 bridge,

10-year flood

1D model without U.S.-13 bridge,

10-year flood

2D model with U.S.-13 bridge,

50-year flood

2D model without U.S.-13 bridge,

50-year flood

1D model with U.S.-13 bridge,

50-year flood

1D model without U.S.-13 bridge,

50-year flood

U.S.-13 bridge

Green Street bridges

U.S.-13 bridge

Green Street bridges

2D model with U.S.-13 bridge,

100-year flood

2D model without U.S.-13 bridge,

500-year flood

1D model without U.S.-13 bridge,

100-year flood

2D model with U.S.-13 bridge,

500-year flood

24.0

23.5

23.0

22.5

22.0

21.5

21.0

20.5

20.0

19.5

19.0

18.5

18.0

17.5

17.0

16.5

27.5

27.0

26.5

26.0

25.5

25.0

24.5

24.0

23.5

23.0

22.5

22.0

21.5

DISTANCE UPSTREAM FROM MODEL BOUNDARY, IN FEET

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 14,000 15,000

B.

A.

1D model with U.S.-13 bridge,

100-year flood

1D model with U.S.-13 bridge,

500-year flood

2D model without U.S.-13 bridge,

100-year flood

1D model without U.S.-13 bridge,

500-year flood
Comparisons of One-Dimensional and Two-Dimensional Modeling Results to Field Data 17

Two-Dimensional Model Flow Fields

The flow fields associated with the two-dimensional 

simulations of the scenarios with and without the U.S.-13 

bridge and roadway show the largest disparity in the areas 

around the bridges and along the roadway with the maximum 

velocity differences (ranging from 3 to 6.5 ft/s for the modeled 

floods) occurring at the location of the right abutment of 

overflow bridge 730057. Difference maps of the simulated 

flow fields for the model scenarios with and without the 

U.S.-13 bridge and roadway are illustrated in the appendix. 

Comparisons of One-Dimensional and 

Two-Dimensional Modeling Results to 

Field Data

The results of the one-dimensional (HEC-RAS) and 

two-dimensional (FESWMS) models of the U.S.-13 bridge 

over the Tar River at Greenville were compared to determine 

whether the two-dimensional model is a more appropriate tool 

for simulating site conditions than the one-dimensional model. 

Water-surface elevations, velocity distributions, and scour 

estimates are compared in the following sections.

Water-Surface Elevations

The water-surface elevations simulated by the twodimensional and one-dimensional models were within 0.2 and 

0.6 ft, respectively, of the measured water-surface elevations 

on the downstream side of the U.S.-13 bridge, and the models 

are generally in good agreement downstream from the U.S.-13 

bridge (fig. 6). However, appreciable disparity occurred 

between the one- and two-dimensional models in simulating 

water-surface elevations upstream from the U.S.-13 bridge. 

The disparity upstream from the U.S.-13 bridge can be attributed mainly to differences in momentum loss at U.S.-13. The 

simulated water-surface slopes for the two models are similar 

upstream from U.S.-13; however, the two-dimensional model 

simulates more energy loss through the U.S.-13 main channel 

bridge, U.S.-13 overflow bridges, and channel bend directly 

upstream from U.S.-13. The flow conditions directly upstream 

and through the U.S.-13 bridge are two dimensional in nature, 

and the associated energy losses are not fully represented by 

a one-dimensional model, which explains the large discrepancies in simulating the water-surface elevations (fig. 6). 

To evaluate model performance in predicting water-surface elevations upstream from the U.S.-13 bridge, simulated 

water levels at the upstream model boundary for both highflow events were compared to stage data collected at USGS 

streamgaging station 02083893 (Tar River at U.S. 264 Bypass 

near Rock Springs, North Carolina), located approximately 

1 mile upstream from the upstream model boundary (fig. 1). 

The water-surface slope in the upper 3,500 ft of both models 

was used to extrapolate simulated water-surface elevations 

upstream to USGS streamgaging station 02083893. The comparison indicated that the extrapolated water levels from the 

one- and two-dimensional models were within 1.7 and 0.8 ft 

of the measured gage data, respectively. Therefore, based on 

the available data from USGS streamgaging station 02083893, 

the two-dimensional model more accurately simulated the 

water-surface elevations in the study reach.

To quantify the effect of debris on the water-surface 

elevations, the two-dimensional model was applied to the 

study reach to account for both the presence and absence of 

debris accumulation at the U.S.-13 bridge. For both high-flow 

events, the two-dimensional model that simulated debris 

resulted in slightly higher water-surface elevations upstream 

from the U.S.-13 bridge relative to the two-dimensional model 

that did not simulate debris (fig. 6). The debris (simulated with 

disabled elements and increased roughness values) impedes 

flow through the U.S.-13 bridge, thereby creating a damming 

effect that raises the upstream water level and is more in line 

with recorded stage data from USGS streamgaging station 

02083893.

Table 5. Modeled water-surface elevations at the approach section of U.S.-13 bridge over the Tar River at Greenville, North 

Carolina, for the existing bridge and pre-roadway scenarios. 

[Values are in feet. 2D, two dimensional; 1D, one dimensional]

Return-period 

flood

2D modeled

water-surface elevation

at approach with 

U.S.-13 bridge

1D modeled

water-surface elevation

at approach with 

U.S.-13 bridge

2D modeled

water-surface elevation

at approach without 

U.S.-13 bridge

1D modeled

water-surface elevation

at approach without

U.S.-13 bridge

500-year 26.88 26.90 26.52 26.78

100-year 24.03 22.93 22.45 22.69

50-year 22.74 21.44 21.12 21.27

10-year 18.86 17.91 17.90 17.80
18 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

Figure 6. Modeled water-surface elevations for high-flow conditions associated with (A) Hurricane Charley in August 2004 

and (B) Tropical Storm Alberto in June 2006.

0 3,000 6,000 9,000 12,000 15,000 18,000 21,000

14.0

13.5

13.0

12.5

12.0

11.5

11.0

10.5

10.0

9.5

9.0

18.0

17.5

17.0

16.5

16.0

15.5

15.0

14.5

14.0

WATER-SURFACE ELEVATION, IN FEET ABOVE NAVD 88

One-dimensional model

Two-dimensional model (with debris)

Two-dimensional model (no debris)

One-dimensional model

Two-dimensional model (with debris)

Two-dimensional model (no debris)

Measured water-surface

elevation

U.S.-13 bridge

Green Street

bridges

DISTANCE UPSTREAM FROM MODEL BOUNDARY, IN FEET

U.S.-13 bridge

Green Street

bridges

Measured water-surface elevation

Figure 6. Modeled water-surface elevations for high-flow conditions associated with (A) Hurricane Charley in

 August 2004 and (B) Tropical Storm Alberto, June 2006.

A.

B.
Comparisons of One-Dimensional and Two-Dimensional Modeling Results to Field Data 19

Velocity Distributions

Velocity distributions through bridge openings can have 

the greatest effect on the location of potential scour; therefore, 

accurate representations of these distributions are essential 

for cost-effective bridge design. To evaluate the capability 

of each model to accurately represent velocity distributions 

at the U.S.-13 bridge over the Tar River, simulated one- and 

two-dimensional velocity distributions were compared to 

field data (fig. 7). Velocity distributions were extracted 

from the one-dimensional model using the velocity from 45 

conveyance tubes uniformly distributed through the U.S.-13 

bridge opening and from the two-dimensional model based 

on 200 values extracted from the grid cells distributed 

across the bridge opening. The raw field data consisted of 

approximately 200 depth-averaged velocity measurements 

across the bridge opening. It is evident from the comparisons 

that the one-dimensional model is less representative than the 

two-dimensional models of measured velocity magnitudes and 

lateral distributions for the surveyed cross sections. In general, 

the velocities from the one-dimensional model were biased 

low and more uniformly distributed than velocities from 

the two-dimensional model and measured data. The mean 

differences in velocity between the two-dimensional model 

and measured field data for the Hurricane Charley (August 19, 

2004) and Tropical Storm Alberto (June 20, 2006) conditions 

were 0.66 and 0.47 ft/s, respectively. The mean differences in 

velocity between the one-dimensional model and field data for 

the Hurricane Charley and Tropical Storm Alberto conditions 

were 0.84 ft/s and 0.93 ft/s, respectively. 

A comparison of the maximum velocities simulated 

by the one- and two-dimensional models is summarized in 

table 6. The approach velocity is an important parameter 

used to predict scour at bridges. To further compare the 

simulated velocities, a summary of the approach velocities 

upstream from the U.S.-13 piers simulated by the one- and 

two-dimensional models is presented in table 7.

Debris accumulation at the U.S.-13 bridge had an 

appreciable effect on the velocity distributions simulated 

by the two-dimensional model (fig. 4). The difference was 

negligible between the one-dimensional model results with 

and without debris; therefore, both results are not depicted 

in figure 7 for the sake of legibility. The two-dimensional 

model, with debris factored in, most accurately simulated the 

contracted-flow distribution (fig. 7) and direction (figs. 8, 9) 

through the bridge opening, which makes it a better tool for 

safe and efficient bridge design. 

The graphical and statistical comparisons of the modeled 

velocity distributions are slightly biased by the fact that there 

are different sample sizes between the output of the two 

models. Output from HEC-RAS is limited to a maximum 

of 45 individual velocity points or conveyance tubes in a 

cross section. Reducing the number of velocity points output 

from the two-dimensional model to be consistent with the 

one-dimensional model would greatly diminish the resolution 

provided by the two-dimensional simulation and, therefore, 

is not a practical approach. The quality of the statistical and 

graphical comparisons between the one- and two-dimensional 

models is limited by the difference in output capabilities of the 

model interfaces.

Scour Estimates 

To further compare the results of the one- and twodimensional models, simulated hydraulic parameters (flow 

depths, velocities, attack angles, blocked flow width) for both 

measured high-flow conditions were used to predict scour 

depths at the U.S.-13 bridge by using the HEC-18 (Richardson 

and Davis, 2001) methods. The absence of available data on 

sediment size (D50 ) in the study reach was a limiting factor 

for scour calculations; therefore, contraction scour was not 

computed because the corresponding HEC-18 equations 

require sediment size. Pier and abutment scour were computed 

because the prediction equations in HEC-18 do not require 

precise sediment-size information (aside from computing 

the K4

 factor for pier scour, which is included to account for 

armoring in course-grained soil but is not applicable to the Tar 

River at Greenville). 

Pier-scour estimates using HEC-18 methods (Richardson 

and Davis, 2001) are sensitive to the attack angle of flow (the 

angle of flow directly upstream from the pier, measured in 

degrees from parallel or in line with the pier). Measured field 

data and the two-dimensional model results at the upstream 

bridge face were in good agreement (figs. 8, 9) and showed 

appreciable attack angles at 5 of the 11 piers, ranging from 

30 to 80 degrees. The one-dimensional model is not capable 

of computing flow angles, yet the HEC-18 computations 

within HEC-RAS require manual input of those angles in 

order to compute pier scour. Without the field data and(or) 

two-dimensional model results, the accuracy of flow angles 

for pier-scour analysis using a one-dimensional model is 

limited to engineering judgment and visual estimations based 

on channel and floodplain alignment relative to the bridge. 

The flow angles used in the one-dimensional model scour 

computations were based on visual estimations of channel and 

floodplain alignment from 2-ft black and white aerial photography of the site. Pier-scour estimates using the hydraulic 

parameters derived from the one- and two-dimensional models 

for the two high-flow surveys are summarized in tables 8 and 

9. Comparisons of pier-scour estimates from both models for 

the U.S.-13 bridge indicate that the two-dimensional scour 

estimates are more often deeper than those from the onedimensional model. The two-dimensional pier-scour estimates 

differ by as much as 4.4 ft with a mean difference of 1.5 ft for 

the measured flow conditions relative to the one-dimensional 

model estimates. To account for potential shifting of the 

thalweg, NCDOT often uses the highest velocity flow tube 

in HEC-RAS to compute scour for all piers. This procedure 

was applied using the results of the HEC-RAS simulations 

and is summarized in tables 8 and 9. The use of the highest 

velocity tube estimate for all pier-scour estimates resulted in 
20 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

Figure 7. Measured and simulated velocity distributions through the U.S.-13 bridge over the Tar River at Greenville, North 

Carolina, for high-flow conditions associated with (A) Hurricane Charley, August 2004, and (B) Tropical Storm Alberto, June 2006.

DISTANCE FROM LEFT BANK, IN FEET

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Field data

Two-dimensional

model (with debris)

One-dimensional

model (with debris)

DEPTH-AVERAGED VELOCITY, IN FEET PER SECOND

0 50 100 150 200 250 300 350

DISTANCE FROM LEFT BANK, IN FEET

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360

Field data

Two-dimensional

model (with debris)

One-dimensional

model (with debris)

Pier 8 Pier 7 

Pier 6 Pier 5 Pier 4 Pier 3 Pier 2 

Pier 7 Pier 6 

Pier 5 Pier 4 Pier 3 Pier 2 

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

A.

B.

Figure 7. Measured and simulated velocity distributions through the U.S.-13 bridge over the Tar River

 at Greenville, North Carolina, for high-flow conditions associated with (A) Hurricane Charley and

 (B) Tropical Storm Alberto, June 2006.
Comparisons of One-Dimensional and Two-Dimensional Modeling Results to Field Data 21

Table 6. One- and two-dimensional model simulated maximum velocities for the main channel and overflow 

U.S.-13 bridges over the Tar River at Greenville, North Carolina.

[Values are in feet per second. 2D, two dimensional; 1D, one dimensional]

Location

Hurricane Charley,

August 2004

Tropical Storm Alberto,

 June 2006

2D model 

maximum 

velocity

1D model 

maximum 

velocity

2D model 

maximum 

velocity

1D model 

maximum 

velocity

U.S.-13 bridge main channel 4.2 2.6 4.0 3.4

U.S.-13 bridge left overbank 1.1 0.94 1.9 1.5

U.S.-13 bridge right overbank 2.5 1.1 3.2 1.4

Overflow bridge 730057 2.2 0.5 4.0 0.9

Overflow bridge 730070 2.1 0.4 4.0 0.7

Table 7. One- and two-dimensional model simulated approach velocities for the piers supporting the U.S.-13 

bridge over the Tar River at Greenville, North Carolina.

[Values are in feet per second. 2D, two dimensional; 1D, one dimensional]

Pier number

(from right to left, 

looking downstream, 

fig. 3)

Hurricane Charley, 

August 2004

Tropical Storm Alberto, 

June 2006

2D model 

approach 

velocity

1D model 

approach 

velocity

2D model 

approach 

velocity

1D model 

approach 

velocity

Pier 1 0.8 1.3 0.8 0.6

Pier 2 1.5 1.6 1.2 2.3

Pier 3 1.7 1.9 1.6 2.6

Pier 4 2.2 1.9 2.8 2.6

Pier 5 3.3 1.6 2.8 2.3

Pier 6 2.6 1.5 1.6 2.2

Pier 7 1.7 1.4 1.4 2.0

Pier 8 0.7 0.7 1.2 1.1

Pier 9 0.6 0.7 1.2 1.1

Pier 10 0.2 0.7 1.0 1.1

Pier 11 0.04 0.7 0.6 1.1
22 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

Figure 8. Measured and simulated velocity vectors at the upstream side of the U.S.-13 bridge over the Tar River at Greenville, North Carolina, 

for high-flow conditions associated with Hurricane Charley, August 2004.

2,478,240 2,478,280 2,478,320 2,478,360 2,478,400 2,478,440 2,478,480

EASTINGS, IN FEET

NORTHINGS, IN FEET

EXPLANATION

Acoustic Doppler current profiler (ADCP) field data

Model data contoured by velocity magnitude

State plane coordinates, North Carolina

Blue arrows

Multi-colored arrows

Horizontal datum

Figure 8. Measured and simulated velocity vectors at the upstream side of the U.S. 13 bridge over the Tar River

 at Greenville, North Carolina, for high-flow conditions associated with (A) Hurricane Charley and

 (B) Tropical Storm Alberto, June 2006.

4.00

3.75

3.50

3.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00

683,680

683,700

683,720

683,740

683,760

683,780

683,800

683,820

683,840

683,860

683,880

683,900

683,920

Velocity magnitude, in feet per second (ft/s)

2 ft/s

U.S.-13 bridge deck

ADCP cross section 5

Individual piles

Pier 6

Pier 5

Pier 4

Pier 3

Pier 2
Comparisons of One-Dimensional and Two-Dimensional Modeling Results to Field Data 23

Figure 9. Measured and simulated velocity vectors at the upstream side of the U.S.-13 bridge over the Tar River at Greenville, North Carolina, 

for high-flow conditions associated with Tropical Storm Alberto, June 2006.

4.00

3.75

3.50

3.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00

683,675

683,700

683,725

683,750

683,775

683,800

683,825

683,850

683,875

683,900

683,925

683,950

Velocity magnitude, in feet per second (ft/s)

2 ft/s

U.S.-13 bridge deck

ADCP cross section 5

Individual piles

Pier 6

Pier 7

Pier 5

Pier 4

Pier 3

Pier 2

2,478,200 2,478,300 2,478,400 2,478,500

EASTINGS, IN FEET

EXPLANATION

Acoustic Doppler current profiler (ADCP) field data

Model data contoured by velocity magnitude

State plane coordinates, North Carolina

Blue arrows

Multi-colored arrows

Horizontal datum

Figure 9. Measured and simulated velocity vectors at the upstream side of the U.S.-13 bridge over the Tar River

 at Greenville, North Carolina, for high-flow conditions associated with (A) Hurricane Charley and

 (B) Tropical Storm Alberto, June 2006.

NORTHINGS, IN FEET
24 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

Table 8. Pier-scour estimates for the U.S.-13 bridge over the Tar River at Greenville, North Carolina, using modeled 

hydraulic data for high-flow conditions associated with Hurricane Charley, August 2004. 

[Values are in feet. 2D, two dimensional; 1D, one dimensional; —, not applicable (no debris)]

Pier number

(from right to left, 

looking downstream, 

fig. 3)

2D model

scour 

depth

2D model

highest 

approach 

velocity scour 

depth

2D model

debris scour 

depth

1D model

scour 

depth

1D model

highest 

velocity 

tube scour 

depth

1D model

debris scour 

depth

Pier 1 1.7 2.9 — 2.2 2.6 —

Pier 2 2.6 3.3 7.0 2.7 2.9 7.3

Pier 3 2.8 3.4 10.0 2.9 3.0 10.4

Pier 4 7.3 7.9 20.3 3.0 3.0 19.2

Pier 5 7.7 7.7 — 4.5 4.8 —

Pier 6 6.5 6.6 — 5.2 5.7 —

Pier 7 2.7 3.3 — 4.1 4.7 —

Pier 8 4.0 7.1 — 1.7 2.6 —

Pier 9 3.2 6.3 — 3.2 4.9 —

Pier 10 2.0 6.3 — 3.1 4.9 —

Pier 11 0.4 2.6 — 1.4 2.1 —

Table 9. Pier-scour estimates for the U.S.-13 bridge over the Tar River at Greenville, North Carolina, using modeled 

hydraulic data for high-flow conditions associated with Tropical Storm Alberto, June 2006.

[Values are in feet; 2D, two dimensional; 1D, one dimensional; —, not applicable (no debris)]

Pier number

(from right to left, 

looking downstream, 

fig. 3)

2D model

scour 

depth

2D model

highest 

approach 

velocity scour 

depth

2D model

debris scour 

depth

1D model

scour 

depth

1D model

highest 

velocity 

tube scour 

depth

1D model

debris scour 

depth

Pier 1 1.8 3.2 — 1.6 3.1 —

Pier 2 2.4 3.5 9.4 3.2 3.4 12.6

Pier 3 2.8 3.6 17.4 3.4 3.5 21.3

Pier 4 7.9 7.9 20.7 3.5 3.5 20.0

Pier 5 7.3 7.3 18.4 5.4 5.6 17.0

Pier 6 2.7 3.5 — 6.1 6.7 —

Pier 7 2.5 3.4 — 5.0 5.5 —

Pier 8 5.2 7.6 — 2.2 3.1 —

Pier 9 4.9 7.0 — 4.3 6.2 —

Pier 10 4.2 6.5 — 4.3 6.2 —

Pier 11 1.5 2.9 — 1.9 2.8 —
Comparisons of One-Dimensional and Two-Dimensional Modeling Results to Field Data 25

an increase in one-dimensional and two-dimensional model 

scour estimates that ranged from 0.1 to 1.9 ft and 0.1 to 4.3 ft, 

respectively. Separate pier-scour estimates also were computed 

for the piers with observed debris accumulation by using the 

interim procedure outlined in HEC-18 (Richardson and Davis, 

2001, appendix D). The accumulated debris nearly tripled the 

original pier-scour estimates of both models. The differences 

in pier-scour estimates can be attributed mainly to the appreciable flow angles simulated by the two-dimensional model, 

as previously discussed, at piers 5–11, which were included in 

the two-dimensional scour computations.

Abutment scour was estimated using the hydraulic 

parameters derived from the one- and two-dimensional models 

for the two high-flow surveys (table 10). The characteristics 

of the right and left U.S.-13 bridge abutments are different. 

The Froehlich prediction equation was applied to the right 

abutment because the site conditions do not fit the criteria for 

using the HIRE equation (Richardson and Davis, 2001), which 

was based on field data of scour at the end of spur dikes in the 

Mississippi River and is applicable when the ratio of projected 

abutment length (L) to the flow depth at the abutment (y1) 

is greater than 25. In contrast, the left abutment blocks an 

appreciable length of flow and, therefore, is more appropriate 

for application of the HIRE equation. The scour estimates 

of the two models for the left abutment are identical for the 

Hurricane Charley high-flow conditions and within 1.6 ft for 

the Tropical Storm Alberto high-flow conditions. The onedimensional model overpredicted scour at the right abutment 

relative to the two-dimensional model for both high-flow 

conditions, which is attributed mainly to the higher velocities 

simulated by the one-dimensional model on the right overbank 

at the approach section.

Suggestions for Selecting Appropriate Modeling 

Approach

Little guidance is available to indicate whether a one- or 

two-dimensional model would provide a more accurate 

estimate of the hydraulic conditions at a bridge site. Because 

of the additional resources associated with two-dimensional 

models, the absence of guidelines to aid in determining when 

a two-dimensional model is likely to improve a design could 

lead to unnecessary modeling expenditures and time delays. 

One goal of this study is to build the knowledge base from 

which modeling guidelines can be developed. Such modeling 

guidelines can be valuable in directing engineers in the 

selection of the most appropriate modeling approach when 

new bridges are being designed. 

During the planning stages of a new bridge design, little 

or no information is available regarding the hydraulics of 

the river until a predictive model is developed and applied. 

Hydrologic, topographic, and physiographic characteristics 

of the area around a bridge site can be useful in determining 

if a one- or two-dimensional model is needed to accurately 

estimate the hydraulic conditions. By compiling pertinent 

site characteristics and relating them to the results of several 

model-comparison studies, the framework for developing 

guidelines for selecting the most appropriate model for a 

given bridge site can be accomplished. Potentially relevant 

bridge-site characteristics and definitions are listed in table 11, 

including a summary of site characteristics for the U.S.-13 

bridge over the Tar River at Greenville. As additional model 

comparisons are completed, additional relevant site characteristics can be identified and added to those listed in table 11. 

The results of this study indicate that for bridges having skews 

Table 10. Abutment-scour estimates for the U.S.-13 bridge over the Tar River at 

Greenville, North Carolina, using hydraulic data from two high-flow events. 

[2D, two dimensional; 1D, one dimensional; ft, feet]

Scour equationa Abutment 2D model

sour depth (ft)

1D model

sour depth (ft)

Hurricane Charley, August 2004

HIRE Left 11.7 11.8

Froehlich Right 15.5 19.5

Tropical Storm Alberto, June 2006

HIRE Left 20.3 18.7

Froehlich Right 19.7 29.1

a

 Richardson and Davis, 2001. 
26 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

Table 11. Definitions of potentially relevant bridge-site characteristics for the development of modeling guidelines at bridges, including 

site characteristics for the U.S.-13 bridge over the Tar River at Greenville, North Carolina.

[>, greater than; <, less than]

Bridge-site characteristic Definition U.S.-13 bridge over 

Tar River value

Geometric-contraction ratio 

(GCr

)

GCr

 = 1– (b/B), where b = contracted-bridge opening width and B = 100-year floodplain 

width at the approach section.

0.9

Degree of sinuosity Ratio of length of stream reach measured along it centerline to length measured along valley centerline [Straight (1–1.05), Sinuous (1.06–1.25), Meandering (1.26–2.0), Highly 

Meandering (>2.0)].

1.41

Stream size Width of channel measured along perpendicular line drawn between opposing banks in a 

straight section or inflection point in a bend.

200 feet

Valley setting Relief measured from valley bottom to top of nearest adjacent divide. 27 feet

Debris potential High, Medium, Low based on upstream land use/vegetation and visual site inspections. High

Stream slope Slope of the stream in feet per feet estimated from surveys or topographic maps. 0.000064

Radius of curvature of 

bend(s)

The radius of curvature of a channel bend within five channel widths upstream from the 

bridge.

225 feet

Ratio of floodplain to channel 

width

Floodplain width divided by channel width. Floodplains are defined as the surface presently 

under construction by a stream that is flooded with a frequency of about 1 1/2 years. 

[Little or None (<2 x channel width), Narrow (2–10 x channel width), Wide (>10 x channel width)].

15

Floodplain eccentricity Ratio of the general left and right floodplain widths at the approach section (F1

/F2, where 

F1

 is always the smaller of the two widths).

0.055

Braiding The degree of braiding of the channel. A braided stream is one that consists of multiple and 

interlacing channels that are generally formed as bars of sediment are deposited within 

the main channel, causing the overall channel system to widen. [None (Not braided to <5 

percent), Locally (5–35 percent), Generally (>35 percent)].

None

Anabranching A description of the degree of anabranching of the channel. An anabranched stream 

differs from a braided stream in that the flow is divided by islands rather than bars, and 

the islands are relatively large in relation to the channel width. The anabranches, or individual channels, are more widely and distinctly separated and more fixed in position than 

the braids of a stream. [Not Anabranched (<5 percent), Locally Anabranched 

(5–35 percent), Generally Anabranched (>35 percent)].

None

Drainage area The contributing drainage area of the stream at bridge location in square miles. 2,660 square miles

Bridge length The length of the bridge (abutment to abutment). 540 feet

Bridge width The width, railing to railing, of the bridge deck. 31.25 feet

Parallel bridges Are there separate parallel bridges at the site? Yes

Distance between centerlines Stream distance between the centerlines of parallel bridges. 65 feet

Bridge skew The acute angle a bridge makes with a perpendicular to flow. Skew is positive if rotated 

clockwise from perpendicular (the left abutment is pointing downstream).

60

Abutment/Contracted 

opening type

Define the type of contracted bridge opening based on classifications found in Shearman 

(1990).

Type I - Vertical embankments and vertical abutments, with or without wingwalls.

Type II - Sloping embankments and vertical abutments without wingwalls.

Type III - Sloping embankments and sloping spillthrough abutments.

Type IV - Sloping embankments and vertical abutments with wingwalls.

Other - If above definitions are not adequate.

Type III

Abutment setback Maximum distance measured from abutment toe to bank of main channel. 70 feet

Guidebanks The presence of any guidebanks defined as Straight, Elliptical, None, Other. Guidebanks 

(also referred to as spur dikes) guide approach flows through the opening, to reduce abutment scour potential and increase bridge conveyance efficiency.

None

Pier type The type of piers on the bridge. Single (single column or wall piers) or Group (form multicolumn or pile bent piers).

Group of piles

Pier width The actual pier/pile width. For tapered piers, enter a representative width. 1.67 feet

Pier contraction ratio Ratio = Ap/(Area of bridge opening), where Ap = Area of piers/piles projected onto a plane 

defined by the bridge opening.

0.087

Number of piers List the number of piers for the bridge(s). If piers consist of multiple-piles, list total number 

of piles in parentheses.

22 (146)

Number of relief bridges/

openings

How many relief bridges or culverts are proposed or present in the floodplains. Two
Summary 27

of 60 degrees, seven piers in the main channel, debris potential 

that is more than three times the pier widths, and a meander 

bend directly upstream, a two-dimensional model provides a 

more accurate representation of water-surface elevations and 

velocity magnitudes and directions through the bridge.

Summary

One- and two-dimensional models of the hydraulically 

complex U.S.-13 bridge over the Tar River at Greenville, 

North Carolina, were developed, and detailed water-surface 

elevations, discharge, and velocity distributions were collected 

in the field for two high-flow events—Hurricane Charley 

in August 2004 and Tropical Storm Alberto in June 2006. 

Comparisons of the field data relative to the results of the 

one- and two-dimensional models provided the basis for 

evaluating the differences between the two models as well as 

the implications of these differences. Water-surface profiles, 

velocity magnitudes and distributions, and scour estimates 

from the one- and two dimensional models were compared. 

The water-surface elevations for both models generally 

agreed downstream from the U.S.-13 bridge; however, 

appreciable disparity occurred between the one-dimensional 

and two-dimensional models upstream from the U.S.-13 

bridge. The disparity upstream from the U.S.-13 bridge mainly 

can be attributed to differences in momentum loss at U.S.-13. 

The simulated water-surface slopes for the two models are 

similar upstream from U.S.-13; however, the two-dimensional 

model simulates more energy loss through the U.S.-13 main 

channel bridge, U.S.-13 overflow bridges, and channel bend 

directly upstream from U.S.-13. The flow conditions directly 

upstream and through U.S.-13 are two dimensional in nature, 

and the associated energy losses are not fully represented by 

a one-dimensional model, which explains the large discrepancies in simulating the water-surface elevations. Based on a 

comparison of measured stage at USGS streamgaging station 

02083893 (located approximately 1 mile upstream from 

the upstream model boundary) and simulated water-surface 

elevations extrapolated upstream to the gage location, the 

two-dimensional model more accurately simulated the watersurface elevations in the study reach.

Comparisons of the modeled and measured velocity 

distributions through the U.S.-13 bridge opening revealed 

that the one-dimensional model results are less representative, 

relative to the two-dimensional model, of the measured velocity magnitudes and distributions. In general, the velocities 

from the one-dimensional model are biased low and are more 

uniformly distributed than the velocities from the twodimensional model and measured data. The two-dimensional 

model most accurately simulates the contracted-flow magnitudes and direction through the bridge opening, which makes 

it a better tool for safe and efficient bridge design. 

Large floating debris rafts between piers 2 and 5 were 

observed during both high-flow hydrographic surveys. The 

general location of the debris accumulation was consistent in 

both high-flow surveys, although the extent and quantity of 

debris were different. Uncertainty, therefore, is associated with 

modeling hypothetical scenarios and(or) conditions that have 

not been surveyed because of the natural variability in debris 

supply and configuration at various flows, which can greatly 

affect the simulated flow fields through a bridge. The NCDOT 

current (2007) designation of debris potential at bridges is 

“high, moderate, or low” based on field observations and 

interviews with bridge maintenance personnel. The results of 

this study indicate that the potential for debris accumulation 

is moderate to high at the U.S.-13 bridge, which appreciably 

affects the velocity magnitudes and distribution through the 

bridge. A three-dimensional model would provide a more 

representative simulation of the hydraulics through the U.S.-13 

bridge opening for conditions in which accumulated debris is 

present.

To further compare the results of the one- and twodimensional models, hydraulic parameters estimated by the 

models for the two measured high-flow conditions were used 

to predict scour depths at the U.S.-13 bridge using HEC-18 

methods. Pier and abutment scour were computed at the 

U.S.-13 bridge; however, contraction scour was not computed 

because sediment grain-size data were not available. 

Comparisons of pier-scour estimates from both models 

indicated that the two-dimensional scour estimates are 

deeper than those from the one-dimensional model. The 

two-dimensional pier-scour estimates differed by as much 

as 5.0 ft, with a mean difference of 1.8 ft for the measured 

conditions relative to the one-dimensional model estimates. 

The inconsistencies in the pier-scour estimates can be attributed mainly to the appreciable flow angles simulated by the 

two-dimensional model at piers 5–11, which were included in 

the two-dimensional scour computations. 

The scour estimates of the two models for the left 

abutment are identical for the Hurricane Charley condition and 

within 1.6 ft for the Tropical Storm Alberto condition. The 

one-dimensional model overpredicts scour at the right abutment relative to the two-dimensional model for both high-flow 

conditions, which is attributed mainly to the higher velocities 

simulated by the one-dimensional model on the right overbank 

at the approach section.

Little or no information is available during the planning 

and design stages of a new bridge regarding the hydraulics of 

the river until a predictive model is developed and applied. 

Hydrologic, topographic, and physiographic characteristics 

of the area around a bridge site can be useful in determining 

whether a one- or two-dimensional model is needed to 

accurately estimate the hydraulic conditions. By compiling 

pertinent site characteristics and relating them to the results of 

several model-comparison studies, the framework for developing guidelines for selecting the most appropriate model for 

a given bridge site can be accomplished. Potentially relevant 

bridge-site characteristics for the development of modeling 

guidelines have been defined, including a summary of the 
28 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

characteristics of the U.S.-13 bridge over the Tar River at 

Greenville. 

The results of this study indicate that for bridges having 

skews of 60 degrees, seven piers in the main channel, debris 

potential that is more than three times the pier widths, and a 

meander bend directly upstream, a two-dimensional model 

provides a more accurate representation of water-surface 

elevations and velocity magnitudes and directions through 

the bridge. By combining information from several similar 

projects and incorporating comparisons of existing models 

from other DOTs in the Southeast, NCDOT engineers and 

staff can be provided with the tools and data that are essential 

in improving bridge design and mitigating structural hazards at 

a range of hydraulically complex sites. 

References Cited 

Bales, J.D., Wagner, C.R., Cassingham, K., and Terziotti, S., 

2006, Flood inundation maps for real-time flood mapping 

applications, Tar River Basin, North Carolina: U.S. Geological Survey Scientific Investigations Report 2007-5032, 34 p.

Bates, P.D., Wilson, M.D., Horritt, M.S., Mason, D.C., Holden, 

N., and Currie, A., 2004, Remote sensing and flood inundation modelling: Hydrological Processes, v. 18, 

p. 2593–2597.

Brigham Young University, 2005, Surface-Water Modeling System (SMS) Reference Manual (ver. 9.0): Provo, Utah, Environmental Modeling Research Laboratory [variously paged].

Donnell, B.P., Letter, J.V., McAnally, W.H., and others, 2005, 

User’s guide for RMA2 version 4.5: Vicksburg, MS, U.S. 

Army, Engineer Research and Development Center, Waterways Experiment Station, Coastal and Hydraulics Laboratory; 

accessed March 10, 2005, at http://chl.wes.army.mil/software/

tabs/docs.htp. 

Federal Emergency Management Agency, 2002, Flood Insurance Study—A report of flood hazards in Pitt County, North 

Carolina, and unincorporated areas: Atlanta, GA, Federal 

Insurance and Mitigation Administration [variously paged].

Froehlich, D.C., 2002, Finite Element Surface-Water Modeling 

System—Two-dimensional depth-averaged flow and sediment 

transport model user’s manual, release 3: Mclean, VA, Federal 

Highway Administration, Office of Research, Development, 

and Technology, Publication No. FWHA-RD-03-053 [variously paged].

Hydrology Subcommittee of the Interagency Advisory Committee on Water Data, 1982, Guidelines for determining flood 

frequency: Reston, VA, U.S. Geological Survey Bulletin 17B, 

Office of Water Data Collection, 183 p.

McDonald, R.R., Nelson, J.M., and Bennett, J.P., in press, Multidimensional surface-water modeling system user’s guide: 

U.S. Geological Survey Techniques and Methods 6-B2, 136 p.

Mueller, D.S., 1996, Scour at bridges—Detailed data collection during floods, in 6th Federal Interagency Sedimentation 

Conference, Proceedings—Subcommittee on Sedimentation 

Interagency Advisory Committee on Water Data, 1996, Las 

Vegas, NV, p. IV-41–IV-48.

Oberg, K.A., Morlock, S.E., and Caldwell, W.S., 2005, Qualityassurance plan for discharge measurements using acoustic 

Doppler current profilers: U.S. Geological Survey Scientific 

Investigations Report 2005-5183, 35 p.

Oberg, K.A., and Mueller, D.S., 1994, Recent applications 

of acoustic Doppler current profilers, in Fundamentals and 

advancements in hydraulic measurements and experimentation, Proceedings—Hydraulics Division/American Society of 

Civil Engineers (ASCE), 1994, Buffalo, NY, p. 341–350.

Pope, B.F., Tasker, G.D., and Robbins, J.C., 2001, Estimating the magnitude and frequency of floods in rural basins of 

North Carolina—Revised: U.S. Geological Survey WaterResources Investigations Report 01-4207, 44 p.

Richardson, E.V., and Davis, S.R., 2001, Evaluating scour at 

bridges: Federal Highway Administration Hydraulic Engineering Circular No. 18, Publication FHWA NHI 01-001, 

378 p.

Shearman, J.O., 1990, User’s manual for WSPRO—A computer 

model for water-surface profile computations: Federal Highway Administration, Report No. FHWA-IP-89-027, 175 p.

Simpson, M.R., and Oltmann, R.N., 1991, Dischargemeasurement system using an acoustic Doppler current 

profiler with applications to large rivers and estuaries: 

U.S. Geological Survey Water-Resources Investigations 

Report 91-487, 49 p.

U.S. Army Corps of Engineers, 2003, HEC-RAS river analysis 

system user’s manual, version 3.1.1: Davis, CA, Hydrologic 

Engineering Center [variously paged].

Wagner, C.R., and Mueller, D.S., 2001, Calibration and validation of a two-dimensional hydrodynamic model of the Ohio 

River, Jefferson County, Kentucky: U.S. Geological Survey 

Water-Resources Investigations Report 01-4091, 33 p.

Wagner, C.R., Mueller, D.S., Parola, A.C., Hagerty, D.J., and 

Benedict, S.T., 2005, NCHRP Project 24-14 scour at contracted bridges: Washington, DC, Transportation Research 

Board, National Research Council [variously paged].

Zevenbergen, L.W., Edge, B.L., Lagasse, P.F., and Richardson, 

E.V., 2002, Development of hydraulic computer models to 

analyze tidal and coastal stream hydraulic conditions at highway structures, Phase III Report: South Carolina Department 

of Transportation, Pooled Fund Study Research Project No. 

591, Report No. FHWA-SC-02-03, 39 p.
Appendix 29

Appendix

Difference maps of simulated velocity magnitudes for the existing and pre-roadway model scenarios for U.S.-13 over the Tar River 

at Greenville, North Carolina.
30 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

Figure A1. Difference map of the simulated velocity magnitudes for the existing bridge and pre-roadway model scenarios for the estimated 

10-year return-period flow at U.S. 13 over the Tar River at Greenville, North Carolina. (Pre-roadway model results are subtracted from the 

existing model results.)

3537’55”

3537’09”

7723’53” 7722’38”

Appendix A. Difference map of the simulated velocity magnitudes for the existing bridge and pre-roadway model scenarios for

 the estimated 10-year return-period flow at U.S. 13 over the Tar River at Greenville, North Carolina. (Pre-roadway model results

 are subtracted from the existing model results.)

Velocity magnitude difference, in feet per second

3.50

3.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-1.25

-1.50
Appendix 31

Figure A2. Difference map of the simulated velocity magnitudes for the existing bridge and pre-roadway model scenarios for the estimated 

50-year return-period flow at U.S. 13 over the Tar River at Greenville, North Carolina. (Pre-roadway model results are subtracted from the 

existing model results.)

3537’55”

3537’09”

7723’53” 7722’38”

Appendix B. Difference map of the simulated velocity magnitudes for the existing bridge and pre-roadway model scenarios for

 the estimated 50-year return-period flow at U.S. 13 over the Tar River at Greenville, North Carolina. (Pre-roadway model results

 are subtracted from the existing model results.)

Velocity magnitude difference, in feet per second

3.50

3.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-1.25

-1.50
32 Simulation of Water-Surface Elevations and Velocity Distributions at the U.S. 13 Bridge, Tar River at Greenville, NC

Figure A3. Difference map of the simulated velocity magnitudes for the existing bridge and pre-roadway model scenarios for the estimated 

100-year return-period flow at U.S. 13 over the Tar River at Greenville, North Carolina. (Pre-roadway model results are subtracted from the 

existing model results.)

3537’55”

3537’09”

7723’53” 7722’38”

Appendix C. Difference map of the simulated velocity magnitudes for the existing bridge and pre-roadway model scenarios for

 the estimated 100-year return-period flow at U.S. 13 over the Tar River at Greenville, North Carolina. (Pre-roadway model results

 are subtracted from the existing model results.)

Velocity magnitude difference, in feet per second

3.50

3.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-1.25

-1.50
Appendix 33

Figure A4. Difference map of the simulated velocity magnitudes for the existing bridge and pre-roadway model scenarios for the estimated 

500-year return-period flow at U.S. 13 over the Tar River at Greenville, North Carolina. (Pre-roadway model results are subtracted from the 

existing model results.)

3537’55”

3537’09”

7723’53” 7722’38”

Appendix D. Difference map of the simulated velocity magnitudes for the existing bridge and pre-roadway model scenarios for

 the estimated 500-year return-period flow at U.S. 13 over the Tar River at Greenville, North Carolina. (Pre-roadway model results

 are subtracted from the existing model results.)

Velocity magnitude difference, in feet per second

3.50

3.25

3.00

2.75

2.50

2.25

2.00

1.75

1.50

1.25

1.00

0.75

0.50

0.25

0.00

-0.25

-0.50

-0.75

-1.00

-1.25

-1.50

Prepared by:

USGS Publishing Network

Raleigh Publishing Service Center

3916 Sunset Ridge Road

Raleigh, NC 27607

For additional information regarding this publication, contact:

Director

USGS North Carolina Water Science Center

3916 Sunset Ridge Road

Raleigh, North Carolina 27607

phone: 1-919-571-4000

email: dc_nc@usgs.gov

Or visit the North Carolina Water Science Center website at:

http://nc.water.usgs.gov
Wagner—Simulation of Water-Surface Elevations and Velocity Distributions at the U.S.-13 Bridge, Tar River at Greenville, NC—Scientific Investigations Report 2007–5263