Calculation of Scour Depth at the Parks Highway 

Bridge on the Tanana River at Nenana, Alaska, 

Using One- and Two-Dimensional Hydraulic Models

U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with the 

Alaska Department of Transportation and Public Facilities and 

Federal Highway Administration

Scientific Investigations Report 2006-5023
Cover: Photograph of the Tanana River at Nenana, Alaska, looking south from the northern highway 

bridge abutment. (Photograph taken by Robert Burrows, U.S. Geological Survey, May 4, 1989).
Calculation of Scour Depth at the 

Parks Highway Bridge on the Tanana River at 

Nenana, Alaska, Using One- and 

Two-Dimensional Hydraulic Models

By Dustin E. Langley 

Prepared in cooperation with the 

Alaska Department of Transportation and Public Facilities and 

Federal Highway Administration

Scientific Investigations Report 2006-5023

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

P. Patrick Leahy, Acting Director

U.S. Geological Survey, Reston, Virginia: 2006

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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:

Langley, D.E., 2006, Calculation of scour depth at the Parks Highway Bridge on the Tanana River at Nenana, Alaska, 

using one- and two-dimensional hydraulic models: U.S. Geological Survey Scientific Investigations Report 2006-5023, 

19 p. 
iii

Contents

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

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

Purpose and Scope ................................................................................. 3

Description of Study Area ........................................................................ 3

Hydraulic Modeling ....................................................................................... 4

Input Requirements ................................................................................. 4

Construction and Calibration of One-Dimensional Hydraulic Model ........................ 6

Construction and Calibration of Two-Dimensional Hydraulic Model ........................ 8

Scour Calculations ....................................................................................... 11

Contraction Scour ................................................................................. 11

Pier Scour .......................................................................................... 11

Comparison of Models.................................................................................... 13

Summary and Conclusions .............................................................................. 18

References Cited.......................................................................................... 19

Figures

Figure 1. Map showing location of the Parks Highway Bridge (Alaska Department of 

Transportation and Public Facilities Bridge #201) scour-analysis site on the 

Tanana River at Nenana, Alaska, and the reach included in hydraulic models...... 2

Figure 2. Hydrograph showing maximum, mean, and minimum daily discharge for 

38 years of record (1962-2000) for U.S. Geological Survey streamflow-gaging 

station 15515500, Tanana River at Nenana, Alaska .................................... 3

Figure 3. Graph showing grain-size distribution of bed-sediment samples collected 

by the U.S. Geological Survey from Tanana River at Nenana, Alaska, 

June 7, 1964 ................................................................................. 4

Figure 4. Plan view showing cross sections and river stations, hydraulic model center 

lines, and river junctions used in the one-dimensional model for scour 

analysis of Tanana River at Nenana, Alaska ............................................. 7

Figure 5. Plan view showing model mesh and streambed elevations used for the 

two-dimensional model of Tanana River at Nenana, Alaska ........................... 9

Figure 6. Graphs showing water-surface profiles for six discharge scenarios on 

Tanana River at Nenana, Alaska, simulated using one- and two-dimensional 

hydraulic models ........................................................................... 10

Figure 7. Plan views showing velocity vectors and magnitudes on the Tanana River 

near the mouth of the Nenana River, Alaska, simulated using a 

two-dimensional hydraulic model ......................................................... 14

Figure 8. Graph showing comparison of discharge in Tanana Slough for six discharge 

scenarios simulated using one- and two-dimensional hydraulic models ............ 18
iv

Tables

Table 1. Estimated annual sediment load of the Tanana River, Alaska, 1977–79............... 4

Table 2. Boundary conditions for discharge scenarios for the Tanana River at Nenana, 

Alaska, simulated using one- and two-dimensional hydraulic models ............... 5

Table 3. Material types and associated roughness values for the Tanana River at 

Nenana, Alaska .............................................................................. 6

Table 4. Values used to calibrate the two-dimensional hydraulic model for the 

Tanana River at Nenana, Alaska ......................................................... 8

Table 5. Calculated depths of pier scour, contraction scour, and angles of attack at 

pier 3, and associated variables, Tanana River at Nenana, Alaska .................. 11

Figure 9. Graph showing depth of pier scour, calculated using output from one- and 

two-dimensional hydraulic models, and angle of attack at bridge pier 3 for 

five discharge scenarios representing floods on the Tanana River near 

Nenana, Alaska .............................................................................. 18

Figure 10. Graph showing streamflow velocity along cross-section 1.377 on the 

Tanana River near Nenana, Alaska, measured on August 19, 1998, and 

simulated using one- and two-dimensional hydraulic models ........................ 18

Figures—Continued

Conversion Factors and Datums

Conversion Factors

Multiply By To obtain

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

foot (ft) 0.3048 meter

feet per foot (ft/ft) 1 meter per meter

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

foot per square second (ft/s2) 0.3048 meter per square second

mile (mi) 1.609 kilometer

million gallons per year (Mgal/yr) 0.04381 cubic meter per year

pound per second per square foot (lb/s)/ft2) 4.882 kilograms per second per square meter

Grain size in streambed sediments is given in millimeters (mm).

Slope is given in feet per foot (ft/ft).

Datums

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

(NGVD 29).

Horizontal coordinate information was arbitrarily set at time of survey.
Abstract

The Parks Highway crossing of the Tanana River at 

Nenana, Alaska, is a hydraulically complex site. Both the 

confluence of the Nenana River and the division of the Tanana 

River by an island into a main channel and a side channel, or 

slough, affect flow. A recent study determined that the large pier 

on the bridge over the main channel was susceptible to damage 

by scour. Further investigations were required to estimate the risk 

of pier scour and contraction scour at high flows.

The reach of the Tanana River that includes the 

confluence of the Nenana River and the Tanana Slough was 

surveyed on August 17-20, 1998. Channel geometry from 

this survey was used as input for two hydraulic models: a 

one-dimensional model and a two-dimensional model. Each 

model was calibrated to a high discharge measurement taken 

on August 17, 1967. Discharge scenarios were simulated for 

the discharge of August 17, 1967, and for floods in the Tanana 

River with 100- and 500-year recurrence intervals, each run 

with a low and a high discharge in the Nenana River. Low 

discharge simulated for the Nenana River was the discharge at 

the time of the survey. The high discharge was the discharge in 

the Nenana River with a 100-year return interval. Output from 

each model was used to calculate pier scour. Contraction scour 

was calculated using only output from the one-dimensional 

model.

Water-surface profiles, pier- and contraction-scour 

estimates, and slough discharge simulated by the models 

were compared to determine the effectiveness of using a 

one-dimensional model to simulate two-dimensional flow. 

The models yielded similar pier scour estimates, but results 

in areas of two-dimensional flow, such as at the mouth of the 

Nenana River, varied considerably.

Introduction

Scour is a complex hydraulic process consisting of 

lowering a streambed by erosive forces. These forces are 

caused by acceleration of streamflow around obstructions or 

through channel contractions. Bridge scour is erosion of the 

streambed resulting from local flow accelerations caused by 

bridge piers, abutments, and, during extreme flows, the bridge 

structure and deck. According to Holnbeck and Parrett (1997), 

“the most common cause of bridge failure has historically 

been the scour or erosion of foundation material away from 

piers and abutments during large floods.” 

To address scour concerns, the Federal Highway 

Administration (FHWA) established a national bridge-scour 

program in 1991. The purposes of this program are to evaluate 

existing bridges for scour potential and to conduct research 

in scour-related areas (Holnbeck and Parrett, 1997). In 1994, 

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

Alaska Department of Transportation and Public Facilities 

(ADOT&PF) and the FHWA, began a cooperative study 

to analyze scour potential at bridges in Alaska. The initial 

phase of this project consisted of screening a large number of 

bridge sites for scour susceptibility using a one-dimensional 

hydraulic model at each bridge. Inputs for the models were 

derived from bridge plans provided by ADOT&PF, along with 

other historical data. Methodology and results of this study are 

available in a report by Heinrichs and others (2001).

The USGS, in cooperation with the FHWA and 

ADOT&PF, chose the Parks Highway crossing of Tanana 

River’s main channel, near the town of Nenana, Alaska 

(fig. 1), for a further, in-depth study because the results of 

the phase 1 study indicated large scour potential. This site is 

hydraulically complicated. Streamflow in the Tanana River 

Calculation of Scour Depth at the Parks Highway 

Bridge on the Tanana River at Nenana, Alaska, 

Using One-and Two-Dimensional Hydraulic Models

By Dustin E. Langley 
Figure 1. Location of the Parks Highway Bridge (Alaska Department of Transportation and Public Facilities Bridge #201) scour-analysis 

site on the Tanana River at Nenana, Alaska, and the reach included in hydraulic models. 

Location of figures 4 and 5

ak19601_fig01

Base from U.S.Geological Survey

Fairbanks (C-5) Quadrangle, Alaska

1:63,360, 1978 

R 8 W

T

4

N

Figure

location ALASKA

Tanana

River

Nena na

River

1967 Gaging Station 1998 Gaging Station Alaska

Railroad

Bridge

Main

Bridge

Slough

Bridge Parks Highway

Parks Highway

North Nenana

Nenana

0 1,000 2,000 3,000 4,000 5,000 FEET

0 500 1,000 1,500 METERS

 Calculation of Scour Depth at Parks Highway Bridge, Tanana River at Nenana, Alaska
at the site is divided between the main channel and a slough, 

and the Nenana River enters the Tanana River just downstream 

of the bridge. Tanana Slough re-enters the main channel 

downstream of the mouth of the Nenana River. Bridges cross 

both the main channel (ADOT&PF bridge 201, referred to in 

this report as the main bridge) and the slough (ADOT&PF 

bridge 202, referred to in this report as the slough bridge). The 

main bridge has a large pier, pier 3, that is oriented at an angle 

to streamflow. A one-dimensional hydraulic model used in 

phase 1 estimated a large scour value at the pier. Two types of 

scour were examined for the phase 2 study—contraction scour, 

caused by increased velocity in a reach where the flow area 

of the stream has been reduced, such as by bridge abutments 

or natural constrictions, and pier scour, erosion around piers 

caused by local flow acceleration and a resulting increase in 

turbulence (Richardson and Davis, 1995).

The primary concern at the Tanana bridge site is pier 

scour at pier 3 on the main bridge. Contraction scour is a 

secondary concern. Depth of pier scour is affected by several 

variables, including pier geometry, flow depth and velocity, 

and angle of attack. Pier geometry can be measured or taken 

from historical records such as bridge plans; flow depth and 

velocity can be measured or estimated with a computer model; 

and angle of attack must be estimated from visual observation 

or by using a two-dimensional model. In the phase 2 study, 

both one-dimensional and two-dimensional hydraulic 

models were used to simulate several discharge scenarios, to 

determine if a two-dimensional model might provide a better 

flow characteristic simulation. Hydraulics and scour estimates 

from each model were compared to each other to determine 

their applicability in studies at complex sites.

Purpose and Scope

This report (1) presents depths of pier scour, calculated 

using output from one-and two-dimensional hydraulic 

models, and contraction scour, calculated using output from 

the one-dimensional model for five discharge scenarios in 

the Tanana and Nenana Rivers; (2) documents construction 

and calibration of the hydraulic models; and (3) compares 

effectiveness of both types of hydraulic models in scour 

analyses at complex sites. Using both model types with the 

same geometry and flows will aid in choosing the correct 

approach to scour investigations at other complex sites.

The study required establishing and surveying 20 cross 

sections on the Tanana River, developing water-surface and 

top-of-bank profiles, and measuring discharge and velocity 

at each cross section. Historical discharge data were used to 

calibrate and run the hydraulic models. The one-dimensional 

model consisted of 43 cross sections, 20 surveyed cross 

sections, and 23 interpolated cross sections. The twodimensional model consisted of 8,198 nodes. The models 

simulated measured discharge for a large flood on the Tanana 

River and 100- and 500-year recurrence-interval flows on the 

Tanana River. Each flow was simulated with a high and a low 

discharge on the Nenana River. 

The survey layout and setup of the models focused on 

accurately simulating high flows. This approach allowed 

larger spacing between cross sections and a coarser mesh for 

the two-dimensional model. Flow at the time of the survey 

was simulated to determine the applicability of the models to 

relatively low flows.

Description of Study Area

Tanana River is a glacially fed river with headwaters 

originating in the Alaska Range. The study reach includes 

the confluence with the Nenana River and extends from the 

Alaska Railroad Bridge to about 6,200 ft downstream of 

the highway bridge and about 1,600 ft up the Nenana River 

(fig. 1). Total length of the reach on the Tanana River main 

channel is about 10,000 ft.

As a glacially fed river, the Tanana has a distinctive 

hydrograph in which high summer flows begin with snowmelt 

runoff, but are sustained throughout the summer by glacial 

melt (fig. 2; Brabets and others, 2000). Extreme high flows 

result from rainfall and typically are in late summer. Flow in 

autumn and winter gradually decreases until snowmelt begins 

again in spring. Ice cover usually forms in October and the 

river remains frozen until spring breakup, usually in April 

or May. Breakup of the surface ice generally is caused by 

increased flow rather than melting in place.

As is common with glacially fed rivers, the sediment 

load of the Tanana River is quite high. A sediment sampling 

study in the late 1970s estimated annual sediment loads based 

on discharge records from USGS streamflow-gaging station 

Tanana River at Fairbanks (15485500) and on sediment 

samples taken near the gaging station and near the city 

of North Pole, Alaska (USGS site ID 644322147192900) 

(table 1, modified from Burrows and others, 1981). Average 

water-surface slope at the Fairbanks gaging station was 

OCT NOV DEC JAN FEB MAR APR MAY JUNE JULY AUG SEPT 1,000

10,000

100,000

1,000,000 DISCHARGE, IN CUBIC FEET PER SECOND 

WATER YEAR 1962-2000 

Maximum

Mean

Minimum

Figure 2. Maximum, mean, and minimum daily discharge 

for 38 years of record (1962-2000) for U.S. Geological Survey 

streamflow-gaging station 15515500, Tanana River at Nenana, 

Alaska.

Introduction 
Figure 3. Grain-size distribution of bed-sediment samples 

collected by the U.S. Geological Survey from Tanana River at 

Nenana, Alaska, June 7, 1964.

0.00051 ft/ft and at the North Pole gaging station was 

0.00118 ft/ft (Burrows and Harrold, 1983). These gaging 

station sites are about 60 river miles upstream of Nenana. 

Major tributaries between these sites include the Chena River 

(non-glacial, relatively low sediment load) and the Wood River 

(glacial, relatively high sediment load).

Bed-material samples were collected by the USGS at 

Tanana River at Nenana on June 7, 1964 (fig. 3). The average 

grain diameter in these samples ranged from less than 0.05 to 

10 mm. Average diameter of samples collected from Fairbanks 

and North Pole ranged from 0.12 to 34 mm, depending on 

sampling site and location in the channel (Burrows and others, 

1981). Bed-material size is closely tied to the water-surface 

slope. When the water surface is steeper, more energy is 

available for sediment transport and larger particles can be 

moved. The largest grain sizes were from the steepest site, 

North Pole. The water-surface slope at Nenana is about 0.0003 

ft/ft. This is similar to the Fairbanks sampling site, in which 

average grain diameter for the composite of the channel was 

0.23 mm.

Table 1. Estimated annual sediment load of the Tanana River, Alaska, 

1977–79.

[Modified from Burrows and others, 1981. Values are in million gallons per 

year. –, not available]

Year

Fairbanks

(15485500) North Pole(644322147192900)

Suspended Bedload Suspended Bedload

1977 26,800,000 326,000 – –

1978 21,200,000 254,000 20,900,000 274,000

1979 27,500,000 440,000 26,700,000 369,000

0.01 0.1 1 10 100

SIEVE SIZE, IN MILLIMETERS

20

40

60

80

100

120

PERCENTAGE, BY WEIGHT, 

FINER THAN INDICATED SIZE 0

Sample 1

Sample 2

Sample 3

Sample 4

Sample 5

Sample 6

Hydraulic Modeling

The U.S. Army Corps of Engineers’ Hydrologic 

Engineering Center River Analysis System (HEC-RAS) 

model (Brunner, 1997) was used as the one-dimensional flow 

model for this project. This model is based on the standard 

step-backwater computation. It balances the energy equation 

from one cross section to the next. Energy losses between 

sections are from friction, expansion, and contraction. Friction 

losses are computed with Manning’s equation. Expansion and 

contraction losses are determined by applying a coefficient 

to the change in velocity head. The model requires that the 

following assumptions are valid (Brunner, 1997):

• Flow is steady in time.

• Flow is gradually varied in space. This assumption 

is not required at hydraulic structures such as 

bridges or culverts because the momentum or other 

empirical equations can be used. HEC-RAS does the 

computations and can be set to use the most applicable 

method.

• Flow is one dimensional (velocity is always 

perpendicular with the cross section).

• Channel slope is less than 10 percent.

The two-dimensional model chosen for this project 

was RMA2 (Donnell and others, 2000) with the Surface 

Water Modeling System (SMS; Environmental Modeling 

Research Laboratory, 1999), a graphical user interface. 

RMA2 is a two-dimensional, depth-averaged, finite-element 

hydrodynamic numerical model (Donnell and others, 2000). 

The model solves for flow properties of two-dimensional 

elements, rather than for entire cross sections as does a onedimensional model. Depth-averaged velocity is computed in 

the X and Y horizontal directions. Velocities in the vertical (Z) 

direction are not accounted for and are assumed negligible. 

The model also assumes gradually varied sub-critical flow. 

Flow can be either steady (constant with time) or unsteady 

(varying with time). This program’s computational procedure 

is based on the solutions of the Reynolds form of the NavierStokes equations for turbulent flows (Donnell and others, 

2000). SMS is used as a pre- and post-processor, automating 

much of the set-up process for a finite-element network and 

providing various graphical outputs.

Input Requirements

Data requirements for one- and two-dimensional models 

are similar, except that a two-dimensional model requires 

more geometry information. One-dimensional models 

essentially require two-dimensional geometry data, whereas 

two-dimensional models require three-dimensional data. 

   Calculation of Scour Depth at Parks Highway Bridge, Tanana River at Nenana, Alaska
Both models require various additional information such as 

bridge geometry, bed roughness, and discharge. Water-surface 

profiles for a known discharge are used to calibrate each 

model type.

Two methods were used to survey channel geometry. 

Dry-land surface was surveyed with a total station using 

standard techniques. Channel geometry was surveyed with 

a vessel mounted acoustic Doppler current profiler (ADCP). 

This device uses sonar to measure water depth, vessel velocity 

in relation to the bed, and water velocity. Water-surface 

elevations were surveyed at each cross section. Twenty cross 

sections were surveyed using this method. Additional points 

along the banks between cross-sections also were surveyed for 

the two-dimensional model.

Bridge datum provided by ADOT&PF was used for 

vertical datum. Horizontal coordinates were established at 

the downstream left-bank corner of the main bridge deck at 

N 10,000 ft, E 10,000 ft.

The roughness value in a one-dimensional model 

accounts for various factors that provide resistance to flow. 

These factors include (Arcement and Schneider, 1989):

• Basic bed-material roughness,

• Surface irregularities,

• Variation in cross section shape and size,

• Obstructions to the flow,

• Vegetation and flow conditions, and

• Meandering of the channel.

Channel roughness can be estimated using established 

techniques (Arcement and Schneider, 1989), or computed with 

a hydraulic model using surveyed water-surface elevations 

for a measured discharge. If roughness is determined with a 

hydraulic model, then all these factors affect the value. The 

difficulty with computing a roughness is that flood flows 

usually are quite different from surveyed flows. Higher flows 

can change bed geometry and are less affected by obstructions 

and small surface irregularities. Extreme flows may go over 

the banks, for which only estimated roughness is available. 

Less confidence can be placed in a model run at flows that 

vary greatly from the calibration discharge.

A two-dimensional model also relies on roughness 

values to compute energy loss. Similar factors apply, except 

that, because the model computes velocity in both X and Y 

directions, several factors do not affect the apparent roughness 

value. As noted above, roughness in a one-dimensional 

model accounts for factors such as channel meanders and 

flow that is not perpendicular to the cross sections. The 

two-dimensional model simulates the effect of these losses 

with non-perpendicular velocity, so they are not reflected in 

the roughness value. As a result, the roughness value used in 

the two-dimensional model often will be lower for the same 

conditions than the value used in the one-dimensional model.

Both model types require boundary conditions: a 

discharge and an initial water-surface elevation. Flow at this 

study site is sub-critical for all discharges; each model requires 

a discharge at the upstream boundary and a water-surface 

elevation at the downstream boundary. The six discharges used 

in the models were the discharge measured on August 19, 

1998, the discharge measured during the flood on August 17, 

1967, and floods with return intervals of 100 and 500 years 

on the Tanana River, with low and high discharges on the 

Nenana River (table 2). The Tanana River flood-frequency 

calculations were based on 32 years of record, 1962-94, at 

USGS streamflow-gaging station Tanana River at Nenana 

(15515500), using standard flood-frequency analyses 

(Interagency Advisory Committee on Water Data, 1982).

The only direct measurement of discharge at the mouth of 

the Nenana River was made on August 19, 1998. Discharges 

for the Nenana River for the other discharge scenarios were 

either estimated or determined as follows. Floods with 

return intervals of 100 and 500 years for the Nenana River 

were estimated using the regional regression flood estimates 

outlined in Jones and Fahl (1994). Nenana River discharge 

on August 17, 1967, was estimated at 30,800 ft3/s, based on 

the ratio between the computed 100- and 500-year floods at 

the mouth and those at streamflow-gaging station Nenana 

River at Healy (15518000). This ratio then was applied to the 

flow from the gage record for August 16, 1967, to determine 

discharge at the mouth for the models. Low discharge for 

Nenana River (12,000 ft3/s) was determined by rounding the 

measured discharge from the survey. High discharge was the 

computed 100-year flood at the mouth (69,000 ft3/s).

Table 2. Boundary conditions for discharge scenarios for the Tanana 

River at Nenana, Alaska, simulated using one- and two-dimensional 

hydraulic models.

[Discharge scenario: Q100 (Nenana Low, High), calculated flood on 

Tanana River with return interval of 100 years and low, high discharge on 

Nenana River. Q500 (Nenana Low, High), calculated flood on Tanana River 

with return interval of 500 years and low, high discharge on Nenana River. 

Discharge, Tanana Slough: Discharge determined by one-dimensional 

model (HEC-RAS, Hydrologic Engineering Center River Analysis System), 

two-dimensional model (RMA2, Resource Management Associates). 

Abbreviations: ft3/s, cubic foot per second; ft, foot]

Discharge scenario

Boundary conditions

Discharge (ft3/s) Initial watersurface 

elevation at 

river station 0

(ft)

Tanana 

River

Nenana 

River 

Tanana Slough

HEC-RAS RMA2

August 19, 1998 42,700 11,800 3,680 1,800 343.7

August 17, 1967 171,000 30,800 13,300 13,400 352.9

Q100 (Nenana Low) 162,000 12,000 11,600 11,500 351.6

(High) 162,000 69,000 13,200 18,400 354.0

Q500 (Nenana Low) 203,000 12,000 16,200 14,900 353.4

(High) 203,000 69,000 18,000 22,000 355.6

Hydraulic Modeling   
Initial water-surface elevations either were known (at the 

surveyed discharge) or were estimated as the normal depth. 

Normal depths were computed using the water-surface slope 

from the discharge measurement made on August 17, 1967, 

and the roughness value from the calibrated model.

Construction and Calibration of 

One-Dimensional Hydraulic Model

Geometry for the one-dimensional model was a 

combination of surveyed and interpolated channel data and 

pier and abutment geometries from the as-built plans. The 

only bridge parts affecting flow characteristics are the piers 

and the south abutment of the main bridge. The other bridge 

abutments (the north one on the main bridge and both on the 

slough bridge) had little effect on the flow because they either 

are not in the water or do not project from the bank. The lowsteel elevations for the bridges are 389.58 ft (main bridge) and 

379.74 ft (slough bridge). (Low steel is the lowest part of the 

bridge superstructure between supports over the river.) These 

are well above the water surface, even during extreme floods; 

the water-surface elevation on August 17, 1967, was 356.9 ft.

Twenty cross sections were surveyed for use in the 

one-dimensional model, but the model can better simulate 

expansions and contractions with additional sections. 

HEC-RAS includes a routine that interpolates between cross 

sections to generate synthetic cross sections (Brunner, 1997). 

Channel geometry between the surveyed cross sections 

changed little, so the interpolation is valid through this reach. 

In all, 43 cross sections were used in the one-dimensional 

model analysis (fig. 4).

Once the geometry data were input to HEC-RAS, 

boundary conditions and discharges were entered to calibrate 

the model. Two discharges were used for model calibration: 

the discharge at the time of the survey on August 19, 1998, 

and the discharge measured on August 17, 1967. Four flooding 

situations were then modeled for the scour estimation. 

The 100- and 500-year recurrence-interval flows on the 

Tanana River were simulated with a high and a low discharge 

in the Nenana River. Simulated discharges and associated 

initial downstream water-surface elevations used as boundary 

conditions are summarized in table 2. Initial downstream 

water-surface elevation used with the discharge on August 19, 

1998, was surveyed. Starting water-surface elevations for the 

other scenarios were estimated from the computed watersurface slope of the August 17, 1967, discharge measurement.

The model computed flow in the Tanana Slough using 

an iterative process beginning with an assumed flow division 

between the main channel and the slough. Water-surface 

elevations then were computed along each channel to the 

upstream junction. If the total energy head at the upstream 

cross section in each channel is equal, the flow division 

between channels is assumed to be correct. If they are not 

equal, the model changed the flow division and recomputed 

the water-surface profiles in the channels. Iterations continued 

until the total energy heads balanced.

The model was calibrated by running it with a given 

discharge having a known water-surface elevation and then 

adjusting the streambed roughness until the output closely 

matched the known elevation. Roughness can change with 

depth, so a calibration discharge near the magnitude of the 

flood discharge is desirable. The high-measurement discharge 

(August 17, 1967) was between the 100- and 500-year 

recurrence-interval flows, so the roughness was calibrated to 

this discharge (table 3). 

The calibrated model was used to simulate four discharge 

scenarios on the Nenana River: the 100-year recurrenceinterval flow with both low and high flows and the 500-

year recurrence interval-flow with both low and high flows 

(Q100/500, Nenana Low/High in table 2). Pier and contraction 

scour were computed using output from these scenarios, and 

the results were used to compare the one-dimensional model 

with the two-dimensional model.

Table 3. Material types and associated roughness values for the Tanana 

River at Nenana, Alaska.

[Abbreviations: RMA2, Resource Management Associates; HEC-RAS, 

Hydrologic Engineering Center River Analysis System; (lb/s)/ft2, pound per 

second per square foot; –, not applicable]

Material type 

description

RMA2 roughness

calibrated from

discharge

SMS eddy 

viscosity 

[(lb/s)/ft2]

HEC-RAS roughness

calibrated from

discharge

Aug. 17,

1967

Aug. 19,

1998

Aug. 17,

1967

Aug. 19,

1998

Tanana River: 

main channel

0.023 0.015 100 0.0245 0.0245

Tanana River: 

slough

.040 .022 45 .037 .037

Railroad yard .045 – 20 .045 –

Bridge abutment .045 – 20 .045 –

Tanana and 

Nenana 

Rivers: bank

.045 – 20 .045 –

Nenana River: 

main channel

.025 – 75 .026 .026

Logjam at 

mouth of 

slough

.110 .016 45 .100 .100

   Calculation of Scour Depth at Parks Highway Bridge, Tanana River at Nenana, Alaska
Figure 4. Cross sections and river stations, hydraulic model center lines, and river junctions used in the one-dimensional model for scour analysis of Tanana River at Nenana, Alaska. 

NOT TO SCALE

Main Bridge

Slough Bridge

Tanana Slough

Nenana River

Tanana River

Tanana River

2

3

4

1.811*

1.728

1.894

1.197

1.174

1.377

1.287*

1.456*

1.535*

1.614

0.295

0.221*

0.147

0.116*

1.163

0.074167*

0

0.148333*

0.2225*

0.296667*

0.370833*

0.445

0.603

0.6798*

0.7566*

0.8334*

0.9102*

0.085

0.987

0.110

0.184*

0.258*

0.332

0.42

0.418

0.472

0.800667*

0.880333*

0.960

0.721

0.527

0.591667*

0.656333*

1.095

EXPLANATION

LINE OF CROSS SECTION—Location used in one-dimensional model, and distance of river station upstream from model boundary, in miles. Stations with an asterisk are interpolated sections. HYDRAULIC MODEL CENTER LINESTREAMFLOW DIRECTIONRIVER JUNCTION—Defined in model as point where two streams join

2

ak19601_fig04

1.811*

Locationof figure 7

Hydraulic Modeling   
Construction and Calibration of 

Two-Dimensional Hydraulic Model

Surveyed cross sections were spaced too widely to create 

an adequate topographic map to run the RMA2 model, so 56 

additional cross sections were interpolated from the surveyed 

cross sections by the HEC-RAS software. Interpolated cross 

sections, surveyed cross sections, and additional surveyed 

points along the banks were input to Computer Aided Drafting 

(CAD) software to add breaklines and boundaries to the data 

set. (Breaklines are where the simulated topographic surface 

slope is allowed to change abruptly. For example, the top of a 

cut bank. A boundary is a line defining the edge of the data.) 

The data set then was exported into SMS.

The next step in setting up the two-dimensional model 

was to generate a computational mesh (fig. 5). The mesh 

consisted of triangular and quadrilateral elements that cover 

the entire simulated area. A well-designed mesh will increase 

model stability. Properties of a well designed mesh are 

discussed in Donnell and others (2000).

Elevations and material properties then were assigned to 

the mesh nodes. Elevations were assigned by overlaying the 

mesh with the geometry data set. SMS interpolates elevations 

for nodes that do not reside directly over a known point. 

Roughness and eddy viscosity were assigned to each element. 

Roughness was entered as a Manning’s n, but, as discussed 

earlier, the value for the two-dimensional model tends to 

be lower than the value for a one-dimensional model. Eddy 

viscosity is a term used to define the effect that velocity in 

one element will have on adjacent elements. Eddy viscosity 

and roughness values were defined as properties of a specific 

material type. Each element in the mesh was then given a 

material type (table 3). This allowed the modeler to rapidly 

change the properties of all similar material types during 

calibration runs.

Boundary conditions are defined by assigning flow to 

the upstream model boundaries and a water-surface elevation 

to the downstream boundaries. The two-dimensional model 

used two upstream boundaries (Tanana River and Nenana 

River) and one downstream boundary (Tanana River below 

the confluence). Discharges and downstream water surfaces 

for this model were the same as was used for the HEC-RAS 

model (table 2).

Model calibration begins with selecting a tolerance 

level for the change in water-surface elevations between 

computational iterations. When this tolerance level is met, 

the model has converged on a solution. The two-dimensional 

model was considered converged when the change was less 

than 0.1 ft. Increasing eddy viscosity causes the model to 

converge more easily, but a value that is too high causes the 

velocity vectors to be parallel and the model to appear onedimensional. Values used with this model were the lowest that 

would result in model convergence. Eddy viscosities ranged 

from 20 to 100 (lb/s)/ft2 (table 3), which are well within the 

range of the 0.2 to 1,000 (lb/s)/ft2 suggested by Donnell and 

others (2000).

The model was calibrated using the measured discharges 

(August 19, 1998, and August 17, 1967) and their associated 

water-surface elevations. The model divided flow between the 

main channel of the Tanana River and the slough. Changing 

the roughness in the main channel of the Tanana River varied 

the simulated water-surface elevation. The simulated flow 

division was varied by changing the roughness of the slough 

channel and a logjam at the upper end of the slough. Values 

used to calibrate the two-dimensional model are presented in 

table 4, and a comparison of water-surface profiles simulated 

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

figure 6A. Different roughness values were required for low 

and high discharge in the two-dimensional model. The survey 

data and mesh design were developed to optimize model 

use for high flows. As a result, the model did not perform 

well simulating low discharges. Channel roughness used in 

the low discharge simulation is lower than that used in the 

high-discharge scenarios. Roughness was reduced to offset 

the affects of using a coarse mesh designed for the high-flow 

simulations. Roughness was reduced to account for ragged 

edges of coarse high-flow mesh and to accommodate a 

decreased flow area produced by turning off edge elements to 

increase model stability. To accurately simulate low discharge 

conditions, a denser topographic data set would have to be 

gathered and a finer computational mesh built.

Once the model was calibrated, runs were made with 

the five discharge scenarios that represent floods (table 2). 

Results from these simulations were used to determine flow 

depths and angles of attack for input to the scour calculations. 

The results show definite areas of two-dimensional flow that 

cannot be described with the one-dimensional model.

Table 4. Values used to calibrate the two-dimensional hydraulic model 

for the Tanana River at Nenana, Alaska.

[Abbreviations: ft, foot; ft3/s, cubic foot per second]

Calibration 

parameter

High flow,

Aug. 17, 1967

Low flow,

Aug. 19, 1998

Measured Modeled Measured Modeled

Water-surface 

elevation at 

streamflow-gaging 

station (ft)

1

356.9 356.9 2346.5 346.2

Discharge through 

main channel 

(ft3/s)

158,000 158,000 38,400 41,200

Discharge through 

slough (ft3/s)

13,300 13,400 4,200 1,800

1

 Streamflow-gaging station 15515500 at 1967 location.

2

 Streamflow-gaging station 15515500 at 1998 location.

   Calculation of Scour Depth at Parks Highway Bridge, Tanana River at Nenana, Alaska
Figure 5. Model mesh and streambed elevations used for the two-dimensional model of Tanana River at Nenana, Alaska.

Nenana River

Tanana River

Slough Bridge

Main Bridge

EXPLANATION

364.7258.7352.7346.7340.6334.6328.6322.5316.5

STREAM BED ELEVATION, in feet above NGVD of 1929

STREAMFLOW DIRECTION

ak19601_fig05

Hydraulic Modeling   
Figure 6. Water-surface profiles for six discharge scenarios on Tanana River at Nenana, Alaska, simulated using 

one- and two-dimensional hydraulic models. 

River stationing is along center of channel from downstream to upstream. 

358

356

354

352

350

WATER-SURFACE ELEVATION, IN FEET ABOVE NGVD OF 1929 348

346

344

342

ak19601_fig06

0 0.5 1.0 1.5 2.0

DISTANCE UPSTREAM FROM MODEL BOUNDARY, IN MILES 

A. DISCHARGE SCENARIOS FOR CALIBRATION

B. DISCHARGE SCENARIOS FOR 100- AND 500-YEAR FLOODS WITH LOW AND HIGH FLOW IN NENANA RIVER

August 17, 1967, discharge 

Surveyed

One-dimensional model 

Two-dimensional model 

Streamflow-gaging station 

15515500, 1967 location 

Streamflow-gaging station 

15515500, 1998 location 

August 19, 1998, discharge (during survey) 

VERTICAL SCALE EXAGGERATED

One-dimensional model

Two-dimensional model

362

360

358

356

354

352

350

WATER-SURFACE ELEVATION, IN FEET ABOVE NGVD OF 1929

0 0.5 1.0 1.5 2.0

DISTANCE UPSTREAM FROM MODEL BOUNDARY, IN MILES Main bridge location Main bridge location 

500-year flood discharge,

Nenana high flow

100-year flood discharge,

Nenana high flow

500-year flood discharge,

Nenana low flow

100-year flood discharge,

Nenana low flow

10 Calculation of Scour Depth at Parks Highway Bridge, Tanana River at Nenana, Alaska
Scour Calculations

Two forms of scour studied at the main pier on the 

bridge crossing the main channel of the Tanana River were 

contraction scour and pier scour. The primary concern is 

pier scour, which was calculated using the one- and twodimensional models for the five high discharge scenarios. 

Contraction scour was calculated using output from the 

one-dimensional model. Because contraction scour was 

not of primary concern and was of minimal magnitude, the 

two-dimensional model was not used to further evaluate 

contraction.

Procedure and scour estimation equations used in this 

analysis are described in “Evaluating Scour at Bridges; 3d ed.” 

(Richardson and Davis, 1995). This publication is also known 

as HEC-18, and describes the scour estimation methods used 

by FHWA.

Contraction Scour

Contraction scour was calculated with the live-bed 

equation from HEC-18 (Richardson and Davis, 1995). 

Sediment samples taken at Fairbanks by Burrows and others 

(1981) show that the Tanana River carries a considerable bed 

load during all stages; the same can be inferred for the Nenana 

River. This means that the bed is always ‘live’. Contractionscour calculation results from the HEC-RAS models and 

variables used in the calculations are shown in table 5.

Pier Scour

Pier scour was calculated using the methods in HEC-18 

(Richardson and Davis, 1995) and hydraulic data output from 

both the one- and two-dimensional models. The equation is 

applicable to both live-bed and clear-water scour conditions. 

Input variables from both models are in table 5. 

Angle of attack can make a significant difference in 

the calculated pier scour. Partly for this reason, the twodimensional model was used. The estimated angle of attack 

from the discharge measurement of August 17, 1967, was 

used for the one-dimensional model pier scour calculations. 

The angles of attack simulated by the two-dimensional model 

(table 5) were used for the calculations with two-dimensional 

data. The two-dimensional model demonstrated that the angle 

of attack is affected by discharge in the Nenana River.

The one-dimensional model divided the channel into 

20 subsections of equal conveyance. Depth and velocity for 

the calculation can be taken from directly upstream of the 

pier or from the deepest, fastest channel subsection. The 

subsectioning is based on the assumption that flow is evenly 

distributed across the channel. If this is not the case, then the 

depth and velocity values could be in error.

The two-dimensional model calculated the depths and 

velocities at many points across the channel, so the values just 

upstream of the pier are presumed to be more reliable. The 

values directly upstream of the pier were used to calculate 

pier scour for both models. This does not give the most 

conservative answer, but did provide a basis for comparison of 

the models.

Pier Scour calculated using output from 

one-dimensional HEC-RAS model Discharge scenario

y

y

K K K a

y

Fr ps

1

1 2 3

1

0 65

0 43 = 2 0 



 



. 

.

.

 

Discharge, 

Aug. 17,

1967

100-year flood 500-year flood

Low flow High flow Low flow High flow

Velocity at nose of pier (ft/s) v1 10.51 10.81 8.90 12.21 10.23

Depth at nose of pier (ft/s) y1 21.3 19.6 22.9 21.3 24.5

Gravity constant (ft/s2) g 32.17 32.17 32.17 32.17 2.2

Froude number at nose of pier Fr = v1

/(gy1)1/2 .40 .43 .33 .47 .36

Pier shape Sharp nose Sharp nose Sharp nose Sharp nose Sharp nose

Pier shape correction factor K1 1.0 1.0 1.0 1.0 1.0

Angle of attack (degree) AA 15 15 15 15 15

Pier width (ft) a 14.0 14.0 14.0 14.0 14.0

Pier length (ft) L 62 62 62 62 62

Ratio L/a 4 4 4 4 4

Angle of attack correction factor K2

 = f(AA, L/a) 1.6 1.6 1.6 1.6 1.6

Pier Scour (ft) yps 37.8 37.9 35.6 40.3 38.1

Table 5. Calculated depths of pier scour, contraction scour, and angles of attack at pier 3, and associated variables, Tanana River at Nenana, Alaska.

[Abbreviations: HEC-RAS, Hydrologic Engineering Center River Analysis System; RMA2, Resource Management Associates; ft, foot; ft/s, foot per second; 

ft/s2, foot per square second; ft3/s, cubic foot per second]

Scour Calculations 11
Pier Scour calculated using output from 

two-dimensional RMA2 model

 

Discharge scenario

y

y

K K K a

y

Fr ps

1

1 2 3

1

0 65

0 43 = 2 0 



 



. 

.

.

 

Discharge, 

Aug. 17,

1967

100-year flood 500-year flood

Low flow High flow Low flow High flow

Velocity in the X direction at nose of pier (ft/s) vx -10.93 -11.23 -8.82 -12.68 -10.20

Velocity in the Y direction at nose of pier (ft/s) vy -1.42 -1.72 -0.84 -1.83 -0.98

Resultant velocity at nose of pier (ft/s) v1 11.02 11.36 8.86 12.81 10.25

Depth at nose of pier (ft/s) y1 23.9 22.4 26.5 24.1 28.0

Gravity constant (ft/s2) g 32.17 32.17 32.17 32.17 32.2

Froude number at nose of pier Fr = v1

/(gy1)

1/2 .40 .42 .30 .46 .34

Pier shape Sharp nose Sharp nose Sharp nose Sharp nose Sharp nose

Pier shape correction factor K1 1.0 1.0 1.0 1.0 1.0

Angle of flow (degree) 263 261 265 262 265

Angle of pier (degree) 248 248 248 248 248

Angle of attack (degree) AA 15 13 17 14 17

Pier width (ft) a 14.0 14.0 14.0 14.0 14.0

Pier length (ft) L 62 62 62 62 62

Ratio L/a 4 4 4 4 4

Angle of attack correction factor K2

 = f(AA, L/a) 1.6 1.5 1.6 1.5 1.6

Bed condition (dunes) correction factor K3 1.1 1.1 1.1 1.1 1.1

Pier Scour (ft) yps 38.9 38.0 37.3 40.8 40.0

Live-bed contraction scour simulated using output from

one-dimensional HEC-RAS model Discharge scenario

Discharge, 

Aug. 17,

1967

100-year flood 500-year flood

y

y

Q

Q

W

W

y y y

K

cs

2

1

2

1

6

7 1

2

2 1

1

= 



 



 



 





= − = (average scour depth)

 

Low flow High flow Low flow High flow

Total discharge in Tanana River main channel (ft3/s) Q 158,000 150,000 149,000 187,000 185,000

Exponent determined from mode of bed material transport K1 .69 .69 .69 .69 .69

Discharge in main channel of approach section (ft3/s) Q1 156,700 148,000 142,000 180,600 173,700

Discharge in main channel of contracted (bridge) section (ft3/s) Q2 155,800 148,100 143,400 182,200 176,600

Width of main channel of approach section (ft) W1 796 796 796 796 796

Width of main channel of contracted (bridge) section (ft) W2 706 706 710 706 710

Average depth of main channel of approach section (ft) y1 20.7 19.1 22.2 20.9 23.8

Average depth in contracted (bridge) section (ft) y2 22.3 20.7 24.2 22.9 26.2

Contraction Scour (ft) ycs 1.7 1.7 2.0 2.0 2.3

Table 5. Calculated depths of pier scour, contraction scour, and angles of attack at pier 3, and associated variables, Tanana River at Nenana, Alaska—

Continued

[Abbreviations: HEC-RAS, Hydrologic Engineering Center River Analysis System; RMA2, Resource Management Associates; ft, foot; ft/s, foot per second; 

ft/s2, foot per square second; ft3/s, cubic foot per second]

12  Calculation of Scour Depth at Parks Highway Bridge, Tanana River at Nenana, Alaska
Comparison of Models

Water-surface profiles from each model are shown in 

figure 6. The water-surface elevations from RMA2 are from 

the approximate center of the main channel. Those from HECRAS are the average water surface from each cross section. 

The largest difference in the profiles was less than 1.5 ft, just 

downstream of the main bridge (at 1.18 mi upstream of the 

downstream boundary), where the models are affected most 

by the two-dimensional nature of the flow. The difference 

between the models is much greater when the discharge in the 

Nenana River is high (fig. 6B).

When the Nenana River has relatively low discharge 

and the Tanana River discharge is high, the flow in the main 

channel of the Tanana River appears as parallel velocity 

vectors in the two-dimensional model (figs. 7A, 7C). When 

the Nenana River discharge is high, the velocity vectors 

indicate that it forces flow in the Tanana River to cross the 

channel from left to right (figs. 7B, 7D). Once the flow vectors 

return to mainly parallel at about 0.75 mi upstream of the 

downstream boundary, the two models match reasonably 

well. The difference in flow patterns at the convergence of the 

channels between the models with low and high flow in the 

Nenana River is shown in figure 7.

The profiles show some variation in the reach upstream 

of the bridge (fig. 6B). RMA2 computed a larger backwater 

effect from the increased discharge in the Nenana River. 

When the Nenana River is low and the flow is mostly onedimensional, then the RMA2 and HEC-RAS profiles are quite 

similar (fig. 6B).

Comparing the flows in Tanana Slough also demonstrates 

the difference in backwater simulated by each model (fig. 8). 

Simulations were similar for scenarios with low discharge in 

the Nenana River, but RMA2 simulated considerably more 

flow in the slough for scenarios with high discharge in the 

Nenana River.

Pier-scour depth calculated using output from the 

two-dimensional model was slightly greater than that using 

the output from the one-dimensional model, because the 

two-dimensional model computed slightly different angles 

of attack than were used in the one-dimensional model 

calculations (fig. 9). Differences in values were less than 

6 percent and were negligible.

Streamflow velocities along the cross section at river 

mile 1.377, measured on August 19, 1998, and calculated 

from each model type also were used to compare the models 

(fig. 10). Velocities for 1998 were measured with a Price AA 

current meter using standard USGS methods (Buchanan and 

Somers, 1969). Velocities calculated from the two-dimensional 

model are the total velocity magnitude. Flow direction at this 

cross section is perpendicular to the cross section, so neither 

velocity data set was adjusted for angles. Velocity calculated 

from the one-dimensional model is the average velocity for the 

cross section. Velocities from all three sources match well.

Comparison of Models 13
Figure 7. Velocity vectors and magnitudes on the Tanana River near the mouth of the Nenana River, Alaska, simulated using a two-dimensional hydraulic model.

0.910

1.095

1.163

1.197 Location of pier 3

1.377

0.085

0.147

GROUND SURFACE—Dry in this areaLINE OF SECTION—Location used in one-dimensional model, and distance upstream from model boundary, in milesVELOCITY VECTOR SCALE Length of arrow corresponds to velocity. 0 length equals 0 feet per second. Example is 10 feet per second

EXPLANATION

A. 100-YEAR FLOOD IN TANANA RIVER, LOW FLOW IN NENANA RIVER

1210

8

642

VELOCITY MAGNITUDE, in feet per second

ak19601fig07a

1.377

14 Calculation of Scour Depth at Parks Highway Bridge, Tanana River at Nenana, Alaska
0.910

1.095

1.163

1.197 Location of pier 3

1.377

0.085

0.147

VELOCITY MAGNITUDE, in feet per second

1816141210

8642

EXPLANATION

B. 100-YEAR FLOOD IN TANANA RIVER, HIGH FLOW IN NENANA RIVER

LINE OF SECTION—Location used in one-dimensional model, and distance upstream from model boundary, in milesVELOCITY VECTOR SCALE Length of arrow corresponds to velocity. 0 length equals 0 feet per second. Example is 10 feet per second

1.377

GROUND SURFACE—Dry in this area

Comparison of Models 15 Figure 7. Continued..
0.910

1.095

1.163

1.197

1.377

0.085

0.147

Location of pier 3

VELOCITY MAGNITUDE, in feet per second

1816141210

8642

EXPLANATION

C. 500-YEAR FLOOD IN TANANA RIVER, LOW FLOW IN NENANA RIVER

LINE OF SECTION—Location used in one-dimensional model, and distance upstream from model boundary, in milesVELOCITY VECTOR SCALE Length of arrow corresponds to velocity. 0 length equals 0 feet per second. Example is 10 feet per second

1.377

GROUND SURFACE—Dry in this area

16 Calculation of Scour Depth at Parks Highway Bridge, Tanana River at Nenana, Alaska

Figure 7. Continued..
0.910

1.095

1.163

1.197

1.377

0.085

0.147

Location of pier 3

D. 500-YEAR FLOOD IN TANANA RIVER, HIGH FLOW IN NENANA RIVER

ak19601fig07d

VELOCITY MAGNITUDE, in feet per second

1816141210

8642

EXPLANATION

LINE OF SECTION—Location used in one-dimensional model, and distance upstream from model boundary, in milesVELOCITY VECTOR SCALE Length of arrow corresponds to velocity. 0 length equals 0 feet per second. Example is 10 feet per second

1.377

GROUND SURFACE—Dry in this area

Comparison of Models 17 Figure 7. Continued..
Figure 8. Comparison of discharge in Tanana Slough for six 

discharge scenarios simulated using one- and two-dimensional 

hydraulic models.

Figure 9. Depth of pier scour, calculated using output from oneand two-dimensional hydraulic models, and angle of attack at bridge 

pier 3 for five discharge scenarios representing floods on the Tanana 

River near Nenana, Alaska.

See table 5 for values.

5,000

ak19601_fig08

Nenana

High Flow 

Nenana

Low Flow 

Nenana

High Flow 

Nenana

Low Flow 

100-YEAR FLOOD 500-YEAR FLOOD 

August 19, 1998 August 17, 1967 0

10,000

15,000

20,000

25,000

DISCHARGE IN TANANA SLOUGH, 

IN CUBIC FEET PER SECOND 

DISCHARGE SCENARIO

Measured

Two-dimensional model 

One-dimensional model 

15 15 13 15 17 15 14 15 17 15

30

35

40

45

CALCULATED SCOUR DEPTH 

 AT PIER 3, IN FEET 

Nenana

High Flow 

Nenana

Low Flow 

Nenana

High Flow 

Nenana

Low Flow 

100-YEAR FLOOD 500-YEAR FLOOD 

August 17, 1967 

DISCHARGE SCENARIO AND ANGLE OF ATTACK

Two-dimensional model 

One-dimensional model 

17 15

Figure 10. Streamflow velocity along cross-section 1.377 on the 

Tanana River near Nenana, Alaska, measured on August 19, 1998, and 

simulated using one- and two-dimensional hydraulic models.

Discharge for August 19, 1998, was 42,700 cubic feet per second.

Measured velocity 

Simulated average velocity from one-dimensional model

Simulated total magnitude of velocity from two-dimensional model 

0 200 400 600 800 1,000

DISTANCE FROM LEFT BANK, IN FEET, ALONG CROSS-SECTION 1.377 

0

1

2

3

4

5

6

STREAMFLOW VELOCITY, IN FEET PER SECOND

Summary and Conclusions

Parks Highway Bridge at Nenana, Alaska, crosses a 

hydraulically complex reach of the Tanana River. The Tanana 

River is divided into two channels, the main channel and 

the slough channel, and both are crossed by bridges. The 

Nenana River enters the main channel several hundred feet 

downstream of the bridge and affects flow at the bridge 

crossing. A large pier at the bridge over the main channel is at 

an angle to the flow. 

This site was selected for a comprehensive scour 

assessment that included a test case for a two-dimensional 

hydraulic model because of the site’s complexity and 

preliminary study results. The site was fully surveyed and 

modeled with a one-dimensional hydraulic model, HEC-RAS. 

The geometry data then were input into a two-dimensional 

model, RMA2. Output from both models was used to calculate 

pier-scour estimates. Contraction scour was calculated using 

only output from the one-dimensional model.

A high discharge measurement made on August 17, 1967, 

at the Tanana River, was used to calibrate both models. The 

models were run with four discharge scenarios using discharge 

in the Tanana River for 100- and 500-year recurrence intervals, 

and, because discharge in the Nenana River has a considerable 

effect on the flow conditions at the bridge, using low and high 

discharges in the Nenana River. Discharge measured in the 

Nenana River during the study survey was used for low flow 

and the discharge for a 100-year recurrence interval in the 

Nenana River was used as high flow. 

The models also were used to simulate the discharge 

at the time of the survey. The one-dimensional model did 

relatively well using the same roughness values as used for the 

higher flows. The simulated water surface was 0.5 to 1 foot 

higher than that surveyed in the field. The two-dimensional 

model required a reduction in roughness to properly simulate 

the lower flow. Surveyed data and computational mesh were 

too coarse, creating an artificial roughness from the jagged 

edges. This shortcoming was offset by reducing the roughness 

factor. Additional surveying and a refinement of the mesh 

would be required to use the two-dimensional model for 

reliable low-flow simulations.

Water-surface profiles computed by each model were 

similarly shaped. The greatest difference in water surface 

elevation was less than 1.5 feet, near the mouth of the Nenana 

River, the area with the greatest horizontal two-dimensional 

flow variability. In reaches where flow directions are not as 

variable, the shape and slope of the profiles match closely. 

In scenarios with high discharge in the Nenana River, water 

surfaces upstream of the bridge were higher in the twodimensional model than those in the one-dimensional model. 

This is due to the increase in cross-channel flow, which was 

simulated by the two-dimensional model but not by the onedimensional model.

18 Calculation of Scour Depth at Parks Highway Bridge, Tanana River at Nenana, Alaska
The models also determined the division of flow between 

the Tanana River main channel and the slough channel. With 

low flow in the Nenana River, the flows in the slough were 

similar between the models. For high flows in the Nenana 

River, the two-dimensional model simulated significantly 

higher flows in the slough because of the higher computed 

water surface upstream of the bridge. Pier-scour depth 

was calculated for all flood scenarios using output from 

both models. Estimates of pier-scour depth from the twodimensional model output were within 6 percent of those from 

the one-dimensional model output.

Flow characteristics near the mouth of the Nenana River 

and upstream of the bridge over the main channel varied 

considerably between the two models. However, results from 

the scour calculations for the two-dimensional model were 

slightly higher, but within 5 percent of those from the onedimensional model. The ability to compute an angle of attack 

from the two-dimensional model output rather than estimating 

an angle for the one-dimensional output greatly improved 

reliability of the scour estimate. Although the final results 

were similar, the two-dimensional model provided additional 

information about flow characteristics throughout the study 

reach and would be more useful for design or analysis than the 

one-dimensional model.

References Cited

Arcement, G.J., Jr., and Schneider, V.R., 1989, Guide for 

selecting Manning’s roughness coefficients for natural 

channels and flood plains: U.S. Geological Survey WaterSupply Paper 2339, 38 p.

Brabets, T.P., Meade, R.H., and Wang, B., 2000, 

Environmental and hydrologic overview of the Yukon River 

basin, Alaska and Canada: U.S. Geological Survey WaterResources Investigations Report 99-4204, 106 p.

Brunner, G.W., 1997a, HEC-RAS, River analysis system 

hydraulic reference manual—Version 2.0: U.S. Army Corps 

of Engineers Hydrologic Engineering Center, 241 p.

Brunner, G.W., 1997b, HEC-RAS, River analysis system 

user’s manual—Version 2.0: U.S. Army Corps of Engineers 

Hydrologic Engineering Center, 243 p.

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References Cited 19
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20 Calculation of Scour Depth at Parks Highway Bridge, Tanana River at Nenana, Alaska
Manuscript approved for publication, January 20, 2006

Prepared by the U.S. Geological Survey Publishing Network, 

Publishing Service Center, Tacoma, Washington 

Bill Gibbs 

Linda Rogers

Debra Grillo

Bobbie Jo Richey

For more information concerning the research in this report, contact the 

Director, Alaska Water Science Center

U.S. Geological Survey, 4230 University Drive

Anchorage, AK 99508

http://ak.water.usgs.gov
SIR 2006-5023 Langley

Calculation of Scour Depth at the Parks Highway Bridge on the Tanana River at Nenana, Alaska, 

Using One- and Two-Dimensional Hydraulic Models

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