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Cover: Photographs taken from the Dalles Bridge looking downstream at the slope-area study reach, Skagit River near Concrete, Washington. 

(Cover photo: D. Miller, U.S. Geological Survey, 2004; Inset, F. Veatch, U.S. Geological Survey, 1962) 
Verification of 1921 Peak Discharge at

Skagit River near Concrete, Washington, 

Using 2003 Peak-Discharge Data

By M.C. Mastin and D.L. Kresch

Scientific Investigations Report 2005-5029

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2005

For sale by U.S. Geological Survey, Information Services

Box 25286, Denver Federal Center

Denver, CO 80225

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endorsement by the U.S. Government.

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:

Mastin, M.C., and Kresch, D.L., 2005, Verification of 1921 peak discharge at Skagit River near Concrete, Washington, 

using 2003 peak-discharge data: U.S. Geological Survey Scientific Investigations Report 2005-5029, 18 p. 
iii

Figures

Figure 1. Map showing location of cross sections, discharge measurement

cableway, Dalles Gorge, and streamflow-gaging station Skagit River

near Concrete, Washington ............................................................... 3

Figure 2. Relief map showing Skagit River basin and streamflow-gaging stations,

Skagit River near Concrete, Washington ................................................ 5

Figure 3. Plan view of cross sections, high-water marks, survey reference line,

survey reference points, Dalles Bridge, and streamflow-gaging station,

Skagit River near Concrete, Washington ................................................ 7

Figure 4. Cross section showing high-water marks (HWMs), flattest- and steepest-sloped

water-surface profiles, and a HEC-RAS water-surface profile near cross

sections XS1, XS2, and XS3, at Skagit River near Concrete, Washington ............ 8

Figure 5. Photographs showing comparison of two n-verified river reaches with

n values of 0.028 ........................................................................... 10

Figure 6. Photograph showing Skagit River near Concrete, Washington, recording

gage house and barren island/cobble bar in the study reach in 1937 ............... 11

Figure 7. Photograph showing Skagit River near Concrete, Washington, and

vegetated island/cobble bar in the study reach in 2001 ................................. 12

Figure 8. Cross section showing historical and recent soundings made during

discharge measurements at the cableway at Skagit River near Concrete, 

Washington, 1924-2004 ..................................................................... 12

Figure 9. Cross sections showing comparison of three cross sections, XS1, XS2,

and XS3, surveyed in 1923 and 2004, and peak water surfaces of the 1921

and 2003 floods at Skagit River near Concrete, Washington ........................ 13

Figure 10. Graph showing current rating and rating No. 1 stage-discharge

ratings for Skagit River near Concrete, Washington, with historical

peak-flow discharges and recalculated high and low estimates of the peak 

discharge of the 1921 flood ............................................................... 14

Contents

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

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

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

Previous Investigations ........................................................................... 4

Description of Skagit River Basin and Study Site ............................................. 4

Methods ................................................................................................... 6

n-Verification Analyses ........................................................................... 6

Recalculating 1921 Peak Discharge ............................................................ 9

Verification of the 1921 Peak Discharge ............................................................... 11

Summary and Conclusions .............................................................................. 16

References Cited .......................................................................................... 17
iv

Conversion Factors and Datum

Conversion Factors

Multiply By To obtain

cubic foot (ft3) 0.02832 cubic meter

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

foot (ft) 0.3048 meter

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

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

inch (in.) 2.54 centimeter

inch (in.) 25.4 millimeter

mile (mi) 1.609 kilometer

square mile (mi2) 2.590 square kilometer

Datum

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

(NGVD 29).

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

Tables

 Table 1. Peak discharges for historical floods in Skagit River near

Concrete, Washington ..................................................................... 15

 Table 2. The 100-year flood discharges of Skagit River near Concrete, Washington, using 

annual peak discharges for 1897, 1909, 1917, and 1921 in conjunction

with unregulated annual peak discharges for water years 1944-2004 ............... 16
Abstract 

The 1921 peak discharge at Skagit River near Concrete, 

Washington (U.S. Geological Survey streamflow-gaging 

station 12194000), was verified using peak-discharge data 

from the flood of October 21, 2003, the largest flood since 

1921. This peak discharge is critical to determining other high 

discharges at the gaging station and to reliably estimating 

the 100-year flood, the primary design flood being used in a 

current flood study of the Skagit River basin.

The four largest annual peak discharges of record 

(1897, 1909, 1917, and 1921) were used to determine the 

100-year flood discharge at Skagit River near Concrete. 

The peak discharge on December 13, 1921, was determined 

by James E. Stewart of the U.S. Geological Survey using 

a slope-area measurement and a contracted-opening 

measurement. An extended stage-discharge rating curve based 

on the 1921 peak discharge was used to determine the peak 

discharges of the three other large floods. Any inaccuracy in 

the 1921 peak discharge also would affect the accuracies of 

the three other largest peak discharges. 

The peak discharge of the 1921 flood was recalculated 

using the cross sections and high-water marks surveyed 

after the 1921 flood in conjunction with a new estimate 

of the channel roughness coefficient (n value) based on 

an n-verification analysis of the peak discharge of the 

October 21, 2003, flood. The n value used by Stewart for his 

slope-area measurement of the 1921 flood was 0.033, and the 

corresponding calculated peak discharge was 240,000 cubic 

feet per second (ft3/s). Determination of a single definitive 

water-surface profile for use in the n-verification analysis 

was precluded because of considerable variation in 

elevations of surveyed high-water marks from the flood 

on October 21, 2003. Therefore, n values were determined 

for two separate water-surface profiles thought to bracket a 

plausible range of water-surface slopes defined by high-water 

marks. The n value determined using the flattest plausible 

slope was 0.024 and the corresponding recalculated discharge 

of the 1921 slope-area measurement was 266,000 ft3/s. The 

n value determined using the steepest plausible slope was 

0.032 and the corresponding recalculated discharge of the 

1921 slope-area measurement was 215,000 ft3/s. The two 

recalculated discharges were 10.8 percent greater than (flattest 

slope) and 10.4 percent less than (steepest slope) the 1921 

peak discharge of 240,000 ft3/s. The 1921 peak discharge 

was not revised because the average of the two recalculated 

discharges (240,500 ft3/s) is only 0.2 percent greater than the 

1921 peak discharge.

Introduction 

Large-scale capital improvement projects currently 

(2004) are being planned to reduce flood impacts on the 

Skagit River basin. The size and cost of each of these 

projects are dictated by the size of the floods that can be 

expected based on historical floods. The design floods for 

these projects are based on the historical peak discharges at 

Skagit River near Concrete, Wash. (U.S. Geological Survey 

streamflow-gaging station 12194000) and any error in the 

calculation of these peak discharges could result in large, 

unnecessary expenditures, or inadequate protection measures. 

The peak discharge of the October 21, 2003, flood, the largest 

peak since 1921, offered an opportunity to verify the peak 

discharge of the 1921 flood that is critical to estimating the 

other large historical floods; and therefore, the magnitude of 

future flooding of the Skagit River.

Verification of 1921 Peak Discharge at

Skagit River near Concrete, Washington,

Using 2003 Peak-Discharge Data

By M.C. Mastin and D.L. Kresch
The U.S. Army Corps of Engineers (USACE) manages 

two of the five major dams in the Skagit River basin for 

flood-control storage, and the other three are managed for 

power generation without any flood-control regulation. 

Pursuant to section 209 of the Flood Control Act of 1962, 

the USACE, with Skagit County as a local sponsor, recently 

has completed a draft of a flood damage reduction study of 

the Skagit River basin. A critical element of that study was 

the determination of discharge on the mainstem of the Skagit 

River for a flood with a 0.01 annual exceedance probability 

the—100-year flood. Annual peak discharges at Skagit 

River near Concrete were used to determine the 100-year 

flood because the station has a long period of record, has a 

stable rating due to a bedrock control, and is downstream 

of all major tributaries in the Skagit River basin. The two 

largest peak discharges of record (500,000 ft3/s in 1815 

and 350,000 ft3/s in 1856) were downgraded to estimates 

because the times and validity of the peak stages could not 

be validated (R.A. Kimbrough, U.S. Geological Survey, 

oral commun., 2004). Therefore, they were not used in the 

calculation of the 100-year flood. The four largest annual peak 

discharges of record used to determine the 100-year flood 

discharge occurred in 1897, 1909, 1917, and 1921.

Procedures and cross-section properties used to 

determine the peak discharge of December 13, 1921 

(240,000 ft3/s), are documented in “Stage and Volume of Past 

Floods in Skagit Valley and Advisable Protective Measures 

Prior to the Construction of Permanent Flood Controlling 

Works” (J.E. Stewart, U.S. Geological Survey, written 

commun., 1923). Based on the 1921 flood peak, the upper end 

of the stage-discharge rating curve was extended and used to 

estimate peak discharges for the 1897, 1909, and 1917 floods. 

Therefore, any inaccuracy in the peak discharge of the 1921 

flood would affect accuracies of the peak discharges of the 

other three largest floods.

The slope-area measurement of the 1921 peak discharge 

was based on (1) three surveyed cross sections, along a reach 

of the river a short distance downstream of Skagit River near 

Concrete, (2) surveyed high-water marks, used to define the 

slope of the water-surface profile along the reach, and (3) 

an estimated roughness coefficient (n value) of 0.033 for 

both subreaches [XS1 to XS2 and XS2 to XS3 (fig. 1)] of the 

measurement. This n value was based on an n-verification 

analysis of a reach near Skagit River near Sedro Woolley 

(gaging station 12199000), about 32 mi downstream from 

the gaging station near Concrete. The n value accounts 

for resistance to flood flows resulting from physical 

characteristics of a stream channel or floodplain. The most 

important factors that affect the n value of a stream channel 

are the type and size of materials that compose the bed and 

banks of the channel and the shape of the channel. Effects 

of depth of flow on the selection of an n value also must be 

considered. A relatively small inaccuracy in estimating or 

determining the actual n value of a stream reach can have 

a significant impact on the magnitude of the calculated 

discharge. The sensitivity of the recalculated peak discharges 

of the 1921 flood to the n values used (0.024 and 0.032) was 

evaluated by calculating discharge for several different n

values between them. The resulting discharges decreased by 

about 2.5 percent for each 0.001 increase in the n value.

Purpose and Scope

Peak discharge for the 1921 flood at Skagit River 

near Concrete needed to be verified in order to determine 

the magnitude of the other three large floods (1897, 1909, 

and 1917) and therefore, the flood frequency discharges 

at the site. Specifically, the validity of the n value used by 

James E. Stewart (U.S. Geological Survey, written commun., 

1923) to calculate peak discharge needed to be verified 

because of concerns about the river reach and discharge from 

which it was determined. The n value was determined by 

an n-verification analysis of a reach of the river near Skagit 

River near Sedro Woolley, which is about 32 mi downstream 

of Concrete. The n value at Concrete may be higher than 

the n value near Sedro Woolley because bed material in the 

reach near Concrete was somewhat coarser (J.E. Stewart, 

U.S. Geological Survey, written commun., 1923). The 

n-verification analysis was based on a discharge of only 

40,200 ft3/s measured on June 12, 1908, which is less than 

20 percent of the magnitude of the peak discharge of the 

December 13, 1921, flood (210,00 ft3/s) at the Sedro Woolley 

gaging station. 

The flood peak on October 21, 2003, at Skagit River near 

Concrete (166,000 ft3/s), the largest peak since 1921, offered 

an opportunity to calculate the n value for a much higher 

flow than the flow originally used by Stewart (40,200 ft3/s), 

and for the study reach. The 1921 peak discharge was 

verified using n values determined from the peak discharge, 

cross-section data, and high-water marks for the flood peak on 

October 21, 2003, in conjunction with Stewart’s cross-section 

data and high-water marks for the 1921 flood. Only Stewart’s 

slope-area measurement reach downstream of Dalles Gorge 

was used for verification because hydraulics within the 

gorge, where several directions of flow and unusual flood 

profiles were observed, were considered too complicated to 

yield reliable results using the contracted-opening method. 

Furthermore, Stewart’s determination of peak discharge 

for the 1921 flood using the contracted-opening method 

(246,000 ft3/s) was only 2.5 percent larger than the discharge 

determined by averaging results of the two methods.

2 Verification of 1921 Peak Discharge at Skagit River near Concrete, Washington, Using 2003 Peak-Discharge Data
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Figure 1. Location of cross sections, discharge measurement cableway, Dalles Gorge, and streamflow-gaging station Skagit 

River near Concrete, Washington.

Introduction 3
Previous Investigations

The importance of knowing the actual peak discharge of 

the 1921 flood was recognized by the U.S. Geological Survey 

(USGS) in the 1950s when an n-verification analysis was done 

by H.C. Riggs and W.H. Robinson (U.S. Geological Survey, 

written commun., 1950). The peak discharge determined 

by Riggs and Robinson was later revised by F.J. Flynn and 

M.A. Benson (U.S. Geological Survey, written commun., 

1951-52), whose analysis was given a final review by 

G.L. Bodhaine (U.S. Geological Survey, written commun., 

1954).

The 1950s analyses were based on four surveyed cross 

sections, a water-surface profile of the November 27, 1949 

flood, and a peak discharge of 153,000 ft3/s, which was 

determined from a stage-discharge rating curve extension. The 

upper end of the rating used for the extension was defined by 

a series of high-flow measurements made in 1932. The highest 

measurement used to define the rating was a current-meter 

measurement made at a discharge of 135,000 ft3/s. The 

upper end of this rating was essentially the same as the rating 

currently in use. The reach defined by the four cross sections 

used for the 1950s analyses was practically the same as the 

reach used for the slope-area measurement of the 1921 flood.

The n values determined by Riggs and Robinson for 

their upstream, middle, and downstream subreaches were 

0.040, 0.0276, and 0.0325, respectively. They recalculated the 

peak discharge of the 1921 flood as 209,000 ft3/s using an 

n value of 0.040 for Stewart’s upstream reach and 0.033 for 

Stewart’s downstream reach. They noted that there was a large 

expansion in the middle of the upstream reach and questioned 

whether the 50-percent energy recovery due to expansion 

that was assumed for that reach was too high. The general 

procedure used by the USGS assumes a 50-percent energy 

recovery in expanding reaches unless otherwise indicated 

(Dalrymple and Benson, 1984. p. 3).

Flynn and Benson revised Riggs and Robinson’s analysis 

by not using their most upstream subreach because of the 

expansion problem and a poorly defined water-surface 

profile on the right bank at their most upstream cross 

section. They computed an average n value of 0.0305 for 

Riggs and Robinson’s middle and downstream subreaches. 

Using only Stewart’s downstream reach and an n value of 

0.030, Flynn and Benson, using a two-section slope-area 

equation, recalculated peak discharge of the 1921 flood 

as 225,000 ft3/s. Bodhaine did not revise the 1921 peak 

discharge of 240,000 ft3/s because Flynn and Benson’s 

revised peak discharge varied from Stewart’s calculated 

discharge by only 6.2 percent. Several years later, a thorough 

history of flooding in the basin that included descriptions of 

high-water marks from the major floods and their discharges 

at gaging stations throughout the basin was documented in 

Stewart and Bodhaine (1961). The peak discharge listed in 

that report for the December 13, 1921, flood at Skagit River 

near Concrete gaging station is 240,000 ft3/s.

Description of Skagit River Basin 

and Study Site

Skagit River near Concrete has an average discharge of 

15,030 ft3/s and drains a 2,737 mi2 basin (Kimbrough and 

others, 2004) that extends to the Cascade Range divide and 

into Canada. Streamflow originates from rain, which falls 

primarily in late autumn to early spring and from glacier 

and snow melt that makes up a large percentage of the flow 

in late spring and summer. Precipitation ranges from 60 in. 

near Skagit River near Concrete to as much as 170 in. in the 

southeastern part of the Skagit River basin near Glacier Peak. 

Altitudes range from 190 ft at the gaging station to 10,773 ft 

at the highest point on Mount Baker (fig. 2). The basin, which 

is situated on the western slopes of the Cascade Range, lies in 

the path of the prevailing westerlies that bring moisture from 

the Pacific Ocean. About three-fourths of the annual peak 

discharges at Skagit River near Concrete occur in the rainy 

months of October through January. Typically, these floods 

are generated from heavy, long-duration rainfall sometimes 

augmented with snowmelt.

Since 1924, when Low Gorge Dam on the Skagit River 

was completed, flows on Skagit River have been regulated 

and flood discharges have been reduced by storage in 

reservoirs. Construction of dams continued with completion 

of Lower Baker River Dam in 1925, Diablo Dam in 1929, 

Ross Dam in 1949, 2nd Gorge Dam in 1950, Upper Baker 

Dam in 1959, and High Gorge Dam in 1961. The peak 

discharge on October 21, 2003, at Skagit River near Concrete 

(166,000 ft3/s) is the largest discharge recorded since the 

dams were constructed.

The reach of Skagit River used for this analysis is 

essentially the same as the reach used by Stewart for his 

slope-area measurement (fig. 1, cross sections XS1-XS3). 

The Skagit River near Concrete gaging station is in Dalles 

Gorge, a steep-sided bedrock channel, where the river 

4 Verification of 1921 Peak Discharge at Skagit River near Concrete, Washington, Using 2003 Peak-Discharge Data
Figure 2. Skagit River basin and streamflow-gaging stations, Skagit River near Concrete, Washington.

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narrows as it enters from around a right-angle bend. Stewart 

referenced cross sections used in his slope-area measurement 

relative to the “lower end of the Dalles” (J.E. Stewart, 

U.S. Geological Survey, written commun., 1923). For this 

verification study, it was assumed that Stewart was referring 

to the downstream end of the prominent bedrock knob on the 

right bank (looking downstream) about 400 ft downstream 

of the streamflow-gaging station where the channel begins to 

abruptly widen along the right bank. Cross sections were field 

surveyed at the same distances downstream of this knob, as 

reported by Stewart, in order to place them as close as possible 

to his survey locations.

Introduction 5
Methods

USGS computer program NCALC v.2.6 (Jarrett and 

Petsch, 1985) was used in conjunction with peak discharge, 

cross-section data, and high-water marks for the October 21, 

2003 flood, to determine the n value of the same reach of 

Skagit River that Stewart used to calculate peak discharge 

of the 1921 flood. That n value was used in conjunction with 

Stewart’s cross-section and high-water mark data for the 1921 

flood and a two-section slope-area equation to recalculate 

peak discharge of the 1921 flood. Although the peak stage of 

the 1921 flood (47.60 ft) was more than 5 ft higher than the 

peak stage of the 2003 flood (42.21 ft), n values for the two 

flood events are expected to be similar because in most stream 

channels, the n value does not vary much with depth once 

the ratio of depth of flow to the size of bed material exceeds 

5, provided that flow width is large relative to flow depth 

(Benson and Dalrymple, 1967, p. 21). Streambed material of 

Skagit River near Concrete consists primarily of cobbles and 

small boulders with an estimated average size of about 10 in. 

The ratio of depth of flow to this size of material exceeds 5 at 

a flow depth of about 4 ft. Average flow depths at Skagit River 

near Concrete during the 1921 and 2003 floods were about 

27 and 22 ft, respectively. Both flow depths are much smaller 

than the width of the channel, which was more than 700 ft 

during both floods.

 NCALC and the slope-area method are based on the 

Manning equation:

 Q n = ( . 1 486 / )AR S

2

3

1

2 , (1)

where

Q is discharge, in cubic feet per second,

A is cross-sectional area, in square feet,

R is hydraulic radius, in feet,

S is friction slope, in feet per foot, and

n is Manning’s roughness coefficient.

The Manning equation is used as shown in equation 1 

to calculate discharge by the slope-area method. Using the 

Manning equation to calculate n values in NCALC requires 

that it be rearranged to solve for n.

The friction slope S between any two consecutive cross 

sections is defined as the total energy loss between them 

divided by the reach length L. Total energy at each cross 

section is determined as the sum of both the static head, 

represented by the water-surface elevation and the velocity 

head, which is a function of the flow velocity. Thus, the 

friction slope is determined by the equation:

 S h = + (∆ ∆h k v v − (∆h L ))/ , (2)

where

∆h is difference in water-surface elevation 

(upstream minus downstream) between two 

consecutive cross sections, in feet,

L is length of the reach, in feet,

h v g v = α 2 / 2 is velocity head, in feet,

α is velocity head coefficient = 1.0 (for 

this study because the shapes of the cross 

sections are basically prismatic with 

minimal bank overflow),

v is flow velocity, in feet per second,

g is acceleration due to gravity = 32.2

(feet per square second),

S is friction slope, in feet per foot,

∆hv is difference in velocity head (upstream 

minus downstream) between two 

consecutive cross sections, in feet, and

k hv ( ) ∆ is energy loss due to contraction or 

expansion of the channel in the reach, in 

feet, where k = energy loss coefficient 

varying from 0 to 1.

Stewart used the Chezy and Kutter equations (Corbett, 

1962, p. 81-83) for his slope-area measurement of the peak 

discharge of the 1921 flood. However, the slope factor S

used by Stewart in his application of these equations was the 

water-surface slope rather than the friction slope.

n-Verification Analyses

The peak discharge on October 21, 2003, at Skagit 

River near Concrete (166,000 ft3/s) was determined 

from the recorded peak stage (42.21 ft) using the current 

stage-discharge rating curve for the gaging station. The 

accuracy of the upper end of the rating was verified 

by a current-meter discharge measurement made at a 

stage of 38.68 ft shortly after the river had crested on 

October 21, 2003. The measured discharge of 138,000 ft3/s 

is only 1.2 percent greater than the discharge indicated by the 

rating for a stage of 38.68 ft.

6 Verification of 1921 Peak Discharge at Skagit River near Concrete, Washington, Using 2003 Peak-Discharge Data
Three cross sections and high-water marks along both 

banks were surveyed during July and August 2004 for the 

n-verification analysis of the peak discharge on October 21, 

2003. A plan view of the entire survey and the reference line 

used to compute stationing of cross sections and high-water 

marks is shown in figure 3. The cross sections were placed as 

near as could be determined to the cross sections surveyed by 

Stewart for his 1921 slope-area measurement. However, only 

cross-sections XS2 and XS3 were used in the n-verification 

analysis. Cross-section XS1, the farthest upstream of the three 

cross sections, was not used in the n-verification analysis 

because the water-surface elevation at that cross section 

was not well defined by the surveyed high-water marks and 

because that cross section is about 600 ft downstream of a 

major river expansion where energy losses may not be fully 

dissipated and accounted for by the calculated energy slope. 

For the same reasons, a cross section in the same area was not 

used in the 1950’s n-verification analysis by Flynn and Benson 

in their recalculation of the 1921 peak discharge.

Figure 3. Plan view of cross sections, high-water marks, survey reference line, survey reference points, 

Dalles Bridge, and streamflow-gaging station, Skagit River near Concrete, Washington.

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Methods 7
High-water marks from the October 21, 2003, flood 

were difficult to find and were of poor quality because they 

were not surveyed until about 9 months after the flood. 

Consequently, elevations of surveyed high-water marks varied 

considerably. 

Cross-sections and high-water marks surveyed for the 

October 21, 2003, flood were processed and plotted using 

USGS software SAM 2.1 (Hortness, 2004). The peak flood 

elevation must be determined for each cross section in order 

to calculate the n value for each subreach. Water-surface 

profiles based on high-water mark elevations were plotted 

(fig. 4) to determine the peak flood elevation at each cross 

section. The high-water mark elevations near cross-section 

XS2 were in relatively close agreement, but those near 

cross-section XS3 were not, especially those along the right 

bank (the bank on the right when looking downstream). In 

addition, most high-water mark elevations along the left bank 

near cross-section XS3 were higher than most high-water 

mark elevations along the right bank near cross-section 

XS3. Consequently, two profiles were drawn in an attempt 

to bracket a plausible range of water-surface slopes for the 

actual water-surface profile, and n values were determined 

on the basis of both profiles. Both profiles began at the same 

elevation at cross-section XS2. However, the elevation at 

cross-section XS3 for the profile with the flattest plausible 

slope primarily was based on left bank high-water mark 

elevations, and the elevation at cross-section XS3 for the 

profile with the steepest plausible slope primarily was based 

on right bank high-water mark elevations.

Figure 4. High-water marks (HWMs), flattest- and steepest-sloped water-surface profiles, and a HEC-RAS water-surface profile 

near cross sections XS1, XS2, and XS3, at Skagit River near Concrete, Washington.

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8 Verification of 1921 Peak Discharge at Skagit River near Concrete, Washington, Using 2003 Peak-Discharge Data
The n values determined for the flattest and steepest 

of the two water-surface profiles are 0.024 and 0.032, 

respectively. Relative accuracy of these n values was 

considered fair because of the variability of high-water mark 

elevations near cross-section XS3. The average of the n values 

determined for the two water-surface profiles was 0.028.

A one-dimensional, steady-flow, step-backwater 

computer model, HEC-RAS version 3.1 (U.S. Army Corps of 

Engineers, 2002), was used to determine the reasonableness 

of the slopes for the two water-surface profiles. The 

HEC-RAS model contains 10 cross sections. Seven cross 

sections, beginning at river mile 50.05, 3.7 mi downstream 

of the study reach, were surveyed by USACE in 1975 (Ted E. 

Perkins, written commun., 2004), and the remaining three 

cross sections, XS1-XS3, were surveyed by the USGS in 2004. 

Discharge used in the HEC-RAS model was 166,000 ft3/s, the 

same discharge used for the n-verification analysis of the peak 

discharge on October 21, 2003. The starting water-surface 

elevation at the most downstream cross section was obtained 

from the output of a USACE HEC-RAS model of Skagit 

River basin. The n value used for the first seven cross sections 

was changed from 0.040, as used in the USACE Skagit 

River basin model, to 0.036 so the simulated water-surface 

elevation at XS3 would most closely agree with high-water 

marks near that cross section. For the remaining three cross 

sections (XS1-XS3), the n value used was 0.028—the average 

of n values determined from the flattest- and steepest-sloped 

water-surface profiles. Coefficients for contraction and 

expansion losses were 0.0 and 0.5, respectively, at all cross 

sections. The HEC-RAS water-surface profile was plotted 

along with the flattest and steepest profiles determined based 

on surveyed high-water marks (fig. 4). The decline in water 

surface between cross-sections XS2 and XS3 is 2.90 ft for 

the steepest-sloped profile and 1.50 ft for the flattest-sloped 

profile. The average decline for these two profiles was 2.20 ft, 

which was within 0.08 ft of the 2.12 ft decline between the 

two cross sections in the HEC-RAS model profile.

The relative accuracy of the NCALC results was 

measured by comparing the mean velocities calculated 

at cross-sections XS2 and XS3 with the mean velocity of 

the discharge measurement made on October 21, 2003. 

Velocities calculated at XS2 and XS3 for the flattest (11.11 

and 11.45 ft/s) and the steepest (11.11 and 12.20 ft/s) of the 

two water-surface profiles compare well with the mean 

velocity of 11.09 ft/s from the current-meter measurement 

of 138,000 ft3/s on October 21, 2003. The accuracy of 

the average of the two calculated n values (0.028) can be 

evaluated by comparing it with verified n values on other 

rivers such as Clark Fork at St. Regis, Montana, where Barnes 

(1967) determined an n value of 0.028. The bed material and 

bank vegetation (fig. 5A) for Clark Fork at St. Regis appear to 

be similar to the channel characteristics of Skagit River near 

Concrete (fig. 5B), although vegetation along the banks of 

Skagit River probably is more dense.

Recalculating 1921 Peak Discharge

Two n values (0.024 and 0.032) were determined in the 

n-verification analysis of the October 21, 2003, flood peak for 

water-surface profiles thought to bracket the plausible range 

in the actual water-surface slope. These n values were used 

in conjunction with Stewart’s cross section and high-water 

mark data for the 1921 flood and a two-section slope-area 

equation to recalculate peak discharge of the 1921 flood. 

Corresponding peak discharges of the 1921 flood calculated 

using these two n values are 266,000 and 215,000 ft3/s, 

respectively. Although these two discharges were 10.8 percent 

greater than and 10.4 percent less than the peak discharge 

calculated by Stewart, respectively, the average of the two 

discharges (240,500 ft3/s) was only 0.2 percent greater than 

the peak discharge of 240,000 ft3/s calculated by Stewart.

USGS policy concerning revision of previously published 

peak discharges is to revise them only if the revised discharge 

is reliable and different from the original discharge by 

more than 10 percent (Novak, 1985, p. 103). Therefore, the 

peak discharge calculated by Stewart was not revised. Peak 

discharges of the 1897, 1909, and 1917 floods were not revised 

either because they were all determined from an extension of 

the stage-discharge rating curve based on the peak discharge 

of the 1921 flood.

A relatively small inaccuracy in estimating or 

determining the actual n value of a stream reach can have 

a significant impact on the magnitude of the calculated 

discharge. The sensitivity of the recalculated peak discharges 

of the 1921 flood to the n values used (0.024 and 0.032) was 

evaluated by calculating discharge for several different n

values between them. The resulting discharges decreased by 

about 2.5 percent for each 0.001 increase in the n value.

Methods 9
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Figure 5. Comparison of two n-verified river reaches with n values of 0.028.

10 Verification of 1921 Peak Discharge at Skagit River near Concrete, Washington, Using 2003 Peak-Discharge Data
Verification of the 1921 Peak 

Discharge

Use of an n value determined from October 21, 2003, 

flood data to verify peak discharge of the 1921 flood is valid 

only if the reach used for both analyses has not changed 

significantly since 1921. A comparison of historical and 

current aerial photographs of the reach (figs. 6 and 7) 

indicates that the reach has not significantly changed. The size 

and shape of an island near the right (north) bank of the river 

in the study area reach (left of center in the photographs) has 

not changed much over time, but the density of vegetation on 

the island has changed significantly. In the 1937 photograph 

(fig. 6), the island is bare of vegetation. Historical photographs 

from 1948 and 1962 show a gradual increase in vegetation 

on the downstream part of the island. As of 2004, the 

downstream part of the island is covered with a dense forest 

of mostly alders (many more than 2-ft diameter), maples, and 

cottonwoods.

The cross section at the cableway used for making 

discharge measurements appears to have changed little 

since the gaging station was established in 1924 (fig. 8). The 

cableway was replaced once, but information indicates that 

the current cableway is at the same location as the previous 

cableway. Discharge measurements 475 and 476 (fig. 8) 

made on October 21 and 22, 2003, indicate some scour in the 

deepest sections and fill on the right half of the cross section, 

but by May 13, 2004, when discharge measurement 479 was 

made, the cross section had adjusted back to its long-term 

shape.

Figure 6. Skagit River near Concrete, Washington, recording gage house and barren island/cobble bar in the 

study reach in 1937 (Skagit County, 2003).

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Verification of the 1921 Peak Discharge 11
Figure 7. Skagit River near Concrete, Washington, and vegetated island/cobble bar in the study reach in 2001

(Skagit County, 2003).

Figure 8. Historical and recent soundings made during discharge measurements at the cableway at Skagit River near 

Concrete, Washington, 1924-2004.

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12 Verification of 1921 Peak Discharge at Skagit River near Concrete, Washington, Using 2003 Peak-Discharge Data
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Figure 9. Comparison of three cross sections, XS1, XS2, and XS3, surveyed in 1923 and 2004, and peak water surfaces 

of the 1921 and 2003 floods at Skagit River near Concrete, Washington. 

Peak water-surface elevations are based on high-water marks.

Stewart’s cross-sections XS1, XS2, and XS3 were 

compared with cross sections surveyed after the peak 

discharge on October 21, 2003. The sizes and shapes of these 

cross sections compare well with each other as shown in 

figure 9.

The accuracy of recalculated peak discharge for the 1921 

flood is contingent on accuracies of the n values determined 

from the n-verification analyses of the October 21, 2003, flood 

peak. A considerable amount of variation was observed in 

the elevations of the surveyed high-water marks, especially 

Verification of the 1921 Peak Discharge 13
among those along the right bank near cross-section XS3, 

used to define water-surface profiles from which the n values 

were determined. Therefore, the accuracy of recalculated peak 

discharge is considered fair, which means that it may be in 

error by as much as 15 to 25 percent (Benson and Dalrymple, 

1967, p. 30).

Because the island extending from cross section 

XS1 to a point downstream from cross section XS2 has 

significantly revegetated since the 1921 flood, the current 

channel roughness is undoubtedly greater than in 1921. 

The recalculation of Stewart’s slope-area measurement of 

the 1921 flood peak does not take this into consideration. 

To accurately recalculate peak discharge of the 1921 

flood, an n value less than 0.028—the average of the n

values determined using the flattest and steepest plausible 

water-surface profiles—probably should be used. However, 

how much the n value should be decreased would be difficult 

to determine. A decrease in average n value would have the 

effect of increasing the recalculated peak discharge of the 

1921 flood. Increased roughness of the island may explain 

why Stewart’s calculated discharge measurement plots to the 

right of the relatively stable stage-discharge rating for the 

streamflow-gaging station (fig. 10). At river stages above the 

island’s ground elevation, slightly higher gage heights are 

expected for a given peak discharge as the island’s emerging 

forest resists flow.

Figure 10. Current rating and rating No. 1 stage-discharge ratings for Skagit River near Concrete, Washington, with historical peak-flow 

discharges and recalculated high and low estimates of the peak discharge of the 1921 flood.

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14 Verification of 1921 Peak Discharge at Skagit River near Concrete, Washington, Using 2003 Peak-Discharge Data
The effect of change in the island’s roughness was 

tested by adding four more cross sections, each with an n

value of 0.028, to the HEC-RAS model, which extended the 

model upstream beyond the gaging station. Contraction and 

expansion coefficients of 0.4 and 0.7, respectively, were used 

through Dalles Gorge so the simulated water-surface elevation 

at the gaging station would match the recorded peak stage 

of the 2003 flood. The n value at XS2 was decreased from 

0.028 to 0.023 and the resulting simulated water surface at the 

gaging station decreased by 0.17 ft indicating that the island’s 

roughness does affect the stage at the gaging station.

The relative influence of different estimates of the 

peak discharge of the December 13, 1921, flood in the 

determination of the 100-year flood discharge for Skagit River 

near Concrete gaging station was evaluated by comparing 

the 100-year flood discharges determined based on various 

estimates of peak discharge. Annual peak discharges for 

1897, 1909, 1917, and 1921, and water years 1944–2004 were 

used in this analysis. Skagit River flows have been regulated 

since 1924, so estimates of the unregulated annual peak 

discharges for water years 1944-2004 were determined from 

the regulated annual peak discharges by USACE (Ted Perkins, 

U.S. Army Corps of Engineers, written commun., 2004). 

Although the gaging station also was operated during water 

years 1925-43, unregulated annual peak discharges could not 

be determined for those years because necessary streamflow 

data were not available.

Peak discharges for the historical floods of 1897, 1909, 

1917, and 1921 are shown in table 1. Peak discharges were 

not determined in this analysis for the 1897, 1909, and 1917 

floods, and the discharges determined for the 1921 flood 

ranged from 10.8 percent greater than to 10.4 percent less than 

the discharge determined by Stewart. Assuming that the same 

approximate range in percentage of differences would apply 

to the other three peak discharges, columns were included in 

table 1 for discharges 10 percent greater than and 10 percent 

less than those determined by Stewart. Peak discharges for the 

1921 flood determined by Riggs and Robinson and by Flynn 

and Benson were 12.5 and 6.2 percent less than the peak 

discharge determined by Stewart.

The 100-year flood discharges (table 2) were determined 

using a log-Pearson Type III distribution of the annual peak 

discharges for the historic floods of 1897, 1909, 1917, and 

1921 and USACE estimates of unregulated annual peak 

discharges for water years 1944–2004. Using the historical 

peak discharges calculated by Riggs and Robinson and those 

calculated by Flynn and Benson in the flood-frequency 

analysis results in 100-year flood discharges 8.4 and 2.8 

percent less than the 100-year flood discharge using Stewart’s 

calculated peak discharges. Using Stewart’s historical peak 

discharges plus or minus 10 percent results in 100-year flood 

discharges of 4.8 percent greater than and 6.2 percent less 

than the 100-year flood discharge determined using Stewarts 

unaltered historical peak discharges.

Source of data Peak discharge, in cubic feet per second

1897 1909 1917 1921

H.C. Riggs and W.H. Robinson (U.S. Geological Survey, 

written commun., 1950)

230,000 220,000 190,000 209,000

F.J. Flynn and M.A. Benson (U.S. Geological Survey, 

written commun., 1951-52)

265,000 240,000 205,000 225,000

James E. Stewart (U.S. Geological Survey, written 

commun., 1923)

275,000 260,000 220,000 240,000

Plus 10 percent 302,500 286,000 242,000 264,000

Minus 10 percent 247,500 234,000 198,000 216,000

Table 1. Peak discharges for historical floods in Skagit River near Concrete, Washington.

Verification of the 1921 Peak Discharge 15
The poor quality of the surveyed high-water marks 

and the fact that channel conditions may have changed over 

80 years precludes any definitive determination of the peak 

discharge of the December 13, 1921, flood. However, all the 

evidence from this investigation suggests that the discharge 

calculated by Stewart was reasonably accurate; therefore, 

neither the peak discharge of the 1921 flood nor the peak 

discharges of the 1897, 1909, or 1917 floods should be revised.

Summary and Conclusions

The 1921 peak discharge at Skagit River near Concrete, 

Washington (U.S. Geological Survey streamflow-gaging 

station 12194000), was verified using peak-discharge data 

from the flood of October 21, 2003—the largest flood since 

1921. This peak discharge is critical to determining other high 

discharges at the gaging station and to reliably estimating the 

100-year flood—the primary design flood being used in a 

current flood study of the Skagit River basin.

The four largest annual peak discharges of record (1897, 

1909, 1917, and 1921) were used to determine the 100-year 

flood discharge for Skagit River near Concrete, Washington. 

A peak discharge of 240,000 cubic feet per second (ft3/s) 

for the flood on December 13, 1921, was determined by 

James E. Stewart of the U.S. Geological Survey by means 

of slope-area and contracted-opening measurements. Peak 

discharges of the other three largest floods were determined 

from a stage-discharge rating curve after extending the 

rating on the basis of the peak discharge of the 1921 flood. 

Therefore, any inaccuracy in the peak discharge of the 1921 

flood also would affect the accuracies of the other three 

largest peak discharges.

The validity of the peak discharge of the 1921 flood 

was evaluated by recalculating the slope-area measurement 

using a channel roughness coefficient (n value) based 

on an n-verification analysis of the peak discharge on 

October 21, 2003. A U.S. Geological Survey computer 

program, NCALC was used in conjunction with peak 

discharge, cross-section data, and high-water marks for the 

flood on October 21, 2003, to determine the n value for the 

same reach of the Skagit River used by Stewart to calculate 

peak discharge for the 1921 flood. That n value then was used 

in conjunction with Stewart’s cross-section and high-water 

mark data and a two-section slope-area equation to recalculate 

the 1921 peak discharge.

Peak discharge of the flood on October 21, 2003, at 

Skagit River near Concrete (166,000 ft3/s) was determined 

from the recorded peak stage (42.21 ft) using the current 

stage-discharge rating curve for the gaging station. Accuracy 

of the upper end of the rating was verified by a current-meter 

discharge measurement made on the same day as the flood 

peak. The measured discharge of 138,000 ft3/s is only 

1.2 percent greater than the discharge indicated by the rating 

for a stage of 38.68 ft.

The n value used for Stewart’s slope-area measurement 

was 0.033, and the corresponding calculated peak discharge 

was 240,000 ft3/s. Because a considerable amount of variation 

was present in the elevations of high-water marks surveyed for 

the flood peak on October 21, 2003, two water-surface profiles 

were used in the n-verification analysis to bracket a plausible 

range of slopes for the actual water-surface profile. Analysis 

using the flattest-sloped profile resulted in an n value of 0.024 

and a peak discharge of 266,000 ft3/s. The n-verification 

analysis using the steepest-sloped profile resulted in an n

value of 0.032 and a peak discharge of 215,000 ft3/s. Although 

these two discharges are 10.8 percent greater than and 10.4 

percent less than Stewart’s 1921 peak discharge, respectively, 

the average of the two discharges (240,500 ft3/s) is only 

0.2 percent greater than Stewart’s 1921 peak discharge.

U.S. Geological Survey’s policy concerning the revision 

of previously published peak discharges is to revise them 

only if the revised discharge is reliable and different from 

the original discharge by more than 10 percent. Therefore, 

Stewart’s 1921 peak discharge of 240,000 ft3/s was not 

revised. The peak discharges of the 1897, 1909, and 1917 

floods were not revised either because they were determined 

from an extension of the stage-discharge rating curve based on 

the peak discharge of the 1921 flood.

16 Verification of 1921 Peak Discharge at Skagit River near Concrete, Washington, Using 2003 Peak-Discharge Data

Source of data

100-year flood

discharge, in cubic 

feet per second

H.C. Riggs and W.H. Robinson (U.S. Geological 

Survey, written commun., 1950)

256,700

F.J. Flynn and M.A. Benson (U.S. Geological 

Survey, written commun., 1951-52)

272,400

James E. Stewart (U.S. Geological Survey, 

written commun., 1923)

280,200

Plus 10 percent 293,700

Minus 10 percent 262,700

Table 2. The 100-year flood discharges of Skagit River near Concrete, 

Washington, using annual peak discharges for 1897, 1909, 1917, and 1921 

in conjunction with unregulated annual peak discharges for water years 

1944-2004.
References Cited

Barnes, H.H., Jr., 1967, Roughness characteristics of natural 

channels: U.S. Geological Survey Water-Supply Paper 1849, 

213 p.

Benson, M.A., and Dalrymple, Tate, 1967, General field and 

office procedures for indirect discharge measurements: 

U.S. Geological Survey Techniques of Water-Resources 

Investigations, Book 3, Chap. A1, 30 p.

Corbett, D.M., 1962, Stream-gaging procedure—A manual 

describing methods and practices of the Geological Survey: 

U.S. Geological Survey Water-Supply Paper 888, 245 p.

Dalrymple, Tate, and Benson, M.A., 1984, Measurement of 

peak discharge by the slope-area method: U.S. Geological 

Survey Techniques of Water-Resources Investigations, 

Book 3, Chap. A2, 12 p.

Hortness, J.E., 2004, A computer program for plotting and 

formatting surveying data for estimating peak discharges by 

the slope-area method: U.S. Geological Survey Fact Sheet 

2004-3028, 6 p.

References Cited 17

Jarrett, R.D., and Petsch, H.E., Jr., 1985, Computer program 

NCALC user’s manual—Verification of Manning’s 

roughness coefficient in channels: U.S. Geological Survey 

Water-Resources Investigations Report 85-4317, 27 p.

Kimbrough, R.A., Smith, R.R., Ruppert, G.P., and Wiggins, 

W.D., 2004, Water-resources data, Washington, water year 

2003: U.S. Geological Survey Water-Data Report WA-03-1, 

626 p.

Novak, C.E., 1985, WRD data reports preparation guide: U.S. 

Geological Survey, Water Resources Division, 199 p.

Skagit County, 2003, Digital data warehouse: Geographic 

data for your mapping system, Skagit County, Washington, 

accessed February 2004 at URL: http://www.skagitcounty.

net/Common/Asp/Default.asp?d=GIS&c=General&p=Di

gital/main.htm

Stewart, J.E., and Bodhaine, G.L., 1961, Floods in the 

Skagit River Basin Washington: U.S. Geological Survey 

Water-Supply Paper 1527, 66 p. 

U.S. Army Corps of Engineers, 2002, HEC-RAS, River 

Analysis System User’s Manual, v. 3.1: Davis, California, 

Hydrologic Engineering Center, 420 p.
This page is intentionally blank.

18 Verification of 1921 Peak Discharge at Skagit River near Concrete, Washington, Using 2003 Peak-Discharge Data
Manuscript approved for publication, February 11, 2005.

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

Washington Water Science Center, Tacoma, Washington.

USGS Publishing staff

Bill Gibbs

Debra Grillo

Ginger Renslow

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

Director, Washington Water Science Center, 

U.S. Geological Survey,

1201 Pacific Avenue–Suite 600 

Tacoma, Washington 98402

http://wa.water.usgs.gov
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