Surges in

Natural Stream Channels

By S. E. RANTZ

RIVER HYDRAULICS

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1369-C

Prepared in cooperation with the 

California DepartmentoffFater Resources

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1961
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington 25, D.C. - Price 15 cents (paper cover)
CONTENTS

Page

Abstract______._____________________________-__--________ 77

Introduction_ ___________________________________________________ 78

Purpose and scope_____________________________________________ 78

Acknowledgments ___ _ ________________________________________ 78

Hydraulic characteristics of the Mokelumne River____________________ 78

Seddon's principle of wave travel_____________________________ 82

Observed and computed wave velocity of initial disturbance ____________ 83

Flattening of the surge profile_________________________________ 87

Computation of the Clements hydrograph____________________________ 88

Summary____ __________________________________________________ 89

References. _______________-__________--_-__-____-_-__-___-_---__-_ 90

ILLUSTRATIONS

Page

FIGURE 10. Map of the Mokelumne River showing location of staff gages

between Lancha Plana and Clements_ _________________ 79

11. Typical stage hydrograph at Lancha Plana, May 1958 __ 80

12. Discharge hydrographs for Lancha Plana and Clements, 1958_ 81

13. Graphical representation of discharge, velocity, and area relations at a gaging station for a rising or falling surge. _ ___ 82

TABLES

Page

TABLE 1. Sample computation of velocity of initial disturbance in Lancha

Plana-Clements reach___ 84 

2. Travel of surges on Mokelumne River from Lancha Plana to

Clements.. _______________________ _ 85

xn
RIVER HYDRAULICS

SURGES IN NATURAL STREAM CHANNELS

By S. E. RANTZ

ABSTRACT

This report presents the results of an investigation of the travel of surges in a 

natural stream channel of irregular cross section, slope, and alinement. For the 

purpose of this study, a surge is defined as a rapid change in discharge from one 

condition of steady flow to another. The channel studied is a 12.7-mile reach of 

Mokelumne River below Pardee Reservoir in central California, and in the reach 

there are 22 rated river gages.

The surges studied were both positive (rising) and negative (falling), and both 

types had extremely flat wave fronts. Results of the investigation indicate that 

the time of travel of the initial element of a surge, or the initial disturbance to 

steady flow, can be computed reliably in accordance with Seddon's principle. 

Channel properties such as shape, dimension, roughness, and slope affect the 

velocity of the initial disturbance, and the variation of these factors produces 

changes in the velocity of the initial element of the surge as it traverses the reach. 

Given a sufficient number of rated cross sections that are favorably situated, it 

is possible to compute these changes in wave velocity, because the effect of channel geometry and roughness in a subreach is integrated in the stage-discharge 

relation for that subreach.

The wave form flattens progressively downstream as a result of channel storage. 

An actual measure of the varying channel storage between the profiles of steady 

flow for the initial and final discharges is provided by the rating curves for the 

cross sections in the reach. Because these rating curves represent the integrated 

effect of channel geometry and roughness, it follows that the volume of channel 

storage and consequently the degree of flattening of the wave form are affected 

by the hydraulic characteristics of the reach. Given the upstream hydrograph 

and sufficient intermediate rated cross sections, the downstream hydrograph, 

following the arrival of the initial disturbance, may be computed in accordance 

with the principle of conservation of mass; that is, the net change in volume of 

discharge equals the change in storage. In this study the upstream hydrograph 

was routed downstream by use of a multiple-phase reservoir-type routing technique. Very close agreement was obtained between the computed and recorded 

downstream hydrographs.

77
78 RIVER HYDRAULICS

INTRODUCTION 

PURPOSE AND SCOPE

The theoretical considerations governing wave travel in prismatic 

channels of mild slope are well understood and have been corroborated 

by laboratory analysis. Efforts to obtain supporting data from observations of natural streams have been less successful. This study 

was made, therefore, in an attempt to fill the need for a rigorous test 

of the applicability of classic wave theory to natural channels.

The last study of note of this nature, with|which the author is 

familiar, is that of Wilkinson (1945) on the Clinch and lower Tennessee 

Rivers. Wilkinson obtained reasonably close agreement between observed and computed wave velocities, but he had too few rated cross 

sections available to him to permit a complete test. For a truly 

satisfactory test of theory, one should be able to reproduce the hydrograph at the downstream end of a reach of river from a knowledge of 

the upstream hydrograph and the hydraulic properties of the stream. 

Because of the nonuniformity of these properties in a natural channel, 

a stream can rarely be found for which sufficient data are available 

to permit such a test. Fortunately for this study, a suitable channel 

is found in a 12.7-mile reach of Mokelumne River below Pardee Reservoir in central California. Reservoir operations there afforded an 

exceUent opportunity for studying the travel of surges, which are 

defined in this report as rapid changes in discharge from one condition 

of steady flow to another.

ACKNOWLEDGMENT

The study described in this report was done under a cooperative 

agreement between the U.S. Geological Survey and the California 

Department of Water Resources.

The cooperation of the East Bay Municipal Utility District in 

furnishing data for the 20 staff-gage sites hi the Lancha Plana-Clements reach of Mokelumne River is gratefuUy acknowledged.

HYDRAULIC CHARACTERISTICS OF THE MOKELUMNE

RIVER

The reach of the Mokelumne River under investigation extends 

from the upstream gaging station at Lancha Plana to the downstream 

gaging station near Clements. The river is controlled 3 miles upstream from Lancha Plana by Pardee Reservoir, which is operated 

for municipal water supply and power by the East Bay Municipal 

Utility District. Between the two gaging stations the river drains 

46 square miles of low foothill area, and at Clements the river debouches onto the rich agricultural valley floor. The fall in the 12.7- 

mile reach of river is 92 feet, but the streambed gradient of the upper 

half of the reach is approximately twice as steep as that of the lower
SURGES IN NATURAL STREAM CHANNELS 79

half. Like most natural streams, the cross-sectional shape of the 

channel is irregular and varies considerably in the reach, and the 

channel alinement is marked by numerous bends.

Except for periods immediately after rams or during protracted dry 

spells, this reach of river is virtually in static equilibrium with the 

ground-water table; that is, there is no measurable difference in discharge at the Lancha Plana and Clements gaging stations while steady 

flow is maintained at the Pardee Reservoir outlet works. This is 

consistent with the known characteristics of the channel, the Mokelumne River being an effluent or gaining stream upstream from the 

reach and an influent or losing stream downstream from Clements. 

However, there are significant losses in discharge between Lancha 

Plana and Clements during protracted dry periods. Conversely, during and immediately after rains there is an appreciable amount of 

local inflow into the reach, but this local inflow is generally of short 

duration after the cessation of rainfall. The surges selected for study 

occurred during periods when local inflow or seepage loss was negligible.

Much is known of the hydraulic properties of the stream channel. 

In 1930, as part of a study in connection with a water-rights litigation, 

the East Bay Municipal Utility District established staff gages at 

20 sites on the river between the Lancha Plana and Clements recording 

gages. These staff gages were located at obvious changes in channel 

geometry of the river and their location is shown on figure 10. Cross 

sections were obtained and the stage-discharge relation determined 

at each of the staff-gage sites during periods of steady outflow from 

Pardee Reservoir. The rating curves for the staff-gage sites were 

revised in 1938 and again in 1940, and a few observations were 

obtained in 1955 and 1956 for the purpose of checking the revised

EXPLANATION

 669 

Recording gage

 637 

Staff gage

Numbers indicate distance from 

Lmteln Plana, in hundreds of feet

FIGUEE 10. Map of Mokelumne[River showing location of staff gages between Lancha Plana and Clements.
80 RIVER HYDRAULICS

stage-discharge relations. It was found that all ratings were prone 

to shift when the channel carried unusually high flows, but the shifts 

were essentially parallel. For example, consider two discharges, 

$1 and Q2, at a given gaging site, that differ by a relatively small 

amount, A#. On several occasions during the years, the corresponding 

water-surface elevations, hi and h2 , at the site will have changed, but 

at all times the difference in water-surface elevation, Ah, corresponding 

to AQ, will remain essentially unchanged. Therefore, the slope of 

the curve that relates the discharge to cross-sectional area is virtually 

constant for any particular discharge at any gaging site in the reach. 

The method of operating Pardee Keservoir makes the downstream 

reach of river ideal for studying the travel of surges in natural channels. 

Flows of less than 5,000 cfs (cubic feet per second) are completely 

controlled and pass through either the turbines at the base of the 

dam or through the sluice valves of the dam. The actual operating 

procedures of the reservoir are somewhat complicated by varying 

demands for hydroelectric generation and by the necessity of complying with the legal rights of downstream water users. Large abrupt 

changes in water release must be avoided in order to prevent damage 

to the levees downstream from Clements. Usually the outlet works 

are operated so that the changes produced in water-surface elevation 

infthe Lancha Plana-Clements reach are less than 1 foot. When it is 

necessary to change the reservoir release by large amounts, several 

successive small changes in outflow are made, with at least an hour 

elapsing between successive gate operations. Figure 11 is a typical 

stage hydrograph for the upstream gage at Lancha Plana.

6.0

^5.5

5.0

1

/J

12m 12m 12m 

May 6 May 7 May 8

FIGURE 11. Typical stage hydit>graph at Lancha Plana, May 1958.
SURGES IN NATURAL STREAM CHANNELS 81

The surges shown in figure 11 flatten in their travel downstream 

from Lancha Plana and this is evident from the discharge hydrographs 

shown in figure 12 for the gages at Lancha Plana and Clements. The

o 

o

§600

500

300 6pm 9pm 12pm Sam 6am 

January 8 *^« January 9

2400

Q

0 2200 

L^

Crt

cr

LU 

Q.

ti 2000

LU 

Uo

m Z) 

o

^ 1800

uT 

O 

cr

<

X

Q 1600

1400

>4_

 f /

f

I

/

/

i

L

 ^

12m 6pm 12

S_lJ>*-^

jm 6 am 12 m

2400

Q z. 2300

0 

<f>

cr

LU°- 2200

LU 

Uo

COZ) 

o omn

UJ

cc

 E

& 2000

Q

1900

A ___?A

I

-V 

I

\

^T

\

V

1

I

?

V

^

P^OWv^ *-

9 am 12m 3 pm 6 pm 9 pm 

April 13

EXPLANATION

Recorded discharge hydrograph 

for Lancha Plana

Recorded discharge hydrograph 

for Clements

Computed discharge hydrograph 

for Clements

Initial disturbance to 

steady flow

FIOURE 12. Discharge hydrographs for Lancha Plana and Clements, 1958.

circles shown on the hydrographs for Clements represent computed 

values of outflow from the reach, and they indicate the close agreement 

between the recorded flow and that computed by routing the Lancha 

Plana hydrograph through the reach. A knowledge of Seddon's

582008 61 2
82 RIVEE HYDRAULICS

principle (Thomas, 1935) is essential to an understanding of the 

methodology used and the results obtained in the routing process. 

Although the general aspects of this principle are familiar to most 

hydraulic engineers, some of the details will bear repeating and are 

discussed in the paragraphs that follow.

SEDDON'S PRINCIPLE OF WAVE TRAVEL

Seddon's principle is best explained by reference to figure 13, 

where for a given gaging site, discharge is plotted as the ordinate, 

and the corresponding cross-sectional area as determined from the 

rating curve for steady flow is plotted as the abscissa. The curve 

of figure 13 is concave upward, a shape typical of all ordinary channel 

sections where the velocity increases as the area increases. In accordance with Seddon's principle, Vw dQ/dA, where Vw is the absolute 

wave velocity of a disturbance to steady flow. Thus, for either a 

rising (positive) or a falling (negative) surge, preceded by a steady 

flow Q2) the velocity of the initial disturbance, or initial element of 

the surge, is represented by the slope of the tangent to the curve at 

P2, or tan 02| . It should be emphasized that Seddon's law is strictly 

applicable only to extremely flat wave fronts, a condition that permits

13. Graphical representation of discharge, velocity, and area relations at a gaging station for a 

rising or falling surge. Subscripts: /, falling (negative) surge; r, rising (positive) surge; t, tangent to 

curve.
SURGES IN NATURAL STREAM CHANNELS 83

the term dQ/dA to be determined from the rating curve for steady 

flow. Figure 13 illustrates graphically the fact that the wave velocity 

corresponding to any discharge is greater than the velocity of flow 

for that discharge. With a discharge Q2, for example, the wave velocity equals tan 02f, whereas the flow velocity equals the smaller value, 

tan 0; .

It is customary in computing wave velocity by the Seddon formula 

to substitute for dQ the difference between initial and final discharges, 

and to substitute for dA the difference between initial and final crosssectional areas. The computed wave velocity for the initial disturbance is then too large for rising surges and too small for falling surges. 

The larger the increment A<2, the greater the error. All this is evident 

from a further inspection of figure 13. For an initial steady flow Q2 , 

any change in discharge whether an increase or a decrease will 

create a wave whose initial element travels with a velocity equal to 

tan 02 r If the discharge rises to Q3 , the computed wave velocity will be 

(Qz~ 0,2) I (As A2}, or tan 82r. The computed velocity will then be too 

large, since 0ar>02 r However, should the discharge fall from Q2 to Qi} 

the computed wave velocity will be (Q2 Qi)/(A2 Ai}} or tan 02/. The 

computed wave velocity is now too small, since 62f<^62t.

Identical wave velocities will be computed for a rise from Qi to Q2 

or a fall from Q2 to Qi} because both AQ and AA are identical in the 

two computations. Nevertheless, it is apparent from 0^ and 02j that 

the initial disturbance to steady flow Q2 will travel faster than the 

initial disturbance to steady flow Qi. These aspects of Seddon's 

principle have been pointed out because of their direct bearing on the 

interpretation of the results of this investigation.

OBSEKVED AND COMPUTED WAVE VELOCITY OF INITIAL,

DISTUKBANCE

The wave velocity of the initial disturbance to steady flow was 

computed by the Seddon formula for 10 surges that occurred in 1957 

and 1958. The term "initial disturbance", as previously explained, 

refers to the beginning of the change from steady flow and is illustrated 

by points labeled A on the discharge hydrographs of figure 12. The 

method of computing the mean wave velocity is shown in the sample 

computation of table 1. The wave velocity at each of the 22 gage sites 

was computed from [the formula VM =AQ/A4, where A<2 represents 

the difference in discharge between the two steady flow conditions and 

AA is the increment of the cross-sectional area corresponding to AQ. 

The mean wave velocity in each subreach between two gages was 

obtained by averaging the computed wave velocities at the ends of 

the subreach. The length of each subreach was then divided by the 

subreach wave velocity to obtain the traveltime. Finally, the total
84 RIVER HYDRAULICS

TABLE 1. Sample computation of velocity of initial disturbance in Lancha Plana 

Clements reach

[Date of determination, Jan. 8,1958. Qi, 349 cfs; Q2, 665 cfs; AQ, +316 cfs]

Station (See fig. 10)

0

16 _

77 3--. . ...

614 . _ . . 

637 . ........

669............................

Length of 

subreach 

(ft)'

} 1,600

6,100

| 2,300

3,200

Difference 

in crosssectional 

area, AA 

(sqft)

{

at

60

87

/ 146

X 100

98

Wave 

velocity 

Vw (fps)

3.81

5.27

3.63

2.16

3.16

3.22

Mean wave 

velocity in 

subreach 

(fps)

} 4.54

4.45

} 2.66

3.19

Traveltime in 

subreach 

(sec)

352

1,371

865

1,003

Sum of 

traveltimes (sec)

1 0

X 352

1,723

f 15, 145

X 16, 010

17,013

. , . . , 66,900ft Average wave velocity in reach= =3.93 fps I7,oio sec

1 Distance from preceding station.

2 Stations 133 through 598 omitted.

length of the reach, 12.7 miles, was divided by the total traveltime 

to give the average wave velocity between Lancha Plana and Clements.

Pertinent data concerning the surges selected for study are found in 

table 2, where the surges are listed hi order of magnitude of the initial 

discharge. It is apparent from columns 8 and 9 that for the range of 

discharges investigated, the velocity of the surge increases as the initial 

discharge increases. It was not feasible to study higher discharges, 

as this would have involved uncontrolled releases over the dam spillway. The hydrographs of spillway discharges show well-rounded 

peaks and troughs, whose time of occurrence cannot be pinpointed 

with sufficient accuracy for use in a study involving traveltimes of 3 

hours or less. The surges studied are amenable to treatment in accordance with Seddon's principle because the wave fronts are extremely flat and actually are not discernible to the eye. The flatness 

of the wave front is evident from an inspection of columns 5 and 6 of 

table 2 which show, respectively, the time elapsed during the change in 

discharge at Lancha Plana and the range in increments of stage at the 

22 gages for each surge. The rate of change of stage for a flat wave 

front has no effect on the velocity with which the initial disturbance 

travels, but does affect the degree to which the surge profile is flattened by channel storage. This effect is discussed later in the report.

An inspection of column 11 of table 2 reveals how closely the 

computed wave velocities agree with the recorded values. Even more 

important is the fact that the 5 positive (rising) surges have computed 

velocities that are slightly high and the 5 negative (falling) surges 

have computed velocities that are somewhat low, which is strikingly 

demonstrated in the 2 groups of surges with initial discharges of 

approximately 700 and 2400 cfs, respectively. As explained in the 

previous discussion of Seddon's principle, these departures of the
TABLE 2. Travel of surges on Mokelumne River from Lan

Date

(1)

Jan. 8, 1958.. ___

Jan. 13, 1958. . __ .

Mar. 13, 1958......

May 29, 1957... _ .

Mar. 4, 1958.... ....

Apr. 13, 1958.......

Mar. 10, 1958....i._

May 31, 1957.......

June 6, 1957..--. 

June 21, 1958 ___ .

Discharge (cfs)

Initial Qi

(2)

349 

665 

690 

700 

1,445 

2,380 

2,400 

2,460 

3,270 

4,210

Final Qa

(3)

665 

337 

1,080 

1,440 

2,020 

1,890 

1,875 

2,920 

2,900 

3,720

Change A Q

(4)

+316 

-328

+390 

+740 

+575 

-490

-525 

+460 

-370 

-490

Time for 

change in discharge at 

Lancha Plana 

(hours)

(5)

1.00 

1.50 

.75 

1.00 

.67 

.67 

.67 

.75 

.75 

.50

Range in increments 

between Qi and Qj

Stage Aft 

(feet)

(6)

0. 45-0. 89 

.51- .95 

. 34- . 98 

. 66-1. 82 

.44-1.07 

,37- .89 

.42- .93 

. 31- . 84 

. 26- . 65 

. 31- . 82

Crosssectional area 

&A (sqft)

(7)

52-146 

52-154 

43-142 

87-258 

61-173 

51-146 

58-162 

44-134 

37-99 

46-133

Recor

travel 

of ini

disturb

(hou

(8)
86 RIVER HYDRAULICS

computed from the observed velocities are precisely the result to be 

expected in a valid demonstration of the theory.

Particularly interesting is the group of surges whose initial discharge 

is approximately 700 cfs. It will be noted that the computed velocities 

of the two positive surges agree closely with the recorded velocities, 

whereas the computed velocity of the negative surge shows a much 

greater departure from the recorded value. The situation here is 

similar to that depicted in figure 13, where Q2 on the figure may be 

said to represent 700 cfs, and P2 is located at a change in the curvature 

of the discharge-area relationship. Figure 13 shows that the wave 

velocity computed for a positive surge (tan 02r) will agree closely with 

the true wave velocity (tan 02r), but that the wave velocity computed for 

a negative surge (tan 02/) will be considerably less than the true wave 

velocity. To go a step further, if Qi on figure 13 is assumed to 

represent a discharge of 350 cfs, then figure 13 depicts the situation 

involving the first two surges listed in table 2. These two surges, 

one positive and the other negative, have approximately the same 

absolute AQ (320 cfs) and the final discharge of the rising surge is 

equal to the initial discharge of the falling surge. The computed 

wave velocities for both surges will be identical, since 0ir=02r However, the true wave velocity of the rising surge (tan 0: t) is slower than 

the true wave velocity of the falling surge (tan 02{), since 9i t<^92t. 

This agrees with the values shown in column 9 of table 2. Also, from 

the position of points Pt and P2 on the discharge-area relation curve 

of figure 13, it is expected that the computed wave velocity of the 

rising surge will agree more closely with its true velocity, than will 

the velocity of the falling surge. This too, is borne out by the 

percentage error shown in column 11 of table 2.

From the above analysis it may be concluded that for surges with 

flat fronts in natural channels, the velocity of the initial disturbance 

to steady flow may be computed reliably in accordance with Seddon's 

principle, if a sufficient number of rated cross sections, favorably 

situated, are available. The reliability of the computed velocity will 

vary inversely with the magnitude of the AQ selected.

Column 7 of table 2 shows the wide range in increments of crosssectional area, AA, at the 22 gages for each surge. This variation in 

AA for any given surge results in a wide range of computed wave 

velocities for the individual subreaches between Lancha Plana and 

Clements, as indicated in column 12. Furthermore, the value of AA 

at any gage site is related to the shape of the rating curve for that gage, 

and the rating curve itself integrates the effect of channel geometry 

and roughness of the adjacent subreach. It is concluded, therefore, 

that channel properties, such as shape, dimension, roughness, and 

slope affect the velocity of the initial disturbance, and the variation
SURGES IN NATURAL STREAM CHANNELS 87

of these factors produces changes in the velocity of the surge as it 

traverses the reach. It is evident, too, that there is a degree of risk 

involved in computing the average wave velocity for a long reach of 

natural channel when the computations are based on only a few rated 

cross sections. The results may be seriously in error if the rated cross 

sections are not typical of the reach.

FLATTENING OP THE SURGE PROFILE

It is evident from the discharge hydrographs of figure 12 that the 

flat wave front at Lancha Plana is flattened considerably more by the 

time the surge reaches Clements. This flattening of the profile is 

attributable to the effect of channel storage, the mechanics of which 

are explained in the following example.

Assume that the initial steady flow at Lancha Plana is increased by 

300 cfs in 1 hour to a new state of steady flow, and that the initial 

disturbance travels 4 miles to a site A during this hour, and 3 miles 

more to a site B during the second hour. At the end of the first hour 

the initial disturbance will have reached site A, but there will have been 

no increase in discharge at site A. During this first hour, the storage 

space available in the 4-mile reach between the profiles of steady flow 

for the initial and final discharges will have been decreased by the 

inflow of a volume equivalent to 150 cfs-hrs, 150 cfs being the average 

value of AQ during the first hour. During the second hour, an 

additional volume of 300 cfs-hrs will have entered the reach between 

Lancha Plana and site A, but the discharge at site A at the end of the 

second hour will have increased by something less than 300 cfs, 

because some of the inflow into the reach remains in the reach as 

channel storage. In the meantime, the initial disturbance will 

have reached site B at the end of the second hour, but there will be 

no increase in discharge at site B. There is no need to carry this 

example any further; it is already evident that some flattening of the 

surge profile has occurred at site A, and the flattening becomes progressively more pronounced as the surge moves downstream.

The channel storage effect is associated with the channel geometry 

and the roughness, because the combined effect of the geometry and 

roughness establishes the Ah corresponding to the difference in discharge between any two rates of steady flow. In turn, Ah establishes 

the amount of storage between the profiles of these two rates of steady 

flow.

The example given in a preceding paragraph may be used to illustrate how the flattening of the surge is affected by the length of time 

that elapses at the upstream site while the flow changes from steady 

discharge Qi to steady discharge Q2 . It was shown that in the first 

hour, the original storage space between Lancha Plana and site A
88 RIVER HYDRAULICS

decreased by a volume equivalent to 150 cfs-hrs. Had the AQ of 300 

cfs occurred at Lancha Plana in one-half hour, the original storage 

available in the reach would have decreased in the first hour by 225 

cfs-hrs (an average flow of 150 cfs for the first half hour and the full 

flow of 300 cfs for the second half hour). Storage differences, such as 

those discussed above, may have an important effect on the flattening 

of the surge profile, particularly in short reaches.

COMPUTATION OF THE CLEMENTS HYDROGRAPH

In order to demonstrate the effect of channel storage on the flattening of the wave profile, the hydrographs at Clements were computed 

for three surges for comparison with the recorded flows. The method 

used is based on the principle of the conservation of mass for an incompressible fluid; that is, the net change in volume of discharge equals 

the change in storage. The surges selected for study are those shown 

in figure 12. A complication arises in the computations, owing to the 

fact that the difference between recorded inflow at Lancha Plana 

and recorded outflow at Clements gives values for change in storage 

that are somewhat greater than the computed channel storage between the profiles of initial and final discharge. The additional increment of storage space required for consistency definitely can be 

attributed to bank storage.

Earlier in this report it was mentioned that local inflow into the 

Lancha Plana-Clements reach ceases very shortly after the cessation 

of rainfall. The extremely permeable coarse alluvium composing the 

river banks and underlying the flood plain, which is so effective in 

draining off subsurface water during wet periods, apparently transmits 

water rapidly in a lateral direction as the river level fluctuates. Down- 

 stream from Clements, diurnal fluctuations in the river level have been 

observed to cause similar diurnal fluctuation in water levels in wells 

as far as 700 feet from the river (Piper and others, 1939, p. 162-163). 

The increment of bank storage required for consistency in this study 

is relatively small, amounting to the equivalent of a wedge of water 

with a depth of Aft at the bank, tapering to zero depth at a distance 

25 to 75 feet away from the stream, depending on the stage.

Before proceeding with the computation of the Clements hydrographs, the computed channel storage was increased by the amount of 

bank storage required to make the total volume of storage equal to the 

difference between recorded inflow and outflow volumes. The volume 

of bank storage added was distributed uniformly over the 12.7 miles 

of river channel. It is emphasized that this bank storage does not 

enter into the computation of wave velocity, because there is little 

downstream movement of water temporarily stored in the banks.
SURGES IN NATURAL STREAM CHANNELS 8&

The procedure used in routing the Lancha Plana hydrograph to 

Clements can be described as a multiple-phase reservoir-type routing 

technique. The 12.7-mile reach was first divided into 4 or 5 subreaches of varying length. The lengths used were determined in the 

following manner. For a given surge, a graph of accumulated distance versus accumulated wave traveltime was prepared. This graph 

is not shown in the report, but it is merely a plot of the values found 

in two of the columns of table 1; namely, column 1 versus column 7. 

The length used for the upstream subreach was that value on the 

graph that corresponds to a wave traveltime equal to the time that 

elapsed at Lancha Plana during the change in discharge from Qi to Q2 . 

Lengths of the other subreaches were likewise determined from this 

graph, using time intervals that were approximately equal to onefourth or one-fifth of the total traveltime between Lancha Plana and 

Clements. Thus, the time of arrival of the initial disturbance was 

known for each site marking the downstream end of a subreach.

For each subreach, a lag-and-route procedure was then used. It 

will be recalled that any change of inflow into a subreach that occurs 

while the initial disturbance is traveling to the downstream end of 

that subreach causes no change in outflow but merely changes the 

storage in the subreach. The traveltime of the initial disturbance 

in each subreach, therefore, constitutes the lag in outflow for the 

subreach. The subsequent routing, using the modified storage, was 

simplified by making the following two assumptions. First, storage in 

the subreach is uniquely related to the outflow (reservoir-type routing),, 

and second, the storage-outflow relation for each subreach is linear. 

These assumptions usually lead to no serious error in computing the 

final outflow for a reach, if a sufficient number of subreaches are used 

and the change in stage is small.

The actual routing procedure used for each subreach was the semigraphical Goodrich method. No details of this method are given here, 

as a description of the Goodrich method is in most standard hydrology 

texts (for example, Johnstone and Cross, 1949, p. 167-171). Successive applications of the lag-and-route procedure to each subreach resulted in the computed hydrographs for Clements shown in figure 12. 

The agreement between the recorded and computed discharge is very

satisfactory.

SUMMARY

For the purpose of this report, a surge is defined as a rapid change 

in discharge from one state of steady flow to another. The surges 

studied were both positive (rising) and negative (falling), and both 

types had extremely flat wave fronts.

It was found that the time of travel of the initial disturbance to 

steady flow can be computed reliably in accordance with Seddon's
90 RIVER HYDRAULICS

principle. Channel properties such as shape, dimension, roughness, 

and slope affect the velocity of the initial disturbance, and the variation of these factors produces changes in the velocity of the initial 

element of the surge as it traverses the reach. Given a sufficient 

number of rated cross sections that are favorably situated, it is 

possible to compute these changes in wave velocity, because the 

effect of channel geometry and roughness in a subreach is integrated 

in the stage-discharge relation for the subreach.

The wave form flattens progressively downstream as a result of 

channel storage. An actual measure of the varying channel storage 

between the profiles of steady flow for the initial and final discharges 

is provided by the rating curves for the cross sections in the reach. 

Because these rating curves represent the integrated effect of channel 

geometry and roughness, it follows that the volume of channel 

storage and consequently the degree of flattening of the wave form 

are affected by the hydraulic characteristics of the reach. Given the 

upstream hydrograph and sufficient intermediate rated cross sections, 

the downstream hydrograph, following the arrival of the initial 

disturbance, may be computed in accordance with the principle of 

conservation of mass; that is, the net change in volume of discharge 

equals the change in storage.

REFERENCES

Johnstone, Don, and Cross, W. P., 1949, Elements of applied hydrology: New

York, Ronald Press. 

Piper, A. M., Gale, H. S., Thomas, H. E., and Robinson, T. W., 1939, Geology

and ground-water hydrology of the Mokelumne area, Calif.: U.S. Geol.

Survey Water-Supply Paper 780. 

Thomas, H. A., 1935, The hydraulics of flood movement in rivers: Carnegie Inst.

Technol. Eng. Bull. 

Wilkinson, J. H., 1945, Translatory waves in natural channels: Am. Soc. Civil

Engineers Trans., v. 72, p 1203-1236.

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