k 261964

Stream Hydrology Related 

to the Optimum Discharge 

for King Salmon Spawning 

in the Northern California 

Coast Ranges

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1779-AA

Prepared in cooperation with the 

California Department of Fish and Game
Stream Hydrology Related 

to the Optimum Discharge 

for King Salmon Spawning 

in the Northern California 

Coast Ranges

By S. E. RANTZ

CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES 

GEOLOGICAL SURVEY WATER-SUPPLY PAPER 1779-AA

Prepared in cooperation with the 

California Department of Fish and Game

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1964
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, D.G. 20402
CONTENTS

	Page 

Abstract_______________________-_____----___-_--_-_-__----_---- AA1

Introduction . ________________-__.__--_---_----___---------_ 1

Purpose and scope____________________________________________ 1

Definition of terms___________________-_-__-___-_-___-----_--_- 2

Acknowledgments. ________________________________________ 3

Characteristics of a spawning area________--__-_______-_-_--__---- 4

Determination of optimum discharge_____ ___________________ 5

Relation of optimum discharge to hydrologic characteristics___-___.__. 9

Application of the derived relation_________________________________ 14

Summary and recommendations__-___--____---______----___-----___- 15

References cited_____-_____---__-____-__-_--_-_-__----____--_--__-_ 16

ILLUSTRATIONS

Page 

FIGURE 1. Sketch map showing location of salmon spawning sites studied

in northern California Coast Ranges.._...._______ AA3

2. Sketch map of spawning site on Van Duzen River near Carlotta. 7

3. Graph for determination of optimum discharge at selected

spawning sites.______ _______ ___ ___ 8

4. Graph showing the relation of optimum discharge to mean

discharge and to ratio of stream width to drainage area__ 13

5. Graph showing the comparison of measured and computed

optimum discharge.________________________ 14

TABLES

Page 

TABLE 1. Summary of field data collected at spawning sites.__________ AA6

2. Pertinent streamflow and physical characteristics of spawning

sites studied..________________________ 8

3. Stream-gaging stations whose records are pertinent to this

study..___ ________.________________ 10

4. Comparison of measured and computed optimum discharge_ 12

m

CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

STREAM HYDROLOGY RELATED TO THE OPTIMUM

DISCHARGE FOR KING SALMON SPAWNING IN THE

NORTHERN CALIFORNIA COAST RANGES

By S. E. KANTZ

ABSTRACT

This report presents the results of a reconnaissance study to test the hypothesis 

that in a geologically homogeneous region, such as the northern California Coast 

Ranges, the optimum discharges for king salmon spawning are related to some 

characteristic discharge of the streams and to an index of their channel geometry. 

For the purpose of this study, optimum discharge is defined as the minimum 

discharge that will give the maximum spawning area. Verification of the existence 

of a significant correlation between optimum discharge and hydrologic characteristics that are readily determined would provide a means of estimating optimum 

discharge at a fraction of the cost in time and money now spent for that purpose.

A short spawning reach was selected for study on each of nine streams in the 

Eel and Mad River basins of northern California. Optimum discharge was 

determined at each reach by field observations made in accordance with criteria 

and methods developed by the California Department of Fish and Game and by 

other conservation agencies. These optimum discharges (Q0) were then correlated with mean discharge (Qm) and ratio of stream width to drainage area (^ ) 

The computed regression equation is 00 =0.89(0m) 1 -09 ( -=- V'44 . The multiple

\ d, o/

correlation coefficient, 0.912, is highly significant from a statistical standpoint.

This study was of an exploratory nature; the general applicability of its 

methodology should be tested further.

INTRODUCTION

PURPOSE AND SCOPE

California's increasing population and burgeoning economy place a 

heavy demand on the available water supply. To meet the expanding 

and conflicting water requirements of the various segments of the 

economy, the development of surface-water supplies is being planned 

along multiple-purpose lines. In most of these multiple-purpose 

projects the conservation of fishlife is an important element, and 

although the water requirements for fishlife do not constitute a consumptive use of water, they frequently conflict with the demand for

AA1
AA2 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

water for hydroelectric generation and for other beneficial uses, such 

as irrigation and domestic or municipal supply. If fishlife is to be 

protected, or possibly enhanced, in a stream whose natural regimen 

is to be changed by a manmade development, it is necessary that 

streamflow requirements for fish reproduction, transportation, and 

rearing of the young be determined while the proposed development 

is still in the planning stage.

Present methods of determining the flows needed for fishlife 

require extensive field study of the hydrography and fish-spawning 

patterns in each stream. The purpose of this study was to explore 

the possibility that the discharge required for fishlife in streams in 

a geologically homogeneous region is related to hydrologic characteristics of the region. Establishment of such a relation would provide 

a means of estimating the flows needed for fishlife at a fraction of the 

cost in time and money now spent for that purpose.

This investigation was limited to a study of the optimum discharge 

for king salmon spawning in streams in a single physiographic region, 

the northern California Coast Ranges (fig. 1). Determination of 

the flow regimen needed for the transportation of king salmon adults 

to, and the young salmon from, spawning areas will require a study 

of broader scope.

DEFINITION OF TERMS

Several terms used in the preceding paragraphs require explanation. 

"Geologically homogeneous region/' as used in this report, refers 

to the physiographic subdivisions of the country described by Fenneman (1931). By Fenneman's classification there are two distinct 

physiographic sections, or geologically homogeneous regions, in north 

coastal California, namely the Klamath Mountains and the California 

Coast Ranges. This study was limited to streams in the Coast 

Ranges.

The term "optimum discharge" refers to the minimum discharge 

that will give the maximum spawning area for king salmon. If, 

for example, a spawning area is at a maximum when the river discharge ranges from 300 to 400 cfs (cubic feet per second), the optimum 

discharge is 300 cfs. A spawning area is defined as a reach of stream 

which king salmon are likely to select for spawning, that is, a reach 

having the proper combination of depth, bottom velocity, water 

temperature, and streambed composition. Usable criteria have been 

established by various conservation agencies for these spawning-area 

elements for king salmon. Similar criteria remain to be established 

for silver salmon and steelhead trout in coastal streams before a 

study similar to this one can be made for these other two species of 

anadromous fish.
OPTIMUM DISCHARGE, KING SALMON SPAWNING, CALIFORNIA AA3

EXPLANATION

_. 8 

Spawning site studied

FIOUBE 1. Sketch map showing location of salmon spawning sites studied in northern California Coast

Ranges.

ACKNOWLEDGMENTS

This study was authorized by a cooperative agreement between 

the U.S. Geological Survey and the California Department of Fish 

and Game. The report was prepared under the general direction of 

Walter Hofmann, district engineer of the Geological Survey. The 

assistance of C. K. Fisher, Jr., and John M. Hayes, fishery biologists
AA4 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

of the Department of Fish and Game, is gratefully acknowledged. 

Mr. Hayes assisted in selecting the spawning sites used in the study, 

and Mr. Fisher instructed Geological Survey personnel in the methods 

used by the Department to sample streambed material and determine 

optimum discharge from field observations.

CHARACTERISTICS OF A SPAWNING AREA

Bed material of spawning areas must consist of gravel of such size 

that king salmon can excavate redds (nests) in which their eggs can be 

deposited, fertilized, and hatched. The preferred areas are either in 

riffles or at the downstream end of pools, where velocities are fairly 

rapid. The force of the current assists the salmon in moving the 

gravel; the larger the gravel, the faster the current required. If, 

however, the current is too fast, the eggs will be washed downstream. 

Immediately after the eggs are deposited and fertilized, the salmon 

move some gravel into the redds to cover the eggs. Thereafter, a 

continuous circulation of water through the gravel and over the eggs 

is required to insure successful hatching. The gravel must therefore 

be large enough to provide the interstices needed for this circulation. 

Water temperatures should be between 42°F and 53 °F for proper 

incubation of the eggs. In the north Coast Ranges region, the spawning season, mid-October to the end of February, coincides with the 

high-water season, and during this period water temperatures are 

usually in the desired range.

The criteria for favorable spawning conditions used in this study are:

1. Depth of water: 10 inches or more.

2. Bottom velocity (measured 0.3 foot above streambed): 1 to 3 feet 

per second.

3. Streambed composition:

Weight fraction of

total sample 

Size (inches) (Percent)

Silt and sand____________________________________ 20 or less

%2 to %_________________________________________ 20 or less

J_ to !___-_._________________________ 20 or less 

1 to 3___________________________-_-___--_-__-_--_ 50 or less

3 to 6_____________________________-_-_-_-__-___ 10 or more

6 to 12_______________________________ 30 or less

These criteria were not developed specifically for conditions in the 

streams studied, but are rather a composite of criteria derived from 

studies of various streams by the California Department of Fish and 

Game (Westgate, 1958) and by other Pacific Coast conservation 

agencies. The gravel classification shown in the table refers to bed 

material sampled to a depth of 1 foot, which is the approximate depth 

of king salmon redds. The bed material is considered unsatisfactory 

if the percentage present in any size classification fails to meet the 

criterion shown.
OPTIMUM DISCHARGE, KING SALMON SPAWNING, CALIFORNIA AA5 

DETERMINATION OF OPTIMUM DISCHARGE

The first step in this study was to determine the optimum discharge 

at nine selected salmon-spawning sites on streams in the north Coast 

Ranges region. Optimum discharge, it will be recalled, is the minimum discharge that will give the maximum spawning area. Furthermore, an area is considered to be favorable for spawning if it meets the 

criteria of depth, bottom velocity, and streambed composition listed 

above. In general, spawning sites were selected in the vicinity of 

stream-gaging stations where the streamflow characteristics were 

known. An exception was the spawning site on Canon Creek (site 

8 on fig. 1), an ungaged stream that the California Department of 

Fish and Game wished to study. All sites selected were in the Eel 

or Mad River basins. A prime consideration in the selection of sites 

was that they sample a wide range of drainage-area sizes. Table 1 

lists the selected spawning sites and the size of drainage area upstream 

from each site. Spawning had been observed in previous years at 

some of the sites, and all sites selected had reaches of streambed that 

were at least partly composed of gravel of favorable size. The length 

of reach used as a representative spawning area was dependent, at 

each site, on the areal extent of the gravel of favorable size. The 

lengths chosen ranged from as little as 40 feet on one small stream to 

200 feet on the medium and large streams.

On each reach of channel selected for study, three to five cross 

sections, or transects, were established at right angles to the direction 

of flow. Within each reach, 6 to 12 samples of bed material were 

taken, where needed, to delineate the potentially usable spawning 

area, that is, the actual area that had gravel of favorable size. A 

potentially usable spawning area needs only to have proper combination of depth of water and bottom velocity to be a favorable area for 

salmon spawning. The bed sampling equipment consisted of a toothedged cylindrical "cookie-cutter," a set of graduated sieves, and a 

spring weighing scale. The "cookie-cutter" was 14 inches in diameter, 

2 feet long, and made of light steel plate. In the sampling process, it 

was forced into the streambed to a depth of 1 foot, and the bed material 

within it was removed by hand, sorted in the sieves, and weighed on 

the scale. Figure 2, a map of the site selected on the Van Duzen 

River near Carlotta, illustrates a typical study area. On this figure 

are shown the streambed sampling points, the potentially usable 

spawning area, and the transect lines. It is along these transects that 

depth and bottom velocity were measured at various discharges to 

determine the area favorable for spawning. Table 1 indicates the 

potentially usable spawning area at each site, as planimetered from 

large-scale maps similar to figure 2; the dates when measurements of

723-773 64 2
AA6 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES 

TABLE 1. Summary of field data collected at spawning sites

No. 

(fig. 1)

1... .... 

2.... ...

3..........

4..........

5.... ...

6..........

7 .... ...

8... ...... .

9..........

Spawning site

Name and location

south of Long vale). 

Black Butte River near Covelo (0.3

mile upstream from mouth). 

Middle Fork Eel River near Covelo

(0.6 mile upstream from Williams 

Creek).

Williams Creek near Covelo (0.6 mile

upstream from mouth).

(0.2 mile upstream from Jack of 

Hearts Creek).

South Fork Eel River near Leggett

(0.3 mile north of Lane's Redwood 

Flat resort and 4.7 miles north of 

Leggett).

mile upstream from Grizzly Creek) .

upstream from mouth).

downstream from Canon Creek).

Drainage 

area 

(sq mi)

95.4

162

374

30.5

43.9

258

222

16.2

393

Potentially

usable 

spawning area 

(SQft)

10,280

7,150

19,450

760

1,880

3,720

15,290

2,620

27, 400

Date of 

measurement

11-19-62

12- 6-62 

1- 3-63 

2-13-63 

2-20-63 

12-20-62

1- 9-63 

2-14-63 

2-19-63 

3- 6-63 

3-18-63 

12-20-62

1-8-63 

1-21-63 

2-14-63 

2-18-63 

3- 6-63 

12-21-62

1-9-63 

2-13-63 

2-18-63 

3- 6-63 

3-18-63 

12-21-62

1- 3-63 

2- 7-63 

2-14-63 

11-20-62

12-20-62 

1-28-63 

2-14-63 

2-19-63 

2-25-63 

3- 8-63 

11- 6-62

2- 4-63 

2- 7-63 

2- 9-63 

2-11-63 

2-20-63 

2-22-63 

2- 1-63

2- 2-63 

2- 3-63 

2-13-63 

3-28-63 

3-29-63 

11- 7-62

2- 2-63 

2- 3-63 

2- 3-63 

2- 4-63 

2- 6-63 

2-11-63 

2-13-63

Discharge 

(cfs)

15.7

275 

71.1 

536 

149 

305

86 

688 

418 

155 

142 

1,090

255 

162 

1,890 

1,160 

396 

72.8

15.8 

139 

71.2 

26.3 

29.8 

186

68.6 

301 

298 

202

1,270 

173 

1,700 

906 

585 

327 

136

2,740 

2,010 

1,560 

1,080 

1,080 

784 

190

114 

123 

81.8 

266 

378 

333

8,460 

7,150 

6,860 

4,730 

3,220 

1,410 

2,840

Ratio of 

favorable

spawning 

area to 

potentially 

usable area 

(percent)

0

47.7 

20.9 

73.5 

55.5 

82.7

8.4 

0 

33.9 

37.8 

33.6 

50.4

52.3 

41.4 

16.2 

39.3 

70.7 

59.2

1.3 

0

57.8 

9.9 

11.6 

52.5

19.6 

42.5 

39.8 

60.4

26.8 

45.3 

20.1 

32.2 

100.0 

93.3 

0

28.4 

47.7 

58.7 

84.0 

75.9 

56.9 

70.2

63.5 

67.4 

57.6 

53.3 

41.0 

13.0

8.0 

19.8 

22.1 

28.0 

25.8 

58.4 

49.1

discharge, depth, and bottom velocity were made; the measured 

discharges on those dates; and the percentages of potentially usable 

spawning area that had favorable depths and bottom velocities on 

those dates.

The data in the last two columns of table 1 were plotted, and 

curves were fitted to the plotted points to obtain values of optimum 

discharge for each site. For illustrative purposes the plotted data 

for three sites are shown on figure 3. The curves on figure 3 are ex-
OPTIMUM DISCHARGE, KING SALMON SPAWNING, CALIFORNIA AA7

R-5

L-l

L-5

S.I

Transect line

Potentially usable 

spawning area

Gravel sampling point

FIGURE 2. Sketch map of spawning site on Van Duzen Elver near Carlotta (site 7).

plained as follows: At the lower flows, favorable spawning area increases with discharge as the increasing flows submerge additional 

areas of gravel. A maximum value of favorable spawning area is 

reached when the discharge attains such a value that any further increase in flow creates bottom velocities in excess of 3 feet per second 

and thereby decreases the favorable spawning area. While the plotted 

points usually provided enough information to define the shape of the 

curves of discharge versus favorable spawning area, additional information concerning the shape of the curves was often obtained by inspection of the depth and bottom velocity observations made at the 

various flow rates. The optimum discharges ontained from the curves 

are listed in column 3 of table 2.

During the investigation, streambed conditions at several of the 

sites varied with time. This occurrence is normal in streams in this 

region. High flows will often move the gravels, and during the 

recession phase of these rises fine materials such as sand and silt may
AA8 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

"N. Van Duzen River near Carlotta (site 7)

Middle Fork Eel River 

near Covelo (site 3)

South Fork Eel 

near Leggett (site 6)

400 800 1200 1600 2000 

DISCHARGE, IN CUBIC FEET PER SECOND

2400 2800

FIGUBE 3. Graph for determination of optimum discharge at selected spawning sites. Letter "A" indicates optimum discharge for each of the spawning sites.

TABLE 2. Pertinent streamflow and physical characteristics of spawning sites studied

Spawning site

No.

1

! ......

2.......

3__._.___

4........

«... ..

6........

7.... .

8.. _ ...

Name and location

2

Outlet Creek near Arnold. 

Black Butte River near 

Covelo. 

Middle Fork Eel River 

near Covelo. 

Williams Creek near Covelo. 

South Fork Eel River near 

Branscomb. 

South Fork Eel River 

near Leggett. 

Van Duzen River near 

Carlotta. 

Canon Creek near Korbel. 

Mad River near Korbel _

Streamflow characteristics

Optimum discharge 

(eft)

3

480 

280

400 

73 

185 

400 

1,000

165 

1,400

Percent 

of time optimum discharge is exceeded

4

13 

31

44 

22 

20 

34 

19

4 

23

Mean discharge 

(eft)

5

261 

285

951 

76 

168 

958 

810

37

1,280

Median discharge 

(cfs)

6

23

78

260 

13 

29 

165 

165

8 

273

Physical characteristics

Drainage 

area

(square 

miles)

7

95.4 

162

374 

30.5 

43.9

258 

222

16.2 

393

Stream 

width 

at mean discharge 

(ft)

8

94 

93

164 

31 

57 

122 

141

31 

271

Ratio 

of 

stream 

width 

to drainage 

area

9

0.99

.57

.44 

1.02 

1.30 

.47 

.64

1.91 

.69

Channel 

slope 

(feet 

per 

foot)

10

0.0028 

.0042

.0034 

.0100 

.0044 

.0033 

.0080

.0096 

.0025

be deposited on the coarse gravels. Later, this fine material may 

be removed by ensuing medium-stage flows. These changes are
OPTIMUM DISCHARGE, KING SALMON SPAWNING, CALIFORNIA AA9

generally ephemeral. Stream-gaging sites in the region do not show 

a steady pattern of either aggradation or degradation, but indicate 

a state of what might be called "unstable equilibrium"; scour at a 

local site is generally followed by fill, and vice versa. Consequently 

streambed conditions at the selected study sites are assumed to be 

generally representative of those at most spawning sites in the 

streams, although in some years the gravel composition at the selected 

sites may be unfavorable at times when the salmon are spawning. 

For these reasons, the boundaries of potentially usable gravel that 

were delineated at each site at the start of the study were considered 

to be constant throughout the investigation.

The reader may wonder what justification can be made for basing 

the optimum discharge of a stream on observations made at a single 

spawning site. Normally when the Department of Fish and Game 

makes a similar study of a stream, long reaches of the channel are 

studied. It is obviously not feasible to study the entire channel, 

and consequently even the extensive investigations of the Department 

represent only a statistical sampling of all possible spawning reaches 

of the stream being investigated. In this study a sampling procedure was also used but, instead of taking a sample of nine spawning 

reaches on a single stream, our sample consists of one spawning 

reach on each of nine streams of various drainage area size. In the 

next section of this report the nine optimum discharges listed in 

column 3 of table 2 are considered in relation to the hydrologic 

characteristics of the streams. A good correlation would indicate 

that the value of optimum discharge of a stream, shown by the 

derived relationship, is probably more reliable than that obtained by 

observing the single short spawning reach. That is, because the 

observed optimum discharges are subject to random error, the curve 

of relation may be more reliable than the individual values on which 

the curve is based.

RELATION OF OPTIMUM DISCHARGE TO HYDROLOGIC 

CHARACTERISTICS

After values of optimum discharge for each of the nine sites were 

obtained, an attempt was made to relate these discharges to hydrologic characteristics of the region. It was hypothesized that in a 

geologically homogeneous region, such as the northern Coast Ranges 

province, the optimum discharges are related to some characteristic 

discharge of the streams and to an index of their channel geometry. 

With a sample of only nine sites available, it was almost mandatory 

that any relationship investigated be limited to a linear or simple 

exponential function involving two, or at most, three variables in 

order to conserve "degrees of freedom." A discussion of the statistical
AA10 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

concept of degrees of freedom is beyond the scope of this paper. 

Suffice it to say that the number of degrees of freedom is equal to 

the number of items in the sample (nine) minus the number of constants in the regression equation and that, when small samples are 

used, the reliability of the regression equation decreases markedly 

as the number of degrees of freedom decreases. Therefore, few 

variables were used in the correlations testing our hypothesis, although 

many were considered; variables considered are in table 2.

The figures shown in columns 4, 5, and 6 of table 2 were derived 

from Geological Survey records. The stream-gaging stations whose 

records are pertinent to this study are given in table 3 and are shown 

on figure 1.

TABLE 3. Stream-gaging stations whose records are pertinent to this study

Identifying 

letter (fig. 1)

A....... ..__.

B _ . _ . ___

C... .........

D . ............

E. _ . __ . ....

F._. ._._.__._

Q. ..............

H._ ...........

Name of station

Drainage 

area 

(square 

miles)

161

162

367

30.4

43.9

216

40.5

485

Period of 

record

1956-63

1968-63

1951-63

1961-63

1946-63

1911-13,

1939-63 

1957-63

1910-13.

1950-63

In table 2, all values shown in columns 4, 5, and 6 are for the 60-year 

base period 1900-59. Column 4 is the percent of time on the longterm flow-duration curve that the optimum discharge is exceeded. 

Column 5 is the long-term mean discharge and column 6 is the longterm median discharge at each of the nine spawning sites. In general, 

the mean discharge of streams in the northern California Coast Ranges 

is exceeded about 24 percent of the time. A previous study (Rantz, 

1964) was the source of the values in columns 4, 5, and 6 for Black 

Butte River near Covelo (site 2), Middle Fork Eel River near Covelo 

(site 3), South Fork Eel River near Branscomb (site 5), and Van 

Duzen River near Carlotta (site 7). The remaining figures in the 

three columns were obtained by applying standard Geological Survey 

correlation procedures to the records for the gaging stations listed in 

table 3 and the discharge measurements listed in table 1.

Physical characteristics of the spawning sites are shown in the last 

four columns of table 2. The latest topographic maps were used to 

obtain drainage areas (column 7) and channel slopes (column 10). 

The stream widths (column 8) corresponding to the mean discharges 

(column 5) were obtained from discharge-measurement data. Column 

9 is the ratio of column 8 to column 7.
OPTIMUM DISCHARGE, KING SALMON SPAWNING, CALIFORNIA AA11

After all pertinent data was compiled, the analysis was begun. 

It was originally theorized that the stream-channel geometry in a 

geologically homogeneous region might be related to some characteristic discharge and to size of drainage area. In other words, all 

streams of a given drainage-area size might tend to have common 

geometric characteristics at discharges that have equal probability of 

being exceeded. For example, the optimum discharge for a 50 squaremile drainage basin might be one that is exceeded 20 percent of the 

time; for a 100 square-mile basin it might be the discharge that is 

exceeded 25 percent of the time. To test this hypothesis a linear 

correlation was computed; percent of time that optimum discharge 

is exceeded (column 4 of table 2) and drainage area (column 7) were 

used in the computation. The correlation coefficient, 0.673 for 7 

degrees of freedom, was significant at the 5 percent level. However, 

the differences between measured and computed optimum discharges 

were excessive. The explanation for these excessive differences is: 

The percentages in column 4 of table 2 were obtained from flowduration curves. Because of the great variability of flow in streams 

in the northern California Coast Ranges, the flow-duration curves are 

very steep and a small increment of percentage represents a large 

increment of discharge. Thus the computed standard error, 9.3 percent in this correlation, represented a large error when converted to 

cubic feet per second. Additional parameters such as channel slope, 

ratio of stream width to drainage area, and mean annual runoff per 

square mile were next considered, but they offered no improvement in 

the correlation.

A second approach to the problem was more successful. Inspection 

of columns 3 and 5 of table 2 showed that optimum discharge and 

mean discharge are roughly of the same magnitude. A linear correlation computed with these two variables had a correlation coefficient 

of 0.783 (7 degrees of freedom), which is significant at the 2 percent 

level. The agreement between measured and computed optimum 

discharges was increased but was still unsatisfactory. However, when 

the differences between the measured and computed values were 

compared with the ratios of stream width to drainage area (column 9 

table 2), the computed values of optimum discharge were low 

when the ratios were low and high when the ratios were high. This 

variation can be explained thus: For streams having equal mean 

discharge, optimum discharge tends to increase directly with increase 

in stream width, because increased stream width usually means a 

greater width of potentially usable gravel and higher flows are generally required to submerge the wider expanse of gravel. Stream width 

in turn varies with drainage area, and those streams that are disproportionately wide, that is, that have a large ratio of stream width
AA12 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

to drainage area, will therefore tend to have disproportionately high 

optimum discharges. A multiple linear correlation was therefore 

computed with optimum discharge (Q0) as the dependent variable 

and mean discharge (Qm) and ratio of stream width to drainage area

( Ej as the independent variables. A logarithmic transformation of

the data was used to eliminate the "joint relation" that existed when 

natural values of the variables were used. (A joint relation exists 

when neither of the independent variables can be considered individually to determine its effect on the dependent variable; the associated 

or joint effect of both independent variables must be considered.) 

The computed regression equation is

This equation is shown as a family of curves on figure 4. Also 

shown on the figure are the plotted points; the number above the 

point identifies the spawning site and the number below is the ratio 

of stream width to drainage area. The multiple correlation coefficient 

0.912, is highly significant. (For 6 degrees of freedom, a multiple 

correlation coefficient of 0.886 would be significant at the 1 percent 

level.) Figure 5 provides a visual comparison of measured and 

computed optimum discharge, values of which are listed in table 4.

TABLE 4. Comparison of measured and computed optimum discharge

Spawning site

No. (fig. 1)

1 . -

2.. .........

3...........

4...........

5.-..... .

6...... 

7. ....

8.. .........

9.... ....

Name and location

Middle Fork Eel River near Covelo. ________ 

South Fork Eel River near Leggett- ___ ____

Optimum discharge

Measured 

(cfs)

480 

280 

400 

73 

185 

400 

1,000 

165 

1,400

Computed 

(cfs)

379 

189 

481 

103 

346 

533 

694 

116 

1,270

Percent 

difference 

referred to 

measured 

discharge

-21 

-32 

+20 

+41 

+87 

+33 -31 

-30 

-9

The regression equation will probably give more reliable estimates 

of optimum discharge for a stream than will current-meter and depth 

observations made over a range of discharges at a single short spawning 

reach. However, it is not to be inferred that the optimum discharges 

computed in this study are necessarily more reliable than those 

observed. What is meant is that the regression equation may give 

more reliable estimates if the stream width used in the equation is the 

average width of the stream, observed at many long potential spawning reaches when the discharge is at or near its mean value. Nor is
OPTIMUM DISCHARGE, KING SALMON SPAWNING, CALIFORNIA AA13

2000 -

z 1000 -

500 -

100

50 100 500 1000 2000

MEAN DISCHARGE (Qm), IN CUBIC FEET PER SECOND

FIGURE 4. Graph showing the relation of optimum discharge to mean discharge and to ratio of 

stream width to drainage area.

it to be inferred that optimum discharges so computed will be as 

reliable as those determined in the extensive investigations made on 

individual streams by the Department of Fish and Game. The 

regression equation does, however, offer a quick, cheap method of 

making preliminary estimates of optimum discharges that appear 

to be of acceptable accuracy. Unfortunately, there is no way, at 

the moment, of making a quantitative check on the reliability of the 

optimum discharges, either observed or computed, that were obtained 

in this study. The only stream in this study that had been investigated by the Department of Fish and Game was Middle Fork Eel 

River near Covelo (site 3), and there the Department had observed
AA14 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES 

2000

1000

500

p 100

CL

o

50

30

EXPLANATION

O9 

Spawning site

I I I I I I I

30 50 100 500 1000 2000

MEASURED OPTIMUM DISCHARGE, IN CUBIC FEET PER SECOND 

FIGURE 5. Graph showing the comparison of measured and computed optimum discharge.

discharges only as high as 270 cfs. The Department study established 

the fact that of the discharges observed, 270 cfs gave the greatest 

amount of favorable spawning area. In this study the observed 

optimum discharge was 400 cfs and the computed optimum discharge 

was 481 cfs.

APPLICATION OF THE DERIVED RELATION

The procedure for applying the regression-equation method to the 

determination of optimum discharge at a spawning reach in the northern California Coast Ranges is as follows:

1. Determine the long-term mean discharge at the spawning reach: If 

the spawning reach has been gaged for 10 years or more, the 

desired figure is available in Rantz (1964). If the gaging station 

at the spawning reach is a recent installation, the long-term 

mean discharge may be obtained by correlating concurrent 

monthly mean discharges at the spawning-site gage and at the 

nearest comparable gaging station for which the long-term 

mean discharge is known. If the spawning reach is ungaged,
OPTIMUM DISCHARGE, KING SALMON SPAWNING, CALIFORNIA AA15

the first step is to make five or six discharge measurements over 

a wide range of discharge at the spawning reach. To obtain 

the desired mean, the measured flows are then correlated 

with concurrent discharges at the nearest comparable gaging 

station for which the long-term mean discharge is known.

2. Determine the drainage area at the spawning reach: If the spawning reach is gaged, the drainage area may be obtained from 

Geological Survey streamflow publications. If ungaged, the 

drainage basin above the reach is first outlined on topographic 

maps. The desired drainage area is then measured by 

planimeter.

3. Determine the average stream width at the spawning reach when 

the discharge is at or near its mean value: If the spawning reach 

is gaged, the stage of the mean discharge will be known. If the 

spawning reach is ungaged, the stage corresponding to mean 

discharge can be deduced from the discharge measurements that 

had been made at the reach. Observations of stream width 

corresponding to the desired stage should be made in sufficient 

numbers to establish the average width for the full extent of the 

spawning reach or reaches. Commonly in the northern California Coast Ranges, the lowest line of vegetation on the stream 

banks is approximately at the stage of mean discharge.

4. Determine optimum discharge at the spawning reach by use of the 

regression equation or curves. The optimum discharge may be 

calculated from the data obtained in the three steps described 

above, by use of the regression curves on figure 4, or by substitution in the regression equation

where Q0 is optimum discharge in cubic feet per second, Qm is 

mean discharge in cubic feet per second, Rw^ is the ratio of

do

stream width, in feet, to drainage area, in square miles.

SUMMARY AND RECOMMENDATIONS

For the purpose of this study, optimum discharge is defined as the 

minimum discharge that will provide the maximum spawning area 

for king salmon and an area is considered favorable for king salmon 

spawning if it meets the criteria for depth, bottom velocity, water 

temperature, and streambed composition currently being used by 

fishery biologists of the California Department of Fish and Game. 

These criteria were used in field observations made to determine the
AA16 CONTRIBUTIONS TO THE HYDROLOGY OF THE UNITED STATES

optimum discharge at a short spawning reach on each of nine streams 

in the Eel and Mad River basins in the northern California Coast 

Ranges. These optimum discharges correlated well with a characteristic discharge of the streams (mean discharge) and an index of 

their channel geometry (ratio of stream width to drainage area). 

The relation obtained should prove useful for making preliminary 

estimates of optimum discharge that are reasonably reliable and which 

yet require only a small expenditure of time and money.

This investigation has been of an exploratory nature; it is recommended that it be pursued further along the lines indicated in this 

report. Extensive studies, such as those customarily made by the 

California Department of Fish and Game, should be carried out on 

streams in the northern California Coast Ranges to test the validity 

of the derived relation more completely. The methodology used in 

that region should also be applied in other physiographic provinces 

to test its general applicability. To broaden the scope of the investigation, criteria for favorable spawning conditions for silver salmon 

and steelhead trout should be established and a similar study should 

be made for these two species of anadromous fish.

REFERENCES CITED

Fenneman, N. M., 1931, Physiography of Western United States: New York, 

McGraw-Hill Book Co., 534 p.

Rantz, S. E., 1964, Surface-water hydrology of coastal basins of northern California: U.S. Geol. Survey Water-Supply Paper 1758. (In press.)

Westgate, John, 1958, The relationship between flow and usable salmon spawning 

gravel, Cosumnes River, 1956: Calif. Dept. Fish and Game Administrative 

Rept. 58-2, 8 p.