U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2004–5068

Prepared in cooperation with the

California State Water Resources Control Board

Evaluation of Methods Used for Estimating Selected 

Streamflow Statistics, and Flood Frequency and Magnitude, 

for Small Basins in North Coastal California

Evaluation of Methods Used for Estimating 

Selected Streamflow Statistics, and Flood 

Frequency and Magnitude, for Small Basins 

in North Coastal California

By Michael P. Mann, Julé Rizzardo, and Richard Satkowski

Prepared in cooperation with the California State Water Resources Control Board

Scientific Investigations Report 2004-5068

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: 2004

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

Box 25286, Denver Federal Center

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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:

Mann, M.P., Rizzardo, Julé, and Satkowski, Richard, 2004, Evaluation of methods used for estimating selected 

streamflow statistics, and flood frequency and magnitude, for small basins in north coastal California: U.S. Geological 

Survey Scientific Investigations Report 2004-5068, 92 p.
 iii

Contents

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

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

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

Acknowledgments ................................................................................. 2

Description of Study Area .............................................................................. 2

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

Selection of Study Stations ........................................................................ 4

SWRCB Flow-Statistic Estimation Methods ................................................... 5

SWRCB Rational Equation Method ......................................................... 9

SWRCB Drainage Basin Area-Ratio Method ............................................. 9

USGS Flood-Frequency Equations ......................................................... 9

USGS Flow-Statistic Determination Methods ................................................... 10

Extension of Study-Station Statistics to Long-Term Conditions ........................ 11

Selection of Index Stations ............................................................ 11

Mean-Daily-Flow Regression Analyses ............................................. 12

Adjustment of Flow Statistics via Regression Equations ........................... 12

December 15 to March 31 Mean Daily Flows for 25- and 50-Percentile Years ...... 14

Flood-Frequency Analysis .................................................................. 14

Low-Outlier Thresholds ............................................................... 14

Two-Station Comparison ............................................................... 15

Historical Adjustment .................................................................. 15

Comparison Between SWRCB Estimated Flow Statistics and USGS Flow Statistics ............ 17

Annual and Seasonal Runoff and February Median Flow Statistics ........................ 18

SWRCB Annual and Seasonal Runoff and February Median Flow-Statistics 

Estimates versus USGS Statistics ................................................ 18

Annual and Seasonal Runoff and February Median Flow Estimates: Station Percent 

Differences versus Basin Characteristics ....................................... 23

Peak-Flow Statistics .............................................................................. 23

SWRCB Peak-flow Estimates vs. USGS Peak Flows .................................... 23

Peak-flow Estimates: Station Percent Differences versus Basin Characteristics ... 24

December 15 to March 31 Mean Daily Flows for 25- and 50-Percentile Years ............ 26

SWRCB Mean-Daily-Flow Estimates versus USGS Published Mean Daily Flows ... 26

Average December 15 to March 31 Mean-Daily-Flow Comparisons .................. 30

December 15 to March 31 Mean-Daily-Flow Estimates for 25- and 50-Percentile 

Years: Relative Standard Errors versus Basin Characteristics ............... 31

Summary and Conclusions .............................................................................. 33

Recommendations for Future Studies .................................................................. 34

References ................................................................................................ 34

Appendixes ................................................................................................ 37
iv 

Figures

Figure 1. Map showing north coast region of California .......................................... 3

Figure 2. Map showing median elevationby hydrologic unit, north coast region of California 4

Figure 3. Map showing mean annual precipitation in northern California ..................... 4

Figure 4. Map showing geographic distribution of selected study stations, north coast 

region of California ........................................................................ 8

Figure 5. Graph showing example of curved versus straight-line relationship of studystation flow and index-station flow ...................................................... 13

Figure 6. Graph showing example of regression residuals plotted versus time ............... 13

Figure 7. Graph showing example of extension of streamflow statistics for a short record 

station, using streamflow statistics from a long-record station ..................... 14

Figure 8. Graph showing example of graphical determination of low-outlier threshold for 

flood-frequency analysis .................................................................. 15

Figure 9. Graphical determination of high-outlier threshold and historic period for floodfrequency analysis ........................................................................ 17

Figure 10. Graph showing SWRCB rain-based annual runoff estimates versus USGS annual 

runoffs for all 40 study stations ............................................................ 21

Figure 11. Graph showing SWRCB rain-based October 1 to March 31 runoff estimates versus 

USGS October 1 to March 31 runoffs for all 40 study stations ........................ 21

Figure 12. Graph showing SWRCB rain-based December 15 to March 31 

runoff estimates versus USGS December 15 to March 31 runoffs for all 40 study 

stations ....................................................................................... 21

Figure 13. Graph showing SWRCB flow-based annual runoff estimates versus USGS annual

runoffs for all 40 study stations ............................................................ 22

Figure 14. Graph showing SWRCB flow-based October 1 to March 31 runoff estimates versus 

USGS October 1 to March 31 runoffs for all 40 study stations ........................ 22

Figure 15. Graph showing SWRCB flow-based December 15 to March 31 runoff estimates 

versus USGS December 15 to March 31 runoffs for all 40 study stations ............ 22

Figure 16. Graph showing SWRCB flow-based February median flow estimates versus USGS 

February median flows for all 40 study stations .......................................... 22

Figure 17. Graph showing SWRCB estimated 2-year peak flows versus USGS 2-year 

peak-flow statistics ........................................................................ 25

Figure 18. Graph showing SWRCB estimated 5-year peak flows versus USGS 5-year 

peak-flow statistics ........................................................................ 25

Figure 19. Graph showing SWRCB estimated 10-year peak flows versus USGS 10-year peakflow statistics .............................................................................. 25

Figure 20. Graph showing SWRCB estimated 25-year peak flows versus USGS 25-year peakflow statistics .............................................................................. 25

Figure 21. Graph showing SWRCB estimated 50-year peak flows versus USGS 50-year peakflow statistics .............................................................................. 26

Figure 22. Graph showing SWRCB estimated 100-year peak flows versus USGS 100-year 

peak-flow statistics ........................................................................ 26

Figure 23. Graph showing rain-based dry (25 percent) year SWRCB average December 15 to 

March 31 mean daily flows versus USGS average December 15 to March 31 mean 

daily flows .................................................................................... 30

Figure 24. Graph showing flow-based dry (25 percent) year SWRCB average December 15 to 

March 31 mean daily flows versus USGS average December 15 to March 31 mean 

daily flows .................................................................................... 30
 v

Tables

Table 1. Basin characteristics used in study ...................................................... 5

Table 2. Desired versus final criteria for study station selection .............................. 5

Table 3. Study stations and their basin characteristics .......................................... 6

Table 4. Streamflow statistics estimated by State Water Resources Control Board ......... 9

Table 5. Values of regression constants and exponents for U.S. Geological Survey’s 

California peak-flow equations, North Coast and Central Coast hydrologic 

regions ....................................................................................... 10

Table 6. Average standard errors for U.S. Geological Survey’s California peak-flow 

equations .................................................................................... 11

Table 7. Required input parameters for two-station adjustment ................................. 16

Table 8. Summary of flood-frequency methods applied and years of annual peak-flow 

record at 30 study stations with flood-frequency analysis ........................... 18

Table 9. Computed errors between State Water Resources Control Board and U.S. 

Geological Survey annual and seasonal runoffs and February median flows ...... 19

Table 10. Percent differences between State Water Resources Control Board rain-based 

flow-statistic estimates and U.S. Geological Survey flow statistics at 40 study 

stations ....................................................................................... 19

Table 11. Percent differences between State Water Resources Control Board flow-based 

flow-statistic estimates and U.S. Geological Survey flow statistics at 40 study 

stations ....................................................................................... 20

Table 12. Average computed errors between State Water Resources Control Board and 

U.S. Geological Survey peak flows ...................................................... 23

Table 13. Percent differences between State Water Resources Control Board peak-flow 

estimates and U.S. Geological Survey peak-flow statistics at 30 study stations 

used for flood-frequency analysis ......................................................... 24

Table 14. Water year for 25- and 50-percentile rain- and flow-based December 15 to 

March 31 mean-daily-flow estimates ................................................... 27

Table 15. Computed relative bias and standard error between State Water Resources Control 

Board estimates and U.S. Geological Survey published data for 25-percentile year, 

for each station .............................................................................. 28

Table 16. Computed relative bias and standard error between State Water Resources 

Control Board estimates and U.S. Geological Survey published data for 

50-percentile year, for each station ...................................................... 29

Table 17. Computed percent difference between December 15 to March 31 average mean 

daily flows for State Water Resources Control Board estimates and U.S. 

Geological Survey published data for each station .................................... 32

Table 18. Results of the 25- and 50-percentile year rain- and flow-based average December 

15 to March 31 mean-daily-flow estimates’ relative standard errors versus basin 

characteristics’ Kendall τ correlation tests ............................................. 33

Figure 25. Graph showing rain-based median (50 percent) year SWRCB average 

December 15 to March 31 mean daily flows versus USGS average December 15 

to March 31 mean daily flows ............................................................ 30

Figure 26. Graph showing flow-based median (50 percent) year SWRCB average 

December 15 to March 31 mean daily flows versus USGS average December 15 

to March 31 mean daily flows ............................................................ 31
vi 

Multiply By To obtain

acre 0.4047 hectometer

acre-foot (acre-ft) 0.001233 cubic hectometer 

foot (ft) 0.3048 meter

foot per mile (ft/mi) 0.1894 meter per kilometer

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

inch (in.) 25.4 millimeter

mile (mi) 1.609 kilometer

square mile (mi2) 2.590 square kilometer 

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

(NAVD 88).

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

Abbreviations

ADAPS USGS Automated Data Processing System

DEM Digital Elevation Model

GIS Geographic Information Systems

LOC Line of Organic Correlation

OLS Ordinary Least Squares

PEAKFQ USGS computer program

USGS U.S. Geological Survey

SWRCB State Water Resources Control Board

WRC U.S. Water Resources Council

Conversion Factors, Datum, and Abbreviations

Appendixes

Appendix 1. Matrix of study station and index station pairings for both daily value regressions 

for streamflow statistic adjustment and two-station adjustment for flood 

frequency analysis ........................................................................ 38

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with 

estimates provided by SWRCB ......................................................... 39

Appendix 3. Computed relative standard errors plotted versus basin characteristics for all 

stations’ 25- and 50-percentile December 15 to March 31 mean-daily-flow 

estimates .................................................................................... 74
Evaluation of Methods Used for Estimating Selected 

Streamflow Statistics, and Flood Frequency and 

Magnitude, for Small Basins in North Coastal California

By Michael P. Mann1, Julé Rizzardo2, and Richard Satkowski2

Abstract

Accurate streamflow statistics are essential to water 

resource agencies involved in both science and decisionmaking. When long-term streamflow data are lacking at a site, 

estimation techniques are often employed to generate streamflow statistics. However, procedures for accurately estimating 

streamflow statistics often are lacking. When estimation procedures are developed, they often are not evaluated properly 

before being applied. Use of unevaluated or underevaluated 

flow-statistic estimation techniques can result in improper 

water-resources decision-making. The California State Water 

Resources Control Board (SWRCB) uses two key techniques, 

a modified rational equation and drainage basin area-ratio 

transfer, to estimate streamflow statistics at ungaged locations. 

These techniques have been implemented to varying degrees, 

but have not been formally evaluated. For estimating peak 

flows at the 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals, the SWRCB uses the U.S. Geological Survey’s (USGS) 

regional peak-flow equations. In this study, done cooperatively 

by the USGS and SWRCB, the SWRCB estimated several 

flow statistics at 40 USGS streamflow gaging stations in the 

north coast region of California. The SWRCB estimates were 

made without reference to USGS flow data. The USGS used 

the streamflow data provided by the 40 stations to generate 

flow statistics that could be compared with SWRCB estimates 

for accuracy. While some SWRCB estimates compared favorably with USGS statistics, results were subject to varying 

degrees of error over the region. Flow-based estimation techniques generally performed better than rain-based methods, 

especially for estimation of December 15 to March 31 mean 

daily flows. The USGS peak-flow equations also performed 

well, but tended to underestimate peak flows. The USGS equations performed within reported error bounds, but will require 

updating in the future as peak-flow data sets grow larger. Little 

correlation was discovered between estimation errors and geographic locations or various basin characteristics. However, for 

25-percentile year mean-daily-flow estimates for December 

15 to March 31, the greatest estimation errors were at east San 

Francisco Bay area stations with mean annual precipitation 

less than or equal to 30 inches, and estimated 2-year/24-hour 

rainfall intensity less than 3 inches. 

1

U.S. Geological Survey

2

California State Water Resources Control Board, Division of Water Rights

Introduction

Better flow-statistic estimation procedures at ungaged 

locations have long been needed in water-resource science 

and decision-making. Such procedures are especially lacking 

for small drainage basin areas (especially less than 30 mi2) 

because of a general lack of long-term flow data for small 

basins. Regional regression equations have been derived in 

many locales across the United States for such purposes. In 

California, peak-flow equations were produced by the U.S. 

Geological Survey (USGS) in 1977 (Waananen and Crippen, 

1977), but have not been revised with updated precipitation 

and flow data. Agencies involved in water-related decision 

making often have a need for other various streamflow statistics that are not available at ungaged sites. Methods for estimating such statistics are numerous and rarely standardized. 

In general, the accuracies of various estimation procedures are 

often not thoroughly evaluated prior to implementation. The 

California State Water Resources Control Board (SWRCB) 

has developed flow-statistic estimation procedures for use 

in water-rights appropriations, but these procedures have 

not been thoroughly evaluated for accuracy. This study was 

designed to formally evaluate these SWRCB procedures, as 

well as to assess the accuracy of the USGS peak-flow equations for the north coast region. 

The SWRCB has a need to estimate selected streamflow 

statistics at ungaged locations in northern coastal California 

(north coast region) in order to appropriate water rights. 

Many of these locations are in small drainage basins (30 mi2

and smaller) where long-term historical flow data tend to be 

lacking. The statistics of interest, estimated by the SWRCB, 

include total annual and seasonal runoffs, February median 

flows, daily mean streamflows, and magnitudes of selected 

flood frequencies. 
2 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Description of Study Area

The north coast region of California is delineated in 

figure 1 by the grey, green, and orange shaded areas. The study 

area covers about 340 mi north to south and ranges in width 

from about 85 mi in the north to about 45 mi in the south. 

Major river drainage basins include the Klamath, Trinity, Eel, 

and Russian Rivers, along with several other smaller drainage basins. These basins drain directly into the Pacific Ocean. 

Because of both its inland extent and differences in geology 

and meteorology, the upper Klamath River basin was excluded 

from the study region, as this area undoubtedly would belong 

in a different region for the purposes of estimating streamflow 

statistics. In addition, because of its proximity to the coast and 

need for a representative geographic distribution of study sites, 

a small portion of the Sacramento River basin around Clear 

Lake was added to the study (orange shaded area in figure 1). 

Elevations range from sea level to over 9,000 ft in the 

north coast region. The map in figure 2 shows the median 

(50-percentile) elevation for the hydrologic units in the study 

region. The highest elevations are in the Klamath and Coast 

Ranges in the northern two-thirds of the study region, with 

peaks ranging from about 6,000 to over 9,000 ft. Most of the 

crests of these ranges are within 50 mi of the coast. The Coast 

Ranges extend to the southernmost portion of the study region, 

with a break in the San Francisco Bay area. Drainage basins 

typically are steep in their upland portions, and flatten near 

the coast at the generally narrow coastal plain. The upland 

portions of the Klamath and northern Coast Ranges are largely 

coniferous (redwood and Douglas fir) forest cover. Southward, 

coniferous forests are found at the highest elevations, but 

mixed pines and hardwoods (oaks, maple, and madrone) are 

dominant at lower elevations. Also southward, chaparral (manzanita, sage, and scrub oak) tends to be dominant on windand sun-exposed slopes. The soils of the Klamath Range are 

derived largely from plutonic and metamorphic rocks, whereas 

the Coast Range soils are derived largely from sedimentary 

rocks. 

The semipermanent high-pressure area of the northern 

Pacific Ocean largely controls the climate of the north coast 

region. This pressure system moves northward in the summer, 

holding storm tracks well to the north. In the late fall to early 

spring, the system migrates southward, bringing storms across 

California. This results in a markedly wet season from October 

to April, and a generally dry season the remainder of the year. 

Most precipitation and associated runoff happens during the 

October to April period. Pacific Ocean-generated storms are 

regional and strong during winter months. This can result in 

regional flooding during winter months. Summer convective 

thunderstorms are possible in summer months, especially at 

higher elevations, but usually result in smaller peak flows than 

the regional wintertime storms. Such summertime storms are 

also limited to much smaller areas than wintertime storms. 

Because of oceanic influences, temperatures in the region are 

moderate year-round and daily fluctuations are limited. Therefore, most precipitation occurs as rain, with snow only at the 

highest elevations of the Klamath and northern Coast Ranges. 

Annual precipitation varies from more than 100 inches in the 

north to 20 inches in the San Francisco Bay area, and generally 40 to 70 inches in the Coast Ranges (Rantz, 1969). The 

map in figure 3 shows mean annual precipitation in the north 

coast region of California. 

Acknowledgments

The California State Water Resources Control Board’s 

Division of Water Rights provided funding for this study. 

Kenyatte Williams, Camille Valenti, and Rudolph Akoutey of 

the California State Water Resources Control Board’s Division 

of Water Rights provided technical assistance in Geographic 

Information Systems (GIS) analysis and flow-statistic estimation. 

Purpose and Scope

The purpose of this report is to present a characterization 

of the accuracy and bias of streamflow statistics resulting from 

application of estimation techniques commonly employed by 

the SWRCB. In order to evaluate these estimation techniques, 

40 actively or previously gaged streamflow study stations were 

chosen to act as ungaged locations. The SWRCB estimated 

various streamflow statistics at these gages without reference 

to the streamgage data. The USGS then used the streamgage 

data to estimate various streamflow statistics for comparison 

with SWRCB’s estimates. This report presents the results of 

the comparisons.

The study included tests for parametric and geographic 

error and bias, with examination of accuracy and bias as 

related to common basin characteristics (drainage area, mean 

channel slope, mean elevation, mean annual precipitation, 

location, etc.). The study was not intended to produce new 

estimation techniques, but to evaluate whether or not SWRCB 

methods are accurate and suitable for their needs, and to investigate whether geographic location or basin attributes have an 

effect upon errors in estimation. The study also was intended 

to serve as a useful model for future assessments of streamflow-statistic estimation techniques, and may promote future 

efforts to improve the techniques.

Two general methods have been developed by the 

SWRCB for estimating flow statistics, depending on the availability and applicability of streamflow or precipitation data. 

These two methods are (1) a modified rational equation, and 

(2) a drainage-basin-area ratio approach. Both methods are 

used by the SWRCB for estimating the streamflow statistics, 

with the exception of the February median flow (for which the 

SWRCB uses method 2 only) and peak flows (USGS peakflow equations).
Figure 1. North coast region of California. 

Numbered regions are Regional Water Quality Control Board regions. The study area is shaded.

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Description of Study Area 3
4 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Figure 2. Median elevation (in meters) by hydrologic unit, north 

coast region of California.

Elevation is shown in meters; 1 meter = 3.281 feet. 

Source: http://www.esg.montana.edu/gl/huc/hucs.

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Figure 3. Mean annual precipitation in northern California.

Selection of Study Stations

The SWRCB has a need to estimate streamflow statistics 

at ungaged sites for small drainage basins (30 mi2 and smaller) 

in the north coast region. To evaluate the SWRCB estimates, 

it was necessary to utilize study sites that are either active or 

previously active gaging stations. A total of 323 streamflow 

stations (both active and inactive) were available in the north 

coast region. A good geographic distribution of study stations 

over the north coast region was desired. Also desired was a 

good distribution of stations over a broad range of drainage 

basin areas (less than 30 mi2), and over the other basin characteristics of interest (table 1). The ultimate goal of the station 

selection was to select a statistically significant number of 

stations (about 30) that are unaffected by storage, diversions, 

or urbanization, with drainage basin areas less than 30 mi2 and 

at least 10 complete years of daily flow record. However, most 

of the long-term periods of record for gaging stations in the 

region are for stations with drainage basin areas greater than 

100 mi2. 

More confidence in streamflow-statistic estimation is 

achieved from longer periods of record (preferably greater 

than 30 years), which limit the effects of short-term variability in long-term climatic conditions. Because of the lack 

of long-term periods of record for small basins, the original 

and desired criteria for station selection had to be altered in 

order to come up with enough study stations to represent the 

geographic variability in the region. Table 2 lists desired and 

final limits for criteria in station selection. Strict application 

of the basic criteria (and avoiding duplication of stations in 

close proximity to one another and with similar basin characteristics) resulted in a selection of 10 stations. Relaxing the 

drainage-area criterion to 45 mi2 resulted in only 13 selected 

stations, and accepting stations with a minimum 5 years of 

Methods

Forty actively or previously gaged streamflow study stations were chosen to act as ungaged locations. The SWRCB 

used a modified rational equation method and a drainagebasin-ratio approach to estimate various streamflow statistics 

at these stations.
Table 1. Basin characteristics used in study.

[USGS, U.S. Geological Survey]

Basin characteristic Units Source

Drainage area (above gage) (DA) square miles USGS Site file

Station altitude (A) feet USGS Site file 

Mean annual precipitation (1900-1960) (P) inches Rantz, 19691

2-year, 24-hour rainfall intensity (I) inches U.S. Weather Bureau, 19612

Mean annual Class A pan evaporation (E) inches U.S. Weather Bureau, 19593

Mean channel slope (determined between 10% and 85% distances from 

gage to basin divide) (S)

-- USGS Site file

Channel length (between gage and basin divide) (L) miles USGS Site file

Altitude index (determined between 10% and 85% distances from gage to 

basin divide) (H)

103 feet USGS Site file

Distance from gage to ocean (mean of west-to-ocean and southwest-toocean distances) (DO)miles Determined from USGS 7.5’ topographic 

quadrangles

1

Rantz, S.E., 1969, Mean annual precipitation in the California Region: U.S. Geological Survey open-file map.

2

U.S. Weather Bureau, 1961, Rainfall frequency atlas of the United States: Technical Paper No. 37, 13 p.

3

U.S. Weather Bureau, 1959, Evaporation maps for the United States: Technical Paper No. 40, 115 p

Table 2. Desired versus final criteria for study station selection.

Criterion Desired limit Final limit

Drainage area Less than 30 square miles Less than 100 square miles

Period of streamflow record Greater than or equal to 30 years Greater than or equal to 4 years

Degree of regulation and/or urbanization None Minor

Number of stations 30 40

Methods 5

SWRCB Flow-Statistic Estimation Methods

The SWRCB used a modified rational equation, 

area-ratio methods, and USGS flood-frequency equations 

(Waananen and Crippen, 1977) to estimate all the streamflow 

statistics listed in table 4. The rational equation was used for 

annual runoff, wet season (October 1 to March 31) runoff, and 

winter season (December 15 to March 31) runoff mean daily 

flows. The area-ratio method was used for all these same statistics and also to estimate February median flows. The USGS 

regional flood-frequency equations were used for estimating 

peak flows at the 2-, 5-, 10-, 25, 50-, and 100-year recurrence 

intervals. The SWRCB does not currently estimate mean daily 

flows for water-rights appropriations, but these estimates were 

added to the study in order to evaluate the limitations of such 

estimates. In order to facilitate comparison between SWRCB 

estimates of December 15 to March 31 mean daily flows and 

USGS gaged mean daily flows, it was important to restrict 

the SWRCB estimates to the period of record at the study 

station. In determining the 25- and 50-percentile years (dry 

and median years) for generating December 15 to March 31 

mean-daily-flow estimates, the SWRCB ranked annual flows 

from a nearby streamgage with a period of record that bracketed at least the same period of record as the study station of 

interest. The SWRCB then selected the years within the period 

of record at the study station whose ranks were closest to the 

computed 25- or 50-percentile years at the nearby reference 

gage. 

record resulted in only 20 selected stations. Accepting stations 

with minor regulation, small diversions, and minor urbanization increased the total number of selected stations to 32. 

However, a reasonable geographic distribution of stations over 

the region was not achieved with these 32 stations. In order to 

fill in holes in the distribution, 6 additional stations with drainage basin areas ranging from 45 to 100 mi2

 and 2 stations with 

periods of records of only 4 years were added. Thus, by relaxing the desired criteria, 40 stations were selected that provided 

a good geographic distribution over the north coast region and 

over the range of basin characteristics in the region. Table 3

lists the 40 selected stations and their basin characteristics. 

The map in figure 4 shows the geographic distribution of the 

40 stations over the north coast region. 
6 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Station 

number Station name

Drainage 

area,

DA

(mi2)

Altitude,

A

(ft)

Precipitation, 

P

(in.)

Rainfall 

intensity,

I

(in.)

Pan 

evaporation,

E

(in.)

Channel 

slope,

S

(ft/mi)

Channel 

length,

L 

(mi)

Altitude 

index,

H

(1,000 ft)

Distance 

to ocean,

DO

(mi)

11162540 Butano Creek near Pescadero, 

CA

18.3 70.0 38 4.5 49 126 11.2 0.6 2.9

11162600 Purisima Creek near Half 

Moon Bay, CA

4.83 380.0 38 3.4 49 336 3.8 0.9 3.8

11172100 Upper Penitencia Creek at San 

Jose, CA

21.5 265.3 16 2.0 56 303 7.7 1.3 32.8

11180500 Dry Creek at Union City, CA 9.39 85.1 22 2.9 57 233 5.1 0.6 28.0

11182500 San Ramon Creek at San 

Ramon, CA

5.89 530.0 23 2.3 58 102 5.7 0.8 31.3

11183700 Little Pine Creek near Alamo, 

CA

1.22 520.0 22 2.3 59 920 2.2 1.3 36.7

11449500 Kelsey Creek near 

Kelseyville, CA

36.6 1,475.4 45 5.0 61 80 15.9 2.0 41.9

11451100 North Fork Cache Creek at 

Hough Spring near Clearlake Oaks, CA

60.2 1,840.0 50 3.0 63 53 17.1 2.0 57.8

11453200 Dry Creek near Middletown, 

CA

8.35 1,172.2 80 5.8 62 466 3.9 1.9 39.5

11458200 Redwood Creek near Napa, 

CA

9.79 166.2 30 2.4 61 258 8.9 1.1 36.9

11460100 Arroyo Corte Madera del Presidio at Mill Valley, CA4.69 1.9 38 2.6 52 181 3.3 0.3 4.8

11460800 Walker Creek near Tomales, 

CA–Pre-regulation (1979)

40.1 56.7 38 2.8 52 24 19.3 0.3 6.7

11460920 Salmon Creek at Bodega, 

CA

15.7 81.0 44 4.5 52 50 10.9 0.3 4.2

11463900 Maacama Creek near Kellogg, CA43.4 188.9 60 5.5 58 166 10.6 0.9 29.4

11464860 Warm Springs Creek near 

Asti, CA

12.2 625.0 67 6.0 54 128 6.4 0.9 16.9

11465150 Pena Creek near Geyserville, CA22.3 195.0 50 6.0 56 48 11.1 0.4 22.4

11465800 Santa Rosa Creek near 

Santa Rosa, CA

12.5 318.6 36 3.2 57 150 8.2 1.0 26.6

11467600 Garcia River near Point 

Arena, CA

98.5 55.3 65 5.0 44 32 35.1 0.5 4.6

11467850 Soda Creek Tributary near 

Boonville, CA

1.53 1,551.3 55 4.3 54 284 1.9 1.8 21.7

11468070 South Fork Big River near 

Comptche, CA

36.2 500.0 50 3.8 53 91 9.2 0.9 16.9

11468540 Pudding Creek near Fort 

Bragg, CA

12.5 88.9 51 3.3 48 90 7.5 0.4 6.1

11469500 North Fork Mattole River at 

Petrolia, CA

37.6 50.0 90 4.0 40 126 12.8 0.7 4.0

Table 3. Study stations and their basin characteristics.

[DA, drainage area above gage; A, station altitude; P, mean annual precipitation (1900–1960); I, 2-year, 24-hour rainfall intensity; E, mean annual Class A pan 

evaporation; S, mean channel slope (determined between 10 and 85 percent distances from gage to basin divide); L, channel length (between gage and basin 

divide); H, altitude index (mean of elevations at 10 and 85 percent distances from gage to basin divide); DO, distance from gage to ocean (mean of west-to-ocean 

and southwest-to-ocean distances). mi2, square miles; ft, feet; in., inches; mi, miles. See fig. 4 for location of stations and table 1 for sources of data]
Table 3. Study stations and their basin characteristics.—Continued

[DA, drainage area above gage; A, station altitude; P, mean annual precipitation (1900–1960); I, 2-year, 24-hour rainfall intensity; E, mean annual Class A pan 

evaporation; S, mean channel slope (determined between 10 and 85 percent distances from gage to basin divide); L, channel length (between gage and basin 

divide); H, altitude index (mean of elevations at 10 and 85 percent distances from gage to basin divide); DO, distance from gage to ocean (mean of west-to-ocean 

and southwest-to-ocean distances). mi2, square miles; ft, feet; in., inches; mi, miles. See fig. 4 for location of stations and table 1 for sources of data]

Station 

number Station name

Drainage 

area,

DA

(mi2)

Altitude,

A

(ft)

Precipitation, 

P

(in.)

Rainfall 

intensity,

I

(in.)

Pan 

evaporation,

E

(in.)

Channel 

slope,

S

(ft/mi)

Channel 

length,

L 

(mi)

Altitude 

index,

H

(1,000 ft)

Distance 

to ocean,

DO

(mi)

11471800 Tomki Creek near Willits, 

CA

43.4 1,591.9 48 4.0 57 43 16.9 1.9 33.4

11473600 Short Creek near Covelo, 

CA

15.2 1,438.2 43 3.3 58 150 7.7 1.9 41.7

11474781 Combined flow of 

11474750 + 11474780

20.66 1,480.0 57 4.5 54 135 10.0 2.1 31.6

11475560 Elder Creek near Branscomb, CA6.5 1,391.1 80 4.3 50 420 5.0 2.4 10.2

11475940 East Branch South Fork Eel 

River near Garberville, 

CA

74.3 385.3 65 5.7 50 87 22.7 1.2 15.4

11476600 Bull Creek near Weott, CA 28.1 269.4 100 5.0 46 136 9.9 0.8 18.1

11477700 Little Van Duzen River near 

Bridgeville, CA

36.2 2,283.0 70 4.3 50 119 13.7 3.0 36.7

11480000 Jacoby Creek near Freshwater, CA5.8 50.0 58 3.4 41 299 3.8 1.5 19.6

11480390 Mad River above Ruth 

Reservoir near Forest 

Glen, CA

93.8 2,700.0 60 3.7 59 58 23.8 3.2 48.1

11481200 Little River near Trinidad, 

CA

40.5 17.6 55 4.0 41 139 15.2 0.9 2.3

11481500 Redwood Creek near Blue 

Lake, CA

67.7 850.0 80 3.9 47 131 22.1 2.0 30.3

11482125 Panther Creek near Orick, 

CA

6.07 400.0 85 5.0 44 435 3.8 1.1 15.1

11482468 Little Lost Man Creek at 

Site No 2 near Orick, CA

3.46 50.0 75 5.8 39 392 4.4 1.0 4.6

11522200 Elk Creek near Happy 

Camp, CA

90.4 1,300.0 65 3.8 45 209 18.1 2.9 50.0

11522260 Ti Creek near Somes Bar, 

CA

9.46 700.0 70 5.3 45 677 6.0 2.5 37.2

11529800 Willow Creek near Willow 

Creek, CA

40.9 585.5 75 4.0 47 207 13.2 2.2 39.0

11532620 Mill Creek near Crescent 

City, CA

28.6 180.0 85 6.0 38 84 9.1 0.5 3.2

11533000 Lopez Creek near Smith 

River, CA

0.92 38.8 80 4.8 37 375 2.0 0.6 0.3

Maximum 98.5 2,700.0 100 6.0 63 920 35.1 3.2 57.8

Minimum 0.9 1.9 16 2.0 37 24 1.9 0.3 0.3

Methods 7
8 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

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Figure 4. Geographic distribution of selected study stations, north coast region of California.
Table 4. Streamflow statistics estimated by State Water Resources Control Board.

Streamflow statistic Units

Annual runoff acre-feet

October 1 to March 31 runoff (wet season runoff) acre-feet

December 15 to March 31 runoff (winter season runoff) acre-feet

February median flow (50-percentile of February daily flows) cubic feet per second

50-percentile (median) year December 15 to March 31 mean daily streamflows cubic feet per second

25-percentile (dry) year December 15 to March 31 mean daily streamflows cubic feet per second

Peak flows at 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals cubic feet per second

Methods 9

USGS Flood-Frequency Equations

The USGS regional peak-flow equations for specified 

regions in California (Waananen and Crippen, 1977) were 

used by the SWRCB for peak-flow estimates at the 2-, 5-, 10-, 

25-, 50-, and 100-year recurrence intervals. These equations 

SWRCB Drainage Basin Area-Ratio Method

The drainage basin area-ratio method assumes that the 

streamflow at an ungaged site is the same per unit area as at 

a nearby hydrologically similar streamgaging station. The 

area-ratio method is used for transferring known flows from 

one point to another location where flow is not known. This 

method is generally best used for transferring flows within 

the same drainage basin; however, the SWRCB also used 

area-ratio methods to transfer flow statistics from one basin 

to another. Typically, the SWRCB selected a streamgage that 

is closest in distance to the point of interest for transfer of the 

streamflow statistic from the gaged location to the ungaged 

location. The SWRCB incorporated not only a drainage basin 

area-ratio for statistic transfer, but also a precipitation ratio 

in order to account for differences in precipitation between 

basins. The area-ratio equation used by the SWRCB to estimate streamflow statistics is:

SWRCB Rational Equation Method

The rational equation is a simple rainfall-runoff equation designed for estimating peak flows in small (less than 1 

mi2) drainage basins (Bendient and Huber, 1992). The rational 

equation is defined as:

Qpeak = C  I  A (1)

where

Qpeak is peak flow (ft3/s),

C is a dimensionless runoff coefficient, less than or 

equal to 1,

I is rainfall intensity (inches per hour), and

A is watershed area above point of interest (acres).

The SWRCB used two different modifications of the rational 

formula for streamflow-statistic estimates in this study. For 

estimating runoff volumes (annual and seasonal runoffs), the 

rational equation appears similar to the equation above, but the 

parameter I was defined differently:

Qrunoff = C  I  A (2)

where

Qrunoff is total runoff (acre-ft) and

I is rainfall total depth for period of interest (ft).

For estimating mean daily flows, a conversion factor was 

added to the equation and the parameter I was again defined 

differently:

Qmean = K  C  I  A (3)

where

Qmean is mean daily streamflow (cubic feet per second),

K is a conversion factor used to convert acre-feet to 

cubic feet per second, and

I is daily rainfall total depth from a nearby raingage 

(ft).

Q (4) ug Qg

Aug

Ag

× -------- Iug

Ig

= × ------

where

Qug is flow volume (acre-ft), mean daily flow (ft3/s), or 

February median flow (ft3/s) at ungaged location,

Qg is flow volume (acre-ft), mean daily flow (ft3/s), or 

February median flow (ft3/s) at gaged location,

Aug is watershed area above ungaged site (acres),

Ag is watershed area above gaged site (acres),

I

ug is mean annual precipitation above ungaged site, 

from GIS-based isohyetal map (ft), and 

I

g

 is mean annual precipitation above gaged site, 

from GIS-based isohyetal map (ft).
10 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Table 5. Values of regression constants and exponents for U.S. Geological Survey’s California peak-flow equations, North Coast and 

Central Coast hydrologic regions.

[From Waananen and Crippen, 1977, USGS Water-Resources Investigations Report 77-21. Peak flow, Qpeak, at a specified recurrence interval = C x Aa x Pb x Hc, 

where C is a regression constant based upon return period and region, A is watershed area above point of interest, P is mean annual precipitation, H is altitude 

index, and a, b, c are regression exponents based upon return period and region]

Recurrence interval

(years)

Regression constant

C

Regression exponents

a b c

North Coast Hydrologic Region

2 3.52 0.90 0.89 -0.47

5 5.04 0.89 0.91 -0.35

10 6.21 0.88 0.93 -0.27

25 7.64 0.87 0.94 -0.17

50 8.57 0.87 0.96 -0.08

100 9.23 0.87 0.97 0

Central Coast Hydrologic Region

2 0.0061 0.92 2.54 -1.10

5 0.118 0.91 1.95 -0.79

10 0.583 0.90 1.61 -0.64

25 2.91 0.89 1.26 -0.50

50 8.20 0.89 1.03 -0.41

100 19.7 0.88 0.84 -0.33

USGS Flow-Statistic Determination Methods

Annual and seasonal runoff and February median flow 

can be determined directly using USGS streamflow data 

available in the USGS’s Automated Data Processing System 

(ADAPS). However, as 34 of the 40 study stations had periods 

of record shorter than desired (less than at least 30 years of 

streamflow record), streamflow statistics generated from 

short-record stations were not considered to be representative of long-term conditions. For these stations, the runoff 

and February median streamflow statistics were adjusted to 

long-term conditions via correlation with long-term reference 

(index) gaging stations. For the years selected by the SWRCB 

as the 25- and 50-percentile (dry and median) years, mean 

daily streamflows available in ADAPS were used as generated. 

were derived through multiple regressions of peak-flow data 

and basin characteristics (table 1) for estimating peak flows in 

specified hydrologic regions in California. The general form 

of the USGS’s California regional peak-flow equations is as 

follows:

Qpeak = C  Aa  Pb  Hc (5)

where 

Qpeak is peak flow at specified recurrence interval 

(ft3/s),

C is a regression constant based upon return period 

and region,

A is watershed area above point of interest (square 

miles),

P is mean annual precipitation (inches),

H is altitude index (mean of altitude taken at points 

10 percent and 85 percent distance between point 

of interest and basin divide; 103 ft), and

a, b, c are regression exponents based upon return period 

and region.

Table 5 lists the values of the regression coefficient (C) 

and regression exponents (a, b, and c) for the north coast and 

central coast hydrologic regions at the 2-, 5-, 10-, 25-, 50-, 

and 100-year recurrence intervals. Table 6 lists the average 

standard errors associated with peak-flow estimates at the 2-, 

5-, 10-, 25-, 50-, and 100-year recurrence intervals using the 

USGS California flood-frequency equations. The isohyetal 

precipitation map “Mean Annual Precipitation in the California Region” for the years 1900 to 1960 (Rantz, 1969) was used 

to derive the USGS’s regional flood-frequency equations. The 

SWRCB did not use Rantz’s map for their estimates, but used 

a Geographic Information Systems (GIS) coverage based upon 

similar isohyetal precipitation data (1900-1960).
Table 6. Average standard errors for U.S. Geological Survey’s 

California peak-flow equations.

Recurrence interval

(years)

Average standard error

(percent)

2 54.8

5 44.9

10 44.0

25 44.7

50 46.6

100 49.4

Methods 11

Selection of Index Stations

Several long-term reference, or index, stations (periods of 

record ranging from 30 to 89 years) were available throughout 

the north coast region for adjustment of short-record statistics 

at study stations. To serve as a useful index station, preference 

was given to index stations similar in size and characteristic 

to a study station. However, as most index stations are from 

larger drainage basins than many of the study stations, index 

stations were selected based upon proximity to study stations. Two criteria were required to be met: (1) The regression 

coefficient of determination (R2) for index-station daily mean 

flows versus study-station daily mean flows was required 

to be greater than 0.8 for concurrent flow data, and (2) the 

index station was required to have at least twice the years of 

record of the study station (Ries and Friesz, 2000). Of the 34 

short-record stations, 2 stations did not have index stations 

that met these criteria (11460100 did not meet criterion 1, and 

11481500 did not meet criterion 2). The streamflow statistics 

at these two stations were not adjusted to long-term conditions. If more than one potential index station was identified 

for a particular study station, all were used for record extension at that site. Results from multiple index stations were 

combined into a single streamflow-statistic estimate. 

In order to adjust study-station flow statistics using 

long-term index stations, tests for trends in flow data should 

be considered. Improper regression can result if trends are 

evident in the long-term record for the north coast region, or 

for individual index stations. If regional trends are indicated, 

station-to-station correlation techniques would be required to 

first employ ‘de-trending’ of the streamflow data. It is also 

undesirable to adjust short-record statistics to individual longterm stations if trends are indicated at a particular index station 

but not for the region. Trend tests involved first plotting mean 

annual flow versus year for each potential index station for 

qualitative detection of trends in mean annual flow data. Kendall τ correlation tests, at 0.05 significance (Helsel and Hirsch, 

Extension of Study-Station Statistics to LongTerm Conditions

The SWRCB estimates of annual flow, winter season 

flow, wet season flow, and February median flow were made 

with the assumption that these flows are representative of 

long-term conditions for each station. That is, the estimates 

of these statistics are not necessarily representative of the 

period of record of the USGS gaging station. Therefore, it was 

important that the USGS-generated statistics were not calculated from short periods of record and compared with SWRCB 

estimates of these statistics for long-term conditions. Of the 40 

study stations, 34 stations had periods of records shorter than 

desired (longer than 30 years) to be representative of longterm conditions. 

Searcy (1959) recognized that for gaging-station record 

comparison, each record must represent, or be adjusted to, 

concurrent periods. Thus, the differences between records will 

be due to differences in climatic or drainage basin characteristics and not to the fact that different periods of time are 

represented. Searcy suggested using gaging-station correlation 

with concurrent-record flow-duration curves to effectively 

extend the periods of record from a short-record (study) station to that of a long-term (reference or index) station. Ries 

and Friesz (2000) used a similar approach in extending the 

effective record length of various estimated flow statistics in 

Massachusetts. 

In this study, flow-duration-curve coordinates between 

short-record and long-record stations were either regressed 

using the MOVE-1 regression technique or graphically if 

curvature was noticeable in the relation. Because several of 

the north coast region stations had very short periods of record 

(as short as 4 years of record), it was decided that computed 

flow-duration statistics would not be reliable for these record 

extension techniques. The method of record extension used in 

this study is similar to Searcy’s and Ries and Frieszs’ methods; however, the statistic used for station correlation was the 

concurrent period of mean-daily-flow values. This significantly increased the number of points for station-to-station 

correlation, and better defined the relation between short- and 

long-record gaging stations. 

Several long-record stations with drainage basin areas 

in excess of 100 mi2 were available in the region to serve as 

reference, or index, stations for adjustment of flow statistics at 

short-term stations to long-term conditions. The six study stations with periods of record greater than 30 years also served 

as index stations. The streamflow statistics were not adjusted 

at these stations. Station-to-station linear (Ordinary Least 

Squares) or second-order polynomial regression of concurrent 

daily values served as the methods for adjustment. 

Flood-frequency analysis was used to determine peak flows 

at the 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals. 

Flood-frequency analysis was performed at 30 of the 40 study 

stations using U.S. Water Resources Council (WRC) methods 

outlined in Guidelines for Determining Flood Flow Frequency, 

Bulletin 17B (U.S. Interagency Advisory Committee on Water 

Data, 1982). Annual peak-flow records of less than 10 years 

prevented flood-frequency analysis at 10 study stations. 
12 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Adjustment of Flow Statistics via Regression Equations

The regression equations derived from the daily-value 

regressions were used in the adjustment of the study-station 

streamflow statistics. The first step in study-station statistics 

adjustment involved computation of the long-term streamflow 

statistics at each index station. These values were then used 

in the regression equation developed between each study and 

index station in order to compute long-term statistics for each 

study station. Figure 7 demonstrates the use of this record 

extension technique for estimating long-term streamflow 

statistics at short-record study stations. For study stations that 

have multiple index stations, the individually computed longterm statistics were averaged by weighting via the regression 

coefficients of determination (R2) and length of period of 

record, as the following equation indicates:

Mean-Daily-Flow Regression Analyses

Concurrent mean-daily-flow values at study stations 

were plotted versus mean-daily-flow values at index stations. 

This relation was used to develop a regression equation (that 

described the study-station streamflows as a function of the 

index-station streamflows) that could be used to compute 

long-term study-station statistics from index-station statistics. 

The Ordinary Least Squares (OLS) fit was used if the relation 

was determined to be linear, and second order polynomial fit 

was used for curved relations. OLS regression was selected in 

lieu of the MOVE-1 (also known as line of organic correlation) 

technique because all statistics of interest generally were close 

to the center of the distribution of daily flows, rather than over 

a wide range of flows as MOVE-1 is recommended for. OLS 

also was chosen because of its more similar computational 

methodology to the polynomial regression. The criterion used 

in determining curvature was that if the R2 for the polynomial fit was larger by 0.01 than that of the OLS fit, then the 

polynomial fit was used for adjustment. Degree of linearity or 

curvature was also evaluated qualitatively by graphical evaluation of study-station flow versus index-station flow plotting. 

It was found that stations with curved relationships met the R2

criteria well. Figure 5 shows such a curved relationship and 

resulting higher R2 value for the polynomial fit. It was found 

that because most of the streamflow statistics of interest were 

not at the extremes (low or high) of the distribution of mean 

daily streamflows, the polynomial fits were not drastically 

different than the OLS in the region of interest, but that the 

polynomial trend lines matched the curvature better. Figure 5

demonstrates this point as well.

For each regression, the computed residuals (the difference between regression-equation predicted and observed 

dependent variables) were plotted versus time in order to 

qualitatively evaluate possible issues with heteroscedasicity (nonconstant variance in datasets with respect to time). 

Residual plots from only a few sites indicated possible 

heteroscedasicity. The residual versus time plot in figure 6

demonstrates possible heteroscedasicity; the residuals appear 

to slightly decrease over time in this example. Quantitative 

trend tests (Kendall τ correlation test, at 0.05 significance) 

were run between computed residuals and time. Only very 

slight trends (τ values within (+/-) 0.5) were indicated at 

the stations that had indicated possible heteroscedasicity in 

residual-versus-time plotting. Due to the short-term periods 

of record when restricted to concurrent flow data, the cyclical nature of hydrologic data was determined to be more the 

cause of this phenomenon than improper regression approach. 

Hydrologic data sets that do not indicate long-term trends may 

have detectable trends in subsets of the data set. This is due to 

the tendency for short-term below- and above-average periods 

of flow seen in most hydrologic time-series data. Therefore, 

regressions that indicate slight heteroscedasicity were still 

used for statistic adjustments, as trends were determined to be 

nonpersistent with time, and as no alternate means for record 

extension were available.

1993), were run on each index station’s mean annual flows to 

quantitatively determine if any long-term trends were evident. 

No regional long-term trends were detected, so no de-trending was required. However, slight trends in annual mean flow 

data were indicated at two potential index stations (11451500 

and 11475800); these index stations were dropped from the 

analysis, as several other index stations were available for 

adjustment. A matrix of study-station and index-station pairings used in daily-value regression analysis for short-record 

streamflow-statistic adjustment is shown in Appendix 1.

Q (6) study

R2

study index – ( – 0.8)( ) POR Qstudy index – � { ( )}

R2

study index – � ( – 0.8)( ) POR

= ---------------------------------------------------------------------------------------------------------------------

where

Qstudy is the long-term streamflow statistic at the 

study station,

R2

study-index is the regression coefficient of determination 

from regression of each study-index pairing,

POR is the period of record (in years) of each index 

station used in study-index pairing, and

Qstudy-index is the streamflow statistic of interest computed 

from the regression equation developed in each 

study-index pairing.
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Figure 5. Example of curved versus straight-line relationship of study-station flow and index-station flow.

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Figure 6. Example of regression residuals plotted versus time.

Methods 13
14 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Figure 7. Example of extension of streamflow statistics for a short record station, using streamflow statistics 

from a long-record station.

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Low-Outlier Thresholds

Outliers are data points that depart significantly from 

the trend of the remaining data. Low annual peak values that 

depart significantly from the trend of the remaining peaks 

are excluded from the systematic record used to define the 

frequency curve. A conditional probability adjustment, as 

described in Bulletin 17B, is applied to account for peaks 

below the low-outlier threshold. Flood-frequency analysis 

first was computed with default parameter values in PEAKFQ 

using the systematic record. An adjustment to the low-outlier 

threshold then was determined graphically from the resulting 

frequency plot of annual peaks generated by PEAKFQ. This 

value was selected on the basis of the point at which the lowermagnitude annual peak values began to depart from the trend 

Flood-Frequency Analysis

Flood-frequency analysis was performed on 30 of the 40 

study stations using U.S. Water Resources Council (WRC) 

methods outlined in Guidelines for Determining Flood Flow 

Frequency, Bulletin 17B (U.S. Interagency Advisory Committee on Water Data, 1982). A minimum of 10 years of 

peak-flow data is required under WRC guidelines for floodfrequency analysis. Of the 40 study stations, 10 stations did 

not meet this requirement, and were dropped from the analysis. WRC methods assume that the logarithms of annual peak 

flows at a given station follow a log-Pearson Type III probability distribution. A log-Pearson Type III frequency curve is 

calculated based on the mean, standard deviation, and skewness of the logarithms of annual peak flows. These procedures were implemented using the USGS computer program 

PEAKFQ (Thomas and others, 1998). PEAKFQ uses WRC 

methods for flood-frequency computations. Additional adjustments to the frequency curve recommended in Bulletin 17B, 

but not available in PEAKFQ, are described in the following 

sections. 

December 15 to March 31 Mean Daily Flows for 

25- and 50-Percentile Years

The SWRCB determined the specific years, as described 

in a preceding section, used to estimate the December 15 to 

March 31 mean daily streamflows for 25- and 50-percentile 

(dry and median) years. The USGS mean daily streamflows 

used for comparison with SWRCB estimated mean daily 

streamflows were obtained directly from ADAPS. 
Figure 8. Example of graphical determination of low-outlier 

threshold for flood-frequency analysis.

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Methods 15

Historical Adjustment

Historical adjustment of frequency distributions is also 

recommended in Bulletin 17B. This analysis involves extending the record of the largest events to a historic period longer 

than that of the systematic record. As PEAKFQ has builtin capability for historic adjustment of frequency curves, 

this process involved only determination of the high-outlier 

threshold and historic period for input into PEAKFQ. The 

historic period and high-outlier threshold work in combination in flood-frequency analysis. The historic period is a 

period beyond the systematic gaging record in which there is 

confidence that no unknown peaks exceed the magnitude of 

Two-Station Comparison

Bulletin 17B recommends adjusting the logarithmic mean 

and standard deviation of a short-record flood-frequency distribution to a station with a longer period of record. As longrecord index stations were available for each of the 30 study 

stations used for flood-frequency analysis, all stations were 

pre-determined to be suitable candidates for two-station comparison. However, two-station comparisons were applied only 

for study stations where a suitable index station had at least 

double the period of record of the study station and where the 

R2 from the study-station versus index-station annual peak 

regression was greater than 0.8. A total of 24 study stations 

met these requirements. 

As with the index stations used for streamflow-statistic 

adjustment, trend tests were run for annual peak flows versus 

time for all potential long-term index stations to determine 

if long-term trends in peak data were evident. Trend tests 

involved first plotting annual peak flows versus year, and then 

running Kendall τ correlation tests at 0.05 significance. No 

regional long-term trends were evident for annual peak flows. 

At one potential index station (11482500), a slight negative 

trend in annual peak flows over time was detected. This station 

was dropped from this analysis, as several other index stations 

were available that did not indicate trends. 

The matrix of study-station and index-station pairings 

in Appendix 1 also shows the index stations used for two-station adjustment. For index-station selections, mean-daily-flow 

records and peak-flow records did not always result in similar 

index-station selection for study-station correlations with 

mean-daily-flow regressions and two-station analysis. For a 

given study station, a given index station can correlate well 

with either mean-daily-flow records or peak-flow records, but 

not necessarily with both. Thus several study stations have different assigned index stations for two-station comparison than 

for short-record extension via mean-daily-flow regressions.

A spreadsheet program, previously developed and used 

by the USGS California District (Robert W. Meyer, U.S. 

Geological Survey, written commun., 2002), was used for 

two-station computations. Two-station comparison requires 

flood-frequency analysis for the following periods of record, 

as applicable, in order to adjust the mean and standard deviation for the short-term (study) station: (1) short-record station 

systematic period of record, (2) short-term station concurrent 

record with long-term station record (in many cases this is 

the same as the study-station systematic period of record), (3) 

long-term station systematic period of record, (4) long-term 

station concurrent record with short-term station record, and 

(5) long-term station nonconcurrent record with short-term 

record. Table 7 lists the required input parameters for the twostation spreadsheet program. The routines performed by the 

two-station spreadsheet program are the same as detailed in 

Appendix 7 of Bulletin 17B. The logarithmic means, logarithmic standard deviations, and station skew were computed 

using PEAKFQ for each of the five required peak records for 

each two-station adjustment. The value ‘b’ refers to the slope 

of the regression line computed between concurrent short- and 

long-record peak flows. This value was computed using the 

Program for Robust Regression (PROGRESS) (Rousseeuw 

and Leroy, 1987) with the re-weighted least median of squares 

method (Rousseeuw, 1984). The generalized skew values for 

the north coast were taken from a map developed by the USGS 

of median skew values for six hydrologic regions in California 

(Richard M. Bloyd, U.S. Geological Survey, written commun., 

1979). Values for generalized skew in the north coast region 

were either –0.2 (north of San Francisco Bay) or –0.5 (San 

Francisco Bay and south).

of the plot of the annual peaks. Figure 8 shows an example 

of graphical determination of a low-outlier threshold. Lowoutlier threshold analysis was performed for each of the 30 

study stations used for flood-frequency analysis (and for each 

long-term index station for the methods described in following sections). If a low-outlier threshold was determined, this 

value was entered into the input file for subsequent PEAKFQ 

computations. Of the 30 study stations, 18 stations were determined to have low-outlier thresholds.
16 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Table 7. Required input parameters for two-station adjustment.

Parameter Description

N1 Number of years of concurrent flow between short- and long-term stations.

N2 Number of years of flows observed at long-record station for nonconcurrent period.

N3 Number of years of flows at short-record station.

Sx1 Standard deviation, log10 of flows at long-record station, for concurrent period.

Sx2 Standard deviation, log10 of flows at long-record station, for nonconcurrent period.

Sy1 Standard deviation, log10 of flows, at short-record station, for concurrent period.

Sy3 Standard deviation, log10 of flows, at short-record station, for nonconcurrent period.

X1 Mean, log10 of flows, at long-record station, for concurrent period.

X2 Mean, log10 of flows, at long-record station, for nonconcurrent period.

X3 Mean, log10 of flows, at long-record station, for entire period of record.

Y1 Mean, log10 of flows, at short-record station, for concurrent period.

Y3 Mean, log10 of flows, at short-record station, for entire period of record.

b Regression coefficient (slope) from robust regression long- versus short-record flows.

Gs Station skew, log10 of flows, computed from entire short-record period of record.

G Generalized skew, from map.

a threshold value (high-outlier threshold). A peak that occurs 

outside of the systematic gaging record is defined as a historic 

peak, and is flagged as such in the USGS annual peak-flow 

(highest peak occurring each year) dataset, or peak-flow file. 

Peaks that occur within the systematic gaging record are 

treated as a random sample of events, as per the fundamental 

assumptions of flood-frequency analysis. Peaks outside of the 

systematic gaging record are not considered to be random. If 

any historic peaks are greater in magnitude than the high-outlier threshold and a historic period is defined, then those peaks 

are considered to be the only peaks that exceed the threshold 

during the historic period. However, if no historic period is 

defined, or if any historic peaks are less in magnitude than the 

high-outlier threshold, those peaks are dropped from the floodfrequency calculations in PEAKFQ. 

For two-station comparisons, all five required peak 

records received historical analysis. Historical analysis was 

performed using a spreadsheet program previously developed 

and used by the USGS California District. Many gaging stations, including the long-record stations used for two-station 

comparison, have periods of record that are not representative of long-term conditions. Long-term stations were used to 

determine the high-outlier threshold and historic periods for 

short- and long-record stations. This process involves plotting 

concurrent annual peak-flow records from long-term index 

stations against the peak-flow record of the study station. Six 

index stations were chosen for peak comparison with each 

study station. The Line of Organic Correlation (LOC) (also 

known as MOVE-1) regression technique was used to adjust 

the index-station peak record to study-station peak magnitudes. The LOC regression technique was selected over OLS 

due to its usefulness over a large range of values. For LOC, a 

high-outlier threshold value is determined such that no peaks 

outside the systematic record exceed the threshold for the 

period of time specified. The resulting plot of adjusted multiple-index-station and station-of-interest peak flows versus 

time was used to determine appropriate high-outlier thresholds 

and historic periods, as shown in figure 9.

If two-station analysis was not appropriate or possible 

at a given study station (owing to above criteria for 

appropriateness), historical analysis was used as the final 

adjustment for flood frequency at that study station. A total 

of five study stations not suitable for two-station analysis 

received only historical analysis. Two stations were not 

suitable for historic adjustment due to either poor index-station 

relationships or gaps in the annual peak-flow record that 
Figure 9. Graphical determination of high-outlier threshold and historic period for flood-frequency analysis.

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Comparison Between SWRCB Estimated Flow Statistics and USGS Flow Statistics 17

Comparison Between SWRCB 

Estimated Flow Statistics and USGS 

Flow Statistics

Three comparative statistics (relative bias, relative standard error, and percent difference) were computed between 

SWRCB streamflow-statistic estimates and USGS streamflow 

statistics, or multi-station averages for a given statistic. All 

three statistics are expressed as percentages. Bias is a measure of the average difference between two data sets, while 

standard error describes the error of the fit of the two data sets. 

Bias is defined as the systematic error that is manifested as a 

consistent positive or negative deviation from the known or 

true value. Bias is a measure of precision, and standard error 

and percent difference are measures of accuracy. The bias and 

standard errors are expressed in relative form because data 

varies over orders of magnitude and the relative forms of these 

statistics are less affected by over-weighting of a relatively few 

large values. Percent difference (relative error) is the measured 

percentage difference between estimated and known or true 

values. Standard error is an estimate of the population error, 

while percent difference (relative error) is simply the error 

between estimated and known or true values. Computations 

for relative bias and percent difference are similar in form, but 

relative bias can be computed over a range of estimates while 

percent difference can be computed for individual estimates 

or for the averages of ranges of estimates. For example, relative bias was used for comparison of December 15 to March 

31 mean daily flows, while percent difference was used for 

comparison of the average December 15 to March 31 mean 

missed important regional flood events. Of these two stations, 

station 11481500 did receive two-station adjustment. This 

left only station 11180500 that received no frequency curve 

adjustment aside from low-outlier threshold determination. 

Table 8 summarizes the flood-frequency methods used 

for each of the 30 study stations that were used for floodfrequency analysis. If two-station analysis was done for a 

particular study station, the index station that was used is 

identified in table 8. Table 8 also lists the number of years of 

record of annual peak flows for each study station.
18 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Table 8. Summary of flood-frequency methods applied and years 

of annual peak-flow record at 30 study stations with flood-frequency analysis.

[See fig. 4 for station locations]

Station 

number

Two-station 

adjustment 

(index 

station)

Historic 

adjustment

Lowoutlier 

threshold

Number 

of years 

of annual 

peak flows

11162540 11162500 X X 13

11162600 11182500 X -- 11

11172100 11176000 X X 27

11180500 -- -- X 45

11182500 -- X X 48

11183700 11160500 X -- 15

11449500 -- X X 54

11451100 11456000 X X 29

11453200 11456000 X X 15

11458200 11456000 X X 15

11460100 11182500 X X 18

11460800 -- X X 20

11463900 11453500 X X 20

11464860 11456000 X X 10

11465150 11456000 X -- 12

11465800 11456000 X -- 11

11467600 11468000 X X 26

11468070 11468000 X -- 12

11473600 11476500 X -- 12

11475560 11477000 X X 34

11476600 11477000 X X 40

11477700 11477000 X -- 12

11480000 -- X X 19

11480390 11478500 X -- 20

11481200 11477000 X -- 45

11481500 11532500 -- X 29

11482125 11522500 X -- 12

11482468 11532500 X -- 13

11529800 11532500 X -- 15

11533000 -- X X 12

the relative standard error is computed as:

SWRCB Annual and Seasonal Runoff and 

February Median Flow-Statistics Estimates 

versus USGS Statistics

The computed average relative biases and relative standard errors between SWRCB runoff and February median 

flow estimates and USGS flow statistics are tabulated in table 

9. Tables 10 and 11 list the computed percent differences 

between SWRCB estimated streamflow statistics and USGS 

streamflow statistics for all 40 stations, including summary 

statistics, for rain-based (table 10) and flow-based (table 11) 

estimates. Plots of SWRCB estimates of annual and seasonal 

runoff and February median flow statistics versus USGS 

statistics are shown in figures 10 to 16. Percent differences 

were scattered across the north coast region, but mean percent 

differences for each recurrence interval were similar in magnitude to relative biases. 

Annual and Seasonal Runoff and February 

Median Flow Statistics

The mean annual runoffs, mean wet season (October 

1 to March 31) runoffs, mean winter season (December 15 

to March 31) runoffs, and February median flow estimated 

by the SWRCB were compared against USGS calculated 

statistics. SWRCB estimates of these statistics were plotted 

against USGS statistics for an overall qualitative evaluation of 

SWRCB results and to help detect trends in results. Relative 

biases and relative standard errors for each statistic (lumpedstation) and percent differences for each station (per statistic) 

were computed for comparison between SWRCB peak-flow 

estimates and USGS peak-flow statistics. Percent differences between SWRCB and USGS estimates were mapped 

to determine whether or not SWRCB estimation errors were 

associated with geographic locations. Percent differences were 

also plotted against basin characteristics (drainage-basin area, 

station altitude, mean annual precipitation, 2-year/24-hour 

rainfall intensity, mean annual Class A pan evaporation, mean 

channel slope, channel length, altitude index, and distance 

to ocean) in order to test for estimation errors resulting from 

basin attributes. 

daily flows. Computed relative bias and average percent difference usually are similar in magnitude. However, for mean 

daily flow estimates, when flow can be estimated as zero, 

relative bias and percent difference can vary from one another. 

In the following equations, QSWRCB refers to a given SWRCB 

estimate of a streamflow statistic or multi-station average of 

estimates and QUSGS refers to the USGS streamflow statistic or 

multi-station average of statistics. In this analysis, relative bias 

is computed as

R.bias(%) = 100 (7)

QSWRCB QUSGS –

QUSGS � -----------------------------------------

n – 1 -------------------------------------------------

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Std.error(%) 100 (8)

QSWRCB QUSGS –

QUSGS

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n – 1 = -------------------------------------------------------

%.difference 100 (9) QSWRCB QUSGS –

QUSGS

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and the percent difference (relative error) is computed as:
Table 9. Computed errors between State Water Resources Control Board and U.S. Geological Survey annual and seasonal runoffs and 

February median flows.

[N/A, not applicable]

Flow statistic

Rain-based Flow-based

Relative bias

(percent)

Standard error

(percent)

Relative bias

(percent)

Standard error

(percent)

Annual flow -6.4 46.8 6.6 42.1

Oct. 1- March 31 flow -4.5 46.7 2.0 41.4

Dec. 15- March 31 flow -24.3 44.1 0.4 39.9

February median flow N/A1 N/A1 -0.5 50.3 1

The State Water Resources Control Board uses only flow-based methods for this statistic.

Table 10. Percent differences between State Water Resources Control Board rain-based flow-statistic estimates and U.S. Geological 

Survey flow statistics at 40 study stations. 

[See fig. 4 for station locations]

Station Annual runoff Oct. 1 – March 31 runoff Dec. 15 – March 31 runoff

11162540 -1.1 4.0 -17.3

11162600 -25.1 -13.0 -28.5

11172100 -51.5 -50.4 -62.6

11180500 97.8 96.8 46.8

11182500 16.8 23.8 -4.7

11183700 140.5 159.7 104.3

11449500 -44.9 -42.8 -54.9

11451100 -44.9 -43.6 -52.6

11453200 -37.9 -38.8 -51.1

11458200 12.6 9.7 -16.0

11460100 -11.1 -13.4 -29.9

11460800 -6.9 -27.4 -51.5

11460920 59.6 51.1 9.5

11463900 -8.1 -7.1 -27.0

11464860 -25.1 -22.8 -36.3

11465150 -4.9 -9.4 -26.0

11465800 -7.3 -4.7 -23.8

11467600 -45.7 -43.4 -55.3

11467850 108.8 95.6 46.1

11468070 9.9 11.4 -10.7

11468540 42.9 22.6 -15.0

11469500 -32.4 -29.6 -41.3

11471800 -24.4 -30.7 -47.8

11473600 62.3 37.8 -1.1

11474781 -1.6 -0.1 -26.6

11475560 -18.5 -14.7 -33.3

11475940 -20.5 -18.7 -34.3

11476600 -53.0 -53.6 -61.8

11477700 -48.1 -45.6 -54.6

11480000 -14.6 -8.4 -24.7

11480390 -4.6 -7.4 -26.5

11481200 -36.1 -36.5 -44.9

11481500 -37.0 -34.6 -45.5

11482125 -43.7 -37.8 -45.7

11482468 -12.5 -13.6 -29.1

11522200 -12.3 28.9 9.8

11522260 -16.3 17.6 1.9

11529800 13.8 43.4 56.0

11532620 -91.7 -92.1 -93.7

11533000 -34.3 -36.3 -49.5

Maximum 140.5 159.7 104.3

Minimum -91.7 -92.1 -93.7

Median -13.5 -13.2 -28.8

Number of stations within +/- 25 percent 19 18 11

Number of stations within +/- 10 percent 8 8 5

Comparison Between SWRCB Estimated Flow Statistics and USGS Flow Statistics 19
20 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Table 11. Percent differences between State Water Resources Control Board flow-based flow-statistic estimates and U.S. Geological 

Survey flow statistics at 40 study stations.

[See fig. 4 for station locations]

Station Annual runoff Oct. 1 – March 31 runoff Dec. 15 – March 31 runoff February median runoff

11162540 -36.7 -37.3 -37.1 -51.8

11162600 -56.5 -51.1 -47.2 -62.3

11172100 -65.5 -66.3 -67.6 -88.4

11180500 -51.4 -52.6 -53.6 -86.5

11182500 -4.2 -6.5 -13.0 -48.0

11183700 117.3 117.4 105.7 55.2

11449500 -4.2 1.2 2.4 -39.3

11451100 -34.5 -77.3 -76.8 -94.7

11453200 13.6 8.7 8.2 8.3

11458200 12.5 5.4 6.1 58.4

11460100 96.6 97.9 103.5 75.0

11460800 64.6 33.3 13.3 12.3

11460920 25.6 23.8 16.7 16.7

11463900 -19.7 -18.4 -23.9 -46.3

11464860 2.8 7.5 6.8 21.4

11465150 9.4 5.7 4.2 31.2

11465800 1.5 6.4 2.7 6.3

11467600 -43.9 -40.9 -39.2 -45.7

11467850 5.6 -6.9 -9.3 170.6

11468070 21.3 22.2 23.4 8.4

11468540 73.9 49.8 36.3 39.6

11469500 3.7 5.8 7.0 -1.6

11471800 -26.6 -31.9 -36.2 -29.2

11473600 85.3 61.0 52.5 26.9

11474781 29.3 26.0 31.2 21.7

11475560 -2.2 -0.3 -0.3 -22.7

11475940 17.4 17.5 18.0 16.1

11476600 -4.3 -5.5 -4.1 -19.3

11477700 10.8 11.9 9.9 5.3

11480000 21.1 26.1 24.1 34.5

11480390 41.3 33.6 22.2 21.9

11481200 0.3 -2.2 -5.3 12.5

11481500 -15.8 -13.2 -19.8 -22.2

11482125 -5.7 2.4 10.9 3.7

11482468 14.1 10.6 12.6 20.7

11522200 36.7 52.9 58.7 48.5

11522260 -3.8 -37.4 -30.0 -9.8

11529800 -7.8 -10.7 -6.3 11.9

11532620 -79.2 -82.9 -82.3 -80.8

11533000 13.7 -9.0 -7.4 2.6

Maximum 117.3 117.4 105.7 170.6

Minimum -79.2 -82.9 -82.3 -94.7

Median 3.3 3.9 3.4 7.3

Number of stations within +/- 25 percent 23 22 25 20

Number of stations within +/- 10 percent 13 14 14 8
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Figure 10. SWRCB rain-based annual runoff estimates versus 

USGS annual runoffs for all 40 study stations.

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Figure 11. SWRCB rain-based October 1 to March 31 runoff estimates versus USGS October 1 to March 31 runoffs for all 40 study 

stations.

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Figure 12. SWRCB rain-based December 15 to March 31 runoff 

estimates versus USGS December 15 to March 31 runoffs for all 40 

study stations.

Comparison Between SWRCB Estimated Flow Statistics and USGS Flow Statistics 21

Rain-based estimates generally were biased low (ranging from -4.5 percent to -24.3 percent), with standard error 

bounds ranging from 44.1 percent to 46.8 percent. Flow-based 

estimates generally were biased slightly high for annual and 

seasonal runoffs (ranging from 0.4 percent to 6.6 percent), 

with standard error bounds ranging from 39.9 percent to 42.1 

percent. For the February median flow estimates, notable scatter in errors was apparent, but relative bias was -0.5 percent 

with a standard error bound of 50.3 percent. Thus, SWRCB 

rain-based estimates of annual and seasonal runoff totals were 

biased low with standard errors of estimation of about 45 

percent. SWRCB flow-based estimates of annual and seasonal 

runoffs were biased slightly high with standard errors of estimation of about 40 percent. February median flow estimates 

were biased slightly low, but with notable scatter throughout 

the north coast region, and with standard errors of estimate of 

about 50 percent. Therefore, flow-based estimation methods 

performed better than rain-based methods in the north coast 

region, but either method is subject to large standard error. No 

geographic trends for estimation errors were apparent with any 

of the annual and seasonal runoff and February median flow 

statistics, as the errors appeared randomly distributed across 

the north coast region when mapped. 
22 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

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Figure 13. SWRCB flow-based annual runoff estimates versus 

USGS annual runoffs for all 40 study stations.

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Figure 14. SWRCB flow-based October 1 to March 31 runoff estimates versus USGS October 1 to March 31 runoffs for all 40 study 

stations.

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Figure 15. SWRCB flow-based December 15 to March 31 runoff 

estimates versus USGS December 15 to March 31 runoffs for all 40 

study stations.

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Figure 16. SWRCB flow-based February median flow estimates 

versus USGS February median flows for all 40 study stations.
SWRCB Peak-flow Estimates vs. USGS Peak 

Flows

The computed average relative biases and relative 

standard errors between SWRCB’s peak-flow estimates and 

USGS’s peak-flow statistics are tabulated in table 12. The 

computed percent differences between SWRCB estimates and 

USGS statistics for each of the 30 stations used for flood-frequency analysis are tabulated in table 13 along with summary 

statistics. Plots of SWRCB peak-flow estimates versus USGS 

peak-flow statistics are shown in figures 17 to 22. Percent 

differences had a wide range for study sites in the north coast 

region. Computed mean percent differences for each recurrence interval were similar in magnitude to computed relative 

biases. 

SWRCB peak-flow estimates were biased low for 2-, 5-, 

10-, 25-, 50-, and 100-year peak-flow estimates. However, 

negative relative bias was strongest for 2-year estimates and 

weakest for 100-year estimates. This is also indicated in the 

plots in figures 17 to 22. A reasonable explanation for this 

is that the USGS flood-frequency regional regression equations (Waananen and Crippen, 1977) are lacking the last two 

decades of peak-flow records since they were developed. 

Regionally, the largest floods were the 1956 and 1964 floods, 

and these were incorporated in the USGS equations; therefore, 

50- and 100-year estimates may be more accurate. However, because more than two decades of smaller floods have 

occurred, the lower recurrence interval floods may be subject 

to the greatest error as the USGS equations become further 

out of date. Relative standard errors were fairly similar for 

all recurrence intervals, and ranged from 46.3 percent to 55.3 

percent, and were similar to reported values for the USGS 

peak-flow equations (table 6). Thus, SWRCB estimates, in 

general, for 2-, 5-, 10-, 25-, 50-, and 100-year peak flows in 

the north coast region tended to be underestimated and subject 

to errors averaging about 50 percent. Mean percent differences 

for the 2-, 5-, 10-, 25-, 50-, and 100-year recurrence intervals 

were plotted on maps of the north coast region in order to 

Table 12. Average computed errors between State Water 

Resources Control Board and U.S. Geological Survey peak flows.

Recurrence 

interval 

(years)

Average relative 

bias 

(percent)

Average relative standard 

error 

(percent)

2 -24.3 55.3

5 -23.9 49.5

10 -19.0 47.7

25 -16.0 46.3

50 -8.5 47.3

100 -5.7 48.6

Comparison Between SWRCB Estimated Flow Statistics and USGS Flow Statistics 23

Peak-Flow Statistics

Peak flows at the 2-, 5-, 10-, 25-, 50-, and 100-year 

recurrence intervals estimated by the SWRCB were compared 

against the USGS peak-flow statistics determined using floodfrequency analysis. SWRCB peak-flow estimates were plotted 

against USGS peak-flow statistics for an overall qualitative 

evaluation of SWRCB results. Relative biases and relative 

standard errors for each statistic (lumped-station) and percent 

differences for each station (per statistic) were computed for 

comparison between SWRCB peak-flow estimates and USGS 

peak-flow statistics. Percent differences between SWRCB and 

USGS estimates were mapped to determine whether or not 

there was geographic bias and error associated with SWRCB 

methods. Percent differences were also plotted against basin 

characteristics (drainage basin area, station altitude, mean 

annual precipitation, 2-year/24-hour rainfall intensity, mean 

annual Class A pan evaporation, mean channel slope, channel 

length, altitude index, and distance to ocean) in order to detect 

error or bias throughout the north coast region. 

Annual and Seasonal Runoff and February 

Median Flow Estimates: Station Percent 

Differences versus Basin Characteristics

Computed station percent differences for annual and seasonal runoffs and February median flows were plotted against 

station basin characteristics (drainage-basin area, station 

altitude, mean annual precipitation, 2-year/24-hour rainfall 

intensity, mean annual Class A pan evaporation, mean channel 

slope, channel length, altitude index, and distance to ocean) 

in order to qualitatively determine error correlation related 

to basin characteristics. Correlation tests (Kendall τ correlation test, at 0.05 significance) also were calculated between 

station percent differences for each statistic of interest and 

stations’ basin characteristics to quantitatively determine if 

errors are correlated with basin characteristics. If a correlation 

coefficient signifies a trend, a scatter plot (error versus basin 

characteristic) should also confirm the correlation (Helsel and 

Hirsch, 1993). Therefore, Kendall τ correlation test results 

that signified a trend were disregarded if the correlation was 

not apparent in plotting. No significant correlations between 

estimation errors and basin characteristics could be identified 

from these analyses. Thus, none of the basin characteristics 

available to this study have an effect upon errors in estimation 

of annual and seasonal runoffs or February median flows.
24 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Table 13. Percent differences between State Water Resources Control Board peak-flow estimates and U.S. Geological Survey peakflow statistics at 30 study stations used for flood-frequency analysis.

[See fig. 4 for station locations]

Station Recurrence interval (years)

2 5 10 25 50 100

11162540 -19.7 23.7 49.3 78.7 103.4 124.1

11162600 20.2 39.9 46.6 49.6 51.8 53.4

11172100 -94.0 -89.7 -86.5 -82.7 -79.6 -76.7

11180500 -65.7 -61.1 -56.5 -50.5 -44.3 -38.8

11182500 -86.7 -78.3 -72.0 -64.1 -57.3 -50.9

11183700 -59.7 -45.6 -35.3 -23.9 -14.6 -4.6

11449500 -70.8 -67.2 -63.0 -59.1 -53.1 -49.6

11451100 -41.6 -50.1 -50.9 -53.0 -50.6 -50.9

11453200 -68.1 -66.2 -62.3 -59.0 -48.5 -50.9

11458200 -56.8 -41.9 -29.3 -17.2 -4.5 2.7

11460100 -24.5 -33.5 -33.0 -35.0 -33.0 -34.6

11460800 -96.0 -89.4 -82.9 -72.7 -62.2 -51.5

11463900 -69.9 -62.8 -55.5 -47.6 -36.4 -28.5

11464860 -58.8 -53.0 -45.8 -38.9 -28.4 -22.1

11465150 -23.2 -32.8 -33.8 -37.8 -36.8 -39.4

11465800 -35.5 -40.5 -39.8 -41.6 -39.8 -41.3

11467600 -59.8 -60.3 -58.0 -56.9 -52.9 -51.6

11468070 -0.1 -14.9 -18.1 -25.2 -25.5 -29.7

11473600 -22.1 -15.1 -8.3 -6.5 0.2 -0.2

11475560 20.0 1.7 -0.8 -8.8 -7.3 -12.0

11476600 -9.4 -19.0 -18.4 -21.0 -17.4 -18.6

11477700 -55.2 -43.4 -30.7 -16.7 3.2 17.9

11480000 -23.9 -24.7 -21.4 -22.5 -19.3 -21.5

11480390 -23.8 -11.0 3.9 18.6 43.0 59.3

11481200 -24.3 -25.3 -20.7 -18.9 -11.9 -10.2

11481500 5.5 17.0 29.5 37.3 54.5 61.2

11482125 115.4 69.9 64.1 52.7 56.1 50.6

11482468 70.7 48.5 47.8 39.5 41.5 35.1

11529800 85.1 82.4 92.5 92.7 110.7 113.3

11533000 19.8 1.8 0.7 -6.0 -6.0 -11.5

Maximum 115.4 82.4 92.5 92.7 110.7 124.1

Minimum -96.0 -89.7 -86.5 -82.7 -79.6 -76.7

Median -24.4 -33.1 -30.0 -23.2 -18.4 -20.0

Number of stations within 

+/- 25 percent

13 9 8 10 9 10

Number of stations within 

+/- 10 percent

3 2 4 3 5 3

Peak-flow Estimates: Station Percent 

Differences versus Basin Characteristics

Computed station percent differences for 2-, 5-, 10-, 

25-, 50-, and 100-year peak flows for the 30 stations used for 

flood-frequency analysis were plotted against basin characteristics for each of these stations in order to qualitatively determine error correlation related to basin characteristics. Correlation tests (Kendall τ correlation test, at 0.05 significance) also 

were run between station percent differences for each peakflow statistic and stations’ basin characteristics to quantitatively determine if errors are correlated with basin characteristics. No significant correlations between estimation errors and 

basin characteristics could be identified from these analyses. 

Thus, none of the basin attributes examined in this study have 

an important effect upon peak-flow estimation errors. 

detect whether or not there was geographic bias with SWRCB 

estimation methods. Magnitudes of percent differences were 

randomly distributed across the north coast region, and no 

geographic bias was detected.
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Figure 17. SWRCB estimated 2-year peak flows versus USGS 

2-year peak-flow statistics.

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Figure 18. SWRCB estimated 5-year peak flows versus USGS 

5-year peak-flow statistics.

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Figure 19. SWRCB estimated 10-year peak flows versus USGS 

10-year peak-flow statistics.

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Figure 20. SWRCB estimated 25-year peak flows versus USGS 

25-year peak-flow statistics.

Comparison Between SWRCB Estimated Flow Statistics and USGS Flow Statistics 25
26 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

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Figure 21. SWRCB estimated 50-year peak flows versus USGS 

50-year peak-flow statistics.

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Q100

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Figure 22. SWRCB estimated 100-year peak flows versus USGS 

100-year peak-flow statistics.

SWRCB Mean-Daily-Flow Estimates versus 

USGS Published Mean Daily Flows

Appendix 2 contains hydrographs of combined SWRCB 

and USGS December 15 to March 31 mean daily flow for 

both 25- and 50-percentile years, for each station that had 

estimates provided by the SWRCB. Inspection of the December 15 to March 31 mean-daily-flow hydrographs provided 

the following general qualitative information about SWRCB 

estimation techniques. For flow-based estimates, the SWRCB 

mean-daily-flow hydrograph generally followed the trend of 

December 15 to March 31 Mean Daily Flows for 

25- and 50-Percentile Years

December 15 to March 31 rain-based and flow-based 

mean daily flows for 25- and 50-percentile years for all stations with estimates provided by the SWRCB were compared 

with USGS published mean daily flows. The SWRCB was not 

able to provide mean-daily-flow estimates for all 40 study stations owing to the unavailability of nearby concurrent raingage 

or streamflow gage data when restricted to the study-station 

period of record. Table 14 lists the water year of the December 

15 to March 31 mean-daily-flow estimates provided by the 

SWRCB for 25- and 50-percentile rain- and flow-based estimates. For some stations no nearby raingage or streamgage 

data were available, and for some no concurrent study-station 

data were available. For both 25- and 50-percentile rain-based 

methods, a total of 32 stations had estimates provided by the 

SWRCB that were comparable with USGS streamflow data. 

For both 25- and 50-percentile flow-based methods, a total 

of 34 stations had estimates provided by the SWRCB that 

were comparable with USGS streamflow data. Hydrographs 

(plotting SWRCB rain- and flow-based estimates and USGS 

published data) of 25- and 50-percentile year December 15 to 

March 31 mean daily flows were plotted for each station with 

estimates provided by the SWRCB. 

For each station with estimates provided by the SWRCB, 

relative biases, relative standard errors, and percent differences were computed for both rain- and flow-based 25- and 

50-percentile years’ mean daily flows. Percent differences for 

each station for the average mean daily flow for the period 

of interest were calculated between SWRCB estimates and 

USGS published data. The computed relative biases, relative 

standard errors, and percent differences for each station were 

mapped in order to determine whether or not there was any 

geographic bias and error associated with SWRCB estimates. 

The computed relative standard errors from all stations’ 

rain- and flow-based estimates, for both 25- and 50-percentile 

years, were plotted versus the various basin characteristics in 

order to qualitatively determine correlation between estimate 

errors and basin attributes. Kendall τ correlation tests, at 0.05 

significance, were also run between standard errors and basin 

characteristics in order to quantitatively verify correlation 

between estimation error and basin characteristics. 
Table 14. Water year for 25- and 50-percentile rain- and flow-based December 15 to March 31 mean-daily-flow estimates.

[See fig. 4 for station locations. POR, period of record]

Station

25-percentile 50-percentile

Rain-based Flow-based Rain-based Flow-based

11162540 1964 1964 1971 1971

11162600 1968 1968 1967 1967

11172100 1972 1972 1970 1970

11180500 1990 1990 1971 1971

11182500 1988 1988 1985 1985

11183700 1976 1976 1975 1975

11449500 1959 1959 1971 1971

11451100 1985 1985 1989 1989

11453200 1972 1972 1971 1971

11458200 1959 1959 1962 1962

11460100 Outside POR Outside POR Outside POR Outside POR

11460800 1972 No Data 1970 No Data

11460920 1972 1972 1971 1971

11463900 1968 1968 1965 1965

11464860 1979 1979 1975 1975

11465150 1979 1979 Outside POR Outside POR

11465800 1961 1961 1967 1967

11467600 1979 1979 1965 1965

11467850 Outside POR Outside POR 1967 1967

11468070 1962 1962 1965 1965

11468540 1968 1968 1965 1965

11469500 1957 1957 Outside POR Outside POR

11471800 1964 1964 1970 1970

11473600 1960 1960 1969 1969

11474781 No Data 1990 No Data 1995

11475560 1970 1970 1968 1968

11475940 Outside POR Outside POR 1970 1970

11476600 1964 1964 1961 1961

11477700 1962 1962 1963 1963

11480000 1962 1962 1961 1961

11480390 1985 1985 1984 1984

11481200 1962 1962 1961 1961

11481500 No Data 1987 No Data 1984

11482125 1985 1985 Outside POR Outside POR

11482468 1985 1985 1979 1979

11522200 1962 1962 1961 1961

Comparison Between SWRCB Estimated Flow Statistics and USGS Flow Statistics 27

the USGS hydrograph for most of the stations. Overall, the 

SWRC flow-based methods tended to underestimate mean 

daily flows, but results were variable by station. During lowerflow conditions there tended to be greater differences between 

SWRCB flow-based hydrographs and the USGS hydrographs. 

Overall, the SWRCB flow-based methods for estimating mean 

daily flows appeared viable, but subject to varying degrees 

of error. This may indicate the need for additional adjustment parameters beyond drainage basin area and precipitation 

ratios, in order to achieve greater accuracy with the flow-based 

method. For rain-based mean daily flows, the most important 

limitation with the rational method is that for days with no 

precipitation, streamflow also was calculated as zero. Thus for 

each day lacking rainfall, the rational method cannot be used 

to compute streamflow. During low-flow periods with low 

antecedent moisture conditions, SWRCB rain-based estimates 

were generally tremendously overestimated. For back-to-back 

storms, when antecedent moisture conditions are higher, the 

SWRCB rain-based estimates were generally closer to USGS 

streamflow data, but estimates were variably high or low with 

little consistency. Temporal changes in antecedent moisture 

conditions appeared to invalidate the use of a single value for 

the ‘C’ parameter in the rational equation. Overall, SWRCB 

rain-based methods for estimating mean daily flow did not 

appear to be a viable method for estimating mean-daily-flow 

hydrographs.

Tables 15 and 16 list (for 25- and 50-percentile years, 

respectively) the computed relative bias and relative standard 
28 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Table 15. Computed relative bias and standard error between State Water Resources Control Board estimates and U.S. Geological 

Survey published data for 25-percentile year, for each station.

[See fig. 4 for station locations. N/A, not applicable]

25-percentile year

Rain-based Flow-based

Relative bias 

(percent)

Standard error 

(percent)

Relative bias 

(percent)

Standard error 

(percent)

11162540 64.7 416.9 -38.4 45.9

11162600 34.3 350.1 -42.7 52.9

11172100 94.5 794.8 -12.9 276.7

11180500 9,038.7 62,365.4 552.2 2,940.6

11182500 290.6 1,357.4 151.4 191.9

11183700 1,131.3 5,294.7 894.7 1,043.5

11449500 -27.2 216.7 -50.1 61.8

11451100 -34.9 262.6 -67.3 76.3

11453200 -59.0 126.7 -12.8 33.7

11458200 1,167.4 7,770.1 72.4 110.1

11460100 N/A N/A N/A N/A

11460800 -71.6 128.7 N/A N/A

11460920 2.6 273.0 12.7 71.7

11463900 -26.2 211.2 -14.1 18.2

11464860 44.6 553.4 9.2 41.9

11465150 5.1 269.2 70.2 97.9

11465800 26.9 395.8 38.8 63.8

11467600 23.6 576.3 -44.9 46.4

11467850 N/A N/A N/A N/A

11468070 19.4 309.8 11.9 41.2

11468540 -16.6 180.7 55.7 68.7

11469500 -24.9 211.3 3.4 51.7

11471800 -16.1 172.1 -24.6 36.7

11473600 163.9 728.6 0.8 46.6

11474781 N/A N/A 4.2 35.0

11475560 93.6 378.8 -11.8 26.0

11475940 N/A N/A N/A N/A

11476600 -47.4 111.4 -16.4 29.2

11477700 -50.7 113.3 31.3 45.2

11480000 13.6 437.6 28.1 39.7

11480390 -16.3 257.3 70.8 91.6

11481200 -62.0 105.6 2.9 19.0

11481500 N/A N/A -2.3 21.5

11482125 -49.6 112.9 -12.1 26.0

11482468 0.6 241.6 50.6 62.7

11522200 154.2 554.7 77.0 83.8

11522260 N/A N/A N/A N/A

11529800 N/A N/A -5.1 17.2

11532620 -96.4 96.3 -83.3 83.1

11533000 N/A N/A N/A N/A

Maximum 9,038.7 62,365.4 894.7 2,940.6

Minimum -96.4 96.3 -83.3 17.2

Median 3.9 271.1 3.1 49.1
Table 16. Computed relative bias and standard error between State Water Resources Control Board estimates and U.S. Geological 

Survey published data for 50-percentile year, for each station.

[See fig. 4 for station locations. N/A, not applicable]

50-percentile year

Rain-based Flow-based

Relative bias 

(percent)

Standard error 

(percent)

Relative bias 

(percent)

Standard error 

(percent)

11162540 -10.7 190.4 -29.6 31.1

11162600 -66.7 124.4 -67.0 67.8

11172100 77.0 598.7 -48.6 123.1

11180500 74.0 621.5 -72.9 76.4

11182500 36.2 352.6 -1.6 41.5

11183700 326.0 1,270.3 207.6 318.2

11449500 -72.2 94.3 -30.1 47.3

11451100 18.6 256.1 -80.5 83.1

11453200 -79.9 100.3 27.8 41.2

11458200 29.0 519.2 11.7 32.2

11460100 N/A N/A N/A N/A

11460800 -74.9 112.2 N/A N/A

11460920 -52.2 132.8 -8.0 42.3

11463900 -40.1 171.1 -43.2 45.8

11464860 -36.8 198.8 15.8 36.3

11465150 N/A N/A N/A N/A

11465800 -62.3 126.5 -2.7 27.1

11467600 -57.8 124.5 -39.0 41.9

11467850 946.8 6,164.9 977.2 2,354.4

11468070 -18.8 217.3 9.2 44.7

11468540 -44.7 146.9 65.0 76.4

11469500 N/A N/A N/A N/A

11471800 -61.1 104.6 -20.2 26.2

11473600 -61.7 82.9 6.6 21.5

11474781 N/A N/A 50.3 73.5

11475560 112.8 491.9 -17.7 31.8

11475940 -53.2 109.5 32.8 66.9

11476600 -71.1 92.8 -19.6 38.2

11477700 -59.7 126.0 12.9 20.6

11480000 14.0 241.0 45.5 59.2

11480390 -43.5 179.9 40.1 49.2

11481200 -50.2 83.3 -2.2 19.0

11481500 N/A N/A -15.1 20.9

11482125 N/A N/A N/A N/A

11482468 -2.9 237.2 19.5 45.9

11522200 3.6 315.4 41.6 57.7

11522260 -7.3 124.7 -10.6 21.6

11529800 N/A N/A 4.6 21.2

11532620 -95.9 95.9 -83.0 82.7

11533000 N/A N/A N/A N/A

Maximum 946.8 6,164.9 977.2 2,354.4

Minimum -95.9 82.9 -83.0 19.0

Median -41.8 159.0 -1.9 43.5

Comparison Between SWRCB Estimated Flow Statistics and USGS Flow Statistics 29
30 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

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Figure 23. Rain-based dry (25 percent) year SWRCB average 

December 15 to March 31 mean daily flows versus USGS average 

December 15 to March 31 mean daily flows.

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Figure 24. Flow-based dry (25 percent) year SWRCB average 

December 15 to March 31 mean daily flows versus USGS average 

December 15 to March 31 mean daily flows.

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Figure 25. Rain-based median (50 percent) year SWRCB average 

December 15 to March 31 mean daily flows versus USGS average 

December 15 to March 31 mean daily flows.

Average December 15 to March 31 Mean-DailyFlow Comparisons

Computing the average December 15 to March 31 mean 

daily flow provided another useful comparison between 

SWRCB estimates and USGS published data. Figures 23 to 

26 show SWRCB average December 15 to March 31 mean 

daily flows versus USGS average December 15 to March 31 

mean daily flows for the 25- and 50-percentile years for both 

rain- and flow-based estimates. Percent differences between 

SWRCB estimates and USGS data were computed for average mean daily flow for each station’s 25- and 50-percentile 

rain- and flow-based estimates. Table 17 lists the computed 

percent difference between average December 15 to March 31 

error between SWRCB rain- and flow-based estimates and 

USGS published data for each station, and summary statistics. 

For individual stations, relative biases and relative standard 

errors for mean-daily-flow estimates were variable across 

the north coast region. In order to detect geographic effects 

on estimate error, relative bias and relative standard error for 

each study station were plotted on north coast region maps. 

Geographic effect upon estimation error was indeterminate for 

most of the north coast region. However, very large estimation 

errors were found at the four east San Francisco Bay stations 

(11183700, 11182500, 11180500, and 11172100) and at station 11458200 to the north of these stations. 
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Figure 26. Flow-based median (50 percent) year SWRCB average 

December 15 to March 31 mean daily flows versus USGS average 

December 15 to March 31 mean daily flows.

Comparison Between SWRCB Estimated Flow Statistics and USGS Flow Statistics 31

December 15 to March 31 Mean-Daily-Flow 

Estimates for 25- and 50-Percentile Years: 

Relative Standard Errors versus Basin 

Characteristics 

Relative standard errors for each station’s mean-dailyflow estimates were plotted versus basin characteristics in 

order to detect errors correlated to specific basin characteristics. These plots are shown in Appendix 3. Standard errors 

plotted versus both mean annual precipitation and 2-year/24-

hour rainfall intensity demonstrate a negative correlation 

for both 25-percentile rain- and flow-based estimates. For 

50-percentile rain- and flow-based estimates, mean annual precipitation, 2-year/24-hour rainfall intensity, and channel length 

demonstrate negative correlation with standard error. That is, 

standard errors tend to decrease for increasing mean annual 

precipitation, 2-year/24-hour rainfall intensity, and channel 

length (50-percentile estimates only). 

Kendall τ correlation tests, at 0.05 significance, also were 

run to quantitatively demonstrate any correlation between relative standard errors and specific basin characteristics. Results 

of the correlation tests between 25- and 50-percentile rain- and 

flow-based standard errors and basin characteristics are tabulated in table 18. If a correlation coefficient signifies a trend, 

a scatter plot (error versus basin characteristic) also should 

confirm the correlation (Helsel and Hirsch, 1993). Therefore, 

Kendall τ correlation test results that signified a trend were 

disregarded if the correlation was not apparent in plotting. 

In summary, the greatest relative biases and standard 

errors between the 25-percentile year SWRCB estimated 

mean daily flows and USGS actual mean daily flows were for 

stations with mean annual precipitation less than or equal to 

30 inches, and for estimated 2-year/24-hour rainfall intensity 

less than 3 inches. All of these stations are in the east San 

Francisco Bay area. For the 50-percentile year mean-dailyflow estimates, standard errors were various across the north 

coast region, but the east San Francisco Bay stations had 

large estimation errors for rain-based estimates. Mean annual 

precipitation and 2-year/24-hour rainfall intensity appeared to 

be the most important basin characteristics in correlation with 

estimation errors associated with 25- and 50-percentile year 

December 15 to March 31 mean-daily-flow estimates. 

mean daily flows for SWRCB rain- and flow-based estimates 

and USGS published data for each station, and summary 

statistics. For the 25-percentile year rain-based estimates, 25 

of the 32 stations had percent differences between SWRCB 

estimates and USGS data that were within (+/-) 25 percent and 

13 were within (+/-) 10 percent. For the 25-percentile flowbased estimates, 28 of the 34 percent differences were within 

(+/-) 25 percent and 24 were within (+/-) 10 percent. For the 

50-percentile rain-based estimates, 28 of the 32 percent differences were within (+/-) 25 percent and 10 were within (+/-) 

10 percent. For the 50-percentile flow-based estimates, 27 of 

the 34 percent differences were within (+/-) 25 percent and 25 

were within 10 percent. Therefore, both rain- and flow-based 

methods generally would be viable methods for estimating 

average December 15 to March 31 mean daily flows.
32 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

Table 17. Computed percent difference between December 15 to March 31 average mean daily flows for State Water Resources Control 

Board estimates and U.S. Geological Survey published data for each station.

[See fig. 4 for station locations]

Station

25-percentile 50-percentile

Rain-based 

(percent)

Flow-based

(percent)

Rain-based

(percent)

Flow-based

(percent)

11162540 31.21 -15.20 4.89 -11.24

11162600 24.02 -19.57 -23.41 -37.98

11172100 602.65 -114.66 -18.48 -47.19

11180500 -153.20 -66.78 22.09 -86.38

11182500 -1,096.75 -649.02 19.00 -8.34

11183700 -82.58 -59.07 -269.38 -177.52

11449500 -11.49 -2.20 -15.79 -0.07

11451100 -7.08 -35.59 -7.50 -64.03

11453200 -13.13 -8.78 -24.85 -0.50

11458200 27.08 8.73 -12.88 1.04

11460100 No Data No Data No Data No Data

11460800 -21.56 No Data -31.12 No Data

11460920 10.75 7.75 -8.36 -6.03

11463900 -5.06 -2.64 -12.29 -5.01

11464860 -2.88 2.82 -11.29 2.45

11465150 8.07 9.18 No Data No Data

11465800 3.41 10.70 -13.28 -2.45

11467600 -4.17 -8.50 -19.15 -5.87

11467850 No Data No Data 38.53 73.39

11468070 -2.75 1.92 -8.89 -2.06

11468540 -3.45 5.11 -15.83 11.20

11469500 -4.92 3.58 No Data No Data

11471800 -11.97 -8.46 -12.66 -5.46

11473600 8.29 7.44 -11.84 0.43

11474781 No Data -2.37 No Data 7.77

11475560 17.33 -1.35 23.24 -4.01

11475940 No Data No Data -8.32 4.72

11476600 -15.64 0.16 -19.92 -2.29

11477700 -8.43 6.72 -11.08 3.59

11480000 -11.25 6.55 -7.32 9.85

11480390 -2.82 9.49 -9.11 4.83

11481200 -12.26 1.03 -2.64 0.62

11481500 No Data 0.52 No Data -1.78

11482125 -16.37 -0.73 No Data No Data

11482468 -4.05 7.38 -11.59 2.32

11522200 14.22 12.27 -3.83 7.75

11522260 No Data No Data 3.43 -3.72

11529800 No Data -2.89 No Data 0.26

11532620 -50.92 -30.17 -47.73 -29.64

11533000 No Data No Data No Data No Data

Maximum 602.65 12.27 38.53 73.39

Minimum -1,096.75 -649.02 -269.38 -177.52

Median -4.55 -0.28 -11.44 -1.92
Table 18. Results of the 25- and 50-percentile year rain- and flow-based average December 15 to March 31 mean-daily-flow estimates’ 

relative standard errors versus basin characteristics’ Kendall τ correlation tests.

[Bold indicates significant correlation at α = 0.05]

Basin characteristic

25-percentile year 

Rain-based

25-percentile year 

Flow-based

50-percentile year 

Rain-based

50-percentile year 

Flow-based

Kendall τ p-value Kendall τ p-value Kendall τ p-value Kendall τ p-value

DA, drainage area (above 

gage)

-0.21 0.088 -0.14 0.25 -0.26 0.036 -0.14 0.24

A, station altitude 0.02 0.99 -0.02 0.84 0.01 0.91 -0.05 0.70

P, mean annual precipitation (1900-1960)-0.46 0.0002 -0.43 0.0003 -0.23 0.06 -0.21 0.08

I, 2-year/24-hour rainfall 

intensity 

-0.36 0.004 -0.33 0.0065 -0.30 0.016 -0.13 0.26

E, mean annual Class A 

pan evaporation

0.23 0.059 0.20 0.09 0.15 0.23 0.11 0.36

S, mean channel slope 

(determined between 

10% and 85% distances from gage to 

basin divide)

0.16 0.20 -0.12 0.32 0.27 0.031 0.02 0.84

L, channel length (between gage and basin 

divide)

-0.17 0.17 -0.07 0.54 -0.28 0.023 -0.21 0.08

H, altitude index (determined between 10% 

and 85% distances 

from gage to basin 

divide)

0.04 0.72 -0.16 0.19 0.09 0.45 -0.12 0.30

DO, distance from gage 

to ocean (mean of 

west-to-ocean and 

southwest-to-ocean 

distances)

0.18 0.14 0.10 0.38 0.12 0.35 -0.01 0.92

Summary and Conclusions 33

Summary and Conclusions

While no new streamflow-statistic estimation techniques 

were developed in this study, a thorough evaluation of the 

SWRCB’s estimation techniques has identified problems with 

currently used procedures. In order to properly allocate water 

rights, it is vital that the streamflow statistics used for such 

allocation are as accurate as possible and also are representative of long-term conditions. In general, the SWRCB’s flowbased methods had smaller errors for flow-statistic estimation 

than rain-based methods. This was most apparent in meandaily-flow estimation. Rain-based methods were universally 

unsuccessful in generating valid individual December 15 

to March 31 mean-daily-flow hydrographs. However, for 

estimating the overall average of the December 15 to March 

31 mean daily flow, both rain-based and flow-based methods 

performed well. For annual and seasonal runoffs, the flowbased methods performed better than the rain-based methods, 

but the errors between the two methods were not as large as 

for mean-daily-flow estimates. In general, both methods performed reasonably well, but with notable scattering in results 

across the north coast region. Rain-based methods for annual 

and seasonal runoff estimation were biased low with standard 

errors of estimation of about 45 percent. Flow-based methods 

for annual and seasonal runoff estimation were biased slightly 

high with standard errors of estimation of about 40 percent. 

The flow-based methods for estimating February median flow 

resulted in a greater range of values, but overall the estimates 

were slightly low with standard errors of estimation of about 

50 percent. 

The SWRCB used the USGS peak-flow equations 

(Waananen and Crippen, 1977) for estimating 2-, 5-, 10-, 25-, 

50-, and 100-year peak flows in the north coast region. Thus, 

this study provided an opportunity to evaluate the accuracy 

of the USGS regional peak-flow equations. It was found that 

errors were greatest with lower recurrence interval (2-, 5-, and 

10-year) peak flows and least with higher recurrence interval 

(25-, 50-, and 100-year) peak flows. Peak flows generally 
34 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

References

Bendient, P.B., and Huber, W.C., 1992, Hydrology and floodplain analysis: Addison-Wesley Publishing Company, 692 p.

Helsel, D.R., and Hirsch, R.M., 1993, Statistical methods in 

water resources: Elsevier Science, 522 p.

Rantz, S.E., 1969, Mean annual precipitation in the California 

Region: U.S. Geological Survey Open-File Map (reprinted 

1972, 1975).

Ries, K.G., and Friesz, P.J., 2000, Methods for estimating lowflow statistics for Massachusetts streams: U.S. Geological 

Survey Water-Resources Investigations Report 00-4135, 

42 p.

Ries, K.G., Steeves, P.A., Freeman, A., and Singh, R., 2000, 

Obtaining streamflow statistics for Massachusetts streams 

on the World Wide Web: U.S. Geological Survey Fact Sheet 

104-00, 4 p.

Recommendations for Future Studies

This study was designed as a three-phase study, under 

which the work described in this report was the first phase. 

This phase was designed to be an evaluation of current flowstatistic estimation techniques, and a lead-in to future phases 

that would provide improved estimation techniques. Phases 2 

and 3 were designed to produce improved estimation techniques in a format widely available to both the public and 

water resources agencies. Because of funding constrictions, 

phases 2 and 3 presently have been abandoned. However, 

future funding may allow for implementation of these phases. 

The second phase was designed to develop multiple 

regression equations for estimating streamflow statistics by 

using basin characteristics developed with Geographic Information Systems (GIS). The GIS application was intended to 

develop a more robust set of various basin characteristics, than 

are currently available, using various topographic GIS coverages and Digital Elevation Models (DEMs). The basin characteristics then could be combined with published flow data, 

using multiple regression techniques, to produce improved 

estimation equations. Included in this phase, the north coast 

regional flood-frequency equations (Waananen and Crippen, 

1977) would have been revised with updated peak-flow data 

and would have used the basin characteristics developed by 

GIS. The regression equations from phase 2 would be a valuable tool for the many agencies involved in water resources 

decision-making in the north coast region of California. Phase 

2 efforts also could be expanded to other regions in California 

if a more statewide approach were desired. 

The third phase was designed to use the USGS’s StreamStats software to couple the multiple regression streamflowestimating procedures from phase 2 with GIS coverages and 

software in a World Wide Web (Web) application (Ries and 

Friesz, 2000; Ries and others, 2000). StreamStats incorporates 

a map-based user interface for site selection, a database that 

provides streamflow statistics, and other information for datacollection stations, and a GIS program that measures physical 

characteristics of the drainage basins for ungaged sites and 

solves regression equations to estimate streamflow statistics 

for the sites. StreamStats users simply point and click on a 

map to get information for data-collection sites and ungaged 

sites. If phase-2 work were to be expanded into a statewide 

effort, the StreamStats Web application would be a valuable 

tool for use by both the general public and various water 

resources agencies in California. As future funding allows, 

implementation of phases 2 and 3 would provide valuable 

information and flow estimation techniques in a user-friendly 

format to a variety of interests in California.

were underestimated with the USGS equations, and standard 

errors were about 50 percent. The standard errors computed in 

this study are similar to the standard errors associated with the 

USGS peak-flow equations. Relative bias ranged from -24.3 

percent for 2-year peak flows to -5.7 percent for 100-year peak 

flows. The USGS equations likely are out of date, because 

they lack more than two decades of peak-flow data. Because 

the largest recorded floods are contained in the peak-flow data 

sets used to derive the USGS peak-flow equations, the lower 

recurrence interval peak-flow equations appear to be the most 

out of date. Revision of the USGS peak-flow equations with 

updated peak-flow data sets would be a valuable effort for the 

future. Nevertheless, the USGS peak-flow equations performed reasonably well in this study.

Little correlation was found between estimation errors 

and geographic location or various basin characteristics 

(drainage basin area, station altitude, mean annual precipitation, 2-year/24-hour rainfall intensity, mean annual Class A 

pan evaporation, mean channel slope, channel length, altitude 

index, and distance to ocean). For both rain- and flow-based 

annual and seasonal runoff estimates, February median flow 

estimates, and 2-, 5-, 10-, 25-, 50-, and 100-year peak-flow 

estimates, no important correlations were identified between 

estimation errors and geographic location or basin characteristics. For 25-percentile mean-daily-flow estimates, the 

greatest estimation errors were at stations with mean annual 

precipitation less than or equal to 30 inches, and estimated 

2-year/24-hour rainfall intensity less than 3 inches. All of 

these stations are in the east San Francisco Bay area. For 50-

percentile mean-daily-flow estimates, estimation errors varied 

more widely across the north coast region, but the east San 

Francisco Bay stations had larger estimation errors for rainbased estimates. Mean annual precipitation and 2-year/24-hour 

rainfall intensity appeared to be the most important basin 

characteristics in correlation with estimation errors associated 

with 25- and 50-percentile year December 15 to March 31 

mean-daily-flow estimates. 
References 35

Rousseeuw, P.J., 1984, Least median of squares regression: 

Journal of the American Statistical Association, vol. 79, 

p. 871-880.

Rousseeuw, P.J., and Leroy, A.M., 1987, Robust regression 

and outlier detection: John Wiley & Sons, 352 p.

Searcy, J.K., 1959, Flow-duration curves, Manual of Hydrology; Part 2—Low Flow Techniques: U.S. Geological 

Survey Water-Supply Paper 1542-A, 33 p.

Thomas, W.O., Lumb, A.M., Flynn, K.M., and Kirby, W.H., 

1998, Users manual for Program PEAKFQ, annual flood 

frequency analysis using Bulletin 17B guidelines: written 

communication, 89 p.

U.S. Interagency Committee on Water Data, 1982, Guidelines 

for determining flood flow frequency, Bulletin 17B of the 

Hydrology Subcommittee: U.S. Geological Survey, Office 

of Water Data Coordination, 183 p.

U.S. Weather Bureau, 1959, Evaporation maps for the United 

States: Technical Paper No. 40, 115 p.

U.S. Weather Bureau, 1961, Rainfall frequency atlas of the 

United States: Technical Paper No. 37, 13 p.

Waananen, A.O., and Crippen, J.R., 1977, Magnitude and 

frequency of floods in California: U.S. Geologcial Survey 

Water-Resources Investigations Report 77-21, 96 p.
36 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendixes

Appendixes 37
Appendix 1. Matrix of study station and index station pairings for both daily value regressions for streamflow statistic adjustment and 

two-station adjustment for flood-frequency analysis.

Study stations Regional index stations

Number Name

111605001116250011176000111764001118050011182100111825001144950011451500 *1145350011456000114610001146450011468000114685001146900011472200114739001147556011475800 *114765001147660011477000114785001148120011482500 **11521500115225001152870011532500

11162540 Butano C nr Pescadero D DP

11162600 Purisima C nr Half Moon Bay D D P

11172100 Up Penitencia C at San Jose DP D D

11180500 Dry C at Union City***

11182500 San Ramon C at San Ramon***

11183700 Little Pine C nr Alamo P D D

11449500 Kelsey C nr Kelseyville***

11451100 NF Cache C at Hough Spring nr 

Clearlake Oaks 

D P D

11453200 Dry C nr Middletown D P D

11458200 Redwood C nr Napa DP

11460100 Arroyo Corte Madera D Pres at 

Mill Valley  

P

11460800 Walker C nr Tomales-PreregulationD

11460920 Salmon C at Bodega@ D

11463900 Maacama C nr Kellogg DP D D

11464860 Warm Springs C nr Asti D DP D

11465150 Pena C nr Geyserville DP D

11465800 Santa Rosa C nr Santa Rosa D DP D

11467600 Garcia R nr Point Arena D D DP

11467850 Soda C Trib nr Boonville # D D

11468070 SF Big R nr Comptche D DP D

11468540 Pudding C nr Fort Bragg # D D

11469500 NF Mattole R at Petrolia # D

11471800 Tomki C nr Willits # D D

11473600 Short C nr Covelo D D D P

11474781 Combined flow of 11474750 + 

11474780 #

D D D D D

11475560 Elder C nr Branscomb** * P

11475940 EB SF Eel R nr Garberville # D D D D

11476600 Bull C nr Weott*** P

11477700 Little Van Duzen R nr 

Bridgeville

D D P D

11480000 Jacoby C nr Freshwater D D

11480390 Mad R abv Ruth Res nr 

Forest Glen

D P D

11481200 Little R nr Trinidad*** P

11481500 Redwood C nr Blue Lake**** P

11482125 Panther C nr Orick D D P

11482468 Little Lost Man C at Site No 2 

nr Orick

D D P

11522200 Elk C nr Happy Camp # D D

11522260 Ti C Nr Somes Bar # D

11529800 Willow C nr Willow C D D P

11532620 Mill C nr Crescent City # D D

11533000 Lopez C nr Smith R D D

D Index station used to improve daily-values flow statistics (may be several per study station).

P Index station used to improve flood-frequency statistics (one per study station).

* Trend in daily-values. Not suitable for use as index station for daily-value flow statistics adjustments.

** Trend in annual peak flows. Not suitable for use as index station for flood-frequency statistics adjustments.

*** Also used as an index station. Daily-values flow statistics computed directly from station data, without adjustment.

**** No suitable index station for daily-values flow statistics. Flow statistics computed directly from station data, without adjustment.

# Insufficient annual peak flow data. Flood-frequency statistics not determined.

@ Questionable peaks in record. Flood-frequency statistics not determined.

38 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2 39

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.

11162540

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11162600

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet pe second)

SWRCB.rain

SWRCB.flow

USGS
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11172100

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.001

0.01

0.1

1

10

100

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11180500

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.0001

0.001

0.01

0.1

1

10

100

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

0

40 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
11182500

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11183700

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.01

0.1

1

10

100

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

0

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

Appendix 2 41
11449500

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.01

0.1

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

0

11451100

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

42 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
11453200

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily fow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11458200

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.01

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

0

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

Appendix 2 43
11460800

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

USGS

11460920

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

44 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
11463900

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11464860

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

Appendix 2 45
11465150

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.01

0.1

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

0

11465800

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

46 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
11467600

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily fow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11468070

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2 47
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11468540

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11469500

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

48 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11471800

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11473600

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.01

0.1

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

0

Appendix 2 49
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

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50 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11476600

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11477700

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2 51
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11480000

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily fow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11480390

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

52 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11481200

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11481500

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.flow USGS

Appendix 2 53
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

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54 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11522200

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11529800

25% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.flow

USGS

Appendix 2 55
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

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11162540

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

56 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2 57

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11172100

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.01

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11162600

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11180500

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.01

0.1

1

10

100

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11182500

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

58 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
11183700

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.01

0.1

1

10

100

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11449500

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

0

Appendix 2 59
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11451100

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11453200

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

60 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11458200

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

0

11460800

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

USGS

Appendix 2 61
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11460920

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11463900

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

62 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11464860

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11465800

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2 63
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11467600

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

100000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11467850

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

0.0001

0.001

0.01

0.1

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

0

64 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11468070

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11468540

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2 65
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11471800

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cfubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11473600

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

66 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

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Appendix 2 67
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

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11476600

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

68 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
11477700

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11480000

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

Appendix 2 69
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11480390

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11481200

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

70 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11481500

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.flow

USGS

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Appendix 2 71
Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

11522200

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

11522260

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

1

10

100

1000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.rain

SWRCB.flow

USGS

72 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
11529800

50% Year 

Dec 15 to Mar 31 Mean Daily Flow

10

100

1000

10000

15-Dec 4-Jan 24-Jan 13-Feb 4-Mar 24-Mar

Date

Mean daily flow (cubic feet per second)

SWRCB.flow

USGS

Appendix 2. SWRCB and USGS hydrographs of mean daily flows for all stations with estimates provided by SWRCB.—Continued

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Appendix 2 73
Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 

15 to March 31 mean-daily-flow estimates.

25% Year Flow-based Daily Values 

Relative Standard Error vs. Station Altitude

10

100

1000

10000

0 500 1000 1500 2000 2500 3000

Station altitude (feet)

Relative standard error

25% Year Flow-based Daily Values 

Relative Standard Error vs. Drainage Area

10

100

1000

10000

0 20 40 60 80 100 120

Drainage area (square miles)

Relative standard error

74 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

25% Year Flow-based Daily Values 

Relative Standard Error vs. Distance to Ocean 

10

100

1000

10000

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00

Distance to ocean (miles)

Relative standard error

25% Year Flow-based Daily Values 

Relative Standard Error vs. Mean Annual Class A Pan Evaporation

10

100

1000

10000

30 35 40 45 50 55 60 65

 Mean annual class A pan evaporation (inches)

Relative standard error

Appendix 3 75
25% Year Flow-based Daily Values 

Relative Standard Error vs. Altitude Index

10

100

1000

10000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Altitude index (1000's of feet)

Relative standard error

25% Year Flow-based Daily Values 

Relative Standard Error vs. 2-year, 24-hour Rainfall Intensity

10

100

1000

10000

1.0 2.0 3.0 4.0 5.0 6.0 7.0

2-year, 24-hour rainfall intensity (inches)

Relative standard error 

Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

76 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
25% Year Flow-based Daily Values

Relative Standard Error vs. Stream Length between 10% and 85% Distances

0.1

1

10

100

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Stream length between 10% and 85% distances (miles)

Relative standard error

25% Year Flow-based Daily Values 

Relative Standard Error vs. Mean Annual Precipitation

10

100

1000

10000

0 20 40 60 80 100 120

Mean annual precipitation (inches)

Relative standard error

Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

Appendix 3 77
25% Year Flow-based Daily Values 

Relative Standard Error vs. Slope of Stream between 85% and 10% Distances

10

100

1000

10000

0 100 200 300 400 500 600 700 800 900 1000

Slope of stream (feet per mile)

Relative standard error 

25% Year Rain-based Daily Values 

Relative Standard Error vs. Station Altitude

10

100

1000

10000

100000

0 500 1000 1500 2000 2500 3000

Station altitude (feet)

Relative standard error

Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

78 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
25% Year Rain-based Daily Values 

Relative Standard Error vs. Drainage Area

10

100

1000

10000

100000

0 20 40 60 80 100 120

Drainage area (square miles)

Relative standard error

25% Year Rain-based Daily Values 

Relative Standard Error vs. Distance to Ocean 

10

100

1000

10000

100000

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00

Distance to ocean (miles)

Relative standard error

Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

Appendix 3 79
25% Year Rain-based Daily Values 

Relative Standard Error vs. Mean Annual Class A Pan Evaporation

10

100

1000

10000

100000

30 35 40 45 50 55 60 65

 Mean annual class A pan evaporation (inches)

Relative standard error

25% Year Rain-based Daily Values 

Relative Standard Error vs. Altitude Index

10

100

1000

10000

100000

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

Altitude index (1000's of feet)

Relative standard error

Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

80 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
25% Year Rain-based Daily Values 

Relative Standard Error vs. 2-yr, 24-hour Rainfall Intensity

10

100

1000

10000

100000

1.0 2.0 3.0 4.0 5.0 6.0 7.0

 2-yr, 24-hour rainfall intensity (inches)

Relative standard error

25% Year Rain-based Daily Values 

Relative Standard Error vs. Stream Length From Gage to Basin Divide

10

100

1000

10000

100000

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0

Stream length (miles)

Relative standard error

Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

Appendix 3 81
25% Year Rain-based Daily Values 

Relative Standard Error vs. Mean Annual Precipitation

10

100

1000

10000

100000

0 20 40 60 80 100 120

Mean annual precipitation (inches)

Relative standard error

25% Year Rain-based Daily Values 

Relative Standard Error vs. Slope of Stream between 85% and 10% Distances

10

100

1000

10000

100000

0 100 200 300 400 500 600 700 800 900 1000

Slope of stream (feet per mile)

Relative standard error

Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

82 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
Appendix 3 83

Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

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Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

84 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
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Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

Appendix 3 85
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Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

86 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
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to March 31 mean-daily-flow estimates.—Continued

Appendix 3 87
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Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

88 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California
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Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

Appendix 3 89
90 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California

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Appendix 3. Computed relative standard errors plotted versus basin characteristics for all stations’ 25- and 50-percentile December 15 

to March 31 mean-daily-flow estimates.—Continued

Appendix 3 91
92 Evaluation of Methods for Estimating Streamflow Statistics, Flood Frequency, Magnitude, North Coastal California