Prepared in cooperation with the Federal Emergency Management Agency, the U.S. Army Corps 

of Engineers, and the U.S. Forest Service

Regional Skew for California, and Flood Frequency for 

Selected Sites in the Sacramento-San Joaquin River Basin, 

Based on Data through Water Year 2006

U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010-5260
Cover: Photogrph showing flooding on the South Yuba River on January 1, 2006 at the 

Old Highway 49 crossing near Nevada City, California. Photograph was taken by Ian 

O’Halloran.
Regional Skew for California, and Flood 

Frequency for Selected Sites in the 

Sacramento–San Joaquin River Basin, 

Based on Data through Water Year 2006

By Charles Parrett, U.S. Geological Survey, Andrea Veilleux and J.R. Stedinger, 

Cornell University; N. A. Barth, Donna L. Knifong, and J.C. Ferris, U.S. Geological 

Survey

Prepared in cooperation with Federal Emergency Management Agency, 

U.S. Army Corps of Engineers, and U.S. Forest Service

Scientific Investigations Report 2010–5260

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, product, or firm names is for descriptive purposes only and does not imply 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:

Parrett, C., Veilleux, A., Stedinger, J.R., Barth, N.A., Knifong, D.L., and Ferris, J.C., 2011, Regional skew for California, 

and flood frequency for selected sites in the Sacramento–San Joaquin River Basin, based on data through water year 

2006: U.S. Geological Survey Scientific Investigations Report 2010–5260, 94 p.
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................6

Study Area Description........................................................................................................................6

Data Used........................................................................................................................................................7

Regional Skew Database ....................................................................................................................7

Elimination of Redundant Sites and Other Non-typical Sites...............................................8

Basin and Climatic Characteristics ..........................................................................................8

Test for Trends in Long-Term Data Used for Regional Skew Analysis................................9

Database for Stations at Key Dam Sites...........................................................................................9

Database for Flood-Frequency Analysis in the Sacramento–San Joaquin River Basin ..........9

Analytical Methods......................................................................................................................................10

Flood Frequency Based on LP3 Distribution ..................................................................................10

Expected Moments Algorithm (EMA)..............................................................................................10

Statistical Analysis of Regional Skew.............................................................................................11

Regional Regression Models...................................................................................................12

Cross-Correlation Model of Concurrent Annual-Peak Discharge.....................................13

Methodology Adjustments for California...............................................................................15

Flood-Frequency Results............................................................................................................................16

Summary........................................................................................................................................................20

References Cited..........................................................................................................................................21

Glossary.........................................................................................................................................................39

Appendix A. Move Methods for Estimating Unregulated Annual-Peak-Flow 

Data at Key Dam Sites ..................................................................................................................41

Appendix B. Extended Bayesian GLS Regional Skew Analysis for California .................................87

Appendix C. Bayesian GLS Regression Diagnostics ............................................................................93
iv

Figures

Figure 1. California map showing stations in northern, central, and southern

Californiaselected for regional skew analysis outside the desert exclusion

area and flood-frequency analysis in the Sacramento-San Joaquin River

Basin, California ........................................................................... 3

Figure 2. Graph showing relation between the average timing of peak discharge and

mean basin elevation for 158 sites used for regional skew analysis in California ... 7

Figure 3. Graph showing relation between the Fisher Z transform (Z) of logs of

annual-peak discharge and distance between basin centroids for 159

station-pairs in California .................................................................. 13

Figure 4. Graph showing relation between the cross-correlation of logs of annual-peak

discharge and the distance between basin centroids based on data from 159

station-pairs in California and 1,317 station-pairs in the Southeastern United

States ....................................................................................... 14

Figure 5. Graph showing histogram of relative frequency of calculated cross-correlation

values in California and in the Southeastern United States ........................... 14

Figure 6. Graph showing relations between the unbiased at-site skew and the mean

basin elevation for 158 sites in California ................................................ 16

Figure 7. Graph showing flood-frequency curves for Saratoga Creek, California, based

on 73 years of recorded data with no censoring of annual-peak discharge ......... 17

Figure 8. Graph showing flood-frequency curves for Kingsbury Creek, California, based

on 11 years of recorded data with no censoring of annual-peak discharge ......... 18

Figure 9. Graph showing flood-frequency curves for West Walker River, California,

based on 81 years of data recorded during an historical period of 106 years

with a perception threshold discharge equal to the largest discharge during

the 81-year record period .................................................................. 19

Figure 10. Graph showing flood-frequency curves for Cantua Creek , California, based on

49 years of recorded data with all peaks smaller than the 50-percent

exceedance probability censored as low outliers....................................... 20

Tables

Table 1. Streamflow-gaging stations and statistical data used to analyze regional skew

in California and to determine flood frequency for the Sacramento-San

Joaquin River Basin, California ............................................................ 23

Table 2. Basin characteristics for analyzing regional skew in California ..................... 23

Table 3. Basin characteristics for sites used in the regional skew analysis, California ...... 24

Table 4. Results of trend tests for annual peak discharge at selected sites in California ... 24

Table 5. Key dam sites and drainage areas, periods of estimated unregulated

annual-maximum-daily discharge, and periods of concurrent unregulated

annual-maximum-daily and peak-discharge data ....................................... 25

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California ...... 26

Table 7. Regional skew models for California ...................................................... 38

Table 8. Average regional skew, variance of prediction (VPnew) and equivalent record

length (ERL) for nonlinear regional skew model NL-Elev for various values of

mean basin elevation (ELEV), California ................................................ 38
v

Conversion Factors, Datums, and Acronyms

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

SI to Inch/Pound

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square centimeter (cm2) 0.001076 square foot (ft2)

square meter (m2) 10.76 square foot (ft2) 

square centimeter (cm2) 0.1550 square inch (ft2) 

square kilometer (km2) 0.3861 square mile (mi2)

Volume

square centimeter (cm2) 0.03531 cubic foot (ft3) 

square meter (m2) 35.31 cubic foot (ft3)

square centimeter (cm2) 1.308 cubic yard (yd3) 

square kilometer (km2) 0.2399 cubic mile (mi3) 

Flow rate

cubic meter per second (m3/s) 35.31 cubic foot per second (ft3/s)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C=(°F-32)/1.8
vi

Datums

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

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Elevation refers to distance above or below NAVD 88.

Water year is the 12-month period, October 1 through September 30, and is designated by the 

calendar year in which it ends. Thus, the water year ending September 30, 2001 is called “water 

year 2001.”

Acronyms

ACOE Army Corps of Engineers

ANOVA analysis of variance

ASEV average sampling error variance

AVP average variance of prediction

B-GLS Bayesian generalized least squares

B-WLS Bayesian weighted least squares

DAR drainage area ratio

DWR Department of Water Resources

ELEV mean basin elevation

EMA expected moments algorithm

ERL effective record length

EVR error variance ratio

FEMA Federal Emergency Management Agency

GIS geographic information system

GLS generalized least squares

LP3 log Pearson Type 3

MBV misrepresentation of the beta variance

MHDP Multi-Hazards Demonstration Project

MM-WLS method-of-moments weighted least squares

MOVE.1 maintenance of variance extension type I

MOVE.2 maintenance of variance extension type II

MOVE.3 maintenance of variance extension 3

MOVE.4 maintenance of variance extension 4

MSE mean square error

ND normalized distance

NHDPlus National Hydrologic Dataset

NLCD National Land-Cover Dataset

NL-Elev nonlinear regional skew model

NWIS National Water Information System

PRISM Parameter-Elevation Regressions on Independent Slopes Model

USGS U.S. Geological Survey

VP variance of prediction 

WLS weighted least squares

Conversion Factors, Datums, and Acronyms—Continued
Regional Skew for California and Flood Frequency for 

Selected Sites in the Sacramento–San Joaquin River 

Basin Based on Data through Water Year 2006 

By Charles Parrett1, Andrea Veilleux2, J.R. Stedinger2, N. A. Barth1, Donna L. Knifong1, and J.C. Ferris1

Abstract 

Improved flood-frequency information is important 

throughout California in general and in the Sacramento–San 

Joaquin River Basin in particular, because of an extensive 

network of flood-control levees and the risk of catastrophic 

flooding. A key first step in updating flood-frequency 

information is determining regional skew. A Bayesian 

generalized least squares (GLS) regression method was used 

to derive a regional-skew model based on annual peakdischarge data for 158 long-term (30 or more years of record) 

stations throughout most of California. The desert areas in 

southeastern California had too few long-term stations to 

reliably determine regional skew for that hydrologically 

distinct region; therefore, the desert areas were excluded 

from the regional skew analysis for California. Of the 158 

long-term stations used to determine regional skew, 145 have 

minimally regulated annual-peak discharges, and 13 stations 

are dam sites for which unregulated peak discharges were 

estimated from unregulated daily maximum discharge data 

furnished by the U.S. Army Corp of Engineers. Station skew 

was determined by using an expected moments algorithm 

(EMA) program for fitting the Pearson Type 3 flood-frequency 

distribution to the logarithms of annual peak-discharge data. 

The Bayesian GLS regression method previously 

developed was modified because of the large cross correlations 

among concurrent recorded peak discharges in California 

and the use of censored data and historical flood information 

with the new expected moments algorithm. In particular, 

to properly account for these cross-correlation problems 

and develop a suitable regression model and regression 

diagnostics, a combination of Bayesian weighted least squares 

and generalized least squares regression was adopted. This 

new methodology identified a nonlinear function relating 

regional skew to mean basin elevation. The regional skew 

values ranged from -0.62 for a mean basin elevation of 

zero to 0.61 for a mean basin elevation of 11,000 feet. This 

relation between skew and elevation reflects the interaction 

of snow with rain, which increases with increased elevation. 

The equivalent record length for the new regional skew 

ranges from 52 to 65 years of record, depending upon mean 

basin elevation. The old regional skew map in Bulletin 17B, 

published by the Hydrology Subcommittee of the Interagency 

Advisory Committee on Water Data (1982), reported an 

equivalent record length of only 17 years.

The newly developed regional skew relation for 

California was used to update flood frequency for the 158 

sites used in the regional skew analysis as well as 206 selected 

sites in the Sacramento–San Joaquin River Basin. For these 

sites, annual-peak discharges having recurrence intervals of 

2, 5, 10, 25, 50, 100, 200, and 500 years were determined 

on the basis of data through water year 2006. The expected 

moments algorithm was used for determining the magnitude 

and frequency of floods at gaged sites by using regional skew 

values and using the basic approach outlined in Bulletin 17B. 

Introduction 

Reliable estimates of peak discharge for various 

exceedance frequencies, commonly referred to as floodfrequency estimates, are needed by engineers, land-use 

planners, resource managers, and scientists. Flood-frequency 

information is required for flood-hazard assessment, safe and 

cost-effective design of water conveyance and transportation 

structures in or near streams, and floodplain delineation for 

flood insurance and land-use management. Water Science 

Centers within the U.S. Geological Survey (USGS) commonly 

provide updated flood-frequency estimates for streamflowgaging stations every 5 to 10 years based on cooperator needs 

and funding availability. The USGS provides methods for 

estimating flood-frequency at ungaged sites also. State-wide 

updates of flood-frequency at gaged sites and methods for 

estimation at ungaged sites in California were last completed 

1

 U.S. Geological Survey, California Water Science Center, Placer Hall, 

6000 J Street, Sacramento, California 95819

2 Cornell University, School of Civil & Environmental Engineering, 220 

Hollister Hall, Ithaca, New York 14853
2 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

in 1977 (Waananen and Crippen, 1977). The additional 30 

years of flow record and new analytical methods together 

with an increasing need for essential levee improvements 

and flood-frequency information due to increased population 

fully justify updating the frequency information. Accordingly, 

the USGS, in cooperation with the U.S. Forest Service, 

Federal Emergency Management Agency (FEMA), and 

the USGS Multi-Hazards Demonstration Project (MHDP), 

initiated a regional flood-frequency study for California in 

2008. This comprehensive study consists of (1) updating 

flood-frequency information for all suitable USGS gages 

that have minimally regulated peak-discharge records for at 

least 10 years, (2) developing methodologies for estimating 

flood-frequency information for ungaged sites in California, 

and (3) implementing a StreamStats (Ries and others, 

2008) application for California. The StreamStats webpage application will initially provide basin and climatic 

characteristics data and flood-estimation equations based on 

two earlier flood-frequency reports for California (Waananen 

and Crippen, 1977; Thomas and others, 1997). As new 

flood-estimation equations are developed for use throughout 

California, they will be incorporated into the California 

StreamStats web page.

Bulletin 17B of the Hydrology Subcommittee of the 

Interagency Advisory Committee on Water Data (1982), 

hereinafter referred to as Bulletin 17B, recommends that 

the log Pearson Type 3 probability distribution be used to 

estimate flood frequency at gaged sites. A key to accurately 

fitting this distribution to recorded flood data is to reliably 

estimate the shape or skewness of the distribution, which is 

often significantly affected by the presence of very small or 

very large discharges in the record (outliers). Accordingly, 

Bulletin 17B also recommends that at-site skew calculated 

from recorded data be weighted with regional skew 

determined from pooled data at nearby long-term sites. Recent 

studies described by Reis and others (2005), Weaver and 

others (2009), Feaster and others (2009), and Gotvald and 

others (2009) have shown that Bayesian generalized least 

squares (GLS) regression provides an effective statistical 

framework for estimating regional skew. The regional 

skewness estimators are more accurate and have smaller mean 

square errors than those attributed to the Bulletin 17B skew 

map. Thus, an important contribution of this study was the 

development of new regional skew relations for California 

using extensions to Bayesian GLS regression. A key first 

step in the regional skew analysis was determining at-site 

(station) skew values for selected long-term (30 or more 

years of peak-discharge record) stations. The desert areas 

in southeastern California had too few long-term stations to 

determine regional skew with reasonable reliability for that 

hydrologically distinct region, so the desert region shown 

on figure 1 was excluded from the regional skew analysis 

for California. Station skew was determined using a new 

expected moment algorithm (EMA) program for fitting the 

Pearson Type 3 flood-frequency distribution to the logarithms 

of annual peak-flow data developed by the USGS (Cohn and 

others, 1997, 2001; Griffis and others, 2004). 

An area of particular interest and need for updated floodfrequency data is the combined Sacramento and San Joaquin 

River Basin in central California. Large population centers, 

including the capital city of Sacramento, Stockton, Modesto, 

and Fresno, and widespread suburban development between 

the cities are at least partially located on floodplains of the 

Sacramento and San Joaquin Rivers and their tributaries. An 

extensive network of levees provides flood protection, but 

many of the levees are in need of upgrades and rehabilitation. 

To ensure that levee upgrades are designed in accordance 

with the latest and most complete hydrologic information, the 

U.S. Army Corps of Engineers (ACOE), in cooperation with 

the California Department of Water Resources (DWR), has 

begun a hydrologic analysis of floodplain areas protected by 

the Federal-State levee system within the Sacramento and San 

Joaquin combined drainage basin. As part of their hydrologic 

analysis, the ACOE requires flood-frequency information for 

simulated unregulated peak discharges at stream sites where 

peak discharges are partially or completely regulated. 

Because the USGS and ACOE share a common interest 

and need for updated flood-frequency information in central 

California, both agencies developed a secondary cooperative 

flood-frequency program. This program tasked the USGS with 

developing a method for estimating unregulated annual-peak 

discharge at 16 selected key dam sites in the Sacramento–San 

Joaquin River Basin and using the estimated annual-peak 

discharges at the sites as part of the regional skew analysis 

already begun by the USGS for all of California outside the 

southeastern desert region. Results from the regional skew 

analysis were to be used to update flood-frequency data also 

for the 16 key sites.

To provide updated flood-frequency in the timeliest 

manner possible for the area of special interest in central 

California, the USGS focused initially on updates at gaged 

sites in a study area that consists of the Sacramento and San 

Joaquin-Tulare Basins. This study area (fig. 1) generally 

conforms to the Sacramento–San Joaquin River Basin study 

area defined by the ACOE. For consistency, the study area 

for the flood-frequency determinations in this report will be 

hereinafter referred to as the Sacramento–San Joaquin River 

Basin. 
Introduction 3

Sacramento

184

197 199 76

206 204 205

211

202 215

331

324

344

323

342 346

312

340

341

305

304

347 345

273

270

296

348

298

350

268 269

266

351

352

265

10

264

258

250

353

246

242

355 354

225

230

362

357

356

361

358

359

360 364

3

4

5

6

363

301

271

196

207

7

8

9

11

12

13

14

175

189 188 176 190

192 191

193 194

198 195

203

208 209

210

212 213

214

216

217

218

219

220

221

223

224

226

227

229

231

232

233

234

235

236

237

238

239

240

241

243

244

245

247

248

249

251

252

253

254

256

257

260

262

263

267

272

274

275 276

277

278

279

280

281

282

283

284 285

286

287 289 288

290

292 291

293

294

295

297

299

300

302

303

307 306

309 308

310

313 311

314

315

317 316

318

319

320

321

322 325

326

327

328 329

330

332 333

334

335 336 337

338

339

343

261

259

255

349

Streamflowgaging stations

Flood

frequency

Regional

skew

Key

dam

X X X

X X

X

X X

IP017136_Figure 1a

Pacific

Ocean

0 20 40 Miles

0 20 40 Kilometers

CALIFORNIA

Sacramento Basin

San Joaquin -

Tulare Basin

Desert

exclusion

area

SIERRA

NEVAD

Pacific A

Ocean

A

Figure 1. Stations in northern (A), central (B), and southern California (C) selected for regional skew analysis outside the desert 

exclusion area and flood-frequency analysis in the Sacramento-San Joaquin River Basin, California.
4 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

46

49 50

48 47

51

83

54

82

93

55

95

56

98

57

97

58

106 105

107

125

109

59

141

60 52

123

53

112

61

63

134

62

128

64

145 151

65

135

66

127

67

68

163

155

69 73

180

169

170

70

174

72

75

173

166

178

74

71

77

184

197

181

199

76

206 204 205

211

202 215

331

344

1

2

139

179

185

196

207

78

78

79

81

84

85

86

87

88

89

90

91 92

94

96 99

100

102 101

103

104

108

110

111

113 114

115

117 116

118

119120

121

122

124

126

129

130

131

132

133

136 137

138

140

144

143

144

146

148

149

150

152

153

154

156

158 157

159

160 161

162

165

167

168

171

172

175

176

177

182

183

186

187

188

189

190

192 191

193 194

195

198

200 201

203

208 209

210

212 213

214

216

217

218

219

220

221

222

329

332 333 330

336 335 337

338

339

343

164

228

147

Sacramento

Stockton

San

Francisco

Modesto

Fresno

0 20 40 Miles

0 20 40 Kilometers

Pacific

Ocean

Flood

frequency

Regional

skew

Key

dam

X X X

X X

X

X X

35°

IP017136_Figure 1b

CALIFORNIA

Sacramento Basin

San Joaquin -

Tulare Basin

Desert

exclusion

area

SIERRA

NEVADA

Pacific

Ocean

Streamflowgaging stations

B

Figure 1.—Continued
Introduction 5

15

16

17 19

18

26

20

21 22

23 25 27

24

32

31

29 30 33 28

34 35

36 37 38

39

40

41

43 42

49

50

47 48

82 83

93

95

97 98

106 105

107

109

78

79

80

81

84

85

86

87

88

89

90

91 92

94

96 99

100

101 102

103

104

108

0 20 40 Miles

0 20 40 Kilometers

IP017136_Figure 1c. 

Pacific

Ocean

Flood

frequency

Regional

skew

Key

dam

X X

X

Los

Angeles

San

Bernardino

San

Diego

CALIFORNIA

Sacramento Basin

San Joaquin -

Tulare Basin

Desert

exclusion

area

SIERRA

NEVADA

Pacific

Ocean Streamflowgaging stations

C

Figure 1.—Continued
6 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Purpose and Scope

The primary purposes of this report are to (1) convey 

the results of the regional skew analysis for California, 

outside the southeastern desert region, and (2) present floodfrequency information for the 158 sites used in the regional 

skew analysis and for an additional 206 selected sites in the 

Sacramento-San Joaquin River Basin. The databases for 

annual-peak discharge used for the regional skew analysis 

and the determination of flood frequency at selected sites are 

described. Because key dam sites identified by the ACOE 

were included in the regional skew analysis, unregulated, 

annual-peak discharge data at those sites needed to be 

constructed from estimated unregulated annual-maximumdaily discharge data. The maintenance of variance extension 

(MOVE) method was used to estimate peak-discharge data at 

the key dam sites and is described in Appendix A. The new 

EMA method was used to compute moments of the logarithms 

for the LP3 distribution to determine a station skew at each 

site to use in the regional skew analysis and to subsequently 

update flood frequency at all selected sites. Finally, the 

Bayesian GLS regression method used for the regional skew 

analysis is described in some detail, and extensions to the 

method required for use in this California study and various 

diagnostics for analyzing regional skew results are presented 

in Appendixes B and C. 

 Updated flood-frequency data at selected sites in the 

study area, based on the new regional skew relations and 

applying the LP3 method, are presented in table format, and 

some example flood-frequency curves are shown. Specific 

flood-frequency information provided are peak discharges 

having annual exceedance probabilities (frequencies) of 0.50, 

0.20, 0.10, 0.05, 0.02, 0.01, 0.005, and 0.002. Exceedance 

probabilities often are expressed in terms of their reciprocals 

as recurrence intervals. A peak discharge having an annual 

exceedance probability of 0.01, for example, has an associated 

recurrence interval of 100 years. Data in this report are 

presented both in terms of annual exceedance probability and 

recurrence interval.

Study Area Description

The study area for the regional skew analysis for 

California consists of the entire state outside the southeastern 

desert region (fig. 1). The excluded desert region largely 

conforms to the desert regions previously shown for California 

in a flood-frequency study for the southwestern desert region 

of the United States (Thomas and others, 1997). That previous 

study used data from several states to determine regional skew 

for the desert. The regional skew adopted by Thomas and 

others (1997) for the desert regions of the southwestern United 

States was zero. 

 Streamflow-gaging stations used in the regional skew 

analysis provided data for the broad range of hydrologic 

conditions throughout the study area. Along the California 

coast, streams drain the moderately rugged mountains of the 

Coastal Range, and annual-peak discharge most often results 

from large winter rainstorms. Annual-peak discharge from 

small streams, particularly those in drier areas of California 

may occasionally result from summer thunderstorms. 

Drainage within the flat valley floor of the Sacramento–San 

Joaquin River Basin is diffuse and often unpredictable because 

of the flat topography and agricultural land use, including 

extensive irrigation withdrawals and canal systems. Floods on 

the generally small streams that drain only the low-elevation 

foothills and valley floor areas commonly are the result of 

large winter rain storms, although floods may occasionally be 

a result of infrequent spring and summer rainstorms. 

About a third of the stream sites selected for the regional 

skew analysis and many of the additional sites selected for the 

flood-frequency analysis in the Sacramento–San Joaquin River 

Basin are in the Sierra Nevada region near the eastern border 

of central California (fig. 1). This rugged, mountainous area 

has numerous streams that drain westward into the Sacramento 

and San Joaquin Rivers. The elevation of the northern part of 

the Sierra Nevada region is generally lower than the elevation 

of the southern part. Annual-peak discharges from streams 

draining the Sierra Nevada almost always occur during the 

winter and spring (November through June), and result from 

a complex interaction of rain and snow. A large winter storm 

might produce rain on the lower parts of a basin and snow on 

the colder, higher parts of the basin. Peak discharge from this 

kind of event would be less than if rain had fallen throughout 

the basin. Alternatively, the runoff from a large basin-wide 

rainstorm can be exacerbated if the higher-elevation part of 

the basin has a large volume of snowpack that is available for 

melting and subsequent runoff.

This complicated interaction of rain and snow on the 

production of annual-peak discharge is most prevalent for 

streams draining the Sierra Nevada, but it also occurs in 

other mountainous areas of California (Mount, 1995). The 

strength of the interaction depends largely upon the elevation 

of the basins above the gaged locations. The relation between 

average month of occurrence (timing) of the annual-peak 

discharge and mean basin elevation is shown in figure 2. 

The average month of occurrence of annual-peak discharge 

for each gaged site used in the regional skew analysis was 

computed, starting with October equal to 1, and plotted 

against mean basin elevation. Because relatively few annual 

peaks in California occur in July through September, those 

months were not used to compute the averages in figure 2. 

Annual-peak discharges from streams with mean basin 

elevations less than about 4,000 ft have an average timing 

clustered between mid-November and mid-January and thus 

most likely represent runoff from rainstorms. On the other 
Data Used 7

hand, the average timing of annual-peak discharge for mean 

basin elevations greater than 4,000 ft generally increases with 

increasing elevation up to about 8,000 ft, where the average 

timing generally flattens at about April. March through May is 

generally the snowmelt period, so that floods that occur during 

this period are generally the result of snowmelt, or rain and 

snowmelt.

The implication of this trend in annual peak-discharge 

timing is that rain is the main cause of peak discharge in 

basins with mean elevations lower than about 4,000 ft, and 

that the interaction of rain and snow increases as elevation 

increases above 4,000 ft. For basins with mean elevations 

above about 8,000 ft, the effects of snow on peak discharge 

are predominant. As discussed later in the section titled 

Methodology Adjustments for California, the rain-snow 

interaction significantly affects regional skew in California 

and, at some sites, the degree of interaction may be so great 

that the annual-peak discharges may require separation into 

two groups for flood-frequency analysis (mixed-population 

analysis) as described in Bulletin 17B. The need for a mixedpopulation flood-frequency analysis is expected to be most 

appropriate for sites with mean basin elevations greater than 

about 8,000 ft. 

Data Used

Annual-peak discharge data were used for several specific 

purposes. The databases for each purpose are described in the 

following sections.

Regional Skew Database

New regional skew values were developed for California 

by using a database of 145 USGS gaged sites having 

essentially unregulated annual peak-flow records of at least 

30 years through water year 2006. In addition, the regional 

skew database included 13 of the 16 stations at key dam 

sites for which unregulated peak flow data were estimated 

from unregulated daily maximum discharge data furnished 

by the ACOE. All sites used for the regional skew analysis 

are shown in figure 1. Station locations and names, together 

with information about the annual peak-discharge and skew 

data are shown in table 1. Table 1 includes information about 

stations in the Sacramento–San Joaquin River Basin for which 

flood frequency information was developed. 

MEAN BASIN ELEVATION, IN FEET

AVERAGE TIMING OF ANNUAL-PEAK DISCHARGE

Oct (1)

Dec (3)

Nov (2)

Jan (4)

Mar (6)

Feb (5)

Apr (7)

May (8)

Jun (9)

0 2,000 4,000 6,000 8,000 10,000 12,000

IP017136_Figure 02

Figure 2. Relation between the average timing of peak discharge and mean basin 

elevation for 158 sites used for regional skew analysis in California. A small number of 

peaks in July, August and September were not used to determine average month of 

occurrence.
8 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Although peak-discharge information for some of the 

145 sites was recorded in the National Water Information 

System (NWIS) database with codes indicating that discharges 

were affected by regulation or diversion, the effects on 

peak discharge were considered negligible or the periods 

significantly affected by regulation or diversion were excluded 

from the analysis (table 1). Peak-discharge records at two sites 

on the San Benito River (stations 11158500 and 11158600) 

were combined into a single, longer record that was assigned 

an artificial station number of 11158699. Artificial station 

numbers ending in digits 99 were also assigned to the 16 

stations at key dam sites for which unregulated peak flow data 

were estimated from unregulated daily maximum discharge 

data. 

Elimination of Redundant Sites and Other Nontypical Sites

 Redundancy results when the drainage basins of two 

gaged sites are nested, meaning that one is contained inside 

the other, and the sizes of the two basins are similar. Then, 

instead of providing two independent spatial observations 

depicting how drainage basin characteristics are related to 

skew (or flood quantiles), these two basins will likely have the 

same hydrologic response to a given storm and thus represent 

only one spatial observation. When sites are redundant, 

a statistical analysis using both gaged sites incorrectly 

represents the information in the regional data set (Gruber and 

Stedinger, 2008). To determine if two sites are redundant and 

thus represent the same hydrologic response, two pieces of 

information are considered: (1) whether their watersheds are 

nested and (2) the ratio of the basin drainage areas.

The first metric, normalized distance, is used to determine 

the likelihood the basins are nested. The normalized distance 

between two basin centroids, ND, is defined as (Veilleux, 

2009)

4

,

where

is the distance between centroids of basin

 and basin ,and

and are the drainage areas at sites and .

ij

i j

ij

i j

D

ND

DA DA

D

i j

DA DA i j

= (1)

The second measure, drainage area ratio (DAR), is used to 

determine if two nested basins are sufficiently similar in size 

to conclude that they essentially represent the same watershed 

for the purposes of developing a regional hydrologic model. 

The DAR is defined as 

, i j

j i

DA DA

DAR Max

DA DA

é ù

= ê ú ê ú ê ú ë û

, (2) 

where DAi and DAj have already been defined. 

Two basins might be expected to be redundant if they 

are close together and similar in size. A previous study in the 

southeastern United States (Veilleux, 2009) determined that 

site pairs having ND less than or equal to 0.5 and DAR less 

than or equal to 5 were likely to have redundancy problems 

for determining regional skew, and therefore one of each site 

pair was removed from the regional skew analysis. The same 

values for ND and DAR were used to screen and remove sites 

from the regional skew analysis in California. Following 

screening, basin boundaries of identified pairs were examined 

to determine if the two sites were really nested.

The two key dam sites removed because of redundancy 

(Sacramento River at Keswick [station 11370599] and Feather 

River at Oroville [station 11407099]) had the two largest 

basins considered for the regional skew analysis. These large 

basins included several subbasins used in the regional skew 

analysis and thus truly were nested even though computed ND 

and DAR were greater than 0.5 and 5.0, respectively. 

One key dam site, Fresno River below Hidden Dam near 

Daulton (station 11258099), was removed from the regional 

skew database because preliminary analysis indicated that an 

LP3 distribution provided only a very poor fit to the estimated 

annual peak-discharge record for both the lower and upper 

tail. Thus, station skew for this site likely did not represent the 

general variation in skew throughout the study area. 

Basin and Climatic Characteristics

Various basin characteristics for each of the 158 sites in 

the regional skew analysis were derived from various national 

geographic information system (GIS) databases, including 

the National Hydrologic Dataset (NHDPlus), the National 

Land-Cover Dataset (NLCD), and the Parameter-Elevation 

Regressions on Independent Slopes Model (PRISM) climatic 

dataset based on data from 1970 to 2000. Table 2 gives the 

basin-characteristic names, descriptions, units, and sources 

of information. Table 3 shows basin characteristics for the 

158 sites used in the regional skew analysis. At most of the 

sites shown in table 3, the drainage area determined from 

the NHDPlus GIS dataset closely matched the drainage area 

manually determined from topographic maps and reported in 

the NWIS peak-flow database. At two sites, station 11063000 

and the key dam site at station 11259099, the drainage area 

determined from the GIS dataset differed from the drainage 

area reported in NWIS by more than 10 percent. For these 

two sites, the only basin characteristics considered to be 
Data Used 9

reliable were those relating to basin elevation, and no other 

basin characteristics are given in table 3. For the two sites 

on the San Benito River where peak-discharge records were 

combined (station 11158500 and station 11158600), the basin 

characteristics measured for station 11158600 were used for 

the artificial combined-record station 11158699.

Test for Trends in Long-Term Data Used for 

Regional Skew Analysis

Flood-frequency analysis requires annual peak-flow data 

at each site that are random, independent, and generated by a 

process that is invariant (stationary) over time. Peak-flow data 

that indicate trends over time may reflect watershed or climatic 

changes that can significantly change flood characteristics 

and make flood-frequency estimates difficult to interpret and 

unreliable. To determine whether annual peak-discharge data 

are showing trends in California, 69 sites used in the regional 

skew analysis that had complete annual discharge records 

from 1977 to 2006 (30 years) were tested for monotonic trends 

using Kendall’s tau, a non-parametric test for trends described 

by Helsel and Hirsch (1992). The locations of the 69 sites 

represented the locations of all 158 sites used for the regional 

skew analysis. The two primary outputs from the test were the 

tau value and the p-value. The tau value measures the strength 

of the correlation between the annual peak-flow values and 

time. Positive values of tau indicate increasing trends and 

negative values indicate decreasing trends. Trends generally 

are considered to be significant when the p-value is less than 

or equal to 0.05. A p-value of 0.05 indicates that there is a 

5 percent probability that the test will identify a trend when 

there is no actual trend present. 

Of the 69 sites tested for a trend in annual-peak discharge 

from 1977 to 2006, none had tests with p-values less than 

or equal to 0.05 Table 4 lists the long-term sites used for the 

trend test and the data from that test. On the basis of the trendtest results, monotonic trends in annual-peak discharge are 

not considered to be a factor anywhere in California and thus 

do not affect the interpretation or overall reliability of floodfrequency results. 

Database for Stations at Key Dam Sites

Unregulated peak-discharge data were estimated for 16 

key dam sites selected by the ACOE. Ten of the 16 selected 

sites had concurrent recorded unregulated, annual-peak 

discharge and annual-maximum-daily discharge data obtained 

before dams were constructed. In addition to the concurrent 

unregulated peak-discharge and maximum-daily-discharge 

data, all sites had longer records of estimated, unregulated 

annual-maximum-daily discharge data that were developed 

and provided by the ACOE (John High, Chief, Hydrology 

Section, Sacramento District, U.S. Army Corps of Engineers, 

written commun., March 2009). These longer records of 

estimated, unregulated annual-maximum-daily discharge were 

used to estimate long-term records of annual-peak discharge 

that were subsequently used in the regional skew analysis for 

California. The 16 sites for which annual-peak discharges 

were estimated are shown in table 5 with a brief indication of 

the periods of discharge records. The estimated, unregulated 

annual-maximum-daily discharge data provided by the ACOE 

generally are the same values as those synthesized for a 

previous hydrologic study of streams in the Sacramento–San 

Joaquin River Basin (U.S. Army Corps of Engineers, 2002). 

The unregulated annual-maximum-daily discharge data 

provided by the ACOE for the 16 selected sites are shown in 

table 6. 

Database for Flood-Frequency Analysis in the 

Sacramento–San Joaquin River Basin

Flood-frequency statistics were calculated for 256 sites 

in the Sacramento–San Joaquin River Basin in California. 

Included in the 256 sites were 50 of the 158 sites used in 

analyzing regional skew for all of California. Flood-frequency 

statistics were calculated for all 16 key dam sites also, even 

though only 13 of the 16 sites were used in the regional skew 

analysis. All sites for which flood-frequency was analyzed 

had minimally regulated peak-discharge records for at least 

10 years. Periods of regulated peak-discharge record were 

excluded from analysis for sites that had at least 10 years of 

unregulated record. Some otherwise eligible sites also were 

excluded from flood-frequency analysis if 25 percent or more 

of the recorded peak discharges were zero, or if the number 

of peak discharges other than zero were less than 10. Finally, 

some otherwise eligible sites also were excluded if the LP3 

distribution provided only a very poor fit to the recorded 

data. The very poor fits were most often the result of one or 

more large outliers in a short record period. Peak-discharge 

records for two sites on Panoche Creek (stations 11255500 

and 11255575) were combined into a single, longer record 

that was assigned the artificial station number of 11255599. 

All sites that were analyzed for flood frequency are shown in 

figure 1 and listed in table 1. 
10 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Analytical Methods

Various methods were used to analyze annual-peak 

discharge data in order to determine flood frequency at gaged 

sites. Those methods are described in the following sections.

Flood Frequency Based on LP3 Distribution

Flood-frequency estimates for gaged sites are computed 

by fitting a mathematical probability distribution to the series 

of annual-peak discharges as described in Bulletin 17B. The 

LP3 distribution, the Pearson Type 3 distribution applied to 

the logarithms (base 10) of annual-peak discharge data, is 

commonly used to estimate flood frequency in the United 

States and was used for the current California study. 

The LP3 distribution is a three-parameter distribution 

that requires estimates of the mean, the standard deviation, 

and the skew coefficient of the population of logarithms of 

annual-peak discharge at each gaged site. The basic equation 

for determining flood frequency from the three parameters is 

the following:

log ,

where

is the annual-peak discharge for the 

exceedance probability, ,

is the mean of the logarithms of the annualpeak discharge,

is a factor based on the weighted skew

 coefficient and th

P p

p

p

Q X KS

Q

P

X

K

= +

e exceedance probability,

, which can be obtained from Appendix 3

in Bulletin 17B, and

is the standard deviation of the logarithms of 

the annual-peak discharge, which is a 

measure of the degree of vari

P

S

ation in the

annual values about the mean value.

(3)

The mean, the standard deviation, and the skew 

coefficient can be estimated from the available sample 

data (recorded annual-peak discharges). However, a skew 

coefficient calculated from a small sample tends to be an 

unreliable estimator of the population skew coefficient. 

Accordingly, the guidelines in Bulletin 17B indicate that the 

skew coefficient calculated from at-site sample data (station 

skew) needs to be weighted with a generalized, or regional, 

skew determined from an analysis of selected long-term gaged 

sites in the study region. The value of the skew coefficient 

used in equation 3 is this weighted skew that is based on 

station skew and regional skew. As previously described, 

Bayesian generalized least squares (GLS) regression, a newly 

developed method for determining regional skew, was used 

for the current study. The regional skew analysis is described 

in detail in a later section of the report titled Statistical 

Analysis of Regional Skew. Some of the more technical details 

of the mathematics involved are more fully presented in 

Appendixes B and C. 

Equation 3 forms the basis for calculating flood 

frequency at gaged sites, but Bulletin 17B also provides 

methods for adjusting the results for zero flows, testing and 

adjusting for low outliers, and adjusting for historical floods 

that occur outside the period of systematic peak-discharge data 

collection. While these adjustments generally improve floodfrequency estimates, the new expected moments algorithm 

(EMA) incorporates historical discharges more efficiently and 

allows peak discharges that are known only to be within some 

range of plausible values (interval or bounded discharges) to 

be used in flood-frequency analysis. Consequently, the EMA 

was used in the current study. 

Expected Moments Algorithm (EMA)

The EMA method was used for an initial LP3 frequency 

analysis in order to determine station skew for all sites used 

in the regional skew analysis. For sites that have systematic 

annual-peak discharge records for complete periods, no low 

outliers, and no historical flood information, the EMA method 

calculates identical values of the LP3 parameters (mean, 

standard deviation, and station skew) as the conventional 

method-of-moments described in Bulletin 17B. The EMA 

method, however, can incorporate into the analysis censored 

peak-discharge data. Censored data may be expressed in terms 

of discharge perception thresholds during historical periods 

outside the period of systematic data collection. For example, 

a site may have some historical information that indicates that 

a large recorded peak discharge of Qhist was the largest since 

1900, before systematic data collection was started in 1930. 

Each annual peak from 1900 to 1930 can thus be characterized 

as a censored discharge whose value is known not to have 

exceeded the perception threshold, Qhist, and estimates of 

those bounded discharges between 0 and Qhist can be used in 

the LP3 flood-frequency analysis. In the same way, the EMA 

method allows use of bounded discharges to characterize any 

missing data during periods of systematic data collection. 

These missing peak discharges can be described by perception 

thresholds or, if we have more knowledge about the likely 

range of missing discharge, by interval discharges that have 

specific upper and lower bounds. For example, if a peak was 

not recorded because the peak stage did not reach the elevation 

of the gage, the missing peak might be characterized as an 

interval discharge with a range that is bounded by zero and 

the peak discharge associated with the elevation of the gage. 

Missing peaks during periods of systematic data collection 

typically are ignored when the conventional LP3 method is 

used.

Censored data also can be low outliers in the systematic 

record. Low outliers are peak discharges that are significantly 

smaller than other recorded peak discharges and consequently 
Analytical Methods 11

often have a large effect on the LP3 distribution fit to all 

the recorded data. The primary focus of flood-frequency 

studies is the upper tail of the distribution (larger, rarer peak 

discharges), so closely fitting the upper tail is more important 

than fitting all data points, particularly abnormally low peak 

discharges. The LP3 distribution only has three adjustable 

parameters and thus may not be able to always fit the smallest 

and the largest flood flows. Accordingly, the conventional LP3 

method described in Bulletin 17B incorporates a Grubbs-Beck 

statistical test to determine when a recorded peak discharge 

is unusually small compared with all other recorded peaks 

and should be treated as a low outlier. Bulletin 17B further 

describes a conditional probability adjustment that is made 

when low outliers are identified. The EMA also makes use of 

the Grubbs-Beck test to identify low outliers. In this case, the 

test is iterated to determine if censoring an outlier causes any 

of the remaining peaks to be identified as an outlier. The EMA 

computation used to fit an LP3 distribution when low outliers 

are censored is different from that described in Bulletin 17B. 

Although the Grubbs-Beck test provides a reasonable way to 

identify low outliers that may result in fitting problems with 

the LP3 distribution, sometimes not all low peak discharges 

that cause fitting problems are identified in either the 

conventional LP3 method or in the EMA program. Thus, when 

either method is applied, sometimes a user-specified lowoutlier threshold that is larger than the values identified by the 

Grubbs-Beck test is used. Individual flood-frequency curves 

were visually inspected to determine whether one or more 

peak discharges in the lower tail (discharges with an annual 

exceedance probability of 0.50 or greater) of the distribution 

might be adversely affecting the fit of the upper tail of the 

frequency curve and thus require censoring. For a few sites, 

the curve fit for the upper tail was substantially improved by 

censoring the complete lower tail of the distribution. However, 

the substantial improvement came at the expense of a large 

increase in the mean square error (MSE) of the station skew as 

computed by the EMA program. All sites for which a userspecified low-outlier threshold was used are noted in table 1. 

Although the EMA allows the use of censored data 

that can significantly improve flood-frequency analyses, 

establishing reasonable bounds on the discharges can require 

considerable judgment on the part of the analyst. Fortunately, 

results from the EMA program generally are not sensitive to 

small changes in the perception thresholds or bounds used for 

interval discharges. 

In practice, the EMA provides estimates of missing, but 

bounded, discharge in a 5-step iterative process described by 

England (2003b):

1. Estimate an initial set of the three sample statistics (mean, 

standard deviation, and skew) from the logarithms of 

peak-discharge data with known magnitudes. These 

discharges are typically recorded peaks from the gaging 

station records and possibly some historical discharges. At 

this step, interval (bounded) discharges are not included. 

2. Use the initial sample statistics from step (1) to estimate a 

set of LP3 distribution parameters . 

3. Use the set of LP3 parameters from step (2) to estimate 

a new set of sample statistics based on the complete 

data set, including unknown discharges less than a 

threshold, unknown discharges that exceed a threshold, 

and unknown discharges with specific lower and upper 

bounds. The threshold values and lower and upper 

bounds are used as the initial estimates of the unknown 

discharges. 

4. Use this new set of moments to estimate a new set of 

LP3 parameters. These estimates are based on expected 

values given that the unknown discharges are less than the 

upper thresholds and bounds and greater than the lower 

thresholds and bounds.

5. Compare the parameters from step (4) with those 

computed from step (2). Repeat steps (3) and (4) until the 

parameter estimates converge. The main equations used 

by EMA to make the estimates in the iterative process 

are listed by Cohn and others (1997), England (1999), 

and England and others (2003a,b). Cohn and others 

(2001) describe the EMA computation for evaluating the 

sampling variance of parameters and quantiles.

Statistical Analysis of Regional Skew

Tasker and Stedinger (1986) developed a weighted 

least squares (WLS) procedure for estimating regional 

skew coefficients that is based on sample skew coefficients 

corresponding to the logarithms of annual peak-discharge 

data. Their method of regional analysis of skewness estimators 

accounts for the precision of the skewness estimator for each 

station, which depends on the length of record for each station 

and the accuracy of the regional skew model. More recently, 

Reis and others (2005), Gruber and others (2007), and Gruber 

and Stedinger (2008) developed a Bayesian generalized least 

squares (GLS) regression model for regional skew. While 

WLS regression accounts for the precision of the regional 

model and the effect of the record length on the variance of 

skewness estimators, GLS regression considers the cross 

correlations among the skewness estimators also. As explained 

later in the report section titled Methodology Adjustments 

for California, the cross correlations among the skewness 

estimators were important for the California regional skew 

study. The new Bayesian GLS regression procedures describe 

the precision of the estimated model error variance, a pseudo 

analysis of variance and enhanced diagnostic statistics (Griffis 

and Stedinger, 2007). A Bayesian GLS regional skew analysis 

was used in recently completed flood-frequency studies for the 

Southeastern United States (Feaster and others, 2009; Gotvald 

and others, 2009; Weaver and others, 2009).
12 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

The California regional skew study described here 

is based on use of Bayesian GLS regression procedures. 

However, the statistical procedures used in the Southeastern 

United States regional flood-frequency study had to be 

extended because of two problems that arose in the analysis 

of the California data set. The first problem was the difficulty 

in estimating the cross correlation of at-site skew estimators 

that were determined from the EMA analysis of the California 

regional-skew data set. This difficulty arose because EMA 

allows for censoring of low outliers and the use of estimated 

interval discharges for missing recorded data, and computing 

cross correlations when peak discharges are not represented 

by single values is difficult. The second problem was the 

extensive cross-correlation among concurrent recorded peak 

discharges in California. This extensive cross-correlation was 

not present in previous regional skew studies using Bayesian 

GLS regression procedures and required special attention in 

the analysis. To properly account for the cross-correlation 

problems and develop a suitable regression model and 

regression diagnostics, Bayesian WLS and GLS regressions 

were combined. In essence, the regression parameters of the 

regional skew model for California were determined using 

Bayesian WLS regression procedures, and the accuracy 

of the regression parameters and the regression models 

were determined using a special Bayesian GLS regression 

procedure. Those procedures are described in Appendixes B

and C. 

Regional Regression Models

The basic model for a regional (or generalized) skew 

analysis when there are k explanatory variables and n stations 

is





where

is an ( 1) vector of the unbiased estimated

at-site skew coefficients for every station

(see Appendix B for more discussion about

unbiased skew estimators),

is an ( ) matrix of basin cha

n

nk k

=

 ́

 ́

X

X

γ βε

γ

+ ,

racteristics

with a column of ones corresponding to a

constant in the model,

is a ( 1) vector of model coefficients,

is the ( 1) vector of total errors, including

both model and sampling errors where 

[

k

n

E

 ́

 ́

β

ε

ε]= 0 and is the covariance matrix

that represents . T E é ù ê ú ë û

Λ

εε

 

(4)

The matrix Λ is computed as the sum of two covariance

matrices (Reis and others, 2005) 2 ( ) σ δI + Σ γ , where 2 σ δ is

the model error variance describing the precision with which 

the proposed model Xβ can predict the true skews, which

are denoted γi, and the matrix  Σ(γ) represents the sampling

variances and covariances of the skewness estimators 

i γ . The

value of  Σ(γ) is determined by the length of record at each 

station, the regional skew, and the cross-correlation of the 

concurrent flows. 

The standard WLS or GLS estimator of β, which for 

given Λ is unbiased with minimum variance, is

  ( )  1 T T 1 1 - - - β γ = X XX L L . (5)

In WLS, the Λ matrix has non-zero elements only on 

the diagonal. In GLS, the Λ matrix nominally has the same 

diagonal elements, but the off-diagonal elements are also nonzero to reflect the cross-correlation among the at-site skewness

estimators 

i γ . 

A critical step for a GLS analysis is estimating the 

cross-correlation of the skewness estimators. Martins and 

Stedinger (2002) used Monte Carlo experiments to derive a 

relation between the cross-correlation of the skew coefficient 

estimators at two stations i and j as a function of the crosscorrelation of concurrent annual maximum flows, ρij: 

   ( ) , , ( )

where

is the cross-correlation of concurrent annualpeak discharges for two gaged stations,

is a constant between 2.8 and 3.3, and

is a factor that accounts for the sample

i j ij ij ij

ij

ij

Sign cf

cf

= κ

κ

ργ γ ρ ρ

ρ

size

difference between stations and their

concurrent-record length and is defined as

 follows:

(6)

/ , ( )( )

where

is the length of the period of concurrent

record,

and are the number of nonconcurrent 

observations corresponding to sites 

and , respectively.

ij ij ij i ij j

ij

i j

cf n n n n n

n

n n

i

j

= ++

(7)
Analytical Methods 13

Cross-Correlation Model of Concurrent AnnualPeak Discharge

 A cross-correlation model for the annual- peak 

discharges in California was developed using 21 sites with 

more than 65 years of concurrent records containing no 

censored peaks. None of the key dam sites identified by 

the ACOE were used in this analysis because annual-peak 

discharge at those sites was estimated. Various models 

relating the cross-correlation of the concurrent annual-peak 

discharge at two sites, ρij, to various basin characteristics 

were considered. In general, a logit model using the Fisher 

Z Transform (Z = log[(1+r)/(1-r)] ) provided a convenient 

transformation of the sample correlations rij from the 

(-1, +1) range to the (-¥,+¥) range. The adopted model 

for estimating the cross–correlations of concurrent annualpeak discharge at two stations, which used the distance 

between basin centroids, Dij, as the only explanatory variable, 

is 

 ( )

( )

exp 2 1

exp 2 1

ij

ij

ij

Z

Z

- = +

ρ , (8)

where

 Z D ij = - exp 0.27 0.0037 ( ij). (9)

 An ordinary least squares regression analysis based 

on 159 station-pairs indicated that this model is as accurate 

as one having 52 years of concurrent annual peaks from 

which to calculate a cross-correlation. Figure 3 shows the 

fitted relation between Z and the distance between the basin 

centroids together with the plotted sample data from the 159 

station-pairs of data. Figure 4 shows the functional relation 

between the untransformed cross correlation and the distance 

between the basin centroids in the California study and the 

Southeastern United States study. The cross correlations 

decrease more gradually with increasing distance between the 

basin centroids in California than they do in the Southeastern 

United States. This difference between California and 

the Southeastern United States indicates that large floodproducing storms cover more area in California than in the 

Southeastern United States. 

The cross-correlation model was used to estimate 

site-to-site cross correlations for concurrent annual-peak 

discharges at all pairs of sites. Figure 5 is a histogram of the 

relative frequency of the distribution of the estimated cross 

correlations among the 158 sites in the California data set 

and, for comparison, the distribution of the cross correlations 

among 342 sites in the Southeastern United States. 

DISTANCE BETWEEN BASIN CENTROIDS, IN MILES

FISHER Z TRANSFORM OF CROSS CORRELATION

0.0

0 100 200 300 400 500 600

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Data for 159 site pairs each having

 65 or more years of concurrent record

Z = exp (0.27 - 0.0037D)

Figure 3. Relation between the Fisher Z transform (Z) of logs of annual-peak discharge and 

distance between basin centroids for 159 station-pairs in California.
14 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006 CALCULATED CROSS CORRELATION OF LOGS OF ANNUAL-PEAK DISCHARGE

0.0

0.2

0.4

0.6

0.8

1.0

California 

Southeastern United States

DISTANCE BETWEEN BASIN CENTROIDS, IN MILES

0 100 200 300 400 500 600

IP017136_Figure 04

Figure 4. Relation between the cross-correlation of logs of annual-peak discharge and the 

distance between basin centroids based on data from 159 station-pairs in California and 1,317 

station-pairs in the Southeastern United States.

CROSS CORRELATION OF ANNUAL-PEAK DISCHARGE

RELATIVE FREQUENCY

0.0

0 to 0.1 0.1 to 0.2 0.2 to 0.3 0.3 to 0.4 0.4 to 0.5 0.5 to 0.6 0.6 to 0.7 0.7 to 0.8 0.8 to 0.9 0.9 to 1

0.1

0.2

0.3

0.4

0.5

California data-158 sites, 12,403 station pairs

Southeast U.S. data-342 sites, 58,311 station pairs

Figure 5. Histogram of relative frequency of calculated cross-correlation values in California 

(158 sites) and in the Southeastern United States (342 sites).
Analytical Methods 15

Methodology Adjustments for California

The Southeastern United States regional skew analysis 

illustrates how a Bayesian GLS analysis would generally 

proceed (Feaster and others, 2009; Gotvald and others, 2009; 

Veilleux, 2009; and Weaver and others, 2009). However, 

when a Bayesian GLS analysis of the California data set was 

attempted, reliable results were not obtained because of the 

large cross correlations. Thus, an alternative procedure that 

uses a combination of Bayesian WLS and GLS was developed 

so that the regional skew analysis would provide more stable 

and defensible results. The need for the alternative procedure 

and the specific computational steps for the procedure are 

described in Appendix B. The results of the California regional 

skew regression using the alternative procedure are provided 

below.

All of the available basin characteristics were initially 

considered as explanatory variables in the regression analysis 

for regional skew. The one key basin characteristic that was 

statistically significant in explaining the site-to-site variability 

in skew was the mean basin elevation (ELEV). Table 7 gives 

the final results for three models: a constant skew denoted 

“Constant,” a model that uses a linear relation between skew 

and mean basin elevation denoted “Elev,” and a model that 

uses a nonlinear relation between skew and mean basin 

elevation denoted “NL-Elev.” 

As shown in table 7, the linear Elev model has a Pseudo 2 Rδ of 41 percent, while the nonlinear NL-Elev model has a

larger Pseudo 2 Rδ of 48 percent and a slightly smaller AVPnew.

The Pseudo 2 Rδ values describe the fraction of the variability 

in the true skews explained by each model (Gruber and others, 

2007). A Constant model does not explain any variability, so

the Pseudo 2 Rδ is equal to 0 percent. Also, the posterior mean

of the model error variance, 2 σ δ , for the NL-Elev model is 

0.10, which is smaller than that for the linear Elev model 

( 2 σ δ = 0.12) and substantially smaller than that for the 

Constant model ( 2 σ δ = 0.20). The average sampling error 

variance (ASEV) in table 7 is the average error in the regional 

skewness estimator at the sites in the data set. 

The average variance of prediction at a new site (AVPnew) 

corresponds to the mean square error (MSE) used in Bulletin 

17B to describe the precision of the generalized skew. In 

table 7, the NL-Elev model has the lowest AVPnew, equal to 

0.14. However, this AVPnew is an average value computed by 

averaging the variance of prediction at a new site (VPnew) for 

all of the 158 sites in the California study. Just as generalized 

skew varies from site to site, depending upon mean basin 

elevation, so too do the values of VPnew. Table 8 gives values 

of the variance of prediction for the regional skew, VPnew , 

and effective record length (ERL) for the NL-Elev model for 

values of mean basin elevation between 0 and 11,000 ft. 

Thus, the NL-Elev regional skew model for California 

has effective record lengths ranging from 52 years to 65 

years, depending upon the mean basin elevation. A VPnew

ranging from about 0.13 to 0.17 is a marked improvement 

over the Bulletin 17B skew map, whose MSE is 0.302 

(Interagency Advisory Committee on Water Data, 1982) for a 

corresponding effective record length of only 17 years.

The nonlinear elevation model provides a reasonable fit 

for the California regional skew data (fig. 6). While the more 

complicated nonlinear model is not that different from the 

simpler linear elevation model, the nonlinear model provides 

smaller values of positive skew at high elevations and less 

negative values of skew for low elevations. For example, when 

a mean basin elevation is zero at sea level, the nonlinear model 

provides a regional skew of -0.62, while the linear elevation 

model provides a regional skew of -0.76. Conversely, when 

a mean basin elevation is 11,000 ft, the nonlinear model 

provides a regional skew of 0.61, while the linear model 

provides a regional skew of 0.79. These differences, though 

subtle, are significant, and the nonlinear model indicates that 

regional skew flattens out in the tails instead of continually 

increasing in absolute value. This flattening of skew at both 

low and high elevations is consistent with the relation between 

the timing of annual-peak discharge and the elevation, which 

is largely reflective of the degree of rain-snow interaction 

affecting peak discharge. Annual peak-discharges from basins 

that have mean elevations less than about 4,000 ft have little 

rain-snow interaction (fig. 2) and thus, might be expected to 

have constant or near-constant regional skews. Likewise, at 

the other extreme, basins at very high elevations tend to have 

annual-peak discharges that are predominantly the result of 

spring snowmelt events. Thus, beyond some point, higher 

elevation has less effect on the distribution of annual maxima 

because few, if any, of the flood peaks are caused by winter 

rainfall events. 

Only six sites that have a mean basin elevation greater 

than about 8,000 ft were used in the regional skew analysis 

(fig. 2). Because of the scarcity of such high-elevation sites, 

the calculated regional skew values for high-elevation sites 

may be less reliable than those for lower-elevation sites. In 

addition, combining a few large, winter-rain caused peaks 

with many more smaller, spring snowmelt peaks often results 

in fitted frequency curves from the LP3 distribution with a 

sharp upward curvature that may poorly represent the true 

frequency of the largest floods. Peak-discharge data for sites 

that have mean basin elevations above about 8,000 ft need 

to be examined to determine if a mixed-population analysis 

for determining flood frequency described in Bulletin 17B 

might be more appropriate than the standard LP3 method. 

When a mixed-population analysis is used the rain-caused 

floods and snowmelt floods are analyzed separately, and the 

separate frequency curves are combined to represent the joint 
16 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

probability of flooding from any cause (Murphy, 2001). The 

Sierra Nevada in California has previously been indicated 

as an area having a mixture of rain and snowmelt events 

(Interagency Advisory Committee on Water Data, 1982, 

p. 16), and the ACOE commonly analyzes rain-caused floods 

separately from snowmelt-caused floods in this area (U.S. 

Army Corps of Engineers, Sacramento District, 2002). 

Flood-Frequency Results

Flood-frequency estimates for 158 stations used in the 

regional skew analysis and 206 additional stations in the 

Sacramento–San Joaquin River Basin are shown in table 1

at the back of the report. Table 1 includes information about 

peak-discharge record lengths, historical record periods, 

censored data and thresholds, and skew coefficients also. All 

flood-frequency estimates in table 1 were developed by using 

the EMA program.

The flood-frequency estimates were calculated by 

applying the LP3 probability distribution, with a weighted 

skew as described in Bulletin 17B, to the annual peakdischarge data at the stations. The weighted skew is 

determined by weighting the station skew and the regional 

skew inversely proportional to their respective mean square 

errors, as shown in the following equation:

( ) ( ),

where

is the weighted skew,

is the station skew,

is the regional skew, and

 and are the mean square error of the 

regional and station skew,

respectively.

Rs sR

w

R s

w

s

R

R s

MSE G MSE G

G

MSE MSE

G

G

G

MSE MSE

+ = + (10)

Figure 6. Relations between the unbiased at-site skew and the mean basin elevation for 

158 sites in California. The lines represent a model based on a constant skew (Constant), a 

model with a linear relation between skew and mean basin elevation (Elev), and a model with 

a nonlinear relation between skew and mean basin elevation (NL-Elev). The models were 

developed from Bayesian weighted least squares and generalized least squares (WLS-GLS) 

analyses.

MEAN BASIN ELEVATION, IN FEET

UNBIASED AT-SITE SKEW

-1.5

-1.0

-0.5

0.0

0.5

0 2,000 4,000 6,000 8,000 10,000

1.0

1.5

At-site data

Constant model

Elevation model 

Nonlinear elevation model 

IP017136_Figure 06
Flood-Frequency Results 17

The MSER is equivalent to the variance of prediction for 

a new site (VPnew) described in the previous section. Bulletin 

17B provides equations for calculating MSES, but these 

equations may not be reliable when peak-flow data are heavily 

censored. The EMA program, which can use heavily censored 

data, uses a first-order approximation for MSES, developed by 

Cohn and others (2001). 

Flood-frequency curves show the LP3 distribution fitted 

to the recorded annual peak-discharge data for selected sites 

in California (figs. 7–10). Each figure shows the fitted curves 

based on station skew and weighted skew with the 90-percent 

confidence interval for the true flood-frequency distribution 

based on use of the weighted skew. The confidence interval 

determined by the EMA program defines a confidence band 

(difference between the upper and lower confidence limits) 

that generally is wider than the confidence band calculated 

using the conventional LP3 analysis, because the EMA results 

include the uncertainty in the estimated skew. As described 

by Cohn and others (2001), the EMA program produces more 

realistic confidence intervals than does the simple method used 

in the conventional LP3 analysis.

Figures 7 and 8 contain typical flood-frequency curves 

for stations that have no censored peak-flow data (no low 

outliers or historical periods) and that have mean basin 

elevations below 4,000 ft. These EMA-developed curves are 

identical to those that would be produced by a conventional 

LP3 frequency analysis and also represent flood-frequency 

curves for stream sites with little or no snowmelt runoff. The 

flood-frequency curves in figure 7 are for a station that has 

a relatively long period of record,73 years (Saratoga Creek, 

station 11169500), whereas the flood-frequency curves in 

figure 8 are for a station that has a short flow record, 11 years 

(Kingsbury Creek, station 11402700). The fitted curves based 

on station skew and on weighted skew are different in figure 7, 

indicating a substantial difference between regional skew and 

station skew for this long-record site. Also, the confidence 

interval for the long-record site in figure 7 is narrower than 

the confidence interval for the short-record site in figure 8. 

Many of the sites for which flood-frequency estimates were 

developed are for sites that had little or no censored data 

(table 1). Thus, the flood-frequency curves shown in figures 7

and 8 are typical—with varying degrees of scatter, widths of 

confidence intervals, and record lengths—of those for many of 

the sites where snow has little or no effect on peak discharge. 

ANNUAL EXCEEDANCE PROBABILITY, IN PERCENT

708090959899 50 0.20.5125102030

PEAK DISCHARGE, IN CUBIC FEET PER SECOND 

10

100

1,000

10,000

LP3 fit using weighted skew

LP3 fit using station skew

Drainage area = 9.2 mi2

Mean basin elevation = 1,750 ft

Station skew = -0.08

Regional skew = -0.53

Saratoga Creek 

(Station 11169500)

Flood-frequency curves

90-percent confidence interval

Recorded data

Figure 7. Flood-frequency curves for Saratoga Creek, California, (station 11169500) based on 

73 years of recorded data with no censoring of annual-peak discharge. LP3, log Pearson Type 3; 

mi2

, square mile; ft, foot.
18 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Flood-frequency curves in figure 9 are for a highelevation (mean basin elevation is 8,610 ft) station (West 

Walker River, station 10296500) that had censored data (an 

historical period with a perception threshold discharge equal 

to the largest recorded discharge in the systematic record). 

The largest recorded discharge plots above the fitted LP3 

curves, but it is well within the relatively narrow 90-percent 

confidence interval for the true distribution. The fitted curves 

based on station skew and weighted skew are almost identical 

for this site. Only three of the 81 recorded peak discharges 

at station 10296500 occurred during the winter-storm rainy 

season (generally November through March), but the two 

largest annual-peak discharges were winter-storm rainy 

season peaks (fig. 9). In contrast, almost all of the annual 

floods on Kingsbury Creek (station 11402700) were from 

the November–March period. Thus, figures 8 and 9 represent 

the shift from a low-elevation flood hydrology, dominated by 

winter rainfall events, to a high-elevation flood hydrology, 

dominated by snow-melt events with only a few—usually the 

largest—annual peaks resulting from winter rainfall. 

Figure 9 generally represents sites where rain-snow 

interaction affected the annual-peak discharges. Winter-storm 

rain season peaks tend to be the largest recorded peaks at these 

sites, and the differences between the large rain peaks and the 

other peaks are large enough to result in positively skewed 

LP3 distributions. The differences between winter-storm 

season rain peaks and the other peaks may be so large that an 

LP3 distribution, limited by three parameters, cannot provide a 

reasonable fit to the data, and a mixed-population analysis may 

be the only way to reasonably determine flood frequency. 

ANNUAL EXCEEDANCE PROBABILITY, IN PERCENT

0.512510203050708090959899 0.2

PEAK DISCHARGE, IN CUBIC FEET PER SECOND 

1

10

100

1,000

10,000

Drainage area = 1.4 mi.2

Mean basin elevation = 3,900 ft.

Station skew = -0.16

Regional skew = -0.23

Kingsbury Creek 

(Station 11402700)

IP017136_Figure 08

LP3 fit using weighted skew

LP3 fit using station skew

Flood-frequency curves

90-percent confidence interval

Recorded data

Figure 8. Flood-frequency curves for Kingsbury Creek, California, (station 11402700) based on 11 

years of recorded data with no censoring of annual-peak discharge. LP3, log Pearson Type 3; mi2

, 

square mile; ft, foot.
Flood-Frequency Results 19

Figure 9. Flood-frequency curves for West Walker River (station 10296500), California, 

based on 81 years of data recorded during an historical period of 106 years with a perception 

threshold discharge equal to the largest discharge during the 81-year record period. LP3, log 

Pearson Type 3; mi2

, square mile; ft, foot. 

ANNUAL EXCEEDANCE PROBABILITY, IN PERCENT

708090959899 50 0.20.5125102030

PEAK DISCHARGE, IN CUBIC FEET PER SECOND 

1,000

10,000

Drainage area = 244 mi.2

Mean basin elevation = 8,610 ft.

Station skew = 0.40

Regional skew = 0.46

West Walker River 

(Station 10296500)

IP017136_Figure 09

LP3 fit using weighted skew

LP3 fit using station skew

Flood-frequency curves

90-percent confidence interval

Recorded data—winter rainy season

Recorded data—snowmelt season

Figure 10 shows frequency curves for a site (Cantua Creek, 

station 11253310) that had heavily censored data (the complete 

lower tail consisting of 24 recorded peaks, including one zero 

value, were considered to be low outliers). While the frequency 

curves generally fit the upper tail of the data, the confidence 

intervals are especially wide owing to the large number of 

censored peaks. 

The flood-frequency curve examples in figures 7 through 

10 illustrate how well the LP3 distribution fit the recorded flood 

data for a variety of different record lengths, data-censoring 

conditions, and mean basin elevations. Overall, using the newly 

developed regional skew function and applying the EMA 

for fitting the LP3 distribution provide reasonable estimates 

of flood frequency at gaged sites in the Sacramento–San 

Joaquin River Basin in California. Flood-frequency estimates 

at some higher-elevation sites might be improved by using 

a mixed-populations analysis. Although mixed-population 

analyses were beyond the scope of the current report, the 

flood-frequency study is ongoing in California and mixedpopulation analysis will be considered for some sites tied to 

poor-fitting LP3 frequency curves. 
20 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Summary

Reliable estimates of peak discharge for various 

exceedance probabilities, commonly referred to as floodfrequency estimates, are needed by engineers, land-use 

planners, resource managers, and scientists. Accordingly, 

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

U.S. Forest Service, Federal Emergency Management Agency 

(FEMA), and the USGS Multi-Hazards Demonstration Project 

(MHDP), initiated a regional flood-frequency study for 

California in 2008. An important aspect of the comprehensive 

USGS flood-frequency study for California was developing 

new regional skew relations for California. 

Because of the common interest and the need for updated 

flood-frequency information in the Sacramento and San 

Joaquin River Basin by the USGS and the U.S. Army Corps

of Engineers (ACOE), both agencies developed a secondary 

cooperative program for estimating unregulated annualpeak discharge at 16 selected key dam sites in the basin and 

using these estimated discharges as part of the regional skew 

analysis. A method using maintenance of variance extension 

(MOVE) techniques was used to estimate annual-peak 

discharge at the key dam sites.

Annual-peak discharges on streams draining the 

Sierra Nevada almost always occur during the winter and 

spring (November through June) and result from a complex 

interaction of rain and snow. Rain is the predominant cause 

of peak discharge in basins that have mean elevations below 

about 4,000 ft, and the interaction of rain and snow increases 

with increasing elevation above that elevation. For basins 

that have mean elevations above about 8,000 ft, snowmelt 

is the predominant cause of peak discharges. The rain-snow 

interaction significantly affects regional skew in California. 

To determine whether annual peak flow data indicate 

trends in California, 69 sites that were used in the regional 

skew analysis and had complete annual discharge records 

from 1977 to 2006 (30 years) were tested for monotonic 

trends using Kendall’s tau, a non-parametric test for trends. 

The locations of the 69 sites represented the locations of all 

158 sites used for the regional skew analysis. Of the 69 sites 

tested for trends in annual-peak discharge over the 30-year 

period, none had p-values less than or equal to 0.05. On the 

basis of the trend-test results, monotonic trends in annual-peak 

discharge were not considered to be a factor in California and 

thus do not affect the interpretation or overall reliability of 

flood-frequency results.

ANNUAL EXCEEDANCE PROBABILITY, IN PERCENT

0.512510203050708090959899 0.2

PEAK DISCHARGE, IN CUBIC FEET PER SECOND 

1

10

100

1,000

100,000

10,000

Drainage area = 46.4 mi.2

Mean basin elevation = 2,540 ft.

Station skew = -0.64

Regional skew = -0.44

Cantua Creek 

(Station 11253310)

IP017136_Figure 10

LP3 fit using weighted skew

LP3 fit using station skew

Flood-frequency curves

90-percent confidence interval

Recorded data

Censored low outliers not used

 for fitting LP3 curve

Figure 10. Flood-frequency curves for Cantua Creek (station 11253310), California, based on 

49 years of recorded data with all peaks smaller than the 50-percent exceedance probability 

censored as low outliers.
References Cited 21

Flood-frequency estimates for gaged sites are computed 

by fitting a mathematical probability distribution to the series 

of annual-peak discharges. The LP3 distribution, which is the 

Pearson Type 3 distribution applied to the logarithms (base 10) 

of annual-peak discharge data, commonly is used to estimate 

flood frequency in the United States and was used for the 

current California study. The expected moment algorithm 

(EMA) was used for an initial LP3 frequency analysis in order 

to determine station skew for all sites used in the regional 

skew analysis, with an adjustment for zero flows, floods 

identified as low outliers, and historical flood information.

The California regional skew study was based on 

Bayesian regression procedures. To properly account for 

problems caused by large cross correlations among annualpeak discharges, a combination of Bayesian weighted least 

squares (WLS) and generalized least squares (GLS) regression 

was adopted to ensure that the regression model and the 

diagnostics for the regression would be reliable.

 Various basin characteristics were considered as possible 

explanatory variables in the regression analysis for regional 

skew. The characteristic that best explained the site-to-site 

variability in skew was the mean basin elevation (ELEV). 

Three models were developed: (1) a constant skew denoted 

“Constant,” (2) a model that used a linear relation between 

skew and mean basin elevation denoted “Elev,” and (3) a 

model that used a nonlinear relation between skew and mean 

basin elevation denoted “NL-Elev.” The average variance 

of prediction at a new site (AVPnew) corresponds to the mean 

square error (MSE) to describe the precision of the generalized 

skew. AVPnew was lowest for the NL-Elev model (0.14). Just 

as generalized skew varies from site-to-site depending upon 

mean basin elevation, so too do the values of variance of 

prediction at a new site, VPnew . The NL-Elev regional skew 

model for California has VPnew values ranging from about 

0.13 to 0.17 and effective record lengths between 52 years and 

65 years, depending upon the value of mean basin elevation. 

A VPnew between 0.13 and 0.17 is a marked improvement over 

the Bulletin 17B skew map, whose reported MSE is 0.302 

with a corresponding effective record length of only 17 years.

Flood-frequency estimates for 158 sites used in the 

regional skew analysis and 206 additional sites in the 

Sacramento–San Joaquin River Basin were developed 

using the EMA program and applying the LP3 probability 

distribution with a weighted skew as described in Bulletin 17B 

to the annual-peak discharge data at the sites. Overall, using 

the newly developed regional skew function and applying the 

EMA program for fitting the LP3 distribution provide the best 

available estimates of flood frequency at gaged sites in the 

Sacramento–San Joaquin River Basin in California.

References Cited

Cohn, T.A., Lane, W.L., and Baier, W.G., 1997, An algorithm 

for computing moments-based flood quantile estimates 

when historical flood information is available: Water 

Resources Research, v. 39, no. 9, p. 2089–2096.

Cohn, T.A., Lane, W.L and Stedinger, J.R.,2001, Confidence 

intervals for EMA flood quantile estimates: Water 

Resources Research, v. 37, no. 6, p. 1695–1706 .

England, J.F., Jr., 1999, Draft user’s manual for program 

EMA, at-site flood frequency analysis with historical/

paleohydrologic data: Bureau of Reclamation, 52 p.

England, J.F., Jr., Jarrett, R.D., and Salas, J.D., 2003a, 

Data-based comparisons of moments estimators that use 

historical and paleoflood data: Journal of Hydrology, v. 278, 

no. 1–4, p. 170–194.

England, J.F., Jr., Salas, J.D., and Jarrett, R.D., 2003b, 

Comparisons of two moments-based estimators that utilize 

historical and paleoflood data for the log-Pearson type III 

distribution: Water Resources Research, v. 39, no. 9, p. 

1243, doi:10.1029/2002WR001791.

Feaster, T.D., Gotvald, A.J., and Weaver, J.C., 2009, 

Magnitude and frequency of rural floods in the southeastern 

United States, 2006: Volume 3, South Carolina: U.S. 

Geological Survey Scientific Investigations Report 2009-

5156, 226 p. 

Gotvald, A.J., Feaster, T.D., and Weaver, J.C., 2009, 

Magnitude and frequency of rural floods in the southeastern 

United States, 2006: Volume 1, Georgia: U.S. Geological 

Survey Scientific Investigations Report 2009–5043, 120 p. 

Griffis, V.W. , Stedinger, J.R., and Cohn, T.A. , 2004, LP3 

quantile estimators with regional skew information and 

low outlier adjustments: Water Resources Research, v. 40,

W07503, doi:1029/2003WR002697, 17 p.

Griffis, V.W., and Stedinger, J.R., 2007, The use of GLS 

regression in regional hydrologic analyses: Journal of 

Hydrology, v. 344, p. 82–95. 

Griffis, V.W., and Stedinger, J.R., 2009, Log-Pearson type 3 

distribution and its application in flood frequency analysis, 

III: sample skew and weighted skew estimators: Journal of 

Hydrology, v. 14, no. 2, p. 121–130. 
22 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Gruber, A.M., Reis, D.S., Jr., and Stedinger, J.R., 2007, 

Models of regional skew based on Bayesian GLS 

regression, Paper 40927-3285, in Kabbes, K.C., ed., World 

Environmental and Water Resources Congress 2007 - 

Restoring our Natural Habitat, American Society of Civil 

Engineers, Tampa, Florida, May 15–19, 2007.

Gruber, A.M., and Stedinger, J.R., 2008, Models of LP3 

regional skew, data selection, and Bayesian GLS regression, 

Paper 596, in Babcock, R., and Walton, R., eds., World 

Environmental & Water Resources Congress 2008 - 

Ahupua‘a, American Society of Civil Engineers, Honolulu, 

Hawaii, May 12–16, 2008.

Helsel, D.R., and Hirsch, R.M., 1992, Statistical methods in 

water resources: New York, Elsevier, 522 p. 

Hirsch, R.M., 1982, A comparison of four streamflow record 

extension techniques: Water Resources Research, v. 18, no. 

4, p. 1081–1088.

Interagency Advisory Committee on Water Data, 1982, 

Guidelines for determining flood-flow frequency, Bulletin 

#17B of the Hydrology Subcommittee: Office of Water 

Data Coordination, U.S. U.S. Geological Survey, 183 p. 

Available at http://water.usgs.gov/osw/bulletin17b/dl_flow.

pdf.

Martins, E.S., and Stedinger, J.R., 2002, Cross-correlation 

among estimators of shape: Water Resources Research, v. 

38, no. 11, 7p. 

Mount, J. F., 1995, California rivers and streams - The 

conflict between fluvial process and land use: University of 

California Press, p. 94–100.

Murphy, P.J., 2001, Evaluation of mixed-population flood 

frequency evaluation: Journal of Hydrologic Engineering, v. 

6, p. 62–70.

Reis, D.S., Jr., Stedinger, J.R., and Martins, E.S., 2005, 

Bayesian generalized least squares regression with 

application to the log Pearson type III regional skew 

estimation: Water Resources Research, v. 41, W10419, 

doi:10.1029/2004WR003445, 14 p.

Ries, K.G., Guthrie, J.D., Rea, A.H., Steeves, P.A., and 

Stewart, D.W., 2008, Streamstats: A water resources web 

application: U.S. Geological Survey Fact Sheet 2008-3067, 

6 p.

Stedinger, J.R., and Tasker, G.D., 1985, Regional hydrologic 

analysis—Ordinary, weighted and generalized least squares 

compared: Water Resources Research, v. 21, no. 9, p. 

1421–1432. [with correction, Water Resources Research, 

v. 22, no. 5, p. 844, 1986.]

Tasker, G.D., and Stedinger, J.R., 1986, Regional skew 

with weighted LS regression: Journal of Water Resources 

Planning and Management, v.112, no. 2, p. 225–237. 

Thomas, B.E., Hjalmarson, H.W., and Waltemeyer, S.D., 1997, 

Methods for estimating magnitude and frequency of floods 

in the southwestern United States: U.S. Geological Survey 

Water-Supply Paper 1997-2433, 205 p.

U.S. Army Corps of Engineers, 2002, Sacramento and San 

Joaquin River Basins comprehensive study: Technical 

studies documentation Appendix B - Synthetic hydrology 

technical documentation, accessed May 10, 2010, at 

http://www.compstudy.net/docs/techstudies/app_b_

synthetichydrology_001.pdf.

Veilleux, A.G., 2009, Bayesian GLS regression for 

regionalization of hydrologic statistics, floods, and Bulletin 

17B skew: Ithaca, New York, Cornell University, M.S. 

Thesis, August, 170 p.

Vogel, R.M., and J.R., Stedinger, 1985, Minimum variance 

streamflow record augmentation procedures: Water 

Resources Research, v. 21, no. 5, p. 715–723. 

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

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

Water-Resources Investigations Report 77-21, 96 p..

Weaver, J.C., Feaster, T.D., and Gotvald, A.J., 2009, 

Magnitude and frequency of rural floods in the southeastern 

United States, 2006—Volume 2, North Carolina: U.S. 

Geological Survey Scientific Investigations Report 

2009–5158, 113 p. Available at http://pubs.usgs.gov/

sir/2009/5158/.
Table 1 23

Table 1. Streamflow-gaging stations and statistical data used to analyze regional skew in California and to determine flood frequency 

for the Sacramento-San Joaquin River Basin, California.

Table 1 is available in a Microsoft© Excel spreadsheet and can be accessed and downloaded at URL http://pubs.usgs.gov/

sir/2010/5260.

Table 2. Basin characteristics for analyzing regional skew in California.

[Abbreviations: DRNAREA is the drainage area of the basin. BASINPERIM is the perimeter of the basin. DEM is digital elevation model. NHDPlus is the 

National Hydrography Dataset. RELIEF is the difference between the maximum and minimum elevations in the basin. ELEVMAX and ELEVMIN are the 

maximum and minimum elevations in the basin, respectively. LAKEAREA is the percentage of the basin drainage area covered by lakes and ponds. EL6000 

is the percentage of the basin above 6,000 feet in elevation. OUTLETELEV is the basin elevation at the gage. RELRELF is the basin RELIEF divided by the 

BASINPERIM. DIST2COAST is the distance from the gage to the Pacific Ocean measured perpendicular to the eastern border of California. ELEV is the 

mean basin elevation. BSLDEM30 is the average basin slope computed from a 30-meter digital elevation model (DEM). FOREST is the percentage of the 

basin covered by forest. IMPERV is the percentage of the basin covered by impervious area. PRECIP is the basin averaged mean annual precipitation. PRISM 

is the Parameter-Elevation Regressions on Independent Slopes Model. JANMAX is the basin averaged January maximum temperature. JANMIN is the basin 

averaged January minimum temperature. LAT_CENT is the latitude of the basin centroid. LONG_CENT is the longitude of the basin centroid. m, meter; >, 

greater than]

Name Description Data source

DRNAREA Area, in square miles 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

BASINPERIM Distance, in miles 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

RELIEF Relief, in feet 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

ELEVMAX Maximum elevation, in feet 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

ELEVMIN Minimum elevation, in feet 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

LAKEAREA Percentage of area covered by lakes and ponds 2001 National Land Cover Database (NLCD) - Land 

Cover http://www.mrlc.gov/nlcd_multizone_map.php

EL6000 High Elevation Index - Percentage of area with elevation 

>6,000 feet

30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

OUTLETELEV Elevation at outlet, in feet 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

RELRELF Relative relief, in feet per mile 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

DIST2COAST Distance, in miles, from basin centroid to coast along a line 

perpendicular to the eastern California border

30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

ELEV Average basin elevation, in feet 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

BSLDEM30M Average basin slope, in percent 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

FOREST Percentage of basin covered by forest 2001 National Land Cover Database (NLCD) - Percent 

Canopy http://www.mrlc.gov/nlcd_multizone_map.php

IMPERV Percentage of basin covered by impervious surface 2001 National Land Cover Database (NLCD) - Percent 

Impervious http://www.mrlc.gov/nlcd_multizone_map.

php

PRECIP Mean annual precipitation, in inches 800M resolution PRISM 1971-2000 data http://www.

prism.oregonstate.edu/products/

JANMAX Average maximum January temperature, in degrees Fahrenheit 800M resolution PRISM 1971-2000 data http://www.

prism.oregonstate.edu/products/

JANMIN Average minimum January temperature, in degrees Fahrenheit 800M resolution PRISM 1971-2000 data http://www.

prism.oregonstate.edu/products/

LONG_CENT Longitude of the basin centroid, in degrees 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/

LAT_CENT Latitude of the basin centroid, in degrees 30-m DEM, NHDPlus elev_cm grid http://www.horizonsystems.com/NHDPlus/
24 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table 3. Basin characteristics for sites used in the regional skew analysis, California.

Table 3 is available in a Microsoft Excel spreadsheet and can be accessed and downloaded at URL http://pubs.usgs.gov/

sir/2010/5260.

Table 4. Results of trend tests for annual peak discharge at selected sites in California.

Site 

number Station number Station name Kendall's tau p-value

2 10296500 West Walker River near Coleville, California 0.20 0.12

4 10336676 Ward Creek at Hwy 89 near Tahoe Pines, California 0.10 0.43

6 10343500 Sagehen Creek near Truckee, California 0.03 0.86

15 11015000 Sweetwater River near Descanso, California –0.17 0.20

16 11028500 Santa Maria Creek near Ramona, California –0.16 0.21

18 11042400 Temecula Creek near Aguanga, California –0.23 0.08

20 11055500 Plunge Creek near East Highlands, California –0.12 0.35

21 11055800 City Creek near Highland, California –0.03 0.84

26 11075800 Santiago Creek at Modjeska, California –0.18 0.16

29 11098000 Arroyo Seco near Pasadena, California –0.04 0.76

42 11124500 Santa Cruz Creek near Santa Ynez, California 0.12 0.37

44 11132500 Salsipuedes Creek near Lompoc, California 0.09 0.48

47 11136800 Cuyama River below Buckhorn Canyon near Santa Maria, California –0.03 0.86

51 11141280 Lopez Creek near Arroyo Grande, California 0.12 0.35

52 11143000 Big Sur River near Big Sur, California 0.08 0.53

53 11143200 Carmel River at Robles del Rio, California 0.10 0.46

56 11147500 Salinas River at Paso Robles, California 0.10 0.46

57 11148500 Estrella River near Estrella, California –0.11 0.38

58 11148900 Nacimiento River below Sapaque Creek near Bryson, California 0.08 0.54

59 11151300 San Lorenzo Creek below Bitterwater Creek near King City, California 0.05 0.72

60 11152000 Arroyo Seco near Soledad, California 0.13 0.34

62 11152600 Gabilan Creek near Salinas, California 0.17 0.20

66 11159200 Corralitos Creek at Freedom, California 0.24 0.06

67 11160000 Soquel Creek at Soquel, California 0.21 0.10

68 11160500 San Lorenzo River at Big Trees, California 0.13 0.34

69 11162500 Pescadero Creek near Pescadero, California 0.18 0.18

71 11162630 Pilarcitos Creek at Half Moon Bay, California 0.13 0.34

72 11164500 San Francisquito Creek at Stanford University, California 0.14 0.27

73 11169500 Saratoga Creek at Saratoga, California 0.03 0.83

75 11176400 Arroyo Valle below Lang Canyon near Livermore, California 0.11 0.41

77 11182500 San Ramon Creek at San Ramon, California 0.07 0.59

96 11200800 Deer Creek near Fountain Springs, California 0.08 0.53

126 11224500 Los Gatos Creek above Nunez Canyon near Coalinga, California 0.00 1.00

135 11237500 Pitman Creek below Tamarack Creek, California 0.05 0.69

136 11242400 North Fork Willow Creek near Sugar Pine, California 0.00 0.99

142 11253310 Cantua Creek near Cantua Creek, California –0.04 0.78

164 11274500 Orestimba Creek near Newman, California 0.09 0.47

165 11274630 Del Puerto Creek near Patterson, California 0.12 0.34

175 11284400 Big Creek above Whites Gulch near Groveland, California 0.02 0.90

185 11294500 North Fork Stanislaus River near Avery, California –0.07 0.58

205 11316800 Forest Creek near Wilseyville, California 0.00 0.99

206 11317000 Middle Fork Mokelumne River at West Point, California 0.06 0.67

207 11318500 South Fork Mokelumne River near West Point, California 0.03 0.83

226 11342000 Sacramento River at Delta, California 0.13 0.33

231 11348500 Pit River near Canby, California 0.10 0.43

251 11374000 Cow Creek near Millville, California 0.00 0.99

256 11376000 Cottonwood Creek near Cottonwood, California 0.11 0.41

267 11381500 Mill Creek near Los Molinos, California –0.04 0.79

270 11383500 Deer Creek near Vina, California 0.04 0.75

274 11390000 Butte Creek near Chico, California 0.10 0.45
Table 4 25

Site 

number Station number Station name Kendall's tau p-value

297 11402000 Spanish Creek above Blackhawk Creek at Keddie, California 0.05 0.71

324 11427700 Duncan Canyon Creek near French Meadows, California 0.05 0.71

325 11431800 Pilot Creek above Stumpy Meadows Reservoir, California 0.03 0.84

332 11439500 South Fork American River near Kyburz (river only), California 0.02 0.90

341 11449500 Kelsey Creek near Kelseyville California 0.14 0.29

346 11461000 Russian River near Ukiah, California –0.02 0.89

348 11468000 Navarro River near Navarro, California 0.07 0.59

349 11468500 Noyo River near Fort Bragg, California 0.11 0.40

350 11469000 Mattole River near Petrolia, California –0.02 0.89

353 11475560 Elder Creek near Branscomb, California 0.15 0.26

354 11476500 South Fork Eel River near Miranda, California –0.11 0.38

355 11477000 Eel River at Scotia, California 0.06 0.63

356 11478500 Van Duzen River near Bridgeville, California 0.18 0.18

357 11481200 Little River near Trinidad, California 0.04 0.78

359 11482500 Redwood Creek at Orick, California 0.09 0.49

360 11519500 Scott River near Fort Jones, California –0.03 0.80

362 11522500 Salmon River at Somes Bar, California –0.03 0.80

363 11523200 Trinity River above Coffee Creek near Trinity Center, California 0.10 0.45

365 11532500 Smith River near Crescent City, California 0.04 0.78

Table 4. Results of trend tests for annual peak discharge at selected sites in California.—Continued

Table 5. Key dam sites and drainage areas, periods of estimated unregulated annual-maximum-daily discharge, and periods of 

concurrent unregulated annual-maximum-daily and peak-discharge data.

[ACOE, U.S. Army Corps of Engineers; USGS, U.S. Geological Survey]

Station number 1 Station name as shown in USGS or ACOE records Drainage area 

(square mile)

Period of estimated 

unregulated, 

annual-maximumdaily-discharge 

record

Period of concurrent 

unregulated annualmaximum-daily and 

peak-discharge record

11222099 Kings River at Piedra, California 1,681 1896–1999 1900–02, 1904–07, 

1909–50

11251099 San Joaquin River below Friant, California 1,678 1911–99

11258099 Fresno River below Hidden Dam, California 258 1942–99 1942–75

11259099 Chowchilla River below Buchanan Dam, California 235 1922–23, 1932–99 1932–72

11270099 Merced River at Exchequer, California 1,038 1902–14, 1916–99 1902–13, 1916–25

11288099 Tuolumne River above La Grange Dam, California 1,532 1897–1999

11299599 Stanislaus River below Melones Dam, California 904 1932–99

11308999 Calaveras River below New Hogan Dam, California 373 1964–98

11323599 Mokelumne River below Camanche Dam, California 628 1905–97 1905–28

11335099 Cosumnes River at Michigan Bar, California 535 1908–97 1908–54

11344099 Littlejohns Creek below Farmington Reservoir, California 2 208 1951–99

11370599 Sacramento River at Keswick, California 3 6,468 1932–98 1932–43

11388099 Stony Creek below Black Butte Dam, California 742 1964–98

11407099 Feather River at Oroville, California 3,624 1902–97 1902–10

11413599 North Yuba River below Bullards Bar Dam, California 487 1941–66, 1970–97 1941–66

11446599 American River at Fair Oaks, California 1,888 1905–98 1905–54

1

 Station number is the USGS station number with the last two digits (usually zeros) replaced by 99. 

2

 All available flow data collected by ACOE.

3

 Peak-flow records available at this site from 1939-P. Peak-flow records from upstream site at Kennett (11369500—drainage area = 6,355 square miles) for 

1926–1938 were also used at this site.
26 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table 6. Unregulated, annual-maximum-daily discharge or key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Kings River San Joaquin River Fresno River Chowchilla River

11222099 11251099 11258099 11259099

Date Discharge Date Discharge Date Discharge Date Discharge

1896 9,400

1897 17,800

1898 8,140

1899 24,000

1/3/1900 13,400

1/7/1901 33,200

4/7/1902 20,800

5/13/1903 15,000

5/16/1904 13,800

6/13/1905 9,780

6/20/1906 24,900

6/3/1907 16,200

4/29/1908 6,460

6/4/1909 20,300

1/1/1910 14,700

1/31/1911 20,500 1/31/1911 41,069

5/30/1912 12,400 6/5/1912 15,481

5/23/1913 7,210 5/28/1913 6,865

1/26/1914 30,400 1/26/1914 27,426

6/1/1915 16,300 6/9/1915 15,249

6/9/1916 16,300 5/6/1916 13,559

6/9/1917 13,200 6/10/1917 13,812

6/13/1918 12,800 6/11/1918 11,618

5/29/1919 11,200 10/2/1918 11,217

5/20/1920 14,900 5/21/1920 12,867

6/8/1921 12,800 6/11/1921 12,445

6/5/1922 17,100 6/5/1922 18,184 2/11/1922 3,620

5/16/1923 11,500 5/17/1923 11,653 4/10/1923 1,990

5/8/1924 3,930 5/9/1924 4,199

5/26/1925 9,240 5/27/1925 9,928

5/5/1926 9,490 5/5/1926 10,095

5/17/1927 14,000 5/17/1927 13,778

5/15/1928 6,750 3/25/1928 11,047

6/16/1929 9,560 6/16/1929 8,669

5/28/1930 7,070 6/13/1930 6,594

5/7/1931 5,030 5/7/1931 4,358

5/17/1932 12,800 2/7/1932 14,642 12/28/1931 4,520

6/14/1933 11,900 6/15/1933 11,290 1/30/1933 331

12/13/1933 4,690 4/16/1934 3,588 2/23/1934 1,010

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California.

[Discharge is in cubic feet per second]
Table 6 27

Table 6. Unregulated, annual-maximum-daily discharge or key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Kings River San Joaquin River Fresno River Chowchilla River

11222099 11251099 11258099 11259099

Date Discharge Date Discharge Date Discharge Date Discharge

6/4/1935 12,500 6/5/1935 13,637 4/8/1935 2,980

5/14/1936 11,600 5/14/1936 10,690 2/23/1936 3,530

2/6/1937 25,600 2/6/1937 18,639 2/6/1937 8,890

12/11/1937 37,800 12/11/1937 40,497 2/11/1938 7,760

4/22/1939 5,780 4/22/1939 5,341 3/10/1939 525

5/15/1940 12,000 5/13/1940 11,205 1/26/1940 3,340

6/6/1941 15,300 5/24/1941 16,145 2/12/1941 5,080

5/25/1942 14,000 5/26/1942 14,652 12/29/1941 1,680 12/29/1941 2,730

1/22/1943 16,200 1/22/1943 17,074 1/22/1943 2,300 3/10/1943 2,760

5/9/1944 8,490 5/9/1944 8,250 3/4/1944 1,190 3/4/1944 1,260

2/2/1945 32,200 2/2/1945 34,376 2/2/1945 4,610 2/2/1945 5,200

5/7/1946 11,600 5/7/1946 10,959 3/30/1946 1,840 3/30/1946 1,990

5/6/1947 9,580 5/3/1947 8,716 12/27/1946 794 11/23/1946 649

5/16/1948 10,400 5/27/1948 10,615 4/10/1948 1,450 4/10/1948 2,490

5/27/1949 9,240 5/27/1949 9,864 3/4/1949 942 3/4/1949 1,760

5/31/1950 10,500 5/31/1950 10,664 2/6/1950 807 2/6/1950 1,720

11/19/1950 51,600 11/19/1950 42,352 11/19/1950 5,130 11/19/1950 6,000

6/6/1952 15,500 5/28/1952 18,149 1/25/1952 3,760 1/25/1952 4,950

6/16/1953 7,390 4/27/1953 8,460 12/31/1952 819 1/14/1953 1,090

5/19/1954 11,596 5/19/1954 10,744 1/25/1954 455 2/14/1954 914

6/8/1955 11,445 6/9/1955 11,572 5/8/1955 312 1/2/1955 448

12/23/1955 77,955 12/23/1955 74,984 12/23/1955 10,400 12/23/1955 18,400

5/19/1957 14,493 5/19/1957 16,847 5/19/1957 672 2/25/1957 600

6/19/1958 14,610 5/19/1958 17,541 4/3/1958 6,700 4/3/1958 7,250

2/16/1959 5,663 2/16/1959 7,928 2/16/1959 630 2/16/1959 914

5/12/1960 5,076 5/12/1960 6,612 2/9/1960 430 2/10/1960 1,100

5/24/1961 3,350 5/24/1961 3,850 12/2/1960 122 12/2/1960 122

5/6/1962 12,746 2/10/1962 13,828 2/11/1962 4,430 2/10/1962 4,620

2/1/1963 35,491 2/1/1963 40,982 2/1/1963 3,540 2/1/1963 4,190

5/21/1964 7,152 5/20/1964 6,655 11/21/1963 200 11/20/1963 397

12/24/1964 15,640 12/23/1964 25,531 12/23/1964 1,970 12/23/1964 3,130

5/6/1966 7,837 5/7/1966 7,445 12/30/1965 625 12/30/1965 1,400

12/6/1966 71,711 12/6/1966 42,394 4/18/1967 4,030 12/6/1966 3,920

5/29/1968 5,689 5/28/1968 5,454 2/21/1968 233 2/18/1968 207

1/25/1969 48,816 1/25/1969 29,324 2/24/1969 7250 2/24/1969 7,010

1/16/1970 16,166 1/16/1970 15,961 1/16/1970 2,330 1/16/1970 4,230

5/16/1971 7,309 6/13/1971 8,583 12/2/1970 252 12/22/1970 348

6/7/1972 5,382 6/8/1972 7,122 12/26/1971 300 2/6/1972 367

5/18/1973 17,501 5/18/1973 17,091 2/11/1973 4,500 2/11/1973 5,160

6/7/1974 14,528 5/28/1974 13,622 4/2/1974 3,240 4/2/1974 3,960

6/1/1975 15,813 6/1/1975 16,941 3/26/1975 740 2/10/1975 1,320
28 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table 6. Unregulated, annual-maximum-daily discharge or key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Kings River San Joaquin River Fresno River Chowchilla River

11222099 11251099 11258099 11259099

Date Discharge Date Discharge Date Discharge Date Discharge

9/11/1976 5,141 5/14/1976 4,864 3/1/1976 176 3/1/1976 216

6/9/1977 4,427 6/9/1977 5,208 1/3/1977 43 1/3/1977 27

6/9/1978 20,898 6/8/1978 19,472 3/4/1978 4,403 2/9/1978 4,784

5/21/1979 14,574 5/22/1979 14,271 3/28/1979 2,104 3/28/1979 2,410

1/13/1980 36,296 1/14/1980 32,001 1/14/1980 3,524 1/14/1980 3,009

5/2/1981 9,161 5/2/1981 8,314 3/20/1981 473 1/29/1981 1,084

4/11/1982 52,007 4/11/1982 59,295 4/11/1982 5,698 1/5/1982 7,514

12/22/1982 28,808 12/22/1982 26,580 1/27/1983 5,665 12/22/1982 7,167

12/25/1983 13,573 12/25/1983 18,185 12/27/1983 1,910 12/25/1983 2,571

4/15/1985 7,461 4/15/1985 6,985 3/28/1985 519 2/9/1985 822

2/18/1986 28,060 2/19/1986 33,515 2/18/1986 5,817 2/18/1986 6,786

5/16/1987 6,014 5/16/1987 7,978 2/13/1987 343 2/13/1987 450

1/5/1988 7,791 5/16/1988 5,672 4/20/1988 203 3/2/1988 132

4/15/1989 6,024 5/9/1989 6,671 3/3/1989 353 3/26/1989 472

5/7/1990 4,666 5/6/1990 4,883 1/14/1990 78 1/14/1990 63

3/4/1991 13,564 6/4/1991 8,989 3/19/1991 1,161 3/19/1991 1,408

4/30/1992 5,830 5/8/1992 6,002 2/13/1992 647 2/15/1992 1,392

1/14/1993 16,489 5/24/1993 15,323 1/14/1993 7,203 1/14/1993 7,574

5/13/1994 7,830 5/12/1994 6,952 2/18/1994 170 2/19/1994 141

3/10/1995 29,959 3/10/1995 39,333 3/11/1995 8,611 3/11/1995 7,982

5/16/1996 28,742 5/16/1996 32,217 2/20/1996 1,888 2/5/1996 2,442

1/2/1997 53,390 1/2/1997 77,467 1/2/1997 7,718 1/2/1997 7,957

6/16/1998 20,884 6/16/1998 20,199 3/25/1998 3,327 3/25/1998 3,920

5/26/1999 8,927 5/27/1999 10,800 2/9/1999 722 2/9/1999 1,100
Table 6 29

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Merced River Tuolumne River Stanislaus River Calaveras River

11270099 11288099 11299599 11308999

Date Discharge Date Discharge Date Discharge Date Discharge

5/25/1897 16,200

4/24/1898 7,600

3/25/1899 26,800

1/3/1900 14,200

2/19/1901 22,560

5/28/1902 5,420 4/7/1902 12,088

4/1/1903 12,000 4/1/1903 19,740

5/14/1904 10,100 3/20/1904 16,365

3/19/1905 8,500 10/11/1904 14,551

1/19/1906 19,800 3/24/1906 26,200

3/19/1907 24,400 3/19/1907 50,425

4/29/1908 3,900 4/30/1908 6,478

1/14/1909 20,400 1/14/1909 26,719

12/9/1909 14,800 12/9/1909 20,900

1/30/1911 37,200 1/30/1911 52,560

6/3/1912 6,100 6/5/1912 13,800

5/23/1913 3,130 5/16/1913 7,590

11/20/1913 204 1/25/1914 31,300

5/13/1915 15,300

3/5/1916 12,600 3/20/1916 17,100

2/22/1917 18,500 2/21/1917 23,000

3/19/1918 14,300 3/12/1918 15,200

5/29/1919 8,740 5/29/1919 13,801

5/20/1920 8,320 5/21/1920 12,971

1/18/1921 13,000 6/8/1921 12,424

2/11/1922 13,300 6/5/1922 18,376

4/6/1923 8,980 5/15/1923 14,326

5/3/1924 2,490 5/3/1924 8,762

2/6/1925 9,280 2/7/1925 17,998

2/14/1926 6,360 4/26/1926 14,437

5/17/1927 8,640 2/19/1927 16,305

3/25/1928 15,973 3/25/1928 43,351

6/16/1929 5,819 6/17/1929 15,279

5/21/1930 3,962 6/12/1930 8,407

5/7/1931 2,435 5/7/1931 5,624

2/7/1932 11,430 2/7/1932 22,955 2/7/1932 9,053

5/31/1933 6,039 6/15/1933 13,144 5/29/1933 8,590

1/1/1934 4,632 1/2/1934 6,227 3/30/1934 2,681

4/8/1935 21,991 4/8/1935 23,450 4/8/1935 10,433

2/23/1936 14,712 2/23/1936 21,865 2/22/1936 14,475

2/6/1937 25,203 2/7/1937 24,389 5/14/1937 9,584
30 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Merced River Tuolumne River Stanislaus River Calaveras River

11270099 11288099 11299599 11308999

Date Discharge Date Discharge Date Discharge Date Discharge

12/11/1937 33,964 12/12/1937 74,424 12/12/1937 36,983

4/12/1939 3,469 5/1/1939 6,185 4/9/1939 3,842

2/27/1940 11,344 3/31/1940 29,396 3/31/1940 20,741

12/27/1940 13,575 12/28/1940 17,575 5/12/1941 10,555

5/26/1942 8,470 12/3/1941 22,728 5/26/1942 10,671

1/23/1943 13,475 1/22/1943 23,155 3/10/1943 20,796

5/9/1944 5,482 5/9/1944 9,772 5/10/1944 6,636

2/2/1945 33,046 2/2/1945 45,472 2/3/1945 18,982

12/22/1945 11,592 12/22/1945 18,914 5/6/1946 7,562

5/3/1947 5,290 5/3/1947 9,972 5/4/1947 4,688

5/27/1948 6,761 5/27/1948 12,613 5/27/1948 9,480

5/14/1949 6,275 5/14/1949 11,734 5/14/1949 8,633

5/28/1950 6,061 5/31/1950 12,056 5/22/1950 7,706

11/19/1950 46,545 11/19/1950 67,047 11/19/1950 58,648

1/25/1952 13,320 6/5/1952 16,997 5/28/1952 11,889

6/6/1953 5,385 4/27/1953 14,511 4/28/1953 10,543

5/9/1954 5,769 3/9/1954 17,015 3/10/1954 11,428

5/23/1955 5,340 6/12/1955 10,974 5/23/1955 5,448

12/23/1955 74,838 12/23/1955 121,555 12/23/1955 80,805

5/19/1957 9,274 5/19/1957 18,042 5/19/1957 12,588

4/3/1958 19,784 4/3/1958 18,867 4/3/1958 13,127

2/16/1959 6,701 2/16/1959 10,985 5/14/1959 2,933

2/9/1960 6,182 2/9/1960 10,533 2/9/1960 7,866

4/7/1961 2,828 5/23/1961 5,097 4/4/1961 2,342

2/10/1962 12,894 2/10/1962 16,487 5/6/1962 6,745

2/1/1963 38,354 2/1/1963 70,087 2/1/1963 38,248

5/20/1964 3,384 11/15/1963 10,602 5/20/1964 3,872 1/22/1964 2,623

12/24/1964 33,093 12/23/1964 72,700 12/24/1964 43,062 12/23/1964 12,789

11/24/1965 6,548 11/24/1965 10,075 4/2/1966 3,794 12/30/1965 2,020

12/7/1966 17,197 12/6/1966 30,014 5/24/1967 16,162 1/22/1967 6,738

5/1/1968 2,856 2/20/1968 9,032 2/21/1968 4,963 2/21/1968 1,647

1/21/1969 33,467 1/21/1969 49,822 1/21/1969 23,881 1/21/1969 14,674

1/16/1970 14,724 1/16/1970 30,681 1/22/1970 28,084 1/21/1970 7,200

5/16/1971 4,940 6/8/1971 9,896 6/27/1971 9,492 12/2/1970 2,983

6/8/1972 3,808 5/30/1972 8,402 5/16/1972 4,200 12/25/1971 4,922

2/11/1973 12,763 5/19/1973 16,736 5/20/1973 12,498 1/16/1973 7,695

4/1/1974 11,061 11/12/1973 23,383 4/2/1974 9,734 3/2/1974 9,124

6/1/1975 10,329 6/12/1975 62,744 6/2/1975 18,115 3/25/1975 5,783

5/13/1976 2,380 10/27/1975 5,851 10/27/1975 1,831 3/2/1976 240

6/10/1977 2,238 9/8/1977 5,778 6/4/1977 940 3/16/1977 112

2/9/1978 15,068 3/4/1978 18,298 3/5/1978 22,572 3/5/1978 5,770
Table 6 31

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Merced River Tuolumne River Stanislaus River Calaveras River

11270099 11288099 11299599 11308999

Date Discharge Date Discharge Date Discharge Date Discharge

1/11/1979 13,504 1/11/1979 20,027 5/22/1979 9,164 2/22/1979 5,388

1/13/1980 31,413 1/14/1980 60,099 1/13/1980 45,520 1/14/1980 8,648

4/30/1981 4,738 5/1/1981 9,017 4/24/1981 5,590 1/29/1981 3,160

4/11/1982 39,147 2/16/1982 49,812 2/15/1982 42,930 1/5/1982 12,321

12/22/1982 21,355 3/1/1983 26,349 3/13/1983 18,340 3/13/1983 10,433

12/25/1983 17,797 12/26/1983 28,544 12/26/1983 18,700 12/25/1983 8,029

4/14/1985 4,255 4/15/1985 9,011 4/15/1985 5,130 2/8/1985 3,769

2/17/1986 31,917 2/19/1986 57,956 2/19/1986 45,320 2/17/1986 23,494

5/16/1987 3,075 2/13/1987 7,268 2/13/1987 3,460 3/6/1987 1,761

5/16/1988 2,726 5/16/1988 5,798 4/14/1988 1,582 1/17/1988 403

4/10/1989 4,085 3/8/1989 12,046 3/8/1989 6,570 3/25/1989 927

4/28/1990 2,707 10/24/1989 6,213 4/23/1990 2,263 2/17/1990 695

5/25/1991 4,746 3/5/1991 10,952 6/4/1991 5,580 3/26/1991 3,939

4/30/1992 4,608 4/18/1992 6,388 2/15/1992 3,150 2/15/1992 5,114

1/14/1993 13,758 1/14/1993 15,188 1/22/1993 8,479 1/13/1993 5,317

5/12/1994 3,153 4/19/1994 7,476 5/31/1994 2,394 2/20/1994 909

3/10/1995 38,212 3/10/1995 46,631 3/10/1995 24,027 3/11/1995 10,146

5/16/1996 16,251 5/16/1996 38,549 5/16/1996 21,081 2/21/1996 5,653

1/2/1997 67,040 1/2/1997 117,709 1/2/1997 72,865 1/2/1997 16,801

2/3/1998 16,813 3/25/1998 28,439 3/24/1998 11,753 2/3/1998 16,919

2/9/1999 8,560 2/9/1999 16,629 2/9/1999 11,017
32 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Mokelumne River Cosumnes River Little Johns Creek Sacramento River

11323599 11335099 11344099 11370599

Date Discharge Date Discharge Date Discharge Date Discharge

5/17/1905 4,940

6/12/1906 9,000

3/19/1907 23,000

4/30/1908 3,020 1/21/1908 2,020

1/14/1909 12,600 1/14/1909 20,800

11/21/1909 7,200 3/21/1910 7,200

1/30/1911 16,700 1/31/1911 22,400

6/3/1912 4,920 3/7/1912 1,100

5/18/1913 3,840 1/19/1913 1,220

1/26/1914 11,100 1/22/1914 13,900

6/1/1915 7,750 2/2/1915 5,920

3/20/1916 8,040 3/20/1916 8,920

6/10/1917 7,550 2/22/1917 13,500

3/12/1918 6,940 3/12/1918 10,800

2/11/1919 7,060 2/11/1919 13,100

5/20/1920 5,500 3/21/1920 3,210

1/18/1921 7,350 1/18/1921 11,500

6/3/1922 7,970 2/9/1922 7,970

5/16/1923 5,430 12/13/1922 9,570

5/2/1924 1,770 2/8/1924 910

2/6/1925 9,700 2/6/1925 15,200

4/8/1926 3,100 2/12/1926 2,950

5/17/1927 6,160 4/3/1927 8,630

3/26/1928 20,300 3/25/1928 17,400

6/16/1929 3,530 2/4/1929 2,800

5/21/1930 3,319 3/5/1930 4,360

5/6/1931 2,022 2/19/1931 879

5/14/1932 5,616 2/6/1932 7,340 12/27/1931 34,921

5/30/1933 5,105 5/30/1933 783 3/28/1933 19,476

3/29/1934 2,858 1/1/1934 4,920 1/2/1934 24,437

4/8/1935 6,214 4/8/1935 11,300 4/8/1935 44,755

2/22/1936 15,034 2/22/1936 15,600 2/22/1936 53,145

5/15/1937 6,194 2/6/1937 7,800 3/13/1937 29,107

12/11/1937 22,970 2/11/1938 15,500 12/11/1937 102,046

4/8/1939 2,570 3/9/1939 1,500 3/13/1939 37,858

3/31/1940 10,740 3/31/1940 16,700 2/28/1940 161,435

5/12/1941 6,214 3/2/1941 4,600 4/4/1941 71,408

1/27/1942 10,397 1/27/1942 14,100 2/6/1942 79,872

3/10/1943 11,380 3/10/1943 18,700 1/23/1943 44,393

5/9/1944 3,964 3/4/1944 4,660 11/21/1943 6,771

2/2/1945 12,891 2/2/1945 13,100 7/30/1945 9,519
Table 6 33

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Mokelumne River Cosumnes River Little Johns Creek Sacramento River

11323599 11335099 11344099 11370599

Date Discharge Date Discharge Date Discharge Date Discharge

12/22/1945 6,133 12/23/1945 8,510 1/4/1946 28,300

5/4/1947 4,046 3/10/1947 2,610 2/12/1947 33,936

5/27/1948 5,415 3/24/1948 3,140 1/7/1948 62,689

5/13/1949 5,108 3/3/1949 9,010 3/19/1949 42,520

6/1/1950 5,227 2/6/1950 5,410 1/23/1950 29,204

11/21/1950 30,862 11/21/1950 16,700 12/8/1950 5,284 10/29/1950 51,803

5/28/1952 7,447 1/12/1952 8,300 3/15/1952 5,019 12/27/1951 77,184

4/27/1953 5,342 4/28/1953 2,630 1/14/1953 725 1/9/1953 81,549

3/10/1954 5,491 3/10/1954 3,020 3/17/1954 723 1/17/1954 61,599

5/23/1955 4,191 1/1/1955 3,160 1/1/1955 3,556 12/6/1954 31,992

12/23/1955 34,657 12/23/1955 32,789 12/24/1955 8,497 12/22/1955 140,880

5/19/1957 7,874 3/5/1957 6,544 3/5/1957 2,232 2/24/1957 77,415

4/3/1958 9,679 4/3/1958 20,090 4/3/1958 7,272 2/24/1958 83,075

2/16/1959 2,719 2/17/1959 2,847 2/16/1959 1,419 1/12/1959 64,496

2/8/1960 5,426 2/8/1960 6,833 2/10/1960 1,402 2/8/1960 65,202

5/23/1961 2,143 3/25/1961 470 2/2/1961 102 1/31/1961 43,389

2/10/1962 5,241 2/15/1962 6,163 2/15/1962 5,086 2/13/1962 70,179

2/1/1963 29,861 2/1/1963 27,560 2/13/1963 3,205 4/14/1963 61,885

5/15/1964 3,321 1/22/1964 2,959 1/22/1964 898 1/20/1964 62,888

12/23/1964 36,173 12/23/1964 29,883 12/26/1964 8,760 12/22/1964 169,171

5/7/1966 2,845 12/31/1965 1,999 1/30/1966 2,071 1/4/1966 37,155

5/23/1967 8,651 1/22/1967 7,148 1/22/1967 4,324 1/29/1967 62,545

2/21/1968 3,352 2/20/1968 3,482 2/21/1968 1,241 2/23/1968 48,582

1/21/1969 15,415 1/21/1969 19,384 1/21/1969 3,707 1/21/1969 91,765

1/21/1970 14,756 1/21/1970 11,475 1/21/1970 3,953 1/23/1970 164,653

3/26/1971 5,335 3/26/1971 5,786 11/29/1970 2,624 3/26/1971 62,285

5/14/1972 3,818 12/25/1971 3,143 12/25/1971 1,267 1/22/1972 38,269

5/18/1973 5,987 1/12/1973 9,692 2/11/1973 5,368 1/16/1973 74,532

11/12/1973 7,905 3/2/1974 6,657 3/2/1974 4,749 1/16/1974 190,847

6/7/1975 6,733 3/25/1975 7,361 3/22/1975 2,742 3/19/1975 56,295

10/27/1975 2,355 3/2/1976 347 9/11/1976 10 2/29/1976 22,709

5/23/1977 1,122 2/23/1977 170 10/1/1976 0 9/29/1977 8,340

5/15/1978 6,211 3/5/1978 6,472 2/9/1978 3,447 1/16/1978 95,610

5/22/1979 6,292 3/1/1979 4,015 2/21/1979 5,080 2/13/1979 30,570

1/13/1980 31,924 1/14/1980 20,311 1/12/1980 4,921 2/18/1980 89,540

4/30/1981 4,873 3/26/1981 3,262 1/29/1981 3,890 1/28/1981 30,480

4/11/1982 24,642 2/16/1982 25,608 3/31/1982 6,522 12/19/1981 81,790

5/26/1983 12,304 3/13/1983 18,455 11/30/1982 6,620 3/13/1983 92,570

12/25/1983 13,559 12/26/1983 14,218 12/25/1983 5,755 12/11/1983 66,160

4/15/1985 3,766 2/8/1985 3,062 2/8/1985 2,411 11/12/1984 23,980

2/17/1986 27,878 2/17/1986 35,933 2/19/1986 9,555 2/17/1986 126,980
34 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Mokelumne River Cosumnes River Little Johns Creek Sacramento River

11323599 11335099 11344099 11370599

Date Discharge Date Discharge Date Discharge Date Discharge

4/30/1987 2,689 3/13/1987 1,531 3/6/1987 2,891 3/13/1987 39,673

4/29/1988 2,255 1/17/1988 991 1/18/1988 63 12/6/1987 32,897

3/8/1989 5,492 3/25/1989 5,839 3/4/1989 45 3/9/1989 72,974

5/31/1990 2,273 3/5/1990 1,044 4/16/1990 25 5/27/1990 31,487

6/4/1991 4,654 3/25/1991 3,631 3/26/1991 2,718 3/4/1991 28,971

4/22/1992 3,298 2/15/1992 3,083 2/15/1992 4,517 2/20/1992 35,598

5/17/1993 6,262 1/21/1993 7,560 1/13/1993 2,697 3/17/1993 82,188

5/11/1994 2,790 2/18/1994 929 2/20/1994 281 1/24/1994 17,942

5/1/1995 15,637 3/11/1995 18,236 1/27/1995 4,854 1/9/1995 111,630

5/16/1996 18,015 3/5/1996 7,917 2/21/1996 3,941 2/21/1996 68,733

1/2/1997 76,137 1/2/1997 61,822 1/2/1997 7,777 1/1/1997 215,623

2/3/1998 11,270 2/3/1998 78,535

2/9/1999 4,517
Table 6 35

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Stony Creek Feather River North Yuba River American River

11388099 11407099 11413599 11446599

Date Discharge Date Discharge Date Discharge Date Discharge

4/6/1902 38,100

3/30/1903 93,000

2/24/1904 106,000

12/30/1904 68,400 3/19/1905 21,200

1/18/1906 96,300 1/19/1906 44,500

3/19/1907 187,000 3/19/1907 105,000

1/21/1908 16,300 12/27/1907 8,460

1/16/1909 137,000 1/14/1909 98,000

12/9/1909 31,000 12/2/1909 47,000

1/31/1911 75,400 1/31/1911 69,100

1/26/1912 16,400 6/2/1912 11,300

5/9/1913 14,200 5/10/1913 11,600

12/31/1913 88,110 1/1/1914 57,700

5/11/1915 69,049 5/12/1915 41,800

3/20/1916 43,093 3/20/1916 33,200

2/25/1917 73,106 2/25/1917 37,600

3/26/1918 28,566 4/10/1918 12,400

2/11/1919 46,335 2/11/1919 45,000

4/16/1920 21,383 4/16/1920 18,800

11/19/1920 51,792 1/18/1921 32,800

5/20/1922 35,090 5/18/1922 23,200

4/6/1923 20,890 12/13/1922 29,800

2/8/1924 32,786 2/8/1924 10,600

2/6/1925 51,084 2/6/1925 68,200

4/8/1926 46,655 4/6/1926 22,700

2/21/1927 82,287 2/21/1927 48,200

3/26/1928 125,168 3/25/1928 119,000

2/4/1929 12,046 2/4/1929 14,800

12/15/1929 77,702 3/5/1930 18,800

3/19/1931 9,731 3/19/1931 7,920

3/20/1932 18,570 2/7/1932 18,900

5/31/1933 9,235 5/30/1933 12,700

3/29/1934 16,971 1/2/1934 13,300

4/8/1935 53,306 4/8/1935 49,300

2/22/1936 57,064 2/22/1936 46,400

4/15/1937 19,379 2/14/1937 22,500

12/11/1937 158,984 12/11/1937 81,100

3/27/1939 8,309 3/9/1939 8,500

3/30/1940 134,761 3/30/1940 69,600

2/11/1941 73,315 2/10/1941 14,400 2/11/1941 26,900

2/6/1942 89,118 2/6/1942 21,800 1/27/1942 54,600
36 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Stony Creek Feather River North Yuba River American River

11388099 11407099 11413599 11446599

Date Discharge Date Discharge Date Discharge Date Discharge

1/23/1943 65,063 1/21/1943 22,200 1/22/1943 73,800

3/4/1944 18,745 5/8/1944 4,610 3/4/1944 12,400

2/2/1945 47,628 2/2/1945 18,600 2/2/1945 70,900

12/29/1945 46,425 12/29/1945 15,300 12/22/1945 32,400

2/12/1947 32,263 2/12/1947 10,100 2/13/1947 20,100

4/17/1948 33,318 4/17/1948 11,500 4/18/1948 17,600

4/23/1949 14,223 4/23/1949 4,690 3/3/1949 25,500

2/6/1950 40,459 2/6/1950 10,200 2/6/1950 22,800

11/21/1950 69,883 11/21/1950 29,900 11/21/1950 132,000

2/2/1952 47,154 2/2/1952 15,400 2/2/1952 30,500

1/9/1953 98,847 1/9/1953 25,600 4/28/1953 27,600

3/10/1954 48,137 3/9/1954 18,100 3/10/1954 36,500

5/9/1955 11,869 5/9/1955 4,650 5/9/1955 10,528

12/23/1955 181,528 12/23/1955 57,000 12/23/1955 189,073

2/24/1957 63,111 2/24/1957 17,200 5/19/1957 36,924

2/25/1958 76,631 2/25/1958 18,800 4/3/1958 42,302

2/17/1959 28,718 2/17/1959 6,170 2/17/1959 15,394

2/8/1960 99,125 2/8/1960 32,600 2/8/1960 63,014

1/31/1961 15,718 2/10/1961 3,050 4/4/1961 6,914

2/10/1962 36,020 2/10/1962 11,800 2/10/1962 35,216

2/1/1963 136,203 2/1/1963 42,000 2/1/1963 152,614

1/20/1964 3,487 1/21/1964 20,465 11/15/1963 5,850 11/15/1963 17,002

12/22/1964 36,993 12/23/1964 178,544 12/22/1964 63,700 12/23/1964 183,242

1/4/1966 15,562 4/10/1966 17,029 4/11/1966 4,040 4/2/1966 8,659

1/21/1967 12,288 1/30/1967 54,276 3/17/1967 36,197

1/14/1968 8,642 2/21/1968 40,151 2/21/1968 24,697

1/20/1969 14,195 1/21/1969 137,082 1/21/1969 83,526

1/24/1970 23,530 1/24/1970 117,684 1/23/1970 39,008 1/22/1970 88,316
Table 6 37

Table 6. Unregulated, annual-maximum-daily discharge for key dam sites, California.—Continued

[Discharge is in cubic feet per second]

Stony Creek Feather River North Yuba River American River

11388099 11407099 11413599 11446599

Date Discharge Date Discharge Date Discharge Date Discharge

1/16/1971 12,177 3/26/1971 64,381 3/26/1971 14,839 3/26/1971 34,047

1/23/1972 3,694 2/29/1972 19,994 1/23/1972 7,722 3/4/1972 10,046

1/18/1973 12,304 1/16/1973 48,339 1/16/1973 13,955 1/12/1973 49,291

1/16/1974 26,751 3/30/1974 108,249 3/30/1974 25,317 1/17/1974 40,631

3/7/1975 10,523 2/13/1975 31,924 3/25/1975 11,352 3/25/1975 30,037

2/27/1976 1,560 2/29/1976 12,079 2/29/1976 3,761 10/27/1975 10,389

3/16/1977 376 2/21/1977 4,289 2/22/1977 1,234 6/10/1977 2,359

1/16/1978 23,978 1/16/1978 54,954 1/15/1978 13,573 1/17/1978 31,169

3/27/1979 6,164 2/14/1979 23,413 1/11/1979 7,203 1/12/1979 18,301

1/13/1980 20,968 1/13/1980 137,623 1/13/1980 54,716 1/14/1980 124,915

1/27/1981 9,586 2/14/1981 18,864 1/28/1981 6,519 3/26/1981 15,531

12/19/1981 13,599 12/20/1981 98,900 12/20/1981 40,045 2/16/1982 113,126

3/1/1983 30,136 3/13/1983 98,773 3/13/1983 29,853 3/13/1983 68,791

12/25/1983 18,068 12/25/1983 74,706 12/25/1983 24,655 12/26/1983 65,182

2/8/1985 4,140 2/8/1985 17,547 2/8/1985 6,024 2/8/1985 13,473

2/17/1986 36,446 2/17/1986 217,024 2/17/1986 69,649 2/18/1986 170,960

3/13/1987 3,268 2/13/1987 30,978 2/13/1987 11,885 2/14/1987 11,690

1/4/1988 9,539 12/2/1987 18,756 12/10/1987 4,491 1/17/1988 5,447

3/11/1989 4,376 3/10/1989 86,723 3/10/1989 23,377 3/25/1989 33,949

1/13/1990 2,076 1/13/1990 14,726 5/31/1990 6,092 5/31/1990 7,606

3/4/1991 7,080 3/4/1991 49,728 3/4/1991 21,656 3/5/1991 27,362

2/12/1992 7,192 2/20/1992 24,208 2/20/1992 9,439 2/20/1992 13,266

1/20/1993 21,429 3/18/1993 59,057 1/22/1993 14,230 1/22/1993 34,244

2/7/1994 3,057 3/6/1994 9,457 12/8/1993 2,566 5/11/1994 5,009

1/9/1995 44,984 3/10/1995 134,188 1/14/1995 29,405 3/11/1995 68,260

2/4/1996 9,981 2/5/1996 57,809 2/5/1996 21,784 5/16/1996 54,315

1/1/1997 29,246 1/1/1997 312,893 1/1/1997 87,988 1/2/1997 252,431

2/3/1998 29,811 2/3/1998 41,819
38 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table 7. Regional skew models for California.

[Constant is the linear regression model with a constant skew. β0 is the regression model constant, and β1 and β2 are regression model coefficients. 2 σ δ is the 

model error variance. ASEV is the average sampling error variance. AVPnew is the average variance of prediction for a new site. Pseudo 2 Rδ describes the 

fraction of the variability in the true skews explained by each model (Gruber and others, 2007). Standard deviations are in parentheses. Elev is the linear 

regression model relating skew to ELEV. NL-Elev is the non-linear model relating skew to ELEV. %, percent] 

Model Model equation β0 β1 β2

2 σ δ ASEV AVPnew

Pseudo 

R δ

2

Constant:  = 0 γ β –0.23 — — 0.20 0.03 0.23 0%

(0.17) (0.06)

Elev: 

γβ β = (ELEV) 0 1 + –0.76 1.4E-04 — 0.12 0.03 0.15 41%

(0.22) (3.4E-05) (0.04)

NL-Elev:  { } 2 = 1 exp (ELEV / 6,500) 0 2 γβ β + --é ù ê ú ë û –0.62 — 1.3 0.10 0.03 0.14 48%

(0.19) (0.31) (0.04)

Table 8. Average regional skew, variance of prediction (VPnew) 

and equivalent record length (ERL) for nonlinear regional skew 

model NL-Elev for various values of mean basin elevation (ELEV), 

California.

Elevation,

in feet

Average

regional

skew

VPnew ERL

0 –0.62 0.14 65

1,000 –0.59 0.14 65

2,000 –0.50 0.14 62

3,000 –0.37 0.13 58

4,000 –0.21 0.13 55

5,000 –0.04 0.13 53

6,000 0.13 0.14 52

7,000 0.28 0.14 52

8,000 0.40 0.15 53

9,000 0.49 0.16 54

10,000 0.56 0.16 55

11,000 0.61 0.17 55
Glossary 39

Glossary

Annual Exceedance Probability The probability, often 

expressed as a decimal fraction less than 1.0, that an 

annual peak discharge will be exceeded in a 1-year period. 

Exceedance probabilities can be expressed in terms of their 

reciprocals as recurrence intervals or return periods in years.

Annual-Maximum-Daily Discharge The maximum daily 

mean discharge occurring during a water year.

Annual Peak The maximum instantaneous discharge 

occurring during a water year. 

Basin Centroid The center of a basin area, which is 

represented by an irregular polygon. For irregularly shaped 

polygons, the centroid is derived mathematically and 

represents an approximate “center of gravity.”

Bayesian Generalized Least Squares Regression (B-GLS) A 

form of GLS regression that uses a Bayesian statistical 

framework to estimate the regression model parameters and 

the model error variance and the precision of those estimators.

Effective Record Length (ERL) A representation of the 

precision of an estimator of a streamflow statistic, or in a 

regression analysis, the at-site variance of prediction. The 

effective record length represents the length of gaged record 

required to estimate a flow statistic at a site with the same 

accuracy as a regional regression for that region. 

Mean Basin Elevation (ELEV) The area-weighted average 

height of the basin above a vertical datum, usually the North 

American Vertical Datum of 1988 (NAVD 88).

EL6000 The percentage of a basin that is more than 6,000 

feet in elevation.

Expected Moments Algorithm (EMA) A method for fitting 

a probability distribution to annual peak-discharge data using 

a generalized method of moments that uses different types of 

censored data. The censored data often occur with historical 

information, where we have only limited knowledge about 

floods outside the period of systematic data collection at a 

gage. For example, we may have information that no floods 

have overtopped a road built near a gage 50 years before the 

gage was established. Censored data also may be in the form 

of interval discharges, where we know that an annual peak 

discharge was between some lower bound and some upper 

bound, such as zero and the smallest recordable discharge for 

a crest-stage gage. 

Generalized Least Squares Regression (GLS) A regression 

method that accounts for differences in the variances and 

cross correlations of the errors associated with different 

recorded discharges. Differences in variances can result from 

differences in the length of record for each site, whereas cross 

correlations among concurrent annual peak discharges results 

in cross-correlation between estimated flood statistics, such as 

quantiles and skewness coefficients.

Historical Flood Information Information about the 

magnitude of flood flows, including recorded or estimated 

annual peak discharges, outside the systematic period of 

record.

Maintenance of Variation Extension (MOVE) A linear 

regression technique used for filling in missing streamflow 

data measurements or producing a unique extended streamflow 

sequence that maintains the mean and variance for the sample.

Mean Square Error (MSE) The average of the squares of the 

differences between the estimated values and the measured 

values. This metric represents how closely, on average, an 

estimated value matches a measured value. Of particular 

concern in this report is the MSE of of the regional skewness 

estimator.

Mixed Population Analysis A method for analyzing flood 

frequency at a site whose annual flood series is a mixture 

of two populations of flood discharges caused by different 

hydroclimatic events. In these situations, the frequency curve 

of annual events can best be described by computing separate 

curves for each type of event and then statistically combining 

the separate curves to derive a distribution applicable to the 

entire annual flood series. 

Outlier A data point that departs from the trend of the rest of 

a data set as described by a distribution or other mathematical 

relationship. 

Skewness Coefficient (γ) A statistical measure of the lack 

of symmetry in a flood-frequency distribution. Station skew 

generally is computed from the logarithms of annual peak 

discharge at a streamflow-gaging station. Because station 

skew is sensitive to outliers, it may be an unreliable estimate 

of the true population skew, especially for small samples. For 

that reason, Bulletin 17B (Interagency Committee on Water 

Data, 1982) recommends that station skew be weighted with 

a regional, or generalized, skew that is based on data from 

many long-term stations to produce at-site flood-frequency 

estimates.

Standard Error (SE) A measure of the precision of an 

estimator, equal to the square root of the variance of the 

sampling error. 

Variance of Prediction (VP) A measure of the likely 

difference between the prediction provided by a regression 

model and the actual value of the variable.

Variance of Prediction, new site (VPnew) A measure of 

the likely difference between the prediction provided by a 

regression model and the actual value of the variable for a 

new site that was not used to calibrate a model or estimate its 

parameters.
40 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Weighted Least Squares Regression (WLS) A regression 

method that accounts for the variation in the errors due to 

unequal record lengths at gaging stations used to estimate the 

flood characteristics of interest. WLS incorporates weights 

associated with each data point into the fitting criterion. 

The size of the weights corresponds to the precision of the 

information contained in the record. 

100-Year Flood (Q100) An annual peak discharge having an 

average recurrence interval of 100 years, corresponding to an 

annual exceedance probability of 0.01.
Appendix A 41

A method based on a linear relation between the 

logarithms of annual-peak discharge and the logarithms 

of annual-maximum-daily discharge was used to estimate 

unregulated, annual-peak discharge for the 16 key dam sites 

selected by the U.S. Army Corps of Engineers (ACOE). At ten 

sites, the log-linear relation was used to extend the period of 

unregulated annual-peak discharge record already available, 

and at six sites that had no unregulated annual-peak discharge 

record, a log-linear relation based on data from a nearby 

site was used to estimate unregulated annual-peak discharge 

values. 

For streamflow record extension, a linear relation 

between concurrent flows or their logarithms is often used 

to estimate missing flow values or to extend the record at a 

short-record station using flow values at a site with a longer 

record. Hirsch (1982) showed that using simple ordinary least 

squares (OLS) regression estimators to extend a short record 

results in a variance for the extended record that is on average 

smaller than that for the short record. Because of this variance 

reduction problem, Hirsch (1982) developed maintenance of 

variance extension methods denoted type I (MOVE.1) and 

type II (MOVE.2) for extending a short record to preserve the 

expected variance of the flows at the short-record station. The 

MOVE.1 procedure estimates the coefficients of the linear 

transformation for extending the short record using only the 

period of concurrent record, whereas MOVE.2 uses the entire 

record at the long-record site to estimate the coefficients. 

Hirsch (1982) showed that the MOVE.2 method was slightly 

better and less biased than the simpler MOVE.1 method. 

Vogel and Stedinger (1985) developed two additional MOVE 

methods (MOVE.3 and MOVE.4), which also use information 

from both the shorter concurrent records and the longer 

record; MOVE.3 and MOVE.4 are intended to ensure that 

the original and generated flow values together have a sample 

mean and variance that are identical to the best estimates of 

the mean and the variance of the flows at the short-record site. 

To estimate periods of unregulated annual-peak 

discharge record from concurrent periods of unregulated 

annual-maximum-daily discharge in this study, MOVE.1 and 

MOVE.3 were considered. The general equation for estimating 

missing values of discharge at a short-record site is 

( )1 ,

where

is the logarithm of estimated flow for year 

at the short-record site,

is the linear equation constant,

is the linear equation coefficient,

is the logarithm of flow for year at t

i i

i

i

Y a bX X

Y i

a

b

X i

=+ -

1

1

he

long-record site, and

is the mean of the logarithms of flow at the

long-record site for the concurrent record

(whose length is ). 

X

n

(A1)

The MOVE.1 equation for estimating missing data is

( ) 1

1 1

1

1

1

1

,

where

is the mean of the logarithms of flow values at

the short-record site,

is the standard deviation of the logarithms of 

flow values at the short-record site,

is the standard 

Y

i i

X

Y

X

S

YY XX

S

Y

S

S

=+ -

deviation of the logarithms of

flow values at the long-record site for the

period of concurrent record, and the other

terms are as defined above.

(A2)

Thus, for MOVE.1, the linear equation constant and 

coefficient in equation A1 can be written as 

1 a Y = , (A3)

and

1

1

Y

X

S

b

S = (A4)

where all terms are defined as above. 

Appendix A. Move Methods for Estimating Unregulated Annual-Peak-Flow 

Data at Key Dam Sites 
42 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

The MOVE.3 equation can be written in a form similar to 

the general linear equation A1 as follows:

Y a bX X i i =+ - ( ) 2 , (A5)

where X 2 is the mean of the logarithms for the long-record 

site for the nonconcurrent record period (whose length is 

n2) and the other terms are as defined above. For MOVE.3 

described by Vogel and Stedinger (1985), the estimates of the 

constant and the slope in equation A5 are

  1 12 1

2

( ) y n n nY a n+ - μ = , (A6)

and

 



 

1

2

2 2

1 2 1

2 2

1 1 2 2

2

2

( 1) ( 1)

( )( )

( 1)

y Y

y y

X

nn n S

nY n a

b

n S

σ

μ μ

é ù ê ú +- - -

- - -- ë û = -

, (A7)

where μ y and σ y are the Matalas-Jacobs estimators of the 

mean and the variance at the short record site. The MatalasJacobs estimator for the mean is

  1 2 1

2

1 2

( ) y

n Y XX n n μ β =+ -

+ , (A8)

where X 2 is defined above for A5 and β is calculated from

 1

1 1

1

1

1

2

1

( )( )

( )

n

i i i

n

i i

X XYY

X X

β =

=

- - = -

å

å . (A9)

The Matalas-Jacobs estimator for the variance is



( ) ( ) ( ) 

( )  ( )

1 2 1

2 1

2

1 2

2 2 2 2 22

12 2

2 2 1 2

1 2

1

1

1 1 11

y

y x y

n n

nS n S n S

n n X X n n

σ

β αρ

β

= + -

ì ü ï ï æ ö

- +- +- -ç ÷ ï ç ï ÷ ç ÷ ï ï è ø í ý ï ï

+ -

+ î þ, (A10)

where

2 21 1

211

( 4)( 1)

( 1)( 3)( 2)

nn n

nnn α - - = --- , (A11)

and 

   1

1

X

Y

S

S ρ β = . (A12)

To determine whether the simpler MOVE.1 method 

would produce peak flow estimates that are as reliable as those 

produced from the MOVE.3 method, the two procedures were 

compared using data from stations that had long concurrent 

records of both annual-peak and annual-maximum-daily 

discharge. The four selected sites, in the Sacramento–San 

Joaquin River Basin, are listed in table A1 along with their 

concurrent record lengths and the Pearson cross-correlation 

between the logs of annual-peak discharge and annualmaximum-daily discharge. For each site, six samples of a 

10-year short record period (ns1) were selected and assumed to 

be the only concurrent records available.

The complete record periods available (n1 + n2) varied 

from 76 to 95 years (table A1); for each sample, ns1 = 10 

and ns2 varied from 66 to 85 years. The six 10-year samples 

of concurrent record at each site were determined by using 

(1) the first 10 years of actual concurrent record, (2) the 

second 10 years of actual concurrent record, (3) the third 

10 years of actual concurrent record, (4) the last 10 years of 

actual concurrent record, (5) the next to last 10 years of actual 

concurrent record, and (6) the third to last 10 years of actual 

concurrent record. For each sample at each site, the MOVE.1 

and MOVE.3 methods were used to estimate annual-peak 

discharges for the ns2 years assumed to have no actual peakdischarge record. The means and the standard deviations of 

the logarithms of the annual-peak discharge for the complete 

record period (ns2 years of estimated peak discharge plus ns1

= 10 years of concurrent and recorded peak discharge) were 

then compared with the means and the standard deviations of 

the logarithms of the actual recorded peak discharge for the 

complete record period. The results of the comparisons of 

the 6 samples from each of the 4 test sites (24 comparisons) 

are shown as box plots in figure A1. The box plots indicate 

that both MOVE.1 and MOVE.3 produced estimated means 

that were slightly biased on the low side for the 24 replicates 

(median log residuals less than zero and the vertical boxes 

centered below zero). Both methods produced estimates of 

standard deviation with little or no bias (median log residuals 

were very close to zero, and the vertical boxes were centered 

near zero. Differences between MOVE.1 and MOVE.3 were 

negligible for both the mean and the standard deviation. 

Figures A2 and A3 show how well MOVE.1 and MOVE.3 

functioned for each of the 24 samples. Figure A2 shows 

the residual from the actual mean for each sample for both 

methods, and figure A3 shows the residual from the actual 

standard deviation for each sample. Both MOVE methods 

produced positive and negative residuals for the same samples, 

and the differences between the MOVE.1 and the MOVE.3 

residuals for each sample were very small. On the basis of 

these results, the simpler MOVE.1 method was adopted to 

estimate annual-peak discharge from annual-maximumdaily discharge in California. Thus, the MOVE.1 method 

was used for the ten sites that had some concurrent records 

of unregulated annual-peak discharge and annual-dailymaximum discharge before dam construction. 
Appendix A 43

Station 

number

Abbreviated names 

of stations

Period of concurrent 

annual maximumdaily and peak 

discharge record

Number of years of 

concurrent record

 (n1

 + n2) 

Pearson correlation 

coefficient (r) relating 

concurrent annual 

maximum-daily discharge 

and peak discharge

11230500 Bear Creek near Lake Thomas 1922–88, 1992–2006 82 0.96

11317000 MF Mokelumne River at West Point 1912–2006 95 0.98

11338500 Deer Creek near Vina 1913–15, 1921–2006 89 0.95

11390000 Butte Creek near Chico 1931–2006 76 0.98

Table A1. Four long-record sites used to test MOVE.1 and MOVE.3 methods in the Sacramento–San Joaquin River Basin, California.

Figure A1. Comparing the MOVE.1 method with the MOVE.3 method to estimate the mean and standard 

deviations of the logs of annual-peak discharges from the logs of annual-maximum-daily discharge based 

on data from four sites (24 samples) in California. Each sample had a short, concurrent record of 10 years 

and an estimation period varying from 66 to 85 years. LOG RESIDUALS FROM ACTUAL LONG-RECORD MEAN AND STANDARD DEVIATION -0.2

-0.1

0.0

0.1

0.2

MEAN STANDARD DEVIATION

MOVE.1 MOVE.3 MOVE.1 MOVE.3

IP017136_Figure A01

75th percentile

Median

25th percentile

Outlier

Outlier

90th percentile

10th percentile

EXPLANATION
44 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

SAMPLE NUMBER

LOG RESIDUALS FROM ACTUAL LONG-RECORD MEAN 

-0.20

0 2 4 6 8 10 12 14 16 18 20 22 24

-0.15

-0.10

-0.05

0.00

0.05

0.10

MOVE.1

MOVE.3

IP017136 Figure A02

LOG RESIDUALS FROM ACTUAL LONG-RECORD STANDARD DEVIATION 

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

MOVE.1

MOVE.3

SAMPLE NUMBER

0 2 4 6 8 10 12 14 16 18 20 22 24

Figure A2. Sample by 

sample comparison of 

MOVE.1 and MOVE.3 to 

estimate the mean of 

the logs of annual-peak 

discharges from the logs 

of annual-maximum-daily 

discharge based on 

data from four sites (24 

samples) in California.

Figure A3. Sample by 

sample comparison of 

MOVE.1 and MOVE.3 to 

estimate the standard 

deviation of the logs of 

annual-peak discharges 

from the logs of annualmaximum-daily discharge 

based on data from four 

sites (24 samples) in 

California.
Appendix A 45

The site-specific MOVE.1 equations developed for the 

ten sites were converted to power relations based on discharge 

rather than the logarithms of discharge to generate unregulated 

annual-peak discharge estimates for each year after dam 

construction for which the ACOE had previously estimated 

unregulated, annual-maximum-daily discharge. The power 

equations are of the form

,

where

are the calculated annual-peak discharges,

are the unregulated, annual- maximum-dailydischarges, and

is the power equation exponent already defined

in equation (A4).

b

i i

i

i

y Ax

y

x

b

= (A13)

The power equation coefficient can be expressed using terms 

already defined in the basic MOVE.1 equations (A1 through 

A4) as 

( )1 10 a bX A - = . (A14)

Table A2 shows the ten sites for which a MOVE.1 equation 

was developed and pertinent data for the MOVE.1 relation,

including record lengths n1 and n2, the power equation 

coefficient and exponent, and the Pearson correlation 

coefficient. The correlations between the concurrent 

unregulated, annual-maximum-daily-discharges and the 

annual-peak discharges exceeded 0.90 for every site. Thus, the 

MOVE analysis provided a reliable extension of the annual 

peak-discharge records. All but one of the exponents were 

greater than one, indicating that the annual-peak discharge 

values varied more than the annual-maximum-daily discharge 

values.

For 6 of the 16 sites that had no earlier periods of 

concurrent unregulated, annual-peak-discharge and annualmaximum-daily discharge record, a MOVE.1 equation 

developed for a nearby and similar site that had long 

concurrent records for the two series was adjusted for scale 

and used to generate unregulated, annual-peak discharges 

for the entire period for which the ACOE had developed 

unregulated, annual maximum-daily-discharge estimates. The 

general MOVE equation (eq. A1) for the nearby site is written

( ) 1 Y a bX X i i =+ - , where Y and X refer to the concurrent

records of logarithms of annual-peak discharge and annualmaximum-daily discharge data for each nearby site. Because 

the six “estimation sites” do not have concurrent records 

of annual-peak and daily-maximum discharge of length n1

and separate extension periods, there is no MOVE.1 versus 

MOVE.3 problem, and the method can be described as a 

general MOVE procedure. 

Table A2. Ten sites for which MOVE.1 was used to extend unregulated peak flow record in the Sacramento–San Joaquin River Basin, 

California.

[n1 is the length of concurrent daily-maximum and peak-flow record, in years. n2 is the length of the non-concurrent maximum-daily-discharge record, in years. 

N, north]

Station 

number 1 Names of stations

Period of unregulated, annual-maximum 

flow record Power equation Pearson 

correlation

Daily Peak 2 Coefficient Exponent coefficient (r)

(n1

 + n2) in parentheses (n1) in parentheses

11222099 Kings River at Piedra 1896–1999 (104) 1900–02, 1904–07, 

1909–53 (52)

0.179 1.215 0.91

11258099 Fresno River below Hidden Dam 1942–99 (59) 1942–75 (34) 0.961 1.075 0.98

11259099 Chowchilla River below Buchanan Dam 1922–23,1932–99 (70) 1932–72 (41) 1.34 1.056 0.97

11270099 Merced River at Exchequer 1902–14,1916–99 (96) 1902–13,1916–25 

(22)

0.737 1.059 0.97

11323599 Mokelumne River below Camanche 

Dam

1905–97 (93) 1905–28 (24) 1.115 1.012 0.97

11335099 Cosumnes River at Michigan Bar 1908–97 (90) 1908–54 (47) 1.099 1.031 0.98

11370599 Sacramento River at Keswick 1932–98 (67) 1932–43 (12) 3.40 0.908 0.92

11407099 Feather River at Oroville 1902–97 (96) 1902–10 (9) 0.472 1.077 0.99

11413599 N Yuba River below Bullards Bar Dam 1941–66,1970–97 (54) 1941–66 (26) 0.486 1.116 0.98

11446599 American River at Fair Oaks 1905–98 (94) 1905–09, 1911–17, 

1919–54 (48)

0.835 1.045 0.99

1

 The station number is the U.S. Geological Survey station number with the last two digits replaced by “99.”

2

 Peaks recorded during years when no daily maxima were available are not included in n1.
46 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Using a MOVE relation developed for a nearby site is 

based on the assumption that flows at the estimation site are 

k times larger or smaller than the corresponding flows at the 

nearby site. Thus, for each of the six estimation sites, the 

logarithms of annual-peak discharge are log ( ) UY k i i = +

and the logarithms of annual-maximum-daily discharge are 

log ( ) VX k i i = + . Substituting these relations in the basic

MOVE equation (eq. A1) yields

log ( ) log ( ) U k a bV k X i i - =+ - - é ù ê ú ë û , (A15)

which can be rewritten to show the relation between the values 

that have been measured at the estimation site (Vi ) and the 

values that are to be generated (Ui):

( ) ( ) 1 log ( ) U a bX b k bV i i = - +- + é ù ê ú ë û . (A16)

Finally, log(k) is estimated as the mean logarithm of annualmaximum-daily discharge at the estimation site (V ) minus the 

mean logarithm of annual-maximum-daily discharge at the

nearby site ( X). With that estimator for log(k), the MOVE 

equation for annual-peak discharge at the estimation site can 

be expressed simply in terms of the annual-maximum-daily 

discharge at the estimation site and the MOVE constant and 

coefficient developed for concurrent discharges at the nearby 

site so that 

U a V X bV V i i ( ) ( ) = +- + - é ù ê ú ë û . (A17)

Thus, the term log(k), which equals V X - becomes a scaling 

factor that is added to the MOVE constant for the nearby site 

to correct for differences in discharge magnitudes at the two 

sites.

To help determine which nearby site was most suitable 

for each of the six estimation sites, a correlation analysis of the 

logs of concurrent annual-maximum-daily discharges at the 

estimation site and at several nearby sites was used. In general, 

the nearby site for which the Pearson correlation coefficient 

was the greatest was selected; however, some sites that had a 

smaller Pearson correlation coefficient but a longer period of 

concurrent annual-maximum-daily discharges or that had a 

MOVE relation based on a longer period of concurrent annualpeak discharge and annual-maximum-daily discharge were 

selected. Table A3 shows the selected nearby site for each of 

the six estimation sites, the Pearson correlation coefficient, and 

the period of concurrent annual-maximum-daily discharges. 

The nearby sites had reasonably similar hydrologic responses 

to the estimation sites based on the correlation coefficients and 

the periods of concurrent discharge. All values of the Pearson 

correlation coefficient were greater than 0.75 and several 

exceeded 0.90 (table A3).

The final MOVE equations were converted to a power 

form and used to calculate annual-peak discharges at 

each of the six estimation sites from the record of annualmaximum-daily discharge. Table A3 also includes the scaling 

(adjustment) factor applied to the MOVE constant for the

nearby site [ log ( ) k VX = - ] and values of the adjusted 

power equation coefficient (A) and exponent (b) for each 

MOVE equation. The adjusted power equation coefficient 

(A) was calculated after adding the needed scaling factor. 

Table A3. Six sites that had no unregulated peak flow record, selected nearby sites, Pearson correlation coefficients, and concurrent 

records for paired sites, scaling factors, and power equation coefficients and exponents for the Sacramento–San Joaquin River Basin, 

California.

[USGS, U.S. Geological Survey]

Station 

numbers 1

Names of stations 

that had no 

unregulated 

peak-flow 

record 

Names and USGS 

numbers for 

correlation stations 

selected nearby

Pearson 

correlation

coefficient 

(r)

Period of 

concurrent

record

Scaling

factors

[log (k)]

Power equation

Adjusted

coefficient

(A)

Exponent

(b)

11251099 San Joaquin River Kings River (11222099) 0.92 1911–99 0.0097 0.179 1.215

11288099 Tuolumne River Mokelumne River 

(11323599)

0.90 1905–97 0.3977 1.103 1.011

11299599 Stanislaus River Mokelumne River 

(11323599)

0.91 1932–97 0.1496 1.003 1.011

11308999 Calaveras River Cosumnes River (11335099) 0.86 1964–97 –0.1281 1.109 1.031

11344099 Littlejohns Creek Cosumnes River (11335099) 0.76 1951–97 –0.5834 1.145 1.031

11388099 Stony Creek Fresno River (11258099) 0.88 1982–98 0.9484 0.817 1.075

1

 Station number is the USGS station number with the last two digits replaced by “99.”
Appendix A 47

Kings River at Piedra

(Station 11222099)

Data from 1901-02,

 1904-07, 1909-55 

ANNUAL 1-DAY MAXIMUM DISCHARGE, IN CUBIC FEET PER SECOND

ANNUAL PEAK DISCHARGE, IN CUBIC FEET PER SECOND

1,000

1,000 10,000 100,000

10,000

100,000

Measured data

MOVE.1 line

y = 0.179 x 1.215

r = 0.91

IP017136_Figure A04

Figure A4. MOVE.1 line relating annual-peak discharge to annual-maximum-daily discharge 

for Kings River at Piedra, California, (station 11222099) based on data from 1901–02, 1904–07, 

and 1909–55. r, Pearson correlation coefficient.

All exponents are greater than one, indicating that the 

annual-peak discharges have more variability than the annualmaximum-daily discharges. 

The MOVE relations for each of the ten sites for which 

concurrent periods of recorded unregulated annual-peak 

discharges and annual-maximum-daily discharges were 

available are shown in figures A4 through A13. Correlations 

between annual-peak discharge and annual-maximum-daily 

discharge were compared with correlations between annualpeak discharge and annual-maximum 3-day discharge for 

each of the ten sites to test whether annual-maximum 3-day 

discharge might predict annual-peak discharge better than 

annual-maximum-daily discharge. For all ten sites, the 

correlations between annual-peak discharge and annualmaximum-daily discharge were larger than those between 

annual-peak discharge and annual-maximum 3-day discharge. 

On the basis of the tests at the ten sites having concurrent 

records of recorded unregulated annual-peak discharges and 

annual-maximum-daily discharges, annual-maximum-daily 

discharge was selected as the best predictor for annual-peak 

discharge for all 16 key dam sites. 

Unregulated, annual-peak discharges for the 16 key dam 

sites are shown in table A4. These data are displayed in a 

form similar to that used by the version of the EMA program 

used for flood-frequency analyses in California. Most of 

the tabulated annual-peak discharges were calculated from 

the MOVE.1 relations described above, although periods of 

recorded, unregulated annual-peak discharges at the ten sites 

are also included and noted in the table. 
48 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Fresno River below Hidden Dam

(Station 11258099)

Data from 1942-75

ANNUAL 1-DAY MAXIMUM DISCHARGE, IN CUBIC FEET PER SECOND

ANNUAL PEAK DISCHARGE, IN CUBIC FEET PER SECOND

100

1,000

10 100 1,000 10,000 100,000

10,000

100,000

Measured data

MOVE.1 line

y = 0.961 x 1.075

r = 0.98

IP017136_Figure A05

Figure A5. MOVE.1 line relating annual-peak discharge to annual-maximum-daily discharge 

for Fresno River below Hidden Dam, California, (station 11258099) based on data from 1942–75. 

r, Pearson correlation coefficient.

Chowchilla River below

Buchanan Dam

(Station 11259099)

Data from 1932-72

ANNUAL 1-DAY MAXIMUM DISCHARGE, IN CUBIC FEET PER SECOND

ANNUAL PEAK DISCHARGE, IN CUBIC FEET PER SECOND

100

1,000

10 100 1,000 10,000 100,000

10,000

100,000

Measured data

MOVE.1 line

y = 1.34 x 1.056

r = 0.97

Figure A6. MOVE.1 line relating annual-peak discharge to annual annual-maximum-daily 

discharge for Chowchilla River below Buchanan Dam, California (station 11259099) based on 

data from 1932–72. r, Pearson correlation coefficient.
Appendix A 49

Merced River at Exchequer Dam 

(Station 11270099)

Data from 1902-13, 1916-25

ANNUAL 1-DAY MAXIMUM DISCHARGE, IN CUBIC FEET PER SECOND

ANNUAL PEAK DISCHARGE, IN CUBIC FEET PER SECOND

1,000

1,000 10,000 100,000

10,000

100,000

Measured data

MOVE.1 line

y = 0.737 x 1.059

r = 0.97

IP017136_Figure A07

Figure A7. MOVE.1 line relating annual-peak discharge to annual-maximum-daily discharge 

for Merced River at Exchequer Dam, California, (station 11270099) based on data from 1902–13, 

1916–25. r, Pearson correlation coefficient.

Mokelumne River below

Camanche Dam 

(Station 11323599)

Data from 1905-28

ANNUAL 1-DAY MAXIMUM DISCHARGE, IN CUBIC FEET PER SECOND

ANNUAL PEAK DISCHARGE, IN CUBIC FEET PER SECOND

1,000

1,000 10,000 100,000

10,000

100,000

Measured data

MOVE.1 line

y = 1.115 x 1.012

r = 0.97

Figure A8. MOVE.1 line relating annual-peak discharge to annual-maximum-daily discharge 

for Mokelumne River below Camanche Dam, California, (station 11323599) based on data from 

1905–28. r, Pearson correlation coefficient.
50 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Cosumnes River at Michigan Bar

(Station 11335099)

Data from 1908-54

ANNUAL 1-DAY MAXIMUM DISCHARGE, IN CUBIC FEET PER SECOND

ANNUAL PEAK DISCHARGE, IN CUBIC FEET PER SECOND

100

1,000

100 1,000 10,000 100,000

10,000

100,000

Measured data

MOVE.1 line

y = 1.099 x 1.031

r = 0.98

IP017136_Figure A09

Figure A9. MOVE.1 line relating annual-peak discharge to annual-maximum-daily discharge 

for Cosumnes River at Michigan Bar, California, (station 11335099) based on data from 

1908–54. r, Pearson correlation coefficient.

Sacramento River at Keswick

Station (11370599)

Data from 1932-43

ANNUAL 1-DAY MAXIMUM DISCHARGE, IN CUBIC FEET PER SECOND

ANNUAL PEAK DISCHARGE, IN CUBIC FEET PER SECOND

10,000

10,000 100,000 1,000,000

100,000

1,000,000

Measured data

MOVE.1 line

r = 0.92

y = 3.4 x 0.908

Figure A10. MOVE.1 line relating annual-peak discharge to annual-maximum-daily discharge 

for Sacramento River at Keswick, California (station 11370599) based on data from 1932-43. r, 

Pearson correlation coefficient.
Appendix A 51

Feather River at Oroville

(Station 11407099)

Data from 1902-10

ANNUAL 1-DAY MAXIMUM DISCHARGE, IN CUBIC FEET PER SECOND

ANNUAL PEAK DISCHARGE, IN CUBIC FEET PER SECOND

10,000

10,000 100,000 1,000,000

100,000

1,000,000

Measured data

MOVE.1 line

y = 0.472 x 1.077

r = 0.99

IP017136_Figure A11

Figure A11. MOVE.1 line relating annual-peak discharge to annual-maximum-daily discharge 

for Feather River at Oroville, California, (station 11407099) based on data from 1902–10. r, 

Pearson correlation coefficient.

North Yuba River below

Bullards Bar Dam

(Station 11413599)

Data from 1941-66

ANNUAL 1-DAY MAXIMUM DISCHARGE, IN CUBIC FEET PER SECOND

ANNUAL PEAK DISCHARGE, IN CUBIC FEET PER SECOND

1,000

10,000

1,000 10,000 100,000

100,000

1,000,000

Measured data

MOVE.1 line

y = 0.486 x 1.116

r = 0.98

Figure A12. MOVE.1 line relating annual-peak discharge to annual-maximum-daily discharge 

for North Yuba River below Bullards Bar Dam, California, (station 11413599) based on data 

from 1941–66. r, Pearson correlation coefficient.
52 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

American River at Fair Oaks

(Station 11446599)

Data from 1905-09, 1911-17,

 1919-54

ANNUAL 1-DAY MAXIMUM DISCHARGE, IN CUBIC FEET PER SECOND

ANNUAL PEAK DISCHARGE, IN CUBIC FEET PER SECOND

1,000

10,000

1,000 10,000 100,000 1,000,000

100,000

1,000,000

Measured data

MOVE.1 line

y = 0.835 x 1.045

r = 0.99

IP017136_Figure A13

Figure A13. MOVE.1 line relating annual-peak discharge to annual-maximum-daily discharge 

for American River at Fair Oaks, California, (station 11446599) based on data from 1905–09, 

1911–17, 1919–54. r, Pearson correlation coefficient.
Appendix A 53

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11222099 Kings River at Piedra, California (simulated unregulated peaks)

Q 1896 12,000

Q 1897 26,100

Q 1898 10,100

Q 1899 37,600

Q 1900 14,600 1

Q 1901 33,200 1

Q 1902 20,800 1

Q 1903 21,200

Q 1904 19,500 1

Q 1905 10,800 1

Q 1906 25,400 1

Q 1907 19,500 1

Q 1908 7,630

Q 1909 32,800 1

Q 1910 44,800 1

Q 1911 30,500 1

Q 1912 15,700 1

Q 1913 8,900 1

Q 1914 59,700 1

Q 1915 18,300 1

Q 1916 45,400 1

Q 1917 17,900 1

Q 1918 13,500 1

Q 1919 13,200 1

Q 1920 17,000 1

Q 1921 15,600 1

Q 1922 19900 1

Q 1923 13,600 1

Q 1924 5,210 1

Q 1925 11,300 1

Q 1926 11,600 1

Q 1927 1,9200 1

Q 1928 10,200 1

Q 1929 14,700 1

Q 1930 8,430 1

Q 1931 6,250 1

Q 1932 23,800 1

Q 1933 14,900 1

Q 1934 6,690 1

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–San 

Joaquin River Basin, California.

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row of 

data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD row show 

the first and last year of missing record. The next number represents a large discharge threshold that presumably was 

not reached during the missing years. The INF following the threshold discharge simply indicates the largest possible 

discharge during the missing years (infinitely large). The first column after the STATION and THRESHOLD rows 

indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). Second column is the 

water year for each discharge. For each single-valued discharge, the third column is the discharge in cubic feet per 

second, and for each interval discharge, the third and fourth columns represent the range in discharge in cubic feet per 

second. For each single-valued discharge, a value of 1 in the last column indicates that the discharge is a recorded, 

unregulated, discharge. A value of 2 in the last column indicates that the discharge was a recorded, regulated discharge]
54 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11222099 Kings River at Piedra, California (simulated unregulated peaks)—Continued

Q 1935 20,100 1

Q 1936 24,600 1

Q 1937 34,800 1

Q 1938 80,000 1

Q 1939 6,500 1

Q 1940 14,800 1

Q 1941 17,900 1

Q 1942 16,600 1

Q 1943 46,900 1

Q 1944 9,950 1

Q 1945 49,300 1

Q 1946 16,500 1

Q 1947 17,300 1

Q 1948 13,000 1

Q 1949 11,500 1

Q 1950 12,900 1

Q 1951 91,000 1

Q 1952 15,500

Q 1953 7,950

Q 1954 15,500

Q 1955 15,300

Q 1956 157,000

Q 1957 20,400

Q 1958 20,600

Q 1959 6,500

Q 1960 5,690

Q 1961 3,430

Q 1962 17,400

Q 1963 60,400

Q 1964 8,630

Q 1965 22,300

Q 1966 9,640

Q 1967 142,000

Q 1968 6,640

Q 1969 89,000

Q 1970 23,200

Q 1971 8,860

Q 1972 6,110

Q 1973 25,600
Appendix A 55

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11222099 Kings River at Piedra, California (simulated unregulated peaks)—Continued

Q 1974 20,400

Q 1975 22,600

Q 1976 780

Q 1977 4,820

Q 1978 31,800

Q 1979 20,500

Q 1980 62,100

Q 1981 11,700

Q 1982 96,100

Q 1983 46,900

Q 1984 18,800

Q 1985 9,080

Q 1986 45,400

Q 1987 6,990

Q 1988 9,570

Q 1989 7,010

Q 1990 5,140

Q 1991 18,800

Q 1992 6,730

Q 1993 23,800

Q 1994 9,630

Q 1995 49,200

Q 1996 46,800

Q 1997 99,200

Q 1998 31,700

Q 1999 11,300

Station - 11251099 San Joaquin River below Friant, California (simulated unregulated peaks)

Q 1911 1,800

Q 1912 21,900

Q 1913 8,170

Q 1914 43,900

Q 1915 21,500

Q 1916 18,700

Q 1917 19,100

Q 1918 15,500

Q 1919 14,800

Q 1920 17,500

Q 1921 16,800
56 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11251099 San Joaquin River below Friant, California (simulated unregulated peaks)—

Continued

Q 1922 26,700

Q 1923 15,500

Q 1924 4,500

Q 1925 12,800

Q 1926 13,100

Q 1927 19,000

Q 1928 14,600

Q 1929 10,800

Q 1930 7,780

Q 1931 4,700

Q 1932 20,500

Q 1933 15,000

Q 1934 3,720

Q 1935 18,800

Q 1936 14,000

Q 1937 27,500

Q 1938 70,600

Q 1939 6,020

Q 1940 14,800

Q 1941 23,100

Q 1942 20,500

Q 1943 24,700

Q 1944 10,200

Q 1945 57,800

Q 1946 14,400

Q 1947 10,900

Q 1948 13,900

Q 1949 12,700

Q 1950 14,000

Q 1951 74,500

Q 1952 26,600

Q 1953 10,500

Q 1954 14,100

Q 1955 15,400

Q 1956 149,000

Q 1957 24,300

Q 1958 25,500

Q 1959 9,730

Q 1960 7,810
Appendix A 57

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11251099 San Joaquin River below Friant, California (simulated unregulated peaks)—

Continued

Q 1961 4,050

Q 1962 19,100

Q 1963 71,600

Q 1964 7,870

Q 1965 40,300

Q 1966 9,020

Q 1967 74,600

Q 1968 6,180

Q 1969 47,700

Q 1970 22,800

Q 1971 10,700

Q 1972 8,540

Q 1973 24,700

Q 1974 18,800

Q 1975 24,500

Q 1976 5,380

Q 1977 5,840

Q 1978 29,000

Q 1979 19,900

Q 1980 53,000

Q 1981 10,300

Q 1982 112000

Q 1983 42,300

Q 1984 26,700

Q 1985 8,340

Q 1986 56,100

Q 1987 9,810

Q 1988 6,480

Q 1989 7,890

Q 1990 5,400

Q 1991 11,300

Q 1992 6,940

Q 1993 21,700

Q 1994 8,300

Q 1995 68,100

Q 1996 53,400

Q 1997 155,000

Q 1998 30,300

Q 1999 14,200
58 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11258099 Fresno River below Hidden Dam near Daulton, California (simulated unregulated 

peaks)

Threshold 1939–1941 17,500 -INF 

Q 1938 15,000 1

Q 1942 2,580 1

Q 1943 3,620 1

Q 1944 2,670 1

Q 1945 8,090 1

Q 1946 2,460 1

Q 1947 1,600 1

Q 1948 2,470 1

Q 1949 1,510 1

Q 1950 1,180 1

Q 1951 10,700 1

Q 1952 5,020 1

Q 1953 1,200 1

Q 1954 723 1

Q 1955 333 1

Q 1956 17,500 1

Q 1957 1,360 1

Q 1958 10,400 1

Q 1959 1,180 1

Q 1960 616 1

Q 1961 257 1

Q 1962 5,340 1

Q 1963 6,290 1

Q 1964 278 1

Q 1965 3,460 1

Q 1966 882 1

Q 1967 5,590 1

Q 1968 273 1

Q 1969 17,300 1

Q 1970 4,420 1

Q 1971 461 1

Q 1972 367 1

Q 1973 11,200 1

Q 1974 8,620 1

Q 1975 877 1 

Q 1976 249
Appendix A 59

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11258099 Fresno River below Hidden Dam near Daulton, California (simulated unregulated 

peaks)—Continued

Q 1977 54.8

Q 1978 7,940

Q 1979 3,590

Q 1980 6,250

Q 1981 721

Q 1982 10,500

Q 1983 10,400

Q 1984 3,230

Q 1985 797

Q 1986 10,700

Q 1987 511

Q 1988 291

Q 1989 527

Q 1990 104

Q 1991 1,890

Q 1992 1,010

Q 1993 13,500

Q 1994 240

Q 1995 16,300

Q 1996 3,190

Q 1997 14,500

Q 1998 5,870

Q 1999 1,140

Station - 11259099 Chowchilla River below Buchanan Dam near Raymond, California (simulated 

unregulated peaks)

Q 1931 156 1

Q 1932 9,610 1

Q 1933 620 1

Q 1934 2,170 1

Q 1935 5,510 1

Q 1936 11,000 1

Q 1937 13,600 1

Q 1938 18,900 1

Q 1939 765 1

Q 1940 8,750 1

Q 1941 12,100 1

Q 1942 5,800 1
60 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11259099 Chowchilla River below Buchanan Dam near Raymond, California (simulated 

unregulated peaks)—Continued

Q 1943 8,460 1

Q 1944 5,020 1

Q 1945 9,610 1

Q 1946 3,450 1

Q 1947 2,870 1

Q 1948 5,660 1

Q 1949 3,360 1

Q 1950 4,250 1

Q 1951 22,500 1

Q 1952 6,040 1

Q 1953 1,710 1

Q 1954 1,390 1

Q 1955 1,070 1

Q 1956 30,000 1

Q 1957 1,230 1

Q 1958 14,000 1

Q 1959 2,120 1

Q 1960 1,620 1

Q 1961 200 1

Q 1962 6400 1

Q 1963 9,740 1

Q 1964 855 1

Q 1965 8,380 1

Q 1966 2,460 1

Q 1967 6,880 1

Q 1968 292 1

Q 1969 13,700 1

Q 1970 8,700 1

Q 1971 574 1

Q 1972 634 1

Q 1973 11,200 

Q 1974 8,440 

Q 1975 2,650 

Q 1976 391

Q 1977 43.5

Q 1978 10,300

Q 1979 4,990

Q 1980 6,310
Appendix A 61

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11259099 Chowchilla River below Buchanan Dam near Raymond, California (simulated 

unregulated peaks)—Continued

Q 1981 2,150

Q 1982 16,600

Q 1983 15,800

Q 1984 5,350

Q 1985 1,600

Q 1986 14,900

Q 1987 849

Q 1988 233

Q 1989 893

Q 1990 106

Q 1991 2,830

Q 1992 2,800

Q 1993 16,700

Q 1994 249

Q 1995 17,700

Q 1996 5,060

Q 1997 17,600

Q 1998 8,350

Q 1999 2,180

Station - 11270099 Merced River at Exchequer, California (simulated unregulated peaks)

Threshold 1915–1915 107,000–INF 

Q 1902 9,120 1

Q 1903 19,000 1

Q 1904 10,700 1

Q 1905 11,000 1

Q 1906 26,600 1

Q 1907 25,200 1

Q 1908 3,970 1

Q 1909 25,800 1

Q 1910 18,700 1

Q 1911 47,700 1

Q 1912 6,840 1

Q 1913 3,480 1

Q 1914 206 1

Q 1916 22,000 1

Q 1917 21,700 1

Q 1918 17,700 1
62 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11270099 Merced River at Exchequer, California (simulated unregulated peaks)—Cont.

Q 1919 9,580 1

Q 1920 10,000 1

Q 1921 19,400 1

Q 1922 17,200 1

Q 1923 11,500 1

Q 1924 2,970 1

Q 1925 15,400 1

Q 1926 11,100 2

Q 1927 10,900 1

Q 1928 20,800 1

Q 1929 7,150 1

Q 1930 4,760 1

Q 1931 2,840 1

Q 1932 14,600 1

Q 1933 7,440 1

Q 1934 5,620 1

Q 1935 29,200 1

Q 1936 19,100 1

Q 1937 33,800 1

Q 1938 46,300 1

Q 1939 4,140 1

Q 1940 14,500 1

Q 1941 17,500 1

Q 1942 10,600 1

Q 1943 17,400 1

Q 1944 6,710 1

Q 1945 45,000 1

Q 1946 14,800 1

Q 1947 6,470 1

Q 1948 8,380 1

Q 1949 7,750 1

Q 1950 7,470 1

Q 1951 64,700 1

Q 1952 17,200 1

Q 1953 6,590 1

Q 1954 7,090 1

Q 1955 6,530 1

Q 1956 107,000 1

Q 1957 11,700 1
Appendix A 63

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11270099 Merced River at Exchequer, California (simulated unregulated peaks)—Cont.

Q 1958 26,100 1

Q 1959 8,310 1

Q 1960 7,630 1

Q 1961 3,330 1

Q 1962 16,600 1

Q 1963 52,700 1

Q 1964 4,030 1

Q 1965 45,100 1

Q 1966 8,100 1

Q 1967 22,500 1

Q 1968 3,370 1

Q 1969 45,600 1

Q 1970 19,100 1

Q 1971 6,010 1

Q 1972 4,560 1

Q 1973 16,400

Q 1974 14,100

Q 1975 13,100

Q 1976 2,770

Q 1977 2,600

Q 1978 19,600

Q 1979 17,400

Q 1980 42,600

Q 1981 5,750

Q 1982 53,800

Q 1983 28,300

Q 1984 23,400

Q 1985 5,130

Q 1986 43,400

Q 1987 3,640

Q 1988 3,200

Q 1989 4,920

Q 1990 3,180

Q 1991 5,760

Q 1992 5,590

Q 1993 17,800

Q 1994 3,740

Q 1995 52,500

Q 1996 21,200
64 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11270099 Merced River at Exchequer, California (simulated unregulated peaks)—Cont.

Q 1997 95,200

Q 1998 22,000

Q 1999 10,800

Station - 11288099 Tuolumne River above La Grange Dam near La Grange, California (simulated 

unregulated peaks)

Threshold 1863–1896 130,000–INF 

Threshold 2000–2006 153,000–INF 

Q 1862 130,000 1

Q 1897 20,000

Q 1898 9,290

Q 1899 33,200

Q 1900 17,500

Q 1901 27,900

Q 1902 14,900

Q 1903 24,400

Q 1904 20,200

Q 1905 17,900

Q 1906 32,500

Q 1907 63,000

Q 1908 7,900

Q 1909 33,100

Q 1910 25,800

Q 1911 65,700

Q 1912 17,000

Q 1913 9,280

Q 1914 38,900

Q 1915 18,800

Q 1916 21,100

Q 1917 28,500

Q 1918 18,700

Q 1919 17,000

Q 1920 15,900

Q 1921 15,300

Q 1922 22,700

Q 1923 17,600

Q 1924 10,700

Q 1925 22,200

Q 1928 54,100

Q 1929 18,800
Appendix A 65

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11288099 Tuolumne River above La Grange Dam near La Grange, California (simulated 

unregulated peaks)—Continued

Q 1930 10,300

Q 1931 6,850

Q 1932 28,400

Q 1933 16,200

Q 1934 7,590

Q 1935 29,000

Q 1936 27,000

Q 1937 30,200

Q 1938 93,400

Q 1939 7,540

Q 1940 36,500

Q 1941 21,700

Q 1942 28,100

Q 1943 28,700

Q 1944 12,000

Q 1945 56,700

Q 1946 23,400

Q 1947 12,200

Q 1948 15,500

Q 1949 14,400

Q 1950 14,800

Q 1951 84,000

Q 1952 21,000

Q 1953 17,900

Q 1954 21,000

Q 1955 13,500

Q 1956 153,000

Q 1957 22,300

Q 1958 23,300

Q 1959 13,500

Q 1960 12,900

Q 1961 6,200

Q 1962 20,300

Q 1963 87,900

Q 1964 13,000

Q 1965 91,200
66 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11288099 Tuolumne River above La Grange Dam near La Grange, California (simulated 

unregulated peaks)—Continued

Q 1966 12,400

Q 1967 37,300

Q 1968 11,100

Q 1969 62,200

Q 1970 38,100

Q 1971 12,100

Q 1972 10,300

Q 1973 20,600

Q 1974 28,900

Q 1975 78,600

Q 1976 7,130

Q 1977 7,040

Q 1978 22,600

Q 1979 24,700

Q 1980 75,200

Q 1981 11,000

Q 1982 62,200

Q 1983 32,700

Q 1984 35,400

Q 1985 11,000

Q 1986 72,500

Q 1987 8,880

Q 1988 7,060

Q 1989 14,800

Q 1990 7,580

Q 1991 13,400

Q 1992 7,790

Q 1993 18,700

Q 1994 9,130

Q 1995 58,200

Q 1996 48,000

Q 1997 148,000

Q 1998 35,300

Q 1999 20,500
Appendix A 67

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11299599 Stanislaus River below Melones powerhouse near Sonora, California (simulated 

unregulated peaks)

Threshold 2000–2006 102,000–INF 

Q 1932 11,200

Q 1933 10,600

Q 1934 3,260

Q 1935 12,900

Q 1936 17,900

Q 1937 11,800

Q 1938 46,400

Q 1939 4,690

Q 1940 25,800

Q 1941 13,000

Q 1942 13,200

Q 1943 25,900

Q 1944 8,150

Q 1945 23,600

Q 1946 9,310

Q 1947 5,740

Q 1948 11,700

Q 1949 10,600

Q 1950 9,490

Q 1951 73,900

Q 1952 14,700

Q 1953 13,000

Q 1954 14,100

Q 1955 6,680

Q 1956 102,000

Q 1957 15,600

Q 1958 16,300

Q 1959 3,570

Q 1960 9,680

Q 1961 2,840

Q 1962 8,290

Q 1963 48,000

Q 1964 4,730

Q 1965 54,100

Q 1966 4,630

Q 1967 20,100

Q 1968 6,080

Q 1969 29,800

Q 1970 35,100

Q 1971 11,700
68 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11299599 Stanislaus River below Melones powerhouse near Sonora, California (simulated 

unregulated peaks)—Continued

Q 1972 5,130

Q 1973 15,500

Q 1974 12,000

Q 1975 22,500

Q 1976 2,220

Q 1977 1,130

Q 1978 28,100

Q 1979 11,300

Q 1980 57,200

Q 1981 6,860

Q 1982 53,900

Q 1983 22,800

Q 1984 23,300

Q 1985 6,290

Q 1986 56,900

Q 1987 4,220

Q 1988 1,910

Q 1989 8,070

Q 1990 2,750

Q 1991 6,840

Q 1992 3,840

Q 1993 10,400

Q 1994 2,910

Q 1995 30,000

Q 1996 26,300

Q 1997 92,000

Q 1998 14,500

Q 1999 13,600

Station - 11308999 Calaveras River below New Hogan Dam near Valley Springs, California (simulated 

unregulated peaks)

Q 1964 3,710

Q 1965 19,000

Q 1966 2,830

Q 1967 9,800

Q 1968 2,290

Q 1969 21,900

Q 1970 10,500
Appendix A 69

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11308999 Calaveras River below New Hogan Dam near Valley Springs, California (simulated 

unregulated peaks)—Continued

Q 1971 4,230

Q 1972 7,090

Q 1973 11,200

Q 1974 13,400

Q 1975 8,370

Q 1976 315

Q 1977 144

Q 1978 8,350

Q 1979 7,780

Q 1980 12,700

Q 1981 4,490

Q 1982 18,300

Q 1983 15,400

Q 1984 11700

Q 1985 5,390

Q 1986 35,500

Q 1987 2,460

Q 1988 538

Q 1989 1,270

Q 1990 943

Q 1991 5,640

Q 1992 7,380

Q 1993 7,680

Q 1994 1,240

Q 1995 14,900

Q 1996 8,180

Q 1997 25,100

Q 1998 25,300

Station - 11323599 Mokelumne River below Camanche Dam, California (simulated unregulated peaks)

Threshold 1998–2006 97,200–INF 

Q 1905 5,540 1

Q 1906 9,960 1

Q 1907 25,500 1

Q 1908 3,100 1

Q 1909 13,100 1

Q 1910 10,800 1

Q 1911 18,900 1
70 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11323599 Mokelumne River below Camanche Dam, California (simulated unregulated 

peaks)—Continued

Q 1912 6,520 1

Q 1913 5,580 1

Q 1914 13,300 1

Q 1915 8,290 1

Q 1916 10,700 1

Q 1917 9,300 1

Q 1918 8,620 1

Q 1919 7,540 1

Q 1920 6,820 1

Q 1921 11,100 1

Q 1922 8,970 1

Q 1923 6,400 1

Q 1924 2,260 1

Q 1925 18,500 1

Q 1926 3,740 1

Q 1927 7,870 1

Q 1928 25,600 1

Q 1929 4,340

Q 1930 4,080

Q 1931 2,470

Q 1932 6,950

Q 1933 6,310

Q 1934 3,510

Q 1935 7,690

Q 1936 18,800

Q 1937 7,670

Q 1938 28,900

Q 1939 3,150

Q 1940 13,400

Q 1941 7,690

Q 1942 13,000

Q 1943 14,200

Q 1944 4,880

Q 1945 16,100

Q 1946 7,590

Q 1947 4,980

Q 1948 6,690

Q 1949 6,310
Appendix A 71

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11323599 Mokelumne River below Camanche Dam, California (simulated unregulated 

peaks)—Continued

Q 1950 6,460

Q 1951 39,000

Q 1952 9,240

Q 1953 6,600

Q 1954 6,790

Q 1955 5,160

Q 1956 43,800

Q 1957 9,780

Q 1958 12,000

Q 1959 3,330

Q 1960 6,710

Q 1961 2,620

Q 1962 6,480

Q 1963 37,700

Q 1964 4,080

Q 1965 45,700

Q 1966 3,490

Q 1967 10,800

Q 1968 4,120

Q 1969 19,300

Q 1970 18,500

Q 1971 6,590

Q 1972 4,700

Q 1973 7,410

Q 1974 9,820

Q 1975 8,340

Q 1976 2,880

Q 1977 1,360

Q 1978 7,690

Q 1979 7,790

Q 1980 40,300

Q 1981 6,020

Q 1982 31,000

Q 1983 15,400

Q 1984 16,900

Q 1985 4,640

Q 1986 35,100

Q 1987 3,300
72 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11323599 Mokelumne River below Camanche Dam, California (simulated unregulated 

peaks)—Continued

Q 1988 2,760

Q 1989 6,790

Q 1990 2,780

Q 1991 5,740

Q 1992 4,050

Q 1993 7,750

Q 1994 3,420

Q 1995 19,600

Q 1996 22,600

Q 1997 97,200

Station - 11335099 Cosumnes River at Michigan Bar, California (simulated unregulated peaks)

Threshold 1998–2006 95,600–INF 

Q 1907 71,000 1

Q 1908 2,200 1

Q 1909 28,400 1

Q 1910 9,640 1

Q 1911 28,400 1

Q 1912 1,700 1

Q 1913 1,700 1

Q 1914 18,200 1

Q 1915 8,200 1

Q 1916 10,400 1

Q 1917 22,900 1

Q 1918 11,900 1

Q 1919 22,000 1

Q 1920 3,700 1

Q 1921 20,600 1

Q 1922 10,600 1

Q 1923 11,600 1

Q 1924 1,120 1

Q 1925 23,800 1

Q 1926 3,850 1

Q 1927 11,400 1

Q 1928 22,900 1

Q 1929 3,160 1

Q 1930 6,090 1

Q 1931 1,620 1
Appendix A 73

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11335099 Cosumnes River at Michigan Bar, California (simulated unregulated peaks)—

Continued

Q 1932 10,600 1

Q 1933 890 1

Q 1934 7,170 1

Q 1935 20,100 1

Q 1936 18,200 1

Q 1937 15,300 1

Q 1938 19,300 1

Q 1939 1,930 1

Q 1940 26,200 1

Q 1941 9,280 1

Q 1942 24,500 1

Q 1943 22,900 1

Q 1944 8,490 1

Q 1945 21,100 1

Q 1946 12,600 1

Q 1947 3,930 1

Q 1948 6,240 1

Q 1949 13,500 1

Q 1950 8,360 1

Q 1951 27,600 1

Q 1952 12,500 1

Q 1953 4,080 1

Q 1954 3,860 1

Q 1955 4,460

Q 1956 49,700

Q 1957 9,440

Q 1958 30,000

Q 1959 4,340 2

Q 1960 1,1200 2

Q 1961 625

Q 1962 8,880

Q 1963 41,600

Q 1964 4,170

Q 1965 45,200

Q 1966 2,880 2

Q 1967 15,900 2

Q 1968 4,930

Q 1969 28,900

Q 1970 16,900
74 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11335099 Cosumnes River at Michigan Bar, California (simulated unregulated peaks)—

Continued

Q 1971 8,590 2

Q 1972 4,430

Q 1973 15,000 2

Q 1974 9,610 

Q 1975 11,000 2

Q 1976 457

Q 1977 219

Q 1978 9,340

Q 1979 6,990 2

Q 1980 34,200 2

Q 1981 5,890 2

Q 1982 38,600

Q 1983 27,500

Q 1984 21,000

Q 1985 6,290 2

Q 1986 54,700

Q 1987 2,110

Q 1988 1,350

Q 1989 8,400

Q 1990 1,420

Q 1991 6670 2

Q 1992 5340 2

Q 1993 11,000

Q 1994 1,260

Q 1995 27,200

Q 1996 11,500

Q 1997 95,600

Station - 11344099 Littlejohns Creek below Farmington Reservoir (simulated unregulated peaks; U.S. 

Army Corps of Engineers station)

Q 1951 7,870

Q 1952 7,460

Q 1953 1,020

Q 1954 1,010

Q 1955 5,230

Q 1956 12,800

Q 1957 3,240

Q 1958 10,900

Q 1959 2,030

Q 1960 2,000
Appendix A 75

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11344099 Littlejohns Creek below Farmington Reservoir (simulated unregulated peaks; U.S. 

Army Corps of Engineers station)—Continued

Q 1961 135

Q 1962 7,560

Q 1963 4,700

Q 1964 1,270

Q 1965 13,200

Q 1966 3,000

Q 1967 6,400

Q 1968 1,770

Q 1969 5,460

Q 1970 5,830

Q 1971 3,820

Q 1972 1,810

Q 1973 8,000

Q 1974 7,050

Q 1975 4,000

Q 1976 12.3

Q 1977 0

Q 1978 5,070

Q 1979 7,550

Q 1980 7,310

Q 1981 5,740

Q 1982 9,770

Q 1983 9,920

Q 1984 8,590

Q 1985 3,500

Q 1986 14,500

Q 1987 4,230

Q 1988 81.9

Q 1989 57.9

Q 1990 31.6

Q 1991 3,970

Q 1992 6,690

Q 1993 3,930

Q 1994 382

Q 1995 7,210

Q 1996 5,810

Q 1997 1,1700

Q 1998 1,7200

Q 1999 6,690
76 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11370599 Sacramento River at Keswick, California (simulated unregulated peaks)

Threshold 1999–2006 237,000–INF

Q 1926 66,000 1

Q 1927 92,800 1

Q 1928 94,900 1

Q 1929 25,800 1

Q 1930 64,000 1

Q 1931 14,300 1

Q 1932 45,400 1

Q 1933 44,200 1

Q 1934 38,900 1

Q 1935 56,800 1

Q 1936 85,500 1

Q 1937 38,400 1

Q 1938 132,000 1

Q 1939 48,800 1

Q 1940 186,000 1

Q 1941 86,800 1

Q 1942 96,100 1

Q 1943 56,400 1

Q 1944 10,200

Q 1945 13,900

Q 1946 37,500

Q 1947 44,200

Q 1948 77,100

Q 1949 54,200

Q 1950 38,600

Q 1951 64,900

Q 1952 93,200

Q 1953 98,000

Q 1954 75,900

Q 1955 41,900

Q 1956 161,000

Q 1957 93,400

Q 1958 99,600

Q 1959 79,200

Q 1960 80,000

Q 1961 55,200

Q 1962 85,500

Q 1963 76,200
Appendix A 77

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11370599 Sacramento River at Keswick, California (simulated unregulated peaks)—

Continued

Q 1964 77,400

Q 1965 190,000

Q 1966 48,000

Q 1967 77,000

Q 1968 61,200

Q 1969 109,000

Q 1970 185,000

Q 1971 76,700

Q 1972 49,300

Q 1973 90,300

Q 1974 212,000

Q 1975 70,000

Q 1976 30,700

Q 1977 12,400

Q 1978 113,000

Q 1979 40,200

Q 1980 107,000

Q 1981 40,100

Q 1982 98,200

Q 1983 110,000

Q 1984 81,000

Q 1985 32,200

Q 1986 146,000

Q 1987 50,900

Q 1988 43,000

Q 1989 8,860

Q 1990 41,300

Q 1991 38,300

Q 1992 46,200

Q 1993 98,700

Q 1994 24,800

Q 1995 130,000

Q 1996 83,900

Q 1997 237,000

Q 1998 947,00
78 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11388099 Stony Creek below Black Butte Dam near Orland, California (simulated unregulated 

peaks)

Q 1964 5,230

Q 1965 66,200

Q 1966 26,100

Q 1967 20,300

Q 1968 13,900

Q 1969 23,700

Q 1970 40,700

Q 1971 20,100

Q 1972 5,570

Q 1973 20,300

Q 1974 46,700

Q 1975 17,100

Q 1976 2,200

Q 1977 478

Q 1978 41,500

Q 1979 9,650

Q 1980 36,000

Q 1981 15,500

Q 1982 22,600

Q 1983 53,100

Q 1984 30,700

Q 1985 6,290

Q 1986 65,200

Q 1987 4,880

Q 1988 15,400

Q 1989 6,680

Q 1990 3,000

Q 1991 11,200

Q 1992 11,400

Q 1993 36,800

Q 1994 4,540

Q 1995 81,700

Q 1996 16,200

Q 1997 51,400

Q 1998 52,500
Appendix A 79

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11407099 Feather River at Oroville, California (simulated unregulated peaks)

Threshold 1998–2006 391,000–INF 

Q 1902 41,000 1

Q 1903 102,000 1

Q 1904 118,000 1

Q 1905 81,000 1

Q 1906 128,000 1

Q 1907 230,000 1

Q 1908 16,300 1

Q 1909 140,000 1

Q 1910 31,000 1

Q 1911 84,500

Q 1912 16,300

Q 1913 14,000

Q 1914 99,900

Q 1915 76,900

Q 1916 46,300

Q 1917 81,700

Q 1918 29,700

Q 1919 50,000

Q 1920 21,700

Q 1921 56,400

Q 1922 37,100

Q 1923 21,200

Q 1924 34,500

Q 1925 55,600

Q 1926 50,400

Q 1927 92,800

Q 1928 146,000

Q 1929 11,700

Q 1930 8,7300

Q 1931 9,310

Q 1932 18,700

Q 1933 8,800

Q 1934 17,000

Q 1935 58,200

Q 1936 62,600

Q 1937 19,600

Q 1938 189,000
80 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11407099 Feather River at Oroville, California (simulated unregulated peaks)—Cont.

Q 1939 7,860

Q 1940 158,000

Q 1941 82,000

Q 1942 101,000

Q 1943 72,100

Q 1944 18,900

Q 1945 51,500

Q 1946 50,100

Q 1947 33,900

Q 1948 35,100

Q 1949 14,000

Q 1950 43,200

Q 1951 77,900

Q 1952 51,000

Q 1953 113,000

Q 1954 52,100

Q 1955 11,500

Q 1956 218,000

Q 1957 69,800

Q 1958 86,000

Q 1959 29,900

Q 1960 113,000

Q 1961 15,600

Q 1962 38,100

Q 1963 160,000

Q 1964 20,700

Q 1965 214,000

Q 1966 17,000

Q 1967 59,300

Q 1968 42,900

Q 1969 161,000

Q 1970 136,000

Q 1971 71,300

Q 1972 20,200

Q 1973 52,300

Q 1974 125,000

Q 1975 33,500
Appendix A 81

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11407099 Feather River at Oroville, California (simulated unregulated peaks)—Cont.

Q 1976 11,800

Q 1977 3,850

Q 1978 60,100

Q 1979 24,000

Q 1980 162,000

Q 1981 19,000

Q 1982 113,000

Q 1983 113,000

Q 1984 83,700

Q 1985 17,600

Q 1986 264,000

Q 1987 32,400

Q 1988 18,900

Q 1989 98,200

Q 1990 14,600

Q 1991 54,000

Q 1992 24,900

Q 1993 64,900

Q 1994 9,030

Q 1995 157,000

Q 1996 63,500

Q 1997 391,000

Station - 11413599 North Yuba River below Bullards Bar Dam, California (simulated unregulated 

peaks)

Threshold 1939–1940 160,000–INF 

Threshold 1967–1969 160,000–INF 

Threshold 1998–2006 160,000–INF 

Q 1938 69,800 1

Q 1941 30,600 1

Q 1942 28,100 1

Q 1943 44,200 1

Q 1944 5,110 1

Q 1945 26,400 1

Q 1946 20,000 1

Q 1947 18,600 1

Q 1948 15,200 1

Q 1949 5,060 1

Q 1950 13,300 1
82 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11413599 North Yuba River below Bullards Bar Dam, California (simulated unregulated 

peaks)—Continued

Q 1951 47,100 1

Q 1952 23,200 1

Q 1953 34,000 1

Q 1954 31,600 1

Q 1955 5,160 1

Q 1956 70,000 1

Q 1957 30,200 1

Q 1958 34,600 1

Q 1959 10,100 1

Q 1960 43,600 1

Q 1961 3,540 1

Q 1962 21,000 1

Q 1963 83,000 1

Q 1964 10,400 1

Q 1965 91,600 1

Q 1966 4,420 1

Q 1970 6,4600

Q 1971 22,000

Q 1972 10,600

Q 1973 20,500

Q 1974 39,900

Q 1975 16,300

Q 1976 4,750

Q 1977 1,370

Q 1978 19,900

Q 1979 9,810

Q 1980 94,300

Q 1981 8,780

Q 1982 66,500

Q 1983 47,900

Q 1984 38,700

Q 1985 8,040

Q 1986 123,000

Q 1987 17,200

Q 1988 5,790
Appendix A 83

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11413599 North Yuba River below Bullards Bar Dam, California (simulated unregulated 

peaks)—Continued

Q 1989 36,500

Q 1990 8,140

Q 1991 33,500

Q 1992 13,300

Q 1993 21,000

Q 1994 3,100

Q 1995 47,100

Q 1996 33,700

Q 1997 160,000

Station - 11446599 American River at Fair Oaks, California (simulated unregulated peaks)

Threshold 1848–1861 300,000–INF 

Threshold 1863–1904 300,000–INF 

Threshold 1999–2006 300,000–INF 

QINT 1862 300,000–336,000

Q 1905 24,200 1

Q 1906 59,700 1

Q 1907 156,000 1

Q 1908 10,300 1

Q 1909 119,000 1

Q 1910 47,000 1

Q 1911 81,300 1

Q 1912 12,100 1

Q 1913 12,700 1

Q 1914 74,100 1

Q 1915 47,900 1

Q 1916 40,700 1

Q 1917 42,300 1

Q 1918 15,800

Q 1919 67,500 1

Q 1920 20,100 1

Q 1921 39,200 1

Q 1922 31,600 1

Q 1923 39,000 1

Q 1924 14,000 1

Q 1925 99,500 1

Q 1926 27,400 1
84 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11446599 American River at Fair Oaks, California (simulated unregulated peaks)—Cont.

Q 1927 67,700 1

Q 1928 163,000 1

Q 1929 26,000 1

Q 1930 24,400 1

Q 1931 9,900 1

Q 1932 21,100 1

Q 1933 16,500 1

Q 1934 22,600 1

Q 1935 60,900 1

Q 1936 58,300 1

Q 1937 33,000 1

Q 1938 114,000 1

Q 1939 10,900 1

Q 1940 89,200 1

Q 1941 38,800 1

Q 1942 83,200 1

Q 1943 152,000 1

Q 1944 20,100 1

Q 1945 94,400 1

Q 1946 42,200 1

Q 1947 27,900 1

Q 1948 21,000 1

Q 1949 37,500 1

Q 1950 34,400 1

Q 1951 180,000 1

Q 1952 37,200 1

Q 1953 49,700 1

Q 1954 42,600 1

Q 1955 13,300

Q 1956 273,000

Q 1957 49,500

Q 1958 57,000

Q 1959 19,800

Q 1960 86,500

Q 1961 8,590

Q 1962 47,100

Q 1963 218,000
Appendix A 85

Table A4. Estimated, unregulated annual peak discharge for key dam sites in the Sacramento–

San Joaquin River Basin, California.—Continued

[For some stations, missing discharges are represented by interval discharge thresholds. These sites have a row 

of data after the STATION row with THRESHOLD indicated. The next two numbers in the THRESHOLD 

row show the first and last year of missing record. The next number represents a large discharge threshold that 

presumably was not reached during the missing years. The INF following the threshold discharge simply indicates 

the largest possible discharge during the missing years (infinitely large). The first column after the STATION and 

THRESHOLD rows indicates whether discharge is a single-valued discharge (Q) or an interval discharge (QINT). 

Second column is the water year for each discharge. For each single-valued discharge, the third column is the 

discharge in cubic feet per second, and for each interval discharge, the third and fourth columns represent the range 

in discharge in cubic feet per second. For each single-valued discharge, a value of 1 in the last column indicates that 

the discharge is a recorded, unregulated, discharge. A value of 2 in the last column indicates that the discharge was a 

recorded, regulated discharge]

Station - 11446599 American River at Fair Oaks, California (simulated unregulated peaks)—Cont.

Q 1964 22,000

Q 1965 264,000

Q 1966 10,900

Q 1967 48,500

Q 1968 32,500

Q 1969 116,000

Q 1970 123,000

Q 1971 45,500

Q 1972 127,00

Q 1973 66,900

Q 1974 54,700

Q 1975 39,900

Q 1976 132,00

Q 1977 27,90

Q 1978 41,500

Q 1979 23,800

Q 1980 177,000

Q 1981 20,000

Q 1982 159,000

Q 1983 94,800

Q 1984 89,600

Q 1985 17,300

Q 1986 246,000

Q 1987 14,900

Q 1988 6,700

Q 1989 45,300

Q 1990 9,490

Q 1991 36,200

Q 1992 17,000

Q 1993 45,700

Q 1994 6,140

Q 1995 94,100

Q 1996 74,100

Q 1997 369,000

Q 1998 56,400
This page intentionally left blank.
Appendix B 87

Appendix B. Extended Bayesian GLS Regional Skew Analysis for California 

The U.S. Geological Survey (USGS) Southeastern 

United States regional skew study shows how a Bayesian 

generalized least squares (B-GLS) analysis typically is 

conducted (Feaster and others, 2009; and Gotvald and others, 

2009; Veilleux, 2009; Weaver and others, 2009). The cross 

correlations between annual-peak discharges in California 

were considerably larger than those in the Southeastern United 

States study (fig. 4). When a B-GLS analysis was attempted 

on the California data set, results were not consistent because 

of the high cross correlations. A Bayesian GLS analysis seeks 

to exploit the cross correlations among the sample skews 

to obtain the best possible estimates of model parameters. 

If the cross correlations are large, the GLS estimators can 

become more complicated as a result of the effort to find 

the most efficient estimator of the parameters. The accuracy 

of the model (eq. 9) used to calculate the cross correlations 

of concurrent annual-peak discharges in California was 

equivalent to 52 years of actual at-site data. While this 

model describes the overall structure of the California data 

set, the calculated cross correlation between any two sites 

is not precise enough to justify the sophisticated weights 

(both positive and negative) that the Bayesian GLS analysis 

generates. Thus, an alternative procedure was developed so 

that the regional skew analysis would provide reliable results.

To this end, a weighted least squares (WLS) analysis 

that does not use cross correlations was first used to develop 

estimators of the regression coefficients for each regional 

skew model. After the regression model coefficients were 

determined using WLS, the precision of the model and the 

precision of the regression coefficients were estimated using 

a modified GLS analysis. However, because of the extensive 

use of low-outlier censoring and historical information in 

the expected moments algorithm (EMA) analysis used in 

California, the simple formulas provided in Bulletin 17B 

and by Griffis and Stedinger (2009) do not reliably represent 

the variance of the sample skewness estimators. Thus, a 

Monte Carlo study was done to determine the actual sample 

variance of the skewness coefficient when a low outlier 

test is employed to identify samples for special treatment. 

Finally, a modified Bayesian GLS analysis using only data 

from pristine sites (that is, sites without low outliers, zero 

flows, reconstructed records at key dam sites, or historical 

information) provided the estimate of the model error variance 

(the precision of the model) and the precision of the estimated 

model parameters. 

The specific computational steps used in the California 

regional skew analysis are described below.

1. A WLS analysis was used to derive the regression model 

parameter estimates using the complete set of records. The 

resultant model yielded an unbiased regional estimator of 

the skew at any site. The WLS analysis explicitly reflects 

variations in record length, but as previously described, 

does not consider cross correlations among the skewness 

estimators. 

The WLS analysis was done in two steps using unbiased 

at-site sample skewness estimators and variances of at-site 

unbiased skewness estimators when possible. A correction 

factor developed by Tasker and Stedinger (1986) and 

applied by Reis and others (2005) was used to unbias 

the at-site skews and the estimates of their variance. 

Equations to derive the unbiased at-site skews and their 

variances are given below.

 6 1 i i

i

G

N

é ù

= +ê ú ê ú ë ûγ , (B1)

and

  [ ]



2

6 ,

where

is the unbiased at-site skew for site ,

is the traditiional biased at-site skew estimator

for site , and

is the systematic record length at site .

i i

i

i

i

i

Var Var G

N

i

G

i

N i

γ

γ

= 1+

é ù é ù ê ú ê ú ë û ê ú ë û

(B2)

When unbiasing the skew, only the number of systematic 

peaks was considered. Thus, any historical flood periods 

in the EMA analysis were not included in the calculation 

of the correction factors.
88 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento—San Joaquin River Basin, Based on Data through WY 2006

These weights were used to compute the final estimates of the 

regression parameters 

β as

  





,

where

is an ( 1) vector of regression parameters,

and

is an ( 1) vector of unbiased at-site sample

skewness estimators.

k

n

=

 ́

 ́

β γ W

β

γ

(B5)

Both the B-WLS and the MM-WLS analyses include 

sites that had historical information, zero flows, and low 

outliers.

2. After estimating the regression parameters, the true 

model error variance needs to be estimated. However, 

the extensive censoring of low outliers, the occurrence of 

zero flows, and the addition of regional historical flood 

information for some sites in the data set complicated the 

estimation of the model error variance. Thus, to estimate 

the true model error variance, a simpler, “pristine” data 

set was developed. The pristine data set is a subset of 

the larger data set used in the WLS estimation of the 

regression parameters, and it does not include sites that 

had zero flows, low outliers as determined by EMA, 

or any reconstructed flow records. Any historical flood 

information was ignored. 

Because the pristine data set excluded sites with low 

outliers, the formulas provided in Bulletin 17B and by 

Griffis and Stedinger (2009) misrepresented the variance 

of the sample skewness estimators. Thus, a new Monte 

Carlo study was done to determine the actual variance of 

the skewness coefficient when a low outlier test is used to 

exclude some data. The Monte Carlo analysis of sample 

skews from an LP3 distribution used only complete 

samples with no low outliers. Results from the Monte 

Carlo analysis were used to determine the bias associated 

with the sample skewness coefficient G when samples 

with low outliers were dropped from the analysis. Two 

functions were computed: the mean of the sample skew, 

denoted m(γ, N), and its variance, denoted v(γ, N), 

( ) { } [ ] | , | , i

m E γ γ N = x no outliers - G N , (B6)

and

( ) { } [ ] | , | , i x no outliers v Var γ γ N = - G N . (B7)

In the first step of the WLS analysis, BayesianWeighted 

Least Squares (B-WLS) was used to estimate the model 

error variance, denoted 2 σ δ ,B WLS - . Then, 2 σ δ ,B WLS - was 

used in a method-of-moments WLS (MM-WLS) analysis 

to generate the weights, W, needed to estimate

the regression parameters 

β . In order to compute the 

MM-WLS weights, a diagonal covariance matrix,

2

, WLS B-WLS ( ) Λ σ δ , was created. The diagonal elements of 

the covariance matrix are the sums of the estimated error 

variance, 2 σ δ ,B WLS − , and the variance of the unbiased

 at-site skew,  Var i

é ù ê ú ë û γ , which depends only on the at-site

annual peak flow record length, and the estimated skew 

for that site. The at-site skew, Gi, and the variance of 

the at-site skew estimator, Var[Gi], were calculated 

from the entire flow record, including historical and 

systematic peaks, using the EMA method (Cohn and 

others, 1997). These biased estimates of the skew and 

the variance of the skew produced by EMA were then 

unbiased using equations B1 and B2, respectively, 

which gave estimates of the unbiased at-site skew, 

i γ

and the at-site skew variance Var[ 

i γ ]. The off-diagonal 

elements of 2

, ΛWLS B-WLS ( ) σ δ were zero, because cross 

correlations between gage sites were not considered in 

the WLS analysis. Thus, the (n × n) covariance matrix, 

2

, ΛWLS B-WLS ( ) σ δ , was

( ) 



2 2 = ( ),

where

is an ( ) identity matrix,

is the number of gage sites in the study, and

( ) is an ( ) matrix containing the variances

of the unbiased atWLS B-WLS B-WLS Var

n n

n

Var n n

σ σ δ δ , , I diag

I

diag

+ é ù ê ú ë û

 ́

é ù ê ú  ́ ë û

Λ γ

γ



site sample skewness

estimators, , on the diagonal and

zeros on the off-diagonal.

Var é ù ê ú ë û γ

(B3)

Using that covariance matrix, the MM-WLS weights are 

calculated as

( ) ( ) 1 1 2 1 2

, , ,

where

is ( ) matrix of weights,

is an ( ) matrix of basin parameters, and

is the number of basin characteristics.

T T

WLS B-WLS WLS B-WLS

k n

n k

k

W X σ σ δ δ X X

W

X

- é ù - - = ê ú ë û

 ́

 ́

Λ Λ (B4)
Appendix B 89

These expectations were computed using only those LP3 

samples,{xi}, that did not contain low outliers, as determined 

by a 10 percent Grubbs-Beck test recommended by Bulletin 

17B. Figure B1 summarizes the Monte Carlo results for 1,000 

simulations of N = 50 years of at-site annual-peak discharges. 

The x-axis represents the population (true) skew, γ, and the 

y-axis represents both the mean of the estimated skew m(γ, N) 

and the standard deviation of the estimated skew [the square 

root of the variance v(γ, N)] for LP3 samples that had no low 

outliers. Figure B1 shows that when only samples without low 

outliers are considered, the mean of the estimated skews (the 

POPULATION (TRUE) SKEW

ESTIMATED MEAN AND STANDARD DEVIATION OF ESTIMATED MEAN 

-1.0

-0.5

0.0

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

0.5

1.0

Relation between estimated

 and true skew

Standard deviation of

 estimated skew

Mean estimated skew

 excluding low outliers

IP017136_Figure B01

Figure B1. Relation between estimated skew and population (true) skew based on 1,000 

Monte Carlo simulations of 50-year samples in California. The dashed line represents the 

mean, m(γ,N), of the estimated skew across samples without outliers, and the dotted line 

represents the standard deviation [the square root of the variance, v (γ,N)] of that estimated 

skew across LP3 samples that do not contain low outliers. 

dashed line) can be significantly biased. Samples with low 

outliers are very likely to be negatively skewed, so analyzing 

data using an unbiased estimator and omitting samples with 

low outliers is expected to yield a regional skewness estimator 

that is positively biased if the bias is not corrected. When 

the true skew is highly positive, the bias is small and slightly 

negative, as few samples are omitted because of low outliers. 

When the true skew is highly negative, the standard deviation 

of the sample is greatly reduced, as shown by the dotted line in 

figure B1.
90 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento—San Joaquin River Basin, Based on Data through WY 2006

when the at-site record length was 50 years and the skew 

was 0.3, only 2 percent of the samples were rejected. 

When the skew was 0.5 or greater, none of the 50,000 

samples generated contained low outliers (table B1). 

 The pattern evident in table B1 shows why the standard 

deviation of the estimated skew in samples without 

outliers increases as the true skew increases. 

3. The Monte Carlo experiments provided the expected 

value and variance of the sample skewness estimator 

based on samples without outliers. These values can 

be used with the pristine data set in the computations 

of the model error variance using B-GLS. By using the 

relationship for regional skew generated by the WLS 

analysis, the WLS mean regional skew estimate, mR(i), 

can be calculated for each site i in the pristine data set as

 

( )

( ) 

,

where

is an 1 vector of WLS regional skew

estimates for each site in the pristine data 

set,

is an matrix of basin parameters,

is an ( 1) vector of WLS regression 

parameters,

is the numb

R

R p

p

p

n

n k

k

n

=

 ́

 ́

 ́

m X

m

X

β

β

er of gage sites in the pristine

data set, and

k is the number of basin characteristics.

(B8)

Skew was more negative when the dataset had more 

samples with low outliers (table B1). For example, 

32 percent of the samples with a true at-site skew of -0.5 

had low outliers and were therefore dropped, but only 

10 percent of the samples with a true at-site skew of 0.0 

were dropped. On the other hand, when the true at-site 

skew was highly positive, few samples were rejected, 

resulting in very little impact on the sampling distribution 

of the estimated skew. In the Monte Carlo simulation, 

Table B1. Monte Carlo results showing the percent of samples, for different at-site skew values, dropped from the simulation 

due to the presence of low outliers

Skew: -1.5 -1.0 -0.8 -0.5 -0.3 0.0 0.3 0.5 0.8 1.0 1.5

% of Samples Dropped: 71% 56% 47% 32% 22% 10% 2% 0% 0% 0% 0%

4. The last step (4) is to estimate the model error variance 

using the pristine data set. If the model error variance,

2 σ δ , −B GLS were zero, then all of the observed variability

 would be sampling error, and we would have

{ ( )} ( ) 2 , , EG m N v N i ii ii γ γ

é ù ê ú - = ë û . (B9)

However, we anticipate that the model will not be perfect, 

and thus estimating the model error variance will be 

challenging. The derivative 

dm d { } ( ) γ γ , 1 N 1 (B10)

will be used to correct the GLS analysis. Let the 

derivative in B10 be replaced by r, 

r dm d = { } ( ) γ γ ,N , (B11)

and let 2 σ δ ,B-GLS be the model error variance. Then a firstorder approximation of the expected value of regional 

skew variability would be

 { }

2 2 2 (, ) (, ) EG m N r v N i ii δ B-GLS i i γ γ σ , é ù ê ú - =+ ë û . (B12)
Appendix B 91

Thus, the GLS covariance matrix for the pristine data set 

is

( )

( ) ( )

( )

( )

2 2 2

, ,

2

,

( ),

where

is an GLS covariance

matrix,

is an identity matrix, and

( ) is an matrix containing the 

sampling variances of the biased

skewness estimato

p B GLS B GLS p

p B GLS p p

p pp

p p

r

n n

n n

n n

δ δ

δ

σ σ

σ

I G

I

G

- -

-

= +

 ́

 ́

 ́

Λ ∑

Λ

∑

[ ] ( )2

rs 

, and the

covariances of the skewness

estimators in the pristine data

set.

i ii

i

Var G v N

G

= γ

(B13)

The values of Σ(G) were determined by the the crosscorrelation of concurrent systematic annual peak flows 

(eq. 6) and the cf factor (eq. 7). In calculating the cf factor 

used to determine the ratio of the number of concurrent 

peak flows at a pair of sites to the total number of peak 

flows at both sites, only the systematic records were 

considered. 

The covariance matrix for the skewness coefficients for

the pristine data set, ( ) 2 Λp B-GLS σ δ , , and the conditional

means of the sample skews, m(γ,N) are used in a Bayesian 

framework to compute the posterior distribution of the 

model error variance, and in particular, the posterior mean 

of the true model error variance. 

The B-GLS model error variance can then be used to 

compute the precision of the regression parameters, 

β ,

that were calculated with the WLS weights, W, as

 = W β γ . Using the posterior mean of the true model

error variance in Λ, the variance of 

β is simply

 ( ) 2

,

T Var B GLS - é ù ê ú = ë û β Λ W W σ δ , (B14)

where ( ) 2 Λ σ δ ,B-GLS is an (n × n) covariance matrix that

uses all of the sites, not just those listed in the pristine

data set, and ( ) 2 σ δ ,B-GLS is the posterior mean of the

model error variance calculated from the B-GLS analysis

described above. It is important to note that ( ) 2 Λ σ δ ,B-GLS

is not the same as the covariance matrix ( ) 2 ΛWLS B-WLS σ δ ,

used in the MM-WLS analysis of all of the sites or the

( ) 2 Λp B-GLS σ δ , used in the B-GLS analysis of just the

pristine sites. Instead, ( ) 2 Λ σ δ ,B-GLS is

( ) 

( ) ( )

( )

 ( )



2 2

, ,

2

,

( ),

where

is an GLS covariance matrix,

is an identity matrix, 

( ) is an matrix containing the 

sampling variances of the unbiased

skewness estimators 

B-GLS B-GLS

B-GLS

i

n n

n n

n n

Var

δ δ

δ

σ σ

σ

γ

I

I

= +

 ́

 ́

 ́

é ù ê

ë

Λ ∑ γ

Λ

∑ γ



and the

covariances of the skewness

estimators , based upon the size 

and the WLS estimator of the skew

at each site.

i γ

ú

û

(B15) 

Off-diagonal elements of  ∑ γ( ) were estimated by the 

the cross-correlation of concurrent systematic annual 

peak flows (eq. 6) and the cf factor (eq. 7), which 

depends on the record lengths and concurrent record 

lengths. In calculating the cf factor used to determine the 

ratio of the number of concurrent peak flows at a pair 

of sites to the total number of peak flows at both sites, 

only the systematic records were considered. Thus, any 

historical floods used in the EMA analysis were not used 

to calculate the cross-correlation of peak flows or the cf

factor.
This page intentionally left blank.
Appendix C 93

Appendix C. Bayesian GLS Regression Diagnostics

To determine if a model is a good representation of 

the data and which regression parameters, if any, should be 

included in a regression model, diagnostic statistics have 

been developed to evaluate how well a model fits a regional 

hydrologic data set (Griffis and Stedinger, 2006; Gruber and 

others, 2008). In this report, the goal was to determine the set 

of possible explanatory variables that best fit the California 

peak-discharge data affording the most accurate skew 

prediction while also keeping the model as simple as possible. 

This appendix presents the diagnostic statistics for a Bayesian 

weighted least squares (WLS) or generalized least squares 

(GLS) analysis, and discusses the specific values obtained for 

the California regional skew study. 

Table C1 presents a Pseudo analysis of variance (Pseudo 

ANOVA) table for the California regional skew analysis. The 

table contains regression diagnostics/goodness of fit statistics 

which are explained below. 

In particular, the table provides equations for determining 

how much of the variation in the observations can be 

attributed to the regional model, and how much of the residual 

variation can be attributed to model error and sampling error, 

respectively. Difficulties arise in determining these quantities. 

The model errors cannot be resolved because the values of the 

sampling errors, ηi

, for each site, i, are not known. However, 

the total sampling error sum of squares can be determined by



1

[ ]

n

i

i

Var

=

å γ . Because there are n equations, the total model

error sum of squares due to the model error, δ, for a model 

with k parameters is 2 n k( ) σ δ . Thus, the residual variation 

attributed to the sampling error is 

1

[ ]

n

i

i

Var

=

å γ , and the

residual variation attributed to the model error is 2 n k( ) σ δ .

For a model with no parameters other than the mean 

(that is, the constant skew model), the estimated model error 

variance ( ) 2 0 σ δ describes all of the anticipated variation in 

i = + i γ μδ , where μ is the mean of the estimated at-site

sample skews. Thus, the total expected sum of squares 

variation due to model error, δi, and due to sampling error,



i i ηγγ i = - should equal 

( ) 2

1

(0) i

n

i

n Var

=

σ γ δ +å . Therefore,

the expected sum of squares attributed to a regional skew

model with k parameters equals 2 2 n k [ (0) ( )] σ σ δ δ - , because the

sum of the model error variance 2 n k( ) σ δ and the variance

explained by the model must sum to ( ) 2 n 0 σ δ . Table C1 shows 

results from models when k = 0 and 1.

Table C1. Pseudo ANOVA table for the Constant model and the NL-Elev model for regional skew in California.

[ANOVA, analysis of variance; NL-Elev model, nonlinear regional skew model; k, the number of parameters used in the regional regression; n, the number of

stations used in the regional skew regression; EVR, error variance ratio; MBV*, misrepresentation of the beta variance; 2 Rδ , Pseudo- 2 Rδ , %, percent] 

Source Degrees of freedom Equations Sum of squares

Constant NL-Elev Constant NL-Elev

Model k 0 1 2 2 n k (0) ( ) é ù ê ú - ë û σ σ δ δ 0.0 15

Model error n-k-1 157 156 2 n k( ) σ δ 32 17

Sampling error n 158 158 

1 i

n

i

Var

=

é ù ê ú å ë û γ 34 34

Total 2n-1 315 315 2 

1

(0) i

n

i

n Var

=

+ é ù ê ú å ë û σ γ δ 66 66

EVR 1.1 2.1

MBV* 13 16

0% 48% 2 Rδ
94 Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento–San Joaquin River Basin, Based on Data through WY 2006

This division of the variation in the observations is 

referred to as a Pseudo ANOVA because the contributions of 

the three sources of error were estimated or constructed, rather 

than being determined from the computed residual errors and 

the model predictions, while ignoring the impact of correlation 

among the sampling errors. 

Table C1 compares the Pseudo ANOVA results for the 

Constant model and the NL-Elev model. Both models have the 

same sampling error because both use the same set of at-site 

skew data. Both have sampling error variances greater than 

their model error variances. However, the model

error attributed to the NL-Elev model, ( ) 2 1 σ δ , is slightly

more than half of the model error variance attributed to

the Constant model, ( ) 2 0 σ δ . This difference is accounted

for by the variation in the sample that the NL-Elev model 

appears to explain. Because the Constant model does not 

have any explanatory variables, the variation attributed to 

that model is 0.0. On the other hand, the NL-Elev model 

has one explanatory variable, which causes the variation 

attributed to the model to increase to 15. This reduces the 

model error variance from 32 with the Constant model to 17 

with the NL-Elev model; thus, adding the nonlinear elevation 

explanatory variable in the NL-Elev model greatly improves 

the ability of the model to describe the observed skew 

coefficients. This impact is described by the Pseudo

2 Rδ , which in this case is 48 percent because the NL-Elev

model explains 48 percent of the estimated variation, ( ) 2 0 σ δ , 

in the true skew among the sites.

The Pseudo analysis of variance also provides the 

information needed to evaluate whether or not a sophisticated 

WLS or GLS analysis is needed to correctly interpret the data. 

In particular, the error variance ratio (EVR) is a modeling 

diagnostic used to evaluate whether a simple ordinary least 

squares (OLS) regression is sufficient or a more sophisticated 

WLS or GLS analysis is appropriate. EVR is the ratio of the 

average sampling error variance to the model error variance. 

Generally, an EVR greater than 20 percent indicates that the 

sampling variance is not significant when compared to the 

model error variance, suggesting the need for a WLS or GLS 

regression analysis. The EVR is calculated as 



( )

1

2

(sampling error) EVR , (model error) ( )

where

is the sum of squares.

n

i

i

Var

SS

SS n k

SS

δ

γ

σ

= = =

å

(C1)

The EVR was 1.1 for the constant model and 2.1 for 

the NL-Elev model. The sampling variability of skewness 

estimators was larger than model error variance of the regional 

model. Thus, given the variation of record lengths from 

site-to-site, using a WLS or GLS analysis is important for for 

evaluating the final precision of the model rather than using a 

simpler analysis that neglects the sampling error in the at-site 

skewness estimators. 

The misrepresentation of the beta variance (MBV*) 

statistic is used to determine whether a WLS regression is 

sufficient or a GLS regression is appropriate to determine the 

precision of the estimated regression parameters (Griffis and 

Stedinger, 2006). The MBV* describes the error produced by 

a WLS regression analysis by evaluating the precision of

0

WLS b , which is the estimator of the WLS regression constant,

0

WLS β . The correlation among estimated at-site skews, which 

is ignored in WLS regression, generally has its greatest impact 

on the precision of the regression constant term (Stedinger and 

Tasker, 1985). If the MBV* is substantially greater than 1, a 

GLS error analysis should be used. The MBV* is calculated as

0

0

1

|

MBV* , |

where

1 .

WLS T

WLS n

i

i

i

ii

Var b GLS analysis

Var b WLS analysis w

w

=

é ù ê ú ë û = = é ù ê ú ë û

=

å

w w

Λ

Λ (C2)

For the California regional skew study, the MBV* was 

equal to 16 for the NL-Elev model and 13 for the Constant 

model. This is a very large value indicating that the crosscorrelation among the skewness estimators has had a major 

effect on the precision with which the regional average skew 

coefficient can be estimated; if a WLS precision analysis 

had been used for the estimated constant parameter in the 

NL-Elev model, the variance would have been underestimated 

by a factor of 16. Thus a WLS analysis would have seriously 

misrepresented the variance of the constant in the Constant 

model and in the NL-Elev model of regional skew. This would 

have caused the variance of prediction to be underestimated 

given that the sampling error in the constant term in both 

models was large enough to contribute appreciably to the 

average variance of prediction. 
Publishing support provided by the U.S. Geological Survey

Publishing Network, Sacramento and Tacoma Publishing Service 

Centers

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

 Director, California Water Science Center

Placer Hall

6000 J street

Sacramento, CA 95819

http://ca.water.usgs.gov/
Parrett and others—Regional Skew for California, and Flood Frequency for Selected Sites in the Sacramento-San Joaquin River Basin,

 Based on Data through Water Year 2006

SIR 2010-5260

Printed on recycled paper