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Scientific Investigations Report 2010-5260

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

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

Thumbnail of and link to report PDF (4.6 MB)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 peak-discharge 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.

First posted March 24, 2011

For additional information contact:
Director, California Water Science Center
Placer Hall
6000 J street
Sacramento, CA 95819

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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.




Data Used

Analytical Methods

Flood-Frequency Results


References Cited


Appendix A. Move Methods for Estimating Unregulated Annual-Peak-Flow Data at Key Dam Sites

Appendix B. Extended Bayesian GLS Regional Skew Analysis for California

Appendix C. Bayesian GLS Regression Diagnostics.

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