Parameter estimation method and updating of regional prediction equations for ungaged sites in the desert region of California

By:  and 



The U.S. Geological Survey (USGS) is currently updating at-site flood frequency estimates for USGS streamflow-gaging stations in the desert region of California. The at-site flood-frequency analysis is complicated by short record lengths (less than 20 years is common) and numerous zero flows/low outliers at many sites. Estimates of the three parameters (mean, standard deviation, and skew) required for fitting the log Pearson Type 3 (LP3) distribution are likely to be highly unreliable based on the limited and heavily censored at-site data. In a generalization of the recommendations in Bulletin 17B, a regional analysis was used to develop regional estimates of all three parameters (mean, standard deviation, and skew) of the LP3 distribution. A regional skew value of zero from a previously published report was used with a new estimated mean squared error (MSE) of 0.20. A weighted least squares (WLS) regression method was used to develop both a regional standard deviation and a mean model based on annual peak-discharge data for 33 USGS stations throughout California’s desert region. At-site standard deviation and mean values were determined by using an expected moments algorithm (EMA) method for fitting the LP3 distribution to the logarithms of annual peak-discharge data. Additionally, a multiple Grubbs-Beck (MGB) test, a generalization of the test recommended in Bulletin 17B, was used for detecting multiple potentially influential low outliers in a flood series. The WLS regression found that no basin characteristics could explain the variability of standard deviation. Consequently, a constant regional standard deviation model was selected, resulting in a log-space value of 0.91 with a MSE of 0.03 log units. Yet drainage area was found to be statistically significant at explaining the site-to-site variability in mean. The linear WLS regional mean model based on drainage area had a Pseudo- 2 R of 51 percent and a MSE of 0.32 log units. The regional parameter estimates were then used to develop a set of equations for estimating flows with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities for ungaged basins. The final equations are functions of drainage area.Average standard errors of prediction for these regression equations range from 214.2 to 856.2 percent.

Study Area

Additional publication details

Publication type Conference Paper
Publication Subtype Conference Paper
Title Parameter estimation method and updating of regional prediction equations for ungaged sites in the desert region of California
DOI 10.1061/9780784412312.238
Year Published 2012
Language English
Publisher American Society of Civil Engineers
Contributing office(s) California Water Science Center
Description 11 p.
First page 2356
Last page 2366
Conference Title World Environmental and Water Resources Congress 2012
Conference Location May 20-24, 2012
Conference Date Albuquerque, New Mexico, United States
Country United States
State California
Other Geospatial Desert region
Online Only (Y/N) N
Additional Online Files (Y/N) N