Magnitude, frequency, and trends of floods at gaged and ungaged sites in Washington, based on data through water year 2014

Scientific Investigations Report 2016-5118
Prepared in cooperation with the Washington State Department of Transportation and the Washington State Department of Ecology
By: , and 



An investigation into the magnitude and frequency of floods in Washington State computed the annual exceedance probability (AEP) statistics for 648 U.S. Geological Survey unregulated streamgages in and near the borders of Washington using the recorded annual peak flows through water year 2014. This is an updated report from a previous report published in 1998 that used annual peak flows through the water year 1996. New in this report, a regional skew coefficient was developed for the Pacific Northwest region that includes areas in Oregon, Washington, Idaho and western Montana within the Columbia River drainage basin south of the United States-Canada border, the coastal areas of Oregon and western Washington, and watersheds draining into Puget Sound, Washington. The skew coefficient is an important term in the Log Pearson Type III equation used to define the distribution of the log-transformed annual peaks. The Expected Moments Algorithm was used to fit historical and censored peak-flow data to the log Pearson Type III distribution. A Multiple Grubb-Beck test was employed to censor low outliers of annual peak flows to improve on the frequency distribution. This investigation also includes a section on observed trends in annual peak flows that showed significant trends (p-value < 0.05) in 21 of 83 long-term sites, but with small magnitude Kendall tau values suggesting a limited monotonic trend in the time series of annual peaks. Most of the sites with a significant trend in western Washington were positive and all the sites with significant trends (three sites) in eastern Washington were negative.

Multivariate regression analysis with measured basin characteristics and the AEP statistics at long-term, unregulated, and un-urbanized (defined as drainage basins with less than 5 percent impervious land cover for this investigation) streamgages within Washington and some in Idaho and Oregon that are near the Washington border was used to develop equations to estimate AEP statistics at ungaged basins. Washington was divided into four regions to improve the accuracy of the regression equations; a set of equations for eight selected AEPs and for each region were constructed. Selected AEP statistics included the annual peak flows that equaled or exceeded 50, 20, 10, 4, 2, 1, 0.5 and 0.2 percent of the time equivalent to peak flows for peaks with a 2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence intervals, respectively. Annual precipitation and drainage area were the significant basin characteristics in the regression equations for all four regression regions in Washington and forest cover was significant for the two regression regions in eastern Washington. Average standard error of prediction for the regional regression equations ranged from 70.19 to 125.72 percent for Regression Regions 1 and 2 on the eastern side of the Cascade Mountains and from 43.22 to 58.04 percent for Regression Regions 3 and 4 on the western side of the Cascade Mountains. The pseudo coefficient of determination (where a value of 100 signifies a perfect regression model) ranged from 68.39 to 90.68 for Regression Regions 1 and 2, and 92.35 to 95.44 for Regions 3 and 4.

The calculated AEP statistics for the streamgages and the regional regression equations are expected to be incorporated into StreamStats after the publication of this report. StreamStats is the interactive Web-based map tool created by the U.S. Geological Survey to allow the user to choose a streamgage and obtain published statistics or choose ungaged locations where the program automatically applies the regional regression equations and computes the estimates of the AEP statistics.

Suggested Citation

Mastin, M.C., Konrad, C.P., Veilleux, A.G., and Tecca, A.E., 2016, Magnitude, frequency, and trends of floods at gaged and ungaged sites in Washington, based on data through water year 2014 (ver 1.2, November 2017): U.S. Geological Survey Scientific Investigations Report 2016–5118, 70 p.,

ISSN: 2328-0328 (online)

Study Area

Table of Contents

  • Abstract
  • Introduction
  • Trends in Peak Flows
  • Estimating Magnitude and Frequency of Floods
  • Summary
  • References Cited
  • Appendix A. Regional Skewness Regression Analysis for the Pacific Northwest, Including Idaho, Montana, Oregon, and Washington
Publication type Report
Publication Subtype USGS Numbered Series
Title Magnitude, frequency, and trends of floods at gaged and ungaged sites in Washington, based on data through water year 2014
Series title Scientific Investigations Report
Series number 2016-5118
DOI 10.3133/sir20165118
Edition Version 1.0: Originally post September 20, 2016; Version 1.1: October 4, 2016; Version 1.2: November 2017
Year Published 2016
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Washington Water Science Center
Description Report: vi, 69 p.; 3 Tables
Country United States
State Washington
Online Only (Y/N) Y
Additional Online Files (Y/N) Y
Google Analytic Metrics Metrics page
Additional publication details