Regional precipitation-frequency analysis and spatial mapping for 24-hour and 2-hour durations for Washington State
Hydrology and Earth System Sciences
This preamble explains why a paper on precipitation probabilities at the 2-hour and 24-hour time periods for the State of Washington, USA, was solicited for a special symposium honouring Dr. McCullochs contributions to hydrology. Indeed, the specific subject of the paper has no particular connection with Dr. McCullochs technical specialties or the thrust of IH work, but it does have much to do with Dr Mc Cullochs prowess and vision for running a research institute. In 1984, I was invited to
... was invited to spend a Sabbatical year at IH to work on the then new technique of Regional Probability Weighted Moments (PWM) in connection with Generalised Extreme Value (GEV) distribution. The IH Flood Studies Report (FSR) had used the GEV distribution with a graphical method involving rather arbitrary and subjective steps in its fitting procedure for determining the regional distributions to use in different parts of the UK. Because physically impossibly-large flood probabilities had been produced by the FSR in connection with some Scottish dams, there was a controversy with large economic and social implications. I, working together with Jon Hosking, a young, very bright mathematical statistician employed by IH, addressed the problem and devised a PWM solution for the GEV so that the FSR flood probability estimation difficulty was resolved which was invaluable to IH at the time. After much more research in the UK and the USA, a book Regional Frequency Analysis; An Approach Based on L-Moments by J.R.M. Hosking and J.R. Wallis was published by Cambridge University Press. It is worth noting that the Regional L-moment algorithm is numerically equivalent to the Regional PWM algorithm, but the Regional L-moment approach is much more complete and powerful; and has appeared in a myriad of other investigations published in hydrological and meteorological journals worldwide, as well as in other studies reported at this General Assembly. Presumably Regional L-moments would have been discovered eventually, but their prompt appearance can be largely attributed to Dr. McCullochs stewardship of IH, and in particular on his insistence on the value of inviting outside scientists to IH. Abstract This study is an update of the information contained in the precipitation-frequency atlas published by the US National Weather Service in 1973. Data collection for the NWS study ended in 1966 while this study uses the current data base which more than doubles the record length used in the NWS study. Washington State has highly variable topography and climate; in particular Mean Annual Precipitation (MAP) varies from over 260 inches a year to less than 7 inches. Steep high mountain ranges provide very wet slopes as well as pronounced rain shadows with large climate changes occurring in relatively short distances. In addition there are four distinct sources for the atmospheric moisture needed for precipitation which gives rise to complex seasonal and spatial interactions. The PRISM mapping system used in this study has greatly improved the spatial mapping of precipitation and increased the reliability of estimates of precipitation in the broad areas between precipitation measurement stations. Further, the development and use of regional L-Moments has greatly improved the reliability of precipitation magnitude-frequency estimates, particularly for the rarer and more extreme storms. Washington State could be specified adequately by 12 regions for the purposes of estimating the 2-hour and 24 hour precipitation frequencies. Within each region algorithms were developed for L-CV and L-Skewness expressed as functions of the MAP. The GEV distribution was acceptable statistically for all regions up to the 1 in 500 recurrence interval, beyond which the four-parameter Kappa distribution is recommended. The estimated changes in precipitation magnitudes for a given frequency as regional boundaries were crossed were found to be small, and well within the expected differences likely from sampling errors. An interesting transition zone was observed at the eastern edge of the Cascade foothills, associated with the maxima having a seasonal change from autumnwinter synoptic scale general storms in the west to springsummer maxima in the east that were produced by a mix of storm types. (Comment: storms were a mix of general storms and more-isolated convective storms).