A case study: calculating a precipitation frequency curve using L-moment statistics with emphasis on the uncertainties in the analysis

Regional frequency analyses, such as L-moments statistics developed by Hosking and Wallis (1997), assume that it is possible to augment a short record length of data at one location with data from a surrounding homogeneous region. Regional frequency statistics are thus appealing to precipitation studies since precipitation observation records generally date back 100 years at best, and a greater record length is desirable. For dam safety objectives at the Bureau of Reclamation, precipitation frequency curves extrapolated to the Probable Maximum Precipitation (PMP) are required as input into hydrologic models to create flood hydrographs. This paper assesses the application of L-moment statistics as a method to produce a precipitation frequency curve for East Park Dam, located in North Central California. The sources of uncertainty that were encountered during the statistical analysis will also be identified and discussed.

Dam safety studies using L-moment statistics are often time-consuming and expensive. Traditionally, these studies were contracted to MGS Software, LLC, the first to develop precipitation frequency curves utilizing the L-moments approach. Recently, Reclamation's meteorological experience and expertise has allowed us to conduct in-house L-moment analyses to meet the schedule and budget of current dam safety projects, such as the East Park Dam study.

L-moments regional frequency statistics were applied to daily precipitation observations to all rain gauge sites within a climatologically similar homogeneous region about the East Park, CA, watershed. The precipitation observations were measured at National Weather Service (NWS) Cooperative Observer Program (COOP) rain gauge sites and were transmitted via the National Climatic Data Center (NCDC) Summary of the Day product. From these statistics, a precipitation frequency curve was created using the Generalized Logistic distribution and extrapolated to the PMP. Two assumptions are made by utilizing this curve: first, future events are similar to past events in magnitude and frequency of occurrence, and second, that the frequency of occurrence does not deviate from a Generalized Logistic distribution. PMP, calculated from ‘Hydrometeorological Report 59: Probable Maximum Precipitation for California,' was assumed to be the physical upper bound of the frequency curve.

A great deal of uncertainty is associated with the L-moments approach based on the assumptions stated above. The statistical uncertainty may be quantified by confidence intervals included on a graph of the frequency curve. However, it is vastly more difficult to quantify the uncertainty involved with extreme precipitation events and a changing climate. The assumption is made that the past will dictate the future, with the past represented by antiquated storm data. For example, ‘HMR 51: Probable Maximum Precipitation Estimates United States East of the 105th Meridian,' the document currently used to calculate PMP for the Eastern half the United States, was published in 1978 using storm data from 1878 to 1972. New storm data (post 1972) does not exist for this region. With a changing climate, it is unclear whether or not the old storm data continues to be representative of the current, or future, climate. Communicating, and accounting for, the uncertainty pertaining to utilizing old storm data for new research remains problematic.