Precipitation-Frequency Applied Research and Development for the United States Army Corps of Engineers Dam and Levee Safety Program

The United States Army Corps of Engineers (USACE) has been assessing risks at all USACE dams over the last ten years to manage its dam portfolio in a risk informed manner. For each risk assessment, the reservoir stage-frequency curve must be estimated. This critical piece of information conveys the probability of exceeding each reservoir stage within a given year and forms the foundation for estimating probabilities of failure. Within USACE, the stage-frequency curve is usually derived using an inflow volume-based approach that makes use of historical stream gage data and potentially rainfall-runoff data when considering extreme events. For performing a rainfall-runoff analysis, areal precipitation-frequency estimates are needed. The only national scale precipitation-frequency product is the NOAA Atlas 14, which is unfortunately limited to a precipitation frequency of 1 in 1,000 years, or an annual exceedance probability (AEP) of 0.001. Dam safety studies routinely evaluate risks out to frequencies of 1 in 1,000,000 years (1E-6 AEP) or less frequent. As such, the NOAA Atlas 14 dataset is not sufficient for higher level issue evaluation study dam safety risk assessments, and project specific studies must be conducted to obtain the necessary point and areal precipitation-frequency estimates.

Current practice in precipitation-frequency for dam safety uses L-moments and areal reduction factors. However, advances from the field of extreme value theory (EVT) have demonstrated the capacity to efficiently, flexibly, and credibly model spatial extremes of pointwise maxima using a max-stable process (MSP), the infinite-dimensional analog of the multivariate extreme value distribution. With their application one can not only compute pointwise return level maps, but also model the joint distribution, and more complex areal-based assessments of risk while working within the theoretically justified mathematical framework provided by EVT. They do not depend upon the subjective assumptions associated with a Regional Precipitation Frequency Analysis (RFA), for example, the definition of homogeneous subareas and the need to convert point estimates into areal average depths using uncertain, empirical regional depth-area reduction factors. The RFA approach does not construct explicit spatial models for marginal parameters, which is a disadvantage of this approach. In contrast, the MSP based modeling approach allows for spatially varying trend surfaces for parameters, and the ability to directly estimate areal-based exceedances within an EVT-based framework. Importantly, the MSP modeling approach has a strong and coherent mathematical basis for model fitting, selection, extrapolation, and uncertainty quantification.

Lessons learned regarding the practical application of MSP models for precipitation-frequency analysis are provided by considering two distinct extreme storm types from two separate geographical locations that were used for MSP model development and application.