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, a reservoir stage–frequency curve is 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 the 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 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 with frequencies of up to 1 in 1,000,000 years (1E-6 AEP) or less. As such, 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 in 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. Applying this, one can not only compute pointwise return level maps but also model the joint distribution and carry out more complex areal-based assessments of risk while working within the theoretically justified mathematical framework provided by EVT. The MSP-based modeling approach allows for spatially varying trend surfaces for parameters and the ability to directly estimate area-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.