Impacts of Max-Stable Process Areal Exceedance Calculations to Study Area Sampling Density, Surface Network Precipitation Gage Extent and Density, and Model Fitting Method

Max-stable process (MSP) models can be fit to data collected over a spatial domain to estimate areal-based exceedances while accounting for spatial dependence in extremes. They have theoretical grounding within the framework of extreme value theory (EVT). In this work, we fit MSP models to three-day duration cool season precipitation maxima in the Willamette River Basin (WRB) of Oregon and to 48 h mid-latitude cyclone precipitation annual maxima in the Upper Trinity River Basin (TRB) of Texas. In total, 14 MSP models were fit (seven based on the WRB data and seven based on the TRB data). These MSP model fits were developed and applied to explore how user choices of study area sampling density, gage extent, and model fitting method impact areal precipitation-frequency calculations. The impacts of gage density were also evaluated. The development of each MSP involved the application of a recently introduced trend surface modeling methodology. Significant reductions in computing times were achieved, with little loss in accuracy, applying random sample subsets rather than the entire grid when calculating areal exceedances for the Cougar dam study area in the WRB. Explorations of gage extent revealed poor consistency among the TRB MSPs with modeling the generalized extreme value (GEV) marginal distribution scale parameter. The gauge density study revealed the robustness of the trend surface modeling methodology. Regardless of the fitting method, the final GEV shape parameter estimates for all fourteen MSPs were greater than their prescribed initial values which were obtained from spatial GEV fits that assumed independence among the extremes. When two MSP models only differed by their selected fitting method, notable differences were observed with their dependence and trend surface parameter estimates and resulting areal exceedances calculations.