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.

Urban flood frequency analysis faces unique challenges as land development alters watershed hydrology, producing nonstationary flood records. This study demonstrates nonstationary flood frequency analysis (NSFFA) using RMC-BestFit, an open-source Bayesian software, through two Texas case studies. Brays Bayou at Houston (96 years of record) exemplifies an urbanized watershed with increasing flood trends; a step-logistic model captures both the abrupt increase in mean flood magnitude around 1968 and the progressive decrease in log-space variance as urbanization homogenized runoff response. O.C. Fisher Reservoir (169 years of record) exhibits decreasing trends attributed to brush encroachment and groundwater extraction; despite a sinusoidal model achieving best information criteria, a step function was selected based on physical reasoning, demonstrating that statistical fit alone should not dictate model selection. Results reveal contrasting frequency curve patterns: at O.C. Fisher, stationary and nonstationary curves differ uniformly (53\% reduction in 100-year flood), while at Brays Bayou, curves differ substantially for frequent events (48\% increase in 2-year flood) but converge in the extreme tail due to opposing trends in location and scale parameters. These findings underscore that NSFFA relevance depends on decision context. Bayesian methods offer key advantages including flexible integration of diverse data sources, comprehensive uncertainty quantification, and principled model comparison. Open-source software democratizes access to these methods, promoting transparency and reproducibility.

Urban flood frequency analysis faces unique challenges as land development alters watershed hydrology, producing nonstationary flood records. This study demonstrates nonstationary flood frequency analysis (NSFFA) using RMC-BestFit, an open-source Bayesian software, through two Texas case studies. Brays Bayou at Houston (96 years of record) exemplifies an urbanized watershed with increasing flood trends; a step-logistic model captures both the abrupt increase in mean flood magnitude around 1968 and the progressive decrease in log-space variance as urbanization homogenized runoff response. O.C. Fisher Reservoir (169 years of record) exhibits decreasing trends attributed to brush encroachment and groundwater extraction; despite a sinusoidal model achieving best information criteria, a step function was selected based on physical reasoning, demonstrating that statistical fit alone should not dictate model selection. Results reveal contrasting frequency curve patterns: at O.C. Fisher, stationary and nonstationary curves differ uniformly (53% reduction in 100-year flood), while at Brays Bayou, curves differ substantially for frequent events (48% increase in 2-year flood) but converge in the extreme tail due to opposing trends in location and scale parameters. These findings underscore that NSFFA relevance depends on decision context. Bayesian methods offer key advantages including flexible integration of diverse data sources, comprehensive uncertainty quantification, and principled model comparison. Open-source software democratizes access to these methods, promoting transparency and reproducibility.

This study utilized a max-stable process (MSP) model with a dependence structure defined via a non-Euclidean distance metric, with the goal of modelling extreme flood data on a river network. The dataset was composed of mean daily discharge observations from 22 United States Geological Survey streamflow gaging stations for river basins in Missouri and Arkansas. The analysis included the application of the elastic-net penalty to automatically build spatially varying trend surfaces to model the marginal distributions. The dependence model accounted for the river distance between hydrologically connected gaging sites and the hydrologic distance, defined as the Euclidean distance between the centers of site’s associated drainage areas, for all stations. Modelling the marginal distributions and spatial dependence among the extremes are two key components for spatially modelling extremes. Among the 16 covariates evaluated for marginal fitting, 7 were selected to spatially model the generalized extreme value (GEV) location parameter (for each gaging station’s contributing drainage basin, its outlet elevation, centroid x coordinate, centroid elevation, area, average basin width, elevation range, and median land surface slope). The three covariates selected for the GEV scale parameter included the area, average basin width, and median land surface slope. The GEV shape parameter was assumed to be constant throughout the entire study area. Comparisons of estimates obtained from the spatial covariate model with their corresponding “at-site” estimates resulted in computed values of 0.95, 0.95, 0.94 and 0.85, 0.84, 0.90 for the coefficient of determination, Nash–Sutcliffe efficiency, and Kling–Gupta efficiency for the GEV location and scale parameters, respectively. Brown–Resnick MSP models were fit to independent multivariate events extracted from a set of common discharge data, transformed to unit Fréchet margins while considering different permutations of the non-Euclidean dependence model. Each of the fitted model’s log-likelihood values indicated improved fits when using hydrologic distance rather than Euclidean distance. They also demonstrated that accounting for flow-connected dependence and anisotropy further improved model fit. In this study, the results from both parts were illustrative; however, further research with larger datasets and more heterogeneous systems is recommended.