Physically Informed Estimation of Spatial Precipitation Extremes
Improving the analysis of the intensity and frequency of spatial extreme precipitation is essential for regional hazard preparedness and infrastructure design. Extreme precipitation events are highly variable across space and time, and current methods for analyzing extremes are often based on simplifying assumptions. For example, the commonly used assumption of spatial independence among extreme precipitation observations may be unrealistic for non-localized events (e.g., hurricane precipitation, large stratiform rainfall events). This can result in the misestimation of risk. Given the additional challenges of data records that are relatively too short for adequately estimating the rarest of events, sparse sensor networks, highly localized events, and integrating spatial data and their drivers across regions, methods for estimating exceedance probabilities that enable the proper modeling of spatially varying extreme marginal parameters and account for spatial dependence between sites need to be explored and refined. The overarching goal of this thesis is to improve the estimation of spatial extreme precipitation by including information based on the physical processes that influence the generation of storms. Here I outline the need for the inclusion of additional physically informed covariates and improved methods for covariate selection that not only improve computation time but also automate the process to reduce the bias of a manual selection approach. Consideration should be given to incorporating assessments of relevant covariates and the spatial dependence of extreme events within the methods used by practitioners to ensure the selection of conservative estimates for infrastructure design. Applying a latent variable modeling approach for analysis of annual maximum (AM) precipitation, I explore the benefits of including additional climatic covariates on regional model performance across two climatically different regions and a region of overlap. These covariates include temperature and dew point temperature, extending beyond what is classically used in practice (geographic only) and within the literature (geographic and mean precipitation). The results indicate that including additional physically informed covariates improves estimates within relatively heterogeneous regions. I introduce a framework for the selection of relevant geographic and climatic covariates for spatially distributing marginal parameters using elastic-net regularization. Using two climatically different regions, I demonstrate the application of elastic-net regularization for trend surface development. This approach aids in automating the selection of relevant covariates in a way that is less biased than manual selection, and that is computationally more efficient than cross-validation using full model simulations for a large set of physically relevant covariates. To quantify the impact of assuming spatial independence, a max-stable process model that accounts for inter-site dependence of the observed AM precipitation will be explored in two climatically different regions. Estimation of areal-based exceedance probabilities is of critical importance, and their calculation depends on properly modeling the spatial dependence structure and the spatially varying generalized extreme value (GEV) marginal distributions. A results comparison between the max-stable process model and a regional frequency analysis is conducted. This comparison indicates that assessing the spatial dependence and the characterization of the spatially varying marginal parameters are worth including to insure conservative estimates.