A penalized maximum likelihood approach for m-year precipitation return values estimation with lattice spatial data

Climate models are useful tools for simulating the uncertainties of climate change under different emission scenarios. Regional Climate Models are high resolution climate models which generate high-dimensional spatio-temporal output. To effectively summarize such output without subsampling is important but difficult. One important aspect in climate assessment is the characteristic of extreme precipitation events and m-year precipitation return values are often computed as the summary statistics of the extreme precipitation events. In this paper we present a Penalized Maximum Likelihood (PML) method to estimate precipitation return values with Generalized Extreme Value distribution (GEV). With PML models, we have a different set of GEV parameters at each spatial location and we add smoothness penalties on parameters based on prior belief that the neighboring parameters should vary smoothly. The penalization terms are selected by data-driven approaches. We evaluate the uncertainty of the estimates using pointwise standard deviations.