Spatially Penalized Regression for Extremes Dependence Analysis and Prediction: Case of Precipitation Extremes

The inability to predict precipitation extremes under nonstationary climate remains a crucial science gap. Precipitation is not a state-variable within climate models, exhibits space-time heterogeneities, and is subject to thresholds and intermittences. Atmospheric variables in the spatiotemporal neighborhood, like temperature, humidity and updraft velocity, are often better predicted than precipitation from these models, and may have information relevant for precipitation extremes. Model-simulated atmospheric variables have been used to enhance model-predicted precipitation extremes in two ways: statistical downscaling routinely uses regression methods including neural networks and recently physics-based formulations have been developed. The former may not generalize under non-stationary climate while the latter is more interpretable but may not be able to discover or leverage the full information content in atmospheric covariates. We propose robust data-mining strategies to complement these approaches. The challenges are to discover spatiotemporal neighborhoods of influence, extract dependence structures, and determine predictive power, under non-stationary climate. We have developed a data-dependent method to discover sparse spatiotemporal dependence structure using spatially-penalized elastic net regression focused on extremes of target variables. The approach addresses neighborhood discovery, dependence discovery and predictive modeling of precipitation extremes. The methods show promise, specifically to improve our understanding of precipitation extremes and hence inform stakeholders and policy-makers in the water sector. In addition, further developments may generalize to problems in multi-physics simulations and to other complex, nonlinear and spatiotemporal dynamical systems where extremes are of interest.