Distribution Regularized Regression Framework for Climate Modeling

Regression-based approaches are widely used in climate modeling to capture the relationship between a climate variable of interest and a set of predictor variables. These approaches are often designed to minimize the overall prediction errors. However, some climate modeling applications emphasize more on fitting the distribution properties of the observed data. For example, histogram equalization techniques such as quantile mapping have been successfully used to debias outputs from computer-simulated climate models to obtain more realistic projections of future climate scenarios. In this paper, we show the limitations of current regression-based approaches in terms of preserving the distribution of observed climate data and present a multiobjective regression framework that simultaneously fits the distribution properties and minimizes the prediction error. The framework is highly flexible and can be applied to linear, nonlinear, and conditional quantile models. The paper demonstrates the effectiveness of the framework in modeling the daily minimum and maximum temperature as well as precipitation for climate stations in the Great Lakes region. The framework showed marked improvement over traditional regression-based approaches in all 14 climate stations evaluated.