A new approach to statistical downscaling using Tweedie compound Poisson gamma response and lasso regularization

Abstract

Statistical Downscaling (SDS) is a technique in climatology to analyze the functional relationship of global scale GCM (Global Circulation Model) output data as predictor variables and local scale rainfall data as a response variable. Rainfall contains continuous and discrete components. The continuous component is related to the intensity of rainfall more than zero which can be assumed to be Gamma distribution while the discrete component is related to the occurrence of rain including zero which can be assumed to be Poisson distribution. A combination of both distributions is called Tweedie compound poisson gamma (TCPG). SDS modeling with TCPG response can be used to predict the occurrence of rain and also the rainfall intensity simultaneously. GCM output data generally contain multicollinearity problems which can be overcome by Lasso regularization. This study discusses SDS modeling which assumes TCPG distributed response and uses Lasso to predict some characteristics of rainfall such as the average number of daily rainfall events per month (, shape parameter , the average intensity of daily rainfall per month , probability of no rain event per month ,  the number of no rain per month . Based on the smallest RMSEP and the high correlation of the actual and predicted data, the TCPG model with Lasso regulation is more reliable and needs to be considered for modeling rainfall than TCPG-generalized linear models and TCPG-principal component analysis.