Gamma distribution linear modeling with statistical downscaling to predict extreme monthly rainfall in Indramayu

Abstract

Rainfall is an important factor in the agricultural process. Several methods to predict the rainfall have been carried out in Indonesia, such as the modeling of Statistical Downscaling (SDS). SDS models might involve ill-conditioned covariates (large dimension and high correlation/multi collinear). This problem could be solved by a variable selection technique such as L1 regularization/LASSO or a dimension reduction approach such as principal component analysis (PCA). In this paper, both methods were applied to generalized linear modeling with gamma distribution and compared in order to predict extreme monthly rainfall at 11 rain posts in Indramayu. Simulations were conducted to compare L1 regularization technique and principal component analysis in the prediction of responses. Two scenarios were based on the coefficient of beta and the distribution of response scenarios. The covariates used in this study were in observational data of GPCP version 2.2. The coefficient of beta scenarios were the combination of beta less than 1, equal 0, and greater than 1 vs all betas less than 1. Gamma distributions were used for distribution of response scenario with three different shape parameters. The simulation showed that L1 regularization technique resulted in almost better prediction than principal component analysis as the shape parameter was larger. The Root Mean Square Error (RMSE) of generalized linear model with Gamma distribution was less than that of principal component regression. However, all generalized linear models with Gamma distribution gave the smaller RMSE values for extreme value prediction above outliers. In this case, the quantiles, Q(0.90) and Q(0.95), were better prediction of extreme monthly rainfall.