Semiparametric modeling in statistical downscaling to predict rainfall

Abstract

Semiparametric model in statistical downscaling (SD) consists of parametric and nonparametric functional relationship between a local scale variable as the response and global scale variables as the predictors. The local variable is rainfall intensity and the global variables are the precipitation of Global Circulation Model (GCM) output. Because of the multicollinearity problem in GCM output, principal component analysis is used to reduce dimension of the predictors to a number of orthogonal components. Usually, SD uses principal component regression (PCR) as a parametric model with the components as predictors. However, the rainfall prediction using the PCR is not quite accurate. In this research the rainfall prediction is improved using a semiparametric model. This model treats some components as parametric and the others as non parametric predictors because of the fact that not all of the components used in the model are linearly related to rainfall. The semiparametric model development uses mixed model approach where the nonparametric relationship is represented using spline with truncated power basis. The model is developed without and with dummy variables. The dummy variables are based on heterogeneous residual variance resulted from partial least square regression. The model performance is evaluated based on the values of RMSEP (Root Mean Square Error of Prediction) and R 2 (Coefficient of Determination). The result shows that the model with dummy 4372 Aji Hamim Wigena, Anik Djuraidah, and Akbar Rizki variables (RMSEP=32.58 and R 2 =97.08%) is better than that without dummy variables (RMSEP=68.88 and R 2 =79.94%).

Quantile spline regression on statistical downscaling model to predict extreme rainfall in Indramayu

“…The number of spline knot in a model depended on the number of parameter and degree the basic model. The cubical model with the spline combination knot of 14, 8, 7, 5 were the best spline combination knot [14]. Figure 4).…”

“…The study of the SD modeling with nonparametric approach that was used was spline multivariate additive regression [11]. The study of the SD modeling with semiparametric that was used was penalty spline regression (P-sline) with mixed linear model approach [14]. However, the SD modeling predicted the average rainfall.…”

“…The type of the functional relationship in the quantile regression could be developed into nonparametric type. The best type of the functional relationship between rainfall and GCM was the spline [14]. Quantile spline regression had been used to predict the air pollution in Surabaya [1].…”

Two-Stage Statistical Downscaling Modeling with Multi-Class Random Forest on Rainfall Prediction

“…GCM output can be used to estimate climate parameters on a local scale using downscaling techniques. One of the downscaling techniques that can be used to obtain localscale information from GCM output data is statistical downscaling (SD) [2]. SD uses a statistical model to connect functionally between global climate parameters obtained from GCM output with local climate parameters obtained from climatology observation stations.…”