Quantile Regression with Functional Principal Component in Statistical Downscaling to Predict Extreme Rainfall
Extreme rainfall events have been great interest in statistical downscaling (SD). This paper is concerned with SD using quantile regression (QR) and functional principal component analysis (FPCA) to estimate extreme monthly rainfall. SD, usually with principal component analysis (PCA) to reduce dimension of predictors, relates functionally local scale response and global scale predictors. PCA analyzes non-functional data while FPCA analyzes functional data. FPCA is used to overcome autocorrelation and multi collinear problems. SD with FPCA and PCA are compared. The response is monthly rainfall from 1979 to 2008 at Indramayu Indonesia and the predictors are monthly precipitation of 64 grid of Global Circulation Model (GCM) output in the same period. Before applying FPCA, GCM output data are firstly transformed to be functional data using Fourier function such that the patterns before and after transformation are similar. Number of components is determined based on cumulative variances. The results show that the number of components from FPCA (two components) is less than that from PCA (five components) at 98% cumulative variances and both methods give similar results. At 90th quantile the patterns of forecasted rainfall in January to December 2008 using FPCA and PCA are similar to the actual rainfall with correlation 0.9 but FPCA gives the estimate of extreme rainfall more accurate and more consistent than PCA. The forecasted rainfall of FPCA in February 2008 is 460 mm considered as the extreme rainfall which confirms well to the highest actual rainfall (439 mm) while that of PCA is 512 mm.
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