A statistical downscaling model based on multi-way functional principal component analysis for southern Australia winter rainfall

We propose a statistical downscaling model based on multi-way functional principal component analysis (FPCA) for rainfall prediction. The model mainly explains the relationship between the winter mean sea level pressure (MSLP) and rainfall in southern Australia from the perspective of functional data. Compared with the traditional approach of feature extraction based on principal component analysis, the multi-way FPCA needs not only fewer principal components to capture most variance in MSLP, bus also greatly avoid the loss of spatial information. A functional principal component (FPC) regression is further developed to simulate both current and future rainfall. The main results show that the first five leading FPCs are sufficient to capture the spatial characteristics of winter MSLP, achieving the purpose of efficient dimensionality reduction. Specifically, no more than three FPCs are required to develop the functional dowscaling models for the winter rainfall over four studied regions. The functional downscaling model provides a good skill in terms of the correlation higher than 0.7 between the predictions and observations, and the ratio of root mean square error to the climatology of winter rainfall below 20% over four regions. The developed downscaling models are further used to interpret the MSLP patterns from four CMIP5 climate models (ACCESS1.3, BCC-CSM1.1-m, CESM1-CAM5 and MPI-ESM-MR), which have been used to simulate both present-day and future climate. The resulting downscaled values based on ensemble MSLP provides (1) a closer representation of observed present-day rainfall than the raw climate model values; (2) alternative estimates of future changes in rainfall that arises from changes in MSLP.