Development of statistical downscaling model based on Volterra series realization, principal components and ridge regression

Impacts of the global climate change in hydrology and water resources are accessed by downscaling of local daily rainfall from large-scale climate variables. This study developed a statistical downscaling model based on the Volterra series, principal components and ridge regression. This model is known, hereafter as SDCRR. The proposed model is applied at four different stations of the Manawatu River basin, in the North Island of New Zealand to downscale daily rainfall. The large-scale climate variables from the National Centers for Environmental Predictions (NCEP) reanalysis data are used in the present study to obtain with the wide range (WR) and the restricted range (RR) of predictors. The developed SDCRR model incorporated the climate change signals sufficiently by working with WR predictors. Further, principal component analysis (PC) was applied to the set of WR predictors, which were also used as the orthogonal filter in the ridge regression model to deal with the multi-collinearity. The ridge regression coefficients determined were less sensitive to random errors, and were capable of reducing the mean square error between the observed and the simulated daily precipitation data. Thus, the combined application of principal component analysis (PCA) and ridge regression improved the performance of the model. This combination is steady enough to capture appropriate information from predictors of the region. The performance of the SDCRR model is compared with that of the widely used statistical downscaling model (SDSM). The results of the study show the SDCRR model has better performance than the SDSM.