Development of Statistical Downscaling Model Based on Volterra Series Realization, Principal Components, Climate Classification, and Ridge Regression

Abstract

This paper applied the fuzzy function approach, combined with the ridge regression model, to produce daily rainfall projections from large-scale climate variables. This study developed a statistical downscaling model based on principal components, c-means fuzzy clustering, Volterra series, and ridge regression. The model is known, hereafter as SDC2R2. In the developed downscaling model, the use of ridge regression, instead of multiple linear regression, is proposed to downscale daily rainfall with wide range (WR) predictors. The WR predictors were applied to sufficiently incorporate climate change signals. The developed model also captured the non-linear interactions of the climate variables by applying the transformation of Volterra series realization over WR predictors. This transformation was performed by applying principal components as orthogonal filters. Further, these principal components were clustered by using c-means clustering and non-linear transformations were applied on these membership functions, to improve the prediction ability of the model. The reanalysis of climate data from the National Centres for Environmental Prediction (NCEP) was used to develop the model and was validated by using the Global Climate Model (GCM) for four locations in the Manawatu River basin. The developed model was used to obtain future daily rainfall projections from three Representative Concentrative Pathways (RCP 2.6, RCP 4.5, and RCP 8.5) scenarios from the Canadian Earth System Model (CanESM2) GCM. The performance of the model was compared with a widely used statistical downscaling model (SDSM). It was observed that the model performed better than SDSM in downscaling rainfall on a daily basis. Every scenario indicated that there is a probability of obtaining high future rainfall frequency. The results of this study provide valuable information for decision-makers since climate change may potentially impact the Manawatu basin.