Comparison of transfer functions in statistical downscaling models for daily temperature and precipitation over Canada

This study compares three linear models and one non-linear model, specifically multiple linear regression (MLR) with ordinary least squares (OLS) estimates, robust regression, ridge regression, and artificial neural networks (ANNs), to identify an appropriate transfer function in statistical downscaling (SD) models for the daily maximum and minimum temperatures (T_max and T_min) and daily precipitation occurrence and amounts (P_occ and P_amount). This comparison was made over twenty-five observation sites located in five different Canadian provinces (British Columbia, Saskatchewan, Manitoba, Ontario, and Québec). Reanalysis data were employed as atmospheric predictor variables of SD models. Predictors of linear transfer functions and ANN were selected by linear correlations coefficient and mutual information, respectively. For each downscaled case, annual and monthly models were developed and analysed. The monthly MLR, annual ANN, annual ANN, and annual MLR yielded the best performance for T_max, T_min, P_occ and P_amont according to the modified Akaike information criterion (AICu). A monthly MLR is recommended for the transfer functions of the four predictands because it can provide a better performance for the T_max and as good performance as the annual MLR for the T_min, P_occ, and P_amount. Furthermore, a monthly MLR can provide a slightly better performance than an annual MLR for extreme events. An annual MLR approach is also equivalently recommended for the transfer functions of the four predictands because it showed as good a performance as monthly MLR in spite of its mathematical simplicity. Robust and ridge regressions are not recommended because the data used in this study are not greatly affected by outlier data and multicollinearity problems. An annual ANN is recommended only for the T_min, based on the best performance among the models in terms of both the RMSE and AICu.