ORIGINAL PAPER Comparison of transfer functions in statistical downscaling models for daily temperature and precipitation over Canada D. I. Jeong • A. St-Hilaire • T. B. M. J. Ouarda • P. Gachon Ó Springer-Verlag 2011 Abstract 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 sta- tistical downscaling (SD) models for the daily maximum and minimum temperatures (T max and T min ) and daily precipi- tation 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 Que ´bec). Reanalysis data were employed as atmospheric predictor variables of SD models. Predictors of linear transfer func- tions and ANN were selected by linear correlations coeffi- cient and mutual information, respectively. For each downscaled case, annual and monthly models were devel- oped 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 recom- mended 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 predict- ands 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 recom- mended only for the T min , based on the best performance among the models in terms of both the RMSE and AICu. Keywords Artificial neural network  Climate change  Statistical downscaling  Precipitation  Temperature  Transfer function  Multiple linear regression 1 Introduction Atmosphere–Ocean Global Climate Models (AOGCMs) are known as fairly accurate tools to reproduce atmospheric variables at an annual and seasonal time scale over broad continental areas (McAveney et al. 2001; Schoof et al. 2007). AOGCM outputs, however, are usually generated on a coarse global-scale grid with horizontal resolutions gen- erally larger than 2° latitude by 2° longitude (e.g., IPCC 2007). Thus, they cannot be applied directly to a local scale for climate change impact studies (Wilby et al. 2002; Huth 2002; Cavazos and Hewitson 2005; Dibike et al. 2008). A regression-based statistical downscaling (SD) approach is one of the common ways of obtaining local-scale climate change scenarios from global-scale AOGCM predictors (Huth 2002; Wilby et al. 2004). In this approach, an empirical relationship between AOGCM predictors (e.g., atmospheric variables near the surface or at the upper air) and surface predictands (e.g., observed temperature or precipitation) is derived directly by linear or non-linear transfer functions. D. I. Jeong (&)  A. St-Hilaire  T. B. M. J. Ouarda INRS-ETE, University of Que ´bec, 490 de la Couronne, Montre ´al, QC G1K 9A9, Canada e-mail: dae_il_jeong@ete.inrs.ca P. Gachon Adaptation and Impacts Research Section (AIRS), Climate Research Division, Environment Canada, Montre ´al, QC, Canada 123 Stoch Environ Res Risk Assess DOI 10.1007/s00477-011-0523-3