2 Methodology

The proposed SVATARK downscaling method mainly consists of both trend and residual models. In this section, we briefly describe the downscaling model components SVR and ATAK and the experimental downscaling scheme.

2.1 Support vector regression method

Support vector machines (SVMs) have been widely applied to classification and regression, which minimize both empirical risk and structural risk to seek the best compromise between the complexity and learning capability of a model (Srivastava et al., 2013; Sujay and Deka, 2014). For regression, SVR was first introduced by Vapnik et al. (1997). Let \(\chi=\{x_{i},y_{i};i=1,\cdots,n\}\) be the training dataset with ancillary vectors \(x_{i}\) and corresponding targets \(y_{i}\). The input space \(\chi\) can be mapped into some feature space \(\Phi\)using the nonlinear function \(\varphi=\chi\rightarrow\Phi\). In the feature space \(\Phi\), the training data may exhibit linearity, which can be approximated by linear regression. The general form of the nonlinear SVR function can be expressed as: