Novel Supervised Nonlinear Dimensionality Reduction Techniques for Improvement of Statistical Downscaling Processes

English Abstract:

Statistical downscaling approaches relying on developing a statistical and quantitative relationship between large-scale atmospheric variables and fine scale hydro-climate variables at particular sites have gained popularity for predicting climate change impacts on hydro-climate variables. Due to the complexity of climate-associated processes, one of the main challenges in development of the statistical downscaling approaches for climate change projection is identification of predictor variables from high dimensional atmospheric variables conveying climate change information with respect to the hydro-climate variable of interest. Due to the inherent complexity, nonlinearity, and interdependency among explanatory large-scale atmospheric parameters, using conventional unsupervised linear dimensionality reduction methods leads to unsatisfactory predictive performance of data-driven models in statistical downscaling. To improve the performance of the machine learning-based models, the present paper proposes a new approach to supervised dimensionality reduction, which is called “Supervised Principal Component Analysis (Supervised PCA)” for regression-based statistical downscaling with high-dimensional input data. This method is a generalization of PCA, extracting the principal components of atmospheric variables along which the dependency between target hydro-climate variable and projectors is maximized. Moreover, a dual formulation is derived for supervised PCA, which significantly reduces the high computational complexity of iterative optimization procedures. To capture the nonlinear variability between hydro-climatic response variables and projectors, a kernelized version of supervised PCA is also proposed for nonlinear dimensionality reduction. The effectiveness of the proposed supervised PCA method in comparison with some state-of-the-art algorithms for dimensionality reduction is evaluated for precipitation under a statistical downscaling process using two soft computing nonlinear machine learning methods, Support Vector Regression (SVR) and Relevance Vector Machine (RVM). The results indicate a significant improvement over supervised PCA methods in terms of performance and computational efficiency.