• Open Access

Least square support vector and multi-linear regression for statistically downscaling general circulation model outputs to catchment streamflows



This study employed least square support vector machine regression (LS-SVM-R) and multi-linear regression (MLR) for statistically downscaling monthly general circulation model (GCM) outputs directly to monthly catchment streamflows. The scope of the study was limited to calibration and validation of the downscaling models. The methodology was demonstrated by its application to a streamflow site in the Grampian water supply system in northwestern Victoria, Australia. Probable predictors for the study were selected from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis data set based on the past literature and hydrology. Probable variables that displayed the best significant correlations, consistently with the streamflows over the entire period of the study (1950–2010) and under three 20-year time slices (1950–1969, 1970–1989 and 1990–2010) were selected as potential predictors. To better capture seasonal variations of streamflows, downscaling models were developed for each calendar month. The standardized potential predictors were introduced to the LS-SVM-R and MLR models, starting from the best correlated three and then, others one by one, based on their correlations with the streamflows, until the model performance in validation was maximized. This stepwise model development enabled the identification of the optimum number of potential variables for each month. The model calibration was performed over the period 1950–1989 and validation was done for 1990–2010. LS-SVM-R model parameter optimization was achieved using simplex algorithm and leave-one-out cross-validation. The MLR models were optimized by minimizing the sum of squared errors. In both modelling techniques, validation was performed as an independent simulation. In calibration, LS-SVM-R and MLR models displayed equally good performances with a trend of under-predicting high flows. During validation, LS-SVM-R outperformed MLR, though both techniques over-predicted most of the streamflows. It was concluded that LS-SVM-R is a better technique for statistically downscaling GCM outputs to streamflows than MLR, but still MLR is a potential technique for the same task. Copyright © 2012 Royal Meteorological Society