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

Abstract

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 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.

Modeling the potential impacts of climate change on the water table level of selected forested wetlands in the southeastern United States

“…The correlation analysis between any two of the selected explanatory variables was executed to distinguish paired collinearity. To reduce the multicollinearity, each of the paired collinear variables was removed by turns, and the other selected explanatory variables were then individually reintroduced to the stepwise regression procedures to seek a balance between the best statistical performance of the model and minimal multicollinearity of the explanatory variables (Sachindra et al, 2013). The correlation analysis and the stepwise regression model procedures were combined in this study to obtain an optimized model with the least number of variables and best statistical performance.…”

“…Conversely, in spite of the weakness of assumption of static relationships between climate and hydrological response patterns in the future, statistical models have advantages of both high efficiency in computation and acceptable performance in modeling when applied over multiple sites. The performance of empirical models in climate change studies appears to be powerful when incorporating downscaled general circulation model (GCM) outputs (Sachindra et al, 2013;Li et al, 2016). For example, Li et al (2016) used log-linear models for 21 rainfall stations and 7 hydrometric stations to predict hydrological drought.…”

Coupling a Markov Chain and Support Vector Machine for At-Site Downscaling of Daily Precipitation

“…Anandhi et al (2008) used LS-SVM to downscale monthly precipitation to the river basin scale in India and found that the LS-SVM model was a feasible choice for obtaining future precipitation projections at a river basin scale, but that it was unable to mimic observed extreme precipitation events. More recently, LS-SVM has been widely used in regression-based downscaling methods (Raje and Mujumdar 2011;Sachindra et al 2013).…”

Research of correcting distorted X-ray images based on least squares and biharmonic spline surface

“…The approach consists of least squares and biharmonic spline surface. The technique of least squares has been widely used in many fields: statistics [14], image processing [15] and physics [16,17], and so on [18]. Biharmonic spline surface has been used in some fields, such as marine satellite measurement data [19], integration of logging and seismic data [20], image deformation [21], to name a few [22].…”