A Multivariate Quantile-Matching Bias Correction Approach with Auto- and Cross-Dependence across Multiple Time Scales: Implications for Downscaling

Rajeshwar Mehrotra Water Research Centre, School of Civil and Environmental Engineering, The University of New South Wales Australia, Sydney, New South Wales, Australia

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Ashish Sharma Water Research Centre, School of Civil and Environmental Engineering, The University of New South Wales Australia, Sydney, New South Wales, Australia

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Abstract

A novel multivariate quantile-matching nesting bias correction approach is developed to remove systematic biases in general circulation model (GCM) outputs over multiple time scales. This is a significant advancement over typical quantile-matching alternatives available for bias correction, as they implicitly assume that correction of individual variable attributes will lead to correction of dependence biases between multiple variables. Furthermore, existing approaches perform bias correction at a given time scale (e.g., daily), whereas applications often require biases to be addressed at more than one time scale (such as annual in the case of most water resources planning projects). The proposed approach addresses all these issues, and additionally attempts to correct for lag-1 dependence (and cross-dependence) attributes across multiple time scales. The approach is called multivariate recursive quantile nesting bias correction (MRQNBC). The fidelity of the approach is demonstrated by applying it to a vector of CSIRO Mk3 GCM atmospheric variables and comparing the results with the commonly used quantile-matching approach. Following this, the implications of the approach in hydrology- and water resources–related applications are demonstrated by feeding the bias-corrected data to a rainfall downscaling model and comparing the downscaled rainfall attributes for current and future climate. The proposed approach is shown to represent the variability and persistence related attributes better and can thus be expected to have important consequences for the simulation of occurrence and intensity of extreme events such as floods and droughts in downscaled simulations, of importance in various climate impact assessment applications.

Corresponding author address: Rajeshwar Mehrotra, Water Research Centre, School of Civil and Environmental Engineering, Botany St., The University of New South Wales, Sydney 2052, Australia. E-mail: raj.mehrotra@unsw.edu.au

Abstract

A novel multivariate quantile-matching nesting bias correction approach is developed to remove systematic biases in general circulation model (GCM) outputs over multiple time scales. This is a significant advancement over typical quantile-matching alternatives available for bias correction, as they implicitly assume that correction of individual variable attributes will lead to correction of dependence biases between multiple variables. Furthermore, existing approaches perform bias correction at a given time scale (e.g., daily), whereas applications often require biases to be addressed at more than one time scale (such as annual in the case of most water resources planning projects). The proposed approach addresses all these issues, and additionally attempts to correct for lag-1 dependence (and cross-dependence) attributes across multiple time scales. The approach is called multivariate recursive quantile nesting bias correction (MRQNBC). The fidelity of the approach is demonstrated by applying it to a vector of CSIRO Mk3 GCM atmospheric variables and comparing the results with the commonly used quantile-matching approach. Following this, the implications of the approach in hydrology- and water resources–related applications are demonstrated by feeding the bias-corrected data to a rainfall downscaling model and comparing the downscaled rainfall attributes for current and future climate. The proposed approach is shown to represent the variability and persistence related attributes better and can thus be expected to have important consequences for the simulation of occurrence and intensity of extreme events such as floods and droughts in downscaled simulations, of importance in various climate impact assessment applications.

Corresponding author address: Rajeshwar Mehrotra, Water Research Centre, School of Civil and Environmental Engineering, Botany St., The University of New South Wales, Sydney 2052, Australia. E-mail: raj.mehrotra@unsw.edu.au
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