# Correcting systematic biases across multiple atmospheric variables in the frequency domain

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## Abstract

A procedure for correcting systematic biases across multiple variables is presented. This procedure operates in the frequency domain, using the cross-spectrum across variables to correct bias across each frequency band. The proposed approach is termed multivariate frequency bias correction or MFBC. The approach is illustrated using global climate model (GCM) simulations of multiple atmospheric variables, with variables selected based on recommended usage in downscaling applications. Results indicate clear benefits of using MFBC in representing both intra- and inter-variable dependence in corrected simulations. This has important implications in applications which require multiple atmospheric variables, and a need to correctly simulate both inter- and intra-variable dependence attributes. MFBC offers a mean to correct raw GCM atmospheric variables prior to downscaling or correct dynamically or statistically downscaled simulations prior to derived simulations of other variables of interest. Use of MFBC can have significant implications on derived hydrologic simulations, such as in sizing of storage reservoirs, or devising water sharing plans for the future.

## Keywords

Bias correction Downscaling Multivariate bias correction Frequency bias correction Multivariate frequency bias correction## Notes

### Acknowledgements

We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modelling groups (the two GCMs listed below) for producing and making available their model output. For CMIP the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. The GCM data is downloaded from. For this study, we used the two GCMs, including MIROC5 [Atmosphere and Ocean Research Institute (The University of Tokyo), National Institute for Environmental Studies, and Japan Agency for Marine-Earth Science and Technology, Japan] and IPSL-CM5A-MR IPSL-CM5A-MR (Institut Pierre Simon Laplace, France). We also acknowledge the reanalysis datasets obtained from the National Center for Environmental Prediction (NCEP) reanalysis2 dataset provided by the NOAA-CIRES Climate Diagnostics Centre, Boulder, Colorado, USA, from their web site at http://www.cdc.noaa.gov/. The first author would like to acknowledge the financial support from the Australian Awards Scholarships (AAS). Authors gratefully acknowledge funding support from the Australian Research Council for making this work possible.

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