Regression-based distribution mapping for bias correction of climate model outputs using linear quantile regression

Impact models are a major source of information for quantifying the consequences of future climate change for humans and the environment. To provide plausible outputs, these models require unbiased high resolution meteorological data as input for atmospheric conditions. State of the art regional climate models (RCMs) often fail to provide such data, since they can exhibit large systematic biases. Therefore, bias correction methods (BCMs) have become a common tool in climate impact studies. Bias correction, however, comes with strong assumptions and limitations, often resulting from the fact that most BCMs are unable to appropriately calibrate a time dependent and conditional transfer function. To address this problem, we introduce here regression quantile mapping (RQM), a bias correction approach based on (linear) regression models which allow to design transfer functions based on expert knowledge. The new RQM algorithm is described in full detail in its basic (linear model) version and applied to RCM generated precipitation data for entire Europe. Based on the latter example, we provide a thorough comparison with another established BCM, quantile delta mapping (QDM) regarding the seasonal characteristics of precipitation sums. Our results demonstrate that RQM already achieves good results when a simple linear model is used. The relationship between precipitation and temperature was properly evaluated by RQM and representation of seasonal variations and key characteristics of precipitation were improved for most seasons. Systematic biases where reduced significantly during this process. Particular improvements in comparison with QDM are found regarding the shape and width of the distribution of bias corrected model precipitation. Furthermore, the representation of precipitation extremes within the data was largely improved when RQM was used instead of QDM.