A multi-criteria evaluation of the performance of bias correction using Delta Quantile Mapping for simulated precipitation over Germany

Bias correction techniques are often used as effective and reliable approaches to improve the representation of current and past conditions in climate models. This study aims to evaluate the performance of Quantile Delta Mapping (QDM) as a bias correction method for daily precipitation simulations from climate models: the Icosahedral Nonhydrostatic Model (ICON), the Regional Climate Model COSMO-CLM (CCLM), and the Regional Climate Model (REMO) at a spatial resolution of 3 km over Germany. The dataset consists of historical observations from HYRAS and climate model simulations between 1961 and 1990, split into a calibration period (1961–1980) and an independent validation period (1981–1990). To assess performance, we considered four aspects: 1) sequence of events, 2) distribution of values, 3) spatial structure, and 4) visual inspection of distance metrics, ultimately providing an integrative qualitative ranking across these aspects. Performance metrics included correlation, Nash-Sutcliffe efficiency (NSE), Kling-Gupta efficiency (KGE), and error metrics such as BIAS, mean square error (MSE), and root mean squared error (RMSE). Additional metrics considered were the Kolmogorov-Smirnov (KS) statistic, Perkins Skill Score (S_score), probability density function (PDF), 80th, 90th, and 95th percentiles, and spatial autocorrelation. As a preliminary assessment of the simulated precipitation from ICON, results show only slight improvements in the time and spatial distribution of precipitation metrics. For example, the KS statistic improved from 0.0314 to 0.0190, while the S_score improved from 0.0314 to 0.0195 when comparing HYRAS vs. ICON raw and HYRAS vs. ICON bias-corrected using QDM, respectively. Therefore, limited improvement is expected from bias correction when the climate model already performs well, whereas significant improvements can be achieved when the climate models perform only acceptably.