Stochastic bias correction of dynamically downscaled precipitation fields for Germany through copula-based integration of gridded observation data

Dynamically downscaled precipitation fields from regional climate model (RCM) often cannot be used directly for local climate change impact studies. Due to their inherent biases, i.e. systematic over- or underestimations compared to observations, several correction approaches have been developed. Most of the bias correction procedures such as the quantile mapping approach employ a transfer function that based on the statistical differences between RCM output and observations. Apart from such transfer function based statistical correction algorithms, a stochastic bias correction technique, based on the concept of Copula theory, is developed here and applied to correct precipitation fields from the Weather Research and Forecasting (WRF) model. As Dynamically downscaled precipitation fields we used high resolution (7 km, daily) WRF simulations for Germany driven by ERA40 reanalysis data for 1971–2000. The REGNIE data set from Germany Weather Service is used as gridded observation data (1 km, daily) and rescaled to 7 km for this application. The 30 year time series are splitted into a calibration (1971–1985) and validation (1986–2000) period of equal length. Based on the estimated dependence structure between WRF and REGNIE data and the identified respective marginal distributions in calibration period, separately analyzed for the different seasons, conditional distribution functions are derived for each time step in validation period. This finally allows to get additional information about the range of the statistically possible bias corrected values. The results show that the Copula-based approach efficiently corrects most of the errors in WRF derived precipitation for all seasons. It is also found that the Copula-based correction performs better for wet bias correction than for dry bias correction. In autumn and winter, the correction introduced a small dry bias in the Northwest of Germany. The average relative bias of daily mean precipitation from WRF for the validation period is reduced from 10% (wet bias) to −1% (slight dry bias) after the application of the Copula-based correction. The bias in different seasons is corrected from 32% (MAM), −15% (JJA), 4% (SON) and 28% (DJF) to 16% (MAM), −11% (JJA), −1% (SON) and −3% (DJF), respectively. Finally, the Copula-based approach is compared with linear scaling and quantile mapping correction approaches by analysing the RMSE and quantile RMSE. The results show that the Copula-based correction has improved performance in all of the quantiles, except for the extremes.