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

Abstract

Abstract. Dynamically downscaled precipitation fields from regional climate models (RCMs) often cannot be used directly for regional climate 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 is based on the statistical differences between RCM output and observations. Apart from such transfer functionbased 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. For dynamically downscaled precipitation fields we used high-resolution (7 km, daily) WRF simulations for Germany driven by ERA40 reanalysis data for 1971-2000. The REG-NIE (REGionalisierung der NIEderschlagshöhen) data set from the German Weather Service (DWD) is used as gridded observation data (1 km, daily) and aggregated to 7 km for this application. The 30-year time series are split into a calibration (1971-1985) and validation (1986-2000) period of equal length. Based on the estimated dependence structure (described by the Copula function) between WRF and REGNIE data and the identified respective marginal distributions in the calibration period, separately analyzed for the different seasons, conditional distribution functions are derived for each time step in the 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 % March-April-May (MAM), −15 % June-July-August (JJA), 4 % September-October-November (SON) and 28 % December-January-February (DJF) to 16 % (MAM), −11 % (JJA), −1 % (SON) and −3 % (DJF), respectively. Finally, the Copula-based approach is compared to the quantile mapping correction method. The root mean square error (RMSE) and the percentage of the corrected time steps that are closer to the observations are analyzed. The Copula-based correction derived from the mean of the sampled distribution reduces the RMSE significantly, while, e.g., the quantile mapping method results in an increased RMSE for some regions.

Multivariate bias adjustment of high-dimensional climate simulations: the Rank Resampling for Distributions and Dependences (R<sup>2</sup>D<sup>2</sup>) bias correction

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“…It is therefore crucial to adjust not only the marginal distributions of the climate simulations but also their multivariate dependence structures, which is the goal of the present study. A few multivariate methodologies have been proposed over the last few years (e.g., Bardossy and Pegram, 2012;Piani and Haerter, 2012;Mao et al, 2015;Vrac and Friederichs, 2015;Cannon, 2017;Dekens et al, 2017;Li et al, 2017). Most of these methods can be categorized into one of the two following approaches: the "marginal/dependence" correction approach and the "successive conditional" correction approach.…”

Three novel copula-based bias correction methods for daily ECMWF air temperature data

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“…Mao et al (2015) investigated daily precipitation data and showed that a copula-based bias correction performs better than quantile mapping. Vogl et al (2012) proposed the "Multiple Theta" and the "Maximum Theta" approaches for bias correction of rainfall data.…”

Bias Correction of MRI-WRF Dynamic Downscaling Datasets

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