Abstract

Two dimensional bias correction of temperature and precipitation copulas in climate models.

C. Piani and J. O. Haerter

In common climate model bias-correction procedures, temperature and precipitation are corrected separately, thereby degrading the dynamical link represented within the model. We propose a methodology that advances the state-of-the-art by correcting not just the 1D intensity distributions separately but the full two-dimensional statistical distribution. To assess the effectiveness of the proposed method, it is applied to the REMO regional climate model output using point measurements of hourly temperature and precipitation from 6 weather stations over Germany as observations. A standard cross-validation is performed by dividing the data into two non-overlapping 15 year periods. Results show that the methodology effectively improves the temperature-precipitation copula in the validation period, unlike separate 1D temperature and precipitation corrections which, by construction, leave the copula unchanged. An unexpected result is that a relatively small number (<5) of temperature bins are required to achieve significant improvements in the copula. Results are similar for all stations.

Figure 1. Map of station locations over Germany

Figure 2. Example of bias correction transfer function (TF). The asterisks are the (simulated, observed) pairs of precipitation values. The thick red line is the emerging piecewise perfect transfer function (PTF). The dashed line is the linear interpolation. The solid line is the X = Y line, for visual reference.

Figure 3. Synthetic histograms of simulated (dashed color filled contours) and observed (solid contours) of temperature and precipitation. (a) Uncorrected simulated data. (b) Simulated data corrected with separate 1D linear TFs. (c) Simulated data corrected with PTFs. (d) Simulated data corrected with linear, though full 2d, bias correction methodology. Thin vertical lines are temperature quantile limits. (e) T&P copula of the observed dataset. (f) T&P copula of the corrected data set shown in Figure 3d (color filled dashed contours) together with superimposed T&P copula from observed data set (solid non colored contours). Temperature quantile limits are shown as in Figure 3d. The color bar units are non-dimensional frequency per unit area.

Figure 4. Cross-validation of 2D bias correction with regional model REMO output and Aachen station data. (a) 2D T&P histogram of simulated (REMO) data. (b) Copula derived from Figure 4a. (c) 2D histogram of separately corrected T&P. (d) Copula derived from Figure 4c. (e) 2D histogram of T&P corrected with 2D bias correction method. Thin vertical lines are the limits of the temperature quantiles used. f) Copula derived from Figure 4e. (g) 2D histogram of observed T&P from the Aachen station. (h) copula derived from Figure 4g. The color bar units are non-dimensional frequency per unit.

Abstract

Corresponding author: C. Piani, Department of Computer Science,Mathematics, and Science, American University of Paris, 31, AvenueBosquet, Paris FR-75007, France. (cpiani@aup.edu)Article: Piani, C., and J. O. Haerter: Two dimensional bias correction of temperature and precipitation copulas in climate models. Geophys. Res. Lett., vol.. 39, LXXXXX, doi:10.1029/2012GL053839, 2012