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

Abstract

Abstract. Climate simulations often suffer from statistical biases with respect to observations or reanalyses. It is therefore common to correct (or adjust) those simulations before using them as inputs into impact models. However, most bias correction (BC) methods are univariate and so do not account for the statistical dependences linking the different locations and/or physical variables of interest. In addition, they are often deterministic, and stochasticity is frequently needed to investigate climate uncertainty and to add constrained randomness to climate simulations that do not possess a realistic variability. This study presents a multivariate method of rank resampling for distributions and dependences (R 2 D 2 ) bias correction allowing one to adjust not only the univariate distributions but also their inter-variable and inter-site dependence structures. Moreover, the proposed R 2 D 2 method provides some stochasticity since it can generate as many multivariate corrected outputs as the number of statistical dimensions (i.e., number of grid cell × number of climate variables) of the simulations to be corrected. It is based on an assumption of stability in time of the dependence structure -making it possible to deal with a high number of statistical dimensions -that lets the climate model drive the temporal properties and their changes in time. R 2 D 2 is applied on temperature and precipitation reanalysis time series with respect to high-resolution reference data over the southeast of France (1506 grid cell). Bivariate, 1506-dimensional and 3012-dimensional versions of R 2 D 2 are tested over a historical period and compared to a univariate BC. How the different BC methods behave in a climate change context is also illustrated with an application to regional climate simulations over the 2071-2100 period. The results indicate that the 1d-BC basically reproduces the climate model multivariate properties, 2d-R 2 D 2 is only satisfying in the inter-variable context, 1506d-R 2 D 2 strongly improves inter-site properties and 3012d-R 2 D 2 is able to account for both. Applications of the proposed R 2 D 2 method to various climate datasets are relevant for many impact studies. The perspectives of improvements are numerous, such as introducing stochasticity in the dependence itself, questioning its stability assumption, and accounting for temporal properties adjustment while including more physics in the adjustment procedures.

A quantile–quantile adjustment of the EURO‐CORDEX projections for temperatures and precipitation

“…The quantile–quantile correction methodology has three main limitations to be considered (Boé et al ., ): the temporal autocorrelation properties of the series are not corrected (e.g., wet spells in the RCM may still exist after the correction); second, each variable is corrected independently, whereas for instance, bias in precipitation might not be independent of bias in temperature; finally, climate model outputs have a strong spatial autocorrelation which may be biased. Recent studies deal with the characterization of the above limitations (Maraun et al ., ), while other authors address the need for methods adjusting not only the marginal distributions of the climate simulations but also their multivariate dependence structures (e.g., Ivanov et al ., ; Vrac, ).…”

Characterizing and avoiding physical inconsistency generated by the application of univariate quantile mapping on daily minimum and maximum temperatures over Hudson Bay

“…SPP of climate model simulations represents an active area of applied research (e.g., Bellprat et al ., ; Wilcke et al ., ; Rocheta et al ., ; Vrac, ), and it responds to a diverse community of users' needs for plausible climate scenarios (Mearns et al ., ; Hewitson et al ., ). Plausibility is of course subjective, but in the case of climate scenarios, it arguably starts with trajectories that are in good statistical equivalence with observations over a relatively long recent‐past period and that present physically based future long‐term trends (Gennaretti et al ., ); SPP is intended to achieve this by blending information from simulations and observation‐based reference products (Cannon, ).…”

New Approach for Bias Correction and Stochastic Downscaling of Future Projections for Daily Mean Temperatures to a High-Resolution Grid

“…Model output statistics (MOS) approaches apply a statistical transfer function between simulated and observed data, and are employed for both bias correction and downscaling. Depending on the specific needs of the climate information user, a wide variety of such methods are in use, ranging from simple mean adjustment to flexible, potentially multivariate quantile mapping methods (Maraun et al, 2010;Piani and Haerter, 2012;Vrac et al, 2012;Vrac and Friederichs, 2015;Cannon, 2016;Vrac, 2018). For downscaling, perfect prognosis (PP) methods establish a statistical link between large-scale predictors and local-scale predictands typically in a regression framework, while weather generators (WGs) are stochastic models that explicitly model marginal and higher order structures.…”

“…For full-field downscaling without PP assumptions, techniques of shuffling the time series produced by univariate bias correction have been proposed (e.g. "Schaake shuffle" Clark et al, 2004), both for temporal (Vrac and Friederichs, 2015), and multi-site and multivariate reordering (Vrac, 2018). The shuffling techniques impose historical rank correlation structure on the bias-corrected data.…”

“…The shuffling techniques impose historical rank correlation structure on the bias-corrected data. They have, in some instances, been shown to underrepresent the dependence structure (Vrac, 2018). Moreover, the size of the shuffled data set is restricted to the size of the observational data set.…”