Multivariate bias corrections of climate simulations: which benefits for which losses?

Abstract

Abstract. Climate models are the major tools to study the climate system and its evolutions in the future. However, climate simulations often present statistical biases and have to be corrected against observations before being used in impact assessments. Several bias correction (BC) methods have therefore been developed in the literature over the last 2 decades, in order to adjust simulations according to historical records and obtain climate projections with appropriate statistical attributes. Most of the existing and popular BC methods are univariate, i.e., correcting one physical variable and one location at a time and, thus, can fail to reconstruct inter-variable, spatial or temporal dependencies of the observations. These remaining biases in the correction can then affect the subsequent analyses. This has led to further research on multivariate aspects for statistical postprocessing BC methods. Recently, some multivariate bias correction (MBC) methods have been proposed, with different approaches to restore multidimensional dependencies. However, these methods are not yet fully apprehended by researchers and practitioners due to differences in their applicability and assumptions, therefore leading potentially to different results. This study is intended to intercompare four existing MBCs to provide end users with aid in choosing such methods for their applications. For evaluation and illustration purposes, these methods are applied to correct simulation outputs from one climate model through a cross-validation method, which allows for the assessment of inter-variable, spatial and temporal criteria. Then, a second cross-validation method is performed for assessing the ability of the MBC methods to account for the multidimensional evolutions of the climate model. Additionally, two reference datasets are used to assess the influence of their spatial resolution on (M)BC results. Most of the methods reasonably correct inter-variable and intersite correlations. However, none of them adjust correctly the temporal structure as they generate bias-corrected data with usually weak temporal dependencies compared to observations. Major differences are found concerning the applicability and stability of the methods in high-dimensional contexts and in their capability to reproduce the multidimensional changes in the model. Based on these conclusions, perspectives for MBC developments are suggested, such as methods to adjust not only multivariate correlations but also temporal structures and allowing multidimensional evolutions of the model to be accounted for in the correction.

Impact of bias nonstationarity on the performance of uni- and multivariate bias-adjusting methods

“…For these two reasons, Vrac (2018) advocates for the use of the more robust and coherent 'marginal/dependence' approach. Robin et al (2019) and François et al (2020) extended this classification by introducing the all-in-one approach, which adjusts the marginal variables and the correlations simultaneously, 'dynamical Optimal Transport Correction' (dOTC) (Robin et al, 2019) being such a method.…”

“…Thus, to adjust the multivariate distribution, the ranks of the climate model are replaced by those of the observations, using methods such as the 'Schaake Shuffle' (Clark et al, 2004;Vrac and Friederichs, 2015). This implies that the temporal structure and trends of the climate model will be altered, which may have a considerable impact (François et al, 2020). This impact is especially large when multiday characteristics strongly matter, such as in applications as the hydrological example we use in this study (Addor and Seibert, 2014).…”

“…The oldest method in the comparison is 'Multivariate Recursive Quantile Nesting Bias Correction' (Mehrotra and Sharma, 2016). This method completely replaces the simulated correlations by those of the observations and is a 'marginal/dependence' method according to François et al (2020). 'Multivariate Bias Correction in n dimensions' (Cannon, 2018) is both a 'marginal/dependence' method and a method that tries to combine information from the climate model and the observations.…”

Evaluating the dependence structure of compound precipitation and wind speed extremes

“…Because both coefficients χ andχ are defined as a limit value, a usual way to analyse the behaviour of a bivariate tail dependence structure between two variables is to compute empirical estimates for varying threshold levels q and then visually inspect their behaviour as q → 1. We estimate χ andχ with the function taildep from the R package extRemes (Gilleland and Katz, 2016).…”

R<sup>2</sup>D<sup>2</sup> v2.0: accounting for temporal dependences in multivariate bias correction via analogue rank resampling

“…Those projections are performed under various greenhouse gas emission scenarios, prescribed for instance within the fifth international Coupled Model Intercomparison Project (CMIP5; IPCC, 2013) or the ongoing CMIP6 (Eyring et al, 2016) and are widely used by the scientific community investigating climate changes and their manifold impacts. Indeed, climate changes have been anticipated to affect multiple domains: hydrology and water resources (e.g., Gleick, 1989;Christensen et al, 2004;Piao et al, 2010), agronomy and crops (e.g., Ciais et al, 2005;Ben-Ari et al, 2018), ecology and biodiversity (e.g., Brown et al, 2011;Bellard et al, 2012), economy (e.g., OCDE, 2015;Tol, 2018) or human migrations (e.g., Defrance et al, 2017) are examples of domains where expected impacts of climate evolution can be high and therefore quite problematic for society.…”