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

Abstract

Abstract. Over the last few years, multivariate bias correction methods have been developed to adjust spatial and/or inter-variable dependence properties of climate simulations. Most of them do not correct – and sometimes even degrade – the associated temporal features. Here, we propose a multivariate method to adjust the spatial and/or inter-variable properties while also accounting for the temporal dependence, such as autocorrelations. Our method consists of an extension of a previously developed approach that relies on an analogue-based method applied to the ranks of the time series to be corrected rather than to their “raw” values. Several configurations are tested and compared on daily temperature and precipitation simulations over Europe from one Earth system model. Those differ by the conditioning information used to compute the analogues and can include multiple variables at each given time, a univariate variable lagged over several time steps or both – multiple variables lagged over time steps. Compared to the initial approach, results of the multivariate corrections show that, while the spatial and inter-variable correlations are still satisfactorily corrected even when increasing the dimension of the conditioning, the temporal autocorrelations are improved with some of the tested configurations of this extension. A major result is also that the choice of the information to condition the analogues is key since it partially drives the capability of the proposed method to reconstruct proper multivariate dependences.

Should Multivariate Bias Corrections of Climate Simulations Account for Changes of Rank Correlation Over Time?

“…More generally, based on the same reasoning, the use of a multi‐run single GCM for investigating climate changes is not recommended, except for analyzing its internal variability and potentially compare it to a larger multi‐model ensemble. For multi‐model ensembles (such as from CMIPs), as the inter‐model uncertainty in the evolution of the correlations is quite large, the use of the non‐stationarity (“NSt”) assumption is not recommended and the stationarity (“St”) assumption (i.e., considering the Spearman correlations of the reference as an approximation for the correlations in future periods) has to be favored. This has important consequences for studies relying on changes of inter‐variable dependence, as well as for MBC methods designed either to keep the dependence structures stationary with respect to a reference (e.g., as in Vrac, 2018; Vrac & Thao, 2020) or to make the dependencies evolve in agreement with the changes provided by the biased climate model simulations to correct (e.g., as in A. Cannon, 2017; Robin et al., 2019). Based on the results of this study, both approaches can make sense, but their appropriate use clearly depend on the confidence the MBC user puts on the model simulations and on their changes in inter‐variable correlations and dependencies. When an MBC method has to be applied based on a single run, the Stationary approach is preferable, rather than a non‐stationarity assumption.…”

“…Whereas 1d‐BC methods mostly keep the copula dependence function (e.g., its Spearman correlation) of the climate model untouched (see Vrac, 2018, among others), MBCs can rely on various assumptions regarding the possible evolutions (i.e., changes over time) of the multivariate dependencies between climate variables, such as the inter‐variable (rank) correlation. Some MBCs try reproducing—generally implicitly—the future correlation changes projected by the climate model (e.g., A. Cannon, 2017; Robin et al., 2019), while other MBCs assume a stationary dependence between variables, sticking to the observational copula function (e.g., Vrac, 2018; Vrac & Thao, 2020). In this study, without correcting any multivariate simulation, we have thus investigated what these “stationarity” and “non‐stationarity” assumptions imply in terms of biases of the inter‐variable Spearman (rank) correlation between temperature and precipitation.…”

“…Either explicitly or implicitly, all MBC methods already incorporate one of these two assumptions. For example, the evolution of the multivariate dependencies is (mostly) reproduced by methods such as the “MBCn” (A. Cannon, 2017) or “dynamical Optimal Transport Correction” (“dOTC,” Robin et al., 2019) methods; while the assumption of stationary rank dependence features is made in the “Rank Resampling for Distribution and Dependency” (“R2D2,” Vrac, 2018) correction method and its extension (“R2D2v2,” Vrac & Thao, 2020). Knowing the robustness of the changes in dependencies simulated by climate models is thus also crucial to choose the proper assumption (stationarity or non‐stationarity) regarding changes in multivariate properties, and therefore the proper MBC methods to use in climate change context.…”

Impact of bias nonstationarity on the performance of uni- and multivariate bias-adjusting methods: a case study on data from Uccle, Belgium

“…The resampling is applied through the search for an analogue for the ranks of a simulated reference dimension in the observed time series, which makes this an application of the analogue principle (Lorenz, 1969;Zorita and Von Storch, 1999) in bias adjustment. A detailed mathematical description can be found in Vrac (2018) and Vrac and Thao (2020b).…”

“…By comparing four bias-adjusting methods in a climate change context with possible bias nonstationarity, some of the remaining questions in François et al (2020) and Guo et al (2020) can be answered. The four multivariate biasadjusting methods compared in this study are "multivariate recursive quantile nesting bias correction" (MRQNBC, Mehrotra and Sharma, 2016), MBCn (Cannon, 2018), "dynamical optimal transport correction" (dOTC, Robin et al, 2019) and "rank resampling for distributions and dependences" (R 2 D 2 , Vrac, 2018;Vrac and Thao, 2020b). These four methods give a broad view of the different multivariate bias adjustment principles, which we will elaborate on in Sect.…”