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.
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