Multivariate distribution correction of climate model outputs: A generalization of quantile mapping approaches

Climate change impact studies necessitate the estimation of climate variable evolution in the future. These are given by climate model simulations made under different greenhouse gas and aerosol emission scenarios agreed at the international level. However, climate model outputs have biases, especially at the local scale, and need to be corrected against observations. Common bias correction methods are distribution based and form the well‐known quantile mapping approaches. This paper presents a generalization of such techniques to the consideration of multivariate distributions. This approach uses the basic lemma of Lévy and Rosenblatt, which allows the transport of a distribution on another one, in every dimension. It needs convenient nonparametric estimations of conditional repartitions. The approach is first tested in a controlled framework, by use of statistical simulations, then in the real setting of climate simulation, in the bivariate case. An important issue of these types of distribution corrections is the different kinds of hypotheses of stationarity over a long enough period: stationarity of the link between model and observations whatever the period or stationarity of the change between the present and future for model and observations. This choice differentiates approaches like quantile mapping and cumulative distribution function transform, for example, in the univariate framework, and makes them more efficient, in the univariate as well as in the multivariate context, when the data to be corrected best verify the assumed hypothesis.