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Percentile adjustment function: application to direct and component-wise bias correction of a multi-variate climate index

Multi-variate climate indices (CIs) are frequently used for many sectoral climate change impact applications. These indices combine two or more essential climate variables that are frequently individually corrected prior to the CI calculation. This poses the question of whether the bias correction (BC) method modifies the inter-variable dependencies and eventually the climate change signal. The direct bias correction of the multi-variate CI stands as an alternative, since it preserves the physical and temporal coherence among the primary variables as represented in the dynamical model output. This comes at the expense of incorporating the individual biases on the CI computation with an effect difficult to foresee, particularly in the case of complex CIs bearing in their formulation non-linear relationships between components. Such is the case of the Fire Weather Index (FWI), a meteorological fire danger indicator frequently used in forest fire prevention and research.

In the present work, we test the suitability of the direct BC approach on FWI as a representative multi-variate CI, assessing its performance in present climate conditions and its effect on the climate change signal when applied to future projections. Moreover, the results are compared with the common approach of correcting the input variables separately. To this aim, we apply the widely used empirical quantile mapping method (QM). We introduce the percentile adjustment function (PAF) as a tool to provide insight into the effect of the QM on the climate change signal. Although both approaches present similar results under present climate, the direct correction introduces a greater modification of the original change signal. These results warn against the blind use of QM, even in the case of essential climate variables or uni-variate CIs.