Distribution-based pooling for combination and multi-model bias correction of climate simulations

Abstract. For investigating, assessing, and anticipating climate change, tens of global climate models (GCMs) have been designed, each modelling the Earth system slightly differently. To extract a robust signal from the diverse simulations and outputs, models are typically gathered into multi-model ensembles (MMEs). Those are then summarized in various ways, including (possibly weighted) multi-model means, medians, or quantiles. In this work, we introduce a new probability aggregation method termed “alpha pooling” which builds an aggregated cumulative distribution function (CDF) designed to be closer to a reference CDF over the calibration (historical) period. The aggregated CDFs can then be used to perform bias adjustment of the raw climate simulations, hence performing a “multi-model bias correction”. In practice, each CDF is first transformed according to a non-linear transformation that depends on a parameter α. Then, a weight is assigned to each transformed CDF. This weight is an increasing function of the CDF closeness to the reference transformed CDF. Key to the α pooling is a parameter α that describes the type of transformation and hence the type of aggregation, generalizing both linear and log-linear pooling methods. We first establish that α pooling is a proper aggregation method by verifying some optimal properties. Then, focusing on climate model simulations of temperature and precipitation over western Europe, several experiments are run in order to assess the performance of α pooling against methods currently available, including multi-model means and weighted variants. A reanalysis-based evaluation as well as a perfect model experiment and a sensitivity analysis to the set of climate models are run. Our findings demonstrate the superiority of the proposed pooling method, indicating that α pooling presents a potent way to combine GCM CDFs. The results of this study also show that our unique concept of CDF pooling strategy for multi-model bias correction is a credible alternative to usual GCM-by-GCM bias correction methods by allowing handling and considering several climate models at once.