ClimLoco1.0: CLimate variable confidence Interval of Multivariate Linear Observational COnstraint

Abstract. Projections of future climate are key to society's adaptation and mitigation plans in response to climate change. Numerical climate models provide projections, but the large dispersion between them makes future climate very uncertain. To refine them, approaches called observational constraints (OCs) have been developed. They constrain an ensemble of climate projections using some real-world observations. However, there are many difficulties in dealing with the large literature on OC: the methods are diverse, the mathematical formulation and underlying assumptions are not always clear, and the methods are often limited to the use of the observations of only one variable. To address these challenges, this article proposes a new statistical model called ClimLoco1.0, which stands for “CLimate variable confidence Interval of Multivariate Linear Observational COnstraint”. It describes, in a rigorous way, the confidence interval of a projected variable (its best guess associated with an uncertainty at a confidence level) obtained using a multivariate linear OC. The article is built up in increasing complexity by expressing three different cases – the last one being ClimLoco1.0, the confidence interval of a projected variable: unconstrained, constrained by multiple real-world observations assumed to be noiseless, and constrained by multiple real-world observations assumed to be noisy. ClimLoco1.0 thus accounts for observational noise (instrumental error and climate-internal variability), which is sometimes neglected in the literature but is important as it reduces the impact of the OC. Furthermore, ClimLoco1.0 accounts for uncertainty rigorously by taking into account the quality of the estimators, which depends, for example, on the number of climate models considered. In addition to providing an interpretation of the mathematical results, this article proposes graphical interpretations based on synthetic data. ClimLoco1.0 is compared to some methods from the literature at the end of the article and is used in a real case study in the appendix.