A Statistical Reduced Complexity Climate Model for Probabilistic Analyses and Projections

Abstract We propose a new statistical reduced complexity climate model. The centerpiece of the model consists of a set of physical equations for the global climate system, which we show how to cast in nonlinear state-space form. The parameters of the model are estimated using the method of maximum likelihood with the likelihood function being evaluated by the extended Kalman filter. Our statistical framework is based on well-established methodology and is computationally feasible. In an empirical analysis, we estimate the parameters for a dataset comprising the period 1959–2022. A likelihood ratio test sheds light on the most appropriate equation for converting the level of atmospheric concentration of carbon dioxide into radiative forcing. Using the estimated model, and different future paths of greenhouse gas emissions, we project the global mean surface temperature until the year 2100. Our results illustrate the potential of combining statistical modeling with physical insights to arrive at rigorous statistical analyses of the climate system. Significance Statement Existing climate models are predominantly deterministic, which complicates their integration with statistical analysis. In this paper, we introduce a fully statistical reduced complexity climate model (Stat-RCM) that explicitly incorporates stochastic processes to account for both epistemic uncertainty (our incomplete knowledge of the climate system) and aleatoric uncertainty (the inherent variability of the climate system). We illustrate the advantages of our approach by using Stat-RCM for statistical model selection, exploring how accurately the parameters of the model can be estimated in a Monte Carlo study, assessing parameter uncertainty when applied to historical data, performing statistical validation of the model against observed records, and computing probabilistic projections of the future climate.