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 non-linear state space form. The parameters in 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 data set 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 global mean surface temperature until the year 2100. Our results illustrate the potential of combining statistical modelling with physical insights to arrive at rigorous statistical analyses of the climate system.