Bayesian Inference of Climate Parameters Using Multibox EBMs

Reliable climate projections in face of global warming require a firm and detailed understanding of climate variability. Variations in climate can be externally-forced, for example by anthropogenic emissions, or internally-generated, for example from chaotic atmosphere and ocean dynamics. To investigate the climatic response to radiative forcing, a common concept is the equilibrium climate sensitivity (ECS). Many studies estimate the ECS by fitting simple energy balance models (EBMs) to observational data. This approach has benefitted from advances in numerical analysis and statistics, enabling a fully Bayesian analysis. Via Bayes theorem, it quantifies the probability of certain climate parameters given observations, for example of surface temperature. To this end, it combines the goodness of the model fit with assumptions on measurement errors and climate variability as well as prior information. Here, we analyse and discuss Bayesian inference of climate parameters such as ECS from global mean temperatures using multibox EBMs. We therefore present an R package which relies on the Markov Chain Monte Carlo algorithm and includes an extension of the one-box model with a time-dependent feedback parameter. Using measurements from the instrumental period as well as temperature reconstructions and model data from the last millennium, we validate and demonstrate the package. We find that the two-box model performs significantly better in fitting the observations than the one-box model, and generates 21st century projections that agree more closely with AR5 estimates. Further, we evaluate the robustness of the estimate against uncertainties in temperature and forcing data through synthetic experiments. To this end, we quantify how estimation errors depend on the strength of noise in temperature data and compare the influence of dating and amplitude uncertainties in forcing reconstructions. In summary, we provide an effective tool for Bayesian estimation of climate parameters and elaborate its potential for studying the response to external forcing.