A New Statistical Reduced Complexity Climate Model

In this paper, we propose a new, fully statistical, reduced complexity climate model. The starting point for our model is a number of physical equations for the global climate system, which we show how to cast in non-linear state-space form. The resulting model incorporates measurement errors, capturing the fact that observations of physical quantities might be contaminated by error, as well as internal stochastic error processes, capturing the fact that the physical equations used are approximations to the true underlying  climate system. The state-space formulation allows for statistical estimation of the parameters in the model, using the method of maximum likelihood, as well as filtering and smoothing of latent quantities in the model, such as ocean and surface temperatures. Further, the explicit statistical formulation of the model allows for conducting a number of useful analyses, such as the estimation of parameter uncertainty, model selection, and probabilistic scenario analysis. 

 

By considering a range of different scenarios for greenhouse gas emissions, we set up simulation studies that can be used to investigate  the effect that a given scenario has on parameter estimates. We find substantial differences in the performance of the estimation procedure, depending on the precise scenario considered. These investigations can help decide what kind of data are best suited for estimating/calibrating the parameters of reduced complexity climate models, e.g. to what extend the historical data record can be used to reliably estimate parameters and/or which CMIP experiments are best suited for calibrating such models.

 

Using a data set of historical observations from 1959-2020, we estimate the model and report key parameter estimates and associated standard errors. A likelihood ratio test sheds light on the most appropriate equation for converting the atmospheric concentration of carbon dioxide (GtC) into forcings (W/m2). We then use the estimated model and assumptions on future greenhouse gas emissions to project global mean surface temperature out to the year 2100. The statistical nature of the model allows us to attach uncertainty bands to the projections, as well as quantify how much of the uncertainty is "aleatoric" (uncertainty arising from the internal variability of the climate system) and how much is "epistemic" (uncertainty arising from unknown model parameters). We find that epistemic uncertainty is by far the most important contributor to the uncertainty on the projected future global temperature increase.