Global Mean Surface Temperature Projection Constrained by Historical Observations

In this paper, we propose a state space representation (EBM-SS model) of the two-component energy balance model (EBMs). The EBM-SS model incorporates three extensions to the two-component EBM. First, we include ocean heat content (OHC) as a measurement of the temperature in the deep ocean layer. Second, we decompose the latent state of radiative forcing into a natural component and an anthropogenic component. The anthropogenic component is modeled as a random walk process with a local linear trend to represent the deterministic and stochastic trends of anthropogenic forcing, while the natural component captures the variations in solar irradiance and transitory episodes in forcing following major volcanic eruptions. Lastly, we use multiple GMST anomaly data sources from separate research groups as measurements for the latent state -- the temperature in the mixed layer in the two-component EBM. 

We estimate the EBM-SS model using observations at the global level during the period 1955 -- 2020 by maximum likelihood. We show in empirical estimation and in simulations that using multiple data sources for the latent process reduces parameter estimation uncertainty. When fitting eight global mean surface temperature anomaly observational series, the physical parameter estimates are comparable to those obtained by using datasets from Coupled Model Intercomparison Project 5 (CMIP 5) in other literature.  We find that using this set of parameter estimates, the GMST projection results under Representative Concentration Pathway (RCP) 4.5, 6.0, and 8.5 scenarios considerably agree with the outputs from the climate emulator Model for the Assessment of Greenhouse Gas Induced Climate Change (MAGICC) 7.5 and CMIP 5 models. We show that utilizing a simple climate model and historical records alone can produce meaningful GMST projections.