  This paper estimates the two-component energy balance model as a linear state
space system (EBM-SS model) using historical data. It is a joint model for the
temperature in the mixed layer, the temperature in the deep ocean layer, and
radiative forcing. The EBM-SS model allows for the modeling of non-stationarity
in forcing, the incorporation of multiple data sources for the latent
processes, and the handling of missing observations. We estimate the EBM-SS
model using observational datasets at the global level for the period 1955 -
2020 by maximum likelihood. We show in the empirical estimation and in
simulations that using multiple data sources for the latent processes reduces
parameter estimation uncertainty. When fitting the EBM-SS model to eight
observational global mean surface temperature (GMST) anomaly series, the
physical parameter estimates and the GMST projection under Representative
Concentration Pathway (RCP) scenarios are comparable to those from Coupled
Model Intercomparison Project 5 (CMIP5) models and the climate emulator Model
for the Assessment of Greenhouse Gas Induced Climate Change (MAGICC) 7.5. This
provides evidence that utilizing a simple climate model and historical records
alone can produce meaningful GMST projections.
