  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.
