Our aim is to estimate the climate sensitivity by modeling the relationship between (estimates of) radiative forcing and measurements of hemispheric temperatures and global ocean heat content in post-industrial time. Complex general circulation models are computationally expensive for this purpose, and we use instead a simple climate model of reduced complexity. This climate model is deterministic, and we combine it with a stochastic model to do properly inference.

Our combined model can be written as

yt = mt(xt-,theta) + f(zt) + nt

Here, yt is a vector with the measurements of temperatures and ocean heat content in year t and mt the corresponding output from the simple climate model. The model input xt- is the unknown radiative forcing in year t and previous years back to pre-industrial time. Furthermore, theta is a vector with time-constant model parameters, whereof the climate sensitivity is the parameter of main interest. The function f(zt) is an empirical motivated term added to the model to account for the El Nino effect and zt is an El Nino index. Finally, nt is an autoregressive error term representing model and measurements errors.

The output from the climate model mt is three-dimensional, consisting of the air temperature on the northern and southern hemispheres and the global ocean heat content. The temperature observations yt consist of three different time series of hemispheric temperature measurements from around 1850, and three series of ocean heat content measurements from around 1955. The three temperature time series are all based on observations at various measurement stations around the earth, but differs by how these are weighted.

This is a joint project with Center for International Climate and Environmental Research in Oslo (CICERO).