Bayesian estimation of the climate sensitivity based on a simple climate model fitted to global temperature observations
Magne Aldrin, Norwegian Computing Center and University of Oslo Marit Holden, Norwegian Computing Center Peter Guttorp, Norwegian Computing Center and University of Seattle
The climate sensitivity is a central parameter in understanding climate change. It is defined as the increase in global temperature due to a doubling of CO2 compared to pre-industrial time. Our aim is to estimate the climate sensitivity by modelling the relationship between (estimates of) radiative forcing and observations of global temperature and 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 proper inference.
Our combined model is
yt = mt(xt-, S, theta) + nt
Here, yt is the observed vector of global temperature and ocean heat content in year t and mt the corresponding output from the simple climate model. Furthermore, the model input xt- is the unknown radiative forcing in year t and previous years. S is the climate sensitivity which is the parameter of interest andtheta is a vector with other model parameters. Finally, nt is an autoregressive error term accounting for model errors and measurement errors. We use a flat prior for the climate sensitivity and informative priors for most other parameters.
The model was fitted to observations of global temperatures from 1850 to 2007 and of ocean heat content from 1955 to 2007. The work is still in progress, so the estimate of the climate sensitivity is preliminary. However, this preliminary estimate is a few degrees Celsius above zero, which is comparable with other estimates.
We believe that this approach is a valuable addition to other methods for estimating the climate sensitivity, where physical knowledge and observed data are linked together by statistical modelling and estimation methods.
From a statistical point of view, it is an example of calibration of computer models, but with more emphasis on modelling the discrepancy between the observations and the computer model, than on using an emulator or surrogate model for the computer model, that has been central in much of the recent work in this area.