Assimilation of paleo-data in a simple Earth system model

We describe the use of a Monte Carlo Markov Chain (MCMC) method based on Bayes' Theorem and the Metropolis-Hastings algorithm for estimation of model parameters in a climate model. We use the model of Saltzman and Maasch (1990). This is a computationally simple model. but with seven free parameters and substantial non-linearity it would be difficult to tune with commonly used data assimilation methods. When forced with solar radiation, the model can reproduce mean ocean temperature, atmospheric CO2 concentration and global ice volume reasonably well over the last 500 ka. The MCMC method samples the multivariate probability density function of model parameters, which makes it a powerful tool for estimating not only parameter values but also for calculating the model's sensitivity to each parameter, A major attraction of the method is the simplicity and the ease of the implementation of the algorithm. We have used cross-validation to show that the model forecast for the next 50-100 ka is of similar accuracy to the hindcast over the last 500 ka. The model forecasts an immediate cooling of the Earth, with the next glacial maximum in around 60 ka. An anthropogenic pulse of CO2 has a short-term effect but does not influence the model prediction beyond 30 ka. Beyond 100 ka into the future, the model ensemble diverges widely, indicating that there is insufficient information in the data which we have used to determine the longer term evolution of the Earth's climate.