A Markov chain Monte Carlo method for estimation and assimilation into models

The arrival of satellite-borne ocean colour sensors means that there will soon be a wealth of observations of the surface concentration of chlorophyll in the worlds oceans. These observations can be used to improve our understanding of the oceanic ecosystem if the appropriate data assimilation techniques are available to combine them with an ecosystem model. In this paper we explore a novel method, based on Bayes Theorem and a Monte Carlo Markov Chain algorithm, of estimating a subset of the parameters in a seven compartment ecosystem model. The model describes the flows of nitrogen amongst phytoplankton, zooplankton, nitrate, bacteria, ammonium, dissolved organic nitrogen and detritus. We first generate synthetic observations from the model and then, in three separate experiments, try to recover subsets of the model parameters from clean and noisy versions of these. Bayes Theorem allows us to combine both prior information on the parameter values and the observations to generate a posterior probability density function of the parameters. The Metropolis-Hastings algorithm then allows us to produce Markov chains that sample this posterior probability density function and recover the parameter means, variances and standard errors. We find that the technique is very successful in recovering information on a small number of parameters but that the time required to solve the model makes it impractical to find second order properties of more than about ten of the model parameters.