On the capability of Monte Carlo and adjoint inversion techniques to derive posterior parameter uncertainties in terrestrial ecosystem models

Terrestrial ecosystem models (TEMs) contain the coupling of many biogeochemical processes with a large number of parameters involved. In many cases those parameters are highly uncertain. In order to reduce those uncertainties, parameter estimation methods can be applied, which allow the model to be constrained against observations. We compare the performance and results of two such parameter estimation techniques - the Metropolis algorithm (MA) which is a Markov Chain Monte Carlo (MCMC) method and the adjoint approach as it is used in the Carbon Cycle Data Assimilation System (CCDAS). Both techniques are applied here to derive the posterior probability density function (PDF) for 19 parameters of the Biosphere Energy Transfer and Hydrology (BETHY) scheme. We also use the MA to sample the posterior parameter distribution from the adjoint inversion. This allows us to assess if the commonly made assumption in variational data assimilation, that everything is normally distributed, holds. The comparison of the posterior parameter PDF derived by both methods shows that in most cases an approximation of the PDF by a normal distribution as used by the adjoint approach is a valid assumption. The results also indicate that the global minimum has been identified by both methods for the given set up. However, the adjoint approach outperforms the MA by several orders of magnitude in terms of computational time. Both methods show good agreement in the PDF of estimated net carbon fluxes for the decades of the 1980s and 1990s.