Development of an ensemble-adjoint optimization approach to derive uncertainties in net carbon fluxes

Abstract. Accurate modelling of the carbon cycle strongly depends on the parametrization of its underlying processes. The Carbon Cycle Data Assimilation System (CCDAS) can be used as an estimator algorithm to derive posterior parameter values and uncertainties for the Biosphere Energy Transfer and Hydrology scheme (BETHY). However, the simultaneous optimization of all process parameters can be challenging, due to the complexity and non-linearity of the BETHY model. Therefore, we propose a new concept that uses ensemble runs and the adjoint optimization approach of CCDAS to derive the full probability density function (PDF) for posterior soil carbon parameters and the net carbon flux at the global scale. This method allows us to optimize only those parameters that can be constrained best by atmospheric carbon dioxide (CO₂) data. The prior uncertainties of the remaining parameters are included in a consistent way through ensemble runs, but are not constrained by data. The final PDF for the optimized parameters and the net carbon flux are then derived by superimposing the individual PDFs for each ensemble member. We find that the optimization with CCDAS converges much faster, due to the smaller number of processes involved. Faster convergence also gives us much increased confidence that we find the global minimum in the reduced parameter space.