Propagating uncertainty through prognostic carbon cycle data assimilation system simulations

One of the major advantages of carbon cycle data assimilation is the possibility to estimate carbon fluxes with uncertainties in a prognostic mode, that is beyond the time period of carbon dioxide (CO₂) observations. The carbon cycle data assimilation system is built around the Biosphere Energy Transfer Hydrology Scheme (BETHY) model, coupled to the atmospheric transport model TM2. It uses about 2 decades of observations of the atmospheric carbon dioxide concentration from a global network to constrain 57 process parameters via an adjoint approach. The model's Hessian matrix of second derivatives provides uncertainty estimates for the optimized process parameters that are consistent with the assumed uncertainties in the observations and the model. With those estimated parameter values, the model can predict the response of the terrestrial biosphere to prescribed climate forcing beyond the assimilation period. We develop a methodological framework that is able to propagate parameter uncertainties through such a prognostic simulation and provide uncertainty estimates for the simulation results. We demonstrate the concept for a 4-year hindcast simulation from 2000 to 2003 following a 21-year assimilation period from 1979 to 1999. We discuss prognostic uncertainties for surface fluxes and atmospheric carbon dioxide.