An example of an automatic differentiation-based modelling system

We present a prototype of a Carbon Cycle Data Assimilation System (CCDAS), which is composed of a terrestrial biosphere model (BETHY) coupled to an atmospheric transport model (TM2), corresponding derivative codes and a derivative-based optimisation routine. In calibration mode, we use first and second derivatives to estimate model parameters and their uncertainties from atmospheric observations and their uncertainties. In prognostic mode, we use first derivatives to map model parameters and their uncertainties onto prognostic quantities and their uncertainties. For the initial version of BETHY the corresponding derivative codes have been generated automatically by FastOpt's automatic differentiation (AD) tool Transformation of Algorithms in Fortran (TAF). From this point on, BETHY has been developed further within CCDAS, allowing immediate update of the derivative code by TAF. This yields, at each development step, both sensitivity information and systematic comparison with observational data meaning that CCDAS is supporting model development. The data assimilation activities, in turn, benefit from using the current model version. We describe generation and performance of the various derivative codes in CCDAS, i.e. reverse scalar (adjoint), forward over reverse (Hessian) as well as forward and reverse Jacobian plus detection of the Jacobian's sparsity.