Adjoint Implementation of Rosenbrock Methods Applied to Variational Data Assimilation Problems

In the past decade the variational method has been successfully applied in data assimilation problems for atmospheric chemistry models. In 4D-var data assimilation, a minimization algorithm is used to find the set of control variables which minimizes the weighted least squares distance between model predictions and observations over the assimilation window. Using the adjoint method, the gradient of the cost function can be computed fast, at the expense of few function evaluations, making the optimization process very efficient. For large-scale models, the high storage requirements and the difficulty of implementing the adjoint code when sophisticated integrators are used to solve the stiff chemistry make the assimilation a very intensive computational process. If the sparse structure of the chemical models is carefully exploited, Rosenbrock methods have been proved to be reliable chemistry solvers because of their outstanding stability properties and conservation of the linear invariants of the system. In this paper we present an efficient implementation of the adjoint code for the Rosenbrock type methods, which can reduce the storage requirements of the forward model and is suitable for automatization. The adjoint code is completely generated using symbolic preprocessing and automatic differentiation tools which allow flexibility and require minimal user intervention.