Inverse three-dimensional variational data assimilation for an advection-diffusion problem: Impact of diffusion and hybrid application

In this study, the performance of inverse three-dimensional variational assimilation (13D-Var) is investigated in terms of dissipation process for an advection-diffusion problem. The performance of 13D-Var becomes poorer with larger diffusion coefficients. However, even for strong dissipation, the cost function during early iterations in the 13D-Var decreases still much faster than it does in the standard four-dimensional variational assimilation (4D-Var). Based on this observation a hybrid approach that combines the 13D-Var and the 4D-Var is suggested to accelerate the performance of 4D-Var. Application of this hybrid method demonstrates that the 13D-Var can serve as a preconditioner for carrying minimization in the full 4D-Var framework. Using the initial conditions obtained through the 13D-Var, the 4D-Var showed much faster convergence in minimizing the cost function.