Adaptive observations using HSV and TESV in a 4D-Var framework with a finite volume shallow-water model
I.M. Navon, Yanhua Cao, D. N. Daescu
A comparative analysis of observation targeting methods based on total energy singular vectors (TESVs) and Hessian singular vectors (HSVs) is performed with a finite volume global shallow-water model, along with its first and second order adjoint model. A 4D-Var data assimilation framework is considered that allows for adaptive observations distributed in both time and space domain. To obtain the HSVs a generalized eigenvalue problem was solved using the generalized Jacobi- Davidson algorithm. A full 4D-Var procedure without incremental approximation was used leading to an accurate second order adjoint and derivation of a consistent Hessian matrix. Numerical experiments involving TESV and HSV as alternative targeting strategies were carried out to assess the potential benefits of targeting methods using second order adjoint information. The results obtained point to an advantage of using HSV as a tool for observation targeting where interaction between targeted observations taken at distinct instants in time has a significant impact on efficiency of both adaptive strategies. Additional metrics such as similarity indices between HSV and TESV also point to the same conclusion.