An Adjoint-Free CNOP-4DVar Hybrid Method for Identifying Sensitive Areas in Targeted Observations: Method Formulation and Preliminary Evaluation

This paper proposes a hybrid method, called CNOP-4DVar, for the identification of sensitive areas in targeted observations, which takes the advantages of both the conditional nonlinear optimal perturbation (CNOP) and four-dimensional variational assimilation (4DVar) methods. The proposed CNOP-4DVar method is capable of capturing the most sensitive initial perturbation (IP), which causes the greatest perturbation growth at the time of verification; it can also identify sensitive areas by evaluating their assimilation effects for eliminating the most sensitive IP. To alleviate the dependence of the CNOP-4DVar method on the adjoint model, which is inherited from the adjoint-based approach, we utilized two adjoint-free methods, NLS-CNOP and NLS-4DVar, to solve the CNOP and 4DVar sub-problems, respectively. A comprehensive performance evaluation for the proposed CNOP-4DVar method and its comparison with the CNOP and CNOP-ensemble transform Kalman filter (ETKF) methods based on 10 000 observing system simulation experiments on the shallow-water equation model are also provided. The experimental results show that the proposed CNOP-4DVar method performs better than the CNOP-ETKF method and substantially better than the CNOP method.