An Adjoint-Free CNOP–4DVar Hybrid Method for Identifying Sensitive Areas 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.摘要本文将非线性最优扰动方法(CNOP)与四维变分同化技术(4DVar)相融合, 提出了一种确定目标观测敏感区域的新方法CNOP-4DVar. CNOP-4DVar方法首先利用CNOP方法确定造成检验时刻最大模式扰动的最优初始扰动CNOP, 进而利用4DVar方法依照消除最优初始扰动同化效果的方式计算不同区域的敏感指数, 从而根据敏感指数的降序排列确定观测时刻的敏感区域. 不难看出, 以上的CNOP-4DVar由求解非线性最优扰动CNOP以及四维变分同化4DVar两个非线性最优化问题组成, 一般而言这类方法都严重依赖于伴随模式、计算与编程代价昂贵, 这一难题可以采用集合的非线性最小二乘策略, 也就是分别利用集合非线性最小二乘CNOP(NLS-CNOP)方法以及4DVar (NLS-4DVar)方法加以解决, 从而给出了联合目标观测方法CNOP-4DVar的无伴随依赖、计算经济的解决方案. 完备的数值表明该方法明显优于目前通常采用的ETKF目标观测方法, 在天气预报于气候预测中的应用潜力巨大.

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