Study of conservation laws with the Local Ensemble Transform Kalman Filter
Study of conservation laws with the Local Ensemble Transform Kalman Filter
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DOI：
10.1002/qj.2829
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发表时间：
2016-07
影响因子：
8.9
通讯作者：
Yuefei Zeng;T. Janjić
中科院分区：
文献类型：
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作者：
Yuefei Zeng;T. Janjić
数值离散格式在结合连续系统的最重要的守恒性质以改进非线性流动的预测方面有着悠久的历史。问题是，数据同化算法是否应该遵循类似的方法。为了解决这个问题，我们探索数据同化过程中的守恒特性，使用完美的模型实验，2D浅水模型保留了真实非线性流的重要特性。这里使用的数据同化方案是具有变化的观测变量、膨胀、局部化半径和变薄间隔的局部包围变换卡尔曼滤波。结果表明，在同化过程中，分析集合平均的总能量随时间向自然运行值收敛。然而，涡度拟能、散度和能谱受资料同化设置的强烈影响。考虑到在无辐散流的情况下，动量平流方案对动能和涡度拟能的守恒会防止系统性的和不切实际的能量级联向高波数，我们根据初始条件中的误差类型来测试对预测的影响。在同化过程中，我们通过标量，域平均噪声测量来评估向下的非线性能量级联。我们发现，同化过程中积累的噪声和分析误差是预测质量的良好指标。
Numerical discretization schemes have a long history of incorporating the most important conservation properties of the continuous system in order to improve the prediction of the nonlinear flow. The question arises whether data assimilation algorithms should follow a similar approach. To address this issue, we explore the conservation properties during data assimilation using perfect model experiments with a 2D shallow‐water model preserving important properties of the true nonlinear flow. The data assimilation scheme used here is the Local Ensemble Transform Kalman Filter with varying observed variables, inflation, localization radius and thinning interval. It is found that, during the assimilation, the total energy of the analysis ensemble mean converges with time towards the nature run value. However, enstrophy, divergence and the energy spectra are strongly affected by the data assimilation settings. Having in mind that the conservation of both the kinetic energy and enstrophy by the momentum advection schemes in the case of non‐divergent flow prevents a systematic and unrealistic energy cascade towards the high wave numbers, we test the effects on the prediction depending on the type of error in the initial condition. During the assimilation, we assess the downward nonlinear energy cascade through a scalar, domain‐averaged noise measure. We show that the accumulated noise during assimilation and the error of analysis are good indicators of the quality of the prediction.