SIAM Journal on Applied Dynamical Systems, Volume 20, Issue 1, Page 299-332, January 2021.
In this study, we develop model bias estimators based on an asymptotic expansion of the model dynamics for small time scales and small perturbations in a model parameter, and then use the estimators to improve the performance of a data assimilation system. We employ the well-known Lorenz (1963) model so that we can study all aspects of the dynamical system and model bias estimators in a detailed way that would not be possible with a full physics numerical weather prediction model. In particular, we first work out the asymptotics of the Lorenz model for small changes in one of its parameters and then use statistics from cycled data assimilation experiments to demonstrate that the asymptotics accurately represent the behavior of the model and that the coefficients of the nonlinear asymptotical expansion can be reasonably estimated by solving a least squares minimization problem. In data assimilation, the background error covariance matrix usually estimates the uncertainty of the model background, which is then used along with the observation error covariance matrix to produce an updated analysis. If the uncertainty of the model background is strongly influenced by time-dependent model biases, then the development of nonlinear bias estimators that also vary with time could improve the performance of the assimilation system and the accuracy of the updated analysis. We demonstrate this improvement through the combination of a constant background error covariance matrix with a dynamically varying matrix computed using the model bias estimators. Numerical tests using the Lorenz (1963) model illustrate the feasibility of the approach and show that it leads to clear improvements in the analysis and forecast accuracy.

中文翻译：

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数据同化的非线性条件模型偏差估计

SIAM应用动力系统杂志，第20卷，第1期，第299-332页，2021年1月。
在这项研究中，我们基于模型动力学的渐近展开（对于模型参数的小时间尺度和小扰动）开发模型偏差估计器，然后使用估计器来改善数据同化系统的性能。我们采用了著名的Lorenz（1963）模型，因此我们可以详细研究动力学系统的各个方面并为模型偏差估计器研究，而这是完整的物理数值天气预报模型所无法实现的。特别是，我们首先研究Lorenz模型的渐近性，以了解其参数之一的细微变化，然后使用循环数据同化实验中的统计数据来证明渐近性准确地表示了模型的行为，并且非线性渐近展开的系数可以是通过解决最小二乘最小化问题来合理估算。在数据同化中，背景误差协方差矩阵通常估算模型背景的不确定性，然后将其与观察误差协方差矩阵一起使用以生成更新的分析。如果模型背景的不确定性受到与时间有关的模型偏差的强烈影响，然后开发随时间变化的非线性偏差估计器也可以提高同化系统的性能和更新分析的准确性。我们通过将恒定的背景误差协方差矩阵与使用模型偏差估算器计算出的动态变化矩阵相结合，证明了这一改进。使用Lorenz（1963）模型进行的数值测试说明了该方法的可行性，并表明该方法可以显着提高分析和预测的准确性。