模式误差与序列资料同化。确定性公式
Model error and sequential data assimilation. A deterministic formulation
摘要：
由于对大气动力学的描述不完善，资料同化方案面临着模式误差的存在。这些误差通常是建立在简单假设的基础上的，如偏差、白噪声、一阶马尔可夫过程。在目前的工作中，提出了一个公式的顺序扩展卡尔曼滤波器，根据最近的研究结果的普遍确定性行为的模型误差与以前的方法（Nicolis，2004年）形成鲜明对比。这个新的方案被应用在Lorenz（1996）提出的空间分布系统的背景下。结果表明：（1）在短时间内，模型误差的方差（假定为确定性过程）服从二次律的演化规律，可以准确地逼近估计误差。此外，与初始条件误差的相关性似乎在估计误差协方差的短时间动态中起次要作用。(ii)模型误差演化的确定性描述，纳入经典的扩展卡尔曼滤波方程，表明与经典的白噪声假设相比，滤波精度可以得到实质性的改善。普遍的，短时间的，二次律的模式误差协方差矩阵的演变似乎非常有前途的建模估计误差动态序列数据同化。
英文摘要：
Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modeled on the basis of simple assumptions such as bias, white noise, first order Markov process. In the present work, a formulation of the sequential extended Kalman filter is proposed, based on recent findings on the universal deterministic behavior of model errors in deep contrast with previous approaches (Nicolis, 2004). This new scheme is applied in the context of a spatially distributed system proposed by Lorenz (1996). It is found that (i) for short times, the estimation error is accurately approximated by an evolution law in which the variance of the model error (assumed to be a deterministic process) evolves according to a quadratic law, in agreement with the theory. Moreover, the correlation with the initial condition error appears to play a secondary role in the short time dynamics of the estimation error covariance. (ii) The deterministic description of the model error evolution, incorporated into the classical extended Kalman filter equations, reveals that substantial improvements of the filter accuracy can be gained as compared with the classical white noise assumption. The universal, short time, quadratic law for the evolution of the model error covariance matrix seems very promising for modeling estimation error dynamics in sequential data assimilation.
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