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首页> 外文期刊>Nonlinear processes in geophysics >Ensemble variational assimilation as a probabilistic estimator – Part?1: The linear and weak non-linear case
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Ensemble variational assimilation as a probabilistic estimator – Part?1: The linear and weak non-linear case

机译：集合变分同化作为概率估计器–第一部分：线性和弱非线性情况

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Data assimilation is considered as a problem in Bayesian estimation, viz. determine the probability distribution for the state of the observed system, conditioned by the available data. In the linear and additive Gaussian case, a Monte Carlo sample of the Bayesian probability distribution (which is Gaussian and known explicitly) can be obtained by a simple procedure: perturb the data according to the probability distribution of their own errors, and perform an assimilation on the perturbed data. The performance of that approach, called here ensemble variational assimilation (EnsVAR), also known as ensemble of data assimilations (EDA), is studied in this two-part paper on the non-linear low-dimensional Lorenz-96 chaotic system, with the assimilation being performed by the standard variational procedure. In this first part, EnsVAR is implemented first, for reference, in a linear and Gaussian case, and then in a weakly non-linear case (assimilation over 5?days of the system). The performances of the algorithm, considered either as a probabilistic or a deterministic estimator, are very similar in the two cases. Additional comparison shows that the performance of EnsVAR is better, both in the assimilation and forecast phases, than that of standard algorithms for the ensemble Kalman filter (EnKF) and particle filter (PF), although at a higher cost. Globally similar results are obtained with the Kuramoto–Sivashinsky (K–S) equation.
机译：在贝叶斯估计中，数据同化被认为是一个问题。确定以可用数据为条件的被观察系统状态的概率分布。在线性加性高斯情况下，可以通过一个简单的过程获得贝叶斯概率分布的蒙特卡洛样本（它是高斯并已明确知道）：根据数据自身误差的概率分布扰动数据，并进行同化在扰动的数据上。在这一由两部分组成的关于非线性低维Lorenz-96混沌系统的论文中，研究了这种方法的性能，这里称为集合变分同化（EnsVAR），也称为数据同化集合（EDA）。通过标准变分程序进行同化。在第一部分中，首先在线性和高斯情况下实现EnsVAR，以供参考，然后在弱非线性情况下（系统5天的同化时间）实现EnsVAR。在两种情况下，被视为概率估计或确定性估计器的算法的性能非常相似。进一步的比较表明，在同化和预测阶段，EnsVAR的性能都比集成卡尔曼滤波器（EnKF）和粒子滤波器（PF）的标准算法要好，尽管成本更高。使用Kuramoto-Sivashinsky（KS）方程可获得全球相似的结果。

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