Data Assimilation Challenges Posed by Nonlinear Operators: A Comparative Study of Ensemble and Variational Filters and Smoothers
Data Assimilation Challenges Posed by Nonlinear Operators: A Comparative Study of Ensemble and Variational Filters and Smoothers
复制标题
非线性算子带来的数据同化挑战：集成和变分滤波器和平滑器的比较研究
DOI：
10.1175/mwr-d-20-0368.1
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发表时间：
2021
影响因子：
3.2
通讯作者：
Poterjoy, J.
中科院分区：
文献类型：
--
作者：
Kurosawa, K;Poterjoy, J.
集合卡尔曼滤波器 (EnKF) 和 4D 变分法 (4DVar) 是大气科学中最常用的滤波器和平滑器。这些方法通常使用高斯近似先验密度，并求解后验均值和协方差的线性方程组。因此，强非线性模型动力学和测量算子可能会导致后验估计出现偏差。为了提高非线性状态下的性能，4DVar 成本函数的最小化通常遵循多组迭代（称为“外循环”），这有助于减少由线性假设引起的偏差。或者，“迭代集成方法”遵循类似的策略，定期重新线性化模型和测量算子。这些方法带有不同的、可能更合适的假设，用于从后验密度中抽取样本，但在数值天气预报 (NWP) 社区中很少受到关注。最后，粒子滤波器（PF）提出了一种用于状态估计的纯贝叶斯滤波方法，它避免了上述方法所做的许多假设。最近提出了几种将局部 PF 应用到 NWP 的策略。当前的研究调查了当前数据同化方法对于需要非线性测量算子的应用的内在局限性。在此过程中，它针对的是与遥感测量同化相关的特定问题，例如雷达反射率和全天辐射率，这对基于高斯的数据同化系统提出了挑战。这种比较包括最近为非线性/非高斯应用设计的多种数据同化方法，以及目前用于数值天气预报的方法。
The ensemble Kalman filter (EnKF) and the 4D variational method (4DVar) are the most commonly used filters and smoothers in atmospheric science. These methods typically approximate prior densities using a Gaussian and solve a linear system of equations for the posterior mean and covariance. Therefore, strongly nonlinear model dynamics and measurement operators can lead to bias in posterior estimates. To improve the performance in nonlinear regimes, minimization of the 4DVar cost function typically follows multiple sets of iterations, known as an “outer loop,” which helps reduce bias caused by linear assumptions. Alternatively, “iterative ensemble methods” follow a similar strategy of periodically relinearizing model and measurement operators. These methods come with different, possibly more appropriate, assumptions for drawing samples from the posterior density, but have seen little attention in numerical weather prediction (NWP) communities. Last, particle filters (PFs) present a purely Bayesian filtering approach for state estimation, which avoids many of the assumptions made by the above methods. Several strategies for applying localized PFs for NWP have been proposed very recently. The current study investigates intrinsic limitations of current data assimilation methodology for applications that require nonlinear measurement operators. In doing so, it targets a specific problem that is relevant to the assimilation of remotely sensed measurements, such as radar reflectivity and all-sky radiances, which pose challenges for Gaussian-based data assimilation systems. This comparison includes multiple data assimilation approaches designed recently for nonlinear/non-Gaussian applications, as well as those currently used for NWP.