Abstract The ocean state off Oregon-Washington, U.S. West coast, is highly variable in time. Under these conditions the assumption made in traditional 4-dimensional variational data assimilation (4DVAR) that the prior model (background) error covariance is the same in every data assimilation (DA) window can be limiting. A DA system based on an ensemble of 4DVARs (En4DVar) has been developed in which the background error covariance is estimated from an ensemble of model runs and is thus time-varying. This part describes details of the En4DVar method and ensemble statistics verification tests. The control run and 39 ensemble members are forced by perturbed wind fields and corrected by DA in a series of 3-day windows. Wind perturbations are represented as a linear combination of empirical orthogonal functions (EOFs) for the larger scales and Daubechies wavelets for the smaller scales. The variance of the EOF expansion coefficients is based on estimates of the wind field error statistics derived using scatterometer observations and a Bayesian Hierarchical Model. It is found that the variance of the wind errors relative to the natural wind variability increases as the horizontal spatial scales decrease. DA corrections to the control run and ensemble members are calculated in parallel by the newly developed, cost-effective cluster search minimization method. For a realistic coastal ocean application, this method can generate a 30% wall time reduction compared to the restricted B-conjugate gradient (RBCG) method. Ensemble statistics are generally found to be consistent with background error statistics. In particular, ensemble spread is maintained without inflating. However, sea-surface height background errors cannot be fully reproduced by the ensemble perturbations.

中文翻译：

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沿海海洋环流模型中的 4DVARs (En4DVar) 数据同化，第一部分：方法论和集合统计

摘要 美国西海岸俄勒冈-华盛顿附近的海洋状态随时间变化很大。在这些条件下，传统 4 维变分数据同化 (4DVAR) 中做出的假设，即先验模型（背景）误差协方差在每个数据同化 (DA) 窗口中都相同，可能会受到限制。已经开发了基于 4DVAR 集合 (En4DVar) 的 DA 系统，其中背景误差协方差是从模型运行的集合中估计的，因此是随时间变化的。这部分描述了 En4DVar 方法和集成统计验证测试的详细信息。控制运行和 39 个集合成员受到扰动风场的强迫，并在一系列 3 天的窗口中由 DA 进行校正。风扰动表示为较大尺度的经验正交函数 (EOF) 和较小尺度的 Daubechies 小波的线性组合。EOF 扩展系数的方差基于使用散射计观测和贝叶斯分层模型得出的风场误差统计的估计。发现风误差相对于自然风变率的方差随着水平空间尺度的减小而增加。对控制运行和集合成员的 DA 校正是通过新开发的、具有成本效益的集群搜索最小化方法并行计算的。对于实际的沿海海洋应用，与受限 B 共轭梯度 (RBCG) 方法相比，该方法可以减少 30% 的壁面时间。整体统计通常被发现与背景误差统计一致。特别是，在不膨胀的情况下保持整体散布。然而，海面高度背景误差不能完全由集合扰动重现。