Data assimilation combines (imperfect) knowledge of a flow’s physical laws with (noisy, time-lagged, and otherwise imperfect) observations to produce a more accurate prediction of flow statistics. Assimilation by nudging (from 1964), while non-optimal, is easy to implement and its analysis is clear and well-established. Nudging’s uniform in time accuracy has even been established under conditions on the nudging parameter χ and the density of observational locations, H, Larios et al. (2019). One remaining issue is that nudging requires the user to select a key parameter. The conditions required for this parameter, derived through á priori (worst case) analysis are severe (Section 2.1 herein) and far beyond those found to be effective in computational experience. One resolution, developed herein, is self-adaptive parameter selection. This report develops, analyzes, tests, and compares two methods of self-adaptation of nudging parameters. One combines analysis and response to local flow behavior. The other is based only on response to flow behavior. The comparison finds both are easily implemented and yields effective values of the nudging parameter much smaller than those of á priori analysis.

中文翻译：

---

基于微移的数据同化中的自适应参数选择


数据同化将流的物理定律的（不完美）知识与（嘈杂、滞后和其他不完美的）观察相结合，以产生更准确的流统计预测。通过轻推进行同化（从 1964 年开始）虽然不是最优的，但很容易实现，并且其分析清晰且成熟。在微移参数 χ 和观测位置密度的条件下，甚至已经建立了轻推的均匀时间精度，H， Larios et al. （2019）。剩下的一个问题是，轻推需要用户选择一个关键参数。通过先验（最坏情况）分析得出的此参数所需的条件非常严格（本文第 2.1 节），远远超出了在计算经验中发现有效的条件。本文开发的一种解决方案是自适应参数选择。本报告开发、分析、测试和比较了两种自适应轻推参数的方法。一个将分析和响应局部流动行为相结合。另一个仅基于对流行为的响应。比较发现两者都很容易实现，并且产生的轻推参数的有效值比先验分析的小得多。