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 $\chi$ and the density of observational locations, $H$, Larios, Rebholz, and Zerfas \cite{larios2019global}. One remaining issue is that nudging requires the user to select a key parameter. The conditions required for this parameter, derived through $\acute{a}$ priori (worst case) analysis are severe (Section \ref{aprior-analysis} 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 yield effective values of the nudging parameter much smaller than those of $\acute{a}$ priori analysis.

翻译：数据同化通过结合流动物理定律的（不完美）知识与（含噪声、存在时滞及其他不完美的）观测数据，以生成更精确的流动统计量预测。基于推力的同化方法（始于1964年）虽非最优，但易于实现，且其分析框架清晰完善。在满足推力参数$\chi$与观测点密度$H$的特定条件下，推力方法的时间一致性精度已得到严格证明（Larios、Rebholz与Zerfas \cite{larios2019global}）。当前遗留的关键问题在于推力方法需要用户选择核心参数。通过先验（最坏情况）分析推导出的参数条件极为严苛（见本文第\ref{aprior-analysis}节），远超计算实践中发现的有效参数范围。本文提出的解决方案是自适应参数选择。本报告开发、分析、测试并比较了两种推力参数的自适应方法：一种结合理论分析与局部流动特性响应，另一种仅基于流动行为响应。比较结果表明，两种方法均易于实现，且能获得远小于先验分析值的有效推力参数。