Adaptive Parameter Selection in Nudging Based Data Assimilation

TL;DR

This paper introduces and compares two self-adaptive methods for selecting nudging parameters in data assimilation, improving practicality and effectiveness over traditional a priori approaches.

Contribution

It develops and analyzes two novel self-adaptive parameter selection methods for nudging in data assimilation, enhancing ease of implementation and accuracy.

Findings

Both methods are easy to implement.

Adaptive methods yield smaller, more effective nudging parameters.

Self-adaptive approaches outperform a priori analysis in practice.

Abstract

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 [1]. One remaining issue is that nudging requires the user to select a key parameter. The conditions required for this parameter, derived through \'a 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 yield effective values of the nudging parameter much smaller than those of \'a priori analysis.