Robust data assimilation using $L_1$ and Huber norms

TL;DR

This paper introduces robust data assimilation algorithms that replace traditional least squares with L1 and Huber norms, effectively handling outliers in observational data to improve analysis quality.

Contribution

It develops a systematic framework for robust data assimilation using L1 and Huber norms, demonstrating improved performance over traditional methods in the presence of outliers.

Findings

Outperforms traditional methods with outlier data

Effective in Lorenz-96 and shallow water models

Maintains analysis quality despite faulty observations

Abstract

Data assimilation is the process to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a physical system of interest. Presence of large errors in some observational data, e.g., data collected from a faulty instrument, negatively affect the quality of the overall assimilation results. This work develops a systematic framework for robust data assimilation. The new algorithms continue to produce good analyses in the presence of observation outliers. The approach is based on replacing the traditional $\L_2$ norm formulation of data assimilation problems with formulations based on $\L_1$ and Huber norms. Numerical experiments using the Lorenz-96 and the shallow water on the sphere models illustrate how the new algorithms outperform traditional data assimilation approaches in the presence of data outliers.