Robust data assimilation using l1 and huber norms

Abstract

© 2017 Society for Industrial and Applied Mathematics. Data assimilation is a process used to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a physi- cal 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 estimates of parameters or state in the presence of observation outliers. The approach is based on replacing the traditional L2 norm formulation of data assimilation problems with formulations based on L1 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.