Robust data assimilation using $L_1$ and Huber norms

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.