Structurally informed data assimilation in two dimensions

Accurate data assimilation (DA) for systems with piecewise-smooth or discontinuous state variables remains a significant challenge, as conventional covariance-based ensemble Kalman filter approaches often fail to effectively balance observations and model information near sharp features. In this paper we develop a structurally informed DA framework using ensemble transform Kalman filtering (ETKF). Our approach introduces gradient-based weighting matrices constructed from finite difference statistics of the forecast ensemble, thereby allowing the assimilation process to dynamically adjust the influence of observations and prior estimates according to local roughness. The design is intentionally flexible so that it can be suitably refined for sparse data environments. Numerical experiments demonstrate that our new structurally informed data assimilation framework consistently yields greater accuracy when compared to more conventional approaches.