A local ensemble Kalman filter for atmospheric data assimilation

TLDR

Ensemble Kalman filters constrain analyses to a forecast‑error subspace, and this work hypothesizes that local regions of the Earth’s surface have a much lower‑dimensional forecast‑error subspace, enabling a local formulation. The paper introduces a local formulation of the ensemble Kalman filter for atmospheric data assimilation. The method performs local analyses on low‑dimensional forecast‑error subspaces, enabling parallel computation and constructing global states, as demonstrated in Lorenz‑96 experiments. The local ensemble Kalman filter achieves accurate analyses at a modest cost, with computational scaling that improves over sequential methods as data volume grows.

Abstract

In this paper, we introduce a new, local formulation of the ensemble Kalman filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earth’s surface is divided up into local regions of moderate size, vectors of the forecast uncertainties in such regions tend to lie in a subspace of much lower dimension than that of the full atmospheric state vector of such a region. Ensemble Kalman filters, in general, take the analysis resulting from the data assimilation to lie in the same subspace as the expected forecast error. Under our hypothesis the dimension of the subspace corresponding to local regions is low. This is used in our scheme to allow operations only on relatively low-dimensional matrices. The data assimilation analysis is performed locally in a manner allowing massively parallel computation to be exploited. The local analyses are then used to construct global states for advancement to the next forecast time. One advantage, which may take on more importance as ever-increasing amounts of remotely-sensed satellite data become available, is the favorable scaling of the computational cost of our method with increasing data size, as compared to other methods that assimilate data sequentially. The method, its potential advantages, properties, and implementation requirements are illustrated by numerical experiments on the Lorenz-96 model. It is found that accurate analysis can be achieved at a cost which is very modest compared to that of a full global ensemble Kalman filter.