A Local Least Squares Framework for Ensemble Filtering

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Abstract
Many methods using ensemble integrations of prediction models as integral parts of data assimilation have appeared in the atmospheric and oceanic literature. In general, these methods have been derived from the Kalman filter and have been known as ensemble Kalman filters. A more general class of methods including these ensemble Kalman filter methods is derived starting from the nonlinear filtering problem. When working in a joint state–observation space, many features of ensemble filtering algorithms are easier to derive and compare. The ensemble filter methods derived here make a (local) least squares assumption about the relation between prior distributions of an observation variable and model state variables. In this context, the update procedure applied when a new observation becomes available can be described in two parts. First, an update increment is computed for each prior ensemble estimate of the observation variable by applying a scalar ensemble filter. Second, a linear regression of th... Abstract Many methods using ensemble integrations of prediction models as integral parts of data assimilation have appeared in the atmospheric and oceanic literature. In general, these methods have been derived from the Kalman filter and have been known as ensemble Kalman filters. A more general class of methods including these ensemble Kalman filter methods is derived starting from the nonlinear filtering problem. When working in a joint state–observation space, many features of ensemble filtering algorithms are easier to derive and compare. The ensemble filter methods derived here make a (local) least squares assumption about the relation between prior distributions of an observation variable and model state variables. In this context, the update procedure applied when a new observation becomes available can be described in two parts. First, an update increment is computed for each prior ensemble estimate of the observation variable by applying a scalar ensemble filter. Second, a linear regression of th...