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Center for Nonlinear Studies |
A new type of Ensemble Kalman Filter (EnKF) is developed, one that stores and updates its state information in an efficient square-root information filter form. It addresses two shortcomings of conventional EnKFs, the lack of a process noise model and the overly optimistic approximation of the estimation error statistics. The new filter uses an assumed a priori covariance approximation that is full-rank but sparse, possibly with a dense low-rank increment. This matrix can be used to develop a nominal square-root information equation for the system state and uncertainty. The measurements are used to develop an additional low-rank set of square-root information equations. Special algorithms provide forecasts and analyses of these increments at a computational cost comparable to that of existing EnKFs. Process noise effects are implicit in the a priori covariance time history, thereby obviating the need for an ad hoc inflation operation. The use of an a priori full-rank covariance allows the analysis operations to improve the state estimate without the need for an ad hoc localization adjustment. This new filter exhibits superior performance to a typical covariance square-root EnKF when operating on truth-model simulation data from a model of a 200-state spring-mass-damper network.
This new EnKF is being developed to solve data assimilation problems in the upper atmosphere. One target application is the assimilation of data into the Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIEGCM). An existing EnKF assimilates in situ neutral-density and electron-density data that are measured by satellites. The new EnKF is being considered to enable augmentation of this filter to assimilate GPS slant TEC from satellite-based radio occultations. This data type presents a challenge for traditional EnKFs because of its non-local nature. Another target application is to develop a real-time International Reference Ionosphere model that assimilates GPS slant TEC data from radio occultations and from a network of ground receivers along with data from a network of ground-based ionosondes. The challenges and opportunities of these two proposed applications will be discussed along with the potential for the new EnKF to meet the challenges.
Host: Humberto C. Godinez