SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Mass Conservation and Positivity Preservation with Ensemble-type Kalman Filter Algorithms

T.J. Pfander, D.B. McLaughlin, S.E. Cohn and M. Verlaan

Abstract
This paper considers incorporation of constraints to enforce physically-based conservation laws in the ensemble Kalman filter. In particular, equality and inequality constraints are used both to conserve mass and to maintain positivity through measurement updates. In order to ensure mass conservation, a projection matrix that corrects for localization effects is constructed. In order to maintain both mass conservation and positivity preservation through the analysis step, we construct two data assimilation algorithms based on quadratic programming and ensemble Kalman filtering. We demonstrate the benefits of imposing these constraints in two simple experimental setups: a solid body rotation experiment and idealized problems of environmental pollution. The results show clear improvements in both analyses and forecasts, particularly in the presence of localized features.

Organized by         Universidad de Valladolid     IMUVA