Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms
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Janjic-2014-Conservation of Mass.pdf
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Author(s)
Janjic, Tijana
McLaughlin, Dennis
Cohn, Stephen E.
Verlaan, Martin
Date Issued
February 2014
Journal
Monthly Weather Review
Publisher
American Meteorological Society
Citation
Janjic, Tijana, Dennis McLaughlin, Stephen E. Cohn, and Martin Verlaan. “Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter Algorithms.” Monthly Weather Review 142, no. 2 (February 2014): 755–773. © 2014 American Meteorological Society
Version
Final published version
Abstract
This paper considers the incorporation of constraints to enforce physically based conservation laws in the ensemble Kalman filter. In particular, constraints are used to ensure that the ensemble members and the ensemble mean conserve mass and remain nonnegative through measurement updates. In certain situations filtering algorithms such as the ensemble Kalman filter (EnKF) and ensemble transform Kalman filter (ETKF) yield updated ensembles that conserve mass but are negative, even though the actual states must be nonnegative. In such situations if negative values are set to zero, or a log transform is introduced, the total mass will not be conserved. In this study, mass and positivity are both preserved by formulating the filter update as a set of quadratic programming problems that incorporate nonnegativity constraints. Simple numerical experiments indicate that this approach can have a significant positive impact on the posterior ensemble distribution, giving results that are more physically plausible both for individual ensemble members and for the ensemble mean. In two examples, an update that includes a nonnegativity constraint is able to properly describe the transport of a sharp feature (e.g., a triangle or cone). A number of implementation questions still need to be addressed, particularly the need to develop a computationally efficient quadratic programming update for large ensemble.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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DOI of Published Version
https://doi.org/10.1175/mwr-d-13-00056.1
