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Conservation of Mass and Preservation of Positivity with Ensemble-Type Kalman Filter AlgorithmsThis 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 non-negativity 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 non-negativity 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.
Document ID
20150010241
Acquisition Source
Goddard Space Flight Center
Document Type
Reprint (Version printed in journal)
External Source(s)
doi:10.1175/MWR-D-13-00056.1
Authors
Janjic, Tijana (Massachusetts Inst. of Tech. Cambridge, MA, United States)
Mclaughlin, Dennis (Massachusetts Inst. of Tech. Cambridge, MA, United States)
Cohn, Stephen E. (NASA Goddard Space Flight Center Greenbelt, MD United States)
Verlaan, Martin (Technische Univ. Delft, Netherlands)
Date Acquired
June 9, 2015
Publication Date
February 1, 2014
Publication Information
Publication: Monthly Weather Review
Publisher: American Meteorological Society
Volume: 142
Issue: 2
Subject Category
Numerical Analysis
Meteorology And Climatology
Report/Patent Number
GSFC-E-DAA-TN23354
Distribution Limits
Public
Copyright
Public Use Permitted.
Keywords
EnKF
ETKF
Algorithms

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