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Ensemble-type Kalman filter algorithm conserving mass, total energy and enstrophy


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Zeng, Yuefei ; Janjić, Tijana ; Ruckstuhl, Yvonne ; Verlaan, Martin:
Ensemble-type Kalman filter algorithm conserving mass, total energy and enstrophy.
In: Quarterly journal of the Royal Meteorological Society. 143 (2017) 708. - S. 2902-2914.
ISSN 1477-870x ; 0035-9009


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For numerical discretization schemes, the violation of enstrophy conservation causes a systematic and unrealistic energy cascade towards high wave numbers. The same occurs in data assimilation schemes, where the total energy, enstrophy and divergence could be strongly affected. In this article, we construct an ensemble data assimilation algorithm that conserves mass, total energy and enstrophy. The algorithm uses B-spline functions for localization and sequential quadratic programming to solve nonlinear constrained minimization problem. Idealized experiments are performed using a 2D shallow-water model, with selected contraints derived from the nature run. It is found that all experiments exhibit comparable root-mean-square errors, with a slight advantage for those that include the conservation constraint on the globally integrated enstrophy. However, the kinetic energy and enstrophy spectra in experiments with the enstrophy constraint are considerably closer to the true spectra, in particular at the smallest resolvable scales. Therefore, imposing conservation of enstrophy within the data assimilation algorithm effectively avoids the spurious energy cascade of the rotational part and thereby successfully suppresses the noise generated by the data assimilation algorithm. The 14 day deterministic free forecast, starting from the initial condition enforced by both total energy and enstrophy constraints, produces the best prediction. The same holds for the ensemble free forecasts.

Weitere Angaben

Sprache des Eintrags:Englisch
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Heisenberg Professur für Datenassimilation
DOI / URN / ID:10.1002/qj.3142
Open Access: Freie Zugänglichkeit des Volltexts?:Nein
Die Zeitschrift ist nachgewiesen in:
Titel an der KU entstanden:Ja
Eingestellt am: 06. Dez 2021 18:43
Letzte Änderung: 31. Aug 2023 09:25
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