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Weak constraints in four-dimensional variational data assimilation

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The formulation of four-dimensional variational data assimilation allows the incorporation of constraints into the cost function which need only be weakly satisfied. In this paper we investigate the value of imposing conservation properties as weak constraints. Using the example of the two-body problem of celestial mechanics we compare weak constraints based on conservation laws with a constraint on the background state. We show how the imposition of conservation-based weak constraints changes the nature of the gradient equation. Assimilation experiments demonstrate how this can add extra information to the assimilation process, even when the underlying numerical model is conserving.

Die vierdimensionale variationelle Datenassimilation ermöglicht es, in der Kostenfunktion zusätzliche Nebenbedingungen zu definieren, welche nur schwach erfüllt sein müssen. Hier untersuchen wir, welchen Nutzen es bringt, die Erhaltungsgrößen als schwache Nebenbedingungen einzuführen. Am Beispiel des Zweikörperproblems der Himmelsmechanik vergleichen wir die Kostenfunktion im Falle schwacher Nebenbedingungen für Erhaltungsgrößen mit der Standardformulierung der Kostenfunktion. Wir zeigen wie die Einführung der schwachen Nebenbedingung für Erhaltungsgrößen die mathematischen Eigenschaften der Gleichung verändert, welche den Gradienten der Kostenfunktion beschreibt. Unsere Assimilationsexperimente demonstrieren, wie auf diese Weise Zusatzinformationen in den Assimilationsprozess eingeführt werden, auch wenn das verwendete Modell die Erhaltungsgrößen nicht verändert.

Document Type: Research Article

DOI: http://dx.doi.org/10.1127/0941-2948/2007/0249

Publication date: December 1, 2007

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  • Meteorologische Zeitschrift (originally founded in 1866) is the joint periodical of the meteorological societies of Austria, Germany and Switzerland. It accepts high-quality peer-reviewed manuscripts on all aspects of observational, theoretical and computational research out of the entire field of meteorology, including climatology. Meteorologische Zeitschrift represents a natural forum for the meteorological community of Central Europe and worldwide.
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