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Original Articles

An Anomaly in the Behaviour of the Time Filter Used with the Leapfrog Scheme in Atmospheric Models

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Pages S3-S15 | Published online: 26 Jul 2011
 

ABSTRACT

Integration techniques such as the explicit leapfrog scheme or the semi-implicit method carry out their calculations over three time levels. Because of this characteristic, these algorithms can produce computational modes that appear as superimposed onto the physical solution of the meteorological equations. These computational modes can cause problems and in order to avoid these problems or remove them, a common practice is to use a rime filter. The rime filter that is frequently used for this purpose efficiently damps the computational mode while it has little effect on the physical solution.

This filter does not always behave exactly as expected and in some cases, strange results are observed. A series of simple numerical experiments are carried out in order to show that the filter can display an anomalous behaviour under certain conditions. An attempt is made to explain this behaviour by numerical analysis. This analysis gives some information as to how to avoid this anomalous behaviour in atmospheric models.

RÉSUMÉ

Les techniques d'intégration telles que le schéma explicite saute-mouton ou la méthode semi-implicite effectuent leurs calculs sur trois niveaux temporels. À cause de ce fait, ces algorithmes peuvent engendrer des modes numériques qui se superposent à la solution physique des équations météorologiques. Ces modes numériques peuvent causer des problèmes et, afin de les éliminer, une pratique courante consiste en l'utilisation d'un filter temporel. Le filter temporel qui est utilisé fréquemment dans ce but amortit efficacement le mode numérique tout en ayant peu d'effet sur la solution physique.

Ce filter ne se comporte pas toujours exactement comme prévu et, dans certains cas, on observe des résultats étranges. Une série d'expériences numériques simples ont été réalisées afin de montrer que le filtre peut présenter un comportement anormal sous certaines conditions. On utilise l'analyse numérique pour tenter d'expliquer ce comportement. L'analyse nous renseigne sur la façon d'éviter ce comportement anormal dans les modèles atmosphériques.

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