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A generalization of Ertel's potential vorticity to a cloudy, precipitating atmosphere

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This paper discusses the generalization of Ertel's PV to a cloudy, precipitating atmosphere. The recommended generalization is = ∇, where is the total density of moist air, is the absolute vorticity, and is the virtual potential temperature. Associated with this form are three important properties: (1) the solenoidal term is annihilated (i.e., ∇ (∇∇) = 0, where is the total pressure, the sum of the partial pressures of dry air and water vapor); (2) the limiting form for a dry atmosphere is the classical Ertel PV; (3) is invertible, i.e., it carries all the necessary dynamical information about the balanced wind and mass fields. Two other possible generalizations are discussed,∇ and ∇, where is the equivalent potential temperature and is the saturation equivalent potential temperature. The former is rejected because properties (1) and (3) are lost, while the latter is rejected because property (2) is lost.

In diesem Artikel wird die Verallgemeinerung von Ertels potenzieller Vorticity für feuchte Luft diskutiert. Die vorgeschlagene Verallgemeinerung hat die Form P = ρ–1ζ ˙ρ wobie ρ die Dichte feuchter Luft ist, ζ die absolute Vorticity und ρ die virtuelle potenzielle Temperatur. Diese Formulierung hat drei wichtige Eigenschaften: (1) der Solenoidterm verschwindet (d.h. ∇ρ˙ (∇ρ × p ) = 0, wobei p die Summe der Partialdrücke von trockener Luft und Wasserdampf ist); (2) der Grenzfall für trockene Luft ist Ertels klassische Form der potenziellen Vorticity; (3) P ist invertierbar, d.h. P enthält alle notwendige dynamische Information über die balancierten Wind- und Massefelder. Zwei weitere Verallgemeinerungen werden diskutiert: ρ–1ζ ˙e und ρ–1ζ ˙*e , wobei e die equivalente potentielle Temperature ist, und *e die equivalente potentielle Temperatur für gesättigte Luft. Beide Verallgemeinerungen werden verworfen. In der einen gehen die erste (1) und dritte (3) der oben genannten Eigenschaften verloren, während in der anderen Formulierung die zweite (2) Eigenschaft verloren geht.

Document Type: Research Article


Publication date: December 1, 2004

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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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