A diagnostic mean velocity potential equation and its application to lee cyclogeneses

Abstract

Similar to the horizontal wind, the horizontal pressure gradient force in σ-coordinates, - φ- RT ln p * (where p * is the pressure at the earth's surface), can be separated into its irrotational and rotational parts and expressed by Ñ φe - k ´ h , where φe and h are referred to as equivalent geopotential and geo-streamfunction, respectively. In this expression, the small difference between two large terms near steep slopes in the horizontal pressure gradient force in σ-coordinates is eliminated. The equivalent geopotential φe can be used in sigma-coordinates in the same way as φ (x,y,p,t) is used in p-coordinates. This method has been used in synoptic analyses over Greenland and Tibetan Plateau and used in developing a generalized omega-equation in sigma coordinates (1999, Mon. Wea. Rev., 127, 145-172).

Due to use of the streamfunction y , the equivalent geopotential φe is separated into a geostrophic geopotential φg and an ageostrophic geopotential φa, where φg=f y and φa=φe - f y . The geostrophic and ageostrophic geopotential can be used over the globe including the equator, and this is one important advantage over the geostrophic and ageostrophic winds. The streamfunction, velocity potential and ageostrophic can reveal the ageostrophic characteristics of the atmospheric motion clearly and explicitly.

The ageostrophic geopotential equation is derived and its advection term combines the vorticity and temperature advection together. The effects of advection on the cyclogenesis can be shown much more explicitly and specifically by the advection of the ageostrophic geopotential than by those of the vorticity and temperature separately. A mean velocity potential equation is developed based on the hydrostatic model in sigma-coordinates, and it can diagnose the effect of various individual factors on the development of weather systems.

The equivalent geopotential φe is used in a spectral limited-area model (Chen et al. 1997, Mon. Wea. Rev. p.143) instead of the generalized geopotential to study lee cyclogenesis when synoptic-scale troughs cross the Rockies. The 24-48 h predictions are done by the models with and without φe , respectively. The other physical processes and resolutions of these two models are the same. In this example, it is shown that although lee cyclogenesis can be predicted by both models, the position and strength of the lee cyclone are predicted more accurately by the model with φe than by that without φe . This example has also been diagnosed by the mean velocity potential equation to show why the lee cyclogenesis is predicted accurately with the equivalent geopotential and geo-streamfunction.