# Global omega equation: derivation and application to tropical cyclogenesis in the north Atlantic Ocean

## Date

2012

## Authors

Dostalek, John F., author

Schubert, Wayne, advisor

DeMaria, Mark, advisor

Estep, Don, committee member

Johnson, Richard, committee member

Vonder Haar, Tom, committee member

## Journal Title

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## Volume Title

## Abstract

The quasi-geostrophic omega equation has been used extensively to examine the large-scale vertical velocity patterns of atmospheric systems. It is derived from the quasi-geostrophic equations, a balanced set of equations based on the partitioning of the horizontal wind into a geostrophic and an ageostrophic component. Its use is limited to higher latitudes, however, as the geostrophic balance is undefined at the equator. In order to derive an omega equation which can be used at low latitudes, a new balanced set of equations is developed. Three key steps are used in the formulation. First, the horizontal wind is decomposed into a nondivergent and an irrotational component. Second, the Coriolis parameter is assumed to be slowly varying, such that it may be moved in and out of horizontal derivative operators as necessary to simplify the derivation. Finally, the mass field is formulated from the nondivergent wind field. The resulting balanced set of equations and the omega equation derived from them are valid over the whole sphere. In addition, they take a similar form to the quasi-geostrophic equations. The global omega equation is applied to the problem of tropical cyclogenesis in the Atlantic Ocean. The omega fields are used to compare those disturbances that eventually undergo cyclogenesis with those that dissipate. Composite analysis is employed and, in order to account for the different regional behavior of tropical cyclogenesis, the Atlantic is divided into three subbasins: the Tropics, the Subtropics, and the Gulf of Mexico. It is found that the large-scale omega is not strong enough to account for the magnitude of vertical velocities found in tropical cyclones, but acts to provide a favorable environment for convection to develop. The greatest difference between the developing composite and dissipating composite is seen in the Tropics, where the large-scale ascent at low levels on the leading edge of the disturbance due to frictional forcing in the developing composite is significantly greater than the ascent at the leading edge of the dissipating disturbance. The other two subbasins do not exhibit such large statistical differences, but examining the omega fields and the dominant forcing terms do lend insight into the physical differences between those distubances which develop and those that do not. As an additional application, the 850-hPa omega is used as a predictor in an operational tropical cyclogenesis probability product. Overall, the inclusion of the omega field improves the performance of the product, as measured in terms of the Brier skill score. Due to a difficulty in interpreting how the linear discriminant analysis handles the omega field however, it may be that the large-scale omega may be of more value in the genesis product's screening step than in its prediction step.