# Global Omega Equation: Derivation and Application to Tropical Cyclogenesis in the North Atlantic Ocean

June 25, 2012

Jack Dostalek

*Hosted by* Wayne Schubert (advisor), Mark DeMaria (co-advisor), Tom Vonder Haar, Dick Johnson, Don Estep (Mathematics)

## Abstract

The quasi-geostrophic (QG) omega equation is a tool which has been available to meteorologists for decades, but its use restricted to the midlatitudes due to the problems with the geostrophic balance at low latitudes. An omega equation valid for the entire sphere is derived. The wind field is not decomposed into geostrophic and ageostrophic components as in QG theory, but rather into nondivergent and irrotational components, and a slowly-varying Coriolis parameter is assumed. The resulting omega equation is similar in appearance to the well-known QG omega equation, with forcing from the vertical derivative of vorticity advection and the laplacian of the thermal advection, or from the divergence of the Q vector. The effect of friction is also included. The solution to the global omega equation is accomplished by using a normal mode transform in the vertical and a spherical harmonic transform in the horizontal.

Tropical cyclogenesis in the Atlantic basin is examined using a â€˜QG approachâ€™, by comparing the large-scale vertical motion and its forcing for two composite systems created from tropical systems from the 2001-2009 seasons. The first composite is created from Global Forecasting System (GFS) fields of disturbances which developed into tropical cyclones. The second composite is created from GFS fields of disturbances which dissipated before becoming a cyclone. The composites are created for four different times: 24, 18, 12, and 6 hours before development or dissipation. Since the nature of cyclogenesis varies with location, composites are created for three regions: the tropical Atlantic, the subtropical Atlantic, and the Gulf of Mexico. In addition to the composite analysis, the potential use of the omega field as a predictor in the Cooperative Institute for Research in the Atmosphereâ€™s Tropical Cyclone Formation Probability Guidance Product is discussed.