Global Omega Equation: Its Derivation and Use in Tropical Cyclogenesis

The quasi-geostrophic (QG) omega equation is a tool that has been available to meteorologists for decades, but its use restricted to the midlatitudes due to deficiencies of 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 solution to the global omega equation is accomplished by using a spherical harmonic transform in the horizontal and a normal mode transform in the vertical.

Tropical cyclogenesis in the Atlantic basin is examined using a ‘QG approach', 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 that developed into tropical cyclones, and 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 CIRA's Tropical Cyclone Formation Probability Guidance Product is discussed.