omega equation

A diagnostic equation by which the vertical velocity in pressure coordinates (ω = Dp/Dt) may be calculated according to quasigeostrophic theory:

for which f is the Coriolis parameter, σ is the static stability, v_g is the geostrophic velocity vector, ζ_g is the geostrophic relative vorticity, φ is the geopotential, ∇_H² is the horizontal Laplacian operator, and ∇_H is the horizontal del operator.
The right-hand side of the omega equation can also be expressed in terms of the divergence of the Q vector.
Holton, J. R. 1992. An Introduction to Dynamic Meteorology. 3d edition, Academic Press, . 166–175.

1. The study of the physics, chemistry, and dynamics of the earth's atmosphere, including the related effects at the air–earth boundary over both land and the oceans. Fundamental topics include the composition, structure, and motion of the atmosphere. The goals ascribed to meteorology are the complete understanding and accurate prediction of atmospheric phenomena.