Before revision: Similar to Chapter 6.3 in Holton 2004, we start from horizontal momentum (15), mass continuity (16), hydrostatic (17), and thermodynamic (18) equations on a beta plane, while assuming that the flow is inviscid and hydrostatic, (15) (16) (17) (18) where represents the geostrophic evolution, , is the diabatic heating term in , is the geopotential height, is the geostrophic component of horizontal velocity, is the geostrophic velocity, is horizontal gradient operator in (x, y, p) coordinates.
After revision: Similar to Chapter 6.3 in Holton 2004, we start from horizontal momentum (15), mass continuity (16), hydrostatic (17), and thermodynamic (18) equations on a beta plane, while assuming that the flow is inviscid and hydrostatic, (15) (16) (17) (18) where represents the ageostrophic evolution, , is the diabatic heating term in , is the geopotential height, is the geostrophic component of horizontal velocity, is the geostrophic velocity, is horizontal gradient operator in (x, y, p) coordinates.