Mesoscale Nonhydrostatic and Hydrostatic Pressure Gradient Forces—Theory

A theory is presented for the evaluation of the different terms of the pressure gradient force, when mesoscale flow is driven by a sensible heat source in the planetary boundary layer (PBL), or by an elevated confined heat source, such as the release of the latent heat of condensation in a cloud. The nonlinear and linear, and the nonhydrostatic and the hydrostatic pressure gradient contributions are evaluated. The validity of the different approximations is discussed as a function of time and space scales. In addition, the validity of this approach is explored as a function of atmospheric environmental parameters, such as static stability, large-scale flow, and dissipation. By accessing the relative importance of each contribution, specific solution techniques for mesoscale atmospheric flows can be adopted. For example, when the linear contributions dominate, an exact analytic model could be used, rather than relying on numerical approximation solution techniques. When the hydrostatic contribution dominates, the spatial variation of the vertical temperature profile can be used to uniquely define the horizontal pressure gradient force.