An Analysis of Dynamic Balance in a Mesoscale Model

Abstract

The degrees to which mesoscale model simulations satisfy forms of the quasi-geostrophic omega-equation and nonlinear balance equation are determined for various vertical and horizontal scales. The forms of the equations are those consistent with the application of Bourke and McGregor's initialization scheme to the simulation model, and the vertical scales are those determined by the model's vertical modes. Results indicate that the degree of balance is primarily a function of vertical (rather than horizontal) scale, with the larger vertical scales better balanced. The balance is observed simultaneously for the fields of velocity divergence and ageostrophic vorticity. Also, it is primarily an adiabatic balance, although at very small horizontal scales, diabatic processes (presumably model diffusion) are an important component of the balance. The degree of balance at any scale is apparently not strongly dependent on synoptic situation, although many significant exceptions are likely. In contrast, the initial interpolated analyses do not show similarly strong degrees of balance suggesting that those analyses require some form of nonlinear normal mode initialization. Important conclusions are that both the quasi-geostrophic omega-equation and nonlinear balance equation are very applicable on the mesoscale if they are applied only to large vertical scales and if all significant nonlinear and diabatic processes are considered.