Quasi-geostrophic aspeccts of seasonal development of lee-side trough and resulting dryline east of Rockies

Pages 10-12 of Bluestein Vol II

The simplified Equation of Continuity (synoptic-scaling) is

(1)

Which says that layer horizontal divergence is related to the vertical motion field.

Under weak synoptic forcing (no or weak diff. vort advc and no or weak temp advection--assumptions that become more valid in late spring, summer and early fall) the QG omega equation can be rewritten as given in (2) [with the far right substitution of equation (1)].

(2)

Inverting the Laplacian on the left gives the approximate equation

(3)

which says that if omega is positive (subsidence), then the derivative on the right returns a positive value (horizontal divergence increases with height).

During the summer, it is often observed that very weak westerly flow occurs in the region from the Front Range of the Rockies through the very western high Plains. This means that air is moving from high elevation to low elevation, or subsiding.

In the case of leeside sinking, there is no omega at the nodal surface, and there is great sinking at the surface. If the nodal surface is at 300 mb, a finite difference version of the far right hand term says that divergence must become more positive with height (more negative with decreasing height) if downward motion is occurring. Since subsidence associated with topography is zero at the nodal surface and maximum at the ground, this implies that there is no divergence at the nodal surface. For divergence to increase with height from the ground, this implies that convergence occurs at the ground on the lee side of mountain ranges.

This effect is often seen east of major mountain ranges as the development of a so-called "leeside low" at the surface that weakens with height. This low is not baroclinic, is not associated with pre-existing temperature or vorticity advection. However, once the low is in place (often in the spring and early summer east of the Rockies, for example) significant moisture advection can occur east of it, and, actually, a synoptic scale "warm front" like feature can develop as well.

During the late spring and early fall, this effect can combine with synoptic scale effects as mid and upper tropospheric troughs move eastward across the Rockies. The pressure falls associated with these features can combine with topographic effects to produce a strong trough in the western High Plains.