2.1. Conceptual View of QG Omega: Forcing and Response The QG omega equation is shown below. It states that forcing for vertical motion is related to the differential vorticity advection and the Laplacian of the temperature advection. For both advections, the approximation is made that the geostrophic wind is a good enough approximation for the advecting velocity. Recall that the change in geopotential ☀ with pressure in the second term (the thickness dZ per unit mass layer dp) is a measure of layer-averaged temperature. Recall also that the Laplacian (V²) of the geopotential in the first term is proportional to geostrophic relative vorticity (with some constants). These ideas may help you to recognize the terms in the omega equation. (v¹¸£ 5* )-- € 2 [v,«v[÷vons]] - ²v|(2) + @= V.V + о др2 o ap 8 ap Our objective in this lesson is to understand this diagnostic relationship. In other words, why does cyclonic vorticity advection increasing with height, or a horizontal maximum of warm advection, represent forcing for ascent? This example is inspired by the Durran and Snellman (1987) paper. Consider an idealized jet streak situation. Suppose the 1000-hPa geopotential height surface Z1000 = 0 everywhere (i.e., the 1000-hPa surface is flat, with no geostrophic wind at that level). On the following diagram, the 500-hPa height contours are shown as bold solid lines, and the 500-hPa isotachs are shown as dashed lines. The cross section B-C is marked for later reference. B-50 kt 50 kt 75 kt -100 kt Jet Streak 75 kt 522 dam 100 kt (2.29) 528 dam 534 dam QUASIGEOSTROPHIC THEORY / 35