Part A. Application of QG-omega Equation (120 points)

The simplified quasigeostrophic omega equation is

Here are charts (a) and (b) used in Metr 301 and Metr 698 to evaluate synoptic-scale “dynamics.” ,They are analyzed for cyclonic vorticity advection and warm advection, respectively.

The 500 mb vorticity advection can be used to evaluate the differential vorticity advection term because vorticity advection patterns increase in magnitude upwards from near zero near the ground. Thus, for example, cyclonic vorticity advection at 500 mb diagnoses upward motion (from the first term alone) at a point midway in the layer, say at 700 mb. For this case, the first term diagnoses upward motion (negative omega) at point A at 700 mb (and at 500 mb, if one assumes that the vorticity advection continues to increase with height to 300 mb)

The 700 mb (and 500 mb) temperature advection can be inferred from the analyzed 1000-500 mb thickness advection chart, if one assumes that the sign of the temperature advection in that layer is representative of the temperature advection at 700 mb (and 500 mb). In this case, at Point A, there is very weak warm advection.

The net contribution of both forcing terms would be in the same sense…and thus, we would expect upward vertical motion (negative omega) to occur quasi-geostrophically at A.

The actual vorticity advection patterns at different levels and the 700 mb temperature advection that actually occurred verifies the above discussion. The vorticity advection indeed becomes more cyclonic (more positive) which height from 850 mb to 500 mb and there is weak warm advection (to neutral) at Point A. The results are consistent.

Part B. Relation of Upper Air to Surface Patterns (115 points)

2. The simplified vorticity equation in natural coordinates is