Combining the Two Forcing Terms in the QG­ Omega Equation

In this example, it appears that the vorticity advection and thermal advection terms are opposing one another. How can one decide which is more significant? In this case, it "appears" that the warm advection term is liable to be stronger than the differential negative vorticity advection. This is very difficult to estimate, however, from a visual inspection of patterns.

Click on chart to see full size version. Click on chart to see full size version. The two terms can be combined mathematically. One method yields an expression that states that quasigeostrophic omega is proportional to the ADVECTION OF THE GEOSTROPHIC VORTICITY BY THE THERMAL WIND. There are other terms in the equation that drop out on an order of magnitude basis. This is called the TRENBERTH APPROXIMATION. To visualize this you need only two charts. One showing the absolute (geostrophic) vorticity at a given level (we are cheating and using the real absolute vorticity) (above right) and the other showing the thickness field where the level at which you would like to estimate omega is somewhere in the middle of the layer. In this case, we are using 1000­500 mb thickness (above left). The "thermal wind" blows parallel to the thickness contours, clockwise around highs and counterclockwise around lows. (It is a kind of geostrophic wind). Where the thermal wind blows from high to low values of vorticity (positive isothermal vorticity advection­­piva or positive or cyclonic voriticty advection by the thermal wind), there is quasigeostrophic forcing for upwards omega and vice versa.

Click on chart to see full size version. Click on chart to see full size version. The chart above left shows the 850 mb absolute vorticity contours overlain with the thermal wind streamlines inferred from the 1000­500 thickness map. The orange dashed line shows the inferred area of PIVA and the purple dashed line shows the inferred area of strongest PIVA. These should be proportional to the quasigeostrophically forced upwards omega and strongest upwards omega in the region. The chart above right shows the ETA forecast total omega at 850 mb for 12UTC Monday 12 January. There is considerable similarity, even though the figure at right includes orographic, solenoidal and a host of other effects that produce upward motion.

What is the moral of this story? In this case, it is clear that warm advection dominated the dynamic controls of this pattern. This is despite the negative vorticity advection which might have prevented a forecaster from even considering the possibility that dynamics were favorable for upward motion for this case. Using the idea of "dynamics" as a dominant control on vertical motion is perfectly fine at the synoptic scale. It is important, however, that the forecaster disavow himself or herself of outmoded rules of thumb that reduces "dynamics" to "vorticity advection."