(TERM C )
The last term in the Q-G Omega Equation is the negative of the Laplacian of geopotential thickness advection (infer from above). As Term C appears above, the dot product within the brackets is proportional to the negative of geostrophic advection of thickness. A few important details should be recalled in order to fully understand Term C:
Now we will look at the same figure as for Term B; however, low-level WAA and CAA are depicted:
As indicated in the figure above, rising motion (w > 0) will occur to the east of the surface low in advance of the warm front, where the strongest positive geopotential thickness advection exists. Conversely, sinking motion (w < 0) will occur to the west of the surface low in the region of strongest CAA.
Because WAA under the 500-hPa ridge (to the east of the surface low) will result in an increase in the 500-1000-hPa thickness field (via the hypsometric equation), the height of the 500-hPa surface will bow upward (increase) at this location. Since the geostrophic relative vorticity is proportional to the negative of the geopotential, the geostrophic relative vorticity must decrease at the 500-hPa ridge. In the absence of NVA at the ridge axis, the only means of decreasing the relative vorticity is via horizontal divergence (recall the Q-G Geostrophic Relative Vorticity Equation). Continuity requires upward motion beneath the upper-level divergence (500-hPa ridge axis) and corresponding low-level convergence.
Because CAA under the 500-hPa trough (to the west of the surface low) will result in a decrease in the 500-1000-hPa thickness field (via the hypsometric equation), the height of the 500-hPa surface will bow downward (decrease) at this location, thus amplifying the mid-level trough. Since the geostrophic relative vorticity is proportional to the negative of the geopotential, the geostrophic relative vorticity must increase at the 500-hPa trough. In the absence of PVA at the trough axis, the only means of increasing the relative vorticity is via horizontal convergence (recall the Q-G Geostrophic Relative Vorticity Equation). Continuity requires downward motion beneath the upper-level convergence (500-hPa trough axis) and corresponding low-level divergence.
Realize that the vertical motions induced by the low-level thermal forcing acts to create adiabatic temperature changes that offset the intial temperature perturbations. More specifically, the upward motion (adiabatic cooling) at the 500-hPa ridge axis counteracts the WAA. In addition, sinking air (adiabatic warming) at the 500-hPa trough axis counteracts the low-level CAA. In essence, the ageostrophic motion is trying to return the atmosphere to hydrostatic balance after the initial thermal perturbations.
The main conclusions:
Low-level WAA results in upward vertical motion.
Now lets use IDV to help visualize this process.
1) Uncheck all of the boxes in the display window (except for your background map).
2) Check the box next to “1000-500 hPa Geopotential Thickness”.
Your screen should now look like this:
Q11 – Visualize the idealized surface fronts from this developing shortwave trough. Identify the regions on this map where you would expect to witness the best low-level WAA and best low-level CAA.
Q12 – Do you expect these low-level thermal forcings (i.e., WAA and CAA) to propagate or amplify the ridge/trough?
Remember these important points:
By using the VCR controls in IDV, move through the time series. Each time, pick a place east of the shortwave trough and notice how the heights fall due to PVA. Also, notice that heights rise significantly behind the trough as you move through each frame.