ATSC 5160 Midterm 18% Wednesday, March 24, 2004

1. Define potential vorticity on isentropic surfaces. (write the equation for P and define the terms in it) (2%)

2. Lee cyclones behind the Rockies and the Alps usually evolve into frontal wave cyclones, but the cyclogenesis process differs. In the lee of the Rockies, cyclogenesis is clearly due to subsidence (adiabatic warming and vortex stretching). In the lee of the Alps, this is not necessarily the case, depending on the strength and stability of the upstream flow. Discuss briefly. (3%)

3. (a) Sketch the Palmen-Newton model of the general circulation of the atmosphere, in a meridional transect from the pole to the equator. Ignore seasonal and land/sea differences.(1.5%)

(b) Explain why this model applies better in the southern hemisphere than in the north, especially during the seasonal extremes (Jan/Jul). (1.5%)

4. Draw a schematic of the ageostrophic flow and con/divergence in the entrance and exit regions of a zonal upper-level jet streak, in the northern hemisphere. Start with a map (xy plane), and include the location of the IPV maximum (+) and IPV minimum (-). Then draw two meridional cross sections (yz planes), one across the jet entrance region, another across the jet exit region. In these sections, plot some isentropes (including a hint of the low-level frontal zone), the tropopause, and ageostrophic flow vectors. (3%)

5. Draw a transect of M (absolute momentum) and q_e. Please label the axes, and define M. Also label the M and q_e lines so that it is clear in what direction M and q_e increase. Your transect should contain a region that is potentially symmetrically unstable (PSI), one that is potentially unstable (PI), and the rest of the transect should be statically, inertially, and symmetrically stable (S). (3%)

6. Bluestein question 1.5: in the two Figs below, sketch the area(s) of CVA; and the area(s) of downward motion (w>0 in QG theory). Shown is the 500 mb height in the northern hemisphere. Assume that the 300 mb height pattern is the same, only the height contours are more tightly packed. (2%)

Left image: L is large (long-wave) Right image: L is small (short-wave)

7. Bluestein question 1.31. For what values of x in the Fig below is there rising motion? For what values is there sinking motion? Use QG theory, and in one sentence explain your answer. (2%)

That ‘s it – 18% max.

Here is an extra credit question. It is a tough one, but it uses the same concepts introduced in class to understand midlatitude baroclinic instability from an IPV perspective.

Assume a subtropical region with anomalously high temperatures near the surface. This anomaly is embedded in an environment with an inverted meridional temperature gradient, i.e. it is warmer to the north. This happens in West Africa in summer, and the so-called Cape Verde hurricanes form there. Assume that the PV anomaly in this warm pool is sufficiently strong to induce a circulation that extends to the upper troposphere and that is in thermal wind balance. Now assume that the easterly flow, in the upper troposphere, advects a negative PV anomaly of about the same magnitude and size as the low-level one into the region.

(a) Draw a transect, from west to east, showing some isentropes and isotachs (x means into the page, . is out of the page). Show both the surface PV anomaly (- or + ??), and the upper level PV anomaly (-), at the time that the latter (UL) is a quarter wavelength to the east of the former (LL) anomaly. (3%)

(b) Draw two maps, one aloft and one at low levels, with basic-state gradients of P aloft and q at low levels, to show how in this relative position the UL anomaly will act to strengthen the LL anomaly, and vice versa. This theory has been used to explain tropical cyclogenesis. In a hurricane an UL ridge (cold pool) lies over a low- to mid-level warm pool. (2%)