SAN FRANCISCO STATE UNIVERSITY                                                               Meteorology 430

DEPARTMENT OF GEOSCIENCES                                                                       Fall 2010

Midterm #2 Key

250 Points

Part A. Surface Charts (100 points)

1. The first chart included in the group of charts labeled “Part A  Charts” is a print of sfcwxall showing

surface observations in the eastern Pacific, and nam_maps nam_thick for  12 UTC 12/11/06.  First, draw advection arrows and do a frontal analysis on nam_thick. (30 points)

See chart at bottom.

2. Using your results in 1 above do a surface synoptic analysis on the unanalyzed chart IN THE DASHED BOX.  The analysis will be graded for meteorological accuracy, proper color and analysis conventions AND neatness.  Use the other charts provided (and any other map or chart included in this exam) for insight.  Also, although you will not be contouring outside the dashed box, you should use the observations (that are readable) outside the box to help you (70 points)

See chart at bottom.

Part B. Relation of Upper Air to Surface Patterns (150 points)

1. The simplified vorticity equation in natural coordinates is (1)

a.  Name and describe each term in equation (1).  Then identify the term  that can be dropped from              equation (2) when applying it to the synoptic scale vorticity and divergence fields  in the upper                     troposphere?  (Don't explain WHY the simplification is made. Just state what it is and what the                resulting equation looks like). (50 points)

The handy-dandy handout that you should have used was this one. This handout was the centerpoint of our whole series of discussions in which we scaled the simplified vorticity equation.

The terms in equation 1 are as follows: In the upper troposphere, the vertical advection of absolute vorticity is zero, since there is no vertical motion or it is negligible, in the upper troposphere.  This term can be dropped from Equation (1).

The local change in absolute vorticity is very small since it is dominated by the other terms.  Thus, the local change also can be dropped from the equation on an order of magnitude basis.

This  leaves the remaining terms (a) absolute vorticity advection;  (b) and the horizontal divergence term.  The resulting equation states that vorticity advection patterns can be used to diagnose or deduce divergence patterns in the upper troposphere.

Making the substitutions and solving for the horizontal divergence, equation (1) becomes: (2)

b. In the group of charts labeled “Part B Charts,” you will find the 300 mb absolute vorticity advection contour plot and the contour plot of the 300 mb absolute vorticity field for 1200 UTC 12/11/06.  Using the equation you simplified in the previous questions, provide an estimate of the 300 mb horizontal divergence at location A.  (Show all steps!) (40 points)

From the group of charts, the following values can be obtained:  (a) absolute vorticity advection = 9 X 10 -9 s-2;  (b) absolute vorticity = 4 X 10 -5 s-1.  Substituting these values into the right side of equation (2) gives a divergence at point A of 22.5 X 10 -5 s-1.

c.  Compare/contrast the divergence you computed to that actually observed, as depicted on the contour        plot of the actual 300 mb divergence field provided in Part B Charts. (20 points)

As one would expect from a value of divergence obtained from an approximated equation, the sign of the divergence is correct, but the estimate was one order of magnitude larger than the actual value.

d. One of the charts included in Part B Charts shows the surface pressure tendency for the 3 hours ending.  Does the pattern at A correspond to what you would expect from Dine’s Compensation, assuming that the sign of 300 mb divergence field is an estimate of the net divergence over the region?  Explain. (20 points)

A version of Dine's Compensation is the pressure tendency equation which states that surface pressure change is the result of the net divergence out of the air column extending from the surface to the top of the troposphere.  If one assumes that the sign of the net divergence is just the divergence at 300 mb, since upper tropospheric divergence nearly always exceeds the compensating lower level convergence, then one should expect surface pressure falls at A.  That is what was forecast to occur.

e.  Compare the 500 mb vertical velocity field (given in Part B Charts) for 1200 UTC 12/11/06 with your results in (b) and (c).  Do the vertical velocity values at A qualitatively correspond to what you would expect from the pressure tendency equation, assuming that the sign of 300 mb divergence field is an estimate of the net divergence over the region? Explain. (20 points)

Dines Compensation states that upper tropospheric divergence should be compensated by mid-tropospheric upwards motion, and compensating surface convergence. Since upper tropospheric divergence almost always exceeds lower level convergence, the pressure tendency equation states that upper divergence, upward motion in the mid troposphere and surface pressure falls should be colocated. For the case shown here, upper tropospheric divergence (and surface pressure falls) should be associated with rising motion at the level of non-divergence at location A.  That is verified by the analyses.  