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 ÒPart A ChartsÓ 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 ÒPart B Charts,Ó 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 DineÕs 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. *