SAN FRANCISCO STATE UNIVERSITY Meteorology 430

DEPARTMENT OF GEOSCIENCES Fall
2010

Final Examination

250 Points

Name _______________________________________________

1. For
questions involving use of equations or calculations, lay out all equations carefully,
show all units, show all steps, number equations sequentially.

2. For
questions involving analysis or mapping techniques, use proper color conventions,
use proper mapping techniques (NO grease pencil on final copies).

3. This
examination is open book, open notes.

4. Answer
on separate sheets or on back of exam.

**Part A. Application of QG-omega
Equation (Map Set A) (140 points)**

This question refers
to the NAM 36 hour forecasts for 0000 UTC 12 December 2010: (a) 500 mb
Heights/500 mb Absolute Vorticity;
(b) the
surface isobars overlaid with 1000-500 mb thickness
contours for the same date and
time; (c) the absolute vorticity advection at
600 mb, 500 mb and 400 mb; and (d) the temperature advection at 500 mb.

You may assume that
real wind is geostrophic and the real absolute vorticity is the same as the absolute geostophic
vorticity.

The
simplified quasigeostrophic omega equation is

(i)
Qualitatively discuss the quasi-geostrophic diagnosed
omega that would occur at point A at 500 mb on the
basis of charts (a) and (b).
Be sure to discuss the contribution of each term, any assumptions you
used and the whether the net forcing indicates upward, downward or
indeterminate vertical motion. *This is comparable to what we have been
doing or have done in Metr 201/400/698. (50 points)*

**The question asks for a
qualitative assessment of the quasigeostrophic
forcing for omega at 500 mb at point
A. The charts provided are the 500
mb height and vorticity fields and the 1000-500 mb
thickness and surface pressure fields.
**

**Thus, the differential vorticity advection term, which should be assessed on the
basis of vorticity advection charts for levels
centering at 500 mb, and the
temperature advection term, which should be assessed on the basis of the
temperature advection at 500 mb, cannot be assessed
directly. **

**On the other hand, since
vorticity advection generally is of the same sign but
increases in magnitude with height, the sign of the vorticity
advection can be estimated on the basis of the sign of the vorticity
advection at the level in question.
Also, since temperature advection decreases in magnitude but keeps the
same sign from the lower to middle troposphere, the 500 mb temperature advection can be qualitatively
estimated on the basis of the temperature advection estimated on the basis of
the 1000-500 mb thickness advection by the surface geostrophic wind.
**

**With these simplifications/assumptions
in mind, there is 500 mb cyclonic vorticity advection returning forcing for upward motion and cold thickness (temperature)
advection returning forcing for downward motion at Point A. Thus the two forcing terms are
returning forcing for vertical motion of opposite signs, and this case is
indeterminate.
**

(ii) Qualitatively discuss discuss quasi-geostrophic
diagnosed omega that would occur at point A at 500 mb
on the basis of charts (c) and (d).
Be sure to discuss the contribution of each term in detail. *This
is a more accurate assessment of the nature of the forcing functions learned in
Metr 430.
(50 pts)*

**Charts (c) provide the
actual vorticity advection at levels beneath, at and
above the 500 mb level. Using these charts, one can see
that cyclonic (positive) vorticity advection is
increasing with height--there is differential cyclonic vorticity advection. This would return forcing for upward motion at Point
A. Chart (d) shows the actual
temperature advection at 500 mb. This is cold advection
which would return forcing for downward motion at Point A.
**

**Thus, the forcing terms,
more accurately assessed qualitatively, return forcing for vertical motion of
opposite sign at Point A. Again, the qualitative assessement does not allow us to judge which term will be larger and this case is indeterminate.
**

(iii) Discuss if your Metr
400/698-level analysis (i) would be backed by your Metr 430-level analysis in (ii). (20 points)

**The
two methods return the same results.
Thus, the assumptions made in (i) appear to be
**

**valid**** in this case. This case illustrates the justification for using the conventionally available charts equivalent to nam_vort **

**and nam_thick to assess the relative forcing of the two terms in the middle troposphere is valid.
**

(iv) Discuss how the forcing in the vorticity advection
term would be modulated by INCREASING the stability. (20 pts)

**The static stability
parameter is in the denominator of the multiplier for all of the forcing **

**terms****. Since the parameter is always greater
than zero for a stable atmosphere (relative to **

**the****
dry adiabatic rate), the greater the stability the larger and more positive the
parameter. **

**This has the effect of dampening
each forcing term. Since, for the case considered, the **

**vorticity**** advection term is forcing greater
upward motion, the impact of increasing the static **

**stability****
will be to decrease the resulting upward motion this term is diagnosing.**

**Part B. Dines Compensation**
(**Map Set B) (70 pts)**

Attached
find the WXP analyses of the 36 hour forecast NAM 300 mb
convergence and
500 mb vertical velocity for 00Z 12 December
2010. Examine the pattern at
the same location you used in Part A.

**1. Compute the 500 mb
vertical velocity (in cm/s) that would be expected on the basis of Dines
Compensation as expressed in the simplified continuity equation.**

** **

In
this case, you
can assume that divergence at 300 mb is a good
estimate of the net divergence in the layer from 500 mb
to the tropopause at 300 mb
and that 500 mb is the Level of Nondivergence. The forecast 300 mb height is 888 dm and the forecast 500 mb height is 540 dm.

**First
solve the equation for the 500 mb
vertical motion.**

**Substitute the values into the last
expression.**

**w _{500}=(3.0
X 10-^{5} s^{-1}) (3480 m) = 0.104 m s^{-1} = 10.4 cm s^{-1}**

2. Comment on the degree to which the
actual vertical velocity field is consistent with your result. Careful, the vertical velocity plot
shows omega, not w. However, I am
only asking you to compare the general nature of your result to the actual NAM
forecast vertical velocity.

**The
actual plot of omega indicates a maximum in upward motion at Point A. My result is c
**

**Part C. Interpretation of Cross-sections (Map Set C) (40 points)**

You are given cross-sections of potential temperature, equivalent potential temperature and temperature at the latitude of San Diego stretching along a line of latitude to Florida. You are also given (a) a surface chart showing cross section location and fronts (assume that they are correct) and (c) soundings for San Diego, Albuquerque and Tallahassee at 12 UTC.

1. Sketch in the position of the tropopause on the cross-section of potential temperature, and encircle areas where you would expect the value of the static stability parameter would be the greatest. (20 pts)

**The areas are shown on the cross-section of
potential temperature.**

2. Comment on how the cross-section of potential temperature is verified by the tropopause locations on (c). (20 pts)

**The soundings show that the tropopause is roughly at 200 mb. This
is consistent with the **

**tropopause**** location
indicated on my cross-section.**

Charts For

00 UTC
December 12, 2010

Part A
Charts

Part B
Charts

Part C
Charts--Cross-sections