SAN FRANCISCO STATE UNIVERSITY                         METEOROLOGY 403         

DEPARTMENT OF GEOSCIENCES                                  Fall 2004

                    

Homework No. 2

Due Thursday September 16, 2004

 

Reading:           Bottom of page 84 to 91 (Translation and Divergence)

                        pp 181 (Thermal Wind) to 190

 

Lay out all steps.  Number all equations sequentially.  Maps/charts are to be neatly analyzed using correct color conventions. 

 

1.      Attached find the sounding for KMIA (Miami, FL) for 12 UTC 7 September 2004 and that for 12 UTC 24 May 2004 for KOUN (Oklahoma City – really, Oklahoma University Norman Campus) plotted on a Skew-T/Ln P Diagram.

(a)           Examine the two soundings and describe why the KOUN sounding is indeed an example of a "loaded gun" while that for KMIA is not.  (Before you attempt to do that, please write down the definition of a "loaded gun" sounding.)

Loaded Gun Sounding -- a sounding characterized by a deep moist (i.e., sfc to 850 mb) wet adiabatic , and relatively cool layer surmounted by a potentially warmer and very dry layer with steep lapse rate. The "interface" between these two layers is an inversion or "cap". This cap allows diurnal heating to be "stored" and well-mixed in the layer beneath the inversion, resulting in surface parcels (whether defined on the basis of surface conditions or a mixed parcel) that have greater and greater CAPE. The term "loaded gun" refers to the fact that surface parcels do not "realize" this CAPE unless the cap is reduced to 50 J/kg CIN or less.

(b)          Evaluate the KMIA sounding for convective potential (only due to parcel lift—you don"t have to transform the sounding for afternoon heating)

 

 

2.      Write out the general vector expression for the three dimensional wind in rectangular coordinates?  In natural coordinates?

Rectangular Coordinates
U = u i + v j + w k
Natural Coordinates
V = V t + w k

3.      Write out the equation of  motion in natural coordinates (Eq. 4.1.108 and 109).  Assume that it is early morning, and winds are calm.  How is the above equation set simplified?  (In other words, simply on the basis of these conditions).

t component
(1)
n component
(2)

If winds are calm, there is no "n" component. You are left with equation (1) (Note: just because the wind is zero doesn't mean that dV/dt is zero. What it meanst Vinitial is zero in the finite difference expression (Vfinal - Viniital)/Delta t