Excellent work. Nice graphs, nicely labeled also …. 5.7/6
ATSC5160 Homework2
Qing Yang
1. 2/2
In omega equation,
2
 1
 2
 
2  



f
  f 0 Vg    2  
0

2
p 
p 

 f0


  
 ----------(1)
f    2 Vg   

p




the left hand side term acts to spread the response to a localized forcing.
Because the forcing in the equation tends to be a maximum in the
midtroposphere and  is required to vanish at the upper and lower
boundaries, for qualitative discussion it is permissible to assume that 
has sinusoidal behavior not only in the horizontal but also in the vertical:
=W0sin(p/p0)sin(kx)sin(ly)
we can write
 2
f
2 
  f 02 2   [ (k 2  l 2 )  ( 0 ) 2 ] ---------------(2)
P 
p0

which shows that the left hand side term in the omega equation is
proportional -.
Combine equation 1&2,
 
  
 1
f0
Vg    2  


f
p 
 f0
[ (k 2  l 2 )  ( 0 ) 2 ] 
p0
1


   
 
f    2 Vg   

p

 


It shows that the laplacian of omega is reverse proportional to the static
stability. It tends to decrease the effect of the three factors on the right
side of equation (1) on vertical motion. Based on the same magnitude of
changing, large value of static stability can cause small local minimum of
omega, so it cause less vertical upward motion very good. As a result,
cyclogenesis are hastened by low values of static stability and are slowed
down by high values. If local sounding is unstable, then static stability is
negative, so convection can be triggered by small disturbance. This is
conflict with the no vertical motion assumption of quasigeostrophic
atmosphere. So static stability must be positive in this situation yes.
According to above consideration, it is shown that static stability is a
spoiling term which will decrease the vertical upward motion indicated
by quasigeostrophic effect.
2. 2/2
b.
Q3: Cold front is located at the place of strongest surface temperature
gradient and apparent change of wind direction at the surface. At the region
of backing region, the geostrophic wind has clockwise turning, means cold
air advection.
Q4: see chart.
Q5:At the surface the temperature gradient is strongest at the location of
cold front and the location of temperature gradient tilting to west with
height, so there is moderate temperature gradient at the lower troposphere
west of the cold front. The temperature gradient appears to be decrease with
height, at the level of 300mb, the temperature gradient is 0, which
correspond to the level of jet core. The geostrophic wind is backing in this
region as shown in the region of CAA, where the thermal wind is pointed
into the paper, that is almost northward. Upper level wind is the lower wind
plus thermal wind, so at this region, the goestrophic wind is getting more
and more southernly, and wind speed getting bigger and bigger with height
till the horizontal level of 300mb, where temperature gradient is near 0, and
wind speed is biggest at this level. Very good
3.
1.7/2
show location of cross section LBF-ILN
b. From this chart, agostrophic wind at the entrance region of upper level jet
across the isobar to the low pressure. And at the exit region, ageostrophic
wind also across the isobar to the higher pressure. Analysing pressure
gradient force and corriolice Coriolis force balancing, we know that the
cross isobaric ageostrophic wind at the entrance and exit region allows the
geostrophic wind to accelerate and decelerate respectively. At the region of
the upper level trough ageostrophic wind is blowing reverse the direction of
geostrophic wind, corresponding sub-geostrophic flow, and at the region of
upper level ridge, ageostrophic wind is blowing along the direction of
geostrophic wind, corresponding to super geostrophic flow. For corriolice
force is pointing perpendicular to isobar to the high pressure, pressure
gradient force has the different direction. At the ridge region, corriolice force
should be bigger than pressure gradient force to generate centripetal force,
that means supergeostrophic wind. At the trough region, corrioce force
should be smaller than pressure gradient force to have centripetal force
pointing at the same direction, so there is subgeostrophic wind. Very good
c.
d. The component of ageostrophic wind in this cross section shows that
ahead of frontal region there is large area of rising motion, above the cold
region of frontal region, there is sinking motion. It coherent with the jet
stream pattern at the entrance region yes but the wave is quite short and
highly curved so I think the ageostrophic upper-level divergence between
the sub-geostrophic trof and supergeostrophic ridge is more important (in
terms of QG thinking, PVA). For northen ageostrophic flow across the
isobar, there is convergence at the upper air of LBF side and divergence at
the upper air of ILN side, so corresponding the rising and sinking motion
respectively. Above the cold frontal region ageotrophic wind is more eastly,
and there is temperature gradient above the cold frontal region, so there is
cold front aloft. By the mixing ratio line, there is dry line in the cold frontal
region. It is not a dryline, it is a cold front because a dry line is characterized by
ONLY moisture, no temperature gradient. At the region1 shown in the the picture,
equivalent ??? potential temperature is decreasing with height, where
specifically is de/dz negative (potential instability) ?? this region has CAPE and
has possibility for deep convection.