Geoscience Reference
In-Depth Information
1000 hPa
Figure 6.8 Isobars in the
horizontal plane.
925 hPa
950 hPa
975 hPa
x
Length scale:
= 500 km
absolute angular momentum. Compare this velocity with observed zonal
velocities in
chapter 2.
6.3. The equation
dM
/
dt
0 expresses the principle of conservation of absolute
angular momentum. Substituting Eq. 6.13 into this equation, carry through
the differentiation to find the zonal component of the Coriolis force, Eq.
6.16. (
Hint
: Do not make the thin atmosphere approximation until after
you have carried through the differentiation and set
dz
/
dt
w
.)
6.4. Estimate the magnitude of each term in Eq. 6.25 using the figures of
chapter 2
to choose reasonable orders of magnitude for values for the
dependent variables. (For example, set
u
~
v
~ 10 m/s.) To focus on large
space scales, let
dx
~
dy
~ 1000 km and
dz
~ 10 km, which is about the
full depth of the troposphere. Make one calculation for middle latitudes
(f ~ 45°N or 45°S) and observe whether the irst-order balance of forces
changes in the tropics (f ~ 10°N or 10°S).
6.5. The peak elevation for Mount Rainier is 14,410 feet. Assuming that the
atmosphere is hydrostatic and isothermal at 270 K, estimate the surface
pressure on the top of Mount Rainier. Be sure to check that your answer is
reasonable.
6.6. To what degree of accuracy can the vertical component of the Coriolis
force (per unit mass) be neglected compared with the acceleration due to
gravity?
6.7. Across Texas, the meridional wind is steady and uniform at + 3 m/s (a
southerly wind). The zonal wind at Austin is measured at 4 m/s and at San
Antonio, about 130 km to the south, the zonal wind is 6 m/s. At what rate
will the zonal wind speed at Austin be accelerated due to advection?
6.8. Refer to the figures of
chapter 2
to find a reasonable value for the vertically
averaged tropospheric meridional temperature gradient in middle latitudes
(say, 40°S-60°S) during the Southern Hemisphere winter. Using this value,
integrate the zonal thermal wind equation (Eq. 6.51) from the surface to
200 hPa to estimate the zonal wind speed at 200 hPa. Assume that the
surface wind speed is 6 m/s. Compare your calculated zonal wind speed
with the observed. Are they similar? What might be sources of difference?
6.9.
Figure 6.9
is an idealization of the geopotential height distribution at 200
hPa over eastern Asia between 30ºN and 60ºN in July (see
Fig. 2.3b)
.
