Geography Reference
In-Depth Information
9.4. Show that for stationary flow over an isolated ridge in the broad ridge limit
(k s
m s ), the group velocity vector is directed upward so that energy
cannot propagate up or downstream of the ridge.
9.5. An air parcel at 920 hPa with temperature 20˚C is saturated (mixing ratio
16gkg 1 ). Compute θ e for the parcel.
9.6. Suppose that the mass of air in an entraining cumulus updraft increases
exponentially with height so that m
m 0 e z/H
8kmandm 0 is
the mass at a reference level. If the updraft speed is3ms 1 at 2 km height,
what is its value at a height of 8 km, assuming that the updraft has zero net
buoyancy?
=
where H
=
9.7. Verify the approximate relationship between moist static energy and θ e given
by (9.41).
9.8. The azimuthal velocity component in some hurricanes is observed to have
a radial dependence given by v λ =
V 0 (r 0 /r) 2
for distances from the center
50 m s 1 and r 0
given by r
r 0 . Letting V 0
=
=
50 km, find the total
geopotential difference between the far field (r
→∞
) and r
=
r 0 , assuming
10 5 s 1 . At what distance from the
center does the Coriolis force equal the centrifugal force?
gradient wind balance and f 0 =
5
×
9.9. Starting with (9.61) derive the angular momentum form of the gradient wind
balance for an axisymmetric vortex given by (9.62).
MATLAB EXERCISES
M9.1. The MATLAB script surface front 1.m demonstrates the concentration
of an initial temperature gradient by an imposed deformation field. The
temperature field is initially taken to have a linear decrease in y: T (y)
=
10 2 y, where y is in kilometers. The horizontal wind is given
by the streamfunction ψ (x, y)
300
15k 1 sin (kx) sin (my ), where k
=−
=
3
π 3
10 6 . Evaluate and contour plot the defor-
mation field for this streamfunction, where deformation is defined as
10 6
×
and m
=
×
∂v ∂y . Run the model and observe where the temperature
gradient increases. Modify the code to plot the maximum temperature
gradient as a function of time. For how long does the gradient increase
approximately exponentially? What is the e-folding time for increase of
the temperature gradient at the origin?
M9.2. The MATLAB script profile 1.m and the function Tmoist.m use pressure,
temperature, and humidity data in the file sounding.dat to calculate and
graph vertical profiles of temperature, dewpoint, and the temperature cor-
responding to pseudoadiabatic ascent from the lifting condensation level
∂u ∂x
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