Geography Reference
In-Depth Information
2.6.
Derive an expression for the density ρ that results when an air parcel initially
at pressure p
s
and density ρ
s
expands adiabatically to pressure p.
2.7.
An air parcel that has a temperature of 20˚C at the 1000-hPa level is lifted
dry adiabatically. What is its density when it reaches the 500-hPa level?
2.8.
Suppose an air parcel starts from rest at the 800-hPa level and rises vertically
to 500 hPa while maintaining a constant 1˚C temperature excess over the
environment. Assuming that the mean temperature of the 800- to 500-hPa
layer is 260 K, compute the energy released due to the work of the buoyancy
force. Assuming that all the released energy is realized as kinetic energy of
the parcel, what will the vertical velocity of the parcel be at 500 hPa?
2.9.
Show that for an atmosphere with an adiabatic lapse rate (i.e., constant
potential temperature) the geopotential height is given by
H
θ
1
−
p
p
0
R
c
p
=
Z
where p
0
is the pressure at Z
=
0 and H
θ
≡
c
p
θ/g
0
is the total geopotential
height of the atmosphere.
2.10.
In the
isentropic
coordinate system (see Section 4.6), potential temperature is
used as the vertical coordinate. Because potential temperature in adiabatic
flow is conserved following the motion, isentropic coordinates are useful
for tracing the actual paths of travel of individual air parcels. Show that
the transformation of the horizontal pressure gradient force from z to θ
coordinates is given by
1
ρ
∇
z
p
=
∇
θ
M
c
p
T+ is the
Montgomery streamfunction
.
2.11.
French scientists have developed a high-altitude balloon that remains at
constant potential temperature as it circles the earth. Suppose such a balloon
is in the lower equatorial stratosphere where the temperature is isothermal
at 200 K. If the balloon were displaced vertically from its equilibrium level
by a small distance δz it would tend to oscillate about the equilibrium level.
What is the period of this oscillation?
2.12.
Derive the approximate thermodynamic energy equation (2.55) by using the
scaling arguments of Sections 2.4 and 2.7.
where M
≡
MATLAB EXERCISES
M2.1.
The MATLAB script
standard T p.m
defines and plots the tempera-
ture and the lapse rate associated with the U.S. Standard Atmosphere as
