Geography Reference
In-Depth Information
Section 12.3.1. Run the script for mean wind values of 5, 10, 15, 20, and
25ms
−
1
. Describe how the geopotential and potential temperature per-
turbations change with changing mean wind speed. Explain these results
based on the arguments given in Section 12.3.1.
10
−
6
s
−
3
, N
10
−
2
s
−
1
,
M12.2.
For the situation of Problem 12.4 let J
0
=
=
10
4
m, and γ
10
−
5
s
−
1
. Make contour plots of the fields u, v
∗
, w
∗
, T and discuss the
relationship of these fields to the imposed diabatic heating.
M12.3.
The MATLAB script
sudden warming.m
provides an analogue to the
sudden stratospheric warmings on an extratropical β plane centered at
60
◦
N. The amplitude of a single planetary wave of zonal wave number
s
10
−
4
s
−
1
, l
10
−
6
m
−
1
, m
f
=
=
=
π/H
, w
her
e
H
=
2 is specified at the bottom boundary (taken to be the 16-
km level), and a time integration is carried out to determine the evolution
of the zonal mean wind in the stratosphere forced by the EP flux of the
specified wave. For the cases s
=
1ors
=
1 and 2, run the model for geopotential
heights between 100 and 400 m at a 50-m interval. For each case note
whether the flow tends toward steady state or repeated sudden warm-
ings. Modify the code to plot the time-height evolution of the EP flux
divergence for the case s
=
=
2 and forcing of 200 m.
M12.4.
The MATLAB script
qbo model.m
is a simplified one-dimensional model
of the equatorial QBO originally introduced by Plumb (1977). In this
model the mean zonal flow is forced by two waves of equal amplitude
at the lower boundary and equal and opposite phase speeds. The initial
mean wind profile has a weak westerly shear. If the model is run for suf-
ficiently weak forcing the mean wind approaches a steady state, but for
forcing greater than a critical amplitude a downward propagating oscilla-
tory solution occurs, with period dependent on the amplitude of forcing.
Run the script for a range of forcing between 0.04 and 0.40 and deter-
mine the approximate minimum forcing for a large-amplitude oscillatory
motion to occur, and the dependence of period on the forcing amplitude.
Modify the script to compute the time mean of the zonal wind over the
course of several oscillations. Try a case in which the eastward forcing
is 0.15 and the westward forcing is 0.075. How does the time mean wind
change in this case?
Suggested References
Brasseur and Solomon,
Aeronomy of the Middle Atmosphere
, has an excellent discussion of the chem-
istry of the stratosphere at an advanced level.
Andrews, Holton, and Leovy,
Middle Atmosphere Dynamics
, present a graduate-level treatment of the
dynamics of the stratosphere and mesosphere.
