Geography Reference
In-Depth Information
10 6 m. The MATLAB script Chapter 6 plot1.m produces a contour
plot of the corresponding geopotential height field and provides a template
that can be modified to produce vector and contour plots of various fields
computed for this geopotential distribution in the domain
4
×
3000 km
x
1000 km. The template shows a contour
plot of and a quiver plot of the zonal mean wind U 0 . Derive the symbolic
expression for each of the fields in parts (a)-(d) and plot the horizontal
distributions in MATLAB. (a) Solve for the x and y components of the
geostrophic wind; plot as a quiver plot for time t
≤+
3000 km,
1000
y
0. (b) Solve for the
geostrophic relative vorticity and plot as a contour plot for time t
=
0. (c)
Solve for the relative vorticity advection by the mean zonal wind and plot as
a contour plot for time t
=
10 11 m 1 s 1 ,
solve for the planetary vorticity advection and plot as a contour plot for
time t
=
0. (d) Assuming that β
=
1.67
×
0.
M6.2. For the situation of Problem M6.1: (a) Use the quasi-geostrophic vorticity
equation to solve for the divergence field at 500 hPa and plot the vorticity
tendency, absolute vorticity advection, and divergence fields as contour
plots for time t
=
0 using MATLAB. (b) What is the phase difference
between the divergence field and the vorticity field? Explain in physical
terms (referring to the vorticity balance) why the divergence field has the
phase relationship to vorticity that you observe.
M6.3. Equations (6.16) and (6.17) can be solved for the ageostrophic wind (u a ,v a )
if the geostrophic wind components are known. For the situation of Prob-
lem M6.1, solve for the ageostrophic wind. For simplicity you may approxi-
mate the advective terms by letting V g ·∇
=
U∂u g ∂x and V g ·∇
u g
v g
U∂v g ∂x. Note that the ageostrophic wind has both a divergent and a
nondivergent part. (The nondivergent part of the ageostrophic wind in this
example is proportional to the β-effect.) Compute the divergence of the
ageostrophic wind and plot as a contour map in MATLAB. Compare with
the results of Problem M6.2. Plot the divergent part of the ageostrophic
wind as a quiver plot in MATLAB for time t
0. Compute the vorticity of
the ageostrophic wind and plot as a contour map in MATLAB. Overlay this
plot with a quiver plot showing the nondivergent part of the ageostrophic
wind. Explain why vorticity has an ageostrophic component in this case.
=
M6.4. The MATLAB script pv anomaly.m contains code to compute and plot
the vertical distribution of the geopotential anomaly induced by quasi-
geostrophic potential vorticity advection confined to above the 250-hPa
level. The example given in Fig. 6.11 is for an infinite meridional scale.
Modify the code to compute the dependence of the ratio of the response at
the 600-hPa level to the response at the 100-hPa level for zonal wavelength
6000 km as the meridional scale is varied from 12,000 to 1000 km. Plot
your results as a line graph in MATLAB.
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