Geography Reference
In-Depth Information
exp
−
b
x
2
y
2
where b is a constant. Run the model for
ζ (x, y)
=
+
10
−
7
km
−
2
. Show
in a table or line plot the dependence of the ratio of the horizontal scales
on which vorticity and the streamfunction decay to one-half of their max-
imum values as a function of the parameter b. Note that for geostrophic
motions (with constant Coriolis parameter), the streamfunction defined
here is proportional to geopotential height. What can you conclude from
this exercise about the information content of a 500-hPa height map versus
that of a map of the 500-hPa vorticity field?
10
−
4
km
−
2
several values of b from b
=
1
×
to 4
×
M4.2.
The MATLAB scripts
geowinds 1.m
(to be used when the mapping tool-
box is available) and
geowinds 2.m
(to be used if no mapping toolbox is
available) contain contour plots showing the observed 500-hPa height and
horizontal wind fields for November 10, 1998 in the North American sec-
tor. Also shown is a color plot of the magnitude of the 500-hPa wind with
height contours superposed. Using centered difference formulas (see Sec-
tion 13.3.1), compute the geostrophic wind components, the magnitude of
the geostrophic wind, the relative vorticity, the vorticity of the geostrophic
wind, and the vorticity minus vorticity of the geostrophic wind. Following
the models of Figs. 1 and 2, superpose these fields on the maps of the
500-hPa height field. Explain the distribution and the sign of regions with
large differences between vorticity and geostrophic vorticity in terms of
the force balances that were studied in Chapter 3.
Suggested References
Williams and Elder,
Fluid Physics for Oceanographers and Physicists
, provides an introduction to
vorticity dynamics at an elementary level. This topic also provides a good general introduction to
fluid dynamics.
Acheson,
Elementary Fluid Dynamics
, provides a good introduction to vorticity at a graduate level.
Hoskins et al. (1985) provide an advanced discussion of Ertel potential vorticity and its uses in diagnosis
and prediction of synoptic-scale disturbances.
