Geoscience Reference
In-Depth Information
According to Eq. 6.50, higher geostrophic wind speeds occur where horizontal
geopotential height gradients are large.
Figure 2.14
portrays a clear example of
this relationship since the 200 hPa wind vectors are larger in regions where the
geopotential height lines pinch closer together.
According to Eq. 6.49, the geostrophic wind is perpendicular to geopotential
(and geopotential height) gradients in the horizontal plane and, therefore, flows
parallel to geopotential height lines. This explains the relationship between the
wind direction and geopotential height lines in
Figures 2.13
and
2.14.
The rela-
tionship breaks down at low latitudes because the Coriolis parameter,
f
, becomes
small and the Coriolis force is less able to balance pressure gradients forces. At
these low latitudes, the low is more directly down the pressure gradient.
As diagrammed in
Figure 6.6,
application of the right-hand rule to Eq. 6.49
in the Northern Hemisphere (
f
> 0) indicates that low heights (or pressures) are
located to the left of the wind direction. In the Southern Hemisphere, where
f
< 0, low heights lie to the right of the geostrophic wind vector. Again, these re-
lationships are seen clearly in
Figures 2.13
and
2.14
and explain why cyclonic
low (low about a low-pressure system), for example, is counterclockwise in
the Northern Hemisphere but clockwise in the Southern Hemisphere.
One great advantage of using pressure instead of elevation as a vertical co-
ordinate is that density does not appear explicitly in the geostrophic wind rela-
tion. This makes it easy to derive an expression for the geostrophic wind shear
(the vertical change in the geostrophic wind) by taking derivatives with respect
to pressure. From Eq. 6.48,
2
2
u
u
1
2
2
Φ
2
1
2
RT
R
2
T
.
G
G
=−
=
=
(6.51)
f
p
&
2
p
f
py
f
yp
2
2
2
y
2
ln
p
f
Similarly,
2
v
R
2
T
.
G
=−
(6.52)
2
x
2
ln
p
f
In vector form,
2
v
v
R
kT
t
G
=−
#
d
.
(6.53)
p
2
ln
p
f
(a)
(b)
Northern Hemisphere
Southern Hemisphere
ν
G
ν
G
L
H
H
L
Pressure gradient force
Coriolis force
Coriolis force
Pressure gradient force
Figure 6.6. Balance of forces in the Northern Hemisphere and the Southern
Hemisphere for geostrophic conditions.
