Geoscience Reference
In-Depth Information
#
p
R
#
p
1
1
Φ−=
R dp ZZ
g
ln
−=
Td p
ln
.
(6.44)
&
1
2
1
2
p
p
2
2
Equation 6.44 indicates that the distance between two geopotential height
levels (known as the
thickness
) is proportional to the mass-weighted average
temperature between the two layers.
6.4 GEOSTROPHIC BALANCE
For large spatial scales (hundreds of kilometers or more), away from the sur-
face and the equator, the largest horizontal forces acting on parcels in the at-
mosphere are horizontal pressure gradient forces and Coriolis forces. This is
also the case in the ocean for space scales greater than about 50 km, away from
the coasts and below the mixed layer. When the horizontal pressure gradient
force is balanced by the Coriolis force, the flow is said to be in
geostrophic
balance.
The wind or ocean current speed for the case of geostrophic balance is known
as the
geostrophic velocity
and denoted
v
t t
It can be calculated by
setting the magnitude of the horizontal pressure gradient force (Eq. 6.33) equal
to that of the (approximate) Coriolis force (Eq. 6.26). In the
x
- direction,
vuivj
GGG
=+
.
1
2
p
1
2
p
,
2
Ω−=
v
sin
φ
0
v
=
(6.45)
&
ρ
2
x
G
f
x
2
ρ
and in the
y
- direction,
1
2
p
1
2
p
.
−
2
Ω
u
sin
φ
−
=
0
u
= −
(6.46)
&
ρ
2
y
G
f
y
2
ρ
In vector form,
#
d
ρ
p
t
v
.
vk
f
=
(6.47)
G
Note again that the Coriolis force couples the east/west and north/south di-
rections of motion in the rotating frame of reference. According to Eq. 6.45,
meridional geostrophic velocity is generated by
zonal
pressure gradients, and
zonal geostrophic velocity is generated by
meridional
pressure gradients ac-
cording to Eq. 6.46.
With pressure as a vertical coordinate,
1
2
Φ
Φ
1
t
t
t
t
,
v
vui vj
=+=−
y
i
+
f
x
j
(6.48)
GGG
2
2
f
or
v
t
fv
=
k
#
d
Φ
.
(6.49)
G
p
The magnitude of the geostrophic wind velocity,
V
G
, in
p
- coordinates is
2
Φ
1
.
2
2
Vu
=+=
v
(6.50)
G
G
G
f
n
2
