Geography Reference
In-Depth Information
Equations (11.50), (11.51), and (11.53) are a closed set for prediction of the
boundary layer variables u, v, for a specified boundary layer perturbation virtual
temperature θ
v
. However, because the parameter ε depends on the presence or
absence of convection, the system can only be solved by iteration through using
(11.24) to test for the presence of convection. This model can be used to compute
the steady surface circulation. A sample calculation of the anomalous circulation
for temperature anomalies corresponding to a typical ENSO event is shown in
Fig. 11.16. Note that the region of convergence is narrower than the region of
warm SST anomalies due to the convective feedback in the boundary layer model.
PROBLEMS
11.1.
Suppose that the relative vorticity at the top of an Ekman layer at 15
◦
Nis
ζ
10 m
2
s
−
1
and the water vapor mixing ratio at the top of the Ekman layer be 12 g kg
−
1
.
Use the method of Section 11.3 to estimate the precipitation rate due to
moisture convergence in the Ekman layer.
10
−
5
s
−
1
. Let the eddy viscosity coefficient be K
m
=
=
2
×
11.2.
As mentioned in Section 11.1.3, barotropic instability is a possible energy
source for some equatorial disturbances. Consider the following profile for
an easterly jet near the equator:
u
0
sin
2
[l
(
y
u
(
y
)
¯
=−
−
y
0
)
]
where u
0
, y
0
, and l are constants and y is the distance from the equator.
Determine the necessary conditions for this profile to be barotropically
unstable.
11.3.
Show that the nonlinear terms in the balance equation (11.15)
2
1
ψ
2
ψ
G (x, y)
≡−
∇
2
∇
ψ
·∇
+
∇·
∇
ψ
∇
may be written in Cartesian coordinates as
2
∂
2
ψ/∂x
2
∂
2
ψ/∂y
2
∂
2
ψ/∂x∂y
2
G (x, y)
=
−
11.4.
With the aid of the results of Problem 11.3, show that if f is assumed to
be constant the balance equation (11.15) is equivalent to the gradient wind
equation (3.15) for a circularly symmetric regular low with geopotential
perturbation given by
0
x
2
y
2
/L
2
=
+
