Geography Reference
In-Depth Information
χ
-
δχ
χ
S
2
S
3
S
1
χ
+
δχ
latitude
Fig. 12.6
Projections of parcel motions on the meridional plane for planetary waves in westerlies
with diabatic heating at low latitudes and diabatic cooling at high latitudes. Thin dashed
lines show tilting of iso-surfaces of tracer mixing ratio due to transport by the diabatic
circulation.
12.2.2
The Transformed Eulerian Mean
In many circumstances the transformed Eulerian mean (TEM) equations intro-
duced in Section 10.2.2 provide a useful model for the study of global-scale middle
atmospheric transport. Recall that in this formulation the zonal-mean momentum,
mass continuity, thermodynamic energy, and thermal wind equations have the
form
1
f
0
v
∗
=
ρ
−
1
0
∂u/∂t
−
∇·
F
+
X
≡
G
(12.1)
α
r
T
T
r
(y, z, t)
N
2
HR
−
1
w
∗
=−
∂T/∂t
+
−
(12.2)
∂
ρ
0
w
∗
/∂z
∂v
∗
/∂y
ρ
−
1
0
+
=
0
(12.3)
RH
−
1
∂T/∂y
0 (12.4)
Here the residual circulation (v
∗
,
w
∗
) is as defined in (10.16a,b),
F
designates the
EP flux due to large-scale e
dd
ies, X is the zonal force due to small-scale eddies (e.
g., gravity wave drag), and G designates the total
zonal force
. In (12.2) the diabatic
heating is approximated in terms of a N
ew
tonian relaxation proportional to the
depart
ur
e of the zonal mean temperature T(y,z,t)from its radiative equilibrium
value T
r
(y,z,t)where α
r
is the Newtonian cooling rate.
To understand how eddies can lead to departures of the zonal-mean temperature
distribution in the middle atmosphere from its radiatively determined state, we
use the TEM system of equations to consider an idealized model of extratropical
forcing. The dependence of the
c
irculation on forcing frequency can be examined
in an idealized model in which T
r
is taken to be a function of height alone and the
f
0
∂u/∂z
+
=
1
As in Chapter 10 we express the log-pressure coordinate simply as z rather than z
∗
.
