Geoscience Reference
In-Depth Information
(b)
(a)
750
750
Radiation
800
800
Subsidence
850
850
2230
CDT
2100
CDT
900
900
Turbulence
950
950
10
20
30
−
30
−
20
−
10
0
10
20
30
Temperature (
C)
Temperature change (
C/day)
Figure 18.5
(a) observed change in the profile of potential temperature over a flat uniform site in Oklahoma between 21:00
and 23:30 on a June day in 1983; (b) model-calculated contributions to this observed change associated with subsidence and
the divergence of sensible heat and net radiation. (Redrawn from Carlson and Stull, 1986, published with permission.)
may mean the divergence of net radiation with height is not necessarily small. In
this case the equation describing heat conservation in Table 17.5 simplifies to:
∂
q
∂
θ
∇
R
∂
(
w
′ ′
θ
)
+
= −
n
p
−
(18.3)
w
r
∂
t
∂
z
c
∂
z
a
Thus, the equation now includes terms that describe the nighttime subsidence and
net radiation divergence. Figure 18.5a shows an example of the evolution of the
profile of potential temperature observed over a flat uniform site in Oklahoma
between 21:00 and 23:30 on a June day in 1983, and Fig. 18.5b shows a model-
calculated estimate of how the three height dependent terms in Equation (18.3)
contributed to the observed change over this period.
Higher order moments
Prognostic equations for turbulent departures
In Chapter 17, the basic equations of atmospheric flow defined in Chapter 16 were
developed to provide a suite of equations describing the evolution of mean varia-
bles. These are referred to as
prognostic equations
for the mean atmospheric flow
variables
ū
,
−
,
−
,
θ
,
−
, etc. But it is also possible to derive a similar suite of prog-
nostic equations for the turbulent departures
u
′
,
v
′
,
w
′
,
q
′
,
q
′
, etc., as now illus-
trated for the example of vertical velocity.
Starting from Equation (16.38) and applying the Bossinesq approximation,
expanding each atmospheric variable as mean and fluctuating components, then
multiplying out the resulting equation gives:
