Geoscience Reference
In-Depth Information
and how do these vary seasonally to cause changes in the energy content of the
atmospheric column?
Going through each of the terms on the right of Equation
3.3
, the tendency in
atmospheric energy storage is represented as:
ps
(
)
∫
(3.3)
∂∂=∂ ∂
At
E
/
/
t
1
/
g
cT kLq
+ ++
Φ
dp
p
S
o
where p is pressure, T is temperature in Kelvin, c
p
is the specific heat of the atmo-
sphere at a constant pressure (1005.7 J K
−1
kg
−1
, c
p
T= c
v
T + pV, where c
v
is the
specific heat at constant column, and V is specific volume), k is kinetic energy, L is
the latent heat of evaporation (2.501 × 10
6
J kg
−1
), q is specific humidity (the ratio of
the mass of water vapor in a sample to the total mass of air in a sample), g is gravi-
tational acceleration (approximately 9.81 m s
−2
), and Φ
s
is the surface geopotential.
The last is not a function of pressure (see Trenberth et al.,
2001
). Each of the terms
in parentheses has units of Joules per kilogram (J kg
−1
); that is, energy per unit
mass. Vertical integration by dp and division by the gravitational acceleration yields
units of J m
−2
. Taking the tendency (the time change) in the storage results in the
final desired units of W m
−2
. Hence, atmospheric energy increases with a rise in the
air temperature, a rise in moisture content and a rise in kinetic energy. The vertical
integral of c
p
T, which is the total enthalpy of the atmospheric column in question,
contains both the internal energy and potential energy; if heat is added to the atmo-
sphere, its temperature - and hence internal energy - increases, while at the same
time, potential energy increases because the center of gravity of the atmosphere
shifts upward (i.e., work is done). In the framework of Equation
3.4
, liquid water
is taken to be the zero latent heat state. This means that snowfall would appear as
an energy gain in the atmosphere and an energy loss at the surface. The latent heat
content of the atmosphere also ignores liquid water or ice in the atmosphere such as
that contained in clouds.
As for the convergence of the horizontal flux of atmospheric energy,
ps
(
)
∫
−∇•=−∇•
F
1/
gcT
+ ++
Φ
Lqk dp
v
(3.4)
A
p
o
Here,
v
is the horizontal wind vector. This says that if more energy is being trans-
ported into the column by the horizontal wind than is being transported out of
the column by the horizontal wind, then there is an energy flux convergence that
contributes to an increase in the atmospheric energy storage. Conversely, if more
energy is being transported out of the column by the horizontal wind than is being
transported into of the column by the horizontal wind, then there is an energy flux
divergence (negative convergence) that contributes to a decrease in the atmospheric
energy storage.
The final term in Equation
3.2
, the net surface flux F
sfc
, is the net energy transfer
between the atmospheric column and the underlying column. It is defined here as
positive upward. If there is a net transfer of energy from the underlying column into
the atmospheric column (a positive net surface flux), then this counts as an energy
