Geoscience Reference
In-Depth Information
This is one of Poisson's equations, which express the constraints on changes in
the three state variables of an ideal gas under adiabatic conditions.
Consider a parcel of air with temperature
T
S
originating at the surface.
Equation 5.5 indicates how the temperature of that parcel will change as it
moves around in the atmosphere experiencing various values of air pressure,
p
,
away from the surface. (As an air parcel moves, its pressure equilibrates with
the environmental air pressure very quickly.) According to Eq. 5.3, with
Q
0,
the parcel expands and cools or contracts and warms as pressure changes,
even though no heat is added to the parcel. These temperature changes are
adiabatic
. If the parcel travels back to the surface, it recovers its original tem-
perature,
T
S
. In other words,
T
S
is
conserved
as the parcel moves adiabatically
in the atmosphere.
Based on this idea of a conserved temperature under adiabatic conditions,
potential temperature, , is defined as the temperature a parcel would have if
brought adiabatically to the surface pressure,
p
S
:
p
Rc
p
S
/
T
fp
(5.6)
.
p
In the absence of information about surface pressure,
p
s
in Eq. 5.6 is often
replaced by a reference pressure,
p
0
, which can be set equal to the globally
averaged surface pressure of 1013 hPa, or simply to 1000 hPa. The adiabatic
thermodynamic equation can then be written
d
Θ
=
0.
(5.7)
dt
5.3 HEAT BALANCE EQUATIONS
Constructing heat balance equations allows us to generate expressions that
can be used to understand the flow of heat through the climate system. In an
equilibrium heat balance equation, heat input equals heat output and there is
no temperature trend. If a system (or subsystem) is not in thermal equilibrium,
a temperature trend will occur.
EQUILIBRIUM HEAT BALANCES
At the top of the atmosphere, only radiative processes need be considered in
the heat balance. Energy enters the climate system in the form of shortwave
radiation and the earth system emits longwave radiation. If the earth system is
assumed to be in radiative equilibrium with the sun, the heat balance at the top
of the atmosphere is simply
S
(1
−
α
)
0
4
E
=
εσ
T
,
(5.8)
4
as discussed in section 4.2.
