Geoscience Reference
In-Depth Information
In the limit of small
δ
z
this means:
∂
P
=−
g
ρ
(3.3)
a
∂
z
Adiabatic lapse rates
The word
adiabatic
is used to describe changes in which there is no net change in
energy. Here it is used to indicate that we are defining how the temperature of a
parcel of air of volume
V
would change if it were moved vertically in the atmos-
phere in such a way that there was no net change in the internal energy of the
parcel. The vertical movement of a buoyant air parcel might, for example, be
approximately adiabatic if its ascent is rapid and there is no time for the parcel to
exchange energy with the surrounding air.
The first law of thermodynamics states that the heat added to a system is the
sum of the change in internal energy plus the work done by the system on its sur-
roundings. When applied to the case of an air parcel of volume
V
moving a small
distance
z
in the vertical and undergoing associated small changes
P
in pressure
δ
δ
and
δ
T
in temperature, this law implies:
m
VH* Vc T VP
δ=
ρ
d
−
d
(3.4)
a
p
H
* is the heat added per unit volume of air and
c
p
m
is the specific heat at
constant pressure of moist air. The specific heat of moist air varies slightly, but
because the amount of water vapor in moist air is typically just a few percent, it is
generally considered acceptable to use
c
p
where
δ
1.013 kJ kg
−1
K
−1
, i.e., the specific heat at
constant pressure for
dry
air in Equation (3.4) instead of
c
p
m
.
=
Dry adiabatic lapse rate
When vertical movement of the moist air is adiabatic and the air remains
unsaturated, (
H
*)
δ
=
0. Equation (3.4) can then be rewritten as:
Pc T
δ
=
rd
(3.5)
ap
Combining this last equation with Equation (3.2) gives:
g
T
z
δ
=−
p
δ
(3.6)
c
To a good approximation, both
g
and
c
p
are constants in the lower atmosphere.
Consequently, for vertical movements of an unsaturated air parcel that occur adiabati-
cally in the atmosphere, the resulting rate of temperature change is constant, i.e.:
