Geoscience Reference
In-Depth Information
∂
T
z
=−Γ
(3.7)
∂
g
/
c
p
is the
dry adiabatic lapse rate
which is conventionally defined to be
positive, and which has the value 0.00968 K m
−1
or 9.68 K km
−1
.
where
Γ
=
Moist adiabatic lapse rate
When vertical movement of moist air is adiabatic but the air is saturated,
condensation can occur in the air parcel as it ascends. If its specific humidity
decreases by an amount
q
sat
, latent heat is released and the internal energy of the
parcel changes by an amount
δ
δ
H
*
=
(
l
.
r
a
.
δ
q
sat
). Equation (3.4) therefore becomes:
Vq Vc TVP
λρ δ
=
ρ
δ
−
δ
(3.8)
a
sat
a
p
Combining this last equation with Equation (3.2), rearranging in the limit gives an
equation similar to Equation (3.7), i.e.:
∂
T
z
=−Γ
(3.9)
m
∂
Γ
m
is the
moist adiabatic lapse rate
given by:
where
⎛
⎞
q
λ
∂
sat
Γ=Γ−
(3.10)
⎜
⎟
m
c
∂
z
⎝
⎠
p
Because the temperature of the atmosphere normally decreases with height the
saturated specific humidity also decreases with height, hence the rate at which the
temperature falls in a parcel of air ascending in a saturated atmosphere is
less
than
in an unsaturated atmosphere, i.e.,
. Because
q
sat
depends on temperature,
the
moist adiabatic lapse rate
also depends on temperature. For a specific value of
saturated vapor pressure, because the value of
q
sat
depends on pressure, see
Equation (2.9),
Γ
m
<
Γ
Γ
m
also depends on atmospheric pressure.
Environmental lapse rate
The actual measured rate at which atmospheric temperature changes away from the
ground on a particular day at a particular place depends on the history of heat inputs
and outputs to the air overhead. The locally observed atmospheric lapse rate, which
is called the
environmental lapse rate
,
Γ
e
, therefore varies with location and time.
Near the surface the lapse rate may well be approximately constant, often with
a value intermediate to the dry and moist adiabatic lapse rates. The temperature
