Geoscience Reference
In-Depth Information
10
10
10
8
8
8
6
6
6
4
4
4
Figure 3.2
Temperature
lapse rate, and pressure and
density variations through
the troposphere of the US
Standard Atmosphere.
2
2
2
0
0
0
150
250
0
50
100
0.0
0.5
Air density (kg m
−
3
)
1.0
1.5
Temperature (
K)
Pressure (kPa)
Potential temperature
For an adiabatic atmosphere,
Γ
local
=
g
/
c
p
and Equation (3.14) can therefore be
re-written as:
R
c
a
p
TT
⎛⎞
P
=
2
(3.15)
⎜
⎝⎠
2
1
1
This equation can be used to correct temperature variations in the atmosphere for
the effect of the hydrostatic pressure gradient. If such corrections are made, any
remnant variations in this corrected temperature profile are those which may result
in vertical heat flow as discussed earlier. It is convenient to use Equation (3.15)
to renormalize the observed temperature profile to correspond to a specific value
of pressure, i.e., 100 kPa. When corrected in this way the resulting temperature is
called the
potential temperature,
q
. Potential temperature is therefore defined to be
the temperature that a parcel of air anywhere in the atmosphere would have if it
were to be brought adiabatically to a pressure of 100 kPa. It is calculated from the
actual temperature and pressure using the equation:
R
c
a
p
⎛
100
⎞
θ
=
T
(3.16)
⎜
⎟
⎝
⎠
P
For a parcel of air moving up or down in an adiabatic atmosphere the value of the
potential temperature is conserved and remains constant with height. To a good
approximation, the vertical gradient of the potential temperature can be calculated
from that for temperature using:
∂
=+Γ
∂∂
θ
T
(3.17)
d
z
z
