Geoscience Reference
In-Depth Information
where
g
is the acceleration due to gravity. For an isothermal atmosphere (temperature
constant with height) this yields (combination of Eqs. (
B.1
) and (
B.11
)):
gz
RT
−
pz pe
() ()
=
0
(B.12)
B.3 Potential Temperature
For an adiabatic process (d
q
= 0 in Eq. (
B.10
)) the combination of Eq. (
B.10
) with
the equation of state (
B.1
) yields a relationship between an ininitesimal temperature
change and an ininitesimal pressure change:
d
T
T
R
c
d
p
p
=
(B.13)
p
Integration of (
B.13
) between a reference pressure
p
0
and pressure
p
yields the deini-
tion of the potential temperature:
R
c
θ≡
p
p
p
T
0
(B.14)
Although the temperature changes during an adiabatic process, the potential temper-
ature does not change (i.e., is a conserved variable). Combination of Eqs. (
B.13
) and
(
B.11
) yields an expression for the temperature change with height for an adiabatic
processes in a hydrostatic equilibrium:
d
d
T
z
g
c
=−
(B.15)
p
which is called the dry adiabatic lapse rate.
B.4 Measures of Water Vapour Content
In the
Table B.2
various measures of water vapour content are summarized, indicating
their symbol, name, unit and an indication of their use.
As all variables given in the table relate to the same amount of water vapour in air,
they should all be related. Those relationships are explored in the text that follows.
Because water vapour pressure is the partial pressure of water vapour, it is directly
related to the absolute humidity:
e
=ρ
vv
RT
(B.16)
Search WWH ::
Custom Search