Geography Reference
In-Depth Information
APPENDIX D
Moisture Variables
D.1
EQUIVALENT POTENTIAL TEMPERATURE
A mathematical expression for θ
e
can be derived by applying the first law of
thermodynamics to a mixture of 1 kg dry air plus q kg of water vapor (q, called
the
mixing ratio
, is usually expressed as grams of vapor per kilogram of dry air).
If the parcel is not saturated, the dry air satisfies the energy equation
−
d (p
e)
−
=
c
p
dT
RT
0
(D.1)
p
−
e
and the water vapor satisfies
R
∗
m
v
de
e
c
pv
dT
−
T
=
0
(D.2)
where the motion is assumed to be adiabatic. Here, e is the partial pressure of
the water vapor, c
pv
the specific heat at constant pressure for the vapor, R
∗
the
universal gas constant, and m
v
the molecular weight of water. If the parcel is
saturated, then consdensation of
−
dq
s
kg vapor per kilogram dry air will heat the
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