Moisture Variables
on Skew T Log P Diagram
AOS 330 LAB 8
List of Variables
•
•
•
•
•
•
•
•
•
•
Mixing ratio (w)
Saturation mixing ratio (ws)
Specific Humidity (q)
Vapor pressure (ev)
Saturation vapor pressure (es)
Relative humidity (RH)
Dewpoint (Td)
Dewpoint Depression T
d
Virtual Temperature (Tv)
Wet-Bulb Temperature (Tw)
Mixing Ratio (w or rv)
• Mixing ratio (rv) – a way to tell how much
vapor there is relative to a mass of dry air
• It is conserved as long as there is no
condensation or evaporation.
Rd
-1

 0.622
• Units : g kg
Rv
ev
v RvT ev Rd
ev
rv 



pd
d
pd Rv p  ev

Rd T
Specific Humidity (q)
• Mass of water vapor per unit mass of moist air
v
v
rv
ev
ev
qv 




 d  v 1 rv p  ev (1 )
p
qv
rv 
1 qv
• But mass of water vapor is very small compare to the
total mass (~1-2% of the total mass)

•
ev
ev

• rv 
, (ev<< p)
p  ev
p
rv  q 
ev
p
Vapor Pressure (ev)
• ev – partial pressure of vapor in (Pa)
• es – saturation vapor pressure over plane
surface of pure water
Saturation Vapor Pressure (es)
• Vapor pressure ev - most directly determines
whether water vapor is saturated or not.
• ev < es(T) subsaturated, evaporation
• ev = es(T) saturated
• ev > es(T) supersaturated, condensation
• es only depends on temperature.
• es(T) increases with increasing temperature.
Relative Humidity
ev
RH 
es (T)
•
•
•
•
Subsaturated: RH < 100%
Saturated: RH = 100%
Supersaturated: RH > 100% S  RH100%
Depends on both vapor pressure ev and the air
temperature T

Dewpoint (Td)
• Consider the case ev < es(T), we could always
reduce es(T) to ev by lowering the temperature.
• Dewpoint is the temperature at which moist air
became saturated over a plane surface of pure
water by cooling while holding ev constant.
• Only depends on the vapor pressure ev.
es (Td )  ev
Saturation Mixing Ratio (ws)
• It is the mixing ratio for which air is saturated
at specific T and P.
ws (T, p) 
es (T)
p  es (T)

es (T)
p
Saturation Mixing Ratio (ws)
 s (T, p) 
es (T)
p
Rd

 0.622
Rv
• Depend on both temperature and pressure
• In units of (g kg-1)
• If we choose P to be 622
 hPa, then
0.622es (T)
s (T,622hPa) 
 0.001es (T)
622
 g 
 s (T,622hPa)  es (T)hPa
kg
To find saturation vapor pressure (es)
3 deg C
622hPa
7.8 gkg-1
A temperature of 3 deg C at 622hPa is correspond to a
saturated mixing ratio of 7.8 g kg-1.
The saturation vapor pressure is ~ 7.8 hPa.
Dewpoint, Mixing Ratio, and
Dewpoint Depression
Td
T
P
w
Td  T  Td
ws
Virtual Temperature (Tv)
• To apply ideal gas law to mixture of air and vapor
• Moist air equation of state :
p  Rm T
p  pd  ev  (d Rd  v Rv )T
d Rd  v Rv
 Rd (
)T
Rd


 M d 
rv 
1
 M v 
 Rd
T
1 rv
p  Rd Tv


 M d 
rv 
1
 M v 
Rm  Rd
1 rv
 M d 
rv 
1
 M v 
Tv 
T
1 rv
Tv  T(1 0.61rv )  T(1 0.61q)
Wet-Bulb Temperature (Tw)
• It is the temperature to
which air is cooled by
evaporation until
saturation occurs.
• Assume that all of the
latent heat of vaporization
is supplied by the air
• Normand’s Rule:
To find Tw, lift a parcel of
air adiabatically to its LCL,
then follow moist adiabat
back down to parcel’s
original P
One Other Variable: Θ
• Potential
Temperature Θ
• Temperature of the
parcel if it were
compressed or
expanded dry
adiabatically to
1000 hPa.
• Conserved in dry
adiabatic process
Critical Levels on
Thermodynamic Diagram
Lifting Condensation Level (LCL)
• The level at which a parcel lifted dry
adiabatically will become saturated.
• Find the temperature and dewpoint of the
parcel (at the same level, typically the
surface). Follow the mixing ratio up from the
dewpoint, and follow the dry adiabat from the
temperature, where they intersect is the LCL.
Finding the LCL
References
• Petty, G (2008). A First Course in Atmospheric
Thermodynamics, Sundog Publishing.
• Potter and Coleman, 2003a: Handbook of Weather, Climate
and Water: Dynamics, Climate, Physical Meteorology,
Weather Systems and Measurements, Wiley, 2003