Atmospheric Water
• Goals for today
– Review Exercise 1
– Define measures of water vapor in air
– Define vapor pressure and its relation with
temperature
– Water vapor in an atmospheric column
– Computation of precipitable water
– Patterns of water vapor and precipitable water in
space and time
• Reading for Tues – Applied Hydrology Sec 3.3
and 3.4 on rainfall and precipitation
Energy fluxes, July 2003
Energy flux components, July 2003
Daily average values
Energy fluxes, Jan 2003
Energy flux comparison
January, 2003
July, 2003
Daily average values
Water vapor
Suppose we have an elementary volume of atmosphere dV and
we want quantify how much water vapor it contains
Water vapor density
Air density
mv
v 
dV
ma
a 
dV
dV
ma = mass of moist air
mv = mass of water vapor
Atmospheric gases:
Nitrogen – 78.1%
Oxygen – 20.9%
Other gases ~ 1%
http://www.bambooweb.com/articles/e/a/Earth's_atmosphere.html
Specific Humidity, qv
• Specific humidity
measures the mass of
water vapor per unit
mass of moist air
• It is dimensionless
v
qv 
a
Vapor pressure, e
• Vapor pressure, e, is the
pressure that water vapor
exerts on a surface
• Air pressure, p, is the
total pressure that air
makes on a surface
• Ideal gas law relates
pressure to absolute
temperature T, Rv is the
gas constant for water
vapor
• 0.622 is ratio of mol. wt.
of water vapor to avg mol.
wt. of dry air
e  v RvT
e
qv  0.622
p
Dalton’s Law of Partial Pressures
John Dalton studied the effect of gases in a
mixture. He observed that the Total Pressure of
a gas mixture was the sum of the Partial
Pressure of each gas.
P total = P1 + P2 + P3 + .......Pn
The Partial Pressure is defined as the pressure
of a single gas in the mixture as if that gas
alone occupied the container. In other words,
Dalton maintained that since there was an
enormous amount of space between the gas
molecules within the mixture that the gas
molecules did not have any influence on the
motion of other gas molecules, therefore the
pressure of a gas sample would be the same
whether it was the only gas in the container or if
it were among other gases.
http://members.aol.com/profchm/dalton.html
Saturation vapor pressure, es
Saturation vapor pressure occurs when air is holding all the water vapor
that it can at a given air temperature
 17.27T 
es  611 exp 

 237.3  T 
Vapor pressure is measured in Pascals (Pa), where 1 Pa = 1 N/m2
1 kPa = 1000 Pa
Relative humidity, Rh
es
e
e
Rh 
es
Relative humidity measures the percent
of the saturation water content of the air
that it currently holds (0 – 100%)
Dewpoint Temperature, Td
e
Td
T
Dewpoint temperature is the air temperature
at which the air would be saturated with its current
vapor content
Water vapor in an air column
• We have three equations
describing column:
2
– Hydrostatic air pressure,
dp/dz = -ag
– Lapse rate of temperature,
dT/dz = - a
– Ideal gas law, p = aRaT
• Combine them and
integrate over column to
get pressure variation
elevation
Column
Element, dz
1
 T2 
p2  p1  
 T1 
g / aRa
Precipitable Water
• In an element dz, the
mass of water vapor
is dmp
• Integrate over the
whole atmospheric
column to get
precipitable water,mp
• mp/A gives
precipitable water per
unit area in kg/m2
2
Column
Element, dz
1
Area = A
dm p  qv  a Adz
Precipitable Water, Jan 2003
Precipitable Water, July 2003
January
July