Lecture 6 22-Aug-2016
ATMOSPHERIC WATER
In the last class, we were discussing about atmospheric water.
Two prominent hydrological process involving atmospheric water are:
Evaporation Precipitation
Water exists in gaseous form as vapor
We talked about specific humidity ( ) and vapor pressure (e)
One relation between and e was obtained from ideal gas law and Dalton’s law of partial pressure.
Water vapor pressure in an atmospheric air, (T in K)
=gas constant for water vapor p =total pressure exerted by the atmospheric air p =
From Dalton’s law
p-e=
= dry density.
=gas constant for dry air.
As = +
And
The total pressure, p=
Therefore, from the ratio of e/p, an approximation can be obtained as such: Where
Also
= J/kg K
Therefore the gas constant of moist air increases with specific humidity.
SATURATION VAPOR PRESSURE
For a particular temperature, there is a maximum moisture content that air can hold. This maximum moisture content is the saturated moisture content. The vapor exerted at this saturated moisture is the saturation vapor pressure ( ) At saturated moisture content, the rate of evaporation and condensation are equal.
Over a water surface, the saturated vapor pressure ( ) is related to the temperature (T) as (Raudkivi, 1979)
. T= temperature in degree Celsius.
RELATIVE HUMIDITY
The ratio of actual vapor pressure to its saturation value at a given air temperature
At a given point specific humidity if the observed value of e is at a given temperature, we can evaluate the corresponding dew point temperature(Td) for the corresponding (e)
EXAMPLE
From a weather station the following parameters were measured:
Air pressure=120 kPa; Air temperature = 18 ;
Wet bulb temperature or dew point temp = 15 ;
Calculate the vapor pressure, relative humidity, and specific humidity of the air.
Solution:
Given,
P=120 kPa = 12000 Pa
T= 18 =291 K
Td = 15
We have
=2065 Pa
As
Td = 15 , the vapor pressure ‘e’ at 18 will be same as sat vap pressure at 15
=1706 Pa
Relative humidity =
Specific humidity =0.0088 kg water/kg moist air WATER VAPOR IN A STATIC ATMOSPHERIC COLUMN
Let us talk about water vapor in a static atmospheric column.
The ideal gas equation law states that p =
Pressure obeys the hydrostatic law or pressure of air will be hydrostatic ie
Temperature also varies with elevation and is given as
is the lapse rate.
As
p =
dz= -
Integrating between two elevations and
At , p= , T=
At , p= , T=
i.e. )
Or,
Also note
THE PRECIPITABLE WATER
From the earlier said atmospheric column, how much amount of water is precipitable is of curiousness To evaluate the precipitable water:
dz
z
From atmospheric column, Consider an elemental strip of thickness dz at height ‘z’ Mass of air in the elemental strip = Mass of water (in vapor form) in this strip=
Total mass of precipitable water between any elevation z1 and z2 will be