Lecture 6 22-Aug-2016
In the last class, we were discussing about atmospheric water.
Two prominent hydrological process involving atmospheric water are:
Water exists in gaseous form as vapor
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
= dry density.
=gas constant for dry air.
As = +
The total pressure, p=
Therefore, from the ratio of e/p, an approximation can be obtained as such: Where
= 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.
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)
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.
P=120 kPa = 12000 Pa
T= 18 =291 K
Td = 15
Td = 15 , the vapor pressure ‘e’ at 18 will be same as sat vap pressure at 15
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.
Integrating between two elevations and
At , p= , T=
At , p= , T=
THE PRECIPITABLE WATER
From the earlier said atmospheric column, how much amount of water is precipitable is of curiousness To evaluate the precipitable water:
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