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