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Atmospheric Water 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 .
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