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Water in the Atmosphere

Water in the Atmosphere. Hess pp 43 - 44 pp 58 – 60 Tsonis pp 93 – 97 Wallace & Hobbs pp 66 – 67 pp 79 – 84 Bohren & Albrecht pp 181-188. Reading. Be able to define water vapor pressure Be able to define virtual temperature Be able to define specific humidity

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Water in the Atmosphere

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  1. Water in the Atmosphere

  2. Hess pp 43 - 44 pp 58 – 60 Tsonis pp 93 – 97 Wallace & Hobbs pp 66 – 67 pp 79 – 84 Bohren & Albrecht pp 181-188 Reading

  3. Be able to define water vapor pressure Be able to define virtual temperature Be able to define specific humidity Be able to define mixing ratio Objectives

  4. Be able to calculate the water vapor pressure Be able to calculate virtual temperature Be able to calculate specific humidity Be able to calculate mixing ratio Objectives

  5. H H O Water In the Atmosphere • Unique Substance • Occurs in Three Phases Under Normal Atmospheric Pressures and Temperatures • Gaseous State • Variable 0 – 4%

  6. Water in the Atmosphere • Remember Dalton’s Law? • Law of Partial Pressures • Let’s look at the contribution of water p = p1 + p2 + p3 + ….

  7. Water Vapor Pressure (e) • Ideal Gas Law for Dry Air • Ideal Gas Law for Water Vapor p = pressure of dry air ad = specific volume of dry air Rd = gas constant for dry air e = vapor pressure of water vapor av = specific volume of water vapor Rv = gas constant for water vapor

  8. Water Vapor Pressure (e) • Partial pressure that water vapor exerts Total Pressure p = pO2+pN2+pH2Ov Water Vapor Pressure e = pH2Ov

  9. H H O Water Vapor Pressure (e) • Gas Constant of Water Vapor Molecular Weight (Mw ) Hydrogen = 1kg kmol-1 Oxygen = 16 kg kmol-1 Water = 18 kg kmol-1

  10. Virtual Temperature (Tv) • The temperature dry air must have in order to have the same density as moist air at the same pressure • Fictitious temperature

  11. Virtual Temperature (Tv) • Dry Air Total Pressure = p Volume = V Temperature = T Mass of Air = md

  12. Virtual Temperature (Tv) • Moist Air (Mixture) Total Pressure = p Volume = V Temperature = T Mass of Air = md +mv

  13. Virtual Temperature (Tv) • Density of mixture

  14. Virtual Temperature (Tv) • Ideal Gas Law • For Dry Air • For Water Vapor Alone or or

  15. Virtual Temperature (Tv) • Substitute into density expression

  16. Virtual Temperature (Tv) • Dalton’s Law of Partial Pressure or

  17. Virtual Temperature (Tv) • Substitute or

  18. Virtual Temperature (Tv) • Remove Rd

  19. Virtual Temperature (Tv) • Define e

  20. Virtual Temperature (Tv) • Remove p

  21. Virtual Temperature (Tv) • Rearrange terms

  22. Virtual Temperature (Tv) • By definition, virtual temperature is the temperature dry air must have in order to have the same density as moist air (mixture) at the same pressure or Instead of p = total (mixture) pressure r = mixture density Use

  23. Virtual Temperature (Tv) • Substitution of • Into • Produces

  24. Virtual Temperature (Tv) • Rearrange

  25. Virtual Temperature (Tv) • Start Canceling!

  26. Virtual Temperature (Tv) • Still looks Ugly! Simplify!

  27. Virtual Temperature (Tv) p = total (atmospheric) pressure e = water vapor pressure T = temperature

  28. Virtual Temperature (Tv) • Moist air (mixture) is less dense than dry air • Virtual temperature is greater than actual temperature • Small difference

  29. Specific Humidity (q) • Ratio of the density of water vapor in the air to the (total) density of the air

  30. Mixing Ratio (w) • The mass of water vapor (mv) to the mass of dry air Mass of Dry Air = md Mass of Water Vapor = mv

  31. Mixing Ratio (w) • The mass of water vapor (mv) to the mass of dry air Mass of Dry Air = md Mass of Water Vapor = mv

  32. Mixing Ratio (w) • Expressed in g/kg • Dry Air • 1 to 2 g/kg • Tropical Air • 20 g/kg

  33. Mixing Ratio (w) • Can mixing ratio be expressed in terms of water vapor pressure? • Sure as it will rain on a meteorologist’s picnic!

  34. Mixing Ratio (w) • By definition • Divide top and bottom by volume (V)

  35. Mixing Ratio (w) • But density is so..... w = mixing ratio rv = density of water vapor in air rd = density of dry air

  36. Mixing Ratio (w) • Ideal Gas Law or or

  37. Mixing Ratio (w) • Substitute

  38. Mixing Ratio (w) • Simplify • Remember

  39. Mixing Ratio (w) • Substitute into • But p = total pressure of air (mixture)

  40. Mixing Ratio (w) • Substitute into • Ta-Da!

  41. Mixing Ratio (w) • Expression for Mixing Ratio (w) • Water Vapor Pressure (e) in any units • Atmospheric Pressure (p) in any units

  42. Mixing Ratio (w) • Can be used to determine other water variables • Let’s look at • Specific Humidity • Water Vapor Pressure (e) • Virtual Temperature (Tv)

  43. Specific Humidity (q) • By definition • But q = specific humidity rv = density of water vapor in air r = density of air rd = density of dry air

  44. Specific Humidity (q) • Substitute into • Results in • But

  45. Specific Humidity (q) • Substitute into • Results in

  46. Specific Humidity (q) • Eliminate V

  47. Specific Humidity (q) • Divide top and bottom by md

  48. Specific Humidity (q) • But so

  49. Specific Humidity (q) • Expression for specific humidity (q) • Mixing Ratio (w) in kg kg-1

  50. Water Vapor Pressure (e) • Pressure exerted by water vapor is a fraction of total pressure of air • Fraction is proportional to # of moles in mixture e = water vapor pressure f = fractional amount of water vapor p = total pressure of air

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