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Moisture Relationships

Moisture Relationships. Troposphere. barrier!. Tropopause. Moisture Relationships. Atmospheric Moisture is necessary for Precipitation. That moisture is moved to the atmosphere by Evaporation and Transpiration. Humidity.

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Moisture Relationships

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  1. Moisture Relationships Troposphere barrier! Tropopause

  2. Moisture Relationships • Atmospheric Moisture is necessary for Precipitation. That moisture is moved to the atmosphere by Evaporation and Transpiration

  3. Humidity • The presence of moisture (water vapor, an invisible gas) in the atmosphere is measured by the humidity of the air. • Humidity and condensation are closely related as condensation inevitably occurs when the air is saturated with moisture (100% humidity). 585 calories/gram “Latent Heat of Condensation” Gas to liquid droplet, heat is released to the atmosphere, air molecules move faster, move apart, less dense, rise

  4. Some useful units • One Gram is the mass of liquid water in a little cube, one centimeter on a side. • A centimeter is less than half an inch. It is 1/100 of a meter. • A meter is 39.37 inches, so a centimeter is about 0.394 inches • A mole of anything is 6.023 x 1023 • 1023 means 10x10x10x10x10x … x10 twenty three times

  5. Relative Humidity and Dew Point • Absolute humidity measures the amount of water vapor in air. Grams H2O/m3 of air. This water is a gas, water vapor. • Relative humidity measures the amount of water vapor in air relative to the maximum amount of water vapor the air could hold at that temperature. • Relative humidity increases with increasing water vapor or decreasing temperature. Cold air can’t “carry” as much water vapor as warm air. • The dew point is the temperature to which a given parcel of humid air must be cooled, at constant barometric pressure, for water vapor to condense into liquid water.

  6. Absolute Humidity • Absolute humidity measures the amount (mass) of water in a volume of air. Units are gramsH2O/meters3 • Problem: volume changes as parcel rises So we will need some measures of humidity that do not depend on volume. Same # grams in a larger volume, so abs. humidity decreases

  7. 298.15K 285.15K 25oC 72oF 12oC 53.6oF oC = 5/9(F- 32) K=oC + 273.15 Various Temperature Scales

  8. Gas Laws • 1600’s to 1800’s • Combined as ideal gas law: • n= # moles, and R is the universal gas constant • R = 8.314472 N·m·K−1·mol−1 Pressure times Volume is a constant Increase Temp, Volume increases Increase Temp, Pressure increases Increase moles of gas, Volume increases

  9. Avogadro’s law Equal volumes of gases at the same temperature and pressure contain the same number of molecules regardless of their chemical nature and physical properties. This number (Avogadro's number) is 6.022 X 1023 . These occupy 22.41 L for all gases at temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of 100 kPa. Dry air Moist air Dry air (21% O2, 78% N2, 1% other) Md ~ 0.21*32+0.78*28 ~ 28.9 Water vapor (H2O) Mv = 2*1 + 16 = 18 Moist air is lighter than dry air because number of molecules is the same for equal volumes, and water is lighter than O2 or N2

  10. Moist Air vs. Dry Air 1 • Air with water vapor in it (Moist Air) is lighter than dry air Here’s Why: • When water vapor H2O is added to air, other gases are pushed aside. (Avogadro’s Law, # mol/vol = const) • Recall that dry air is mostly Nitrogen N2 and Oxygen O2 molecules.

  11. Moist Air vs. Dry Air 2 OR “why moist air rises” • Water H2O “weighs” 18 grams per mole. • Nitrogen N2 “weighs” 28 grams per mole • Oxygen O2 “weighs” 32 grams per mole • The number of molecules in air in some volume at constant T and P is constant. • Since light water molecules displace much heavier molecules, air with water vapor in it is “lighter”, less dense, more buoyant. Moist air rises, forms storms.

  12. Dalton’s Law of Partial Pressures John Dalton studied the effect of gases in a mixture. He observed that the Total Pressure of a gas mixture was the sum of the Partial Pressure of each gas. P total = P1 + P2 + P3 + .......Pn The Partial Pressure is defined as the pressure of a single gas in the mixture as if that gas alone occupied the container

  13. Partial Pressure of water vapor e or ew • Partial Pressure is the pressure that would be exerted on a surface by a gas in a mixture if the other gases were absent. e = esat(Td) • The Partial Pressure of water vapor ew is given by a form of the Ideal Gas Law ew =rRT 0.622 • where 0.622 is the ratio of the molecular weights of water (18) to an average molecular weight for air (28.9). • 1 mb [mbar, millibar] = 100 Pascals ew = water vapor pressure in mbars rw = vapor density or absolute hum. R = Dry Air Gas Constant R= 2.87 x 103 mbar cm3/g . K T = absolute temperature Kelvin

  14. Mixing Ratio, w • Air pressure, P, is the total pressure that air makes on a surface • Ideal gas law relates pressure to density and absolute temperature T. • Vapor pressure, e, is the pressure that water vapor exerts on a surface. Rv is the gas constant for water vapor • Mixing Ratio w is the ratio of vapor mass to dry air mass w = rv/rdry • 0.622 is ratio of mol. wt. of water vapor to avg mol. wt. of dry air (=18/28.9) = Notice this mixing ratio doesn’t depend on volume (the v’s in density cancel) , and so will stay constant as a parcel ascends

  15. Curve Fits • Complex situations, such as mixtures of gases, often defeat modeling because the assumptions of physical equations aren’t true. • In this case we do many experiments, plot the data, and fit a curve to the data.

  16. Saturation vapor pressure, esat Saturation vapor pressure occurs when air is holding all the water vapor that it can at a given air temperature, then RH = 100% and T=Tdew point Then T dry bulb = T wet bulb http://hurri.kean.edu/~yoh/calculations/satvap/satvap.html pws = water vapor saturation pressure (Pa) e = the constant 2.718....... T = dry bulb temperature of the moist air (K) http://www.engineeringtoolbox.com/water-vapor-saturation-pressure-air-d_689.html

  17. Relative Humidity • The relative humidity of an air-water mixture is defined as the ratio of the partial pressure of water vapor in the mixture, called ew or e, to the saturated vapor pressure of water at a prescribed temperature, called e*w or esat. I prefer e and esat, respectively. • Relative humidity is normally expressed as a percentage and is calculated by using the following equation: • This equation is useful for calculating e from esat and RH

  18. Appendix C varies slightly Saturated Air Properties http://www.engineeringtoolbox.com/water-vapor-saturation-pressure-air-d_689.html e sat

  19. Dry Air Properties at std. atm. sea-level

  20. Water Vapor Density Curve Fit • The density of water vapor can be expressed as: ρv = 0.0022 pv / T   where • pv = e =partial pressure water vapor (Pa, N/m2) • ρv = density water vapor (kg/m3) • T = absolute dry bulb temperature (K) http://www.engineeringtoolbox.com/water-vapor-saturation-pressure-air-d_689.html

  21. Specific Humidity, qv • Specific humidity measures the mass of water vapor per unit mass of moist air • It is dimensionless • Like mixing ratio, it doesn’t change with volume. • We still need the moist air density.

  22. Density of Moist Air, rm • rm= P/RT (1 - 0.378 e / • We need this to calculate the specific humidity. • Derivation in the handout follows this.

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