Copyright © 2013 R. R. Dickerson AOSC 620 PHYSICS AND CHEMISTRY OF THE ATMOSPHERE, I Lecture 5A, Moist Air Professor Russell Dickerson Room 2413, Computer & Space Sciences Building Phone(301) 405-5364 russ@atmos.umd.edu web site www.meto.umd.edu/~russ Copyright © 2013 R. R. Dickerson 1 1

Copyright © 2013 R. R. Dickerson & Z.Q. Li Skew-T Practice If a parcel of air with T = 15 oC and Td = 2oC rises adiabatically form 1000 hPa to the LCL find the alt, press, temp and sat mix ratio at the LCL. If the parcel continues to rise (pseudo-adiabatically) another 200 hPa how much water can be condensed out? How much rain could this produce? Copyright © 2013 R. R. Dickerson & Z.Q. Li

Dew Point Temperature Td Temperature to which moist air may be cooled with pressure and mixing ratio held constant to just reach saturation with respect to H2O. The “frost point” is the saturation temperature with respect to ice. Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li At the dewpoint w = ws(Td, P) As in Henry’s Law, but L is enthalpy, at a given temperature: Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li gas solid liquid T0 e Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li Phase Diagram of Water The heat of vaporization is zero at and beyond the critical point, and so there is no distinction between the two phases. The fluid is supercritical. Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2014 R. R. Dickerson Relating relative humidity to dew point. Copyright © 2014 R. R. Dickerson

Wet-Bulb Temperature Tw Temperature to which air may be cooled by evaporating water into it at constant pressure. When water is evaporated into air, energy is added to the water. This energy comes at the expense of the dry air, which is cooled. How do we get from Tw to w and RH? Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li Consider 1. Isobaric process 2. Mixing ratio increased by evaporating water into air: w => ws(Tw,p) The heat necessary to evaporate dw grams of water per kilogram of dry air is: dq = Lvdw Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li To find the heat lost to dry air alone due to evaporation of water, we must correct for the mass of the water that the unit mass dry air now contains: Integrate from T to Tw w => ws(Tw,p) Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li Useful for isobaric condensation. Measure using a Sling Pychrometer or aspirated wet and dry bulbs: We measure T and Tw. Since ws is a known function of Tw and p, you can determine w from ws and the above equation. Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li Alternatively, if w and T are known one can calculate the wet bulb temperature, Tw. Example: We may now apply the Clausius Clapeyron equation. Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li From Isobaric Condensation: The Clausius Clapeyron Equation gives: Solve for Tw: (f = w/ws(T)) Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li After extensive algebra: Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li Also note: Copyright © 2013 R. R. Dickerson & Z.Q. Li

Equivalent Temperature Te Temperature a sample of moist air would reach if all the moisture were condensed out at constant pressure (i.e., latent heat converted to sensible heat). Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li

Isentropic Condensation Temperature Tc Tc is the temperature at which saturation is reached when moist air is cooled adiabatically with w held constant. See R&Y Figure 2.3 or W&H Figure 3.10. Not in Salby explicitly. Tc can be determined by the intersection of the adiabatic equation (Poisson’s) and the Clausius Clapeyron equation and found on a SkewT. Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li Constant H2O mixing ratio Dry adiabat SkewT Copyright © 2013 R. R. Dickerson & Z.Q. Li

Copyright © 2013 R. R. Dickerson & Z.Q. Li For completeness Absolute humidity, rv, density of water vapor. Specific humidity, q, g H2O /kg air (not dry air). Same as [H2O]e. Copyright © 2013 R. R. Dickerson & Z.Q. Li

Conservative Properties of Air Parcels Variable dry adiabatic saturated/pseudo adiabatic q C NC qe qw Td Tw w T* Te Tc f The potential virtual temperature (of moist air) is the potential temperature of dry air at the same pressure and density. In theta e all rain falls out. Copyright © 2013 R. R. Dickerson & Z.Q. Li