1!Lecture Ch. 6a!• Saturation of moist air!• Relationship between humidity and dewpoint!– Clausius-Clapeyron equation!• Dewpoint!– Temperature!– Depression!• Isobaric cooling!Curry and Webster, Ch. 6!For Tuesday: Read Ch. 7!How does saturation occur?!• By increasing water vapor!– Evaporation of water at surface!– Evaporation of falling rain!• By cooling!– Isobaric!– Radiative cooling of rising air!• By mixing of two unsaturated air parcels!Curry and Webster, Ch. 6!Saturation of Moist Air!• Dew point temperature!Curry and Webster, Ch. 6!Saturation of Moist Air!• Clausius-Clapeyron equation at dew point!€ vv=RvTp€ dpp=LlvRvT2dTd ln p =LlvRvT2dTd ln pdT=LlvRvT2Clausius Clapeyron!• Recall by integration between two temperatures we had!2!Dewpoint and Humidity!• Integrating from ambient to saturation"• Dew point depression (T-TD)!INCORRECT!!Figure is wrong.!1.00.80.60.40.20.0Relative Humidity20151050Dewpoint Depression (T-Td) T=2C T=24C T=46CCumulus Cloud Base "Altitude Calculator!http://www.csgnetwork.com/estcloudbasecalc.html !Cloud Base Altitude = ((((temperature - dew point) / 4.5) * 1000) + measure station altitude) Assumes: -The rate at which air cools as it rises is averaged at 5.5°F per 1000 feet -The dew point also decreases at about 1.0°F over the same distance. warming cooling3!IPCC!Homework Ch. 5 Prob. 3!€ r* =3baS* =1+4a327brho_l 1000 kg/m3sigma_lv 0.075015 N/m Eqn. 5.7Rv 461.478686 J/K/KGT 280 KI 2M_v 18.016 g/molM_sol 132.1 g/molm_sol 1.00E-18 KGa 1.1611E-09 m a=2sigma/(rho*Rv*T)b 6.5117E-23 m3 b=3i*Mv*msol/(4pi*Msol*rho)r* 4.1018E-07 m r*=sqrt(3b/a)S* 1.00188713 S*=1+sqrt(4a^3/27b)Example Ch. 5 Prob. 7!Curry and Webster, p. 158, Problem 7a-c!€ xmeaxdx =∫xmeaxa−maxm −1eaxdx∫= eax−1( )rm!xm − rm − r( )!ar +1r= 0m∑Integral Tables (521), CRC 1986 p. 330!Example Ch. 5 Prob. 7!€ xmeaxdx =∫eax−1( )rm!xm− rm − r( )!ar +1r= 0m∑x2eaxdx =∫eaxax2−2a2ax −1( ) Integral Tables (521)!CRC 1986 p. 330!€ N = Ar2e−Brdr0∞∫= Ae−Br−Br2−2B2−Br −1( ) 0∞= 0 − −AB2B2 =2AB3Example Ch. 5 Prob. 7!€ xmeaxdx =∫eax−1( )rm!xm− rm − r( )!ar +1r= 0m∑x3eaxdx =∫eaxax3−3x2a+6a3ax −1( ) Integral Tables (521)!CRC 1986 p. 330!€ r =1NAr3e−Brdr0∞∫=ANe−Br−B r3+3r2B−6B3−Br −1( ) 0∞= 0 − −ABN6B3 =3B4!Example Ch. 5 Prob. 7!€ r =3B= 10 ×10−6B = 3 ×105N =2AB3= 200 ×106A = 2.7 ×1024Example Ch. 5 Prob. 7!€ xmeaxdx =∫eax−1( )rm!xm− rm − r( )!ar +1r= 0m∑= 120eaxx5120a−x424a2+x36a3−x22a4+xa5−1a6 Integral Tables (521)!CRC 1986 p. 330!€ wl=4πAρl3ρa r5e−Brdr∫=4πAρl3ρa 120e−Brr5−120B−r424B2+r3−6B3−r22 B4+r−B5−1B6 0∞=4πAρl3ρa 0 −−120B6 =160πAρlB6ρa Cloud in a Jar Demonstration!http://groups.physics.umn.edu/demo/old_page/demo_gifs/4B70_20.GIFCloud Condensation Nuclei!Cloud Processing!0.1!10!Diameter (µm)!0.1!10!Diameter (µm)!dN!dlogD!Diameter (µm)!0.1!10!Hoppel Minimum!• Particle evolution in remote marine conditions!• cloud processing – growth of particles due to coalescence and solute condensation in cloud!7.1 Seinfeld and Pandis, Fig. 15.23 (Hoppel et al., 1990) Number Distributions vs. Population Distributions!1.2 Age!0! 60!Population!Dp (µm)!0.01! 10!dN!dlogDp!Aerosol Particle Size Distribution!(Manhattan)!Human Population Age Distribution (Manhattan) 20! 40!0.1! 1!5!Particle Size Distributions!• Number concentration!– Total number N!– Differential number n!• Mean size!– Geometric!– Arithmetic!– Number-based!– Mass-based!• Size variability!– Standard deviation σ"– Geometric standard deviation σg!Dpg!0.01! 10!Dp (µm)!dN!dlogDp!∼ σg!n(Dp)!0.1! 1!Particle Characteristics!• Concentration and size!• Chemical composition!• Light scattering!Dp (µm)!0.01!0.10!dn!dlogDp!Dpg!∼ σg!n(Dp)!Size Characterization of Particles!• clusters of molecules!• starting at 100 molecules/cluster!• growth by condensation of molecules is nearly continuous!• multiple ways to graph same distribution!2468103246810424681052Concentration (cm-3)2 3 4 5 612 3 4 5 6102Diameter (µm) ni Ni Lognormal ni dN/dlogDp dN/dDp ScaledNiParticle Sizes!Dp (µm)!0.01!0.10!fine mode!coarse mode!Aitken nuclei!1.0! 10.0! 100.0!• range of particle sizes is approximately from 1 nm to 1 mm in diameter!• range of approximately 6 orders of magnitude!• concentrations at each of these sizes also vary !Size Distribution Modes!Dp (µm)!0.01!0.10!dn!dlogDp!fine mode!accumulation mode!nucleation mode!coarse mode!Aitken nuclei!precipitation-!sized droplets!cloud droplets!1.0! 10.0! 100.0!recently nucleated particles!• modes of aerosol are distinguished by !– size!– sources!– behavior!Log-Normal Number Distributions!• Differential !Dp (µm)!0.01!0.10!Cumulative Distribution !(% less than Dp)!Dpg!σg!Cumulative Number!100!0!50!84.1%!15.9%!}!Cumulative Surface!Cumulative Volume!Dp (µm)!0.01!0.10!dn!dlogDp!Dpg!∼ σg!n(Dp)!• Cumulative6!Microphysics!• Aerosol includes both particles and vapor!• Number, area, volume, mass vary nonlinearly!• Deposition velocity depends on size (nano, micro, milli)!• Scavenging, coalescence, activation and condensation change the size distribution!Global Aerosol Distribution!Capaldo et al., Nature, 1999!• Regional variations in aerosol mass and composition [NARSTO, 2002]!Toronto (1997-99)Egbert (1994-99)Abbotsford (1994-95)Quaker City OH (1999)Arendstville PA (1999)Atlanta (1999)Yorkville (1999)Mexico City - Pedregal (1997)Los Angeles (1995-96)Fresno (1988-89)Kern Wildlife Refuge (1988-89)SulfateNitrateAmmoniumBlack carbonOrganic carbonSoilOther12.3 ug m-38.9 ug m-37.8 ug m-312.4 ug m-310.4 ug m-319.2 ug m-314.7 ug m-355.4 ug m-330.3 ug m-323.3 ug m-339.2 ug m-3Washington DC (1996-99)14.5 ug m-3Colorado Plateau (1996-99)3.0 ug m-3 Mexico City - Netzahualcoyotl (1997)24.6 ug m-3Esther (1995-99)St. Andrews (1994-97)5.3 ug m-34.6 ug m-3ROAST
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