3 Air Constituents in Troposphere and Stratosphere N %, O %, H2O 0-2%Inert gases 0.938%Many of the least abundant have a disproportionally large influence on atmospheric transmission.CO2 398ppm absorbs 2.8, 4.3 & 15 mmCH4 1.7ppm absorbs 3.3 & 7.8mmN2O .35ppm absorbs 4.5, 7.8 & 17mmO3 ~ absorbs UV-B, 9.6mmCFCl3, CF2CL2 … absorbs IR
12 Outline I. The atmosphere: composition, profile INEL 6069,OutlineI. The atmosphere: composition, profileII. Gases: many molecules1. Shapes(G, VVW, L): below 100GHz, up to 300GHzwe find interaction with H2O and O22. Total AtmosphericAbsorption kg, opacity tq, and atm-losses Lq3. TB: Downwelling Emission by AtmosphereSky Temp= cosmic + galaxy
13 U.S. Standard Atmosphere INEL 6069,U.S. Standard AtmosphereThermosphere(or Ionosphere) oF!95/120kmMesopauseMesosphereno aircrafts heretoo cold ~-90oF50/60kmStratopauseStratosphere- no H2O or dustozone absorption of UVwarms air to ~40oF8/15kmTropopauseTroposphere – clouds, weatherP= 1013 mbars= 1013 HPaT= 300K
14 Atmospheric Profiles US Standard Atmosphere 1962 INEL 6069,Atmospheric Profiles US Standard Atmosphere 1962TemperatureDensity in kg/m3Pressure P= nRT/V=rairRT/M or Poe-z/H3orRair= 2.87
15 INEL 6069,Water Vapor ProfileDepends on factors like weather, seasons, time of the day.It’s a function of air temperature.Cold air can’t hold waterHot air can support higher humidities.(P dependence)rv(z)= roe-z/H [g/m3]where ro averages in mid latitudesand the total mass of water vapor in acolumn of unit cross section is
16 Relative Humidity Dew point temperature (dew=rocío) Relative Humidity is the T below which the WV in a volume of humid air at a constant barometric P will condense into liquid water.Is the T as which fog formsRelative HumidityWhen Tair is close to Tdew => high %RHAbsolute Humidity, the mass of water per unit volume of air.
17 Equations for RHWhere e = pressure and exp means exponential ex
18 Relative Humidity (RH) simplified equations T is in Celsius
19 Relative Humidity, RH vapor in air INEL 6069,Relative Humidity, RH vapor in airAir TemperatureTVapor air can holdActual Vapor in the air[gr per kg dry air]Relative humidityRH86oF27.610.8339%77oF20.453%68oF14.972%59oF10.8100%
20 Relative Humidity, RH dew Temperature INEL 6069,Relative Humidity, RH dew TemperatureAir TemperatureTDew TemperatureTdpActual Vapor in the air[gr per kg dry air]Relative humidityRH86oF64oF10.8339%77oF60oF53%68oFoF72%59oF100%
22 EM interaction with Molecules INEL 6069,EM interaction with MoleculesTotal internal energy state for a moleculeelectronic energy corresponding to atomic levelvibration of atoms about their equilibrium positionrotation of atoms about center of moleculeE = Ee + Ev + ErBohr condition f lm= (El – Em ) /hValues for energy differences forelectronic: 2 to 10 eVvibrational-rotational: 0.1 to 2 eVpure rotational: 10-4 to 5 x 10-2 eV ( microwaves)
24 Line Shapes where, Slm is the line strength F(f,flm) is the line shape INEL 6069,Line Shapeswhere,Slm is the line strengthF(f,flm) is the line shapeLINE SHAPESLorentzGrossVan-Vleck-WeisskoptOne moleculefrequencyAbsorptionMany molecules:pressure broaden*frequency*caused by collision between molecules
25 Line shapes Lorentz Gross Van-Vleck-Weisskopt Liebe MPM model for INEL 6069,Line shapesLorentzGrossVan-Vleck-WeisskoptLiebe MPM model forMillimeter wave propagation model
26 Absorption Bands Mainly water and oxygen for microwaves INEL 6069,Absorption BandsMainly water and oxygen for microwavesBrightness Temperature [K]Frequency [GHz]
27 Note how line width changes with height due to less pressure broadening
29 Total Atmospheric Absorption kg, Opacity tq, [Np] Loss factor Lq INEL 6069,Total AtmosphericAbsorption kg,Opacity tq, [Np]Loss factor Lq[L en dB]To convert from Np/km to dB/km multiply by for 1-way propagation
30 Atmospheric Emission For clear atmosphere where INEL 6069,Atmospheric EmissionFor clear atmospherewhereAlso there is some background radiationTcos=2.7K from the Big Bang and Tgal~0 above 5GHz
31 Latent Heat – to understand radiation budget need to monitor water content in atmosphere Radiative Transfer,INEL 6069,
32 Scattering from Hydrometeors: Clouds, Snow, Rain
33 Outline: Clouds & Rain Single sphere (Mie vs. Rayleigh) Sphere of rain, snow, & ice (Hydrometeors)Find their ec, nc, sbMany spheres together : Clouds, Rain, Snowa. Drop size distributionb. Volume Extinction= Scattering+ Absorptionc. Volume BackscatteringRadar Equation for MeteorologyTB Brightness by Clouds & Rain
37 EM interaction with Single Spherical Particles AbsorptionCross-Section, Qa =Pa /SiEfficiency, xa= Qa /pr2ScatteredPower, PsCross-section , Qs =Ps /SiEfficiency, xs= Qs /pr2Total power removed by sphere from the incident EM wave, xe = xs+ xaBackscatter, Ss(p) = Sisb/4pR2
38 Mie Scattering: general solution to EM scattered, absorbed by dielectric sphere. Uses 2 parameters (Mie parameters)Size wrt. l :Speed ratio on both media:
39 [Index of Refraction and Refractivity] The Propagation constant depends on the relative complex permittivityWhere the index of refraction isBut n’air≅1.0003So we define N
40 So… Propagation in terms of N is And the attenuation and phase is And the power density carried by wave traveling in the z-direction is :With f in GHz
41 Mie Solution Mie solution Where am & bm are the Mie coefficients given by 8.33a to 8.33b in the textbook.Probl , menos 7,9,10,13 para jueves Abr10
43 Mie Regions Cambio de regiones de acuerdo a razon de e’/e” Rayleigh regionIntermediate or Mie regionOptical regionRayleigh regionIntermediate regionOptical regionCambio de regiones de acuerdo a razon de e’/e”Example: sphere withe =3.2(1-j)Conclusion: regiones se definen de acuerdo a c y a n
44 Intermediate or Mie region BackscatteringIntermediate or Mie regionOptical regionRayleigh region
45 Variations of water dielectric const. with frequency and Temperature
46 Non-absorbing sphere or drop (n”=0 for a perfect dielectric, which is a non-absorbing sphere) Rayleigh region |nc|<<1
48 Plots of Mie xe versus cRayleighIntermediateOpticalFour Cases of sphere in air :n=1.29 (lossless non-absorbing sphere)n=1.29-j0.47 (low loss sphere)n=1.28-j1.37 (lossy dielectric sphere)n= perfectly conducting metal sphereAs n’’ increases, so does the absorption (xa), and less is the oscillatory behavior.Optical limit (r >>l) is xe =2.Crossover forHi conducting sphere at c =2.4Weakly conducting sphere is at c =.06
49 Rayleigh Approximation |nc|<<1 Scattering efficiencyExtinction efficiencywhere K is the dielectric factor
50 Absorption efficiency in Rayleigh region i.e. scattering can be neglected in Rayleigh region(small particles with respect to wavelength)|nc|<<1
51 Scattering from Hydrometeors Rayleigh ScatteringMie Scattering >> particle sizecomparable to particle size--when rain or ice crystals are present.95GHz (3mm)33GHz (9mm)
54 Single Particle Cross-sections vs. c Scattering cross sectionAbsorption cross sectionIn the Rayleigh region (nc<<1) =>Qa is larger, so much more of the signal is absorbed than scattered. ThereforeFor small drops, almost no scattering, i.e. no bouncing from drop since it’s so small.
55 Gas molecules = much smaller than visible l=> Rayleigh approx. is OK. Red 700nmViolet 400nm
56 Mie Scattering Mie scatt. is almost independent of frequency [l dependent] [almost l independent]Mie scatt. is almost independent of frequencyCloud droplets ~20mm compare to 500nmMicrowaves have l~cm or mm (large) – Rayleigh for most atmospheric constituentsLaser have l~nm - Mie
63 Rayleigh-Mie-Geometric/Optics Along with absorption, scattering is a major cause of the attenuation of radiation by the atmosphere for visible.Scattering varies as a function of the ratio of the particle diameter to the wavelength (d/l) of the radiation.When this ratio is less than about one-tenth (d/l<1/10), Rayleigh scattering occurs in which the scattering coefficient varies inversely as the fourth power of the wavelength.At larger values of the ratio of particle diameter to wavelength, the scattering varies in a complex fashion described by the Mie theory;at a ratio of the order of 10 (d/l>10), the laws of geometric optics begin to apply.
64 Mie Scattering (necessary if d/l1), Mie theory : A complete mathematical-physical theory of the scattering of electromagnetic radiation by spherical particles, developed by G. Mie in 1908.In contrast to Rayleigh scattering, the Mie theory embraces all possible ratios of diameter to wavelength. The Mie theory is very important in meteorological optics, where diameter-to-wavelength ratios of the order of unity and larger are characteristic of many problems regarding haze and cloud scattering.When d/l neither Rayleigh or Geometric Optics Theory applies. Need to use Mie.Scattering of radar energy by raindrops constitutes another significant application of the Mie theory.
65 Backscattering Cross-section From Mie solution, the backscattered field by a spherical particle isObserve thatperfect dielectric(nonabsorbent) sphereexhibits largeoscillations for c>1.Hi absorbing and perfectconducting spheres showregularly damped oscillations.
66 Backscattering from metal sphere Rayleigh Region defined asFor conducting sphereWhere,
67 Scattering by Hydrometeors Hydrometeors (water particles)In the case of water, the index of refraction is a function of T & f. (fig 5.16)@T=20CFor ice.For snow, it’s a mixture of both above.
74 Snowflakes Snow is mixture of ice crystals and air The relative permittivity of dry snowThe Kds factor for dry snow
75 Volume Scattering Two assumptions: particles randomly distributed in volume-- incoherent scattering theory.Concentration is small-- ignore shadowing.Volume Scattering coefficient is the total scattering cross section per unit volume.[Np/m]
76 Total number of drops per unit volume in units of mm-3Drop size distribution in terms of radius or diameterDisdrometer- measures DSD
86 Reflectivity & Reflectivity Factor hZ (in dB)Reflectivity, h [cm-1]dBZ for 1g/m3Reflectivity and reflectivity factor produced by 1g/m3 liquid waterDivided into drops of same diameter. (from Lhermitte, 2002).
88 Rain drops A) Raindrops are not tear-shaped, as most people think. B) Very small raindrops are almost spherical in shape.C) Larger raindrops become flattened at the bottom, like that of a hamburger bun, due to air resistance.D) Large raindrops have a large amount of air resistance, which makes them begin to become unstable.E) Very large raindrops split into smaller raindrops due to air resistance.
89 Precipitation (Rain) Volume extinction [eq. 8.85-87] where Rr is rain rate in mm/hr[dB/km] and b are given by various modelcan depend on polarization since large drops are not spherical but ~oblong.[dB/km]Mie coefficients
92 Rain Rate [mm/hr]If know the rain drop size distribution, each drop has a liquid water mass oftotal mass per unit area and timerainfall rate is depth of water per unit timea useful formula
93 Volume Backscattering for Rain For many drops in a volume, if we use Rayleigh approximationMarshall and Palmer developedbut need Mie for f>10GHz.
94 Rain retrieval Algorithms Several types of algorithms used to retrieve rainfall rate with polarimetric radars; mainlyR(Zh),R(Zh, Zdr)R(Kdp)R(Kdp, Zdr)whereR is rain rate,Zh is the horizontal co-polar radar reflectivity factor,Zdr is the differential reflectivityKdp is the differential specific phase shift a.k.a. differential propagation phase, defined as
96 Snow extinction coefficient Both scattering and absorption ( for f < 20GHz --Rayleigh)for snowfall rates in the range of a few mm/hr, the scattering is negligible.At higher frequencies,the Mie formulation should be used.The is smaller that rain for the same R, but is higher for melting snow.
101 These data sets provided information on the structure of precipitation systems. This was from Hurricane Georges passing over the Dominican Rep. while being ripped apart by tall mountains.Extremely strong convection is noted over the mountains that produced huge amounts of rainfall.EDOP flew in conjunction with radiometers. The combined radar/radiometer data sets was used to develop rain estimation algorithms for the Tropical Rainfall Measuring Mission (TRMM).The ER-2 Doppler Radar (EDOP)aboard the high-altitude ER-2 aircraft is a dual-beam 9.6 GHz radar to measure reflectivity and wind structure in precipitation systems.