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## Microwave Interactions with the Atmosphere

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**Microwave Interactions with the Atmosphere**Dr. Sandra Cruz Pol Microwave Remote Sensing INEL 6669 Dept. of Electrical & Computer Engineering, UPRM, Mayagüez, PR**Atmosphere composition**Other components: Carbon dioxide (CO2), Neon (Ne), Helium (He), Methane (CH4), Krypton (Kr), Hydrogen (H2) and Water vapor (highly variable)**Air Constituents in Troposphere and Stratosphere**• N2 78.1%, O2 20.9%, H2O 0-2% • Inert gases 0.938% Many of the least abundant have a disproportionally large influence on atmospheric transmission. • CO2398ppm absorbs 2.8, 4.3 & 15 mm • CH4 1.7ppm absorbs 3.3 & 7.8mm • N2O .35ppm absorbs 4.5, 7.8 & 17mm • O3 ~10-8absorbs UV-B, 9.6mm • CFCl3, CF2CL2 … absorbs IR**Atm. CO2 Concentration**Last 200 years**H2O is less than 2% yet has great effect in climate &**weather**Radiative Transfer in Atmosphereduring Daytime**During daytime only. Nighttime is another story**Atm. Gases & Electromagnetic propagation**• Up to now, we have assumed lossless atm. • For 1 GHz< f< 15 GHz ~lossless • For higher frequencies, =>absorption bands O2 H2O • 22.235 GHz • 183.3 GHz • IR & visible • 50-70GHz • 118.7GHz • IR & visible**Outline**I. The atmosphere: composition, profile II. Gases: many molecules 1. Shapes(G, VVW, L): below 100GHz, up to 300GHz e.g.H2O , O2 2. Total Atmospheric Absorption kg, opacity tq, and atm-losses Lq 3. TB: Downwelling Emission by Atmosphere Sky Temp= cosmic + galaxy**U.S. Standard Atmosphere**Thermosphere (or Ionosphere) 1000-3000oF! 95/120km Mesopause Mesosphere no aircrafts here too cold ~-90oF 50/60km Stratopause Stratosphere- no H2O or dust ozone absorption of UV warms air to ~40oF 8/15km Tropopause Troposphere– clouds, weather P= 1013 mbars = 1013 HPa T= 300K**Atmospheric ProfilesUS Standard Atmosphere 1962**• Temperature • Density in kg/m3 • Pressure P= nRT/V=rairRT/M or Poe-z/H3 or Rair= 2.87**Water Vapor Profile**• Depends on factors like weather, seasons, time of the day. • It’s a function of air temperature. • Cold air can’t hold water • Hot air can support higher humidities.(P dependence) rv(z)= roe-z/H4[g/m3] where ro averages 7.72 in mid latitudes and the total mass of water vapor in a column of unit cross section is**Relative Humidity**• Dew point temperature (dew=rocío) • 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 forms • Relative Humidity • When Tair is close to Tdew=> high %RH • Absolute Humidity, the mass of water per unit volume of air.**Equations for RH**Where e = pressure and expmeans exponentialex**Relative Humidity (RH) simplified equations**T is in Celsius**EM interaction with Molecules**• Total internal energy state for a molecule • electronic energy corresponding to atomic level • vibration of atoms about their equilibrium position • rotation of atoms about center of molecule • E = Ee + Ev + Er • Bohr conditionf lm= (El – Em ) /h • Values for energy differences for • electronic: 2 to 10 eV • vibrational-rotational: 0.1 to 2 eV • pure rotational: 10-4 to 5 x 10-2 eV ( microwaves)**Line Shapes**where, • Slm is the line strength • F(f,flm) is the line shape LINE SHAPES • Lorentz • Gross • Van-Vleck-Weisskopt One molecule frequency Absorption Many molecules: pressure broaden* frequency *caused by collision between molecules**Line shapes**• Lorentz • Gross • Van-Vleck-Weisskopt**Absorption Bands**• Mainly water and oxygen for microwaves Brightness Temperature [K] Frequency [GHz]**Total Atmospheric**• Absorption kg, • Opacity tq, [Np] • Loss factorLq • [L en dB] To convert from Np/km to dB/km multiply by 4.343 for 1-way propagation**Atmospheric Emission**• For clear atmosphere where Also there is some background radiation Tcos=2.7K from the Big Bang and Tgal~0 above 5GHz**Latent Heat – to understand radiation budget need to**monitor water content in atmosphere**Outline: Clouds & Rain**• Single sphere (Mie vs. Rayleigh) • Sphere of rain, snow, & ice (Hydrometeors) Find their ec, nc, sb • Many spheres together : Clouds, Rain, Snow a. Drop size distribution b. Volume Extinction= Scattering+ Absorption c. Volume Backscattering • Radar Equation for Meteorology • TB Brightness by Clouds & Rain**EM interaction with Single Spherical Particles**Definitions: • Absorption • Cross-Section, Qa=Pa /Si • Efficiency, xa=Qa/pr2 • Scattered • Power, Ps • Cross-section , Qs =Ps /Si • Efficiency,xs=Qs /pr2 • Total power removed by sphere from the incident EM wave, xe= xs+ xa • Backscatter, Ss(p) = Sisb/4pR2 Si**Mie Scattering: general solution to EM scattered, absorbed**by dielectric sphere. • Uses 2 parameters (Mie parameters) • Size wrt. l : • Speed ratio on both media:**[Index of Refraction and Refractivity]**• The Propagation constant depends on the relative complex permittivity • Where the index of refraction is • But n’air≅1.0003 • So we define N**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**Mie Solution**• Mie solution • Where am & bm are the Mie coefficients given by eqs 8.33a to 8.33b in the textbook.**Non-absorbing sphere or drop(n”=0 for a perfect**dielectric, which is anon-absorbing sphere) c =.06 Rayleigh region |nc|<<1**Plots of Mie xe versus c**Four 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 sphere • As n’’ increases, so does the absorption (xa), and less is the oscillatory behavior. • Optical limit (r >>l) is xe =2. • Crossover for • Hi conducting sphere at c=2.4 • Weakly conducting sphere is at c=.06**Rayleigh Approximation |nc|<<1**• Scattering efficiency • Extinction efficiency • where K is the dielectric factor**Absorption efficiency in Rayleigh region**i.e. scattering can be neglected in Rayleigh region (small particles with respect to wavelength) |nc|<<1** >> particle size**Scattering from Hydrometeors Rayleigh Scattering Mie Scattering • comparable to particle size --when rain or ice crystals are present. 95GHz (3mm) 33GHz (9mm)**Rayleigh Approximation for ice crystals**Rayleigh scattering (λ >d) Mie scattering (λ ~ d)**Single Particle Cross-sections vs.c**• Scattering cross section • Absorption cross section In the Rayleigh region (nc<<1) =>Qa is larger, so much more of the signal is absorbed than scattered. Therefore For small drops, almost no scattering, i.e. no bouncing from drop since it’s so small.**Gas molecules = much smaller than visible l=> Rayleigh**approx. is OK. Red 700nm Violet 400nm**Mie Scattering**• Mie scatt. is almost independent of frequency • Cloud droplets ~20mm compare to 500nm • Microwaves have l~cm or mm (large) – Rayleigh for most atmospheric constituents • Laser have l~nm - Mie [l dependent] [almost l independent]