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Microwave Interactions with the Atmosphere Microwave Interactions with the Atmosphere Dr. Sandra Cruz Pol Microwave Remote Sensing INEL 6669 Dept. of Electrical & Computer Engineering, UPRM, Mayagüez, PR

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Atmosphere composition Other components: Carbon dioxide (CO 2 ), Neon (Ne), Helium (He), Methane (CH 4 ), Krypton (Kr), Hydrogen (H 2 ) and Water vapor (highly variable)

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Air Constituents in Troposphere and Stratosphere N %, O %, H 2 O 0-2% N %, O %, H 2 O 0-2% Inert gases 0.938% Inert gases 0.938% Many of the least abundant have a disproportionally large influence on atmospheric transmission. CO 2 398ppm absorbs 2.8, 4.3 & 15 m CO 2 398ppm absorbs 2.8, 4.3 & 15 m CH 4 1.7ppm absorbs 3.3 & 7.8 m CH 4 1.7ppm absorbs 3.3 & 7.8 m N 2 O.35ppm absorbs 4.5, 7.8 & 17 m N 2 O.35ppm absorbs 4.5, 7.8 & 17 m O 3 ~10 -8 absorbs UV-B, 9.6 m O 3 ~10 -8 absorbs UV-B, 9.6 m CFCl 3, CF 2 CL 2 … absorbs IR CFCl 3, CF 2 CL 2 … absorbs IR

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Atm. CO 2 Concentration Last 200 years

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Methane

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H 2 O is less than 2% yet has great effect in climate & weather

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Radiative Transfer in Atmosphere during Daytime During daytime only. Nighttime is another story

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Atm. Gases & Electromagnetic propagation Up to now, we have assumed lossless atm. Up to now, we have assumed lossless atm. For 1 GHz< f< 15 GHz ~lossless For 1 GHz< f< 15 GHz ~lossless For higher frequencies, =>absorption bands For higher frequencies, =>absorption bands H2OH2O O2O GHz GHz IR & visible 50-70GHz 118.7GHz IR & visible

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Outline I. The atmosphere: composition, profile II. Gases: many molecules 1. Shapes( G, VVW, L ): below 100GHz, up to 300GHz we find interaction with H 2 O and O 2 2. Total Atmospheric Absorption g, opacity, and atm-losses L Absorption g, opacity, and atm-losses L 3. T B : Downwelling Emission by Atmosphere Sky Temp= cosmic + galaxy

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U.S. Standard Atmosphere Troposphere – clouds, weather Stratosphere- no H 2 O or dust ozone absorption of UV warms air to ~40 o F Mesosphere no aircrafts here too cold ~-90 o F Thermosphere (or Ionosphere) o F! Tropopause Stratopause Mesopause 8/15km P= 1013 mbars = 1013 HPa T= 300K 50/60km 95/120km

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Atmospheric Profiles US Standard Atmosphere 1962 Temperature Temperature Density Density in kg/m 3 Pressure Pressure P= nRT/V= air RT/M nRT/V= air RT/M or P o e -z/H 3 or R air = 2.87

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Water Vapor Profile Depends on factors like weather, seasons, time of the day. Its a function of air temperature. Cold air cant hold water Hot air can support higher humidities.(P dependence) v (z) o e -z/H 4 [g/m 3 ] where o averages 7.72 in mid latitudes total mass of water vapor in a and the total mass of water vapor in a column of unit cross section is

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Relative Humidity Dew point temperature (dew=rocío) 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 Relative Humidity –When T air is close to T dew => high %RH Absolute Humidity, the mass of water per unit volume of air. Absolute Humidity, the mass of water per unit volume of air.

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Equations for RH Where e = pressure and exp means exponential e x

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Relative Humidity (RH) simplified equations T is in Celsius

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Relative Humidity, RH vapor in air Air Temperature T Vapor air can hold Actual Vapor in the air [gr per kg dry air] Relative humidity RH 86 o F % 77 o F % 68 o F % 59 o F %

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Relative Humidity, RH dew Temperature Air Temperature T Dew Temperature T dp Actual Vapor in the air [gr per kg dry air] Relative humidity RH 86 o F 64 o F % 77 o F 60 o F % 68 o F o F o F % 59 o F o F o F %

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Quantum of energy

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EM interaction with Molecules Total internal energy state for a molecule 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 = E e + E v + E r Bohr condition f lm = ( E l – E m ) /h Bohr condition f lm = ( E l – E m ) /h Values for energy differences for Values for energy differences for –electronic: 2 to 10 eV –vibrational-rotational: 0.1 to 2 eV –pure rotational: to 5 x eV ( microwaves)

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Aviris Visible and IR

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Line Shapes where, –S lm is the line strength –F(f,f lm ) is the line shape LINE SHAPES –Lorentz –Gross –Van-Vleck-Weisskopt Absorption frequency One molecule Many molecules: pressure broaden* *caused by collision between molecules

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Line shapes Lorentz Lorentz Gross Gross Van-Vleck-Weisskopt Van-Vleck-Weisskopt Liebe MPM model for Liebe MPM model for –Millimeter wave propagation model

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Absorption Bands Absorption Bands Mainly water and oxygen for microwaves Mainly water and oxygen for microwaves Brightness Temperature [K] Frequency [GHz]

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Note how line width changes with height due to less pressure broadening

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Total Atmospheric Absorption g, Absorption g, Opacity, [Np] Opacity, [Np] Loss factor L Loss factor L [L en dB] [L en dB] To convert from Np/km to dB/km multiply by for 1-way propagation

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Atmospheric Emission For clear atmosphere For clear atmospherewhere Also there is some background radiation T cos =2.7K from the Big Bang and T gal ~0 above 5GHz

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Latent Heat – to understand radiation budget need to monitor water content in atmosphere Latent Heat – to understand radiation budget need to monitor water content in atmosphere

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Scattering from Hydrometeors: Clouds, Snow, Rain

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Outline: Clouds & Rain 1.Single sphere ( Mie vs. Rayleigh ) 2.Sphere of rain, snow, & ice ( Hydrometeors ) Find their c, n c, b Find their c, n c, b 3.Many spheres together : Clouds, Rain, Snow a. Drop size distribution b. Volume Extinction= Scattering+ Absorption c. Volume Backscattering 4.Radar Equation for Meteorology 5.T B Brightness by Clouds & Rain

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Clouds Types on our Atmosphere

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Sizes for cloud and rain drops

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% Cirrus Clouds Composition

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EM interaction with Single Spherical Particles Absorption Absorption –Cross-Section, Q a =P a /S i –Efficiency, a = Q a / r 2 Scattered Scattered –Power, P s –Cross-section, Q s =P s /S i –Efficiency, s = Q s / r 2 Total power removed by sphere from the incident EM wave, e = s + a Total power removed by sphere from the incident EM wave, e = s + a Backscatter, S s ( ) = S i b /4 R 2 Backscatter, S s ( ) = S i b /4 R 2 SiSi

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Mie Scattering: general solution to EM scattered, absorbed by dielectric sphere. Uses 2 parameters (Mie parameters) Uses 2 parameters (Mie parameters) –Size wrt. : –Speed ratio on both media:

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[Index of Refraction and Refractivity] The Propagation constant depends on the relative complex permittivity The Propagation constant depends on the relative complex permittivity Where the index of refraction is Where the index of refraction is But n air But n air So we define N So we define N

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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 : And the power density carried by wave traveling in the z-direction is : –With f in GHz

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Mie Solution Mie solution Mie solution Where a m & b m are the Mie coefficients given by 8.33a to 8.33b in the textbook. Where a m & b m are the Mie coefficients given by 8.33a to 8.33b in the textbook. Probl , menos 7,9,10,13 para jueves Abr10 Probl , menos 7,9,10,13 para jueves Abr10

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Mie coefficients

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Mie Regions Rayleigh region Intermediate or Mie region Optical region Example: sphere with =3.2(1-j) Cambio de regiones de acuerdo a razon de Optical region Intermediate region Rayleigh region Conclusion: regiones se definen de acuerdo a y a n

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Backscattering Rayleigh region Intermediate or Mie region Optical region

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Variations of water dielectric const. with frequency and Temperature

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Non-absorbing sphere or drop (n=0 for a perfect dielectric, which is a non-absorbing sphere) =.06 Rayleigh region |n |<<1

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Conducting (absorbing) sphere =2.4 Rayleigh region Intermediate or Mie region Optical region

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Plots of Mie e versus Plots of Mie e versus As n increases, so does the absorption ( a ), and less is the oscillatory behavior. As n increases, so does the absorption ( a ), and less is the oscillatory behavior. Optical limit (r >> ) is e =2. Optical limit (r >> ) is e =2. Crossover for Crossover for –Hi conducting sphere at =2.4 –Weakly conducting sphere is at =.06 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 Rayleigh Intermediate Optical

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Rayleigh Approximation |n |<<1 Scattering efficiency Scattering efficiency Extinction efficiency Extinction efficiency where K is the dielectric factor where K is the dielectric factor

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Absorption efficiency in Rayleigh region i.e. scattering can be neglected in Rayleigh region (small particles with respect to wavelength) |n |<<1

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Scattering from Hydrometeors Rayleigh Scattering Mie Scattering >> particle size comparable to particle size --when rain or ice crystals are present. 33GHz (9mm) 95GHz (3mm)

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Rayleigh scattering (λ >d) Mie scattering (λ ~ d) Rayleigh Approximation for ice crystals

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Single Particle Cross-sections vs. Single Particle Cross-sections vs. Scattering cross section Scattering cross section Absorption cross section Absorption cross section In the Rayleigh region (n Q a 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 its so small.

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Gas molecules = much smaller than visible => Rayleigh approx. is OK. Red 700nm Violet 400nm

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Mie Scattering Mie scatt. is almost independent of frequency Mie scatt. is almost independent of frequency Cloud droplets ~20mm compare to 500nm Cloud droplets ~20mm compare to 500nm Microwaves have ~cm or mm (large) – Rayleigh for most atmospheric constituents Microwaves have ~cm or mm (large) – Rayleigh for most atmospheric constituents Laser have ~nm - Mie Laser have ~nm - Mie dependent] [almost independent]

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Observe scattering in Visible EM; forward scattering vs. backscattering Mie scattering by dust particles and aerosols Rayleigh scattering by water vapor molecules and gases.

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Mie forward scattering nos impide ver bien a menos que haya alto contraste.

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Forward scattering

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Rayleigh-Mie-Geometric/Optics Along with absorption, scattering is a major cause of the attenuation of radiation by the atmosphere for visible. 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/ ) of the radiation. Scattering varies as a function of the ratio of the particle diameter to the wavelength (d/ ) of the radiation. When this ratio is less than about one-tenth (d/ ), Rayleigh scattering occurs in which the scattering coefficient varies inversely as the fourth power of the wavelength. When this ratio is less than about one-tenth (d/ ), 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 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/ ), the laws of geometric optics begin to apply. at a ratio of the order of 10 (d/ ), the laws of geometric optics begin to apply.

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Mie Scattering (necessary if d/ ), Mie theory : A complete mathematical-physical theory of the scattering of electromagnetic radiation by spherical particles, developed by G. Mie in Mie theory : A complete mathematical-physical theory of the scattering of electromagnetic radiation by spherical particles, developed by G. Mie in 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. 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/ 1 neither Rayleigh or Geometric Optics Theory applies. Need to use Mie. When d/ 1 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. Scattering of radar energy by raindrops constitutes another significant application of the Mie theory.

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Backscattering Cross-section From Mie solution, the backscattered field by a spherical particle is From Mie solution, the backscattered field by a spherical particle is Observe that perfect dielectric perfect dielectric (nonabsorbent) sphere (nonabsorbent) sphere exhibits large oscillations for c>1. Hi absorbing and perfect Hi absorbing and perfect conducting spheres show regularly damped oscillations.

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Backscattering from metal sphere Rayleigh Region defined as Rayleigh Region defined as For conducting sphere Where,

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Scattering by Hydrometeors Hydrometeors (water particles) In the case of water, the index of refraction is a function of T & f. (fig 5.16) In the case of water, the index of refraction is a function of T & f. For ice. For ice. For snow, its a mixture of both above. For snow, its a mixture of both above.

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Liquid water refractivity, n

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Sphere pol signature Co-pol Cross-pol

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Mie Efficiency at 3GHz and 30GHz

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At 300GHz

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Snowflakes Snowflakes Snow is mixture of ice crystals and air Snow is mixture of ice crystals and air The relative permittivity of dry snow The relative permittivity of dry snow The K ds factor for dry snow The K ds factor for dry snow

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Volume Scattering Two assumptions: 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. Volume Scattering coefficient is the total scattering cross section per unit volume. [Np/m]

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Total number of drops per unit volume in units of mm -3 Disdrometer- measures DSD NzNhN/Thies_Laser_Precipitation_Monitor_for_prec ipitation_type_detection_powerpoint_ppt_presentati on Drop size distribution in terms of radius or diameter

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p n (r) for Various Hydrometeors

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Volume Scattering Its also expressed as Its also expressed as or in dB/km units, or in dB/km units, [dB/km] [Np/m] Using... [s,e,b stand for scattering, extinction and backscattering.]

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For Rayleigh approximation Substitute eqs. 41, 44 and 46 into definitions of the cross sectional areas of a scatterer. Substitute eqs. 41, 44 and 46 into definitions of the cross sectional areas of a scatterer. D=2r =diameter

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Noise in Stratus cloud image -scanning K a -band radar

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Volume extinction from clouds Total attenuation is due to gases,cloud, and rain Total attenuation is due to gases,cloud, and rain cloud volume extinction is (eq.8.69) cloud volume extinction is (eq.8.69) Liquid Water Content LWC or m v ) Liquid Water Content LWC or m v ) water density = 10 6 g/m 3 water density = 10 6 g/m 3

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Relation with Cloud water content This means extinction increases with cloud water content. This means extinction increases with cloud water content.where and wavelength is in cm.

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Volume backscattering from Clouds Many applications require the modeling of the radar return. Many applications require the modeling of the radar return. For a single drop [Eq and 8.78] For a single drop [Eq and 8.78] For many drops (cloud) For many drops (cloud)

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Reflectivity Factor, Z Is defined as Is defined as so that and sometimes expressed in dBZ to cover a wider dynamic range of weather conditions. and sometimes expressed in dBZ to cover a wider dynamic range of weather conditions. Z is also used for rain and ice measurements. Z is also used for rain and ice measurements.

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Reflectivity in other books

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Reflectivity & Reflectivity Factor Reflectivity, [cm -1 ] dBZ for 1g/m 3 Reflectivity and reflectivity factor produced by 1g/m3 liquid water Divided into drops of same diameter. (from Lhermitte, 2002). Z (in dB)

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Cloud detection vs. frequency S Ka W

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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.

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Precipitation (Rain) Volume extinction [eq ] Volume extinction [eq ] where R r is rain rate in mm/hr where R r is rain rate in mm/hr [dB/km] and b are given by various model [dB/km] and b are given by various model can depend on polarization since large drops are not spherical but ~oblong. can depend on polarization since large drops are not spherical but ~oblong. Mie coefficients [dB/km]

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e = specific extinction coeff. e = specific extinction coeff.

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W-band UMass CPRS radar

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Rain Rate [mm/hr] If know the rain drop size distribution, each drop has a liquid water mass of If know the rain drop size distribution, each drop has a liquid water mass of total mass per unit area and time total mass per unit area and time rainfall rate is depth of water per unit time rainfall rate is depth of water per unit time a useful formula a useful formula

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Volume Backscattering for Rain For many drops in a volume, if we use Rayleigh approximation For many drops in a volume, if we use Rayleigh approximation Marshall and Palmer developed Marshall and Palmer developed but need Mie for f>10GHz. but need Mie for f>10GHz.

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Rain retrieval Algorithms Several types of algorithms used to retrieve rainfall rate with polarimetric radars; mainly R(Z h ), R(Z h ), R(Z h, Z dr ) R(Z h, Z dr ) R(K dp ) R(K dp ) R(K dp, Z dr ) R(K dp, Z dr )where R is rain rate, Z h is the horizontal co-polar radar reflectivity factor, Z dr is the differential reflectivity K dp is the differential specific phase shift a.k.a. differential propagation phase, defined as

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Raindrops symmetry Differential Reflectivity Z dr

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Snow extinction coefficient Both scattering and absorption ( for f < 20GHz --Rayleigh) Both scattering and absorption ( for f < 20GHz --Rayleigh) for snowfall rates in the range of a few mm/hr, the scattering is negligible. for snowfall rates in the range of a few mm/hr, the scattering is negligible. At higher frequencies,the Mie formulation should be used. At higher frequencies,the Mie formulation should be used. The is smaller that rain for the same R, but is higher for melting snow. The is smaller that rain for the same R, but is higher for melting snow.

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Snow Volume Backscattering Similar to rain Similar to rain

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Radar equation for Meteorology For weather applications For weather applications for a volume for a volume

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Radar Equation For power distribution in the main lobe assumed to be Gaussian function. For power distribution in the main lobe assumed to be Gaussian function.

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Radar Equation R c dB =radar constant (including atmospheric attenuation) For calibrated target

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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. 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).

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