Outline. December 14, Applications Scattering. Chemical components. Forward model Radiometry Data retrieval. Applications in remote sensing

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1 in in December 4, 27 Outline in 2

2 : RTE Consider plane parallel Propagation of a signal with intensity (radiance) I ν from the top of the to a receiver on Earth Take a layer of thickness dz Layer will absorb according Beer-Lambert but also emit according Kirchhoff resp. Planck Change of intensity di ν will be equal to the emission of the gas E ν minus the absorption A ν di ν = E ν A ν = E ν k a I ν dz Emission given by Planck function: E ν = e ν B ν (T ) B ν (T )dν = 2hν ( 3 )dν c 2 e hν kt di ν = k a (B ν (T ) I ν )dz 3 in in Integration of the I ν () = I ν (z )e τ ν(z ) + z B ν (T )k a e τ ν(z) dz In case of microwave frequencies we use the brightness temperature T B T B (ν). = λ2 2k I ν leading to T B (ν) = T B e τ(z ) + z T (z)e τ(z) k a dz Background term T B depends on observation geometry 4

3 , special cases in Assume isothermal, i.e. T = T eff = const. T B (ν) = T t + T eff ( t) optical thin case: opacity low transmissivity t high optical thick case:opacity high transmissivity t low Application to transmission lines: Loss of line L T B (ν) = T in L + T line( L ) 5 Transmissivity of the in 6

4 Transmission of in the infrared to UV in ZENITH ATMOSPHERIC TRANSMITTANCE UV VIS Near IR Thermal IR CO N O 2 CH 4 O 2 O 3 CO 2 H 2 O Total Wavelength [µm] Contribution of different species to transmission 7 Transmission of in the microwave Zenith Microwave Oxygen Water Vapor (2.3 kg m -2 ) Cloud Liquid Water (.2 kg m -2 ) Total Frequency [GHz] Zenith transmission of the for typical midlatitude conditions H 2 O O 2 Zenith Microwave O 2 H 2 O Dry ( kg/m 2 ) Polar (3. kg/m 2 ) Midlatitude (2.3 kg/m 2 ) Tropical (53.6 kg/m 2 ) in Frequency [GHz] Zenith transmission of the for different conditions 8

5 Intensity in the infrared in 9 Different interaction mechanisms in Absorption is not the only mechanism of interaction

6 of radiation In addition to absorption, light may also be scattered by air molecules, cloud droplets and aerosols is a redistribution of radiation in different directions phase function In analogy to absorption define a scattering cross section Effect of absorption plus scattering is called extinction σ ext = σ scat + σ a The scattering cross section is a kind of shadow. However this shadow can be much bigger than the actual geometrical cross section. The ratio of the scattering cross section to the geometrical area A is called scattering efficiency: Q scat = σ scat /A ( ) 2πr 2 Q scat = 2 (2n + )( a n 2 + b n 2 ) λ n= in Why scattering is important in Particles of diameters less than µm are highly effective at scattering incoming solar radiation reduction of incoming solar energy as compared with that in their absence and consequently cool the Earth Mineral dust particles can scatter and absorb both incoming and outgoing radiation Visible part: light scattering dominates and mainly cool In the infrared: mineral dust acts like an absorber and like a greenhouse gas, thus warms Sulfate aerosols and smoke of biomass burning are currently estimated to exert a global average cooling effect. 2

7 Why scattering is important in Aerosols influence climate directly by scattering and absorption of solar radiation and indirectly through their role as cloud condensation nuclei. Aerosol concentrations are highly variable in space and time. Aerosol radiative effects depend in a complicated way on the solar angle, relative humidity, particle size and composition and the albedo of the underlying surface. For the interaction of solar radiation with aerosols, elastic light scattering is the process of interest. The absorption and elastic scattering of light by a spherical particle is a classical problem in, the mathematical formalism of which is called Mie theory 3 Key parameters used in describing scattering Key parameters are:. wavelength λ 2. particle size in relation to λ α = 2rπ λ 3. complex index of refraction N = n r + in i Often the refractive index is normailized to the one of air: m = N N Distribution of scattered radiation as a function of angle is given by the phase function P(ϑ, α, m) = π F (ϑ, α, m) F (ϑ, α, m) sin ϑdϑ F (ϑ, α, m) is the instensity scattered in angle ϑ in = should include scattering... but determination of the phasefunction is extremely difficult 4

8 regimes in x = 2πr λ = α 5 Mie phase functions for water droplets p(θ) in Θ [deg.] x=.. x=.3. x= from G.Petty, Atmospheric Radiation x=3 x= x=3 For x =. classical symmetric Rayleigh phase function For x 3 forward scattering gets important For x paek near ϑ = 4 starts rainbow For x 2 outside Mie-regime but still explains phenomena geomterical optics cannot explain x= x=3 x=, e+6 x=3, e+7 x=, e+8 e+9 Phase Function 6

9 phase functions for water droplets in x= x=3 x= x=. from G.Petty, Atmospheric Radiation 7 phase functions for water droplets in Glory Fogbow x=3 Corona Secondary Rainbow Primary Rainbow x= Forward Diffraction Peak x=, from G.Petty, Atmospheric Radiation logarithmic representation of phasefunction 8

10 in 9 in 2

11 in 2 VMR=number of gas molecules q per molecule of dry air VMR = N q = p q N d p d where p q is the partial pressure of gas q in 22

12 in z T B (ν) = T B e τ(z) + T (z)e τ(z) k a dz Measurements of the in emission or absorption 23 Simulated spectra in T B (ν) = T B e τ(z ) + Helligkeitstemperatur [K] z Mikrowellen!Emissionspektren bei bodengestützter Messung T (z)e τ(z) k a dz Bern Jungfraujoch Frequenz [GHz] D. Feist, Unive. of Berne, ground!5ghz.ps, 2!Oct!997 Simulated spectra for Bern and Jungfraujoch 24

13 Simulated ozone spectra in Brightness Temperature [K] Brightness Temperature [K] Ozone layer!25 km Ozone layer 4!55 km Frequency [GHz] Brightness Temperature [K] Brightness Temperature [K] Ozone layer 25!4 km Frequency [GHz] Total Ozone Frequency [GHz] 25 Simulated ozone spectra in Brightness Temperature [K] Ozone line for specific ozone layers Total!25 km 25!4 km 4!55 km 55!7 km 7!95 km Frequency [GHz] 26

14 Linewidth example in Linewidth of H 2 O line at 83 GHz for different altitudes 27 Application in microwave radiometry in Aircraft experiment Brightness Temperature [K] H2O Spectra at 83.3GHz (km alt.) measured by AMSOS (A)! TROPIC! MIDLAT.! ARCTIC! (A)! Frequency [GHz] Measured spectra of H 2 O at 83 GHz from aircraft Question: What is the distribution of water vapor in the that leads to such a spectrum? 28

15 in gives us the relation between measured signal and state TB (ν) = TB e τ (z ) + Zz T (z)e τ (z) ka dz remember: ka = n(z)s(ν, T (z), p)f (ν, T (z), p(z)) We have to solve for n(z)!! = there is no analytical solution of this integral... but combining a priori knowledge, xa, with measurement, y, in an optimal way allows to retrieve an altitude profile, ˆ x, from the measurements by considering uncertainties in the measurement, Sy and in the a priori knowledge, Sa ˆ x = xa + Sa KT (KSa KT + Sy ) (y Kxa ) K is the so called kernel function 29 in Water vapor radiometry from Zimmerwald 3