Atmospheric radiation and radiative transfer André Butz Institute of Environmental Physics University of Heidelberg 1 Radiation in the atmosphere Radiative energy fluxes run planetary climate. [IPCC, AR5, 2013] 2 Radiation in the atmosphere Zonal mean radiative cooling and heating: radiation surplus in the tropics, radiation deficit at the poles: poleward transport of heat required. Meridionally unbalanced incoming and outgoing radiative fluxes drive large scale atmosphere and ocean dynamics. [Marshall and Plumb, 2008] 3 Radiation in the atmosphere Production of ozone via the Chapman cycle in the stratosphere - initiated by UV radiation that splits oxygen and ozone Radiation drives molecules atmospheric photochemistry: ozone layer, air pollution, … [http://www.ccpo.odu.edu/SEES/ozone/class] 4 Radiation in the atmosphere Radiation measurements are a key tool for understanding the Measuring radiation enables remote sensing of Earth system … planetary properties such as thermodynamic state, and other planets, atmospheric composition, surface types, etc. stars, the universe. [https://sites.physics.utoronto.ca/bit] 5 Electromagnetic waves Usually, we are interested in [Petty, 2006] the electromagnetic energy flux in a certain direction: Poynting vector. 1 W 푆Ԧ = 퐸 × 퐵 휇 m2 6 Electromagnetic waves Usually, we are interested in [Petty, 2006] the electromagnetic energy flux inUsually a certain, wedirectiondo not : Poyntingcarevector about. 1 W 푆Ԧ = 퐸timescales× 퐵 on the 휇 order ofm2em-wave oscillations: time averaging. 7 Electromagnetic waves Usually, we are interested in [Petty, 2006] the electromagnetic energy flux inUsually a certain, wedirectiondo not : Poyntingcarevector about. 1 W Usually, dealing with 푆Ԧ = 퐸timescales× 퐵 on the 휇 order ofm2em-waveindividual waves (of oscillations: timedifferent directions, averaging. different wavelengths, different shapes) is untreatable. 8 Electromagnetic waves Usually, we are interested in [Petty, 2006] the electromagnetic energy flux inUsually a certain, wedirectiondo not : Poyntingcarevector about. 1 W Usually, dealing with 푆Ԧ = 퐸timescales× 퐵 on the 휇 order ofm2em-waveindividual waves (of oscillations: timedifferent directions, So, we need a „continuum“ quantity averaging. different wavelengths, that is something like the sum of all different shapes) is time-averaged Poynting vector untreatable. contributions in a certain direction at a certain place: radiance. 9 Radiometric quantities 푑퐸푛푒푟푦 W Spectral radiance 퐼휆 (or 퐿휆): 퐼 = 퐼 푡; 푥, 푦, 푧; 훺 = 휆 휆 푑푡 푑휆 푑훺 푐표푠휃 푑퐴 m2 nm sr „Radiant power in wavelength element 푑휆 transported through cross-sectional area 푐표푠휃 푑퐴 into/from W direction element 푑훺 (defined via solid angle [steradian]).“ dW = strength of pencil beam of radiation / ray of light [Petty, 2006] 10 Radiometric quantities 푑퐸푛푒푟푦 W Spectral radiance 퐼휆 (or 퐿휆): 퐼 = 퐼 푡; 푥, 푦, 푧; 훺 = 휆 휆 푑푡 푑휆 푑훺 푐표푠휃 푑퐴 m2 nm sr „Radiant power in wavelength element 푑휆 transported through cross-sectional area 푐표푠휃 푑퐴W into/from W direction element 푑훺 (defined via solid angle dA [steradian]).“ dW dW = strength of pencil beam of radiation / ray of light dl 퐼휆 푡; 푥, 푦, 푧; 훺 [Petty, 2006] [http://www.oceanopticsbook.info] 11 Radiometric quantities 푑퐸푛푒푟푦 W Spectral irradiance 퐹휆: 퐹휆 = 퐹휆 푡; 푥, 푦, 푧 = = 푑푡 푑휆 푑퐴 m2 nm ׬2휋 퐼휆 cos 휃 푑훺 = W „Radiant power in wavelength element 푑휆 transported through dW surface area 푑퐴.“ = „radiant energy flux through surface.“ [Petty, 2006] 12 Radiometric quantities 푑퐸푛푒푟푦 W Spectral irradiance 퐹휆: 퐹휆 = 퐹휆 푡; 푥, 푦, 푧 = = 푑푡 푑휆 푑퐴 m2 nm ׬2휋 퐼휆 cos 휃 푑훺 = W in 2p W „Radiant power in wavelength element 푑휆 transported through dW surface area 푑퐴.“ dA = „radiant energy flux through surface.“ [Petty, 2006] 퐹휆 푡; 푥, 푦, 푧 [http://www.oceanopticsbook.info] 13 Radiometric quantities W 퐴 = 퐴 푡; 푥, 푦, 푧 = න 퐼 푑훺 Spectral actinic flux 퐴휆: 휆 휆 휆 2 4휋 m nm ℎ푐 Photons 퐴휆,푝ℎ = 퐴휆,푝ℎ 푡; 푥, 푦, 푧 = න 퐼휆/ 푑훺 2 4휋 휆 s m nm W „Radiant power / Number of photons in wavelength dW element 푑휆 hitting surface 푑퐴.“ = „Radiant energy available for chemical reactions.“ [Petty, 2006] 14 Radiometric quantities W 퐴 = 퐴 푡; 푥, 푦, 푧 = න 퐼 푑훺 Spectral actinic flux 퐴휆: 휆 휆 휆 2 4휋 m nm ℎ푐 Photons 퐴휆,푝ℎ = 퐴휆,푝ℎ 푡; 푥, 푦, 푧 = න 퐼휆/ 푑훺 2 4휋 휆 s m nm W „Radiant power / Number of photons in wavelength dW element 푑휆 hitting surface 푑퐴.“ W in 4p = „Radiant energy available for chemical reactions.“ [Petty, 2006] 퐴휆 푡; 푥, 푦, 푧 [http://www.oceanopticsbook.info] 15 Radiation in the middle atmosphere Actinic flux 푨흀: Driver for photochemistry. Irradiance 푭흀: Energy balance, heating and cooling rates. Radiance 푰흀: Remote sensing of composition. 16 Planetary radiation sources Collimated radiance beam from sun Planck’s law of black body radiation: 2ℎ푐2 퐵 푇 = 휆 ℎ푐 휆5 exp − 1 휆푘푇 For the sun: 푇 ≈ 5800 퐾 (photosphere) + Fraunhofer lines (absorption in the solar atmosphere) [Thomas and Stamnes, 1999] 17 Planetary radiation sources Collimated radiance beam from sun In the deep UV, solar radiation stems Planck’s lawfrom of blackthe dilute body and radiation: hot solar atmosphere. 2ℎ푐2 퐵 푇 = 휆 ℎ푐 휆5 exp − 1 휆푘푇 For the sun: 푇 ≈ 5800 퐾 (photosphere) + Fraunhofer lines (absorption in the solar atmosphere) [Thomas and Stamnes, 1999] 18 Planetary radiation sources Isotropic thermal emission by the Earth’s surface and atmosphere Planck’s law of black body radiation: 2898 휇푚 휆 = 푚푎푥 푇 2ℎ푐2 퐵 푇 = 휆 ℎ푐 휆5 exp − 1 휆푘푇 For the Earth: 푇 ≈ 180 … 320 퐾 [Petty, 2006] Wavelength / micron 19 Planetary radiation sources In the shortwave (< 4 micron) solar radiation dominates, in the longwave (> 4 micron) Comparison of isotropically reflected solar and emitted telluric radiation telluric radiation dominates (under conceptual Planck’s law assumption). … unless one looks directly into the sun or into mirror-like reflections of the sun – then the sun dominates at all wavelengths. 20 Radiative transfer equation 푑퐼 휆 = 푑푠 퐼휆 푥, 푦, 푧; 훺 −퐼휆 ⋅ 푘푎,휆 −퐼휆 ⋅ 푘푠,휆 +퐵휆 ⋅ 푘푎,휆 푑푠 2휋 휋 푘푠,휆 ′ ′ ′ 푑푧 + න න 퐼휆 Ω ⋅ 푝 Ω → Ω 푑Ω 4휋 0 0 퐼휆 푥′, 푦′, 푧′; 훺 [http://www.oceanopticsbook.info] 21 Radiative transfer equation 푑퐼 Properties of the 휆 = medium 푑푠 Absorption coefficient (n, p, T,…) 퐼 푥, 푦, 푧; 훺 −퐼 ⋅ 푘 휆 휆 푎,휆 Scattering coefficient −퐼휆 ⋅ 푘푠,휆 +퐵휆 ⋅ 푘푎,휆 Scattering phase function 푑푠 2휋 휋 푘푠,휆 ′ ′ ′ 푑푧 + න න 퐼휆 Ω ⋅ 푝 Ω → Ω 푑Ω 4휋 0 0 퐼휆 푥′, 푦′, 푧′; 훺 [http://www.oceanopticsbook.info] 22 Examples: Direct-sun Direct sun: • neglect telluric emission (푇퐸푎푟푡ℎ ≪ 푇푆푢푛) • neglect scattering gain (number of scattered photons ≪ direct photons) 푑퐼 휆 ≈ −(푘 + 푘 )퐼 푑푠 푎,휆 푠,휆 휆 (Beer Lambert‘s law) 푠푒푛푠표푟 ׬ 푘푎,휆+푘푠,휆 푑푠 − 퐼휆 = 퐼휆,푠푢푛푒 푠푢푛 23 Examples: Direct-sun Direct sun: • neglect telluric emission (푇퐸푎푟푡ℎ ≪ 푇푆푢푛) • neglect scattering gain (number of scattered photons ≪ direct photons) 푑퐼 휆 ≈ −(푘 + 푘 )퐼 푑푠 푎,휆 푠,휆 휆 (Beer Lambert‘s law) 푠푒푛푠표푟 ׬ 푘푎,휆+푘푠,휆 푑푠 − 퐼휆 = 퐼휆,푠푢푛푒 푠푢푛 24 Examples: Direct-sun Direct sun: • neglect telluric emission (푇퐸푎푟푡ℎ ≪ 푇푆푢푛) 푘푎,휆: here - rotational-vibrational absorption by CO2 • neglect scattering gain (number of scattered photons ≪ direct photons) 푑퐼 휆 ≈ −(푘 + 푘 )퐼 푑푠 푎,휆 푠,휆 휆 (Beer Lambert‘s law) 푠푒푛푠표푟 ׬ 푘푎,휆+푘푠,휆 푑푠 − 퐼휆 = 퐼휆,푠푢푛푒 푠푢푛 25 Examples: Solar occultation sounding Solar occultation from stratospheric balloons – composition profiling Combine a series of direct sun radiance measurements during sunset / sunrise to infer the concentration profiles of substances in the middle atmosphere. 26 Examples: Solar heating The absorbed radiative energy (difference between TOA and sea level) heats the atmosphere. 27 Examples: Solar heating 휌(푧): air density 1 퐾 퐶푝 : specific heat Spectral heating rate 푯흀: 퐻 = − න 훺 ∙ 훻퐼 푑훺 휆 휆 푛푚 푠 capacity at constant p 휌 퐶푝 4휋 „change (per pathlength) of radiance 푑퐼 along direction 훺” (= fancy variant of 휆 ) 푑푠 28 Examples: Solar heating 휌(푧): air density 1 퐾 퐶푝 : specific heat Spectral heating rate 푯흀: 퐻 = − න 훺 ∙ 훻퐼 푑훺 휆 휆 푛푚 푠 capacity at constant p 휌 퐶푝 4휋 „change (per pathlength) of radiance If one is interested only 푑퐼 along direction 훺” (= fancy variant of 휆 ) in vertically (z) layered 푑푠 ↑ ↓ heating rates (plane 퐹휆 푧 + 푑푧 = 퐹 푧 + 푑푧 − 퐹 푧 + 푑푧 1 푑퐹휆 휆 휆 parallel geometry): 퐻휆 = − 푑푧 휌 퐶푝 푑푧 ↑ ↓ 퐹휆 푧 = 퐹휆 푧 − 퐹휆 푧 29 Examples: Solar heating 휌(푧): air density 1 퐾 퐶푝 : specific heat Spectral heating rate 푯흀: 퐻 = − න 훺 ∙ 훻퐼 푑훺 휆 휆 푛푚 푠 capacity at constant p 휌 퐶푝 4휋 „change (per pathlength) of radiance If one is interested only „given the rich spectral structure푑퐼 along direction 훺” (= fancy variant of 휆 ) in vertically (z) layered ∞ of atmospheric absorption, the 푑푠 spectral integral is a complex Totalheating heatingrates rate(plane 푯: 퐻 = න 퐻 푑휆 ↑ ↓ 휆1 푑퐹 undertaking퐹휆 푧 +: band푑푧 =models퐹휆 푧 “+ 푑푧 − 퐹휆 푧 + 푑푧 parallel geometry): 0 휆 퐻휆 = − 퐾 푑푧 휌 퐶푝 푑푧 ↑ ↓ 푠 퐹휆 푧 = 퐹휆 푧 − 퐹휆 푧 30 Examples: Solar heating 1 푑퐹휆 퐻휆 = − 휌 퐶푝 푑푧 ↑ ↓ 퐹휆 푧 + 푑푧 = 퐹휆 푧 + 푑푧 − 퐹휆 푧 + 푑푧 푑푧 ↑ ↓ 퐹휆 푧 = 퐹휆 푧 − 퐹휆 푧 [Brasseur and Solomon, 2006] 31 Examples: Telluric emission 퐼휆 푡; 푥, 푦, 푧; 훺 Telluric emission: • neglect scattering - operate sufficiently far in the infrared such that scattering is negligible (under cloudless W=W conditions) nadir 푑퐼 휆 = −푘 (퐼 − 퐵 ) 푑푠 푎,휆 휆 휆 (Schwarzschild equation) Earth 32 Examples: Telluric emission Telluric emission: • neglect scattering - operate sufficiently far in the infrared such that scattering is negligible (under cloudless conditions) 푑퐼 휆 = −푘 (퐼 − 퐵 ) 푑푠 푎,휆 휆 휆 (Schwarzschild equation) Upwelling longwave radiation: downward looking from satellite / or high-altitude balloon [Petty, 2006] 33 Examples: Telluric emission Telluric emission: • neglect scattering - operate Transparent wavelength