Atmospheric Radiation and Radiative Transfer

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

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

푑퐸푛푒푟𝑔푦 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

푑퐸푛푒푟𝑔푦 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

퐼휆 푡; 푥, 푦, 푧; 훺

[Petty, 2006]

[http://www.oceanopticsbook.info]

11 Radiometric quantities

푑퐸푛푒푟𝑔푦 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

푑퐸푛푒푟𝑔푦 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

= „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:

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 sufficiently far in the infrared (radiance emitted by such that scattering is ground) 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] 34 Examples: Telluric emission

Telluric emission:

• neglect scattering - operate Transparent wavelength sufficiently far in the infrared (radiance emitted by such that scattering is ground) negligible (under cloudless conditions) Opaque wavelength (radiance emitted by ground gets absorbed 푑퐼 휆 = −푘 (퐼 − 퐵 ) by molecules in the 푑푠 푎,휆 휆 휆 atmosphere, atmosphere emits (Schwarzschild equation)upward and downward)

Upwelling longwave radiation: downward looking from satellite / or high-altitude balloon

[Petty, 2006] 35 Examples: Emission limb sounding

Emission limb sounding from stratospheric balloons – composition profiling.

Combine a series of tangential limb emission spectra at different tangent heights to infer the concentration profiles of substances in the middle atmosphere.

[https://www.imk-asf.kit.edu/english/319.php] 36 Examples: Emission limb sounding

Emission limb sounding from O3 O3 stratosphericCO2 balloons – HNO composition profiling.3

Combine a series of tangential limb emission spectra at different tangent heights to infer the concentration profiles of substances in the middle atmosphere.

[courtesy by M. Höpfner, MIPAS-Balloon, KIT] [https://www.imk-asf.kit.edu/english/319.php] 37 Examples: Thermal cooling

Escape of thermal radiation into space cools the atmosphere and the surface. (But absorption in the atmosphere hinders some of the radiation to escape / cooling less efficient than without atmosphere = greenhouse effect.)

Upwelling longwave radiation: downward looking from satellite / or high-altitude balloon

38 Examples: Thermal cooling

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]

39 Examples: Solar heating and thermal cooling

1 푑퐹휆 퐻휆 = − 휌 퐶푝 푑푧 ↑ ↓ 퐹휆 푧 + 푑푧 = 퐹휆 푧 + 푑푧 − 퐹휆 푧 + 푑푧 푑푧 ↑ ↓ 퐹휆 푧 = 퐹휆 푧 − 퐹휆 푧

In a steady state (T constant), net radiative heating/cooling would need to be balanced by dynamic heat transport. [Brasseur and Solomon, 2006]

40 Examples: Scattered sunlight

Scattered sunlight (typically considered at short wavelengths < 4 micron): • neglect telluric emission 푑퐼 휆 = −(푘 + 푘 )퐼 푑푠 푎,휆 푠,휆 휆 2휋 휋 푘푠,휆 ′ ′ ′ + න න 퐼휆 Ω ⋅ 푝 Ω → Ω 푑Ω 4휋 0 0

41 Examples: Skylight limb sounding

Skylight limb sounding from stratospheric balloons – composition profiling.

Combine a series of scattered sunlight spectra at different tangent heights to infer the concentration profiles of substances in the middle atmosphere.

42 Examples: Skylight limb sounding

SkylightAtmospheric limb sounding scattering from stratosphericproperties depend balloons heavily – compositionon size/wavelength, profiling. particle phase/shape 2휋푟 Combine(liquid, ice): a series x = of scattered sunlight spectra at 휆different tangent heights to infer the concentration profiles of substances in the middle atmosphere.

[Petty, 2006] 43 Examples: Skylight limb sounding

SkylightAtmospheric limb sounding scattering from Scattering phase function stratosphericproperties depend balloons heavily – compositionon size/wavelength, profiling. particle phase/shape 2휋푟 Combine(liquid, ice): a series x = of scattered x ≪ 1 (molecules) sunlight spectra at 휆different tangentCirrus heights22°halo to infer the concentration profiles of substances in the middle atmosphere. x > 1 (liquid)

[Petty, 2006] 44 Examples: Cloud radiative effects

Schematic radiative effects of cloudy vs. clearsky conditions in the Clouds backscatter shortwave and longwave regimes solar shortwave Shortwave radiation and trap Longwave clear-sky cloudy clear-sky cloudy longwave telluric radiation.

[Corti and Peter, ACP, 2009]

45 Examples: Cloud radiative effects

Net radiative flux (퐹) changes (referenced to Clouds backscatter clear-sky) for a cirrus at roughly 11 km altitude solar shortwave radiation and trap longwave telluric For high altitude clouds, the longwave trapping radiation.

heating effect typically outweighs the shortwave backscattering effect such that the cloud is a net heating of the below

atmosphere and surface. cooling

[Meerkötter et al., 1999]

46 Examples: Cloud radiative effects

Net radiative flux (퐹) changes (contours) as function of Clouds backscatter cloud optical thickness and clout top height. solar shortwave radiation and trap cooling heating longwave telluric radiation.

SW LW

For the shortwave effect, it does not really matter at what height the cloud is, cloud thickness is important. The thicker, the „brighter“ the cloud. (However, high ice clouds are often thin.) For the longwave effect, cloud height is important (in particular for opaque clouds) since higher clouds at lower T radiate less to space.

[Corti and Peter, ACP, 2009] 47 Examples: Cloud radiative effects

SW LW

NET „High, thin clouds heat cooling the Earth; low, thick For the shortwave effect, it does not really matter at what height the cloud is, cloud thickness is important. The thicker, the „brighter“ the cloud. clouds cool the Earth.“ (However, high ice clouds are often thin.)

For the longwave[Corti and Peter,effect ACP, 2009], cloud height is important (in particular for opaque clouds) since higher clouds at lower T radiate less to space.

48 Summary

Stratospheric ballooning provides a great way to experience the manifold ways of how radiation shapes our environment:

climate physics, atmospheric photochemistry, atmospheric dynamics, balloon thermodynamics, Earth observation, solar physics, astronomy, …

49 Examples: Cloud radiative effects

Clouds backscatter Net radiative flux (퐹) changes (referenced to clear-sky) and solar shortwave heating rate for a thin cirrus (optical thickness 0.5 in the radiation and trap visible) at roughly 11 km altitude. longwave telluric radiation. Cirrus

[Meerkötter et al., 1999] 50