1. © Crown copyright Met Office Radiation scheme for Earth’s atmosphere …and what might not work for exoplanets James Manners 6/12/11

2. © Crown copyright Met Office Table of Contents Two-stream equations Solar and thermal spectrum Gaseous absorption: lines / continuum Rayleigh scattering Aerosols – Mie scattering and absorption (Clouds)

3. © Crown copyright Met Office Some fundamentals…. dI / ds = − k a I + k a B I (n) dsds Kirchhoff’s Law: absorption proportional to emission Requires Local Thermodynamic Equilibrium (LTE) (valid up to ~65km for Earth) Consider a single frequency:

4. © Crown copyright Met Office Some fundamentals…. dI / ds = − k a I + k a B − k s I + k s S I (n) dsds I (n' ) Conservative scattering (no change in frequency)

5. © Crown copyright Met Office Some fundamentals…. dI / ds = − k a I + k a B − k s I + I (n) dsds I (n' ) Phase function: P(n', n): probability of scattering into direction n from n‘

6. © Crown copyright Met Office Two-stream approximation F+F+ F–F– I (n) Height (z) Integrate over up and down directions:

7. © Crown copyright Met Office Two-stream equations Linear simultaneous equations can be solved to give F ± on levels. All we need to know: k a: absorption coefficient k s : scattering coefficient g: asymmetry of scattering (1 st moment of phase function) Q ± : up and down source terms

8. © Crown copyright Met Office Source terms Q ±

9. © Crown copyright Met Office Split between solar (short-wave) and thermal (long-wave) radiation Treat scattering of direct solar radiation Treat thermal emission from atmosphere

10. © Crown copyright Met Office Split between solar (short-wave) and thermal (long-wave) radiation Q−Q− Q+ SW LW Q+ Q−Q− Source term = scattering from direct beam Source term = Plankian emission at temperature of layer

11. © Crown copyright Met Office “Single scattering” properties (k a, k s, g) for each process Gaseous absorption (k a = f(ν), k s = 0) (including continuum absorption) Rayleigh scattering (k a = 0, k s = f(ν), g = 0) Aerosol particles (k a = f(ν), k s = f(ν), g = f(ν) ) Clouds: water droplets and ice crystals

12. © Crown copyright Met Office Gaseous absorption

13. © Crown copyright Met Office Gaseous absorption SW:H 2 O, CO 2, O 3, O 2 LW:H 2 O, CO 2, O 3, N 2 O, CH 4, CFCs, HFCs Absorption line data from HITRAN (HIgh-resolution TRANsmission molecular absorption database). HITRAN data designed for Earth’s atmosphere: Reference Temperature 296K Line broadening coefficients for Earth P/T Isotope abundance for Earth atmosphere

14. © Crown copyright Met Office Gaseous absorption Doppler (temperature) broadening: Gaussian line shape Collision (pressure) broadening: Lorentz line shape Absorption spectrum needs to be adjusted for P/T broadening of lines.

15. © Crown copyright Met Office k-distribution kaka kaka g 0.0 0.5 1.0 kaka weight k-terms Order wavenumber bins by absorption at reference P/T: Number of monochromatic calculations reduced from 50,000 to 6 (in this example).

16. © Crown copyright Met Office Correlated-k method kaka 0.0 0.5 1.0 g Use same ordering (mapping to “g-space”) for all P/T. P / T P ' / T ' kaka 0.0 0.5 1.0 g

17. © Crown copyright Met Office LW bands: overlapping gaseous absorption Relative abundances at 10km (mid-latitude summer, ~ tropopause) 1235789 46 H2OH2O CO 2 O3O3 CH 4 N2ON2O

18. © Crown copyright Met Office SW bands: 123456 line data cross sections HITRAN 2008

19. © Crown copyright Met Office Random overlap of absorption lines H2OH2O N2ON2O CH 4 k-terms Requires 2*2*6 = 24 monochromatic calculations LW band 7

20. © Crown copyright Met Office Equivalent extinction H2OH2O N2ON2O CH 4 k-terms Calculate single “equivalent extinction” coefficient using clear-sky atmosphere with minor gas. Requires 2*1*1 = 2 monochromatic calculations LW band 7 Major gas Minor gas

21. © Crown copyright Met Office “Grey” processes Slowly changing with wavelength (considered constant over band).

22. © Crown copyright Met Office Continuum absorption Absorption poorly modelled far from line centres. Empirical fit to continuum. Add absorption due to: Self-broadened H2O continuum Foreign-broadened H2O continuum Other gases continua may be important for exoplanets.

23. © Crown copyright Met Office Rayleigh scattering Scattering from particles of size << wavelength of light k s  λ -4, k a = 0 Depends linearly on number density Scattering efficiency depends on molecule – will be different for exoplanets. Symmetric phase function (g = 0)

24. © Crown copyright Met Office Aerosol absorption and scattering Particle size >> wavelength of light k a, k s, g calculated using Mie-Debye theory (equivalent to geometric optics for large spherical particles) Assume single size distribution for each aerosol species (+ humidity dependence) Strong forward scattering peak (g > 0)

25. © Crown copyright Met Office δ-rescaling 2-stream approximation loses accuracy for strongly asymmetric scattering k s, g k s ' = k s (1 – f ) g' = (g – f )/(1 – f ) Forward scattering fraction f = g 2

26. © Crown copyright Met Office Cloud droplets and ice crystals Cloud droplets similar to aerosols except: Effective radius depends on number of CCN Sub-grid structure (cloud fraction etc.) Cloud ice based on ice-aggregates: Optical properties parametrised based on external database δ-rescaling required

27. © Crown copyright Met Office New configuration for exoplanets…

28. © Crown copyright Met Office External “spectral files”: Spectral bands Solar spectrum Gases considered k-terms for each gas Coefficients for pressure / temperature scaling Single scattering properties for: Continuum absorption Rayleigh scattering Aerosols & clouds Tools available Corr_k.f90: generates k-terms from line database Scatter.f90: generates properties for aerosol particle size distributions

29. © Crown copyright Met Office Model code and parameter changes: Orbital parameters & solar constant Gas and aerosol species (+ mixing ratios) Surface albedo and emissivity …bound to be others I’ve forgotten

30. © Crown copyright Met Office Questions and answers

31. © Crown copyright Met Office Some fundamentals… Change in radiance (I) for beam direction n Absorption from beam Scattering from beam Scattering into beam n from all other beams n ' Emission into beam