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

© Crown copyright Met Office

Radiation scheme for Earth’s atmosphere…and what might not work for exoplanets

James Manners 6/12/11


Table of Contents

• Two-stream equations

• Solar and thermal spectrum

• Gaseous absorption: lines / continuum

• Rayleigh scattering

• Aerosols – Mie scattering and absorption

• (Clouds)


Some fundamentals….

dI / ds = − kaI + kaB

I (n)

ds

Kirchhoff’s Law: absorption proportional to emission

Requires Local Thermodynamic Equilibrium (LTE)(valid up to ~65km for Earth)

Consider a single frequency:



dI / ds = − kaI + kaB − ksI + ksS

I (n)

ds

I (n' )

Conservative scattering (no change in frequency)



dI / ds = − kaI + kaB − ksI +

I (n)

ds

I (n' )

Phase function:

P(n', n) : probability of scattering into direction n from n‘


Two-stream approximation

F+

F–

I (n)Height (z)

Integrate over up and down directions:


Two-stream equations

Linear simultaneous equations can be solved to give F± on levels.

All we need to know:

• ka : absorption coefficient• ks : scattering coefficient• g : asymmetry of scattering (1st moment of phase function)• Q± : up and down source terms


Source terms Q±


Split between solar (short-wave) and thermal (long-wave) radiation

Treat scattering ofdirect solar radiation

Treat thermal emission from atmosphere


Split between solar (short-wave) and thermal (long-wave) radiation

Q−

Q+

SW LW

Q+

Q−

Source term =scattering from direct beam

Source term =Plankian emission at temperature of layer


“Single scattering” properties(ka, ks, g) for each process

• Gaseous absorption (ka = f(ν), ks = 0)

(including continuum absorption)

• Rayleigh scattering (ka = 0, ks = f(ν), g = 0)

• Aerosol particles (ka = f(ν), ks = f(ν), g = f(ν) )

• Clouds: water droplets and ice crystals


Gaseous absorption


Gaseous absorption

• SW: H2O, CO2, O3, O2

• LW: H2O, CO2, O3, N2O, CH4, 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


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.


k-distribution

ka ka

g0.0 0.5 1.0

ka

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).


Correlated-k method

ka

0.0 0.5 1.0g

• Use same ordering (mapping to “g-space”) for all P/T.

P / T P' / T'

ka

0.0 0.5 1.0g


LW bands:overlapping gaseous absorption

Relative abundances at 10km(mid-latitude summer, ~ tropopause)

1 2 3 5 7 8 9

4 6

H2O

CO2

O3 CH4

N2O


SW bands:

123456

line data

cross sections

HITRAN 2008


Random overlap of absorption lines

H2O

N2O

CH4

k-terms

Requires 2*2*6 = 24 monochromatic calculations

LW band 7


Equivalent extinction

H2O

N2O

CH4

k-terms

Calculate single “equivalent extinction” coefficient using clear-sky atmosphere with minor gas.

Requires 2*1*1 = 2 monochromatic calculations

LW band 7Major gas

Minor gas

Minor gas


“Grey” processesSlowly changing with wavelength (considered constant over band).


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.


Rayleigh scattering

• Scattering from particles of size << wavelength of light

ks λ-4 , ka = 0

• Depends linearly on number density

• Scattering efficiency depends on molecule – will be different for exoplanets.

• Symmetric phase function (g = 0)


Aerosol absorption and scattering

• Particle size >> wavelength of light

• ka, ks, 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)


δ-rescaling

• 2-stream approximation loses accuracy for strongly asymmetric scattering

ks, g

ks' = ks(1 – f )

g' = (g – f )/(1 – f )

Forward scattering fraction f = g2


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


New configuration for exoplanets…


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


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


Questions and answers


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

Documents

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