1 Atmospheric Radiation – Lecture 9 PHY Lecture 9 Infrared radiation in a cloudy atmosphere

2 Atmospheric Radiation – Lecture 9 Clouds The problem with clouds in the Earth’s atmosphere is that they are extremely variable – the statistics of size, shape and frequency are very large. Four main types : –stratus –cumulus –cirrus –wave(orographic)

3 Atmospheric Radiation – Lecture 9 Cloud composition Composition is normally water droplets but optically thin ice clouds and aerosol layers also exist Growth of cloud particles: Cloud particle ~ 10um Rain drop ~ 1mm – 1,000,000 cloud particles Processes: Diffusion of water vapour to the cloud particles and subsequent condensation (first stage) Collision and coalescence of particles (large particles) Both absorption and scattering need to be considered (water vapour is a strong absorber)

4 Atmospheric Radiation – Lecture 9 Infrared radiative transfer of clouds For most problems a relatively simple cloud model is used - a homogeneous plane – parallel cloud layer is assumed Radiative transfer equation for a plane-parallel atmosphere with both scattering and absorption is where  =cos  B v = blackbody function (assuming Kirchoff’s law holds)  e = extinction coefficient  a = absorption coefficient  s = scattering coefficient is the source function involving scattering and absorption processes, and  v is single scattering albedo

5 Atmospheric Radiation – Lecture 9 Blackbody assumption for cloud If the cloud behaves as a blackbody, radiation from above and below would not be able to penetrate the cloud – it would behave like the Earth’s surface with emitted radiance from top and bottom surfaces given by the Planck function. How black are clouds? (Liou Fig 4.12)

6 Atmospheric Radiation – Lecture 9 Exchange of IR radiation between cloud and surface: warming of surface at night (blanket effect) Consider a cloud moving over a (snow) surface Liou, Fig 4.13 T c = cloud bottom temperature T s = surface temperature  s = surface emissivity F c = Flux density emitted from cloud F s = Flux density emitted from surface

7 Atmospheric Radiation – Lecture 9 Calculation of upwards and downwards fluxes Surface upwards flux = surface emission + reflected cloud flux Cloud downwards flux = cloud emission + reflected surface flux Solving simultaneous equations:

8 Atmospheric Radiation – Lecture 9 Rate of warming of surface Net flux: If we assume that both surface & cloud are blackbodies (  s =0) then we can define the cloud forcing as If we assume surface temperature increase due to cloud is  T, then from the definition of heating rate The increase of surface temperature  T dependes on the time period  t that the cloud remains over the surface and the net flux divergence

9 Atmospheric Radiation – Lecture 9 Exact solution of RTE for a cloud layer Using optical depth co-ordinates (  ) our basic RTE becomes: where the source term S is where the azimuth independent scattering term J v has been expanded in terms of phase function, P(  ’) This can be solved exactly by the adding method ( see Liou section 6.4), or the method of discrete ordinates ( see Liou section 6.2)

10 Atmospheric Radiation – Lecture 9 Approximations Next time: Two/four stream approximation Eddington’s approximation Order of scattering approximation MODTRAN results for radiance through cloud layers