Download PHY2505-Lecture9 - Earth, Atmospheric, and Planetary Physics

Atmospheric Radiation – Lecture 9
PHY2505 - Lecture 9
Infrared radiation in a cloudy
atmosphere
1
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)
2
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
3
(water vapour is a strong absorber)
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 m=cos q
Bv = blackbody function (assuming Kirchoff’s law holds)
be= extinction coefficient
ba= absorption coefficient
bs= scattering coefficient
is the source function involving scattering
and absorption processes , and wv is
single scattering albedo
4
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)
5
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
Tc= cloud bottom temperature
Ts = surface temperature
es = surface emissivity
Fc = Flux density emitted from
cloud
Fs= Flux density emitted from
surface
Liou, Fig 4.136
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:
7
Atmospheric Radiation – Lecture 9
Rate of warming of surface
Net flux:
If we assume that both surface & cloud are blackbodies (es=0) then we
can define the cloud forcing as
If we assume surface temperature increase due to cloud is DT, then
from the definition of heating rate
The increase of surface temperature DT dependes on the time period
Dt that the cloud remains over the surface and the net flux divergence
8
Atmospheric Radiation – Lecture 9
Exact solution of RTE for a cloud layer
Using optical depth co-ordinates (t) our basic RTE becomes:
where the source term S is
where the azimuth independent scattering term Jv has been expanded in
terms of phase function, P(m, m’)
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)
9
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
10