Transcript Document

Absorption and scattering by the atmosphere
To compute the solar radiation flux density at the
surface we need to know effects of atmosphere in
filtering and depleting the beam from the top of the
atmosphere to the ground
Scattering
•Rayleigh, for molecules and tiny particles

•Mie for larger particles
1


1
4
Rayleigh, blue sky
Mie, with large particulate
matter. Whitish sky
Absorption, especially due to O3, H2O,CO2
Combined in a simple slab approach, scattering and
absorption reduce transmissivity, so for cloudless
atmosphere:
K  I o cos Zam
am
Depends on turbidity of the air (scattering +
absorption) and path length or optical air mass
(m)
Z
m
slanth path
1

zenith distance cos Z
Typically am varies from about 0.9 (clean) to 0.6
(dirty), typical 0.84
Physically based models
Attempt to account for all physical processes in the chain
I o  K Ex 

K

cloudlesshorizontal surface
K

K


cloudy horizontal surface sloping terrain
Some calculate components of direct (S) and diffuse
(D) radiation
K  S  D
Example: Davies et al. 1975
Cloudless sky
Assumptions:
•Absorption occurs before scattering
•Half of dust deplection is due to absorption
•Scattering occurs equally in forward and backward direction
•Absorption by ozone neglected
Absorption
Scattering
So  I o cos Z wa  da ws  rs ds
Do  I o cos Z wa da
( 1   ws  rsds )
2
 wa  water vapor absorption
 da  aerosol absorption
 ws  water vapor scattering
 are function of w
 rs  Rayleigh scattering
(precipitable water)and m.
 ds  aerosol scattering
Curves fitted on experimental data.
K o  So  Do  I o cos Z wa  da
( 1   ws  rs ds )
2
Davies et al. 1975 (continue)
Cloudy sky
Cloud layers
K   K o   Ci 1   c C g 
n
i 1
 Ci  cloud transmissi on of layer i
(function of the cloud type and cloud fraction)
 c  albedo of cloud base
 c  albedo of the ground
C  total amount of cloud
Comparison with measurements
Physical models are capable of approaching
accuracy of measurements, especially in
cloudless case and for daily averages
Won (1977)
Absorption + Scattering
•It uses hourly reported meteorological parameters
K   K ExTt C t
C t  cloudiness (using quadratic equation)
Tt  TpTwTd
Tp  scattering of dry air
Tw  scattering and absorption of water vapor
Td  scattering due to dust
Tp,w,d  exp onential form (Beer' s Law)
In the computation of the Tp,w,d functions, empirical coefficients
are used. It may be place specific
Beer’s Law (Monteith p. 32-35)
It describes the attenuation of flux density of a parallel
beam of monochromatic radiation through an
homogeneous medium
x
dx
( x )
( x )  k( x )dx
d( x )  k( x )dx
d( x ) is absorption in the layer dx
Integrating
( x )  ( 0 )e  kx
k is extinctioncoefficient (m -1 ) related to
the nature of the medium.
 deplets exponentially withthe distance (x)
from the initial value (0).
It has been found that the very restrictive
assumption about single wave length and
homogeneity of the medium can be relaxed or
modified. So the Beer’s Law can be applied to:
Air (Won, 1977 model),
•k= atmospheric extinction due to turbidity
•x=path length
And also in water, snow, ice, soil, vegetation canopy