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.

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

Absorption and scattering by the atmosphere

Scattering•Rayleigh, for molecules and tiny particles

•Mie for larger particles

41

1

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:

mao ZcosIK

ma Depends on turbidity of the air (scattering +

absorption) and path length or optical air mass (m)

Z Zcosdistance zenith

path slanthm

1

Typically ma 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

terrain sloping

K

surface horizontal cloudy

K

surface horizontal cloudless

KExKoI

Some calculate components of direct (S) and diffuse (D) radiation

DSK

Absorption

Scattering

Example: Davies et al. 1975

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

Cloudless sky

dsrswsdawaoo ZcosIS

2

1 )(ZcosID dsrsws

dawaoo

scattering erosola

scattering ayleighR

scattering vapor water

absorption erosola

absorption vapor water

ds

rs

ws

da

wa

2

1 )(ZcosIDSK dsrsws

dawaoooo

data. alexperiment on fitted Curves

m. and ble water)(precipita

w of functionare

Cloudy skyDavies et al. 1975 (continue)

cloud of amount totalC

groundthe of albedo

base cloud of albedo

fraction) cloud andtype cloudthe of (function

i layer of ontransmissi cloud

CKK

c

c

Ci

gc

n

iCio

11

Cloud layers

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

Law) s(Beer' form onentialexpT

dust todue g scatterinT

vapor waterof absorption and scatteringT

airdry of scatteringT

TTTT

equation)quadratic (using cloudinessC

CTKK

dw,p,

d

w

p

dwpt

t

ttEx

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

dxx

)x( dx)x(k)x(

dx layerthe in absorption is )x(d

dx)x(k)x(d

Integrating

medium.the ofnature the

to related )(m tcoefficien extinction is k

e)()x(1-

kx 0

(0).value initialthe from

(x)distance the lly withexponentia deplets

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