Solar Radiation in the Atmosphere - Short-Wave Solar Radiation in the Earth's Atmosphere - page 15

of the interaction and the phase function for each of M components and then to
calculatethetotalcharacteristicsoftheelementaryvolumewiththeformulas:

M M

α =

1 α i ,

σ =

1 σ i ,

= =

i i

(1.23)

) M

M M

κ =

1 κ i ,

γ =

1 σ i x i (

γ

1 σ i .

x ( )

= = = i i i

These rules also allow calculating characteristics of the molecular and aerosol
scattering and absorption of radiation in the atmosphere separately. Then
(1.23) is transformed to the following:

α = σ m + σ a + κ m + κ a ,

σ = σ m + σ a ,

κ = κ m + κ a , (1.24)

= σ m x m (

γ σ a x a ( γ )+ )

γ x ( ) ,

σ σ

m + a

σ m , κ m , x m ( γ where ) are the volume coefficients of the molecular scattering,

absorption and molecular phase function for the atmospheric gases corre-
spondingly and

σ a , κ a , x a ( γ

)aretheanalogousaerosolcharacteristics.
The rules of summarizing expressed by (1.22)-(1.24) have been derivedwith
the assumption that the particles are interacting with radiation independently.
Here the following question is pertinent: is this assumption correct? From the
view of geometrical optics, which we have appealed to, when introducing the
cross-sections of the interaction, their areas (sections) mustn't intersect within
the elementary volume, i. e. the total area of its projection to the side dS must
be equal to the sum of the areas of all particles. It would be accomplished
if the distances between particles were much larger than the linear sizes of
the cross-sections of the interaction or, roughly speaking, much larger than
the particle sizes. Dividing the elementary volume to small cubes with side d ,
where d is the distinctive size of the particle we are concluding that for this
condition the particle number in the volume dV has to be much less than the
number of cubes - ndV <<dV d 3 ,where n istheparticlenumber

concentration. The second condition - the independency of the interaction
between the particles and radiation - follows from the points of wave optics,
according to which the independency of the interaction occurs if the distances
between the particles are much larger than radiation wavelength

|

d 3 ,i.e. n<< 1

|

λ and that

3 . Using the values of the real molecules and
aerosol particle concentrations in the atmosphere it is easy to test that the
condition n < 1

|λ leads to the inequality n < 1

3 is correct in
the short-wave range for aerosol particles and is broken for molecules of
the atmospheric gases. Nevertheless, it is assumed that light scatters not on

| d 3 |λ is always correct, the condition n < 1