Geoscience Reference
In-Depth Information
The substitution of (1.69) to (1.66) yields the integral equation again for the
source function:
τ
µ
0
)exp
−
τ
d
1
=
ω
0
(
τ
µ
µ
τ
)
µ
)
d
−
B
m
(
τ
µ
µ
0
)
p
m
(
τ
µ
B
m
(
τ
,
µ
,
τ
,
,
,
,
µ
2
0
0
τ
µ
0
)exp
−
τ
d
0
0
−
ω
0
(
τ
µ
µ
τ
)
µ
)
d
−
p
m
(
τ
µ
B
m
(
τ
,
µ
,
τ
,
,
µ
2
τ
−1
+
ω
0
(
τ
)
Sp
m
(
τ
µ
µ
0
)exp(−
τ|µ
0
).
,
,
4
(1.70)
Thus, passing to the phase function expansion over Legendre Polynomials
(1.60) and (1.64) allows obtaining (1.66)-(1.70), where the azimuthal depen-
dence of the functions is absent, that certainly simplifies the analysis and
solution. Besides expansions of the radiance and the source function (1.65)
are called expansions over
the azimuthal harmonics
and the method is called
amethodoftheazimuthalharmonics
.
1.4
Reflection of the Radiation from the Underlying Surface
The ratio of the irradiances reflected from the surface to the irradiances in-
coming to the surface is called
an albedo of the surface
and it is one of the most
important characteristics of the underlying surface:
F
↑
(
τ
0
)
=
A
.
(1.71)
τ
0
)
F
↓
(
This characteristic has a clear physical meaning - it corresponds to the part
of the incoming radiation energy reflected back to the atmosphere. Actually,
if value
A
=
0 then the surface absorbs all radiation (the absolutely black
surface), if value
A
=
1 then, otherwise, the surface absorbs nothing and
reflects all radiation (the absolutely white surface). Generalizing the notion
ofthealbedo,weareintroducing
the albedo of the system of atmosphere plus
surface
,specifyingitatarbitrarylevel
τ
:
F
↑
(
τ
)
τ
=
A
(
)
.
(1.72)
τ
F
↓
(
)
Remember that here and below we are considering values defining the single
wavelength, i. e. the spectral characteristics of the radiation field and surface.
The integral albedo that is called just “albedo” for briefness (do not confuse it
with
the spectral albedo
) is of great importance in atmospheric energetics.
10
10
It is necessary to point out that the albedo (like other reflection characteristics) is formally defined
only for the surface without the atmosphere. In transfer theory, they are often called “true”. Taking
Search WWH ::
Custom Search