Geoscience Reference
In-Depth Information
Ω
angle
is accomplished over the instrument-viewing angle. The instruments
are calibrated so that the measured value of the radiance would be outputting
instantaneously. From the theoretical point it means the normalization of the
instrumental functions.
)
λ
2
(
t
)
t
2
=
f
t
f
t
λ
=
f
λ
λ
f
λ
λ
λ
f
t
(
t
)
(
t
)
dt
,
f
(
)
(
(
)
d
,
λ
t
1
λ
1
f
S
(
x
,
y
)
S
f
S
(
x
,
y
)
dxdy
,
=
f
S
(
x
,
y
)
)
Ω
ϑ
ϕ
=
f
Ω
ϑ
ϕ
f
Ω
ϑ
ϕ
ϑ
ϑ
ϕ
f
(
,
)
(
,
(
,
) sin
d
d
Ω
Then the measured value of radiance
I
is expressed through the real radiance
I
ϑ
ϕ
(
x
,
y
,
,
,
t
)bythefollowing:
λ
λ
t
2
2
=
λ
I
dt
d
dxdy
λ
t
1
S
(1.11)
1
ϑ
ϑ
ϕ
ϑ
ϕ
λ
ϑ
ϕ
×
sin
d
d
I
(
x
,
y
,
,
,
t
)
f
t
(
t
)
f
(
)
f
S
(
x
,
y
)
f
(
,
).
λ
λ
Ω
Ω
=
Actually, the equality
I
I
0
is valid according to (1.11) for normalized instru-
ϑ
ϕ
=
=
mental functions if
I
const.
For the radiance measurements, the instrument viewing angle is chosen
as small as possible. In this case, all the factors except the wavelength are
neglected. Then the following is correct:
(
x
,
y
,
,
,
t
)
I
0
λ
λ
2
=
λ
λ
I
I
f
(
)
d
λ
λ
λ
1
and the main instrument characteristic would be a
spectral instrumental func-
tion
f
λ
), that will be simply called the
instrumental function
. If the radiance is
slightly variable in the wavelength interval [
(
λ
λ
2
] the influence of the specific
features of the instrument on the observational process are possible not to take
into account.
The function
f
λ
1
,
λ
) plays an important role in the observation of the semi-
spherical fluxes because the radiance at the instrument input changes evidently
along the direction (
(
λ
ϑ
ϕ
,
). However, comparing (1.4) and (1.11) it is easy to see
that condition
f
Ω
ϑ
ϕ
=
ϑ
must be implemented specifically during the
measurement of the irradiance. This demand to the instruments, which are
measuring the solar irradiance, is called a Lambert's cosine law.
(
,
)
cos
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