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irradiance F was measured using a second instrument on the ground. The
aluminumplate covered withmagnesiumoxide (manufactured from the burn-
ing of magnesium shavings immediately before the airborne observation) was
used as an absolutely white orthotropic surface. The albedo of this plate was
assumed to be equal to 0.97. Calibration curve
ρ =
0.97 F |
I 0 was a result of
ρ = π
the ground measurements. Mark that relation
for the absolutely white
orthotropic surface follows from albedo definition (1.71) and from the ex-
pression for the upwelling irradiance through radiance I 0 (1.4). The values
of downwelling irradiance F and reflected radiance I (
ϑ
ϕ
)wereregistered
simultaneously by two instruments during the airborne observations. The SBC
was computed according to (3.9) as follows:
,
ϑ
ϕ
= ρ
ϑ
ϕ
|
F
r (
,
)
I (
,
)
.
(3.10)
The formula of the theoretical link between the SBC and surface albedo is
obtained by expressing value I (
ϑ
ϕ
,
) from (3.10) with relations (1.4) and (1.71):
π|
π
2
2
1
π
=
ϕ
ϑ
ϕ
ϑ
ϑ
ϑ
A
d
r (
,
) cos
sin
d
.
(3.11)
0
0
The instruments for the observations and the accuracy of the estimations
have been described in Sect. 3.1. However, two different instrumentsmeasured
the radiance and irradiance and the division (3.10) leads to the additional
uncertainty connected with the random displacement of wavelength scales of
the instruments relative to each other (Table 3.1). When the signal magnitude
is weakly varying with wavelength, the effect of displacement is insignificant,
but within the spectral regions, with the fast signal variations (e. g. within the
oxygen absorption band 760 nm) the uncertainty of the SBC could strongly
increase.
The randomuncertainties of the SBCvalues calculatedwith (3.10) are caused
by the flight factors, especially by the surface heterogeneity, and indicated in the
SBC spectra as fast randomoscillations. For its filtration the smooth procedure
with the triangle weight function (Otnes and Enochson 1978) has been used
that leads to the formulas:
1−
m
1
m +1
j
m +1
=
=
R i
d 0 r i +
d j ( r i j + r i + j ), d j
(3.12)
=
j
1
where r i is the initial spectrumof theSBCand R i is the smoothedone, subscript i
corresponds to the point number of the spectrum, m is the smoothing halfwidth
(wehaveusedthevalue m
=
9).We shouldmention that halfwidth m in (3.12) is
a parameter of the frequency filtration of the data as pointed out in the topic by
Otnes and Enochson (1978) and it does not link with the instrumental function
halfwidth expressed by (3.1). We should emphasize that only smoothed SBC
spectra have been used for further analysis. The SBC spectra were considered
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