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N
3 m
Sample Locations
30 m
Figure 5.2
Light attenuation profile locations every 3 m along the 30-m east to west and south to north
transects.
in the reflectance returned to the sensor. Ability to include or exclude atypical structures is expected
to enhance remote sensing reflectance and canopy structure comparisons.
5.2.1.4
Changing Sun Zenith
Light attenuation measurements collected at different times correspond to different sun eleva-
tions or zeniths. In order to relate PAR recordings at different sun zeniths, we used the following
relationships equating the beam transmittance coefficient to the product of leaf area and canopy
extinction coefficient (Decagon Devices, 1991):
ln
t
/ln
t
= K
/K
=
r
(5.1)
Q
1
Q
2
Q
1
Q
2
where ln
t
= the log of the canopy transmission coefficient (
t
) at sun zenith 1 (
Q
), ln
t
= the
Q
1
1
Q
2
correction factor.
Although this relationship is based on the penetration probability without interference and is directly
relevant to sunfleck measurements, we tested the application of the sun zenith normalization to
PAR measurements. The canopy extinction coefficient expression (K) taken from Decagon Devices
(1991) was presented by Campbell (1986) as:
log of
t
at
Q
, K
= the extinction coefficient at
Q
, K
= at
Q
, and
r
= the
Q
2
Q
1
1
Q
2
2
K = (
x
+ tan
Q
)
/[
x
+ 1.774(
x
+ 1.182)
]
(5.2)
2
2
1/2
-0.733
where
equates to the ratio of area projected by an average canopy element on a horizontal to
vertical plane. An
x
x
of 1000 defines a horizontal, an
x
of 1 a spherical, and an
x
of 0 a vertical leaf
distribution, and the
represents the sun zenith angle.
Accounting for no change in leaf area and
Q
between light attenuation measurements and after
simplification, a correction factor for off-nadir sun angles is constructed as follows:
x
r
= (
x
2
+ tan
2
Q
)
1/2
/(
x
2
+ tan
2
Q
)
1/2
= K
/K
.
(5.3)
1
2
Q
1
Q
2
where the sun zenith at the time of measurement is
Q
. Assuming
x
is 1.0 (spherical) and choosing
2
a standard zenith angle of
Q
= 0 (sun directly overhead), then:
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