AccuPAR LP-80
9
PAR AND LAI THEORY
by:
L
= 2(
A
+
B
)
(19)
An approximate value for
χ
is
χ
= exp(
−
B/
0
.
4
L
).
Example: Readings were obtained as follows:
Table 2: Sample Readings
Θ-deg
Θ-rad
τ
-cosΘ ln
τ
35
0.61
0.21
1.28
41
0.72
0.18
1.29
55
0.96
0.10
1.32
Linear Regression gives:
A = 1.21
B = 0.12
L = 2(1.21 + 0.12) = 2.64
χ
= exp(-0.12 / 0.4 x 2.64) = 0.9
A more precise method for finding
χ
is as follows. We would like
to find values for
χ
and
L
which minimize:
F
=
X
(ln
τ
i
+
K
i
L
)
2
(20)
subject to the constraint,
χ >
0, where
τ
i
are transmission coefficients
measured at several zenith angles, Θ
i
, and the
K
i
are the extinction
coefficients for the corresponding angles.
9.5.1
Correction of PAR for Sun Angle
Canopy transmission (
τ
), measured at one zenith angle, can be used
to predict transmission or radiation interception for other zenith an-
gles. For example, a measurement might be made at Θ = 32
◦
from
which cover (1 - transmission at Θ = 0) is to be calculated. From
equation 16:
ln
τ
1
ln
τ
2
=
K
1
K
2
=
p
(21)
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