Light Attenuation Transformed to KM and LAI
The canopy light attenuation profiles averaged per height above
the ground surface were parameterized to estimates of the
canopy
LAI
and
KM
. The first step in the transformation was the
calculation of the rate of light falloff with depth. We applied the
standard exponential form of light attenuation passing through
a turbid media that has proven a consistently accurate repre-
sentation of light profiles in vegetative canopies (e.g., Goudri-
aan, 1977; Ramsey
et al.
, 2004). To calculate the light extinc-
tion factor without knowing the vertical biomass or
LAI
depth
distribution, we adapted an iterative procedure after Goudriann
(1977) as shown in Equation 1 that began with setting the
LAI
depth profile to small and equal increments (
LS
). We revised
that estimate to fit the field measured vertical increments. For
example, a one meter high marsh profile would include five 20
m depth increments (
J
= 5), or five vertical bins each weighted
as 0.2 (
LS
value). The
PAR
recordings per 20 m interval (see
Appendix 1: Model Flow Section for more details) setting the
top of canopy recording to zero were entered into Goudriann’s
procedure. With these inputs, the procedure iterated until the
calculated and measured profile (summed from 1 to
J
) deviation
was minimized. The optimized site light extinction factor,
KM
,
was then used to calculate
LAI
values matching the
PAR
profile.
DEVIATION
=
EXP
(–
KM
* (
J
– 1)*
LS
(
J
))–
PAR
(
J
).
(1)
The form of the equation relating
PAR
attenuation to
LAI
was
suggested by Norman (1988) and revised to include
KM
and
PAR
canopy leaf absorption (
A
) as Equation 2 (Welles, 1990;
Decagon Devices, Inc., 2014). The optimized site extinction
factor provided the
KM
estimate (Equation 1). Other inputs
including the sky diffuse and direct fraction (
FB
) at the time of
measurement were calculated from coincident above canopy
recordings and above atmosphere sun irradiance (Ramsey and
Nelson, 2005; Decagon Devices, Inc., 2014; Elterman,1970).
LAI z
KM
FB lnPAR z
A
FB
( )
.
.
.
( )
( .
.
)
=
−
−
−
1 0 1 0
2
1 0
1 0 0 47
(2)
The
PAR
canopy absorption
A
was calculated based on
Equation 3 (Decagon Devices, Inc., 2014) as:
A
= 0.283+0.785*
LFABS
-0.159*
LFABS
**2
(3)
and the leaf absorption (
LFABS
) was estimated to be 0.9.
We adjusted Equation 2 to directly calculate the change
in
LAI
per 20 cm sample interval instead of cumulatively.
Because the
KM
estimate was constant per site-profile, the first
order approximation is shown in Equation 4. Equation 4 was
then used to calculate an incremental
LAI
value for each 20-
cm profile depth (z).
∆
∆
∆
LAI z z
KM
FB
A
FB
PAR
( ) /
.
.
.
( ( .
.
)
(
=
−
−
−
1 0 1 0
2
1 0
1 0 0 47
z PAR z
) /
( )
(4)
Next, these newly calculated incremental values of
LAI
were
used to provide an appropriate
KM
estimate by replacing the
0.2 weighted estimates (
LS
) used in the initial
KM
calculation
of equation 1. Up until this point, the
KM
iterations based on
estimated 0.20 increments (
LS
) proceeded until there was min-
imal change in the
PAR
profile. The second pass
KM
calculation
still iterated until minimum error was realized, however, the
process was performed once not repeated multiple times as is
optional in the
KM
calculation (see Appendix 1: Model Flow
Section for more details). The limitation was applied because
LAI
increments were based already on optimized canopy ex-
tinction and the purpose was to adjust the
KM
to better reflect
LAI
profile changes while retaining its relationship to the mea-
sured light profile not to reconstruct the
KM
optimization. In
effect, this transformed the initial
PAR
extinction rates to more
correctly represent the actual
LAI
profile. Based on the impor-
tance on recreating the measured profiles, we standardized
the second pass iteration limitation in the parameterization of
the light profiles. All subsequent
KM
calculations applied the
incremental
LAI
profile estimates obtained from the
PAR
extinc-
tion profile to produce the final
KM
and
LAI
values.
Although the method is reasonable and based on estab-
lished principals and methods, we caution that the solution is
not unique. Changing the increment values in the
KM
solution
or changing the number of iterations may change the results.
For this purpose we closely followed the approach developed
by Goudriaan (1977) and relied on an established relationship
for relating light recordings to
KM
and
LAI
(Norman, 1988).
Accounting for Sun Zenith Variability
The site average
LAD
was estimated by multiplying the
KM
value by the cosine of the average zenith angle during the site
light attenuation measurements (KM
∗
cos (sun zenith)) (Gou-
driaan, 1977; Zheng and Moskal, 2009). Although, the sun
zenith adjustment can be incorporated in the definition and re-
ferred to simply as
KM
(e.g., Norman and Campbell, 1989), we
explicitly separate the two for clarity. Specifically, optimized
KM
values obtained with iteration of Equation 1 were convert-
ed to
LAD
estimates and these estimates used in Equation 4 to
calculate
LAI
. These
LAI
values are referred to as
LAD
-
LAI
. These
LAD
values should reflect the sun zenith angle corrected light
extinction values reported in (Monsi and Saeki, 2005).
The
LAD
offers more direct interpretability, 0 to 0.5 indi-
cates vertical to spherical and above 0.5 indicates an in-
creasingly horizontal canopy orientation (Goudriaan, 1977;
Ramsey and Jensen, 1995). Further, use of
LAI
values based
on
LAD
provides a more intrinsic representation of the canopy
structure;
LAD
and
LAD
-
LAI
are independent of sun elevation.
LAD
-
LAI
cumulative values are listed along with
KM
and
KM
-
LAI
in Table 1. Except where noted,
LAD
and
LAD
-
LAI
estimates
were used in all subsequent descriptions and analyses.
LAI
Based on a Constant
LAD
Although a key objective of this study was the calculation of
density and orientation of the marsh, we evaluated the rami-
fications of applying a fixed
LAD
in the
LAI
calculation and
its representation of the observed canopy structure. In cases
where the extinction coefficient is unknown,
KM
(or
LAD
) can
be estimated based on suggested values (Decagon Devices, Inc.
2014) or a general assumption of the canopy’s average orienta-
tion. In order to conduct the evaluation, we followed the fairly
common practice of assuming a spherical leaf-stem distribu-
tion or a
LAD
of 0.5.
LAI
calculated based on the fixed spherical
distribution and Equation 4 was then compared to
LAI
calcu-
lated based on the
LAD
value optimized to the
PAR
profile.
Results
Field Measures
Marsh biomass quantity and composition varied highly at
each site, between sites, and over time (Table 1; Appendix 2,
Figure A1). Biomass dry weights exhibited an even distribu-
tion from around 400 to 1,600 Kg/m
2
with a single weight at
2,350 Kg/m
2
. The live-dead ratio as an indicator of biomass
composition was distributed nearly evenly from about 0.5
to a little over 1 with a single ratio near zero and two ratios
above 1.5. Although a dieback pattern was documented for the
Golden Meadow region over this time period (Ramsey
et al.,
810
October 2015
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
