160 C. Macfarlane et al. Agricultural and Forest Meteorology 100 2000 155–168
and light scattering, assuming that light scattering for all wavelengths of visible light λ = 400–700 nm is
similar to that for blue light λ 490 nm.
3.5. Statistical treatment of data Variation of L
h
and ¯α
h
owing to sampling position, EV
R
and sharpening of images, was tested using analy- sis of covariance where EV
R
was the covariate. Linear regression was used to develop relationships between
EV
R
, L
h
and ¯α
h
for each stand. Separate relationships were developed for sharpened and unsharpened im-
ages. These relationships were used to determine, iter- atively, the EV
R
that gave agreement between L
h
esti- mated using hemispherical photography, and L and L
e
calculated from L
p
using Eqs. 2 and 3. The ‘correct’ EV
R
estimated by this method was compared to that predicted from Eq. 1 using linear regression. ¯α
h
esti- mated from sharpened and unsharpened photographs
at ‘correct’ EV
R
was compared with a paired t-test. 3.6. Comparison of hemispherical photography and
direct measurement of L After calibrating the hemispherical photography
method against the PCA, the method was tested against a direct estimate of L obtained by destructive
sampling and allometry in four stands of E. globulus located on the Water Authority of Western Australia
effluent disposal treefarm 10 km north of Albany, Western Australia. Three stands were established
with a 2 m spacing between trees within rows which were alternately 2 comprising a ‘double row’ and
5 m apart to give an initial stand density of 1500 stems per hectare Fig. 1b. Trees in these stands
were about 13 m tall. The fourth stand was of similar spacing and density to the stands used to calibrate the
hemispherical photography technique, and trees were about 11.5 m tall.
Three trees within each stand were selected to cover the range of diameters at breast height 1.3 m over
bark D
bh
and felled. For each of the 12 trees, all live branches were removed and stratified into five
groups on the basis of branch diameter 11; 11–16; 16–22; 22–28; 28 mm. The total mass of branches
in each group was measured to the nearest 0.1 kg and two sample branches were selected from each group.
These branches were immediately stripped of leaves and the wood and leaf components weighed. The area
of a 200–250 g sub-sample of leaves from each branch was measured with a calibrated leaf area meter. The
mean ratio of leaf area to total fresh branch mass for all branches from all sample trees in each size class was
calculated and used to estimate the total leaf area of each sample tree. A logarithmic regression was devel-
oped to predict total tree leaf area from tree diameter D
bh
and used to calculate the total leaf area of each stand. The regression was corrected for proportional
bias using Snowden 1991 ratio estimator for bias correction and tested for homogeneity of slope and in-
tercept between stands using analysis of covariance. L for each stand was calculated as the total area of leaves
for the stand divided by the total area of the stand.
3.6.1. Indirect estimation of L by hemispherical photography
Within each of the four stands, three exposures were taken within rows or within the 2 m spaced double
rows; position 1; Fig. 1a, b and between rows posi- tion 2, 3 at EV
R
= − 0.3. Photographic negatives were
scanned and processed as described earlier and all digitised images were sharpened twice. L
h
was esti- mated in HEMIPHOT and the gap fractions at the five
zenith angles used to estimate ¯α
h
after Lang 1986. L
was derived from L
h
using a relationship developed from the other stands. Analysis of variance was used
to test the effect of sampling position within the three double-row stands on L estimated from photography.
A paired t-test was used to compare L estimated from photography and that from allometry within the three
double-row stands.
4. Results
4.1. Effect of EV
R
, sampling position and sharpening on L and ¯
α estimated from hemispherical photography
Analysis of covariance indicated significant re- lationships among EV
R
, L
h
and ¯α
h
and significant differences between stands. Regressions of L
h
against EV
R
were usually highly significant P 0.001 with adjusted R
2
between 0.80 and 0.95 in many cases, but only one regression of ¯α
h
against EV
R
was significant
C. Macfarlane et al. Agricultural and Forest Meteorology 100 2000 155–168 161
Table 2 Slope and intercept of regressions of mean tilt angle ¯α
h
estimated from hemispherical photography against relative exposure value EV
R
of the form: ¯α
h
= EV
R
× a + b
, with adjusted correlation coefficient R
2
, standard error s.e., statistical significance of the slope P and number of observations n
Site Sharpened negatives
Unsharpened negatives a
b R
2
s.e. P
n a
b R
2
s.e. P
n Bunbury
3.78 69.2
0.00 15.4
0.544 9
5.85 66.0
0.00 22.8
0.527 9
Busselton −
0.72 79.8
0.00 12.1
0.886 9
− 0.36
80.6 0.00
10.8 0.937
9 Collie
0.02 63.1
0.00 1.1
0.977 6
− 0.07
62.2 0.00
3.5 0.980
5 Cowaramup
2.04 65.8
0.00 8.6
0.568 9
3.06 70.8
0.00 14.2
0.605 9
Cundinup1 1.33
77.5 0.00
9.4 0.769
9 4.61
80.7 0.09
7.5 0.224
9 Cundinup2
3.60 67.2
0.00 11.5
0.435 9
5.81 69.3
0.04 13.5
0.293 9
Grimwade 3.42
78.1 0.02
7.5 0.312
9 2.93
78.9 0.00
8.4 0.483
8 Mandurah
− 3.70
52.1 0.00
10.8 0.454
9 −
4.10 51.8
0.00 12.1
0.456 9
Northcliffe 2.80
60.6 0.69
1.9 0.004
9 3.35
61.9 0.58
2.8 0.010
9 Scott River
1.31 61.8
0.22 1.8
0.111 9
1.72 63.2
0.33 1.9
0.063 9
Northcliffe, Table 2. L
h
increased by 0.31–0.74 for a one-unit reduction in EV
R
. Later results demonstrated that the slope of the relationship between L
h
and EV
R
increased with increasing L R
2
= 0.86, s.e. = 0.4,
P 0.001 such that the change in L
h
resulting from a one-unit change in EV
R
was approximately 13 ± 0.6 of L. Detailed examination confirmed a linear rela-
tionship between L
h
and EV
R
Fig. 2a but there was evidence of non-linearity in the relationship between
¯ α
h
and EV
R
at Mandurah Fig. 2b. Sampling position had little effect on L
h
P = 0.06 but poor relationships between ¯α
h
and EV
R
resulted partly from large variation in ¯α
h
between sampling positions within stands P 0.001. A significant in-
teraction between position and stand indicated that the effect of sampling position on ¯α
h
was inconsistent. In some stands, ¯α
h
estimated between rows positions 2 and 3; Fig. 1 was larger than that within rows po-
sition 1; Fig. 1 by up to 15
◦
. This could result in an overestimate of ¯α because twice as many measure-
ments were taken from sampling positions between rows where values of ¯α
h
are larger. In stands, where differences between ¯α
h
at position 1 and positions 2 and 3 were large, ¯α may have been overestimated by
as much as 10
◦
. Sharpening significantly reduced L
h
P 0.001 at the same relative exposure and caused an average
3
◦
decrease of ¯α
h
at ‘correct’ exposure P = 0.05. Sharpening increased the contrast between gaps
and foliage resulting in larger gaps when sharpened canopy images were converted from grayscale to
black and white, and reduced L
h
estimated from sharpened compared to unsharpened images Fig. 3.
Small gaps at large zenith angles often disappeared from unsharpened images. In canopies with large L
Grimwade and Collie this sometimes resulted in a gap fraction of zero for the largest zenith angle which
caused excessively large L
h
e.g. 12–15 from some of the most underexposed images. These were not used
for the regressions. A significant interaction between
Fig. 2. The effect of relative exposure value EV
R
on a leaf area index and b mean tilt angle of foliage estimated from sharpened,
digitised negatives photographed within stands of E. globulus at Collie
d
and Mandurah
j
.
162 C. Macfarlane et al. Agricultural and Forest Meteorology 100 2000 155–168
Fig. 3. Comparison of sharpened a, c and unsharpened b, d, digitised images of E. globulus canopies at Collie a, b and
Mandurah c, d. Unsharpened images have smaller gap fractions and fewer gaps at large zenith angles compared to sharpened
images.
sharpening and EV
R
indicated that sharpening digi- tised images also influenced the slopes of regressions
for L
h
P 0.001. Regressions of L
h
on EV
R
de- rived from unsharpened images always had more
negative slopes than those derived from sharpened images Table 3. Larger ¯α
h
from unsharpened com-
Table 3 Slope and intercept of regressions of leaf area index L estimated by hemispherical photography against relative exposure value EV
R
of the form: L = EV
R
× a + b
, with adjusted correlation coefficient R
2
, standard error s.e., statistical significance of the slope P and number of observations n for stands of E. globulus
Site Sharpened negatives
Unsharpened negatives a
b R
2
s.e. P
n a
b R
2
s.e. P
n Bunbury
− 0.367
2.82 0.95
0.08 0.001
9 −
0.400 3.11
0.85 0.15
0.001 9
Busselton −
0.489 3.06
0.86 0.17
0.001 9
− 0.500
3.39 0.90
0.15 0.001
9 Collie
− 0.692
4.33 0.95
0.14 0.001
6 −
0.737 5.21
0.86 0.22
0.015 5
Cowaramup −
0.394 3.18
0.82 0.16
0.001 9
− 0.422
3.58 0.65
0.26 0.005
9 Cundinup1
− 0.390
2.67 0.81
0.14 0.001
9 −
0.474 3.15
0.68 0.24
0.004 9
Cundinup2 −
0.378 3.15
0.45 0.37
0.029 9
− 0.420
3.61 0.41
0.43 0.037
9 Grimwade
− 0.677
4.74 0.96
0.11 0.001
9 −
0.715 5.51
0.97 0.11
0.001 8
Mandurah −
0.312 1.55
0.83 0.11
0.001 9
− 0.376
1.71 0.84
0.13 0.001
9 Northcliffe
− 0.452
3.51 0.87
0.18 0.001
9 −
0.604 4.22
0.85 0.26
0.001 9
Scott River −
0.314 2.74
0.68 0.18
0.004 9
− 0.436
3.28 0.66
0.26 0.005
9 Fig. 4. Comparison of the relative exposure value EV
R
predicted from Eq. 1 to obtain leaf area index
d
and effective plant area index
j
from sharpened, digitised hemispherical photographs with that estimated from the regressions in Table 3 for nine stands
of E. globulus. An outlier Mandurah was not included in the regression.
pared to sharpened images were also the result of the disappearance of small gaps at large zenith angles in
unsharpened images.
4.2. Comparison of predicted and estimated EV
R
The EV
R
required to obtain L
e
or L from hemi- spherical photographs was positively correlated with
the proportion of diffuse radiation penetrating below the canopy as expected Fig. 4. Eq. 1 was a reason-
able predictor of the EV
R
required to obtain L from
C. Macfarlane et al. Agricultural and Forest Meteorology 100 2000 155–168 163
Fig. 5. Comparison of leaf area index
d
and effective plant area index
j
with L
h
from nine stands of E. globulus. An outlier Mandurah was not included in the regression.
hemispherical photographs but was a poor predictor of EV
R
required to obtain L
e
. EV
R
required to obtain L
e
from hemispherical photographs ranged from 0 to 2 while that required to obtain L ranged from −1.5 to 1.
4.3. Calibration of hemispherical photography against the plant canopy analyser
L
h
calculated at EV
R
= 0 intercepts from equations
in Table 3 was strongly correlated with L and L
e
ob- tained from the PCA Fig. 5a, b; R
2
= 0.93, P 0.001,
n = 9. For all regressions, including those of predicted
against estimated EV
R
, the stand at Mandurah had a large residual value and was excluded from the regres-
sions. L ranged from 2.3–5.3 Table 4.
Table 4 Effective plant area index L
e
, leaf area index L and mean tilt angle ¯α, mean ± standard error for stands of E. globulus in south-western Australia measured by the Licor LAI-2000 plant canopy analyser n = 6 and hemispherical photography. For hemispherical photography,
standard errors are those of the regressions used to calculate ¯α
h
Stand L
e
L ¯
α
p
¯ α
h
sharp ¯
α
h
unsharp Bunbury
2.0 ± 0.05 3.0 ± 0.06
63 ± 1 69 ± 15
68 ± 23 Busselton
1.9 ± 0.02 2.9 ± 0.03
62 ± 1 81 ± 12
80 ± 11 Collie
3.5 ± 0.02 5.3 ± 0.03
62 ± 2 61 ± 1
62 ± 4 Cowaramup
2.0 ± 0.03 3.0 ± 0.05
61 ± 5 67 ± 9
75 ± 14 Cundinup1
1.6 ± 0.02 2.4 ± 0.03
62 ± 3 79 ± 9
88 ± 8 Cundinup2
2.2 ± 0.05 3.3 ± 0.06
61 ± 2 67 ± 12
74 ± 14 Grimwade
3.3 ± 0.07 5.0 ± 0.09
62 ± 5 78 ± 8
81 ± 8 Mandurah
1.5 ± 0.05 2.3 ± 0.06
62 ± 5 62 ± 11
58 ± 12 Northcliffe
2.6 ± 0.02 3.9 ± 0.03
59 ± 6 59 ± 2
64 ± 3 Scott River
1.6 ± 0.05 2.4 ± 0.06
69 ± 4 65 ± 2
67 ± 2 Fig. 6. The ratio of the gap fraction estimated using hemispherical
photography to that measured using the Licor LAI-2000 plant canopy analyser at five zenith viewing angles in eight stands
of E. globulus. For each stand, gap fractions are means of six measurements from the PCA, and one image from each of position
1 and either 2 or 3 Fig. 1a taken at an exposure near that required to obtain L
e
.
Within a stand, the gap fraction at small zenith an- gles was usually larger from photographic images than
from the PCA while the gap fraction at large zenith angles was much smaller compared to the PCA Fig.
6. As a result, ¯α
p
was generally less than ¯α
h
from either sharpened or unsharpened photographic images
Table 4. 4.4. Comparison of hemispherical photography and
direct estimation of L in highly clumped stands L
h
of the single row stand of E. globulus Fig. 1a; stand 4 agreed closely with L obtained from destruc-
tive sampling and allometry Table 5. However, for
164 C. Macfarlane et al. Agricultural and Forest Meteorology 100 2000 155–168
Table 5 Leaf area index L measured by allometry and hemispherical photography mean ± s.e. and clumping index of four stands of E.
globulus near Albany, Western Australia. Three stands were planted in closely spaced double-rows and one in evenly spaced single rows.
The positions refer to Fig. 1a, b. is calculated as the ratio of mean L
h
to L from allometry Observations
L
h
Position 1 L
h
Position 2 L
h
Mean L
Allometry
3 3
6 Double row
1 3.53 ± 0.06
2.14 ± 0.11 2.83 ± 0.32
3.37 0.84
2 4.17 ± 0.10
2.16 ± 0.05 3.16 ± 0.45
4.54 0.70
3 4.63 ± 0.11
3.11 ± 0.06 3.87 ± 0.34
4.87 0.79
Single row 4
3.32 ± 0.20 2.97 ± 0.18
3.14 ± 0.14 3.11
1.01
the stands planted in double rows Fig. 1b; stands 1–3, L
h
underestimated L by 16–30 Table 5. L
h
mea- sured beneath the double rows position 1; Fig. 1b
was 1.5–2 times greater than that measured between the double rows position 2; Fig. 1b; P 0.001. L
h
measured only beneath the double rows agreed well with directly measured L.
5. Discussion
