4.2 Angle count samples
One hundred and ten angle count samples of the permanent forest
inventory were used to estimate stand heights. The samples are
permanently marked, and the coordinates of the center points
measured at an accuracy of better than +30 cm. For each of these
points an angle count sample of 300 m? area with a basal area
factor of 4 was collected according to (Bitterlich, 1948). For each
contributing tree in each sample the distance, the diameter at
breast height (DBH), and the tree height was measured. The latter
was collected using the Bitterlich Relascope with a measurement
accuracy of +1.1 m for coniferous trees and +1.7 m for deciduous
trees (standard deviation).
The following common stand heights were estimated for each
sample:
e The dominant height is represented by the mean height of
the three thickest trees according to (Pollanschütz, 1971);
e the maximum height is represented by the mean height of
the three highest trees;
e Lorey’s height, i./e. the mean height weighted by the stem
area in breast height.
These values along with the basal areas were calculated in each
sample for coniferous and deciduous trees separately. Statistics
are shown in Table 1 for the 110 samples.
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999
mo the mode;
me the median;
std the standard deviation;
m2 the quadratic mean;
sk the skewness;
cu the curtosis;
P90 |the 90" percentile.
P95 the 95" percentile.
Table 2: Variables calculated from the laser data
Remark: The estimate used for the penetration rate is only a
rough measure. The reflection rates of both ground and trees
need to be taken into account in order to obtain a correct
value. Unfortunately, these reflection rates are not known and
may differ, therefore the simple measure as described above
was chosen.
These variables are calculated for the three flights, obtaining the
following indices:
WL Winter last pulse
SL Summer last pulse
SF Summer first pulse
All reference heights (Table 1) were checked against the laser
variables by a "stepwise variable selection regression" (software
SPSS ®) with the reference height as dependent and all other
values as independent variables. The results are given in Table 3.
Variable Mean | Std. dev. | Min | Max
Stem density [trees/ha] 671 449 175]. 2077
Basal area [m*/ha] 38.4 83| 16.0] 64.0
Dominant height [m] 25.2 45| 10.6, 34.3
Maximum height [m] 28.0 3.9| 19.5} 36.7
Lorey’s height [m] 284 358| 171] 35.3
Lorey s hgt. / coniferous [m] 26.2 42! 159! 360
Lorey’s hgt. / deciduous [m] 24.6 3.9) 17.6} 350
Table 1: Variables calculated from the 110 angle count samples
Estimating stand heights
Several methods to estimate stand heights from the laser data
were investigated. These are compared with the terrestrially
obtained height values.
For each of the angle count samples all laser points within the
sample radius of 9,77 m (corresponding to the area of 300 m?)
were used to plot histograms as shown in Figures 3 - 5. Since the
laser data show significant "noise" at the ground level, a height
threshold of 3 m was chosen below which points are assumed to
be ground points. The following variables were calculated from
the histograms:
Name Description
p The penetration rate estimated as the percentage of
ground points (height above ground lower than 3 m)
from the total number of points;
dependent independent variable(s) | correl. | std.err. of
variable coeff. estimate
dominant height | P90sr 0.812 +2.65 m
P90sz, pw. 0.850 +2.41 m
maximum P90s 0.839 +2.11 m
height P90sr, pwr. 0.877 +1.87 m
P90sr, pw;, Mow 0.890 +1.79m
P90sr, pw; , mow;, SKsr 0.896 +1.74 m
Lorey's height / | P90sp 0.829 +2.14 m
all trees P90sr, pw. 0.880 +1.83 m
Lorey's height mosr 0.828 i2.32m
for conifers Moser, CUsr 0.844 12.23 m
Lorey's height / | mese 0.881 +1.88 m
deciduous trees | mesg, pwr. 0.896 +1.78 m
Table 3:Results of the regression analysis with absolute term.
The standard errors of the estimates range from +1.7 m to £2.7 m,
which is relatively good compared to the mean standard errors of
the terrestrial observations of +1.1 m for coniferous and 41.7 m
for deciduous trees. Generally the tree heights correlate better
with summer first than with winter last, which is reasonable.
There is a strong relation between the 90" percentile and the
maximum heights. The 95" percentile as being closer to the
extremes does not correlate comparably well.
The mode correlates well with Lorey’s mean heights for conifers,
while for deciduous trees the median is more reliable; this is
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