9-11 Nov. 1999 
  
  
  
  
  
  
  
(d from the laser data 
e penetration rate is only a 
ates of both ground and trees 
in order to obtain a correct 
ction rates are not known and 
. measure as described above 
1e three flights, obtaining the 
| pulse 
st pulse 
rst pulse 
re checked against the laser 
lection regression" (software 
t as dependent and all other 
results are given in Table 3. 
International Archives of Photogrammetry and Hemote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999 
again reasonable since the frequency distributions are skewed to 
the right (approx. -1.1), thus the mode is larger than the median 
(by about 1.7 m), and this corresponds to the observation that 
coniferous trees tend to be higher than deciduous trees within a 
neighborhood. 
Since the intercepts of the regression with only one independent 
variable do not significantly deviate from zero (with the 
exception of the maximum height), the same regression was done 
in a much simpler model without offsets, featuring only summer 
first pulse data. Normally a winter flight needs to be taken once, 
from which the ground model can be derived, which does not 
change over time. Consequently, only summer flights are 
necessary from time to time. Therefore it may be of particular 
interest to restrict the estimators to summer first pulse data. 
The results are shown in Table 4. The regression is shown in 
Figure 8. Note that the coefficient for the regression without 
intercept is not a regression coefficient. Rather, it is the slope of 
the regression line and may reach values of higher than 1. Here it 
shows that the maximum height as estimated from P90 is 
underestimated by 4 % (a value of 1.04) while the other heights 
are overestimated, especially Lorey’s mean height for deciduous 
trees, which is again, reasonable. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
ble(s) | correl. | std.err. of 
coeff. estimate 
0.812 +2.65 m 
0.850 +2.41 m 
0.839 42.11 m 
0.877 +1.87 m 
: 0.890 +1.79m 
, SKsF 0.896 +1.74m 
0.829 +2.14 m 
0.880 +1.83m 
0.828 +2.32 m 
0.844 +2.23m 
0.881 +1.88 m 
0.896 +1.78 m 
  
  
analysis with absolute term. 
range from +1.7 m to £2.7 m, 
o the mean standard errors of 
m for coniferous and +1.7 m 
tree heights correlate better 
er last, which is reasonable. 
| the 90? percentile and the 
ntile as being closer to the 
bly well. 
y's mean heights for conifers, 
ian is more reliable; this 15 
  
  
dependent independent | coeff. | std.err. of 
variable variable(s) (slope) | estimate 
dominant height P90sr 0,939 | 1265m 
maximum height P90sr 1.040 | +2.19m 
Lorey’s height / all trees P90sr 0.945 | +2.16 m 
Lorey’s h. / coniferous trees | P90sr 0.972 | +2.67 m 
Lorey’s h. / deciduous trees | P90sr 0.900 | +2.53m 
  
Table 4: Results of the regression analysis without intercept. 
  
| 
| 6 m 3 s» % 
| : From 90th percentile of summer first pulse 
  
Figure 8 Estimates of maximum stand dash om 90 
percentile of laser flight summer first pulse 
A systematic under-estimation of the tree heights as was observed 
by (Magnussen, 1998) and (Magnussen, 1999) could not be 
found, most likely due to the high point density of the laser 
scanner (6.85 compared to 0.2 points per square meter). 
Furthermore, the correlation coefficients are much higher than 
those of (Magnussen, 1999) who only reached values of 0.6 - 0.7 
and standard errors of 3 - 4 m using recovering-models based on 
Weibull or on smoothed likelihood estimates. 
Basal area proportion of coniferous trees 
The basal area proportion of coniferous trees was estimated for 
the 110 angle count samples. The method is generally quite 
inaccurate, since the mean number of trees per angle sample is 
less than 10 in the test area; a slight shift of the sample point may 
drop a tree of some species and include a tree of another species 
which would significantly change the proportion. Thus, according 
to (Sterba, 1998), at least 3 - 12 angle count samples are 
necessary to estimate the basal area proportion of a stand with an 
accuracy of +10 per cent (standard error). 
The average basal area proportion of conifers for the test area is 
62 % for all samples and ranges from 0 to 100 96. Again, stepwise 
variable selection regression was used successfully to provide a 
model for the basal area proportion of coniferous trees, Ber. The 
resulting equation reads, 
Ber = 48.36 + 1.54 py — 0.0197 pw” + 0.00728 pwr psp (2) 
with a regression coefficient R = 0.86 and a standard error of the 
estimates of +15.7 %. Compared to the accuracy of the ground 
samples, the result is very good and suggests that the estimate by 
the laser data is of similar accuracy as the estimate from the 
ground data. The values px are the penetration rates for the 
respective flights as described in Table 2. Figure 9 shows the 
regression. The massive underestimation of the proportion of 
conifers in some stands is due partly to the fact that holes are not 
considered. Furthermore, in most of these stands there are shrubs 
and shelter present, that are higher than 3m and cause significant 
reflection in winter last pulse flight. In order to obtain more 
reliable results, this regeneration vegetation needs to be 
  
  
considered. 
Basal area proportion of conifers 
120 
y = 0,742x + 8,93 + 
100 R - 0,86 
  
co 
e 
  
  
    
  
EC 
© 
! 
| 
| 
© 
N 
© 
1 
  
  
From laser data [95] 
© 
© 
  
0 20 40 60 80 100 
From reference data [%] 
  
  
Figure 9 Estimates of basal area proportion of conifers 
according to equation (2).