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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
The signal was de-noised, taking care to preserve the energy 
ratio between the bands, assuming that any noise bias does not 
distort the ratio. The ratio of visible to near infra-red was 
smoothed with Gaussians of decreasing width so that the 
smallest Gaussian to leave a single crossing point of the second 
differential (corresponding to a maximum gradient) was used. 
Using the smallest possible Gaussian ensured the best 
localisation of the edge. To avoid the large gradients of the 
signal start and end only a window between the first and last 
crossing points of the third differential (after smoothing) was 
used. The position of the maximum gradient was taken as the 
start, the last return above noise as the end and the average 
taken as the centre of the ground return respectively. Figure 8 
shows the mean error in derived ground position for one 
hundred simulated waveforms with 5% noise added over forests 
with different canopy covers on a 30° slope. Error bars show the 
standard deviations. 
-25 
! 
-30 | 
-35 ' * *- 1 
0 10 20 30 40 50 60 70 80 80 100 
Canopy covar(S) 
Figure 8. Ground position error against canopy cover 
The method performs well provided there is a reasonable 
ground return. For very dense canopies the ground return is less 
than the noise threshold and so would be hard to see, even 
without topography. 
If it can be assumed that the tallest trees are equally spaced 
across the laser footprint then the tree height will be the 
distance between the first signal return and first ground return. 
The forest is unlikely to be so homogeneous over a 30m 
footprint. The measure of canopy height need not be the tree 
top. Lefsky et al (1999) showed the possibilities of using 
parameters such as the median canopy height to estimate 
biomass and other biophysical parameters through allometrics. 
This can be calculated provided the energy returned from the 
canopy and ground can be separated. The ground start and end 
could be used to further constrain the Gaussian fitting then the 
median of the canopy calculated. How this relates to biomass 
will depend upon the forest’s horizontal and vertical 
heterogeneity. 
Conclusions 
This paper has briefly outlined work in progress on the 
development of algorithms for measuring tree height from 
above canopy waveform lidar. The standard method of Gaussian 
decomposition has been implemented, using realistic 
simulations to precisely quantify the technique’s error (mean 
overestimate of 5.7m for <75% cover; refining of the method is 
needed). 
A method for determining ground position of signals blurred by 
topography or understory with dual waveband lidar has been 
introduced and shown to work reliably for all but the densest 
canopy covers and the errors quantified (mean RMSE of 3.2m 
for <65% cover). Relatively few simulations were available 
(100 over sloping and 225 over flat forests); more are being 
processed with a wider range of densities, slopes and tree 
species for use in further investigations. These will explore the 
affect of noise, thresholds, range resolution, canopy cover and 
pulse length on derived tree height error. 
A reliable method for determining a measure of canopy height 
over slopes is needed. The median canopy position may be the 
easiest to derive. Its sensitivity to heterogeneity and noise will 
be investigated. 
The premature estimation of tree top suggests that the threshold 
used was not high enough. This could be increased to the mean 
noise value plus four or more times the standard deviation, but 
having this fixed would increase the chances of thresholding out 
weak ground returns. An adaptive threshold based upon 
estimates of maximum likely tree heights or signal shape (the 
tree top is unlikely to be isolated from the rest of the tree) may 
give a better solution and should be investigated. 
Acknowledgments 
This work was funded by the NCEOI (Natural environment 
research council Centre for Earth Observation and 
Instrumentation) for project SA-014-DJ-2007 (Hyperspectral 
Imaging LiDAR) and the Hollow waveguide technology for 
C0 2 and canopy measurements (A-scope) project through the 
Centre for Terrestrial Carbon Dynamics (CTCD).and the 
EPSRC, studentship no. GR/9054658 
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