the 1064 nm laser wavelength is very low, typically in the range 
0.01 to 0.1 (e.g., Williams, 1991) 
Canopy Height Profile Algorithm 
In order to derive canopy height profiles from the raw SLICER 
waveform distributions we adapted the MacArthur and Horn 
(1969) transformation method. Two assumptions inherent to the 
transformation (Aber, 1979) also apply to the transformation of 
SLICER waveforms. The horizontal distribution of canopy 
components within a layer is assumed to be random with 
respect to layers above and below. In other words a Poisson 
distribution is assumed with no horizontal clumping of canopy 
components. Also, the leaf inclination distribution is assumed 
to be constant as a function of height so that the projected leaf 
area in the direction of observation (up-looking from the 
ground or down-looking for SLICER) is related in a constant 
way to total leaf area. Several additional assumptions specific 
to the SLICER waveforms must also be made. As a 
replacement for the proportion of clear-sky to plant interception 
sightings, defining gap fraction viewed upward from the 
ground, the proportion of ground return to canopy return signal 
strength is used. However, in order for this proportion to 
represent downward-viewed gap fraction the ground return 
signal strength is modified in order to account for any 
difference in the average reflectance at 0° phase angle (i.e., 
direct backscatter) of the ground and canopy at the laser 
wavelength. In most circumstances this ratio between ground 
and canopy reflectance is not known at the scale of the laser 
footprints and a value must be assumed. Application of the 
method to SLICER waveforms also assumes that the reflectance 
of the canopy components is constant as a function of height. 
Whereas for the ground sightings each canopy intercept counts 
equally in the resulting distribution, for SLICER an equivalent 
surface area contributes greater return signal as reflectance 
increases. This assumption inherently implies that the ratio of 
woody to leafy surface area and the woody and leafy 
reflectances are constant as a function of height. Finally, it is 
assumed that multiple scattering, causing lengthened photon 
travel paths, does not contribute significantly to delayed signal 
in the waveform, because either the amount of multiply- 
scattered photons received in the backscatter direction is small 
as compared to singly-scattered photons or the magnitude of 
any resulting delay is small. Implications for each of these 
assumptions are considered in Harding et al., (Submitted). 
The effect of occlusion (the decrease in return energy that 
occurs with increasing depth in the canopy, and which is due to 
the previous interception of the laser energy) on the NCPD is 
corrected by weighting this distribution by -1 x In(1- closure) 
(MacArthur and Horn, 1969; Aber, 1979), transforming the 
result to a cumulative distribution of canopy area projected in 
the direction of the laser beam (Fig. 1c). The cumulative 
distribution is normalized and converted to an incremental 
height distribution, yielding the Canopy Height Profile (CHP), 
which depicts the fraction of projected canopy area per 
measurement interval (Fig. 1d). The heights of the CHP 
intervals are referenced to the absolute backscatter energy and 
no comparison of energy between laser shots is made. 
International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 3W14, La Jolla, CA, 9-11 Nov. 1999 
Software Implementations of Waveform Processing 
Algorithms 
There are two main software implementations of these 
processing algorithms. IMH (Interactive MacArthur-Horn), 
developed by D. Harding and M. Lefsky, computes stand 
height and canopy height profiles, and has served as the 
software for most applications of the processing algorithms. 
The IMH functions are included in the latest version of a 
SLICER data browser and editor implemented in the Interactive 
Data Language (IDL) that is available at 
http://denali.gsfc.nasa.gov/lapf. XLV  (X-windows Lidar 
Viewer) is an extension of those routines developed by M. 
Lefsky, and includes the ability to predict transmittance profiles 
and canopy volume measurements (see below). 
4. VALIDATION OF WAVEFORM LIDAR 
MEASUREMENTS 
Height 
Lefsky (1997) examined field and lidar measurements of 
maximum stand height for a dataset consisting of twelve field 
plots with coincident lidar measurements in eastern deciduous 
forests of Maryland and North Carolina, USA. He found good 
correlation (r°= 78%) between field and lidar measurements, 
but a tendency for the lidar measurements to underestimate the 
height of the tallest stands. Field measurements of maximum 
height were derived from estimates of the canopy height 
profile, using the optical quadrat method (MacArthur and Horn, 
1969) and were therefore not as accurate as those obtained 
using methods based on the trigonometric principle. Means et 
al. (1999) found high correlation (29596) and excellent 
agreement between lidar estimates of height and field estimates 
of "canopy height" (mean height of dominant and co-dominant 
trees) obtained using the trigonometric principle. Subsequent 
analysis of that dataset (Lefsky, Unpublished) indicates high 
correlation between lidar and field estimates of maximum stand 
height (17-9490), and that the relationships between field and 
lidar estimated maximum height and canopy height are not 
significantly different from identity. 
Cover 
Plant cover has been estimated as the total adjusted power of 
the ground return, divided by the total power of the canopy 
return. Lefsky (1997) found good agreement between field and 
lidar measurements of cover (R°=65%), and, with the exception 
of two clearly outlining points, found a relationship near 
identity for the lidar and field estimates of cover. Means et al., 
(1999) found excellent agreement between lidar and field 
estimates of cover (R94), with negligible difference between 
field and lidar estimates of cover (RMS=0.08). 
    
   
   
    
    
   
    
    
   
    
    
   
   
      
    
   
   
    
    
    
    
    
    
    
   
    
    
  
   
   
   
    
   
   
  
  
  
    
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