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EXPLORING THE MEASUREMENT OF FORESTS WITH FULL WAVEFORM LIDAR 
THROUGH MONTE-CARLO RAY TRACING 
Steven Hancock 1 ’ 2 , Mathias Disney', Philip Lewis 1 Jan-Peter Mullef. 
1, Department of Geography, University College London, Gower street, London, WC1E 6BT. United Kingdom and 
NERC Centre for Terrestrial Carbon Dynamics. 
2, Milliard Space Science Laboratory, University College London, RH5 6NT, United Kingdom. 
KEY WORDS: Forestry, structure, lidar, vegetation, simulation, 3D modelling, satellite. 
ABSTRACT: 
This paper presents results from two simulation studies which attempt to measure forest height with full waveform lidar. Monte- 
Carlo ray tracing is used to simulate a full waveform lidar response over explicitly represented 3D forest models. Gaussian 
decomposition and multi-spectral edge detection are used to estimate tree top and ground positions over a range of forest ages, stand 
densities and ground slopes. The error of the height estimates are precisely quantified by comparison with the 3D model height. This 
paper discusses the development and testing of the inversion of tree height from simulations of lidar data, assuming a fixed set of 
lidar characteristics (corresponding to an LVIS-like instrument). It is shown that Gaussian decomposition performs reasonably well 
(mean 5.3m overestimate for <75% cover) for all but the densest canopies over flat ground. The potential of multi-spectral edge 
detection to separate ground and canopy returns from blurred waveform is demonstrated. The methods presented will be refined and 
extended to instrument-specific cases. 
Background 
Carbon flux models are essential for understanding the complex 
processes involved in the Earth’s climate (Woodward et al, 
2004). These models need variables, such as biomass and leaf 
area at a range of scales and locations (Williams et al, 2005). 
Many areas are inaccessible and it would be prohibitively 
expensive to cover the world with airborne sensors. Space- 
borne remote sensing may be the solution. 
Empirical relationships and physical models have been 
developed to relate biomass and leaf area to vegetation indices 
from passive optical instruments, such as MODIS (Myneni et al, 
2002). These indices saturate at moderate canopy densities (LAI 
of 3 or 4, Lovell et al, 2003). Synthetic aperture radar suffers 
from similar saturation problems (Waring et al., 1995). This 
saturation would bias any global remotely sensed data 
assimilation scheme. 
In contrast lidar derived vegetation parameters are less prone to 
saturation over forests as the light can fit through small gaps 
(Lefsky et al., 1999) and it allows a direct measurement of tree 
height. The capabilities of spacebome lidars for measuring 
vegetation were demonstrated by the GLAS instrument aboard 
ICESat (Rosette et al., 2008). 
Simulation system 
There has been a great deal of work on estimating forest 
parameters from full waveform lidar in recent years (Wagner et 
al, 2008, Reitberger et al, 2008). The results of these studies are 
promising; however positional uncertainty of remote 
measurements and the difficulty in seeing the tree top from 
ground level make validation difficult (Hyde et al, 2005). 
Computer simulations allow “validation” as the true parameters 
of the virtual forest are known, unlike reality where there is 
always some uncertainty. This paper will use a Monte-Carlo ray 
tracer based upon the RAT library developed from “frat” 
(Lewis, 1999) to simulate a waveform lidar. Frat has been 
validated in the RAdiation transfer Model Inter-comparison 
exercises (RAMI) two and three, (Pinty et al. 2004, Widlowski 
et al, 2007). These exercises have not yet tested range resolved 
simulations but they have shown that the radiometry of a core 
set of explicit 3D models, including frat, agree to within 1% 
over vegetation for most cases. 
Explicit geometric forest models, in which every needle is 
described (Disney et al, 2006) were used for the simulations. 
Individual Sitka spruce trees of different ages were created 
using the Treegrow model (Leersnijder, 1992). These trees were 
cloned at random locations, with a minimum separation, over a 
variety of slopes to form forests with a range of stand densities 
and different age mixes. The affect of different light regimes in 
different densities on tree structure was ignored. Figure 1 shows 
a ray traced image of a forest with an equal proportion of trees 
of each age on a 20° slope. In addition to the simulated light 
returns the percentage coverage of each material in each range 
bin were recorded and used for validation of derived 
parameters. Spectra from the Prospect model (Jacquemond and 
Baret, 1990), measurements from the LOPEX dataset (Hosgood 
et al, 1995) and the model of Price (1990) were used for leaf, 
bark and soil spectra respectively. Modelled spectra were 
matched against OTTER field data. In a change to the method 
of Disney et al., (2006), needles were allowed to transmit light, 
trusting in the accuracy of Prospect in the absence of reliable 
transmittance data. 
Figure 1, Simulated image of mixed age Sitka spruce forest 
model. 
Using explicit 3D models is computationally expensive but 
avoids assuming that canopies behave as turbid media; an