The early studies manually interpreted lidar waveforms to identify ground and canopy returns (Hyde et al. 2005). Whilst more robust than automatic methods this is obviously not practical for global studies and so more recent studies have concentrated on developing automatic methods.
The first, and easiest step, is to find the tree top. This is taken as the first point at which the signal rises above a noise threshold. To prevent abnormally large noise spikes causing premature triggering a cumulative energy threshold rather than an intensity threshold is used (Hofton et al. 2000). The total energy above a noise threshold is calculated, then the point at which the cumu- lative energy above noise rises to 1% of the total is taken as the signal start. Determining the ground position and the separation between ground and canopy returns is more complex. First features must be identified then classified as ground or canopy. The traditional technique is to fit Gaussians to the waveform by non-linear iterative algorithms (Hofton et al. 2002, Wagner et al. 2006) such as the Levenberg-Marquardt method (Press et al. 1994). This is an unstable process
and previous studies found that around 4% of waveforms could not be fit to (Hofton et al. 2002). It is also a mathematically ill-posed problem (Hofton et al. 2000) and so even if a waveform is successfully fit, the features may not be an accurate representation of reality.
It is difficult to reliably identify the ground, especially in dense forests were returns may be very weak (Hofton et al. 2002). A simple approach is generally taken, labelling the brightest of the last two features as the ground (Hofton et al. 2000) and this is reported to work well, even in very dense tropical forests (Hofton et al. 2002). Some have used the number and arrangement of identified features to perform qualitative land cover classifications (Reitberger et al. 2008), reporting success when used on well defined and separated vegetation types (herbaceous borders, coniferous forests and fields of grass).
Another feature that lidar directly measures is the fraction of energy returned from the canopy and ground. This can be used to calculate canopy cover if the ratio of canopy to ground reflectance is known (Lefsky et al. 1999) by the following equation;
Cover =ρg ρc 1 Eg Ec + ρc ρg (23)
Where Eg is the energy returned from the ground, Ec is the energy returned from the canopy,
ρgis the ground reflectance and ρcis the canopy reflectance (which will depend upon leaf and bark
reflectance and canopy structure as described in section 1.3). So far studies have assumed values
for the ratio of ρc to ρg from ground data. For example (Lefsky et al. 1999) used a factor of 2.
When using a 10m to 30m diameter footprint it is not entirely clear how many trees are being measured and so the relationship between height and forest biomass is not clear. Some have suggested using stand scale metrics (described in section 3.1.2) to relate lidar signals to biomass (Rosette et al. 2008). Lidar’s direct measurement of vertical structure allows new metrics to be developed which can be empirically related to biophysical parameters with ground based data (Lefsky et al. 1999).
It is still early days for relating lidars measurements to forest parameters and so there is currently a profusion of metrics as investigators try to find robust and accurate inversion techniques. There is little agreement on the best metrics as yet. One of the most popular metrics is the height
of median energy (HOME) (Drake et al. 2002). The cumulative, energy from the top down, is calculated and the median value found. The height that this median value is reached above the ground is the HOME. This will depend on both tree height and canopy density with height. Tall, old canopies with the majority of foliage at the top, will have high HOME and also high biomass, whilst shorter or less dense canopies will have much smaller HOME and also low biomass. This way tree height and stand density, the two most important factors in biomass, are taken into account. HOME was linked to biomass through empirical relationships and found not to saturate, even in dense, structurally complex tropical forests (Drake et al. 2002).
Tree height can be converted to biomass through allometric relationships and some authors believe that these relationships are similar for many species, meaning that global allometrics could be used.
Topography presents a big problem for large footprint lidar. The ground return will be spread out by the height variation across the footprint, as will canopy returns depending on its hetero- geneity, reducing their separation. If the ground height variation is greater than the separation between the bottom of canopy and ground the two signals will not be distinguishable and a phys- ically based inversion will not be possible. Figure 103 illustrates this for a 30m footprint over a
30o slope, the ground return is completely indistinguishable from the canopy.
Figure 13: Illustration of topographic blurring of a 30m footprint on a 30o
slope
It is the variation in ground height across the footprint that causes the blurring, so the smaller the footprint the less the blurring. In fact, small discrete return systems report little difficulty
over steep terrain (Takahashi et al. 2005). Any off nadir pointing will cause blurring so large footprint lidar cannot make multi-angular measurements. There have been attempts to use external topographic maps to determine the ground slope within each footprint, this gives an idea of the extent of the ground return which can be overlaid on the waveform, allowing the fraction of energy from the ground to be determined (Harding and Carabajal 2005, Rosette et al. 2008), illustrated in figure 14. The absolute elevations of the two datasets do not have to match, as the end of the lidar waveform must correspond to the end of the ground, but the horizontal location and resolution of the DEM are vital.
Figure 14: ICESat waveform(red) matched up to a DEM (black dotted) to predict the ground return
(black), from Harding and Carabjal (2005)
This method has only been used in areas with very accurate DEMs (Britain’s Ordnance Survey and America’s USGS) but such accurate maps are not available for the whole world (Rosette
et al. 2007). There are remotely derived near global DEMs (such as the shuttle radar topography
mission, SRTM (Werner 2000) and ASTER (Yamaguchi et al. 1998)) but their reliability over forests is questionable (Dowman 2004) and are coarse resolution compared to lidar footprints (90m for SRTM outside North America) so that local topographic variations will be missed.
An attempt has been made to use SRTM (30m resolution within North America) to calculate slope for correcting ICESat (90m footprint) waveforms (Boudreau et al. 2008). They hoped that the radar scattering centre (somewhere within the canopy) would mirror the ground, so that it did not matter that the SRTM DEM was not true ground when calculating slope. This should be
the case in homogeneous canopies but the assumption may not hold for more heterogeneous cases.
They reported an r2 of 0.65 when comparing ICESat/SRTM derived heights to those from small
footprint lidar. This is an encouraging result but far from perfect.
Lefsky et al. (2007) proposed a method to extract the mean tree height within a footprint (a useful metric for evaluating biomass) from a topographically blurred waveform alone. They calcu- lated three metrics from ICESat waveforms, total extent (distance from first to last return above noise threshold), leading edge extent and trailing edge extent (both defined later in section 5.9.3, their exact meaning is not important right now) into empirical correction factors by comparison with intensive ground data. Even for an empirical relationship, the proposed equations lack el- egance (equation 24 shows the equation for the trailing edge correction factor as an example). These factors were subtracted from total waveform extent to get mean tree height.
tf =√te + 0.92 ∗ te − 88.5 ∗wete + 2049.5 + te
we2 − 14171.4 ∗
te
we3 (24)
Where tf is the trailing edge correction factor te is the trailing edge extent
we is the total waveform extent
This approach reduced the tree height errors on slopes to an average of 5m, which they claim to be “consistent with the requirements of a global dataset”, though without further qualification of those requirements. Interestingly they found that the signs of the correction factors were the opposite of what would be expected; highlighting the non-physical nature of the approach. They admit that this is only a first step on the path to measuring sloped forests, however, such a non- physical method will always be species and site specific and a more physically based method would be preferable.
Conclusion The abilities of large footprint waveform lidar to remotely collect forest structural data have been well demonstrated, most importantly the measurements do not saturate until much higher densities than passive optical and radar signals, allowing measurements of previous blind
spots on the Earth’s surface. The link between measured signals and certain biophysical parameters is far more direct than with other techniques, particularly tree height and canopy cover. It is no surprise that the remote sensing community has such an interest in new lidar missions.
There is still some confusion about how best to go about relating lidar data to forest parameters, but this should dissipate as validation campaigns continue and data becomes more widely available. Lidar footprints are smaller than many other remote sensing instrument’s pixels (30m as opposed to 1km for MODIS). At these scales forests are very heterogeneous and so a geolocation error of a few tens of metres of the lidar footprint might mean that ground measurements are made of completely different trees, weakening allometric relationships and frustrating validation attempts (Drake et al. 2002). This is cited as one of the primary causes of uncertainty in lidar inversion (Næsset and Økland 2002, Hyde et al. 2005, Drake et al. 2002) and it is difficult to advance our understanding of the processes involved without reliable validation data. Here radiative transfer modelling offers the potential to aid understanding (North et al. 2008, Ni-Meister et al. 2001), as long as the model can be trusted to capture effects at the scale of a lidar footprint.