Connecting the Dots between Laser Waveforms and Herbaceous Biomass for Assessment of Land Degradation using Smallfootprint Waveform LiDAR Data.
ABSTRACT Measurement and management of vegetation biomass accumulation in ecosystems typically involves extensive field data collection, which can be expensive and time consuming, while leaving the user with relatively crude inputs to intricate biomass models. Light detection and ranging (LiDAR) remote sensing, which provides extensive height measurements of terrain and vegetation, has become an effective alternative to characterize vegetation structure. In this paper, we report on ongoing efforts at developing signal processing approaches to model herbaceous biomass using a new generation of airborne laser scanners, namely fullwaveform LiDAR systems. Structural and statisticbased feature metrics are directly derived from LiDAR waveforms at the pixel level and related to plotlevel field data. Initial results reveal a definite correlation between the LiDAR waveform and herbaceous biomass. Ongoing research focuses on the links between fractional cover estimated from imaging spectroscopy and woody biomass.

Article: A Comparison of Signal Deconvolution Algorithms Based on SmallFootprint LiDAR Waveform Simulation
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ABSTRACT: A raw incoming (received) Light Detection And Ranging (LiDAR) waveform typically exhibits a stretched and relatively featureless character, e.g., the LiDAR signal is smeared and the effective spatial resolution decreases. This is attributed to a fixed time span allocated for detection, the sensor’s variable outgoing pulse signal, receiver impulse response, and system noise. Theoretically, such a loss of resolution can be recovered by deconvolving the system response from the measured signal. In this paper, we present a comparative controlled study of three deconvolution techniques, namely, Richardson–Lucy, Wiener filter, and nonnegative least squares, in order to verify which method is quantitatively superior to others. These deconvolution methods were compared in terms of two use cases: 1) ability to recover the true crosssectional profile of an illuminated object based on the waveform simulation of a virtual 3D tree model and 2) ability to differentiate herbaceous biomass based on the waveform simulation of virtual grass patches. All the simulated waveform data for this study were derived via the “Digital Imaging and Remote Sensing Image Generation” radiative transfer modeling environment. Results show the superior performance for the Richardson–Lucy algorithm in terms of small root mean square error for recovering the true cross section, low false discovery rate for detecting the unobservable local peaks in the stretched raw waveforms, and high classification accuracy for differentiating herbaceous biomass levels.IEEE Transactions on Geoscience and Remote Sensing 01/2011; 49(6):24022414. · 2.93 Impact Factor
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CONNECTING THE DOTS BETWEEN LASER WAVEFORMS AND
HERBACEOUS BIOMASS FOR ASSESSMENT OF LAND DEGRADATION
USING SMALLFOOTPRINT WAVEFORM LIDAR DATA
aJ. Wu, aJ.A.N. van Aardt, bG. P. Asner, cR. Mathieu, bT. KennedyBowdoin, bD. Knapp, cK. Wessels,
dB.F.N. Erasmus, and eI. Smit
aChester F. Carlson Center for Imaging Science, Rochester Institute of Technology, Rochester, NY
bCarnegie Institution for Science, Stanford, CA
cCouncil for Scientific and Industrial Research, Pretoria, South Africa
dSchool of Animal, Plant and Environmental Science, University of the Witwatersrand, Johannesburg,
South Africa
eKruger National Park Scientific Services, Skukuza, South Africa
ABSTRACT
Measurement and management of vegetation biomass
accumulation in ecosystems typically involves extensive
field data collection, which can be expensive and time
consuming, while leaving the user with relatively crude
inputs to intricate biomass models. Light detection and
ranging (LiDAR) remote sensing, which provides extensive
height measurements of terrain and vegetation, has become
an effective alternative to characterize vegetation structure.
In this paper, we report on ongoing efforts at developing
signal processing approaches to model herbaceous biomass
using a new generation of airborne laser scanners, namely
fullwaveform LiDAR systems. Structural and statisticbased
feature metrics are directly derived from LiDAR waveforms
at the pixel level and related to plotlevel field data. Initial
results reveal a definite correlation between the LiDAR
waveform and herbaceous biomass. Ongoing research
focuses on the links between fractional cover estimated from
imaging spectroscopy and woody biomass.
Index Terms—Biomass, LiDAR, waveform, signal
processing
1. INTRODUCTION
Information regarding global carbon sources (e.g.,
emissions) and sinks (e.g., carbon sequestration) is essential
to our understanding of global energy flows and general
carbon stock fluctuations. Such information also plays an
important role in finescale dynamics, specifically those
related to vegetation biomass and its link to land
degradation, i.e., the loss of an ecosystem’s capability to
provide services to communities. However, measurement
and
accumulation typically involves extensive field data
collection, which includes parameters such as foliar area,
crown volume, bare soil coverage, and vegetation height.
Acquisition of these data can be expensive and time
consuming. Traditional remote sensing technology, such as
multispectral data (e.g. 1km2 pixels in NOAA AVHRR data
or 250m x 250m pixels MODIS data), has been applied to
develop regional indicators of vegetation production.
However, these spectrallyandspatially coarse resolution
data cannot unravel changes in the land surface at the scale
at which fine scale plant physiological processes actually
occur (a few meters). Nor can they identify vegetation
composition and structure, especially in the vertical
dimension. Light detection and ranging (LiDAR) remote
sensing, which provides extensive height measurements of
terrain and vegetation, has created novel opportunities for
accurate characterization of vegetation structure. A LiDAR
sensor typically emits a laser pulse and registers the return
trip distance between the sensor and a reflective target,
thereby enabling range measurements. A novel type of
LiDAR sensor, called waveform LiDAR, capable of
recording and digitizing the fullbackscattered signal at high
vertical resolution (~1ns), holds much promise for detailed
vertical characterization of vegetation structure.
Fullwaveform LiDAR data have been widely used for
estimating forest parameters, e.g., canopy height, stem
diameter, woody biomass, etc. [15]. However, these studies
are constrained to tree characterization. In this paper, we
explored the possibility of aboveground herbaceous
biomass estimation via a signalprocessing approach applied
to smallfootprint waveform LiDAR data. The entire
waveform processing workflow consists of denoising,
signal deconvolution, Gaussian decomposition, statistical
management of vegetation biomass (carbon)
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feature extraction, and regression model development. The
research goal is to eventually link woodyherbaceous
biomass assessment and
approaches, even though this paper focuses mainly on
herbaceous biomass modeling.
2. DATA
2.1. Study area
The study area is bounded by (22°8’00” S; 30°34’52”E) and
(25°32’48”s; 32°2’50”E) in South Africa (Figure 1) and
spans a conservationsubsistence farming land use gradient.
This gradient is defined along a transect from the
Bushbuckridge (communal range lands; high rural
population density) to the Sabie Sands game reserve (private
conservation area) and Kruger National Park (stateowned
conservation area) areas.
lidarimaging spectroscopy
Figure.1: Location of the study area that spans a land use
gradient (westtoeast) from heavily exploited range and
farmland, a private game reserve, and the Kruger National
Park, South Africa
2.2. Remote sensing and field data
Waveform LiDAR data (pixel size: 0.56x0.56 m; vertical
resolution: 1ns) were acquired by Carnegie Airborne
Observatory (CAO) during April 2008. Each scene pixel is
represented by an incoming
distribution with 256 bands at 1ns (0.15m) spacing. The
associated waveform of the outgoing pulse was also
available.
Field data for
this research were
collected from 36
sites in the study
area, each 50 x 50 m
in size. A total of 36
plots were laid out
within each site at a
10 m spacing,
resulting in a gridlike
pattern (Figure 2). For
design with 36 plots/site
(received) waveform
each plot, the herbaceous biomass was weighed within a
0.5x0.5m grid, along with assessment of other variables,
e.g., woody biomass, canopy density, etc.
3. HERBACEOUS BIOMASS MODELING
Figure 3 shows the workflow of the waveform LiDARbased
herbaceous biomass modeling procedure. It consists of two
parts, namely signal preprocessing and modeling.
Denoising (FFT)
Figure.3: Workflow of LiDAR waveform based herbaceous
biomass modeling
3.1. Signal preprocessing
The raw incoming (received) waveform typically exhibits a
stretched and featureless character, attributed to a fixed time
span allocated for detection, the sensor’s variable outgoing
pulse signal, the receiver impulse response, and system
noise. Signal preprocessing therefore is necessary to recover
the true response distribution of optically active targets
along the path of the LiDAR waveform.
First, system noise is typically present in the form of
high frequency components of the raw signal in the
frequency domain. Therefore, we smoothed the raw
waveform by setting a cutoff frequency threshold for
removal of noise components in the frequency domain (a
similar effect as a low pass filter), followed by conversion
back to the time domain. The subsequent noisefiltered
waveform can be mathematically modeled as:
Pr(t) = Pt(t)*σ (t)*Γ(t) (1)
where Pt(t) refers to the outgoing waveform (known), σ (t)
represents the crosssection (the true response distribution of
the target), and Γ(t) is the receiver impulse response
(estimated by the return signal from a flat ground area). The
true response of the target can be derived by sequentially
50 m50 m
10 m10 m
Figure.2: Sitelevel sampling
Signal
Preprocessing
Modeling
Biomass model
Deconvolution (RichardLucy)
Gaussian decomposition (EM)
Feature metrics extraction
Linear regression
Raw waveform
Field data
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deconvolving the incoming waveform from the outgoing
waveform and receiver impulse response. We applied the
RichardsonLucy algorithm [6] for this purpose. Richardson
Lucy is an iterative deconvolution procedure, which is based
on Bayes’ statistical theorem. The mathematical solution of
σ (t) can be expressed as:
)
σ i+1(t) =)
σ i(t)
h(t)*)
where h(t) = Pt(t)*Γ(t), and i denotes the iteration. The
residual for each iteration is computed as:
ri(t) = Pr(t) − h(t)*)
The residual will converge as the iteration progresses. The
user can terminate the iteration, either by selecting a specific
residual threshold or by setting a constant iteration number.
Harsdorf and Reuter [7] claimed that the onedimensional
RichardsonLucy algorithm resulted in the most stable
results when compared to Fourier transform and non
negative least squares approaches. This processing step
enhances the vertical signal resolution, which facilitates
extraction of target information from the waveform.
3.2. Modeling
Pr(t)
σ i(t)*h(t)
(2)
σ i(t) (3)
Figure.4: Raw waveform (left) and Gaussian decomposition
of the deconvolved waveform (right)
The last component of a return LiDAR waveform typically
corresponds to the groundlevel response, which may be
composed of bare soil, grass, leaves, stones, etc. We
hypothesized that the herbaceous biomass, directly
associated with the grass abundance, can be linked to the
properties of the last waveform component (e.g. width,
height, area). Figure 4 (left) shows the raw return waveform
(single peak) where there is no tree or shrub. Figure 4 (right)
reveals a dualpeak intensity distribution after deconvolution
of the raw waveform; this was hidden in the raw signal (left)
due to the existence of an imperfect system response and
variable outgoing “pulse”. An expectationmaximization
(EM) algorithm was subsequently employed to decompose
this deconvolved waveform into two individual Gaussian
curves [8]. It is evident from Figure 4 that the second
Gaussian is mainly due to the asymmetric trailing edge,
relative to the leading edge in the raw waveform. This
asymmetric trailing edge typically results from the late
return photons due to the structure of the ground layer (e.g.,
grass), leading to multiple scattering of the return signal. On
the other hand, the first Gaussian was seen as corresponding
mainly to the single scattering from the ground material (e.g.
bare soil, grass, stone, etc). The mathematic description of
this waveform as a mixed Gaussian model is expressed as:
x−u1
()2
2σ1
g(t) = a1e
where a1 and a2 are the amplitudes of the Gaussian peaks
and σ1 and σ2 are the standard deviation (related to width) of
each Gaussian (x and µi are input and mean variables,
respectively). The next step involved extraction of waveform
metrics (independent variables) and linking these to the field
biomass data. Since we have parameterized the waveform in
terms of a Gaussian distribution, feature metrics can be
directly extracted from Eq. 4 (e.g., a1, a2, σ1, and σ2). We
also added two additional metrics, namely s1 and s2, which
correspond to the integration (area) of the two Gaussian
curves. These six independent metrics are not necessarily
uncorrelated, which led to the exclusion of highlycorrelated
(> 0.8) metrics after calculation of correlation coefficients.
The herbaceous biomass model was finally retrieved based
on a linear regression fit between the selected, independent
feature metrics and field data in the form of:
n
∑
−
2
+ a2e
−
x−u2
(
2σ2
)2
2
(4)
Hbiomass=
cnpn+ k
1
(5)
where pn refers to the nth feature metric, cn represents the
associated coefficient, and k is the regression intercept.
4. EXPERIMENTAL RESULTS
The proposed model was tested for 6 different sites, the only
ones that contained waveform lidar data. Herbaceous
biomass in these sites ranged between 0~90 gram/plot (216
plots in total). We only considered waveforms (before
deconvolution) with a single peak, i.e., waveforms that did
not exhibit multiple peaks due to tree canopy returns. This
reduced the number of sample plots to 159. We also
assumed that the GPS locations of the pixelbased
(0.56x0.56m) waveform and the plot center (field sample)
were both representative of the same plot. Herbaceous
biomass samples were then grouped into 5g classes for the
purposes of this study, which led to 18 weightbased
biomass classes (e.g. 0~5, 5~10, …85~90) in the 090g
range. Waveformderived metrics and measured biomass
were averaged within each class.
Table 1 shows the correlation coefficient matrix for the
field data and waveformderived metrics, used to optimize
the variable selection. All the metrics in Table 1 have been
converted into “natural log” space to minimize the
nonlinearity between the parameters. It is evident that pairs
(a1, s1) and (a2, s2) exhibited high correlations. We therefore
discarded a1 and s2 to ensure model robustness, since these
correlated metrics also exhibited a lower correlation to the
biomass, when compared with s1 and a2, respectively.
Single scattering
Multiple
scattering
Deconvolved
1st component
2nd component
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Figure 5 shows the results of herbaceous biomass
estimation using feature metrics σ1, s1, a2, and σ2 (Eq. 6),
where the coefficients were solved by least squares linear
regression. We have concluded that the waveform approach
has potential for estimating aboveground herbaceous
biomass, given the model’s ability to explain almost 60% in
herbaceous biomass variability. However, we feel that the
small range in herbaceous biomass field values, limited
structural information, and senescent state of the vegetation
were detrimental to model performance.
ln()
Table 1: Correlation coefficients between field data and
waveformderived feature metrics
H ) = 6.3*ln(a1) + 5.2*ln(s1) + 0.3* ln(a2) + 0.4 *ln(σ2) −41.6 (6)
Figure 5: Herbaceous biomass estimation using LiDAR
waveformderived metrics
5. CONCLUSIONS
We successfully extracted waveform LiDAR feature metrics
from the deconvolved waveform’s Gaussian responses to
model plotlevel herbaceous biomass  the coefficient of
determination (R2) indicated that our model could explain
60% of the variation in herbaceous biomass. Although this
could be considered as relatively low, it is clear that
significant potential exists for assessment of herbaceous
biomass in savanna ecosystems at fine scales using
waveform LiDAR. We mainly attributed the relatively poor
model performance to a narrow range of field biomass
values. Future research will focus on biomass estimation
during the wet season, linking woodyherbaceous biomass
assessment, and applying spectralbased mixture mapping to
further explore the relative variation of LiDAR returns
across different vegetation species, structures, biomass, etc.,
at the subpixel level.
6. ACKNOWLEDGEMENTS
The Carnegie Airborne Observatory is supported by the
W.M. Keck Foundation and William Hearst III; the study
was funded by the Andrew Mellon Foundation. We are
grateful for field campaign funding from the Council for
Scientific and Industrial Research (SA) and PhD student
funding from the Rochester Institute of Technology (USA).
7. REFERENCES
[1] H.E. Andersen, R. McGaughey, and S. Reutebuch,
“Estimating forest canopy fuel parameters using LIDAR data”,
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[2] J. Anderson, M, Martin, M.L. Dubayah, R. Dubayah, M.
Hofton, P. Hyde, B. Peterson, J. Blair, and R. Knox, “The use of
waveform lidar to measure northern temperate mixed conifer and
deciduous forest structure in New Hampshire”, Remote Sensing of
Environment 105(3), pp. 248261, 2005.
[3] J. Drake, R. Dubayah, D. Clark, R. Knox, J. Blair, M. Hofton,
R. Chazdon, J. Weishampel, and S. Prince, “Estimation of tropical
forest structural characteristics using largefootprint lidar”, Remote
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[4] B. Koetz, F. Morsdorf, G. Sun, K. Ranson, K. Itten, and B.
Allgower, “Inversion of a lidar waveform model for forest
biophysical parameter estimation”, IEEE Geoscience and Remote
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[5] M. Lefsky, D. Harding, W. Cohen, G. Parker, and H. Shugart,
“Surface lidar remote sensing of basal area and biomass in
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Environment 67(1), pp. 8398, 1999b.
[6] L.B. Lucy, “An iterative technique for the rectification of
observed distributions”, The Astronomy Journal 79(6), pp. 745
754, 1974.
[7] S. Harsdorf, and R. Reuter, “Stable deconvolution of noise
lidar signals”, Proceedings of EARSelSIGWorkshop LIDAR,
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[8] A. Dempster, N. Laird, and D. Rubin, “Maximum likelihood
from incomplete data via the EM algorithm”, Journal of the Royal
Statistical Society 39(1), pp. 138, 1977.
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σ1 s1
a2
σ2
s2
Bio
(H)
0.69
a1
σ1
s1
a2
σ2
s2
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(H)
1 0.12 0.98 0.79 0.35 0.59
0.12 1 0.07 0 0.05 0.09 0.21
0.98
0.79
0.35
0.59
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0
0.05
0.09
1 0.80
1
0.52
0.93
0.36
0.52
1
0.57
0.58
0.93
0.57
1
0.75
0.67
0.35
0.50
0.80
0.36
0.58
0.69 0.21 0.75 0.67 0.35 0.50 1
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