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\begin{document}

\title{Voxel Volumes and Biomass: estimating vegetation volume and litter
accumulation of exotic annual grasses using automated ultra-high
resolution SfM and advanced classification techniques}



\author[1]{Josh Enterkine}%
\author[1]{Ahmad Hojatimalekshah}%
\author[2]{Monica Vermillion}%
\author[1]{Thomas Van Der Weide}%
\author[3]{Sergio Arispe}%
\author[3]{William Price}%
\author[4]{April Hulet}%
\author[1]{Nancy Glenn}%
\affil[1]{Boise State University}%
\affil[2]{US Forest Service Forest Health Protection Region 4}%
\affil[3]{Oregon State University}%
\affil[4]{Brigham Young University}%


\vspace{-1em}



  
  \date{May 18, 2024}


\begingroup
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\selectlanguage{english}
\begin{abstract}
Rangelands and semi-arid ecosystems are subject to increasing changes in
ecologic makeup from a collection of factors. In much of the northern
Great Basin, rangelands invaded by exotic annual grasses such as
cheatgrass (Broumus tectorum) and medusahead (Taeniatherum
caput-medusae) are experiencing an increasingly short fire cycle which
is compounding and persistent. Improving and expanding ground-based
field methods for measuring above-ground biomass (AGB) may enable more
sample collections across a landscape and over succession regimes, and
better harmonize with other remote sensing techniques. Developments and
increased adoption of uncrewed aerial vehicles and instrumentation for
vegetation monitoring are enabling greater understanding of vegetation
in many ecosystems. Research towards understanding the relationship of
traditional field measurements with newer aerial platforms in rangeland
environments is growing rapidly, and there is increasing interest in
exploring the potential use both to quantify AGB and fine fuel load at
pasture scales. Our study here uses relatively inexpensive handheld
photography with custom sampling frames to collect and automatically
reconstruct 3D-models of the vegetation within 0.2 m2 quatrats (n =
288). Next, we examine the relationship between volumetric estimates of
vegetation to compare with biomass. We found that volumes calculated
with 0.5 cm voxel sizes (0.125 cm3) most closely represented the range
of biomass weights. We further develop methods to classify ground
points, finding a 2\% reduction in predictive ability compared to using
the true ground surface. Overall, our reconstruction workflow had an R2
of 0.42, further emphasizing the importance of high-resolution imagery
and reconstruction techniques. Ultimately, we conclude that more work is
needed of increasing extents (such as from UAS) to better understand and
constrain uncertainties in volumetric estimations of biomass in
ecosystems with high amounts of invasive annual grasses and fine fuel
litter.%
\end{abstract}%



\sloppy


Josh Enterkine\textsuperscript{1*}, Ahmad
Hojatimalekshah\textsuperscript{2}, Monica
Vermillion\textsuperscript{3}, Thomas Van Der Weide\textsuperscript{1},
Sergio A. Arispe\textsuperscript{4}, William J.
Price\textsuperscript{5}, April Hulet\textsuperscript{6}, Nancy F.
Glenn\textsuperscript{1}.

\textsuperscript{1} Boise State University Department of Geosciences,
Boise ID

\textsuperscript{2} Boise State University Department of Computer
Sciences, Boise ID

\textsuperscript{3} USDA US Forest Service, Forest Health Protection
Region 4, Boise ID

\textsuperscript{4} Oregon State University Extension Service-Malheur
County, Oregon State University, Ontario, OR

\textsuperscript{5} Oregon State University Extension Service-Baker \&
Union Counties, Oregon State University, Baker City, OR

\textsuperscript{6} Brigham Young University, Plant \& Wildlife
Sciences, Provo, UT

*joshenterkine@boisestate.edu, 1910 W. University Dr., Boise, ID,
83725-1535

\subsection*{Abstract}

{\label{abstract}}

Rangelands and semi-arid ecosystems are subject to increasing changes in
ecologic makeup from a collection of factors. In much of the northern
Great Basin of the western United States, rangelands invaded by exotic
annual grasses such as cheatgrass (\emph{Bromus tectorum} ) and
medusahead (\emph{Taeniatherum caput-medusae} ) are experiencing an
increasingly short fire cycle, which is compounding and persistent.
Improving and expanding ground-based field methods for measuring
above-ground biomass (AGB) may enable more sample collections across a
landscape and over succession regimes, and better harmonize with other
remote sensing techniques. Developments and increased adoption of
uncrewed aerial vehicles and instrumentation for vegetation monitoring
are enabling greater understanding of vegetation in many ecosystems.
Research towards understanding the relationship of traditional field
measurements with newer aerial platforms in rangeland environments is
growing rapidly, and there is increasing interest in exploring the
potential use both to quantify AGB and fine fuel load at pasture and
landscape scales. Our study here uses relatively inexpensive handheld
photography with custom sampling frames to collect and automatically
reconstruct 3D-models of the vegetation within 0.2
m\textsuperscript{2}quadrats (n = 288). Next, we examine the
relationship between volumetric estimates of vegetation to compare with
biomass. We found that volumes calculated with 0.5 cm voxel sizes (0.125
cm\textsuperscript{3}) most closely represented the range of biomass
weights. We further develop methods to classify ground points, finding a
2\% reduction in predictive ability compared to using the true ground
surface. Overall, our reconstruction workflow had an
R\textsuperscript{2} of 0.42, further emphasizing the importance of
high-resolution imagery and reconstruction techniques. Ultimately, we
conclude that more work is needed of increasing extents (such as from
UAS) to better understand and constrain uncertainties in volumetric
estimations of biomass in ecosystems with high amounts of invasive
annual grasses and fine fuel litter.

\textbf{Keywords: rangeland, fine fuels, medusahead, SfM, biomass}

\subsection*{Introduction}

{\label{introduction}}

Semi-arid ecosystems act as carbon sinks and are thought to play a major
role in global interannual carbon variations (Ahlstr\selectlanguage{ngerman}öm et al. 2015). In
addition to soil carbon sequestration, semi-arid ecosystems at regional
scales provide important ecosystem services such as wildlife habitat and
mesic refugia. Semi-arid ecosystems, such as in the western U.S. are
water-limited and pressures from climate change and population growth
make these lands vulnerable to degradation. Specifically, the
sagebrush-steppe ecosystem is currently under threat from the invasion
of exotic annual grasses, such as cheatgrass (\emph{Bromus tectorum} L.)
and medusahead (\emph{Taeniatherum caput-medusae} (L.) Nevski), which
are decreasing biodiversity (Knapp, 1996), altering the fire cycle
(Bradley et al., 2018), and reducing carbon storage (Bradley et al.,
2006).

Quantifying vegetation biomass is critical for assessing ecosystem
structure, tracking vegetation growth, and quantifying carbon storage
(Houghton et al., 2009). Above ground biomass (AGB) in semi-arid
ecosystems helps scientists and land managers better understand the
contribution of these ecosystems to the global carbon flux, and the
impacts of ecosystem shifts towards desertification (Chambers et al.,
2014). In particular, AGB is defined as the dried weight of vegetation
above the ground including both alive and dead components, is difficult
to accurately measure in semi-arid ecosystems because of the
heterogeneity and fine-scale structure of vegetation (Fern et al., 2018;
Wijesingha et al., 2019). This is especially so for invasive annual
grasses such as medusahead and cheatgrass, where previous growth can
become a mat of dry litter, decreasing native vegetation growth and
further promoting the invasive annual grass species (Evans \& Young
1970). As a result, an increase in the continuity of fine fuel loads
occurs. This build-up of fine fuels, coupled with senescence early in
the growing season promote ignition and increased fire spread. This
feedback loop, `invasive grass-fire cycle' further results in
degradation of semi-arid ecosystems (Fernández-Guisuraga et al. 2022).

Management approaches to the invasive grass-fire cycle are varied across
techniques and spatial and temporal scales. Approaches such as
re-seeding, grazing, and fuel breaks, aim to effect and observe changes
in a plot, pasture, or regional scales (100s-1000s
km\textsuperscript{2}). Where the sites may be relatively small in
extent (e.g. grazing exclosure scales, or m to km), there is a benefit
of reducing the need to destructively harvest samples to observe changes
while reducing impact on the vegetation. Monitoring data at high spatial
resolutions and with low uncertainty are needed to provide baseline
information to both of these scales to be able to extrapolate
measurements with greater certainty, and where changes over time and in
response to treatments and climate are valuable to observe.

\emph{How AGB is Measured in the Field, Destructively and
Non-Destructively}

Current methods for collecting AGB can be described as a combination of
site-specific and extrapolated measurements. An example of site-specific
measurements is the destructive harvesting of biomass. Often
quantification of biomass at the plot scale is extrapolated to larger
scales (Clark et al., 2008). Further, in the field plot-level data
collection of plants are destructively harvested, dried, and weighed to
obtain a biomass metric, or point frame data is used to relate to
biomass. The manual process itself has uncertainty in the collection
from human error. Often these plots are small, and the biomass can vary
significantly across spatial scales, even within 1 m or less. The act of
removing plants itself alters the landscape and impacts future studies
of those plots. Advances in remote sensing systems like lidar, unmanned
aerial systems (UAS), and structure from motion (SfM) software have led
to advances in quantifying biomass in dryland ecosystems (Anderson et
al., 2018; Cunliffe et al., 2016). Fine (spatial/structural) resolution
remote sensing has potential to help solve the above rangeland
vegetation challenges. SfM is photogrammetry, the method of using 2D
stereoscopic images and detecting common points, resulting in a 3D
reconstruction in the form of a point cloud. SfM provides a similar data
product to lidar: a point cloud in which vegetation structure can be
interpreted. However since SfM is based on optical passive imagery it
does not penetrate the canopy (Salamí et al., 2014). SfM and lidar are
similar in their point cloud reconstruction, however because lidar is
active, it has an intensity associated with each point. Additionally,
lidar can be collected as full-waveform or in discrete returns which can
characterize the understory and ground surface (Wallace et al. 2017).

In contrast, SfM is derived from passive remote sensing relying on
optical imagery to create point clouds where each point has an
associated color value for the spectra of the optical image. This value
is rarely radiometrically calibrated. SfM point clouds are not
discretized from a waveform but developed based on the overlap of
imagery taken. Vegetation parameters such as volume, can be derived from
point clouds to develop allometric relationships between vegetation and
destructively harvested biomass. SfM offers a low-cost, time efficient,
and in some cases, more accurate method compared to terrestrial laser
scanning (TLS) for estimating vegetation structure in dryland ecosystems
(Cooper et al. 2017, Olsoy et al., 2018; Wallace et al., 2017).

Extremely close-range SfM, defined by the use of hand-held instruments
to collect the imagery for the SfM method, has shown success comparable
to TLS in deriving parameters such as height and volume from the
reconstruction of individual trees (Miller et al., 2015). In grasslands,
extremely close-range SfM was shown to outperform TLS and traditional
height measurements in developing allometric equations, in part because
SfM can capture finer details compared to TLS, dependent upon the
experimental setup (Cooper et al., 2017). TLS at plot scale (Anderson et
al. 2017) and TLS and hand-held camera photos at 0.5 m x 0.5 m
(0.46*0.46, Cooper et al. 2017) had high correlations between SfM and
TLS and AGB. SfM has been shown to successfully capture grasses and
reconstruct fine features such as leaves and stems (Cooper et al. 2017,
Kröhnert et al., 2018). These previous studies demonstrate that SfM
shows promise in providing accurate information for allometric equations
used to extrapolate biomass of rangeland grass to a landscape-scale.

Field work for capturing extremely close-range SfM imagery requires less
training for field crews compared to TLS and UAS data collection and
eliminates the need for specialized equipment. Developing an allometric
relationship at a plot scale (cm) will inform future SfM studies that
utilize UAS imagery (Gillan et al., 2019). Furthermore, close range SfM
can be complementary and used as a precursor for extrapolating to scales
that are amenable to commonly available UAS (e.g., m to km). However,
vegetation and soil classification in such a fine resolution dataset
remains challenging. Spectral reflectance in the visible spectrum and
near-infrared may be able to better separate vegetation and dry biomass
litter from one-another, or from the mineral soil or ground surface.
Although differences in the soil composition can cause different types
of confusion with vegetation and litter, possibly reducing
transferability of methods between study sites (Huang et al., 2007), in
areas where the ground surface can be largely obscured may benefit from
other approaches such as structural analyses from either SfM or active
remote sensing technologies may be more successful (Calders et al.,
2015).

A common technique for estimation of AGB relies on Digital Terrain Model
(DTM) and Digital Surface Model (DSM) computation and the retrieved
Canopy Height Model (CHM) and Leaf Area Index (LAI) from them (Ota et
al., 2015, Zhang et al., 2018, Xu et al., 2019). The biomass from lidar
and UAS-derived point clouds CHM is generally classified into ground and
vegetation by setting a height threshold (Cunliffe et al., 2016,
Viljanen et al., 2018, Näsi et al., 2018, Navarro et al., 2020).
However, the accuracy of CHM mostly exceeds the height of short shrubs
and grasses, and thus CHM models are less suitable for aboveground
biomass estimation in dryland ecosystems (Zahawi et al., 2015).
Schulze\selectlanguage{english}-Bruninghoff et al. (2021) suggested a method combining
lidar-derived metrics (sum of voxels, canopy height model, and canopy
surface structure) and vegetation spectral properties to estimate fresh
and dry biomass in a machine learning approach. In addition, by
combining ground camera and UAS, Taugourdeau et al. (2022) extracted
vegetation metrics from RGB bands and height to estimate aboveground
biomass in a random forest model. Therefore, the uncertainty of biomass
estimation is limited to the uncertainty in CHM, data resolution, and
the type of land treatments (grazed or ungrazed). In this regard, the
discrimination between vegetation and bare ground structural properties
(smoothness of the surface, randomness of vegetation foliage, and
curvature) could improve AGB estimation from high-resolution ground
camera and UAS SfM-derived point clouds.

The objectives of this work are to explore the potential for close-range
SfM to quantify fine-fuel AGB, with the thought of replacing
destructively harvested sampling with the methodology, or to utilize the
close-range SfM volumetric estimations to inform potential UAS data
collection. To accomplish this, we first developed a method to acquire
and process field data from photos to point clouds. Second, we explored
how to separate and classify the ground surface through the thick litter
layer found in the study area. Third, we examined the relationship
between the measurement unit of volumetric calculation and the biomass
of the study area's vegetation. Lastly, we discuss some observations on
how the SfM point frame might be used, and how this method may inform
UAS data seeking to estimate biomass or vegetation volume.

\subsection*{Methods}

{\label{methods}}

\begin{enumerate}
\tightlist
\item
  \emph{Study Area}
\end{enumerate}

Our study area is the Three Fingers allotment located in southeastern
Oregon (Fig. 1), approximately 80 km west of Boise, Idaho. The Vale
District U.S. Bureau of Land Management (BLM) manages the allotment,
which has a history of disturbance from grazing, recreation, and fire.
The area has experienced significant departure from native vegetation
communities, with few remaining native shrubs and an extensive cover of
cheatgrass and medusahead, and other annual grasses (\textgreater{}80\%
in all experimental exclosures).

This study was part of a larger study focused on evaluating the effect
of dormant season grazing on fine fuels (Arispe et al. 2022). As part of
the project, data were collected across two years and on three different
pastures on the Three Fingers allotment---approximately 55,000 hectares.
The three pastures within the project included, McIntyre (MCI; 3100 ha),
South Camp Kettle (SCK; 2500 ha), and Saddle Butte (SB; 3800 ha). Within
each pasture a northern and southern exclosure was randomly placed, for
a total of six treatment areas. Each exclosure contained four paddocks
150 m x 150 m in size, for a total of 24 paddocks.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\emph{Fig. 1: Study area in southeast Oregon, USA. At each pasture, two
sites were established for a total of six treatment areas. At each of
the six treatment areas, four paddocks (150 m x 150 m) were established;
within each paddock, three transects are established annually. Each
transect is sampled in at least three places with destructive harvesting
and Structure-from-Motion volumetric estimates.}

\emph{Field Data and Collection Protocol}

Data were collected in June 2020 and June 2021, as supplement to
existing protocol (Arispe et al. 2022) for collecting biomass data in
each of the 24 experimental paddocks. For each of the 24 paddocks, three
transects are established from a randomized central location. Along each
transect, three 0.4 m by 0.5 m areas were photographed for
Structure-from-Motion reconstruction and then destructively harvested.
Vegetation was removed to as near to mineral soil as possible, and
separated into annual grasses, perennial grasses, forbs, and litter
prior to drying. Plots that contained shrubs were excluded, since shrubs
are not destructively harvested for the larger project. Samples were
oven-dried for 48 hours at 60\selectlanguage{ngerman}° in a commercial drying hood and weighed.
Approximately \selectlanguage{english} 1/3  of the plots were photographed again immediately after
harvesting the vegetation but before disturbing the frames so as to
collect the mineral soil surface microtopography.

\emph{Structure-from-Motion Protocol and Reconstruction}

Two custom quadrat frames were constructed from extruded aluminum,
containing custom 3D-printed 0.05 m cubes with coded targets (Fig. 2).
These targets are automatically detected in Agisoft Metashape (version
1.6). We used a Sony a6000 with the stock kit lens (16-50 mm F3.5-5.6)
to collect approximately 75 photographs per quadrat frame. These were
taken approximately 1 m above the plot in a 5 x 5 sampling pattern
repeated three times: once at nadir, once at approximately 20-degree
tilt away from the photographer, and again tilted towards the
photographer. Several additional images were taken at each plot from a
greater height, and at several corner-on angles. Care was taken to stand
so as to avoid casting a shadow on the plot. One of each of the six
sites was collected per day. In total, approximately 216 plots were
collected over the six treatment areas in both 2020 and 2021.

Our processing workflow in Agisoft was automated using Python; each plot
was processed at high-quality image alignment and medium-quality dense
cloud reconstruction. Resulting point clouds had typical densities of
0.5- to 4-million points per square meter with a minimum of 0.001 m
spacing between points. After processing and quality assessment, there
were 114 plots for 2020 and 174 plots for 2021.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\emph{Fig. 2: Point cloud reconstruction of a typical 0.4 m x 0.5 m plot
before destructive harvesting, including quadrat frame with coded
targets. Vegetation (primarily Taeniatherum caput-medusae) colored by
height.}

\emph{Point Cloud Classification and Volumetric Processing}

Following reconstruction, point clouds were imported into Matlab
(version R2021a) for classification into ground and vegetation classes
and volumetric measurements (Fig. 3). After clipping the point clouds
inside the frames, we applied the point cloud denoising algorithm
presented by Rusu et al. (2008) to remove the outliers from the point
cloud. To classify the point cloud into ground and vegetation classes we
applied the simple morphological filter (SMRF) algorithm in Matlab.

The simple morphological filter (SMRF) method (Pingel et al. 2013)
classifies the point clouds into vegetation and ground using the
elevation and slope threshold. The algorithm tiles the data by a grid
resolution, finds the minimum elevation points within each grid and fits
a surface to the minimum points. The points that are excluded from the
elevation difference between the minimum surface and morphological
opened minimum surface by linearly increased window sizes (from 1 to
user defined maximum window radius) in an iterative procedure are
considered as vegetation and the points that satisfy the elevation
threshold are classified as ground (more detail can be found in Pingel
et al. 2013).

We used an elevation threshold of 11 cm, slope threshold of 0.1 (as the
plots were mostly flat), elevation scale of 0.9 (to detect medium size
objects) and max window radius of 10. While this is effective, the
ground classified points still contain some vegetation biomass. To
separate the remaining vegetation points from the ground class, we
applied two gaussian mixture classification algorithms on the curvature
of the point clouds using 50 and 200 neighbors (200 neighbors is applied
on the ground class from 50 neighbors output). In this method we assume
that the ground surface is smoother than the vegetation surface and thus
the curvature on the surface is different for those classes. The
algorithm extracts curvatures and fits a gaussian distribution, and
assumes vegetation and ground curvatures follow two mixed gaussian
distributions. After retrieving the vegetation and ground class we
merged the vegetation class with the previous vegetation class from the
SMRF results.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\emph{Fig. 3: Point cloud processing workflow.}

\emph{Evaluating Volumetric Measurement Methods}

Once the data were classified into ground and vegetation, we
investigated several methods to compare volume with above-ground
biomass. We assessed the data based on a per site (n = 6) and as
combined sites per year, and by combining years. Our interest in
assessing on a per-site basis was to consider possible effects of
changing photography conditions (one site photographed per day), or
influences of the site location such as general vegetation type. Similar
logic was applied to the per year versus both years combined datasets.

We examined how we accounted for voxel volume by using
vegetation-classified points as the volumetric measure (vegetation voxel
volume), and by using the total plot voxel volume with no classification
of vegetation and ground. We performed the latter to test whether litter
or other obstructions had a detrimental effect on the ability to detect
the ground surface. Ultimately, in this model, litter was considered as
part of the biomass volume.

We also computed a vegetation voxel volume above the surface, by fitting
a surface to the ground and computing the vegetation volume above the
surface. Additionally, we examined the relationships between volumes and
vegetation type (e.g. perennial and annual grasses, forbs). Linear
models and logarithmic models were both investigated for the
relationships between voxel volume and biomass.

Finally, we also assessed the scale at which volumetric data is best
reconstructed for sagebrush-steppe vegetation (e.g., fine annual
grasses) and to inform the possibility for using volumes reconstructed
from UAS imagery. This included voxelizing the point clouds at several
resolutions ranging from 2 mm to 100 mm, comparing volumes of all
reconstructed points and volumes of vegetation-classified points only.

\subsection*{Results}

{\label{results}}

\begin{enumerate}
\tightlist
\item
  \emph{Volume and Biomass Allometry Modeling and Sensitivity Analysis}
\end{enumerate}

Table 1 depicts the models we tested that had a significant
(\textgreater{} 0.30 R\textsuperscript{2}) relationship between voxel
volume and field biomass. We found the best correlation
(R\textsuperscript{2} = 0.48) with a logarithmic regression between 5 mm
voxel volumes of vegetation-classified points with above ground biomass
for all sites across years (Table 1). We generally found that
logarithmic models performed better than linear models when all plots
were grouped together across years.

A linear regression of plots (n = 36) from both years from South Camp
Kettle (South site) attained an R\textsuperscript{2} of 0.62 between
classified vegetation points at 5 mm voxel sizes with the biomass of
only annual and perennial grasses (i.e. no litter biomass was included).
However, generally there was no pattern of linear or logarithmic
modeling performing better for any of the comparisons when modeling by
site or by year.

Generally, our vegetation voxel volume calculated from classified
vegetation points (from Fig. 3, workflow) performed better than using a
fitted surface to identify vegetation points and calculate a volume.
Using a total plot voxel volume along with only annual and perennial
grasses had a relatively high R\textsuperscript{2}. No relationship with
forb biomass was found due to their relative rarity in the study area.

\emph{Table 1. The retrieved R\textsuperscript{2} by applying a linear
and logarithmic regression between biomass and vegetation volume. The
reported values are the significant ones according to the
f\textsuperscript{2} test for the sample size. The minimum threshold for
power is 90\% here. AG and PG here means annual and perennial grass,
respectively. Plot volume is the voxelized volume of the total plot
without classification, and vegetation volume is also voxelized volume
but after classification per the workflow (Fig. 3).}\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
Comparison (5mm voxel) & Linear regression R\textsuperscript{2} &
Logarithmic regression R\textsuperscript{2}\tabularnewline
Vegetation voxel volume vs vegetation biomass & 0.35 &
0.48\tabularnewline
Vegetation voxel volume vs vegetation biomass + litter & &
0.32\tabularnewline
Vegetation voxel volume above reconstructed ground surface with total
biomass & 0.30 &\tabularnewline
Vegetation voxel volume and AG+PG & 0.33 & 0.40\tabularnewline
Plot voxel volume and AG+PG & 0.32 & 0.39\tabularnewline
\bottomrule
\end{longtable}

\emph{Voxel Size Comparison}

Investigating the effects of volumetric resolution on data distributions
was conducted by voxelizing the point clouds in intervals from 2 mm to
100 mm. Distributions of calculated volumes with the differing voxel
sizes were all statistically different from one-another (Fig. 4) as
determined by a Wilcoxon test (Table 2).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\emph{Fig. 4. Biomass and vegetation volume distribution at different
voxel sizes for 2020-2021 data.}

\emph{Table 2. Wilcoxon test results on plot volume among different
voxel sizes. The null hypothesis assumes that the paired volumes are not
different. P-values less than 0.05 significance level (5\% confidence
level) rejects the null hypothesis, meaning that the computed volumes
using different voxel sizes are significantly different. As the voxel
volumes are not normally distributed, we used the Wilcoxon test.}\selectlanguage{english}
\begin{longtable}[]{@{}llllllll@{}}
\toprule
Voxel size & 2 mm & 5 mm & 10 mm & 20 mm & 30 mm & 50 mm & 100
mm\tabularnewline
2 mm & & & & & & &\tabularnewline
5 mm & \textless{} 0.05 & & & & & &\tabularnewline
10 mm & \textless{} 0.05 & \textless{} 0.05 & & & & &\tabularnewline
20 mm & \textless{} 0.05 & \textless{} 0.05 & \textless{} 0.05 & & &
&\tabularnewline
30 mm & \textless{} 0.05 & \textless{} 0.05 & \textless{} 0.05 &
\textless{} 0.05 & & &\tabularnewline
50 mm & \textless{} 0.05 & \textless{} 0.05 & \textless{} 0.05 &
\textless{} 0.05 & \textless{} 0.05 & &\tabularnewline
100 mm & \textless{} 0.05 & \textless{} 0.05 & \textless{} 0.05 &
\textless{} 0.05 & \textless{} 0.05 & \textless{} 0.05 &\tabularnewline
Biomass & \textless{} 0.05 & \textless{} 0.05 & \textless{} 0.05 &
\textless{} 0.05 & \textless{} 0.05 & \textless{} 0.05 & \textless{}
0.05\tabularnewline
\bottomrule
\end{longtable}

\emph{Reference Surface vs. Reconstructed Surface}

Comparing the plots where we collected imagery after destructive
harvesting and reconstructed the `true' reference ground surface using
SfM (n = 35) with our reconstructed interpolated ground surface showed a
decrease in R\textsuperscript{2} from 0.44 to 0.42 at 5 mm voxels (Fig.
5). The mean absolute difference in volumes was 20\% of the volume
calculated using the reference ground surface.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\emph{Fig. 5. Calculated vegetation and litter voxel volumes using
reference ground surface and reconstructed ground surface.}

Discussion

The outcome of this research illuminates some considerations specific to
the vegetation of the study area, chiefly the gracile structure of
medusahead and the layer of litter that it deposits. Broadly, we found
that the largest cause for uncertainty in our estimations resulted from
the fine fuel litter layer obscuring the ground surface. However, with
some additional processing, we were able to attain some informative
results.

\emph{Structure-from-Motion Sample Frame and Reconstruction}

Reconstructing point clouds from the field photography is a feasible
sampling strategy for studies of this scale. However an effort must be
taken to automate as much as possible, since it can be labor- and
processing-intensive. The addition of coded targets at known, local
coordinates greatly reduces the need for manual steps in the process. We
observed that reconstruction success of the point clouds was mostly
dependent on the photo quality (e.g. not blurry), amount of overlap, and
that the targets were not obstructed by even a small amount of
vegetation. Environmental conditions also played a role in the success
of the point cloud reconstruction; occasionally, lighting conditions
created too many shadows or too much variability during the
photographing process. Due to the relatively delicate structure of the
site vegetation, small gusts of wind can be troublesome and cause a plot
to fail reconstruction quality thresholds, or fail to process
altogether.

Because the per-year and per-site regressions did not have significant
relationships (excepting 2020-2021 South Camp Kettle South, n = 36,
R\textsuperscript{2} = 0.62, 5 mm voxel size), we hypothesize that the
conditions for all fields were similar and that the reconstructed point
clouds were of similar quality and captured the variability of
vegetation types equally across the study environment. We observed no
significant relationship between vegetation types and volume
calculations. The fidelity of the reconstructed point clouds to the
vegetation structure was mostly influenced by whether the ground surface
was visible, and whether there was a dense layer of litter or stand of
vegetation.

\emph{Ground and Vegetation Classification and Separability in Point
Clouds}

Vegetation in the Three Fingers Allotment can often contain a dense
layer of dead medusahead from previous growing seasons, or a thick cover
of living medusahead, or both. This means that passive remote sensing
techniques such as Structure-from-Motion may have difficulty measuring
both the internal volume and the ground surface. Such obstructions
likely decreased the correlation between calculated volume and measured
biomass. Iterative classification of the ground surface points increased
the observed relationship between volume and biomass for all
combinations of vegetation types and biomass. In addition to occluding
the ground surface, the layer of litter also confounded the ability to
accurately characterize the ground surface.

However, our comparison between our reconstructed ground surface with
the `true' reference ground surface elucidates two points. First, the
decrease in predictive ability between the reference surface and our
reconstruction is only 2\% (from R\textsuperscript{2} of 0.44 to
R\textsuperscript{2} of 0.42), which assists in constraining
uncertainties in volumetric calculations using our ground and vegetation
classification or similar process. Second, the range of litter biomass
in this regression ranged from 20\% to 100\% of the total vegetation
biomass with evenly distributed errors. This indicates that the
disagreement between calculated volumes is independent from the
proportion of litter in the total biomass. Thus, it may be possible to
adequately quantify uncertainty in volumetric measurements at
pasture-scales. It is possible that the observed relationship is related
to the compaction of the litter layer over time. However, a larger and
more varied sample size at the smaller plot scale would help further
understand this relationship.

Additionally, we explored using a convex hull volumetric calculation to
compare to the voxel volume calculations. While the convex hull method
may better handle the under-sampled volumes internal to a mat of litter
or dense vegetation, we found that although the results were similar to
the voxel models, the convex hull method generally performed worse
across the different classifications and comparison models.

\emph{Voxel Volume Analysis}

Because the total volumetric calculations were statistically significant
for each voxel size, we ascertain that the volumetric calculations are
highly dependent on the resolution of the final point cloud. Volumes
from decreasing voxel sizes were increasingly similar to the measured
biomass, up to a point: the distribution of voxel volumes at 5 mm more
closely matched the biomass distribution than the 2 mm voxel sizes. This
may indicate that the scale of obscured volume is exacerbated as
decreasing voxel sizes are employed for the vegetation communities; the
smaller voxel sizes may be more reflective of the surface of the
vegetation. More simply, it may be that the density of such plant
communities is beyond the limits of the resolution of the imagery
(Wallace et al. 2017).

\emph{Considerations for Future UAS-Derived and Non-Destructive Biomass
Data}

Our study helps inform UAS-derived spatial and structural data in two
ways. Primarily, the unique characteristics of the vegetation and
ecological communities in this study area (perennial and annual
grass-dominated, of varying densities and heights, and with significant
layers of litter cover) strongly favor higher-resolution UAS data. While
it is not uncommon for UAS sensors to routinely output models at 5 cm
pixel sizes, our analysis suggests that additional mission planning and
sensor considerations to achieve closer to 1 cm pixel sizes may be
important to enable volumetric estimates of biomass in such
environments, as found by Cunliffe et al. (2016). Additionally, the
complications of our analysis given the common occlusion of the ground
surface indicate that volumetric estimations on such a scale (e.g.
centimeter to tens of centimeter litter layers, typically shorter than 1
m vegetation heights) are sensitive to the spatial resolution of the
remote sensing product and that using an elevation model (e.g. DSM) may
be insufficient to reconstruct a ground surface.

Given the uncertainty of identifying ground surface, whether from
classified points or a reconstructed surface, our proposed method would
benefit from refinement before being considered a replacement for
destructive harvesting. Such refinements might include systematic
comparisons with other commonly-used biomass sampling techniques for
grasslands such as rising plate meter devices. Separating ground from
vegetative biomass, or litter from ground and standing biomass may
benefit greatly from using multispectral imagery. Active remote sensing
techniques such as lidar, whether in conjunction with imaging or alone,
may also more reliably return ground points through litter layers and
dense vegetation, as well as providing other data such as intensity that
may enable greater discernment between ground, litter, and other
vegetation.

Other avenues to explore with our proposed method may explore other
calculations and measurements from the dense and high-resolution point
clouds, such as vegetation height or other allometry (Cunliffe et al.
2022, Schulze-Br\selectlanguage{ngerman}üninghoff et al. 2021). This may include relationships
between biomass and structure, or as a more direct replacement of other
field-measured data such as canopy cover. With other passive sensor
types such as multispectral or hyperspectral imaging, or active sensors
such as lidar, other metrics such as moisture level or classifications
may be possible. Fusion of such data types has shown more success
together in grasslands in predicting biomass as well as other properties
such as moisture content (Schulze-Brüninghoff et al. 2021).

Conclusion

In this paper we explored using Structure-from-Motion at ultra-fine
scales in an environment dominated by exotic annual grasses and
associated litter. Understanding the amount of biomass and litter in
these rangeland environments is important for managing forage and fuels,
and understanding treatments and changes. UAS offer the possibility to
scale up traditional field methods to larger areas, yet challenges still
remain. This research aims to develop field methods and processes to
understand the limits of using Structure-from-Motion in semi-arid
ecosystems to estimate biomass. We believe that our research adds to
this process by establishing a methodology to further collect and
process small plots of biomass into classified point clouds in a
largely-automated fashion, so that additional work may be conducted and
expanded. Our results indicate that the ability to detect the ground may
be the limiting factor in attaining satisfactory volume-to-biomass
relationships in similar environments, and reiterating that fine spatial
resolutions are needed for fine-scale vegetation.

Author's Contributions

\textbf{Josh Enterkine:} Methodology, Software, Validation,
Investigation, Resources, Data Curation, Writing - Review \& Editing,
Supervision, Visualization. \textbf{Ahmad Hojatimalekshah:} Methodology,
Software, Validation, Formal Analysis, Data Curation, Writing - review
\& editing, Visualization. \textbf{Monica Vermillion:} Methodology,
Software, Investigation, Writing -- Original Draft. \textbf{Thomas Van
Der Weide:} Software. \textbf{Sergio A. Arispe:} Conceptualization,
Investigation, Supervision, Project administration, Funding
acquisition.\textbf{William J. Price:} Methodology, Investigation,
Resources, Data Curation, Supervision. \textbf{April Hulet:}
Conceptualization, Methodology, Investigation, Resources, Funding
acquisition.\textbf{Nancy F Glenn:} Conceptualization, Methodology,
Writing -- Review \& Editing, Supervision, Project administration,
Funding acquisition.

\subsection*{Running Title}

{\label{running-title}}

\emph{SfM Volume for Exotic Annual Grass Biomass and Fine Fuels}

\subsection*{Conflicts of Interest}

{\label{conflicts-of-interest}}

The authors declare that they have no conflicts of interest.

\subsection*{Funding}

{\label{funding}}

Funding: this work is supported by the National Institute of Food and
Agriculture, US Department of Agriculture {[}2019-68008-29914{]}.

\subsection*{Permission to Reproduce Materials from Other
Sources}

{\label{permission-to-reproduce-materials-from-other-sources}}

None/not applicable.

\subsection*{Data Availability
Statement}

{\label{data-availability-statement}}

Data and code is available for reviewers at
https://drive.google.com/drive/folders/1TnYQKFnTyV3aBjx9bWQavYnS7JqHlv2e?usp=sharing
and will be published via DOI through Boise State University
ScholarWorks preceding publication of manuscript.

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