BGBiogeosciencesBGBiogeosciences1726-4189Copernicus PublicationsGöttingen, Germany10.5194/bg-15-3811-2018Estimating aboveground carbon density and its uncertainty in Borneo's
structurally complex tropical forests using airborne laser scanningEstimating aboveground carbon density and its uncertainty in Borneo's tropical forestsJuckerTommasohttps://orcid.org/0000-0002-0751-6312AsnerGregory P.DalponteMichelehttps://orcid.org/0000-0001-9850-8985BrodrickPhilip G.PhilipsonChristopher D.https://orcid.org/0000-0001-8987-7260VaughnNicholas R.TehYit Arnhttps://orcid.org/0000-0001-7976-6794BrelsfordCraighttps://orcid.org/0000-0001-7084-352XBurslemDavid F. R. P.DeereNicolas J.EwersRobert M.KvasnicaJakubLewisSimon L.MalhiYadvinderMilneSolNilusReubenPfeiferMarionPhillipsOliver L.QieLanRenneboogNathanReynoldsGlenRiuttaTerhiStruebigMatthew J.https://orcid.org/0000-0003-2058-8502SvátekMartinTurnerEdgar C.CoomesDavid A.dac18@cam.ac.ukhttps://orcid.org/0000-0002-8261-2582Forest Ecology and Conservation group, Department of Plant Sciences,
University of Cambridge, Cambridge CB2 3EA, UKCSIRO Land and Water, 147 Underwood Avenue, Floreat, 6014, Western
Australia, AustraliaDepartment of Global Ecology, Carnegie Institution for Science, 260
Panama Street, Stanford, CA 94305, USADepartment of Sustainable Agro-ecosystems and Bioresources, Research
and Innovation Centre, Fondazione E. Mach, Via E. Mach 1, 38010 San Michele
all'Adige, ItalyDepartment of Environmental Systems Science, ETH Zürich,
Universitätstrasse 16, 8092 Zürich, SwitzerlandCentre for Environmental Change and Human Resilience, University of
Dundee, Dundee DD1 4HN, UKSchool of Biological Sciences, University of Aberdeen, Cruickshank
Building, St Machar Drive, Aberdeen AB24 3UU, UKDepartment of Biosciences, Viikki Plant Science Center (ViPS),
University of Helsinki, 00014 Helsinki, FinlandDurrell Institute of Conservation and Ecology (DICE), School of
Anthropology and Conservation, University of Kent, Canterbury CT2 7NR, UKImperial College London, Silwood Park Campus, Buckhusrt Road, Ascot
SL5 7PY, UKFaculty of Forestry and Wood Technology, Department of Forest Botany,
Dendrology and Geobiocoenology, Mendel University, Brno, Czech RepublicSchool of Geography, University of Leeds, Leeds LS2 9JT, UKDepartment of Geography, University College London, London WC1E 6BT,
UKEnvironmental Change Institute, School of Geography and the
Environment, University of Oxford, Oxford OX1 3QY, UKForest Research Centre, Sabah Forestry Department, P.O. Box 1407,
90715 Sandakan, Sabah, MalaysiaSchool of Biology, Newcastle University, Newcastle NE1 7RU, UKPermian Global, Savoy Hill House, 7-10 Savoy Hill, London WC2R 0BU,
UKSouth East Asia Rainforest Research Partnership (SEARRP), Danum
Valley Field Centre, P.O. Box 60282, 91112 Lahad Datu, Sabah, MalaysiaDepartment of Zoology, University of Cambridge, Downing Street,
Cambridge CB2 3EJ, UKDavid A. Coomes (dac18@cam.ac.uk)22June20181512381138307February20189March201824May20188June2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://bg.copernicus.org/articles/15/3811/2018/bg-15-3811-2018.htmlThe full text article is available as a PDF file from https://bg.copernicus.org/articles/15/3811/2018/bg-15-3811-2018.pdf
Borneo contains some of the world's most biodiverse and carbon-dense tropical
forest, but this 750 000 km2 island has lost 62 % of its
old-growth forests within the last 40 years. Efforts to protect and restore
the remaining forests of Borneo hinge on recognizing the ecosystem services
they provide, including their ability to store and sequester carbon. Airborne
laser scanning (ALS) is a remote sensing technology that allows forest
structural properties to be captured in great detail across vast geographic
areas. In recent years ALS has been integrated into statewide assessments of
forest carbon in Neotropical and African regions, but not yet in Asia. For
this to happen new regional models need to be developed for estimating carbon
stocks from ALS in tropical Asia, as the forests of this region are
structurally and compositionally distinct from those found elsewhere in the
tropics. By combining ALS imagery with data from 173 permanent forest plots
spanning the lowland rainforests of Sabah on the island of Borneo, we
develop a simple yet general model for estimating forest carbon stocks using
ALS-derived canopy height and canopy cover as input metrics. An advanced
feature of this new model is the propagation of uncertainty in both ALS- and
ground-based data, allowing uncertainty in hectare-scale estimates of carbon
stocks to be quantified robustly. We show that the model effectively captures
variation in aboveground carbon stocks across extreme disturbance gradients
spanning tall dipterocarp forests and heavily logged regions and clearly
outperforms existing ALS-based models calibrated for the tropics, as well as
currently available satellite-derived products. Our model provides a simple,
generalized and effective approach for mapping forest carbon stocks in
Borneo and underpins ongoing efforts to safeguard and facilitate the
restoration of its unique tropical forests.
Introduction
Forests are an important part of the global carbon cycle
(Pan
et al., 2011), storing and sequestering more carbon than any other ecosystem
(Gibbs et al., 2007). Estimates of tropical deforestation
rates vary, but roughly 61 300 km2 of forest were lost each year
between 2000 and 2012, and an additional 30 % were degraded by logging or
fire (Asner et al., 2009; Hansen et
al., 2013). Forest degradation and deforestation result in about 1–2 billion tonnes of carbon
being released to the atmosphere each year, which equates to about 10 % of global emissions
(Baccini et al., 2012). Even
if nations decarbonize their energy supply chains within agreed schedules,
a rise of 2 ∘C in mean annual temperature is unavoidable unless
300 million hectares of degraded tropical forests are protected and land
unsuitable for agriculture is reforested (Houghton et al.,
2015). Signatories to the Paris Agreement, brokered at COP21 in 2015, are
now committed to reducing emissions from tropical deforestation and forest
degradation (i.e. REDD+; Agrawal et al., 2011),
whilst recognizing that these forests also harbour rich biodiversity and
support livelihoods for around a billion people (Vira et al.,
2015).
The accurate monitoring of forest carbon stocks underpins these initiatives to
generate carbon credits through REDD+ and similar forest conservation and
climate change mitigation programmes (Agrawal et al.,
2011). Airborne laser scanning (ALS) has shown particular promise in this
regard because it generates high-resolution maps of forest structure from
which aboveground carbon density (ACD) can be estimated
(Asner
et al., 2010; Lefsky et al., 1999; Nelson et al., 1988; Popescu et al.,
2011; Wulder et al., 2012). The principle of ALS is that laser pulses are
emitted downwards from an aircraft, and a sensor records the time it takes
for individual beams to strike a surface (e.g. leaves, branches or the
ground) and bounce back to the emitting source, thereby precisely measuring
the distance between the object and the airborne platform. Divergence of the
beam means it is wider than leaves and allows for penetration into the canopy,
resulting in a 3-D point cloud that captures the vertical structure of the
forest. By far the most common approach to using ALS data for estimating
forest carbon stocks involves developing statistical models relating ACD
estimates obtained from permanent field plots to summary statistics derived
from the ALS point cloud, such as the mean height of returns or their skew
(Zolkos et al., 2013). These
“area-based” approaches were first used for mapping the structural attributes of
complex multi-layered forests in the early 2000s
(Drake et al.,
2002; Lefsky et al., 2002) and have since been applied to carbon mapping in
several tropical regions
(Asner
et al., 2010, 2014; Jubanski et al., 2013; Laurin et al., 2014;
Réjou-Méchain et al., 2015).
Panel (a) shows the location of the Sepilok and Kuamut Forest
Reserve, the Danum Valley and Maliau Basin Conservation Area, and the SAFE
landscape within Sabah (Malaysia). Green shading in the background
represents forest cover at 30 m resolution in the year 2000
(Hansen et al., 2013). In panel (b), the
relationship between field-measured aboveground carbon density and
ALS-derived top-of-canopy height found across the study sites (coloured
circles, n=173) is compared to measurements taken mostly in the
Neotropics (Asner and Mascaro, 2014; grey
circles, n=754).
This paper develops a statistical model for mapping forest carbon and its
uncertainty in South-east Asian forests. We work with ALS and plot data
collected in the Malaysian state of Sabah on the north-eastern end of the
island of Borneo (Fig. 1), which is an important test bed for international
efforts to protect and restore tropical forests. Borneo lost around 62 %
of its old-growth forest in just 40 years as a result of heavy logging and
the subsequent establishment of oil palm and forestry plantations
(Gaveau et al., 2014, 2016). Sabah lost its forests at
an even faster rate in this period (Osman et al., 2012),
and because these forests are amongst the most carbon dense in the tropics,
carbon loss has been considerable
(Carlson
et al., 2012a, b; Slik et al., 2010). In response to past and ongoing
forest losses, the Sabah state government has recently taken a number of
concrete steps towards becoming a regional leader in forest conservation and
sustainable management. Among these was commissioning a new high-resolution
wall-to-wall carbon map for the entire state, which will inform future
forest conservation and restoration efforts across the region. Here we
develop the ALS-based model that underpins this new carbon map
(Asner et al., 2018).
The approach we take builds on the work of
Asner and Mascaro (2014), who proposed
a general model for estimating ACD (in MgCha-1) in tropical forests
using a single ALS metric – the mean top-of-canopy height (TCH, in m) – and
minimal field data inputs. The method relates ACD to TCH, stand basal area (BA; in
m2ha-1) and the community-weighted mean wood density (WD; in gcm-3)
over a prescribed area of forest, such as 1 ha, as follows:
ACDGeneral=3.836×TCH0.281×BA0.972×WD1.376.
Asner and Mascaro (2014) demonstrated
that tropical forests from 14 regions differ greatly in structure.
Remarkably, they found that a generalized power-law relationship could be
fitted that transcended these contrasting forests types, once regional
differences in structure were incorporated as sub-models relating BA and WD to
TCH. However, this general model may generate systematic errors in ACD estimates
if applied to regions outside the calibration range, and
Asner and Mascaro (2014) make clear
that regional models should be obtained where possible. Since South-east
Asian rainforests were not among the 14 regions used to calibrate the
general model and are phylogenetically and structurally distinct from
Neotropical and Afrotropical forests
(Banin
et al., 2012), new regional models are needed before Borneo's forest carbon
stocks can be surveyed using ALS. Central to the robust estimation of ACD using
ALS data is identifying a metric which captures variation in basal area among
stands. Asner and Mascaro's (2014)
power-law model rests on an assumption that basal area is closely related to
top-of-canopy height, an assumption supported in some studies, but not in
others
(Coomes
et al., 2017; Duncanson et al., 2015; Spriggs, 2015). The dominance of Asian
lowland rainforests by dipterocarp species makes them structurally unique
(Banin
et al., 2012; Feldpausch et al., 2011; Ghazoul, 2016) and gives rise to
greater aboveground carbon densities than anywhere else in the tropics
(Avitabile
et al., 2016; Sullivan et al., 2017), highlighting the need for new
ALS-based carbon estimation models for this region.
Here we develop a regional model for estimating ACD from ALS data that
underpins ongoing efforts to map Sabah's forest carbon stocks at high
resolution to inform conservation and management decisions for one of the
world's most threatened biodiversity hotspots
(Asner et al.,
2018; Nunes et al., 2017). Building on the work of
Asner and Mascaro (2014), we combine
ALS data with estimates of ACD from a total of 173 permanent forests plots
spanning the major lowland dipterocarp forest types and disturbance
gradients found in Borneo to derive a simple yet general equation for
predicting carbon stocks from ALS metrics at hectare resolution. As part of
this approach we also develop a novel framework for propagating uncertainty
in both ALS- and ground-based data, allowing uncertainty in hectare-scale
estimates of carbon stocks to be quantified robustly. To assess the accuracy
of this new model, we then benchmark it against existing ALS-derived
equations of ACD developed for the tropics
(Asner and Mascaro, 2014) and
satellite-based carbon maps of the region
(Avitabile et al.,
2016; Pfeifer et al., 2016).
Summary of permanent forest plot data collected at each study site
and description of which ALS sensor was used at each location. Plot size
is in hectares, while minimum stem diameter thresholds (Dmin) are given
in centimetres.
Study siteCensus yearNo. plotsPlot sizeNo. treesDminHeightSpecies IDALS sensorSepilok Forest Reserve2013–201536122 43010✓✓NERC ARFKuamut Forest Reserve2015–2016390.265a558810✓✓CAO-3Danum Valley Conservation Area CTFS plot2010–2016451215 0161✓✓NERC ARF CAO plots2017200.271a277110✓✓CAO-3SAFE landscape SAFE experiment201438b0.062584441✓NERC ARF SAFE experiment2010101b0.0625251710NERC ARF Riparian buffers201448b0.0625147210✓NERC ARF GEM plots201441190010✓✓NERC ARFMaliau Basin Conservation Area SAFE experiment201027b0.062589410NERC ARF GEM plots20142190510✓✓NERC ARF
a Mean plot size after applying slope correction (see Sect. 2.2.2
for further details).b Plots established as part of the SAFE experiment, and those located
along riparian buffer zones in the SAFE landscape were aggregated into
spatial blocks prior to statistical analyses (n=27 with a mean plot size
of 0.5 ha; see Sect. 2.2.4 for further details).
Materials and methodsStudy region
The study was conducted in Sabah, a Malaysian state in northern Borneo (Fig. 1a).
Mean daily temperature is 26.7 ∘C and annual rainfall is
2600–3000 mm (Walsh and Newbery, 1999). Severe droughts
linked to El Niño events occur about once every 10 years
(Malhi and Wright, 2004; Walsh
and Newbery, 1999). Sabah supports a wide range of forest types, including
dipterocarp forests in the lowlands that are among the tallest in the
tropics (Fig. 1b;
Banin et al., 2012).
Permanent forest plot data
We compiled permanent forest plot data from five forested landscapes across
Sabah (Fig. 1a): Sepilok Forest Reserve, Kuamut Forest Reserve, Danum Valley
Conservation Area, the Stability of Altered Forest Ecosystems (SAFE)
experimental forest fragmentation landscape
(Ewers et al., 2011) and Maliau Basin
Conservation Area. Here we provide a brief description of the permanent plot
data collected at each site, which are summarized in Table 1. Additional
details are provided in Supplement S1.
Sepilok Forest Reserve
The reserve is a protected area encompassing a remnant of coastal lowland
old-growth tropical rainforest (Fox, 1973) and is
characterized by three strongly contrasting soil types that give rise to
forests that are structurally and functionally very different
(Dent et
al., 2006; DeWalt et al., 2006; Nilus et al., 2011): alluvial dipterocarp
forest in the valleys (hereafter alluvial forests), sandstone hill
dipterocarp forest on dissected hillsides and crests (hereafter sandstone
forests), and heath forest on podzols associated with the dip slopes of
cuestas (hereafter heath forests). We used data from nine permanent
4 ha
forest plots situated in the reserve, three in each forest type. These were
first established in 2000–2001 and were most recently re-censused in
2013–2015. All stems with a diameter (D, in cm) ≥ 10 cm were recorded and
identified to species (or closest taxonomic unit). Tree height (H, in m) was
measured for a subset of trees (n=718) using a laser range finder. For
the purposes of this analysis, each 4 ha plot was subdivided into
1 ha
subplots, giving a total of 36 plots 1 ha in size. The corners of the plots
were geolocated using a Geneq SXBlue II global positioning system (GPS)
unit, which uses satellite-based augmentation to perform differential
correction and is capable of a positional accuracy of less than 2 m (95 %
confidence intervals).
Kuamut Forest Reserve
The reserve is a former logging area that is now being developed as a
restoration project. Selective logging during the past 30 years has left
large tracts of forest in a generally degraded condition, although the
extent of this disturbance varies across the landscape. Floristically and
topographically the Kuamut reserve is broadly similar to Danum Valley –
with which it shares a western border – and predominantly consists of
lowland dipterocarp forests. Within the forest reserve, 39 circular plots
with a radius of 30 m were established in 2015–2016 spanning a range of
forest successional stages, including young secondary forests characterized
by the presence of species with low wood densities (e.g. Macaranga spp.).
Coordinates for the plot centres were taken using a Garmin GPSMAP 64s device
with an accuracy of ±10 m (95 % confidence intervals). Within each
plot, all stems with D≥10cm were recorded and identified to species
(or the closest taxonomic unit), and H was measured using a laser range finder.
Because the radius of the plots was measured along the slope of the terrain
(as opposed to a horizontally projected distance), we slope-corrected the
area of each plot by multiplying by cos(θ), where θ is the
average slope of the plot in degrees as calculated from the digital
elevation model obtained from the ALS data. The average plot size after
applying this correction factor was 0.265 ha (6 % less than if no slope
correction had been applied).
Danum Valley Conservation Area
The site encompasses the largest remaining tract of primary lowland
dipterocarp forest in Sabah. Within the protected area, we obtained data
from a 50 ha permanent forest plot which was established in 2010 as part of
the Centre for Tropical Forest Science (CTFS) ForestGEO network
(Anderson-Teixeira
et al., 2015). Here we focus on 45 ha of this plot for which all stems with
D≥1cm have been mapped and taxonomically identified (mapping of the
remaining 5 ha of forest was ongoing as of January 2017). For the purposes
of this study, we subdivided the mapped area into 45 1 ha plots, the
coordinates of which were recorded using the Geneq SXBlue II GPS. In
addition to the 50 ha CTSF plot, we also secured data from 20 circular plots
with a 30 m radius that were established across the protected area by the
Carnegie Airborne Observatory (CAO) in 2017. These plots were surveyed
following the same protocols as those described previously for the plots at
Kuamut in Sect. 2.2.2.
SAFE landscape and Maliau Basin Conservation Area
Plot data from three sources were acquired from the SAFE landscape and the
Maliau Basin Conservation Area: research plots established through the SAFE
project, plots used to monitor riparian buffer zones and plots from the
Global Ecosystem Monitoring (GEM) network (http://gem.tropicalforests.ox.ac.uk, last access: 20 June 2018).
As part of the SAFE project, 166
plots 25×25m in size were established in forested areas
(Ewers
et al., 2011; Pfeifer et al., 2016). Plots are organized in blocks which
span a land-use intensity gradient ranging from twice-logged forests that
are currently in the early stages of secondary succession within the SAFE
landscape to relatively undisturbed old-growth forests at Maliau Basin
(Ewers et al., 2011; Struebig
et al., 2013). Plots were surveyed in 2010, at which time all stems with D≥10cm were recorded and plot coordinates were taken using a Garmin
GPSMAP60 device (accurate to within ±10 m; 95 % confidence
intervals). Of these 166 plots, 38 were re-surveyed in 2014, at which time
all stems with D≥1cm were recorded and tree heights were measured
using a laser range finder. Using these same protocols, a further 48 plots
were established in 2014 along riparian buffer zones in the SAFE landscape.
As with the SAFE project plots, riparian plots are also spatially clustered
into blocks. The small size of the SAFE and riparian plots (0.0625 ha) makes
them prone to high uncertainty when modelling carbon stocks from ALS
(Réjou-Méchain
et al., 2014), especially given the relatively low positional accuracy of
the GPS coordinates. To minimize this source of error, we chose to aggregate
individual plots into blocks for all subsequent analyses (n=27, with a
mean size of 0.5 ha). Lastly, we obtained data from six GEM plots – four
within the SAFE landscape and two at Maliau Basin. The GEM plots are 1 ha in
size and were established in 2014. All stems with D≥10cm were mapped,
measured for height using a laser range finder and taxonomically
identified. The corners of the plots were georeferenced using the Geneq
SXBlue II GPS.
Estimating aboveground carbon density and its uncertainty
Across the five study sites we compiled a total of 173 plots that together
cover a cumulative area of 116.1 ha of forest. For each of these plots we
calculated aboveground carbon density (ACD, in MgCha-1) following the
approach outlined in the BIOMASS package in R (R Core
Development Team, 2016; Réjou-Méchain et al., 2017). This provides a
workflow to not only quantify ACD, but also propagate uncertainty in ACD estimates
arising from both field measurement errors and uncertainty in allometric
models. The first step is to estimate the aboveground biomass (AGB, in kg) of
individual trees using Chave et
al.'s (2014) pantropical biomass equation: AGB=0.067×D2×H×WD0.976. For trees with no height measurement in the
field, H was estimated using a locally calibrated H–D allometric equation,
while wood density (WD, in gcm-3) values were obtained from the global
wood density database
(Chave et al., 2009;
Zanne et al., 2009; see Supplement S1 for additional details on both H and
WD estimation).
In addition to quantifying AGB, Réjou-Méchain et al.'s (2017) workflow
uses Monte Carlo simulations to propagate uncertainty in biomass estimates
due to (i) measurement errors in D (following
Chave et al.'s (2004)
approach, in which 95 % of stems are assumed to contain small measurement
errors that are in proportion to D, while the remaining 5 % is assigned a
gross measurement error of 4.6 cm), (ii) uncertainty in H–D allometries,
(iii) uncertainty in WD estimates arising from incomplete taxonomic identification
and/or coverage of the global wood density database, and (iv) uncertainty in
the AGB equation itself. Using this approach, we generated 100 estimates of
AGB for each recorded tree. ACD was then quantified by summing the AGB of all trees
within a plot, dividing the total by the area of the plot and applying a
carbon content conversion factor of 0.47
(Martin and
Thomas, 2011). By repeating this across all simulated values of AGB, we
obtained 100 estimates of ACD for each of the 173 plots that reflect the
uncertainty in stand-level carbon stocks (note that a preliminary analysis
showed that 100 iterations were sufficient to robustly capture mean and
standard deviation values of plot-level ACD, while also allowing for efficient
computing times). As a last step, we used data from 45 plots in Danum Valley
– where all stems with D≥1cm were measured – to develop a
correction factor that compensates for the carbon stocks of stems with D<10cm that were not recorded (Phillips et
al., 1998; see Eq. S2 in Supplement S1).
Stand basal area and wood density estimation
In addition to estimating ACD for each plot, we also calculated basal area
(BA, in m2ha-1) and the community-weighted mean WD, as well as their
uncertainties. BA was quantified by summing π×D/22 across all stems within a plot and then applying a correction
factor that accounts for stems with D<10cm that were not measured
(see Eq. S3 in Supplement S1). In the case of BA, uncertainty arises from
measurement errors in D, which were propagated through following the approach
of Chave et al. (2004)
described in Sect. 2.3. The community-weighted mean WD of each plot was
quantified as ∑BAij×WDi, where BAij is the
relative basal area of species i in plot j, and WDi is the mean wood
density of species i. Uncertainty in plot-level WD reflects incomplete
taxonomic information and/or lack of coverage in the global wood density
database.
Airborne laser scanning data
ALS data covering the permanent forest plots described in Sect. 2.2 were
acquired through two independent surveys, the first undertaken by NERC's
Airborne Research Facility (ARF) in November of 2014 and the second by the
Carnegie Airborne Observatory (CAO) in April of 2016. Table 1 specifies
which plots were overflown with which system. NERC ARF operated a Leica
ALS50-II lidar sensor flown on a Dornier 228-201 at an elevation of
1400–2400 m a.s.l. (depending on the study site) and a flight speed of
120–140 knots. The sensor emits pulses at a frequency of 120 kHz, has a
field of view of 12∘ and a footprint of about 40 cm. The average
point density was 7.3 pointsm-2. The Leica ALS50-II lidar sensor
records both discrete point and full-waveform ALS, but for the purposes of
this study only the discrete-return data, with up to four returns recorded
per pulse, were used. Accurate georeferencing of the ALS point cloud was
ensured by incorporating data from a Leica base station running in the study
area concurrently to the flight. The ALS data were preprocessed by NERC's
Data Analysis Node and delivered in LAS format. All further processing was
undertaken using LAStools software (http://rapidlasso.com/lastools, last access: 20 June 2018).
The CAO campaign was conducted using the
CAO-3 system, a detailed description of which can be found in
Asner et al. (2012).
Briefly, CAO-3 is a custom-designed, dual-laser, full-waveform system that
was operated in discrete-return collection mode for this project. The
aircraft was flown at 3600 m a.s.l. at a flight speed of 120–140 knots. The
ALS system was set to a field of view of 34∘ (after 2∘
cut-off from each edge) and a combined-channel pulse frequency of 200 kHz.
The ALS pulse footprint at 3600 m a.s.l. was approximately 1.8 m. With
adjacent flight-line overlap, these settings yielded approximately 2.0 pointsm-2.
Despite differences in the acquisition parameters of the
two surveys which can influence canopy metrics derived from ALS data
(Gobakken and Næsset, 2008; Roussel et al., 2017),
a comparison of regions of overlap between the flight campaigns showed
strong agreement between data obtained from the two sensors (Supplement S2).
Airborne laser scanning metrics
ALS point clouds derived from both surveys were classified into ground and
non-ground points, and a digital elevation model (DEM) was fitted to the
ground returns to produce a raster at 1 m resolution. The DEM was then
subtracted from the elevations of all non-ground returns to produce a
normalized point cloud, from which a canopy height model (CHM) was
constructed by averaging the first returns. Finally, any gaps in the raster
of the CHM were filled by averaging neighbouring cells. From the CHMs we
calculated two metrics for each of the permanent field plots: top-of-canopy
height (TCH, in m) and canopy cover at 20 m aboveground (Cover20). TCH is the mean
height of the pixels which make up the surface of the CHM. Canopy cover is
defined as the proportion of area occupied by crowns at a given height
aboveground (i.e. 1 – gap fraction). Cover20 was calculated by creating a
plane horizontal to the ground in the CHM at a height of 20 m aboveground,
counting the number of pixels for which the CHM lies above the plane and
then dividing this number by the total number of pixels in the plot. A
height of 20 m aboveground was chosen as previous work showed this to be the
optimal height for estimating plot-level BA in an old-growth lowland
dipterocarp forest in Sabah
(Coomes et al.,
2017).
Accounting for geopositional uncertainty
Plot coordinates obtained using a GPS are inevitably associated with a
certain degree of error, particularly when working under dense forest
canopies. However, this source of uncertainty is generally overlooked when
attempting to relate field estimates of ACD to ALS metrics. To account for
geopositional uncertainty, we introduced normally distributed random errors
in the plot coordinates. These errors were assumed to be proportional to the
operational accuracy of the GPS unit used to geolocate a given plot: ±2 m
for plots recorded with the Geneq SXBlue II GPS and ±10 m for
those geolocated using either the Garmin GPSMAP60 or Garmin GPSMAP 64s
devices. This process was iterated 100 times, and at each step we calculated
TCH and Cover20 across all plots. Note that for plots from the SAFE project and
those situated along riparian buffer zones, ALS metrics were calculated for
each individual 0.0625 ha plot before being aggregated into blocks (as was
done for the field data).
Modelling aboveground carbon density and associated uncertainty
We started by using data from the 173 field plots to fit a regional form of
Asner and Mascaro's (2014) model, in which
ACD is expressed as the following function of ALS-derived TCH and field-based
estimates of BA and WD:
ACD=ρ0×TCHρ1×BAρ2×WDρ3,
where ρ0-3 represent constants to be estimated from empirical data.
In order to apply Eq. (2) to areas where field data are not available, the
next step is to develop sub-models to estimate BA and WD from ALS metrics. Of
particular importance in this regard is the accurate and unbiased estimation
of BA, which correlates very strongly with ACD (Pearson's correlation coefficient
(ρ)=0.93 across the 173 plots).
Asner and Mascaro (2014) found that a
single ALS metric – TCH – could be used to reliably estimate both BA and WD
across a range of tropical forest regions. However, recent work suggests
this may not always be the case
(Duncanson et al., 2015; Spriggs,
2015). In particular,
Coomes et al. (2017) showed that ALS metrics that capture information about canopy cover
at a given height aboveground – such as Cover20 – were better suited to
estimating BA. Here we compared these two approaches to test whether
Cover20 can prove a useful metric to distinguish between forests with
similar TCH but substantially different BA.
Basal area sub-models
Asner and Mascaro (2014) modelled BA as
the following function of TCH:
BA=ρ0×TCH.
We compared the goodness-of-fit of Eq. (3) to a model that additionally
incorporates Cover20 as a predictor of BA. Doing so, however, requires
accounting for the fact that TCH and Cover20 are correlated. To avoid issues
of collinearity (Dormann et al., 2013), we therefore
first modelled the relationship between Cover20 and TCH using logistic
regression and used the residuals of this model to identify plots that have
higher or lower than expected Cover20 for a given TCH.
lnCover201-Cover20=ρ0+ρ1×lnTCH
Predicted values of canopy cover (Cover^20) can be obtained from
Eq. (4) as follows:
Cover^20=11+e-ρ0×TCH-ρ1.
From this, we calculated the residual cover (Coverresid) for each of the 173
field plots as Cover20-Cover^20 and then modelled BA as the
following non-linear function of TCH and Coverresid:
BA=ρ0×TCHρ1×1+ρ2×Coverresid.
Equation (6) was chosen after careful comparison with alternative functional
forms. This included modelling BA directly as a function of Cover20, without
including TCH in the regression. We discarded this last option as BA estimates
were found to be highly sensitive to small variations in canopy cover when
Cover20 approaches 1.
Wood density sub-models
Following Asner and Mascaro (2014), we
modelled WD as a power-law function of TCH:
WD=ρ0×TCHρ1.
The expectation is that, because the proportion of densely wooded species
tends to increase during forest succession
(Slik et al., 2008), taller forests
should on average have higher stand-level WD values. While this
explicitly ignores the well-known fact that WD is also influenced by
environmental factors that have nothing to do with disturbance
(e.g.
soils or climate; Quesada et al., 2012), we chose to fit a single function
for all sites, as from an operational standpoint applying forest-type-specific equations would require information on the spatial
distribution of these forest types across the landscape (something which may
not necessarily be available, particularly for the tropics). For comparison,
we also tested whether replacing TCH with Cover20 would improve the fit of the
WD model.
Error propagation and model validation
Just as deriving accurate estimates of ACD is critical to producing robust and
useful maps of forest carbon stocks, so too is the ability to place a degree
of confidence on the mean predicted values obtained from a given model
(Réjou-Méchain et al., 2017). In order to fully
propagate uncertainty in ALS-derived estimates of ACD, as well as robustly
assessing model performance, we developed the following approach based on
leave-one-out cross validation: (i) of the 173 field plots, 1 was set
aside for validation, while the rest were used to calibrate models; (ii) the
calibration dataset was used to fit both the regional ACD model (Eq. 2)
and the BA and WD sub-models (Eqs. 3, 6–7); and (iii) the fitted models
were used to generate predictions of BA, WD and ACD for the validation plot
previously set aside. In each case, Monte Carlo simulations were used to
incorporate model uncertainty in the predicted values. For Eqs. (4) and (6),
parameter estimates were obtained using the L-BFGS-B non-linear optimization
routine implemented in Python (Morales and Nocedal, 2011). For
power-law models fit to log–log-transformed data (i.e. Eqs. 2 and 7), we
applied the Baskerville (1972) correction factor by
multiplying predicted values by expσ2/2,
where σ is the estimated standard deviation of the residuals (also
known as the residual standard error); (iv) model fitting and prediction
steps (ii)–(iii) were repeated 100 times across all estimates of ACD, BA, WD, TCH and
Cover20 that had previously been generated for each field plot. This allowed
us to fully propagate uncertainty in ACD arising from field measurement errors,
allometric models and geopositional errors; (v) lastly, steps (i)–(iv) were
repeated for all 173 field plots.
Once predictions of ACD had been generated for all 173 plots, we assessed model
performance by comparing predicted and observed ACD values (ACDpred
and ACDobs, respectively) on the basis of root mean square error (RMSE)
calculated as 1N∑i=1NACDobs-ACDpred2 and
relative systematic error (or bias), which we calculated as
1N∑i=1NACDpred-ACDobsACDobs×100 (Chave et al., 2014).
Additionally, we tested how plot-level errors (calculated for each
individual plot as ACDobs-ACDpredACDobs×100) varied as a function of forest carbon
stocks and in relation to plot size
(Réjou-Méchain
et al., 2014).
The modelling and error propagation framework described above was chosen
after a thorough comparison with a number of alternative approaches. The
objective of this comparison was to identify the approach that would yield
the lowest degree of systematic bias in the predicted values of ACD, as we
consider this to be a critical requirement of any carbon estimation model,
particularly if – as is the case here – that model is to underpin the
generation of a carbon map designed to inform management and conservation
policies (Asner et al., 2018). Of
the two alternative approaches we tested, the first relied on fitting a
combination of ordinary and non-linear least squares regression models to
parameterize the equations presented above. As with the modelling routine
described above, this approach did not account for potential spatial
autocorrelation in the residuals of the models, which could result in a
slight underestimation of the true uncertainty in the fitted parameter
values. We contrasted this approach with one that used generalized and
non-linear least squares regression that explicitly account for spatial
dependencies in the data. Both these approaches underperformed compared to
the routine described above, as they substantially overestimated ACD values in
low-carbon-density forests and underestimated ACD in carbon-rich ones (see
Supplement S3 for details). This tendency to introduce a systematic bias in
the ACD predictions was particularly evident in the case of the spatially
explicit models (see Fig. S4b in the Supplement). In light of this we opted for the approach
presented here, even though we acknowledge that it may slightly
underestimate uncertainty in modelled ACD values due to spatial
non-independence in the data.
Comparison with satellite-derived estimates of aboveground carbon
density
We compared the accuracy of ACD estimates obtained from ALS with those of two
existing carbon maps that cover the study area. The first of these is a
carbon map of the SAFE landscape and Maliau Basin derived from RapidEye
satellite imagery (Pfeifer
et al., 2016). The map has a resolution of 25×25m and makes use
of textural and intensity information from four wavebands to model forest
biomass (which we converted to carbon by applying a conversion factor of
0.47; Martin
and Thomas, 2011). The second is a recently published consensus map of
pantropical forest carbon stocks at 1 km resolution
(Avitabile et al., 2016). It makes use of field data and
high-resolution locally calibrated carbon maps to refine estimates from
existing pantropical datasets obtained through satellite observations
(Baccini
et al., 2012; Saatchi et al., 2011).
Relationship between field-estimated and modelled aboveground
carbon density (ACD). Panel (a) shows the fit of the regionally calibrated
ACD model (Eq. 8 in Sect. 3), which incorporates field-estimated basal area
(BA) and wood density (WD), while panel (b) corresponds to
Asner and Mascaro's (2014) general
ACD model (Eq. 1 in Sect. 1). Panels (c)–(d) illustrate the predictive
accuracy of the regionally calibrated ACD model when field-measured BA and WD
values are replaced with estimates derived from airborne laser scanning. In
panel (c) BA and WD were estimated from top-of-canopy height (TCH) using Eqs. (9) and
(11), respectively. In contrast, ACD estimates in panel (d) were obtained by
modelling BA as a function of both TCH and canopy cover at 20 m aboveground
following Eq. (10). In all panels, predicted ACD values are based on
leave-one-out cross validation. Dashed lines correspond to a 1 : 1
relationship. Error bars are standard deviations and the RMSE of each
comparison is printed in the bottom right-hand corner of the panels.
Relationship between ALS-derived canopy cover at 20 m
aboveground and top-of-canopy height. Panel (a) shows the distribution of
the field plots with a line of best fit passing through the data, with error
bars corresponding to standard deviations. Panel (b) illustrates how
estimates of aboveground carbon density (ACD; obtained using Eq. 8 with Eqs. 10 and 11
as inputs) vary as a function of the two ALS metrics for the
range of values observed across the forests of Sabah.
Relationship between field-measured basal area and (a) top-of-canopy
height and (b) canopy cover at 20 m aboveground as
measured through airborne laser scanning. Error bars correspond to standard
deviations.
Relationship between community-weighted mean wood density (from
field measurements) and top-of-canopy height (from airborne laser scanning).
Error bars correspond to standard deviations.
To assess the accuracy of the two satellite products, we extracted ACD values
from both carbon maps for all overlapping field plots and then compared
field and satellite-derived estimates of ACD on the basis of RMSE and bias. For
consistency with previous analyses, ACD values for SAFE project plots and those
in riparian buffer zones were extracted at the individual plot level (i.e.
0.0625 ha scale) before being aggregated into the same blocks used for
ALS model generation. In the case of Avitabile et al. (2016), we acknowledge that because of the large difference in resolution
between the map and the field plots, comparisons between the two need to be
made with care. This is particularly true when only a limited number of
field plots are located within a given 1 km2 grid cell. To at least
partially account for these difference in resolution when assessing
agreement between Avitabile et al.'s (2016) map and the
field data, we first averaged ACD values from field plots that fell within the
same 1 km2 grid cell. We then compared satellite- and plot-based
estimates of ACD for (i) all grid cells within which field plots were sampled,
regardless of their number and size (n=135), and for (ii) a subset
of grid cells for which at least five plots covering a cumulative area ≥ 1 ha
were sampled in the field (n=8). The expectation is that grid
cells for which a greater number of large plots have been surveyed should
show closer alignment between satellite- and plot-based estimates of ACD.
Results
The regional model of ACD – parameterized using field estimates of wood density
and basal area and ALS estimates of canopy height – was
ACDRegional=0.567×TCH0.554×BA1.081×WD0.186.
The model had an RMSE of 19.0 MgCha-1 and a bias of 0.6 % (Fig. 2a;
see Supplement S4 for confidence intervals on parameter estimates for all
models reported here). The regional ACD model fit the data better than
Asner and Mascaro's (2014) general
model (i.e. Eq. 1 in Sect. 1), which had an RMSE of 32.0 MgCha-1
and tended to systematically underestimate ACD values (bias =-7.1 %; Fig. 2b).
Basal area sub-models
When modelling BA in relation to TCH, we found the best-fit model to be
BA=1.112×TCH.
In comparison, when BA was expressed as a function of both TCH and Coverresid we
obtained the following model:
BA=1.287×TCH0.987×1+1.983×Coverresid,
where Coverresid=Cover20-11+e12.431×TCH-4.061 (Fig. 3). Of the two sub-models used to predict
BA, Eq. (10) proved the better fit to the data (RMSE = 9.3 and 6.6 m2ha-1,
respectively; see Supplement S5), reflecting the fact that in our
case BA was more closely related to canopy cover than TCH (Fig. 4).
Wood density sub-model
When modelling WD as a function of TCH, we found the best-fit model to be
WD=0.385×TCH0.097.
Across the plot network WD showed a general tendency to increase with TCH (Fig. 5;
RMSE of 0.056 gcm-3). However, the relationship was weak and Eq. (11)
did not capture variation in WD equally well across the different forest types
(see Supplement S5). In particular, heath forests at Sepilok, which have
very high WD despite being much shorter than surrounding lowland dipterocarp
forests (0.64 against 0.55 gcm-3), were poorly captured by the WD
sub-model. We found no evidence to suggest that replacing TCH with canopy cover
at 20 m aboveground would improve the accuracy of these estimates (see
Supplement S5).
Model errors (calculated for each individual plot as ACDobs-ACDpred/ACDobs×100) in relation to
(a) field-estimated aboveground carbon density (ACD) and (b) plot size. Curves
(±95 % shaded confidence intervals) were obtained by fitting linear
models to log–log-transformed data. Black lines correspond to the
regionally calibrated ACD model (Eq. 8 in Sect. 3). Orange lines show model
errors when basal area (BA) was estimated from top-of-canopy height (TCH) using
Eq. (9). In contrast, blue lines show model errors when BA was expressed as a
function of both TCH and canopy cover at 20 m aboveground following Eq. (10).
Vertical dashed lines along the horizontal axis show the distribution
of the data (in panel b plot size values were jittered to avoid
overlapping lines).
Comparison between field-estimated aboveground carbon density
(ACD) and satellite-derived estimates of ACD reported in (a) Pfeifer et al. (2016)
and (b) Avitabile et al. (2016). In panel (b) large black
points correspond to grid cells in Avitabile et al.'s
(2016) pantropical biomass map for which at least five plots covering a
cumulative area ≥ 1 ha were sampled in the field. By contrast, grid
cells for which comparisons are based on less than five plots are depicted
by small grey circles. Error bars correspond to standard deviations, while
the RMSE of the satellite estimates is printed in the bottom right-hand
corner of the panels (note that for panel b the RMSE in grey is that
calculated across all plots, whereas that in black is based only on the
subset of grid cells for which at least five plots covering a cumulative
area ≥ 1 ha were sampled in the field). For comparison with ACD estimates
obtained from airborne laser scanning, a kernel density plot fit to the
points in Fig. 2d is displayed in the background.
Estimating aboveground carbon density from airborne laser
scanning
When field-based estimates of BA and WD were replaced with ones derived from
TCH using Eqs. (9) and (11), the regional ACD model generated unbiased estimates of
ACD (bias =-1.8 %). However, the accuracy of the model decreased
substantially (RMSE = 48.1 MgCha-1; Fig. 2c). In particular, the
average plot-level error was 21 % and remained relatively constant across
the range of ACD values observed in the field data (yellow line in Fig. 6a). In
contrast, when the combination of TCH and Cover20 was used to estimate BA
through Eq. (10), we obtained more accurate estimates of ACD (RMSE = 39.3 MgCha-1,
bias = 5.3 %; Fig. 2d). Moreover, in this instance
plot-level errors showed a clear tendency to decrease in large and
high-carbon-density plots (blue line in Fig. 6a), declining from an average
25.0 % at 0.1 ha scale to 19.5 % at 0.25 ha, 16.2 % at 0.5 ha and
13.4 % at 1 ha (blue line in Fig. 6b).
Comparison with satellite-derived estimates of aboveground carbon
density
When compared to ALS-derived estimates of ACD, both satellite-based carbon maps
of the study area showed much poorer agreement with field data (Fig. 7).
Pfeifer et al.'s (2016)
map covering the SAFE landscape and Maliau Basin systematically
underestimated ACD (bias =-36.9 %) and had an RMSE of 77.8 MgCha-1
(Fig. 7a). By contrast, Avitabile et al.'s (2016)
pantropical map tended to overestimate carbon stocks. When we compared
field and satellite estimates of ACD across all grid cells for which data
were
available we found that carbon stocks were overestimated by 111.2 % on
average, with an RMSE of 100.1 MgCha-1 (grey circles in Fig. 7b).
As expected, limiting this comparison to grid cells for which at least five
plots covering a cumulative area ≥ 1 ha were sampled led to greater
agreement between field and satellite estimates of ACD (large black circles in
Fig. 7b). Yet the accuracy of the satellite-derived estimates of ACD remained
much lower than that derived from ALS data (RMSE = 82.8 MgCha-1;
bias = 59.3 %).
Discussion
We developed an area-based model for estimating aboveground carbon stock
from ALS data that can be applied to mapping the lowland tropical forests of
Borneo. We found that adding a canopy cover term to estimate BA to
Asner and Mascaro's (2014) general
model substantially improved its goodness-of-fit (Fig. 2c–d), as it allowed
us to capture variation in stand basal area much more effectively compared
to models parameterized solely using plot-averaged TCH. In this process, we
also implemented an error propagation approach that allows various sources
of uncertainty in ACD estimates to be incorporated into carbon mapping efforts.
In the following sections we place our approach in the context of ongoing
efforts to use remotely sensed data to monitor forest carbon stocks,
starting with ALS-based approaches and then comparing these to
satellite-based modelling. Finally, we end by discussing the implication of
this work for the conservation of Borneo's forests.
Including canopy cover in the Asner and Mascaro (2014) carbon
model
We found that incorporating a measure of canopy cover at 20 m aboveground in
the Asner and Mascaro (2014) model improves its goodness-of-fit
substantially without compromising its generality. Asner and Mascaro's
(2014) model is grounded in forest and tree geometry, drawing its basis from
allometric equations for estimating tree aboveground biomass such as that of
Chave et al. (2014), in which a tree's biomass is expressed as a multiplicative
function of its diameter, height and wood density: AGB=ρ0×WD×D2×Hρ1. By
analogy, the carbon stock within a plot is related to the product of mean
wood density, total basal area and top-of-canopy height (each raised to a
power). Deriving this power-law function from knowledge of the tree size
distribution and tree–biomass relationship is far from straightforward
mathematically (Spriggs, 2015;
Vincent et al., 2014), but this analogy seems to hold up well in a practical
sense. When fitted to data from 14 forest types spanning aridity gradients
in the Neotropics and Madagascar, Asner and Mascaro (2014) found that a
single relationship applied to all forests types once regional differences
in structure were incorporated as sub-models relating BA and WD to TCH. However,
the model's fit depends critically on there being a close relationship
between BA and TCH, as BA and ACD tend to be tightly coupled (ρ=0.93 in our
case). Whilst that held true for the 14 forest types previously studied, in
Bornean forest we found that the BA sub-models could be improved considerably
by including canopy cover as an explanatory variable, particularly when it
came to estimating BA in densely packed stands. This makes intuitive sense if
one considers an open forest comprised of just a few trees; the crown area
of each tree scales with its basal area, so the gap fraction at the ground level
of a plot is negatively related to the basal area of its trees
(Singh et al., 2016). A
similar principle applies in denser forests, but in forests with multiple
tiers formed by overlapping canopies such as those that occur in Borneo, the
best-fitting relationship between gap fraction and basal area is no longer
at ground level, but is instead further up the canopy
(Coomes et al.,
2017). Meyer et al. (2018)
recently came to a very similar conclusion, showing that the cumulative
crown area of emergent trees estimated at a height of 27 m aboveground using
ALS data was strongly and linearly related to ACD across a diverse range of
Neotropical forest types.
The functional form used to model BA in relation to TCH and residual forest cover
(i.e. Eq. 10 presented above) was selected for two reasons: first, for a
plot with average canopy cover for a given TCH, the model reduces to the
classic model of Asner and Mascaro (2014), making comparisons
straightforward. Second, simpler functional forms (e.g. ones relating
BA directly to Cover20) were found to have very similar goodness-of-fit, but
predicted unrealistically high ACD estimates for a small fraction of pixels
when applied to mapping carbon across the landscape. This study is the first
to formally introduce canopy cover into the modelling framework of Asner and
Mascaro (2014), but several other studies have concluded that gap fraction
is an important variable to include in multiple regression models of forest
biomass
(Colgan
et al., 2012; Meyer et al., 2018; Ni-Meister et al., 2010; Pflugmacher et
al., 2012; Singh et al., 2016). Regional calibration of the Asner and
Mascaro (2014) model was necessary for the lowland forests of South-east
Asia because dominance by dipterocarp species makes them structurally unique
(Ghazoul, 2016; Jucker et al., 2018): trees in the
region grow tall but have narrow stems for their height
(Banin
et al., 2012; Feldpausch et al., 2011), creating forests that have among the
greatest carbon densities of any in the tropics
(Avitabile
et al., 2016; Sullivan et al., 2017).
The structural complexity and heterogeneity of Sabah's forests is one reason
why even though accounting for canopy cover substantially improved the
accuracy of our model (particularly in the case of tall, densely packed
stands), a certain degree of error remains in the ACD estimates (Fig. 6). This
error also reflects an inevitable trade-off between striving for generality
and attempting to maximize accuracy when modelling ACD using ALS. In this
regard, our modelling framework differs from the
multiple-regression-with-model-selection approach that is typically adopted
for estimating the ACD of tropical forests using ALS data
(Chen
et al., 2015; Clark et al., 2011; D'Oliveira et al., 2012; Drake et al.,
2002; Hansen et al., 2015; Ioki et al., 2014; Jubanski et al., 2013;
Réjou-Méchain et al., 2015; Singh et al., 2016). These studies,
which build on 2 decades of research in temperate and boreal forests
(Lefsky et
al., 1999; Nelson et al., 1988; Popescu et al., 2011; Wulder et al., 2012),
typically calculate between 5 and 25 summary statistics from the height
distribution of ALS returns and explore the performance of models
constructed using various combinations of those summary statistics as
explanatory variables. The “best-supported” model is then selected from
the list of competing models on offer by comparing relative performance
using evaluation statistics such as R2, RMSE or AIC.
There is no doubt that selecting regression models in this way provides a
solid basis for making model-assisted inferences about regional carbon
stocks and their uncertainty
(Ene et al.,
2012; Gregoire et al., 2016). However, a well-recognized problem is that
models tend to be idiosyncratic by virtue of local fine-tuning, so they cannot be
applied more widely than the region for which they were calibrated and
cannot be compared very easily with other studies. For example, it comes as
no surprise that almost all publications identify mean height or some metric
of upper-canopy height (e.g. 90th or 99th percentile of the
height distribution) as being the strongest determinant of biomass. But
different choices of height metric make these models difficult to compare.
Other studies have included variance terms or measures of laser penetration
to the lower canopy in an effort to improve goodness-of-fit. For instance, a
combination of 75th quantile and variance of return heights proved
effective in modelling ACD of selectively logged forests in Brazil
(D'Oliveira
et al., 2012). Similarly, a model developed for lower montane forests in
Sabah included the proportion of last returns within 12 m of the ground
(Ioki et al., 2014), while the proportions of returns in
various height tiers were selected for the ALS carbon mapping of sub-montane
forest in Tanzania (Hansen et al., 2015).
Working with Asner and Mascaro's (2014) power-law model may well sacrifice
goodness-of-fit compared with these locally tuned multiple regression
models. However, it provides a systematic framework for the ALS modelling of
forest carbon stocks, which we expect will prove hugely valuable for
calibrating and validating the next generation of satellite sensors being
designed specifically to monitor the world's forests.
Quantifying and propagating uncertainty
One of the most important applications of ACD estimation models is to infer
carbon stocks within regions of interest. Carbon stock estimation has
traditionally been achieved by networks of inventory plots designed to
provide unbiased estimates of timber volumes within an acceptable level of
uncertainty using well-established design-based approaches
(Särndal et al.,
1992). Forest inventories are increasingly supported by the collection of
cost-effective auxiliary variables, such as ALS-estimated forest height and
cover, that increase the precision of carbon stock estimation when used to
construct regression models, which are in turn used to estimate carbon across
areas where the auxiliary variables have been measured
(e.g. McRoberts et al., 2013). But just as
producing maps of our best estimates of carbon stocks across landscapes is
critical to informing conservation and management strategies, so is the
ability to provide robust estimates of the uncertainty associated with these
products (Réjou-Méchain et al., 2017).
Assessing the degree of confidence which we place on a given estimate of
ACD requires uncertainty to be quantified and propagated through all
processes
involved in the calculation of plot-level carbon stocks and statistical
model fitting (Chen et al., 2015). Our Monte Carlo
framework allows field measurement errors, geopositional errors and model
uncertainty to be propagated in a straightforward and robust manner
(Yanai et al., 2010). Our approach uses
Réjou-Méchain et al.'s (2017) framework as a starting point for
propagating errors associated with field measurements (e.g. stem diameter
recording, wood density estimation) and allometric models (e.g.
height–diameter relationships, tree biomass estimation) into plot-level
estimates of ACD. We then combine these sources of uncertainty with those
associated with co-location errors between field and ALS data and propagate
these through the regression models we develop to estimate ACD from ALS
metrics. This approach, which is fundamentally different to estimating
uncertainty by comparing model predictions to validation field plots, is
not widely used within the remote sensing community (e.g.
Gonzalez et al., 2010) despite being the more
appropriate technique for error propagation when there is uncertainty in
field measurements (Chen et al., 2015).
Nevertheless, several sources of potential bias remain. Community-weighted
wood density is only weakly related to ALS metrics and is estimated with
large errors (Fig. 5). The fact that wood density cannot be measured
remotely is well recognized, and the assumptions used to map wood density
from limited field data have major implications for carbon maps produced by
satellites (Mitchard
et al., 2014). For Borneo, it may prove necessary to develop separate wood
density sub-models for estimating carbon in heath forests versus other
lowland forest types (see Fig. 5). Height estimation is another source of
potential bias (Rutishauser et al., 2013):
four published height–diameter curves for Sabah show similar fits for small
trees (< 50 cm diameter) but diverge for large trees
(Coomes et al.,
2017), which contain most of the biomass
(Bastin et al., 2015).
Terrestrial laser scanning is likely to address this issue in the coming
years, providing not only new and improved allometries for estimating tree
height, but also much more robust field reference estimates of ACD from which
to calibrate ALS-based models of forest carbon stocks
(Calders et al., 2015;
Gonzalez de Tanago Menaca et al., 2017). As this transition happens, careful
consideration will also need to be given to differences in acquisition
parameters among ALS campaigns and how these in turn influence ACD estimates
derived from ALS metrics. While we found strong agreement between canopy
metrics derived from the two airborne campaigns (Supplement S2), previous
work has highlighted how decreasing ALS point density and changing footprint
size can impact the retrieval of canopy parameters
(Gobakken and Næsset, 2008; Roussel et al., 2017).
In this regard new approaches designed to explicitly correct for differences
among ALS flight specifications (e.g. Roussel et
al., 2017) offer great promise for minimizing this source of bias.
Lastly, another key issue influencing uncertainty in ACD estimates derived from
ALS data is the size of the field plots used to calibrate and validate
prediction models. As a rule of thumb, the smaller the field plots the
poorer the fit between field estimates of ACD and ALS-derived canopy metrics
(Asner
and Mascaro, 2014; Ruiz et al., 2014; Watt et al., 2013). Aside from the
fact that small plots inevitably capture a greater degree of heterogeneity
in ACD compared to larger ones (leading to more noise around regression lines),
they are also much more likely to suffer from errors associated with poor
alignment between airborne and field data, as well as exhibiting strong edge
effects (e.g. large trees whose crowns straddle the plot boundary). As
expected, for our best-fitting model of ACD we found that plot-level errors
tended to decrease with plot size (blue curve in Fig. 6b), going from
25.0 % at 0.1 ha scale to 13.4 % for 1 ha plots. This result is
remarkably consistent with previous theoretical and empirical work conducted
across the tropics, which reported mean errors of around 25–30 % at
0.1 ha
scale and approximately 10–15 % at 1 ha resolution
(Asner
and Mascaro, 2014; Zolkos et al., 2013). These results have led to the
general consensus that 1 ha plots should become the standard for calibrating
against ALS data. That being said, because there is a trade-off between the
number of plots one can establish and their size, working with 1 ha plots
inevitably comes at the cost of replication and representativeness. As such,
in some cases it may be preferable to sacrifice some precision (e.g. by
working with 0.25 ha plots, which in our case had a mean error
of 19.5 %) in order to gain a better representation of the wider landscape
– so long as uncertainty in ACD is fully propagate throughout.
Comparison with satellite-derived maps
Our results show that when compared to independent field data,
existing satellite products systematically underestimate or overestimate ACD
(depending on the product; Fig. 7). While directly comparing
satellite-derived estimates with independent field data in not entirely
straightforward, particularly when the resolution of the map is much
coarser than that of the field plots
(Réjou-Méchain
et al., 2014), as is the case with Avitabile et al. (2016),
it does appear that ALS is able to provide much more robust and accurate
estimates of ACD and its heterogeneity within the landscape than what is
possible with current satellite sensors. This is unsurprising given that in
contrast to optical imagery, which only captures the surface of the canopy,
ALS data provide high-resolution information on the 3-D structure of
canopies, which directly relates to ACD. However, ALS data are limited in
their
temporal and spatial coverage due to high operational costs. Consequently,
there is a growing need to focus on fusing ALS-derived maps of ACD
with satellite data to advance our ability to map forest carbon stocks
across large spatial scales and through time (e.g.
Asner et al., 2018). In this regard,
NASA plans to start making high-resolution laser-ranging observations from
the international space station in 2018 as part of the GEDI mission, while
the ESA BIOMASS mission will use P-band synthetic aperture radar to monitor
forests from space from 2021. Pantropical monitoring of forest carbon using
data from a combination of space-borne sensors is fast approaching, and
regional carbon equations derived from ALS data such as the one we develop
here will be critical to calibrate and validate these efforts.
Conclusions
Since the 1970s Borneo has lost more than 60 % of its old-growth forests,
the majority of which have been replaced by large-scale industrial palm oil
plantations (Gaveau et al., 2014, 2016). Nowhere else
has this drastic transformation of the landscape been more evident than in
the Malaysian state of Sabah, where forest clearing rates have been among
the highest across the entire region (Osman et al., 2012).
Certification bodies such as the Roundtable on Sustainable Palm Oil (RSPO)
have responded to criticisms by adopting policies that prohibit planting on
land designated as high conservation value (HCV) and have recently proposed
to supplement the HCV approach with high carbon stock (HCS) assessments that
would restrict the expansion of palm oil plantations onto carbon-dense forests.
Yet enforcing these policies requires an accurate and spatially detailed
understating of how carbon stocks are distributed cross the entire state,
something which is currently lacking. With the view of halting the further
deforestation of carbon-dense old-growth forests and generating the
necessary knowledge to better manage its forests into the future, in 2016
the Sabah state government commissioned CAO to deliver a high-resolution
ALS-based carbon map of the entire state
(Asner et al., 2018). The regional
carbon model we develop here underpins this initiative
(Asner et al.,
2018; Nunes et al., 2017) and more generally will contribute to ongoing
efforts to use remote sensing tools to provide solutions for identifying and
managing the more than 500 million ha of tropical lands that are currently
degraded (Lamb et al., 2005).
The data supporting the results of this paper have been archived on the
NERC Open Research Archive
website (https://nora.nerc.ac.uk/, last access: 20 June 2018).
The supplement related to this article is available online at: https://doi.org/10.5194/bg-15-3811-2018-supplement.
DAC and YAT coordinated the NERC airborne campaign, while GPA led
the CAO airborne surveys of Sabah. TJ and DAC designed the study, with
input from GPA and PGB; TJ, MD, PGB and NRV processed the airborne
imagery, while other authors contributed field data; TJ analysed the data,
with input from DAC, GPA, PGB and CDP; TJ wrote the first draft
of the paper, with all other authors contributing to revisions.
The authors declare that they have no conflict of interest.
Acknowledgements
This study was funded by the UK Natural Environment Research Council's
(NERC) Human Modified Tropical Forests research programme (grant numbers
NE/K016377/1 and NE/K016407/1 awarded to the BALI and LOMBOK consortiums,
respectively). We are grateful to NERC's Airborne Research Facility and Data
Analysis Node for conducting the survey and preprocessing the airborne
data and to Abdullah Ghani for manning the GPS base station. David A. Coomes
was supported in part by an International Academic Fellowship from the
Leverhulme Trust. The Carnegie Airborne Observatory portion of the study was
supported by the UN Development Programme, the Avatar Alliance Foundation,
the Roundtable on Sustainable Palm Oil, the World Wildlife Fund and the Rainforest
Trust. The Carnegie Airborne Observatory is made possible by grants and
donations to Gregory P. Asner from the Avatar Alliance Foundation, the Margaret A. Cargill
Foundation, the David and Lucile Packard Foundation, the Gordon and Betty
Moore Foundation, the Grantham Foundation for the Protection of the Environment,
the W. M. Keck Foundation, the John D. and Catherine T. MacArthur Foundation, the Andrew Mellon
Foundation, Mary Anne Nyburg Baker and G. Leonard Baker Jr., and
William R. Hearst III. The SAFE project was supported by the Sime Darby
Foundation. We acknowledge the SAFE management team, Maliau Basin Management
Committee, Danum Valley Management Committee, South East Asia Rainforest
Research Partnership, Sabah Foundation, Benta Wawasan, the State Secretary,
the Sabah Chief Minister's Departments, the Sabah Forestry Department, the Sabah
Biodiversity Centre and the Economic Planning Unit for their support, access
to the field sites and permission to carry out fieldwork in Sabah. Field
data collection at Sepilok was supported by an ERC Advanced Grant (291585,
T-FORCES) awarded to Oliver L. Phillips, who is also a Royal Society Wolfson
Research Merit Award holder. Martin Svátek was funded through a grant from
the Ministry of Education, Youth and Sports of the Czech Republic (grant
number INGO II LG15051), and Jakub Kvasnica was funded through an IGA grant
(grant number LDF_VP_2015038). We are
grateful to the many field assistants who contributed to data collection.
Edited by: Nobuhito Ohte
Reviewed by: two anonymous referees
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