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Using biomass distributions to determine probability
and intensity of tropical forest disturbance
Mathew Williams
a
a b
, Timothy C. Hill
a b
& Casey M. Ryan
a
School of GeoSciences, University of Edinburgh, UK
b
NERC National Centre for Earth Observation
Accepted author version posted online: 14 Jun 2012.Version of record first published: 24
Sep 2012.
To cite this article: Mathew Williams , Timothy C. Hill & Casey M. Ryan (2013): Using biomass distributions to determine
probability and intensity of tropical forest disturbance, Plant Ecology & Diversity, 6:1, 87-99
To link to this article: http://dx.doi.org/10.1080/17550874.2012.692404
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Plant Ecology & Diversity, 2013
Vol. 6, Issue 1, 87–99, http://dx.doi.org/10.1080/17550874.2012.692404
Using biomass distributions to determine probability and intensity of tropical forest disturbance
Mathew Williamsa,b*, Timothy C. Hilla,b,c and Casey M. Ryana
a
School of GeoSciences, University of Edinburgh, UK; b NERC National Centre for Earth Observation; c Current address: School of
Geography and Geosciences, University of St Andrews, St Andrews, UK
Downloaded by [University of Edinburgh] at 13:21 15 April 2013
(Received 20 September 2011; final version received 7 May 2012)
Background: Tropical forest biomass is not at steady state, being determined by a balance between deterministic growth
and stochastic disturbances. Understanding tropical carbon sources and sinks therefore requires better characterisation of the
incidence and intensity of disturbance at critical scales.
Aims: We determine if information from remotely sensed biomass maps (ALOS-PALSAR) can constrain estimates of
miombo woodland biomass dynamics and disturbance.
Methods: We analyse biomass maps created over Mozambican woodlands undergoing varied disturbances. We use a simple
ensemble model of biomass dynamics to test the hypothesis that biomass distributions can diagnose disturbance processes in
specified areas, and use the model to explore the sensitivity of biomass to disturbance parameters.
Results: Ensemble runs can reproduce qualitatively similar biomass patterns to those observed in miombo, through varying
two parameters that determine frequency and intensity of biomass loss. Using sensitivity analyses, we show for a synthetic
case that these two disturbance parameters can be retrieved from satellite observations.
Conclusions: Biomass distributions provide enough information to constrain the two critical parameters of the disturbance
model, the local probability of disturbance, and its intensity (fraction of biomass lost). These results provide a proof of
concept for assimilating biomass maps into models of carbon cycling.
Keywords: carbon model; data assimilation; deforestation; degradation; land-use change; miombo; Mozambique; REDD;
synthetic aperture radar
Introduction
Large parts of the tropical land surface are acting as
either sources of CO2 due to land-use change, or sinks
due to hypothesised increases in growth (Pan et al. 2011).
The location of these areas, and their source or sink
strength, remains poorly characterised. This uncertainty
arises because total stocks of C in tropical forests, particularly in wood biomass, are poorly quantified and mapped
(Houghton et al. 2009). Accurate estimates of biomass and
biomass change are hampered by the high spatial variability of woody biomass in tropical forests (Keith et al. 2009).
Variation in soils, climate and hydrology affect biomass pattern at related scales (Toledo et al. 2011; Woollen et al. in
press) through effects on growth rates. Variability is also
determined by disturbance, both natural and anthropogenic.
Natural processes that remove biomass include wildfire,
storm damage, pest outbreaks and floods. Human pressure
on biomass is linked to resource extraction, clearance for
agriculture and increased fire frequency, causing deforestation and forest degradation (Houghton and Hackler 2006).
Carbon cycle models have been used to analyse forest carbon cycling and support predictions of source and
sink dynamics. These models have tended to represent tropical forests as steady state systems (Ciais et al. 2011),
for simplicity. In reality, non-steady state dynamics are
more common, with forest biomass determined by a combination of deterministic growth processes and stochastic
*Corresponding author. Email: [email protected]
© 2013 Botanical Society of Scotland and Taylor & Francis
disturbance processes (Fisher et al. 2010). In the steady
state case, the dynamics of the woody C pool (C w , t C
ha−1 ) are set by the net primary production of the ecosystem (PN , t C ha−1 year−1 ), the fraction of net production
allocated to wood growth (aw ), and the turnover rate of
wood (tw, year−1 , the inverse of lifespan). In the non-steady
state case, a further loss term is introduced (final term in
Equation 1), linked to the probability (P, year−1 ) and severity (F, fraction of C lost) of disturbance events (natural and
anthropogenic):
Cw = aw PN − tw Cw − P F Cw
(1)
Correctly representing forest dynamics in models, particularly the stochastic parameters P and F, is crucial for
an integrated understanding of the global C cycle (Delbart
et al. 2010), because the response (source/sink behaviour)
of steady state versus non-steady state forests to climate
change and human usage will be different. There is a pressing need, therefore, to determine and model the current
incidence and intensity of disturbance in tropical forests,
at appropriate scales, in order to better understand current
biomass distributions and predict their future dynamics.
Novel satellite remote sensing approaches have recently
been used to generate tropical biomass maps (Saatchi
et al. 2011; Baccini et al. 2012). Depending on the sensor
used, the maps can resolve spatial variation in biomass
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88
M. Williams et al.
at scales < 1 ha, providing unprecedented insights into
biomass pattern (Ryan et al. 2012). With repeated observations, time series of maps provide quantification of dynamic
patterns in biomass. There is the tantalising possibility,
therefore, to gain insights into disturbance processes from
these rich datasets. High-resolution biomass maps have
been generated with the ALOS-PALSAR sensor, an L-band
radar (Kimura and Ito 2000). This instrument has been
most effective with lower biomass forests, hence the focus
here on miombo woodlands. Miombo are open woodlands,
with a grass understory and frequent fire disturbance, covering 2.7 M km2 in southern Africa (Campbell 1996).
Human pressure on these woodlands is rising, and derives
from clearance for small-holder agriculture and selective
harvesting for wood and fuel.
The objective of this paper is to determine if the information from remotely sensed biomass maps can constrain
estimates of miombo woodland biomass dynamics and disturbance. First, we analyse biomass maps created from
radar scenes collected over Mozambican miombo undergoing varied disturbances. We then use a simple model
of forest biomass dynamics to test the hypothesis that
biomass distributions can be used to diagnose disturbance
processes in specified areas. Second, we use the biomass
model to explore the sensitivity of biomass to stochastic
parameters related to disturbance. We hypothesise that
varying parameters relating to both probability (P) and
intensity of disturbance (F) will recreate qualitatively the
observed biomass distributions. Third, we determine the
information on model disturbance parameters that can be
retrieved from biomass distributions. We discuss the application of a model–data fusion (data assimilation) system
(Williams et al. 2009) in this context.
Methods
Study site
The study area is located within an area of 1160 km2 in the
Gorongosa and Nhamatanda Districts of Sofala province in
Mozambique (18◦ 58 44 S, 34◦ 10 34 E) (see Figure 1).
The area receives 850 mm mean annual precipitation (ranging from 407–1219 mm), 96% of which falls between
October and April (Williams et al. 2008). Soils are highly
weathered and generally freely drained sandy loams or
sandy silt loams. The terrain varies in altitude from 60–
330 m a.s.l., and is gently undulating in most of the study
area (97% has slopes of <10◦ at 90 m resolution) (Ryan
et al. 2012). Climate differences across the area are likely to
be insignificant, due to its compact scale (∼20 km across)
and minor elevation changes.
The vegetation is largely miombo, seasonally dry deciduous woodland. Miombo woodlands are dominated by
Figure 1. Map of the study region in central Mozambique. Rivers are indicated in solid lines, roads as parallel solid lines (tarmac) or
dashed lines (dirt). The Gorongosa National Park is shaded. The outline of the ALOS PALSAR scene from which biomass data were
generated is shown as the dashed polygon.
Determining forest disturbance using biomass distributions
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the trees of the genera Brachystegia and Julbernardia,
have an open canopy, and a grass understory. In central
Mozambique, mean above-ground biomass (AGB) is 21 t C
ha−1 , but is highly variable over the study region, ranging
from 5–50 t C ha−1 , (Ryan et al. 2011). Disturbance, both
natural and anthropogenic, is a major influence on biomass
variability. There are also topographic trends, with biomass
higher on well-drained ridges with sandy soils compared
with valley bottoms with more clay soils (Woollen et al.
2012).
Disturbance processes
Fire is a common disturbance agent in Mozambique during the dry season (July–September), fuelled largely by the
senesced grass layer. Fires cause mortality of trees among
all stem size classes. While mortality is greatest among
saplings (< 5 cm diameter at breast height), large stems are
vulnerable, particularly to intense fires (Ryan and Williams
2011). In seven experimental fires at the site, the mean number of trees top-killed as a result of fire was 4.7%, and
the mean mortality for saplings was 92.4%. These mortality data, in the context of chronosequence estimates of
forest growth rate (Williams et al. 2008) and modelling of
tree population dynamics (Ryan and Williams 2011), suggest that variability in biomass over miombo landscapes is
strongly linked to degradation from fire-induced mortality
(Furley et al. 2008).
The study area is also undergoing rapid land-use
change, which began in the 1990s with the end of the
Mozambican civil war and the start of road and bridge
construction. Deforestation is primarily the result of clearance for small-scale agriculture, involving the removal of
nearly all AGB at the scale of hectare(s) (Ryan et al.
2012). Anthropogenic degradation is likely to be linked to
wood fuel and timber collection, fire, and charcoal production. Following abandonment, woody cover regrows rapidly
(Williams et al. 2008).
To sample areas with distinct disturbance histories,
landscape biomass estimates were generated for two contrasting areas. The Gorongosa National Park buffer zone
was chosen as it is a protected area, relatively remote from
human settlement or transport, with low human impacts.
Biomass variability and dynamics in this region are hypothesised to be largely driven by disturbance processes resulting from fires. High-resolution satellite imagery shows
no small-holder activity. Charcoal activity is not visible
from the main highway past this area. The Mucombezi
area was chosen as an area with a high degree of human
impacts, and therefore where anthropogenic disturbance
was dominant. Mucombezi is south of the Pungue River,
and accessible to areas of high population via the Beira
Corridor to the south, a major regional transportation route.
Small-holder activity in this area is intense, and clearly
visible from the main highway. Biomass variability and
dynamics in this region are hypothesised to be largely
driven by anthropogenic disturbance processes, principally
deforestation (high biomass loss).
89
Radar imagery
Synthetic aperture radar (SAR) is a particularly suitable
instrument for generating biomass maps. At appropriate
wavelengths the backscatter from the SAR signal is related
to the physical structure of the land surface. L-band (23
cm) backscatter has been shown to provide a reasonable,
continuous estimate of biomass up to saturation of 100 t
ha−1 (Le Toan et al. 1992). Radar is to be preferred to
optical reflectance approaches, which rely on classifying
land cover into forest or non-forest, and then using local
biomass estimates to generate maps according to land cover
(Houghton et al. 2009).
Biomass maps generated from ALOS data and in situ
plot data were used to test the modelling approach. The
generation of these data is described in detail in Ryan
et al. (2012), and a summary is provided here. Images
of radar backscatter (denoted σ 0 ) were obtained from the
Phased Array L-band SAR sensor on the Advanced Land
Observing Satellite (ALOS-PALSAR) in the Fine-Beam
Double mode. Data were generated from a scene collected
in 2009, with pixel resolution of 0.06 ha (25 m × 25 m).
σ 0 data were converted into t C ha−1 using a regression
equation based on inventories of 96 plots in the study area.
These data come from a range of inventories conducted during 2006–2009, and include plots of sizes ranging from
0.1–2.2 ha (mean ± SD 0.63 ± 0.33 ha). Thirty-seven
plots were located in small-holder agricultural land, and the
remainder in woodland and savanna. In each plot all stems
above a diameter threshold (typically 5 cm) were sampled,
and a site-specific allometric equation was used to estimate stem biomass (Ryan et al. 2011). AGB estimates from
stem inventories ranged from 0–56 t C ha−1 . The regression of backscatter against biomass gave values of R2 from
0.40–0.58 over the 10 ALOS scenes. The validation procedure estimated root mean square errors of 8.7–10.9 t C
ha−1 for the different scenes, and mean absolute bias of
1.6 ± 0.1 t C ha−1 (Ryan et al. 2012).
Modelling biomass
Recognising the importance of stochastic processes in
biomass dynamics, we generated a large ensemble of simulations of a C mass balance model, each ensemble member
representing the C cycle of a forest patch, in the manner of
gap models (Friend and Schugart 1993; Ryan and Williams
2011). A typical patch size corresponds to the area of a fully
sized tree crown (an 8 m radius crown covers a patch of 0.02
ha). The area sampled by the proposed BIOMASS mission
(Le Toan et al. 2011), which would use a specific SAR
instrument to generate global biomass maps from radar, is
1 ha. So it is reasonable to state that 50 patches comprise
an observed area of 1 ha.
We used a simple model of ecosystem C mass balance,
the Data Assimilation Linked Ecosystem Carbon (DALEC)
model (Williams et al. 2005; Fox et al. 2009). DALEC
is adjusted to run on an annual timescale and to separate
the woody C pool into above- and below-ground components. The resulting Annual-DALEC (A-DALEC) model
90
M. Williams et al.
Ra
Respiration
Flux
GPP
Af
Cf
Tf
Ar
Cr
Rloss
Cl
(litter)
(foliage)
Rloss
Tr
Awbg
Cwbg
Twbg
(wood below
ground)
Awag
Cwag
Rhs
Cdbg
Rloss
(wood debris
below ground)
Twag
(wood above
ground)
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Cs
(Soil organic
matter)
(fine roots)
Cdag
Rloss
(wood debris
above ground)
Figure 2. Structure of the A-DALEC model showing carbon pools (boxes), fluxes (arrows). Dotted lines: disturbance fluxes (stochastic).
Dashed lines: annual flux of entire donor pool. C, C stock. Fluxes: A, allocation; T, turnover; f, foliage; r, roots; w, wood; l, litter; d,
debris; bg, below ground; ag, above ground; GPP, gross primary production; Ra , autotrophic respiration; Rhs , heterotrophic respiration;
Rloss , respiration during fractionation.
(Figure 2) allows rapid computation time, more suitable
for ensemble runs and data assimilation (see Appendix for
full details on model structure and calibration). The focus
on woody biomass makes this annual time-step acceptable,
because the woody pool has typical time constants approximating annual to decadal. The critical models parameters
are the allocation ratios for net primary production to each
biomass pool, and the turnover rates of each pool. The
dynamics of the above-ground woody C pool therefore follow the basic structure of Equation (1), but are also linked
to primary production through a coupling between woody
biomass and leaf area index. The model parameters for
production and allocation were calibrated with local data
on forest growth rates and stem allometry (see Appendix).
Disturbance was modelled stochastically over the simulated
patches. A random number generator determined if disturbance has occurred in each patch, according to a given
probability (P). The intensity of the disturbance (F) is variable, covering a range (0–1) through light degradation to
complete deforestation.
The calibration of A-DALEC to the Mozambican
woodlands was constrained by local measurements of
closed canopy (i.e. low disturbance) forest in the Marrameu
region (Ryan and Williams 2011), north of the study region,
but with similar climate and soils. Local calibration data
included estimates of leaf area index and total biomass,
with soil C stocks and above-ground:below-ground wood
ratios available from the study region (Ryan et al. 2011).
The A-DALEC model was run in an ensemble of 150
1 ha grid-cells over a 250-year period to determine the
landscape distribution of biomass stocks. Each grid-cell
is the aggregate of 50 modelled patches, each simulated
individually by an instance of A-DALEC (7500 simulations in total). This patch approach represents the gap phase
dynamics typical of natural forests with varied age structures. An intra-grid-cell, inter-patch disturbance covariance
was included. This can vary from 0 (i.e. all patches are
randomly and independently disturbed) to 1 (i.e. what happens to one patch, happens to all other patches in that same
grid-cell). We pick a value of 0.5, so that a disturbance in
one patch means that other disturbances are more likely
within that grid-cell. Thus, most disturbances cover a fraction of a hectare, consistent with estimates from radar data
(Ryan et al. 2012). Large fires would, of course, cover more
extensive areas.
Modelling experiments
We determined the sensitivity of the landscape biomass distribution to changes in probability (P) and intensity (F) of
disturbance (Equation (1)). We first quantified the probability density functions (PDFs) for a selection of probabilities
and intensities of disturbance. We characterised the reduction in biomass from the steady state (undisturbed) landscape, and the range in biomass for each distribution. We
then undertook a more complete sensitivity analysis, determining the landscape mean biomass and its range, varying
the probability of disturbance and the intensity of disturbance across their full potential ranges and interactions
(0–100%).
The landscape of central Mozambique now includes
areas with non-steady state biomass distributions. Any
potential steady state has been disrupted by an historical
increase in anthropogenic disturbance with increasing population and economic growth, and improved roads since the
early 1990s (Figure 1). South of the Pungue, in Mucombezi,
increased anthropogenic disturbance has been on-going for
a longer period than to the north, at least four decades.
Determining forest disturbance using biomass distributions
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To simulate this transient response to recent anthropogenic
changes in disturbance regime, an initial spin-up with low
disturbance (P = 1%, F = 68%) was used to generate
a nominal estimate of a mid-late twentieth century landscape, based on outputs from the sensitivity analysis and
qualitative comparison with miombo woodland field plots.
From this spin-up, new simulations were run for 20–40
years with increased disturbance probabilities (P = 5%)
linked to deforestation intensities (F = 95%), to explore
the transient disturbance response of biomass distributions
to rising anthropogenic effects. We generated a more complete sensitivity analysis of transient biomass distributions,
determining the mean and range of biomass 20 years after
a change in disturbance, across the full range of potential
frequencies and probabilities, including their interactions.
Results
Biomass mapping
The biomass mapping was focussed on two disturbance
end-members for the study region, using radar data
from 2009; firstly, the buffer zone of the Gorongosa
National Park, north of the river Pungue; and secondly,
the Mucombezi area south of the river Pungue (Figure 1).
The PDFs of estimated biomass for these two regions
(Figure 3) show distinctly different biomass distributions.
For Mucombezi, the radar-generated maps indicated that
most of the landscape had negligible AGB, with a median of
2.5 t C ha−1 . The distribution was skewed to low biomass,
with a tail of higher biomass. However, less than 10% of
the area had AGB > 20 t C ha−1 . In contrast, the National
Park buffer zone in 2009 had a more normal distribution of
biomass, with a median AGB of 20.5 t C ha−1 , and a range
from 10th –90th percentiles of 36.9 t C ha−1 .
Modelling biomass distributions
The undisturbed calibration run reached a steady state for
foliage and fine roots within a decade, while woody C
took ca. 200 years to reach 57 t C ha−1 . Rates of woody
biomass accumulation during initial growth (0–25 years)
were ∼0.7 t C ha−1 , similar to those recorded on a local
chronosequence, tracking regrowth following disturbance
91
(Williams et al. 2008). In these runs the lack of any stochastic disturbance resulted in a deterministic modelled steady
state comparable with the observations from Marrameu
(Table 1).
The effects of disturbance on steady state biomass were
assessed over a 250 year simulation of primary succession
(i.e. running from an initial small seeding of vegetation C
stocks). The stochastic disturbance modelling introduced
variable trajectories into the ensemble of modelled patches,
and the aggregated grid-cells at 1 ha scale. Examples
(Figure 4) show that landscape variability in biomass
resulted from the imposition of disturbance over the modelled grid-cells. With a low disturbance probability (P =
1% per annum) and two-thirds of C removed by the disturbance (F = 68%), the median AGB was 44.7 t C ha−1 ,
a drop of 22% from the undisturbed state states, with an
inter-quartile (IQ) range of 6.4 t C ha−1 . Increasing P to
5% reduced the median AGB to 21.0 t C ha−1 , similar to
the mean observed value of local miombo woodland (Ryan
et al. 2011), and widened the IQ range to 8.2 t C ha−1 . A
further increase of P to 10% continued the trend, reducing
median AGB to 11.4 t C ha−1 . This decline also resulted in
a smaller IQ range of 6.32 t C ha−1 . It was possible to produce a similar median C stock (12.1 t C ha−1 ) with a higher
P (20%) but with F reduced by half (34%). This more frequent, lower intensity disturbance regime reduced the IQ
range to 4.4 t C ha−1 .
The transient effects of rising anthropogenic pressures
on forest resources, resulting from a step change increase in
deforestation, were explored in another set of model runs.
An increase in disturbance magnitude over 20–40 years
Table 1. Mean values of plant C pools for undisturbed (closed
canopy) and fire disturbed (open canopy) woody ecosystems in
central Mozambique. AG, above ground; BG, below ground.
Standard errors are shown, and are determined from sampling of
multiple sites in Ryan et al. (2011). Errors were not directly determined in the undisturbed plots (Ryan and Williams 2011), and are
here estimated pro rata.
Pool
Foliage C
AG Wood C
BG Wood C
Undisturbed (t C ha−1 )
Disturbed (t C ha−1 )
1.33 ± 0.14
57.5 ± 3.8
23.0 ± 1.2
0.72 ± 0.07
21.3 ± 1.4
8.6 ± 0.46
Figure 3. Histograms of biomass from the buffer area of Gorongosa National Park (left) and from the Mucombezi regions (right) in
central Mozambique, developed from ALOS-PALSAR images calibrated against 96 field plots. Negative values are present because of
random error on the biomass estimates.
92
M. Williams et al.
0.25
P = 0.01
F = 0.68
P = 0.05
F = 0.68
Frequency
0.20
0.15
0.10
0.05
0.00
0.25
P = 0.20
F = 0.34
P = 0.10
F = 0.68
Frequency
0.20
0.15
0.10
0.00
10
20
30
40
50
60
10
20
30
40
50
60
Figure 4. Simulated landscape variability in biomass stocks for a Mozambican calibration of A-DALEC under stochastic disturbance
over 150 ha. The four panels show varying levels of disturbance probability (P) and intensity (F, fraction of C biomass lost in disturbance).
0.25
0.20
Frequency
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0.05
20 yrs of
P = 0.05
F = 0.95
40 yrs of
P = 0.05
F = 0.95
0.15
0.10
0.05
0.00
10
20
30
40
50
60
10
20
30
40
50
60
Figure 5. The effect of increased disturbance over 40 years (left) and 20 years (right) on a steady state forest structure resulting from
lower disturbance (P = 0.01, F = 0.68, see top left panel in Figure 4). The histograms show the distribution of biomass after this period of
increased disturbance.
resulted in clear shifts in biomass distributions (Figure 5).
After 20 years of increased disturbance frequency and
intensity (P = 5%, F = 95%), the median biomass
decreased by 42%, from 44.7 to 25.6 t C ha−1 . After 40
years of increased disturbance, the median biomass has
decreased further to 23.0 t C ha−1 . The shapes of the distributions after 20 and 40 years differed. There was increased
skew towards low biomass after 40 years (skew rose from
0.15 to 0.34). The mode dropped sharply, from 26.1 t C
ha−1 after 20 years to 17.1 t C ha−1 after 40 years.
Sensitivity analysis of disturbance parameters
A two-dimensional analysis varying P and F revealed the
sensitivity of biomass distributions to these disturbance
parameters. With 121 simulations to spanned the dimensions, the distributions are most parsimoniously shown as
contour plots of the median AGB and the AGB range from
10th –90th percentiles over the 150 simulated 1 ha stands.
The results for the steady state analysis, based on a 250year run with fixed P and F values, clearly show that the
highest median biomass is associated with low values of
either parameter (Figure 6a). Nonetheless, the interaction
of the two parameters was clear, with median biomass
very sensitive to small changes in either parameter when
the other is large. The range of biomass values showed a
different response (Figure 6b), with a much stronger sensitivity to changes in probability of disturbance (P) compared
with changes in intensity of disturbance (F). Frequent lowintensity disturbance resulted in more uniform biomass
distributions than less frequent deforestation events. Note
that with very low P or F the range shrank to a small value
as the landscape approached the undisturbed steady state.
The sensitivity analysis of the transient, 20-year
response of biomass distributions to altered disturbance
showed similar patterns of sensitivity (Figures 7a and b).
Determining forest disturbance using biomass distributions
5500
0.9
5000
0.8
4500
Probability of disturbance (P)
(a) 1.0
4000
0.7
3500
0.6
3000
0.5
2500
0.4
2000
0.3
1500
0.2
1000
0.1
500
0
0
0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Intensity of disturbance (fraction of C lost, F )
1.0
(b) 1.0
Probability of disturbance (P)
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93
0
1000
0.9
900
0.8
800
0.7
700
0.6
600
0.5
500
0.4
400
0.3
300
0.2
200
0.1
100
0
0
0.1
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Intensity of disturbance (fraction of C lost, F )
1.0
0
Figure 6. The sensitivity of combined changes in disturbance probability (per annum) and disturbance intensity on steady state median
biomass stocks (a), and range from 10th –90th percentiles (b), using A-DALEC run to steady state over 250 years. Colour bars units are
in g C m−2 .
The sensitivity of median biomass to changes in both P
and F were reduced, due to the shortened period in which
disturbances could alter the structure of the simulated landscape. As a result of the broad distribution of biomass at
the start of the 20-year simulation (see top left panel in
Figure 4), there has not been enough time for the new
steady state to impose itself strongly at very low values of
P or F.
Discussion
The spatial characterisation of biomass from radar remote
sensing can be summarised in a PDF, showing the frequency of particular stocks of biomass over the observed
range of observations (Figure 3). Such PDFs encapsulate
the history of the analysed region, containing information
on the balance between growth and loss of biomass. As
maps of tropical biomass have recently become available,
the variability in stand structure observable at fine scales
(ha) has become clear (Asner et al. 2010). Over large
enough samples (km2 ), we hypothesise that the stochastic
processes driving biomass loss are identifiable and can be
quantified.
Relating biomass maps to known patterns of disturbance
Field plot studies are complicated by the selection of
sites, leading to concerns about representivity (Fisher et al.
2008). The advantage of satellite data is that a complete
coverage of landscape is possible. For analyses, there is still
a need to stratify images into consistent areas for analysis. In this example, the stratification was assisted by the
94
M. Williams et al.
(a) 1.0
4500
0.9
4000
Probability of disturbance (P)
0.8
3500
0.7
3000
0.6
2500
0.5
2000
0.4
0.3
1500
0.2
1000
0.1
500
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Intensity of disturbance (fraction of C lost, F )
0.9
1.0
0
(b) 1.0
1800
0.9
1600
0.8
Probability of disturbance (P )
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0
1400
0.7
1200
0.6
1000
0.5
800
0.4
600
0.3
0.2
400
0.1
200
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Intensity of disturbance (fraction of C lost, F )
0.9
1.0
0
Figure 7. The sensitivity of combined changes in disturbance probability (per annum) and disturbance intensity on transient median
biomass stocks (a), and range from 10th –90th percentiles (b), using A-DALEC run for 20 years with altered disturbance from a steady state
with low disturbance over 250 years (P = 0.01, F = 0.68). Colour bars units are in g C m−2 .
presence of a protected area (National Park and its buffer
zone) which was largely free of direct human disturbance.
The biomass distribution from the buffer zone was close
to a normal distribution (Figure 3), similar to that simulated by a long-term disturbance probability P = 0.05, and
intensity F = 0.68 (Figure 4, top right panel). The normal
distribution shape here is suggestive of a steady state system, subject to consistent disturbance over a long period.
This conclusion is consistent with our historical knowledge
of the region as a protected area, though still subject to
major, probably fire, disturbance, and some minor human
impacts. The earth observation data have a broader distribution than the modelled PDF. This difference is likely to
be a result of observational noise (RMSE of 9.8 t C ha−1 ) of
the ALOS-PALSAR products. The calibration of the radar
image does generate some estimates of negative biomass,
for example (Ryan et al. 2012).
The Mucombezi area has a history of increased disturbance from the 1960s onwards. This pressure is clearly
revealed in the biomass distribution for the area, which is
strongly skewed towards lower biomass values, with a small
but clear tail of higher biomass. It is noteworthy that the
Mucombezi distribution was not recreated by the modelled
biomass distributions (Figure 4), generated with 250 years
of consistent disturbance parameters. On the other hand,
there is a closer resemblance to the distribution of biomass
generated by 40 years of increased disturbance (Figure 5),
imposed on a distribution generated from less disturbed
Determining forest disturbance using biomass distributions
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landscapes. This similarity is consistent with our knowledge of increased land-use pressures on the Mucombezi
area in recent decades.
The modelling studies here indicated that strongly
left-skewed biomass distributions were the result of a
transient response to increased disturbance. The steady
state response to biomass produces either right-skewed
distributions if disturbance is low, due to the maximum
biomass limit for the undisturbed case, or more normal
distributions.
Deriving disturbance models from biomass maps
If spatial data can identify dynamic processes, then biomass
maps become a novel means to calibrate and evaluate carbon cycle and/or dynamic vegetation models. Currently
such models are evaluated against global networks of flux
measurements (Williams et al. 2009) or against optical
satellite data or atmospheric concentration data (Cadule
et al. 2010). However, recent analyses have shown that
many critical internal parameters, relating to C allocation
and particularly to the balance of C stored in wood versus
soils, are not well constrained by flux data alone (Fox et
al. 2009; Richardson et al. 2010). C stock data provide a
powerful orthogonal constraint on models, particularly on
parameters relating to disturbance, which are less amenable
to identification through a relatively sparse flux network,
forest plot networks, or highly aggregated atmospheric
measurements. Uncertainty in these parameters is likely to
account for divergent predictions of the twenty-first century C cycle (Friedlingstein et al. 2006). An ultimate goal
is to assimilate biomass maps into appropriate models to
improve estimates of current C sources and sinks, and better constrain projections with such models (Bellassen et al.
2011).
The challenge to understanding forest disturbance lies
in its stochastic nature. These systems are not deterministic, so modelling analyses are hard to constrain (Delbart et
al. 2010). Information about the median biomass of an area
is clearly insufficient to understand its disturbance history.
The sensitivity analysis (Figure 6) clearly showed that a particular median biomass could result from the interaction of
disturbance probability and disturbance intensity across a
broad curved swath of parameter space. A doubling of disturbance probability and a halving of disturbance intensity
results in a forest landscape with similar median biomass
(Figure 4, lower panels).
However, the distribution of biomass, the PDF, provided
extra information that assisted in separating disturbance
probability from intensity. A higher probability of disturbance tended to result in a narrower distribution of
biomass (Figure 4, lower panels). The full sensitivity analysis showed this clearly, for both steady state and transient
forest systems (Figures 6 and 7). These analyses indicate
that median data combined with information on the range
of biomass values can provide a constraint on disturbance
probability and intensity. For instance, a landscape with a
median AGB of 20.0 t C ha−1 could result from disturbance
95
intensities ranging from 70–100%, linked to specific disturbance probabilities ranging from 7–100%. However, if the
10th –90th percentile range is measured at 5.0 t C ha−1 , then
the parameters P (∼40%) and F (∼10%) are constrained –
the area of parameter space that fits the statistics of the
distribution is restricted.
Complicating factors
In determining model parameters for disturbance, there are
several complicating factors. Existing unmanaged forests
are not in a steady state, given more than a century of
changing atmospheric CO2 concentrations and climate, and
increased nutrient deposition in some locations and rising
anthropogenic pressure. Thus, the biomass observed in a
region must be interpreted in the context of a transient productivity caused by changing external forcings alongside
likely variable disturbance over recent decades.
An assisting factor can be any data on landscape history, such as timing of agricultural abandonment, and prior
information on forest yield class, tree life span, and wood
increment. Local eddy flux data can provide detailed understanding on climate interactions with productivity, for constraining those components of the modelling (Richardson
et al. 2010). Wherever the time since wood C accumulation began is known (e.g. a chronosequence study), an extra
constraint on process rates, and thus parameters, is available (Williams et al. 2008). We have assumed similar rates
of growth across the landscape, but these may vary due to
soils and topography. Current process models are capable of
predicting the impacts of rising CO2 and changing climate
on plant production (Sitch et al. 2008), although the effects
of nutrient deposition are not always modelled, or modelled
with such consistency. It is vital to use dynamic models in
this regard for interpreting maps of wood C stocks.
Another complicating factor is that there will be uncertainty associated with any biomass map. In the analyses
here, we have assumed perfect knowledge of the biomass
distribution. Adding uncertainty to the biomass estimate
for each observation grid-cell will degrade the quality of
the distribution, resulting in a broadening of the PDF.
This is clearly seen in the maps derived from ALOSPALSAR (Figure 3), with some grid-cells registering <0
biomass. The risk is that uncertainty in biomass maps will
reduce their information content. The retrieval of disturbance model parameters then becomes more challenging.
There are two answers to this problem. The first is to
rely only on high-quality data with small uncertainties.
However, even the proposed BIOMASS mission (Le Toan
et al. 2011) will still have a large enough error to cause
problems. The second approach is to rely on biomass PDF
time series, recording biomass change, rather than a single, static PDF of biomass. By using consecutive biomass
maps, a picture of biomass change can be generated. By differencing biomass maps, the errors of the approach should
be reduced, strengthening the signal. A companion paper
investigates the necessary techniques for assimilation with
such an approach in detail (Hill et al. in review). Even
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96
M. Williams et al.
given these problems, it is worth noting that a single ALOSPALSAR image does show clear patterns that can be related
to known land-use history in the Park buffer zone and
Mucombezi. So the errors in these data seem manageable for identifying and calibrating significant differences
in disturbance across landscapes.
The approach shown here represents a relatively simple
usage of biomass distribution data for inferring dynamical processes. There are clearly alternative approaches, and
developments of this approach, that will generate further
insights. The raw distribution data do not make use of
the spatial correlations in biomass dynamics. For instance,
the type of disturbance will be linked to typical scales of
impact, related to farm size, the search radius around charcoal kilns, the size of fire. Human disturbance will often
be linked to previous disturbance, as farms are extended,
and transport networks develop. Assimilation schemes that
can use these spatial relationships will be able to gather
further critical constraints on process models for dynamic
landscapes, albeit those with homogeneous disturbance
histories.
Conclusions
We analysed biomass maps created from radar scenes collected over tropical woodlands in Mozambique. Our analysis supports our hypothesis that biomass distributions are
sensitive to known disturbance agents in specified areas.
Areas with known recent intensive disturbance show distributions skewed to low biomass. These distributions are
consistent with model simulations of biomass under an
intensification of disturbance over the past decades. Remote
areas with protected status display a distribution of biomass
close to normal. By changing the frequency and intensity of
disturbance in our C model, we were able to recreate qualitatively the observed biomass distributions. Thus, applied
on a regional scale, the approach here could be used to
quantify the spatial variation in disturbance probability and
intensity at scales of km2 .
Biomass distributions provide enough information to
constrain the two critical parameters of the disturbance
model, the probability of disturbance for a patch, and
the intensity of disturbance (the fraction of biomass lost).
These results provide a proof of concept for assimilating
biomass maps into models of C cycling. Further work is
required to determine the best ways to deal with uncertainties in biomass maps in such assimilation schemes. The
development of models that can interface with biomass
maps provides critical new ecological information. These
models and analyses also have policy relevance for activities such as the proposed REDD mechanism, focusing on
tropical deforestation and forest degradation.
Acknowledgements
ESA and JAXA provided the ALOS imagery (C1P.7493). Funding
was provided by the European Space Agency, UK NCEO, the
NERC International Opportunities CarbonFusion project, the
Mpingo Conservation and Development Initiative under their
REDD Pilot Project funded by the Royal Norwegian Embassy
in Tanzania, and the EU FP7 iREDD+ project. We thank Emily
Woollen for producing the map.
Notes on contributors
Mathew Williams is an ecologist who uses simulation models
and field observations to explore dynamic processes in terrestrial
ecosystems.
Timothy Hill is an environmental scientist whose research focuses
on the interface between models and measurements of terrestrial
ecosystems.
Casey Ryan’s research is focused on the miombo woodlands of
southern Africa, their ecology and the ecosystem services.
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Appendix
A-DALEC structure
A-DALEC is a mass balance model of forest carbon cycling operating at an annual time-step and resolving multiple plant, litter and
soil carbon pools. Carbon accumulates through photosynthesis
and is lost through respiration and disturbance-related processes.
There are four biomass pools representing trees; foliage, fine
roots, above-ground wood and below-ground wood (grasses are
not simulated). There are three litter pools, fed from the foliage
and the two woody pools, and a single soil C pool. Net primary
production (NPP) each year is allocated to the four biomass pools.
Each biomass pool, and the litter and soil pools, has a specified turnover rate. In A-DALEC, the variation of leaf area index
(LAI) across landscapes (the model ensemble) drives differences
in gross primary production (GPP).
The values and definitions of the variables and parameters
used are shown in Table A1. For each time-step, GPP (G) is calculated from the previous time-step foliar C (Cf t-1 ) (Equation (A1)).
A minimum Cf (Cf,min ) of 10 g C m−2 is assumed to allow regrowth
from intense deforestation events. Equations (A1)–(A11) are
applied to individual patches.
Gt = f Cft−1 , LCA
(A1)
where G is a function of LAI (determined from Cf /LCA, Equation
(A19)). Superscripts t indicate the current time-step and t – 1
the previous time-step. G is then used to estimate the NPP (N),
Equation (A2).
N t = Gt (1 − Ra )
(A2)
The total respiration is calculated as the sum of the
autotrophic respiration and the various heterotrophic respiration
terms (Equation (A3)).
Rt = Gt Ra + Cst−1 Rhs + [Clt−1 Tl_s + Crt−1
(A3)
t−1
t−1
+ Cdbg
Tdbg_s + Cdag
Tdag_s ]Rloss
The carbon pools are then updated (Equations (A4)–(A11)).
Cst = Cst−1 − Cst−1 Rhs + [Clt−1 Tl_s + Crt−1
(A4)
t−1
t−1
+ Cdbg
Tdbg_s + Cdag
Tdag_s ](1 − Rloss )
Clt = Clt−1 − Clt−1 Tl_s + Cft−1
(A5)
t−1
t−1
t−1
t
= Cdbg
− Cdbg
Tdbg_s + Cwbg
Twbg−dbg
Cdbg
(A6)
t−1
t−1
t
t−1
= Cdag
− Cdag
Tdag_s + Cwag
Twag−dag
Cdag
(A7)
98
M. Williams et al.
Cft = N t Af
(A8)
Clt = 0
(A13)
Crt = N t Ar
(A9)
τ
=0
Cdag
(A14)
Cft = Cft (1 − F)
(A15)
t
t
= Cwag
(1 − F)
Cwag
(A16)
t
t
t
= Cdbg
+ Cwbg
F
Cdbg
(A17)
t
t
= Cwbg
(1 − F)
Cwbg
(A18)
t−1
t−1
t
Cwbg
= Cwbg
− Cwbg
Twbg_dbg + N t Awbg
(A10)
t
t−1
t−1
= Cwag
− Cwag
Twag_dag + N t Awag
Cwag
(A11)
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Disturbance modelling
An intra-grid-cell, inter-patch multivariate random number
(∈[0, 1]) is generated for each patch simulated. If for a given
patch, this random number is greater than, or equal to P (∈[0,
1]) then the patch is considered to be disturbed and the following
equations (A12)–(A18) are applied. These equations assume that
all above-ground litter is lost to fire in the disturbance (Equations
(A13) and (A14)). A fraction (F∈[0, 1]) of the living aboveground biomass is considered to be burnt (Equations (A15) and
(A16)). Burnt fractions are allocated to a disturbance flux (D),
(Equation (A12)). An equivalent fraction (F) of below-ground live
biomass is assumed to be lost and added to the below-ground litter pool (Equations (A17) and (A18)). Apart from the correlation
imposed by the multivariate random number, these dynamics are
applied to patches independently.
In this application to Mozambican woodlands, the model was
first parameterised for an undisturbed site at Marrameu, in central Mozambique (Ryan and Williams 2011), with closed canopy
forest, very low fire incidence, and protection from disturbance.
The relationship between GPP and LAI was determined from a
detailed modelling analysis (Ryan and Williams 2011) based on
phenological observations of LAI and leaf level photosynthesis
estimates in miombo woodlands. A third order polynomial was fitted to the relationship (Table A1), and then GPP (g C m−2 year−1 )
can be estimated directly for each patch from its specific LAI (L).
t
t
F + Clt + Cdag
Dt = Cft F + Cwag
GPP = p3 L3 + p2 L2 + p1 L + p0
(A12)
Model calibration
Table A1. A-DALEC model parameters and variables. Unless otherwise specified m−2 refer to ground area. Values
noted as ‘SV’ are state variables, requiring initial conditions, but then dynamically determined.
Symbol
Value
Af
Ar
Awag
Awbg
Cdag
Cdbg
Cf
Cf,min
Cl
Cr
Csom
Cwag
Cwbg
Dc
F
P
LCA
P0
p1
p2
p3
Ra
Rhs
Rloss
Tdag_s
Tdbg_s
Tl_S
Twag_dag
Twbg_dbg
0.2845
0.2845
0.3078
0.1232
SV
SV
SV
SV
SV
SV
SV
SV
SV
0.5
Varies
Varies
50
118.64
367.52
−24.05
0.44378
0.5
0.021
0.5
0.1
0.1
0.5
0.025
0.025
Units
gC gC−1
gC gC−1
gC gC−1
gC gC−1
gC m−2
gC m−2
gC m−2
gC m−2
gC m−2
gC m−2
gC m−2
gC m−2
gC m−2
gC gC−1
year−1
gC m−2 leaf area
gC m−2 year−1
gC m−2 year−1
gC m−2 year−1
gC m−2 year−1
gC gC−1
gC gC−1 year−1
gC gC−1
gC gC−1 year−1
gC gC−1 year−1
gC gC−1 year−1
gC gC−1 year−1
gC gC−1 year−1
Parameter Description
Fraction of NPP allocated to C f
Fraction of NPP allocated to C r
Fraction of NPP allocated to C wag
Fraction of NPP allocated to C wbg
Wood debris pool (above ground)
Wood debris pool (below ground)
Foliar pool
Minimum foliar pool
Litter pool (from fine roots and foliage)
Fine root pool
Soil organic matter pool
Coarse wood pool (above ground)
Coarse wood pool (below ground)
Inter-patch disturbance correlation
Fraction of C f , C r , C wag and C wbg lost per disturbance
Probability of a disturbance happening each year
Leaf carbon mass per unit leaf area
Polynomial fit parameter, see Eqn. A19
Polynomial fit parameter, see Eqn. A19
Polynomial fit parameter, see Eqn. A19
Polynomial fit parameter, see Eqn. A19
Fraction of GPP respired autotrophically
Fraction of C som respired heterotrophically
Fraction of fluxes into C som lost in respiration
Annual turn over rate from C dag to C som
Annual turn over rate from C dbg to C som
Annual turn over rate from C l to C som
Annual turn over rate from C wag to C dag
Annual turn over rate from C wbg to C dbg
(A19)
Determining forest disturbance using biomass distributions
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Foliar carbon is linked to LAI via the leaf mass per unit leaf area
(LMA).
The ratio of foliar C to woody C declines in patches with
greater woody biomass. We used data from 15 permanent sample
plots in central Mozambique to examine this relationship between
LAI and woody biomass. By fitting a simple model to this relationship, we determined the annual allocation of C to foliage for
a given patch woody biomass. The LAI of a patch is directly
determined by the foliar C and a carbon mass per leaf area.
Leaves turn over annually, as the system is deciduous. We assume
that a fixed proportion of GPP is respired by autotrophs (Waring
et al. 1998).
From detailed excavations at N’hambita, the ratio of stem
wood to coarse root C is known (Ryan et al. 2011), and this ratio
is maintained in the model by allocating woody C in the proportions 71% above ground and 29% below ground. There are sparse
data on fine root C, and so we assume that allocation and turnover
99
is the same as for foliage. To ensure mass balance the following
equation must be maintained in each time-step:
Ar + Af + Awag + Awbg = 1
(A20)
To calibrate the steady state conditions at the undisturbed
site at Marrameu, the turnover rates for the two woody pools
were adjusted so that allocation to wood balanced losses at this
observed biomass (Table 1). This calibration resulted in an estimated annual woody C turnover of 2.5%, giving a typical woody
lifespan of 40 years. Turnover rates of woody debris were arbitrarily set at 0.1 per annum. 50% of debris turnover is respired
and the remainder is transferred to soil organic matter. The annual
turnover rate is set at 0.02% to give a steady state value of 110 t C
ha−1 in the undisturbed state, matching the observed tendency for
soil C store to exceed woody biomass C stocks (Ryan et al. 2011).