NPGNonlinear Processes in GeophysicsNPGNonlin. Processes Geophys.1607-7946Copernicus PublicationsGöttingen, Germany10.5194/npg-24-113-2017A matrix clustering method to explore patterns of land-cover transitions in satellite-derived maps of the Brazilian AmazonMüller-HansenFinnmhansen@pik-potsdam.deCardosoManoel F.https://orcid.org/0000-0003-2447-6882Dalla-NoraEloi L.DongesJonathan F.https://orcid.org/0000-0001-5233-7703HeitzigJobsthttps://orcid.org/0000-0002-0442-8077KurthsJürgenThonickeKirstenhttps://orcid.org/0000-0001-5283-4937Potsdam Institute for Climate Impact Research, Telegrafenberg A31, 14473 Potsdam, GermanyDepartment of Physics, Humboldt University Berlin, Newtonstraße 15, 12489 Berlin, GermanyCenter for Earth System Science, National Institute for Space Research, Rodovia Presidente Dutra 40, 12630-000 Cachoeira Paulista, São Paulo, BrazilStockholm Resilience Center, Stockholm University, Kräftriket 2B, 114 19 Stockholm, SwedenFinn Müller-Hansen (mhansen@pik-potsdam.de)28February201724111312314September201611October201612January201728January2017This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://npg.copernicus.org/articles/24/113/2017/npg-24-113-2017.htmlThe full text article is available as a PDF file from https://npg.copernicus.org/articles/24/113/2017/npg-24-113-2017.pdf
Changes in land-use systems in tropical regions, including deforestation, are
a key challenge for global sustainability because of their huge impacts on
green-house gas emissions, local climate and biodiversity. However, the
dynamics of land-use and land-cover change in regions of frontier expansion
such as the Brazilian Amazon are not yet well understood because of the
complex interplay of ecological and socioeconomic drivers. In this paper, we
combine Markov chain analysis and complex network methods to identify regimes
of land-cover dynamics from land-cover maps (TerraClass) derived from
high-resolution (30 m) satellite imagery. We estimate regional transition
probabilities between different land-cover types and use clustering analysis
and community detection algorithms on similarity networks to explore patterns
of dominant land-cover transitions. We find that land-cover transition
probabilities in the Brazilian Amazon are heterogeneous in space, and adjacent
subregions tend to be assigned to the same clusters. When focusing on
transitions from single land-cover types, we uncover patterns that reflect
major regional differences in land-cover dynamics. Our method is able to
summarize regional patterns and thus complements studies performed at the
local scale.
Introduction
Land-use/cover change does not only affect local ecosystems and climate but
has global consequences for the Earth system . Land use
emits about 25 % of annual greenhouse gases to the atmosphere worldwide.
Particularly in tropical regions, increasing demand for food, fiber and
biofuels drives land conversion from forest biomes to agriculturally used
areas . In order to analyze the causes of tropical
deforestation, it is thus crucial to understand the dynamics of land-cover
changes that occur after deforestation, compare them between regions and
connect them to socioeconomic and political drivers. Furthermore, this could
help to better understand the effects of land-use intensification that can
potentially reverse deforestation trends, as hypothesized in forest
transition theory .
The Brazilian Amazon is one of the world's key regions with highly dynamic
land-use change and is subject to multiple pressures . Economic activities such as unsustainable logging
and agricultural expansion of cattle ranching and soybean cultivation lead
to a fragmentation of the landscape resulting in biodiversity loss
. Global climate change may decrease precipitation and
increase forest fires . All these pressures are increasing
the risk of destabilizing the ecosystem and crossing a tipping point with
irreversible consequences .
In the 1970s and 1980s, deforestation was mostly driven by large infrastructure
and settlement programs, but more recent years saw mainly market drivers
pushing the deforestation frontier further, while government programs tried
to contain it . Since 2005, deforestation rates in the
Brazilian Amazon have been reduced enormously. In recent years, the rates are
fluctuating around 6000 km2 per year, which is a reduction
of about 80 % compared to the peak of deforestation activities in 2004
. The changes are explained by new monitoring programs,
public policies and supply chain interventions . However, there are warnings that deforestation
may increase again .
In order to understand deforestation rates, it is crucial to take subsequent
land uses and their dynamics into account. This paper focuses on developing
methods to detect patterns of land-cover dynamics using data from remote
sensing and identifying large-scale differences between subregions of the
Brazilian Amazon as a sample region. To do so, we draw on the theory of
Markov chains that has been used in the context of land-system science to
describe and analyze land-cover dynamics . Markov
chains are stochastic systems that are described by transition probabilities
between discrete states, here referring to a specific land-use or land-cover
type. An ensemble of such chains describes a collection of land patches that
undergo stochastic transitions between land-cover classes. Because simple
Markov models do not take spatial correlations into account, they often form
only one part of hybrid land-cover models that introduce stochasticity into
the model see, e.g.,. For example,
applied a Markov analysis to estimate greenhouse gas
emissions from land-use change in the Brazilian Amazon and found that carbon
storage in the land system decreases as it approaches an equilibrium.
In the past, most studies using Markov analysis focused on small regions due
to limited data availability. Modern geographic information systems (GISs)
enable the detection of land-cover changes at an unprecedented scale using
satellite images . Automated algorithms allow the
classification of land use and land cover of vast regions. Furthermore, it is
possible to compare the land-use dynamics between different subregions and
find differences and similarities based on consistent data sets. For example,
combined different sources of land-use indicators and used
self-organizing maps to identify archetypical land uses and regions with
similar land-use change in Europe.
In this study, we use Markov transition probability matrices as a descriptor
of aggregate land-cover dynamics estimated from high-resolution land-cover
data for three time slices of land cover over 6 years in the Brazilian Amazon. To
our knowledge, Markov analysis has so far not been applied to investigate
interregional heterogeneity of land-cover dynamics. This paper explores this
idea by comparing transition matrices from different subregions in the
Brazilian Amazon to identify patterns of similar land-cover dynamics drawing
on large data sets derived from satellite imagery. While previous studies
mostly worked with predefined regions to compare land-cover dynamics, we
develop methods to identify regions with similar land-cover dynamics, which
allows a large-scale analysis of land-cover change patterns. With this
methodology, we approach the hypothesis that different land-cover dynamics can
be identified by the characteristics of their transition matrix and a
partition of subregions, for example, into remote, frontier and consolidated
areas, can be detected from the data.
Map of the Brazilian legal Amazon and its nine federal states: Acre
(AC), Amapá (AP), Amazonas (AM), Maranhão (MA), Mato Grosso (MT),
Pará (PA), Rondônia (RO), Roraima (RR) and Tocantins (TO).
The paper is structured as follows. In the subsequent Sects.
and , we present the details of the proposed method and
describe the data that we apply it to. Section gives
results from the analysis and discusses them, pointing to possible
interpretations but also restrictions of the method.
Section concludes with an outlook on how the method
could be applied to further analyses.
Illustration of the geometric union operation that combines the
information of two land-cover maps into a transition map and how the
transition matrices are obtained from this map.
Data: land-cover maps of the Brazilian Amazon
In this study, we use land-cover maps of the Brazilian legal Amazon (cf.
Fig. ) produced by the TerraClass project
for the years 2008, 2010 and 2012. The land-cover maps are
derived from high-resolution Landsat-5 thematic mapper (TM) and MODIS imagery
using a mix of techniques including supervised learning and classification by
spectral properties of different land-cover types and their annual variations
for details, see. The maps consist of
polygons that represent patches of land attributed to 1 of 16 specific
land-cover types (see Table S1 in the Supplement). The maps are based on the
PRODES project that distinguishes between forest, patches not belonging to
the rain forest biome (mainly savanna), hydrography (i.e., lakes and rivers)
and deforested patches larger than 6.25 ha . TerraClass
further specifies the land cover of formerly deforested areas according to 12
types, including different kinds of pasture land, secondary vegetation and
annual crops. evaluated the accuracy of land-cover
detection using the method described in . Considering a
very small sample of the data set, they found up to 58 % commission and up
to 34 % omission errors. found that the dominant land
cover on previously deforested land is pasture (62 % as of 2008) followed
by secondary vegetation (21 %). Annual crops only covered about 5 % of
the total deforested areas.
This paper focuses on relevant transitions between major land-cover classes
occurring in different subregions of the Brazilian Amazon. Therefore, we
first exclude patches that could not be classified, e.g., due to cloud cover.
Second, we discard land-cover types that do not change by definition, i.e.,
lakes and rivers and patches not belonging to the rain forest biome. Third,
we aggregate similar land-cover types into six new classes. These classes
combine different types of less intensively used pasture as well as types
that only make up small fractions of the Amazon like mining and urban patches
(see Table S1) and group land-cover types between which high confusion errors
exist, thus decreasing them. In a final step of the data preparation, we
assign patches to N different subregions. Depending on the scale of spatial
aggregation of our analysis, the subregions either correspond to the legal
municipalities of the Brazilian Amazon (N=770, as of 2007) or to the
mesoregions (N=30) as defined by the Instituto Brasileiro de Geografia e
Estatística (Brazilian Institute of Geography and Statistics,
).
A method to explore patterns of land-cover transitions
In order to compare land-cover dynamics between different subregions of the
Amazon, we proceed in two steps. First, we calculate the area in a given
region that undergoes a transition from one land-cover type to another
between two reference years (including the lumping of several land-cover
types into one class) and normalize the obtained matrices. Second, we compare
the transition matrices between subregions by means of cluster analysis and
network methods. In this section, we describe the steps of the method in
detail.
Extraction and normalization of transition matrices
Markov chains are stochastic systems, in which the probability distribution
of the next time step only depends on the current state of the system; hence,
the system has no memory. A subregion can be thought of as consisting of a
number of land patches that undergo transitions between land-cover classes.
Markov analysis then describes how the set of patches may change over time.
Although the Markov property, i.e., that the transition probability only
depends on the present state of the system, can be shown to hold
approximately for land-use systems , the transition rates
are generally not constant over time, which means the system is not
stationary. This is not surprising because of the various climatological and
socioeconomic drivers and political decisions influencing land-cover
dynamics . Even though Markov chain analysis may
oversimplify land-cover dynamics because it does not take the underlying
processes explicitly into account and may therefore not be suitable to
project future land-cover change, it serves here as a first approximation in
obtaining a general understanding of the land-cover dynamics observed in the
data.
We obtain the transition matrices of subregions by calculating the areas in a
given subregion that undergo a transition from a land-cover class i to
another class j. The transition matrix of one subregion T(t) is
an n×n matrix with elements Tij(t), i,j∈{1,…,n},
where n is the number of land-cover classes. The transition matrix depends
on time, indicating the nonstationarity of the Markov process. In the
following, however, we omit the time dependence for ease of notation. With
the aggregation described above, the number of land-cover classes n is 6. We estimate T from the data
by first projecting the coordinates of the patches (in the data given in the
South American Datum (SAD69) coordinate system) to the South
America Albers Equal Area Conic projection. Second, we compute the geometric
union with GIS software combining the information contained in the two
land-cover maps of the reference years into one data set. Finally, we sum up
the area of all patches in one subregion that undergo the same transition.
Figure illustrates the creation of the
transition matrix T from the data.
To estimate transition probabilities, we have to normalize the transition
matrices. Thereby, we also make subregions of different total area
comparable. We normalize the rows of the transition matrices to 1, which
allows us to focus on relative changes in single land-cover classes
pij=Tij∑kTikfori,j:1…n.
The normalization does not work if one land-cover class i does not figure
in the data of one subregion, as ∑kTik would be equal to zero. In
such cases, we set the diagonal element Tii=1 and all other elements of the ith row to zero, implying that we handle
the land-cover class in the particular subregion as if no change occurs.
In statistical terms, p=(pij) is a stochastic matrix
compare with the properties pij≥0 and ∑jpij=1 for i=1…n. It corresponds to the maximum likelihood
estimation of the transition probability matrix of a first-order Markov chain
where land-cover classes correspond to the states of the Markov chain and the
rows of p specify the transition probabilities between the states
.
Illustration of the normalized transition matrices between
simplified classes derived for the whole Brazilian Amazon from the TerraClass
data set (changes between 2010 and 2012): (a) Markov transition
matrix p (self-loops omitted) and (b) conditional transition
matrix q. The strengths of the arrows are scaled with the
transition probabilities except for those representing small values. Arrows
with very small values (below 0.005) are not shown. The values are given in
Tables S2 and S3.
Figure a presents a visualization of the Markov chain and the
calculated transition probabilities estimated for the whole Brazilian Amazon.
The figure shows that there are transitions between almost all aggregated
classes, but they occur with very different probabilities. After
deforestation, about two-thirds of the areas are used as pasture, whereas the
rest is mostly classified as secondary vegetation. Furthermore, transitions
occur frequently between pasture partly covered with woody vegetation (dirty
pasture) and clean pasture. The former makes also frequent transitions to
secondary vegetation. Finally, there are considerable transitions from and to the “other” class,
in which we aggregated the following minor land-cover types from the original TerraClass classification: “mosaic
of uses”, “urban area”, “mining”, “reforestation” and “others”.
Alternatively to the Markov analysis, one could normalize the sum of the
transition matrix elements Tij to 1. Such a normalization would keep
the information on the initial distribution of land-cover classes in one
subregion but would not allow to analyze relative changes in individual
land-cover classes.
The transition probability matrix p, representing the dynamics of
an underlying Markov chain process, includes information on the patches that
undergo changes and the patches that remain in their land-cover class. To
only consider changes, we set the diagonal elements to zero before
normalizing the rows of T to 1:
qij=Tij∑k≠iTikfori≠j0fori=j.
Hence, q=(qij) estimates the probability to make a transition
from a single land-cover class i conditional on there being a transition
to a different land-cover class j. Figure b shows a
visualization of this conditional transition matrix for the whole Brazilian
Amazon. For land-use classes that have a high proportion of patches remaining
in the same class, this figure allows inspecting the relative shares of
transitioning patches more easily.
The normalized matrices p and q describe the
transitions between all land-cover classes. In the following, we are
particularly interested in comparing transition probabilities from a single
land-cover class to all others, formally represented by the rows of the
normalized matrices. If we only focus on the rows, we solve the
above-mentioned problem of missing land-cover classes in a subregion by
simply discarding the respective subregions from the analysis. To increase
the robustness, we also discard subregions having less than 1 km2 of
the considered land-cover class.
As described above, we estimated the normalized transition matrices
p and q for all mesoregions and municipalities
separately. This spatial segmentation was chosen because it makes the
analysis compatible with other data (e.g., socioeconomic data sets provided
by the IBGE). Additionally, the areas of the municipalities reflect to some
degree the population density and therefore potential land-use activities. In
principle, a segmentation into regular grid cells could provide complementary
information and insights. However, to keep the presentation clear, we focus
here on mesoregions and municipalities.
In general, the lower the spatial aggregation, i.e., the smaller the size of
the subregions, the higher the variability in space and in time. We can
observe this when comparing the mesoregion and municipality maps and
transitions between different times. Figure
shows two exemplary components of the matrices q calculated for
each municipality. The two maps highlight these subregions in darker colors
in which the transition probability from clean pasture to secondary
vegetation and vice versa is high compared to transitions to other land
covers. In Fig. a, we can observe that
transitions from clean pasture to secondary vegetation are infrequent
compared to other transitions except in the central north and the southwest.
Figure b suggests that along a horizontal
band from the west to the east and in the north (state of Roraima) the
transition probability from secondary vegetation to clean pasture is higher
than in the other parts of the Brazilian Amazon. The maps in
Fig. and similar maps for all other
possible transitions contain the information that we aim to aggregate using
clustering analysis. The next section therefore describes this second step of
our method.
Map of two selected components of the conditional transition
matrices q for each municipality of the Brazilian legal Amazon.
Colors indicate the shares of areas that make a transition from
(a) clean pasture to secondary vegetation and (b) secondary
vegetation to clean pasture.
Construction of similarity networks and clustering analysis of land-cover transitions
Clustering methods are a basic technique described in the machine learning
and data mining literature . In recent years, the
basic problem of clustering nodes in complex networks has also gained a lot
of interest in complex systems science . In this paper,
we choose a combination of established and more recent clustering methods to
compare and test the robustness of our results. The chosen established
methods are hierarchical clustering and the k means algorithm. The other
methods are based on complex networks that we construct from a difference
measure. To partition the network, we apply two different community detection
algorithms, the fast greedy and Louvain algorithms .
The first method applies hierarchical clustering that merges data points or
clusters based on their distance in the abstract data space. In the context
of this analysis, a data point x is either a full normalized
transition matrix (flattened, such that x∈Rn2) or a
single row of such a matrix (x∈Rn). Each data point
corresponds to an individual subregion. We choose to calculate the distance
between two data points x and y by the ℓ1 norm, also
called Manhattan distance, d(x,y)=∑iabs(xi-yi). This distance is easy to interpret in the context of probabilities and
compared to the euclidean metric does not punish outliers of a cluster as
much. The distances between two clusters or one cluster and one data point
are calculated using the complete linkage algorithm that takes the maximal
distance between the points of two clusters. This algorithm identifies
compact clusters with small diameters . Hierarchical
clustering produces a dendrogram of cluster partitions. The clusters are
obtained by cutting the dendrogram at a certain level determining the number
of clusters.
The second method uses the k means algorithm. The algorithm works in an
iterative manner: it associates data points to centroids and adjusts the
position of the centroids by minimizing the within-cluster sum of squared
distances. The k means algorithm inherently requires the choice of the
euclidean metric to calculate distances.
The network methods both require the construction of a similarity network
first. In the network, each node vα represents a subregion and nodes
with similar dynamics are linked by an edge eαβ, where the
Greek character indices refer to subregions. The connectivity of the network
can also be represented by an adjacency matrix A=(Aαβ). To determine the similarity, we use a normalized version of the
Manhattan distance as the difference measure d(x,y)=12k∑iabs(xi-yi), where k is the number of
land-cover classes n if we compare whole transition matrices and k=1 if
we only consider transitions from single land-cover classes. The metric is
0 if and only if transition probabilities are equal and 1 if they are
completely different. We set a threshold dth to transform the
data into a network with the adjacency matrix A:
Aαβ=1ifd(xα,xβ)<dth0else.
This adjacency matrix contains all information on the similarity network. The
threshold dth, which determines the subregions that are
connected, is chosen such that only links that are significantly different
from a distribution of difference measures of random vectors or matrices are
realized. In order to obtain dth, we use a Monte Carlo
simulation: we generate a large number (106) of random samples of vectors
or matrices, the values of which are drawn from a uniform distribution and
rows are normalized. From the computed distribution of pairwise difference
measures, we use the fifth percentile to determine the threshold
dth.
A visualization of such a similarity network is shown in
Fig. for transitions from clean pasture to other
land-cover types. The nodes of the network represent data points for the
municipality drawn around it. Links are present between regions that have a
difference measure below the significant threshold dth=0.11,
which we obtain as described above from a Monte Carlo simulation of
normalized random vectors of dimension 4 (because transitions to four other
classes are possible). A visual inspection of the network suggests that
similar transition probabilities are detected in regions of the eastern and
the southern Amazon, whereas there are less similar transitions in the
northern part. The inset in Fig. furthermore
shows a histogram of all pairwise differences. The threshold is indicated as
a red vertical line. From tests with different thresholds and different
underlying data, we can conclude that the patterns observed in the similarity
networks hardly depend on the exact choice of the threshold (or link
density). Thus, the construction of the network is robust with respect to
variations of the threshold.
Illustration of a similarity network with a spatial division in
municipalities for transitions from clean pasture to other land-cover classes
between 2010 and 2012. Inset: histogram of difference metric values with
threshold in red.
The visual inspection of similarity networks is difficult and may not be
reliable. Therefore, we applied community detection algorithms to the
networks to infer information about the network structure. These algorithms
identify clusters of nodes on the network (in the literature the clusters are
often called communities, hence the name) that have a high internal
connectivity. Most of these algorithms are based on the idea of optimizing
modularity Q, a network measure that compares the frequency of links inside
of communities to the frequency of links between communities
. For a network with adjacency matrix A and
clusters C, the modularity is given by
Q=12m∑α,βAαβ-kαkβ2mδ(Cα,Cβ),
where kα=∑βAαβ is the degree of node
α and m is the number of edges in the network. The term δ(Cα,Cβ) only gives a contribution if nodes α and β
belong to the same cluster. In the following, we constrain our comparison to
the fast greedy and the Louvain algorithms, which are computationally
efficient and yield comparatively high modularity values. The general idea of
the fast greedy algorithm as described in is to
subsequently join clusters such that the increase in modularity is highest
after the join. This produces a dendrogram, similar to the output of the
hierarchical clustering method, which can be cut at the level of highest
modularity Q. In contrast, the Louvain algorithm developed in
proceeds in two iterative steps. It first checks
subsequently if the reassignment of single nodes to other clusters leads to
an improvement in modularity. In a second step, it builds a new network
combining all nodes of a community found in the previous step into one node
and sums up all edges between communities to form weighted new edges.
In the following, we apply these algorithms to the same heterogeneous data. A
comparison between the different methods will show whether the clustering can
be considered robust.
Spatial heterogeneity of land-cover transitions and discussion of clustering patterns
This section describes patterns of land-cover change found in the Brazilian
Amazon when applying the clustering algorithms of differently normalized
transition matrices or single rows of them. We show the spatial comparison of
transitions between 2010 and 2012 with the threshold for the construction of
the similarity networks set to dth=0.11 (see
Sect. ). Comparisons of transitions between other years
are shown in the Supplement.
As explained in the methods section, we considered different normalizations
of the transition matrices: the Markov matrices p that also
contain information about patches remaining in the same land-cover class and
conditional transition matrices q that disregard this information.
First, we note that the majority of land patches do not change their class
from one time step to the next. This is illustrated in
Fig. , where the relative area of patches that make
a transition to a different land-cover class is plotted (excluding primary
forest), i.e., the sum of the diagonal elements of the transition matrix
divided by the sum of all elements. Only in the central Amazon and in some of
the smaller municipalities there are considerable fractions of up to 50 %
of the area undergoing a change in land-cover class. Because we are
interested in the changes, we will focus our discussion first on the
conditional transitions matrices q and compare only single rows
between the municipalities.
Relative areas that undergo changes in land-use classes between the
years 2010 and 2012 (excluding primary forest).
As an example, Fig. displays the
result of the clustering analysis for transitions from clean pasture to other
land-cover classes. To make the clustering comparable, we fixed the number of
clusters for the hierarchical and k means clustering to the one obtained
from the fast greedy network clustering algorithm. As we can see from the
figure, there are clearly distinguishable clusters in the south and the
northwest of the Amazon colored in orange and cyan for all four different
clustering algorithms. These clusters are identified independently of the
chosen clustering algorithm. In the other parts of the Amazon region, the
clusters vary dependent on the applied clustering algorithm. Both network
community detection algorithms identify similar clusters, even though the
Louvain algorithm finds seven and the fast greedy algorithm reveals five
communities in the data. Also, some clustering algorithms seem to find two
clusters for a group of municipalities, where other algorithms only find one
(compare, e.g., the fast greedy with the k means algorithm). In addition to
the two relatively stable clusters, we can observe in
Fig. that most clusters consist of
adjacent municipalities. This suggests that neighboring municipalities have a
high likelihood to exhibit similar relative land-cover changes.
Comparison of network (a, b) and classical (c, d)
clustering algorithms for conditional transitions from clean pasture to other
land-cover classes between 2010 and 2012. Each cluster is visualized by one
color. White regions lack data to estimate the transition matrix, grey
regions are not connected to the similarity network. The number of clusters
for the hierarchical and k means clusters was chosen to match the outcome of
the fast greedy algorithm (five). The Louvain algorithm detects seven clusters.
In order to interpret the clusters, we analyzed the cluster centroids, i.e.,
the mean of all data points in a cluster weighted by the area of the
considered land patches in the subregion.
Figure shows the cluster centroids
from the hierarchical clustering. The bars indicate the shares of patches
making a transition from clean pasture to another land-cover class and thus
show which transitions are dominating or are absent in the cluster. They
allow a straightforward interpretation of different clusters. For instance,
in municipalities belonging to the orange cluster, most of the areas are
converted to annual crops while only a small fraction makes the transition to
dirty pasture. This is in line with a previous study by
who found that cropland expanded mostly into pasture in the region between
2006 and 2010. The orange cluster is located inside the Mato Grosso state,
one of the biggest producers of soybeans in Brazil, which are detected as
annual crops in the data. As we can see, the clusters generally differ by
their relative shares of land-cover types such as dirty pasture and secondary
vegetation. When comparing the cluster centroids between algorithms, these
shares differ for the unstable clusters while the cluster centroids of the
stable clusters are almost the same.
(a) Hierarchical clustering with conditionally normalized
transition probabilities from clean pasture to other land-cover classes
between 2010 and 2012, as in Fig. c.
(b) Cluster centroids showing the conditional transition
probabilities of the average over the respective cluster indicated by cluster
color.
So far, we discussed transitions from clean pasture to other land-cover
classes as one example. But our analysis has shown that the stable clusters
identified in Fig. can also be
found when considering transitions from other land-cover classes, e.g., from
secondary vegetation (see Figs. S1 and S2). However, the same patterns are
not found for all transitions from single land-cover types. This is not
surprising considering typical land-cover sequences (often called land-use
trajectories) that follow total deforestation and are discussed in the
literature . According to
these studies, a common trajectory is that cleared forest patches are
converted to pasture land or used for small-scale subsistence agriculture.
After a while, as the soil degrades, the areas are often abandoned, leaving
them for regrowth of secondary vegetation. Later, they may be cleared again
and reused as pasture or they are converted to more intensive agricultural
cropland, e.g., for soybean cultivation. These accounts are generally
consistent with our results.
In addition to the clustering based on transitions from single land-cover
classes, we tried to identify regions that are similar regarding the
transitions between all land-cover classes. The clustering based on the full
Markov matrices p proved to be very unreliable due to the high
heterogeneity and dimensionality of the data (see Fig. S3). Furthermore, the
analysis of the difference measure showed that only a small fraction of
municipalities are significantly similar to each other compared to random
matrices. The clustering based on the full conditional transition matrix
q turned out to be highly dependent on the assumptions we made to
fill in missing data. Thus, we can conclude that a general classification of
land-cover dynamics only based on the full transition probability matrices
between different land-cover types is not reliable.
This may have several reasons. First, the underlying processes of land-cover
change in the Amazon are very heterogeneous in space and time and are
therefore difficult to compare. Second, the areas of the municipalities may
be too small for a reliable estimation of transition probabilities. For this
reason, we also analyzed the transition matrices at the level of mesoregions
(see Fig. S5). However, there was no reliable clustering at this spatial
aggregation either. Third, the classification of land-cover types in the
TerraClass data set comes with considerable errors. We tried to reduce the
errors by aggregating some of the original classes. However, there is not yet
an evaluation of the performance of change detection available for this data
set, which makes an estimation of the errors in our analysis difficult.
The Brazilian Amazon has been broadly divided into mostly undisturbed,
frontier and consolidated areas. For example,
distinguishes between the arch, i.e., densely populated areas in the south and
the east of the legal Amazon, new frontier regions in the central Amazon and
the mostly undisturbed west. used this partition to
analyze interregional differences in factors potentially determining
deforestation and found that the importance and combination of factors such
as protected areas, distance to roads and access to markets differs between
the three subregions. Although these studies focus on the 1990s and
large-scale socioeconomic patterns may have changed since then, our analysis
suggests that there are no clear patterns in the estimated transition
probabilities which correspond to a spatial partition such as the one
proposed by .
Conclusions
This paper has explored variations of a method that is able to provide
important information on the dynamics of land covers, including the ability
to quantify and compare land-cover transition frequencies and identify
regions of similar patterns of land-cover change. We have applied different
clustering techniques to find patterns in the subregional transition
probabilities between land-use classes and detected patterns of subregions
presenting similar transition dynamics that are consistent with other
studies. In some regions, such as northern Mato Grosso where transitions from
pasture to annual crops dominate, spatial patterns of relative land-use
changes are consistent between different clustering methods. However, our
analysis also indicates that relative land-use changes do not follow clearly
distinguishable patterns that are linked to earlier socioeconomic partitions
of the Brazilian Amazon.
The integration of socioeconomic data into the framework described in this
paper could potentially yield insights about the underlying drivers and
processes of land-cover transitions and how regionally different transition
probabilities are determined. Furthermore, the analysis presented in this
paper could potentially be used to parameterize models of land-cover change
that track aggregate areas with different land-cover types. By controlling
specific transition rates as functions of socioeconomic drivers, such
models, to be developed in future research, could give rough ideas about
possible future developments of land cover and thus support the planning of
future land-use policies in the Amazon region.
The input data were downloaded from the public archives indicated in Sect. 2
(INPE and EMBRAPA, IBGE). The code for the preparation of the data and the analysis
as well as the processed data are stored in the long-term archive of the Potsdam
Institute for Climate Impact Research. They will be made available upon request by email to the corresponding author.
The Supplement related to this article is available online at doi:10.5194/npg-24-113-2017-supplement.
The authors declare that they have no conflict of interest.
Acknowledgements
Finn Müller-Hansen acknowledges funding by the DFG (IRTG 1740/TRP
2011/50151-0). Jonathan F. Donges is grateful for financial support by the
Stordalen Foundation (via the Planetary Boundary Research Network
PB.net) and the EarthLeague's EarthDoc program. We thank Ana Cano
Crespo for help with the TerraClass data and Tim Kittel, Catrin Ciemer and
Silvana Tiedemann as well as the members of the ECOSTAB and COPAN flagships
at PIK for fruitful discussions. The data preparation for this paper was
carried out using ArcGIS with a licence provided by the German Research
Centre for Geosciences (GFZ, Potsdam). The data analysis relies on the
following python packages: scipy, scikit-learn, pandas, igraph, networkx,
shapefile and matplotlib. We thank all the contributors and developers of
these packages. Edited by:
S. Vannitsem Reviewed by: A. Tsonis and one anonymous referee
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