Introduction
Precipitation is the primary constraint for the presence of woody
vegetation in Africa. Although the mean annual rainfall determines the maximum
woody cover , large variation in vegetation cover
is observed across a broad range of rainfall bands . It
suggests that the actual cover fraction is significantly influenced by other
factors and increases the difficulty of projecting ecosystem responses to future
climate change. Obviously only precipitation is not sufficient to interpret
the dynamics of ecosystems. Explicit climate conditions and mechanisms should
enhance our understanding of current and future woody cover distributions.
From satellite observations, and
showed that the distribution of the tropical woody cover fraction was not
unimodal. For a given mean annual precipitation (P‾), a range of
ecosystems including grass (no trees), savanna (sparse tree cover) and forest
states are observed, suggesting that alternative stable states of vegetation
may exist . The alternative stable states are caused
by feedback mechanisms due to the
interactions between vegetation and its local climate
.
demonstrated that due to a positive fire feedback the savanna state can
maintain in water sufficient areas. The positive fire feedback implies that
fire will decrease woody cover and the burned area will be colonized
by herbaceous plants relatively quickly, which in turn provide more fuel for fire in
the next dry season. On the other hand, fire hardly occurs when woody cover
exceeds 60 % as the amount of fuel is limited . Trees
then colonize spaces from grass and the high degree of woody cover can be kept.
Simultaneously, if water supply by precipitation is not sufficient, high
transpiration rates by forest can lead to more enhanced convective cloud cover
than by savanna , which can reduce incoming
shortwave radiation and avoid further water loss .
Consequently forest can keep a wet environment for a longer time. This cloud
feedback plays an important role for the stability of the forest state,
especially during drought conditions.
Although alternative stable states can lead to bimodality in woody cover,
it can also be caused by discontinuities in environmental drivers or
variation in for instance the growth rates of woody plants .
Thus a better understanding of the cause of the observed bimodality is
needed, for instance to evaluate the resilience of the current ecosystem to
climate variation and to predict potential shift
of vegetation states.
To address the proposed questions, we focus on feedback mechanisms
that can explain the essential cause of the alternative stable states
. Assuming that the observed bimodality is related to the
alternative stable states, the proposed feedback mechanisms should exist.
Consequently, bimodality should also be found in variables that interact in
the feedback loops. For instance, the mean annual shortwave radiation
(R‾) is a key factor in the cloud feedback. High and low
R‾ are expected to associate with low and high woody cover
respectively if the cloud feedback is significant. Thus also R‾
should have a bimodal distribution, corresponding to the bimodality of
woody cover. The existence of bimodality in specific variables is
therefore an extra piece of evidence for the existence of alternative stable states.
More importantly, these feedback-integrated variables indicate the strength of
a specific feedback loop, through which we are able to assess the stability
of the current ecosystem.
Via vegetation–climate feedbacks, vegetation states and climatic
variables are clearly linked. Obviously, these interactions comprise
a wider set of characteristics than just mean annual rainfall and
woody cover. Seasonality of rainfall has a clear impact on the
dynamics of soil water, and consequently available water, for vegetation
. To explore the effects of rainfall
seasonality on current ecosystem states, scientists have made use of the
length of the dry season , entropy of the rainfall time
series and a seasonality index . Moreover,
vegetation states can clearly be controlled by climatic factors other than
precipitation; radiation and its seasonality also result in spatial and
temporal growth patterns, particularly under energy limited evaporation
regimes . Ignoring these additional drivers in the
coupled vegetation climate system may lead to an incomplete picture of the
prevailing mechanisms, probably misinterpreting the detected areas of
potential bistability.
In this paper we hypothesize that bimodality should not only be found
in woody cover, but due to the strong climate-vegetation interaction they
should also be found in some related variables. Above-ground biomass B
and mean shortwave radiation R‾
are chosen to verify our hypothesis. B can be seen as
a proxy for the development age of woody plants. It is also a measure of the
fire feedback as high fire frequency and severity can reduce
woody biomass significantly and lead to low B. R‾ is a
climatic variable for estimating the strength of the cloud feedback. A
low R‾ is interpreted as an environment with a more uniformly
distributed precipitation regime, where fire is rare and woody plants can
extend their canopies to increase woody cover W. And high W can in turn
diminish R‾ by affecting cloud cover through reinforcing
evapotranspiration . We first expect that the bimodality
can be found in both B and R‾. Moreover, the mode of low W in
the bimodality is expected to match with low B and high R‾; and
high W is expected to match with high B and low R‾.
After the detection of areas with bimodal states in B, W and
R‾, we use conditional histograms to attribute distributions of
one quantity to other quantities. As such we create a predictive set of
equations for W, driven by the climate data for diagnosing areas displaying
potential bimodality in the vegetation states. By analysing observations of
multiple climatic indicators and classified land cover types, we investigate
different prediction accuracies of these climatic indicators to different land
cover types. A new method is proposed to predict potential land cover by
combining predictions of these climatic indicators. Then we readdress the
spatial distribution of potential land cover types in western and central Africa
to illustrate areas where land cover change might occur in response to changes
in the driving climatic conditions.
Data and analysis methods
Data
The region of interest covers western Africa ((20∘ W,
30∘ E) × (5∘ S, 20∘ N), see
Fig. a and b). The MODIS (Moderate Resolution Imaging Spectroradiometer) Vegetation Continuous
Fields (VCF) product MOD44B; provides high-resolution
(500 m) satellite retrieved woody cover W averaged over the period
October 2000 to December 2001. Four consecutive annual cycles (2000–2003) of
above-ground biomass B are taken from , with 1 km
spatial resolution. This data set only comprises biomass of woody plants,
which is consistent with the woody cover data set. Six years (2002–2007) of
precipitation (P) and radiation (R) data are calculated from a 3 hourly
observation based data set intended for use as a climate forcing for the AMMA
(African Monsoon Multidisciplinary Analysis) Land Surface Model
Intercomparison Project ALMIP;. The spatial resolution is 0.5∘.
(a, b) Map of averaged woody cover (W) and above-ground
biomass (B) in western Africa. In one climatic grid cell
(0.5∘ × 0.5∘), about 12 321 data points of W and B (at
500 m resolution) are located. From this set 50 samples of W and B are
taken randomly and averaged to estimate the mean value of W and B in
each climatic grid cell. Note that the region covered by B-observations
(denoted by black contour) is smaller than for W. Total rainfall in area
covered by W-observations ranges between 212 and 4340 mmyr-1,
while B data are only available where P‾>641 mmyr-1.
(c, d, e) Histograms of observed W, B
and R‾ in the area where B-observation is available (the dark
contour region in (b)). The y axis is the density of the histograms.
Solid and dashed curves represent savanna and forest states from the
bimodality test respectively.
Figure a and b shows grid-cell-averaged values of W
and B from observations. The areal extent of B is smaller than
that of W, indicated by the dark contour line. In the
overlapping region (where the conditional histogram analysis is
carried out; see below), the mean annual precipitation P‾
ranges from 950 to 1350 mmyr-1 and the mean annual
radiation R‾ from 173 to 260 W m-2. Note that
P‾ ranges between 0 and 4340 mmyr-1 when the
entire western Africa is considered.
Anthropogenic land use is filtered from the data sets of W and B,
using data from the GlobCover project of the European Space Agency
(ESA; http://due.esrin.esa.int/page_globcover.php). This data set
provides 300 m resolution global land cover data in 2005–2006 and
2009. As the 2009 version improves the classification of deforested
patterns in tropical regions, it is used in this study.
Conditional histograms
The B data set was resampled from 1 km to 500 m to adjust the W
data set by bilinear interpolation. In each 0.5∘ grid cell of the
climate data set, samples with zero W or zero B are filtered out first.
A random subsample of 50 data points of W and B was assigned to every
climate data grid cell. Next a statistical bimodality test was applied using the “flexmix” package (version 2.3–13) in R version
3.2.2;, evaluating the integrated completed likelihood (ICL)
criterion . For various numbers of assumed data clusters
the expectation maximization (EM) algorithm is used to
determine the number of clusters best matching the observations
. For cases where a bimodal distribution is found to
provide the best data fit, the thresholds of the modes of W, B and
R‾ are calculated. For instance, in a mixture of savanna and
forest (S–F), Wl indicates the low woody cover biome (the
savanna state), while Wh indicates the forest state. Similarly,
Bl and Bh refer to the savanna and forest states
respectively, while R‾h corresponds to the savanna
state as high radiation levels are associated with a shorter rainfall season
limiting the maximum potential W . Consequently,
R‾l refers to the forest state.
Conditional histograms are compiled by selecting data of one
distribution conditioned on whether or not the corresponding data in
the other distribution belong to the savanna or forest categories. For
instance, histograms of W under both low and high conditions of
R‾ are constructed (that is, (W|R‾l) and (W|R‾h) respectively), and subsequently it is tested whether the bimodality
still exists.
Currently there is a contentious debate about the availability of the MODIS
VCF product for multimodality research. The classification
and regression tree (CART) method used for woody cover retrieval can lead to
artificial bias, which is suggested to be the real reason for the observed
multimodality . However through MODIS data
calibration, figure out that the bimodality of woody cover
larger than 30 % is not attributable to artificial bias. Similarly bias
also exists in the above-ground biomass product . The
discontinuity in the satellite estimation is accompanied by the same
discontinuity in validation data , implying that the
bimodality is not a reflection of the CART method . Thus we
conclude that both the woody cover and the above-ground biomass data sets are
appropriate for a bimodality analysis of the coexistence of savanna and
forest. More details are discussed in the Supplement.
Spatial classification of land cover
The filtering of anthropogenic land use change is applied to all W data for
the entire western African area. For this, all vegetation cover data in every
0.5∘ climatic grid cell (containing 12 321 MODIS
500 m × 500 m grid cells each) in this larger domain are
processed, and GlobCover data points flagged as human activities are removed.
These include the GlobCover classifications: post-flooding or irrigated
croplands, rainfed croplands, mosaic cropland (50–70 %)/vegetation
(grassland, shrubland, forest) (20–50 %), water bodies, artificial
surfaces and associated areas (urban areas >50 %) and mosaic
vegetation (grassland, shrubland, forest) (50–70 %)/cropland
(20–50 %) . If the number of remaining W samples
in a climatic grid cell is less than 500, the entire grid cell is considered
to be anthropogenic and no bimodality testing is applied. Classification into
treeless, savanna and forest states is calculated using a bimodality test
. A positive detection of a bimodal distribution is followed
by a check on the location of the peak values in the histogram to distinguish
between grass–savanna (G–S) or savanna–forest (S–F) states. In addition,
the relative proportion of the size of the two modes is calculated. We find
that if the proportion of one mode is less than 5 %, large uncertainty
will occur in the bimodality test. In cases with less than 5 % in one
mode, we assume an unimodal grid cell occupation by either grass, savanna or
forest. More details are shown in the online Supplement.
Climatology and potential shifts of ecosystem states
The degree to which potential woody cover distributions can be explained by
mean annual precipitation (P‾) and rainfall seasonality has been
addressed in various studies . In these studies, rainfall seasonality is
characterized by different indicators ,
which may lead to different sensitivities in the shift of climate regimes and
ecosystem states. By including the precipitation seasonality in their
analysis, find a somewhat surprising potential bimodality
in the heart of the Congo basin, in spite of a high precipitation amount even
in the dry season of that region. The studies listed above did not include an
analysis of climatic features that exclude the existence of a bistable
vegetation regime, like seasonality patterns that do not allow fire or other
processes that are essential for vegetation states.
We review a number of climatic indicators for expressing the
variability of rainfall, and we explore the degree to which these
indicators explain variations in ecosystem states. The relationships,
trained with observed vegetation and climate characteristics, are used
to determine the stability of woody cover and its sensitivity to
potential shifts in climatic indicators in western Africa.
Indicators for rainfall seasonality
We use six climatic indicators to express the temporal dynamics of the
water and energy cycle in western Africa. The mean annual precipitation
(P‾) represents the amount of water available to the land
surface and is calculated from daily observations during the
6-year ALMIP period between 2002 and 2007 . The
mean annual shortwave radiation (R‾) describes the total
amount of solar energy intercepted by the land surface and is
calculated from the measured daily-averaged incoming shortwave
radiation over the same 6-year period.
Two commonly used indicators of rainfall seasonality are the relative
length of the dry season LD in
and the entropy of relative monthly rainfall Ep
in. LD is indicative for the length of the
vegetation growing season, which in turn is related to the maximum
potential woody cover. It is calculated by ranking the monthly
rainfall (pm) in ascending order. LD is
defined as the fraction of months with a cumulative rainfall amounts
less than 10 % of the total rainfall in the record.
Ep is also determined using the monthly
rainfall amount (pm). For each year, the hydrological
year is defined to start after the month with the minimum of
pm. A climatological monthly rainfall amount
pm is derived by averaging the monthly rainfall in these
hydrological years. When qi is the relative rainfall amount in
a hydrological month (pm/P‾), Ep
can be obtained:
Ep=∑i=112qilog2qiph,
where ph (=1/12) is the uniform distribution of
pm. Although the value of Ep varies
greatly across climatic regimes (especially in monsoon areas in western
Africa), the difference of Ep between the Sahara and
tropical regions is very small, as rainfall seasonality is low in both
regimes.
The final indicator is the normalized difference of precipitation
(Δp):
Δp=max(p‾m)-min(p‾m)max(p‾m)+min(p‾m),
where max(p‾m) and min(p‾m) are maximum
and minimum of climatologically averaged monthly precipitation respectively. A low value of Δp reflects tropical
precipitation regimes, characterized by a small difference between
minimum and maximum monthly precipitation and a high annual mean
precipitation amount. The use of
max(p‾m)+min(p‾m) as
a denominator in Eq. () limits the range of Δp
in [0,1]. Compared with LD and Ep,
Δp is able to discriminate between low and wet
precipitation regimes with a strong seasonality of both.
Another indicator is the correlation coefficient of monthly mean
precipitation and shortwave radiation across the number of years
ρP‾m,R‾m, which
accounts for seasonally varying magnitude of land–atmosphere coupling. The
transpiration–precipitation feedback promotes cloud cover, which in turn
blocks the incoming shortwave radiation and decreases
ρP‾m,R‾m. Thus high
negative correlation between P‾m and
R‾m occurs in regions with strong land–atmosphere
coupling .
Relationship between climatic indicators and ecosystem states
We analyse the relationship between climatic indicator (CI) and land
cover (LC) for five different types: forest (F), grass (G), savanna (S)
and coexisting grass–savanna (G–S) and savanna–forest (S–F). Note
that bare ground is not considered in this analysis. For each of the six
climatic indicators CIk (k∈[1,6] corresponding to
P‾, R‾, Ep,
Δp, LD and ρP‾m,R‾m), n equal width bins are defined, spanning the
range of that indicator in our data set. A CIk × LC
matrix, consisting of the number of grid cells (vi,j, i is the
number of bins and j is LC) found in our data set of n CIk
ranges and five LC types, is constructed:
CI1kCI2k⋮CInkGG–SSS–FFv1,1v1,2v1,3v1,4v1,5v2,1v2,2v2,3v2,4v2,5⋮⋮⋮⋮⋮vn,1vn,2vn,3vn,4vn,5.
We test how for a given value of CIk, grid cells are distributed over the
five LC types. For this we use the probability qk,j, defined as follows:
qk,j=vi,j∑j=15vi,j,
where k∈[1,6] represents the specific CIk, and j is the LC type.
i indicates the band CIik (Eq. ) where the given CIk
value is located. With this probability matrix, a prediction of potential
land cover in every grid cell is constructed by giving the value of a climatic
indicator. For different types of climatic indicators these predictions will
be different, as different sensitivities of LC types to different climatic
indicators are found. For instance, by using the mean annual rainfall
(P‾), every land cover type in a given grid cell can be predicted
with equal possibility (20 % for G, G–S, S, S–F, F), while
Δp indicates a different probability distribution (0 %
for G, G–S, S, S–F and 100 % for F). To evaluate the predicted
uncertainty of each climatic indicator to climate regimes, we define an
entropy-like quantity wk:
wk=-∑j=15qk,jlog2qk,j.
Note that both qk,j and wk are grid cell dependent. Each grid cell
has its own qk,j and wk. So do variables which appear in
Sect. .
Predicted land cover types by climatic indicators
The probability qk,j and uncertainty index wk can be used to
predict the potential land cover for a given CI-combination. The two-step
prediction procedure first redistributes the probability of mixed vegetation
states (G–S and S–F) over uniform vegetation probabilities ck,g, ck,s and ck,f for grass, savanna
and forest respectively:
ck,g=qk,1+12qk,2ck,s=12qk,2+qk,3+12qk,4ck,f=12qk,4+qk,5.
In the second step the weighted mean of cg, cs and
cf is calculated. For cg this is the following:
cg=∑1wkck,g∑1wk,
where the weights wk are taken as the uncertainty index of CIk
(Eq. ). For wk=0 (100 % probability for a given
vegetation structure) a low value (10-3) is chosen. Similar equations
exist for savanna and forest.
From Eqs. (), () and (), we can find that
cg+cs+cf=1. A probability exceeding 90 %
for a certain land cover type is considered a stable, unimodal vegetation
structure. A probability less than 90 % but exceeding 50 % is
considered to be an unstable ecosystem dominated by a single land cover type.
Coexistence of grass, savanna and forest (each having considerable cover
fractions) is found to be rare. As a result, the vegetation structure in western
Africa can be classified by seven types: stable grass (Gs),
savanna (Ss) and forest (Fs); and bimodal types
dominated by grass (Gb), savanna (Sb) and forest
(Fb), where the bimodal structure dominated by savanna includes
two cases: G–S and S–F.
Difference between observed and predicted land cover types
To evaluate the stability and potential transition of current land
cover in western Africa, we compare the predicted potential land cover
with the observed land cover classification (Sect. ). In
this exercise the prediction uses the combination of climatic
indicators P‾, LD and Δp,
and the comparison comprises each land cover type (G, S and F)
individually. For grass, G and G–S are combined as grass in the
observation, while predicted stable and grass-dominated vegetation
types are similarly combined into a single grass category. By comparing
the predicted and observed grass cover distributions we can
distinguish three situations:
Area currently covered by grass with predicted grass cover.
Area currently covered by grass with other predicted cover
types.
Area currently covered by other types with predicted grass
cover.
The same method is applied for savanna and forest. Note that G–S in
the observation is shared by grass and savanna, while S–F is shared by savanna and
forest. This overlap has no significant effect on the analysis in principle.
Histograms of observed woody cover for different categories of mean
annual radiation R‾, being R‾l
(<220 W m-2, grey bars) and R‾h (>220 W m-2,
shaded bars). Panels represent samples taken under different total
precipitation regimes.
Results
Conditional histograms
Figure c–e show the histograms of observed woody
vegetation cover W, above-ground biomass B and mean annual radiation
R‾ for the research area after filtering the anthropogenic
land use out of the data. The bimodal distribution of W and B are
clearly illustrated. Related bimodality analyses are implemented by
and respectively. In the online Supplement
we provide the evaluation of potential classes of R‾. Based on the
ICL and the density distributions of R‾ under different
P‾ bands, two classes are determined as the best fit.
A clear threshold between the savanna and forest states is found for W
(0.6), B (7 kg C m-2) and R‾
(220 W m-2). Low R‾ is generally associated with
forest, while high R‾ corresponds to the savanna state.
Based on the detected thresholds while including the whole research
area in the analysis, we apply the conditional histogram method
(Sect. ) after stratifying the data into different
P‾ regimes (1000±50, 1100±50, 1200±50
and 1300±50 mmyr-1). Figure shows these
conditional histograms of W under fixed R‾ intervals for
the four precipitation regimes. The histograms
(W|R‾h) successfully classify all data that
obey the calculated threshold (<0.6) for all four precipitation
bands. This implies that under high radiation only low W is found. In
contrast, the histograms (W|R‾l) are bimodal,
indicating that alternative states coexist under low R‾
conditions. The distribution of W samples over Wl and
Wh is listed in Table . For all four precipitation
regimes at least 94 % of the data with R‾>220 W m-2 have a low W (<0.6). For the low R‾
class, however, only 19 to 62 % of the W data correspond to the
high W class.
Histograms of above-ground biomass B conditioned on woody
cover Wl (<0.6, shaded bars) and Wh (>0.6,
grey bars) under different precipitation regimes.
Percentage of woody cover fraction W and above-ground biomass B
falling into different R‾ and W categories respectively, being
high radiation (R‾h, R‾>220 W m-2) and low radiation (R‾l). High
and low values of W (higher or lower than 0.6) are denoted by
Wh and Wl, while biomass is categorized into high
(Bh) and low (Bl) values by taking
7 kg m-2 as threshold.
Conditions
Expected state
1000 mm
1100 mm
1200 mm
1300 mm
R‾h
W<0.6
98.55
98.01
94.21
96.33
R‾l
W>0.6
18.54
37.68
62.84
48.32
Wl
B<7 kgC m-2
97.88
96.75
94.83
95.96
Wh
B>7 kgC m-2
55.91
68.02
78.91
78.91
Figure shows the histograms of B conditioned on the W class.
The histograms (B|Wl) successfully classify all data below the
threshold B<7 kg C m-2. Again, at least 94 % of all data
with a low W (<0.6) are associated with low B (Table ).
However, for (B|Wh) a bimodal distribution is found,
indicating that two B modes exist with low W. Only 55 to 78 % of the
high B data are associated with Wh.
Table summarizes the results. We found that the W state can
be determined under two conditions: (1) low R‾ and high B, (2)
high R‾ and low B. The only regime where a bimodality is found
is the combination of low B and low R‾. In the study area,
a combination of high B and high R‾ did not occur.
Spatial patterns of bimodal regimes
We analysed all natural W samples and applied the bimodality test on
each climatic grid cell (Sect. ). In Fig. a, western
Africa is classified into six different W classes using thresholds of 0,
0.1 and 0.6 to separate the unimodal classes: bare soil (B, W=0), grass (G,
0<W<0.1), savanna (S, 0.1<W<0.6) and forest (F, W>0.6). If a bimodal
distribution was found, it was classified as either grass–savanna (G–S) or
savanna–forest (S–F) depending on the location of the individual peaks.
Figure a reveals that bimodal distributions only occur in the
transition zones between unimodal land cover types. The coexistence of savanna
and forest is only found in the south of Liberia and Ghana as well as in the Congo
basin. In the Congo basin, the tropical forest is surrounded by the bimodal
savanna–forest states.
Woody cover states determined by radiation (R‾) and
biomass (B) states. Bimodality is considered to be a coexistence of
savanna and forest states.
Low B
High B
Low R‾
Bimodality
High W
High R‾
Low W
N/A
(a) Bimodality classification of woody cover in western
Africa according to the integrated completed likelihood (ICL) criterion in the
bimodality test. (b, c) Classification of mean
annual precipitation P‾ vs. mean annual radiation
R‾ based on Fig. a. B: bare soil. G: grass. G–S:
grass–savanna. S: savanna. S–F: savanna–forest. F: forest.
To demonstrate the relations between land cover types and climate
forcing, we distinguished between unimodal and bimodal cells in
a P‾–R‾ scatter plot (Fig. b
and c). For a given P‾, different unimodal or bimodal
classes can be found, while R‾ appears to be a better
discriminator between the different classes.
Sensitivity of land cover types to climatic indicators
The six climatic indicators (CI, Sect. ) are calculated
from the ALMIP climate data and stratified by land cover type (LC) as
shown in Fig. . P‾ (top left panel of
Fig. ) increases with an LC shift from G to F, suggesting
that precipitation is the main driver of LC. However, the response of
different LC types shows a large mutual overlap, implying that
with a given P‾ multiple LC states can
exist. Precipitation is a poor predictor for LC. The precipitation
range where LC overlap occurs reflects the bimodality regime found by
P‾.
Box plot of six climatic indicators versus land cover types.
P‾ is mean annual precipitation, R‾ is mean annual
shortwave radiation, Ep is entropy of relative monthly
precipitation, Δp is normalized difference of averaged
monthly precipitation, LD is the maximum length of the dry
season and ρP‾mR‾m is
correlation coefficient of monthly precipitation and monthly
radiation.
For R‾ a negative relation with the woody cover fraction (from G
to F) is shown. R‾ shows stronger sensitivity to the LC type than
P‾. Both G and G–S are found for R‾ exceeding
240 W m-2. For higher R‾ (>262 W m-2) only G is found, suggesting that high R‾
is a necessary condition for stable G. A LC type consisting of S is
found in a narrow window (218<R‾<238 W m-2),
implying that the savanna state is very stable in this range of
R‾. Some samples of G and G–S are also found in this range.
However, they are in the tail of the specific distributions.
F is found when R‾<228 W m-2, which contains the LC
type S–F as well. As shown in Table , a low value of R‾
is necessary but not exclusive for finding F.
The covariation between LC and Ep is similar to the pattern
shown for R‾. However the range of Ep where
grass is found is larger than the range occupied by forest.
Ep>1.3 is sufficient to predict the existence of
grassland, which is thus a good climatic indicator for G. Both
Ep and R‾ focus on the detection of
a seasonality of the forcing. However, they are not sufficient to predict
a stable forest state. For instance, in spite of a strong seasonality in
precipitation, if the amount of precipitation during the dry season is high
enough to prevent fire occurrence, a stable F state can exist.
To distinguish the forest state from other LC types, we analyse the
covariation between the normalized difference of precipitation
(Δp, Eq. ) and LC. Δp=1
occurs when
max(p‾m)≫min(p‾m) or
min(p‾m)=0. A low value of Δp
requires a small seasonality in combination with a high value of
minimum p‾m. This quantity successfully segregates
the range of climate regimes according to rainfall seasonality, amplified in
a regime with a high precipitation amount. The results (middle right panel of
Fig. ) illustrate a successful introduction of new piece of
information to the previously discussed climate indicators. G and G–S are
dominant for a specific value of Δp. A shift from grass to
forest is accompanied by a strong decrease of Δp. For
Δp<0.90, forest will surely be present and very
stable for Δp<0.59, which provides a sufficient
diagnostic of the occurrence of forest.
The length of the dry season (LD, Fig. ) is
another indicator expressing the climate seasonality. Although
LD is defined differently from Ep, their
results are similar.
The ρP‾m,R‾m
represents the coupling between monthly precipitation and radiation,
which is predominantly negative (Fig. ). The observed range
of ρP‾m,R‾m is between
-0.81 and 0.54. G, G–S, S–F and F are all found in large ranges of
ρP‾m,R‾m-values, which
complicates its use as LC predictor. Detection of savanna vegetation types
could be linked to its dominant coexistence with negative values of
ρP‾m,R‾m meaning that
savanna apparently requires an environment with a strong rainfall–radiation
coupling, although its distribution has a fairly long tail.
Each of the climatic indicators does give useful information about the
vegetation states, but they are not mutually statistically independent.
Figure shows the correlations between all climatic indicators. The
highest correlation is found between Ep and LD,
demonstrating that the prediction ability of the Ep is
equivalent to that of the LD. R‾ is highly
correlated with both Ep and LD, since rainfall is
strongly correlated to the downward radiation flux. The P‾ is
highly correlated with R‾, Ep and LD,
but is not a good discriminator for LC due to the large overlapping LC regimes
for a given precipitation amount (Fig. ). Δp
behaves similarly to P‾, having a high correlation with Ep
and LD. However, Δp provides new information
compared to the other climatic indicators, shown by the scatter plot of
Ep vs. Δp (row 4, column 3 in
Fig. ). Ep can distinguish grass from other LCs, but
this is not true for S, F and S–F, which show great overlapping regions. In
contrast, Δp is able to detect the differences between
these LCs.
Correlation matrix of the six climatic indicators: r is the
correlation coefficient and p is the p value. Woody cover samples are
coloured based on land cover types: red is G, blue is S, magenta is
F, green is G–S and cyan is S–F.
ρP‾m,R‾m is fairly
independent from other climatic indicators. The scatter plots between
ρP‾m,R‾m and other
climatic indicators confirm the negative relation between rainfall and
radiation, but quite different values of
ρP‾m,R‾m are shown for
different land cover types. The U-shaped curves (the last row of
Fig. ) indicate that the strongest rainfall–radiation coupling is
apparent for the savanna region. The tails of this distribution are populated
by grass (dry climate) and forest (wet climate) where the correlation
between rainfall and radiation is weaker.
Figure illustrates the spatial distribution of the uncertainty
index (wk defined in Eq. ) of six climatic indicators in our
analysis domain. In two regions P‾ provides LC predictions with
high confidence (Fig. a). In the Sahara this is obviously related
to the stationary low precipitation regime (<300 mmyr-1)
without vegetation. At the boundary between Nigeria and Cameroon near the
Gulf of Guinea (10∘ E, 5∘ N), in contrast, a high
P‾ (>3000 mm) makes the prediction of forest vegetation very
robust (see also top left panel of Fig. ). Low R‾ is
found in three regions (Fig. b). The first region is the long band
of savanna between 5 and 12∘ N. Intermediate R‾ is
strongly related to stable savanna vegetation (top right panel of
Fig. ). The other two regions are the west and the east of the
Congo basin ((10∘ E, 3∘ S–5∘ N) and
(25–30∘ E, 3∘ S–3∘ N)). In these regions
R‾ is low (<180 Wm-2). However,
R‾ cannot determine the vegetation type in the majority of the
Congo basin area (0.65<wk<1.0), which is forest dominated. The
uncertainty estimations for Ep and LD are similar
(Fig. c and e). The predicted band of savanna is narrower than
produced with R‾. However, the Congo basin is mainly
highlighted with low uncertainty (0.39<wk<0.54). The stable forest
vegetation predicted by Δp occupies a larger area than
produced with Ep and LD with lower uncertainty
(wk<0.4), which demonstrates Δp to be a better
climatic indicator for stable forest. Savanna can be well predicted by
ρP‾m,R‾m with relatively
low uncertainty, but the result is not as good as produced with
R‾, Ep or LD. However,
ρP‾m,R‾m can predict
the land cover in the west of the Congo basin, where a weak positive
correlation between rainfall and radiation is displayed.
Uncertainty index of the six climatic variables for land cover
prediction. A low value (wk is defined in Eq. ) denotes
a high confidence of the specific variable to predict the local
land cover types.
Prediction and potential shifts of land cover
Figure a–c displays the predicted land cover using three
combinations of climatic indicators. In Fig. a LC is
predicted using solely precipitation as climatic indicator. Stable
forest is only found for several grid cells around (10∘ E,
5∘ N) with high rainfall (>3000 mmyr-1). The
area where both savanna and forest can exist ranges from the coast of
Guinea to the Congo basin. The Congo basin is currently covered by
forest, but is predicted to be unstable and has the potential to shift to
the savanna state using P‾ only. The region around
(14∘ W, 10∘ N) is also predicted to be forest dominated,
while in reality it is covered by a G–S vegetation type (Fig. a).
With high LD (>0.7) and radiation (>230 W m-2), S–F hardly occurs.
(a, b, c) Predicted
land cover type using different combinations of climatic indicators.
(a) Only total rainfall P‾, (b)
P‾ and length of the dry season LD, (c)
P‾, LD and the entropy of the relative monthly
precipitation Δp. B is bare soil, Gs is stable
grass; Gb is bimodality dominated by grass, Sb is bimodality
dominated by savanna, Ss is stable savanna, Fb is bimodality
dominated by forest and Fs is stable forest. Note that Sb appears
twice. The top Sb is a bimodality between savanna and forest, and the
bottom one represents a bimodality between grass and savanna. (d, e, f) Difference between predicted and observed
land cover based on Figs. c and a respectively. In
(d), the area marked by “+” is predicted to be dominated by
forest but currently is covered by other states. The area marked by “-”
is predicted to be covered by other states but currently is dominated by
forest. The area marked by “=” is predicted to be dominated by forest and
currently is dominated by forest. For (e) and (f) the same
signs are used for savanna and grass.
Figure b shows LC prediction generated using both
P‾ and LD as climatic indicators. Stable
forest vegetation is predicted in a small area of the Congo basin. The
forest-dominated area occurs on the south coast of Liberia and Ghana
((10∘ W, 5∘ N) to (1∘ W, 5∘ N)),
which coincides with observations. In addition, stable savanna is present as
a shallow band around 10∘ N. Δp is added as
climatic indicator in Fig. c, which leads to an increase of the
area with stable forest cover. The stable savanna region shown in
Fig. b is reduced in areal extent.
Figure d–f illustrates the difference between observed and
predicted LC (Fig. c). For each pattern, the mean value of
P‾, Δp and LD are listed
in Table . Note that Fig. d–f only shows the
potential shift of the specific state, whereas the values in
Table show the explicit direction of the potential
shift. For instance, the “+” in Fig. e indicates the
regions that have potential to shift from other land cover types to
the savanna state. This includes two possibilities: F → S and
G → S (in Table ), representing patterns where
current forest and current grass can shift to savanna.
The mean value of P‾, Δp and LD of different
patterns shown in Fig. d–f. The first column represents the
status of the specific patterns. For instance, F → S indicates the
patterns that are observed as forest but predicted to be savanna.
Land cover
P‾
Δp
LD
change
(mm yr-1)
(–)
(1)
F → F
1601
0.70
0.30
F → S
1481
0.92
0.40
S → F
1513
0.78
0.32
S → S
1174
0.96
0.49
S → G
695
1.00
0.66
G → S
887
1.00
0.59
G → G
525
1.00
0.68
G → B
259
1.00
0.75
B → G
378
1.00
0.70
Figure d shows that a large area covered by forest has
the potential for a transition to savanna. It includes the forest area
in Guinea and a large boundary of the Congo basin. However, forest
recovery can only occur in a few areas at the border between F and S
states, including the south coast of Ghana and Côte d'Ivoire. The
P‾ (1513 mmyr-1, Table ) of the
S → F patterns is slightly higher than the P‾
(1481 mmyr-1) of the F → S patterns, but
the Δp (0.78 for S → F; 0.92 for
F → S) and LD (0.32 for
S → F; 0.40 for F → S) show a considerable
difference. It implies that in such regions the seasonality of
precipitation is more important to forest than the mean annual
precipitation. The regions with low Δp and
LD are more likely to be covered by forest. The
potential transition of savanna into another vegetation type is shown
in two regions (Fig. e). For the S → G
transition, there is an increasing trend of savanna between
8∘ W and 19∘ E, suggesting regreening of the
Sahel. This is compensated by a replacement of savanna by grass in the
adjacent areas. Compared with the transitions between forest and
savanna, the differences between S → G and
G → S mainly exist in P‾ (695 and
887 mmyr-1) and LD (0.66 and 0.59) rather
than in Δp (Table ). A large area of the
Sahara has the potential to be recovered by grassland due to
sufficient P‾ (378 mmyr-1) to sustain
grassland (Fig. f and Table ). The main recovery
occurs in the northern Sahel front between 15∘ W and
20∘ E. Especially in the centre of this front (between
0∘ E and 10∘ E), the regreening trend can promote
vegetation extension approximately 3 ∘ northward.
Discussion
Conditional analysis of bimodalities
Multiple studies e.g. found that the observed distribution of woody cover
(W) provides evidence that alternative vegetation states may exist under
a given precipitation regime. Due to the interactions between vegetation and
local climate , alternative
stable states can exist. Therefore we have hypothesized that bimodality
should be found in both vegetation and climate variables, especially for western
Africa, where land surface is strongly coupled with atmosphere
.
Our results confirm our hypotheses and show that alternative states also
exist in above-ground biomass (B) and mean shortwave radiation
(R‾). Two modes of W generate different amounts of evapotranspiration
under the same P‾. It strongly influences radiation regimes
through cloud formation . Furthermore,
rainfall seasonality, which can be represented by R‾, affects the
temporal distribution of water and the fire
frequency , which in turn
influences the W. Although the interactions between W and R‾
are extremely complex, the bimodality found in both variables reveals the
existence of vegetation–climate interactions.
By applying conditional histograms in the analysis of distributions of
B and R‾ we found that our hypothesis was not totally true.
For instance, vegetation under high R‾ must have low W, but low
W does not mean that it correlates with high R‾. Low W
indicates that the vegetation has low B, but high W occurs in both low and
high B cases. These results are summarized in Table , containing
four cases. The first case is that with low B and high R‾ only
low W is found. It is a typical condition for savanna states. Low B
implies weak colonization ability of woody plants while high R‾
represents high rainfall seasonality. Both of them provide ideal
conditions for grass growth in the wet season and fire occurrence during the
dry season, suggesting that the savanna state here is very stable. This is
consistent with findings of for areas where annual
rainfall exceeds 1000 mmyr-1: in areas with a long dry season
(associated with high radiation), only savannas with low woody cover were
observed.
The second case is that only high W can exist under the condition of
high B and low R‾. It suggests that high biomass and low
variation of rainfall seasonality are sufficient conditions for a stable forest
state. The importance of rainfall seasonality on vegetation cover was
highlighted before in various studies .
Furthermore, did find for Africa that areas with similar
annual rainfall amounts have higher woody cover if the rainfall climatology is
dominated by frequent low-intensity precipitation events.
For the previous two cases, the mode of W can be determined because the
vegetation–climate interactions under the given conditions are very strong.
For instance, low R‾ provides a steady rainfall climatology for
high B and in turn high B reinforces the stability of low R‾.
With a disturbance, for instance rainfall decreasing during the dry season,
the high B can remain as high cloud cover through evapotranspiration to
avoid further water loss, which in turn keeps R‾ at a low level.
However, apart from these two stable states we also find two unstable states.
The first is high B and high R‾, which is rarely
observed in our study. It suggests that the system would
fast shift to the two stable states once this situation occurs.
The most interesting condition is low B and low R‾, where
the bimodality of W is still found. This status can be observed at the
boundary between savanna and forest. In this region, B is low due to the fire
effect from the savanna side but woody plants can benefit from high cloud cover
from the forest side. Thus they can produce both low and high W, which is
subject to the strength of fire and cloud cover. In this case the system can
easily shift from one state to another. If high W occurs, it can reinforce the
transpiration-cloud feedback and get rid of fire. Consequently, this region
will be colonized by forest. Otherwise, fire frequency increases due to low
W and the savanna will extend to the forest.
Based on the bifurcation theory, ecosystems may form alternative stable
states under the same climate condition due to different feedback mechanisms.
In this study, the mean annual precipitation is the general climate condition.
Thus the observed bimodalities of B and R‾ are strong evidence
for alternative stable states under different P‾ bands. Moreover we
notice that R‾ can be an ideal measure of the strength of the
vegetation–climate interactions, through which we can estimate the stability
of the two W modes. Our results (in Table ) demonstrate that
unimodality of W is found under specific conditions of W and
R‾. It implies that the W state is stable under such
conditions. However bimodality of W still exists under an intermediate
status: low B and low R‾, revealing where critical transitions
might occur. Numerous studies tried to find early warning signals of possible
critical transitions through different approaches . However they only focused on
indicators from the dynamics of vegetation to estimate ecosystem states. The
essential cause of most alternative stable states in ecology, feedback
mechanisms , is not explicitly
considered. This study uses a climatic variable R‾ and a proxy
variable of woody plants' age B to estimate the stability of vegetation
states through measuring the strength of the specific feedback mechanism.
This approach does not need long time series data of vegetation dynamics,
only a screen shot of vegetation biomass and short time observations of a
proper climatic variable. However we agree that this approach does not allow
the quantification of complex feedbacks between, e.g. land cover and local
climate, for which more complex observations and analyses are needed.
This study simply tests the climatic approach in western Africa. In the next
step, this approach will be extended to the whole tropical region to estimate
the stability of vegetation states at global scale. Recently a new version of
MODIS VCF (Collection 5) has become available .
found that the multimodality of boreal plants still exists in the new
version, but the density distribution varies significantly compared with the
previous version Collection 3,. Thus the difference
between the two VCF versions in the tropical area should be carefully investigated
before analysis. Moreover, it will be of interest to investigate whether the two
modes of W from Collection 3 are equal to that from Collection 5 according to the
conditional histogram.
Climate indicators and land cover prediction
Although rainfall is the primary driver of the maximum woody cover in
Africa , the land cover predicted
by the mean annual precipitation is highly uncertain due to complex
ecohydrological processes and sensitivities. It is
essential to consider rainfall seasonality , and clearly helps
in understanding vegetation pattern anomalies, for instance during
drought conditions . However, other climatic
indicators play important roles as well.
In this study, we link vegetation patterns to six climatic
indicators, including mean annual precipitation, rainfall seasonality,
incoming shortwave radiation and correlation coefficient of
P‾m and R‾m. Taking total
rainfall as the only indicator results in high uncertainty of the LC
prediction (Fig. a). Overlapping vegetation states for a given
precipitation climate (Fig. ) can be misinterpreted as the
existence of a bimodal vegetation structure. Mean annual shortwave
radiation explains more variability in observed LC patterns
(Fig. b). It is closely related to savanna and increases
confidence in estimated vegetation states in the west of the Congo basin.
This is also found from
ρP‾m,R‾m, indicating
a relatively strong positive correlation between P‾m and
R‾m. The precipitation seasonality relates to
the strong monsoon season modulates cloud cover, which leads to a low or
negative value of
ρP‾m,R‾m. The western
Congo basin, however, has a continuous high cloud coverage. The variation of
the radiation is thus strongly linked to the solar zenith angle and the
correlation between rainfall and radiation is weakly positive instead of
negative as is found in most regions.
Predictions of LC with three incremental combinations of climatic
indicators are illustrated and compared to observed LC distributions
(Fig. ). Using P‾ alone
(Fig. a) yields similar LC patterns to the findings of
. In the Congo basin with intermediate rainfall amounts
(1300<P‾<2500 mmyr-1) a potential bimodal S–F
vegetation structure (currently covered by forest) is found
(Fig. a). However, the rainfall seasonality in this area is
relatively low compared to other climatic zones. The precipitation amount
during the dry season is high enough to prevent fire occurrence, leading to
a relatively stable ecosystem with low probability of bimodal vegetation
states.
A new analysis in this comparison is the climate driven potential LC
transition in western Africa. The results (Fig. ) show that
a strong reduction in tropical forest area is possible due to high seasonality
(Table ). Predicted grassland expansion around 15∘ N
coincides well with observations . However, the regreening
trend of savanna around 10∘ N was not detected by observations as the
remote sensing data used are fairly insensitive to possible changes in woody
cover during the growing season .
Our analysis is limited by the use of a short (6 years)
climate data set . Prediction of future LC transition
related to climate change is hard , but could be
complemented by including climate model data .
Changes in CO2 concentration and factors
like soil type , plant diversity
and topography
have not been included in our analysis. Including dynamic
vegetation-climatic interactions , vegetation competition for limited resources
and grazing pressure in these systems
further promotes the understanding of the complexity
of the potential woody cover prediction .
Apart from natural factors, human activities (e.g. deforestation,
grazing and urbanization) also significantly influence the tropical ecosystem.
In fact, based on the GlobCover data we found that over 80 % of an area
can be affected by humans in specific climatic grid cells (0.5∘
resolution). Estimating the amount and type of land use change is difficult as
it involves many different social processes, such as economy, cultivation culture and
policy both on local and global scales. In turn these land use changes
interact with climate change as well. Thus its contributions to climate
change and ecosystems should be carefully investigated to improve the
prediction of potential land cover change.