In times of global change, we must closely monitor the state of the planet in
order to understand the full complexity of these changes. In fact, each of the
Earth's subsystems – i.e., the biosphere, atmosphere, hydrosphere, and
cryosphere – can be analyzed from a multitude of data streams.
However, since it is very hard to jointly interpret multiple monitoring data
streams in parallel, one often aims for some summarizing indicator. Climate
indices, for example, summarize the state of atmospheric circulation in a
region.
Although such approaches are also used in other fields of science, they are
rarely used to describe land surface dynamics.
Here, we propose a robust method to create global indicators for the terrestrial
biosphere using principal component analysis based on a high-dimensional set
of relevant global data streams.
The concept was tested using 12 explanatory variables representing the
biophysical state of ecosystems and land–atmosphere fluxes of water, energy, and carbon
fluxes. We find that three indicators account for 82 % of the variance of the
selected biosphere variables in space and time across the globe. While the
first indicator summarizes productivity patterns, the second indicator
summarizes variables representing water and energy availability. The third
indicator represents mostly changes in surface albedo. Anomalies in the
indicators clearly identify extreme events, such as the Amazon droughts (2005
and 2010) and the Russian heat wave (2010). The anomalies also allow us to
interpret the impacts of these events. The indicators can also be used to
detect and quantify changes in seasonal dynamics. Here we report, for instance,
increasing seasonal amplitudes of productivity in agricultural areas and
arctic regions. We assume that this generic approach has great potential for
the analysis of land surface dynamics from observational or model data.
Introduction
Today, humanity faces negative global impacts of land use and land cover change
, global warming , and
associated losses of biodiversity
, to only mention the most
prominent transformations. Over the past decades, new satellite missions
e.g., along with the continuous
collection of ground-based measurements e.g., and
the integration of both have increased our capacity to monitor the Earth's surface
enormously. However, there are still large knowledge gaps limiting our capacity
to monitor and understand the current transformations of the Earth system
.
Many recent changes due to increasing anthropogenic activity are manifested in long-term transformations. One prominent example is “global greening” that has been attributed to fertilization effects, temperature increases, and land use intensification . It is also known that phenological patterns change in the wake of climate change . However, these phenological patterns vary regionally. In “cold” ecosystems one may find decreased seasonal amplitudes on primary production due to warmer winters . Elsewhere, seasonal amplitude may increase in agricultural areas, for example, due to the so-called “green revolution” .
Another change in terrestrial land surface dynamics is induced by increasing
frequencies and magnitudes of extreme events
. The consequences for
land ecosystems have yet to be fully understood and require novel detection and attribution methods
tailored to the problem .
While extreme events are typically only temporary deviations from a normal
trajectory, ecosystems may change their qualitative state permanently, for
example shift from grassland to shrubland. Such shifts or tipping points can be
induced by changing environmental conditions or direct human influence, and they pose
yet another problem that needs to be considered . The
question we address here is how to uncover and summarize changes in
land surface dynamics in a consistent framework. The idea is to simultaneously
take advantage of a large array of global data streams, without addressing each
observed phenomenon in a specific domain only. We seek to develop an integrated
approach to uncover changes in the land surface dynamics based on a very generic
approach.
The problem of identifying patterns of change in high-dimensional data streams
is not new. Extracting the dominant features from high-dimensional observations
is a well-known problem in many disciplines. One approach is to manually define
indicators that are known to represent important properties such as the “Bowen
ratio” find a more complete description of the concept in Sect. . Another one consists in using machine
learning to extract unique, and ideally independent features from the data. In
the climate sciences, for instance, it is common to summarize atmospheric states
using empirical orthogonal functions (EOFs), also known as principal component
analysis (PCA; ). The rationale is that
dimensionality reduction only retains the main data features, which makes them
more easily accessible for analysis. One of the most prominent examples is the
description of the El Niño–Southern Oscillation (ENSO) dynamics in the
multivariate ENSO index (MEI; ), an
indicator describing the state of the regional circulation patterns at a certain
point in time. The MEI is a very successful index that can be easily interpreted
and used in a variety of ways; most basically it provides a measure for the
intensity and duration of the different quasi-cyclic ENSO events, but it can also
be associated with its characteristic impacts, e.g., seasonal warming, changes
in seasonal temperatures, and overall dryness in the Pacific Northwest of the
United States ; drought-related fires in the
Brazilian Amazon ; and crop yield anomalies
.
In plant ecology, indicators based on dimensionality reduction methods are used
to describe changes to species assemblages along unknown gradients
. The emerging gradients can be interpreted using additional environmental
constraints, or based on internal plant community dynamics
. It is also common to compress satellite-based Earth observations via
dimensionality reduction to get a notion of the underlying dynamics of
terrestrial ecosystems. For instance, showed that one can understand the
impacts of droughts and heat waves based on a compressed view of the relevant
vegetation indices. In general, dimensionality reduction is the method of choice to compress
high-dimensional observations in a few (ideally) independent components with
little loss of information .
Understanding changes in land–atmosphere interactions is a complex problem, as
all aforementioned patterns of change may occur and interact: land cover change
may alter biophysical properties of the land surface such as (surface) albedo
with consequences for the energy balance . Long-term
trends in temperature, water availability, or fertilization may impact
productivity patterns and biogeochemical processes
. In fact, these land surface
dynamics have implications for multiple dimensions and require monitoring of
biophysical state variables such as leaf area index, albedo, etc., as well as
associated land–atmosphere fluxes of carbon, water, and energy.
Here, we aim to summarize these high-dimensional surface dynamics and make them
accessible for subsequent interpretations and analyses such as mean seasonal
cycles (MSCs), anomalies, trend analyses, breakpoint analyses, and the
characterization of ecosystems. Specifically, we seek a set of uncorrelated, yet
comprehensive, state indicators. We want to have a set of very few indicators
that represent the most dominant features of the above-described temporal
ecosystem dynamics. These indicators should also be uncorrelated, so that one
can study the system state by looking and interpreting each indicator
independently. The approach should also give an idea of the general complexity
contained in the available data streams. If more than a single indicator is
required to describe land surface dynamics accurately, then these indicators
shall describe very different aspects. While one indicator may describe global
patterns of change, others could be only relevant in certain regions, for
certain types of ecosystems, or for specific types of impacts. The indicators
shall have a number of desirable properties: (1) represent the overall state
of observations comprising the system in space and time, (2) carry sufficient
information to allow for reconstructing the original observations faithfully
from these indicators, (3) be of much lower dimensionality than the number of
observed variables, and (4) allow intuitive interpretations.
In this work, we first introduce a method to create such indicators, and then we apply the method to a global set of variables describing the biosphere. Finally, to prove the effectiveness of the method, we interpret the resulting set of indicators and explore the information contained in the indicators by analyzing them in different ways and relating them to well-known phenomena.
Variables used describing the biosphere. For a description of the variables, see Appendix .
VariableDetailsSourceBlack-sky albedoDirectional reflectanceEvaporation(mmd-1)Evaporative stressModeled water stressfAPARfraction of absorbed photosyntheticallyactive radiationGross primary productivity (GPP)(gCm-2d-1), Latent energy (LE)(Wm-2), Net ecosystem exchange (NEE)(gCm-2d-1), Root-zone soil moisture(m3m-3)Sensible heat (H)(Wm-2), Surface soil moisture(mm3mm-3)Terrestrial ecosystem respiration (TER)(gCm-2d-1), White-sky albedoDiffuse reflectanceMethodsData
Table gives an overview of the data streams used in this analysis
(for a more detailed description see Appendix ). For an
effective joint analysis of more than a single variable, the variables have to
be harmonized and brought to a single grid in space and time. The Earth System
Data Lab (ESDL; https://www.earthsystemdatalab.net, last access: 23 April 2020;
) curates a comprehensive set of data streams to
describe multiple facets of the terrestrial biosphere and associated climate
system. The data streams are harmonized as analysis-ready data on a common
spatiotemporal grid (equirectangular grid 0.25∘ in space and 8 d
in time, 2001–2011), forming a 4D hypercube, which we call a “data cube”. The
ESDL not only curates Earth system data, but also comes with a toolbox to
analyze these data efficiently. For this study, we chose all available variables
in the ESDL v1.0 (the most recent version available at the time of analysis),
divided the available variables into meteorological and biospheric variables and
discarded the atmospheric variables. We also discarded variables with
distributions that are badly suited for a linear PCA (e.g., burned area contains
mostly zeros) and variables with too many missing values. The only dataset that
was added post hoc was fAPAR, which represents an important aspect of vegetation
which was not available in the data cube at the time of analysis (it is part of
the most recent version of the data cube).
The datasets taken from and are
derived from flux tower measurements . The flux towers
are not equally distributed in climate space; i.e., there are many flux towers
in temperate areas but much fewer in tropic and arctic regions, which may lead
to less accurate data in these regions. These datasets also exclude large arid
areas such as the Sahara and Gobi deserts and parts of the Arabian Peninsula
which may affect the resulting loadings of the PCA slightly.
In this study, each variable was normalized globally to zero mean and unit
variance to account for the different units of the variables, i.e., transform
the variables to have standard deviations from the mean as the common unit.
Because the area of the pixel changes with latitude in the equirectangular
coordinate system used by the ESDL, the pixels were weighted according to the
represented surface area. Only spatiotemporal pixels without any missing values
were considered in the calculation of the covariance matrix.
Dimensionality reduction with PCA
As a method for dimensionality reduction, we used a modified principal component
analysis to summarize the information contained in the observed variables. PCA
transforms the set of d centered and, in this case, standardized variables
into a subset of p, 1≤p≤d, principal components (PCs). Each
component is uncorrelated with the other components, while the first PCs explain
the largest fraction of variance in the data.
The data streams consist of d=12 observed variables at the same time and
location. Each observation is defined in a d-dimensional space,
xi∈Rd, and we define the dataset by collecting all
samples in the matrix X=[x1|⋯|xn]∈Rd×n. The observations are repeated in space and time and
lie on a grid of lat×long×time. In our case,
we have n=|lat|×|long|×|time|=720×1440×506=524,620,800 observations, where |⋅| denotes the
cardinality of the dimension. Note that the actual number of observations was
lower, n=106,360,156, because we considered land points only and removed
missing values.
The fundamental idea of PCA is to project the data to a space of lower
dimensionality that preserves the covariance structure of the data. Hence, the
fundament of a PCA is the computation of a covariance matrix, Q.
When all variables are centered to global zero mean and normalized to unit
variance, the covariance matrix can in principle be estimated as
Q=1n-1XXT=1n-1∑i=1nxixiT.
However, in our case the data cube lies on a regular 0.25∘ grid and
estimating Q as above would lead to overestimating the influence of
dynamics in relatively small pixels of high latitudes compared to lower
latitudes where each data point represents a larger area. Hence, one needs a
weighted approach to calculate the covariance matrix,
Q=1w∑i=1nwixixiT,
where wi=cos(lati) and lati is the latitude of
observation i, w=∑i=1nwi is the total weight, and n is the
total number of observations. Equation () has the
additional property that it can be computed sequentially on very big datasets,
such as our Earth System Data Cube, by a consecutively adding observations to
an initial estimate.
Note that the actual calculation of the covariance matrix is even more
complicated, because summing up many floating-point numbers one by one can lead
to large inaccuracies due to precision issues of floating-point numbers and
instabilities of the naive algorithm (; the same
holds for the implementations of the sum function in most software used
for numerical computing). Here, we used the Julia package
WeightedOnlineStats.jl (10.5281/zenodo.3360311, repository:
https://github.com/gdkrmr/WeightedOnlineStats.jl/, last access: 23 April 2020) (implemented by the first author of this paper), which uses numerically stable
algorithms for summation, higher-precision numbers, and a map-reduce scheme that
further minimizes floating-point errors.
Based on this weighted and numerically stable covariance matrix, the PCA can be
computed using an eigendecomposition of the covariance matrix,
Q=VΛVT∈Rd×d.
In this case, the covariance matrix Q is equal to the correlation
matrix because we standardized the variables to unit variance.
Λ is a diagonal matrix with the eigenvalues,
λ1,…,λd, in the diagonal in decreasing order and
V∈Rd×d, the matrix with the corresponding
eigenvectors in columns. V can project the new incoming input data
xi (centered and standardized) onto the retained PCs,
yi=VTxi∈Rd,
where yi is the projection of the observation xi
onto the d PCs.
The canonical measure of the quality of a PCA is the fraction of explained
variance by each component, σi2, calculated as
σi2=λi∑i=1dλi.
To get a more complete measure of the accuracy of the PCA, we used the
“reconstruction error” in addition to the fraction of explained variance. PCA
allows a simple projection of an observation onto the first p PCs and a
consecutive reconstruction of the observations from this p-dimensional
projection. This is achieved by
Yp=VpTX∈Rp×nandXp=VpYp∈Rd×n,
where Yp is the projection onto the first p PCs,
Vp the matrix with columns consisting of the eigenvectors
belonging to the p largest eigenvalues, and Xp the
observations reconstructed from the first p PCs.
The reconstruction error, ei, was calculated for every point,
xi, in the space–time domain based on the reconstructions from the
first p principal components:
ei=VpVpTxi-xi∈Rd.
As this error is explicit in space, time, and variable, it allows for
disentangling the contribution of each of these domains to the total error. This
can be achieved by estimating the (weighed) mean square error,
MSE=1w∑iwiei2.
This approach can give a better insight into the compositions of the error than
a single global error estimate based on the eigenvalues.
Pixel-wise analyses of time series
The principal components estimated as described above are ideally
low-dimensional representations of the land surface dynamics that require
further interpretation. These components have temporal dynamics that need to
be understood in detail. One crucial question is how the dynamics of a system of
interest deviate from its expected behavior at some point in time. A
classical approach is inspecting the “anomalies” of a time series, i.e., the
deviation from the mean seasonal cycle at a certain day of year.
Another key description of such system dynamics are trends. We estimated trends
of the indicators as well as of their seasonal amplitude using the Theil–Sen
estimator. The advantage of the Theil–Sen estimator is its robustness to up to
29.3 % of outliers , while
ordinary least-squares regression is highly sensitive to such values. The
calculation of the estimator consists simply in computing the median of the
slopes spanned by all possible pairs of points,
slopeij=zi-zjti-tj,
where zi is the value of the response variable at time step i and
ti the time at time step i.
In our experiments, we computed the slopes separately per pixel and principal
component with time as the predictor and the value of the principal component as
the response variable.
To test the slopes for significance, we used the Mann–Kendall statistics
and adjusted the resulting
p values with the Benjamini–Hochberg method to control for the
false discovery rate . Slopes with an adjusted
p<0.05 were deemed significant.
To identify disruptions in trajectories, breakpoint detection provides a good
framework for analysis. For the estimation of breakpoints, the generalized
fluctuation test framework was used to test for
the presence of breakpoints. The framework uses recursive residuals
such that a breakpoint is identified when the mean
of the recursive residuals deviates from zero. We used the implementation in
. For practical reasons, here we only focus on
the largest breakpoint.
Example polygons and their areas,
Eq. (); the arrows indicate the directionality.
(a) Clockwise polygon with a negative area.
(b) Counterclockwise polygon with a positive area.
(c) Chaotic polygon with a very low area.
(d) Polygon with a single intersection and both a clockwise and
counterclockwise portion. The clockwise portion is slightly larger than
the counterclockwise portion; therefore the area is slightly negative.
The analysis of a different type of dynamic considers bivariate relations. In
the context of oscillating signals it is particularly instructive to quantify
their degree of phase shift and direction – even if both signals are not
linearily related. A “hysteresis” would be such a pattern describing how the
pathways A→B and B→A between states A and
B differ . We estimated hysteresis by
calculating the area inside the polygon formed by the mean seasonal cycle of the
combinations of two components.
Area=12∑i=1nxi(yi+1-yi-1),
where n=46, the number of time steps in a year, and xi and yi are the
mean seasonal cycle of two PCs at time step i. The polygon is
circular; i.e., the indices wrap around the edges of the polygon so that x0=xn and xn+1=x1. This formula gives the actual area inside the
polygon only if it is non-self-intersecting and the vertices run
counterclockwise. If the vertices run clockwise, the area is negative. If the
polygon is shaped like an 8, the clockwise and counterclockwise parts will
cancel each other (partially) out. Trajectories that have larger amplitudes
will also tend to have larger areas as illustrated in
Fig. .
Results and discussion
In the following, we first briefly present and discuss the quality of the global
dimensionality reduction (Sect. ) and interpret the individual
components from an ecological point of view (Sect. ). We
summarize the global dynamics that we uncovered in the low-dimensional space
(Sect. ). We characterize the contained seasonal dynamics
(Sect. ), including spatial patterns of hysteresis
(Sect. ). We then describe global anomalies of the identified
trajectories (Sect. ) and discuss the identified anomalies
in depth based on local phenomena (Sect. ). Finally, we present
global trends and their breakpoints (Sect. ).
(a) Fraction of explained variance of the PCA by component. The knee at
component three suggests that components four and higher do not contribute
much to total variance.
(b) Rotation matrix of the global PCA model (also called loadings,
Eq. ). The columns of the rotation matrix describe
the linear combinations of the (centered and standardized) original
variables that make up the principal components.
PC1 is dominated by primary-productivity-related
variables,
PC2 by variables describing water availability,
and PC3 by variables describing albedo.
Values of the rotation matrix are clamped to the range [-0.5, 0.5]; the
actual range of the values is [-0.73, 0.74] and [-0.46, 0.54] for
the first three components.
Quality of the PCA
Figure a shows the explained fraction of variance
(Eq. ) for the global PCA based on the entire data cube. The two leading components explain 73 % of the variance from the 12 variables; additional components contribute relatively little additional variance (PC3 contributes 9 % and all subsequent PCs less than 7 %) each. This results in a “knee” at component 3, which suggests that two indicators are sufficient to capture the major global dynamics of the terrestrial land surface, but we will also consider the third components in the following analyses .
Reconstruction error of the data cube using varying numbers of principal components aggregated by the mean squared error. Reconstruction errors aggregated over all time steps and variables are shown in the left column: (a) using only the first component, (c) using the first two, (e) and using the first three. Corresponding right plots (b, d, f) show the mean reconstruction error aggregated by latitude.
We estimated the reconstruction error sequentially up to the first three principal components (Fig. ). Regions that do not fit the model well show a higher reconstruction error. Considering one component only, the highest reconstruction errors appear in high latitudes but decrease strongly with each additional component and nearly vanish if the third component is included.
Interpretation of the PCA
The first PC summarizes variables that are closely related to primary
productivity (GPP, LE, NEE, fAPAR) and therefore are highly interrelated (see
Fig. b). The energy for photosynthesis comes from
solar radiation, and fAPAR is an indicator for the fraction of light used for
photosynthesis. The available photosynthetic radiation is used by photosynthesis
to fix CO2 and to produce sugars that maintain the metabolism of
the plant. The total uptake of CO2 is reflected in GPP, which
is also closely related to water consumption. The flow of water within the plant
is not only essential to enable photosynthesis but also drives the transport of
nutrients from the roots. The uplift of water in the plant is ultimately driven
by transpiration – together with evaporation from soil surfaces one can observe
the integrated latent energy needed for the phase transition (LE). However,
ecosystems also respire; CO2 is produced by plants in energy-consuming processes as well as by the decomposition of dead organic materials
via soil microbes and other heterotrophic organisms. This total respiration can
be observed as terrestrial ecosystem respiration (TER). The difference between
GPP and TER is the net ecosystem exchange (NEE) rate of CO2
between ecosystems and the atmosphere . GPP and
TER are also well represented in the first dimension.
The second component represents variables related to the surface hydrology of
ecosystems (see Fig. b). Surface moisture,
evaporative stress, root-zone soil moisture, and sensible heat are all
essential indicators for the state of plant-available water. While surface
moisture is a rather direct measure, evaporative stress is a modeled quantity
summarizing the level of plant stress: a value of zero means that there is no
water available for transpiration, while a value of 1 means that transpiration
equals the potential transpiration . Root-zone soil
moisture is the moisture content of the root zone in the soil, the moisture
directly available for root uptake. If this quantity is below the wilting point,
there is no water available for uptake by the plants. Sensible heat is the
exchange of energy by a change in temperature; if there is enough water
available, then most of the surface heat will be lost due to evaporation (latent
heat), and with decreasing water availability more of the surface heat will be lost
due to sensible heat, making this an indicator of dryness as well.
We observe that the third component is most strongly related to albedo
(Fig. b). Albedo describes the overall
reflectiveness of a surface. Here we refer to broadband (400–3000 nm) surface
albedo; for an exact definition see Appendix . Light
surfaces, such as snow and sand, reflect most of the incoming radiation, while
surfaces that have a high liquid water content or active vegetation absorb most
of the incoming radiation. Local changes to albedo can be due to many causes, e.g., snowfall, vegetation greening and browning, or land use change.
The relation of PC3 to productivity and hydrology is opposite to what we would expect from an albedo axis. Because vegetation uses radiation as an energy source, albedo is negatively correlated with the productivity of vegetation, hence the negative correlation of albedo with PC1. Given that water also absorbs radiation, we can observe a negative correlation of albedo with PC2 (see Fig. b). We
observe that PC1 and PC2 are positively correlated with PC3 on the positive portion of their axes (see Fig. d and f), which means counterintuitively that the index representing albedo is positively correlated with primary productivity and moisture content.
Finally we can observe that PC1 and PC2 have a
much higher reconstruction error in snow-covered regions, which is strongly
improved by adding PC3 (see Fig. f).
Therefore the third component should be regarded mostly as a binary variable that
introduces snow cover, as the other information that is usually associated with
albedo is already contained in the first two components.
Trajectories of some points (colored lines) and the area-weighted density
over principal components one and two (the gray background shading shows the
density) for (a, c, e) the raw trajectories and (b, d, f) the mean
seasonal cycle. The trajectories are shown in the space of
PC1–PC2 (first row),
PC1–PC3 (second row), and
PC2–PC3 (third row).
The trajectories were chosen to cover a large area in the space of the first
two principal components. Some of the trajectories have an arrow indicating
the direction. The numbers illustrate the value of some variables; for units
see Table . Description of the points is as follows.
Red: tropical rain forest, 2.625∘ S, 67.625∘ W;
blue: maritime climate, 52.375∘ N, 7.375∘ E;
green: monsoon climate, 22.375∘ N, 82.375∘ E;
purple: subtropical, 34.875∘ N, 117.625∘ W;
orange: continental climate, 52.375∘ N, 44.875∘ E;
yellow: arctic climate, 72.375∘ N, 119.875∘ E.
Distribution of points in PCA space
The bivariate distribution of the first two principal components forms a
“triangle” (gray background in Fig. a). At the high end of
PC1 we find one point of the triangle in which ecosystems have a
high primary productivity (high values of GPP, fAPAR, LE, TER, and evaporation),
mostly limited by radiation. On the lower end of the first principal component we
find the other two points of the triangle describing two alternative states of
low productivity. These can happen either when the second principal component
coincides with temperature limitation (the negative extreme of the second
principal component) as seen in the lower left corner of the distribution in
Fig. a and b or due to water limitation (positive extreme of
the second principal component, the upper left corner in
Fig. a). This pattern reflects the two essential global
limitations of GPP in terrestrial ecosystems .
Both components form a subspace in which most of the variability of ecosystems
takes place. Component one describes productivity and component two the limiting
factors to productivity. Therefore, we can see that most ecosystems with high
values on component one (a high productivity) are at the approximate center of
component two. When ecosystems are found outside the center of component two,
they have lower values on component one (lower productivity) because they are
limited by water or temperature (see Fig. b).
The background shading shows the distribution of the mean seasonal cycle of
the spatial points (see Fig. ). The contour lines
represent the reconstruction of the variables from the first two principal
components. The reconstructed variables are
(a) latent heat (LE),
(b) sensible heat (H), and
(c)log10SensibleHeatLatentHeat, the log10 of the Bowen ratio.
Note that the LE and H have been considered in the construction of the PCs
and hence are a linear function of the PCs. The Bowen ratio, instead, was
not considered here and clearly responds in a nonlinear form.
To further interpret the triangle we analyze how the Bowen ratio embeds in
the space of the first two dimensions.
Energy fluxes from the surface into the atmosphere can represent either a
radiative transfer (sensible heat) or evaporation (latent heat). Their ratio is
the “Bowen ratio”, B=HLE,
(; see also Fig. ). When water is
available most of the available energy will be dissipated by evaporation, B<1, resulting in a high latent heat flux. Otherwise, the transfer by latent
heat will be low and most of the incoming energy has to be dissipated via
sensible heat, B>1. In higher latitudes, there is relatively limited
incoming radiation and temperatures are low; therefore there is not much energy
to be dissipated and both heat fluxes are low. A high sensible heat flux is an
indicator of water limitation.
Seasonal dynamics
The leading principal components represent most of the variability of the space
spanned by the observed variables, summarizing the state of a spatiotemporal
pixel efficiently. This means that the PCs track the state of a local ecosystem
over time (Fig. a) or, in the case of the mean seasonal
cycle, time of the year (Fig. b). For a
representation of the state of the first three components in time and space, see
Appendix Fig. .
A first inspection reveals a substantial overlap of seasonal cycles of very
different regions of the world. We also see that very different ecosystems may
reach very similar states in the course of the season, even though their
seasonal dynamics are very different. For instance, a midlatitude pixel (blue
trajectory in Fig. ) shows very similar characteristics to
tropical forests during peak growing season. This indicates that an ecosystem of
the midlatitudes can reach similar levels of productivity and water
availability as a tropical rain forest (see also Appendix
Fig. ). Likewise, for the first two components, many high-latitude areas show similar characteristics to midlatitude areas during winter (low latent and sensible energy release as well as low GPP), and many dry
areas such as deserts show similar characteristics to areas with a pronounced
dry season, e.g. the Mediterranean.
Depending on their position on Earth, ecosystem states can shift from limitation
to growth during the year (Fig. b, e.g. ). For example, the orange trajectory in
Fig. , an area close to Moscow, shifts from a temperature-limited state in winter to a state of very high productivity during summer.
Other ecosystems remain in a single limitation state with only slight shifts,
such as the red trajectory in Fig. . In the corner of maximum
productivity of the distribution, we find tropical forests characterized by a
very low seasonality. We also observe that very different ecosystems can have
very similar characteristics during their peak growing season; e.g. green
(located in northeast India), blue (northwest Germany), and orange (located
close to Moscow) trajectories have very similar characteristics during peak
growing season compared to the red trajectory.
The third component shows a different picture. Due to a consistent winter snow
cover in higher latitudes, the albedo is much higher and the amplitude of the
mean seasonal cycle is much larger than in other ecosystems. Other areas show
comparatively little variance on the third component and their relation to
productivity and moisture content is even positively correlated to the third
component, which is the opposite of what is expected from an albedo axis.
Mean seasonal cycle of the first three principal components (in columns)
during the seasons (in rows).
Left column: first principal component.
Middle column: second principal component.
Right column: third principal component.
Rows from top to bottom: equally spaced intervals during the year.
Values have been clamped to 0.7 times their range to increase contrast.
The global pattern of the first principal component follows the productivity
cycles during summer and winter (Fig. , left column) of the
Northern Hemisphere, with positive values (high productivity, green) during
summer and negative values (low productivity, brown) during winter. The tropics
show high productivity all year. The global pattern shows the well-known green
wave because the
first dimension integrates over all variables that correlate with plant
productivity.
The second principal component (Fig. , middle column) tracks
water deficiency: red and light red areas indicate water deficiency, light blue
areas excess water, and dark blue areas water growth limitation due to cold. Areas
which are temperature limited during winter but have a growing season during
summer, such as boreal forests, change from dark blue in winter to light blue
during the growing season. Areas which have low productivity during a dry season
change their coloring from red to light red during the growing season, e.g the
northwest of Mexico and southwest of the United States.
The third principal component (Fig. , right column) tracks
surface reflectance. Therefore we can see the highest values in the arctic
region during winter, and other areas vary much less in their reflectance throughout
the year. Again, the third component shows a counterintuitive behavior in the
midlatitudes, as it is positively correlated with productivity and therefore
shows the opposite behavior of what would be expected from an indicator
tracking albedo.
Although the principal components are globally uncorrelated, they covary locally
(see Fig. ). Ecosystems with a dry season have a negative
covariance between PC1 and PC2, while ecosystems
that cease productivity in winter have a positive covariance. Cold arid steppes
and boreal climates show a negative covariance between PC1
and PC3. While other ecosystems that have a strong seasonal
cycle show a positive correlation, many tropical ecosystems do not show a large
covariance. A very similar picture is painted between the covariance of
PC2 and PC3: boreal and steppe ecosystems
show a negative covariance, while most other ecosystems show a more or less
pronounced positive covariance, again depending on the strength of the
seasonality.
Observing the mean seasonal cycle of the principal components gives us a tool to
characterize ecosystems and may also serve as a basis for further analysis, such
as a global comparison of ecosystems .
The area inside the mean seasonal cycles of
(a) PC1–PC2,
(b) PC1–PC3, and
(c) PC2–PC3.
The area is positive if the direction is counterclockwise and negative if the
direction is clockwise. Most of the trajectories need a strong seasonal
cycle to show a pronounced hysteresis effect. If the mean seasonal cycle
intersects, the areas cancel each other out, e.g. the green trajectory
of Fig. b.
Hysteresis
The alternative return path between ecosystem states forming the hysteresis
loops arises from the ecosystem tracking seasonal changes in the environmental
condition, e.g. summer–winter or dry–rainy seasons
(Fig. b). Hysteresis is a common occurrence in ecological
systems . For instance, a hysteresis loop can be found when plotting
soil respiration against soil temperature . The
sensitivity of soil respiration to soil temperature changes seasonally due to
changing soil moisture and photosynthesis (by supplying carbon to the
rhizosphere), producing a seasonally changing hysteresis effect
. Biological variables also show a hysteresis effect in
their relations with atmospheric variables; e.g. found a hysteresis effect between seasonal
NEE, temperature, and a number of other ecosystem and climate-related variables.
Here we look at the mean seasonal cycles of pairs of indicators and the area
they enclose.
The orange trajectory (area close to Moscow) in Fig. b shows
that the paths between maximum and minimum productivity can be very different,
in contrast to the blue trajectory located in the northwest of Germany which
also has a very pronounced yearly cycle but shows no such effect.
Figure also indicates that the area inside the mean seasonal
cycles of PC1–PC2 and
PC1–PC3 shows important characteristics while
hysteresis in PC2–PC3 is a much less pronounced
feature; i.e., we can only see a pronounced area inside the yellow curve in
Fig. f.
The trajectories that show a more pronounced counterclockwise hysteresis effect in
PC1–PC2 (Fig. a) are areas
with a warm and temperate climate and partially those that have a snow climate
with warm summers, i.e., areas that have pronounced growing, dry, and wet
seasons and therefore shift their limitations more strongly during the year.
That means the moisture reserves are depleted during growing season, and therefore the
return path has higher values on the second principal component (the climatic
zones are taken from the Köppen–Geiger classification;
). We can also see that areas with dry winters tend
to have a clockwise hysteresis effect, e.g. many areas in East Asia. Due to the
humid summers there is no increasing water limitation during the summer months
which causes a decrease for PC2 instead of an increase. Other
areas with clockwise hysteresis can be found in winter dry areas in the Andes
and the winter dry areas north and south of the African rain forests. Tropical
rain forests do not show any hysteresis effect due to their low seasonality. In
general we can say that the area inside the mean seasonal cycle trajectory of
PC1–PC2 depends mostly on water availability in
the growing and non-growing seasons, i.e., the contrast of wet summer and dry
winter vs. dry summer and wet winter.
The hysteresis effect on PC1–PC3
(Fig. b) shows a pronounced counterclockwise MSC trajectory
mostly in warm temperate climates with dry summers, while it shows a clockwise
MSC trajectory in most other areas; again tropical rain forests are an exception
due to their low seasonality. The most pronounced clockwise MSC trajectories can
be found in tundra climates in arctic latitudes, where we have a consistent
winter snow cover and a very short growing period.
A counterclockwise rotation can be found in summer dry areas, such as the
Mediterranean and California, but also some more humid areas, such as the
southeast United States and the southeast coast of Australia. In these areas
we can find a decrease for PC3 during the non-growing phase
which probably corresponds to a drying out of the vegetation and soils.
The hysteresis effect on PC2–PC3
(Fig. c) mostly depends on latitude. There is a large
counterclockwise effect in the very northern parts, due to the large amplitude
of PC3. The amplitude gets smaller further south until the
rotation reverses in winter dry areas at the northern and southern extremes
of the tropics and disappears at the equatorial humid rain forests.
We can see that the hysteresis of pairs of indicators represents large-scale
properties of climatic zones. The enclosed area and the direction of the rotation provide interesting
information. Hysteresis can provide
information on the seasonal availability of water, seasonal dry periods, or
snowfall. With the method presented here, we can not observe intersecting
trajectories, which would probably provide even more interesting insights (e.g. the green trajectory in Fig. b).
Anomalies of the first three principal
components. The brown–green contrast shows the anomalies on
PC1, a relative low productivity or greening, respectively.
The blue–red contrast shows the anomalies on PC2, a relative
wetness or dryness, respectively. The brown–purple contrast shows the anomaly
on PC3, a relative deviation in albedo.
Panels (a), (e), and (i) are maps showing the anomalies of
PC1–PC3, respectively, on 1 January 2001.
Panels (b), (c), and (d) show longitudinal cuts of
PC1–PC3, respectively, at the red vertical line in
(a). The effects of the floods on the Horn of
Africa (2006) and the Russian heat wave (2010) are highlighted by circles.
Panels (f), (g), and (h) show longitudinal cuts of
PC1–PC3, respectively, at the red vertical line in
(e). Strong droughts in the Amazon during 2005 and
2010 can be observed as large red spots on the fringes of the Amazon basin
(highlighted by circles).
Panels (j), (k), and (l) show longitudinal cuts of
PC1–PC3, respectively, at the red vertical line in
(i). A strong snowfall event affecting central and
southern China is marked as circles.
Anomalies of the trajectories
The deviation of the trajectories from their mean seasonal cycle should reveal
anomalies and extreme events. These anomalies have a directional component which
makes them interpretable the same way the original PCs are. Therefore one can
infer the state of the ecosystem during an anomaly. For instance the well-known
Russian heat wave in summer 2010 appears in
Fig. as a dark brown spot in the southern part of the
affected area, indicating lower productivity, and as a thin green line in the
northern parts, indicating increased productivity. This confirms earlier
reports in which only the southern agricultural ecosystems were negatively
affected by the heat wave, while the northern predominantly forest ecosystems
rather benefited from the heat wave in terms of primary productivity
.
Another example of an extreme event that we find in the PCs is the very wet
November rainy season of 2006 in the Horn of Africa after a very dry rainy
season in the previous year. This event was reported to bring heavy rainfall and
flooding events which caused an emergency for the local population but also
increased ecosystem productivity . The rainfall
event appears as green and blue spots in Fig. b and c,
preceded by the drought events which appear as red and brown spots.
Figure f and g also show the strong drought events in
the Amazon, particularly the droughts of 2005 and 2010
appear strongly north and
south of the Amazon basin. The central Amazon basin does not show these strong
events, because the observable response of the ecosystem was buffered due to the
large water storage capacity in the central Amazon basin.
Another extreme event that can be seen is the extreme snow and cold event
affecting central and south China in January 2008, causing the temporary
displacement of 1.7 million people and economic losses of approximately USD 21 billion . This event shows up clearly on
PC2 and PC3 as cold and light anomalies,
respectively (see Fig. k and f).
Trajectories of the first two principal components for single pixels. (a) Deforestation increases the seasonal amplitude of the first two PCs
(Brazilian rain forest, 9.5∘ S, 63.5∘ W). The red line shows the trajectory
before 2003 and the blue line the trajectory 2003 and later. A strong increase
in seasonal amplitude can be observed after 2003. (b) The heat wave is
clearly visible in the trajectory (red, Russian heat wave, summer 2010, 56∘ N,
45.5∘ E).
(c) Rainfall in the short rainy season (November–December) influences
agricultural yield and can cause flooding (extreme flooding after drought,
November 2006, 3∘ N, 45.5∘ E).
(d) The European heat wave in summer 2003 was one of the strongest on record
(France, 47.2∘ N, 3.8∘ E). The mean seasonal cycle of the trajectories is shown
in purple.
Single trajectories
Observing single trajectories can give insight into past events that happened at
a certain place, such as extreme events or permanent changes in ecosystems. The
creation of trajectories is an old method used by ecologists, mostly on species
assembly data of local communities, to observe how the composition changes over
time (e.g. ).
In this context, we observe how the states of the ecosystems inside the
grid cell shift over time, which comprises a much larger area than a local
community but is probably also less sensitive to very localized impacts than a
community-level analysis. One of the main differences of the method applied here
from the classical ecological indicators is that the trajectories observed here
are embedded into the space spanned by a single global PCA, and therefore we can
compare a much broader range of ecosystems
directly.
(a, c, e) Trends in PC1–PC3,
respectively (2001–2011).
(b, d, f) Bivariate distribution of trends. Trends were calculated
using the Theil–Sen estimator. Panels (a), (c), and (e) show significant trends
only (p<0.05, Benjamini–Hochberg adjusted).
The seasonal amplitude of the trajectory in the Brazilian Amazon increases due
to deforestation and crop growth cycles. Figure a shows an
area in the Brazilian Amazon in Rondônia (9.5∘ S,
63.5∘ W) which was affected by large-scale land use change and
deforestation. It can be seen that the seasonal amplitude increases strongly
after the beginning of 2003. This increased amplitude could be due to
any of the following reasons or a combination of them: deforestation decreases
water storage capability and dries out soils, causing larger variability in
ecosystem productivity. Therefore, during periods of no rain, large-scale
deforestation can cause a shift in local-scale circulation patterns, causing
lower local precipitation . Crop growth and harvest
cause an increased amplitude in the cycle of productivity. An analysis of the
trajectory can point to the nature of the change; however finding the exact
causes for the change requires a deeper analysis.
The 2010 Russian heat wave has a very clear signal in the trajectories.
Figure b shows the deviation of the trajectory during the
Russian heat wave (red line) in an area east of Moscow (56∘ N, 45.5∘ E). In the
southern grass- and croplands, the heat wave caused the productivity to drop
significantly during summer due to a depletion of soil moisture. In the northern
forested parts affected, the heat wave caused an increase in ecosystem
productivity during spring due to higher temperatures combined with sufficient
water availability. This shows the compound nature of this extreme event (see
Fig. a and ). The
analysis of the trajectory points directly towards the different types of
extremes and responses that happened in the biosphere during the heat wave.
Variability of rainfall during the November rainy season in the Horn of Africa
(3∘ N, 45.5∘ E, Fig. c) shows the trajectory and points in
November of the observed time. The November rain has implications for food
security because the second crop season depends on it. In 2006, the rainfall
events were unusually strong and caused widespread flooding and disaster but
also higher ecosystem productivity (see also Fig. ). This
was especially devastating because it followed a long drought that caused crop
failures. Note also the two rainy seasons in the mean seasonal cycle (purple
line in Fig. c).
The 2003 European heat wave is reflected in the trajectories just like the 2010
Russian heat wave. Figure d shows the trajectory during the
August 2003 heat wave in Europe (France, 47.2∘ N, 3.8∘ E). The heat wave was
unprecedented and caused large-scale environmental, health, and economic losses
.
The 2010 heat wave was stronger than the 2003 heat wave but the strongest parts of
the 2010 heat wave were in eastern Europe (see Fig. ),
while the center of the 2003 heat wave was located in France.
As we have seen here, observing single trajectories in reduced space can give us
important insights into ecosystem states and changes that occur. While the
trajectories can point us towards abnormal events, they can only be the starting
points for deeper analysis to understand the details of such state changes.
Trends in trajectories
The accumulation of CO2 in the atmosphere should cause an
increase in global productivity of plants due to CO2
fertilization, while larger and more frequent droughts and other extremes may
counteract this trend. Satellite observations and models have shown that during
the last decades the world's ecosystems have greened up during growing seasons.
This is explained by CO2 fertilization, nitrogen deposition,
climate change, and land cover change
.
Tropical forests especially showed strong greening trends during the growing season.
General patterns of trends that can be observed are a positive trend (higher
productivity) on the first principal component in many arctic regions. Many of
these regions also show a wetness trend, with the notable exception of the
western parts of Alaska, which have become drier.
This is important, because wildfires play a major role in these ecosystems
.
These changes are also accompanied by a decrease for PC3 due to a
loss in snow cover.
A large-scale dryness trend can also be observed across large parts of western
Russia. Increasing productivity can also be observed for large parts of the
Indian subcontinent and eastern Australia. Negative trends in the first
component can also be observed: they are generally smaller and appear in regions
around the Amazon and the Congo Basin, but also in parts of western Australia.
The main difference from previous analyses on the observations presented here is
that , for example, looked only at trends during the growing
season, while this analysis uses the entire time series to calculate the slope.
In the Amazon basin, we find a dryness trend accompanied by a decrease in
productivity and a slight increase in PC3. In the Congo Basin,
we find a wetness trend and an increasing productivity in the northern parts,
while the southern part and woodland south of the Congo Basin show a strong
dryness trend with decreased productivity. This is different to the findings of
, who found a widespread browning of vegetation in
the entire Congo Basin for the April–May–June seasons during the period
2000–2012. The findings of are not reflected in our
data, especially compared to the areas surrounding the Congo Basin. We can find
only minor browning effects inside the basin, and our findings are more in line
with the global greening , which shows a browning mostly
outside the Congo Basin.
In eastern Australia we find a strong wetness and greenness trend which is due
to Australia having a “millennium drought” since the mid-1990s with a peak
in 2002 and extreme floods
in 2010–2011 .
Large parts of the Indian subcontinent show a trend towards higher productivity
and an overall wetter climate. The greening trend in India happens mostly over
irrigated cropland. However browning trends over natural vegetation have been
observed but do not emerge in our analysis . A very
notable greening and wetness trend can be observed in Myanmar due to an increase
in intense rainfall events and storms, although the central part experienced
some strong droughts at the same time . In Myanmar
we also find one of the strongest trends in PC3 outside of the
Arctic.
In large parts of the Arctic, a trend towards higher productivity can be
observed. Vegetation models attribute this general increase in productivity to
CO2 fertilization and climate change. The changes also cause
changes to the characteristics of the seasonal cycles
. found a decreased
seasonal amplitude of surface temperature over northern latitudes due to winter
warming.
The seasonal amplitude of atmospheric CO2 concentrations has
been increasing due to climate change, causing longer growing seasons and
changing vegetation cover in northern ecosystems
.
Therefore we checked for trends in the seasonal amplitude, but because each time
series only consists of 11 values (one amplitude per year), after adjusting the
p values for false discovery rate, we could not find a
significant slope. However, there were many significant slopes with the
unadjusted p values; see the appendix,
Fig. .
Another way to detect changes to the biosphere consists in the detection of
breakpoints, which has been applied successfully to detect changes in global
normalized difference vegetation index (NDVI) time series or generally
to detect changes in time series . A proof-of-concept analysis can be found in Fig. . We hope that
applying this method to indicators instead of variables can detect a wider range
of breakpoints analyzing a single time series.
Relations to other PCA-type analyses
One of the most popular applications of PCA in meteorology are EOFs, which
typically apply PCA to a single variable, i.e., on a dataset with the
dimensions lat×long×time, although EOFs can be
calculated from multiple variables. EOFs can be calculated in S mode and
R mode. If we matricize our data cube so that we have time in rows and
lat×long×variables in columns, then S mode
PCA works on the correlation matrix of the combined variable and space
dimension. In T mode, the PCA works on the correlation matrix formed by the
time dimension . The PCA presented here works slightly
differently. (1) We performed a different matricization
(lat×long×time in rows and variables in
columns) and then (2) the PCA works on the correlation matrix formed by the
variables. Therefore in this framework we could call this a V mode PCA.
Ecological analyses usually use PCA with matrices of the shape
object×descriptors. When calculating the PCA on the
correlation matrix formed by the objects, then it is called a Q mode
analysis. When the PCA is applied to the correlation matrix formed by the
variables, then it is called an R mode analysis
. The PCA carried out in this study is closest to an
R mode analysis. In the present case the descriptors are the various data
streams and the objects are the spatiotemporal pixels.
Using PCA as a method for dimensionality reduction means that we are assuming
linear relations among features. A nonlinear method could possibly be more
efficient in reducing the number of variables but would also have significant
disadvantages. In particular, nonlinear methods typically require tuning
specific parameters, objective criteria are often lacking, a proper weighting of
observations is difficult, the methods are often not reversible, and it is
harder to interpret the resulting indicators due to their nonlinear nature
. The salient feature of PCA is that an inverse
projection is well defined and allows for a deeper inspection of the errors,
which is not the case for nonlinear methods which learn a highly flexible
transformation that is hard to invert. Therefore interpretability of the
transform in meaningful physical units in the input space is often not possible.
In the machine-learning community, this problem is known as the “pre-imaging
problem” and is a matter of
current research.
Conclusions
To monitor the complexity of the changes occurring in times of an increasing
human impact on the environment, we used PCA to construct indicators from a
large number of data streams that track ecosystem state in space and time on a
global scale. We showed that a large part of the variability of the terrestrial
biosphere can be summarized using three indicators. The first emerging indicator
represents carbon exchange, the second indicator shows the availability of water
in the ecosystem, while the third indicator mostly represents a binary variable
that indicates the presence of snow cover. The distribution in the space of the
first two principal components reflects the general limitations of ecosystem
productivity. Ecosystem production can be limited by either water or energy.
The first three indicators can detect many well-known phenomena without
analyzing variables separately due to their compound nature. We showed that the
indicators are capable of detecting seasonal hysteresis effects in ecosystems,
as well as breakpoints, e.g. large-scale deforestation. The indicators can also
track other changes to the seasonal cycle such as patterns of changes to the
seasonal amplitudes and trends in ecosystems. Deviations from the mean seasonal
cycle of the trajectories indicate extreme events such as the large-scale
droughts in the Amazon during 2005 and 2010 and the Russian heat wave of 2010.
The events are detected in a similar fashion as with classical multivariate
anomaly detection methods while directly providing information on the underlying
variables.
Using multivariate indicators, we gain a high level overview of phenomena in
ecosystems, and the method therefore provides an interesting tool for analyses
where it is required to capture a wide range of phenomena which are not
necessarily known a priori. Future research should consider nonlinearities,
adding data streams describing other important biosphere variables (e.g. related to biodiversity and habitat quality), and including different
subsystems, such as the atmosphere or the anthroposphere.
Description of variables
Variables used describing the biosphere can be found in Table .
Here we provide a more complete description of all variables.
Black-sky albedo is the reflected fraction of total incoming radiation
under direct hemispherical reflectance, i.e., direct illumination
. This dataset is the broadband surface albedo including
the visible, the near-infrared, and the shortwave-infrared spectrum (400–3000 nm). It is
derived from the SPOT4-VEGETATION, SPOT5-VEGETATION2, and MERIS satellite
sensors.
White-sky albedo is the reflected fraction of total incoming radiation
under bihemispherical reflectance, i.e., diffuse illumination
. Together with black-sky albedo it can be used to
estimate the albedo under different illumination conditions. This dataset is the
broadband surface albedo including the visible, the near-infrared, and the
shortwave-infrared spectrum (400–3000 nm). This dataset is derived from the
SPOT4-VEGETATION, SPOT5-VEGETATION2, and MERIS satellite sensors.
Evaporation (mm d-1) is the amount of water evaporated per day, depending on the amount of available water and energy.
This dataset is based on the GLEAMv3 model , using satellite data from ESA CCI and SMOS to derive a number of variables.
Evaporative stress is modeled water stress for plants. Zero means that the vegetation has no water available for transpiration and 1 means that transpiration equals potential transpiration.
This dataset is based on the GLEAMv3 model , using satellite data from ESA CCI and SMOS to derive a number of variables.
fAPAR is the fraction of absorbed photosynthetically active radiation, a proxy for plant productivity . This dataset is based on the GlobAlbedo dataset (http://globalbedo.org, last access: 23 April 2020) and the MODIS fAPAR and leaf area index (LAI) products.
Gross primary productivity (GPP) is (gC m-2 d-1) the total amount of carbon fixed by photosynthesis .
This dataset is derived from upscaling eddy covariance tower observations to a global scale using machine-learning methods.
Terrestrial ecosystem respiration (TER) is (gC m-2 d-1) the total amount of carbon respired by the ecosystem, including autotrophic and heterotrophic respiration .
This dataset is derived from upscaling eddy covariance tower observations to a global scale using machine-learning methods.
Net ecosystem exchange (NEE) is (gC m-2 d-1) the total exchange of carbon of the ecosystem with the atmosphere NEE=GPP-TER.
This dataset is derived from upscaling eddy covariance tower observations to a global scale using machine-learning methods.
Latent energy (LE) is (W m-2) the amount of energy lost by the surface due to evaporation .
This dataset is derived from upscaling eddy covariance tower observations to a global scale using machine-learning methods.
Sensible heat (H) is (W m-2) the amount of energy lost by the surface due to radiation .
This dataset is derived from upscaling eddy covariance tower observations to a global scale using machine-learning methods.
Root-zone soil moisture is (m3 m-3) the moisture content of the root zone.
This dataset is based on the GLEAMv3 model , using satellite data from ESA CCI and SMOS to derive a number of variables.
Surface soil moisture is (mm3 mm-3) the soil moisture content at the soil surface.
This dataset is based on the GLEAMv3 model , using satellite data from ESA CCI and SMOS to derive a number of variables.
Time–space patterns of Components 1–3
Time and space patterns of PC1–PC3, where the cut points are the same as in Fig. .
The brown–green contrast shows the state of PC1,
from low to high productivity.
The blue–red contrast shows the state of PC2,
from cold to dry.
The brown–purple contrast shows the state of PC3,
from dark to light.
Panels (a), (e), and (i) are maps showing the state of PC1–PC3, respectively, on
1 January 2001.
Panels (b), (c), and (d) show longitudinal cuts of PC1–PC3, respectively, at the red
vertical line in (a).
Panels (f), (g), and (h) show longitudinal cuts of PC1–PC3, respectively, at the red
vertical line in (e).
Panels (j), (k), and (l) show longitudinal cuts of PC1–PC3, respectively, at the red
vertical line in (i).
Mean seasonal cycle extrema
The minimum (a, c, e) and maximum (b, d, f) mean seasonal cycles of
GPP (a, b),
latent heat (c, d), and
sensible heat (e, f).
This illustrates the similarity of possibly very different ecosystems in terms of productivity and limitations.
During peak growing season, many midlatitude areas have a similar productivity and latent energy release as tropical rain forests (b, d).
The highest maximum seasonal sensible heat loss can be found in dry areas around the world and is lowest in areas with a wet climate such as tropical rain forests and maritime climates (f).
Spatial covariances of the components
Pairwise covariances of the first three principal components mean seasonal cycles by space.
(a)cov(PC1,PC2),
(b)cov(PC1,PC3), and
(c)cov(PC2,PC3).
The bar charts show the distribution of the covariances.
It can be seen that although two principal components are globally uncorrelated by their way of construction, they covary locally.
Changes in the seasonal amplitude
Trends in the amplitude of the yearly cycle, 2001–2011. Only Theil–Sen
estimators for significant slopes (p<0.05, unadjusted) are
shown. Because there is only a single amplitude per year and therefore
only 11 data points per time series, the Benjamini–Hochberg adjusted
p values are not significant.
Breakpoints in trajectories
Breakpoint detection,
(a) on PC1,
(b) on PC2, and
(c) on PC3. The color indicates the year of the biggest
breakpoint if a significant breakpoint was found, with gray if there was no
significant breakpoint found.
As the environmental conditions change, due to climate change and human
intervention, the local ecosystems may change gradually or abruptly. Detecting
these changes is very important for monitoring the impact of climate change and
land use change on the ecosystems. We applied breakpoint detection to the
trajectories (Fig. ).
Breakpoints on the first component were found in the entire Amazon, and the
largest breakpoint is dated to the year 2005 during the large drought event. The
entire eastern part of Australia shows its largest breakpoint towards the end of
the time series because of a La Niña event, which caused lower temperatures and
higher rainfall than usual during the years 2010 and 2011.
Code and data availability
The data are available and can be processed at
https://www.earthsystemdatalab.net/index.php/interact/data-lab/, last
access: 30 March 2020.
The exact dataset and a docker container to reproduce the analysis can be
found under 10.5281/zenodo.3733766.
The code to reproduce this analysis is available under
10.5281/zenodo.3733783 and
https://github.com/gdkrmr/summarizing_the_state_of_the_biosphere, last access: 23 April 2020.
Author contributions
GK and MDM designed the study in collaboration with MR and GCV. GK conducted
the analysis and wrote the manuscript with contributions from all co-authors.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
We thank Fabian Gans and German
Poveda for useful discussions. We thank Jake Nelson for proofreading a previous version of the
manuscript. We thank Gregory Duveiller and the three anonymous reviewers for very helpful suggestions and
Kirsten Thonicke for editorial advice that improved the manuscript greatly.
Financial support
This study is funded by the Earth System Data Lab – a project by the European Space Agency. Miguel D. Mahecha and Markus Reichstein have been supported by the Horizon 2020 EU project BACI under grant agreement no. 640176.
Gustau Camps-Valls' work has been supported by the EU under the ERC consolidator grant SEDAL-647423.
The article processing charges for this open-access publication were covered by the Max Planck Society.
Review statement
This paper was edited by Kirsten Thonicke and reviewed by Gregory Duveiller and three anonymous referees.
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