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remote sensing
Article
Spectro-Temporal Heterogeneity Measures from
Dense High Spatial Resolution Satellite Image
Time Series: Application to Grassland Species
Diversity Estimation
Mailys Lopes 1,*, Mathieu Fauvel 1, Annie Ouin 1and Stéphane Girard 2
1Dynafor, University of Toulouse, INRA, INPT, INPT-EI PURPAN, Chemin de Borde-Rouge,
31326 Castanet Tolosan, France; mathieu.fauvel@ensat.fr (M.F.); annie.ouin@ensat.fr (A.O.)
2Team Mistis, Inria Grenoble Rhône-Alpes, LJK, 655 Avenue de l’Europe, 38334 Montbonnot, France;
stephane.girard@inria.fr
*Correspondence: mailys.lopes@inra.fr; Tel.: +33-534-323927
Received: 25 July 2017 ; Accepted: 22 September 2017; Published: 25 September 2017
Abstract:
Grasslands represent a significant source of biodiversity that is important to monitor over
large extents. The Spectral Variation Hypothesis (SVH) assumes that the Spectral Heterogeneity
(SH) measured from remote sensing data can be used as a proxy for species diversity. Here, we
argue the hypothesis that the grassland’s species differ in their phenology and, hence, that the
temporal variations can be used in addition to the spectral variations. The purpose of this study is to
attempt verifying the SVH in grasslands using the temporal information provided by dense Satellite
Image Time Series (SITS) with a high spatial resolution. Our method to assess the spectro-temporal
heterogeneity is based on a clustering of grasslands using a robust technique for high dimensional
data. We propose new SH measures derived from this clustering and computed at the grassland
level. We compare them to the Mean Distance to Centroid (MDC). The method is experimented on
192 grasslands from southwest France using an intra-annual multispectral SPOT5 SITS comprising
18 images and using single images from this SITS. The combination of two of the proposed SH
measures—the within-class variability and the entropy—in a multivariate linear model explained the
variance of the grasslands’ Shannon index more than the MDC. However, there were no significant
differences between the predicted values issued from the best models using multitemporal and
monotemporal imagery. We conclude that multitemporal data at a spatial resolution of 10 m do not
contribute to estimating the species diversity. The temporal variations may be more related to the
effect of management practices.
Keywords:
spectral variation hypothesis; spectral heterogeneity; dense satellite image time series;
alpha-diversity; grasslands
1. Introduction
Grasslands represent one of the largest land covers on Earth. They are an important source of
biodiversity in farmed landscapes, thanks to their plant and animal composition [
1
,
2
]. This biodiversity
supports many ecosystem services such as carbon regulation, erosion regulation, food production,
biological control of pests and crop pollination [
3
,
4
]. However, global grassland surface area is
decreasing, and grassland diversity is declining because of agriculture intensification, abandonment
and urbanization [
3
], leading to a loss of biodiversity and associated services. To understand
these effects, it is of utmost importance to determine and monitor grassland species diversity and
composition over large extents.
Remote Sens. 2017,9, 993; doi:10.3390/rs9100993 www.mdpi.com/journal/remotesensing
Remote Sens. 2017,9, 993 2 of 23
Biodiversity can be characterized by alpha-diversity [
5
], which is related to the diversity in species
of a community. Alpha-diversity is commonly measured by the species richness (number of species in
the sampling area). However, this diversity can also be quantified with heterogeneity measures, such
as the Shannon index [
6
], which combines richness and evenness (even abundance between species),
and the Simpson index [7], which measures the dominance of species over the others.
Usually, ecologists measure and monitor biodiversity during field surveys. However, these
surveys are time consuming, and they require important human and material resources, making them
costly and limited in time and space [
8
,
9
]. Moreover, they tend to be influenced by the assessor [
10
],
which can make the comparison between study areas difficult. Ecological field surveys are thus limited
to a local scale, whereas there is an important need to monitor biodiversity over larger extents (national
to international scales). To circumvent this issue, remote sensing appears to be an appropriate tool.
Indeed, thanks to the broad spatial coverage and regular revisit frequency of satellite sensors, remote
sensing provides continuous, regular and repeatable observations over large extents [
11
,
12
]. It has
already proven its ability for habitat mapping [
11
,
13
], and it can be seen as an indirect approach for
biodiversity estimation [8,9].
Considerable progress has been made in the remote sensing of biodiversity during the last few
decades [
10
]. Many works are based on the Spectral Variation Hypothesis (SVH) [
14
,
15
], which
assumes that the spectral heterogeneity in the image is correlated with the heterogeneity of the
habitat.
The diversity
of species being related to the heterogeneity of the habitat [
16
,
17
], the spectral
heterogeneity can be used as a proxy for species diversity [10].
The measures of grasslands’ species diversity in the context of SVH have been discussed in the
work of Oldeland et al. [
18
]. Most of the studies are based on species richness. However, this measure
gives equal weight to every species, regardless of their proportion in the community. The contribution
of rare individuals in the spectral heterogeneity can be doubtful. Abundance-based measures of species
diversity, such as the Shannon index, give more weight to species with higher proportions. Therefore,
these measures should be preferred to species richness in the context of SVH [18,19].
Many ways to quantify the Spectral Heterogeneity (SH) and to relate it to alpha-diversity have
been developed in the remote sensing community [
8
]. SH has been quantified with the standard
variation or the coefficient of variation of the Normalized Difference Vegetation Index (NDVI) [
14
,
20
],
using Principal Components Analysis (PCA) [
18
,
21
] and with the mean Euclidean distance to the
spectral centroid [
15
,
18
,
19
,
22
]. However, these measures do not describe well the variability in the
spectral space. Recently, Féret and Asner [
23
] developed an original approach to account for both
the spatial and the spectral information of imaging spectroscopy. Their approach is based on the
hypothesis that species can be categorized according to their spectral reflectance. They performed an
unsupervised clustering using the k-means algorithm, assigning each pixel of the image to a cluster
called a “spectral species”. Then, they computed the “spectral species distribution”, which is the
entropy (Shannon index) of the spectral species and which was found highly correlated with the
ground Shannon index of a tropical forest. However, since they were using hyperspectral data with
very high spatial resolution (2 m), simplifying steps were necessary prior to the clustering because
k-means is not suitable for high dimensional data, resulting in a significant loss of spectral information
and possibly of the heterogeneity.
Most of the aforementioned works were performed with hyperspectral data issued from a field
spectroradiometer or an airborne sensor, thus with a very high spatial resolution. Although these
works showed good results, they were limited to a very local scale, because of the costs involved
by such a mission. Conversely, new satellite missions for continuous vegetation monitoring, such
as Sentinel-2 [
24
], provide freely multispectral time series with high spatial and high temporal
resolutions. Therefore, a tradeoff could be considered by using time series of satellite images
to monitor grasslands biodiversity over large extents. Indeed, species communities differ in
their temporal and seasonal behaviors, i.e., their phenology, making the phenological diversity
related to the species
diversity [25,26].
Therefore, in this study, we argue the hypothesis that the
Remote Sens. 2017,9, 993 3 of 23
spectro-temporal heterogeneity of a community can be related to its species diversity, such as suggested
by
Rocchini et al.
[
10
]: “Multispectral satellite sensors with high to very high spatial resolution and
short revisit period, such as Sentinel-2, Ven
µ
s, and other high spatial resolution multispectral sensors
may be good candidates for biodiversity mapping based on spectro-temporal variations”. We could
name this hypothesis the “Spectro-Temporal Variation Hypothesis” (STVH) in reference to the SVH.
However, the use of both the spectral and the temporal information in dense time series involves
big data issues. Indeed, we have to deal with a high number of spectro-temporal variables, but with a
small number of samples, because grasslands in Europe are relatively small objects in the landscape
(around one hectare). Even with high spatial resolution sensors (around 10 m), on average, only a
hundred pixels compose these grasslands, while there is about the same number of spectro-temporal
variables during a year of acquisitions. Clustering algorithms and measures of spectral heterogeneity
that are suitable for high dimensional data are thus required.
The objective of this study is to verify if the spectro-temporal variations in grasslands are related
to their species diversity, using dense Satellite Image Time Series (SITS) with a high spatial resolution
(10 m). To verify this hypothesis, we propose to link spectro-temporal and spectral-only heterogeneity
measures derived from the unsupervised clustering of grasslands to their species diversity through
linear regression models. To address the high dimensional issue, we propose to use a robust clustering
algorithm that does not require dimension reduction prior to the clustering. We introduce new SH
measures derived from the clustering and computed at the grassland level, to be consistent with
ecological studies that usually estimate the biodiversity at the grassland level. The SH measures make
possible the comparison of grasslands of varying sizes.
The proposed method is experimented on the Shannon index measured in 192 grasslands from
southwest France with a dense intra-annual SPOT5 (Take5) multispectral time series and with single
images extracted from this SITS. Note that contrary to [
23
], the spatial units are determined by the
grasslands’ spatial limits that are defined in a GIS, such as a land cover database.
In the next section, we present the materials used in this study. Then, the method proposed to
measure the spectro-temporal heterogeneity is detailed in Section 3. Finally, the results are given in
Section 4and discussed in Section 5. Conclusions are given in Section 6.
2. Materials
2.1. Study Area
The study area is part of the Long-Term Ecological Research site “Coteaux et Vallées de Gascogne”
(LTER_EU_FR_003), located in Gascony, in southwest France near the city of Toulouse (43
◦
17
0
N, 0
◦
54
0
E,
Figure 1). This hilly area of around 900 km
2
is characterized by a mosaic of crops, small woods and
grasslands. It is dominated by mixed crop-livestock farming. Grasslands provide food for cattle
by grazing and/or producing hay or silage. They range from monospecific grasslands sown with
ryegrass (improved with mineral fertilizing and mown up to three times a year) to semi-natural
grasslands composed of spontaneous plant species (not fertilized and mown once a year). Grasslands
are mainly located on steep slopes, whereas annual crops are in the valleys on the most productive
lands.
The climate
is sub-Atlantic with sub-Mediterranean and mountain influences (mean annual
temperature, 12.5 ◦C; mean annual precipitation, 750 mm) [27,28].
Remote Sens. 2017,9, 993 4 of 23
Figure 1.
Location of the study area in southwest France and of the grasslands within the study area. The
background is an aerial photograph issued from the French orthophoto database “BD ORTHO
R
” (
c
IGN).
2.2. Satellite Image Time Series
The time series issued from the SPOT5 (Take5) mission (https://www.spot-take5.org) was used
in this study. Eighteen images at a spatial resolution of 10 m were available from April–September
2015 (Table 1).
Table 1. Characteristics of SPOT5 (Take5) imagery used in this study.
Pixel Size 10 m
Spectral bands
B1 “Green” (500–590 nm)
B2 “Red” (610–680 nm)
B3 “Near-Infrared” (780–890 nm)
B4 “Short Wave Infrared” (1580–1750 nm)
Acquisition dates
20-04-2015, 25-04-2015, 30-04-2015, 10-05-2015, 20-05-2015, 04-06-2015,
24-06-2015, 29-06-2015, 04-07-2015, 09-07-2015, 14-07-2015, 19-07-2015,
24-07-2015, 13-08-2015, 18-08-2015, 28-08-2015, 02-09-2015, 07-09-2015
The images were orthorectified, radiometrically and atmospherically corrected by the French
Spatial Agency (CNES). They were provided in reflectance with a mask of clouds and shadows issued
from the MACCS (Multi-sensor Atmospheric Correction and Cloud Screening) processor [29].
To reconstruct the time series due to missing data (clouds and their shadows), the Whittaker
filter [
30
,
31
] was applied pixel-by-pixel on the reflectances in each spectral band. The smoothing
parameter was the same for all the pixels and all the spectral bands. It was fixed to 10
4
after an ordinary
cross-validation done on a subset of the pixels.
Remote Sens. 2017,9, 993 5 of 23
The smoothed time series associated with each of the spectral bands were
concatenated to get a unique spectro-temporal vector
xk
per pixel
k
, such as
xk=
[xkB1(t1)
,
. . .
,
xkB1(tT)
,
xkB2(t1)
,
. . .
,
xkB2(tT)
,
xkB3(t1)
,
. . .
,
xkB1(tT)
,
xkB4(t1)
,
. . .
,
xkB4(tT)]>
, where
xkB1(tj)
is the value of pixel
k
in band
B
1 at the
j
-th acquisition, and
T=
18 is the number
of acquisitions.
2.3. Field Data
Grasslands composing the dataset have been monitored for several years in the frame of different
research projects. They represent more than 200 managed grasslands. The management practices and
their intensity (i.e., number of mowings, intensity of grazing) are known for some grasslands.
The grasslands were digitalized in a GIS from aerial photographs (“BDORTHO
R
” French
database of orthophotos,
c
IGN). For this study, an inner buffer of 10 m was removed from all the
grasslands’ polygons to avoid edge effects due to mixed pixels at the parcel edges. After rasterizing
the polygons, only the grasslands composed of at least 10 pixels of 10-m resolution, i.e., having an
area higher than 1000 m2, were kept to ensure a minimum number of pixels per grassland. After this
treatment, the dataset is composed of 192 grasslands. Their location can be seen in Figure 1.
A botanical survey was conducted in the spring of 2015 and 2016 after the flowering and before
the mowing (April–May), to record the botanical composition of these grasslands. The grassland
composition is supposed to remain stable from one year to the following year. The survey consisted of
an exhaustive visual recording of all the species present in the grassland. The recording was processed
while walking on a “W-shaped” transect, and the percentage of cover of each species was estimated
at the grassland scale. The cover was estimated with the Braun-Blanquet abundance-dominance
coefficients [
32
] for each present species (*: one individual, +: cover <1%, 1: 1–5%, 2: 5–25%, 3: 25–50%,
4: 50–75%, 5: 75–100%). An average abundance was kept for each coefficient (*: 0.1%, +: 0.2%, 1: 2.5%,
2: 15%, 3: 37.5%, 4: 62.5%, 5: 87.5%). From these absolute abundance-dominance covers, relative
proportions of cover in the grassland can be retrieved for each species.
In this study, the species richness (number of species in the plot) was not considered because it
accounts for rare species in the grassland, which might impact its functional diversity, but which do not
have an impact on the spatio-spectral heterogeneity [
18
]. Therefore, an abundance-based biodiversity
index was preferred to measure the alpha-diversity, the Shannon index (H):
H=−
R
∑
s=1
psln ps(1)
where
ps
is the proportion of the
s
-th species with
∑R
s=1ps=
1 and
R
is the total number of species in
the grassland (species richness). H values usually range between 0 and 5, increasing as the diversity
increases. The Shannon index is a measure of the entropy in the grassland. It reflects the evenness
of a population: a community with one or two dominating species is considered less diverse than a
community that has different species with a similar number of individuals [18].
Most of the grasslands are semi-natural grasslands with a medium to high level of biodiversity
(H > 2) (Figure 2a). Only a few are monospecific grasslands (sown with one species, H < 0.5). Three
examples of grasslands’ temporal profiles along the H axis, from a low to a high level of biodiversity,
are shown in Figure 3.
The average grassland size in pixels is 135 pixels, and the median is 94 pixels (Figure 2b).
In total
,
there are 25,903 pixels in the dataset.
Remote Sens. 2017,9, 993 6 of 23
0 0.5 1 1.5 2 2.5 3 3.5
0
10
20
H
Number of grasslands
0 200 400 600 800
0
10
20
30
40
Number of pixels ni
Number of grasslands
(a) (b)
Figure 2. Histogram of (a) Shannon index H and (b) grasslands’ size in number of pixels ni.
120 140 160 180 200 220 240
0.0
0.2
0.4
0.6
0.8
1.0
120 140 160 180 200 220 240
0.0
0.2
0.4
0.6
0.8
1.0
120 140 160 180 200 220 240
0.0
0.2
0.4
0.6
0.8
1.0
(a) H = 0.10 (b) H = 1.57 (c) H = 2.89
Figure 3.
SPOT5 NDVI temporal profiles of all the pixels belonging to three grasslands along the
H gradient: (
a
) grassland with a low level of biodiversity, (
b
) grassland with a medium level of
biodiversity and (
c
) grassland with a high level of biodiversity. The floristic record of these three
grasslands can be found in Appendix A, Table A1. The x-axis corresponds to the day of the year of
2015, and the y-axis corresponds to the NDVI. Grasslands have been voluntarily chosen by their high
number of pixels for better visualization.
3. Method
The objective of this part is to describe the proposed method to measure the spectro-temporal
heterogeneity in the grasslands from SITS and to link it with the Shannon index measured in the field
in order to verify the STVH.
Each pixel
k
is represented by a vector
xk
of dimension
d
,
d
being the number of variables.
For instance,
in the case of hyperspectral data,
d
is the number of spectral bands, which is a few
hundred. In the case of multitemporal data, usually a vegetation index is used, and
d
corresponds to
the number of temporal measurements. In this study, where we use both the spectral and the temporal
information,
d=nBnT
, with
nB
the number of spectral bands and
nT
the number of temporal
acquisitions, as presented in Section 2.2.
3.1. Measures of Spectral Heterogeneity in the Literature
In the literature, the measure of spectral heterogeneity is based on measures of dispersion [
8
]
such as the standard deviation [
14
] or the coefficient of variation [
20
]. However, these measures
require selecting single bands or performing band reduction, such as using a vegetation index or using
ordination methods like Principal Components Analysis (PCA), and thus, they lose some relevant
information. To enable the use of all the spectral information, Rocchini [
22
] proposed the mean of
the pairwise Euclidean distances from the spectral centroid (MDC) [
15
] for all the pixels covering the
sampling plot:
Remote Sens. 2017,9, 993 7 of 23
MDCi=1
ni
ni
∑
k=1
kxik −µik2(2)
where
ni
is the number of pixels in the plot
i
,
xik
is the spectral vector associated with pixel
k
,
µi
is
the plot’s spectral centroid and
k · k2
stands for the Euclidean distance. In our case, the plot is the
grassland. Hence, the centroid is the grassland’s pixels’ centroid, i.e., the mean spectro-temporal value
of the grassland’s pixels.
To reduce the dimensional-space, some studies compute the MDC on the first few components
of PCA performed on the spectral variables [
18
,
19
,
22
]. Theoretically, it is almost equivalent to the
original MDC.
MDC is in fact the trace of the pixels’ empirical covariance matrix
Vi
, which measures the spectral
variability in the plot:
Vi=1
ni
ni
∑
k=1
(xik −µi)(xi k −µi)>(3)
and:
trace(Vi) = 1
ni
ni
∑
k=1
kxik −µik2. (4)
However, several drawbacks can be raised from the MDC. This measure is flawed because it
assumes homoscedasticity of the variables (same variance), and it does not differentiate between
monomodal and multimodal distributions in the spectral space. Different spectral configurations can
have the same distance to the centroid [23] as illustrated in a two-dimensional space in Figure 4.
−5 0 5
−5
0
5
−5 0 5
−5
0
5
(a) MDC = 13.9 (b) MDC = 13.6
Figure 4.
Simulated pixels’ distributions for two different plots (
a
) and (
b
). Pixels are displayed in
blue, and the centroids of the plots are displayed in red. The estimated MDC are very close while the
spectral distributions of the plots are clearly different.
To address this issue, Féret and Asner [
23
] introduced a clustering step to account for the global
distribution in the spectral space. The unsupervised clustering is used to obtain “spectral species”
(clusters), which are related to one or several species sharing similar spectral signatures. The clusters
were estimated through a PCA and a k-means procedure. Although this clustering algorithm is often
used, it is not robust in a high dimensional space [
33
]. Moreover, it assumes homoscedasticity of the
clusters (same variance for each cluster), and it does not reflect well the distribution in the spectral
space. An illustration can be seen in Figure 5where (a) a simulated plot made of three different spectral
species was clusterized by (b) the pipeline PCA + k-means and (c) by Gaussian mixture models. With
PCA + k-means, the spectral species (clusters) are not well found contrary to the clustering using
Gaussian mixture models.
Remote Sens. 2017,9, 993 8 of 23
−2024−2
0
2
−2
0
2
4
−2024−2
0
2
−2
0
2
4
−2024−2
0
2
−2
0
2
4
(a) (b) (c)
Figure 5.
(
a
) Simulated distributions of three spectral species (blue, yellow, red) in a 3-dimensional
space. (
b
) Clustering of the three distributions with PCA and k-means. (
c
) Clustering of the three
distributions with Gaussian mixture models.
Thus, in the following, we propose a clustering technique that is robust to high dimensional data.
Hence, no dimension reduction such as PCA is necessary. Moreover, it assumes heteroscedasticity of
the clusters, i.e., each cluster could have a different variability. This clustering algorithm enables the
computation of other measures of spectral heterogeneity.
3.2. Spectral Clustering Algorithm for High Dimensional Data and Derived Measures of Spectral Heterogeneity
We suggest to use a robust clustering algorithm that encompasses k-means, but that is suitable in a
context of a small sample size with a large number of variables: the High Dimensional Data Clustering
(HDDC) [
34
] (available in the R package at https://cran.r-project.org/web/packages/HDclassif/
index.html). HDDC is based on a mixture model where each mixture component follows a Gaussian
distribution. Under this model, a given sample (i.e, pixel)
x
is the realization of a random vector, for
which distribution pis such that [35]:
p(x) =
C
∑
c=1
πcfc(x|µc,Σc)(5)
where
C
is the number of clusters,
πc
is the proportion of cluster
c
and
fc(x|µc
,
Σc)
is a Gaussian
distribution with parameters µcand Σc, i.e.,
fc(x|µc,Σc) = 1
(2π)d
2|Σc|1
2
exp −1
2(x−µc)>Σ−1
c(x−µc). (6)
The parameters of the mixture model are estimated using a conventional expectation-
maximization algorithm. Once the optimal parameters are found, each sample
x
is assigned to
the cluster cfor which the log-probability Qc(x)is maximal. Qc(x)is computed as:
Qc(x) = 1
2×−(x−µc)>Σ−1
c(x−µc)−log(|Σc|) + 2 log(πc)−dlog(2π). (7)
The computation of Equation (7) requires the inversion of the covariance matrix
Σc
and the
computation of the logarithm of its determinant, which can be numerically unstable in a high
dimensional context. To circumvent these issues, HDDC assumes that the last (lowest) eigenvalues of
the covariance matrix are equal. It results that the inverse of the covariance matrix and its determinant
can be computed explicitly while the numerical stability is controlled [36].
In this study, the clustering is applied to all the grasslands’ pixels
xk∈Rd
, regardless of the
grassland to which they belong. The clustering splits all the pixels into
C
clusters. Then, for each
grassland
gi
, its corresponding pixels
xik
are assigned to
Ci
clusters with
k∈ {
1, ...,
ni}
;
ni
is the number
of pixels in gi,Ci∈ {1, . . . , C}and CiC.
Remote Sens. 2017,9, 993 9 of 23
For each cluster
c
in the grassland, the mean vector
µic
and the covariance matrix associated
with the pixels belonging to this cluster are updated from the initial clustering on all the pixels.
The proportion
of this cluster
pic
is also updated,
pic =nic
ni
with
nic
the number of pixels of
gi
associated
with
c
. Hence, by considering several clusters inside a given grassland, it is possible to assess the
between-class variability, the within-class variability and the entropy within the grassland. They
provide additional information with respect to MDC to assess the spectral heterogeneity, and they are
defined in the next subsections.
3.2.1. Between- and Within-Class Variabilities
The covariance matrix of gican be decomposed as [37]:
Vi=Bi+Wi(8)
with:
•Bi=∑Ci
c=1pic (µic −µi)(µic −µi)>is the between-class covariance matrix,
•µic is the spectro-temporal mean of pixels in giassigned to cluster c,
•µiis the mean spectro-temporal value computed from all the pixels of gi,
•Wi=1
ni∑Ci
c=1∑k∈c(xik −µic )(xik −µic )>=∑Ci
c=1pic Vic is the within-class covariance matrix,
•Vic is the empirical covariance matrix of pixels of giassigned to cluster c.
Therefore, using Equation (4), the MDC associated with gican be written as:
MDCi=trace(Vi) = trace(Bi) + trace(Wi). (9)
From Equation (9), two measures of spectral heterogeneity can be extracted: the between-class
variability and the within-class variability. The trace of Biquantifies the between-class variability:
trace(Bi) =
Ci
∑
c=1
pic kµic −µik2. (10)
This measure reflects the inter-classes variance: how the means of clusters in the grassland are
different or similar. The more the clusters are different, the higher the between-class variability. If there
is only one class in the grassland, then trace(Bi) = 0.
The within-class variability is quantified by the trace of Wi:
trace(Wi) = 1
ni
Ci
∑
c=1
∑
k∈c
kxik −µic k2. (11)
This measure represents the mean of the clusters variances. The more the grassland has
heterogeneous clusters with high variance, the higher the within-class variability. However, if the
grassland has many homogeneous clusters, trace(
Wi
) will be low. Contrary to the between-class
variability, if there is only one cluster, the within-class variability still provides information on the
heterogeneity in the grassland.
3.2.2. Entropy
Another measure of spectral heterogeneity that can be derived from the spectral clustering of
grasslands is the entropy. The entropy is linked to the proportions of clusters within the grassland
gi
and is quantified by:
Ei=
Ci
∑
c=1
−pic log(pic ). (12)
Remote Sens. 2017,9, 993 10 of 23
The more the dataset has equally-balanced clusters, the higher
Ei
. The least balanced is the dataset,
the closer Eiis to 0. If there is only one cluster in the grassland, Ci=1 and pi1=1, then Ei=0.
The HDDC algorithm provides for each pixel the probability that it belongs to each cluster, which
can be understood as a soft assignment with respect to the hard assignment of k-means (Figure 6).
Therefore, a “finer” measure of entropy can be computed using the probability of assignment of the
grassland’s pixels to each cluster cof the global clustering, πic :
πic =1
ni∑
k∈gi
πick (13)
with
πick
the assignment probability of pixel
k
from
gi
to cluster
c
provided by the algorithm,
∑C
c=1πick =
1 (Figure 6). Therefore, a finer measure of entropy can be written by replacing
pic
by πic in Equation (12) and by summing it to the total number of clusters C:
Esi=
C
∑
c=1
−πic log(πic ). (14)
This measure of entropy hardly ever reaches null values, unless all the pixels of the grasslands
are assigned to the same cluster with a probability of 1.
(a) (b) (c) (d)
Figure 6.
Grassland clustered with an initial clustering of the landscape into 8 clusters. (
a
) Hard
assignment of the pixels. One color corresponds to one cluster (orange, yellow, blue). (
b
–
d
) Soft
assignment of the pixels. The grey-scaled color corresponds to the assignment probability
πick
to
cluster (b) orange, (c) yellow and (d) blue.
The entropy reflects the grassland’s clusters evenness: whether it is dominated by one cluster or
numerous equally-distributed clusters.
3.3. Methodology
To link the proposed SH measures issued from SITS to the Shannon index measured from the
species, univariate and multivariate (combining several SH measures), linear regressions are performed.
The response variable is the Shannon index, and the explanatory variables are the global variability
or MDC (Equation (9)), the between-class variability (Equation (10)), the within-class variability
(Equation (11)) and the entropy with soft assignment (Equation (14)).
Since the linear regressions assume normality of the distributions, the global variability, the
between-class variability and the within-class variability are log-transformed to Gaussianize them [
38
],
as done in [
19
,
39
]. In the following, the entropy with soft assignment is denoted by E, and the
log-transformed global (or MDC), within-class and between-class variabilities are denoted by V, W
and B, respectively.
The adjusted coefficient of determination
¯
R2
is used to measure the goodness of fit of the
regressions. It is defined as the proportion of variance explained by the regression model adjusted for
the number of explanatory variables.
The proposed methodology including the clustering is synthesized in Figure 7. To assess the
contribution of temporal variations to the SVH through the use of multitemporal data, we also applied
the same methodology using only one acquisition issued from the SITS. We compared the results
Remote Sens. 2017,9, 993 11 of 23
obtained with the SITS and obtained with a single image by computing a Wilcoxon signed-rank test
between the two distributions of predicted values issued from their best models.
SITS of the
grasslands’ pixels
HDDC
clustering
Cluster map
of grasslands Compute SH SH map of
grasslands
Linear regression
Shannon index
(field data)
Figure 7.
Overview of the method to compare the Spectral Heterogeneity (SH) measures (explanatory
variables) to the Shannon index (response variable). Square rectangles correspond to data, and rounded
rectangles correspond to a process.
The clustering algorithm, the computation of the SH measures and the statistical analysis
were performed in Python through the SciPy (https://www.scipy.org), scikit-learn [
40
] and pandas
(http://pandas.pydata.org) libraries.
The initial number of clusters for the clustering has an influence on the clusters found in each
grassland (Figure 8). Hence, the correlations are studied for different numbers of initial clusters, from
2–150 clusters (every 2 clusters in the range
[
2, 60
]
and every 25 clusters in the range
[
75, 150
]
). For each
number of clusters, 10 runs of the algorithm with different random initializations are performed, and
the best result in terms of the Integrated Classification Likelihood (ICL) [41] is kept.
(a) (b) (c)
Figure 8.
(
a
) False color image of a grassland acquired on 30 April 2015. The same grassland clustered
using HDDC on multitemporal data with an initial clustering into (
b
) 8 clusters and (
c
) 150 clusters.
Each cluster is represented by one color.
4. Results
The proposed SH measures were computed using the spectro-temporal data for all the grasslands
for different numbers of clusters. Then, the adjusted coefficient of determination of the linear regression
between the Shannon index measured in the field (H) and the individual or combined SH measures
was calculated (Figure 9). The entropy computed with soft assignment (Equation (14)) was slightly
better correlated with H than the “simple” entropy (Equation (12)); therefore, the usual entropy is
not shown.
Remote Sens. 2017,9, 993 12 of 23
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
0.00
0.05
0.10
0.15
Number of clusters C
¯
R2
V W
B E
W and E W, B, V and E
Figure 9.
Adjusted coefficient of determination in the multivariate linear regression between different
combinations of SH measures (V: log-transformed global variability or MDC, W: log-transformed
within-class variability, B: log-transformed between-class variability, E: entropy) computed from
multitemporal data and the Shannon index (response variable) depending on the number of clusters.
4.1. Univariate Correlation with Multitemporal Data
The global variability, or MDC computed at the grassland scale, is significantly correlated with
the Shannon index (
¯
R2=
0.071, p-value <0.001). Depending on the number of clusters, the entropy and
the within-class variability reach higher correlation coefficients than the global variability. For instance,
for the entropy, with
C=
8 and
C=
75, the adjusted coefficient of determination is
¯
R2=
0.099
and
¯
R2=
0.105, respectively (p-value <0.001). Its minimum is
¯
R2=−
0.005 and not significant for
C=
2. The within-class variability reaches maximum correlation values of
¯
R2=
0.097 for
C=
2 and
¯
R2=
0.074 for
C=
6 (p-value <0.001). Its minimum value is
¯
R2=
0.034 for
C=
75 (p-value <0.05).
The between-class variability never reaches as high values as MDC except for
C=
14 (
¯
R2=
0.072,
p-value < 0.001). The problem with this measure lies with its null values, which make it not continuous.
The relationships between H and the proposed SH measures for each grassland that reach the
highest coefficients of determination are shown in Figure 10. The entropy is the SH measure showing
the highest coefficient of determination with H. All the SH measures tend to increase with the Shannon
index suggesting that the spectro-temporal heterogeneity is linked to the species diversity.
0 0.5 1 1.5
0
1
2
3
E
H
C=75, ¯
R2=0.105**
810 12
0
1
2
3
V
¯
R2=0.071**
810 12
0
1
2
3
W
C=2, ¯
R2=0.097**
0 5 10
0
1
2
3
B
C=14, ¯
R2=0.072**
Figure 10.
Shannon index (H) best univariate linear correlations with different SH measures
(E: entropy, V: log-transformed global variability or MDC, W: log-transformed within-class
variability, B: log-transformed between-class variability) computed from multitemporal data.
C
is
the corresponding number of clusters,
¯
R2
is the adjusted coefficient of determination and ** signifies
p-value <0.001. The black line is the linear regression line.
Remote Sens. 2017,9, 993 13 of 23
4.2. Multivariate Correlation with Multitemporal Data
Multivariate linear regressions were run with different combinations of SH measures to assess
which combinations of variables are the most related to H.
The models combining several variables explain better the Shannon index than the univariate
models (Figure 9, blue and red lines). Indeed, the multivariate model combining the entropy (E) and
the within-class variability (W) and the model combining the four proposed SH measures (E, W, B
and V) always has higher coefficients of determination than SH measures alone, regardless of the
number of clusters. Moreover, for the number of clusters reaching the maximum adjusted coefficient
of determination (
C=
8), the variables contributing the most to explain H are W and E (p-value <0.05),
whereas V and B do not contribute much (p-value >0.05, Table 2). Therefore, the combination of W
and E (
¯
R2=
0.131) explains H better than the combination of W, B, V and E (
¯
R2=
0.127, Figure 9and
Table 2). This is the case for most of the numbers of clusters. Additionally, the combination of V and E
(data not shown) is worse to explain H than the combination of W and E.
Table 2.
Multivariate linear models for
C=
8 to explain the Shannon index (H) from the SH
measures (V: log-transformed global variability or MDC, W: log-transformed within-class variability,
B: log-transformed between-class variability, E: entropy) computed from multitemporal data. Reg.
Coeff. is the regression coefficient; Std Err. is the standard error; F stands for the F-value with
degrees of freedom in brackets;
R2
is the coefficient of determination; and
¯
R2
is the adjusted coefficient
of determination.
Response Variable Explanatory Variables Reg. Coeff. Std Err. p-Value
H W 0.29 0.14 0.04
B 0.01 0.02 0.61
V−0.15 0.14 0.30
E 0.40 0.13 0.003
intercept 0.73 0.51 0.16
Model summary: F(4, 187)= 8.0, p-value <0.001, R2= 0.145, ¯
R2=0.127
H W 0.16 0.06 0.005
E 0.37 0.09 <0.001
intercept 0.65 0.51 0.20
Model summary: F(2, 189)= 15.4, p-value <0.001, R2= 0.140, ¯
R2=0.131
4.3. Univariate and Multivariate Correlation with Monotemporal Data
To evaluate the contribution of multitemporal data to the SVH, we compared the above results
to results obtained from monotemporal data. We chose two acquisitions dates from the time series:
30 April
(near the growth peak, before the occurrence of the management practices such as mowing
and grazing) and 29 June (after most of the management practices occurred).
Higher coefficients of correlations are obtained with only one acquisition (Figure 11). Using the
image of 30 April, the maximum adjusted coefficient of determination is 0.139 (p-value <0.001) with
the model combining W and E for
C=
150 and
¯
R2=
0.169 (p-value <0.001) with the model combining
W, B, V and E for
C=
150 (for higher numbers of clusters,
¯
R2
was lower, data not shown). Using the
image of 29 June,
¯
R2=
0.137 with the model combining W and E, and
¯
R2=
0.140 (p-value <0.001)
with the model combining W, B, V and E, both for C=20.
For both images, the combination of the four proposed SH and the combination of W and E are
better at explaining the Shannon index than MDC. However, the contributions of each SH measure in
the model are not the same as for the model using multitemporal data.
We compared the distributions of the predicted Shannon index values issued from the best models
using the three types of data (i.e., multitemporal data:
C=
8, explanatory variables: W and E;
30 April
image:
C=
150, explanatory variables: W, B, V and E; and 29 June image:
C=
20, explanatory
Remote Sens. 2017,9, 993 14 of 23
variables: W, B, V and E) by conducting a Wilcoxon signed-rank test. There were no significant
differences between the values predicted by the best models for each data type (p-value >0.05 for each
pair of distributions). Therefore, the models are equivalent in terms of predicted H values.
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
0.00
0.05
0.10
0.15
Number of clusters C
¯
R2
V W
B E
W and E W, B, V and E
(a)
10 20 30 40 50 60 70 80 90 100 110 120 130 140 150
0.00
0.05
0.10
0.15
Number of clusters C
¯
R2
V W
B E
W and E W, B, V and E
(b)
Figure 11.
Adjusted coefficient of determination in the multivariate linear regression using
one image acquired on (
a
) 30 April and (
b
) 29 June between different combinations of SH
measures (V: log-transformed global variability or MDC, W: log-transformed within-class variability,
B: log-transformed
between-class variability, E: entropy) and the Shannon index (response variable)
depending on the number of clusters.
5. Discussion
5.1. Spectral Heterogeneity Measures
Globally, the variance of the species diversity (represented by the Shannon index) explained by
the SH measures derived from the clusterings of grasslands using SITS is weak.
Indeed, low species diversity grasslands are not associated with low SH measures, except for
E (Figure 10). High species diversity grasslands can be associated with any SH measures: low to
medium E values, medium V values, high W values and medium B values. Medium species diversity
grasslands, that represent a great percentage of the dataset, can be associated with any SH measures.
As a result, the unexplained variance of H is very high (87%) with the model combining E and W
(
C=
8). Indeed, it predicts a much smaller range of values than the actual ones (Figure 2a): the
maximum predicted H is 2.8, while the minimum is 1.8 with a mean of 2.3 and a standard deviation 0.2.
The spatial, but also the spectral resolution of the sensor may have limited the analysis. Indeed,
individual grassland’s species are particularly small and mixed. A spatial resolution of 10 m is too
Remote Sens. 2017,9, 993 15 of 23
coarse to detect individual species. In a pixel of 10 m, there can be a large number of mixed grassland
plant species. Moreover, some species are spectrally too similar to be discriminated with low spectral
resolution [
42
,
43
]. Consequently, if a grassland has a high level of biodiversity, with a large number
of species, and if these species are homogeneously mixed within the grasslands, the pixels will be
spectrally similar even if they contain a mix of species. Thus, there would be one cluster in the
grassland. This would result in a low spectral entropy, although this grassland has a high Shannon
index. This could explain the wide range of SH values associated with grasslands with high species
diversity. These SH measures seem to reflect more the variability of homogeneous species assemblages
(i.e., the clusters) in the grasslands than the diversity of species, explaining the low, but significant
relationship with the ground Shannon index.
Despite the weak relationship with the Shannon index, we proposed SH measures that provide
supplementary information on the grassland’s heterogeneity with regard to MDC. Indeed, the
combination of the entropy and the within-class variability was always more correlated with the
species diversity than the MDC alone, regardless of the type of imagery used. These two SH measures
contributed the most to explain H.
The within-class variability is an interesting measure since it provides a quantitative information
on the grassland’s heterogeneity even if there is only one cluster, which cannot be provided by the
entropy. Thus, the within-class variability and the entropy are complementary. Their combination
was better than the combination of the four proposed SH measures together, or the univariate models,
regardless of the number of clusters (Figures 9and 11, blue line).
Beyond the relationship with species diversity of the SH measures, the proposed method
makes possible the detection of assemblages of species within the grasslands, which share
common spectro-temporal properties. These assemblages can indirectly give information about
the heterogeneity within the grasslands. The heterogeneity of these groups of species can be quantified
with their spectral variability (Figure 12). Such a spectral map at the grassland scale would not be
possible using MDC.
(a) (b) (c)
Figure 12.
Maps of spectral heterogeneity inside three grasslands (
a
–
c
). The first row shows the
grasslands’ polygon limits in yellow on the SPOT5 false color image acquired on 10 May 2015. The
second row shows the clusters after an HDDC clustering into eight clusters using multitemporal data.
The color scale corresponds to the log-transformed variability of each cluster
c
in the grassland
gi
.
(a) H = 0.10,
E = 0, V = 10.13, W = 10.13, B = 0; (
b
) H = 1.57, E = 0.68, V = 10.06, W = 9.41, B = 9.33;
(c) H = 2.89,
E = 1.06, V = 9.58, W = 9.22, B = 8.42. The floristic record of these three grasslands can be
found in the Appendix A, Table A1.
Remote Sens. 2017,9, 993 16 of 23
5.2. Clustering
To understand the meaning of the clusters found using multitemporal data (
C=
8), the mean
vectors corresponding to each cluster were extracted, and their NDVI temporal profiles were computed
(Figure 13). The profiles seem consistent with typical profiles of grasslands. The pixels associated
with cluster C7 in Figure 13 belong to grasslands varying in species diversity, but all intensively-used.
These pixels usually represent the whole grasslands, while grasslands less intensively used can be
associated with several other clusters.
05 06 07 08 09
0.2
0.3
0.4
0.5
0.6
0.7
0.8
C1 C2 C3 C4
C5 C6 C7 C8
Figure 13.
Mean NDVI temporal profiles of each cluster from the clustering into
C=
8 clusters using
multitemporal data. The x-axis is the month of year 2015, and the y-axis is the NDVI.
Hence, the clusters seem to be more related to phenological profiles linked to management
practices than to phenological profiles of species. Indeed, the management practices have an influence
on the species distribution and composition [
44
], but they may have a stronger impact on the spatial,
temporal and spectral profiles of the grasslands because they induce abrupt changes in the grassland
(mowing, grazing, fertilizing). In particular, due to the use of acquisitions from April–September, the
effect of management practices that usually occur within this period may be very significant.
More precisely, we suspect that clusters are related to the intensity of practices. Indeed, an
intensive use with constant defoliation does not allow for the expression of the phenology of species.
However, when the grassland is extensively used, species can express different phenologies (during
the regrowth after the mowing for instance), and different clusters related to these phenologies can be
detected. This could explain the multiple clusters found in extensively-used grasslands (for instance,
in Figure 12c), while intensively-used grasslands are represented by one cluster, which has a typical
signature of intensively-used grassland (Figure 12a).
Hence, at a spatial resolution of 10 m, the clusters found using multitemporal data seem to reflect
more the intensity of practices in the grasslands than the species composition. This could explain the
weak correlations with the Shannon index.
Regarding the number of clusters, the proposed clustering algorithm (HDDC) provides model
selection criteria (ICL and BIC) that were not efficient in our experiment. Indeed, the theoretical optimal
number of spectral clusters may not correspond to the number of expected clusters of species [
45
].
Therefore, our strategy was to test a wide range of numbers of clusters and to keep the one that gives
the best
¯
R2
. From an operational viewpoint, this strategy can be time consuming, but it can adapt to
any spatial configurations (size and location).
5.3. Contribution of Multitemporal Imagery
In this study, we made the assumption that the spectro-temporal variations of a grassland could
be related to its species diversity. The results obtained with the monotemporal imagery showed that
the multitemporal data do not improve the relationship with the Shannon index. Indeed, higher
Remote Sens. 2017,9, 993 17 of 23
coefficients of determination were reached with the two dates proposed than with the full SITS.
Hence, the SVH with temporal variations, the so-called STVH, is not verified in this work, at a spatial
resolution of 10 m.
However, the clusters found in the grasslands using the full SITS create homogeneous patterns
within the grasslands, contrary to the clusters found with one image, which are quite “pixelized” and
do not seem spatially consistent (Figure 14). Considering that the predicted values with models issued
from these three datasets were not significantly different, we can also doubt the relationship of the
clusters found using one image with the species diversity. However, this would require verification in
the field, but this was not possible in the frame of this work.
(a) (b) (c)
(d) (e) (f)
Figure 14.
Clustering of the same grassland (false color image of (
a
) 30 April and (
d
) 29 June) with
an initial clustering into 150 clusters, using (
b
) the image of 30 April and (
c
) the full SITS, and into
20 clusters, using (e) the image of 29 June and (f) the full SITS.
As previously suggested, the temporal variations measured by the sensor seem to be more related
to the management practices than to the species diversity. Indeed, we used a time series covering the
period from mid-April–September. Most of the management practices such as mowing and/or grazing
usually occur within this period. To circumvent this effect, the time series could be limited to a period
or a combination of periods when there is no management practices, such as the beginning of the
growing season, before the growth peak. Moreover, previous studies have shown that the relationships
between species diversity and remote sensing metrics can be season-dependent [
46
]. Therefore, specific
care should be considered regarding the dates of the imagery selected.
5.4. Limitations
The weak relationships found in this work can be due to the unbalanced H values present in our
dataset. Indeed, it was mostly composed of grasslands with a medium level of biodiversity (
H between
two and 2.5, Figure 2a). The H gradient was not very well sampled, with very few grasslands low in
species diversity (H < 1) and rich in species diversity (H > 3). Hence, the regression models were more
calibrated on medium level biodiversity and lacked generality. This may be why the models have an
average predicted H value of around 2.3 (Section 5.2).
Moreover, we obtained lower coefficients of determination than in other studies that related
the species diversity in grasslands with the SH using monotemporal imagery at a very high spatial
resolution. For instance, Oldeland et al. [
18
] used airborne hyperspectral data at a spatial resolution
Remote Sens. 2017,9, 993 18 of 23
of 5 m and found significant correlations between the Shannon index of savannah plots and the
MDC computed from PCA. They reached significant
R2
ranging from 0.31–0.62 depending on the
20 m
×
50 m plots. Möckel et al. [
19
] investigated the prediction of grassland species diversity
(species richness and inverse Simpson’s diversity) in Sweden from airborne hyperspectral data with a
spectral response approach and a spectral heterogeneity approach. However, they failed to detect a
significant relationship between species diversity and spectral heterogeneity (PCA + MDC) at the plot
scale, contrary to the spectral response approach. In the same study area, Hall et al. [
39
] related the
species richness (alpha-diversity) and the species turnover (beta-diversity) measured in three plots per
grassland with the spectral heterogeneity in the four bands of the QuickBird sensor (2.4 m resolution)
and other field variables. The spectral heterogeneity was measured as the mean difference between
the mean of each individual 3
×
3 pixel window (corresponding to each plot) and the mean of all
three pixels windows within each grassland site. It can be assimilated to the between-class variability,
but with three plots of the same size. They found low, but significant linear correlations between
the species richness and the spectral heterogeneity measured with the NIR band (
R2=
0.08) and
between the species turnover and the spectral heterogeneity measured in the red band (
R2=
0.10), the
NIR band (
R2=
0.19) and the NDVI (
R2=
0.14). Better correlations were found with multivariate
models,
but only
the model predicting the species turnover included the spectral heterogeneity (NIR,
¯
R2=0.33).
However, these studies were conducted at the plot scale, both for the floristic record and the
associated spectral information. They used the pixels corresponding only to the sampling unit.
Our protocol
was different, since the botanical survey was conducted at the grassland scale by a
random walk strategy, and only one biodiversity index was computed from it. Yet, grasslands are
characterized by patterns of small scale species composition and spatial distribution [
47
–
49
]. Hence,
this estimation of the biodiversity at the grassland level may be difficult to relate to remote sensing
data and might have limited our analysis.
Furthermore, the influence of the topography should be considered for future studies because it
is known that the topography influences the reflectance.
5.5. Outlooks
In terms of methodology, the proposed method could be used to assess the beta-diversity among
grasslands. Indeed, in light of the Bray–Curtis dissimilarity [
50
], a spectral dissimilarity could easily
be computed from the proportions of clusters in each grassland [
23
]. It could be improved by using
the probability of belonging to each cluster, similarly to the way done with the entropy.
The pairwise
spectral Bray–Curtis dissimilarity between grasslands giand gjwould be defined as:
BCijspectral =∑C
c=1|πic −πjc |
∑C
c=1πic +πjc
(15)
where
πic
and
πjc
are the mean assignment probabilities to cluster
c
of pixels of grasslands
gi
and
gj
,
respectively, defined in Equation (13).
In terms of application, the proposed method is not specific to grasslands, and it could be used to
assess the species diversity of other habitats. For instance, it could be used on forest, since the method
is not required to work at a specific object scale: it can be applied to a plot of fixed size.
In addition, this work could be extended to the relationship of the spectral heterogeneity with the
functional diversity of the habitat. Indeed, some functional traits are related to the way plants
reflect light and thus to the signal measured by the sensor [
9
,
51
–
53
] and may be related to the
spectral heterogeneity. However to our knowledge, functional diversity has not yet been related
to remotely-sensed measures [
53
,
54
] and has not been discussed in the context of SVH [
8
,
10
]. The
stakes would be to determine which traits and which measures of functional diversity are the most
consistent with SVH. Using SITS, we would suggest to select functional traits that are linked to the
phenology of the species such as the flowering date, the flowering length and the leaf life span.
Remote Sens. 2017,9, 993 19 of 23
6. Conclusions
The aim of this work was to attempt to verify the Spectral Variation Hypothesis (SVH) in
grasslands under the assumption that the temporal variations could be used in addition to the spectral
variations of the habitat as a proxy of its species diversity: the Spectro-Temporal Variation Hypothesis
(STVH). To do so, we proposed a method based on an unsupervised clustering of the grasslands using
multitemporal and multispectral data, allowing for the derivation of spectro-temporal heterogeneity
measures computed at the grassland level: the within-class variability, the between-class variability
and the entropy. We compared them to the commonly-used mean distance to the centroid. The method
was applied on 192 grasslands from southwest France using an inter-annual multispectral time series
of SPOT5 images. Univariate and multivariate regression models combining several spectro-temporal
heterogeneity measures were run with different numbers of clusters to assess their correlation with the
Shannon index measured from field data.
The tested spectral heterogeneity measures were found significantly, but weakly correlated with
the Shannon index. The combination of the within-class variability and the entropy was found
always better correlated with the Shannon index than the mean distance to the centroid, regardless
of the number of clusters. The best regression model explained 13.1% of the variance of the ground
Shannon index while the mean distance to the centroid explained 7.1% of the variance. Hence, the
clustering makes possible the extraction of spectral heterogeneity measures that give supplementary
information to the mean distance to the centroid. However, equivalent results were obtained using
monotemporal imagery.
Therefore, the spectro-temporal variation hypothesis was not verified using multispectral
multitemporal imagery at a spatial resolution of 10 m. The proposed spectro-temporal heterogeneity
measures seemed to be more related to the management practices performed in the grasslands than
to the species diversity. The use of a whole time series covering the growing season or the season
when the management practices occur does not seem to be suitable to detect the diversity in species.
A period when no practice occurs should be more appropriate.
More research should be conducted on the extension of the SVH to the functional diversity.
The STVH might be more related to functional traits linked to the phenology of species.
Acknowledgments:
This work was partially supported by the French National Institute for Agricultural Research
(INRA) and the French National Institute for Research in Computer Science and Automation (INRIA) Young
Scientist Contract (CJS INRA-INRIA) and by the project SEBIOREF (“Promouvoir les Services Ecosystémiques
rendus par la Biodiversité à l’agriculture”, Région Occitanie, INRA, IRSTEA (French National Institute for Research
in Sciences and Technologies for Environment and Agriculture)). The authors would like to thank the botanists
who made possible the constitution of the field dataset used in this study: Philippe Caniot, Jérôme Willm, Emilie
Andrieu and Gérard Balent. We would also like to thank the people accompanying the botanists: François
Calatayud, Romain Carrié, Jean-Philippe Choisis, Donatien Dallery,
Bruno Dumora
, Camille Gouwy, Wilfried
Heintz, Marc Lang and Anne-Sophie Mould. Specials thanks to Clélia Sirami, Romain Carrié, Rémi Duflot and
Nicolas Gross for sharing their knowledge about grasslands’ species diversity.
The authors
would like to thank
CNES for providing the pre-processed SPOT5 (Take5) data. We thank the anonymous reviewers for their valuable
comments that greatly improved the manuscript.
Author Contributions:
M.L. and M.F.designed the methodology. M.L. performed the experiments. M.L., M.F.
and A.O. analyzed the data. M.L. and M.F. wrote the paper with feedback from A.O. and S.G.
Conflicts of Interest:
The authors declare no conflict of interest. The founding sponsors had no role in the design
of the study; in the collection, analyses or interpretation of data; in the writing of the manuscript; nor in the
decision to publish the results.
Abbreviations
The following abbreviations are used in this manuscript:
B Log-transformed between-classes variability
CNES Centre National d’Etudes Spatiales (French spatial agency)
E Entropy computed from soft assignment
GIS Geographic Information System
Remote Sens. 2017,9, 993 20 of 23
H Shannon index
HDDC High Dimensional Discriminant Clustering
ICL Integrated Classification Likelihood
MDC Mean Distance to Centroid
NDVI Normalized Difference Vegetation Index
NIR Near-Infrared
PCA Principal Components Analysis
SH Spectral Heterogeneity
SITS Satellite Image Time Series
STVH Spectro-Temporal Variation Hypothesis
SVH Spectral Variation Hypothesis
V Log-transformed global variability
W Log-transformed within-class variability
Appendix A
Table A1.
Braun-Blanquet abundance-dominance coefficients associated with each plant species
recorded in three grasslands a, b and c having a Shannon index of 0.10, 1.57 and 2.89, respectively.
“spp.” means that the species from the given genus was not identified.
Species a b c
Agrimonia eupatoria +
Agrostis capillaris 1
Anthoxanthum odoratum 1
Arrhenatherum elatius 1
Bellis perennis 1
Bromus erectus 1
Carex divulsa +
Carex flacca 1
Centaurea nigra +
Cirsium arvense 1
Cirsium dissectum 1
Cirsium vulgare +
Convolvulus arvensis 1 1
Crepis capillaris 1
Crepis spp. +
Dactylis glomerata 1 3
Daucus carota 1
Festuca arundinacea 2 3
Festuca rubra 1
Galium mollugo 1
Gaudinia fragilis 1
Holcus lanatus 1
Hypericum perforatum +
Hypochaeris radicata 1 1
Lathyrus pratensis 2
Leucanthemum vulgare 1
Linum usitatissimum 1
Lolium perenne 5
Lotus corniculatus 1
Remote Sens. 2017,9, 993 21 of 23
Table A1. Cont.
Species a b c
Medicago spp. +
Muscari comosum +
Orchis purpurea +
Plantago lanceolata 1
Poa pratensis 2
Poa trivialis + 5
Potentilla reptans 1 1
Prunus spinosa 1
Rafanus spp. +
Ranunculus acris 1
Ranunculus bulbosus 1
Ranunculus repens 2
Rasica oleacera +
Rhinanthus minor +
Rubus spp. +
Rumex acetosa 1
Rumex crispus 1 +
Senecio jacobaea 1
Sonchus asper +
Stachys officinalis +
Taraxacum officinalis 1 1
Tragopogon pratensis + +
Trifolium dubium 2
Trifolium pratense 1 2
Trifolium repens 1
Verbena officinalis 1
Veronica arvensis +
Vicia sativa + 1
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