gremlin97/RemoteSensingCorpus · Datasets at Hugging Face

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Step 2 The trend coef ﬁcients, αjandβjforj=1,…,m, are then
computed using robust regression of Eq. (1)based on M-
estimation ( Venables and Ripley, 2002 ). The trend estimate is
then set to T ̂t=α ̂j+β ̂jtfort=t j−1⁎+1,…,tj⁎.
Step 3 If the OLS-MOSUM test indicates that breakpoints are
occurring in the seasonal component, the number and
position of the seasonal break points ( t1#,…,tp#) are estimated
from the detrended data, Yt−T ̂t.
Step 4 The seasonal coef ﬁcients, γi,jforj=1,…,mandi=1,…,s−1,
are then computed using a robust regression of Eq. (4)based
on M-estimation. The seasonal estimate is then set to ˆSt=Ps−1
i=1 ˆγi;jdt;i−dt;0/C0/C1
fort=t j−1#+1,…,tj#.These steps are iterated until the number and position of the
breakpoints are unchanged. We have followed the recommendations
ofBai and Perron (2003) and Zeileis et al. (2003) concerning the
fraction of data needed between the breaks. For 16-day time series,
we used a minimum of one year of data (i.e. 23 observations) between
successive change detections, corresponding to 12% of a 9 year data
span (2000 –2008). This means that if two changes occur within a
year, only the most signi ﬁcant change will be detected.
3. Validation
The proposed approach can be applied to a variety of time series,
and is not restricted to remotely sensed vegetation indices. However,
validation has been conducted using Normalized Difference Vegeta-
tion Index (NDVI) time series, the most widely used vegetation index
in medium to coarse scale studies. The NDVI is a relative and indirect
measure of the amount of photosynthetic biomass, and is correlated
with biophysical parameters such as green leaf biomass and the
fraction of green vegetation cover, whose behavior follows annual
cycles of vegetation growth ( Myneni et al., 1995; Tucker, 1979 ).
We validated BFAST by (1) simulating 16-day NDVI time series, and
(2) applying the method to 16-day MODIS satellite NDVI time series(2000 –2008). Validation of multi-temporal change detection methods
is often not straightforward, since independent reference sources for a
broad range of potential changes must be available during the change
interval. Field validated single-date maps are unable to represent the
type and number of changes detected ( Kennedy et al., 2007 ). We
simulated 16-day NDVI time series with different noise, seasonality,
and change magnitudes in order to robustly test BFAST in a controlled
environment. However, it is challenging to create simulated time
series that approximate remotely sensed time series which contain
combined information on vegetation phenology, interannual climate
variability, disturbance events, and signal contamination (e.g. clouds)
(Zhang et al., 2009 ). Therefore, applying the method to remotely
sensed data and performing comparisons with in-situ data remains
necessary. In the next two sections, we apply BFAST to simulated and
MODIS NDVI time series.
3.1. Simulation of NDVI time series
NDVI time series are simulated by extracting key characteristics from
MODIS 16-day NDVI time series. We selected two MODIS NDVI time
series (as described in Section 3.2 ) representing a grassland and a pine
plantation ( Fig. 1 ), expressing the most different phenology in the study
area, to extract seasonal amplitude, noise level, and average value.
Simulated NDVI time series are generated by summing individually
simulated seasonal, noise, and trend components. First, the seasonal
component is created using an asymmetric Gaussian function for each
season. This Gaussian-type function has been shown to perform well
when used to extract seasonality by ﬁtting the function to time series
(Jönsson and Eklundh, 2002 ). The amplitude of the MODIS NDVI time
series was estimated using the range of the seasonal component derived
with the STL function, as shown in Fig. 2 . The estimated seasonal
amplitudes of the real forest and grassland MODIS NDVI time series
were 0.1 and 0.5 ( Fig. 1 ). Second, the noise component was generated
using a random number generator that follows a normal distribution N
(µ=0,σ=x), where the estimated xvalues were 0.04 and 0.02, to
approximate the noise within the real grass and forest MODIS NDVI time
series ( Lhermitte et al., submitted for publication ). Vegetation index
speciﬁc noise was generated by randomly replacing the white noise by
noise with a value of −0.1, representing cloud contamination that often
remains after atmospheric correction and cloud masking procedures.
Third, the real grass and forest MODIS NDVI time series were
approximated by selecting constant values 0.6 and 0.8 and summingthem with the simulated noise and seasonal component. A comparison
between real and simulated NDVI time series is shown in Fig. 1 .108 J. Verbesselt et al. / Remote Sensing of Environment 114 (2010) 106 –115
Based on the parameters required to simulate NDVI time series
similar to the real grass and forest MODIS NDVI time series ( Fig. 1 ), we
selected a range of amplitude and noise values for the simulation
study ( Table 1 ). These values are used to simulate NDVI time series of
different quality (i.e. varying signal to noise ratios) representing a
large range of land cover types.
The accuracy of the method for estimating the number, timing and
magnitude of abrupt changes was assessed by adding disturbances with
as p e c i ﬁc magnitude to the simulated time series. A simple disturbance
was simulated by combining a step function with a speci ﬁc magnitude
(Table 1 ) and linear recovery phase ( Kennedy et al., 2007 ). As such, the
disturbance can be used to simulate, for example, a ﬁre in a grassland or
an insect attack on a forest. Three disturbances were added to the sum of
simulated seasonal, trend, and noise components using simulation
parameters in Table 1 . An example of a simulated NDVI time series with
three disturbances is shown in Fig. 3 . A Root Mean Square Error (RMSE)
was derived for 500 iterations of all the combinations of amplitude,
noise and magnitude of change levels to quantify the accuracy of
estimating: (1) the number of detected changes, (2) the time of change,

Step 2 The trend coef ﬁcients, αjandβjforj=1,…,m, are then

computed using robust regression of Eq. (1)based on M-

estimation ( Venables and Ripley, 2002 ). The trend estimate is

then set to T ̂t=α ̂j+β ̂jtfort=t j−1⁎+1,…,tj⁎.

Step 3 If the OLS-MOSUM test indicates that breakpoints are

occurring in the seasonal component, the number and

position of the seasonal break points ( t1#,…,tp#) are estimated

from the detrended data, Yt−T ̂t.

Step 4 The seasonal coef ﬁcients, γi,jforj=1,…,mandi=1,…,s−1,

are then computed using a robust regression of Eq. (4)based

on M-estimation. The seasonal estimate is then set to ˆSt=Ps−1

i=1 ˆγi;jdt;i−dt;0/C0/C1

fort=t j−1#+1,…,tj#.These steps are iterated until the number and position of the

breakpoints are unchanged. We have followed the recommendations

ofBai and Perron (2003) and Zeileis et al. (2003) concerning the

fraction of data needed between the breaks. For 16-day time series,

we used a minimum of one year of data (i.e. 23 observations) between

successive change detections, corresponding to 12% of a 9 year data

span (2000 –2008). This means that if two changes occur within a

year, only the most signi ﬁcant change will be detected.

3. Validation

The proposed approach can be applied to a variety of time series,

and is not restricted to remotely sensed vegetation indices. However,

validation has been conducted using Normalized Difference Vegeta-

tion Index (NDVI) time series, the most widely used vegetation index

in medium to coarse scale studies. The NDVI is a relative and indirect

measure of the amount of photosynthetic biomass, and is correlated

with biophysical parameters such as green leaf biomass and the

fraction of green vegetation cover, whose behavior follows annual

cycles of vegetation growth ( Myneni et al., 1995; Tucker, 1979 ).

We validated BFAST by (1) simulating 16-day NDVI time series, and

(2) applying the method to 16-day MODIS satellite NDVI time series(2000 –2008). Validation of multi-temporal change detection methods

is often not straightforward, since independent reference sources for a

broad range of potential changes must be available during the change

interval. Field validated single-date maps are unable to represent the

type and number of changes detected ( Kennedy et al., 2007 ). We

simulated 16-day NDVI time series with different noise, seasonality,

and change magnitudes in order to robustly test BFAST in a controlled

environment. However, it is challenging to create simulated time

series that approximate remotely sensed time series which contain

combined information on vegetation phenology, interannual climate

variability, disturbance events, and signal contamination (e.g. clouds)

(Zhang et al., 2009 ). Therefore, applying the method to remotely

sensed data and performing comparisons with in-situ data remains

necessary. In the next two sections, we apply BFAST to simulated and

MODIS NDVI time series.

3.1. Simulation of NDVI time series

NDVI time series are simulated by extracting key characteristics from

MODIS 16-day NDVI time series. We selected two MODIS NDVI time

series (as described in Section 3.2 ) representing a grassland and a pine

plantation ( Fig. 1 ), expressing the most different phenology in the study

area, to extract seasonal amplitude, noise level, and average value.

Simulated NDVI time series are generated by summing individually

simulated seasonal, noise, and trend components. First, the seasonal

component is created using an asymmetric Gaussian function for each

season. This Gaussian-type function has been shown to perform well

when used to extract seasonality by ﬁtting the function to time series

(Jönsson and Eklundh, 2002 ). The amplitude of the MODIS NDVI time

series was estimated using the range of the seasonal component derived

with the STL function, as shown in Fig. 2 . The estimated seasonal

amplitudes of the real forest and grassland MODIS NDVI time series

were 0.1 and 0.5 ( Fig. 1 ). Second, the noise component was generated

using a random number generator that follows a normal distribution N

(µ=0,σ=x), where the estimated xvalues were 0.04 and 0.02, to

approximate the noise within the real grass and forest MODIS NDVI time

series ( Lhermitte et al., submitted for publication ). Vegetation index

speciﬁc noise was generated by randomly replacing the white noise by

noise with a value of −0.1, representing cloud contamination that often

remains after atmospheric correction and cloud masking procedures.

Third, the real grass and forest MODIS NDVI time series were

approximated by selecting constant values 0.6 and 0.8 and summingthem with the simulated noise and seasonal component. A comparison

between real and simulated NDVI time series is shown in Fig. 1 .108 J. Verbesselt et al. / Remote Sensing of Environment 114 (2010) 106 –115

Based on the parameters required to simulate NDVI time series

similar to the real grass and forest MODIS NDVI time series ( Fig. 1 ), we

selected a range of amplitude and noise values for the simulation

study ( Table 1 ). These values are used to simulate NDVI time series of

different quality (i.e. varying signal to noise ratios) representing a

large range of land cover types.

The accuracy of the method for estimating the number, timing and

magnitude of abrupt changes was assessed by adding disturbances with

as p e c i ﬁc magnitude to the simulated time series. A simple disturbance

was simulated by combining a step function with a speci ﬁc magnitude

(Table 1 ) and linear recovery phase ( Kennedy et al., 2007 ). As such, the

disturbance can be used to simulate, for example, a ﬁre in a grassland or

an insect attack on a forest. Three disturbances were added to the sum of

simulated seasonal, trend, and noise components using simulation

parameters in Table 1 . An example of a simulated NDVI time series with

three disturbances is shown in Fig. 3 . A Root Mean Square Error (RMSE)

was derived for 500 iterations of all the combinations of amplitude,

noise and magnitude of change levels to quantify the accuracy of

estimating: (1) the number of detected changes, (2) the time of change,