Quantifying intra-annual persistent behaviour in SPOT-VEGETATION NDVI data for Mediterranean ecosystems of southern Italy

Remote Sensing of Environment 101 (2006) 95 – 103 www.elsevier.com/locate/rse

Quantifying intra-annual persistent behaviour in SPOT-VEGETATION NDVI data for Mediterranean ecosystems of southern Italy Luciano Telesca *, Rosa Lasaponara Istituto di Metodologie Avanzate di Analisi Ambientale, Consiglio Nazionale delle Ricerche, Area della Ricerca di Potenza, Tito, Italy Received 18 April 2005; received in revised form 7 December 2005; accepted 10 December 2005

Abstract Multi-temporal series of satellite SPOT-VEGETATION Normalized Difference of Vegetation Index (NDVI) data from 1998 to 2003 were exploited for studying persistence in Mediterranean ecosystems of southern Italy. We used Multiple Segmenting Method (MSM), which is well suited to analyze scaling behaviour in short time series, and the Detrended Fluctuation Analysis (DFA), which permits the detection of persistent properties in nonstationary signal fluctuations. Our findings point out to the characterization of Mediterranean ecosystems as governed by persistent mechanisms. D 2005 Elsevier Inc. All rights reserved. Keywords: SPOT-VEGETATION NDVI; Mediterranean; Southern Italy; Vegetation

1. Introduction Variations in the composition and distribution of vegetation can arise in response to natural hazard (drought, wind, floods, rain erosion) and anthropic stress (industry, overgrazing, fires, land abandonment) and represents one of the main source of systematic change on local, regional, or global scale. The characterization of land surface conditions and land surface variations can be efficiently approached by using satellite remotely sensed data mainly because they provide a wide spatial coverage and internal consistency of data sets. In particular, the Normalized Difference Vegetation Index (NDVI) is an expression of contrasting reflectance between red and near-infrared regions of a surface spectrum (Rouse et al., 1974). This expression is a readily usable quantity that can be linked with the green vegetation cover or measure of vegetation abundance, and is given by the following formula: NDVI = (R NIR
R RED) / (R NIR + R RED), where R NIR is nearinfrared (NIR) reflectance and R RED is the red reflectance. This index is sensitive to the presence of green vegetation (Sellers, 1985), and has been well correlated with biomass and green leaf area index in chaparral and grassland of California * Corresponding author. Tel.: +39 0971 427201; fax: +39 0971 427271. E-mail address: [email protected] (L. Telesca). 0034-4257/$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.rse.2005.12.007

(Gamon et al., 1995). It has been used for several regional and global applications in studies concerning the distribution and the potential photosynthetic activity of vegetation (Deblonde & Cihlar, 1993; Myneni et al., 1995; Prince & Tucker, 1986). Due to its formulation, NDVI allows a normalization of red / NIR ratio, and therefore it robustly describes green vegetation in spite of varying atmospheric conditions in the red and NIR bands (Fraser & Kaufman, 1985; Holben et al., 1990). This index is also regarded as a reliable indicator for land cover variations (e.g. Cuomo et al., 2001; Huemmrich et al., 1999; Lanfredi et al., 2003; Myneni et al., 1996) since its temporal evolution is strongly linked to changes in the state of the surface. In particular, surface energy and water balance (Betts et al., 1996; Chase et al., 1996) as well as carbon cycle (Betts, 2000; Eastman et al., 2001) are strongly influenced by dynamic changes in vegetation cover. Further, natural hazards (drought, wind, floods, rain) and anthropic activity have a direct impact on vegetation, which, in turn, feeds back on climate (Eswaran et al., 2001; Foley et al., 1994). The existence of feedback mechanisms involving anthropic activity, ecological patterns, different subsystems of climate and the Earth’s surface gives rise to correlation structures and memory phenomena. The vegetation patterns constrain and at the same time are constrained by the processes that influence them. Within this feedback framework, the concept of persistence,

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developed through the concept of fractals (Feder, 1988), is very useful in order to characterize the stability/instability properties of vegetation dynamics. In this context it is crucial to characterize the vegetation dynamics by means of methodologies which are able to determine time scale structures in an observational time series in order to obtain information on features and causes of variations at different time scales. Actually, establishing of effective methodologies for the analysis of satellite multi-temporal data is one of the most arduous challenges that the remote sensing community will face. Investigations of satellite time series require robust methodologies for the extraction of valuable information stored because the methods currently used for historical time series analysis cannot be applied to the short time series available from satellite data since satellite remote sensing is a rather recent technique. In this paper, we discuss the use of three methodological approaches that we applied to a temporal series 1998 to 2003 of NDVI SPOT VEGETATION data acquired for southern Italy. Such methodologies allow for the characterization of persistence properties of the signal fluctuations, so provide valuable information about the inherent memory of the system. Persistence means that the system under investigation is governed by positive feedback mechanisms, which tend to destabilize the system under external forces or perturbations. 2. Study area The analysis was performed in vegetated areas of the South of Italy which includes most of the Mediterranean part of the Italian peninsula. The different vegetation covers were recognized by using the Corine land cover map (Fig. 1, left) provided by the European Topic Centre on Land Cover at Environmental

N

satellite data Center in Kiruna, Sweden. The Corine map was recoded and re-sampled at the same spatial resolution (1 km) as NDVI satellite data (Fig. 1, right). The prevailing land covers are (Fig. 1, left): agricultural areas, conifer stands (Pinus pinea, Pinus halepensis, Pinus nigra, Pinus laricio), deciduous stands (Eucalyptus, Castanea sativa, Fagus silvatica, Quercus pubescens and Quercus cerris), Mediterranean maquis, that is Quercus ilex (small, thickly packed trees, shrubs and bushes) as well as urban areas. The vegetation covers investigated were: forests (13%), shrub-lands (7.4%), and mixed made up of herbaceous and agricultural land covers (30.7%). The study area is characterized by a typically Mediterranean climate with a pronounced biseasonality regime having hot/dry summers and cold/rainy winters. During the last decades, temperature in the South of Italy as in other Mediterranean regions has shown an overall warming trend. Precipitation in the region has oscillated throughout the past decades however, there seem to have been no general trends in the seasonality of precipitation. Nevertheless, increase in the duration and severity of summer drought was recorded during the last years. In conjunction with warming, summer reductions in precipitation will have subjected vegetation to significant increases in the duration and severity of drought, potentially affecting temporal patterns, modifying photosynthetic activity and limiting primary productivity. Therefore, seasonal droughts, the very high rainfall variability and sudden and high-intensity rainfall, are likely to have had complex effects on Mediterranean vegetation, but the net impact of these remains uncertain. Undoubtedly, the investigated area is regarded as one of the most vulnerable in the Mediterranean basin, as shown by

Artificial surfaces Pastur Cultivated Little Vegetated Maquis Forests Low NDVI Fig. 1. (Left) Corine land cover for the study area. (Right) SPOT-VGT NDVI decadal composition.

i NDVI High

L. Telesca, R. Lasaponara / Remote Sensing of Environment 101 (2006) 95 – 103

ground surveys and satellite-based investigations (Cuomo et al., 2001; Lanfredi et al., 2003) and by a number of studies regarding the mapping of the desertification risk in Italy performed within different framework from global (Eswaran & Reich, 1998), continental (DISMED, 2003), national scale (Kosmas et al., 1999) down to regional scale (UNCCD-CRIC, 2002). The environmental equilibrium of southern Italy is fragile and highly vulnerable to perturbations and, therefore, it is expected that its ecosystems should be more sensitive to the changes that are presently affecting the whole Mediterranean basin.

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1999). If a = 0 the temporal fluctuations are purely random, typical of white noise processes, characterized by completely uncorrelated samples; in this case the process is memoryless. If a > 0, the temporal fluctuations are persistent, meaning that positive (negative) variations of the signal will be very likely followed by positive (negative) variations; this feature is typical of systems which are governed by positive feedback mechanisms. If a < 0, the temporal fluctuations are antipersistent, meaning that positive (negative) variations of the signal will be very likely followed by negative (positive) variations; this feature is typical of systems which are governed by negative feedback mechanisms.

3. Methods 3.2. Multiple segmenting method To quantitatively characterize NDVI dynamics, techniques able to extract robust features hidden in their complex fluctuations are needed. Fractality is one of the features of such complexity. What does fractality mean? A fractal is an object whose sample path included within some radius scales with the size of the radius. It is clear from the definition of fractal, that fractal processes are characterized by scaling behaviour, which leads naturally to power-law statistic. In fact, consider a statistics f(x), which depends continuously on the scale x, over which the measurements are taken. Suppose that changing the scale x by a factor a, will effectively scale the statistics f(x) by another factor g(a), f ðaxÞ ¼ g ðaÞf ð xÞ:

ð1Þ

The only nontrivial solution for this scaling equation is given by f ð xÞ ¼ bgð xÞ;

ð2Þ

g ð xÞ ¼ xc ;

ð3Þ

for some constants b and c (Thurner et al., 1997). Therefore, power-law statistics and fractals are very closely related concepts. 3.1. Power spectral density The fractality of a signal can be investigated in order to characterize its temporal fluctuations; in this case, we need to perform second-order fractal measures, which furnish information regarding the correlation properties of a time series. The spectral analysis represented the standard method to detect correlation features in time series fluctuations. The power spectrum is obtained by means of the Fourier Transform of the signal. It describes how the power is concentrated at various frequency bands. Thus, the power spectrum reveals periodic, multi-periodic or nonperiodic signals. The scaling behaviour of a time series is revealed by a power-law dependence of the spectrum upon the frequency, S ð f Þ¨1=f a ;

ð4Þ

where the scaling (spectral) exponent a gives information about the type and the strength of the time-correlation structures intrinsic in the signal fluctuations (Havlin et al.,

Therefore, by estimating the scaling coefficient we are able to obtain quantitative information on the strength of persistent correlations of the signal and to gain insight into the kind of mechanisms that may be responsible of its generation. The strength of these correlations provides useful information about the inherent memory of the system (Miramontes & Rohani, 2002). A good estimation of the scaling exponent a can be performed by means of several methods, but in a recent study, Pilgrim and Kaplan (1998) argued that, after reviewing a number of different techniques for estimating a, the linear regression of Fourier transform (FT)-estimated power spectrum plotted on log – log scales is very accurate. But the performance of the FT regression method is sensitive to the length of the record. Recently, Miramontes and Rohani (2002) have introduced the multiple segmenting method (MSM), which works for much shorter time series (less than 100). Let x i , i = 1, . . . N, be a time series of length N. The estimate of a is performed by means of the Fast Fourier Transform (FFT) on different segments of this series each of length n. The length n of the segments is chosen as a power of two (n = 2q , q Z N, q > 2). The sub-series {x 1, x 2, . . ., x n }, {x 2, x 3, . . ., x n+1}, . . ., {x N
n+1, x N
n+2, . . ., x N
n+1} are obtained. Using the linear regression of the log – log FFT-estimated power spectra, we obtain N
n + 1 pseudo-replicates of the exponent. Among these replicates the average and the standard deviation have to be considered. There is a drawback in using the MSM: as the segment size is shortened the information regarding the signal correlations is lost. But, the statistical advantage by the possibility of estimating the scaling exponent a number of times for any given time series. It is demonstrated that the average of the scaling exponents for the segments will furnish an accurate estimate of the scaling behaviour of the data. It has been shown (Miramontes & Rohani, 2002) that the estimate of a scales with the segment size according to the following ansatz: b gðnÞ ¼ a þ pffiffiffi ; n

ð5Þ

where a and b are constants. Fitting the function g(n) to the data generated using the MSM, and after substituting the values of the constants a and b, the value g(N) gives an estimated value of the scaling exponent a.

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3.3. Detrended fluctuation analysis The Detrended Fluctuation Analysis (DFA) (Peng et al., 1995) avoids spurious detection of correlations that are artifacts of trends and nonstationarity, that often affects experimental data. Such trends have to be well distinguished from the intrinsic fluctuations of the system in order to find the correct scaling behaviour of the fluctuations. Very often we do not know the causes and the scales of these underlying trends (Kantelhardt et al., 2001). The DFA method works as follows. With x ave we indicate the mean value of the series. The signal is first integrated, k

yð k Þ ¼

~ ½ xðiÞ
xave :

ð6Þ

i¼1

Next, the integrated time series is divided into boxes of equal length n. In each box a least-squares line is fit to the data, representing the trend in that box. The y coordinate of the straight line segments is denoted by y n (k). Next we detrend the integrated time series y(k) by subtracting the local trend y n (k) in each box. The root-mean-square fluctuation of this integrated and detrended time series is calculated by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 N F ð nÞ ¼ ~ ½ yðk Þ
yn ðk Þ2 : ð7Þ N k¼1 Repeating this calculation over all box sizes, we obtain a relationship between F(n), that represents the average fluctuation as a function of box size, and the box size n. If F(n) behaves as a power-law function of n, data present scaling: F ðnÞ”nd :

ð8Þ

Under these conditions the fluctuations can be described by the scaling exponent d, representing the slope of the line fitting log F(n) to log n. For a white noise process, d = 0.5. d > 0.5 indicates the presence of persistent correlations, meaning that a large (compared to the average) value is more likely to be followed by large value and vice versa. d < 0.5 indicates the presence of antipersistent correlations, meaning that a large (compared to the average) value is more likely to be followed by small value and vice versa. The exponents d and a are related to each other by (Buldyrev et al., 1995) d¼

1þa : 2

ð9Þ

4. Data analysis and discussion The investigations were performed on NDVI data derived from the sensor VEGETATION on board the SPOT satellite platforms. Such data are available free of charge at the Vlaamse Instelling voor Technologisch Onderzock (VITO) Image Processing centre (Mol, Belgium) http://www.vgt.vito.be. In particular, we analyzed a temporal series spanning from 1998 to 2003 made up of the ten-day (decadal) maximum value of daily NDVI maps. The temporal evolution of decadal NDVI composition is regarded as an effective time window able to

show the natural seasonal variations, the consequences of extreme climatic events and the man-induced damage suffered by ecosystems. The data were subjected to atmospheric corrections performed by CNES on the basis of the Simplified Method for Atmospheric Corrections (SMAC) (for details see Rahman & Dedieu, 1994). Moreover, the considered NDVI composition also allows for reducing the contamination effects due to residual clouds, atmospheric perturbations, variable illumination and viewing geometry that are generally present in daily NDVI maps. Pixels having residual cloud cover were excluded from our analysis. For each decadal NDVI image and for each cover, we calculated NDVIs, which is the spatial average. Fig. 2a– c shows the time variation of NDVIs from 1998 to 2003 for the three considered land cover types that determine the characteristics of seasonal NDVI curves. The observed temporal patterns characterize the phenological development, typical of the Mediterranean ecosystems, which is characterized by clear periodic trend. In order to eliminate the periodic seasonal trend, for each 10-day composition, we calculated the mean decadal bNDVIs. The mean decadal bNDVIs is calculated for each decade, e.g. 1st decade of January, by averaging over all years in the record. Fig. 3 shows the bNDVIs, whose maximum values correspond to the greenness peaks of the growing seasons; whereas, the minimum values correspond to the dormant seasons. Nevertheless, different magnitudes, amplitudes, and timings of temporal greenness can be observed for mixed covers compared to those observed for forests and shrub-lands. Fig. 3 shows two different modality behaviours. Modality indicates the periodicity of the vegetation production. For any given area, there can be either a single or multiple peak greenness depending on land cover/use and geographic location. Multi-modality occurs in areas with double cropping, or with vegetation highly responsive to bimodal temperature and/or precipitation regime, or with diverse land cover types. In our case, forests and shrub-lands exhibit a single-peak greenness as it is expected due to their structural characteristics. Whereas, the mixed cover class exhibits two peaks of greenness occurring at different times. This fact is mainly due to the heterogeneity of this class, that is mostly made up of hay/pasture, shrub-land, grassland and forest, grassland, and some deciduous forest. As in the case of forests and shrub-lands the main greenness peak is associated with the spring green up of vegetation, whereas the second peak is mainly due to the precipitation regime which allows for a larger availability of water during the main precipitation season occurring in autumn during the months of October and November. Studies of intra-annual NDVI variability not caused by phenology and/or vegetation growth requires the removal of seasonal trends in order to isolate the intrinsic signal fluctuations. The identification and quantification of intra-annual behaviour are highly desired for understanding how vegetation dynamics respond to external forcing such as those caused by short-term climate disturbances including summer drought and winter freezing, or environmental disturbances including soil condition, land use and management.

L. Telesca, R. Lasaponara / Remote Sensing of Environment 101 (2006) 95 – 103

a)

forest cover 0.9 0.8

NDVIS

0.7 0.6 0.5 0.4 0.3 0

50

100

150

200

t (decade)

b)

shrub-land cover 0.8

NDVIS

0.7 0.6 0.5

0.4 0.3 0

50

100

150

200

t (decade)

c)

mixed cover 0.75 0.70

NDVIS

0.65

99

Fig. 5 shows the power spectral density of the three covers analyzed in southern Italy. Firstly, the spectra, plotted in log – log scales, are not flat for all the analyzed frequency bands. This indicates that the vegetational covers under study are not characterized by purely random temporal fluctuations. The three covers are, therefore, not realizations of white noise processes, which are memoryless and uncorrelated, but featured by correlated time structure and presence of memory phenomena. However, the spectra appear very rough, due to the short number of the data. Although the appearance of this roughness, the global trend in all the spectra is linearly decreasing. This allows describing the spectra by power-law functions of the frequency f, with the scaling exponent a estimated as the slope of the line that fits the power spectrum by means of the least square method. The values of the exponent a gives information about the type and the strength of the temporal fluctuations inherent in the data. In our case, all the covers show scaling exponents larger than zero, and this suggests that they are characterized by persistent time fluctuations. All three vegetation types exhibit frequency peaks in the power spectra S( f). In particular the highest frequency peak is at approximately f(1/dec) = 0.03, corresponding to about 1 year for the forest; at approximately f(1/dec) = 0.02 corresponding to about 400 – 500 days for the shrub-land and mixed covers. These peaks indicate that there is a strong annual component of the NDVI fluctuations. In order to investigate the nature of the presence of such frequency peaks and scaling behaviour in power spectra, we analyzed the rain, recorded in the same period of satellite data by ten ground-based meteorological stations. The rain gauge (in accordance with the W.M.O. recommendations) consists of a catchment area of 500 cm2 with an output magnetic reed switch and operating temperature between
20 -C and + 50 -C; the sensitivity threshold is 0.2 mm and accuracy of 2%. We analyzed the departures R d = R a
bR a, where R a is the decadal accumulated rain and bR a is the mean decadal, in order to be consistent with the same analysis performed on NDVId satellite data.

0.60

forest shrub-land mixed

0.85

0.55

0.80 0.50

0.75 0.70

0.40

0.65

0

50

100

150

200

t (decade)



0.45

0.60 0.55 0.50

Fig. 2. Temporal variation of the spatial average over the three NDVI covers from 1998 to 2003; (a) forests, (b) shrub-lands and (c) mixed.

0.45 0.40

Therefore, we focused on the departures NDVI d = NDVIs
bNDVIs from the mean decadal bNDVIs. Fig. 4a to c shows the time variation of NDVId, where the periodic seasonal trend has been removed. The further analyses have been performed on these data sets.

0.35 0

3

6

9

12 15 18 21 24 27 30 33 36 t (decade)

Fig. 3. Temporal variation of the spatial average over the three bNDVIs covers from 1998 to 2003.

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L. Telesca, R. Lasaponara / Remote Sensing of Environment 101 (2006) 95 – 103

forest cover

a) 0.08 0.06

NDVId

0.04 0.02 0.00 -0.02 -0.04

shrub-land cover and the dynamics of rainfall fluctuations. In fact, the behaviour of NDVI signal observed for Mediterranean shrub-land covers is strongly linked to the water availability. Indeed, this is not surprising considering the high correlations that is generally found between the net photosynthetic rates and several parameters of water availability (De Angelis et al., 2005; Larcher, 1995; Llorens et al., 2003). The results obtained from our investigations provided further evidence of the key role of water availability in the

a)

-0.06 0

50

100 t (decade)

150

0.1

200

0.01 shrub-land cover

0.08

1E-3 S(f)

b)

forest cover

1

0.06

αFT=0.75

1E-4 1E-5

0.04

1E-6

NDVId

0.02

1E-7

0.00

1E-8 0.01

-0.02

0.1 f(1/dec)

-0.04

b)

-0.06

shrub-land cover 0.1

-0.08

c)

50

100 t (decade)

150

200 0.01

mixed cover 0.08

S(f)

0

αFT=0.32

1E-3

0.06 0.04

1E-4

NDVId

0.02 0.00

0.01

-0.02

0.1 f(1/dec)

1

c)

-0.04

mixed cover

1 -0.06 0.1

-0.08 50

100 t (decade)

150

0.01

200

Fig. 4. Temporal variation of the departure NDVId = NDVIs
bNDVIs from the mean decadal bNDVIs from 1998 to 2003 for the three covers; (a) forests, (b) shrub-lands and (c) mixed.

Fig. 6 shows the power spectral density averaged on the ten power spectra calculated for the rain data R d. It is visible the frequency peak at about f(1/dec) = 0.02 superimposed to the scaling behaviour with scaling exponent a ¨0.2. These results (the frequency peak and the scaling exponent) suggest a close connection between the vegetational dynamics of

S(f)

0

1E-3

αFT=1.0

1E-4 1E-5 1E-6 1E-7 0.01

0.1 f(1/dec)

Fig. 5. The analysis by means of the Power Spectrum method on the NDVId data plotted in Fig. 4.

L. Telesca, R. Lasaponara / Remote Sensing of Environment 101 (2006) 95 – 103

behaviour more unstable to external perturbations. The analyzed time scales range between 1 month and about 1.4 years. Therefore, the persistent behaviour of the Mediterranean ecosystems under study concerns only intra-annual time dynamics. This means that within this time scale range, the feedback mechanisms express a positive circular causality that

0.01

101

α=0.2

1E-3

a)

forest cover 4

1E-4

Fig. 6. Averaged power spectral density of ten rain time series, recorded by ground-based meteorological stations.

regulation of the photosynthetic rates in Mediterranean shrubland covers. Fig. 7 shows the results of the MSM procedure applied to the three vegetation covers. The length n of the segments has been chosen as a power of two, n = 2q , with q ranging between 4 and 7. The maximum value of q is limited by the length of the series (N = 198). We fit the obtained scaling exponents versus n using the ansatz (5), and obtained for the parameters (a, b) the following estimates: (¨0.607, ¨1.710), (¨0.516, ¨0.829) and (¨0.959, ¨1.417) for the forest, shrub-land and mixed covers, respectively. Substituting these values and computing g(198), we estimated a MSM about 0.73, 0.58 and 1.06 for the considered three covers, respectively. The relation F(n)¨n (shown in Fig. 8) presents a very clear scaling behaviour for time scales ranging from approximately 1 month to 1.4 years, with scaling exponents (d¨0.87, a DFA¨0.74), (d¨0.82, a DFA¨0.64) and (d¨1.05, a DFA¨1.1) for the forest, shrub-land and mixed covers, respectively. These values are consistent with the MSM analysis, and indicate the presence of persistent dynamics in the data. A striking feature of these results is that forests and shrublands have very close values for the scaling exponent, leading to a very similar dynamical behaviour. This study shows the persistent characterization of the temporal fluctuations of the time series of decadal NDVI satellite data in southern Italy. Persistence means that the investigated ecosystems are governed by positive feedback mechanisms, which tend to destabilize the systems under external forces. This means that vegetation, after external shocks, is not yet returned to the initial conditions and very likely it will not return to reference levels for a long time; thus, vegetation reacts to negative shocks attempting to accumulate the positive ones (Lanfredi et al., 2004). Therefore, persistence is closely linked with the concept of resilience, that is the ability of vegetation to recover from disturbances. Similar persistent features are evidenced in natural ecosystems, such as forests and shrub-lands, while mixed covers show a larger persistent character, which leads to a

a=0.60708, b=1.71024 αMSM=0.73

2

1

0

-1 0

20

40

60

80

100

120

140

segment size

b)

shrub-land 8

scaling component

f(1/dec)

a=0.51612, b=0.82997 αMSM=0.575

6

4

2

0

-2 0

20

40

60

80

100

120

140

segment size

c)

mixed cover 4 a=0.95868, b=1.41703 αMSM=1.06 3

scaling component

0.1

scaling component

3 0.01

2

1

0

-1 0

20

40

60

80

100

120

140

segment size Fig. 7. The analysis by means of the MSM on the NDVId data plotted in Fig. 4.

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forest cover

a)

5. Conclusions

-1.0 d=0.87 αDFA=0.74

log10(F(n))

-1.2 -1.4 -1.6 -1.8 -2.0 -2.2 0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

log10(n) (decade)

b) -0.8

shrub-land cover

-1.0 d=0.82 αDFA=0.64

log10(F(n))

-1.2 -1.4 -1.6 -1.8 -2.0 -2.2 0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

log10(n) (decade)

c) -0.6

mixed cover

-0.8 d=1.05 αDFA=1.1

-1.0 log10(F(n))

-1.2 -1.4 -1.6

Efforts in vegetation mapping and monitoring using remotely sensed data have increased in the recent years due to the increasing demand for up-to date information on the Earth’s land cover with respect to climate and ecosystems changes. This requires availability of multi-temporal remotely sensed data and development of time series analysis techniques. The value of remotely sensed data for operational vegetation assessment depends on the ability to accurately, efficiently and cost-effectively retrieve key parameters, useful for the characterization of structural properties and temporal dynamics of vegetation. In particular, the identification and quantification of persistent behaviour are highly requested for understanding how vegetation dynamics respond to external forcing such as those caused by climate disturbances including drought, flood, freezing hazard, and violent wind, or environmental disturbances including wild-land fires, soil conditions, land clearance and dramatic change in land use and management. In this paper, three methodologies for investigating the intra-annual vegetational dynamics of three different land covers have been used, in order to capture their persistent behavioural trend. They rely on estimating the scaling properties of the vegetational dynamics, which give information about the correlation structures and memory phenomena of the Mediterranean ecosystems (forest, shrub-land and mixed covers). The values obtained for the scaling exponents reveal that all the covers are characterized by persistent temporal fluctuations for time scales ranging between 1 month and about 1.4 years. Our results suggest the presence of feedback mechanisms, characterized by a positive circular causality that plays the role of growth-generating phenomenon, driving unstable patterns. Therefore the vegetational processes take memory of external shocks, which drive the time dynamics of the vegetation covers. These methods can be adopted for investigations at a pixel spatial scale, in order to derive local information about the vegetation fluctuation dynamics.

-1.8 -2.0

Acknowledgments

-2.2 -2.4 0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

log10(n) (decade) Fig. 8. DFA method performed on the NDVId data plotted in Fig. 4.

acts as a growth-generating phenomenon and therefore drives unstable patterns. Therefore the vegetational processes take memory of external shocks, which drive the time dynamics of the vegetation covers. Of course, we want to stress that this dynamical behaviour is consistent with the limited range of time scales (from 1 month to 1.4 years), that could be investigated with the available dataset and the adopted analysis procedures.

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