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VEGETATION Normalized Difference Vegetation Index (NDVI) time series to characterize vegetation recovery after fire disturbance
International Journal of Applied Earth Observation and Geoinformation 26 (2014) 441–446
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International Journal of Applied Earth Observation and Geoinformation journal homepage: www.elsevier.com/locate/jag
Fisher–Shannon information plane analysis of SPOT/VEGETATION Normalized Difference Vegetation Index (NDVI) time series to characterize vegetation recovery after fire disturbance Antonio Lanorte a , Rosa Lasaponara a , Michele Lovallo b , Luciano Telesca a,∗ a b
Consiglio Nazionale delle Ricerche, Istituto di Metodologie per l’Analisi Ambientale, C. da S. Loja, 85050 Tito (PZ), Italy ARPAB, 85100 Potenza, Italy
a r t i c l e
i n f o
Article history: Received 10 December 2012 Accepted 24 May 2013 Keywords: Satellite time series Fisher information measure Shannon entropy Fires SPOT
a b s t r a c t The time dynamics of SPOT-VEGETATION Normalized Difference Vegetation Index (NDVI) time series are analyzed by using the statistical approach of the Fisher–Shannon (FS) information plane to assess and monitor vegetation recovery after fire disturbance. Fisher–Shannon information plane analysis allows us to gain insight into the complex structure of a time series to quantify its degree of organization and order. The analysis was carried out using 10-day Maximum Value Composites of NDVI (MVC-NDVI) with a 1 km × 1 km spatial resolution. The investigation was performed on two test sites located in Galizia (North Spain) and Peloponnese (South Greece), selected for the vast fires which occurred during the summer of 2006 and 2007 and for their different vegetation covers made up mainly of low shrubland in Galizia test site and evergreen forest in Peloponnese. Time series of MVC-NDVI have been analyzed before and after the occurrence of the fire events. Results obtained for both the investigated areas clearly pointed out that the dynamics of the pixel time series before the occurrence of the fire is characterized by a larger degree of disorder and uncertainty; while the pixel time series after the occurrence of the fire are featured by a higher degree of organization and order. In particular, regarding the Peloponneso fire, such discrimination is more evident than in the Galizia fire. This suggests a clear possibility to discriminate the different post-fire behaviors and dynamics exhibited by the different vegetation covers. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Wildfire represents one of the main disturbance factors (Trabaud, 1987) throughout the world (IPCC, 2007) and it is particularly relevant in many shrubland and wooded ecosystems of the Mediterranean Basin (Swetnam and Betancourt, 1998; Allen et al., 2002; Pausas, 2004). Wildfire affects both flora and fauna, severely damages ecosystem functionalities and causes considerable economic damages (IPCC, 2007). Fire-induced dynamic processes are very difficult to study since they affect the complex soil–surface–atmosphere system, due to the existence of feedback mechanisms involving human activity, ecological patterns and different subsystems of climate. Fire destroys vegetation and ecosystems rapidly, whereas, in contrast, recovery is a long-term process quite difficult to systematically and consistently assess and monitor over space and time (Gouveia et al., 2010). Accurate and detailed information on the impact of fire on vegetation as well the vegetation capability to recover after fire
∗ Corresponding author. Tel.: +39 0971427277. E-mail address: [email protected] (L. Telesca). 0303-2434/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jag.2013.05.008
are required. Post-fire investigations have been generally performed at stand level even though a wide range of habitats in the Mediterranean-type communities have been analyzed. Due to the necessity of monitoring large areas for long periods, reliable low-cost tools must be set up to consistently and properly assess the ecological consequences of fire disturbance in different ecosystems, geographic regions and vegetation cover types. To cope with these needs and gain information at different temporal and spatial scales, satellite time-series NDVI (Rouse et al., 1974), derived from NOAA/AVHRR, SPOT/VEGETATION or TERRA/MODIS, Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), Temathic Mapper (TM) may be fruitfully used. Long time-series of NDVI data are today available free of charge for all the above mentioned satellite sensors and offer spectral information adequate for monitoring vegetation and, in particular, for assessing post fire vegetation regeneration and recovery. Nevertheless, even if the importance and value of remotely sensed time-series data for vegetation monitoring has been strongly recognized (Goward et al., 1985; Tucker and Sellers, 1986; Lasaponara, 2006; Telesca and Lasaponara, 2006), only a limited number of methods have been today developed in order to extract and analyze the precious information therein stored to capture and explore temporal/spatial feature patterns and their variations.
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Over the years, investigations on post fire vegetation recovery have been conducted mainly using multi-date satellite images such as LANDSAT (Diaz-Delgado et al., 2002, 2003), and only recently satellite time series derived from AVHRR, SPOT/VEGETATION and MODIS (see for example Telesca and Lasaponara, 2005; Van Leeuwen, 2008; Van Leeuwen et al., 2010; Montesano et al., 2011) have been analyzed for monitoring post fire vegetation recovery. The NDVI is the most widely used index for investigating vegetation cover monitoring (Myneni et al., 1997) and post-fire recovery. In particular, the ability of NDVI time series to capture the different fire induced dynamics on vegetation covers has been generally investigated on the basis of satellite multi-date NDVI maps. Viedma et al. (1997) and Diaz-Delgado et al. (2002, 2003) estimated vegetation recovery rates by comparing NDVI ratios of vegetation burned and unburned areas from a limited number of Landsat scenes. To advance the understanding of many phenomena caused by fire disturbance, space monitoring of vegetation phenology, based on post fire trends and metrics, has been carried out by Van Leeuwen (2008) and Van Leeuwen et al. (2010) using long time series of AVHRR (Advanced Very High Resolution Radiometer), SPOT VEGETATION and Moderate Resolution Imaging Spectroradiometer (MODIS) see for example Gouveia et al. (2010) and Montesano et al. (2011). Ricotta et al. (1998) monitored the landscape stability of Mediterranean vegetation in relation to fire using a fractal algorithm applied to satellite NDVI data. Telesca and Lasaponara (2005, 2006) conducted specific statistical analyses using the Detrended Fluctuation Analysis (DFA) in forest areas to analyze and characterize the vegetation fire resilience, namely the capability of vegetation to recovery after fire. In more detail, they considered both a single fire occurrence (Telesca and Lasaponara, 2006) and also repeated wildfire events (Telesca and Lasaponara, 2008) in areas where no mitigation and/or rehabilitation treatments were carried out after fire occurrence. In this paper, the Fisher–Shannon information plane analysis of SPOT/VEGETATION NDVI time series has been used to characterize vegetation dynamics before and after fire occurrence for two test sites selected in Spain and Greece. The main purpose is to extract quantitative information on the temporal fluctuations of SPOT/VEGETATION NDVI time series.
2. Data The investigations were performed by using NDVI data derived from the VEGETATION sensor on board the SPOT satellite platforms. Such data are available free of charge at the Vlaamse Instelling voor Technologisch Onderzock (VITO) Image Processing center (Mol, Belgium) (http://www.vgt.vito.be). The data were subjected to atmospheric corrections performed by CNES on the basis of the simplified method for atmospheric corrections (SMAC). 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. Additionally, for each considered pixel we carefully checked the absence of residual errors due to cloud edges and shadows, image navigation inaccuracy and changing of viewing-illumination conditions by using a visual inspection and additional information obtained from the four single SPOTVGT channels and viewing geometry available on-line from VITO website. The SPOT VEGETATION data have a spatial resolution of 1 km
Fig. 1. Galizia (Spain) 9 August 2006 (MODIS RGB 2-4-3) – green circle: fire event considered. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The investigation was carried out using NDVI time series acquired from April 1998 to December 2010. The NDVI is computed using red (R ) and near-infrared (NIR ) channels as in formula (1). NDVI =
NIR − R NIR + R
(1)
The NDVI is designed as a ratio, in order to limit the atmospheric effects and, therefore, as a consequence its variability is normalize into the range −1 and +1. The NDVI values are less than 0 for water, clouds, snow cover, etc., whereas they exhibit values slightly higher than 0 for bare soils and definitely positive values according to the type and density of vegetation cover and its phenological state. We used the decadal composition of NDVI daily maps, downloaded from the VITO website. The decadal composition enable us to reduce the cloud contaminations, cloud border areas and the atmospheric effects which can strongly alter the actual spectral vegetation spectral responses. We considered two test sites: Galizia (Spain) and Peloponnese (Greece). The fire event in Galizia occurred from the 9th to the 10th of August 2006 (Fig. 1). It has been selected among many fire events that have affected the northwestern of Spain in that period. This fire event affected an area larger than 2000 hectares which was mainly covered by low shrubland vegetation (moorlands) at an altitude of around 100 meter a.s.l. The fire event in Peloponnese occurred from the 24th to the 31st of August 2007 (Fig. 2). Also in this case it is one of the fire events in Greece in August 2007. This fire event affected an area larger than 30,000 hectares which was covered by evergreen vegetation, mainly Leccio at an altitude between 500 and 1000 m a.s.l. The choice of the two study areas was determined by the need to evaluate the technique in two very different ecosystemic contexts both from the point of view of the climate (oceanic and mediterranean) that the vegetation (moorland and sclerophyllus vegetation). Since the analysis is pixel-based, the extension of the burned area, however, is not a relevant factor. 3. The Fisher–Shannon information plane The Fisher–Shannon information plane (FS) represents an efficient tool to investigate the complex temporal fluctuations of nonstationary signals. It is constructed with coordinate axes given by the Fisher Information Measure (FIM) and the Shannon entropy
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a statistical measure of complexity (Romera and Dehesa, 2004), and for 1-dimensional space, the line INX = 1 separates the FS plane in two parts, one allowed (INX > 1) and the other not allowed (INX < 1). The calculation of the FIM and the Shannon entropy depends on the calculation of the probability density function f(x) (pdf). The pdf can be estimated by means of the kernel density estimator technique (Devroye, 1987; Janicki and Weron, 1994) that approximates the density function as 1 fˆM (x) = K Mb M
x − x i
b
i=1
,
(5)
with b the bandwidth, M the number of data and K(u) the kernel function, a continuous non-negative and symmetric function satisfying the two following conditions
+∞
K(u) ≥ 0 and
K(u)du = 1.
(6)
−∞
Fig. 2. Peloponnese (Greece) 26 August 2007 (MODIS RGB 2-4-3) – green circle: fire event considered. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
power (NX ) that are both well known in the context of information theory. The FIM quantifies the amount of organization or order in a system, while NX measures its degree of uncertainty or disorder. The FIM was developed by Fisher (1925) in the context of statistical estimation. Then, it was utilized for different aim. Frieden (1990) used the FIM to describe the evolution laws of physical systems. Martin et al. (1999, 2001) applied it to characterize the temporal fluctuations of electroencephalograms (EEG) and to detect significant dynamical changes. Complex geophysical and environmental phenomena, like volcano-related signals, earthquake-related electromagnetic signals, atmospheric particulate matter benefited of the application of the FIM methodology to gain insight into their inner time dynamics and the mechanisms underlying their temporal fluctuations and to reveal precursory signatures of critical phenomena (Lovallo and Telesca, 2011; Telesca and Lovallo, 2011; Telesca et al., 2009, 2010, 2011). Shannon entropy is used to quantify the uncertainty of the prediction of the outcome of a probabilistic event (Shannon, 1948); in fact, it is zero for deterministic events. For continuous distributions the Shannon entropy can take any real positive and negative value. In order to avoid the difficulty arising with negative information measures, the so-called Shannon power entropy NX (defined below) can be used instead of the Shannon entropy. Let f(x) be the probability density of a signal x, then its FIM I is given by
+∞
I= −∞
2
∂ f (x) ∂x
dx , f (x)
(2)
and its Shannon entropy is defined as (Shannon, 1948):
+∞
HX =
fX (x) log fX (x)dx.
(3)
−∞
As specified above, the notion of Shannon entropy power will be used (Angulo et al., 2008) NX =
1 2HX . e 2e
(4)
The two measures satisfy the so-called ‘isoperimetric inequality’ INX ≥ D (Esquivel et al., 2010) where D is the dimension of the space. The ‘isoperimetric inequality’ indicates that FIM and Shannon entropy power are linked to each other; and the so called Fisher–Shannon (FS) information plane represents a tool for the characterization of signals. The product INX can also be employed as
In our study, we estimated the pdf f(x) by means of the algorithm developed in Troudi et al. (2008) combined with that developed in Raykar and Duraiswami (2006), that uses a Gaussian kernel with zero mean and unit variance:
− (x−xi ) 1 e 2b2 . √ M 2b2 M
fˆM (x) =
2
(7)
i=1
4. Results The time variation of the NDVI time series of six pixels covering the two investigated test sites (Galizia and Peloponnese) is studied. Figs. 3 and 4 show, as an example, the NDVI time series of all examined pixels for the Galizia site (Fig. 3) and for the Peloponnese site (Fig. 4). The pixels selected according to a random criterion constitute a representative sample of the study areas and the main vegetation patterns at the two sites. Selecting more points the results might be different in relation to different levels of fire severity of the pixels considered. However, this element does not affect the correctness of the results achieved. The temporal variation of the NDVI allows us to identify the following three different features: (i) intra-annual variability: both the sites show intra-annual phenomena linked to the seasonal component variations, with NDVI values ranging from around 0.6 to 0.8. This intra-annual variability, driven by the phenological seasonality as well as rainfall and temperature effects, is more evident for the Peloponnese site, due to its more homogeneous land cover mainly made up of Leccio trees; whereas it is less evident for the Galizia area that is mainly covered by low shrubs, with which rainfall interactions have more rapid impacts than tree land cover. (ii) inter-annual variability: observed for both the test sites, it may be linked to the yearly variability of meteoclimatic factors (temperature and precipitations), but also to changes in land management and/or gradual land degradation processes. (iii) abrupt change due to the fire disturbances, revealed by a NDVI value around 0.3 for the Galizia fire and lower than 0.2 for the Peloponnese one. Therefore, in order to eliminate the phenological fluctuations linked with the seasonality, for each pixel we analyzed the time series of the departure of the NDVI from the decadal mean (m), divided by the decadal standard deviation (), by using the following formula (Telesca and Lasaponara, 2005, 2006): NDVId =
NDVI − m(NDVI) . (NDVI)
(8)
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Fig. 3. NDVI time series of six pixel for the test site in Galizia.
Fig. 4. NDVI time series of six pixel for the test site in Peloponnese.
Figs. 5 and 6 show the NDVId series for the same pixels shown in Figs. 3 and 4. Before the occurrence of the fire, the NDVId of the Galizia test site exhibits a higher variability than that of the Pelopponese test site (and this is reasonable considering the diverse plant cover, density and phenologies). In correspondence of the fire occurrence the NDVId clearly evidences in both the sites a drop, which, however, has a different height, being larger for the Peloponnese (Fig. 5) than for the Galizia site (Fig. 6). Such drop in the NDVId may provide information on fire severity. The fire severity is a qualitative indicator of the effects of fire on ecosystems and its assessment is very important to monitor fire effects, to model and evaluate post-fire dynamics and to estimate the ability of vegetation to recover after fire: the Galizia site, in fact, seems to be closer
to the pre-fire situation than the Peloponnese site and, therefore, to recover more rapidly. In order to quantitatively evaluate these two different vegetation recovery behaviors, the time dynamics of the NDVId time series is analyzed by using the statistical approach of the Fisher–Shannon (FS) information plane. The pre-fire and post-fire FS properties of each pixel are investigated, subdividing the NDVId time series of each pixel into two sub-series, one corresponding to the pre-fire and the other to the post-fire variability of the NDVId . Fig. 7 shows the FS information plane for the Galizia site, while Fig. 8 shows that for the Peloponnese one. A common pattern can be identified in both the plots: the pre-fire sub-series are characterized by higher Shannon entropy power and lower FIM than those of the
Fig. 5. NDVId time series for the test site in Galizia corresponding to the NDVI pixel time series shown in Fig. 3.
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Fig. 6. NDVId time series for the test site in Peloponnese corresponding to the NDVI pixel time series shown in Fig. 4.
Galizia pre-fire post-fire
FIM
5. Discussion
1 1
Nx
Fig. 7. FS information plane for the Galizia site.
post-fire sub-series. This indicates that the dynamics of the NDVId time series before the occurrence of the fire is characterized by a larger degree of disorder and uncertainty; while the NDVId time series after the occurrence of the fire feature a higher degree of Peloponnese pre-fire post-fire 100
FIM
organization and order. In particular, regarding the Peloponnese test site, the discrimination between the pre- and post-fire subseries is more evident because the aggregation into two different clusters is more pronounced. Regarding the Galizia test site, this aggregation in two distinct clusters is less evident, even though the post-fire sub-series are characterized by a higher FIM and lower Shannon entropy power than the pre-fire sub-series.
10
Telesca and Lasaponara (2005, 2006) applying an independent statistical method, namely the detrended fluctuation analysis (DFA), found a significant discrimination between pre-fire and post-fire NDVI time series, revealing that post-fire vegetation dynamics is characterized by a higher persistence degree than the pre-fire vegetation dynamics, suggesting, then, a higher regularity of the post-fire pixel sub-series with respect to the pre-fire ones. This higher regularity, which signals the tendency of the vegetation to recover after being affected by the fire, is nicely consistent with the higher order and higher level of organization (indicated by the higher FIM) shown by the post-fire sub-series. Both the DFA and the Fisher–Shannon (FS) information plane provide, then, a quantitative characterization of the vegetation recovery capability. Another important element of interpretation can be related to the different degrees of fire severity between the two analyzed events. It is very likely that the best discrimination obtained for the Peloponnese fire is related to the higher level of fire severity of this event compared to that of the Galicia event. In particular, regarding the Peloponnese site, such discrimination is more evident than for the Galizia site, probably due to the different vegetation covers characterizing the two sites. Therefore, the different post-fire behaviors may refer and be linked to the different recovery abilities, which characterize the different vegetation types: the low shurbland’s recovery rate is faster than the tree cover’s re-growth and pre-fire functional and structural recovery rate. As regards the choice of the two areas, the applied method is independent of the size of the burned area which do not influences the efficiency of the method. Instead, the application of the method to areas that have a different spectral behavior is one of the objectives of this work. 6. Conclusions
1
Nx
1
Fig. 8. FS information plane for the Peloponnese site.
In this paper, the time dynamics of SPOT-VEGETATION NDVI time series were analyzed by using the statistical approach of the Fisher–Shannon (FS) information plane in order to assess and
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monitor vegetation recovery after fire disturbance. The investigation was performed on two test sites, located one in Galizia (North Spain) and the other in Peloponnese (South Greece). They were selected because of two vast fires, occurred during the summers of 2006 and 2007, and for the different vegetation covers, mainly low shrubland in Galizia and evergreen forest I Peloponnese. Data analysis was carried out using the 10-day Maximum Value Composites of NDVI (MVC-NDVI), with a 1 km × 1 km spatial resolution. For both the test sites, the time series of MVC-NDVI have been analyzed before and after the fire occurrence. Results clearly point out that the dynamics of the NDVI time series before the fire occurrence are characterized by a larger degree of disorder and uncertainty, while that of NDVI time series after fire occurrence features a higher degree of organization and order. Of course the FS method needs to be further validated on other cases in order to be considered an efficient and promising method, which applied to multi-temporal space is able to account for NDVI variations and to extract multi-year trends from NDVId variability. Acknowledgements The present study was supported by the CNR-CAS Project “Development of models and time series analysis tools for oceanographic parameters analysis and forecasting”, in the framework of the Bilateral Agreement for Scientific and Technological Cooperation Between CNR and CAS 2011–2013. References Allen, C.D., Savage, M., Falk, D.A., Suckling, K.F., Swetnam, T.W., Schulke, T., Stacey, P.B., Morgan, P., Hoffman, M., Klingel, J.T., 2002. Ecological restoration of Southwestern ponderosa pine ecosystems: a broad perspective. Ecological Applications 12, 1418–1433. Angulo, J.C., Antolin, J., Sen, K.D., 2008. Fisher–Shannon plane and statistical complexity of atoms. Physics Letters A 372, 670–674. Devroye, L., 1987. A Course on Density Estimation. Birkhauser, Boston. Diaz-Delgado, R., Lloret, F., Pons, X., Terradas, J., 2002. Satellite evidence of decreasing resilience in mediterranean plant communities after recurrent wildfires. Ecology 83, 2293–2303. Diaz-Delgado, R., Lloret, F., Pons, X., 2003. Influence of fire severity on plant regeneration by means of remote sensing imagery. International Journal of Remote Sensing 24, 1751–1763. Esquivel, R.O., Angulo, J.C., Antolin, J., Dehesa, J.S., Lopez-Rosa, S., Flores-Gallegos, N., 2010. Analysis of complexity measures and information planes of selected molecules in position and momentum spaces. Physical Chemistry Chemical Physics 12, 7108–7116. Fisher, R.A., 1925. Theory of statistical estimation. Proceedings of the Cambridge Philosophical Society 22, 700–725. Frieden, B.R., 1990. Fisher information, disorder, and the equilibrium distributions of physics. Physical Review A 41, 4265–4276. Gouveia, C., DaCamara, C.C., Trigo, R.M., 2010. Post-fire vegetation recovery in Portugal based on SPOT/VEGETATION data 2010. Natural Hazards and Earth System Sciences 10, 673–684. Goward, S.N., Tucker, C.J., Dye, D.G., 1985. North American vegetation patterns observed with theNOAA-7 advanced very high resolution radiometer. Plant Ecology 64, 3–14. IPCC, 2007. Intergovernmental Panel on Climate Change, fourth assessment report. Climatic Change. Synthesis Report, Summary for Policymakers. Janicki, A., Weron, A., 1994. Simulation and Chaotic Behavior of Stable Stochastic Processes. Marcel Dekker, New York. Lasaponara, R., 2006. On the use of principal component analysis (PCA) for evaluating interannual vegetation anomalies from SPOT/VEGETATION NDVI temporal series. Ecological Modelling 194, 429–434.
Lovallo, M., Telesca, L., 2011. Complexity measures and information planes of X-ray astrophysical sources. Journal of Statistical Mechanics, P03029. Martin, M.T., Pennini, F., Plastino, A., 1999. Fisher’s information and the analysis of complex signals. Physics Letters A 256, 173–180. Martin, M.T., Perez, J., Plastino, A., 2001. Fisher information and nonlinear dynamics. Physica A 291, 523–532. Montesano, T., Lanorte, A., De Santis, F., Lasaponara, R., 2011. Pre and Post Fire Vegetation Behavioral Trends from Satellite MODIS/NDVI Time Series in Seminatural Areas, ICCSA 2011 – International Conference, Santander, Spain, June 20–23. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (Eds.), Computational Science and Its Applications Proceedings, Part II. Lecture Notes in Computer Science, 6783. Springer, ISBN 978-3-642-21886-6, pp. 330– 343. Myneni, R.B., Keeling, C.D., Tucker, C.J., Asrar, G., Nemani, R.R., 1997. Increased plant growth in the northern high latitudes from 1981 to 1991. Nature 386, 698–702. Pausas, J.G., 2004. Changes in fire and climate in the eastern Iberian Peninsula (Mediterranean Basin). Climatic Change 63, 337–350. Raykar, V.C., Duraiswami, R., 2006. Fast optimal bandwidth selection for kernel density estimation. In: In Proceedings of the sixth SIAM International Conference on Data Mining, Bethesda, April 2006, pp. 524–528. Ricotta, C., Avena, G.C., Olsen, E.R., Ramsey, R.D., Winn, D.S., 1998. Monitoring the landscape stability of Mediterranean vegetation relation to fire with a fractal algorithm. International Journal of Remote Sensing 19, 871–881. Romera, E., Dehesa, J.S., 2004. The Fisher–Shannon information plane, an electron correlation tool. Journal of Chemical Physics 120, 8906–8912. Rouse, J.W.J., Haas, R.H., Schell, J.A., Deering, D.W., 1974. Monitoring vegetation systems in the Great Plains with ERTS. In: Third ERTS Symposium, NASA SP-351, Washington, DC, pp. 309–317. Shannon, C.E., 1948. A mathematical theory of communication. Bell System Technical Journal 27, 379–423, 623-656. Swetnam, T.W., Betancourt, J.L., 1998. Mesoscale disturbance and ecological response to decadal climatic variability in the American southwest. Journal of Climate 11, 3128–3147. Telesca, L., Lasaponara, R., 2005. Discriminating dynamical patterns in burned and unburned vegetational covers by using SPOT-VGT NDVI data. Geophysical Research Letters 32, L21401. Telesca, L., Lasaponara, R., 2006. Pre- and post-fire behavioral trends revealed in satellite NDVI time series. Geophysical Research Letters 33, L14401. Telesca, L., Lasaponara, R., 2008. Analysing vegetation response to two successive fires using satellite SPOT-VGT Normalized Difference Vegetation Index time series. In: Proceedings of the 10th IASTED International Conference Signal and Image Processing, Kailua-Kona, Hawaii, USA, August 18–20, 2008, pp. 300– 303. Telesca, L., Lovallo, M., 2011. Analysis of the time dynamics in wind records by means of multifractal detrended fluctuation analysis and the Fisher–Shannon information plane. Journal of Statistical Mechanics, P07001. Telesca, L., Lovallo, M., Ramirez-Rojas, A., Angulo-Brown, F., 2009. A nonlinear strategy to reveal seismic precursory signatures in earthquake-related self-potential signals. Physica A 388, 2036–2040. Telesca, L., Lovallo, M., Carniel, R., 2010. Time-dependent Fisher Information measure of volcanic tremor before 5 April 2003 paroxysm at Stromboli volcano, Italy. Journal of Volcanology and Geothermal Research 195, 78–82. Telesca, L., Lovallo, M., Hsu, H.-L., Chen, C.-C., 2011. Analysis of dynamics in magnetotelluric data by using the Fisher–Shannon method. Physica A 390, 1350– 1355. Trabaud, L., 1987. Dynamics after fire of sclerophyllous plant communities in the Mediterranean basin. Ecologia Mediterranea 13, 25–37. Troudi, M., Alimi, A.M., Saoudi, S., 2008. Analytical plug-in method for kernel density estimator applied to genetic neutrality study. EURASIP Journal on Advances in Signal Processing 2008, Article ID 739082. Tucker, C.J., Sellers, P.J., 1986. Satellite remote sensing of primary production. International Journal of Remote Sensing 7, 1395–1416. Van Leeuwen, W.J.D., 2008. Monitoring the effects of forest restoration treatments on post-fire vegetation recovery with MODIS multitemporal data. Sensors 8, 2017–2042. Van Leeuwen, W.J.D., Casady, G.M., Neary, D.G., Bautista, S., Alloza, J.A., Carmel, Y., Wittenberg, L., Malkinson, D., Orr, B.J., 2010. Monitoring post-wildfire vegetation response with remotely sensed time-series data in Spain, USA and Israel. International Journal of Wildland Fire 19, 75–93. Viedma, O., Melia, J., Segarra, D., Garcia-Haro, J., 1997. Modeling rates of ecosystem recovery after fires by using landsat TM data. Remote Sensing of Environment 61, 383–398.
Contents lists available at ScienceDirect
International Journal of Applied Earth Observation and Geoinformation journal homepage: www.elsevier.com/locate/jag
Fisher–Shannon information plane analysis of SPOT/VEGETATION Normalized Difference Vegetation Index (NDVI) time series to characterize vegetation recovery after fire disturbance Antonio Lanorte a , Rosa Lasaponara a , Michele Lovallo b , Luciano Telesca a,∗ a b
Consiglio Nazionale delle Ricerche, Istituto di Metodologie per l’Analisi Ambientale, C. da S. Loja, 85050 Tito (PZ), Italy ARPAB, 85100 Potenza, Italy
a r t i c l e
i n f o
Article history: Received 10 December 2012 Accepted 24 May 2013 Keywords: Satellite time series Fisher information measure Shannon entropy Fires SPOT
a b s t r a c t The time dynamics of SPOT-VEGETATION Normalized Difference Vegetation Index (NDVI) time series are analyzed by using the statistical approach of the Fisher–Shannon (FS) information plane to assess and monitor vegetation recovery after fire disturbance. Fisher–Shannon information plane analysis allows us to gain insight into the complex structure of a time series to quantify its degree of organization and order. The analysis was carried out using 10-day Maximum Value Composites of NDVI (MVC-NDVI) with a 1 km × 1 km spatial resolution. The investigation was performed on two test sites located in Galizia (North Spain) and Peloponnese (South Greece), selected for the vast fires which occurred during the summer of 2006 and 2007 and for their different vegetation covers made up mainly of low shrubland in Galizia test site and evergreen forest in Peloponnese. Time series of MVC-NDVI have been analyzed before and after the occurrence of the fire events. Results obtained for both the investigated areas clearly pointed out that the dynamics of the pixel time series before the occurrence of the fire is characterized by a larger degree of disorder and uncertainty; while the pixel time series after the occurrence of the fire are featured by a higher degree of organization and order. In particular, regarding the Peloponneso fire, such discrimination is more evident than in the Galizia fire. This suggests a clear possibility to discriminate the different post-fire behaviors and dynamics exhibited by the different vegetation covers. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Wildfire represents one of the main disturbance factors (Trabaud, 1987) throughout the world (IPCC, 2007) and it is particularly relevant in many shrubland and wooded ecosystems of the Mediterranean Basin (Swetnam and Betancourt, 1998; Allen et al., 2002; Pausas, 2004). Wildfire affects both flora and fauna, severely damages ecosystem functionalities and causes considerable economic damages (IPCC, 2007). Fire-induced dynamic processes are very difficult to study since they affect the complex soil–surface–atmosphere system, due to the existence of feedback mechanisms involving human activity, ecological patterns and different subsystems of climate. Fire destroys vegetation and ecosystems rapidly, whereas, in contrast, recovery is a long-term process quite difficult to systematically and consistently assess and monitor over space and time (Gouveia et al., 2010). Accurate and detailed information on the impact of fire on vegetation as well the vegetation capability to recover after fire
∗ Corresponding author. Tel.: +39 0971427277. E-mail address: [email protected] (L. Telesca). 0303-2434/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jag.2013.05.008
are required. Post-fire investigations have been generally performed at stand level even though a wide range of habitats in the Mediterranean-type communities have been analyzed. Due to the necessity of monitoring large areas for long periods, reliable low-cost tools must be set up to consistently and properly assess the ecological consequences of fire disturbance in different ecosystems, geographic regions and vegetation cover types. To cope with these needs and gain information at different temporal and spatial scales, satellite time-series NDVI (Rouse et al., 1974), derived from NOAA/AVHRR, SPOT/VEGETATION or TERRA/MODIS, Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), Temathic Mapper (TM) may be fruitfully used. Long time-series of NDVI data are today available free of charge for all the above mentioned satellite sensors and offer spectral information adequate for monitoring vegetation and, in particular, for assessing post fire vegetation regeneration and recovery. Nevertheless, even if the importance and value of remotely sensed time-series data for vegetation monitoring has been strongly recognized (Goward et al., 1985; Tucker and Sellers, 1986; Lasaponara, 2006; Telesca and Lasaponara, 2006), only a limited number of methods have been today developed in order to extract and analyze the precious information therein stored to capture and explore temporal/spatial feature patterns and their variations.
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Over the years, investigations on post fire vegetation recovery have been conducted mainly using multi-date satellite images such as LANDSAT (Diaz-Delgado et al., 2002, 2003), and only recently satellite time series derived from AVHRR, SPOT/VEGETATION and MODIS (see for example Telesca and Lasaponara, 2005; Van Leeuwen, 2008; Van Leeuwen et al., 2010; Montesano et al., 2011) have been analyzed for monitoring post fire vegetation recovery. The NDVI is the most widely used index for investigating vegetation cover monitoring (Myneni et al., 1997) and post-fire recovery. In particular, the ability of NDVI time series to capture the different fire induced dynamics on vegetation covers has been generally investigated on the basis of satellite multi-date NDVI maps. Viedma et al. (1997) and Diaz-Delgado et al. (2002, 2003) estimated vegetation recovery rates by comparing NDVI ratios of vegetation burned and unburned areas from a limited number of Landsat scenes. To advance the understanding of many phenomena caused by fire disturbance, space monitoring of vegetation phenology, based on post fire trends and metrics, has been carried out by Van Leeuwen (2008) and Van Leeuwen et al. (2010) using long time series of AVHRR (Advanced Very High Resolution Radiometer), SPOT VEGETATION and Moderate Resolution Imaging Spectroradiometer (MODIS) see for example Gouveia et al. (2010) and Montesano et al. (2011). Ricotta et al. (1998) monitored the landscape stability of Mediterranean vegetation in relation to fire using a fractal algorithm applied to satellite NDVI data. Telesca and Lasaponara (2005, 2006) conducted specific statistical analyses using the Detrended Fluctuation Analysis (DFA) in forest areas to analyze and characterize the vegetation fire resilience, namely the capability of vegetation to recovery after fire. In more detail, they considered both a single fire occurrence (Telesca and Lasaponara, 2006) and also repeated wildfire events (Telesca and Lasaponara, 2008) in areas where no mitigation and/or rehabilitation treatments were carried out after fire occurrence. In this paper, the Fisher–Shannon information plane analysis of SPOT/VEGETATION NDVI time series has been used to characterize vegetation dynamics before and after fire occurrence for two test sites selected in Spain and Greece. The main purpose is to extract quantitative information on the temporal fluctuations of SPOT/VEGETATION NDVI time series.
2. Data The investigations were performed by using NDVI data derived from the VEGETATION sensor on board the SPOT satellite platforms. Such data are available free of charge at the Vlaamse Instelling voor Technologisch Onderzock (VITO) Image Processing center (Mol, Belgium) (http://www.vgt.vito.be). The data were subjected to atmospheric corrections performed by CNES on the basis of the simplified method for atmospheric corrections (SMAC). 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. Additionally, for each considered pixel we carefully checked the absence of residual errors due to cloud edges and shadows, image navigation inaccuracy and changing of viewing-illumination conditions by using a visual inspection and additional information obtained from the four single SPOTVGT channels and viewing geometry available on-line from VITO website. The SPOT VEGETATION data have a spatial resolution of 1 km
Fig. 1. Galizia (Spain) 9 August 2006 (MODIS RGB 2-4-3) – green circle: fire event considered. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
The investigation was carried out using NDVI time series acquired from April 1998 to December 2010. The NDVI is computed using red (R ) and near-infrared (NIR ) channels as in formula (1). NDVI =
NIR − R NIR + R
(1)
The NDVI is designed as a ratio, in order to limit the atmospheric effects and, therefore, as a consequence its variability is normalize into the range −1 and +1. The NDVI values are less than 0 for water, clouds, snow cover, etc., whereas they exhibit values slightly higher than 0 for bare soils and definitely positive values according to the type and density of vegetation cover and its phenological state. We used the decadal composition of NDVI daily maps, downloaded from the VITO website. The decadal composition enable us to reduce the cloud contaminations, cloud border areas and the atmospheric effects which can strongly alter the actual spectral vegetation spectral responses. We considered two test sites: Galizia (Spain) and Peloponnese (Greece). The fire event in Galizia occurred from the 9th to the 10th of August 2006 (Fig. 1). It has been selected among many fire events that have affected the northwestern of Spain in that period. This fire event affected an area larger than 2000 hectares which was mainly covered by low shrubland vegetation (moorlands) at an altitude of around 100 meter a.s.l. The fire event in Peloponnese occurred from the 24th to the 31st of August 2007 (Fig. 2). Also in this case it is one of the fire events in Greece in August 2007. This fire event affected an area larger than 30,000 hectares which was covered by evergreen vegetation, mainly Leccio at an altitude between 500 and 1000 m a.s.l. The choice of the two study areas was determined by the need to evaluate the technique in two very different ecosystemic contexts both from the point of view of the climate (oceanic and mediterranean) that the vegetation (moorland and sclerophyllus vegetation). Since the analysis is pixel-based, the extension of the burned area, however, is not a relevant factor. 3. The Fisher–Shannon information plane The Fisher–Shannon information plane (FS) represents an efficient tool to investigate the complex temporal fluctuations of nonstationary signals. It is constructed with coordinate axes given by the Fisher Information Measure (FIM) and the Shannon entropy
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a statistical measure of complexity (Romera and Dehesa, 2004), and for 1-dimensional space, the line INX = 1 separates the FS plane in two parts, one allowed (INX > 1) and the other not allowed (INX < 1). The calculation of the FIM and the Shannon entropy depends on the calculation of the probability density function f(x) (pdf). The pdf can be estimated by means of the kernel density estimator technique (Devroye, 1987; Janicki and Weron, 1994) that approximates the density function as 1 fˆM (x) = K Mb M
x − x i
b
i=1
,
(5)
with b the bandwidth, M the number of data and K(u) the kernel function, a continuous non-negative and symmetric function satisfying the two following conditions
+∞
K(u) ≥ 0 and
K(u)du = 1.
(6)
−∞
Fig. 2. Peloponnese (Greece) 26 August 2007 (MODIS RGB 2-4-3) – green circle: fire event considered. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
power (NX ) that are both well known in the context of information theory. The FIM quantifies the amount of organization or order in a system, while NX measures its degree of uncertainty or disorder. The FIM was developed by Fisher (1925) in the context of statistical estimation. Then, it was utilized for different aim. Frieden (1990) used the FIM to describe the evolution laws of physical systems. Martin et al. (1999, 2001) applied it to characterize the temporal fluctuations of electroencephalograms (EEG) and to detect significant dynamical changes. Complex geophysical and environmental phenomena, like volcano-related signals, earthquake-related electromagnetic signals, atmospheric particulate matter benefited of the application of the FIM methodology to gain insight into their inner time dynamics and the mechanisms underlying their temporal fluctuations and to reveal precursory signatures of critical phenomena (Lovallo and Telesca, 2011; Telesca and Lovallo, 2011; Telesca et al., 2009, 2010, 2011). Shannon entropy is used to quantify the uncertainty of the prediction of the outcome of a probabilistic event (Shannon, 1948); in fact, it is zero for deterministic events. For continuous distributions the Shannon entropy can take any real positive and negative value. In order to avoid the difficulty arising with negative information measures, the so-called Shannon power entropy NX (defined below) can be used instead of the Shannon entropy. Let f(x) be the probability density of a signal x, then its FIM I is given by
+∞
I= −∞
2
∂ f (x) ∂x
dx , f (x)
(2)
and its Shannon entropy is defined as (Shannon, 1948):
+∞
HX =
fX (x) log fX (x)dx.
(3)
−∞
As specified above, the notion of Shannon entropy power will be used (Angulo et al., 2008) NX =
1 2HX . e 2e
(4)
The two measures satisfy the so-called ‘isoperimetric inequality’ INX ≥ D (Esquivel et al., 2010) where D is the dimension of the space. The ‘isoperimetric inequality’ indicates that FIM and Shannon entropy power are linked to each other; and the so called Fisher–Shannon (FS) information plane represents a tool for the characterization of signals. The product INX can also be employed as
In our study, we estimated the pdf f(x) by means of the algorithm developed in Troudi et al. (2008) combined with that developed in Raykar and Duraiswami (2006), that uses a Gaussian kernel with zero mean and unit variance:
− (x−xi ) 1 e 2b2 . √ M 2b2 M
fˆM (x) =
2
(7)
i=1
4. Results The time variation of the NDVI time series of six pixels covering the two investigated test sites (Galizia and Peloponnese) is studied. Figs. 3 and 4 show, as an example, the NDVI time series of all examined pixels for the Galizia site (Fig. 3) and for the Peloponnese site (Fig. 4). The pixels selected according to a random criterion constitute a representative sample of the study areas and the main vegetation patterns at the two sites. Selecting more points the results might be different in relation to different levels of fire severity of the pixels considered. However, this element does not affect the correctness of the results achieved. The temporal variation of the NDVI allows us to identify the following three different features: (i) intra-annual variability: both the sites show intra-annual phenomena linked to the seasonal component variations, with NDVI values ranging from around 0.6 to 0.8. This intra-annual variability, driven by the phenological seasonality as well as rainfall and temperature effects, is more evident for the Peloponnese site, due to its more homogeneous land cover mainly made up of Leccio trees; whereas it is less evident for the Galizia area that is mainly covered by low shrubs, with which rainfall interactions have more rapid impacts than tree land cover. (ii) inter-annual variability: observed for both the test sites, it may be linked to the yearly variability of meteoclimatic factors (temperature and precipitations), but also to changes in land management and/or gradual land degradation processes. (iii) abrupt change due to the fire disturbances, revealed by a NDVI value around 0.3 for the Galizia fire and lower than 0.2 for the Peloponnese one. Therefore, in order to eliminate the phenological fluctuations linked with the seasonality, for each pixel we analyzed the time series of the departure of the NDVI from the decadal mean (m), divided by the decadal standard deviation (), by using the following formula (Telesca and Lasaponara, 2005, 2006): NDVId =
NDVI − m(NDVI) . (NDVI)
(8)
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Fig. 3. NDVI time series of six pixel for the test site in Galizia.
Fig. 4. NDVI time series of six pixel for the test site in Peloponnese.
Figs. 5 and 6 show the NDVId series for the same pixels shown in Figs. 3 and 4. Before the occurrence of the fire, the NDVId of the Galizia test site exhibits a higher variability than that of the Pelopponese test site (and this is reasonable considering the diverse plant cover, density and phenologies). In correspondence of the fire occurrence the NDVId clearly evidences in both the sites a drop, which, however, has a different height, being larger for the Peloponnese (Fig. 5) than for the Galizia site (Fig. 6). Such drop in the NDVId may provide information on fire severity. The fire severity is a qualitative indicator of the effects of fire on ecosystems and its assessment is very important to monitor fire effects, to model and evaluate post-fire dynamics and to estimate the ability of vegetation to recover after fire: the Galizia site, in fact, seems to be closer
to the pre-fire situation than the Peloponnese site and, therefore, to recover more rapidly. In order to quantitatively evaluate these two different vegetation recovery behaviors, the time dynamics of the NDVId time series is analyzed by using the statistical approach of the Fisher–Shannon (FS) information plane. The pre-fire and post-fire FS properties of each pixel are investigated, subdividing the NDVId time series of each pixel into two sub-series, one corresponding to the pre-fire and the other to the post-fire variability of the NDVId . Fig. 7 shows the FS information plane for the Galizia site, while Fig. 8 shows that for the Peloponnese one. A common pattern can be identified in both the plots: the pre-fire sub-series are characterized by higher Shannon entropy power and lower FIM than those of the
Fig. 5. NDVId time series for the test site in Galizia corresponding to the NDVI pixel time series shown in Fig. 3.
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Fig. 6. NDVId time series for the test site in Peloponnese corresponding to the NDVI pixel time series shown in Fig. 4.
Galizia pre-fire post-fire
FIM
5. Discussion
1 1
Nx
Fig. 7. FS information plane for the Galizia site.
post-fire sub-series. This indicates that the dynamics of the NDVId time series before the occurrence of the fire is characterized by a larger degree of disorder and uncertainty; while the NDVId time series after the occurrence of the fire feature a higher degree of Peloponnese pre-fire post-fire 100
FIM
organization and order. In particular, regarding the Peloponnese test site, the discrimination between the pre- and post-fire subseries is more evident because the aggregation into two different clusters is more pronounced. Regarding the Galizia test site, this aggregation in two distinct clusters is less evident, even though the post-fire sub-series are characterized by a higher FIM and lower Shannon entropy power than the pre-fire sub-series.
10
Telesca and Lasaponara (2005, 2006) applying an independent statistical method, namely the detrended fluctuation analysis (DFA), found a significant discrimination between pre-fire and post-fire NDVI time series, revealing that post-fire vegetation dynamics is characterized by a higher persistence degree than the pre-fire vegetation dynamics, suggesting, then, a higher regularity of the post-fire pixel sub-series with respect to the pre-fire ones. This higher regularity, which signals the tendency of the vegetation to recover after being affected by the fire, is nicely consistent with the higher order and higher level of organization (indicated by the higher FIM) shown by the post-fire sub-series. Both the DFA and the Fisher–Shannon (FS) information plane provide, then, a quantitative characterization of the vegetation recovery capability. Another important element of interpretation can be related to the different degrees of fire severity between the two analyzed events. It is very likely that the best discrimination obtained for the Peloponnese fire is related to the higher level of fire severity of this event compared to that of the Galicia event. In particular, regarding the Peloponnese site, such discrimination is more evident than for the Galizia site, probably due to the different vegetation covers characterizing the two sites. Therefore, the different post-fire behaviors may refer and be linked to the different recovery abilities, which characterize the different vegetation types: the low shurbland’s recovery rate is faster than the tree cover’s re-growth and pre-fire functional and structural recovery rate. As regards the choice of the two areas, the applied method is independent of the size of the burned area which do not influences the efficiency of the method. Instead, the application of the method to areas that have a different spectral behavior is one of the objectives of this work. 6. Conclusions
1
Nx
1
Fig. 8. FS information plane for the Peloponnese site.
In this paper, the time dynamics of SPOT-VEGETATION NDVI time series were analyzed by using the statistical approach of the Fisher–Shannon (FS) information plane in order to assess and
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monitor vegetation recovery after fire disturbance. The investigation was performed on two test sites, located one in Galizia (North Spain) and the other in Peloponnese (South Greece). They were selected because of two vast fires, occurred during the summers of 2006 and 2007, and for the different vegetation covers, mainly low shrubland in Galizia and evergreen forest I Peloponnese. Data analysis was carried out using the 10-day Maximum Value Composites of NDVI (MVC-NDVI), with a 1 km × 1 km spatial resolution. For both the test sites, the time series of MVC-NDVI have been analyzed before and after the fire occurrence. Results clearly point out that the dynamics of the NDVI time series before the fire occurrence are characterized by a larger degree of disorder and uncertainty, while that of NDVI time series after fire occurrence features a higher degree of organization and order. Of course the FS method needs to be further validated on other cases in order to be considered an efficient and promising method, which applied to multi-temporal space is able to account for NDVI variations and to extract multi-year trends from NDVId variability. Acknowledgements The present study was supported by the CNR-CAS Project “Development of models and time series analysis tools for oceanographic parameters analysis and forecasting”, in the framework of the Bilateral Agreement for Scientific and Technological Cooperation Between CNR and CAS 2011–2013. References Allen, C.D., Savage, M., Falk, D.A., Suckling, K.F., Swetnam, T.W., Schulke, T., Stacey, P.B., Morgan, P., Hoffman, M., Klingel, J.T., 2002. Ecological restoration of Southwestern ponderosa pine ecosystems: a broad perspective. Ecological Applications 12, 1418–1433. Angulo, J.C., Antolin, J., Sen, K.D., 2008. Fisher–Shannon plane and statistical complexity of atoms. Physics Letters A 372, 670–674. Devroye, L., 1987. A Course on Density Estimation. Birkhauser, Boston. Diaz-Delgado, R., Lloret, F., Pons, X., Terradas, J., 2002. Satellite evidence of decreasing resilience in mediterranean plant communities after recurrent wildfires. Ecology 83, 2293–2303. Diaz-Delgado, R., Lloret, F., Pons, X., 2003. Influence of fire severity on plant regeneration by means of remote sensing imagery. International Journal of Remote Sensing 24, 1751–1763. Esquivel, R.O., Angulo, J.C., Antolin, J., Dehesa, J.S., Lopez-Rosa, S., Flores-Gallegos, N., 2010. Analysis of complexity measures and information planes of selected molecules in position and momentum spaces. Physical Chemistry Chemical Physics 12, 7108–7116. Fisher, R.A., 1925. Theory of statistical estimation. Proceedings of the Cambridge Philosophical Society 22, 700–725. Frieden, B.R., 1990. Fisher information, disorder, and the equilibrium distributions of physics. Physical Review A 41, 4265–4276. Gouveia, C., DaCamara, C.C., Trigo, R.M., 2010. Post-fire vegetation recovery in Portugal based on SPOT/VEGETATION data 2010. Natural Hazards and Earth System Sciences 10, 673–684. Goward, S.N., Tucker, C.J., Dye, D.G., 1985. North American vegetation patterns observed with theNOAA-7 advanced very high resolution radiometer. Plant Ecology 64, 3–14. IPCC, 2007. Intergovernmental Panel on Climate Change, fourth assessment report. Climatic Change. Synthesis Report, Summary for Policymakers. Janicki, A., Weron, A., 1994. Simulation and Chaotic Behavior of Stable Stochastic Processes. Marcel Dekker, New York. Lasaponara, R., 2006. On the use of principal component analysis (PCA) for evaluating interannual vegetation anomalies from SPOT/VEGETATION NDVI temporal series. Ecological Modelling 194, 429–434.
Lovallo, M., Telesca, L., 2011. Complexity measures and information planes of X-ray astrophysical sources. Journal of Statistical Mechanics, P03029. Martin, M.T., Pennini, F., Plastino, A., 1999. Fisher’s information and the analysis of complex signals. Physics Letters A 256, 173–180. Martin, M.T., Perez, J., Plastino, A., 2001. Fisher information and nonlinear dynamics. Physica A 291, 523–532. Montesano, T., Lanorte, A., De Santis, F., Lasaponara, R., 2011. Pre and Post Fire Vegetation Behavioral Trends from Satellite MODIS/NDVI Time Series in Seminatural Areas, ICCSA 2011 – International Conference, Santander, Spain, June 20–23. In: Murgante, B., Gervasi, O., Iglesias, A., Taniar, D., Apduhan, B.O. (Eds.), Computational Science and Its Applications Proceedings, Part II. Lecture Notes in Computer Science, 6783. Springer, ISBN 978-3-642-21886-6, pp. 330– 343. Myneni, R.B., Keeling, C.D., Tucker, C.J., Asrar, G., Nemani, R.R., 1997. Increased plant growth in the northern high latitudes from 1981 to 1991. Nature 386, 698–702. Pausas, J.G., 2004. Changes in fire and climate in the eastern Iberian Peninsula (Mediterranean Basin). Climatic Change 63, 337–350. Raykar, V.C., Duraiswami, R., 2006. Fast optimal bandwidth selection for kernel density estimation. In: In Proceedings of the sixth SIAM International Conference on Data Mining, Bethesda, April 2006, pp. 524–528. Ricotta, C., Avena, G.C., Olsen, E.R., Ramsey, R.D., Winn, D.S., 1998. Monitoring the landscape stability of Mediterranean vegetation relation to fire with a fractal algorithm. International Journal of Remote Sensing 19, 871–881. Romera, E., Dehesa, J.S., 2004. The Fisher–Shannon information plane, an electron correlation tool. Journal of Chemical Physics 120, 8906–8912. Rouse, J.W.J., Haas, R.H., Schell, J.A., Deering, D.W., 1974. Monitoring vegetation systems in the Great Plains with ERTS. In: Third ERTS Symposium, NASA SP-351, Washington, DC, pp. 309–317. Shannon, C.E., 1948. A mathematical theory of communication. Bell System Technical Journal 27, 379–423, 623-656. Swetnam, T.W., Betancourt, J.L., 1998. Mesoscale disturbance and ecological response to decadal climatic variability in the American southwest. Journal of Climate 11, 3128–3147. Telesca, L., Lasaponara, R., 2005. Discriminating dynamical patterns in burned and unburned vegetational covers by using SPOT-VGT NDVI data. Geophysical Research Letters 32, L21401. Telesca, L., Lasaponara, R., 2006. Pre- and post-fire behavioral trends revealed in satellite NDVI time series. Geophysical Research Letters 33, L14401. Telesca, L., Lasaponara, R., 2008. Analysing vegetation response to two successive fires using satellite SPOT-VGT Normalized Difference Vegetation Index time series. In: Proceedings of the 10th IASTED International Conference Signal and Image Processing, Kailua-Kona, Hawaii, USA, August 18–20, 2008, pp. 300– 303. Telesca, L., Lovallo, M., 2011. Analysis of the time dynamics in wind records by means of multifractal detrended fluctuation analysis and the Fisher–Shannon information plane. Journal of Statistical Mechanics, P07001. Telesca, L., Lovallo, M., Ramirez-Rojas, A., Angulo-Brown, F., 2009. A nonlinear strategy to reveal seismic precursory signatures in earthquake-related self-potential signals. Physica A 388, 2036–2040. Telesca, L., Lovallo, M., Carniel, R., 2010. Time-dependent Fisher Information measure of volcanic tremor before 5 April 2003 paroxysm at Stromboli volcano, Italy. Journal of Volcanology and Geothermal Research 195, 78–82. Telesca, L., Lovallo, M., Hsu, H.-L., Chen, C.-C., 2011. Analysis of dynamics in magnetotelluric data by using the Fisher–Shannon method. Physica A 390, 1350– 1355. Trabaud, L., 1987. Dynamics after fire of sclerophyllous plant communities in the Mediterranean basin. Ecologia Mediterranea 13, 25–37. Troudi, M., Alimi, A.M., Saoudi, S., 2008. Analytical plug-in method for kernel density estimator applied to genetic neutrality study. EURASIP Journal on Advances in Signal Processing 2008, Article ID 739082. Tucker, C.J., Sellers, P.J., 1986. Satellite remote sensing of primary production. International Journal of Remote Sensing 7, 1395–1416. Van Leeuwen, W.J.D., 2008. Monitoring the effects of forest restoration treatments on post-fire vegetation recovery with MODIS multitemporal data. Sensors 8, 2017–2042. Van Leeuwen, W.J.D., Casady, G.M., Neary, D.G., Bautista, S., Alloza, J.A., Carmel, Y., Wittenberg, L., Malkinson, D., Orr, B.J., 2010. Monitoring post-wildfire vegetation response with remotely sensed time-series data in Spain, USA and Israel. International Journal of Wildland Fire 19, 75–93. Viedma, O., Melia, J., Segarra, D., Garcia-Haro, J., 1997. Modeling rates of ecosystem recovery after fires by using landsat TM data. Remote Sensing of Environment 61, 383–398.