- Email: [email protected]
Identifying spatial clustering properties of the 1997–2003 Liguria (Northern Italy) forest-fire sequence
Chaos, Solitons and Fractals 32 (2007) 1364–1370 www.elsevier.com/locate/chaos
Identifying spatial clustering properties of the 1997–2003 Liguria (Northern Italy) forest-fire sequence Luciano Telesca a,*, Giuseppe Amatulli a, Rosa Lasaponara a, Michele Lovallo a, Adriano Santulli a,b a
Istituto di Metodologie per l’Analisi Ambientale, CNR, C.da S.Loja, 85050 Tito (PZ), Italy b Istituto di Selvicoltura, Universita` degli Studi della Basilicata, 85100 Potenza, Italy Accepted 23 November 2005
Abstract The spatial clustering of the forest-fire sequence (1997–2003) of Liguria Region (Northern Italy) has been analysed using the correlation dimension DC, calculated by means of the correlation integral method. Studying the variations of this parameter, we recognize the presence of a strong variability of the spatial clusterization, modulated by seasonal cycles. Furthermore, we found that the larger fires (size >400 ha) mark the cyclic behaviour of the correlation dimension. Ó 2005 Elsevier Ltd. All rights reserved.
1. Introduction Fire is one of the most important disturbance factors in natural ecosystems. For millennia fires were recognized as a historic but infrequent element of natural ecosystems, but, currently, the number of wildfires and burned areas have increased dramatically [6] throughout the world and also in the fragile ecosystems of the Mediterranean basin (Portugal, Spain, Italy, Greece) that are known to be at high risk of desertification [26]. Forest fires are a major source of CO and other air pollutants [3,10,12], and the recent increase of fire activity on a global scale (Central America, Amazonia, Africa, boreal regions of North America and Eurasia) has provided a widespread increase in greenhouse gases (such as CO2 and CH4) [11]. As a landscape disturbance, fires result in partial or complete destruction of vegetation cover, leading to permanent changes in the composition of vegetation community, causing decrease in forests, loss of biodiversity, soil degradation, alteration of landscape patterns and ecosystem functioning, and, thus, speeding desertification processes up [26]. Moreover, recent studies found that fires tend to aggregate spatially producing larger interconnected burned patches and creating positive feedbacks in future fire susceptibility, fuel loading, fire spreading and intensity [1,28].
*
Corresponding author. Tel.: +39 971 427206; fax: +39 971 427271. E-mail address: [email protected] (L. Telesca).
0960-0779/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2005.11.075
L. Telesca et al. / Chaos, Solitons and Fractals 32 (2007) 1364–1370
1365
The accurate identification of characteristics of fire regime parameters, such as fire seasonality, fire distribution patterns in time and space, size, intensity and severity [16] is needed for understanding the role of fire in vegetation dynamics in fire-prone areas. In particular, season of fire occurrence is one of the determinants of successive trajectories on which ecosystems are subjected after fire; seasonal phenological state of burned plants has a pronounced effect on the structure of post-fire ecosystems and landscapes [8]. Fire distribution patterns are valuable information for identifying lightning-causes of fires, improving fire occurrence prediction and fire management planning, for supporting investigations relating the role of fire in landscape processes, land-cover changes and degradation, for improving predictive models of plant succession following wildfires, etc. Moreover, detailed information on the spatial pattern of fire locations (fires with a strong degree of clusterization or at some distance from one another) is of interest, being that fires seem to be concentrated in specific areas, and more frequent where it has been already burned, thus contributing to increase of fire incidence [27]. Nevertheless, the landscape dynamics in fire-prone ecosystems are still scarcely known because of the complexities concerning fire ignition and propagation processes, that involve climate and vegetational patterns, topographic features and human factors. More particularly, for understanding the impact of fire, detailed information of fire regime parameters are needed at the local level (landscape or at the administrative level) because aggregate spatially analyses (based on large scale) can mislead or veil the local space/time dynamics of fires. Several studies have been performed in order to capture the main features of fire dynamics and to model fire behaviour. Drossel and Schwabl [5] developed a forest-fire model based on SOC characteristics of forest and forest fires. Recently, Schenk et al. [22] investigated finite-size effect in the SOC forest fire model by taking tree density and fire size distribution into account. Investigations performed on different wildfire time series from different regions and climates, such as USA and Australia [15] or Northern Italy [21] revealed that, despite the complexities concerning fire ignition and propagation, forest fires exhibit a power-law frequency–area statistics over many orders of magnitude. Nevertheless, Ricotta et al. [21] found that cumulative-area distributions of wildfire time series are self-similar only over restricted scaling regions. This was confirmed by additional investigations performed by Ricotta et al. [20] in diverse areas of Mediterranean Basin including Southern Italy, Spain, France and Greece. Song et al. [24] analysed the SOC and fractal characteristics of actual forest fires in China in order to investigate the deviations observed between the occurrence frequency of large fires and the power-law relation. Detailed statistical analyses was recently performed by Lasaponara et al. [14] in order to investigate the time-clustering properties of the temporal distribution of yearly forest-fire sequences occurred (from 1997 to 2001) in Reggio Calabria (southern Italy). The present study aims to analyse the spatial scale invariant characteristics of fire occurrence as revealed from a time series (from 1997 to 2003) of fire records provided by the Italian National Forestry Service for the Liguria Region (Northern Italy), that is classified as highly vulnerable to forest fires [6]. The study area is characterized by a strong micro-climatic variability, complex topography and mixed land cover types, and is generally affected by fire during summer and winter as well. In both of these periods, climate conditions affect vegetated areas adversely, thus determining the conditions which increase occurrence and severity of forest fires.
2. Method A forest-fire sequence can be considered as a realization of a spatial point process, that describes events that occur at some random locations in space [2]. The fractality of such a process is evidenced by the scaling behaviour of some statistics in a certain range of spatial scales. The spatial fractal analysis is based on the correlation integral [9], used to estimate the correlation dimension DC. Indicating with NR
2N R
ð1Þ
The angular distance r in degrees between two events is calculated using the following formula [13]: r ¼ cos1 ½cos h1 cos h2 þ sin h1 sin h2 cosð/1 /2 Þ
ð2Þ
where (h1, h2) and (/1, /2) are the colatitudes and the longitudes of the two events. If the sequence of events is fractal in the space domain, then CðrÞ rDC . DC is estimated by the slope of the line that best fits log C(r) versus log r (converted to a distance using 1° = 111 km) [17] in the linear range of the curve. DC can lie between 0 and 2, because only the geo-
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L. Telesca et al. / Chaos, Solitons and Fractals 32 (2007) 1364–1370
graphical coordinates of the forest-fires are considered. The interpretation of such limit values is that a fire sequence with DC = 0 has all events concentrated (clustered) into one point; DC = 2 indicates that the events homogeneously cover the two-dimensional embedding space [25].
3. Land use of Liguria Region (Northern Italy) Liguria extends from the Roja river to the Magra river (Fig. 1). Most of the territory is mountainous or hilly with narrow strips of level ground along the coast or near alluvial valleys. The highest mountains rise in the west of the region (Saccarello Mount, 2200 m) where the landscape becomes decidedly mountainous: to the east, the mountains are lower and the landscape becomes much gentler, broken at intervals by rocky spurs. Numerous valleys penetrate the mountains and their rivers are generally fast-flowing torrents. On the southern side, the climate is typically Mediterranean with limited variations in temperature, mild winters and cool ventilated summers; in the higher inland areas and the Po Valley side it becomes increasingly continental. The precipitations are more abundant in autumn and winter, increasing from west to east; reaching more than 2000 mm/year. Woodlands cover an area of 283,256 hectares, equal to 52.3% of the territory [19]. The vegetation of the area is Mediterranean up to 500 m a.s.l. with evergreen shrub and vast woods of Aleppo and maritime pines. Beyond this lies the chestnut belt, up to approximately 800 m a.s.l., with some black hornbeams, elm, ash and oaks. From 800 m a.s.l. to 1500 m a.s.l. there are beechwoods and larch, while from 1500 m to 2000 m a.s.l. there is fir. The indigenous vegetation of Liguria, has been partly transformed by human activity, with the introduction of various cultivations and exotic species, which have found an environment favourable to growth. Sowing soils are particularly diffused among the productive agrarian areas (graincrops is very present); vineyards, orange or lemon groves, olive groves and orchards are the most widespread crops and represent a significant economic activity. In particular, orange and lemon groves require a lot of manpower. From a botanical point of view, the Portofino promontory is particularly interesting: two completely different kinds of vegetation, Mediterranean and middle European-mountain, grow in close proximity. It is here that the scrub reaches its highest point and the chestnut woods extend so far down as almost to touch the sea: the thermal inversion phenomenon, causing plant life to exchange roles and environment for climatic and ecological reasons is singularly frequent. More than 700 different species of plants have been listed, on the limited terrain of this promontory. On the southern slopes, facing the sea, the Mediterranean scrub consists of underwood, thick bushes, tangled brushwood, stands of evergreen oak, Aleppo and maritime pinewoods, strips of fragmented meadow and long-tufted grasses [23]. The northern side, on the other hand, is predominantly chestnut woods and mixed woodland, with flowering ash, oak, hazel and black hornbeam; spectacular plants such as the large Mediterranean spurge stand out at intervals and there are interesting indigenous plants, including Saxifraga cochlearis and Centaurea aplolepa lunensis [18]. Another typically Ligurian environment is the Cinque Terre where vines are grown on artificial terracing. The vegetation is largely Aleppo and maritime pinewoods, with the interesting association of evergreen oak and cork trees with an under storey of Mediterranean spurge, fleecy cistus and groundsels. In the Ligurian Apennines (1287 m a.s.l.) the vegetation is woodland (partly planted) with maritime, black,
Fig. 1. Spatial distribution of the fires in Liguria Region (northern Italy) from 1997 to 2003.
L. Telesca et al. / Chaos, Solitons and Fractals 32 (2007) 1364–1370
1367
and scots pines, while the north side is mainly mixed woodland with oak, beech and chestnut trees, mountain meadows and wet peatbogs [7].
4. Forest-fire archive The forest fire fighting service in Italy is made of one at regional level, another at provincial and municipal level depending from the Inspectorate Division of the Forest. It is controlled by the Politic Rural and Forest Ministry, which coordinates the activity of the Nucleo Antincendio Boschivi (A.I.B.). In turn, the nucleus A.I.B. coordinates the activity of the detachments of the forest; these are made of Special Groups well equipped and ready for action. The details of the fires come from the A.I.B. and are collected and carefully prepared by a program managed by the AIB/FN, software given to the State Body of Co-ordination of the Forester at national level. (http:// www.corpoforestale.it). For the current work has been utilized the data kept from the fires of the seven years from 1997 to 2003. In doing so it has been created a detailed statistic of the fires that occurred in the Liguria Region.
5. Results Fig. 2 shows the correlation integral for the sequence of fire locations in Liguria Region from 1997 to 2003. The integral was calculated for distance r ranging from approximately 10 m–100 km. The plot evidences the presence of a scaling region between 1 km and approximately 10 km with correlation dimension DC 1.6. The value suggests the sequence is clusterized at the specified spatial scales. To test the significance of such result, we generated a random set of the same number of fire locations, included in the Liguria area, but uniformly distributed. Fig. 3 shows the result of the correlation dimension analysis. The uniform spatial distribution of the fire locations are characterized by DC 1.98, which indicates absence of clusterization, as expected for an uniform spatial distribution. In order to evaluate the variation of DC with the time, we performed our fractal analysis on a fixed fire events number window, shifting through the entire data set; this approach evidences global scaling relations between fires of the catalogue [4]. The evolution of DC with respect to time has been analysed, using overlapping time windows of 100 fire events. The shift between successive windows was set at one event, permitting sufficient smoothing among the values of the exponents. Each calculated value was associated with the time of the last fire in the window. The correlation dimension has been estimated in the spatial range between 1 km and 10 km, in agreement with the scaling region detected in Fig. 2. In Fig. 4 we show the variation with respect to time of the correlation dimension DC. We observe a clearly strong variability of the correlation dimension between 0.87 and 1.72, indicating a strong variability of the spatial fractal properties. The spatial dynamics of the set of fire locations ranges between a rather clusterized and an approximately ran-
7
log10C(r)
6 DC=1.607±0.002
5
10 Km 4
3
1 Km
2 -2
-1
0
1
2
log10(r) (Km) Fig. 2. Log–log plot of C(r) versus r for the whole data set. A clear linear range is distinguishable in the spatial range 1–10 km (indicated by the line).
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L. Telesca et al. / Chaos, Solitons and Fractals 32 (2007) 1364–1370 8 Uniform
7
log10C(r)
6 5 4 DC=1.978±0.001
3 2 1 0 -2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
log10 r (Km) Fig. 3. Log–log plot of C(r) versus r for an uniform spatial distribution of fires, located in the same area of Fig. 1.
1.8
May-Aug 97 Nov 98-Feb 99 Feb-May 01 Jun-Jul 03 Mar-Jun 98 Dec-Jan 00 Apr-Aug 02 Dec 01
1.6
μ+σ
1.4
μ
1.2
DC
μ- σ
1.0 0.8 0.6
Apr 97 Jul-Aug 98 Apr-Jul 00 Aug-Sep 03 Jun-Jul 99 Jan-Feb 02 Mar 98
0.4 0
500
1000
1500
2000
2500
3000
t (days) Fig. 4. Temporal variation of DC: a cyclic behaviour is clearly observable, with maxima and minima of the dimension, ranging between 0.87 and 1.72.
dom behaviour. It is also evidenced a cyclic behaviour in the time variation of DC, but the dynamics of the maxima are different from those of minima. In fact, the minima are more or less located during the warm seasons of each year, except one minimum lasting during January and February 2002; while the maxima seem to shift during time from warm to cold seasons. Furthermore, it seems that the maximum of the correlation dimension is characterized by an oscillatory behaviour of 5–6 years (as argued from the position of the first and sixth maximum at May–August 1997 and April– August 2002); of course, the oscillatory behaviour is just supposed, since the short duration of the total observation period (only 7 years) does not allow to estimate significantly cyclic components of 5–6 years. Fig. 5 shows the time variation of the correlation dimension DC, as plotted in Fig. 4, but in addition it presents the biggest fires as indicated by the vertical lines. We selected as big fires those with a size larger than 400 ha. A big fire seems to follow the sharp decrease of the correlation dimension. Furthermore, the cyclic behaviour of DC is marked by the occurrence of the major events recorded in the area.
6. Conclusions The fire sequence of Liguria Region from 1997 to 2003 has been investigated to detect the presence of spatial clusterization. The correlation dimension, calculated by the correlation integral, is characterized by a cyclic behaviour, with value ranging between almost 0.8 to about 1.7, indicating a variability between clusterized and uniform spatial dynam-
L. Telesca et al. / Chaos, Solitons and Fractals 32 (2007) 1364–1370 1.8
1369
1600 1400
1.6
1200
DC
1000 1.2
800
1.0
600
Size (ha)
1.4
400 0.8
0
500
1000
1500
2000
2500
t (days) Fig. 5. Temporal variation of DC: the vertical lines indicate the occurrence of the larger fires during the observation period.
ics. The major fires (with size larger than 400 ha) seem to mark such cyclic behaviour. These results highlight the relevance of applying spatial fractal analyses in order to follow in a more exhaustive manner the evolution of the space distribution of fires in relation to the occurrence of large size fires.
References [1] Cochrane MA, Alencar A, Schulze MD, Souza Jr CM, Nepstad DC, Lefebvre P, et al. Positive feedback in the fire dynamic of closely canopy tropical forests. Science 1999;284:1832–5. [2] Cox DR, Isham V. Point processes. London: Chapman and Hall; 1980. [3] Crutzen PJ, Delany A, Greenberg J, Haagenson P, Heidt L, Lueb R, et al. Tropospheric chemical composition measurements in Brazil during the dry season. J Atmos Chem 1985;2:233–56. [4] De Rubeis V, Tosi P, Vinciguerra S. Time clustering properties of seismicity in the Etna region between 1874 and 1913. Geophys Res Lett 1997;24:2331–4. [5] Drossel B, Schwabl F. Self-organized critical forest-fire model. Phys Rev Lett 1992;69:1629–992. [6] FAO, 2001. Global forest fire assessment 1990–2000. Forest Resources Assessment Programme, working paper no. 55. Available from: http://www.fao.org:80/forestry/fo/fra/docs/Wp55_eng.pdf. [7] Fenaroli L. Flora delle alpi e degli altri monti d’Italia. Giunti 1998. [8] Flannigan MD, Stocks BJ, Wotton BM. Climate change and forest fires. The Sci Total Environ 2000;262:221–9. [9] Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D 1983;9:189–208. [10] Greenberg J, Zimmerman P, Heidt L, Pollock W. Hydrocarbon and carbon monoxide emissions from biomass burning in Brazil. J Geophys Res 1984;89:2201–7. [11] Guido R, Van derr Werf JT, Randerson G, James Collatz L, Giglio PS, Kasibhatla AF, et al. Continental-scale partitioning of fire emissions during the 1997–2001 El Nino/La Nina period. Science 2004;303:73–6. [12] Hao WM, Liu MH, Crutzen PJ. Estimates of annual and regional fire releases of CO2 and other trace gases to the atmosphere from fires in the tropics, based on FAO statistics for the period 1975–1980. In: Goldammer JG, editor. Fires in tropical biota. Berlin: Springer-Verlag; 1990. p. 440–62. [13] Hirata T. A correlation between the b value and the fractal dimension of earthquakes. J Geophys Res 1989;94:7507–14. [14] Lasaponara R, Santulli A, Telesca L. Time-clustering analysis of forest-fire sequences in southern Italy. Chaos Solitons & Fractals 2005;24:139–49. [15] Malamud BD, Morein G, Turcotte DL. Forest fires: an example of self-organized critical behaviour. Science 1998;281:1840–1. [16] Malanson GP. Diversity, stability, and resilience: effects of fire regime. In: Trabaud L, editor. The role of fire in ecological systems. The Hague: SPB Academic Publishing; 1987. p. 49–63. ¨ ncel AO, Main I, Alptekin O, Cowie P. Spatial variations of the fractal properties of seismicity in the Anatolian fault zones. [17] O Tectonophysics 1996;257:189–202. [18] Pignatti S. Flora d’Italia. Edagricole, Bologna 1984. [19] Regione Liguria ‘‘Bollettino Regionale di statistica’’, no. 5, 1998 (Secondo quadrimestre). [20] Ricotta C, Arianoutsou M, Dı´az-Delgado R, Duguy B, Lloret F, Maroudi E, et al. Self-organized criticality of wildfires ecologically revisited. Ecol Model 2001;141:307–11. [21] Ricotta C, Avena G, Marchetti M. The flaming sandpile: self-organized criticality and wildfires. Ecol Model 1999;119:73–7. [22] Schenk K, Drossel B, Clar S, Schwabl F. Finite-size effects in the self-organized critical forest-fire model. Eur Phys J 2000;15:177–85. [23] Schonfelder IeP. La flora mediterranea. De Agostini 1996.
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[24] Song W, Weicheng F, Binghong W, Jianjun Z. Self- organized criticality of forest fire in China. Ecol Model 2001;145:61–8. [25] Tosi P. Seismogenic structure behavior revealed by spatial clustering of seismicity in Umbria-Marche Region (Central Italy). Annali di Geofisica 1998;41:215–24. [26] UNCCD, United Nations Convention to Combat Desertification, report, Paris; 1994. [27] Vazquez A, Moreno JM. Spatial distribution of forest fires in Sierra de Gredos (Central Spain). Forest Ecol Manag 2001;147:55–65. [28] Vila M, Lloret F, Ogheri E, Terradas J. Positive fire-grass feedback in mediterranean basin shrubland. Forest Ecol Manag 2001;147:3–14.
Identifying spatial clustering properties of the 1997–2003 Liguria (Northern Italy) forest-fire sequence Luciano Telesca a,*, Giuseppe Amatulli a, Rosa Lasaponara a, Michele Lovallo a, Adriano Santulli a,b a
Istituto di Metodologie per l’Analisi Ambientale, CNR, C.da S.Loja, 85050 Tito (PZ), Italy b Istituto di Selvicoltura, Universita` degli Studi della Basilicata, 85100 Potenza, Italy Accepted 23 November 2005
Abstract The spatial clustering of the forest-fire sequence (1997–2003) of Liguria Region (Northern Italy) has been analysed using the correlation dimension DC, calculated by means of the correlation integral method. Studying the variations of this parameter, we recognize the presence of a strong variability of the spatial clusterization, modulated by seasonal cycles. Furthermore, we found that the larger fires (size >400 ha) mark the cyclic behaviour of the correlation dimension. Ó 2005 Elsevier Ltd. All rights reserved.
1. Introduction Fire is one of the most important disturbance factors in natural ecosystems. For millennia fires were recognized as a historic but infrequent element of natural ecosystems, but, currently, the number of wildfires and burned areas have increased dramatically [6] throughout the world and also in the fragile ecosystems of the Mediterranean basin (Portugal, Spain, Italy, Greece) that are known to be at high risk of desertification [26]. Forest fires are a major source of CO and other air pollutants [3,10,12], and the recent increase of fire activity on a global scale (Central America, Amazonia, Africa, boreal regions of North America and Eurasia) has provided a widespread increase in greenhouse gases (such as CO2 and CH4) [11]. As a landscape disturbance, fires result in partial or complete destruction of vegetation cover, leading to permanent changes in the composition of vegetation community, causing decrease in forests, loss of biodiversity, soil degradation, alteration of landscape patterns and ecosystem functioning, and, thus, speeding desertification processes up [26]. Moreover, recent studies found that fires tend to aggregate spatially producing larger interconnected burned patches and creating positive feedbacks in future fire susceptibility, fuel loading, fire spreading and intensity [1,28].
*
Corresponding author. Tel.: +39 971 427206; fax: +39 971 427271. E-mail address: [email protected] (L. Telesca).
0960-0779/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2005.11.075
L. Telesca et al. / Chaos, Solitons and Fractals 32 (2007) 1364–1370
1365
The accurate identification of characteristics of fire regime parameters, such as fire seasonality, fire distribution patterns in time and space, size, intensity and severity [16] is needed for understanding the role of fire in vegetation dynamics in fire-prone areas. In particular, season of fire occurrence is one of the determinants of successive trajectories on which ecosystems are subjected after fire; seasonal phenological state of burned plants has a pronounced effect on the structure of post-fire ecosystems and landscapes [8]. Fire distribution patterns are valuable information for identifying lightning-causes of fires, improving fire occurrence prediction and fire management planning, for supporting investigations relating the role of fire in landscape processes, land-cover changes and degradation, for improving predictive models of plant succession following wildfires, etc. Moreover, detailed information on the spatial pattern of fire locations (fires with a strong degree of clusterization or at some distance from one another) is of interest, being that fires seem to be concentrated in specific areas, and more frequent where it has been already burned, thus contributing to increase of fire incidence [27]. Nevertheless, the landscape dynamics in fire-prone ecosystems are still scarcely known because of the complexities concerning fire ignition and propagation processes, that involve climate and vegetational patterns, topographic features and human factors. More particularly, for understanding the impact of fire, detailed information of fire regime parameters are needed at the local level (landscape or at the administrative level) because aggregate spatially analyses (based on large scale) can mislead or veil the local space/time dynamics of fires. Several studies have been performed in order to capture the main features of fire dynamics and to model fire behaviour. Drossel and Schwabl [5] developed a forest-fire model based on SOC characteristics of forest and forest fires. Recently, Schenk et al. [22] investigated finite-size effect in the SOC forest fire model by taking tree density and fire size distribution into account. Investigations performed on different wildfire time series from different regions and climates, such as USA and Australia [15] or Northern Italy [21] revealed that, despite the complexities concerning fire ignition and propagation, forest fires exhibit a power-law frequency–area statistics over many orders of magnitude. Nevertheless, Ricotta et al. [21] found that cumulative-area distributions of wildfire time series are self-similar only over restricted scaling regions. This was confirmed by additional investigations performed by Ricotta et al. [20] in diverse areas of Mediterranean Basin including Southern Italy, Spain, France and Greece. Song et al. [24] analysed the SOC and fractal characteristics of actual forest fires in China in order to investigate the deviations observed between the occurrence frequency of large fires and the power-law relation. Detailed statistical analyses was recently performed by Lasaponara et al. [14] in order to investigate the time-clustering properties of the temporal distribution of yearly forest-fire sequences occurred (from 1997 to 2001) in Reggio Calabria (southern Italy). The present study aims to analyse the spatial scale invariant characteristics of fire occurrence as revealed from a time series (from 1997 to 2003) of fire records provided by the Italian National Forestry Service for the Liguria Region (Northern Italy), that is classified as highly vulnerable to forest fires [6]. The study area is characterized by a strong micro-climatic variability, complex topography and mixed land cover types, and is generally affected by fire during summer and winter as well. In both of these periods, climate conditions affect vegetated areas adversely, thus determining the conditions which increase occurrence and severity of forest fires.
2. Method A forest-fire sequence can be considered as a realization of a spatial point process, that describes events that occur at some random locations in space [2]. The fractality of such a process is evidenced by the scaling behaviour of some statistics in a certain range of spatial scales. The spatial fractal analysis is based on the correlation integral [9], used to estimate the correlation dimension DC. Indicating with NR
2N R
ð1Þ
The angular distance r in degrees between two events is calculated using the following formula [13]: r ¼ cos1 ½cos h1 cos h2 þ sin h1 sin h2 cosð/1 /2 Þ
ð2Þ
where (h1, h2) and (/1, /2) are the colatitudes and the longitudes of the two events. If the sequence of events is fractal in the space domain, then CðrÞ rDC . DC is estimated by the slope of the line that best fits log C(r) versus log r (converted to a distance using 1° = 111 km) [17] in the linear range of the curve. DC can lie between 0 and 2, because only the geo-
1366
L. Telesca et al. / Chaos, Solitons and Fractals 32 (2007) 1364–1370
graphical coordinates of the forest-fires are considered. The interpretation of such limit values is that a fire sequence with DC = 0 has all events concentrated (clustered) into one point; DC = 2 indicates that the events homogeneously cover the two-dimensional embedding space [25].
3. Land use of Liguria Region (Northern Italy) Liguria extends from the Roja river to the Magra river (Fig. 1). Most of the territory is mountainous or hilly with narrow strips of level ground along the coast or near alluvial valleys. The highest mountains rise in the west of the region (Saccarello Mount, 2200 m) where the landscape becomes decidedly mountainous: to the east, the mountains are lower and the landscape becomes much gentler, broken at intervals by rocky spurs. Numerous valleys penetrate the mountains and their rivers are generally fast-flowing torrents. On the southern side, the climate is typically Mediterranean with limited variations in temperature, mild winters and cool ventilated summers; in the higher inland areas and the Po Valley side it becomes increasingly continental. The precipitations are more abundant in autumn and winter, increasing from west to east; reaching more than 2000 mm/year. Woodlands cover an area of 283,256 hectares, equal to 52.3% of the territory [19]. The vegetation of the area is Mediterranean up to 500 m a.s.l. with evergreen shrub and vast woods of Aleppo and maritime pines. Beyond this lies the chestnut belt, up to approximately 800 m a.s.l., with some black hornbeams, elm, ash and oaks. From 800 m a.s.l. to 1500 m a.s.l. there are beechwoods and larch, while from 1500 m to 2000 m a.s.l. there is fir. The indigenous vegetation of Liguria, has been partly transformed by human activity, with the introduction of various cultivations and exotic species, which have found an environment favourable to growth. Sowing soils are particularly diffused among the productive agrarian areas (graincrops is very present); vineyards, orange or lemon groves, olive groves and orchards are the most widespread crops and represent a significant economic activity. In particular, orange and lemon groves require a lot of manpower. From a botanical point of view, the Portofino promontory is particularly interesting: two completely different kinds of vegetation, Mediterranean and middle European-mountain, grow in close proximity. It is here that the scrub reaches its highest point and the chestnut woods extend so far down as almost to touch the sea: the thermal inversion phenomenon, causing plant life to exchange roles and environment for climatic and ecological reasons is singularly frequent. More than 700 different species of plants have been listed, on the limited terrain of this promontory. On the southern slopes, facing the sea, the Mediterranean scrub consists of underwood, thick bushes, tangled brushwood, stands of evergreen oak, Aleppo and maritime pinewoods, strips of fragmented meadow and long-tufted grasses [23]. The northern side, on the other hand, is predominantly chestnut woods and mixed woodland, with flowering ash, oak, hazel and black hornbeam; spectacular plants such as the large Mediterranean spurge stand out at intervals and there are interesting indigenous plants, including Saxifraga cochlearis and Centaurea aplolepa lunensis [18]. Another typically Ligurian environment is the Cinque Terre where vines are grown on artificial terracing. The vegetation is largely Aleppo and maritime pinewoods, with the interesting association of evergreen oak and cork trees with an under storey of Mediterranean spurge, fleecy cistus and groundsels. In the Ligurian Apennines (1287 m a.s.l.) the vegetation is woodland (partly planted) with maritime, black,
Fig. 1. Spatial distribution of the fires in Liguria Region (northern Italy) from 1997 to 2003.
L. Telesca et al. / Chaos, Solitons and Fractals 32 (2007) 1364–1370
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and scots pines, while the north side is mainly mixed woodland with oak, beech and chestnut trees, mountain meadows and wet peatbogs [7].
4. Forest-fire archive The forest fire fighting service in Italy is made of one at regional level, another at provincial and municipal level depending from the Inspectorate Division of the Forest. It is controlled by the Politic Rural and Forest Ministry, which coordinates the activity of the Nucleo Antincendio Boschivi (A.I.B.). In turn, the nucleus A.I.B. coordinates the activity of the detachments of the forest; these are made of Special Groups well equipped and ready for action. The details of the fires come from the A.I.B. and are collected and carefully prepared by a program managed by the AIB/FN, software given to the State Body of Co-ordination of the Forester at national level. (http:// www.corpoforestale.it). For the current work has been utilized the data kept from the fires of the seven years from 1997 to 2003. In doing so it has been created a detailed statistic of the fires that occurred in the Liguria Region.
5. Results Fig. 2 shows the correlation integral for the sequence of fire locations in Liguria Region from 1997 to 2003. The integral was calculated for distance r ranging from approximately 10 m–100 km. The plot evidences the presence of a scaling region between 1 km and approximately 10 km with correlation dimension DC 1.6. The value suggests the sequence is clusterized at the specified spatial scales. To test the significance of such result, we generated a random set of the same number of fire locations, included in the Liguria area, but uniformly distributed. Fig. 3 shows the result of the correlation dimension analysis. The uniform spatial distribution of the fire locations are characterized by DC 1.98, which indicates absence of clusterization, as expected for an uniform spatial distribution. In order to evaluate the variation of DC with the time, we performed our fractal analysis on a fixed fire events number window, shifting through the entire data set; this approach evidences global scaling relations between fires of the catalogue [4]. The evolution of DC with respect to time has been analysed, using overlapping time windows of 100 fire events. The shift between successive windows was set at one event, permitting sufficient smoothing among the values of the exponents. Each calculated value was associated with the time of the last fire in the window. The correlation dimension has been estimated in the spatial range between 1 km and 10 km, in agreement with the scaling region detected in Fig. 2. In Fig. 4 we show the variation with respect to time of the correlation dimension DC. We observe a clearly strong variability of the correlation dimension between 0.87 and 1.72, indicating a strong variability of the spatial fractal properties. The spatial dynamics of the set of fire locations ranges between a rather clusterized and an approximately ran-
7
log10C(r)
6 DC=1.607±0.002
5
10 Km 4
3
1 Km
2 -2
-1
0
1
2
log10(r) (Km) Fig. 2. Log–log plot of C(r) versus r for the whole data set. A clear linear range is distinguishable in the spatial range 1–10 km (indicated by the line).
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7
log10C(r)
6 5 4 DC=1.978±0.001
3 2 1 0 -2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
log10 r (Km) Fig. 3. Log–log plot of C(r) versus r for an uniform spatial distribution of fires, located in the same area of Fig. 1.
1.8
May-Aug 97 Nov 98-Feb 99 Feb-May 01 Jun-Jul 03 Mar-Jun 98 Dec-Jan 00 Apr-Aug 02 Dec 01
1.6
μ+σ
1.4
μ
1.2
DC
μ- σ
1.0 0.8 0.6
Apr 97 Jul-Aug 98 Apr-Jul 00 Aug-Sep 03 Jun-Jul 99 Jan-Feb 02 Mar 98
0.4 0
500
1000
1500
2000
2500
3000
t (days) Fig. 4. Temporal variation of DC: a cyclic behaviour is clearly observable, with maxima and minima of the dimension, ranging between 0.87 and 1.72.
dom behaviour. It is also evidenced a cyclic behaviour in the time variation of DC, but the dynamics of the maxima are different from those of minima. In fact, the minima are more or less located during the warm seasons of each year, except one minimum lasting during January and February 2002; while the maxima seem to shift during time from warm to cold seasons. Furthermore, it seems that the maximum of the correlation dimension is characterized by an oscillatory behaviour of 5–6 years (as argued from the position of the first and sixth maximum at May–August 1997 and April– August 2002); of course, the oscillatory behaviour is just supposed, since the short duration of the total observation period (only 7 years) does not allow to estimate significantly cyclic components of 5–6 years. Fig. 5 shows the time variation of the correlation dimension DC, as plotted in Fig. 4, but in addition it presents the biggest fires as indicated by the vertical lines. We selected as big fires those with a size larger than 400 ha. A big fire seems to follow the sharp decrease of the correlation dimension. Furthermore, the cyclic behaviour of DC is marked by the occurrence of the major events recorded in the area.
6. Conclusions The fire sequence of Liguria Region from 1997 to 2003 has been investigated to detect the presence of spatial clusterization. The correlation dimension, calculated by the correlation integral, is characterized by a cyclic behaviour, with value ranging between almost 0.8 to about 1.7, indicating a variability between clusterized and uniform spatial dynam-
L. Telesca et al. / Chaos, Solitons and Fractals 32 (2007) 1364–1370 1.8
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1600 1400
1.6
1200
DC
1000 1.2
800
1.0
600
Size (ha)
1.4
400 0.8
0
500
1000
1500
2000
2500
t (days) Fig. 5. Temporal variation of DC: the vertical lines indicate the occurrence of the larger fires during the observation period.
ics. The major fires (with size larger than 400 ha) seem to mark such cyclic behaviour. These results highlight the relevance of applying spatial fractal analyses in order to follow in a more exhaustive manner the evolution of the space distribution of fires in relation to the occurrence of large size fires.
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