Cluster recognition in spatial-temporal sequences: the case of forest fires

2.1 Study area

Canton Ticino is located in Switzerland in the southern slope of the Swiss Alps (Fig. 1); it has a total area of 2,812 km² and a population of 320,000 inhabitants [10]. Topography in Canton Ticino is characterized by a marked altitudinal gradient (from 200 to 3,400 m above sea level—m.a.s.l.) with a rather heterogeneous geology, dominated by siliceous rocks originating in connection with the tectonics of the Alps. Depending on the elevation and the geographical location, the mean annual precipitation ranges from 1,600 to 2,600 mm and the mean annual temperature from 3 to 12 °C. The climate in this region is demarcated by dry and mild winters comprising few days (40 days per year on average) distinguished by strong gusts of a katabatic (descending) dry wind from the north (foehn), which consequently drops the relative humidity to values as low as 20 %. The high amount of summer rain (800 to 1,200 mm in the period June-September) is characteristic for the whole area. Throughout this season long periods without rain, or even drought, may alternate with thunderstorms and short spells of heavy precipitation [33].

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At the beginning of the last century, Ticino was mainly a rural canton. This situation drastically changed in the post-war period when the canton experienced a large socio-economic transformation towards a more service-oriented economy that ensured prosperity and benefited a strong population growth. Nevertheless, this situation also caused the almost total abandonment of traditional agriculture, livestock breeding and landuse management activities. According to different available sources [2], the forest area grew to more than double its size, passing from ca. 62,900 ha in 1900 to around 129,000 ha in the year 2000, with a remarkable acceleration of the forest extension process since the post-war period [6]. Nowadays the forest cover is dominated at low elevations (up to 900-1,100 m.a.s.l.) by anthropogenic monocultures of chestnut tree (castanea sativa), occasionally interrupted by the presence of other broadleaved species such as Tilia cordata, Quercus petraea, Q. pubescens, Alnus glutinosa, Prunus avium, Acer spp. or Fraxinus spp. At medium elevations (900-1,400 m.a.s.l.) the forests mostly consist of pure stands of Fagus sylvatica followed by coniferous forests (Picea abies), and at higher elevations Larix decidua. On the south-facing slopes the beech belt is sometimes completely missing. The presence of Abies alba has been reduced to small patches on the north-facing slopes in the central part of the area. Pine forests are confined to very particular sites: Pinus sylvestris on dry south-facing slopes and Pinus cembra on the most continental areas of the upper regions [4].

2.2 Forest fire geo-database

Basic information of the forest fires in Canton Ticino has been collected by the Forest Service since 1900. Starting from 1969, the data has been organized in a relational geo-database [28] that stores geo-referenced information of single fire events: XY-coordinates of the ignition points, date of first alarm, date of fire extinction, ignition cause, burned area, slope, altitude, etc.

For the present study, we analyzed all forest fires recorded between January 1^st 1969 and August 31^th 2008 comprising a total of 2,401 fire events. From this geodatabase, several datasets were extracted to perform different simulations regarding fire-origins (anthropogenic and naturally caused fires) with different spanning periods. Only the two more significant studies are reported in this paper: one analysis using all the events enabling an overall analysis of all fires, and the second analysis considering only the events due to lightning.

Because the method proposed in this paper does not distinguish clusters due to an increase risk of fire or due to a different geographical event distribution at different times [19] (details in Section 2.3), the first dataset, which includes all fires, was split into three groups (datasets I, II and III) in order to obtain more homogeneous fire regime conditions as possible for a sound statistical analysis. Dataset I contained 833 fires occurring between 1969 and 1978, dataset II held 762 events happening between 1979 and 1990 and dataset III comprised 806 fires burning between 1991 and 2008. The definition of these three datasets was based on different factors that had conditioned the distribution and frequency of fires in Canton Ticino in the last 40 years. As cited in Section 2.1, this canton experienced an increase in forest area during the post-war period and a rise in the risk of fire. Under this situation, the cantonal authorities gradually put into operation measures lessening the ignition occurrences of the anthropogenic wildfires and actions for early fire-fighting [6]. The most efficient fire-preventative dispositions considered in the analyses of this paper were: the major fire brigades reorganization implemented in 1978, the systematic use of helicopters for both transport of the fire fighters and aerial firefighting since 1980 [6]; and the implementation of two preventive legal acts (1989 and 1991) aiming at prohibiting burning activities in the open spaces.

The lightning fire dataset was separately analyzed over the entire study period (1969-2008) comprising a total of 175 events, given that their fire regime is quite different from the anthropogenic-caused fires, and that their ignition occurrences are not affected by the measures mentioned above.

As shown in Fig. 2a, the distribution of the annual number of fires during the whole study period is rather irregular, with a general drift towards lower fire frequencies (< 60 events per year) after 1990. The annual burnt areas in Fig. 2b are generally of small sizes (< 500 ha per year) with a tendency to lower values after 1976; nevertheless, fires can get out of control when fire-prone conditions are present through the year. Such situations were observed in 1970, 1973, 1981, 1990 and 1997 where fires resulted in extremely large burnt areas. It should be noted that 1973 is an exceptional year with 176 fire events that burned 7,273.88 ha, despite an average of 1,500 ha for the years mentioned above. This trend toward a diminution of the frequency and burnt area size of the fires is mostly the effect of the implementation of several firefighting dispositions achieved by the canton.

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Looking at the fire regime along the year, see Fig. 3, all three considered sub-periods uncovered a major peak in March-April; a time-frame mostly characterized by surface fires (rapid spreading) of anthropogenic origins at low elevations (< 1,000 m.a.s.l.). In the so called winter period, from December to April, lightning fires are not present. In the summer season (May to November, corresponding to the vegetation period), fires are of both natural and anthropogenic origins, with a prominent peak of lightning-fires in July-August, especially in the period 1991-2008.

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Regarding fires of known causes, in the period 1969-1978, human activities were the origin of about 97 % of the fire events, while only 3 % corresponded to lightning. In the period 1979-1990, this proportion shifted to 94 % and 6 % respectively; whereas, in the third period 1991-2008, human behaviour was the cause for the ignition of about 87 % of the total fire events while lightning was responsible for the remaining 13 %. Concerning human-ignited fires, negligence and arson are the origins of the majority of forest fires as shown in Fig. 4. The implementation of preventive measures mitigating the risk of fire-ignition can explain the small presence of other anthropogenic-caused fires such as railways, army activities and electrical lines [5]. Among these minor ignition causes, fires detonated by electric lines and other sources are experiencing a blooming trend.

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2.3 Space-time scan statistics

Scan statistics represents a collection of methods, used and adapted in many domains, to search for local excesses of events (clusters) in both space and/or time. The main purpose is to determine whether or not an observed cluster, assumed to belong to a randomly distributed pattern, is statistically significant or has rather occurred by chance. The method was first developed in health science by Naus [25, 26], and more recently, once more in the health domain, Kulldorff developed spatial [18] and spatio-temporal extensions [20, 21]. Nowadays, these methods are implemented in a large variety of fields.

For the purely spatial scan statistics, the region under study is scanned by a circular window centered on each event. Each window moves across the entire area, varying its radius continuously from zero up to a fixed upper limit. Each circle takes the nearest neighbour events location falling inside and compares them with those lying outside. Under the null hypothesis of spatial randomness, these events are inferred to be distributed according to a known discrete-state random process (Poisson distribution) which parameters can be estimated. Given this assumption, it is then possible to test whether or not these events are randomly and independently distributed in a specific area.

The likelihood function, representing the probability that a specific zone contains a cluster, is computed for every possible scanning window and the one maximising the function represents the most likely cluster, and so on. The statistical significance of the retained potential clusters is then evaluated in order to test whether or not they have occurred by chance. For this purpose, Monte Carlo hypothesis testing was performed with a large number of random replications of the dataset generated under the null hypothesis [19]. The rank of the maximum likelihood from the real dataset is compared with the rank of the maximum likelihood from the random datasets. For instance, if the likelihood ratio for the most likely cluster exceed 95 % of the values in the Monte Carlo simulations, then, the cluster is considered to be significant at the 5 % level (p-value =0.05) [21]. In this way, it is possible to reject a cluster when the corresponding p-value is above the fixed threshold value. Based on the desired threshold, the number of Monte Carlo simulations is established.

The computational method of the space-time scan statistics is an adaptation of the purely spatial scan statistic in space and time. The circular window is replaced by a cylinder with the circular base representing the geographic space and the height corresponding to the time period of the potential clusters. Cylinder’s sizes can increase from zero up to a maximum value in both space (radius) and time (height). As in purely spatial scan statistics, each cylinder visits each event geographical location and, additionally, it visits each possible time period.

The two standard models (Poisson for discrete data and Bernoulli for binary data) demand the definition of a control population in order to compute the expected number of cases inside each scanning window. However, when the control population data is not available or not known, the problem is overcome using the space-time scan statistic permutation model (STSSP). This model only requires case data which corresponds to the single observations of the events under study. Thus, the expected number of cases is estimated on the base of the observed cases under the assumption of no space-time interaction, meaning that the spatial and temporal locations of all events are independent of each other. A complete explanation of the permutation model can be found in Kulldorff et al. [21]; here, the statistics is briefly exposed.

This ratio is calculated and maximized for every possible cylinder and Monte Carlo simulations are performed to test the statistical significance of the detected clusters.

STSSP model is a statistical tool very useful for the analysis of the distribution of environmental data. The main advantage of this model is that it only uses the observed cases instead of requesting both the case data and the population-at-risk. In the case of forest fires, the identification of the control population referring these events is a thorny task. Biomass could be considered as the material risking to be burnt; yet, this element is quite complicated to quantify and to localize at high resolution level and over large areas, becoming the major limitation for the implementation of other scan statistical models.

In the present study calculations were performed with SaTScan™ software developed by Martin Kulldorff [19]. The program allows the user to indicate all the requirements to perform the analysis, such as input data, coordinates system, study period, number of Monte Carlo replications, etc. Concerning the input data and the study period, cluster analyses were conducted for four datasets as described in Section 2.2 and for each one a SaTScan simulation was performed: dataset I with fires that occurred from 1969-1978, dataset II with fires detected in the period 1979-1990, and dataset III with fires that burned during 1991-2008. The fourth dataset comprises only lightning fires and spans the whole study period (1969-2008) for a total of 175 events.

All fire events were specified as individual locations (X,Y-Cartesian coordinates referenced with the Swiss National grid) with each point representing one fire occurrence (case) and the related date of fire-ignition in the format of year-month-day. The results are non-overlapping clusters identified using the retrospective space-time permutation model.

For the definition of the scanning space-time window parameters in SaTScan, multiple simulations were executed using different maximum-size values; for instance, for the upper limit on the geographical size, circles with varying radius from 500 m to 5 km were used, and for the temporal cluster size, maximum lengths from 1-year to 50 % of the study period and time intervals from 1-week to 1-month length were studied. These hyperparameters were also compared with different comprehensive spatial and temporal structural analyses that were completed (out of the scope of this paper) in order to detect the degree of clustering of the forest fires in Canton Ticino. The temporal distribution was analyzed using Allan Factor statistics suited to detect scaling behaviour in point processes [35]. The spatial point pattern of the forest fires was analyzed using a wide variety of spatial structural analysis tools such as topological, statistical and fractal measures [14, 15, 41] and the Ripley’s K-function [42].

Only the two most representative results, consistent with qualitative analyses from the forest fire experts in Canton Ticino, are presented in this paper. The scanning space-time window parameters used in these analyses were set as follows: 1) for the datasets I, II and III, the maximum spatial window size was set to a 3-km radius and the temporal window was set to a maximum size of 25 % of the time-length of each dataset, enabling the detection of clusters spanning several years, and a time interval of 1 month in order to detect clusters with monthly temporal trends. 2) For the lightning induced fires dataset the maximum spatial window size was set to be a 3-km radius, and the temporal window was set to a maximum length of one year and with a time interval of 15-days length in order to detect clusters within one season since lightning fires only take place each year in summer season.

The statistical significance threshold for cluster detection was fixed at 5 % level of confidence (i.e. p-value ≤ 0.05) with the smallest p-value at 0.001. Therefore, 999 Monte Carlo replications were performed.