Detection of clusters using spaceâtime scan statistics

CSIRO PUBLISHING

International Journal of Wildland Fire 2009, 18, 830–836

www.publish.csiro.au/journals/ijwf

Detection of clusters using space–time scan statistics Marj ToniniA,B , Devis TuiaA and Frédéric RatleA A Institute

of Geomatics and Risk Analysis, University of Lausanne, Amphipôle, CH-1015 Lausanne, Switzerland. B Corresponding author. Email: [email protected]

Abstract. This paper aims at detecting spatio-temporal clustering in fire sequences using space–time scan statistics, a powerful statistical framework for the analysis of point processes. The methodology is applied to active fire detection in the state of Florida (US) identified by MODIS (Moderate Resolution Imaging Spectroradiometer) during the period 2003–06. Results of the present study show that statistically significant clusters can be detected and localized in specific areas and periods of the year. Three out of the five most likely clusters detected for the entire frame period are localized in the north of the state, and they cover forest areas; the other two clusters cover a large zone in the south, corresponding to agricultural land and the prairies in the Everglades. In order to analyze if the wildfires recur each year during the same period, the analyses have been performed separately for the 4 years: it emerges that clusters of forest fires are more frequent in hot seasons (spring and summer), while in the southern areas, they are widely present during the whole year. The recognition of overdensities of events and the ability to locate them in space and in time can help in supporting fire management and focussing on prevention measures. Additional keywords: Florida, MODIS active fires.

Introduction Wildfires Wildfires are defined as uncontrolled events occurring in wildland areas that can rapidly spread, affecting houses and agricultural resources. In the United States, wildfires are relatively common, with more than 100 000 reported events every year; Florida accounts for ∼5550 wildfires per year. The primary natural ignition source of wildfires is lightning (Fuquay et al. 1979; Fuquay 1980; Meisner 1993; Rorig and Ferguson 1999): reportedly, it caused nearly 80% of the remote wildland fires in the United States. Lightning strikes are very common in Florida; consequently, fire has always been an integral part of Florida’s natural history. Along with periodic natural fires, a fire-adapted ecosystem has developed in the state. Fire is not just a destructive force, but it can also have ecological benefits, for example by maintaining native fire-adapted ecosystems in a healthy condition, by reducing some weedy and invasive plants and by improving the nutritional quality of plants (Pyne et al. 1996). In this sense, fire management counts prescribed fires as a very important control tool; moreover, prescribed fires help to diminish the occurrence and severity of wildfires by reducing accumulated plant debris, which represents fuel material. When fire is applied in the proper place and time with expert management, or when spontaneous wildfires are dampened, it represents an ally. Nevertheless, if we consider wildfires as unwanted events in the natural environment, their suppression and control are crucial to protect life and its surrounding habitat, and the need for advanced management tools is real. Fire ignition and propagation are influenced by a variety of factors, such as lightning, human neglect, arson, air and soil © IAWF 2009

Debris burning 19%

Incendiary (arson) 26%

Equipment 4% Railroad 2%

Miscellaneous 10%

Lightning 16% Unknown 12%

Smoking 4% Campfires 2%

Children 5%

Fig. 1. Average proportion of wildfires by cause, 1981–2002. From Florida Department of Community Affairs and Florida Department of Agricultural and Consumer Services, Division of Forestry (http://www.fl-dof.com/, accessed 5 October 2009).

humidity, and wind. It is known that wildfires are more common and severe during drought periods and on windy days. The analysis of the dataset of wildfires by causes in Florida, from 1981 to 2002 (Fig. 1), illustrates that lightning accounts only for ∼16% of the total wildfires reported. The major causes are anthropogenic, either from escaped yard-debris fires, act of carelessness, or intentional actions (arson). According to the Florida Division of Forestry (FDOF data, 1981–2002), each year in Florida on average 5550 wildfires affect an area of ∼850 000 km2 . FDOF data (1981 to 2002 time 10.1071/WF07167

1049-8001/09/070830

Wildfire cluster detection using scan statistics

series) indicate that the largest numbers of wildfires occur in January, February and March, and the most acreage burns in wildfires in May and June. The FDOF emphasizes that the fire season in Florida is 12-month-long and that wildfires can occur very easily after 2 weeks without precipitation. Historical data show that wildfires are quite spread out in space and in time. Therefore, the analysis of their distribution to evaluate if they are statistically more frequent in some area and in some period of the year represents a useful management tool. Cluster analysis Cluster analysis is a general term that includes several different algorithms and methods aiming at grouping objects showing similar properties into respective categories (Bailey and Gatrell 1995). Cluster analysis methods are mostly used when little or nothing is known about the internal data structure and no prior hypothesis can be formulated. Generally speaking, cluster analysis methods can be classified as non-specific and specific (Besag and Newell 1991). The first group aims at the general detection of clustering of the process considered. Several non-specific methods can be found in the literature: Moran’s I (Moran 1950), K-functions (Ripley 1977) or fractal dimensions (Lovejoy et al. 1986), to list only a few of them. Specific methods aim at detecting cluster structure and location in space and in time. If the location is predefined, these methods are referred to as focussed; conversely, if to find the cluster’s location is the objective of the analysis, they are said to be non-focussed (Openshaw et al. 1987, 1999). Specific methods are often associated with statistical significance testing of the clusters. Many specific methods can be found in the literature. The most popular are the GAM (Geographical Analysis Machine) (Openshaw et al. 1987), Turnbull’s Cluster Evaluation Permutation Procedure (CEPP) (Turnbull et al. 1990) and the Spatial Scan Statistic (Kulldorff 1997). In geographical space, clusters occur when objects under study are found in spatial proximity. Identification of the clusters and detection of their spatio-temporal extent can help find the causes and are useful for managers to take actions based on risk assessment and containment. The comparison of the detected clusters with environmental and socioeconomic data can highlight possible spatial relationships among them (Shouls et al. 1996; Danfeng et al. 2006; Schweitzer 2006). Several studies demonstrate that ignition sources of fires show spatial clustering (Rorig and Ferguson 1999; Hammer et al. 2004; Genton et al. 2006; Tuia et al. 2008). Others studies analyze the time-clustering phenomena in fire sequences (Lasaponara et al. 2004; Telesca et al. 2005; Telesca and Lasaponara 2006). The aim of the present paper is to detect and to test the significance of clusters of wildfires in space and in time. A case study is represented using Florida daily fire detection using the Moderate Resolution Imaging Spectroradiometer (MODIS) active fire product during the period 2003–06. The method used is the space–time permutation scan statistic (STPSS), a specific non-focussed clustering method. Up to now, scan statistics have been widely applied to health sciences but there is evidence that this analysis has great potential to be applied to other disciplines (Jefferis 1998; Ceccato and Haining 2004; Witham and Oppenheimer 2004). In the field

Int. J. Wildland Fire

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Fig. 2. Principle of scanning window (left) with variable size (center) and locations (right).

of forestry, only few papers have been found in the literature (Coulston and Riitters 2003; Riitters and Coulston 2005; Tuia et al. 2008). The detection of clusters and their relative frame period is a crucial point to support fire management by establishing prevention measures focussing on areas that are more sensitive to wildfires. Space–time scan statistics Scan statistics are a family of methods introduced during the 1960s in the field of health sciences by Naus (1965a, 1965b). Spatial and spatiotemporal extensions of the methods have been introduced by Kulldorff et al. (1998, 2006) and Kulldorff (1997). In a spatial context, the aim of the method is the early detection, localization and significance assessment of clusters. The events are assumed to belong to a random point process following, for instance, Poisson or Bernoulli distributions. In the general case, the region under study is scanned by a circular moving window defining a set of zones z. To each zone zi belong several events ci and a population pi , corresponding to the sums of events and population falling within the zone. The moving window scans the set of all possible zones zi covering the region under study. In order to achieve this, non-overlapping windows of different size and centers are taken into account (Fig. 2). In each zone, the data are assumed to be distributed under the null hypothesis H0 of space and time randomness: X ∼ Poi(λ0 ) X ∼ B(k, n, p0 )

(1)

where λ0 and p0 are the parameters under the null hypothesis of the Poisson and binomial distributions respectively, n is the number of observations and k the number of expected events. Likelihood functions are then computed: • L0 , corresponding to the likelihood function with the parameters w restricted according to Eqn 1. • L1 , which is the same function, but with parameters unrestricted. In each zone z, L1 and L0 have different parameters, from the heterogeneous population distribution. The method searches for the cluster candidates that maximize the likelihood ratio LR: L1 (2) T = max LR(zi ) where LR(zi ) = zi ∈Z L0 zi In order to assess the significance of the most likely cluster candidates, a significance test using a Monte Carlo simulation is run. For each potential cluster, a large number of replications of datasets (usually 999 or 9999) using the restricted parameters

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4

3

2

Clusters 2003–2006

5

Florida counties

1

Fig. 3.

The five most likely clusters of active fires in Florida for the period 2003 to 2006.

is generated. The LR is computed for these regions and a distribution is obtained. If the observed cluster candidate has an LR higher than, for instance, 95% of the datasets generated under the H0 hypothesis, the cluster is said to be significant at the 0.05 level of confidence. The space–time scan statistic follows the same procedure but, instead of using space circles, space–time cylinders are used. Scan statistics do not require prior specification of the size of the clusters: by testing a series of sizes and locations, the size of the clusters is found by the algorithm. Moreover, because the LR is computed locally, i.e. by taking into account specific events and populations within a particular zone, the method is not sensitive to spatial non-stationarity or trends (Coulston and Riitters 2003).

The space–time permutation scan statistic Several scan statistics have been developed so far. In order to deal with fire data, the STPSS (Kulldorff et al. 2005) seems to be the most adequate model: the STPSS does not require the explicit specification of the population-at-risk in each cylinder. Unlike applications dealing with human population and cases of disease, the estimation of the local population-at-risk for an environmental event such as wildfire is difficult. Biomass could be an appropriate choice, but it is very difficult to quantify. For this reason, a space–time permutation model, which needs only case data, has been used instead.

In the STPSS model, the expected cases are estimated using the observed cases in space and time, and the need for a specific population is avoided. The following development can be found in Kulldorff et al. (2005) and is exposed here for clarity reasons. Let czd be the number of cases observed within a zone z in a day d and C be the total number of cases observed. The expected number of cases µA for a space–time cylinder A can be estimated as the sum of µzd (the number of expected cases per day and zone) belonging to cylinder A: µA =

z,d∈A

µzd

where µzd

1 = C

z

czd

czd

(3)

d

Let cA be the number of observed cases in A. If we assume that this variable is hypergeometrically distributed and that C is large compared with z∈A czd and d∈A czd , cA can be considered as Poisson-distributed, with mean µA . Thus, we obtain a Poisson generalized likelihood ratio (GLR), which can be computed as follows: cA C − cA (C−cA ) cA (4) GLR = µA C − µA This ratio is computed and maximized on every possible cylinder to detect the most likely clusters in the sequence. The remainder of the method is similar to the classical space–time scan statistic based on Monte Carlo simulation for significance testing.



Table 1. Results for STPSS (space–time permutation scan statistic) of active fires in Florida for the years from 2003 to 2006 Cluster

Start date

End date

1 2 3 4 5

1 May 2006 1 July 2006 1 April 2004 1 March 2006 1 November 2005

30 June 2006 31 August 2006 30 April 2004 30 April 2006 31 January 2006

(a)

Radius (km)

Relative risk

P value

52.43 5.19 7.13 39.90 63.51

6.21 30.65 34.95 3.76 2.14

0.001 0.001 0.001 0.001 0.001

(b) 1 3

4 2

Clusters 2003

Clusters 2004

3

Florida counties

5

Florida counties 4 5

1

2

(d )

(c) 2

4

3

3

4 2

5 5 Clusters 2005 Florida counties

Fig. 4.

1

Clusters 2006 Florida counties

The five most likely clusters of active fires in Florida for the years 2003 (a), 2004 (b), 2005 (c) and 2006 (d).

1

833

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M. Tonini et al.

Table 2. Results for STPSS (space–time permutation scan statistic) of active forest fires in Florida for the years 2003, 2004, 2005 and 2006 Cluster

Start date

End date

Radius (km)

Relative risk

P value

1 2 3 4 5

1 September 2003 1 May 2003 1 February 2003 1 April 2003 1 January 2003

31 October 2003 31 May 2003 31 March 2003 30 April 2003 31 January 2003

74.02 68.36 68.98 48.55 34.37

5.10 7.41 1.90 3.26 3.70

0.001 0.001 0.001 0.001 0.001

1 2 3 4 5

1 July 2004 1 April 2004 1 March 2004 1 June 2004 1 January 2004

31 August 2004 30 April 2004 30 April 2004 30 June 2004 29 February 2004

39.28 6.94 47.57 8.32 74.08

8.07 10.54 3.20 13.74 1.84

0.001 0.001 0.001 0.001 0.001

1 2 3 4 5

1 November 2005 1 March 2005 1 July 2005 1 September 2005 1 February 2005

31 December 2005 30 April 2005 31 August 2005 30 November 2005 28 February 2005

78.39 61.44 52.07 100.67 63.23

2.48 2.35 5.69 2.17 2.01

0.001 0.001 0.001 0.001 0.001

1 2 3 4 5

1 May 2006 1 July 2006 1 March 2006 1 September 2006 1 April 2006

30 June 2006 31 August 2006 30 April 2006 30 September 2006 31 May 2006

81.29 29.36 55.44 30.82 17.26

3.96 7.70 2.51 12.62 4.37

0.001 0.001 0.001 0.001 0.001

Data source and methods The MODIS fire and thermal anomalies images make up to four daily observations from both Terra and Aqua satellites (Justice et al. 2002). Fire detection is performed using a contextual algorithm that exploits the strong emission of mid-infrared radiation from fires. Subsequently, each pixel of the MODIS image is assigned to one of the following classes: missing data, cloud, water, non-fire, fire or unknown (Giglio et al. 2003). Active fire detections are provided as centroids of pixels of a 1-km resolution grid and compiled into daily Arc/INFO point coverage. The Geographical Information Systems (GIS) dataset from MODISdetected active fires is freely downloadable from the website of the USDA Forest Service (http://www.fs.fed.us/, accessed 5 October 2009). The use of MODIS active fires as a data source for the cluster detection purpose can be questioned. It could be considered more appropriate to use ignition points, but this information is hard to obtain and, in some cases, like in inaccessible zones or in developing countries, it simply does not exist. To overcome this drawback, the MODIS active fire product can represent, in a first approximation, a good alternative. To detect fire clusters in space and in time, the space–time permutation scan statistic analysis was applied. Analyses were performed using SaTScan (Kulldorff 2006). Each fire location is considered as a center of a possible cluster area (zone zi ). A maximal spatial cluster size corresponding to 25% of the total number of cases was imposed: this choice ensures that clusters do not contain large unconnected areas. To detect if seasonality behavior exists in the cluster frame periods, a maximal temporal cluster size of 4 months was set. For the Monte Carlo hypothesis testing, 999 replications were generated.

Two separate analyses were performed: first, the entire MODIS active fires dataset (from 2003 to 2006) was considered. In this way, the most probable clusters of fires in space are highlighted and their frame period is defined. Second, the STPSS model was applied separately for each of the 4 years to test if the clusters recur each year in the same area and during the same frame period. In order to identify the geographic cluster location, the plant community and landcover map dataset for the state of Florida was overlapped with the cluster maps resulted from the analyses above. Habitat and landcover raster digital data were elaborated from the Florida Fish and Wildlife Conservation Commission (http://myfwc.com/, accessed 5 October 2009), using the Landsat Enhanced Thematic Mapper satellite imagery from 2003. Results The results of the space–time scan statistic analyses of active fires in Florida for the period 2003–06 are shown and discussed below. For the most likely cluster and secondary clusters (at least the first eight), the test statistic likelihood ratio is significant at the 0.001 level of confidence (P value). For the secondary clusters having a rank lower than five, the value of the likelihood ratio diminishes abruptly, and for this reason only the first five clusters are considered in the discussion. As stated above, the first analysis considers the entire time series, from 2003 to 2006. Two out of the five most likely clusters detected for the entire frame period are localized in the northwest part of Florida and one in the center-north; the other two clusters are localized in the south (Fig. 3). The overlap with the landcover map of Florida shows that the three clusters in the


northern part of the state correspond to forest areas whereas the clusters detected in the south correspond to agricultural land and the prairies in the Everglades. Four out of the first five clusters fall in 2006 (Table 1). Considering seasonal aspects, cluster frame periods for the forest clusters fall in the hot season: April 2004 for cluster number 3; March–April 2006 for cluster number 4, and July–August 2006 for cluster number 2.The two clusters in the south have the largest spatial extension (∼50 and 60 km radius); the corresponding frame period is May–June 2006 (cluster number 1) and from November 2005 to January 2006 (cluster number 5). In the second analysis, the recurrence of fires is investigated: to this end, space-time cluster analysis was performed separately for each one of the four years (2003, 2004, 2005 and 2006). The first five most probable clusters of fires are mainly concentrated in the north-west and center-south part of the state (Fig. 4). Overlapping the cluster map with the landcover map of Florida, it emerges that clusters in forest areas (in the north-west) are more frequent during hot and dry periods: five clusters follow in March–April, three in September–October and two in July– August (Table 2). It is more difficult to outline a well-defined cluster frame period for the clusters localized in the south, corresponding to agricultural land and prairies in the Everglades: they are scattered from January to June; moreover, one cluster falls in November–December and one in July–August. Conclusions This paper applied the space–time permutation scan statistic to detect clusters of wildfire in Florida, USA. This methodology represents an exploratory step in the task of identifying clusters of fires in a spatial and temporal dimension, which can help in pinpointing vulnerable areas and frame periods more susceptible to the event. Among the several existing specific clustering methods, the space-time scan statistic presents several advantages: (i) it allows detection of the cluster location, extent and frame period without a need for prior knowledge of the phenomenon; (ii) it tests the statistical significance of the detected clusters; (iii) it does not rely on a stationarity hypothesis; (iv) the permutation model allows detection of clusters even if no population-at-risk is available, as it is for wildfires. The use of the STPSS method to detect clusters of wildfires is novel and it is valid under the assumption that the fire event is reduced to a point. MODIS active fire data have been used; the validity of such data has been discussed. In our opinion, this dataset represents a good alternative to the use of ignition points because this information is often hard to obtain. However, scale is an important factor in data usage: as the resolution of the pixel is 1 km, cluster analyses can be performed only for large areas. From the present study, statistically significant clusters have been detected and localized in specific areas and periods of the year. The five most probable clusters are localized in the forest areas of the north and north-west part of Florida, and in the agricultural land and prairies of the Everglades, in the southern part of the state. Forest fire cluster frame periods fall in the hot season, while the clusters of wildfires detected in the south are scattered throughout the entire the year.


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These results can be useful to support fire management and to focus on prevention measures.

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Manuscript received 26 November 2007, accepted 22 January 2009

http://www.publish.csiro.au/journals/ijwf

Detection of clusters using spaceâtime scan statistics

Detection of clusters using spaceâtime scan statistics

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