Non-parametric comparative analysis of the spatiotemporal pattern of human-caused and natural wildfires in Galicia

RESEARCH PAPER https://doi.org/10.1071/WF22030 Non-parametric comparative analysis of the spatiotemporal pattern of human-caused and natural wildfires in Galicia M. F. Marey-Pérez A,* , Isabel Fuentes-Santos B , Paula Saavera-Nieves C and Wenceslao González-Manteiga C ABSTRACT Background. Wildfire is a major environmental threat worldwide and climate change is expected to increase its severity. Galicia has suffered high wildfire incidence during the last decades, most wildfires being from arson, in contrast with the low rate of natural wildfires. Aim. This work aims to characterise the spatiotemporal dynamics of human-caused and natural fires in Galicia. Methods. We apply first- and second-order non-parametric inference to spatiotemporal wildfire point patterns. Key results. The distribution of natural wildfires remained stable over years, with high incidence in summer and in the eastern area of Galicia. Arson wildfires had aggregated patterns, with strong interaction between outbreaks and fires, and their distribution varied both over and within years, with high incidence shifting between the southern and western areas, and high hazard in early spring and late summer. Negligence wildfire patterns showed short-distance aggregation, but large-distance aggregation between outbreaks and fires; their spatial distribution also varied between and within years. Conclusions. Different models and covariates are required to predict the hazard from each wildfire type. Natural fires are linked to meteorological and environmental factors, whereas socioeconomic covariates are crucial in human-caused wildfires. Implications. These results are the basis for the future development of predictive spatiotemporal point process models for human-caused wildfires. Keywords: inhomogeneous point processes, intensity function, non-parametric inference, smooth bootstrap, Spain wildfire, spatiotemporal interactions, wildfire hazard. Introduction Wildfire is a major environmental threat around the world that causes substantial natural damage and socioeconomic losses (Zhang et al. 2016; Costafreda-Aumedes et al. 2017; Bowd et al. 2019; Marrs et al. 2019; Pausas and Keeley 2021). In the southern European Union (EU) countries (Portugal, Spain, France, Italy and Greece), 48 600 forest fires burn on average 447 800 ha (1980–2015) every year, most of this area being burned by a small number (<15%) of large fires (San-Miguel-Ayanz et al. 2013). This high wildfire incidence in Mediterranean Europe can be attributed to climate, environmental and anthropogenic factors. On one hand, climate change has increased temperature and has reduced relative humidity. On the other hand, socioeconomic factors such as the abandonment of farms and rural areas have resulted in an unusual accumulation of forest fuels (Vilar del Hoyo et al. 2011; Aragó et al. 2016). Unravelling wildfire patterns is crucial to understand fire behaviour and to develop prevention and mitigation strategies, as well as landscape restoration plans. The increasing availability of georeferenced wildfire data has enhanced the development of a prolific line of research focused on analysing the spatial distribution of wildfire and on identifying biotic and abiotic risk factors. Spatiotemporal cluster analysis has been proposed as a useful tool to address important scientific challenges such as characterising observed short-term clustering of ignition points, detecting changes in the spatial distribution of ignition points and understanding the causes of those changes, and measuring temporal variations in wildfire clusters (Prestemon et al. 2013). Clustering analysis applied to For full list of author affiliations and declarations see end of paper *Correspondence to: M. F. Marey-Pérez PROePLA Research Group, Department of Crop Production and Engineering Projects, Universidade de Santiago de Compostela, Spain Email: [email protected] Received: 15 March 2022 Accepted: 22 November 2022 Published: 23 December 2022 Cite this: Marey-Pérez MF et al. (2023) International Journal of Wildland Fire 32(2), 178–194. doi:10.1071/WF22030 © 2023 The Author(s) (or their employer(s)). Published by CSIRO Publishing on behalf of IAWF. wildfire research has been conducted through the combination of classical statistics with GIS (Geographic Information System) tools (Rodrigues et al. 2019), and by spatiotemporal point process analysis and modelling (Serra et al. 2013; Wing and Long 2015; Aragó et al. 2016; Díaz-Avalos et al. 2016; Parente et al. 2016; Woo et al. 2017). In addition to the analysis of interactions between fire events, point process modelling also allows estimation of the effect of environmental and socioeconomic covariates on wildfire incidence, and the creation of fire hazard maps. In the analysis of wildfires, we should distinguish between natural and human-caused fires, which, in addition to different origins, have different dynamics (González- Olabarria et al. 2015). Natural fires, mainly caused by lightning, tend to be concentrated in summer months, fostered by the high temperatures, low air humidity and, hence, low fuel moisture content (Pineda et al. 2014; Nampak et al. 2021; He et al. 2022). On the other hand, more than 90% of fires worldwide are directly or indirectly linked to intentional and unintentional human activities (Costafreda- Aumedes et al. 2017). The spatiotemporal dynamics of human-caused fires have been studied for a long time (Crosby 1954; Bruce 1963; Donoghue and Main 1985). Recent studies found that arson fires in the Iberian Peninsula have aggregated patterns (Costafreda-Aumedes et al. 2016) and analysed the biophysical and socioeconomic factors that favour the occurrence of arson and negligence fires (Rodrigues et al. 2016; Parente et al. 2018; Silva et al. 2019; Dupuy et al. 2020), reaching complementary conclusions. In particular, Rodrigues et al. (2016) identified changes in agricultural activity as the main driver of arson wildfires in Spain in the last decade of the 20th and the first decade of the 21st centuries; Dupuy et al. (2020) and Rodrigues et al. (2018) linked human-caused wildfires with climate change, while Silva et al. (2019) suggested that anthropogenic factors are the main cause that explains arson fires in the Iberian Peninsula. Galicia (north-west Spain, Fig. 1 (left)) has suffered high wildfire incidence over several decades, although climaterelated fire danger in this region is lower than in the Mediterranean and southern regions of Spain (Fig. 1, right). This is due to the fact that a large fraction, above 75%, of wildfires in Galicia are arson, 25% higher than the national rate (MAGRAMA 2016). The particular characteristics of wildfires in Galicia, and their severe environmental and socioeconomic consequences, have motivated of a large body of research with the aim of understanding fire dynamics, identifying fire risk drivers and predicting the occurrence of future events. Any progress in these research topics will contribute to improving the effectiveness of current fire prevention and suppression plans. Different studies have proposed the application of a wide variety of statistical analysis and modelling techniques. Boubeta et al. (2015) proposed a semiparametric time series model to predict the burned area in Galicia 1 week in advance. Boubeta et al. (2016, 2019) used area-level mixed effects models to predict the number of fires; the former showed good performance of Poisson mixed regression models and bootstrap techniques, and the latter incorporated time effects into these models. Wildfire occurrence and burned area have also been estimated through structured additive regression (STAR) that incorporates space- and time-varying covariates, as well as spatial and temporal correlations (Ríos-Pena et al. 2017, 2018). Non-parametric first- and Fires/Year 10 sqkm of wildland 0.00 0.01 0.02 0.03–0.05 0.06–0.08 0.09–0.12 0.13–0.18 0.19–0.26 0.27–0.60 0.61–24.98 No fire data Location of Galicia Average meteorological forest fire danger, 1981–2010 Seasonal severity rating <0.4 0.4–1 1–2 2–3 3–4 4–5 5–6 6–7 7–10 10–15 >15 Outside coverage Fig. 1. Left: location of Galicia and annual mean intensity of wildfire in Europe. Source: Birot et al. (2009). Right: average climate-related forest fire danger in Europe (European Environmental Agency). www.publish.csiro.au/wf International Journal of Wildland Fire 179 second-order analysis of spatial point processes was used to study the spatial distribution of wildfire activity in a forest district in Galicia by Fuentes-Santos et al. (2013). In parallel, some studies have developed new non-parametric inference techniques for spatial and spatiotemporal point processes and have used wildfire patterns in Galicia as case studies to illustrate their applicability. Fuentes-Santos et al. (2016) proposed a plug-in bandwidth selector for the kernel intensity estimator, which contributes to obtaining more accurate estimators for the spatial distribution of wildfires. The non-parametric first-order intensities comparison by Fuentes-Santos et al. (2017) can be used to test if fires with different causes have the same spatial distribution, whereas the log-ratio based separability test proposed by Fuentes-Santos et al. (2018) allows us to check if the spatial distribution of wildfires varies over time. In the present work, we analyse a large dataset comprising the ignition points and time of occurrence of the wildfires recorded in Galicia during 16 years (1999–2014). We focused on comparing the patterns of natural, arson and negligence wildfires. Given that over 70% of wildfires in Galicia burn less than 1 ha, we analyse wildfires smaller (outbreaks) and larger (fires) than 1 ha burned separately. The novel non-parametric first-order inference techniques for spatial and spatiotemporal point processes introduced above were applied to describe the distribution of arson, negligence and natural wildfire patterns, and test for differences between years in order to identify a potential change point in wildfire patterns and between the spatial distributions of wildfire causes. We also applied Monte Carlo tests based on the inhomogeneous L-function (Baddeley et al. 2000), the inhomogeneous L-cross (Ripley 1981) and the spatiotemporal K-function (Fuentes-Santos et al. 2018) to test for interactions between fires. Study area and dataset Study area Galicia, located in the north-west of the Iberian Peninsula (Fig. 1), has a surface area of 29 574 km 2 , which represents 5.78% of the surface of Spain, and has a population of 2.7 million (5.84% of the Spanish population), which implies a mean population density of 94.1 inhabitants/ km 2 , close to the mean population density of Spain (Spanish Statistical Office (INE) 2019, https://www.ine.es/). Forests occupy 69% of the surface in Galicia, a large proportion in comparison with the Spanish average (55%, MAGRAMA 2019). Forested land in Galicia is mainly private (97%) and distributed among a large number of small landowners at an average rate of 2 ha/owner (Marey-Pérez et al. 2012). The forestry sector in Galicia generates 20 320 direct and 50 000 indirect jobs, and represents 3.5% of the regional gross domestic product (GDP) (XERA 2018). Indeed, Galicia, with an average income of EUR2652 million/year, is the major timber producer in Spain and the ninth in Europe (Balsa-Barreiro and Hermosilla 2013). As we can see in Fig. 1 (left), Galicia is one of the regions with higher wildfire incidence in Europe (Comas et al. 2014; Álvarez-Díaz et al. 2015; Da Ponte et al. 2019) despite its relatively unfavourable fire weather conditions. In fact, Galicia suffered more than 255 000 forest fires between 1961 and 2014, with an estimated affected area of 1.83 million ha (Ríos-Pena et al. 2017). Wildfire dataset This work analyses the 104 000 wildfires recorded in Galicia from 1999 to 2014. Data were obtained from the Wildfire General Statistics available at the Spanish Government Data Portal (https://datos.gob.es/es/ catalogo/e05068001-estadistica-general-de-incendios-fore- stales). The dataset comprises the spatial location and time of detection of each ignition point together with additional information about the source of ignition, suppression and damage caused by the wildfire. This work focuses on the burned area and the cause of fire. Although the Wildfire General Statistics provide wildfire records form 1983, the period 1983–1998 was discarded in this study after conducting a data quality control of the georeferenced information provided. Data quality control was conducted testing whether the spatial coordinates of each ignition point were within the reported municipality and type of land assigned to the event. Discrepancies found in the period 1999–2014 were corrected, assigning new coordinates to the event through the procedure detailed in Fuentes- Santos et al. (2013), and less than 10% of ignition points needed to be corrected. Forest fires in Spain have been classified with five main causes: natural, arson, accidental or negligence (referred to as negligence hereafter), reproductions (reigniting fires) and unknown cause (MAGRAMA 2016). This work focuses on arson, negligence and natural wildfires. However, as in previous work (Fuentes-Santos et al. 2013), forest fires were also divided into these groups according to burned area (S), outbreaks (S < 1 ha), regular fires (1 ≤ S< 25 ha) and large fires (S ≥ 25 ha). Non-parametric point processes analysis Point processes are mathematical models that govern the occurrence of a random number of events in a bounded domain, Wd (with d being Euclidian space). If each event has any measure or mark associated with it, we have a marked point process. A multitype point process is a marked point process with categorical marks that define different point processes according with the type of event. Spatial point processes generate a random number of events M. F. Marey-Pérez et al. International Journal of Wildland Fire 180 X x x= { , …, } 1 N in a planar region W2 with area |W| > 0. Spatiotemporal point processes comprise the location and time of occurrence of a random number of events, , ,Sx t x t= {( ), …, ( )} 1 1 N N , irregularly placed in W T× × 2 + . Throughout this paper, point processes and patterns are denoted in bold capitals and events are denoted in bold. The wildfires dataset introduced in the previous section, comprising the spatial location of the ignition points and date and time of detection of wildfires in Galicia, can be seen as a realisation of a spatiotemporal point process. Each event is marked by the cause of fire and its burned area. Non-parametric inference techniques recently developed for first- and second-order analysis of spatial and spatiotemporal point processes allow us to answer important questions regarding the distribution and behaviour of different types of forest fires in Galicia. Kernel estimators of the first-order intensity functions (Diggle 1985; Fuentes-Santos et al. 2016; van Lieshout 2020) characterise the spatial distribution of arson and natural fires, and the nonparametric comparison of first-order intensities tests (Fuentes-Santos et al. 2017), for instance, whether arson and natural fires had the same spatial distribution or whether wildfire distribution varied over years. A firstorder spatiotemporal separability test (Fuentes-Santos et al. 2018) checks whether the spatial distribution of wildfire patterns varies over time. Second-order characteristics, which analyse pairwise interactions between events, allow us to test if wildfire patterns are clustered, regular or random, i.e. whether a wildfire at a given location enhances (clustered) or inhibits (regular) wildfire occurrence in its neighbourhood. Second-order characteristics of multitype point processes allow us to analyse the relationship between different types of events. We can test, for instance, if arson outbreaks and fires appear closer or further apart than would be expected if they were independent. First-order analysis One of the main issues in the analysis of any observed pattern is estimating its first-order intensity function, λ(·), which determines the expected number of events per unit domain (Diggle 2013). In this work, we estimate the firstorder intensity of the arson and natural fire patterns under study through kernel smoothing with full bandwidth matrix (Fuentes-Santos et al. 2016). x p x H k H x x ˆ( ) = ( ) | | ( ( )) HHi N i 1 1/2 =1 1/2 (1) where k(·) is a bivariate Gaussian kernel, H is a positively defined bandwidth matrix and |H| denotes the determinant of H· p x H k H x y y( ) = ( ( ))d HW 1/2 1/2 is the edgecorrection term that reduces the bias near the boundary of the observation domain W, and guarantees the consistency of the kernel estimator of the density of event locations, x x m( ) = ( )/ 0 where m x x= ( )d W is the expected number of events in W. The bandwidth parameter, which determines the degree of smoothing of kernel estimators, is crucial for the performance of the kernel intensity estimation. Different bandwidth selectors, such as the mean nearest distance used in the seminar paper of Koutsias et al. (2004), have been used in the analysis of wildfire patterns. In the present work, bandwidth selection was conducted through the two-stage plug-in algorithm introduced by Fuentes-Santos et al. (2016), which minimises the bootstrap estimate of the AMISE (asymptotic mean integrated square error) of the kernel density of event locations. As can be seen in Fuentes-Santos et al. (2016), large bandwidths are obtained for small point patterns of natural wildfires, and small ones for large point patterns of arson wildfires. Taking advantage of the consistency of the kernel density of event locations, Fuentes-Santos et al. (2017) proposed a formal test to compare the spatial distribution of two observed patterns. This test relies on the fact that two spatial point processes, X 1 and X 2 , with the same spatial distribution have the same density of event locations. Thus, we can use an L 2 discrepancy measure to test the null hypothesis, x x x: ( ) = ( ) = ( ) 0 01 02 0 , and define the test statistic T x x x ˆ= ( ˆ( ) ˆ( )) d = ˆ+ˆ (ˆ+ˆ) W01 02 2 1 2 12 21 (2) where ˆ ij and ˆ i are estimators of x x x= ( ) ( )d ij Wi j0 0 for i, j = 1, 2 and x x= ( ) d iWi02 , obtained by kernel smoothing with plug-in bandwidth (Chacón and Duong 2010). The test was calibrated through smooth bootstrap with B = 200 realisations of the null hypothesis. We use this procedure to compare the intensity of arson and natural wildfires and to test if the spatial distribution of each type of fire varied across years. This procedure is referred as the T-test hereafter. Up to now, we have focused on the spatial distribution of wildfire, overlooking the temporal dimension. To fill this gap, we estimate the spatiotemporal intensity of the wildfire patterns under study by kernel smoothing, and apply the log-ratio based separability test proposed by Fuentes-Santos et al. (2018) to check whether the spatial distribution of wildfires varies over time. The kernel intensity estimator is given by x t p x t H h ˆ( , ) = ( , ) | | H h H h ,,1s1/2 t1 s t s t (3) k H x k h tx t( ( )) ( ( )) i N i i =1 ss 1/2 tt 1 where k s (·) and k t (·) are bivariate and univariate Gaussian kernels, H s is the two-dimensional bandwidth matrix for the www.publish.csiro.au/wf International Journal of Wildland Fire 181 spatial component, and h t is the bandwidth for the temporal component. p x t k x u k t v u v( , ) = ( ) ( )d d H h T W H h ,s, t, s t s t is the spatiotemporal edge-correction factor. A spatiotemporal point process is first-order separable if its intensity can be expressed as the product of its spatial and temporal marginals: x t x t( , ) = ( ) ( ) 1 2 and, consequently, the log-ratio between the spatiotemporal and spatial intensities, x t x t x( , ) = log( ( , )/ ( )) 1 , does not depend on the spatial locations x for any t T . Considering this property, Fuentes-Santos et al. (2018) proposed using a no-effect test to check the separability assumption. To implement the test, we first estimate ρ(x, t) as the log-ratio of the kernel spatiotemporal (Eqn 3) and spatial (Eqn 1) intensity functions with diagonal bandwidth matrices selected by least-squares cross-validation. Once x tˆ ( , ) is obtained, we consider a regression problem with a response variable, ,Y y i nx t= { = ˆ ( ), =1, … , } ii i , that may depend on the spatial covariate X x x x i n= { = ( , ), =1, … , } i i i1 2 comprising the event locations, and we test for the effect of X on Y. Thus, following Bowman and Azzalini (1997), we check whether µE Y X[ | ] = or E Y X m X[ | ] = ( ) through the test statistic F=(RSS RSS )/(df df ) RSS /df 0 1 1 0 1 1 (4) where RSS 0 and RSS 1 are the residual sum of squares for non-parametric estimators of the null and alternative models, and df 0 , df 1 denote their respective degrees of freedom. The test is calibrated through a permutation test, which relies on the fact that under 0 , the pairing of any particular X and Y is completely random. This procedure is referred to as the F-test hereafter. Second-order analysis Once the spatial and spatiotemporal distribution of wildfire patterns are characterised, we apply Monte Carlo tests based on the spatial and spatiotemporal inhomogeneous K-functions to check for interaction between ignition points. The K-function of a homogeneous spatial point process is defined as K r N r( ) = [ ( )] 10 where N 0 (r) is the number of further events within distance r of an arbitrary event (Ripley 1977). Given that the homogeneity assumption can be very restrictive and unrealistic when dealing with real data, Baddeley et al. (2000) extended this function to the case of inhomogeneous point processes, K inhom (r), and proposed an empirical estimator ¸ ¸ , K r W I r r r x x x x ˆ( ) = 1 | | ( ) ˆ( ) ˆ( ) ; 0 W i j i j x x X i j i j inhom ,1 max i j (5) where I(·) is the indicator function, r max is the maximum distance at which the function is evaluated, w ij is Ripley's edge-corrector, and x ˆ( ) is the kernel intensity estimator detailed in Eqn 1. The L-function (Besag 1977), defined as L r K r( ) = ( )/ imhom inhom , is a transformation of the K-function widely used in practice. The inhomogeneous L-function of a spatial Poisson point process is L r r( ) = inhom , where values below or above this threshold indicate, respectively, inhibition or clustering between events at distance r. This property suggests testing for interaction between events through a Monte Carlo test, which compares the L-function of the observed patterns, X, with the upper and lower envelopes of B − 1 realisations of the inhomogeneous spatial Poisson point process with the same first-order intensity as X. Spatial interactions between two types of fires, e.g. arson and natural fires in a given year, were tested through Monte Carlo tests based on the inhomogeneous L-cross function, which is the natural extension of the previous procedure to the multitype framework (Ripley 1981; Baddeley et al. 2015). The Monte Carlo procedures introduced above test for spatial interaction in wildfire patterns overlooking the temporal lag between events. However, testing for spatiotemporal interaction, i.e. whether the occurrence of a wildfire increases or reduces the probability of new events in its neighbourhood during the next hours and days, is crucial for a proper analysis of fire behaviour. To address this issue, we applied a Monte Carlo test based on the spatiotemporal inhomogeneous K-function (Gabriel and Diggle 2009), as for a Poisson point process K r t r t( , ) = ST,inhom 2 , where larger and smaller values indicate clustering and inhibition, respectively. To implement the spatiotemporal K-test, we first obtained the empirical estimator of K r t( , ) ST,inhom as follows ¸ ¸ , , , , K r t W T I r tx x t t x t x t ˆ( , ) = 1 | × | ( < , | | < ) ˆ( ) ˆ( ) W T i j i j x x t t i j i j i i j j ST,inhom ,1 i j i j (6) r r t t0 0 max max where I(·) is the indicator function, ω ij is Ripley's spatiotemporal edge-corrector, r max , t max are the maximum spatial and temporal distances at which the function is evaluated, and x t ˆ( , ) is an estimator of the spatiotemporal first-order intensity function. Gabriel and Diggle (2009) assume firstorder separability, i.e. they use a separable estimator of the spatiotemporal intensity, x t x t ˆ( , ) = ˆ( ) ˆ( ) 1 2 , and attribute any non-separable effect to the second-order structure. We used separable or non-separable kernel intensity estimated in agreement with the results of the first-order separability test introduced in the previous section. As well as for the spatial framework, the Monte Carlo test compares the spatiotemporal K-function of the observed pattern, K x t ˆ( , ) ST,inhom , with upper and lower envelopes determined M. F. Marey-Pérez et al. International Journal of Wildland Fire 182 by Monte Carlo realisations of a spatiotemporal Poisson point process with the same intensity as the observed pattern. The maximum values r and t for which K x t ˆ( , ) ST,inhom falls above or below the envelopes determine the spatial and temporal interaction radius, respectively. Software The statistical analysis of the spatial and spatiotemporal wildfire patterns was conducted with the R statistical software (R Core Team 2018). The Spatstat package (Baddeley et al. 2015) was used for kernel intensity estimation and second-order analysis of spatial point patterns, whereas plug-in bandwidths were obtained with the help of the ks package (Duong 2018). The kde.test function in the ks package was adapted by Fuentes-Santos et al. (2017) to implement the L 2 -test for comparison of first-order intensities. Kernel log-relative risk functions and their tolerance contours were estimated using the sparr package (Davies et al. 2018). Fuentes-Santos et al. (2018) extended some functions in the sparr package (Davies et al. 2018) to estimate the spatiotemporal intensity and log-ratio functions to implement the separability test with the help of the sm package (Bowman and Azzalini 2014). Results Exploratory analysis Fig. 2 shows the number of wildfires and area burned by cause of fire and year (see Table A1 in Supplementary Appendix A for further details). The majority of wildfires recorded were arson (>80%), while the incidence of those caused by negligence (~3%)) and natural causes (~1%) was very small. The year 2006 registered a decrease in the number of wildfires in comparison with previous years but had the largest affected area, and we observed a significant reduction in the number of wildfires and affected area from 2007 onward. The correspondence analysis conducted as a preliminary analysis of wildfire behaviour identified 2006 as a change point, as we found association between arson fires and the years 1999–2006, and between negligence fires and 2007–2014 (see details in Supplementary Appendix A). According to the official reports, a large proportion of the wildfires, 72.5%, burned less than 1 ha, and just 2% affected more than 25 ha. Although we do not see large differences between causes, arson wildfires have the lowest rate of events with less than 1 ha burned (see Supplementary Table A1). Taking into account these particular features of wildfire in Galicia, this work considers all events, not only 12 000 8000 No. fires 6000 4000 2000 0 80 000 Burned area (ha) 60 000 40 000 20 000 0 1999 2000 2001 2002 2003 Year Year 2004 2005 2006 2007 2008 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Arson Natural Negligence Reproduction Unknown Fig. 2. Number of ignition points registered in Galicia from 1999 to 2014 (top); and burned area (bottom) by cause of fire. www.publish.csiro.au/wf International Journal of Wildland Fire 183 those with more than 1 ha burned as is usual in wildfire research. Hereafter, 'wildfires' refers to all events, 'outbreaks' to wildfires with S < 1 ha, and 'fires' to those with S ≥ 1 ha. Spatial and spatiotemporal distribution of wildfire We analysed the spatial and spatiotemporal distribution of arson, negligence and natural wildfires, distinguishing between outbreaks (S < 1 ha) and fires (S ≥ 1 ha) when the size of the observed pattern was large enough. Given the large number of analyses conducted, detailed results for the spatial and spatiotemporal analyses are provided as Supplementary Appendices B and C, respectively. The kernel intensity estimators of arson, negligence and natural wildfires shown in Figs 3–5 show clear differences in the spatial patterns of wildfire between the three causes. These differences were confirmed by the non-parametric comparison between intensity functions (T-test, P value < 0.005 for all years with more than 20 natural fires). Now, we focus on testing for interannual variability in the spatial pattern of each cause of wildfire, and on testing for differences between outbreaks and fires for the two types of human-caused wildfires. The non-parametric test found that the spatial distribution of arson wildfires, outbreaks and fires varied across years (T-test, P value < 0.005). In particular, Fig. 3 suggests a trend with wildfire hotspots spreading from the south of Galicia, on the boundary with Portugal, to the west coast every 4 years. We also found differences (T-test, P value < 0.005) between the spatial patterns of outbreaks (Supplementary Fig. B1 in Supplementary Appendix B) and fires (Supplementary Fig. B2); for instance, in 2006, we observed a low intensity of outbreaks, but a high incidence of fires in the SE of Galicia. The spatial distribution of wildfires caused by negligence, outbreaks and fires varied over years, although pairwise 1999 2000 2001 2002 0.2 0.5 1 1.5 2 0.5 0.2 0.6 1 1.4 1 1.5 2 0.6 1 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 0.2 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.1 0.3 0.5 0.1 0.3 0.5 0.1 0.1 0.2 0.3 0.4 0.1 0.2 0.02 0.06 0.3 0.4 0.3 0.5 0.5 1 1.5 2 0.5 0.2 0.4 0.6 0.8 1 1 1.5 2.5 2 0.6 1 Fig. 3. First-order intensity estimator for the spatial patterns of arson wildfires by year (different scales). M. F. Marey-Pérez et al. International Journal of Wildland Fire 184 comparison did not always report significant differences (see Table S3). Fig. 4 shows negligence fires occurred mainly in the Atlantic coastal area of Galicia, with high-incidence areas moving between the northern and southern coastal areas, and some hotspots in the inner region of Galicia. Comparison between outbreaks and fires found significant differences between them in 1999, 2000, 2002, 2003, 2007 and 2008. As observed for arson fires, the inner and southern areas tend to have larger fire than outbreak (details are given in Supplementary Table B2, Supplementary Figs B3, B4). The spatial distribution of natural wildfires was more stable over years, with higher incidence in the east of Galicia (Fig. 5), although the non-parametric comparison detected differences between some pairs of years (Supplementary Table B3). Outbreaks and fires were not analysed separately owing to the small number of events observed. Supplementary Appendix C shows the kernel estimator of the spatial and spatiotemporal intensities, and the temporal density of ignition points for arson, negligence and natural fires by year. As for the spatial distribution, we observed differences between the temporal patterns of human-caused and natural wildfire patterns. The temporal pattern of arson wildfires varied over years, early spring and late summer–autumn being the seasons with the highest fire incidence. Fires caused by negligence occurred mainly in spring and summer, but the highest-incidence period also varied over years. Finally, natural fires occurred mainly in summer. The spatiotemporal separability test rejects the null hypothesis for arson and negligence wildfires (F-test, P value <0.005), i.e. the spatial distribution of wildfire varied over time, as can be seen in the spatiotemporal intensity estimators (see animations in Supplementary Appendix C). Although data sparseness and the small number of natural wildfires recorded each year do not allow the application of 1999 2000 2001 2002 0.002 5e–04 0.0015 0.005 0.015 0.005 0.015 0.01 0.006 0.01 0.01 0.001 0.005 0.01 0.015 0.005 0.01 0.015 0 0.001 0 0 0.004 0.001 0.003 0.008 0.012 4e–04 0.001 0.004 0.007 0.003 0 0.005 0.01 0.015 0 0.005 0.015 0.005 0.002 0.008 0.014 0.015 0.03 0.05 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Fig. 5. First-order intensity estimator for the spatial patterns of natural wildfires by year (different scales). www.publish.csiro.au/wf International Journal of Wildland Fire 185 the separability test for these patterns, visual inspection of the kernel estimators of the spatiotemporal intensity suggests that their distribution also varied over time. Spatial and spatiotemporal interaction between wildfires Table 1 shows the maximum interaction rates found with the inhomogeneous L-tests for arson, negligence and natural wildfire patterns, and for interactions in the outbreak and fire patterns of the two types of human-caused fires. The inhomogeneous L-test detected clustering in the arson wildfire patterns for all years but 2007 with an interaction radius between 1 km in 2004 and 6 km in 2014, and inhibition at large distances (see Supplementary Fig. B4 in Supplementary Appendix B). We also found interactions between the outbreaks (Supplementary Fig. B6) and fires (Supplementary Fig. B7); as observed for the whole wildfire patterns, the interaction radius varied over years. The inhomogeneous L-cross test found evidence of positive interaction between arson outbreaks and fires (Table 2, Supplementary Fig. B8). Arson wildfires also show aggregation between arson events over years (Supplementary Fig. B17), i.e. a higher probability of arson fires in areas that recorded arson fires in previous years. In contrast, we did not find evidence of interactions between fires over sequential years (Supplementary Fig. B18). The spatiotemporal inhomogeneous K-tests (Fig. 6), which test for interactions between events up to 15 km and 15 days after the occurrence of a given event, show that the probability of new wildfires in the neighbourhood of an observed event decreases over time. In this sense, except for 2009 and 2012, which had long-term aggregation up to 15 km, the interaction radius decreases with time. In particular, in 1999, 2005 and 2006, the spatiotemporal K-test detected long-term interaction up to 6–10 km, an 1999 2000 2001 2002 0.005 0.01 0.02 0.03 0.01 0.01 0.03 0.01 0.01 0.02 0.005 0.015 0.03 0.05 0.07 0.02 0.03 0.04 0.01 0.01 0.006 0.002 0.014 0.008 0.002 0.02 0.03 0.04 0.015 0.025 0.005 0.015 0.005 0.015 0.025 0.005 0.015 0.005 0.015 0.005 0.015 0.002 0.006 0.025 0.005 0.015 0.025 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Fig. 4. First-order intensity estimator for the spatial patterns of negligence wildfires by year (different scales). M. F. Marey-Pérez et al. International Journal of Wildland Fire 186 temporal dynamics of fire regime features in mainland Spain. Journal of Environmental Management 241, 575–586. doi:10.1016/j. jenvman.2018.09.107 Koutsias N, Kalabokidis KD, Allgöwer B (2004) Fire occurrence patterns at landscape level: beyond positional accuracy of ignition points with kernel density estimation methods. Natural Resource Modeling 17(4), 359–375. doi:10.1111/j.1939-7445.2004.tb00141.x Krasovskii A, Khabarov N, Migliavacca M, Kraxner F, Obersteiner M (2016) Regional aspects of modelling burned areas in Europe. International Journal of Wildland Fire 25(8), 811–818. doi:10.1071/WF15012 López-Iglesias E (2019) The agricultural and agri-food sector in Galicia; assessment of changes since European integration, 1986-2016. Revista Galega de Economía 28(3), 1–20. doi:10.15304/rge.28. 3.6168 López-Penabad MC, Iglesias-Casal A, Rey-Ares L (2022) Proposal for a sustainable development index for rural municipalities. Journal of Cleaner Production 357, 131876. doi:10.1016/j.jclepro.2022.131876 López-Rodríguez G, Rodríguez-Vicente V, Marey-Pérez MF (2021) Study of forest productivity in the occurrence of forest fires in Galicia (Spain). Sustainability 13(15), 8472. doi:10.3390/ su13158472 Lovreglio R, Leone V, Giaquinto P, Notarnicola A (2010) Wildfire cause analysis: four case-studies in southern Italy. iForest - Biogeosciences and Forestry 3(1), 8–15. doi:10.3832/ifor0521-003 MAGRAMA (2016) Los incendios forestales en Espana. Decenio 2006–2015. (Coord. AL López-Santalla, M López-García). Ministerio de Agricultura, Pesca y Alimentación. Secretaría General Técnica. [In Spanish] MAGRAMA (2019) Anuario de Estadística Forestal 2017. Ministerio de Agricultura Pesca y Alimentación. Secretaría General Técnica. [In Spanish] Marey-Pérez MF, Rodríguez-Vicente V, Álvarez-López JC (2012) Practical application of multivariant analysis techniques to the forest management of active farmers in the northwest of Spain. Small-scale Forestry 11(4), 453–476. doi:10.1007/s11842-012-9195-1 Marey-Pérez MF, Calvo-González A, Domínguez-Torres G (2014) Are the communal forest owners involved in the management of their lands? A qualitative analysis for the case of Galicia (Spain). Bosque (Valdivia) 35(2), 207–215. doi:10.4067/S0717-92002014000200008 Marey-Perez M, Loureiro X, Corbelle-Rico EJ, Fernández-Filgueira C (2021) Different strategies for resilience to wildfires: the experience of collective land ownership in Galicia (northwest Spain). Sustainability 13(9), 4761. doi:10.3390/su13094761 Marrs RH, Marsland E-L, Lingard R, Appleby PG, Piliposyan GT, Rose RJ, O’Reilly J, Milligan G, Allen KA, Alday JG, et al. (2019) Experimental evidence for sustained carbon sequestration in firemanaged, peat moorlands. Nature Geoscience 12(2), 108–112. doi:10.1038/s41561-018-0266-6 Martínez J, Vega-Garcia C, Chuvieco E (2009) Human-caused wildfire risk rating for prevention planning in Spain. Journal of Environmental Management 90(2), 1241–1252. doi:10.1016/j.jenvman.2008.07.005 Mateus S, Ferreira V, Sanches A, Resende P, Pinho C (2021) Determination of combustion kinetic data of some agricultural wastes from the Galicia-northern Portugal Euroregion. Waste and Biomass Valorization 12(6), 3091–3107. doi:10.1007/s12649-020-01227-7 Moreno JM, Morales-Molino C, Torres I, Arianoutsou M (2021). Fire in Mediterranean pine forests: past, present and future. In ‘Pines and their mixed forest ecosystems in the Mediterranean Basin’. (Eds G Ne'eman, Y Osem) pp. 421–456. (Springer) Moreno MV, Conedera M, Chuvieco E, Pezzatti GB (2014) Fire regime changes and major driving forces in Spain from 1968 to 2010. Environmental Science & Policy 37, 11–22. doi:10.1016/j.envsci. 2013.08.005 Nampak H, Love P, Fox-Hughes P, Watson C, Aryal J, Harris RMB (2021) Characterizing spatial and temporal variability of lightning activity associated with wildfire over Tasmania, Australia. Fire 4(1), 10. doi:10.3390/fire4010010 Otero-Varela A, Paül V (2022) The never-ending story of the metropolitan area of Vigo (Galicia, Spain). In ‘International symposium: New metropolitan perspectives’. (Eds F Calabrò, L Della Spina, MJ Piñeira Mantiñán) pp. 946–956. (Springer) https://doi.org/10.1007/978-3- 031-06825-6_90 Palaiologou P, Kalabokidis K, Troumbis A, Day MA, Nielsen-Pincus M, Ager AA (2021) Socio-ecological perceptions of wildfire management and effects in Greece. Fire 4(2), 18. doi:10.3390/fire4020018 Parente J, Pereira MG, Tonini M (2016) Space-time clustering analysis of wildfires: The influence of dataset characteristics, fire prevention policy decisions, weather and climate. Science of the Total Environment 559, 151–165. doi:10.1016/j.scitotenv.2016.03.129 Parente J, Pereira MG, Amraoui M, Tedim F (2018) Negligent and intentional fires in Portugal: Spatial distribution characterization. Science of the Total Environment 624, 424–437. doi:10.1016/j. scitotenv.2017.12.013 Pausas JG, Keeley JE (2021) Wildfires and global change. Frontiers in Ecology and the Environment 19(7), 387–395. doi:10.1002/fee.2359 Pineda N, Rigo T (2017) The rainfall factor in lightning-ignited wildfires in Catalonia. Agricultural and Forest Meteorology 239, 249–263. doi:10.1016/j.agrformet.2017.03.016 Pineda N, Montanyà J, van der Velde OA (2014) Characteristics of lightning related to wildfire ignitions in Catalonia. Atmospheric Research 135–136, 380–387. doi:10.1016/j.atmosres.2012.07.011 Pozo RA, Galleguillos M, González ME, Vásquez F, Arriagada R (2022) Assessing the socio-economic and land-cover drivers of wildfire activity and its spatiotemporal distribution in south-central Chile. Science of the Total Environment 810, 152002. doi:10.1016/j.scitotenv.2021. 152002 Prestemon JP, Hawbaker TJ, Bowden M, Carpenter J, Brooks MT, Abt KL, Sutphen R, Scranton S (2013) Wildfire ignitions: a review of the science and recommendations for empirical modeling. General Technical Reports SRS-GTR-171, 1–20. (USDA Forest Service, Southern Research Station: Asheville, NC) R Core Team (2018) ‘R: A Language and Environment for Statistical Computing.’ (R Foundation for Statistical Computing: Vienna, Austria) Ríos-Pena L, Kneib T, Cadarso-Suárez C, Marey-Pérez M (2017) Predicting the occurrence of wildfires with binary structured additive regression models. Journal of Environmental Management 187, 154–165. doi:10.1016/j.jenvman.2016.11.044 Ríos-Pena L, Kneib T, Cadarso-Suárez C, Klein N, Marey-Pérez M (2018) Studying the occurrence and burnt area of wildfires using zero-one- inflated structured additive beta regression. Environmental Modelling & Software 110, 107–118. doi:10.1016/j.envsoft.2018.03.008 Ripley BD (1977) Modelling spatial patterns. Journal of the Royal Statistical Society: Series B (Methodological) 39, 172–192. doi:10.1111/j.2517-6161.1977.tb01615.x Ripley BD (1981) ‘Spatial statistics.’ (Wiley: New York) Rodrigues M, Jiménez A, de la Riva J (2016) Analysis of recent spatial–temporal evolution of human driving factors of wildfires in Spain. Natural Hazards 84(3), 2049–2070. doi:10.1007/s11069-016- 2533-4 Rodrigues M, Jiménez-Ruano A, Peña-Angulo D, De la Riva J (2018) A comprehensive spatial-temporal analysis of driving factors of humancaused wildfires in Spain using geographically weighted logistic regression. Journal of Environmental Management 225, 177–192. doi:10.1016/j.jenvman.2018.07.098 Rodrigues M, Costafreda-Aumedes S, Comas C, Vega-García C (2019) Spatial stratification of wildfire drivers towards enhanced definition of large-fire regime zoning and fire seasons. Science of the Total Environment 689, 634–644. doi:10.1016/j.scitotenv.2019.06.467 Rodrigues M, Jiménez-Ruano A, de la Riva J (2020) Fire regime dynamics in mainland Spain. part 1: Drivers of change. Science of The Total Environment 721, 135841. doi:10.1016/j.scitotenv.2019.135841 Ruffault J, Mouillot F (2017) Contribution of human and biophysical factors to the spatial distribution of forest fire ignitions and large wildfires in a French Mediterranean region. International Journal of Wildland Fire 26(6), 498–508. doi:10.1071/WF16181 San-Miguel-Ayanz J, Moreno JM, Camia A (2013) Analysis of large fires in European Mediterranean landscapes: lessons learned and perspectives. Forest Ecology and Management 294, 11–22. doi:10.1016/ j.foreco.2012.10.050 Serra L, Juan P, Varga D, Mateu J, Saez M (2013) Spatial pattern modelling of wildfires in Catalonia, Spain 2004–2008. Environmental Modelling & Software 40, 235–244. doi:10.1016/ j.envsoft.2012.09.014 Silva JMN, Moreno MV, Le Page Y, Oom D, Bistinas I, Pereira JMC (2019) Spatiotemporal trends of area burnt in the Iberian Peninsula, www.publish.csiro.au/wf International Journal of Wildland Fire 193 1975–2013. Regional Environmental Change 19(2), 515–527. doi:10.1007/s10113-018-1415-6 Tedim F, Leone V, Xanthopoulos G (2016) A wildfire risk management concept based on a social-ecological approach in the European Union: Fire Smart territory. International Journal of Disaster Risk Reduction 18, 138–153. doi:10.1016/j.ijdrr.2016.06.005 Tonini M, Pereira MG, Parente J, Orozco CV (2017) Evolution of forest fires in Portugal: from spatio-temporal point events to smoothed density maps. Natural Hazards 85(3), 1489–1510. doi:10.1007/ s11069-016-2637-x Urbieta IR, Franquesa M, Viedma O, Moreno JM (2019) Fire activity and burned forest lands decreased during the last three decades in Spain. Annals of Forest Science 76(3), 90. doi:10.1007/s13595-019- 0874-3 van Lieshout MNM (2020) Infill asymptotics and bandwidth selection for kernel estimators of spatial intensity functions. Methodology and Computing in Applied Probability 22, 995–1008. doi:10.1007/s11009- 019-09749-x Venäläinen A, Korhonen N, Hyvärinen O, Koutsias N, Xystrakis F, Urbieta IR, Moreno JM (2014) Temporal variations and change in forest fire danger in Europe for 1960–2012. Natural Hazards and Earth System Sciences 14(6), 1477–1490. doi:10.5194/nhess-14- 1477-2014 Vilar L, Woolford DG, Martell DL, Martín MP (2010) A model for predicting human-caused wildfire occurrence in the region of Madrid, Spain. International Journal of Wildland Fire 19(3), 325–337. doi:10.1071/WF09030 Vilar L, Camia A, San-Miguel-Ayanz J, Martín MP (2016) Modeling temporal changes in human-caused wildfires in Mediterranean Europe based on land use–land cover interfaces. Forest Ecology and Management 378, 68–78. doi:10.1016/j.foreco.2016.07.020 Vilar del Hoyo LV, Isabel MPM, Vega FJM (2011) Logistic regression models for human-caused wildfire risk estimation: analysing the effect of the spatial accuracy in fire occurrence data. European Journal of Forest Research 130(6), 983–996. doi:10.1007/s10342- 011-0488-2 Wing MG, Long J (2015) A 25-year history of spatial and temporal trends in wildfire activity in Oregon and Washington, USA. Modern Applied Science 9(3), . 117–132. doi:10.5539/mas.v9n3p117 Woo H, Chung W, Graham JM, Lee B (2017) Forest fire risk assessment using point process modelling of fire occurrence and Monte Carlo fire simulation. International Journal of Wildland Fire 26(9), 789–805. doi:10.1071/WF17021 XERA (2018) La cadena forestal – madera en Galicia 2017. 2018, Axencia Galega da Industria Forestal. (Coord. J Picos) (Consellera de Economa e Industria, Universidade de Vigo) Zhang Y, Lim S, Sharples JJ (2016) Modelling spatial patterns of wildfire occurrence in south-eastern Australia. Geomatics, Natural Hazards and Risk 7(6), 1800–1815. doi:10.1080/19475705.2016. 1155501 Data availability. Wildfire data used in this were obtained form the Wildfire Statistics dataset of the Wildfire General Statistics available at the Spanish Government Data Portal (https://datos.gob.es/es/catalogo/e05068001-estadistica-general-de-incendios-forestales). Conflicts of interest. Thea authors declare no conflicts of interests. Declaration of funding. This work was supported by Projects MTM2016-76969-P and PID2020-116587GB-I00 (AEI/FEDER, UE), and projects IN607B: Modalidad B – Grupos con potencial crecemento, GPC GI-1716 PROXECTOS E PLANIFICACIÓN (PROEPLA), 2018-PG078 (Ref. ED431B 2018/23) from the Galician Government (Xunta the Galicia). Acknowledgements. We would like to acknowledge Luis Franco for his technical support in the access and pre-processing of wildfire data. Author affiliations A PROePLA Research Group, Department of Crop Production and Engineering Projects, Universidade de Santiago de Compostela, Spain. B Marine Research Institute, Spanish National Research Council, Spain. C Department of Statistics, Mathematical Analysis and Optimisation, University of Santiago de Compostela, Spain. M. F. Marey-Pérez et al. International Journal of Wildland Fire 194