On the comparative importance of fire danger rating ... - CiteSeerX

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International Journal of Wildland Fire 2011, 20, 46–58

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On the comparative importance of fire danger rating indices and their integration with spatial and temporal variables for predicting daily human-caused fire occurrences in Spain M. PadillaA,B and C. Vega-GarcıáA A

Agriculture and Forest Engineering Department, University of Lleida, 191 Alcalde Rovira Roure Avenue, E-25198 Lleida, Spain. B Corresponding author. Email: [email protected]

Abstract. Human-caused forest fires are common in Mediterranean countries. Forest fire management agencies customarily estimate daily fire loads by using meteorological fire danger rating indices, based on variables registered daily by weather stations. This paper is focussed on the evaluation of the relative performance of a comprehensive set of commonly used fire weather indices by developing holistic daily fire occurrence models in Spain involving also other topographic, fuel and human-related geographic factors. The data consisted of historical records of daily fire occurrences, daily weather data and geographic characteristics for the peninsular territory of Spain in a 10-km-spatial resolution grid, for the period from 2002 to 2005. The prediction units were 10 10-km-grid cells but in order to take into account the spatial variation in relationships between explanatory variables and historical occurrences, Spain was divided into 53 ecoregions and a logistic regression model was developed for each one of these regions. The explanatory variables included in the models illustrated which weather and geographic factors primarily affected daily human-caused fires in the ecoregions. The validation of the estimated ignition probabilities with the fire occurrences registered during 2005, reserved for independently testing the model’s predictive capability, resulted in values of total percentage correctly predicted varying from 47.4 to 82.6%. Additional keywords: fire risk, fire weather, human factors, logistic regression, regional analysis, validation.

Introduction Fire is common in Mediterranean countries and it is currently the major threat to the forest ecosystems in the region. Spain is one of the European countries most affected by wildfire. In the 10-year period between 1996 and 2005, more than 200 000 fires burned 1.2 million hectares (2.5% of the country), causing great damage and, more importantly, several human lives were lost. A total of 197 625 (78%) of those fires were caused by people, including also those with unknown causes (DGMNPF 2006). To deal with fire occurrence and reduce damage, forest fire management agencies usually plan the distribution of their resources on their territory relying on estimates of where fires are likely to occur each day (Wotton and Martell 2005), and where fire behaviour could be more severe. Human-caused daily occurrences of fire depend on people’s activity and actions (Syphard et al. 2008), and on the ignition conditions in the fire environment, where weather plays a relevant role (Garcıá Diez et al. 1999; Chuvieco et al. 2010). Despite the importance of the human risk component, daily registers of human activities do not exist or are rarely available (Martell et al. 1987), so human variables are incorporated into prediction models in most studies through surrogate spatial or geographic variables such as accessibility (i.e. distance to urban areas, campgrounds, roads, etc.) Ó IAWF 2011

(Chou et al. 1993; Vega-Garcıá et al. 1995, 1996; Vasconcelos et al. 2001; Maingi and Henry 2007; Romero-Calcerrada et al. 2008; Martıńez et al. 2009), population density and livestock grazing (Romero-Calcerrada et al. 2008), land use (Vasconcelos et al. 2001), urban–forest interface or other socioeconomic variables such as those included in Martıńez et al. (2009) (e.g. density of agricultural machinery, density of agricultural plots, persistence of livestock under traditional management, unemployment rate, rural population decrease, etc.). Fuels have been introduced in fire occurrence studies through geographic data (e.g. fuel model category, Vega-Garcıá et al. 1995, 1996; Syphard et al. 2008) but also as spectral indices computed from Landsat data (Lozano et al. 2007, 2008) or texture measurements of the landscape pattern of the vegetation (Vega-Garcıá and Chuvieco 2006). Meteorology influences fuel moisture conditions and these determine the likelihood of ignition. To evaluate ignition conditions in the forest physical environment, fire management agencies traditionally use meteorological fire danger rating (FDR) indices based on variables registered daily by weather stations. The use of FDR indices is widely accepted and developed all over the world but not as much for specifically evaluating ignition probabilities as for anticipating general 10.1071/WF09139

1049-8001/11/010046

Predicting daily human-caused fire occurrences in Spain

forest fire activity and fire potential for a management area (Andrews et al. 2003). The use of historical occurrence data for testing fire danger rating systems started in 1926 when A. E. Moss tested the relationship between relative humidity and fires per day (Andrews et al. 2003), and since, many other authors have found records of fire-days (days with fires) and no-fire-days to be an appropriate indicator of fire activity within FDRs (i.e. Krusel et al. 1993). More recently, Viegas et al. (1999) compared several FDR methods in southern Europe using fire occurrence (number of fires per day, number of fire-days) and area burned. Andrews et al. (2003) assessed the performance of the US National Fire Danger Rating System (NFDRS) (Deeming et al. 1977; Bradshaw et al. 1983), testing three indices (Spread Component, Energy Release Component, Burning Index) in four fuel models by means of fire-days, large-fire-days (days with at least one fire bigger than 4 ha) and multiple-fire-days (days with five or more fires). On a mirror view of the relationship between fire danger and fire occurrence, Crosby (1954) was the first author to use a lineal regression to predict daily fire occurrence in Missouri, USA, from the danger index used at that time in the United States. He was followed by Cunningham and Martell (1973), Martell et al. (1987), Todd and Kourtz (1991), Loftsgaarden and Andrews (1992), Vega-Garcıá et al. (1995) and Preisler et al. (2004) among others, who relied on the Fine Fuel Moisture Code (FFMC) of the Canadian Forest Fire Weather Index System (CFFWIS) (Van Wagner and Pickett 1985; Van Wagner 1987), the Energy Release Component (ERC) of the NFDRS, or other meteorological, human and environmental variables for daily prediction. The variables were input mainly into logistic regression models, but other types of models have also been used in the past (e.g. artificial neural networks, Vega-Garcıá et al. 1996; Li et al. 2009). All models used just one FDR system, but no systematic attempt has ever been made at evaluating the relative aptitude of the different available danger rating methods or ignition components for daily fire occurrence prediction. Andrews et al. (2003) have pointed out that the decision to use fuel models and indices in the NFDRS is often made subjectively, but the system being climatology-based, proper application and interpretation must be based on the analysis of historical data. Wotton and Martell (2005) found that similar values of a fire danger index in two regions may imply different ignition conditions because of variation in vegetation and forest type structures. FDR systems should be efficient in accounting for weather influence on ignition, but in FDR, fuel and terrain factors are essentially held constant (Andrews et al. 2003). We propose that the optimal way to explain the meaning of fire danger indices in terms of fire activity is to test them within the frame of probability models of daily fire occurrence. Comprehensive modelling of fire occurrence has been proved in the past to require geographic factors as well, related to fuels, terrain and human risk variables (e.g. Badia-Perpinya´ and PallaresBarbera 2006). Consequently, the goal of the present study was to evaluate the relative performance of different FDR systems by developing holistic daily fire occurrence models in Spain. Spain is on the point of shifting from the former Grado Actual de Peligro de Incendios Forestales (named the Spanish

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ICONA method in this manuscript) (Ve´lez 1985; ICONA 1990) of the Spanish Forest Service (Martıńez 2004) to adopt the Canadian Forest Fire Weather Index, which is being calibrated at the provincial level (Mestre et al. 2008). This makes it an ideal study area: appropriate application of FDRs has been an issue in the United States for years (Andrews et al. 2003), and as FDR systems are exported to other countries, and calibrated, appropriate application remains an important issue. Although Viegas et al. (1999) found that the CFFWIS performed well in relative terms in some small areas in Portugal, France and Italy, they did not consider the NFDR system in their work, nor did they attempt to model the daily fire occurrence process with the FDR indices they tested. The selection of prediction units was given considerable attention in this study. In previous work, some daily prediction models were built for a specific weather station and variables input into the models were computed for the areas of influence of the weather station (e.g. Martell et al. 1987). Some prediction models were applied to prediction units of variable size, such as forest districts (Vega-Garcıá et al. 1995), but in others, a regular grid was the prediction unit (e.g. Vega-Garcıá et al. 2008). In non-daily models, prediction units have ranged from forest stands (Gonza´lez et al. 2006), to 30-m pixels (Vega-Garcıá and Chuvieco 2006; Lozano et al. 2007, 2008), 1-km2 units (Lloret et al. 2002), polygons (Chou et al. 1993), townships (Martıńez et al. 2009), and relatively large areas within a country (Viegas et al. 1999). The highest resolution available in Spain from the historical fire records was 10 10-km grid cells. But in the operational application of fire occurrence prediction (FOP) models at the country level, widely varying conditions were to be expected. So, in order to take into account spatial variation over the broad study area, the peninsular territory of Spain (almost 500 000 km2) was divided into 53 ecoregions, used by the Spanish Forest Service, and a separate FOP modelling process was carried out for each one. Methods The data consisted of historical records of daily fire occurrences, daily weather data and geographic characteristics for the peninsular territory of Spain in a 10-km spatial-resolution grid, for the period from 2002 to 2005. The study period was restricted to 4 years owing to data acquisition limitations (the spatially interpolated daily weather data), but this period is in agreement with other studies (e.g. 3–9 years in Viegas et al. 1999; 5 years in Vega-Garcıá and Chuvieco 2006) and with the usual time-frame for fire prevention planning in Spain. Dependent variable – the fire observation The historical fire-start points came from the forest fire database of the Spanish Forest Service of the Ministry of Environment, recorded in a 10 10-km cell system anchored to UTM (Universal Transverse Mercator) coordinates. Observations in the dichotomous dependent variable were set as a fire observation (Y ¼ 1) if at least one human-caused fire happened that day in a cell, or as a no-fire observation (Y ¼ 0) where and when there was none. The grid consisted of 5189 cells, but some irregular cells on the coast line and in the boundaries between UTM zones 29, 30 and 31 were excluded in order to obtain a regular grid of

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M. Padilla and C. Vega-Garcıá

equal-area cells (100 1 km2). The resulting grid of 4651 cells was set as the spatial base for resampling of the explanatory variables and for the analyses of the present study. Explanatory variables – geographical Cartographic information on human factors, vegetation and physiographic characteristics came from the Biodiversity Database of the Spanish Ministry of Environment (see http:// www.mma.es/portal/secciones/biodiversidad/banco_datos/, accessed 22 December 2010). All the original geographic data came in vector format except the physiographic data, which came in raster images (25-m resolution). The human factors provided were forest land tenure (whether public, private, communal or protected) and infrastructures (distance to

towns, reservoirs and recreational areas, and density of population, roads, electric lines and railway tracks). Physiography was described by elevation (minimum, maximum, range, mean and standard deviation observed in each 10 10-km cell), slope (range, mean, standard deviation and surface with slope under 30% in each cell) and aspect variability (number of aspect classes observed in each cell, whether N, NE, E, SE, S, SW, W, NW or flat). The vegetation was represented by the fuel types based on Rothermel’s fuel models (Rothermel 1972), the percentage of each fuel present in each cell was also input into the models, together with an additional variable (heterogeneity) computed to account for the number of different fuel types present in a cell (see Table 1 for a complete list of acronyms for the independent variables).

Table 1. Acronyms and abbreviations of the independent variables selected for modelling Acronyms and abbreviations

Variable

Geographical variables Human factors Forest land tenure MONTE_PV Private MONTE_PB Public MONTE_VC Communal ENPE Protected Infrastructure NUCLEOS_DI Distance to towns RECRE_DIST Distance to recreational areas EMBAL_DIST Distance to reservoirs DENS_POBL Density of population DENS_ELEC Density of electric lines DENS_FER Density of railway tracks DENS_VIAS Density of roads Vegetation Area occupied by each Rothermel’s (1972) fuel type (%) MOD_01 Fuel type 1 MOD_02 Fuel type 2 MOD_03 Fuel type 3 MOD_04 Fuel type 4 MOD_05 Fuel type 5 MOD_06 Fuel type 6 MOD_07 Fuel type 7 MOD_08 Fuel type 8 MOD_09 Fuel type 9 MOD_10 Fuel type 10 MOD_00 No vegetation MOD_SI No data COMB_VAR Number of different fuel types Physiography MDT_MIN Minimum elevation MDT_MAX Maximum elevation MDT_RANGE Elevation range MDT_MEAN Elevation mean MDT_STD Standard deviation of the elevation SLOPE_RANG Slope range SLOPE_MEAN Slope mean SLOPE_STD Standard deviation of the slope SLOPE_30 Surface with slope under 30% ASPECT_VAR Number of aspect classes

Acronyms and abbreviations Meteorological variables Raw weather variables P24 T_min T_max HR_min DewTmpMax Velocidad_Viento Radiacion_Solar Nieve Nubosidad Fire danger rating indices ISI BUI FWI FFMC DMC DC h1 h10 h100 BEHAVE McArth67 KB PortoCif Prob LFMC

Variable

Daily rainfall Minimum temperature Maximum temperature Minimum relative humidity Maximum dew point temperature Wind speed at 1200 hours UTC Solar radiation Presence of snow Cloudiness Canadian Initial Spread Index Canadian Build-up Index Canadian Fire Weather Index Canadian Fine Fuel Moisture Code Canadian Duff Moisture Code Canadian Drought Code American NFDRS 1-hour-Timelag Fuel Moisture American NFDRS 10-hour-Timelag Fuel Moisture American NFDRS 100-hour-Timelag Fuel Moisture BEHAVE fine fuel moisture model McArthur’s 1967 fuel moisture model Keetch–Byram Drought Index Portuguese index Spanish ICONA method Live fuel moisture content


Explanatory variables – meteorological The weather data in this study included daily registers of rainfall, temperature (maximum and minimum), relative humidity (maximum and minimum), maximum dew-point temperature, wind speed at 1200 hours UTC, solar radiation, presence of snow, and cloudiness. These data were provided at a 3-km spatial resolution by the Department of Geography of the University of Alcala´ with permission of Meteolo´gica SA (Madrid, Spain). This department also provided live fuel moisture content (LFMC) estimations for Mediterranean grasslands and shrub species derived from satellite (National Oceanic and Atmospheric Administration Advanced Very High Resolution Radiometer, NOAA-AVHRR) data. The registers of LFMC data were available for 8-day periods, and they were computed from 8-day composites of NOAA-AVHRR images in order to avoid interference from clouds and radiometric problems in satellite data. The LFMC data was derived through an empirical function based on 4 years of field measurements and multitemporal composites of AVHRR’s normalised difference vegetation index and surface temperature values, as well as as a function of the day of the year. A description of this empirical method can be found in Chuvieco et al. (2004). The Meteorological Fire Danger Index Processor (MFDIP) described in Camia et al. (1998), and developed within the European project Megafires (Chuvieco 1998), was used to compute several FDR indices. The computed indices are listed and classified according to the component of fire danger that each represents, after Bovio and Camia (1997): Short-term moisture content (fine dead fuels) McArthur’s 1967 fuel moisture model: part of the Australian Forest Fire Danger Meter, it estimates the moisture content of the surface layer of Eucalyptus litter (McArthur 1967). American NFDRS 1-Hour-Timelag Fuel Moisture (h1): estimates the moisture content of fine dead fuels (Deeming et al. 1977). Canadian FFMC: indicates the relative ease of ignition and flammability of fine dead fuels (Van Wagner and Pickett 1985). BEHAVE fine fuel moisture model: estimates the moisture content of fine dead fuels (Rothermel et al. 1986). Mid-term and long-term moisture content (mid-size dead fuels, large dead fuels and live fuels) American NFDRS 10-Hour- (h10) and 100-Hour-Timelag Fuel Moisture (h100) (Bradshaw et al. 1983). American NFDRS 1000-Hour-Timelag Fuel Moisture (h1000) (Fosberg et al. 1981). Keetch–Byram Drought Index (KB): measures aridity, the effects of a long drying period on litter and duff (Keetch and Byram 1968). Canadian Duff Moisture Code (DMC): estimates the amount of fuel of medium size available for combustion, and relates to water content of a moderately thick organic layer (Van Wagner and Pickett 1985). Canadian Drought Code (DC): rates water content of a deep, compact organic layer in the soil (Van Wagner and Pickett 1985).


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Fire spread potential Canadian Initial Spread Index (ISI): this provides an estimate of the expected propagation of the flame front, combining the effect of FFMC and wind (Van Wagner and Pickett 1985). Extreme fire danger days Canadian Fire Weather Index (FWI): this represents the intensity of the propagating flame front, which depends on the quantity of energy released from a linear unit of the front itself (Van Wagner and Pickett 1985). Canadian Build-Up Index (BUI): represents a rating of the total fuel available for burning, and combines the two codes DMC and DC (Van Wagner and Pickett 1985). Spanish ICONA method (Prob): defines a risk of ignition based on litter and fine dead fuels moisture content (ICONA 1993). Portuguese Index (PortoCif): this is a modified version of the Nesterov index, the fire danger index used in the former Soviet Union, based on the assessment of atmospheric conditions in the proximity of the fuel layer, including precipitation and wind speed (Gonçalves and Lourenço 1990). Modelling approach We used logistic regression analysis to model the probability of daily human-caused fire occurrence in the prediction units within the 53 ecoregions mentioned in the Introduction section. As explained above, widely varying conditions were to be expected at the country level. It is not only the climatology that varies broadly in Spain, but the importance of the human factors also varies regionally. Badia-Perpinya´ and PallaresBarbera (2006) found out in the north-east of Spain that distance to roads is more important as a factor in the metropolitan area of Barcelona than in a typical rural region. These ecoregions (Fig. 1 and Table 2) are based in the Regions of Identification and Utilisation for forest reproductive material (RIUs) defined in Garcıá del Barrio et al. (2001) and also the Biogeoclimatic Regions of the Peninsular territory of Spain described in Elena-Rosello´ (1997). We considered these ecologically based regions optimal for the stated goal of testing the relative performance of different FDR systems in explaining fire activity (measured as occurrence) against other types of variables. By studying the relationship between explanatory variables and historical occurrences in ecoregions, we could also evaluate the spatial variation of this relationship with varying conditions in the fire environment. The logistic regression model has often been successfully used in FOP modelling with binary data (Martell et al. 1987; Vega-Garcıá et al. 1995; Preisler et al. 2004; Chuvieco et al. 2009). It estimates the probability Pi of a fire observation (one or more fires occurring in a cell on a certain day) as a function of a set of explanatory variables: Pi ¼

1 1 þ eZi

ð1Þ

50



Fig. 1. The peninsular territory of Spain (shaded) with the 53 ecoregions used to model fire occurrence prediction (FOP) in Spain.

with Zi being a linear function of the independent variables: Zi ¼ b0 þ

k X

bj Xij

ð2Þ

j¼1

where Xij are the k explanatory variables and b0, b1, b2,y, bk are the k þ 1 parameters to be estimated through maximum likelihood methods from the database of historical fire occurrence and the values of the explanatory variables. The relevant statistics related to the application of the logistic regression in predicting the probability of at least one fire taking place in a prediction unit (a fire observation) have been discussed by Loftsgaarden and Andrews (1992) and Andrews et al. (2003), so they will not be described here. All observations in 2005 were set aside for validation. In the calibration dataset (2002–04), there were 35 296 fire observations and a much larger number of no-fire observations, 4 419 405. Vega-Garcıá et al. (1995) and Preisler et al. (2004) dealt with this problem by randomly sampling the no-fire observations to obtain a balanced dataset for model estimation (Maddala 1987). In the current study, we decided to include all the fire observations and get a random sample of the same size from the rest of the database. Prediction for the entire population with real proportions would be possible by increasing the intercept (b0) of the logistic equation by g, computed as follows (Maddala 1987):

g ¼ ln p1 ln p2

ð3Þ

where p1 is the probability that an observation from the no-fire group would be selected and p2 is the probability that an observation from the fire group would be selected for the calibration dataset (in our case p2 ¼ 1) (Maddala 1987). Model building. Variables selection The large number of explanatory variables derived from the same weather data and the high correlations exhibited by geographic variables ensured that multicollinearity problems would be present in the models. Significance of the variables might get ‘diluted’ among collinear variables contributing in a similar way to the explanation of the response variable (Legendre and Legendre 1998), so we used a mechanical procedure to select the explanatory variables for each model. The method allowed efficient development of the 53 models, one for each ecoregion, within reasonable computing time. The logistic regression analysis was carried out with the statistical package SPSS v.15.0 (http://www.spss.com/, accessed 1 July 2009). We used the Forward procedure taking into account the significance of the variables, their collinearity and also the signs of the estimated parameters. The first variable entered in the model was the one that produced the largest adjusted coefficient of determination Nagelkerke R2, which is a modification of the Cox and Snell coefficient. The Nagelkerke R2 divides Cox and Snell’s R2 by its maximum, in order to



Table 2. Ecoregion numbers (ID), designation and number of fires (from 2002 to 2005) ID

Name of the ecoregion

1 2 3

Galicia Litoral septentrional Galicia Litoral meridional y montanãs occidentales Montanãs y mesetas interiores de Galicia meridionales Montanãs y mesetas interiores de Galicia centro Litoral astur-cańtabro Vertiente septentrional canta´brica Vertiente meridional canta´brica–Lomas de la Maragaterıá I Litoral Vasco Montes vasco-navarros Pirineo axial Prepirineo Litoral Catalań Orla septentrional de la Depresioń del Ebro Depresioń del Ebro Orla meridional de la Depresioń del Ebro La Rioja Sistema Ibe´rico septentrional–Macizo del Moncayo Paramos del Duero meridionales–Fosa de Almazań Paramos del Duero septentrionales Tierras del Pan y del Vino Sierra de Gata Sierra de Gredos septentrional Sierra de Gredos meridional Sierras de Guadarrama–Aylloń septentrional Sierras de Guadarrama–Aylloń meridional Alcarrias Sierra de Albarracıń Sistema Ibe´rico oriental Litoral Levantino septentrional Litoral Levantino meridional Sistema Ibe´rico meridional Serranıá de Cuenca Campo de Criptana Campo Aran˜uelo–Cuenca de Madrid Montes de Toledo–Monfraguë Alcantara–Sierra de San Pedro–Llanos de Caćeres Vegas del Guadiana–La Serena Campo de Calatrava La Mancha Campo de Montiel Sierras de Cazorla y Segura Cordillera Subbe´tica Murciana Litoral Murciano Litoral sur-oriental andaluz Sierras Nevada–Filabres Cordillera Subbe´tica granadina Orla meridional de la Depresioń del Guadalquivir Serranıá de Ronda Litoral meridional andaluz oriental Litoral meridional andaluz occidental Depresioń del Guadalquivir Sierra Morena meridional Sierra Morena septentrional

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

Number of fires 5869 11 822 3456 4986 6250 4786 3833 835 851 212 508 938 646 1042 455 1084 191 285 683 2006 1056 151 1398 87 868 637 171 395 250 554 880 492 452 1404 917 1038 1377 407 562 165 265 637 240 334 285 609 682 288 243 825 422 549 478

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achieve a measure that ranges from 0 to 1, as an interpretation of the proportion of the explained variation (Nagelkerke 1991). Each next variable entered in the model was the one with the next largest partial correlation coefficient. To avoid multicollinearity in the model, each new variable should have a low Spearman correlation (R2o0.5) with the variables already entered in the model in previous steps. This procedure was iteratively repeated until no more significant explanatory variables had a significant partial regression coefficient (Po0.05). Afterwards, to evaluate the influence of individual variables included in each model, the criterion of the computed Wald statistic was used (Martıńez et al. 2009). Model evaluation Goodness-of-fit was examined through the Hosmer and Lemeshow (1989) test as recommended by Loftsgaarden and Andrews (1992). The sign of the estimated parameters of the variables should follow theoretical expectations based on previous knowledge of the fire occurrence problem, when available, and be significant (Po0.05). A sample dataset from 2002 to 2004 was used for calibration as described in the previous paragraphs. The dataset from 2005, with real proportions of fire and no-fire observations, was reserved for testing independently the model’s predictive capability. The large number of observations and models to be processed was an issue, so a maximum of 20 000 observations were selected randomly for each ecoregion to validate the 53 models. To evaluate the performance of the multiple logistic regressions, we compared their predictions with the observed records of historical occurrences. We used two analyses to explore the predictive capabilities of the models in both the validation and the calibration dataset: the receiver operating characteristics (ROC) plot and 2 2 classification tables. In a ROC curve, the true positive rate (sensitivity) is plotted as a function of the false-positive rate (1 specificity) for different available probability thresholds (Fielding and Bell 1997; Hernandez et al. 2006). Each point on the ROC plot represents a sensitivity–specificity pair corresponding to a particular probability threshold. From the ROC plot, we derived (i) the area under curve (AUC), which is a measure of the model’s overall performance and has values usually ranging from 0.5 (random) to 1.0 (perfect accuracy) (Syphard et al. 2008); and (ii) the optimised probability thresholds that maximise the percentage of true absences and presences that are correctly identified (Manel et al. 2001). The threshold for each model can be obtained by identifying the point on the ROC curve where the sum of the sensitivity and specificity is maximised (Hernandez et al. 2006). The predictive capability can be also measured using the 2 2 classification table or cross-tabulation between the real occurrence observed and the binary classification of the estimated occurrence. The probability level (cut-off point) for the binary classification in the validation data is established by the optimal probability threshold obtained in each ROC curve. This probability level is set at 0.5 (the midpoint of the logistic distribution) for the calibration data, where the number of fire-days and nofire-days is balanced as described previously. From the 2 2 classification table, the global accuracy of the prediction can be

52


derived as the sum of the true-positive and the true-negative observations divided by the total number of observations. Results The best logistic models (one for each ecoregion) obtained from the forward selection procedure described above differed in variables chosen, with the number of variables selected in each model ranging between 3 and 21. Table 3 shows the summary of the performance evaluation of the 53 models. For the calibration dataset, the Nagelkerke R2 values varied from 0.25 to 0.77, the P values of the Hosmer–Lemeshow test from 0.000 to 0.989 (39 models with P 4 0.05), the AUC values from 0.74 to 0.95 and the global accuracy of the 2 2 classification table (probability threshold ¼ 0.5) ranged from 64.7 to 89.0%. The validation data showed lower agreement: AUC values varied from 0.52 to 0.86 and the total percentage correctly predicted (thresholds optimised by ROC) from 47.4 to 82.6%. The probability threshold values optimised by the ROC plots ranged from 0.002 to 0.204 and we observed that they increased with the rise of the ratio fire/no-fire observations in the validation data. Fig. 2 displays the geographical variation of the AUC values of the ROC plot in each ecoregion with the calibration (a), and on the validation dataset (b). Fig. 2 exhibits a lack of spatial pattern or aggregation trend in terms of predictive capacity. The individual influence of the variables included in each model was assessed through the computed value of the Wald statistic. Fig. 3 shows the two main explanatory variables in each model, the variable with the first- and the second-highest Wald value. The Canadian FWI was the variable that was most often (11) the most important in the models, but FFMC was relevant in nine regions, all located in the north of Spain. Other indices and meteorological variables (mainly relative humidity, HR_min, and maximum temperature, T_max) were also in the list of the first variables, and only in nine regions was the main explanatory variable geographic. In the second position, geographic variables predominated, particularly road density (DENS_VIAS) and average distance to urban areas (NUCLEOS_DI), but LFMC, FWI, FFMC, DC, HR_min, and h1000 were second in importance in some regions. It was our stated purpose to compare the relative importance of each variable within the global scope of the 53 ecoregions in Spain. Because it was not possible to compare directly the absolute value of the Wald statistics or its related P value in different models, we used their relative position of importance within each ecoregion. The variables in each model were ranked following the value of the Wald statistic (or the related P value); the first position was for the variable with the highest Wald value, the second position was for the variable with the second highest Wald value and so forth for all variables in the given ecoregion. The boxplots in Fig. 4 display the positions of each variable within each model. Variables were first ranked according to the median of the positions and second for the number of models where the given variable was an input. According to these criteria, it was concluded that the main variable for fire occurrence prediction in Spain was the Canadian FWI, included in 16 models out of 53. In at least eight models (50%) FWI was the most important variable, in at least 12 models (75%) was one of the two more important variables and in all cases was within


the three more important variables (Fig. 4). HR_min, T_max and FFMC were also found relevant variables in terms of position in the models, and LFMC was present in 15 models. Road density and distance to urban areas were the most relevant geographic variables (23 and 22 models), but many other were present in most of the models (i.e. COMB_VAR in 22 models). The interpretation of the number of times that one variable is included in the models (number on the left of the parentheses in Fig. 4) must be made with caution because of the variableselection procedure used. In order to avoid multicollinearity problems, two or more highly correlated variables are never in the same model. This means that one variable with high influence in the fire occurrence process can be selected only few times because another exists that explains the fire events slightly better. Although signs in weather-related variables were always in agreement with theoretical expectations, signs in some geographical variables shifted according to the particular characteristics of the ecoregion. Discussion The logistic regression analysis produced 53 regional models following a forward procedure for selecting the set of variables with significant influence and without multicollinearity. The best models included different selections of variables and this fact suggests that a regional analysis is an appropriate choice for modelling fire occurrence in Spain. Those regional models can better integrate the differences in biophysical characteristics of the fire environment and the type of human activities, and hence, the fire occurrence patterns. The accuracy varied among the models, with Nagelkerke R2 values ranging from 0.25 to 0.77. These values were slightly higher than those obtained by Martell et al. (1987) (Nagelkerke R2 values from 0.00 to 0.54) for the daily prediction of forest fires in Ontario, Canada, with different models defined by cause and season of the fire. The AUC values for the calibration data between 0.74 and 0.95 (validation 0.52–0.86) pointed to adequate performance, because it is considered that valueso0.7 indicate low accuracy, values of 0.7–0.9 useful applications and values of 40.9 high accuracy (Swets 1988). The lack of spatial aggregation does not indicate any specific geographic constraint that diminishes the performance in any area of the peninsular territory of Spain. Simply put, different performances are due to intrinsic differences between ecoregions, and the capability of the variables used to account for their fire occurrence trends. Global accuracies of the 2 2 classification table (probability threshold ¼ 0.5) ranged from 64.7 to 89.0% (validation 47.4–82.6%). Other studies predicting human-caused daily forest fires in Alberta, Canada, found similar agreements in the calibration dataset, 79.0% using logistic regression and 81.2% using artificial neural networks (Vega-Garcıá et al. 1995, 1996) and in Catalonia, Spain, 73% using logistic regression and 78% using artificial neural networks (Vega-Garcıá 2007; Vega-Garcıá et al. 2008). The explanatory variables included in the models agree with previous work on the relationship between human variables and fire occurrence (Chou et al. 1993; Syphard et al. 2007) and the influence of the moisture conditions of the fuel (Chuvieco et al.



53

Table 3. Summary of the performance of the 53 models AUC, area under curve; ROC, receiver operating characteristics Calibration data (2002–04) Region 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 Maximum Minimum

2

Validation data (2005)

Nagelkerke R

Hosmer–Lemeshow test (P)

AUC

Global accuracy (%); cut-off ¼ 0.5

AUC

ROC cut-off

Global accuracy (%); ROC cut-off

0.41 0.43 0.46 0.47 0.42 0.50 0.58 0.48 0.45 0.62 0.51 0.38 0.31 0.41 0.25 0.40 0.46 0.58 0.54 0.47 0.49 0.36 0.45 0.63 0.48 0.54 0.53 0.44 0.33 0.35 0.42 0.32 0.43 0.47 0.50 0.71 0.60 0.63 0.52 0.55 0.50 0.42 0.62 0.39 0.47 0.44 0.56 0.43 0.46 0.55 0.77 0.52 0.59 0.77 0.25

0.000 0.000 0.001 0.428 0.000 0.000 0.031 0.708 0.590 0.916 0.524 0.287 0.040 0.140 0.148 0.792 0.783 0.989 0.386 0.459 0.985 0.051 0.543 0.549 0.320 0.004 0.078 0.371 0.326 0.812 0.127 0.386 0.203 0.000 0.006 0.865 0.001 0.110 0.037 0.273 0.284 0.334 0.253 0.024 0.454 0.137 0.029 0.196 0.800 0.568 0.526 0.371 0.365 0.989 0.000

0.82 0.83 0.84 0.85 0.83 0.86 0.89 0.85 0.85 0.91 0.86 0.82 0.78 0.82 0.74 0.82 0.85 0.90 0.88 0.85 0.86 0.79 0.84 0.91 0.86 0.87 0.87 0.84 0.79 0.80 0.83 0.78 0.83 0.84 0.86 0.94 0.89 0.91 0.87 0.88 0.87 0.83 0.91 0.82 0.85 0.84 0.88 0.84 0.85 0.89 0.95 0.86 0.90 0.95 0.74

74.9 75.5 77.1 76.8 74.8 78.1 81.5 78.1 77.5 82.6 76.5 74.3 71.7 73.9 64.7 73.9 78.4 80.7 79.9 78.4 78.3 70.2 77.3 81.4 78.5 78.5 85.3 75.8 70.4 72.0 74.9 70.5 77.1 78.2 78.2 86.6 82.8 82.3 80.5 80.9 78.8 74.1 83.5 75.0 76.8 76.3 80.0 74.7 75.8 80.8 89.0 79.5 80.5 89.0 64.7

0.74 0.71 0.76 0.80 0.77 0.79 0.83 0.80 0.75 0.78 0.73 0.75 0.66 0.70 0.64 0.71 0.70 0.67 0.67 0.70 0.70 0.73 0.73 0.67 0.68 0.75 0.55 0.62 0.52 0.68 0.73 0.60 0.68 0.67 0.62 0.86 0.79 0.71 0.74 0.72 0.78 0.82 0.84 0.70 0.73 0.61 0.76 0.73 0.82 0.76 0.85 0.75 0.65 0.86 0.52

0.091 0.190 0.204 0.127 0.046 0.041 0.025 0.016 0.007 0.004 0.005 0.011 0.007 0.004 0.002 0.007 0.003 0.003 0.007 0.003 0.025 0.008 0.035 0.004 0.012 0.004 0.002 0.002 0.005 0.005 0.005 0.004 0.009 0.018 0.008 0.015 0.017 0.003 0.005 0.003 0.003 0.005 0.010 0.006 0.006 0.005 0.005 0.012 0.013 0.013 0.005 0.005 0.004 0.204 0.002

63.7 64.0 70.3 68.8 68.5 69.0 76.5 75.9 69.0 72.7 73.6 66.8 60.7 66.6 54.7 61.8 64.3 56.8 62.3 62.0 69.8 77.4 69.5 65.2 58.6 66.2 53.3 64.4 47.4 60.6 73.8 63.7 58.8 61.7 65.9 77.4 69.1 57.3 67.4 69.9 68.7 82.2 82.6 69.7 63.5 58.9 65.5 71.4 81.8 71.3 72.9 68.0 57.6 82.6 47.4

54



(a)

(b)

N AUC of ROC plot 100 200 km

0. 50

– 0. 0.5 56 5 – 0. 0.6 61 0 – 0. 0.6 66 5 – 0. 0.7 71 0 – 0. 0.7 76 5 – 0. 0.8 81 0 – 0. 0.8 86 5 – 0. 0.9 91 0 – 0. 0.9 96 5 –1 .0 0

0

Fig. 2. Map showing the area under curve (AUC) values of the receiver operating characteristics (ROC) plot for each model for the calibration (a), and for the validation dataset (b).

2009). The two main geographic variables were proxy variables for human presence and activity, density of roads (DENS_ VIAS) and distance to towns (NUCLEOS_DI). The coefficient of the first was always positive, higher density of roads indicating easier accessibility and a higher probability of ignition. The sign of the second was negative most of the time (21 out of 23 models), indicating that for those regions, increased distance to towns meant a lower probability of ignition. These trends agreed with work by Maingi and Henry (2007), Syphard et al. (2008) and Romero-Calcerrada et al. (2008), among others. Two geographic variables following in importance were related to topography, slope range (topographic roughness) and mean elevation. Though the sign of those variables varies a bit among the ecoregions, the trends suggest that more ignitions are likely to occur in rugged terrain and low-elevation areas. Those results agree with Dickson et al. (2006), who also found relations between probability of occurrence and topographic roughness in northern Arizona, USA, and with VegaGarcıá et al. (2008) in Catalonia for elevation. However, our results allow comparison of the relative performance of FDR indices and raw weather data within the frame of probability models of daily fire occurrence to account for daily fire activity in the peninsular territory of Spain. Given that Spain is on the point of shifting FDR systems to adopt the Canadian Forest Fire Weather Index, the favourable results of this study with regards to FFMC and FWI would seem to support that decision. Nevertheless, the FWI is being calibrated at the provincial level (Mestre et al. 2008), a politically based division of the country, but ecoregions or other zoning strategies may better account for different conditions in the fire risk environment. This analysis at the ecoregion level suggests also that FWI, representing the potential for extreme fire danger days (and its relative ease of ignition and flammability of fine dead fuels code FFMC) may not be the only FDR system to be considered for all of Spain. Relative humidity (HR_min),

maximum temperature (T_max) and also some American NFDRS fuel moisture measures were equally relevant in many regions. LFMC derived from NOAA data was a relevant variable in 15 regions, showing great promise for the future. Attention should be paid also to the fact that five models depending on FFMC as the main variable, all located in the Atlantic north-west of Spain, did not show a good fit to the data according to the Hosmer–Lemeshow test. Models for regions 1, 2, 3, 5 and 6 all had global accuracies over 75% and AUC values over 0.82, with Nagelkerke R2 over 0.40, but the goodness-of-fit test showed lack of fit (Po0.05). These regions corresponded geographically to most of Galicia, Asturias and Cantabria. The first two usually account for almost 50% of all fires in Spain, 4531 (40%) in 2008, 6569 (44%) in 2009 (DGMNPF 2008, 2009), and the numbers of fires per forest area are higher than in the rest of Spain. As almost all fires are human-caused in Cantabria (99.4%), Asturias (over 99%) and Galicia (98%) (78% average in Spain), we believe that socioeconomic and territorial variables not incorporated in this study, because they were not available at the right resolution, would be required to improve these models. Interestingly, the models for these regions, in which 75% of all fires are intentional and related to agricultural burning and pasture improvement, included variables related to forest ownership (MONTE_PV, MONTE_PB or MONTE_VC) and to grass (pastures) fuel models (MOD_01, MOD_02, MOD_03). Hence, it has been often argued that weather by itself cannot explain fire occurrence in Spain (e.g. Garcıá Diez et al. 1999), and our results would seem to support that conclusion. Conclusions This work focussed on the evaluation of the relative performance of a comprehensive set of commonly used fire danger rating indices by developing daily fire occurrence models in Spain involving also some geographic factors. Spain was divided into 53 ecoregions and logistic regression models were successfully



Fig. 3. Two main explanatory variables in the logistic regression of each ecoregion: the variable with the first (a) and the second (b) highest Wald value. (See Table 1 for explanation of variables.)

55

56



Fig. 4. Rank of the variable in ecoregions in the peninsular territory of Spain under the criteria of median position of importance in each model and the number of models where the variable is included (number to the left of the parentheses). Numbers within the parentheses indicate the number of models in which the variable is entered with a positive sign (left) and negative sign (right). (See Table 1 for explanation of variables.)


developed for each region. The explanatory variables included in the models agreed with previous work, but varied with ecoregion, suggesting that a regional analysis is an appropriate choice for modelling fire occurrence in Spain. The results of this study were favourable to the adoption of the Canadian Forest Fire Weather Index as the new FDR system in Spain, but relative humidity, maximum temperature, some American NFDRS fuel moisture measures and LFMC derived from NOAA data were equally relevant in many regions. Lack of significance in a few models in the north-west of Spain suggests that regional differences in human activities may influence fire occurrence patterns more than biophysical characteristics of the fire environment. Acknowledgements This work was funded by the Parc Cientı´fic i Tecnolo`gic Agroalimentari de Lleida and by the Spanish Ministry of Environment. The authors would like to thank the Spanish Forest Service for providing the historical fire database, the Department of Geography of the University of Alcala´ for providing weather and live fuel moisture data and the Institute for Regional Development of the University of Castilla – La Mancha for the latest version of the fuel models cartography. We gratefully recognise the technical support of the Remote Sensing and GIS Laboratory of the University of Lleida and ` ngels Colomer and Ricardo Blanco, from the statistical advice from Maria A University of Lleida.

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Manuscript received 1 December 2009, accepted 17 April 2010

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