Leonardo Guimar?es Ziccardi · Cláudio Roberto Thiersch · Aurora Miho Yanai ·Philip Martin Fearnside · Pedro José Ferreira-Filho

Abstract This study compares the performance of three fire risk indices for accuracy in predicting fires in semideciduous forest fragments, creates a fire risk map by integrating historical fire occurrences in a probabilistic density surface using the Kernel density estimator (KDE)in the municipality of Sorocaba, Sa~o Paulo state, Brazil.The logarithmic Telicyn index, Monte Alegre formula(MAF) and enhanced Monte Alegre formula (MAF+) were employed using data for the period 1 January 2005 to 31 December 2016. Meteorological data and numbers of fire occurrences were obtained from the National Institute of Meteorology (INMET) and the Institute for Space Research(INPE), respectively. Two performance measures were calculated: Heidke skill score (SS) and success rate (SR).The MAF+ index was the most accurate, with values of SS and SR of 0.611% and 62.8%, respectively. The fire risk map revealed two most susceptible areas with high(63 km2) and very high (47 km2) risk of fires in the municipality. Identification of the best risk index and the generation of fire risk maps can contribute to better planning and cost reduction in preventing and fighting forest fires.

Keywords Forest fire risk maps · Forest fire protection ·Monitoring · Monte Alegre formula

Introduction

Forest fire regimes are important components in maintaining function and structure of many terrestrial ecosystems, but can also be considered threats responsible for important negative economic and environmental impacts,e.g., economic losses in the forestry sector, degradation of land cover, changes in atmospheric composition (Malowerschnig and Sass 2014; Duarte and Teododo 2016). If forest fires can have a positive effect in terms of biodiversity and species richness (Keeley et al. 2003; Moretti et al. 2006; Wohlgemuth et al. 2006), they can also impede hydrological processes and interfere with the dynamic equilibrium of forests and with the carbon cycle (Fearnside and Barbosa 1999; Robinne et al. 2016). Considering global warming and expected increase in extreme events in the light of climate changes, there is a firm possibility for increased frequency of forest fire outbreaks, mainly as a result of plant demographic processes that can change the growth of tree species and affect carbon sequestration by forests (Collins et al. 2014).

Monitoring meteorological parameters allows for the adoption of measures to reduce the potential damage of forest fires (Tetto et al. 2010). The main sources of ignition are human activities that are closely linked to the means of access to the forest, with increase in fire risk near roads in rural areas (Díaz-Delgado et al. 2004; Duarte and Teododo 2016). Railways can also be sources of fire ignition,especially in the dry season. Sparks resulting from friction between the train wheels and the rails can start fires in dry vegetation, subsequently spreading to adjacent forests(Martell et al. 1987; Wotton et al. 2010).

An efficient plan to prevent and fight forest fires requires tools that include mapping areas that are most vulnerable to fire (i.e., fire risk mapping), and the creation of forest fire risk indices (Morgan et al. 2001; White et al. 2015). A fire risk map reveals the risk areas and facilitates the logistics for countermeasures by enabling rapid analysis of the situation for decision-making to prevent and combat forest fires (Dalcumune and Santos 2005). Fire risk indices show in advance the likelihood of forest fire occurrence, and the interpretation of these values is linked to prevention plans and pre-suppression of fire (SantAnna et al. 2007; White et al. 2015).

Several methods exist to interpolate historical ignition points and create a continuous wildfire risk map. The Kernel density estimation (KDE) is a nonparametric method that has been broadly used over the last two decades, especially after Koutsias et al. (2004), de la Riva et al. (2004) and Amatulli et al. (2007) explored how this technique was efficient to preserve a more realistic pattern of fire occurrence under broad pixel resolution, allowing appropriate forest fire-risk mapping (Kuter et al. 2011).

Identifying areas of greatest fire risk makes it possible to adopt preventive measures in a timely fashion. These include the construction of firebreaks, restriction of access in critical periods, reorganization of management, and allocation of resources to strategic points (Soares 1972;Sousa 2000). Fire prevention plans in Brazil are mainly focused on protected areas because these areas are fundamental to conserving biodiversity and maintaining ecological processes (Fiedler 2004).

In addition to evaluating fire risk indices, new models can be created to increase accuracy for the area under study. New tools can increase the efficiency resource allocation (White et al. 2015).

The objectives of this study were to evaluate the accuracy of three fire-risk indices in semi-deciduous forest fragments, create a fire risk map of the landscape in the municipality of Sorocaba, and determine the influence of roads and railways on the occurrence of fires.

Materials and methods

Study site

This study was carried out in the rural areas of the municipality of Sorocaba, Sa~o Paulo state (47°31′50′′W;47°31′W; and 23°34′57′′S; 23°35′25′′S) (Fig. 1).

Sorocaba has 659,871 inhabitants and is one of the fastest growing cities in Brazil. Data released on July 1,2017 by the Brazilian Institute of Geography and Statistics(IBGE) show that, compared to 2016, the population increased by 1.1%, more than the 0.8% growth in the country as a whole. In the last 7 years, the city gained 73,246 new residents and is currently 13th among Brazil’s most populous municipalities (excluding state capitals)(IBGE 2017).

The average elevation is 632 m with a maximum of 1028 m. The soil is classified as red latosol (oxisol) and vegetation is a transition ecotone between the Cerrado(central Brazilian savanna) and the Atlantic forest region,the former being degraded and characterized by small fragments of secondary succession (EMBRAPA 2006).According to the Koppen classification, the climate is transitional Cwb (rainy and hot temperate with a moderately hot summer) to Cwa (seasonally dry with a warm to hot summer). Mean annual temperature is 22 °C and mean annual precipitation 1310 mm (Ikematsu et al. 2007).

Meteorological data and occurrence of fires

Daily records of average temperature, relative humidity,wind speed, and precipitation for the preparation of risk indices were obtained from the INMET (National Meteorology Institute) database for 1 January 2005 to 31 December 2016 (Appendix in the Electronic Supplementary Material, Fig. S1).

Hotspots that indicate fires with their dates of occurrence and locations (latitude and longitude) were obtained from the INPE (National Institute of Space Research)database of MODIS satellite (AQUA_M-T) with 1-km spatial resolution. Fire outbreaks were detected from the thermal signal of the wavelengths in the infrared range(Mid InfraRed-MIR) in a 500-m × 500-m pixel (Roberts and Wooster 2008).

Occurrences were examined over the same period (1 January 2005 to 31 December 2016). Fire data were deleted in the case of duplicates, and 83 days were disregarded due to absence of weather data. The result was 4300 days of observation and 69 records of forest fire occurrence in the study area.

Fig. 1 Location of the municipality of Sorocaba, Sao Paulo state

Fire risk map

As there are no uninhabited regions in the municipality, the risk map developed was based on fire hazards associated with anthropogenic factors using a continuous density map of fire occurrences in a historical series of events (Morgan et al. 2001; Narciso et al. 2011). Annual fire outbreaks were mapped based on their coordinates using ArcGIS software,UTM Zone 22 S projection and Datum SAD 69 (22 s).

The Kernel density estimator (KDE) determined critical areas for fire occurrence. This non-parametric density estimator produces a probabilistic density surface based on local information by superimposing a grid on the data for each observed event (Parzen 1962; Gatrell et al. 1996).This adjusts for inaccuracies in the locations of hotspots and is appropriate for manipulating spatial data at the scale of a municipality (Koutsias et al. 2004; De la Riva et al.2004).

Evaluation of the performance of fire risk indices

Fire risk indices are related to daily meteorological elements (Fig. S2) and are considered to be in cumulative form, providing reliable results for the climatic characteristics of a region (Soares and Batista 2007).

To determine the performance of each index, it was necessary to define the limit separating presence and absence of fire risk for which the rating scales of the indices were categorized in binary form. The indices indicate absence of risk when the value is less than the lower limit of the medium risk class, while the presence of risk is indicated when the values are above this limit(Nunes et al. 2010).

The Monte Alegre formula (MAF) is a cumulative index that uses two climatic variables for which values are easy to obtain, these being the number of days without rain (an indirect measure of precipitation) and the relative humidity at 13:00 h (1:00 pm). This index was developed based on data from the central portion of the state of Paraná (Soares 1972), which is adjacent to the state of Sa~o Paulo where this study was carried out. The use of MAF (Eq. 1) to determine the daily risk of forest fires is notable for being relatively easy (Soares 1998).

where MAF is Monte Alegre formula, n the number of consecutive days with precipitation less than 13 mm, i e number of days in a sequence of rainless days, and H is relative humidity (%) measured at 13:00 h.

The index is subject to modifications according to the daily precipitation, which is necessary for obtaining cumulative values (Table S1). Estimates of the degree of danger associated with the calculated value of MAF should be interpreted according to a scale of risk (Table S2).

The enhanced Monte Alegre formula (MAF+) was developed from the inclusion of wind speed as a variable modifying the MAF (Eq. 2). As was the case for MAF, this formula was developed for central Paraná (Nunes et al. 2006).

where

MAF+, Enhanced Monte Alegre formula

n, Number of consecutive days with precipitation less than 13 mm

i, Number of days in a sequence of rainless days H, Relative humidity (%) measured at 13:00 h

e, Base of natural logarithms (2.718282)

v, Wind speed (ms-1).

Since MAF+ is also cumulative in character, this index is subject to modifications in the calculation in accord with daily precipitation (Table S3). As is the case with MAF, the estimate of the degree of danger that is associated with the calculated value of MAF+ must be interpreted according to a scale of risk (Table S4). The variable corresponding to the wind speed (at 13:00 h) is considered to be non-cumulative in the equation.

The logarithmic Telicyn Index (I) was developed in the former Union of Soviet Socialist Republics (Telicyn 1970).The two variables included in this index are air temperature and the dew point at 13:00 h. Like other indices considered in this study, the logarithmic Telicyn Index is also calculated cumulatively up to the moment of each precipitation event, after which a new calculation cycle begins:

where

I, Telicyn index

T, Air temperature (°C)

r, Dew point temperature (°C)

log, Logarithm in base 10

n, Number of days without rain

i, Number of days in a sequence of rainless days.

The degree of danger related to the value calculated(Eq. 3) must also be interpreted according to a scale of risk; this index has only four classes of risk (Table S5). The logarithmic Telicyn index, the Monte Alegre formula(MAF) and the enhanced Monte Alegre formula (MAF+)were employed between 1 January 2005 and 31 December 2016. The predicted values for the occurrence of fires were obtained based on the scales for the three indices, the presence of risk being represented by the ‘‘medium’’,‘‘high’’, and ‘‘very high’’ risk classes and the absence of risk by the ‘‘small’’ and ‘‘null’’ classes.

Comparison of the efficiencies of the models was performed with two test parameters: the Heidke skill score(SS) and the success rate (SR). These parameters are based on a contingency table with observed and predicted values for occurrence of the events (Nunes et al. 2006, 2010 Nunes 2008) (Table 1).

The following parameters were obtained from Table 1:

C, Observed number of correct predictions (hits), where

C = a + d

p, Probability of having at least one event per day, where

p = N1/N

q, Probability of exceeding the limit value of the index,in which q = N2/N

E, Expected number of hits, where E = N × (1 - p) ×(1 - q) + N × p × q

SS, Skill score, where SS = (C - E)/(N - E)

SR, Success rate, where SR = C/N

Table 1 Contingency table used to determine the ability to rate the skill score (SS) and success rate (SR). Adapted from Sampaio (1999)

Where

N, Total number of observations (N = a + b + c + d)

a, Days on which occurrence of fires was predicted and they occurred(correct prediction)

b, Days on which occurrence of fires was predicted and they did not occur (incorrect prediction)

c, Days on which non-occurrence of fires was predicted and they occurred (incorrect prediction)

d, Days on which non-occurrence of fires was predicted and they did not occur (correct prediction)

Results

Outbreaks of forest fires

Of the 4300 days analyzed, 69 (1.6%) had forest fires in the study area. The largest number of outbreaks (15) occurred in 2014, while 2008 and 2013 had the fewest (Amatulli et al. 2007; Fig. 2).

Considering the monthly analysis of the cumulative total of outbreaks, August had the highest number (23) of fire occurrences. The three-month period with the largest number of outbreaks was July, August and September(Soares 1972; Fig. 3).

Performance of fire risk indices

Performance of the indices was quantified by the number of days from 2005 to 2016 for which fires were predicted and the number of days when fires were observed. Days in the study period were segregated into different classes in accordance with each fire risk index (Table 2).

The MAF showed the greatest number (3160 days or 73.5%) of fire risk, considering the sum of ‘‘medium’’,‘‘high’’ and ‘‘very high’’ classes. A tendency for a greater number of days in the classes for the absence of risk was found for MAF+ (2264 days or 52.7%) as the sum of the‘‘small’’ and ‘‘null’’ risk classes (Table 2).

The Telicyn risk index lacks the ‘‘very high’’ risk class and shows an intermediate number of observed days in classes that indicate the presence of risk, with 53.4%considering the values of the ‘‘medium’’ and ‘‘high’’ risk classes. However, the percentage of days in low-risk classes was 46.6%, showing a possible balance between classes (as was also the case for MAF+), possibly related to the climatic characteristics of the region.

Fig. 2 Yearly distribution of forest fire outbreaks from 2005 to 2016 in the municipality of Sorocaba

Fig. 3 Monthly distribution of outbreaks of forest fires from 2005 to 2016 in the municipality of Sorocaba. The red dashed lines represent the period with the greatest fire frequency

Based on the integration between observed fire outbreaks and the adjusted scales of the risk indices, the values for fire occurrences were recorded in a contingency table and used to calculate SS and SR (Table 3).

For the calculation of SR, days with hits or misses were quantified for each index. Hits were either days when fire was predicted and one or more outbreaks occurred, or days when fire was not predicted and no outbreak occurred.

The SR result by MAF+ (62.8%) was higher compared to the other indices, with a SR value of 48.5% for the logarithmic Telicyn index and 28.7% for MAF (Table 4).The SS values (Table 4) mirror the results for SR, with MAF+ achieving the highest value (0.611), followed by Telicyn (0.468) and MAF (0.264).

Fire risk map

The risk map from the smoothed density of fire outbreaks in the study period 2005-2016 identifies areas susceptible to forest fires (Fig. 4). The values generated by the algorithms for calculating Kernel density were categorized into five classes, very low, low, moderate, high and very high,and is a key step as part of a prevention plan in delimitating areas that are most vulnerable to fire (Duarte and Teododo 2016).

Discussion

Many forest fire risk indices derived from daily meteorological variables have been created on the assumption that climate-related variables are the most important indetermining fire risk (Whitlock et al. 2003). The most frequently cited fire risk indices are the Russian Nesterov Index (Nesterov 1949), the Russian Logarithmic Index of Telicyn (Telicyn 1970), the U.S. National Fire Danger Rating System (Deeming et al. 1977), the Swedish Angstrom index (Chandler et al. 1983), the Canadian Forest Fire Danger Rating System (van Wagner 1987), and the Argentine index of Rodriguez and Moretti (Rodriguez and Moretti 1988).

Table 2 Distribution of days in fire risk classes for each index from 2005 to 2016

Table 3 Number of days predicted for forest fire occurrence, and observed outbreaks in satellite data from 2005 to 2016

Table 4 Skill score (SS) and success rate (SR) values from 2005 to 2016 for fire-risk indices

In Brazil, FMA (Soares 1972) is the index most used by forestry and environment protection companies (White et al. 2013). However, some studies have suggested that this is not the most suitable for certain Brazilian regions,especially the north (da Silva and Pontes 2011), northeast(White et al. 2013), mid-west (Narciso et al. 2011), and even the southeast region (Mafalda et al. 2009), which is close to where the index was created. This is because most of the indices based on empirical models are suitable only for local application because of the specific vegetation and climate from where they were developed (Wastl et al.2012).

The SS value for MAF+ in this study (0.611) was higher than the values of Nunes (2007) for the same index in Paraná for the period 1998-2003 in Cambará, Tele?maco Borba, Guarapuava, Pinhais, Campo Moura~o, Cascavel and Londrina (0.088, 0.117, 0.133, 0.283, 0.302, 0.334, and 0.338, respectively). The SR values in this study for MAF(28.7%) and Telicyn (48.5%) were less than for Guarapuava, which had the smallest value (49.3%) of the 13 municipalities evaluated by Nunes (2007).

Much of the rural area of Sorocaba is under eucalyptus plantations and these increased from 233,406 ha in 2002(Kronka et al. 2002) to 323,478 ha in 2008 (Canavesi et al.2011), an increase of 38.6% over a relatively short period.These plantations have high fire risk because, in addition to the availability of timber, a blanket of combustible material is available by a continuous deposition of leaves and twigs on the soil surface (Borges et al. 2011). Generally, the boundaries between zones of high and low risk of fires are consistent with the limits between continuous and fragmented forest (Portier et al. 2016).

Compared to the other indices, MAF + showed the best performance in tests of SS and SR, as has also been reported for 2003-2006 in predicting outbreaks of fire in areas with eucalyptus cultivation in the north of Espírito Santo, with values of 0.18 for SR and 53.5% for SS(Borges et al. 2011).

Fig. 4 Fire risk map for the municipality of Sorocaba

MAF+ includes wind speed as a variable, which differs from the original MAF. With the inclusion of this variable,MAF+ reflects, in addition to the probability of ignition,the potential for fires to spread (Nunes et al. 2006).

The forest fire risk map revealed two areas with the highest occurrences of outbreaks: the northwest and southeast portions of the study area. Of the entire area of the municipality of Sorocaba, 13.7% was ‘‘very high risk’’(47 km2) and 18.5% was ‘‘high risk’’ (63 km2).

The northwestern portion of the municipality has eucalyptus plantations and lies next to the Ipanema National Forest and also has numerous roads. The high productivity of commercial plantations in the areas leads to a high concentration of biomass, which raises the risk of forest fires (Castro et al. 2003).

In the southeastern portion of the municipality, the large number of fire outbreaks can be linked, in part, to the stretch of railway associated with a green area. The presence of the railway may facilitate fire ignition and increase the risk of fire in adjacent vegetation in association with wind patterns (Chuvieco et al. 2010).

Because the scale of the fire risk map is coarse, it is more useful in an informative rather than in an operational context. The spatial statistical analysis of weights of evidence is able to capture the effect of distances of roads and railroads on fire outbreaks. It is a probabilistic method based on a Bayesian approach in log-linear form and applicable when sufficient data are available to estimate the relative influence of different scenarios for the factors considered in the analysis (Bonham-Carter 1994). However, the low spatial resolution of MODIS does not allow discussion of distances of less than 1-km, making this analysis unfeasible for this data set.

One suggestion for future studies aiming to use this analysis is to obtain the hotspots that indicate fire through the LANDSAT 8 thermal band. The spatial resolution of this reference satellite is 30 m (i.e., with much more spatial detail than MODIS), but the temporal resolution is 16 days,leading to the omission of many fire outbreaks.

The scenario for fire in a given location is linked to the socio-economic, political and environmental context of the region. There is a strong connection between the fire regime and territorial dynamics at different temporal scales(Montiel Molina and Galiana-Martín 2016). Recent studies also point to the existence of a relationship between the type of vegetation and the frequency and intensity of forest fires in any given location (Bernier et al. 2016).

Because fire prevention planning requires monitoring of where and when a fire is likely to occur (Kuter et al. 2011),the forest fire risk map and fire risk indices are two objective tools that should be used together for efficient pre-fire planning. While the fire risk map helps managers in planning prevention strategies by showing the most fire susceptible areas (based on historical fire occurrences), the indices indicate which days are most likely for the occurrence of fires (based on daily meteorological factors).Determining the best index for application in municipalities that do not have an index specific to their location is fundamental for planning forest fire prevention.

MAF+ gave the best result among the indices examined in this study. However, Brazil has a wide diversity of climates, which is reflected in the different results of the various indices of forest fire risk in different regions of the country.

Conclusions

Depending on climatic patterns in the region under study,one risk index may be more suitable than another for the prediction of fire events. The MAF+ index had the best performance in the municipality of Sorocaba, with a skill score of 0.611 and a success rate of 62.3%. These indicate that wind speed is an important variable and should be considered for determining the degree of fire hazard in this region.

By developing a risk map, it was possible to identify the areas that are more prone for the occurrence of forest fires.These areas are mainly in the northwestern and southeastern portions of the municipality. The risk of forest fires in Sorocaba is associated with local climatic conditions,and with the network of roads and the railway that crosses the municipality.

AcknowledgementsWe owe personal thanks to Alberto Vicentini,Nathan Gonc?alves, Ricardo Perdizes and Vitor Alves.