Assessment of Three Machine Learning Techniques with Open-Access Geographic Data for Forest Fire Susceptibility Monitoring—Evidence from Southern Ecuador

Abstract

Forest fires have become a habitual threat in all types of ecosystems, which is the reason why it is necessary to improve management of the territories and optimization of prevention and means of extinction. This study compares three machine learning techniques: logistic regression, logistic decision tree, and multivariate adaptive regression spline to identify areas susceptible to forest fires in the Loja canton. In the training of the machine learning models, a multitemporal database with 1436 points was used, fed with the information from seven variables related to fuel moisture, proximity to anthropic activities, and ground elevation. After analyzing the performance of the three models, better results were observed with the LMT, thus offering application ease for local decision-makers. The results show that the technique used allowed generating a model with a good predictive capacity and that the maps resulting from the model can be updated in short periods of time. However, it is necessary to highlight the lack meteorological data availability at the local level and to encourage future researchers to implement improvements in this regard.

1. Introduction

Forest fires are uncertain events, both in terms of their causes and impacts on ecosystems and the economy. Although some forest fires occur spontaneously, most of them are caused by human activities. Hence the importance of identifying the seasons and zones that represent greater risks to inform the citizens, warn the authorities, and streamline the available surveillance and extinction means. To such end, it is recommended to analyze the four basic factors involved in the occurrence of forest fires, namely: weather, type of vegetation cover, topography, and human activity. The first three factors have been analyzed in various publications, converging in that: when information on the fuel type of the vegetation is not available, it is possible to approximate it by using the vegetation spectral indices; the topography, with ground altitude, slope, and orientation factors; and the meteorological conditions, with relevant variables, such as temperature, relative humidity in the air, wind, rainfall, and water vapor pressure [1,2,3,4,5]. All these conditions have the potential to boost or, on the contrary, delay fire propagation [6].

Although forest fires occur in most of the biomes, in countries with Template-Mediterranean climates, especially in Europe and North America, the effect of the seasons is more accentuated, especially with the increase in temperatures and the reduction in rainfall volume [7]. These meteorological changes have driven the creation of several indices to determine the likelihood of fire occurrence in specific areas, with the National Fire Danger Rating System (NFDRS), the McArthur Forest Fire Danger Index (FFDI), the Canadian Forest Fire Weather Index System (FWI), and the Fire Potential Index (FPI) standing out [8]. All these indices use weather data as a basis [9,10,11,12] and, although they have been used for several decades to plan and manage forest fires in North American countries, they are not designed for Ecuadorian tropical zones nor do they include anthropic interaction measurements, as recommended by [13].

The study of forest fires evolves continuously following environmental and social changes. The first meteorological approaches were centered on the likelihood occurrence and on the locations’ susceptibility assessment with regression models, geographically weighted regression, or generalized additive regression [14]. In this sense, protocols for zoning the risk of fires following the Saaty multicriteria analysis methodology also became popular; such methodology allows designing hierarchization models to weight variables with the criteria of professionals from various areas and generate an equation that multiplies the value of each variable by the weight obtained in the technical analysis [15].

In the last decade, forest fire modeling has undergone significant advances thanks to the integration of machine learning algorithms, mainly Artificial Neural Networks (ANNs), Random Forests (RFs), and Supporting Vector Machines (SVMs) [13]. In parallel, the use of the maximum entropy (MaxEnt) algorithm has gained ground, which had, typically, been used in the analysis of species distribution and modeling of ecological niches [16]. The most recent trend is that of the forest fire simulation systems such as FARSITE, FSim, CFast, FlamMap, or Burn-P3, which allow for quantitative estimations of both ignition probability and fire propagation to guide fuel treatment as a forest management measure [17]. A more in-depth analysis of the forest fire modeling techniques can be found in these research studies [18,19,20]. Despite its easy application and interpretation, decision trees have been scarcely employed in similar studies, in which techniques such as ANN, SVMs, or RF have been preferred.

The extremely unstable fire behavior of forest fires is boosted by the topographical, geological, and climatic conditions characteristic of tropical and subtropical countries, such as Ecuador. The low seasonality throughout the year is due to the country’s location above the Ecuadorian line and is the reason why the difference between the regions is only defined in two seasons: wet or winter, and dry or summer [21]. Generally, in the Coastal region, the rain season begins in December and lasts until May, while the dry season is between June and November. In the Sierra and Amazonia region, there is rainfall from October to May, and the dry season extends between June and September, with slight differences in the North Amazonia (province of Sucumbíos), where the rainy season lasts from March to November and the dry season extends from December to February [22].

The altitude range is another conditioning factor for weather in inland Ecuador, since the topography generates a wide gradient of temperatures and exerts an influence on rainfall volume. Generally, the high areas receive low rainfall, while the low zones up to 2000 m.a.s.l. present an ample variation in annual rainfall volume [23]. This division caused by the pluviometric and thermal regimes makes it possible for forest fires to occur in almost all the months throughout the national territory.

As already mentioned, the meteorological variables (temperature, relative humidity, and accumulated rainfall) are habitually used as the cornerstone for the models of forest fire occurrence, regardless of the technique followed [5,24,25]. Some authors, such as [26], add to the analysis information about the vegetation cover, classifying it especially according to the type of fuel. In other models, the distance to access routes or other human infrastructures is also used [27], as well as forestry productivity or demographic density [28] for an approximation to the ignition risk in forest fires.

Although the meteorological variables are present practically in all the models, access to good resolution information in Ecuador is limited. There are several internet services offering weather information, although predominantly at broad scales and as weekly or monthly averages. Such is the case of the ERA5-Land collection [29] with monthly data regarding temperature, rainfall, atmospheric pressure, or wind speed at a resolution of 0.1 arc degrees (approximately 1.11 km). The TerraClimate [30] dataset offers a broader catalog of variables, the following among them: Actual and potential evapotranspiration, water deficit, soil moisture, accumulated rainfall, and the maximum and minimum temperatures of each month at a global level; however, it is only available in a 2.5-km scale. On its part, GLDAS-2.1 [31] offers more than 30 meteorological variables estimated every 3 h at a resolution of 0.25 arc degrees (approximately 25 km).

The experience of modeling the occurrence probability of forest fires in Ecuador is semi-empirical, and little has been published on the subject. The most relevant corresponds to the Metropolitan District of Quito (DMQ), in which case FlamMap software was used to simulate the spread of a forest fire that occurred in 2018 in the Atacazo hill. This study recognizes the lack of baseline information at the country level and how the performance of firefighters is affected by this gap. Other recommendations of the authors are the generation of mapping at local scale mapping with their own models, or, the use of factors that allow adapting or calibrating popular models in other areas of the world [32].

Is it possible to generate, using supervised learning techniques such as decision trees, logistic regression or MARS, a reliable model that allows obtaining fire probability maps periodically? To answer this question, this study was carried out in the Loja canton (province of Loja, Ecuador). The data were obtained from open sources, both to identify hot spots (fires) and explanatory variables. Once the database was generated, the three techniques mentioned above were applied to generate the model which was later validated using cross-validation.

This manuscript begins with an explanation of how to obtain the explanatory variables considered for the forest fire susceptibility model, as well as it is explained the importance analysis and other metrics that allow prioritizing variables and discarding multicollinearity. Aspects of the experimental design for training and validation in machine learning are later discussed. Being this a comparative article of the performance of three different techniques, a section that evaluates their performance and allows to choose a technique was drafted. Given the scarce application of machine learning models in the country, the discussion section recapitulates the most novel aspects of the research and compares it with available studies for similar contexts. The concluding paragraphs emphasize recommendations for future researchers and the challenges to follow after this research.

2. Materials and Methods

2.1. Study Area

Loja canton is a part of the province of Loja, located in southern Ecuador, and has an approximate area of 1928 km². About 31% of the territory is used for agricultural activities (crops and/or animal breeding), 26% corresponds to remnants of native forest and, in a lower proportion, are other types of natural vegetation: 17% shrubs, 13% grass, and only 7% moors; on their turn, the urbanized zones correspond to 6% of the total area of the canton [33].

The average temperature varies from 57 °F (14 °C) in the rainiest months to 63 °F (17 °C) in the driest ones. The south-western part of the canton has higher temperatures (71 °F or 22 °C). In contrast, the north-eastern zone is characterized by low temperatures throughout the year (45 °F or 7 °C). In the central zone, the most urbanized sector, the average annual temperature is 61 °F or 16 °C; the coldest month is July (43 °F or 6 °C), and the hottest month is November (81 °F or 27 °C). A climate variable extremely related to temperature in the study area is humidity, whose ranges goes from 86% between December and July to 75% between August and November.

The average annual rainfall is 1300 mm, the areas that receive the least rainfall are the eastern areas; in terms of seasonality, the months with the least rainfall tend to be august or September, while the months with the highest rainfall are December, January, and February [34].

According to the last population and housing census, 2010, the canton Loja holds a population of 214,855 inhabitants (48% of the province of Loja). The capital Loja is the most populated with 180,617 inhabitants, followed by Malacatos (7114 inhabitants), Vilcabamba (4778 inhabitants), San Lucas (4673 inhabitants), and Taquil (3663 inhabitants). In terms of population density, the city of Loja and the parish capitals are the most populated; in contrast, the parishes of Jimbilla, Malacatos, San Pedro de Vilcabamba, Vilcabamba, and Yangana have extensive uninhabited areas (located to the south-east). Internal migration is a progressive phenomenon in the canton: currently, 80% of the territory is considered urban and only 20% rural.

The canton has multiple natural hazards throughout the year. In recent years, during the rainy season, were reported overflowing canals, landslides, and floods in several areas of the territory. The main risk in the canton is the increasing of forest fires in the driest months. According to official statistics of the National Service for Risk and Emergency Management (Servicio Nacional de Gestión de Riesgos y Emergencias, SNGRE), available since 2016, in 2020 more than 100 events a year were identified in the province of Loja, which represented between 13% and 39% of the burned area in the entire country [35].

The only fire risk map available is a model elaborated in 2014 by several governmental institutions. It uses Multicriteria Evaluation (MCE) techniques based on cartographic information of the fuel, temperature, rainfall, solar radiation, humidity, and cover-soil complex texture model [36]. Although it is the official country-scale model, it is based on subjective criteria, so it is not possible to evaluate its accuracy with objective parameters. As it is a static map, it does not reflect the constant changes that the canton has undergone during these eight years, both in anthropogenic activities and in the state of vegetation.

2.2. Preselection of Explanatory Variables and Generation of the Database

The model was generated based on data collected between 2015 and 2020 in a 5-km influence area around the canton limits. This period was selected due to the availability of Sentinel 2 information. 1910 hot spots (fires) were obtained from the data generated by the VIIRS [37] and MODIS [38] satellites, from which a random selection of 887 points was made. In addition, from Sentinel 2 images [38], 549 points of unburned sites and that were on dates close to those when the hot spots were recorded were identified (Figure 1). From these 1436 points and considering the dates on which the fire took place within the study period, a database with 23 variables related to the topography, vegetation, and proximity to human activities was generated, selecting the images immediately preceding occurrence of the event. These variables were reduced to eight after an importance analysis. The NDVI and NDMI indices were generated from Sentinel 2 imagery using the code editor of Google Earth Engine (GEE).

2.3. Multi-Collinearity Checking of Forest Fire Influencing Variables

In order to test for multicollinearity, we applied the tolerance (Equation (1)), and VIF (variance inflation factor) (Equation (2)), of the R olsrr package [39], definided as:

$$Tolerance=1-R^2{}_d$$

(1)

$$VIF=\left|\frac{1}{Tolerance}\right|$$

(2)

where $R^2{}_d$ is the determining factor for the regression of explanatory variables and d concerns all other explanatory variables, ${\lambda }_{max}$ and ${\lambda }_k$ are the maximum and the kth eigen values, respectively. Tolerance < 0.1, VIF > 10 indicates serious collinearity problem [39,40,41,42].

2.4. Forest Fire Occurrence Probability Models

2.4.1. Logistic Regression (LR)

Logistic regression aims to predict, from independent variables, the probability (from 0 to 1) of occurrence (Equation (3)). The LR equation (Equation (4)) is as follows [43]:

$$Pi=\frac{1}{1+e^{-zi}}$$

(3)

$$zi=\alpha +{\beta }_1{X}_{i1}+{\beta }_2{X}_{i2}+\dots +{\beta }_p{X}_{ip}$$

(4)

where P is the probability of occurrence of the event (dichotomous variable); z is obtained from a linear combination of independent variables based on adjustment of maximum likelihood, with constant α, coefficient of partial lineal regression β, and original values of variables x.

2.4.2. Multivariate Adaptive Regression Spline (MARS)

Multivariate Adaptive Regression Splines (MARS) is a method developed for flexible modelling of high-dimensional data. This method uses classical linear regression, mathematical construction of splines, and binary partitioning to create a local model.

When the response y assumes only two values, linear logistic regression is used. The MARS model predicts a function using “basic function (BF)”, a linear combinations and interactions of the adaptive piecewise linear regression [44]. The basic function of MARS non-parametric regression is [45]:

$$y=f\left(x\right)+\epsilon$$

(5)

where ε shows the error, f(x) is an unknown regression model that calculated by:

$$f\left(x\right)={\beta }_0+{{\displaystyle \sum }}_{m=1}^M{\beta }_m{\beta }_m\left(x\right)$$

(6)

where ${\beta }_0$ is the coefficient of the constant basis function, ${\beta }_m$ is the coefficient of the $m_{th}$ basis function, ${\beta }_m\left(x\right)$ is the $m_{th}$ basis function, and $M$ is the number of basic functions in the model.

2.4.3. Logistic Model Trees (LMT)

The logistic model tree is a classification model, which combines decision tree learning methods and logistic regression (LR). From the number of iterations, a simple regression function is adjusted using the attributes that generate the lowest error and incorporate it into an additive model. The optimum number of iterations is determined by means of cross-validation when performance of the model stops increasing. When no more improvements can be attained by adding more simple linear models, the data are divided, and boosting is resumed separately in each subset. This process takes the logistic model generated up to this moment and de-bugs it separately for the data in each subset. Cross-validation is once again performed in each subset to determine the suitable number of iterations to perform in this subset. To prevent data overfitting, a tree-pruning process is applied, producing smaller but very precise trees with linear-logistic models in the leaves. A more detailed explanation of the model can be found in [46].

2.5. Forest Fire Occurrence Probability Analysis

Data analysis applying (i) LR; (ii) MARS, and (iii) LMT. All models were executed in R using ‘caret’ package [47]. MARS was executed using additionally the ‘earth’ package [48], with the “backward” pmethod for prune the model, and 1 degree of interaction. And for LMT we use RWeka [49], the number of iterations was cross-validated, and the rest of the parameters used were those configured by default (Figure 2).

In addition, the variable importance was calculated using the Varimp command of the caret package in R software. For Varimp interpretation of each model, see the Caret package documentation [47].

2.6. Performance Assessment

Two tools were used to assess performance of the model, namely: Area Under the Curve (AUC) and Cohen’s Kappa Coefficient.

2.6.1. Area under the Curve

The ROC (Receiver Operating Characteristic) curve allows evaluating the ability of the trained model to classify information, regardless of the algorithm used or of the scale of the predictive variables. It measures the relationship between sensitivity (Equation (7)), or “rate of true positives”, and 1-specificity (Equation (8)), or “rate of false positives”.

Sensitivity = TP/((TP + FN))

(7)

TP = true positives, FN = false negatives.

Specificity = TN/((FP + TN))

(8)

TN = true negatives, FP = false positives.

In 1988, the forth some approximate parameters were set to classify precision [40] as follows: 0.50–0.60 = insufficient; 0.60–0.70 = poor; 0.70–0.80 = fair; 0.80–0.90 = good; and 0.90–1.00 = excellent [46].

2.6.2. Cohen’s Kappa Coefficient

The Kappa index was calculated, which is a statistical instrument that estimates agreement between two observers or measuring tools for the same phenomenon, with the intention of adjusting the random effect in the agreement proportion expected, as established by Equation (9) [50].

Kappa = (P₀ − P_e)/(1 − P_e)

(9)

P₀ = observed concordance ratio, and P_e = expected random matching concordance ratio.

The expected value of the Kappa coefficient takes on values between 0 and 1; where 1 represents perfect consistency. To intercept the results, the appraisal scale for the Kappa index proposed by [51] was adopted, which, with 0.2 intervals, proposes the following agreement levels: no agreement (0.00), insignificant (0.00–0.20), discreet (0.21–0.40), moderate (0.41–0.60), substantial (0.61–0.80), and almost perfect (0.81–1.00).

Once the models were generated, they were applied to the entire study area. Additionally, 5 categories were developed (very low: 0–0.2, low: 0.2–0.4, moderate: 0.4–0.6, high: 0.6–0.8, and very high: 0.8–1) using the equal interval method. NDVI and NDMI values for the month of August 2020 were used for this purpose, mainly because it is the month with the lowest cloud cover in Sentinel images. To compare the models, the percentage of estimated area within each of the categories was calculated.

Finally, positive predicted value (PPV) and negative predicted value (NPV) were calculated to determine the proportions of positive and negative results that are true positive and true negative results, respectively.

2.6.3. Wilcoxon Test Rank

With the aim of identifying statistically significant differences between the values observed in the training and test dataset and the results of each model, and to compare any statistically significant differences between the values generated by the models, the Wilcoxon signed-rank test was applied. According to this method, when the p-values are less than the significance level (0.05), the null hypothesis is rejected and, therefore, the performances of the models are significantly different [52].

3. Results

3.1. Multi-Collinearity Analysis

The multi-collinearity test showed strong multicollinearity problems among the variables ‘Accessibility from towns’ and ‘Accessibility from roads’. Once the variable ‘Accessibility from towns’ was eliminated, the achieved tolerance, and variance inflation factor (VIF) values below the upper and lower limits, respectively (

Table 1. Multicollinearity analysis in the current study.

N	Variables	Tolerance	VIF
1	NDVI	0.9543621	1.04782
2	NDMI	0.8127563	1.230381
3	Accessibility from economic center	0.1436906	6.959399
4	Accessibility from roads	0.1273751	7.850826
5	Elevation	0.5045483	1.981971
6	Distance to rivers	0.824852	1.212339
7	Distance to anthropic zones	0.5341745	1.872047

). Therefore, no multicollinearity issues were identified for the seven variables tested (Figure 3).

3.2. Forest Fire Occurrence Mapping Results

The maps generated by each model are shown in Figure 4. Additionally, a bar chart identifying the number of pixels assigned to each class is shown in each map. In the case of LR, the very low class has the largest area (32%), followed by low (21%), moderate (17%), high (15%), and very high (15%). For MARS, the dominant classes are very low (45%), and then very high (20%), although some areas are classified as low (13%), and finally moderate (13%) and high (13%). As for LMT, the largest proportion of area classified as very low has the largest area (59%), followed by very high (30%), while low percentages are classified as low (7%), high (3%), and moderate (2%) (Figure 4).

3.3. Variable Importance

The results of the variable importance are showed in the

Table 2. Variable importance of the forest fire occurrence independent variables using the varImp function from Caret package. In the three algorithms analyzed, the most important variable turned out to be the NDMI index; while the variable with the least impact for the models based on LR and MARS was Distance to anthropic zones, for the LMT algorithm the variable with least importance was the NDVI index.

	LR	MARS	LMT
NDMI	9.6	100.0	0.7921
Accessibility from roads	5.4	35.6	0.6902
NDVI	4.1	39.8	0.5062
Elevation	2.4	65.5	0.6844
Accessibility from economic center	2.3	27.9	0.5547
Distance to rivers	2.0	21.0	0.5683
Distance to anthropic zones	1.0	20.4	0.5256

. According to it, for LR, the most important variables are humidity (NDMI), accessibility from roads and NDVI. Elevation, accessibility from economic center and distance to anthropic zones are of intermediate importance, while the least important variable, is the distance to rivers. For MARS, two variables have a strong weight, namely: humidity and elevation. NDVI and accessibility from roads are of intermediate importance, while accessibility from economic center, distance to anthropogenic zones, and distance to rivers are of less importance. For LMT, humidity, accessibility from roads, and elevation are the most important variables, followed by distance to anthropic zones, accessibility from economic center, distance to rivers, and, finally, NDVI, which are of less importance.

3.4. Models’s Performance

The training and test result of the forest fire occurrence probability is shown in the

Table 3. Performance of models generated by three statistical techniques. LR: logistic regression. MARS: Multivariate adaptive regression spline. LMT: Logistic model tree.

	TRAINING DATA SET			TEST DATA SET
Parameters	LR	MARS	LMT	LR	MARS	LMT
True positive	348	361	378	106	114	116
True negative	304	331	365	99	113	112
False positive	108	81	47	38	24	25
False negative	64	51	34	31	23	21
PPV (%)	0.7632	0.8167	0.8894	0.7361	0.8261	0.8227
NPV (%)	0.8261	0.8665	0.9148	0.7615	0.8309	0.8421
Sensitivity	0.8447	0.8762	0.9175	0.7737	0.8321	0.8467
Specificity	0.7379	0.8034	0.8859	0.7226	0.8248	0.8175
AUC	0.844	0.9061	0.9017	0.825	0.8849	0.8321
KAPPA	0.5825	0.6796	0.8034	0.4964	0.6569	0.6642
Accuracy	0.7913	0.8398	0.9017	0.7482	0.8285	0.8321

. Using the training data, the LR model has a good ability to classify the information (AUC > 0.8), while the ability of MARS and LMT is excellent (AUC > 0.9). Regarding the degree of agreement measured with the kappa index, it is observed that the model generated by LR is moderate, while in the MARS and LMT models it is substantial, with LMT approaching near perfect. It is also observed that the LR model tends to generate a considerable number of false positives, which generates a positive predictive value (PPV) of 0.7632, and a lower accuracy than the other models. In contrast, LMT generates a low number of false positives, yielding a positive predictive value of 0.8894, and a model accuracy of 0.9017.

With the validation dataset, the overall accuracy of the models decreases, but they still maintain good classification accuracy (AUC between 0.8 and 0.9). As with the training data, in the validation data the kappa index is moderate for the LR model (0.4964) and substantial for the MARS and LMT models (0.6569 and 0.6642, respectively). While LR generates a considerable number of false positives, leading to a PPV d 0.7361 and an accuracy of 0.7482, the models generated by MARS and LMT still maintain PPV values and accuracy greater than 0.8.

The pairwise comparisons of the three models and the observed data are shown in

Table 4. Results of the Wilcoxon signed rank test applied to the observed and predicted data generated by each model. Numbers within each cell represent the p-value associated with the null hypothesis being true: no difference between the data generated by a given pair of models. LR: logistic regression; MARS: multivariate adaptive regression splines; and LMT: logistic model tree.

	TRAINING DATA SET			TEST DATA SET
	LR	MARS	LMT	LR	MARS	LMT
BBDD *	0.00	0.00	0.15	0.00	0.00	0.56
LR		0.32	0.00		0.89	0.00
MARS			0.00			0.00

* BBDD means database.

. In both, the training and test databases, the models generated by LR and MARS show a significant difference with respect to the observed data, while LMT does not show a significant difference with respect to the observed data.

Likewise, there are no significant differences between the data generated by the LR and MARS models, while the p-values allow us to infer that there are significant differences between LMT and the other two models, which leads us to conclude that the LMT model is significantly better than LR and MARS in this experiment.

4. Discussion

Our results demonstrate that nonparametric techniques (MARS and LMT) are able to generate more accurate models than traditional logistic regression models, such as LMT, for the identification of the probability of forest fire occurrence, nevertheless, this difference is statistically significant in LMT. The models obtained present a performance level that is similar to that of other studies that have used more complex techniques for the evaluation of risk events, such as forest fires or landslides. In the case of the Random Forests (RFs), its performance is generally high, with AUC values within the 0.80–0.90 range in similar studies conducted in Honduras and China, respectively [13,53]. On their turn, [54] generated a model based on Alternative Decision Trees (ADT) with an AUC value slightly higher than 0.9 and obtained AUC results slightly lower than that in our study when using other techniques, such as LMT, Functional Trees (FTs) and Naïve Bayes Tree (NBT).

One of the advantages of generating models with LMT and MARS is that they allow the generation of zones in which the variables that affect the probability of forest fire occurrence have a greater or lesser influence on the definition of this probability. Another greatest advantage in using LMT and MARS is its simplicity in the final application of the model since, unlike other alternatives such as random forests and artificial neural networks, there is no need to use software programs specialized in machine learning. Both the classification in subgroups and the application of the equations can be adapted to geographic information systems, thus facilitating its implementation by local decision-makers and visualization by citizens.

Part of the elements that ensure usefulness in the modeling processes are related to access to the initial data, as well as to the ease to implement the final model. Regarding the former, it is to be noted that, in our model, the use of weather variables was avoided due to the difficulty in permanent access to good resolution data in developing countries, as already verified by [55,56] in the case of Argentina by [57] at the regional level (South America). Although these research studies analyze several sources of meteorological variables, they all seem to reach the same conclusion: their spatial resolution is useful in large-scale modeling and, as the analysis scale increases, the importance of the meteorological variables decreases. In their absence, variables that result from the interaction of weather conditions were used, such as vegetation moisture (NDMI) and, to a certain extent, NDVI.

For the permanent application of susceptibility models based on satellite images, there is a common inconvenience, the shadows or masking caused by the presence of clouds on the capture date. For this, the recommendation is to build a tile free of clouds during longer periods of time [8,53,58]; or, if not possible, to remove the contaminated pixels, as was the case in this study, with the consequent information sacrifice to obtain more periodic maps. Finally, the incidence of human activities on the occurrence of forest fires was corroborated. Of the seven variables included in the model generated, four corresponded to proximity to anthropic zones. As stated by [59], the ecosystems located farthest away from human activities present more resilience to thermal stress and to sporadic ignition

5. Conclusions

In this study, the predictive ability of models based on LR, MARS, and LMT to determine the probability of forest fire occurrence was evaluated. Several experiments were conducted using a dataset that included a database of burned and unburned points and seven conditioning variables. The performance of the forest fire probability models was evaluated using ROC curves and statistical measures. The LMT and MARS classification models obtained higher AUC values for the training and validation datasets, but only LMT differed significantly in the statistical measures with respect to LR. Nevertheless, the MARS and LMT techniques are promising for mapping probability of forest fire occurrence. Additionally, vegetation moisture, represented by the variable MDMI, proved to be of highest importance in the models generated by the three techniques, while distance to anthropogenic zones was of a low importance in all three models. The accuracy of the forest fire probability model presented in this work, and the ease of obtaining geographic data to apply it, as well as the implementation of the results in more user-friendly environments, such as geographic information systems, make these results useful for the generation, in a simple and fast way, of permanently updated information on the probability of occurrence of forest fires by decision-makers.