Study area

The present work was developed by using information from the state of Jalisco, which is located in the central-western part of Mexico, on a surface area of 78 588 km², of which 68 % has a warm sub-humid climate along the coast and in the central zone, while 18 % is temperate sub-humid in the upper parts of the mountains and 14 % is dry and semi-dry in the north and northeast. At a national scope, the entity occupies the tenth place by the number of registered forest fires, and the fourth place in terms of affected surface. On average, about 22 000 ha are burned each year (Figure 1), which corresponds to 570 fires per year, with an average of 30 ha per fire. The most damaged vegetation type is grassland, with an average of almost 12 000 ha per year; it is followed by forest areas with shrubs and bushes, with about 8 500 ha per year; and the burned area with the presence of adult trees amounts, on average, to 1 100 ha (^{Conafor, 2015}).

Source: ^{Conafor (2015)}.

Número de incendios = Number of forest fires; Superficie incendiada = Area affected.

Figure 1 Number of forest fires and area affected during the 2005-2014 period in the state of Jalisco, Mexico. 

Establishing the risk of fire

Factors such as topography, agricultural activities, fuel models, fire history, etc. are analyzed in order to locate and size the priority areas for forest fire fighting (^{Vilchis et al., 2015}). Based on these, a map of priority attention areas is developed, indicating on it the pertinent preventive actions, under the corresponding management plan (^{Calkin et al., 2014}).

In Mexico, these areas are located and sized according to the determination of risk, hazard and value criteria (^{Conafor, 2010}). Specifically, the concept of risk, in practical terms, refers to the probability of a forest fire occurring in a given area and within a given period (^{Hardy, 2005}); this depends on various factors (^{Julio, 1990}; ^{Conafor, 2010}; ^{Rodríguez et al., 2011}), which in turn are divided into a series of variables that receive a certain weighting (Table 1). Based on these, the spatial variation of risk assessments in the state of Jalisco was determined (Figure 2).

Muy bajo = Very low, Bajo = Low; Medio = Medium; Alto = High; Muy alto = Very high.

Figure 2 Spatial distribution of forest fire risk in the state of Jalisco, considering three and five classes. 

Number and range of classes

The forest fire risk map (Figure 2) was defined at the state level; thus, it was structured from a resolution of 120 × 120 m pixels, each of which was assigned a risk value. Figure 3 shows the frequency of these values, whose distribution tends to be normal, with an average of 5.102 and a variance of 3.929. While most of the pixels with risk are located between values 3 and 10, besides that there were few pixels with high values for risk. Based on this distribution, three and five classes were defined, being the most widely used (^{IDEAM, 2011}; ^{Atienza et al., 2012}; ^{Sevillano et al., 2015}), whose intervals were defined with the following methods: a) Equal intervals (II); b) Quantities (Q); c) Natural breaks (QN); and d) Geometric intervals (IG). Subsequently, a comparative analysis (ANOVA) was made between methods, for each defined class.

Número de pixeles = Number of pixels; Valor de riesgo = Risk value.

Figure 3 Frequency of forest fire risk levels derived for the state of Jalisco. 

Selection criteria

In order to define the number of classes and the most appropriate method to establish the corresponding intervals, 1 000 validation sites (SV) were first located at random throughout the state of Jalisco. Around each one, an area of 100 km² was located (Figure 4), corresponding to the so-called fire risk factor (^{Flores, 2017}; ^{Flores and Macías, 2018}), within which the total number of forest fires that occurred in the 2005-2014 period was counted. Thus, a class per site (SV) was associated with the number of fires counted in the 100 km² area of each SV.

Incendio = Fire; Punto de validación = Validation sites (points); Área de validación = Validation area.

Figure 4 Detail of the location of the validation sites (points) and their corresponding area of 100 km², within the state of Jalisco. 

According to the method used to define the class intervals (three and five), each of the SV was identified with a risk class, which may differ according to the classification method. Based on the values of the number of fires in each one of the SV belonging to a risk class, the standard deviation was estimated as a parameter for comparison between the different classification methods. Finally, the thematic maps were elaborated, with the purpose of making a visual qualitative comparison displaying the differences and similarities between the tested classification methods.

Visual interpretation of risk classes

The analysis of the maps corresponding to three fire risk classes showed that there is no difference between the maps generated with the IG, QN and Q methods; besides, both the definition of the intervals' limits and their spatial distribution on the maps were very similar. However, the difference between method II with the IG, QN and Q methods is clear, since the High-risk class area was reduced, having been was absorbed mainly by the Medium-risk class. This can be seen in the graphic distribution of the limits of each one of the classes.

On the other hand, the maps that resulted from considering five classes were visually very different, which was also observed in the graphs corresponding to the limits of their intervals. However, it was clear the similarity between the maps derived from the GI and Q methods, in which the High and Very High risk classes covered a larger area. As in the case of the three classes, the map generated with thee II method had the largest difference. Although the differentiation between the five classes is evident, visually it is not recommended to use a very large number of classes, as complications may arise in the interpretation of the map when trying to identify the symbology of each class, potentially leading to errors (^{Olaya, 2014}).

Fires by risk class

In order to characterize each of the risk classes, the number of forest fires present was evaluated (Table 2). When considering the classification of only three classes, the number of fires observed in class 1 (low risk) was the same, except when using method II, which exhibited over twice the number, compared to the other methods. As for class 2 (Medium risk), the behavior was similar, unlike the results obtained with the Q method, with registered only 84.5 % of the fires located using the IG and QN methods. Conversely, in class 3 (high risk) 6.54 % more fires were obtained using the Q method than with the IG and QN methods, while the II method exhibited only 43.3 % of fires, compared to IG and QN.

In the five-interval classification, the II method exhibited 82.4 % more fires than the other methods. For class 2, there was variation in all cases, with a difference of 390.3 % between the lowest (IG) and the highest (II) number of fires. Classes 3 and 4 were more similar as to number of fires, while for class 5, the IG and Q methods yielded very similar numbers, although the QN and II methods exhibited 48.89 and 12.46 %, respectively, of the maximum number registered for IG class, which was 2 720 fires.

The average surface area per fire was very similar between methods when comparing the classes in the three-interval classification, although the Q and II methods presented lower values. As for the five-interval classification, in general, there was no definite trend, but the lowest values were obtained with the II method for all classes, except for class 1. The highest values varied by method in each of the five classes.

Variability between risk classes

Given that the definition of risk classes seeks the existence of sufficient variability among classes, Figure 6 shows that when only three classes were used, the variability (standard deviation) was practically the same among the classes defined with the IG, QN, and Q methods. However, when considering all the methods, there was a slight increase in variability in classes 1 and 2. Class 3 (high risk) is widely differentiated in the case of the II method; this agrees with the visual interpretation of the maps (Figure 5), in which the difference in the distribution and amplitude of the classes resulting from the application of method II was clear. On the other hand, when the average number of fires (Figure 6) corresponding to each class was considered, the observed behavior was very similar.

IG = Geometric Intervals; QN = Natural breaks; Q = Quantiles; II = Equal intervals.

Número promedio de incendios = Average number of fires; Desviación Estándar = Standard deviation.

Figure 6 Variation of the average number of fires and standard deviation, for each one of the forest fire risk classes.  

When five classes were considered (Figure 6), the variability among the four methods was virtually the same. However, for risk class 2, the II method determined a greater standard deviation, while the other methods exhibited a similar variability. A better differentiation in the variability between the four methods was observed from class 3 (medium risk) onward.

In class 4 (high risk), the variability resulting from the II method stood out, while with the rest of the methods the variability was very similar and much lower. Finally, class 5 (very high risk) exhibited a clear difference between the variability of all the methods. As in the case of the three classes described above, the II method generated the best differentiation in the variability among its classes, followed by QN. On the other hand, in relation to the average number of fires per class, a slight variation was observed between the first three classes, considering all methods. This trend was also present in class 4, but only with the IG, QN and Q methods, as the II method exhibited a larger number of fires. In class 5, a clearer difference was registered between the number of fires when comparing the four methods.

These results suggest using, first, five class intervals instead of three. The equal interval (II) method was the best for defining the boundaries between classes. Accordingly, the number of classes must: a) not be so small that it will summarize the information excessively; b) allow for adequate detail of the spatial variation of the variable under study, and c) not be too large, so as to prevent the problems that ensued from not dividing the values into classes. In general, it is suggested not to use more than eight classes (^{Olaya, 2014}).

As noted above, one of the purposes in selecting the interval of each of the classes is to ensure a statistically significant difference; thus, the ANOVAS (Table 3) resulting from the comparison of each of the classes supported the results of the analysis shown in Figure 6. For example, with the three-interval classification, no difference was observed in class 1 between the methods used, as confirmed by the resulting probability (p= 0.4430911), which implied the inexistence of a statistically significant difference, while a significant difference between the methods was registered in classes 2 and 3.

On the other hand, in the five-interval classification, classes 2 to 5 exhibited a statistically significant difference when comparing between the methods.

Finally, it must be highlighted that this kind of work has not been done recently; therefore, no comparative analysis of the results obtained could be performed. This implies that since ^{Jenks' study (1967)}, there has been little research on the definition of an analytical process for the selection of the number of classes and the most appropriate method for the delimitation of the intervals of those classes, such as might lead to an adequate classification of forest fire risk. The above research will provide statistical bases for a better location and sizing of the forest fire risk classes.