1 Introduction

Australia has been suffering more from bushfires than other types of natural disasters in recent years due to climate changes which have increased the temperature and decreased rainfalls (Yu et al. 2020). Bushfires can be harmful to the human health and cause devastating impacts on the environment and economy (Zhang et al. 2016). For example, 173 people were killed and 4500 km2 of area were burned during Black Saturday bushfires in Australia in 2009 (Ma et al. 2020). Later, 248 buildings across the New South Wales (NSW) were destroyed by bushfires in 2013 (Ma et al. 2020). The most catastrophic bushfire season occurred in the summer of 2019/2020, which devastated fire fighters, humans, and animals (Milton and White 2020). The frequency and severity of the bushfires are expected to increase in the future as a result of climate changes (Milton and White 2020). It is important to model bushfires and mitigate the negative impacts of bushfires on humans and environment. It is also important to determine areas with a high possibility of bushfire occurrence to achieve a better natural hazard management (Tehrany et al. 2021). Various algorithms and methods have been applied to bushfire susceptibility mapping (Tehrany et al. 2021), including statistical methods, artificial intelligence and machine learning (ML) techniques, ensemble techniques, and evolutionary algorithms.

Statistical methods have been used to generate bushfire susceptibility maps in different studies, such as frequency ratio (FR), evidential belief function (EBF), and weight of evidence (WOE) (Pourghasemi 2016; Hong et al. 2017, 2019; Jaafari et al. 2017). FR uses an understandable procedure and simplifies the problem and outcome, which enables to analyze large datasets in software such as ArcGIS (Pradhan et al. 2007). Statistical methods can be used in the ArcGIS environment, which enables to generate spatial patterns of bushfire prediction maps (Nami et al. 2018).

Forest fire susceptibility mapping in a case study on Minudasht forests in Iran showed that Shannon’s entropy (SE) and FR are two promising methods for the prediction of forest fires with areas under the curve (AUCs) of 83.16% and 79.85%, respectively (Pourtaghi et al. 2015). EBF is also an appropriate statistical method for the prediction of bushfires, with an AUC of 81.03% in the Hyrcanian ecoregion in Iran (Nami et al. 2018).

A study in the Yihuang area, China, showed that the methods such as linear discriminant analysis and quadratic discriminant analysis (LDA and QDA), FR, and WOE were useful for the prediction of bushfires. WOE had the highest AUC (82.20%), followed by FR (80.9%), QDA (78.3%), and LDA (78.0%) (Hong et al. 2017).

The advancement of remote-sensing technologies has improved the bushfire management and monitoring (Jain et al. 2020). The bushfire prediction by data-driven methods has recently been used owing to the improvement in data quality (e.g., weather data) (Jain et al. 2020). The advancement in data quality has also helped scientists to use different ML techniques for bushfire susceptibility mapping (Jain et al. 2020). ML techniques can predict bushfires using input data, regardless of the expert’s knowledge. ML techniques are trained by a portion of the data and find the most fitted model that can be used for the generation of spatial maps for the bushfire prediction in the entire bushfire-prone area (Leuenberger et al. 2018; Tonini et al. 2020).

Recent studies have shown that new artificial intelligence methods generate more accurate results than conventional statistical techniques (Hoang and Tien Bui 2018). Different ML methods such as random forest (RF), artificial neural network (ANN), decision tree (DT), support vector machine (SVM), and genetic algorithms (GAs) have been applied to bushfire prediction (Jain et al. 2020). The application of multiple ML methods, including RF, ANN, multilayer perceptron (MLP), Dmine regression (DR), least-angle regression, radial basis function (RBF), self-organized map, SVM, DT, and LR, showed that RF had the highest AUC (88.0%) for the prediction of bushfires in Mazandaran province, Iran (Gholamnia et al. 2020). Similarly, RF provided promising results during different seasons in the Liguria region of Italy (Tonini et al. 2020). RF exhibited better results than those of SVM, ANN, LR, and Probit regression (Cao et al. 2017; Ghorbanzadeh et al. 2019).

Unlike deterministic (linear) methods, RF does not require prior knowledge of the bushfires, yet achieves a similar accuracy as those of deterministic methods (Leuenberger et al. 2018). Other ML methods such as Bayes network (BN), DT, naive Bayes (NB), and multivariate logistic regression (MLR) have been applied to the bushfire prediction in Pu Mat National Park, Vietnam (Pham et al. 2020). The BN had an AUC of 96.0%, followed by DT (94.0%), NB (93.9%), and MLR (93.7%) (Pham et al. 2020). Kernel logistic regression and SVM were also used to generate bushfire susceptibility maps in Cat Ba National Park, Vietnam, where the kernel logistic regression had the highest AUC of 92.2% for the prediction of bushfires (Bui et al. 2016).

Ensembles of ML methods also showed promising outcomes for bushfire susceptibility mapping. The ensemble of different techniques, including ANFIS, GA, and simulated annealing (SA), had the highest AUC of 90.3% for the bushfire prediction (Razavi-Termeh et al. 2020). Razavi-Termeh et al. (2020) also reported that an ensemble of RBF and an imperialist competitive algorithm had an AUC of 87.8%. A combination of WOE and a knowledge-based analytical hierarchy process was more accurate than the use of WOE alone and LR in Huichang County, China (Hong et al. 2019).

Gene expression programming (GEP) which is a branch of artificial intelligence approaches proposed by Ferreira (2001) can find the explicit function between the response variables and conditioning factors automatically without considering assumptions about the problem’s function form (Ferreira 2001; Emamgolizadeh et al. 2015; Hoang and Tien Bui 2018). GEP determines the relationships between dependent variables and conditioning factors that can be nonlinear (Hosseini and Lim 2021). It can provide robust solutions quicker than traditional methods for complex problems (Alkroosh and Nikraz 2011). GEP is a useful tool for natural disaster prediction such as landslide prediction (Zakaria et al. 2010; Kayadelen 2011; Mousavi et al. 2012; Hoang and Tien Bui 2018; Hosseini and Lim 2021).

GEP is a novel approach which had not been considered in the management and prediction of bushfires. As a result, the main purpose of this research is to investigate the application of GEP for generating bushfire probability maps. GEP is a new approach in bushfire susceptibility mapping which works based on an evolutionary algorithm. Therefore, our models generated by GEP are expected to provide important insights to bushfire susceptibility mapping. To implement GEP and measure its capability to produce bushfire susceptibility maps over NSW which is one of the most bushfire-prone states in Australia, we proposed four ensemble methods: GEP and FR (GEPFR), RF and FR (RFFR), SVM and FR (SVMFR), LR and FR (LRFR), and four baseline methods: GEP, RF, SVM, and FR for the comparison with the ensemble methods. We investigated the use of ensemble methods to evaluate their performance. We compared the results of single and ensemble methods to identify the best method for the prediction of bushfires in our case study area.

2 Methods

2.1 Study area

The study area is NSW, in the eastern part of Australia, located at latitudes of 28° 15′ S to 37° 30′ S and longitudes of 141° E to 153° 30′ E (Fig. 1). NSW has an area of 801,150 km2, and its elevation ranges from − 7 m to 2175 m. Queensland is located to the north of NSW, while South Australia is located on the west side of NSW. NSW borders Victoria to the south. From the east, NSW has coast borders with Coral and Tasman Seas. Plant covers in NSW mainly include grassland, shrubland, savannas, and forests.

Fig. 1
figure 1

Map of the study area. A Australia and the location of NSW and B a bushfire inventory map for NSW in the period of 2010 to 2020. Dark green and red indicate unburned and burned areas, respectively

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2.2 Data preparation

2.2.1 Bushfire inventory map

Data collection is an important step before the generation of bushfire susceptibility maps (Pourtaghi et al. 2015). The generation of an inventory map is the first step in establishing a GIS database (Hoang and Tien Bui 2018). The bushfire inventory map in NSW was generated from the MODIS fire data (MODIS 500-m MCD 64 Monthly). These data were collected for the period of the fire season in Australia (November to February) between 2010 and 2020 (Fig. 1). In this study, 70% of the inventory map was randomly allocated to the training set, while the remaining 30% was used for the testing set (Pourtaghi et al. 2015).

2.2.2 Conditioning factors

Bushfire is a complex phenomenon. Numerous factors can contribute to bushfire occurrence. As a result, the selection of conditioning factors is an important step for the generation of bushfire susceptibility maps (Pourtaghi et al. 2015). In this study, we selected topography, climate, fuel loads, and human-made factors as conditioning factors based on the availability of data (Jaafari et al. 2017, 2019a; You et al. 2017; Sachdeva et al. 2018; Hong et al. 2019; Zhang et al. 2019; Eskandari et al. 2020; Tonini et al. 2020).

Slope, aspect, and digital elevation model (DEM) were used as topographical factors in this study. The DEM (ASTER 30-m GDEM) is illustrated in Fig. 2A. DEM data were collected from the United States Geological Survey (USGS) website (USGS 2021). Elevation is another important factor in bushfire occurrence (Gigović et al. 2019). The aspect and slope were derived from the DEM (Fig. 2C and D, respectively). Slope is the land gradient, represented in percentages or angles, which has a significant impact on the bushfire behavior (Gigović et al. 2019). The burn speed is higher on a steep slope. The slope can impact the direction of the bushfire (Gigović et al. 2019). Aspect is the direction of the slope and influences the slope in connection with insolation and exposure to wind (Gigović et al. 2019).

Fig. 2
figure 2

Maps of topographic factors for NSW. A Elevation, B aspect, C slope. The legend describes the color code for each map

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The climatic factors used in this study are annual mean precipitation and annual maximum temperature. These data were collected from the Bureau of Meteorology of Australia for NSW (Fig. 3A and B) (BOM 2021). The annual temperature is an important weather component that should be considered because the temperature can affect fuel conditions, such as fuel dryness (Gigović et al. 2019). Precipitation is another major factor that contributes to high fuel humidity levels (Gigović et al. 2019). In contrast, a higher precipitation can result in an increase in vegetation, which implies the availability of more fuel loads for bushfires (Zhang et al. 2015).

Fig. 3
figure 3

Maps of climate factors for NSW. A Annual maximum temperature, B annual mean precipitation. The legend describes the color code for each map

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Fuel loads including the normalized difference vegetation index (NDVI) and land cover, and human-made factors such as distance to roads were also used in this study. NDVI and land cover data (Fig. 4A and B) were collected from the USGS (MODIS 1-km MYD13A3 NDVI) (USGS 2021). NDVI, which displays the coverage and density of surface vegetation in an image and land cover, is an element in the preservation of the environment (Gigović et al. 2019). Land cover has been classified into six categories: forest, shrubland, savanna, grassland, cropland, and others. The distance to roads was calculated using the Euclidean distance technique in ArcGIS (Fig. 4C). Distance to roads data were collected from Open Street Map (OSM 2021). Finally, we considered eight conditioning factors for bushfire susceptibility mapping. They are slope, aspect, elevation, annual mean precipitation, annual maximum temperature, NDVI, land cover, and distance to roads.

Fig. 4
figure 4

Maps of fuel load and human activity factors for NSW. A NDVI, B land cover, and C distance to roads

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2.3 GEP

GEP is a population-based algorithm (similar to GA and genetic programming (GP)) introduced by Ferreira (Ferreira 2001). Individuals are selected according to their fitness. One or more genetic operators have been used to bring genetic variation to the population (Ferreira 2001). GEP can solve complex problems more quickly than GP (Alkroosh and Nikraz 2011). Individuals are linear entities with fixed lengths in GEP, but they express themselves in nonlinear expression trees (ETs) with different sizes (Alkroosh and Nikraz 2011).

The GEP algorithm initiates with a population that is randomly generated (Ferreira 2001). Individuals are expressed and evaluated and then are chosen to reproduce based on their fitness (Ferreira 2001). The process of expression, selection, and reproduction is repeated until either a determined number of generations or final solution for the problem is obtained (Ferreira 2001). The replication cannot bring variety to the population, so that the algorithm needs other operators to introduce variation to the population (Ferreira 2001). Chromosomes are copied without any changes in the replication step, but the rest of the operators select the chromosomes to conduct a particular modification (Ferreira 2001). Replication is necessary, but is an unexciting operator because it does not contribute to genetic diversity (Ferreira 2001). Other operators, such as mutation, inversion, and recombination, have been used to vary the population. Mutations can occur anywhere on the chromosome (Ferreira 2001). In mutation, head symbols are allowed to change to function or terminal, but terminals in tails have the option to be replaced by terminals (Ferreira 2001; Ebtehaj et al. 2015). In inversion, a random sequence is selected in the chromosome’s head and inverted (Ebtehaj et al. 2015). In recombination, two chromosomes, which have been randomly selected, parent, combine with each other and introduce two new offspring to the generation (Ferreira 2001).

We selected a population size of 30 and chromosome head length of 12. In addition, five genes were linked to each chromosome (with addition function). Bushfire conditioning factors and constants create a terminal set. The functions were selected by following the steps given in our previous research (Hosseini and Lim 2021).

2.4 FR

FR is a statistical technique based on the correlation between the distribution of bushfire occurrence and bushfire conditioning factors (Jaafari et al. 2019b; Kayet et al. 2020). In the FR approach, weight is assigned to each factor based on the contribution of each factor to the bushfire occurrence (Hosseini and Lim 2021). The FR for each class of conditioning factors is

$$ FR = \frac{{\frac{BF\left( x \right)}{{TBF}}}}{{\frac{N\left( x \right)}{{TN}}}}, $$
(1)

where BF(x) is the number of bushfires occurring in each class x, TBF is the total number of bushfires, N(x) is the number of pixels for each class x, and TN is the total number of pixels for the entire study area. Bushfire susceptibility mapping was created using the total weighted FR for the factors (Hosseini and Lim 2021). A higher FR implies a higher potential for bushfire susceptibility (Pradhan et al. 2015).

2.5 RF

The RF method introduced by Breiman (2001) is a strong and flexible ensemble learning methodology based on DT (Breiman 2001). The RF approach is suitable for nonlinear and high-dimensional problems, such as bushfire susceptibility (Gigović et al. 2019). RF is trained with bootstraps and is tested with out-of-bag samples (Sarica et al. 2017). RF constructs trees based on bootstrapped samples drawn randomly from the training dataset (Couronné et al. 2018). In the implementation of RF, the number of trees (N_tree) and the number of variables for each split (N_try) are parameters that need to be adjusted (Noi and Kappas 2018). N_tree should be sufficiently large such that each conditioning factor has a sufficient probability to be selected. N_try as a default is the square root of the number of conditioning factors for classification (Couronné et al. 2018; Gigović et al. 2019).

N_tree and N_try have been optimized to reduce errors and increase the accuracy (Gigović et al. 2019). In this study, we used the RF package in the R open-source software (R Core Team 2020) with N_tree = 1,000 and N_try = 3.

One of the features of RF is the allowance of variable importance investigation (Gigović et al. 2019). The RF variable importance is calculated using the Gini index (Gigović et al. 2019). The prediction power of conditioning factors based on the principle of impurity reduction is measured by the Gini index in classification or regression (Sarica et al. 2017). Land cover was the most important factor, followed by precipitation and NDVI in our study, based on variable importance.

2.6 SVM

SVM, introduced by Vapnik (1995), is a data mining ML approach used to solve problems in different fields (Vapnik 1995; Gigović et al. 2019; Jaafari and Pourghasemi 2019; Gholamnia et al. 2020). The SVM method is based on the risk minimization principle to separate two different classes using a linear hyperplane (Gigović et al. 2019; Jaafari and Pourghasemi 2019). SVM generates a separating hyperplane and changes the nonlinear problem to a linear problem (Jaafari and Pourghasemi 2019). The optimal hyperplane can be found when there are maximal separations between the margins of the different classes of the problem (Gholamnia et al. 2020).

In SVM implementation, different kernel functions can be applied. RBF, polynomial, linear, and sigmoid kernels are the most common kernels used in SVM classification (Gigović et al. 2019). We used RBF as a kernel function for bushfire susceptibility mapping. The performance of the SVM model depends on two parameters, the kernel width (γ) and regularization constant (C), which should be adjusted properly (Gigović et al. 2019). We tuned the data to find the best values for γ and C for the model using the R open-source software.

2.7 LR

LR is a widely used approach for the natural hazard prediction (Hong et al. 2019). In bushfire modeling, LR creates a statistical relationship between the independent variable (bushfire occurrence) and dependent variables (conditioning factors) to determine the most accurate model to produce the probability of fire occurrence (Hong et al. 2019). LR uses Eq. (2) to find the best-fit model (Hong et al. 2019),

$$ Z = b_{0} + b_{1} x_{1} + b_{2} x_{2} + \ldots + b_{n} x_{n} . $$
(2)

where Z represents the existence or absence of bushfire, b0 is an equation intercept, b1, b2, …, bn are the model coefficients, and xi’s refer to the conditioning factors (Hong et al. 2019).

The probability of fire occurrence obtained by LR in each pixel can be expressed as (Hong et al. 2019)

$$ p = \frac{1}{{1 + e^{ - z} }}, $$
(3)

where p is the probability of fire occurrence (between 0 and 1) (Hong et al. 2019).

2.8 Ensemble methods

In this study, we proposed four ensemble techniques: GEPFR, RFFR, SVMFR, and LRFR. In order to run ensemble methods, we classified the different conditioning factors in ArcGIS. Then, weights for different classes were calculated using the FR given in Eq. (1). Maps of different classes of each factor were obtained using ArcGIS based on results from Eq. (1). The results were introduced as inputs to GEP, RF, SVM, and LR. Finally, the output was mapped in ArcGIS for GEPFR, RFFR, SVMFR, and LRFR.

2.9 Data validation

The area under the curve (AUC) of the receiver operating characteristic (ROC) and accuracy were used to evaluate the models. ROC is a nondependent threshold method commonly used to evaluate bushfire susceptibility models (Gigović et al. 2019). Accuracy is defined as a ratio of cases classified correctly to the total data (Hoang and Tien Bui 2018). Accuracy is another common quality metric between different models, calculated by

$$ {\text{Accuracy }} = \frac{TP + TN}{{TP + TN + FP + FN}}, $$
(4)

where false positive (FP) represents the number of pixels incorrectly classified as fire class, true negative (TN) represents the number of pixels correctly classified as nonfire class, true positive (TP) represents the number of pixels correctly determined as fire class, and false negative (FN) represents the number of pixels incorrectly classified as nonfire class (Hong et al. 2019).

3 Results

We generated the bushfire susceptibility map using ensemble techniques including GEPFR, RFFR, SVMFR, and LRFR and individual methods such as GEP, RF, SVM, and FR.

The mathematical formula generated from GeneExproTools by GEPFR is

$$ \begin{gathered} F = \left( {\frac{{\left( {d_{4} + d_{3} } \right)}}{2}} \right) \times {\text{log}}\left( {d_{3} } \right) + \frac{{\frac{{\left( {d_{1} + d_{2} } \right)}}{2} + \alpha }}{2} + {\text{log}}\left( {d_{6} ) + (d_{7} \times d_{5} } \right) + d_{7} \times {\text{arctan}}(d_{6} - \beta + 2\gamma + d_{7} ), \hfill \\ \alpha = 7.52, \beta = - 5.83 ,\gamma = 7.05, \hfill \\ \end{gathered} $$
(5)

where d1 is the slope, d2 is the altitude, d3 is the NDVI, d4 is the distance to road, d5 is the land cover, d6 is the annual maximum temperature, and d7 is the annual mean precipitation.

The bushfire susceptibility map generated by the GEPFR is presented in Fig. 5A. The majority of the study area was categorized as having a very low possibility of bushfire using the GEPFR method. The coastal area is covered by moderate to very high possibility of bushfire, while the western area has a very low possibility of bushfire. The AUCs of the GEPFR model in the training and testing sets were 0.892 and 0.890, while the accuracies were 92.45% and 92.69%, respectively (Table 1).

Fig. 5
figure 5

Bushfire susceptibility mapping using ensemble methods. A GEPFR, B RFFR, C SVMFR, and D LRFR. The spectrum of dark green (very low) to red (very high) represents the probability of bushfire

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Table 1 Performance of different methods
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We also generated a bushfire susceptibility map using the RFFR model (Fig. 5B), which similarly labeled the majority of the study area as having a very low possibility of bushfire. The northeastern, eastern, and southeastern parts of NSW were predicted to have a very high potential for bushfires. The RFFR model had an AUC of 0.895 for the training set and 0.875 for the testing set. The accuracies for training and testing were 95.29% and 94.70%, respectively (Table 1).

The majority of the map was covered by a low possibility of bushfire in the susceptibility map generated by SVMFR (Fig. 5C). The northeast, east, and southeast were covered by a very high possibility of bushfires, but SVMFR was not successful in finding areas with a high potential for bushfires in the study area. SVMFR had AUCs of 0.796 and 0.753 and accuracies of 94.54% and 94.28% in the training and testing sets, respectively (Table 1).

The bushfire susceptibility map generated by LRFR (Fig. 5D) shows that the west and central parts of NSW have very low possibility of bushfire. The northeast, east, and southeast exhibited moderate to very high potential for bushfires. The AUCs for the training and testing sets were 0.890 and 0.887, respectively. The accuracies in the training and testing sets were 93.50% and 93.67%, respectively (Table 1). The model generated by LRFR is

$$ z = - 5.039 + 0.143 \times A + 0.169 \times S - 0.170 \times E + 0.074 \times N + 0.028 \times D + 0.274 \times L - 0.273 \times T + 0.338 \times P $$
(6)

where A is aspect, S is slope, E is elevation, N is NDVI, D is distance to road, L is land cover, T is annual maximum temperature, and P is annual mean precipitation.

Individual methods were also used to generate susceptibility maps to compare their results with those of ensemble methods. The individual methods included GEP, RF, SVM, and FR.

The bushfire model generated by GEP (Fig. 6A) shows that the study area is mostly covered by a low possibility of bushfire in the western and central parts of NSW. The northeast, east, and southeast are covered by a moderate to very high possibility for bushfires. GEP had AUCs of 0.884 and 0.882 for the training and testing sets, respectively. The accuracies of the GEP model in the training and testing phases were 91.92% and 91.89%, respectively (Table 1).

Fig. 6
figure 6

Bushfire susceptibility mapping using single methods. A GEP, B RF, C SVM, and D FR. The spectrum of dark green (very low) to red (very high) represents the probability of bushfire

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The bushfire map generated by RF (Fig. 6B) in the central and western parts shows a very low possibility of bushfire, while smaller areas in the northeast, east, and southeast are categorized with very high possibilities for bushfires. RF had AUCs of 0.902 and 0.876 in the training and testing sets, while the accuracies were 95.47% and 94.51%, respectively (Table 1).

We also generated a bushfire susceptibility map using SVM (Fig. 6C), which is similar to the map generated by SVMFR. The majority of the study area is categorized as low-possibility class for bushfires. The northeast, east, and southeast are covered by a very high potential for bushfires. SVM had AUCs of 0.868 and 0.781 in the training and testing sets, respectively. The SVM had accuracies of 96.03% and 94.21% in the training and testing sets, respectively (Table 1). Similar to SVMFR, this method is not successful in finding areas with a high potential for bushfire occurrence.

The bushfire susceptibility map generated by FR (Fig. 6D) shows a very low potential in the west and low possibilities in the central NSW. The northeast, east, and southeast of the area are covered by moderate to very high potential for bushfires. FR had an AUC of 0.888 and accuracy of 87.20% (Table 1).

The generated bushfire susceptibility maps (from different individual and ensemble methods) were reclassified using the natural break classification method. Finally, the generated maps were categorized into five different subclasses (very low, low, moderate, high, and very high).

The west and central areas of NSW were categorized with very low to low possibility for bushfire in all maps generated by different individual and ensemble methods. The northeast, east, and southeast of NSW in different methods have moderate to very high potential for bushfires. The bushfire susceptibility maps generated by RF and RFFR categorized the majority of the area into two categories: very low and very high; however, the other methods allocated areas in all five possibility classes.

4 Discussion

We presented a GEPFR approach for modeling bushfires in NSW, Australia. The majority of bushfires occurred in the eastern, northeastern, and southeastern regions of NSW, possibly due to the high vegetation and forest in those areas. Our findings showed that the land cover and precipitation had significant impacts on the occurrence of bushfires. Bushfires are more common in particular land cover types, such as native forests and grazing lands (Deb et al. 2020). Another study also showed that forests had the highest potential for fire occurrence among land covers due to the availability of massive loads of fuel (Zhang et al. 2015).

The majority of bushfires are located in mountainous and coastal regions in our study area. Previous studies also demonstrated that mountainous and coastal areas have a high potential for bushfire occurrence (Zhang et al. 2015; Sun et al. 2016).

The annual mean precipitation was highest in the eastern part of NSW, compared to the western and central parts of NSW. The annual mean precipitation is one of the most important factors in our study area. Our results showed that the precipitation had a strong positive correlation with the bushfire occurrence. Similarly, a previous study has shown that the precipitation increases the amount of vegetation, resulting in a higher risk of flammability (Collins et al. 2014). A positive correlation between bushfires and precipitation was also reported in southeastern Arizona, which indicates the availability of higher fuel loads as a result of a higher precipitation (Crimmins and Comrie 2005; Nicholls and Lucas 2007). The precipitation can increase the moisture content, which is expected to reduce the bushfire occurrence. On a large scale, the precipitation can increase the available fuel for bushfires, which is the reason for the positive correlation between the bushfire occurrence and precipitation (Zhang et al. 2015). Another study also showed a substantial positive nonlinear association between cumulative antecedent rainfall (over several years) and occurrence of fires in central Australia (Nicholls and Lucas 2007; Griffin 2017). Similarly, widespread wildfires in northern Australia occurred after periods of above-average rainfall (Felderhof and Gillieson 2006; Nicholls and Lucas 2007).

In NSW, the temperature is higher in the central and western parts. However, our results indicate that these regions have a low probability of bushfire. The western and central parts also have the highest temperature and lowest annual precipitation rate. As a result, the fuel load in these areas is lower than those in other areas. This could be the reason for the classification of the western areas of NSW with a low possibility for bushfires.

Our results show that forest-covered areas have a moderate to high probability of bushfires in the generated prediction maps. The area with a low potential is mostly covered by shrublands and grasslands. Similarly, other studies have shown that the forest land cover has a strong positive correlation with bushfire occurrence, whereas the lowest bushfire probability belonged to shrublands (Zhang et al. 2016).

One advantage of FR is the simplicity of the procedure while it might not be suitable for complex problems. LR also has an advantage to elaborate the best variable for determining spatial patterns of the problem. SVM and RF can handle nonlinear and complex problems, but SVM takes a longer period of processing time and RF does not create an explicit formula for the problem. However, GEP can provide formula for the problem unlike traditional methods and it is fast and easy to understand for the user.

The comparison of the maps created by different methods show that the GEPFR method has the highest AUC, while the others have almost the same AUCs except SVM and SVMFR which have the lowest AUCs. The predictions by RFFR and RF are similar. They categorized the data in almost two groups, while GEPFR, LRFR, GEP, and FR classified the data in various classes with very low to very high potential of bushfire. The maps obtained by SVM and SVMFR are almost the same, but the map generated by SVM has a higher AUC. GEPFR allocated the majority of the study area to very low potential for bushfire, while GEP categorized the majority of the study area with a low potential for bushfire. GEPFR, RFFR, and LRFR determined that land cover and precipitation were the most important factors in bushfire susceptibility mapping.

5 Concluding remarks

In this study, we investigated an application of GEP for bushfire susceptibility mapping. GEP is a novel approach which can help managers, authorities, and researchers to have better understanding of the bushfire and have better management to reduce adverse impact of bushfires. We applied eight different methods, including ensemble methods of GEPFR, RFFR, SVMFR, and LRFR and individual methods such as GEP, RF, SVM, and FR, for bushfire susceptibility mapping in NSW, Australia. The prediction models in our research showed that the eastern, northeastern, and southeastern parts of NSW had the highest probability of bushfires, which are mostly covered by forest. In contrast, the western and central parts of the study area have a very low potential in the bushfire susceptibility mapping, while these areas have the highest temperature and lowest precipitation. The western and central parts of NSW are also covered with shrublands, grasslands, and croplands. GEPFR was the best method for the prediction of bushfires in NSW, Australia. GEPFR is a user-friendly method and thus suitable for the prediction of bushfires in different bushfire-prone areas. It should be noted that more conditioning factors and applications of other artificial intelligence methods could be used in future research to provide better understanding of bushfire behavior.