Estimating the Surface Fuel Load of the Plant Physiognomy of Cerrado Grassland Using Landsat 8 OLI Products

1. Introduction

Fire is common in the Cerrado biome, mainly in open plant physiognomies predominated by herbaceous and grassland vegetation. According to Miranda et al. [1], fires in the Cerrado, like in other savannas, can be characterized as surface fires that consume the fine fuels of the grass fuel layer. Surface fine fuels represent the layer of particles less than 0.6 cm in thickness, consisting of litter, grasses, herbs, and downed woody material [2]. For Rothermel [3], the fuel represents the organic matter available for ignition and combustion and characterizes the only fire-related factor that can be controlled by human action. Knowing the fuel characteristics is essential to determining fire behavior and decision-making in integrated fire management and wildfire suppression actions. However, determining the characteristics of the fuel is temporally and spatially complex [4,5]. Arroyo et al. [6] reported that determining fuel characteristics demands high costs and considerable time for sampling. Roberts et al. [7] indicate the following essential attributes in understanding fire behavior: fuel type, fuel biomass, fuel moisture, and fuel condition (live or dead). Fuel load is a crucial variable, commonly used fuel characteristic in various fire management strategies, such as fire risk assessments and fire behavior prediction [3]. Nevertheless, there are few studies on the Cerrado that involve determining the characteristics of its flammable material.

Remote sensing techniques are essential for estimating several fuel characteristics as more studies and improvements are made. According to Roberts et al. [7], the products obtained from various remote sensing techniques can help assess wildfire hazards, which include the following: (i) direct measurements of live fuel moisture, (ii) measurements of live herbaceous biomass, (iii) measurements of fuel condition, (iv) detailed classifications of fuel type. Van Wagtendonk and Root [8] note that information relative to fuel is often presented as fuel model maps; fuel models are used to determine fuel load, size, depth, and moisture of extinction. A wide range of studies have estimated fuel variables through remote sensing products. However, there is a significant lack of studies concerning the surface fuel of grassland environments of the Cerrado biome. Several studies characterize and estimate forest biomass using Landsat imagery [9,10,11,12], MODIS products [13,14], and Lidar sensors [15,16]. Various studies that use remote sensing products mostly relate to the characterization of forest variables, but few works with estimates of surface fuel variables, which are more related to the occurrence of surface fires, quite recurrent in grassland and savanna areas.

The use of vegetation indices has been widely addressed. They are utilized in biomass studies and mainly to determine the fuel moisture [17,18]. Other studies using spectral mixture techniques have been conducted [19,20]. However, few are related to determining surface fuel's physical characteristics, except for Franke et al. [21], who applied spectral mixture techniques to map fine fuel accumulation. In this sense, the main objectives of the present study are as follows:

(1)

To evaluate the performance of multiple linear regression equations adjusted for load estimation in classes of live and dead fine fuels, considering the beginning and end of the dry season, based on the reflectance of Landsat 8 OLI images, vegetation indices, and fraction values (F-values) of the spectral mixture analysis (SMA);

(2)

To assess the use of Random Forest and k-Nearest Neighbor algorithms to estimate fine fuel load in different classes in comparison to traditional multiple linear regression analyses;

(3)

To analyze the importance of each predictor variable from remote sensing products in Random Forest models.

2. Materials and Methods

2.1. Study Area

Collections in the field were made in the central southern portion of the Serra Geral do Tocantins Ecological Station (EESGT), a fully protected conservation unit with an area of 716,306 ha located in the Cerrado biome in the Jalapão region. According to the Köppen climate classification, the region’s climate is classified as Aw (tropical savanna climate), and its annual precipitation ranges from 1,400 to 1,500 mm [22], which is higher than the annual potential evapotranspiration. In the region, the summer occurs between October and April and is rainy, and winter occurs between May and September and is dry [23]. The predominant plant physiognomy is grassland: pure grassland (campo limpo), pure wet grassland (campo limpo úmido), grassland with scattered shrubs and trees (campo sujo), wet grassland with scattered shrubs and trees (campo sujo úmido), and rocky grassland (campo rupestre) [24,25]. The predominant type of soil type is quartz sand or quartzipsamments, and it has a sandy or loamy texture at least two meters deep and may have up to 15% clay. The location’s relief varies from relatively flat to gently undulating, with average elevations between 300 and 500 meters [26]. Figure 1 presents the study area and the spatial distribution of sampling data units.

2.2. Field Survey

A field survey of the variables of surface fuel load was conducted by installing data sampling units that were collected during the period from 05/11/2017 to 05/31/2017 (May), from 06/06/2017 to 06/29/2017 (June), from 08/05/2017 to 08/25/2017 (August) and; from 09/08/2017 to 09/24/2017 (September). Average air temperatures at the time of samplings ranged from 24.4 to 31.0 °C from the beginning (May and June) to the end (August and September) of the dry season, respectively. The relative humidity of the air presented averages at the time of samplings, which varied from 41.0 to 27.3% from the beginning to the end of the dry season. Each sampling unit had two 30-meter transects spaced 14 meters apart. Markings were made on the transects to install by prior draw eight sub-samples of surface fuel with an area of 0.25 m² (0.5 x 0.5 cm), and fuel was collected from them by the destructive method. The size of the sub-samples was chosen for a broader sampling that could provide a more significant variability of fuel samples in a shorter time. Accordingly, 64 data sampling units separated by a distance over 100 m from each other were collected for analyses by satellite images. It is noteworthy that data sampling was carried out in the area of viable access, given the existence of an area of difficult access further north (Figure 1).

The destructive sampling involved separating the material according to its physiological state (live or dead) among different diameter classes (timelag), adapting the methodology proposed by Schroeder and Buck [27] and Brown et al. [2]. Thus, the surface fuels were classified as follows: (i) dead grass fuel, (ii) 1-h downed wood debris (<0.64 cm diameter), (iii) live grass fuel, and (iv) live shrub fuel (<0.64 cm diameter). As the study aims to estimate fine fuels under 0.64 cm in diameter, which exert more significant influence on fire spread in regions with open vegetation in the Cerrado biome, the 10-h (0.64 - 2.54 cm) and 100-h (2.54 - 7.62 cm) classes are not considered. In addition to the abovementioned classes, the analyses and estimates took into account the total fine live (grass + shrub <0.64 cm diameter) and fine dead (grass + 1-h downed wood debris) fuels and the total fine fuel load (live and dead; <0.64 cm diameter). After collecting the sub-samples from the field, they were all dried until they reached constant mass. Next, the dry mass was determined, and its respective fuel moisture content was calculated by the ratio between wet mass and dry mass on a dry weight basis and then converted to percentage. Figure 2 presents a diagram exemplifying the collection locations, surface fuel data sampling, and characterization process.

2.3. Obtaining and Processing Satellite Imagery

Images from the Landsat 8 OLI satellite were used in this study. They were obtained for the approximate dates of four collections of field samples during the dry season in May and June (beginning of the dry season) and in August and September (end of the dry season), corresponding to the following dates (mm/dd/yyyy): 05/05/2017, 06/06/2017, 06/22/2017, 07/24/2017, 08/09/2017, and 09/10/2017. To cover the entire study area, images from 3 Landsat 8 OLI scenes were used, namely: 220/067; 221/067, and; 221/068. The reflectance values of the bands were extracted, and the vegetation indices were calculated through the cloud-based geospatial data processing platform Google Earth Engine (GEE). The GEE platform provides easy access to high-performance computing resources for large-scale processing of geospatial datasets [28]. The reflectance values were obtained from the Landsat 8 OLI sensor bands in the following channels: (i) blue (0.45 - 0.51 µm), (ii) green (0.53 - 0.59 µm), (iii) red (0.64 - 0.67 µm), (iv) near-infrared (0.85 - 0.88 µm), (v) short-wave infrared (1.57 - 1.65 µm), and (vi) short-wave infrared (2.11 - 2.29 µm).

2.3.1. Vegetation Indices (VIs)

Based on the combination of reflectance in different spectral bands, vegetation indices (VIs) were calculated. VIs are an efficient way to attain empirical information from multispectral sensors and are frequently used in various scientific studies that set out to explain better or determine the behavior of certain vegetation variables [8,9,29,30]. Therefore, a total of 20 vegetation indices were calculated and incorporated into the analyses as independent variables: (i) Normalized Difference Vegetation Index - NDVI [31]; (ii) Visible Atmospherically Resistant Index - VARI [32]; (iii) Visible Green Index - VIgreen [32]; (iv) Simple Ratio - SR [33]; (v) Structure Insensitive Pigment Index - SIPI [34]; (vi) Soil-adjusted Vegetation Index - SAVI [35]; (vii) Normalized Difference Water Index - NDWI [36]; (viii) Normalized Difference Infrared Index - NDII6 [37]; (ix) Normalized Burn Ratio - NBR [37]; (x) Modified Vegetation Index - MVI [38]; (xi) Modified Simple Ratio - MSR [39]; (xii) Moisture Stress Index - MSI [40]; (xiii) Modified Normalized Difference Water Index - MNDWI [41]; (xiv) Integral - INT [42]; (xv) Global Vegetation Moisture Index - GVMI [29]; (xvi) Enhanced Vegetation Index - EVI [43]; (xvii) Derivative - band 5 (ivp), band 6 (siwir1) - DER56 [44]; (xviii) Derivative - band 4 (vm), band 5 (ivp) - DER45 [44]; (xiv) Derivative - band 3 (vd), band 4 (vm) - DER34 [44]; (xx) Derivative - band 2 (az), band 3 (vd) - DER23 [44]. The vegetation indices analyzed in this study show relationships with fuel load and moisture, as well as with the physiological state of the fuel. The choice of these vegetation indices aimed to analyze their viability for estimating fuel load from Landsat 8 OLI images, considering seasonality during the dry season in a Cerrado environment.

2.3.2. Spectral Mixture Analysis (SMA)

The spatial variability of vegetation within a pixel is a strong limiting factor in ascertaining fuel condition and load information. Spectral Mixture Analysis (SMA) has considerable potential to estimate fuel condition and fuel moisture content at the sub-pixel level [30]. SMA is a widely applied technique in remote sensing for obtaining ecologically relevant and significant components of an image pixel [45]. In SMA, two or more reference spectra (endmembers), such as green vegetation, dry vegetation, soil, and shade, are modeled as linear combinations to estimate the sub-pixel fractions of each component [46].

After retrieving the Landsat 8 OLI images, they underwent the atmospheric correction process to eliminate interferences from the atmosphere to extract data and determine the reflectance values [47]. Next, the color composites were obtained and utilized in subsequent study steps. The color composite of the Landsat 8 OLI image used in the initial collection for the spectral mixture analyses was 7 (short-wave infrared - SWIR 2), 5 (near-infrared), and 4 (red). After processing the satellite images, the creation of a spectral library began. First, the surface targets for the SMA were divided into (i) non-photosynthetic dry vegetation (NPV), (ii) green vegetation (GV), and (iii) exposed soil. This classification was chosen because green vegetation, dry vegetation, and soil dominate Cerrado grassland environments. Figure 7 presents the fuel condition mapping demonstrating the accumulation of GV, NPV fuel, and soil from the EESGT contrasting the early and late dry season condition fuel in the Cerrado biome. Several candidates for “pure pixels,” known as endmembers, were selected from each target. Thus, based on the specific spectral behavior of each target, regions of interest (ROI) whose reflectance presented spectral behaviors that were as faithful as possible to the characteristic spectral curve of the respective target were delimited.

To fulfill the objectives proposed herein, endmembers were chosen in four representative images of the four months of the dry season (May, June, August, and September), according to the dates of the Landsat 8 images previously mentioned. Having chosen all the pure pixel candidates of the features as mentioned earlier based on the spectral curves, the process of selecting the endmembers based on the lowest statistical errors began. The multiple endmember spectral mixture analysis (MESMA) methodology was applied to perform this procedure. MESMA’s results produce gray-scale images whose values (called fraction values – F-values) represent the estimated relative degree in which each pixel corresponds to its respective reference spectrum. Therefore, the images generated with the F-values were for the GV, NPV, and soil components.

2.3.3. Data Extraction

The pixel values associated with the field plots were extracted from a 3 x 3-pixel window around the reference pixel (pixel associated with the field plot). This way, the median values of the pixels in each 3 x 3-pixel polygon related to the field plots were extracted [9,10,48,49,50,51,52]. The data were exported and tabulated to compare the information collected from the plots in the field with the information from the spectral mixture analysis, reflectance, and the calculated vegetation indices.

2.4. Statistical Analysis of the Data

2.4.1. Multiple Linear Regression Analysis

After processing the data from the Landsat 8 OLI satellite images, all the information associated with the collection points in the field were extracted in a 3 x 3-pixel window. Then, all the data were tabulated and correlated with the fuel load values in the different classes. In the multiple linear regression analyses, fuel load was a dependent variable, especially for the fine dead fuels (dead grass fuel, 1-h downed wood debris, and total fine dead fuel) and total fine fuel (live and dead, <0.64 cm diameter) classes. The predictor (independent) variables were divided into three main groups: (i) fraction values (F-values) from the spectral mixture analyses (SMA), (ii) the reflectance of the Landsat 8 OLI images in the different spectral bands, and (iii) the calculated vegetation indices. The stepwise method was adopted to select the most relevant variables for the regression equations. Also, the adjustments of the multiple linear regression equations considered the following: (i) adjusting equations considering 32 plots collected in the initial months of the dry season (May and June), (ii) adjusting equations considering 32 plots collected in the final months of the dry season (August and September), and (iii) adjusting equations for the entire period of the dry season (all 64 plots). Figure 3 presents a flowchart of the methodology applied in this study.

2.4.2. Random Forest Machine Learning Algorithm

The Random Forest (RF) machine learning algorithm is a non-parametric method developed by Breiman [53] that has been widely adopted in various studies [11,14,51,54]. The RF algorithm combines several predictor trees generated by an independently sampled random vector with a similar distribution for all trees in the forest [55]. Compared to traditional linear regression methods, Random Forest models exhibit several advantages in aboveground biomass estimation, such as better accuracy and fewer non-linear problems [56].

Although the training and test sets were divided randomly in R, a specific code command (set seed) was used to guarantee the model’s reproducibility, in other words, to run the model with the same previously defined data sets (training and test). To implement Random Forest, two parameters must be defined: the number of trees (ntree) and the number of features in each split (mtry). Regarding the ntree, in the present study, it was observed that the prediction accuracy by the Random Forest algorithm did not increase significantly when the ntree presented values greater than 1,000. The ideal ntree defined was ntree = 1,000 to guarantee the reliability of the prediction results without affecting computational efficiency [57,58]. For mtry, the values were defined as one-third of the total number of predictor variables [53,59,60,61]. These varied between mtry = 4 and 5 for models adjusted with predictor variables selected by the stepwise method and mtry = 10 for models adjusted with all predictor variables. The “randomForest” package in R program was used to apply the algorithm. The importance of the predictor variables utilized in the Random Forest models was evaluated by the increase in the mean squared error (% IncMSE), which measures the effect of a variable’s predictive potential when subjected to a random permutation. In short, this metric shows how much the model’s accuracy decreases if a particular predictor variable is left out of the model.

2.4.3. K-Nearest Neighbor Machine Learning Algorithm

Another machine learning algorithm used to verify the feasibility of estimating fuel load from satellite imagery products was the k-Nearest Neighbor (k-NN) algorithm. The k-NN algorithm is used for classification and regression. It predicts the values of specific variables based on the similarity in a covariate space between the point and other points representing the values of the variables [62]. The utilization of the k-NN algorithm associated with remote sensing data has played a key role in forest studies, and there have been several applications in forest inventories in the field that aimed to improve the accuracy of estimates [63,64]. The k-NN algorithm was applied employing the “Caret” package in R. There is one essential parameter in this algorithm, K, or the number of neighbors that need to be optimized. This parameter specifies the voting system in the k-NN algorithm wherein the K nearest neighbors are selected, and then it sets the output model [65]. The K values were determined based on the lowest RMSE values, and the optimal values were chosen for each estimated fuel variable. Table 3 provides each estimated fuel variable's selected K values and the respective RMSE values.

2.4.4. Cross-validation

Cross-validation evaluates a model’s performance and provides a nearly unbiased prediction error estimator [66]. The multiple linear regression equations, Random Forest models, and k-NN algorithm models were subjected to cross-validation with the k-fold cross-validation technique, using 10 folds. The k-fold cross-validation technique is a robust method for estimating a model’s accuracy, and it generally provides more accurate estimates of the test error rate [9,67,68]. The following statistical metrics were used to validate the equations: (i) the values of the squared coefficient of determination (R²), (ii) the adjusted squared coefficient of determination (R²adj), (iii) the root-mean-square error (RMSE), and (iv) the mean absolute error (MAE). The validations considered the adjustments of the multiple linear regression models and the Random Forest and k-Nearest Neighbor algorithm models, with an emphasis on the models with the best fit considering all the independent variables of the study and on the models with the best fit considering the independent variables selected by the stepwise method.

3. Results

3.1. Multiple Linear Regression Analysis

Table 1 presents the metrics of the multiple linear regression equations, which were validated by considering the study's independent variables. The multiple linear regression equations performed best with the adjustments by the stepwise method. Table 1 presents only the metrics of the equations adjusted by this method. The equations validated by the k-fold cross-validation method, which were notable about the coefficient of determination (R²), were for the estimation of total fine dead fuel (grass + 1-h downed wood debris), with R² = 0.92, and dead grass fuel, with R² = 0.89. These equations mentioned earlier are for the beginning of the dry season (p < 0.05). However, the lowest RMSE and MAE values were observed for estimates of dead grass fuel at the beginning of the dry season, with values below 0.40. The statistical metrics verified for the end of the dry season were lower than those observed for the equations adjusted for the beginning of the dry season in the study area.

For the entire period of the dry season, the R² values ranged from 0.57 to 0.78. The equation for estimating dead grass fuel performed the best, with R² = 0.78, followed by the stepwise equation for calculating total fine dead fuel (grass + 1-h downed wood debris), with R² = 0.73 (p < 0.05). The R²aj values of the equations subjected to cross-validation may be negative without a lower limit and present a maximum value of one, as noted by Peterson et al. [69], which was the case for the equations at the end of the dry season. The lowest RMSE and MAE values were found to estimate dead grass fuel.

3.2. Estimates by the Random Forest Algorithm

3.2.1. Model Performance Metrics

To use the Random Forest algorithm, the entire dry season was considered for the adjustment of the models. The models were not divided for the dry season's beginning and end, as was done for the multiple linear regression analyses. Like the regression equations, the Random Forest algorithm was adjusted for each estimated variable by considering all the study's independent variables and the variables selected by the stepwise method. Unlike the multiple linear regression equations, the Random Forest models presented a slight advantage in the adjustments with all the independent variables compared to the adjustments with the variables selected by the stepwise method, as shown in Table 2. The R² values by the Random Forest algorithm ranged from 0.52 to 0.83; the highest values were found to estimate dead grass fuel and total fine dead fuel.

To estimate the total fine fuel (live and dead), the best performance was related to the model using all the independent variables, with R² = 0.62. As for the RMSE and MAE values of the estimates by the Random Forest algorithm, the lowest values were recorded for the estimation of dead grass fuel, with 0.33 and 0.23, respectively. In contrast, the highest RMSE and MAE values corresponded to the estimation of total fine fuel load (live and dead). Figure 4 and Figure 5 show the fine fuel load mappings in the Serra Geral do Tocantins Ecological Station, with the best fits for each fuel load category analyzed.

3.2.2. Importance of the Variables in the Random Forest Models

In analyzing the results of the importance of the variables in the RF models presented in Figure 6, the considerable importance of the fraction-soil variable (FS – F-values) from the spectral mixture analysis (SMA) is noteworthy in all the models addressed. In all situations, the FS variable increased the mean squared error (% IncMSE) above 20% in all the models presented. This means that the removal of the predictor variable FS will result in an increase in the mean squared error above 20% for the estimated fuel variables. Among the fuel variables in which FS exerted greater importance, total fine dead fuel (grass + 1-h downed wood debris) and dead grass fuel were notable, presenting values of 33.5% and 29.1%, respectively.

The vegetation indices NDII, NBR, GVMI, and DER56 emerged as the second most essential variables considering the estimates of dead grass fuel, 1-h downed wood debris, total fine dead fuel (grass + 1-h downed wood debris), and total fine fuel (live and dead), respectively. GVMI appeared most frequently among the vegetation indices and was most important in the fitted Random Forest models. It was not a variable of importance only for estimating total fine fuel. Out of the bands' reflectance, the short-wave infrared channel (SWIR2 - 2.11 - 2.29 µm) occurred most frequently and had the most significant importance. Figure 6 graphically illustrates the importance of the Random Forest algorithm models with the best fit.

3.3. Estimates by the K-Nearest Neighbor Algorithm

Similarly, the data from the same database used for the application of the RF algorithm were executed with the k-Nearest Neighbor (k-NN) algorithm so that two models were built for each fuel load variable: one model considering all the independent variables of the study and another model considering only the variables selected by the stepwise method. As a parameter for using the k-NN algorithm, the K values were chosen based on the lowest RMSE values, ranging from 5 to 13. Table 3 demonstrates the K values chosen for each k-Nearest Neighbor algorithm model.

Like the Random Forest models, the k-Nearest Neighbor models presented slightly superior performances for the adjustments made with all the predictor variables of the study in comparison with those selected by the stepwise method. The R² values ranged from 0.30 to 0.68, and the k-NN models with the best fit were for estimating dead grass fuel, followed by the model for estimating total fine dead fuel, with R² = 0.54. Table 4 provides the statistical metrics of the k-NN algorithm models.

Regarding the RMSE and MAE values, the estimates by the k-NN algorithm presented the lowest values for the estimation of dead grass fuel, with 0.37 and 0.30, respectively. The highest RMSE and MAE values about the k-NN models were found to estimate total fine fuel load (live and dead) (Table 4).

4. Discussion

Given the low correlations of the live fuel classes (live grass and live shrub), the statistical analyses for their estimation could not be conducted. However, according to the findings of Santos et al. [70], the low moisture level for Cerrado grassland species is the main factor behind the increase in the fuel’s flammability. Moreover, the proportion of fine dead fuel about the proportion of live fuel during the dry season in the biome can reach 70%, or over 80%, considering only the grass fuel of the area, based on the fuel characterization by Santos et al. [71]. In addition, the fine thickness of 1-h and grass fuels in a physiologically inactive state (e.g., grass and 1-h downed wood debris) makes the moisture content of these fuels more sensitive to changes in atmospheric conditions, thus affecting their ignition capacity and leaving areas with a predominance of these types of fuels more prone to the occurrence of wildfires, especially in the dry season [72]. As reported by Slijepcevic et al. [73] and Soares et al. [74], low fuel moisture is one of the main factors contributing to the occurrence of large fires.

Out of the adjustments of the multiple linear regression equations for the beginning and end of the dry season in the Cerrado biome, the equations adjusted for the beginning of the dry season had the best statistical performance. This may be explained by analyzing the results obtained by Santos et al. [71], who characterized the fuel of Cerrado grassland vegetation. In this study, fuel characteristics, such as the number of individuals, the number of species, the grass height, and the fuel load in different classes (timelag), exhibit different behaviors between the first and last months of the dry season in the physiognomy under analysis. The fuel condition mapping showing fractions of NPV, GV, and soil for the beginning of the dry season (May) in contrast to the fuel condition at the end of the dry season (September) is presented in Figure 7. For example, given the different ages of the fuels present in the area, the load values of dead grass fuel in the first months of the dry season (May and June) showed a statistically significant difference in dead grass fuel between the ages of one and four years. By the end of the dry season (August and September), no statistically significant difference was found among the fuel loads of dead grass fuels between the ages of two and four years (p < 0.05).

Considering all the adjustments of the multiple linear regression equations in the study (beginning, end, and the entire dry period), the R² values ranged from 0.45 to 0.92. For the whole of the dry period, the highest value was 0.78 for the adjusted equation to estimate dead grass fuel (Table 1). Similar results were reported by Tucker et al. [75], who presented more expressive values considering only coefficient of determination (R²) values and the 0.385 µm range of the electromagnetic spectrum as the predictor variable to estimate total dry biomass (R² = 0.80). Using Landsat 5 TM imagery to estimate aboveground biomass in interior Alaska, Ji et al. [9] obtained an R² value of 0.73 in their regression model. In one of the few studies conducted in the Cerrado, Franke et al. [21] found relationships between variables obtained from spectral mixture analyses and the biomass of fine surface fuels in their regression model, with R² values of 0.81 (fraction of non-photosynthetic dry vegetation - FNPV) and 0.65 (fraction-soil - FS). The results of Franke et al. [21] differ from those of the present study: between the variables given by the spectral mixture analysis and fuel load, the most substantial relationships were found for the fraction-soil (FS) values. However, the linear regression models fitted by Franke et al. [21] did not consider a cross-validation analysis. It is possible to note that there are few studies on estimating surface fuel from satellite imagery, especially for the Cerrado biome.

Like the adjustments of the multiple linear regression equations, the models resulting from applying the Random Forest algorithm with better performance based on the evaluation metrics were for estimating dead grass fuel classes and the total fine fuel class (grass + 1-h downed wood debris). They presented higher values than the other classes, reaching an R² = 0.83. The statistical metrics obtained for estimating 1-h downed wood debris fuel load demonstrated poor performance in relation to the other variables (Table 2). This may be explained by less spatial continuity compared to the dead grass fuel present in the study area. Dube and Mutanga [76] used Landsat 8 OLI and 7 ETM+ images and the reflectance of the bands and vegetation indices as predictor variables. They tested the Random Forest algorithm to estimate aboveground biomass in southern Africa and found coefficient of determination (R²) values ranging from 0.43 to 0.65. Pierce et al. [77] used the RF algorithm and information from Landsat 5 TM, field data, and topographic factors for modeling and mapping canopy fuels in California (USA) and attained pseudo-R² values ranging from 0.55 to 0.68. Frazier et al. [11] characterized the aboveground biomass in a boreal forest using Landsat temporal segmentation metrics and found R² values of 0.62 estimated by Random Forest models. Gao et al. [14] found higher R² values (0.75) using MODIS sensor data to estimate aboveground biomass in a region in Asia.

As for the importance of the variables of the RF models with the best fit, for the dead fuel classes (dead grass, 1-h downed wood debris, and total fine dead fuels) and total fine fuel (live and dead), the fraction-soil (FS) variable from the spectral mixture analysis (SMA) was the independent variable that exerted the most significant importance. These results corroborate the higher correlations between the FS variable and the variables obtained from the spectral mixture analysis. The physiognomy of Cerrado grassland is predominantly open (pure grassland and grassland with scattered shrubs and trees) and has a sparse population of tree species. Given the age of the fuel and its level of cover, greater or less soil exposure becomes quite noticeable in the response of the spectral mixture analysis, which demonstrated an inverse relationship with surface fuel load. Despite the importance of the FS variable in the RF models, there is no knowledge of its performance in areas with a greater presence of tree species. At least five vegetation indices, namely NDII, GVMI, DER56, NBR, and MSI, had a degree of importance concerning %IncMSE above 10%. All these vegetation indices reveal the presence of the near-infrared (NIR: 0.85 - 0.88 µm) and short-wave infrared (SWIR1: 1.57 - 1.65 µm, SWIR2: 2.11 - 2.29 µm) channels in their respective calculations. This indicates the importance of the near-infrared and short-wave infrared channels for load estimates by both the RF models and multiple linear regression analyses. The near-infrared and short-wave infrared channels have been utilized to estimate vegetation characteristics in several settings [48,69].

Overall, the statistical metrics used to assess the models were superior for the RF models in relation to the multiple linear regression equations and the k-NN models. Thus, the models estimating the surface fuel of Cerrado grassland by the Random Forest algorithm with data retrieved from satellite images provided better estimates of the surface fuel. Only the total fine fuel variable (live and dead) estimated by the multiple linear regression analysis resulted in a slightly higher coefficient of determination (R²), considering the entire dry period in the study area. However, the RMSE and MAE values were higher than those of the Random Forest algorithm. Aligned with the results of this study, D'Este et al. [78] evaluated the performance of machine learning models in estimating the fine fuel load in a region of Italy. They observed greater predictive power for the Random Forest algorithm, with R² = 0.50, compared to multiple linear regression models (Multiple Linear Regression) and Support-vector Machines, which presented coefficients of determination of 0.40 and 0.39, respectively. Compared with the present study, despite different fuel characteristics, the R² values for estimating the fine dead fuel load (<0.64 cm diameter) by RF had a better performance (R² = 0.83).

The application of the k-NN algorithm to estimate the surface fuel of the plant physiognomy of Cerrado grassland was unsatisfactory, presenting lower statistical metrics than the multiple linear regression analyses and the Random Forest algorithm. This may be because the k-NN algorithm has a better performance and more comprehensive application in estimating forest variables [79,80,81] and due to little knowledge in the assessment of surface fuels.

5. Conclusions

The multiple linear regression analyses showed better statistical results for equations adjusted for the beginning of the dry season (May and June) than those adjusted for the end of the dry season (August and September). This behavior arises from the various changes in fuel characteristics in Cerrado grassland's physiognomy during the dry season's beginning and end. Therefore, modeling to obtain estimates for load, moisture, and other surface fuel characteristics should be performed separately and consider the seasonality throughout the year.

The use of the Random Forest algorithm contributed to improvements in the evaluation metrics for estimating the Cerrado grassland surface fuel load concerning the multiple linear regression analyses and k-Nearest Neighbors algorithm. Out of the predictor variables originating from the products of Landsat 8 OLI images, the fraction-soil variable from the spectral mixture analysis exerted the most significant importance for load estimation in the different classes analyzed herein. Accordingly, applying the RF algorithm and the fraction-soil variable is recommended for estimating the Cerrado's fuel load of open or savanna physiognomies. However, their performance in more closed physiognomies with a greater presence of tree species, for example, is unknown. Further studies must be conducted to verify the feasibility of using the products of different satellite images in different environments, especially in the areas more prone to fires in the biome.