Comparison of maximum likelihood estimators and 2 regression models in Mediterranean forests fires for 3 severity mapping using Landsat TM and ETM + Data 4

The severity of forest fires derived from remote sensing data for research and management 11 has become increasingly widespread in the last decade, where these data typically quantify the pre12 and post-fire spectral change between satellite images on multi-spectral sensors. However, there is 13 an active discussion about which of the main indices (dNBR, RdNBR or RBR) is the most adequate 14 to estimate the severity of the fire, as well about the adjustment model used in the classification of 15 severity levels. This study proposes and evaluates a new technique for mapping severity as an 16 alternative to regression models, based on the use of the maximum likelihood estimation (MLE) 17 automatic learning algorithm, from GeoCBI field data and spectral indices dNBR, RdNBR and RBR 18 applied to Landsat TM, ETM+ Images, for two fires in central Spain. We compare the severity 19 discrimination capability on dNBR, RdNBR and RBR, through a spectral separability index (M) and 20 then evaluated the concordance of these metrics with field data based on GeoCBI measurements. 21 Specifically, we evaluated the correspondence (R2) between each metric and the continuous 22 measurement of fire severity (GeoCBI) and the general precision of the regression and MLE models, 23 for the four categorized levels of severity (Unburned, Low, Moderate, and High). The results show 24 that the RBR has more spectral separability (average between two fires M = 2.00) that the dNBR (M 25 = 1.82) and the RdNBR (M=1.80), additionally the GeoCBI has a better adjustment with the RBR of 26 (R2 = 0.73), than the RdNBR (R2 = 0.72), and dNBR (R2 = 0.71). Finally, the overall classification 27 accuracy achieved with the MLE (Kappa = 0.65) has a better result than regression models 28 (Kappa=0.58) and higher accuracy of individual classes. 29


Introduction
Wildfire is a primary disturbance phenomenon with 200-500 million hectares being burned annually [1].Fires affect large areas in almost all terrestrial ecosystems from tropical to boreal, being more widespread than any other natural disturbance [2,3].In some ecosystems, e.g., savannas and grasslands, fire plays an ecologically significant role in biogeochemical cycles and disturbance dynamics, influencing the temporal variability in carbon, water, and energy fluxes.In other regions, fire may lead to the destruction of forests or to long-term site degradation.Specifically in Mediterranean countries, fire is a major hazard with an average of 45,000 fires being recorded every year, making it a substantial source of land degradation, burning an average of > 4 million hectares based on a 35-year average [4,5].
Therefore, fire constitutes one of the main factors determining the current forest landscape, these wildfires cause extensive ecological and economic losses [6] over hundreds of thousands of hectares.
In Spain, although the last decade (2001-2010) has seen a reduction in the number of fire incidents (averaging 17.127 per year), the occurrence of large fires (>100 ha) has increased, in 2012, 64% of the total area affected by fires was burned in a large fire [4,7].Even though Mediterranean species are adapted to natural fire regimes, changes in land use and the anthropogenic disturbances make vegetation communities more vulnerable to high-intensity wildfires [8]; however, these effects vary across the landscape depending on such factors as severity, intensity or recurrence of the fire [9,10].
Burn severity is a function of physical and ecological changes caused by fire, additionally, wildfires burn heterogeneously across landscapes with sections of unburned and lightly burned patches interspersed among severely burned patches, which is caused by the variability in weather, type of fire, and patch to landscape vegetation patterns.On the other hand, fire severity usually refers to changes in organic matter in stories after the wildfire.Information on burn severity and fire severity modelling is essential for land managers and ecologists who need to understand ecosystem processes especially for vegetation recovery [11], this information is also essential for emergency services for making decisions on allocating time and resources.Burn severity information is also necessary to reduce uncertainty in emission estimates [12], water quality and yield, and for the study of how burn severity affects albedo and energy partitioning [5].
Therefore, scientists and fire managers require the most accurate information available regarding the impact of fire on the environment.The key of this study, is to be able to plan better efforts for wildfire preparedness, and consequently, understand how this efforts translate to changes in actual fuel load/structure, leading this to subsequent changes in fire behavior and consequently, the fire damage potential and as well as for: vegetation recovery monitoring, wildlife studies, soil and hydrologic changes, among various ecological processes [13].Because fire causes a number of physical changes, including consuming different layers of vegetation strata, destroying leaf chlorophyll, exposing soil, charring stems and ground, changing soil chemical composition [14] and altering both above-ground and below-ground moisture [15]; the burn severity can be related directly to the degree of this change.Such physical transformation causes variations in surface reflectance, albedo, moisture and temperature, which can be detected by means of satellite and airborne imagery [16].Therefore, remotely sensed data can be used to measure the severity of the wildfire.
There is a wide range of remotely sensed platforms, along with applicable methods for determining the severity of a wildfire; however, the choice of approach depends on a set of particular circumstances, for instance, the conditions within the study region and the user spatial and temporal resolution needs, and the natural and climatic conditions of the study area; additionally, some sensors do not cover the required part of the electromagnetic spectrum, and vary in the number of available spectral bands.The availability of data also determines which method can be employed, such as burn algorithms, image differencing, spectral mixture analyses or fire radiative power.Within this range of remotely sensed platforms, there is a wide array of applicable methods for determining the mapping of wild land fire effects, commonly called "severity maps" [17].
Many studies have demonstrated the sensitivity of various spectral bands to significant changes in spectral radiance in burned vegetation, these spectral bands can reliably detect burnt areas, burn severity and vegetation changes.For example, near-infrared (NIR), short-wave infrared (SWIR) and thermal bands are found to be sensitive to burn magnitude changes in vegetation and are thus frequently used for fire effects studies in vegetated areas [14,18,19].Among the most common indices for studying burn severity from satellite imagery is the NBR, which is most sensitive to changes in the vegetation.The NBR is formulated like the normalized difference vegetation index (NDVI) except for the SWIR band (2.08 um to 2.35 nm) that is used instead of the red band.The NIR wavelengths are primarily sensitive to chlorophyll, while the SWIR wavelengths are primarily sensitive to water content, ash cover, and soil mineral content [13,18].
The NBR ranges between -1 and 1 but, in common practice, NBR is scaled by 1000 to transform it to integer format [19].The term severity involves a temporal evaluation, that is why the remotely sensed measures of severity aggregate fire effects at the time; Key  version called dNBR, to subtract a post-fire NBR from a pre-fire NBR for mapping fires in an absolute change detection methodology, so that barren areas unchanged by fire would not appear as high severity [19].However, one of the disadvantages of the differential indices used to map the severity is the ambiguity in the definition of the threshold of damage (Table 1), dNBR must be individually calibrated for each assessment of fire severity because of disparities in vegetation types and density [18,20].and RdNBR, improving the detection change even where pre-fire vegetation cover is low.
These spectral indices were calibrated from one-year-post-fire Landsat data to the field-collected through the Composite Burn Index (CBI), developed by Key and Benson [19] within the framework of the Fire Effects Monitoring and Inventory Protocol (FIREMON) project for pine forests in western USA, to sample these changes and to summarize the general effects of a fire at a given plot.The CBI and its modified version GeoCBI have been widely used as means for ground measurements of fire severity [24], and as an operational tool, GeoCBI visually assesses the magnitude of change by fire in five strata (soils, understory vegetation, mid-canopy, overstory, and dominant overstory vegetation) and integrates these for an overall burn severity level plot rated between zero (unburned) and three (highest severity) [19,25].
Usually, map products derived from satellite images-are produced using calibrations between the differenced spectral burn ratios (dNBR, RdNBR, RBR) to the field Burn Index (CBI, GeoCBI) percent change in tree basal area (BA), or in canopy cover (CC) [18].None the less, it can be difficult to relate field Burn Index values to immediate fire effects [18,20,23,25], mainly because the immediate effects of fire that satellite images show, cannot always be explained through the relationship with field-based assessments of burn severity under regression models, since they also depend on factors such as ecosystem type, vegetation structure or spatial distribution among others.For this reason, the identification of complex wildfire patterns and its understanding from remotely sensed images is the key issue of burn severity mapping research programs; and in this regard, data-driven artificial intelligence and machine-learning techniques are being increasingly used to classify multispectral remotely sensed data for practical applications such as wild fire monitoring [24,26]. In

Study Area
Our study area was located in two regions in central Spain within the grounds of the Pantano de San Juan (Madrid), and adjacent lands of Riba de Saelices Town (Guadalajara) (Fig. 1).The forest fire under study of the first area is relatively small, and it is located in south-eastern Madrid; in this case, this fire burned a total of 850 ha, with moderate to high severity, mainly composed of pine trees (Pinus pinea) mixed with semi-deciduous oaks and Mediterranean shrubs (Quercus ilex).This region has a moderate-dry climate with evenly-distributed annual precipitation of approximately 435 mm, and an annual daily mean temperature of 13 °C [27] (Table 2).(b) Riba de Saelices.Guadalajara.

Field Data Collection
The field-based assessment of burn severity used on both fires, was done accordingly to the standard protocol of the Geometrically structured Composite Burn Index (GeoCBI) proposed by De Santis and Chuvieco [25].This method for estimating burn severity have into account the fraction of coverage (FCOV) of each stratum in the original CBI protocol developed by Key and Benson [19], including in the influences of overall reflectance of every plot in the calculation: where m refers to each vegetation stratum and n is the number of strata.All vegetated strata are weighed by their FCOV; the substrates stratum is not weighted.Additionally, it is included the "new sprouts" rating factor to the herbs and low shrubs stratum, including the "percent change in cover" rating factor converted to "change in leaf area index (LAI)".
The GeoCBI plot locations on the two fires were selected via stratified random sampling.Plots were stratified by burn severity, forest cover, and accessibility.GeoCBI field measurements were taken in a maximal interval of twenty-five days after the ignition date of the burnt area.The size of the plots were 30 m per 30 m, in conjunction with another studies and Landsat spatial resolution [19,[28][29][30], the plots were located in fairly homogenous patches of a given burn severity type (90 m x 90 m).The collection of GeoCBI data was established and measured for four strata of the burn severity (unburned, low, moderate, and high), with a total of 190 plots in the two fires.On the Madrid fire, the GeoCBI was assessed with 61 plots, included ten control plots, and 103 plots on the Guadalajara fire plus 26 of control (Table 3).
Digital photos were taken from the center of each plot to the four cardinal directions to record the vegetation structure and soil condition, plus additional information.Individual coordinates of plot centers were recorded with a hand-held meter-level global positioning system (GARMIN 12 GPS), with a final accuracy of the horizontal position of sample points between an average of 5 to 15 meters.

Remote Sensing Data
The satellite images used in this study were acquired according to their availability and cloud  3).
For this study, we used the standard product level L1T (Standard Terrain Correction) processing at-sensor reflectance, which was corrected to ground reflectance in order to reduce the atmospheric effects on the images.The imagery was obtained from the Glovis server of the USGS (http://earthexplorer.usgs.gov),and the ESDI (Earth Science Data Interface) server from the University of Maryland (http://glcfapp.glcf.umd.edu:8080/esdi/).

Workflow
Our workflow (Figure 2) was composed of the following steps: imagery pre-processing (see Section 2.5), spectral index calculation (see Section 2.6), spectral separability analysis (see Section 2.7), burn severity classification (see Section 2.8), and accuracy assessment (see Section 2.9).
After pre-processing ETM+ and TM pre and post-fire images, multiple spectral indices were calculated.Then, the capability of the different spectral indices selected in discriminating the differences in burn severity levels was compared.Third, the adjust values of RMSE and R 2 obtained were determined in order to validate the discrimination accuracy (Section results), next, differentials images were calculated after selecting the optimal index of burn severity.Fourth, based on the targeted spectral index and GeoCBI assessment plots-field, as well as the fire perimeter, we produced a burned mask and classified burned pixels into the four burn severity levels (Unburned, Low, Moderate, and High) using two techniques: the first one, a regression model that used a field data as calibration data to estimate the burn severity; the second one, consists of a maximum likelihood estimation (MLE) approach.Finally, the overall accuracy of the burn severity map was evaluated across four affectation levels by means of a matrix error and Kappa index.The atmospheric correction of satellite images is a critical step in image processing, especially when the objectives of the study are based on the analysis of spectral indices, the use of different sensors, or multitemporal analysis [13,31,32].This correction consists of the conversion of measured radiances above the atmosphere (Top-Of-Atmosphere, -TOA-) to ground-level reflectivity (Bottom-Of-Atmosphere, -BOA-).
This study used the ATCOR atmospheric correction model included in the GEOMATICA PCI-2015 software [33].This model calculates the reflectivity values at ground level based on the input image metadata, eliminating atmospheric effects in satellite images depending on different atmospheric conditions, aerosol types and water vapor.In addition, the spectral response of more or less illuminated areas is homogenized depending on the relief (topographic correction) and the effect of bidirectional reflectivity (BRDF) [33].

Remote Sensed Burn-Severity Indices
Many researchers consider that spectral severity indices analysis from Landsat data has shown promise for improving assessments of burn severity [24,[34][35][36].Most of these indices are derived from an image transformation algorithm known as the Normalized Burn Ratio (NBR), given the sensitivity of the bands of the near-infrared (NIR) and shortwave infrared (SWIR) to detect changes produced by the burn severity.
After imagery pre-processing, 6 of the most common indices used were implemented including the use of single-date and multi-date (pre-and post-burn imagery) to assess forest burn severity mapping.(Table 4).
Table 4. Spectral Indices used to classify burn severity.
RdNBR and RBR have been used previously as an adjusted indices of bare ground and pre-fire vegetation during the detection of burn severity [18,20,23], we expected it could be used to improve the severity accuracy, through the adjust of the effect of the increased bare ground within the burned areas as a result of the fire-caused canopy loss.

The Separability Analysis
, The M index was calculated with the purpose of estimate the capacity of the spectral indices to differentiate the levels of fire severity identified on-field; therefore, assessing the separability of the spectral indices in discriminating burned severity effects from Landsat imagery.
A separability index (Equation ( 8) was used to estimate the discriminating effectiveness (i) between burned and unburned land and (ii) the spectral indices to discriminate between the different levels of burn severity.The separability index (also called normalized distance) has been used before to assess the power of mostly broadband sensors to discriminate burned areas [24,[39][40][41][42].The separability index is computed as follows: where   and   are the mean values of the considered spectral index band of the severity levels respectively,   and   are the corresponding standard deviations.The separability index has been frequently used to assess the degree of discrimination in fire ecology studies for both broadband and imaging spectroscopy sensors [24,39].
Values of M index higher (M > 1) indicate good separability (better discrimination), while values lower (M < 1) represent a large degree of histogram overlap between the severity classes.Since the approach of this study is to find the best way to estimate the burn severity mapping; therefore, the sensitivity analysis was performed on the six spectral indices, based on the classification of four severity levels.

Burn Severity Classificaction
The spectral index of burn severity was obtained by evaluating two parameters: (i) the spectral separability index that revealed the highest discriminatory power on the pooled dataset within each severity class, and (ii) the performance of the spectral indices (NDVI, NBR, dNDVI, dNBR, RdNBR and RBR) evaluating the correspondence of the continuous values -measured on-field GeoCBI with the coefficient of determination value R 2 .Then, two classification methods were applied to map forest burn severity using both a spectral severity index and GeoCBI assessments.
The first method evaluated was based on regression models, this method evaluates the performance of the satellite-derived indices as continuous metrics of burn severity, and we tested their correspondence to GeoCBI using linear regression [18].In previous studies, simple linear and various non-linear regression forms have been used to model the relationship between CBI or GeoCBI, and dNBR or RdNBR (e.g., [5,20,24,44]).To facilitate the comparison between our results and other studies [18,44,45], we chose to use their linear determinate by the next equation: where Y is the satellite-derived metric being evaluated, a is the gain, and b is the offset value of the model.We quantified the correspondence of each metric to GoCBI as the coefficient of determination (i.e., R 2 of a linear regression between predicted and observed values) [23].We conducted the regression for each of the 2 fires and for all 190 plots lumped together.We also conducted a validation on every plot; with 80% of the data used to train the linear model and the remaining 20% to test the model.
Next, we evaluated each remotely sensed burn severity metric's classification accuracy relative to GeoCBI.Four distinct categories (such as the defined in the study) are commonly used when mapping burn severity: unchanged (GeoCBI ≤ 0.1), low (>0.1 and ≤1.25), moderate (>1.25 and ≤2.25), and high (>2.25)[19,25].We calculated the values of each burn severity metric that corresponded to the GeoCBI for each fire, to define the thresholds of every level using the linear regressions described in the equation ( 9).
The second classification method evaluated was a maximum likelihood estimation (MLE) on a spectral index image selected before (see section 2.7.), for detecting levels of ecological damage due to the burn severity.Other studies have already used supervised classifiers for mapping severity [29,46], Mitri and Gitas [47], for instance, were able to increase up to 83% overall accuracy of fire severity mapping using object-based supervised classification; in this case, we hypothesized they could improve the classification through field assessment data (GeoCBI).
Among the conventional methods of classifying multispectral imagery, such as parallelepiped, minimum distance to mean, and MLE, the latter is the most widely used algorithm for pixel-based classification, and has been shown to give the best results for classification of remotely sensed natural resource data, among the algorithms of parametric classifiers [48].
As is well known, the MLE allocates a pixel to the class with which it has the highest probability of correspondence where the likelihood Li(x) that a pixel x is a member of class (i) is given by: where Vi is the covariance matrix of class i, n is the number of spectral bands, and y is the Mahalanobis distance.The rescaling of Li(x) between 0 and 1 yields the MLE a posteriori probability Pi(x) [49].
Training sites were chosen based upon field knowledge of the four severity classes (Figure 3).
Although is possible to generate more classes in the mapping procedure, these four were kept for training purposes due to spectral disparities between them (e.g., moderate and high).It was also important to distinguish fires from other unburned areas, so control plots outside of the perimeter were included in the training procedure.
The fire perimeters were based on remote-sensing and contrasted with the fire management office data [50], therefore, fire perimeters were created based on the remotely sensed burn-severity images, from the pre-fire NBR and the dNBR images [51,52].Then, we applied the "burned mask" to the index-normalized images.

Accuracy Assesment
Finally, using burn severity classification maps, we evaluated classification accuracy for each fire using error matrices detailing producer's, user's, and overall accuracies and estimates of the Kappa statistic to compare the performance of the estimator MLE and regression models.
Producer's accuracy (omission error) is an evaluation of when a plot is not mapped in the correct category.User's accuracy (commission error) is an evaluation of when a plot is mapped in the wrong category.Kappa is a measure of the difference between the actual agreement between reference data and classified data, and the chance agreement between the reference data and randomly classified data.
We calculated the classification accuracy as the percentage of plots correctly classified into each fire individually and all plots together.Therefore, our evaluation of best classification method involves (i) the overall classification accuracy of the fires and (ii), the classification accuracy of all severity levels analyzed; though the GeoCBI thresholds used for this classification are the most common, they are based on ecological conditions defining by the CBI and GeoCBI scale, and allow for consistent interpretation of classes across multiple fires.These GeoCBI thresholds also facilitate comparison with previous studies (e.g., [20,44]).

Correspondence of spectral indeces to GeoCBI
In general, an analysis on the severity classes (excluding unburned) showed that the severity assessment on-field with the GeoCBI was concentrated to a greater extent on the high severity category for the two fires.In the case of Madrid, 56% correspond to High severity, followed by Moderate severity with 42%, while only 2% have Low severity.For the Guadalajara fire, High severity, typical of large Mediterranean fires, with an average GeoCBI value of 2.85, concentrated in 90.3% of the plots, 7.7% in Moderate and only 2% in Low severity (See Figure 4).5), although differences between the three indices were not large.Therefore, there was an indication that RdNBR and RBR consistently performed better than others.The linear regression equation we used to model the relationship between satellite-derived severity metrics and GeoCBI fit the data reasonably well (Figure 5).Averaged among two fires, the correspondence between GeoCBI and RBR was higher (R 2 = 0.727) than both RdNBR (R 2 = 0.725) and dNBR (R 2 = 0.711) (Figure 5).The best adjusted R 2 values for the RBR and RdNBR models were 0.827 and 0.822 respectively, indicating better performance and highest correspondence to the GeoCBI model in explaining the variance in burn severity compared to the rest of spectral indices.

Spectral Index Selection
In general, a high correlation is observed for all the spectral indices in both study areas.In the case of Madrid, the RBR has the highest correlations with GeoCBI (R 2 = 0.827), with separability values higher than (M=2.93) in the remaining indices.In the case Guadalajara, the best fit of R 2 is presented for the RdNBR and RBR index (R 2 =0.63), being also the two indices that presents a greater separability (1.082 and 1.068) respectively.
According to the spectral indices correlation and discrimination results, RBR was selected for subsequent forest burn severity mapping as the best index for discrimination of severity.

Burn Severity Classifications
Based on the previously mentioned RBR index images, the forest burn severity maps were classified, first by a linear regression classification method (Figure 7), and second, by supervised classification method "MLE".
We observed relatively strong correlations in the final burn severity distribution, based on the regression parameters of the RBR.In the fire of Madrid, with a significant Pearson correlation of 0.897 and a RMSE error of 0.4398, while in Guadalajara a Pearson correlation of 0.759 and a RMSE error of 0.734.
The heterogeneity of the burned area is clearly visible, showing different severity effects in the two study areas (Figure 7), some small unburned or low-severity patches were found to be bordered by large moderate to high-severity patches; especially for Guadalajara for the high severity and unburned class, where their spatial distributions were more widespread on the map.

Accuracy Assesment
Overall classification accuracies for individual fires ranged from 58% (Guadalajara) to 92% (Madrid) (Table 7).When averaged among fires, MLE had the highest average overall classification accuracy (75%), being greater than the linear regression model (72.5%).When all severity levels were Classification accuracy in the moderate-and high severity classes decreased when the linear regression model, as opposed to MLE model, was used (Table 7).The increased classification accuracy in the moderate and low severity classes reflects differences between classification models, an effect due to the probabilistic classification of the MLE model in pixels where there is confusion between thresholds (Figure 8).To better understand the performance of the models, we can see the frequency distributions of severity class pixels extracted from the regression model in Guadalajara represented in the Figure 8.
The histograms show that burned and unburned pixels were well separated and relatively easy to discriminate, while that the frequency distribution of the severity classes (low, moderate and high) were superposed between in an upper range, compared with the frequency distribution of unburned.Severity class percentages were significantly different among from GeoCBI-defined field plots, but indicated a general agreement between burn severity classifications and validation field plots.
Overall, the linear regression models with an average of Kappa (57.5) was mostly lower than maximum likelihood estimation model MLE (64.5).

Discussion
The process of burn severity mapping is critical to the understanding of the post-fire landscape change and ecosystem resilience [6,27,34,46], this has led to an increase of studies using moderate resolution satellite sensors as an approach to this issue [19,25,28].The increased availability of moderate resolution (e.g.Landsat or Sentinel series) imagery, provides an important opportunity to map burn severity and research post-fire succession effects, making them an important resource for management activities [4,13,19,25,52].In this study, we explored the differences in the use of supervised classification though MLE, and regression models for burn severity mapping for the first time using remotely sensed spectral indices imagery from Landsat data in a Mediterranean ecosystem.
It is important to note that it is clear that mapping burn severity at moderate spatial scales of the Landsat ETM + and TM satellite measurements, was consistent with the GeoCBI field measurements.
We have observed that the results of GeoCBI in the prediction of the burn rates of remote sensing, with respect to the classification accuracy were satisfactory.In fact, the good performance of the weighted versions of the GeoCBI may be due to the fact that they emphasize the substratum and stratum, and estimate the dominant and intermediate tree strata that are more closely related to the reflectance of the plot -in their calculation [24,25,44].
The findings of our investigation can be explained, at least partially, by the spectral properties of the severity ratings of the burn according to the severity classes.Previous studies of Cansler and McKenzie [44], determined how robust spectral indices are when applied to new regions.
Additionally, our study identified the spectral index that performs the best in the severity discrimination, and also the sensitivity of spectral reflectance values with respect to different levels of burn severity in areas affected by the fire.
In our study, we also assessed the separability of multiple spectral indices in discriminating burned effects in a Spain Mediterranean ecosystem.We found that spectral indices (e.g.dNBR, RdNBR), designed to account for the reflectance from the canopy affected by burn severity and proportion of pre-fire cover, tended to show higher separability (Table 7. Overall classification accuracy for classification models using individual burn severity classes on RBR.), like other studies on the same subject [18,20,24].However, like the Parks et al. study [23], the spectral index RBR was the better corresponded to field-based burn severity measurements and had higher classification accuracy compared to dNBR and RdNBR, when discriminating different levels of severity.
These spectral indices with high discrimination power also depended on the differences between NIR, red and SWIR reflectance values.Where the effects of fire are directly related to decreasing in NIR and red spectral reflectance, as described by the studies [14,39,53].
In their study on the evaluation of spectral indices for burned area discrimination using MODIS/ASTER (MASTER) airborne simulator data Veraverbeke et al. [43], demonstrated that the highest sensitivity of the longer short wave infrared (SWIR) spectral region (1900-2500 nm) was observed in the interval between 2310 and 2360 nm.In our case, we observed, that the VIS (450-690 nm) regions of the indices are therefore very poor and the spectral regions of SWIR (2080-2350 nm) moderate discriminatory power, but the highest spectral separability between severity levels is observed in the spectral region of NIR (760-900 nm).This conclusion is consistent with the studies of Schepers et al. [39] and Arnett et al. [34] finding using high resolution imagery for assessing burned effects in heathlands of Europe and a mixed forest of western Canada, respectively.
User and producer specifications for moderate and low severity categories were poor for two reasons (Table 7): first, High, Low and Moderate categories had less than twice as many plots that others categories, it is therefore important to consider the number of plots evaluated by category, the accuracy of the register of imagery and scale of gravity maps when used for post-fire planning [18].Second, the plot location in relation to the limit of the mapped gravity polygons is important, also plots that do not align perfectly with the 30 m satellite pixel, and how fire can move from the surface to Crown within 30 m according to Miller & Quayle [18] and Safford et al [54].The fire effects can vary considerably within a pixel, this results in less precision in pixels adjacent to the edge of the polygon of wildfire, and burn severity classes.
Based on the overall accuracy of the error matrices, the approach of MLE supervised classification with an overall average accuracy of 76%, is obviously higher than the linear regression models approach, with an overall accuracy of 75%.Therefore, our evaluation of the resulting burn severity maps indicated that our MLE based approach can be used for forest burn severity mapping at moderate spatial scales from Landsat ETM + and TM data with reasonable accuracy (Table 7); additionally, the results were consistent across different forest fire sizes.As such, we observe that ETM+ and TM data can provide valuable information about the burned effects between severity levels.
Finally, Figure 7 indicates that the heterogeneity of burn severity patterns was high in the two fires.Future researches could determine the relationship between the degrees of severity of the changes produced in the landscape, in order to provide information to post-fire management tasks and restoration programs, but also can provide information on changes in plant function associated with fire impacts [3,55].

Conclusions
Our analysis illustrates two cases in which methodological process the regression models and the maximal likelihood estimator (MLE) applied on remotely sensed indices of burn severity from Landsat imagery-in Mediterranean fires, did not show the same accuracies.We find an improved performance of MLE models over the original methods of regression for severity burn mapping, as was observed in the study areas.Nevertheless, calculation of burn severity including more categories, as well as the sensibility analysis to a larger number of ground field based (GeoCBI) training areas should be evaluated in the future.Within our study area in Mediterranean ecosystems there was a difference in the explanatory power and separability of predicting spectral indices: dNBR, RdNBR, and RBR, but the spectral index RBR may be more consistent across regions than the dNBR and RdNBR.The relationships between the geometrically structured Composite Burn Index (GeoCBI) and the RBR have about 5% more of the spectral separability and classify severity with about 10% more accurately, suggesting that the methodology is applicable and useful but could use improvement for severity mapping.

(
Alto Tajo), identified as a critical habitat with its core area protected.This area presents an abrupt topography, with evenly-distributed annual precipitation of approximately 650 mm, and an annual daily mean temperature of 10.2 °C[10].

Figure 1 .
Figure 1.Location of the two fires included in this study: (a) Pantano de San Juan.Madrid;

coverage was Landsat 5 (
TM) and Landsat 7 (ETM +) space-borne platform images.The ETM+ imagery was available prior to the wildfires on June 10, 2003, and 2005.Following the wildfires, TM imagery was acquired on July 06 and August 05, 2003, and 2005 (Table

Figure 2 .
Figure 2. Flowchart of the methodology

PreprintsFigure 3 .
Figure 3. GeoCBI ground plots in field.The background image is the RBR spectral index in grayscale on Pantano de San Juan -Madrid.

Figure 4 .
Figure 4. GeoCBI distribution: (a) Boxplots in Madrid.Pantano de San Juan fire; (b) Boxplots in Guadalajara.Riba de Saelices fire; boxes represent the inter-quartile range, whiskers extend to the 5th and 95th percentiles, horizontal lines represent the median of field plots.

Figure 6 Figure 2 .
Figure6presents graphically the spectral signature plots of the burned severity on vegetation for Landsat ETM+ and TM satellite sensors, based on values extracted from sampling areas located on the satellite images.The spectral signatures of burned areas were compared for the two fires, in order to obtain a better understanding of their spectral behavior and potential discriminatory ability.It was evident that the discrimination offered by the infrared spectral channels is much higher than the visible (450 -690 nm), despite the low spectral distance of bare land with the vegetation in the Band 4 (Near infrared: 760 -900 nm) and the low spectral distance of bare land with the burned areas in the Band 7 Shortwave infrared, (2080 -2350 nm).Among these, spectral Band 4 showed the highest discrimination between the severity levels and the unburned areas, followed by Band 7, Band 5, and Band 3.

Figure 7 . 7 .
Figure 7. Spatial distributions of predicted burn severity: (a) Riba de Saelices-Guadalajara fire produced by using the linear regression; (b) Pantano de San Juan-Madrid fire by using the linear regression; (c) Riba de Saelices-Guadalajara fire produced by using the supervised classification of MLE, and (d) Pantano de San Juan-Madrid fire by the supervised classification of MLE.

Preprints
(www.preprints.org)| NOT PEER-REVIEWED | Posted: 29 March 2018 doi:10.20944/preprints201803.0245.v1analyzed simultaneously, it was observed that the accuracy of classification in the lower and middle classes improved with the use of the MLE in relation to the regression model.

Figure 8 .
Figure 8. Frequency distributions of burn severity levels extracted pixels of RBR.The vertical dash lines show a mean threshold value for discriminating burned pixels: (a) Riba de Saelices-Guadalajara; (b) Pantano de San Juan-Madrid.

Table 1 .
Variability in the definition of the thresholds of burn severity through the dNBR spectral index.
[23]er and Thode[20]present a relativized version of dNBR called RdNBR based upon adjusting in the measuring absolute change, on areas in with a sparse tree canopy.They modified dNBR by dividing by a function of the pre-fire NBR.Subsequently, Parks et al.[23]evaluate a new Landsatbased burn severity metric, the Relativized Burn Ratio (RBR), which provides an alternative to dNBR

Table 2 .
Summary of study areas analyzed in this study.

Table 3 .
List of imagery data used in this study.

Table 5 .
Variance explained and overall correlation for spectral indices, and GeoCBI.

Table 6 .
M index values comparing burned effects separability by level for the spectral indices.

Table 7 .
Overall classification accuracy for classification models using individual burn severity classes on RBR.