Application of Getis-Ord Correlation Index (Gi) for Burned Area Detection Improvement in Mediterranean Ecosystems (Southern Italy and Sardinia) Using Sentinel-2 Data

Abstract

This study collects the results obtained using the Getis-Ord local spatial autocorrelation index (Gi) with the aim of improving the classification of burned area detection maps generated from spectral indices (i.e., dNBR index) derived from Sentinel-2 satellite data. Therefore, the work proposes an adaptive thresholding approach that also includes the application of a similarity index (Sorensen–Dice Similarity Index) with the aim of adaptively correcting classification errors (false-positive burned pixels) related to the spectral response of burned/unburned areas. In this way, two new indices derived from the application of the Getis-Ord local autocorrelation analysis were created to test their effectiveness. Three wildfire events were considered, two of which occurred in Southern Italy in the summer of 2017 and one in Sardinia in the summer of 2019. The accuracy assessment analysis was carried out using the CEMS (Copernicus Emergency Management Service) on-demand maps. The results show the remarkable performance of the two new indices in terms of their ability to reduce the false positives generated by dNBR. In the three sites considered, the false-positive reduction percentage was around 95–96%. The proposed approach seems to be adaptable to different vegetation contexts, and above all, it could be a useful tool for mapping burned areas to support post-fire management activities.

1. Introduction

Historically, and with differences between countries, information on burnt areas has been based on ground-based estimates using GPS and the digitisation of events on digital maps, organised and carried out by the authorities responsible for fire management [1]. The differences in the methods used over the years mean that these sources are not without limitations. The traditional mapping methodology, even if it is the officially recognised one in many countries, provides datasets that often have accuracy problems due to several causes [2,3,4,5].

Currently, Earth Observation (EO) is becoming increasingly effective in solving many of these problems, also thanks to the new tools available [6]. The new knowledge and techniques allow us to have accurate and comparable data with the inventories of the burned areas in extremely short times compared to the field survey without losing accuracy [7,8]. Especially in the last decade, satellite products for the regional or local scale mapping of burned areas have been widely developed using high to medium-resolution sensors [9,10,11,12,13,14].

As a result, a wide range of EO-based spectral indices have been developed with the aim of identifying burned areas in as much detail as possible [15,16,17,18]. Furthermore, the use of spectral indices is increasingly integrated with other analysis techniques such as object-based analysis [19], time-series change detection [20,21], multitemporal analysis [11], contextual growing approaches [22], machine learning approaches [12,14,23,24,25,26], and unsupervised approaches [18,27].

In general, the use of additional analysis techniques for the application of spectral indices aims at improving the estimate of burned areas provided by the latter.

Specifically, the dNBR index, which is based on the NIR and SWIR spectral bands, is one of the key tools on which most remote sensing methodologies applied to fire studies are based [28,29]. Because of its ease of use and flexibility, dNBR is now used in several contexts. However, the use of this index can lead to an overestimation of burned areas as the dNBR index can produce false positives, i.e., pixels are considered to be burned areas when, in fact, they are not [30]. In fact, dNBR is generally classified according to the severity thresholds adopted by Key and Benson [28]. Therefore, a threshold of +0.1 is considered the most appropriate to distinguish burned from unburned areas. This threshold, as in the cases considered in this study, can lead to erroneous results in the classification of burned areas. This criticality is common in several studies of burned area detection using dNBR [28,29,30,31,32,33]. The misclassification of pixels can have many causes but is mainly due to changes in agricultural land cover (harvesting and/or tilling), small water bodies, changes in ground cover and moisture on dark soils and dry vegetation before the fire, and the rapid drying of green vegetation, as occurs in xeric grasslands [34]. Therefore, one of the needs when using dNBR to locate burned areas is to reduce the number of false-positive pixels as much as possible. This is even more true when dNBR is used in an operational environment, where the need to be as accurate as possible is even greater.

With the aim of further contributing to the scientific debate on the use of remote sensing techniques for burned area mapping, this study develops a local thresholding approach based on spatial autocorrelation techniques and spatial analysis to identify burned areas using Sentinel-2 imagery and dNBR maps.

The integration of geostatistical analysis, remote sensing, and wildfire issues can provide interesting results for the analysis of relationships between factors related by a geographical component [35]. In particular, spatial autocorrelation makes it possible to assess how the intensity of a spatially defined phenomenon, such as a fire, in a given area affects the surrounding area [36].

This paper describes the development of the algorithm and the results obtained in improving the burned area mapping in Italy for three different fire events. The validation was based on maps provided by the Copernicus Emergency Management Service (CEMS). These products have often been used in recent years to validate the results of studies on the detection of burnt areas [7,17,37]. The aim of this work is to evaluate if and to what extent the application of the Getis-Ord local spatial autocorrelation index (Gi) can improve the results obtained by calculating spectral indices such as dNBR in the detection of burnt areas.

2. Study Areas and Dataset

2.1. Study Areas and Fire Events

Three different areas with wildfire events were examined in this study. The location and extent of the fires, as reported by the Copernicus Emergency Management Service (CEMS), are shown in Figure 1. All fire events are located in Italy, in a typical Mediterranean environmental and territorial context.

The first case considered occurred between 16 and 21 August 2017 near the village of Brienza (southern Italy-Basilicata region) and burned approximately 230 ha of forest vegetation, shrubs, and natural pastures. The area is mountainous, and the fire occurred at an altitude between 800 and 1200 m a.s.l. During this summer, almost the entire Italian territory, and in particular Southern Italy, experienced a period characterised by high temperatures and a lack of rain. This resulted in a greater impact of the fires, especially in forest areas [38].

Another important event in 2017 also occurred in Southern Italy (Calabria region) in San Fili-Rende. In this case, the main fire and other smaller fires occurred close to inhabited centres. In this case, in addition to the damage to forest areas, many agricultural areas were affected by the fire. The burnt area at the end of the events was about 580 ha [39]. On the other hand, the last event occurred on 28 July 2019 in the region of Sardinia (Tanca-Altara). During this period, many events affected the northeastern part of the Sardinia Region around the area of the town of Siniscola. There were many outbreaks, but the most widespread affected a large part of the Mediterranean scrub and agricultural areas. This event also caused a lot of damage to agricultural activities, as there was a lot of damage to rural houses and livestock deaths [40]. The most important information on the fires is summarised in

Table 1. Main information for fire events.

Location	Data	Burned Area (ha) 1	Centroid Coordinates (EPSG: 4326)
Brienza	16/21 August 2017	229.8	40.48925895 N, 15.59848536 E
San Fili-Rende	27/31 August 2017	582.1	39.35448712 N, 16.16220215 E
Tanca-Altara	28 July–1 August 2019	575.1	40.52711014 N, 9.65008056 E

¹ As reported by CEMS.

, using the official data provided by the CEMS [38,39,40]. In addition, the dates of the satellite images used in this study, which are illustrated later, are given.

2.2. Earth Observation Products

The burned area maps were produced using Sentinel-2 imagery with acquisition dates close to the dates of the fires and comparable to the dates used to process the CEMS maps used for validation.

Sentinel-2 satellite data are powerful and valuable for forest fire monitoring and management. These data, which cover a wide range of spectral bands, allow fires to be detected and tracked in real time. The near-infrared (NIR) and mid-infrared (MIR) bands are particularly sensitive to vegetation and biomass, making them valuable for assessing the extent and impact of fires [41].

Sentinel-2 satellite data are available free of charge from the European Union’s Copernicus program. Sentinel-2 Level-2A Collection 1 imagery was used for this study, which provides orthorectified surface reflectance (referred to as Bottom-Of-Atmosphere or BOA), ensuring accuracy in multispectral and multitemporal registration at the sub-pixel level. The product includes scene classification (which includes clouds and cloud shadows), AOT (an acronym for Aerosol Optical Thickness), and WV (representing water vapour) maps. The main features of the L2A products are summarised in the official documentation [42]. All processed images were downloaded for free from the Copernicus Data Space Ecosystem and then pre-processed using GIS software to calculate the main indices. Due to the bands used, all images were reclassified to a resolution of 20 m. In order to process the data required for this study, a pre-fire image and a post-fire image were taken for each fire (

Table 2. Image data from the Sentinel L2A satellite used in the study of three fire events.

Location	Pre-Fire Image	Post-Fire Image
Brienza	1 August 2017	26 August 2017
San Fili-Rende	29 July 2017	2 September 2017
Tanca-Altara	13 July 2019	2 August 2019

).

As mentioned above, the data for the comparison and validation of the methodology were provided by the CEMS service of the European Communities [43]. The Copernicus EMS Early Warning and Monitoring provides critical geospatial information at both the European and global levels through continuous observations and forecasts for floods, droughts, and forest fires. Specifically for forest fire data, we used the products generated by the European Forest Fire Information System (EFFIS). The EFFIS supports the forest fire protection services in the EU and neighbouring countries and provides the European Commission services and the European Parliament with up-to-date and reliable information on forest fires in Europe.

The datasets provided by CEMS [38,39,40] were used in the GIS environment as data for the validation of the methodology. In addition to the perimeter, both the area of interest (AOI) and the land use classification were used.

3. Methods

The methodology described below aims to identify the burned areas using a local spatial statistical thresholding approach capable of discriminating the pixels in burned and unburned classes.

Specifically, the proposed approach aims to identify and delineate the burned areas using the NBR and dNBR indices as input and developing two new indices (dGiNBR and dNBRGi) obtained by applying the Getis-Ord Gi* statistic, one of the best-known and used local indices of spatial autocorrelation. The two new indices were developed in parallel in order to compare their performance. The flowchart of the methodology used is shown in Figure 2.

Once the satellite tiles were produced, they were pre-processed to remove any areas that could increase the calculation errors and false positives of the Normalised Burn Ratio (NBR) index. Specifically, two binary raster masks were created to eliminate wetlands and water bodies. Although NBR can classify some pixels as high severity, they are water, so it is good to mask these areas as a priority. The method chosen was based on the calculation of the Normalised Difference Water Index (NDWI) [44] by imposing a threshold greater than 0.5 (1).

$$NDWI={\displaystyle \frac{Green-NIR}{Green+NIR}}={\displaystyle \frac{\left(B03-B08\right)}{\left(B03+B08\right)}}$$

(1)

However, the use of Level 2A atmospherically corrected Sentinel-2 imagery allows us to mask other sources of noise, such as clouds, shadows and smoke. Burned areas are then identified by first calculating the NBR spectral index on both Sentinel-2 images (pre- and post-fire) and then the dNBR index according to Equations (2) and (3):

$$NBR={\displaystyle \frac{NIR-SWIR}{NIR+SWIR}}={\displaystyle \frac{\left(B8A-B12\right)}{\left(B8A+B12\right)}}$$

(2)

$$dNBR=NBRprefire-NBRpostfire$$

(3)

Therefore, NBR is the normalised difference ratio in reflectance between the near-infrared (band 8A of Sentinel-2) and shortwave infrared (band 12 of Sentinel-2) parts of the electromagnetic spectrum, while dNBR is the difference between the two NBR indices calculated before and after the fire.

As mentioned above, NBR and dNBR indices are widely used for pre- and post-fire estimation and provide results that are generally considered to be high performance [16,32,45,46,47,48].

In the literature, the scale proposed by Key and Benson [31] was used as a reference to interpret the different values of dNBR, indicating that pixels with values greater than 0.1 are burned areas (Figure 3, Figure 4 and Figure 5).

In the second step of the approach used, the Getis-Ord spatial autocorrelation index (Gi) was applied to the previously calculated spectral indices.

Spatial autocorrelation refers to the degree to which the values of a variable at one location are correlated with the values of the same variable at neighbouring locations in space. According to Anselin and Rey S. [49], spatial autocorrelation can be defined as a territorial area of similar parameter values. If similar parameter values—high or low—are spatially localised, there is a positive spatial autocorrelation of the data. Conversely, the spatial proximity of dissimilar values, i.e., not stable in space, indicates negative spatial autocorrelation (or spatial heterogeneity). These statistics help to analyse the extent to which the occurrence of an event in one area inhibits or makes the occurrence of an event more likely in a neighbouring area.

The presence of spatial autocorrelation indicates the occurrence of anomalies in the distribution of map values, the causes of which require further investigation. According to Haining [50], spatial autocorrelation can occur in several situations, including (a) when there is a mismatch between the (large) scale of variation of a phenomenon and the (small) scale of the spatial framework used to capture or represent that variation; (b) due to measurement error; (c) as a result of spatial diffusion, spillover effects, interactions and dispersal processes; (d) when one variable inherits characteristics from another through a causal association; (e) due to misspecification of the model.

Geographic objects are described by two different types of information: position in space and associated properties. The most interesting feature of spatial autocorrelation is the possibility of analysing the two components of information, the spatial and the attribute components, at the same time [51]. As a result, spatial autocorrelation can be considered a highly effective technique for analysing the spatial distribution of objects while evaluating the degree of influence and relationship with neighbouring elements.

Several techniques are commonly used to assess and measure spatial autocorrelation. The Moran index [52] and the Geary index [53] are both global indicators of spatial autocorrelation that are used to assess whether observations in each geographical area tend to have similar or dissimilar values compared to nearby observations. However, there are some differences between the two indices.

Firstly, the Moran index is based on the covariance between observations in a geographical space, while the Geary index is based on the sum of the squares of the differences between observations. In other words, the Moran index is a measure of spatial association, whereas the Geary index is a measure of spatial dissimilarity. Furthermore, the Moran index is sensitive to both positive and negative relationships between observations, whereas the Geary index is only sensitive to negative relationships. This means that the Geary index is better at detecting clusters of low values (i.e., areas with very different values from the surrounding areas), while the Moran index can detect both high and low-value clusters.

Global indices of spatial autocorrelation are used to assess whether the point elements of a spatial distribution are distributed randomly, in aggregates or uniformly. These indices provide a synthetic measure of the degree of spatial association of the points, i.e., whether nearby points tend to have similar or different values compared to distant points. These global indices are useful for highlighting whether a spatial distribution has positive (aggregates) or negative (dispersion) autocorrelation and for assessing the intensity of this autocorrelation. However, they do not provide information on the spatial variation of the autocorrelation and the local relationships between points.

The localization of high autocorrelation values is instead provided by the so-called local indices of spatial autocorrelation. They are used to assess whether the spatial distribution of a given variable shows clusters or dispersion limited to specific areas of the territory.

The LISA (Local Indicators of Spatial Association) index [54,55] is a local index of spatial autocorrelation that assesses whether a given area of space has a similar distribution of a variable compared to the surrounding areas. The LISA index is calculated for each area of interest and is based on the spatial weight matrix, which indicates the spatial relationship between different areas. The LISA is a local Moran index.

The Geary index also has a local version. For each spatial unit i, the local Geary index evaluates the difference between the value of the variable in that unit and the average of the values of the variable in neighbouring spatial units.

Getis-Ord’s G function [56,57] considers disaggregated measures of autocorrelation, taking into account the similarity or difference of some zones. This index measures the number of events with homogeneous characteristics contained within a distance d identified for each distribution event. This distance represents the extension within which clusters of particularly high or low-intensity values are produced.

The Getis-Ord function is given by Equation (4).

$$G_i^{*}{\displaystyle \frac{\sum _{j=1}^n{w}_{i,j}{x}_j-\overline{X}\sum _{j=1}^n{w}_{i,j}}{S\sqrt{\frac{\left[\sum _{j=1}^n{w}_{i,j}^2-{\left(\sum _{j=1}^n{w}_{i,j}\right)}^2\right]}{n-1}}}}$$

(4)

Here, $x_j$ represents the value of an attribute for feature j, $w_{i,j}$ denotes the spatial weight between features i and j, and n stands for the total count of features. Additionally, $\overline{X}$(5) and S(6) correspond to the mean and variance, respectively.

$$\overline{X}={\displaystyle \frac{\sum _{j=1}^n{x}_j}{n}}$$

(5)

$$S=\sqrt{{\displaystyle \frac{\sum _{j=1}^n{x}_j^2}{n}}-{\left(\overline{X}\right)}^2}$$

(6)

In our approach, the Gi index allows us to perform a statistical clustering of values on a hotspot analysis, where pixels are grouped based on a spatial relationship of proximity. The index identifies clusters of similar values, such as areas of very high or very low values that occur in proximity. In our methodology, the Gi index is applied to both the dNBR index and the previously calculated NBR indices (pre-fire and post-fire).

With the Envi 4.7 software, the calculation of Gi is linked to the Neighbourhood Rule, which compares each pixel with the 8 neighbouring pixels (Queen’s Case Neighbourhood Rule). It also uses the Multiple Interval Statistics calculation function, which calculates the autocorrelation at different lag distances through a correlogram. Thus, the autocorrelation is calculated not only for the central pixels but also for each of the 8 nearest neighbours based on the selected maximum lag. The choice of the most appropriate maximum distance is based on the condition that the fire area (or the area of the main burned area in the case of multiple burned areas in the same image) identified by applying the Gi index is at least equivalent to that obtained with dNBR or, better still, more accurate (using the CEMS maps as ground truth data). In this way, two new indices are calculated, denoted as dNBRGi (derived by applying the Gi index to dNBR) and dGiNBR, as the difference of the Gi index values calculated for each pair of NBR according to the following formula (7):

$$dGiNBR=GiNBRprefire-GiNBRpostfire$$

(7)

To determine the burned/unburned threshold for the two new indices, we first isolate a burned area within the image used, selected as a region of interest (ROI), using the CEMS map. This ROI corresponds to the burned area of the map or, in any case, to the largest burned area (in the case of multiple burned areas in the same image). Figure 6 shows the ROIs selected for the three study areas in the context of the CEMS map.

At this point, the methodology aims to identify the threshold of dNBRGi (and dGiNBR) that selects for them the same number of burned pixels as detected with dNBR (>0.1). Thus, in this way, we determine the threshold for the indices derived from Getis-Ord that gives the same result in terms of burned pixels as dNBR.

We also apply a similarity index, the Sorensen–Dice similarity index [58,59], to the ROI. Using this index, we compare the dNBR index with the other two indices (dGiNBR and dNBRGi) to evaluate their similarity in the detection of burned areas provided by the indices used. The Sorensen–Dice similarity index (SDS) is calculated using the following Equation (8):

$$SDS={\displaystyle \frac{2a}{2a+b+c}}$$

(8)

where a is the number of burned pixels common to dNBR and dNBRGi (or dGiNBR), b is the number of burned pixels according to dNBR, and c is the number of burned pixels according to dNBRGi (or dGiNBR). The SDS index ranges from 0 to 1, where 1 means perfect similarity, and 0 means no similarity between the examined indices. In the three cases considered in this study, the minimum value considered for the SDS index was equal to 0.9.

Therefore, the objective pursued was to identify the threshold of the indices derived from the Gi index, capable of mapping the same number of burned pixels as the dNBR index and with a high similarity of the burned areas provided by the compared indices (

Table 3. Report of the identified threshold and SDS index for each lag distance tested for the dNBRGi and dGiNBR index.

Brienza			San Fili Rende			Tanca Altara
dNBRGi Index
Lag	Threshold	SDS Index	Lag	Threshold	SDS Index	Lag	Threshold	SDS Index
1	31.57	0.993	1	10.73	0.983	1	16.68	0.948
2	51.7	0.99	2	24.46	0.979	2	25.73	0.926
3	64.1	0.99	3	39.13	0.974	3	33.58	0.909
4	74.21	0.99	4	52.19	0.971
5	82.5	0.99	5	63.38	0.968
dGiNBR Index
Lag	Threshold	SDS Index	Lag	Threshold	SDS Index	Lag	Threshold	SDS Index
1	3.93	0.99	1	2.97	0.984	1	7.71	0.946
2	6.3	0.99	2	6.2	0.978	2	11.94	0.926
3	8.62	0.99	3	9.29	0.973	3	15.33	0.91
4	9.98	0.99	4	11.99	0.97
5	10.67	0.99	5	14.34	0.968

). Essentially, the threshold identified by dNBRGi (or dGiNBR) produces a map of the burned area (on the ROI) of the same size as that produced by dNBR and of a shape that is as similar as possible.

The dNBRGi and dGiNBR maps, subsequently applied to the whole image using the previously identified thresholds, provide new burned/unburned areas as a product that can be compared with those identified by the dNBR index. The aim is to evaluate the improvements obtained in terms of correct identification of the burned areas themselves by estimating the reduction in false positives contained in the dNBR maps.

The maps provided by CEMS were used as reference validation data to compare the burned and unburned area results obtained with dNBR, dNBRGi, and dGiNBR.

All operations, except for the Getis-Ord Gi* application, were performed using QGIS 3.34.6-Prizren software.

4. Results

The results obtained by applying the described methodology in different areas are presented below (Figure 7 and

Table 4. Number of burnt pixels calculated with dNBR, dNBRGi, and dGiNBR indices. Pixels were also counted, excluding cropland (derived from CEMS maps). The total number of pixels in the study area and the number of pixels identified as cropland are also given. The dNBRGi and dGiNBR for Brienza and San Fili-Rende refer to the lag 5 distance, while for Tanca-Altara, they refer to the lag 3 distance. Lag 5 (for Brienza and San Fili-Rende) and Lag 3 (for Tanca-Altara) provided the best results respecting the SDS > 0.9 condition.

			CEMS VALIDATION	dNBR	dNBRGi	dGiNBR
BRIENZA	Burned pixel		5825	45,333	7233	7856
	Burned pixel without croplands		3933	29,339	4940	5699
Total burned/unburned pixels: 220,500			Total Cropland pixel: 64,834
SAN FILI	Burned pixel		13,365	122,975	19,125	17,620
	Burned pixel without croplands		6137	85,565	9397	8448
Total burned/unburned pixels: 319,970			Total Cropland pixel: 105,804
TANCA	Burned pixel		14,406	13,847	10,466	10,399
	Burned pixel without croplands		2593	1930	1904	1824
Total burned/unburned pixel: 83,678			Total Cropland pixel: 79,454

).

As mentioned above, to validate the methodology, false positives and negatives were calculated with respect to the burned area reported by CEMS (Figure 8 and

Table 5. For each wildfire event, the types of false positives and false negatives, calculated in terms of both the number of pixels and percentage, are shown. The dNBRGi and dGiNBR for Brienza and San Fili-Rende refer to the lag 5 distance, but for Tanca-Altara, it refers to lag 3.

	N. of Pixel			% of Pixel
BRIENZA	dNBR	dNBRGi	dGiNBR	dNBR	dNBRGi	dGiNBR
False-positive	39,521	1515	2140	18.41	0.71	1.00
False-positive without agricultural areas	25,417	1090	1793	16.75	0.72	1.18
False positive in agricultural areas	14,104	425	347	22.41	0.68	0.55
False-negative	13	107	109	0.22	1.84	1.87
SAN FILI-RENDE	dNBR	dNBRGi	dGiNBR	dNBR	dNBRGi	dGiNBR
False-positive	110,092	6762	5280	35.91	2.21	1.72
False-positive without agricultural areas	79,633	3579	2650	38.28	2.36	1.27
False-positive in agricultural areas	30,459	3183	2630	30.90	3.23	2.67
False-negative	482	1002	1025	3.61	7.50	7.67
TANCA-ALTARA	dNBR	dNBRGi	dGiNBR	dNBR	dNBRGi	dGiNBR
False-positive	3568	205	144	5.15	0.30	0.21
False-positive without agricultural areas	156	97	76	9.56	0.06	4.66
False-positive in agricultural areas	3412	108	68	5.04	0.16	0.10
False-negative	4127	4145	4151	28.65	28.77	28.81

).

At the Brienza site, the false-positive pixels identified by dNBR corresponded to 18.41% of the total study area (excluding true burned pixels). If only non-agricultural pixels were considered (which represent about 69% of the total area), the false-positive dNBR pixels were equal to 16.75%. If only agricultural pixels were considered (which represent about 29% of the total area), the dNBR false-positive pixels were 22.41%. With the two indices, dGiNBR and dNBRGi, a drastic reduction in false-positive pixels was always obtained. In particular, using the lag 5 distance, the best results were obtained with dNBRGi on the total of agricultural and non-agricultural pixels (0.71% of false positives), with dGiNBR considering only the agricultural pixels (0.55% of false positives) and again with dNBRGi considering only the non-agricultural pixels (0.72%).

At the San Fili site, the false-positive pixels identified with dNBR corresponded to 35.91% of the total study area (excluding true burned pixels). If only non-agricultural pixels were considered (which represent about 65% of the total area), the false-positive dNBR pixels were 38.28%. If only agricultural pixels were considered (which represent about 33% of the total area), the dNBR false-positive pixels were 30.9%. Again, the two indices, dGiNBR and dNBRGi, always gave a drastic reduction in false positives. Using lag 5, the best results were obtained with dGiNBR on the total of agricultural and non-agricultural pixels (1.72% false positives), but also when considering only the agricultural pixels (2.67% false positives) and only the non-agricultural pixels (1.27%).

At the Tanca-Altara site, the false-positive pixels identified with dNBR were equal to 5.15% of the total study area (excluding true burned pixels). If only non-agricultural pixels (representing less than 5% of the total area) were considered, the false-positive dNBR pixels represented 9.56%. If only agricultural pixels (representing more than 95% of the total area) were considered, the false-positive dNBR pixels were 5.04%.

Although, in this case, the percentage of dNBR false positives was lower than in the other two cases, the dGiNBR and dNBRGi indices reduced the number of false positives significantly. Using lag 3, the best results were obtained with dGiNBR on the sum of agricultural and non-agricultural pixels (0.21% false positives), but also when considering only agricultural pixels (0.1% false positives) or only non-agricultural pixels (4.66%).

The analysis also includes an evaluation of false negatives, i.e., pixels that are burned but not identified as such by the indices used. The aim is to understand if and to what extent the indices derived from Getis-Ord influence the increase in false negatives compared to dNBR, bearing in mind that, unlike false positives, the methodology used cannot reduce their number.

At the Brienza site, the dNBR false negatives represented only 0.22% of the true burnt area. With the two indices derived from Getis-Ord (lag 5), this percentage increases to about 1.85%. This is, therefore, an extremely limited increase in absolute terms.

At the San Fili site, the dNBR false negatives represented 3.6% of the true area burned. With the two indices derived from Getis-Ord (lag 5), this percentage increases to about 7.5%.

On the Tanca site, the dNBR false negatives were 28.6%, and the Getis-Ord (lag 3) derived indices were at the same percentages, so they did not worsen the dNBR result. The high number of false-negative pixels is most likely due to the extremely dry state of the vegetation before the fire. This makes it more difficult to detect burned areas using spectral indices such as dNBR.

Finally, some accuracy metrics were also calculated (

Table 6. Accuracy metrics for each index. The dNBRGi and dGiNBR refer to lag 5 distance and lag 3 for the Tanca Altara fire.

Accuracy Metrics	dNBR	dNBRGi	dGiNBR
Brienza
User accuracy burned class	0.128	0.791	0.728
User accuracy unburned class	1.000	0.999	0.999
Producer accuracy burned class	0.998	0.982	0.981
Producer accuracy unburned class	0.816	0.993	0.990
Overall accuracy	0.821	0.993	0.990
Kappa (k)	0.189	0.872	0.830
San Fili Rende
User accuracy burned class	0.105	0.646	0.700
User accuracy unburned class	0.998	0.997	0.997
Producer accuracy burned class	0.964	0.925	0.923
Producer accuracy unburned class	0.641	0.978	0.983
Overall accuracy	0.654	0.976	0.980
Kappa (k)	0.123	0.749	0.786
Tanca Altara
User accuracy burned class	0.742	0.980	0.986
User accuracy unburned class	0.941	0.943	0.943
Producer accuracy burned class	0.714	0.712	0.712
Producer accuracy unburned class	0.948	0.997	0.998
Overall accuracy	0.908	0.948	0.949
Kappa (k)	0.672	0.795	0.798

).

The accuracy analysis concerns the estimation of the Producer’s Accuracy (PA), User’s Accuracy (UA), Overall Accuracy (OA), and Kappa Coefficient (k). PA is the probability that the classifier has labelled an image pixel into Class A given that the ground truth is Class A. UA is the probability that a pixel is Class A given that the classifier has labelled the pixel into Class A. OA is computed by summing the number of pixels classified correctly and dividing by the total number of pixels. The Kappa coefficient (k) measures the increase in classification accuracy compared to just randomly assigning values by accounting for omission and commission error [60,61].

The accuracy metrics for the Brienza event showed that dNBR had a slightly higher PA in the burned class than the two Getis-Ord derived indices but a significantly lower UA than the other two indices. This confirms that dNBR strongly overestimates burned areas (many false positives) and slightly reduces false negatives compared to dNBRGi and dGiNBR. Of the latter two, the accuracy analysis confirmed that the former offered a slightly better performance. Both the OA and k values confirmed the previous considerations.

Also, for the San Fili event, the accuracy metrics gave similar results to the previous event, with extremely low dNBR UA values for the burned class and, therefore, an overestimation of the burned area much higher than that provided by the two Getis-Ord derivative indices. In the case of San Fili, however, it was the dGINBR index that performed slightly better than dNBRGi.

Finally, for the Tanca event, the comparison between the UA values of the three indices showed an improvement in the two Getis-Ord derivative indices for the reduction in false positives (the UA of dNBR burned class was 0.742, UA of the other two indices were higher than 0.98 in the burned class). Furthermore, both the OA and the k coefficient showed an improvement in the performance of the classification of burned areas (and dGiNBR was slightly better than dNBRGi).

5. Discussion

The results obtained in this study seem to demonstrate that the Getis-Ord Gi spatial autocorrelation index is highly effective when used to improve the performance of a satellite-derived index such as dNBR in detecting burned/unburned areas. In particular, the use of Gi in conjunction with the Neighbourhood Rule (in Envi 4.7 software), which compares each pixel with its eight neighbours, combined with the use of a correlogram that calculates the autocorrelation at different lag distances, made it possible to identify only the “consistent” clusters, thus reducing the false positives provided by dNBR. In fact, the most significant result was the reduction in scattered and isolated pixels that appeared as “burned” in the dNBR map. An example of this improvement is shown in Figure 9. However, the use of Gi also allowed us to eliminate clusters of pixels that could be identified as false positives. This is because fire causes an autocorrelation that is generally greater than that found in the presence of other significant variations in spectral response between the two images used, which can be determined mainly by the drying out of green vegetation but also by modest changes in ground cover or moisture, as well as the presence of shadows or smoke [34].

The use of the similarity index guarantees a reliable result, as the comparison is made in relation to dNBR, and it is, therefore, reasonable to assume that the burned/unburned thresholds identified for the new indices do not underestimate the result (in fact, it is more likely that they overestimate it, as dNBR gave an overestimated result). However, the improvements are remarkable despite the different conditions of vegetation affected by fire, as found in the three case studies. Therefore, the methodology used allows a drastic reduction in false positives (pixels identified as burned that are, in fact, not burned) compared to dNBR, guaranteeing a detection of a burned area at least equal to that provided by dNBR in terms of number of burned pixels.

As expected, the methodology does not improve the dNBR results in terms of false negatives (pixels identified as unburned that are burned). Therefore, in the case studies analysed, where dNBR identifies a significant presence of false negatives (e.g., Tanca site), their number remains almost unchanged even after the application of Gi. This is mainly the case in burned areas where the vegetation was already very dry and sparse before the fire [34]. On the other hand, when the state of the vegetation is different (less dry or more humid), as in the case of Brienza and San Fili, the number of false negatives is much lower. Or they are low-severity burned areas.

As already highlighted, the number of false negatives in the analysed case studies of Brienza and San Fili increases slightly in absolute terms in both cases using Getis-Ord derivative indices (lag 5) compared to dNBR. However, the difference is reduced by using lower lags. In fact, at the San Fili site, if we use lag 5, the percentage of false negatives corresponds to approximately 7.5% of the actual burnt area (compared to 3.6% for dNBR); if we use a lag distance of 4, it drops to 6.3%, and to 5.3% if we use lag 3. At the same time, the reduction in false positives remains high (1.97% of false positives on the total of agricultural and non-agricultural pixels with lag 4 and 2.24% with lag 3), slightly higher than those identified with lag 5 (1.72%). Therefore, the use of lower lag distances allows the number of false negatives to be minimised, with only a slight deterioration in the results obtained in terms of reducing false positives (

Table 7. False negatives number and percentage of pixels for each fire. Values are calculated for dNBR and for dNBRGi and dGiNBR indices at different lags.

	N. of Pixel	% of Pixel		N. of Pixel		% of Pixel
	dNBR			dNBRGi	dGiNBR	dNBRGi	dGiNBR
			lag 3	88	97	1.51	1.67
Brienza	13	0.22	lag 4	92	102	1.58	1.75
			lag 5	107	109	1.84	1.87
San Fili Rende			lag 3	712	780	5.33	5.84
	482	3.61	lag 4	838	860	6.27	6.43
			lag 5	1002	1025	7.50	7.67
Tanca Altara			lag 1	4129	4125	28.66	28.63
	4127	28.65	lag 2	4136	4139	28.71	28.73
			lag 3	4145	4151	28.77	28.81

).

The persistence of false positives in the maps derived from the new indices mainly depends on the temporal distance between the two images used. As a function of this distance, and if conditions of vegetation drying occur during the period considered, some vegetation typologies radically modify their spectral response and can be confused with areas affected by fire, as they are characterised by a relatively high autocorrelation between contiguous pixels (Figure 10). Alternatively, it may be due to radical changes caused by agricultural practices in the post-fire period in unburned areas. However, it is worth highlighting the high reliability of the method used in agricultural areas, even though these are areas where dNBR maps often show errors (false positives) due to agricultural practices.

The limitation found in the proposed approach concerns the identification of thresholds of dNBRGi and dGiNBR to distinguish burned/unburned areas. These thresholds cannot be standardised and, therefore, have to be determined on a case-by-case basis. This makes the process relatively more complex. This is because a spatial autocorrelation index such as Gi is a measure of how the values associated with a set of spatial features are related to each other. Therefore, this measurement is strictly dependent on the range of values on which the Gi index operates, unlike, for example, the NBR or dNBR index, which gives a value for each pixel regardless of its neighbours. A negative consequence of using the lag distance to calculate the Gi index is the production of smoothing images with a consequent loss of detail. This is also responsible for the relative increase in false negatives compared to dNBR.

The work presented in this article is related to that developed in a previous article [26], in which the authors highlighted the improvements obtained in the detection of burned areas by using local spatial autocorrelation statistics and spectral indices on Modis and Aster satellite images.

This new study aims to demonstrate the potential of the applied tools using a more solid methodology that can be easily replicated in different contexts. Unlike other studies aimed at improving the results obtained with satellite-derived indices in the detection of burnt areas, which work on the variability of the spectral response of burnt areas through different analysis techniques [62,63,64], the use of spatial autocorrelation instead operates at a different level, using, as in this case, sets of values derived from an index calculated on the basis of the spectral responses of “objects”. However, the feature under investigation is how this spectral response is arranged at a spatial level.

A fundamental theoretical implication of this study is precisely the high spatial autocorrelation generated in burned areas, generally higher than that determined by other vegetation dynamics or noise. This aspect facilitates an improvement in the discrimination of burned/unburned pixels compared to what is obtained with a “specialised” index in the detection of burned areas, such as dNBR.

It is interesting to note that other studies [65,66,67] have highlighted how fires contribute to the increase in “persistence” of vegetation dynamics, where persistence means a long-range correlation in temporal fluctuations within complex systems; the presence of such correlations implies the existence of “memory” phenomena in some historical data series. In other words, fire causes an immediate increase in the degree of organisation and spatial order (high autocorrelation), which seems to persist over time in the context of vegetation dynamics.

In addition to the possible theoretical implications, the results of this study may have practical applications for operators in the fire prevention sector by providing a useful tool for the automatic estimation of burned areas.

Future developments of the work presented here may mainly concern the following:

• Application of the same methodology using other spectral indices for the detection of burnt areas:
• Improve the use of separability/similarity indices to identify burned/unburned thresholds;
• Deepen the analysis, based on the methodology used, also for the identification of fire severity classes within the burned category.

6. Conclusions

In this work, a local spatial statistical thresholding approach has been proposed to generate binary maps of areas affected by fire events using Sentinel-2 imagery. The proposed methodology involves the application of the Getis-Ord-Gi statistical local spatial autocorrelation to develop two new indices (dGiNBR and dNBRGi). In the subsequent phase, aimed at defining and applying appropriate thresholds, these indices were used to obtain burned/unburned maps in three study areas. The results obtained show that the approach used can improve the results obtained with a spectral index such as dNBR, which is widely used for burned/unburned discrimination after fires. In particular, the improvements obtained concern the possibility of drastically reducing false positive pixels, which are one of the main problems in the interpretation of dNBR maps. The comparison with reference validation datasets (Copernicus EMS maps) shows that the approach used allows the generation of maps of areas affected by fires with higher accuracy than that obtained by simply applying traditional satellite-derived spectral indices. Therefore, the method, once automated, could be usefully applied by public and private sector personnel interested in the automatic estimation of burnt areas.