Development of a Novel Burned-Area Subpixel Mapping (BASM) Workflow for Fire Scar Detection at Subpixel Level

Abstract

The accurate detection of burned forest area is essential for post-fire management and assessment, and for quantifying carbon budgets. Therefore, it is imperative to map burned areas accurately. Currently, there are few burned-area products around the world. Researchers have mapped burned areas directly at the pixel level that is usually a mixture of burned area and other land cover types. In order to improve the burned area mapping at subpixel level, we proposed a Burned Area Subpixel Mapping (BASM) workflow to map burned areas at the subpixel level. We then applied the workflow to Sentinel 2 data sets to obtain burned area mapping at subpixel level. In this study, the information of true fire scar was provided by the Department of Emergency Management of Hunan Province, China. To validate the accuracy of the BASM workflow for detecting burned areas at the subpixel level, we applied the workflow to the Sentinel 2 image data and then compared the detected burned area at subpixel level with in situ measurements at fifteen fire-scar reference sites located in Hunan Province, China. Results show the proposed method generated successfully burned area at the subpixel level. The methods, especially the BASM-Feature Extraction Rule Based (BASM-FERB) method, could minimize misclassification and effects due to noise more effectively compared with the BASM-Random Forest (BASM-RF), BASM-Backpropagation Neural Net (BASM-BPNN), BASM-Support Vector Machine (BASM-SVM), and BASM-notra methods. We conducted a comparison study among BASM-FERB, BASM-RF, BASM-BPNN, BASM-SVM, and BASM-notra using five accuracy evaluation indices, i.e., overall accuracy (OA), user’s accuracy (UA), producer’s accuracy (PA), intersection over union (IoU), and Kappa coefficient (Kappa). The detection accuracy of burned area at the subpixel level by BASM-FERB’s OA, UA, IoU, and Kappa is 98.11%, 81.72%, 74.32%, and 83.98%, respectively, better than BASM-RF’s, BASM-BPNN’s, BASM-SVM’s, and BASM-notra’s, even though BASM-RF’s and BASM-notra’s average PA is higher than BASM-FERB’s, with 89.97%, 91.36%, and 89.52%, respectively. We conclude that the newly proposed BASM workflow can map burned areas at the subpixel level, providing greater accuracy in regards to the burned area for post-forest fire management and assessment.

1. Introduction

Forest fires represent one of the biggest threats to plant ecological systems and resources [1], and they are partially responsible for the increase of greenhouse gas in the atmosphere [2,3]. Around 350 million hectares of land are affected by forest fires annually due to natural or human causes [4,5,6]. Forest fires happen very frequently. A total of 3.52 million hectares of forests were burned in China from 2001 to 2015 according to National Forest Fire Prevention Plan (2016–2025) [7]. Mapping the burned area accurately and timely is essential for post-forest fire management and assessment [8], quantifying carbon budgets [9], and for analyzing the relationship between vegetation and climate [9]. The traditional methods for mapping burned area were followed using artificial ground surveys [10] and field sketches [11]. These methods for mapping burned area were very inefficient, and these data were unreliable when analyzed at large scale [12].

Satellite-remote sensing can acquire images continuously, even over remote areas, and has the advantage of wide coverage, being timeless, and low cost [13]. Burned area mapping based on satellite image has always been a hot spot of research [14,15,16,17].

Table 1. Overview of eleven widely used burned-area products.

No.	Burned-Area Product	Developer	Sensor	Spatial Resolution	Reference
1	Fire CCI 5.0	ESA	MODIS	250 m	[18]
2	Fire CCI 5.1	ESA	MODIS	250 m	[19]
3	FireCCILT10	ESA	AVHRR	0.25°	[20]
4	Copernicus burnt area	European Commission	PROBA-V	300 m	[21]
5	MCD64A1 c6	NASA	MODIS	500 m	[22]
6	GWIS	JRC	MODIS	500 m	[23]
7	GABAM	IRSDE/CAS	Landsat 8 OLI	30 m	[24]
8	Landsat Burned Area	NASA	Landsat TM Landsat ETM+ Landsat OLI	30 m	[25]
9	TREES	TREES-INPE	MODIS	250 m	[26]
10	DETER B	INPE	AWiFS	64 m	[27]
11	Global Fire Atlas	NASA	MODIS	500 m	[28]

Note: No. = number. ESA = European Space Agency. MODIS = Moderate-resolution Imaging Spectroradiometer. AVHRR = advanced very high resolution radiometer. PROBA = Project for On-Board Autonomy. MCD64A1 = MODIS Direct Broadcast Monthly Burned Area Product Collection 6. NASA = National Aeronautics and Space Administration. GWIS = Global Wildfire Information System. JRC = Joint Research Centre. GABAM = Global Annual Burned Area Mapping. IRSDE/CAS = Institute of Remote Sensing and Digital Earth-Chinese Academy of Sciences. OLI = Operational Land Imager. TM = Thematic mapper. ETM = Enhanced Thematic Mapper. TREES = Tropical Ecosystems and Environmental Sciences lab. INPE = National Institute for Space Research. DETER = near real-time deforestation detection. AWiFS = Advanced Wide-Field Sensor.

summarizes eleven widely used burned-area products.

However, the highest spatial resolution of the burned-area products is 30 m, as derived from Landsat data and shown in Table 1. Research on burned-area mapping with high spatial resolution satellite data, such as Sentinel 2 of 10 m spatial resolution, has been actively pursued [6,8,15,29,30]. Stroppiana et al. [15] mapped burned areas based on the Sentinel 2 data using an automatic machine learning (ML) algorithm from highly reliable fire points. Florath and Keller [14] detected burned areas using a generic approach based on ML and the Sentinel 2 data. Zhang et al. [6] presented a Siamese self-attention (SSA) classification strategy for burned area mapping using the Sentinel-1 & 2 data. Pinto et al. [8] applied a Burned Areas Neural Network (BA-NET) based method to map burned area using Sentinel-2 and Visible Infrared Imaging Radiometer Suite (VIIRS) data.

For any type of image data, pixel mixing is a common phenomenon [31,32,33]. A mixed pixel may contain an unknown composition of land cover types [34], affecting the simulation of radiative characteristics and inversion for land surface parameters from remote sensing data [33]. Mixing pixels has been a barrier in the application of remote sensing to burned area mapping. To overcome the barrier, a series of unmixing methods have been proposed, such as fully constrained least squares (FCLS) [35], maximum margin criterion and derivative weights (MDWSU) [36], minimum volume transform (MVT) [37], vertex component analysis (VCA) [38], simplex growing algorithm (SGA) [39], minimum volume constraint nonnegative matrix factorization (MVC-NMF) [40], successive projection algorithm (SPA) [41], etc. He et al. [42] showed that spectral unmixing methods have advantages over the remote sensing vegetation indices due to their ability to decompose the mixed pixel into several fractional abundances. Nascimento and Dias [38] performed a series of experiments using simulated and real data sets and found that the VCA algorithm performs better than the pixel purity index (PPI) method and better than or similar to the N-FINDR algorithms [43]. Miao and Qi [40] applied the MVC-NMF method to extract unsupervised endmembers from highly mixed image data. Zhang et al. [41] presented SPA that can provide a general guideline to constrain the total number of endmembers. Kumar et al. [44] estimated global land cover fractions from satellite data based on unconstrained lease squares (UCLS), fully constrained least squares (FCLS), modified fully constrained least squares (MFCLS), simplex projection (SP), sparse unmixing via variable splitting and augmented Lagrangian (SUnSAL), SUnSAL and total variation (SUnSAL TV), and Collaborateve SUnSAL (CL SUnSAL), and their results indicated that FCLS outperformed the other techniques. Thus, in this paper, we used FCLS for spectral unmixing of burned area in mixed pixels.

However, spectral unmixing methods only solve the problem of endmember types and abundances without being able to locate endmembers in a mixed pixel. To solve this problem, Atkinson [45,46] proposed the subpixel concept for precise spatial locations of endmembers in a mixed pixel based on unmixing analysis [47]. On the basis of Atkinson’s study, many algorithms have been developed [48], such as the spatial attraction model (SAM), double-calculated spatial attraction model (DSAM) [32], subpixel learning algorithms [44], subpixel edge detection method [49], etc. These subpixel techniques have found many applications [50,51,52,53]. For instance, the random forests and spatial attraction model (RFSAM) was applied to remote sensing images to improve the accuracy of subpixel mapping of wetland flooding [54]. Li et al. [55] predicted a land cover map accurately based on the spatio-temporal subpixel land cover mapping (STSPM) method. Ling et al. [56] monitored variations of reservoir surface water area accurately and timely from daily MODIS images by exploiting information at the subpixel scale. Deng and Zhu [57] successfully applied the Continuous Subpixel Monitoring (CSM) method to map urban impervious surface area (ISA%) at the subpixel scale and characterize its dynamics in Broome County, New York.

However, there are very few applications of these subpixel algorithms for burned area mapping [58]. In order to accurately map burned area, the exact location of the burned area in a mixed pixel is important for post-forest fire management and assessment, quantifying carbon budgets, etc. A good subpixel algorithm can help to map and locate burned area with subpixel accuracy, especially from low-spatial-resolution satellite images. However, current burned area mapping algorithms based on satellite remote sensing data can locate burned area only at the pixel level. The objective of this study is to develop a new algorithm to improve burned area mapping at the subpixel level. To this end, we proposed a burned area subpixel mapping (BASM) workflow. The first step is a spectral unmixing analysis using the fully constrained least squares (FCLS) method. The second step is to process the unmixing analysis results with the modified-pixel swapping algorithm (MPSA). The last step is post-classification after MPSA. We then applied the proposed BASM workflow to the Sentinel 2 data sets. The ground-truth fire-scar information provided by the Department of Emergency Management of Hunan Province, China was used as reference data for assessment.

2. Study Area

Hunan Province, China, is located in the middle Yangtze River, central China, within an area enclosed by 108°47′–114°15′ longitude and 24°38′–30°08′ latitude (Figure 1). Over the course of a year, its temperature typically varies from 7.78 °C to 33.33 °C. The rainiest month is June, with an average rainfall of 177.8 mm. The driest month is December, with an average rainfall of 35.56 mm. The relatively warm and humid weather results in lush vegetation and an evergreen landscape. Hunan Province has a subtropical, evergreen, broad-leaved forest with a forest coverage rate of 59.96%. Hunan Province has a land area of about 211,829 km², and a mountainous area of about 108,472 km² accounting for 51.21% of its total. Hunan Province is surrounded by mountains to the east, south, and west sides and a lake basin plain in the north, undulating in the central section, forming an asymmetrical horseshoe shaped terrain opening to the northeast. The east and south sides are mostly at an altitude of above 1000 m. The west side is 500–2099 m above sea level. The central section elevation is below 500 m. Most of the north side elevations are below 50 m. Forest and wetland ecosystems are the two major natural ecosystems. There are about 200 significant ecological zones around the world, and Hunan Province has two forest and wetland ecosystems, i.e., the subtropical, evergreen, broad-leaved forest ecological zones in Wuling Xuefeng Mountains and Nanling Luoxiao Mountains, known as the world’s most valuable ecological regions in the same latitude zone. Due to the high forest coverage rate and large mountainous area in Hunan Province, forest fire is a great potential hazard. There are many obstacles for post-forest fire management, e.g., accurate burned area mapping has to rely on manual surveys. To improve this situation, it is imperative to map burned area using automation or semi-automation algorithms, such as remote sensing-based detection and mapping methods.

3. Methodology

First, we obtained the locations of the 15 fire-scar sites based on the ground-truth fire scar information that was provided by the Department of Emergency Management of Hunan Province. Then, we downloaded the pre- and post-forest fire Sentinel 2 data sets and processed them. Second, burned area fraction was derived from the four selected Multispectral Instrument (MSI)/Sentinel 2 bands listed in

Table 2. Selected bands of Sentinel 2, GF 1, GF 1B, GF 1C, GF 1D, and GF 2 satellite imagery data sets used in the current study.

Satellite	Sensor	Band Number	Band Width (μm)	Spatial Resolution (m)
Sentinel 2	MSI	2	0.46–0.52	10
		3	0.54–0.58
		4	0.65–0.68
		8	0.79–0.90
GF 1, GF 1B, GF1C, GF1D	PMS	1	0.45–0.90	2
		2	0.45–0.52	8
		3	0.52–0.59
		4	0.63–0.69
		5	0.77–0.89
GF 2	PMS	1	0.45–0.90	1
		2	0.45–0.52	4
		3	0.52–0.59
		4	0.63–0.69
		5	0.77–0.89

using the FCLS method [44,59,60]. Taking burned area fraction as input for the Modified Pixel Swapping Algorithm (MPSA) in Visual Studio 2012 platform edited by C# language, we obtained the burned area at subpixel level as output. Furthermore, after a post-classification clump and sieve procedure on the output, the burned area at the subpixel level was mapped. Finally, a comparison analysis and accuracy assessment of the burned area mapped on subpixel level was performed using high spatial resolution GaoFen (GF) series data sets. The flowchart for mapping burned area at the subpixel is shown in Figure 2. Methodological steps are explained in detail over the following subsections.

3.1. Satellite Data and Preprocessing

3.1.1. Satellite Data

Sentinel 2 is an Earth observation mission of European Space Agency to support environmental services and natural disaster management [61,62]. The Sentinel 2 Multispectral Instrument (MSI) data were used in this study, sampling 13 spectral bands: four bands at 10 m, six bands at 20 m, and three bands at 60 m spatial resolutions over the visible, near infrared (NIR), and short wave infrared (SWIR) (https://sentinels.copernicus.eu/web/sentinel/user-guides/sentinel-2-msi/overview, last accessed on 3 April 2022) [62,63]. This makes it useful for land monitoring studies at local, regional, and global scales.

The sentinel 2 data were downloaded from United States Geological Survey (USGS, https://earthexplorer.usgs.gov/, last accessed on 1 March 2022) as a Level 1C product, which represent orthorectified, top-of-atmosphere (TOA) reflectance. GF series data sets are important component of China High-Resolution Earth Observation System (CHEOS) project sponsored by China National Space Administration (CNSA) [64]. We obtained GF series data sets from the China Centre for Resources Satellite Data and Application (http://www.cresda.com/CN/, last accessed on 2 February 2022) [65]. The GF 1 satellite, launched on 26 April 2013, is the first of China’s series of high resolution earth observation satellites operated by China [66]. The GF 1 satellite is equipped with one four-camera push-broom multispectral system to obtain an 800 km wide image and one two-camera panchromatic/multispectral system (PMS), allowing a temporal resolution of four days [67]. Each camera for the four-camera push-broom multispectral system is a wide field of view (WFV) camera with a resolution of 16 m. Thus, the four-camera push-broom multispectral system is also called a wide field of view system (WFVS). The GF 1 PMS has 5 spectral bands, of which one is the panchromatic band (band 1) of 2 m spatial resolution, and the other 4 bands (bands 2–5) are multispectral bands of 8 m resolution, as shown in Table 2. The GF 1B, GF 1C, and GF 1D satellites were launched on 31 March 2018, in coordination with GF 1 to observe earth surface. They have the same sensor systems as GF 1. The PMS on GF 2 also has 5 spectral bands but with higher spatial resolution, e.g., 1 m resolution for the panchromatic band (band 1) and 4 m resolution for the other multispectral bands (bands 2–5), as shown in Table 2. The Sentinel 2, and GF 1, GF 1B, GF 1C, GF 1D, and GF 2 satellite data sets (abbr. GF series data sets) were re-projected to a common Universal Transverse Mercator (UTM) projection with WGS84 as the datum so that all data sets can be overlaid within the same coordinate system. The Sentinel 2 data set has medium spatial resolution and was used as input to our mapping workflow of burned area at the subpixel level, and the GF series data sets have higher spatial resolution and were used as reference data for the accuracy assessment of burned area mapped at subpixel level. The Sentinel 2 satellite data were processed to bottom-of-atmosphere reflectance after radiometric calibration and atmospheric correction using the algorithm ‘Sen2Cor’ v2.8 (downloadable from http://step.esa.int/main/snap-supported-plugins/sen2cor/sen2cor_v2-8/, last accessed on 3 April 2022) [68,69,70]. Table 2 lists the specification of the Sentinel 2 bands (bands 2–4 and 8) selected for this study.

3.1.2. Data Preprocessing

To make full use of spectral information of the selected bands, we carried out two steps further on the Sentinel 2 data sets:

(1)

Geo-referencing based on Georeferencing tool in ArcMap 10.4 (ESRI) software, adding ten control points to determine the corresponding relationship between the Sentinel 2 data sets and the GF series data sets, and selecting first Order Polynomial (Affine) transformation [71,72,73,74].

(2)

Calculation of Normalized Difference Vegetation Index (NDVI) based on Band Math tool in the Environment for Visualizing Images (ENVI) software (version 5.3, Exelis, Herndon, VA, USA) using Equation (1) [75,76]:

NDVI = (NIR − Red)/(NIR + Red)

(1)

where NIR and Red represent band 2 and band 8 of Sentinel 2, respectively.

To take full advantage of all spectral information, we took four steps to process the GF series data sets (step 1, 3, 4 processed in ENVI 5.3, and step 2 processed in ArcMap 10.4):

(1)

Geometric orthorectification [77,78] was based on the RPC Orthorectification Batch tool using the Advanced Land-Observing Satellite (ALOS) digital elevation model (DEM) of 12.5 m spatial resolution [79,80].

(2)

Geo-referencing was based on the Georeferencing tool by adding ten control points to determine the correspondence between panchromatic band and multispectral bands and selecting first Order Polynomial (Affine) transformation [71,72,73,74].

(3)

Image fusion was based on the Pan Sharpening Batch tool to fuse panchromatic and multispectral bands to obtain images of 2 m resolution [77,81].

(4)

Resampling was based on the GF 2 images at 1 m spatial resolution after image fusion that were resampled to 2 m resolution using the cubic convolution interpolation method [82,83,84].

3.2. True Fire-Scar Information

Tabulated fire information collected (TFIC) that was provided by the Department of Emergency Management of Hunan Province was used as ground-truth fire-scar information for this study. Every forest fire event contained information about location, weather, starting and extinguishing times, burned area, and causes, etc. The Department of Emergency Management of Hunan Province confirmed and reported forest fire in details when a forest fire occurred (as shown in Figure 3). Field measurements, including burned area resulted from forest fire, were conducted with Global Navigation Satellite System (GNSS) survey equipment and Unmanned Aerial Vehicle (UAV). The platform was Phantom 4 Pro V2.0, and the sensor was 1-inch CMOS with 20 million effective pixels by well-trained personnel. Well-trained personnel created manually in situ vector data of burned area [85]. We transformed the vector data based on the GF series data sets into regions of interest (ROIs) to validate the proposed workflow. Within the TFIC between 2018 and 2021, fifteen fire-scar sites that caused the most environmental damages were selected as reference data for ground truth fire-scar information.

Table 3. Fire information at the fifteen selected sites.

No.	Date of the Fire Event	Longitude	Latitude	Extent (ha)
1HYHD	24 September 2019	113°3′	27°8′	1244.42
2CZGY	16 December 2019	112°53′	25°54′	166.82
3YZLS	1 October 2019	112°8′	25°32′	95.32
4HHHJ	6 October 2018	109°53′	27°15′	87.18
5XXFH	6 April 2019	109°40′	28°2′	78.23
6CZGD	4 January 2021	113°54′	25°58′	66.61
7CSNX	19 March 2020	112°0′	28°11′	53.06
8CZGY	31 October 2019	112°41′	25°29′	50.14
9CZBH	6 February 2019	112°52′	25°42′	39.18
10ZZLL	16 April 2020	113°27′	27°25′	37.99
11ZJJSZ	19 March 2020	110°0′	29°25′	34.72
12CZGD	19 January 2021	113°48′	25°49′	21.81
13YYTJ	9 April 2020	111°59′	28°16′	21.62
14YYTJ	9 April 2020	112°0′	28°16′	18.41
15YYTJ	14 March 2020	111°59′	28°14′	8.70

shows information concerning the 15 fire sites in Hengdong County (1HYHD), Guiyang County (2CZGY), Lanshan County (3YZLS), Hongjiang County (4HHHJ), Fenghuang County (5XXFH), Guidong County (6CZGD), Ningxiang County (7CSNX), Guiyang County (8CZGY), Beihu County (9CZBH), Liling County (10ZZLL), Sangzhi County (11ZJJSZ), Guidong County (12CZGD), Taojiang County (13YYTJ), Taojiang County (14YYTJ), and Taojiang County (15YYTJ).

3.3. BASM Approach for Fire Scar Detection

The proposed Burned Area Subpixel Mapping (BASM) workflow consists of three major steps: (1) spectral unmixing using the FCLS Spectral Unmixing tool in ENVI 5.3 software since it outperformed other techniques with the highest classification accuracy and least execution time [44], (2) obtaining burned area spatial distribution information from mixed pixels used modified-pixel swapping algorithm (MPSA), and (3) post-classification after MPSA to denoise the data [86], using the Clump tool in ENVI 5.3 software with Dilate Kernel Value of 3 and Erode Kernel Value of 3. Since burned area mapping at the subpixel level has been rarely investigated, we used the BASM to detect burned area spatial distribution within mixed pixels. The burned area abundance after FCLS was processed with the MPSA to get the final results. Based on the Sentinel 2 satellite data, we divided each pixel into 5 × 5 sub-pixels so that each subpixel has a spatial resolution of 2 m. The final result of burned areas with geographic locations at subpixel level will show the specific spatial distribution of burned areas within a mixed pixel.

3.3.1. Fully Constrained Least Squares (FCLS)

To estimate the abundance of burned area in a mixed pixel in the Sentinel 2 images, we used the well-performed FCLS [35,44,87] method for linear spectral unmixing analysis. There are two constraints imposed on the analysis: (1) endmember abundance sum-to-one ${\displaystyle {\sum }_{j=1}^p{\alpha }_j=1}$, and (2) abundance nonnegativity ${\alpha }_j\ge 0$ (1 ≤ j ≤ p). We extracted spectra of three variable set of endmembers manually: bare land, forest, and burned area from a Sentinel 2 image, and save them as spectral library (.sli format) for FCLS as input.

3.3.2. Modified Pixel Swapping Algorithm (MPSA)

Atkinson [47] proposed the pixel swapping algorithm (PSA) method that was designed to process an image of land cover proportions in K = 2 classes. In this study, the PSA method was applied to the spectral unmixing results after FCLS. If 10 × 10 (=100) subpixels are to be mapped within each mixed pixel, a land cover class (with or without burned area) with a fraction of 57 percent means that 57 subpixels were allocated to that class. Furthermore, these subpixels are randomly located within the mixed pixel. Once allocated, only the spatial arrangement of the subpixels, not the actual attribute values, can vary. The number of subpixels allocated to that class within each mixed pixel remains fixed. PSA is comprised of three basic steps, but we improved the algorithm as the Modified Pixel Swapping Algorithm (MPSA) that has four steps as detailed below: Firstly, in satellite images with 10 m spatial resolutions, we took burned area as a continuous entity. Within the abundance results after applying the FCLS algorithm, some pixels will appear as false burned area due to noise [60,88,89]. In order to minimize misclassification and effects due to noise in the FCLS results on the final burned area at subpixel level, we modified the PSA by adding the object-based approach for classifying burned area, filtered out negative burned area caused by noise, compared with the results from three pixel-based classifiers, and found the most suitable denoising method for this study. We chose a well-known object-based approach and used the three pixel-based classifiers imbedded in the ENVI 5.3 software. Specifically, for the object-based and three pixel-based classifiers, we used four models, including feature extraction rule based (FERB) [90,91], random forest (RF) [92,93], backpropagation neural net (BPNN) [94,95], and support vector machine (SVM) [96,97], that are well-known for their good performance. We manually selected 30% of the clipped image as training samples for RF, BPNN, and SVM, and used the rest as test samples. We took the result of FERB, RF, BPNN, and SVM, respectively, with the result of FCLS as the input of the BASM method. The step of traversing the pixel value of FERB, RF, BPNN, SVM respectively reduced the misclassification and effect due to noise for mapping the burned area at subpixel level. The parameter setup of the four models is shown in

Table 4. Parameter setup of FERB, RF, BPNN, and SVM.

Model	Parameter Setup	Training Percent
FERB	(1) Custom Bands (Normalized Difference) Band 1: Red, Band 2: NIR (2) Segment Settings (Algorithm: Edge, Scale Level: 50.0), Merge Settings (Algorithm: Full Lambda Schedule, Merge Level: 91.8) (3) Rule Attributes Type: Spectral, Name: Spectral Mean	-
RF	(1) Number of Trees: 100 (2) Number of Features: Square Root (3) Impurity Function: Gini Coefficient (4) Min Node Samples: 1 (5) Min Impurity: 0	30%
BPNN	(1) Training Threshold Contribution: 0.9 (2) Training Rate: 0.2 (3) Training Momentum: 0.9 (4) Training RMS Exit Criteria: 0.1 (5) Number of Hidden Layer: 1 (6) (Number of Training Iterations: 100	30%
SVM	(1) Kernel Type: Polynomial (2) Degree of Kernel Polynomial: 2 (3) Bias in Kernel Function: 1 (4) Penalty Parameter: 100 (5) Pyramid Levels: 0	30%

.

Secondly, for every subpixel p_i, its attractiveness A($p_i^c$) in the c-th class is predicted as a distance-weighted function of its j = 1,2, …, J neighbors:

$$A(p_i^c)={\displaystyle \sum _{j=1}^J{\lambda }_{ij}z(x_j^c)}$$

(2)

where z($x_j^c$) is the value of the j-th subpixel belonging to the c-th class (c = 1 or 2), and λ_ij is a distance-dependent weight given by the following equation:

$${\lambda }_{ij}=\exp (\frac{-h_{ij}}{\alpha })$$

(3)

where h_ij is the distance between two subpixels p_i and p_j, and a is the non-linear parameter of the exponential model. In this study, a is chosen to be 3.

Thirdly, once the attractiveness of each subpixel has been calculated based on the current arrangement of subpixel classes, the subpixel algorithm ranks the values on a pixel-by-pixel basis. For each pixel, the least attractive subpixel currently allocated to a “1” (i.e., a “1” surrounded mainly by “0”s) is stored (as shown in Equation (4)):

$$\mathrm{candidate\; A}=(x_i^c:A(p_i^c) = \min (\mathrm{A}\left)\right|z\left(x_i^c\right) = 1)$$

(4)

The most attractive subpixel currently allocated to a “0” (i.e., a “0” surrounded mainly by “1”s) is also stored (as shown in Equation (5)):

$$\mathrm{candidate\; B} = (x_j^c : A(p_j^c) = \max (\mathrm{A})|z(x_j^c) = 0)$$

(5)

Lastly, classes of subpixels are swapped as follows: if the attractiveness of the least attractive subpixel is less than that of the most attractive subpixel, the classes are swapped for the subpixels in question to enhance spatial correlation of the sub-pixels (as shown in Equation (6)):

$$\left.\begin{array}{c}\mathrm{z}(x_i^c)=0\\ z(x_j^c)=1\end{array}\right\}\begin{array}{cc}& \end{array}\mathrm{if}\begin{array}{c}\\ \end{array}{A}_i<A_j$$

(6)

Otherwise no swapping is made.

For the convenience of presenting the results of the proposed BASM traversing through the four models, we named the BASM with FERB as BASM-FERB, with RF as BASM-RF, with BPNN as BASM-BPNN, and with SVM as BASM-SVM, respectively. Furthermore, we directly named BASM without traversing any of the four models as BASM-notra. To demonstrate minimizing misclassification and effect due to noise of the BASM-FERB, BASM-RF, BASM-BPNN, and BASM-SVM, we compared them with BASM-notra. After comparing and analyzing the accuracy assessment of the BASM-FERB, BASM-RF, BASM-BPNN, BASM-SVM, and BASM-notra, the method with the highest accuracy was obtained.

3.4. Accuracy Assessment

To evaluate the performance of the BASM workflow, fifteen fire-scar sites with TFIC were selected as reference to assess the accuracy of burned area mapping at subpixel level. For each fire-scar site in a Sentinel 2 image, we used the extracted burned area vector data from the GF series data sets as the reference image due to their high spatial resolution. Five widely used quality indexes, i.e., overall accuracy (OA) [98,99], user’s accuracy (UA) [100,101], producer’s accuracy (PA) [102,103], intersection over union (IoU) [104,105], and Kappa coefficient (Kappa) [106,107] were calculated for evaluation. OA represents the proportion of the correctly predicted number of pixels to the total. UA represents the proportion of true burned area to the predicted burned area. PA represents the correctly predicted burned area to the true burned area. IoU represents the correct classification accuracy of the models. Kappa represents the agreement between the predictions and ground truth. They can be formulated as follows and calculated from the confusion matrix (as shown in

Table 5. Confusion matrix of ground truth and prediction.

	Ground Truth	Burned Area	Background
Prediction
Burned area		True Positive (TP)	False Positive (FP)
Background		False Negative (FN)	True Negative (TN)

).

Five widely used quality indexes given by the following equation:

$$OA=\frac{TP+TN}{TP+FP+FN+TN}$$

(7)

$$UA=\frac{TP}{TP+FP}$$

(8)

$$PA=\frac{TP}{TP+FN}$$

(9)

$$IoU=\frac{TP}{TP+FP+FN}$$

(10)

$$\begin{array}{l}Kappa = \frac{OA - Pe}{1 - Pe}Where,\\ Pe=\frac{(TP + FP) \times (TP + FN) + (FN + TN) \times (FP + TN)}{{(TP + FP + TN + FN)}^2}\end{array}$$

(11)

4. Results

4.1. Reduction of Misclassification Due to Noise

To solve the misclassification and noise problem in mapping burned areas at the subpixel level, we analyzed misclassification and effects due to noise for the BASM-notra, BASM-FERB, BASM-RF, BASM-BPNN, and BASM-SVM. We chose eleven fire-scar sites in Hunan Province, China as examples from Table 3, and they were 2CZGY, 3YZLS, 4HHHJ, 5XXFH, 6CZGD, 9CZBH, 10ZZLL, 12CZGD, 13YYTJ, 14YYTJ, and 15YYTJ, respectively.

As shown in Figure 4, burned area mapped at the subpixel level based on BASM-FERB (Panel C), BASM-RF (Panel D), BASM-BPNN (Panel E), and BASM-SVM (Panel F) presents less misclassification and effect due to noise than that based on BASM notra (the Panel B). The results indicated that the proposed BASM combining with the four models (classifiers) is effective in minimizing misclassification and effect due to noise. The effect in minimizing misclassification and effect due to noise by BASM-FERB is generally better than BASM-RF, BASM-BPNN, and BASM-SVM.

4.2. Pixel and Subpixel Mapping of Burned Area

To illustrate the advantage of the proposed BASM for mapping burned area at subpixel level compared with the traditional object-based method (FERB) and pixel-based method (RF, BPNN, and SVM), we tested it on the fifteen fire-scar sites using the Sentinel 2 satellite image. We compared results from BASM-FERB with FERB, BASM-RF with RF, BASM-BPNN with BPNN, and BASM-SVM with SVM, respectively. We took two fire-scar sites in Hunan Province, China as examples. The first fire-scar site is located in Ningxiang County with 53.06 ha burned area (i.e., 7CSNX) and the second fire-scar site is located in Guiyang County with 50.14 ha burned area (i.e., 8CZGY).

Results for the two examples were shown in Figure 5, in which we compared the burned area mapped at subpixel level with that mapped at pixel level. Comparing panel B with panel G, panel C with panel H, panel D with panel I, and panel E with panel J, we can see that methods FERB, RF, BPNN, and SVM can roughly classify the burned area range (i.e., panels B–E). However, the boundaries of the burned area mapped at pixel level are rough and the visual effect is poor, in contrast to the boundaries of the burned area mapped at subpixel level (i.e., panels G–J) that are clearer and have more spatial details. Results shown in panels B–E, and G–J in Figure 5, indicate that the burned area mapped was not fully classified. Comparing panels B–E, the burned area mapped at pixel level using the FERB (i.e., panel B) is more similar to the reference map (i.e., panel A) than others (i.e., panels C–E). Comparing panels G–J, the burned area mapped at subpixel level using BASM-FERB (i.e., panel G) is more similar to the reference map (i.e., panel F) than others (i.e., panels H–J).

4.3. Accuracy Assessment of the BASM Approach

To further assess the performance of the proposed BASM method, we evaluated it quantitatively at the fifteen fire-scar sites using the Sentinel 2 satellite images. As in Section 4.2, we took two fire-scar sites in Hendong County (i.e., 1HYHD) with 1244.42 ha burned area and Sangzhi County (i.e., 11ZJJSZ) with 34.72 ha burned area.

The results for the Hendong site are shown in Figure 6a. In the panels E–H, the BASM-FERB, BASM-RF, BASM-BPNN, and BASM-SVM have shown classifying ability in the extraction and classification of burned area. Furthermore, as shown in the green circle in panels E–H, the BASM-FERB is better than BASM-RF, BASM-BPNN, and BASM-SVM, which can minimize misclassification in the burned area mapped at subpixel level and can make the burned area mapped at subpixel level accurate. As shown in

Table 6. A performance comparison among BASM-FERB, BASM-RF, BASM-BPNN, BASM-SVM, and BASM-notra using the Sentinel-2 images (scale = 5).

No.	Algorithm		Ground Truth	Burned Area	Background	OA	UA	PA	IoU	Kappa
		Prediction
1HYHD	BASM-FERB	Burned area		2,026,688	159,559	98.56%	92.70%	94.04%	87.56%	92.56%
		Background		128,375	17,724,410
	BASM-RF	Burned area		2,082,757	288,361	98.20%	87.84%	96.64%	85.24%	91.02%
		Background		72,306	17,595,608
	BASM-BPNN	Burned area		2,073,524	387,511	97.66%	84.25%	96.22%	81.55%	88.52%
		Background		81,539	17,496,458
	BASM-SVM	Burned area		2,086,017	486,179	97.23%	81.10%	96.80%	78.98%	86.70%
		Background		69,046	17,397,790
	BASM-notra	Burned area		2,098,326	3,151,184	83.99%	39.97%	97.37%	39.54%	48.88%
		Background		56,737	14,732,785
2CZGY	BASM-FERB	Burned area		223,195	44,697	98.08%	83.32%	85.82%	73.24%	83.53%
		Background		36,866	3,939,935
	BASM-RF	Burned area		232,539	75,721	97.57%	75.44%	89.42%	69.25%	80.54%
		Background		27,522	3,908,911
	BASM-BPNN	Burned area		225,850	70,289	97.54%	76.26%	86.85%	68.37%	79.90%
		Background		34,211	3,914,343
	BASM-SVM	Burned area		230,479	92,204	97.13%	71.43%	88.62%	65.43%	77.58%
		Background		29,582	3,892,428
	BASM-notra	Burned area		241,068	1,343,544	67.90%	15.21%	92.70%	15.03%	17.45%
		Background		18,993	2,641,088
3YZLS	BASM-FERB	Burned area		200,224	57,503	98.99%	77.69%	88.52%	70.58%	82.23%
		Background		25,973	7,965,280
	BASM-RF	Burned area		205,704	145,159	97.99%	58.63%	90.94%	55.39%	70.30%
		Background		20,493	7,877,624
	BASM-BPNN	Burned area		205,320	192,130	97.42%	51.66%	90.77%	49.08%	64.61%
		Background		20,877	7,830,653
	BASM-SVM	Burned area		204,996	208,250	97.22%	49.61%	90.63%	47.19%	62.80%
		Background		21,201	7,814,533
	BASM-notra	Burned area		205,681	1,036,790	87.18%	16.55%	90.93%	16.29%	24.51%
		Background		20,516	6,985,993
4HHHJ	BASM-FERB	Burned area		184,576	26,509	96.26%	87.44%	86.30%	76.78%	84.68%
		Background		29,306	1,250,957
	BASM-RF	Burned area		184,338	12,439	97.18%	93.68%	86.19%	81.45%	88.15%
		Background		29,544	1,265,027
	BASM-BPNN	Burned area		183,598	20,268	96.61%	90.06%	85.84%	78.41%	85.93%
		Background		30,284	1,257,198
	BASM-SVM	Burned area		185,900	18,787	96.86%	90.82%	86.92%	79.90%	87.00%
		Background		27,982	1,258,679
	BASM-notra	Burned area		187,594	272,474	79.97%	40.78%	87.71%	38.57%	44.88%
		Background		26,288	1,004,992
5XXFH	BASM-FERB	Burned area		128,313	50,831	92.08%	71.63%	95.19%	69.13%	76.82%
		Background		6478	537,928
	BASM-RF	Burned area		128,592	55,431	91.48%	69.88%	95.40%	67.60%	75.37%
		Background		6199	533,328
	BASM-BPNN	Burned area		128,266	59,456	90.88%	68.33%	95.16%	66.03%	73.88%
		Background		6525	529,303
	BASM-SVM	Burned area		128,461	57,418	91.19%	69.11%	95.30%	66.83%	74.64%
		Background		6330	531,341
	BASM-notra	Burned area		129,416	147,370	78.89%	46.76%	96.01%	45.87%	50.48%
		Background		5375	441,389
6CZGD	BASM-FERB	Burned area		113,575	61,535	98.78%	64.86%	83.72%	57.60%	72.48%
		Background		22,081	6,641,201
	BASM-RF	Burned area		108,901	149,392	97.42%	42.16%	80.28%	38.20%	54.09%
		Background		26,755	6,553,344
	BASM-BPNN	Burned area		86,921	100,463	97.82%	46.39%	64.07%	36.81%	52.73%
		Background		48,735	6,602,273
	BASM-SVM	Burned area		90,620	169,078	96.87%	34.89%	66.80%	29.74%	44.39%
		Background		45,036	6,533,658
	BASM-notra	Burned area		117,067	2,076,082	69.37%	5.34%	86.30%	5.29%	6.56%
		Background		18,589	4,626,654
7CSNX	BASM-FERB	Burned area		105,881	9985	99.28%	91.38%	89.65%	82.66%	90.13%
		Background		12,225	2,968,290
	BASM-RF	Burned area		105,414	24,109	98.81%	81.39%	89.25%	74.12%	84.52%
		Background		12,692	2,954,166
	BASM-BPNN	Burned area		101,541	39,733	98.18%	71.88%	85.97%	64.33%	77.35%
		Background		16,565	2,938,542
	BASM-SVM	Burned area		104,017	60,100	97.60%	63.38%	88.07%	58.37%	72.49%
		Background		14,089	2,918,175
	BASM-notra	Burned area		106,945	776,466	74.56%	12.11%	90.55%	11.95%	15.68%
		Background		11,161	2,201,809
8CZGY	BASM-FERB	Burned area		109,602	18,969	99.78%	85.25%	91.69%	79.14%	88.24%
		Background		9927	12,827,564
	BASM-RF	Burned area		106,355	70,008	99.36%	60.30%	88.98%	56.11%	71.58%
		Background		13,174	12,776,525
	BASM-BPNN	Burned area		91,376	101,001	99.00%	47.50%	76.45%	41.43%	58.12%
		Background		28,153	12,745,532
	BASM-SVM	Burned area		92,605	148,864	98.64%	38.35%	77.47%	34.50%	50.70%
		Background		26,924	12,697,669
	BASM-notra	Burned area		110,832	3,116,582	75.90%	3.43%	92.72%	3.42%	4.93%
		Background		8697	9,729,951
9CZBH	BASM-FERB	Burned area		79,646	6466	99.71%	92.49%	84.23%	78.84%	88.02%
		Background		14,909	7,253,485
	BASM-RF	Burned area		81,599	132,326	98.02%	38.14%	86.30%	35.97%	52.05%
		Background		12,956	7,127,625
	BASM-BPNN	Burned area		80,102	33,232	99.35%	70.68%	84.71%	62.68%	76.74%
		Background		14,453	7,226,719
	BASM-SVM	Burned area		80,723	69,095	98.87%	53.88%	85.37%	49.33%	65.52%
		Background		13,832	7,190,856
	BASM-notra	Burned area		81,637	1,361,640	81.31%	5.66%	86.34%	5.61%	8.41%
		Background		12,918	5,898,311
10ZZLL	BASM-FERB	Burned area		79,636	21,504	98.54%	78.74%	96.34%	76.45%	85.89%
		Background		3027	1,575,007
	BASM-RF	Burned area		80,329	31,448	97.99%	71.87%	97.18%	70.40%	81.58%
		Background		2334	1,565,063
	BASM-BPNN	Burned area		79,095	43,596	97.19%	64.47%	95.68%	62.65%	75.60%
		Background		3568	1,552,915
	BASM-SVM	Burned area		79,949	35,429	97.73%	69.29%	96.72%	67.70%	79.57%
		Background		2714	1,561,082
	BASM-notra	Burned area		80,789	415,268	75.16%	16.29%	97.73%	16.22%	21.28%
		Background		1874	1,181,243
11ZJJSZ	BASM-FERB	Burned area		74,445	14,469	98.81%	83.73%	95.12%	80.28%	88.44%
		Background		3816	1,444,226
	BASM-RF	Burned area		76,165	33,209	97.70%	69.64%	97.32%	68.33%	80.00%
		Background		2096	1,425,486
	BASM-BPNN	Burned area		75,969	28,422	98.00%	72.77%	97.07%	71.21%	82.15%
		Background		2292	1,430,273
	BASM-SVM	Burned area		76,088	42,822	97.07%	63.99%	97.22%	62.84%	75.69%
		Background		2173	1,415,873
	BASM-notra	Burned area		76,134	358,382	76.54%	17.52%	97.28%	17.44%	23.05%
		Background		2127	1,100,313
12CZGD	BASM-FERB	Burned area		51,663	16,858	98.00%	75.40%	94.67%	72.33%	82.89%
		Background		2909	915,928
	BASM-RF	Burned area		51,378	11,115	98.55%	82.21%	94.15%	78.22%	87.01%
		Background		3194	921,671
	BASM-BPNN	Burned area		51,823	21,254	97.57%	70.92%	94.96%	68.34%	79.93%
		Background		2749	911,532
	BASM-SVM	Burned area		51,871	23,054	97.39%	69.23%	95.05%	66.82%	78.75%
		Background		2701	909,732
	BASM-notra	Burned area		52,156	248,396	74.60%	17.35%	95.57%	17.22%	22.08%
		Background		2416	684,390
13YYTJ	BASM-FERB	Burned area		56,955	7470	99.10%	88.41%	88.87%	79.59%	88.17%
		Background		7133	1,553,830
	BASM-RF	Burned area		57,249	29,067	97.79%	66.32%	89.33%	61.46%	75.00%
		Background		6839	1,532,233
	BASM-BPNN	Burned area		54,470	46,672	96.54%	53.85%	84.99%	49.18%	64.20%
		Background		9618	1,514,628
	BASM-SVM	Burned area		54,566	41,569	96.86%	56.76%	85.14%	51.64%	66.53%
		Background		9522	1,519,731
	BASM-notra	Burned area		57,299	364,515	77.16%	13.58%	89.41%	13.37%	17.97%
		Background		6789	1,196,785
14YYTJ	BASM-FERB	Burned area		37,597	4881	98.42%	88.51%	76.81%	69.84%	81.42%
		Background		11,354	975,321
	BASM-RF	Burned area		37,398	20,004	96.93%	65.15%	76.40%	54.24%	68.72%
		Background		11,553	960,198
	BASM-BPNN	Burned area		37,517	35,993	95.39%	51.04%	76.64%	44.17%	58.93%
		Background		11,434	944,209
	BASM-SVM	Burned area		36,738	28,961	96.00%	55.92%	75.05%	47.15%	62.02%
		Background		12,213	951,241
	BASM-notra	Burned area		37,882	223,392	77.22%	14.50%	77.39%	13.91%	17.84%
		Background		11,069	756,810
15YYTJ	BASM-FERB	Burned area		17,275	9606	97.30%	64.26%	91.84%	60.80%	74.24%
		Background		1534	384,615
	BASM-RF	Burned area		17,248	12,262	96.65%	58.45%	91.70%	55.51%	69.71%
		Background		1561	381,959
	BASM-BPNN	Burned area		16,632	14,289	96.01%	53.79%	88.43%	50.25%	64.90%
		Background		2177	379,932
	BASM-SVM	Burned area		16,938	16,300	95.60%	50.96%	90.05%	48.24%	62.93%
		Background		1871	377,921
	BASM-notra	Burned area		17,383	92,802	77.19%	15.78%	92.42%	15.57%	20.79%
		Background		1426	301,419
Average	BASM-FERB					98.11%	81.72%	89.52%	74.32%	83.98%
	BASM-RF					97.44%	68.07%	89.97%	63.43%	75.31%
	BASM-BPNN					97.01%	64.92%	86.92%	59.63%	72.23%
	BASM-SVM					96.82%	61.25%	87.68%	56.98%	69.82%
	BASM-notra					77.13%	18.72%	91.36%	18.35%	22.99%

, the BASM-FERB outperformed BASM-RF, BASM-BPNN, and BASM-SVM with OA, UA, IoU, and Kappa being 98.56%, 92.70%, 87.56%, and 92.56% respectively, but with PA being 94.04%, slightly lower than that of BASM-RF’s, BASM-BPNN’s, and BASM-SVM’s.

The results for the Sangzhi site (i.e., 11ZJJSZ) are shown in Figure 6b. BASM-FERB, BASM-RF, BASM-BPNN, and BASM-SVM have shown good classifying ability in deriving burned area from Sentinel 2. Furthermore, the BASM-FERB can more effectively minimize misclassification on the burned area mapped at subpixel level. As shown in Table 6, BASM-FERB also performed better than BASM-RF, BASM-BPNN, and BASM-SVM with OA, UA, IoU, and Kappa being 98.81%, 83.73%, 80.28%, and 88.44% respectively, but in the area encircled by the green circle in panels E–H, BASM-RF, BASM-BPNN, and BASM-SVM could derive burned area from the Sentinel 2 image while BASM-FERB could not.

As shown in Table 6, thirteen out of the fifteen fire-scar sites demonstrated that BASM-FERB outperformed BASM-RF, BASM-BPNN, and BASM-SVM. Furthermore, the average OAs of BASM-FERB, BASM-RF, BASM-BPNN, BASM-SVM, and BASM-notra are 98.11%, 97.44%, 97.01%, 96.82%, and 77.13% respectively. The average UAs of BASM-FERB, BASM-RF, BASM-BPNN, BASM-SVM, and BASM-notra are 81.72%, 68.07%, 64.92%, 61.25%, and 18.72% respectively. The average IoUs of BASM-FERB, BASM-RF, BASM-BPNN, BASM-SVM, and BASM-notra are 74.32%, 63.43%, 59.63%, 56.98%, and 18.35% respectively. The average Kappas of BASM-FERB, BASM-RF, BASM-BPNN, BASM-SVM, and BASM-notra are 83.98%, 75.31%, 72.23%, 69.82%, and 22.99% respectively. The average PAs of BASM-FERB, BASM-RF, BASM-BPNN, BASM-SVM, and BASM-notra are 89.52%, 89.97%, 86.92%, 87.68%, and 91.36% respectively.

5. Discussion

At present, the research on burned area mapping is mainly at pixel scale [6,8,29,58,108]. Based on the moderate spatial resolution Sentinel 2 data sets, we introduced the concept of subpixel for burned area mapping, and the results had relatively high accuracy. In addition, we modified the pixel swapping algorithm by innovatively traversing the four well-performed classifiers, which reduced the misclassification and effect due to noise of burned area mapped at subpixel level. Traditionally, burned area mapping was done by artificial ground surveys and field sketches [12], which is difficult to cover a large area. Data collection and spatialization is difficult too. Burned area mapping using satellite image data has become a subject of extensive research over the past decades [6,8], and research on using remote sensing techniques to generate products of global burned area started in the late 1980s [109]. The advent of remote sensing techniques, either space-borne [15] or airborne [110], gives researchers an alternative or even better way for burned area mapping.

Reduction in noise and misclassification using remote sensing images has always been a classical problem, which has attracted a lot of research interests [111]. There are many methods for noise reduction and classification improvement, including second-generation wavelets [112], rank approximation [113], Asymmetrical Gaussian function-fitting [114], Double logistic function-fitting [114], and so on. In the current study, the burned area abundance obtained using FCLS is hindered by ubiquitous noise, thus we modified Pixel Swapping Algorithm by traversing the four well-performed classifiers or models, and then getting the burned area mapped at subpixel level that performed well in noise reduction and classification improvement.

Based on satellite remote sensing image data and techniques, there are many studies using machine learning algorithms for burned area mapping [15,17,29,75,115]. Xulu et al. [29] adopt Random Forest classifier to separate burned from unburned area using the Sentinel 2 data. Ramo et al. [17] explored the random forest, support vector machine, neural networks, and decision tree algorithm (C5.0) for classifying burned area at global scale based MODIS data. In addition, researchers used deep learning algorithm [8,30,108,116] to classify burned area from images collected by different sensors. For example, Seydi et al. [30] proposed a novel framework based on deep Siamese morphological neural network (DSMNN-Net) for burned area mapping. Zhang et al. [6] presented a Siamese self-attention classification strategy for the multi-sensor burned area mapping.

However, whether using machine learning algorithms or deep learning algorithms based on remote sensing data for burned area mapping, most current research basically performs the mapping at pixel level, and very rarely at subpixel level. In this paper, we proposed the BASM workflow and evaluated it at fifteen fire-scar sites, and the results indicated that using BASM-FERB, BASM-RF, BASM-BPNN, and BPSM-SVM for mapping burned area at subpixel level provides finer resolution when compared to FERB, RF, BPNN, and SVM at pixel level. The efficiency of the BASM-FERB, BASM-RF, BASM-BPNN, and BPSM-SVM was roughly the same, and each method took less than 30 min from the start to the output of results. In addition, burned area mapped at the subpixel level using BASM-FERB agreed very well to the reference data.

Furthermore, burned area mapping at pixel level could cause large errors. Ability to specify the distribution of endmember composition in a mixed pixel can improve such a situation [46]. Ruescas et al. [117] estimated burnt land percentage at subpixel level using Advanced Very High Resolution Radiometer (AVHRR) data with a mean error of 6.5%. In this paper, we selected endmembers manually, which was not as efficient as automatic or semiautomatic procedures and was subject to operator experience. It needs to be considered to adopt automatic or semiautomatic procedures for endmember selection, such as the Pixel Purity Index (PPI) and Sequential Maximum Angle Convex Cone (SMACC) algorithms in ENVI. Furthermore, we derived burned area abundance from the Sentinel 2 data and further output the specific spatial distribution of burned area in mixed pixels. It is widely known that, in mountainous areas, burned area mapping based on unmixing models is confounded by shadows. For example, as shown in Figure 4, the misclassification and effect due to noise, including any red area beyond the yellow line, may be caused by shadows. In order to minimize misclassification and effects confounded by shadows, we modified the PSA by traversing the result of four approaches respectively, then filtered out the negative burned area caused by noise, such as shadows. In this study, we proposed the BASM workflow for mapping burned area at the subpixel level and we compared BASM-FERB, BASM-RF, BASM-BPNN, BASM-SVM, and BASM-notra with each other. Except for the case that the BASM-FERB’s average PA (=89.52%) is slightly lower than that of BASM-RF (average PA = 89.97%) and BASM-notra (average PA = 91.36%), BASM-FERB’s OA, UA, IoU, and Kappa are significantly higher than those of the other four methods. It is of great significance for post-forest fire management and assessment to derive burned area at the subpixel level from remote sensing data. Moreover, the BASM-FERB method was successfully applied to the fifteen fire-scar sites in Hunan Province, China.

6. Conclusions

We proposed an approach named BASM to map burned area at the subpixel level using Sentinel 2 image data. The proposed method contains three main steps: (1) spectral unmixing used FCLS, (2) derivation of burned area at subpixel level using MPSA, and (3) post-classification after MPSA using Clump. The BASM was applied to fifteen fire-scar sites located in Hunan Province, China. Comparing with the traditional mapping methods (FERB, RF, BPNN, and SVM) for burned area mapping at pixel level, BASM-FERB, BASM-RF, BASM-BPNN, and BASM-SVM generated burned area as mapped at the subpixel level. In terms of minimizing misclassification and effects due to noise, a comparison between BASM-notra, BASM-FERB, BASM-RF, BASM-BPNN, and BASM-SVM could optimize the selection of methods to reduce noise effectively. Results showed that BASM-FERB has better mapping accuracy of burned area at the subpixel level, which is reflected in four accuracy evaluation indices i.e., OA, UA, IoU, and Kappa. The mapping accuracy of burned area at subpixel level based on the BASM-FERB has been largely enhanced with average OA (98.11%), average UA (81.72%), average IoU (74.32%), and average Kappa (83.98%), respectively. Even though BASM-RF’s and BASM-notra’s average PA (89.97%), (91.36%) is higher than BASM-FERB’s (89.52%), the difference is very small. We concluded that: (1) the BASM method developed in this study has well demonstrated its better performance in mapping burned area at the subpixel level compared to conventional methods at the pixel level, (2) the BASM in combination with any of the four well-performing classifiers can reduce misclassification and minimize noise effectively when compared with the results obtained by BASM alone, and (3) the BASM-FERB can generate more accurate burned area as mapped at subpixel level than BASM-RF, BASM-BPNN, BASM-SVM, and BASM-notra. This new mapping technique for mapping burned area at the subpixel level can enhance post-fire management and assessment and help in quantifying carbon budgets. We guess that the BASM method will also have better effects in vegetation mapping, snow mapping, and other applications. The result in this paper provides a reference for the refined utilization of satellite remote sensing data sets with moderate spatial resolution.