1. Introduction

2. Data and Methods

2.2. Method

The forest fire discrimination method based on the Angle slope index utilizes the unique characteristics of angles formed by reflectance values in visible, near-infrared, and short-wave infrared bands, as well as brightness temperatures in mid-infrared and far-infrared bands in the spectral images of forested areas and fire points. The method also leverages changes in these angles observed in spectral images during a fire event to construct a forest fire discrimination index. Additionally, a decomposed three-dimensional OTSU adaptive threshold segmentation algorithm is used to calculate the forest fire index thresholds against different backgrounds. The accuracy of this method is evaluated using actual forest fire data. Figure 6 illustrates the data processing and analysis flowchart, which will be elaborated in the subsequent sub-sections.

2.2.1. The Theoretical Basis of Satellite Remote Sensing Fire Point Identification

When forest fires occur, vegetation in the burning area is destroyed, and the decrease of chlorophyll content causes changes in the reflectance of visible, red-edge and near-infrared (NIR) bands, which are specifically reflected in the reflectance of near-infrared band decreases, the short-wave infrared reflectance increases, and the normalized vegetation index ($NDVI=(NIR-R)/(NIR+R)$decreases significantly. At the same time, according to the basic law of thermal radiation (Wien displacement law), the wavelength corresponding to the object's radiation peak is inversely proportional to the temperature, and as the object's temperature increases, the radiation peak moves to the shortwave direction. The main temperature range of forest burning is 600~1300 K, and the corresponding peak wavelength is in the mid-infrared (MIR, 3~5μm) range, while the peak wavelength of surface normal temperature (about 300K) is about 11μm. In the mid-infrared band, the difference between the radiation emitted by combustion and the background radiation can be up to four orders of magnitude. According to Planck's law, this difference in radiation brightness results in that even if the fire area only accounts for 1/104-1/103 of the total area of the pixel, the brightness temperature value of the fire point pixel in the mid-infrared band will be significantly increased, and there is a significant difference with the surrounding pixel. In the far infrared band, this difference in brightness temperature also occurs, but the difference is smaller. This characteristic of bright temperature difference can be used as the main basis for fire point identification.

2.2.2. Forest Fire Discrimination

2.2.2.1. Cloud Detection

Clouds obscure the real information of ground objects when monitoring forest fire with remote sensing imagery, and reduce the quality of image and the accuracy of fire point discrimination. In this study, a multi-spectral comprehensive threshold cloud detection algorithm is adopted. It uses the brightness temperature or reflectivity of clouds in infrared and visible spectrum to identify the characteristics different from other ground objects, and the detection results were corrected by clear sky repair algorithm. The specific algorithm is as follows:

Identify thick cloud conditions:

$$\rho 03>0.3\mathrm{or}0.9<{\displaystyle \frac{\rho 04}{\rho 03}}<1.1,$$

(1)

Identify high cloud conditions:

$$B{T}_{16}<236K\mathrm{or}(0.09<{\displaystyle \frac{\rho 03-\rho 05}{\rho 03+\rho 05}}<0.2\mathrm{and}\rho 01>0.1),$$

(2)

Identify medium cloud conditions:

$${\mathrm{BT}}_{14}<278K\mathrm{or}B{T}_7-B{T}_{14}>20K,$$

(3)

Perform clear sky repair on the identified cloud pixels:

$$-0.18\le NDVI\le 0.2,$$

(4)

Where: $\rho$is the apparent reflectance of channels 3, 4, 5 of AHI, BT is the brightness temperature of channels 7, 14, 16 of AHI, NDVI is the normalized difference vegetation index.

2.2.2.2. Forest Land Discrimination

Considering the dynamic changes of forest resources, the following comprehensive methods are adopted in woodland identification:

• Use land cover data: The product of Global Land Cover with Fine Classification System at 30m in 2020 downloaded from the website of Earth big data science engineering data sharing service system supported by the Institute of Aerospace Information Innovation, Chinese Academy of Sciences.
• Use the Normalized Difference Vegetation Index (NDVI) to confirm:

$$NDVI=\left(NIR-R\right)/\left(NIR+R\right)\mathrm{and}NDVI>0.45,$$

(5)

where $NIR$represents the reflection value of the near infrared band, and $R$represents the reflection value of the red band.

2.2.2.3. Forest Fire Point Discrimination

• Construction of Angel slope Indices and forest fire discrimination.

The Angle slope index, proposed by Palacios-Orueta and Khanna et al., describes the relationship between the three continuous bands by using the geometric shape of the spectra, so it detects not only the reflectance values of bands, but also the relationship between the bands. When forest fires break out, vegetation destruction and thermal radiation have a certain impact on visible, near-infrared and infrared bands (see Figure 7). There is a strong correlation between each independent band in spectral images, and the relationship between bands in spectral data is as important as the reflectivity, radiation and brightness temperature. Therefore, the Angle slope index is more sensitive to the occurrence of forest fires and can better capture the information of forest fire points. In this study, new Angle slope indexes were constructed to analyze the spectrum characteristics and changes of forest fire points.

As shown in the schematic diagram of the spectral curve in Figure 7, the x-axis in the coordinate system represents the identifiers for bands 1-16 of the Himawari-8 satellite, corresponding to integer values 1-16. The y-axis corresponds to reflectance values for bands 1-6, which cover the visible, near-infrared, and short-wave infrared regions, while for bands 7-16, it corresponds to the brightness temperature values in the infrared region.

Angle slope indices ANIR , AMIR and AMNIR are defined as follows:

$$ANIR={\displaystyle \frac{{\left|R_R{R}_N\right|}^2+\left|R_N{R}_S\right|{}_2-{\left|R_R{R}_S\right|}^2}{2\left|R_R{R}_N\right|\left|R_N{R}_S\right|}},$$

(6)

$$AMIR={\displaystyle \frac{{\left|R_S{R}_M\right|}^2+\left|R_M{R}_F\right|{}_2-{\left|R_S{R}_F\right|}^2}{2\left|R_S{R}_M\right|\left|R_M{R}_F\right|}},$$

(7)

In formula (6),$R_R$,$R_N$respectively represent the points corresponding to the reflectance values of the red band and near-infrared band on a coordinate system, $\left|R_R{R}_N\right|$represents the distance between these two points in the coordinate system, similarly, $\left|R_N{R}_S\right|$represents the distance between the points corresponding to the reflectance values of the near-infrared band and short-wave infrared band in the coordinate system, $\left|R_R{R}_S\right|$represents the distance between the points corresponding to the reflectance values of the near-infrared band and short-wave infrared band in the coordinate system. The calculation result is the cosine values corresponding to $\angle R_R{R}_N{R}_S$.

In formula (7), $R_S$represents the point corresponding to the reflectance value of the short-wave infrared in the coordinate system, $B_M$represents the point corresponding to the brightness temperature value of the mid-infrared band in the coordinate system. Similarly, $\left|B_M{B}_F\right|$represents the distance between the points corresponding to the brightness temperature values of the mid-infrared band and far-infrared band in the coordinate system, $\left|R_S{B}_F\right|$represents the distance between the points corresponding to the reflectance value of the short-wave infrared band and the brightness temperature value of the far-infrared band in the coordinate system. The calculation result is the cosine values corresponding to $\angle R_S{B}_M{B}_F$.

Differences in the order of magnitude of the coordinate axes are relatively large and the setting of the same distance scale values on the coordinate axis directly affect the change in the Angle slope index, thus generating different forest fire discrimination thresholds. When the ratio of the same distance scale values on the coordinate axis (y/x, ignoring units) increases, the angles$\angle R_R{R}_N{R}_S$, $\angle R_S{B}_M{B}_F$increase, the threshold decreases, and the threshold difference also decreases; when the y/x ratio decreases, the angles$\angle R_R{R}_N{R}_S$, $\angle R_S{B}_M{B}_F$decrease, the threshold increases, and the threshold difference also increases.

When a forest fire occurs, the pixel points in the fire area show an increase in the angle $\angle R_R{R}_N{R}_S$, the angle slope index ANIR decreases, $\angle R_S{B}_M{B}_F$decreases, the angle slope index AMIR increases, and the difference between AMIR and ANIR is used to construct the angle slope difference index, enhancing the sensitivity and accuracy of fire detection. AMNIR is defined as:

$$AMNIR=AMIR-ANIR,$$

(8)

Angle slope indices in Himawari-8were defined as follows:

$$AMIR={\displaystyle \frac{{\left|R_6{R}_7\right|}^2+\left|R_7{R}_8\right|{}_2-{\left|R_6{R}_8\right|}^2}{2\left|R_6{R}_7\right|\left|R_7{R}_8\right|}},$$

(10)

In formula (9), $R_3$and$R_4$respectively represent the points in the coordinate system corresponding to the reflectance values of bands 3 and 4. $\left|R_3{R}_4\right|$represents the distance between these two points in the coordinate system. Similarly, $\left|R_4{R}_5\right|$represents the distance between the points corresponding to the reflectance values of bands 4 and 5, and $\left|R_3{R}_5\right|$ represents the distance between the points corresponding to the reflectance values of bands 3 and 5. The$ANIR$calculation result is the cosine value corresponding to $\angle R_3{R}_4{R}_5$.

In formula (10), $R_6$represents the point in the coordinate system corresponding to the reflectance value of band 6, $R_7$represents the point corresponding to the brightness temperature value of band 7, and $\left|R_6{R}_7\right|$represents the distance between these two points. Similarly, $\left|B_7{R}_8\right|$represents the distance between the points corresponding to the brightness temperature values of bands 7 and 8, and $\left|R_6{B}_8\right|$ represents the distance between the points corresponding to the reflectance value of band 6 and the brightness temperature value of band 8. The$AMIR$calculation result represents the cosine value corresponding to $\angle R_6{R}_7{R}_8$.

2.

Construction of Time-series Angle slope difference index and forest fire discrimination;

The Angle Slope Difference Index is constructed based on the spectral differences between forested areas and fire points before and after a fire occurs. It is defined as follows:

$$∆ANIR={ANIR}_{t1}-{ANIR}_{\mathrm{t}2},$$

(11)

$$∆AMIR={AMIR}_{\mathrm{t}2}-{AMIR}_{\mathrm{t}1},$$

(12)

$ANI{R}_{t1}$and $AMI{R}_{t1}$represent the angle indices of the forest before a fire, while $ANI{R}_{t2}$and $ANI{R}_{t2}$represent the angle indices of the forest after a fire. $\Delta ANIR$and $\Delta AMIR$represent the difference in the angle slope indices between the forested area and the fire point.

In actual monitoring, ANIR_t1 and AMIR_t1 represent the angle indices of the previous moment image in time-series remote sensing imagery, while ANIR_t2 and AMIR_t2 represent the angle indices of the next moment image in the time-series remote sensing imagery. $\Delta ANIR$ and $\Delta AMIR$ represent the difference in angle indices between the two scenes.

3.

Decomposed 3D OTSU adaptive threshold segmentation algorithm.

To address the misjudgment of fire points in satellite imagery due to background variations in different regions, the decomposed three-dimensional OTSU algorithm is employed for adaptive threshold segmentation. This algorithm not only considers the between-class variance and the clustering within classes but also successfully decomposes the three-dimensional problem into three one-dimensional components. This reduction in dimensionality dramatically decreases the computational complexity from $O(L^3)$to$O(L)$, significantly enhancing the computation speed and practical utility of the algorithm. It outperforms other segmentation algorithms in efficiency. The computation process for the decomposed three-dimensional OTSU algorithm is outlined as follows:

Let value s divide a set of discrete data into two categories (fire points target and background). For these two categories, define their inter-class distance as:

$$sb\left(s\right)=|{\mu }_1\left(s\right)-{\mu }_0\left(s\right)|,$$

(13)

Where ${\mu }_1(s)$, ${\mu }_0(s)$ are the mean values of the elements corresponding to their respective categories. It can be seen the larger $sb(s)$, the greater the inter-class distance, which means the target and background are more distinctly separated, resulting in better segmentation effects.

When values divide a set of discrete data into two categories, where$P_i$is the probability of data i occurrence, $W_0(s)$and$W_1(s)$respectively represent the probabilities of the two categories, and${\mu }_0(s)$and${\mu }_1(s)$are the mean values of the corresponding categories, the intra-class distances for these categories are defined as:

$$d_0\left(s\right)={\displaystyle \frac{\sum _{i=0}^s{P}_i|i-{\mu }_0(s\left)\right|}{W_0\left(s\right)}},$$

(14)

$$d_1\left(s\right)={\displaystyle \frac{\sum _{i=s+1}^{L-1}{P}_i|i-{\mu }_1(s\left)\right|}{W_1\left(s\right)}},$$

(15)

The overall intra-class distance for the two categories is:

$$sw\left(s\right)=W_0\left(s\right)d_0\left(s\right)+W_1\left(s\right)d_1\left(s\right),$$

(16)

which indicates the cohesion within each class. The best segmentation effect is achieved when the value of $sw(s)$ is minimized.

Thus, considering both the aforementioned factors, it is essential to ensure the maximum inter-class distance while also achieving the best possible cohesion within each class to obtain optimal segmentation results. Based on these requirements, upon analyzing Otsu, a new threshold determination function has been proposed, where the formula to find the threshold is:

$$G\left(s\right)={\displaystyle \frac{W_0\left(s\right)W_1\left(s\right)sb\left(s\right)}{sw\left(s\right)}},$$

(17)

The gray level corresponding to the maximum value of $G\left(s\right)$ is considered the optimal threshold $S_0$, that is:

$$s_0=argmax\left\{G\left(s\right)\right\},$$

(18)

For the single-channel imagery constructed using the Angle slope difference index $AMNIR$, three-dimensional OTSU adaptive threshold segmentation is applied. For the segmented anomalous target points, forest fire discrimination is conducted based on the following principles:

If $\Delta AMIR>\Delta AMI{R}_{Threshold}$ and $\Delta ANIR>\Delta ANI{R}_{Threshold}$, The potential fore point is determined.

2.2.3. Flare Removal

When the fire points were identified, it is necessary to perform flare removal to filter false fire points. The removing principle is as follows: if the reflectivity of the visible light and infrared are both greater than 0.3, and the flare angle is less than 30°, then the pixels are identified as flare. The flare angle[1] is calculated as:

$$\cos {\theta }_r=\cos {\theta }_v\cos {\theta }_s-\sin {\theta }_v\sin {\theta }_s\cos \psi ,$$

(19)

Where: ${\theta }_r$ is the angle between the direction of the specular reflection and the vector pointing from the ground to the satellite. ${\theta }_v$ is the observation zenith angle, ${\theta }_{\mathrm{s}}$ is the solar zenith angle, $\psi$ is the relative azimuth.

2.2.4. Precision Evaluation Method

The accuracy rate (P), missed rate (M), and overall evaluation (F) were used to carry out the evaluation in a unified way [2]. The specific formula is as follows:

$$P={\displaystyle \frac{Y_y}{Y_y+Y_n}},$$

(20)

$$M={\displaystyle \frac{N_y}{Y_y+N_y}},$$

(21)

$$F={\displaystyle \frac{2P(1-M)}{1+P-M}},$$

(22)

where $Y_y$is the number of real fire points detected, $Y_n$is the number of falsely detected fire points; $N_y$ is the number of missed fire points, P and M are the accuracy rate and the omission errors respectively, and F is the comprehensive evaluation index of accuracy rate and missed detection rate.

3. Results

4. Discussion

5. Conclusion

6. Patents

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