Quantitatively Mapping Discolored Seawater around Submarine Volcanoes Using Satellite GCOM-C SGLI Data: A Case Study of the Krakatau Eruption in Indonesia in December 2018

: The ﬁnal goal of this paper is to contribute to the difﬁcult task of understanding and forecasting submarine volcanic eruption activity by proposing a method to quantify discolored water. To achieve this purpose, we quantitatively analyzed the discolored seawater seen before and after the eruption of the marine environment around the Indonesian submarine volcano “Anak Krakatau”, which erupted at the end of December 2018, from the viewpoint of the “dominant wavelength”. The atmospherically corrected COM-C SGLI data for 17 periods from the eruption from October 2018 to March 2019 were used. As a result, the following three main items were found. First, the average ± standard deviation of the entire dominant wavelength was 497 nm ± 2 nm before the eruption and 515 nm ± 35 nm after the eruption. Second, the discolored water area around the island derived from SGLI was detected from the contour line with dominant wavelengths of 500 nm and 560 nm. Third, the size of a dominant wavelength of 500 nm or more in the discolored water areas changed in a complicated manner within the range of almost 0 to 35 km 2 . The area of the dominant wavelength of 500 nm or more slightly increased just before the eruption. Finally, it was proven that the “dominant wavelength” from the SGLI proposed in this paper can be a very effective tool in understanding or predicting submarine volcanic activity.


Introduction
Submarine volcanoes have frequently erupted in recent years, such as Indonesia's "Anak Krakatau Island" in 2018 [1], New Zealand's "White Island" in 2019 [2], and Japan's "Nishinoshima" [3] and "Fukutoku Okanoba" in 2021 [4]. In particular, the eruption of "Anak Krakatau Island" on 22 December 2018 caused a tsunami due to the collapse of the mountain body [5], resulting in the loss of many lives. In this way, the explosion of a submarine volcano often affects human life and the flight of airplanes; thus, eruption forecasting is an essential research theme.
Some volcanic activity forecast methods include using volcanic earthquake data and volcanic gas data [6]. However, this activity is difficult to predict even with these methods. On the other hand, for submarine volcanoes, it has been pointed out that there is a possibility to forecast using the "discoloration phenomenon" that occurs in seawater before and after the eruption of the volcano [7,8]. Although the relationship between the chemical composition of discolored water and volcanic activity has been known for a long time, research on the discolored water around submarine volcanoes is globally scarce. This is because the survey of submarine volcanoes itself is dangerous and often difficult since they are far from land. Under such circumstances, satellite remote sensing for the noncontact observation of submarine volcanoes is very helpful. In research on volcanically discolored

Study Area
As shown in Figure 1, the study area of Krakatau is a volcano located in the middle of the Sunda Strait between the Indonesian islands of Java and Sumatra, at the latitude of 6 • 6 2 S and longitude of 105 • 25 29 E. The water depth around the island is about 200-300 m [5]. This island is a relatively new volcanic island formed by the massive eruption of 1983 [17]. An eruption occurred on 22 December 2018 (around 14:00 UTC), accompanied by a tsunami [18] caused by the collapse of the mountain mass [5] from the south-western slope of the island. This tsunami caused a major disaster in the coastal area of Krakatau [19]. Novellino et al. [20] analyzed the area change derived from the coastline extraction before and after the December 2018 eruption using Sentinel-2 satellite data. The island area increased from about 2.8 km 2 on 16 November 2018 to about 3.1 km 2 on 3 April 2019 due to intense explosive activity after the December 2019 eruption [20]. One of the main reasons for the area's expansion is the extension of the eastern shoreline by Surtseyan pyroclastic deposits draping the eastern flank [21]. main reasons for the area's expansion is the extension of the eastern shoreline by Surtseyan pyroclastic deposits draping the eastern flank [21].

Dominant Wavelength Quantification Method
The most crucial method in this study is to derive the "dominant wavelength" from the multispectral reflectance data obtained from satellite data. The dominant wavelength is a numerical value of the wavelength of the color of light perceived by human eyes. The dominant wavelength estimation from satellite data is briefly explained below.
The color system used this time is the XYZ color system [14] adopted in 1931 by the International Commission on Illumination (CIE), which has a proven track record in the color evaluation of crater lakes and hot springs [12,13]. Although it is possible to specify an objective and accurate color by expressing it with the two numerical values (x, y) obtained by this color system, it is not easy to associate the color with the two numbers. Furthermore, there is the advantage that it is easier to explain the characteristics of discolored seawater by showing the two numbers in the image as one number (the dominant wavelength) rather than showing them separately in the image.
On the other hand, the following equation is generally used to convert the reflectance to the XYZ values (X, Y, Z) of the XYZ color system.
Here, S is the "standard spectral distribution of light", x', y', and z' are the "color matching function," R is the "spectral reflectance of the object," and K is the "proportional coefficient" (in fact relative); and λ indicates the wavelength. The values of X, Y, and Z calculated in this way are further relativized by the following equations:

Dominant Wavelength Quantification Method
The most crucial method in this study is to derive the "dominant wavelength" from the multispectral reflectance data obtained from satellite data. The dominant wavelength is a numerical value of the wavelength of the color of light perceived by human eyes. The dominant wavelength estimation from satellite data is briefly explained below.
The color system used this time is the XYZ color system [14] adopted in 1931 by the International Commission on Illumination (CIE), which has a proven track record in the color evaluation of crater lakes and hot springs [12,13]. Although it is possible to specify an objective and accurate color by expressing it with the two numerical values (x, y) obtained by this color system, it is not easy to associate the color with the two numbers. Furthermore, there is the advantage that it is easier to explain the characteristics of discolored seawater by showing the two numbers in the image as one number (the dominant wavelength) rather than showing them separately in the image.
On the other hand, the following equation is generally used to convert the reflectance to the XYZ values (X, Y, Z) of the XYZ color system.
Here, S is the "standard spectral distribution of light", x , y , and z are the "color matching function", R is the "spectral reflectance of the object", and K is the "proportional coefficient" (in fact relative); and λ indicates the wavelength. The values of X, Y, and Z calculated in this way are further relativized by the following equations: Since the variables x, y, and z in these equations have a relationship of "x + y + z = 1", z is not necessary for the scene that essentially expresses color. Therefore, in principle, if only R (λ) of 380 nm to 780 nm is known (commonly included in Equations (1)-(3)), the remaining coefficients can be obtained by using constants such as the Japanese Industrial Standards Handbook [22]. Thus, the sea color can be quantified by two numerical values: x and y. However, for S (λ), the standard light near the solar light source called D65 defined by CIE is used to determine the standard sea color in the field. Figure 2a,b shows the wavelength characteristics of the weighting factor [22], which is the "product of the color matching function and the standard light D65" used in Equations (2)-(4).  The x and y values obtained in this way are shown in the chromaticity coordinates shown in Figure 2c. The outer circumference of this chromaticity coordinate (the numerical value of the wavelength written on the thick black curve) corresponds to the dominant wavelength. For example, when the coordinates (x, y) of C are obtained, the dominant wavelengths are the white point W (x = 0.3333, y = 0.3333) and the point S where the extension line of C and the outer circumference intersect. The "ratio of WS and WC ([WC/WS] × 100%)" is called "purity", and the closer it is to S, the higher the purity of the color (the purity of the S point is represented by 100%). Generally, the dominant wavelength is determined by drawing, but the numerical calculation is not open to the public. Therefore, point B, where the perpendicular line is drawn from point W and intersects with the outer circumference, is set to 0 • , and the clockwise 360 • is set to θ [23]. Then, a polynomial approximation is performed on the relationship between θ and the dominant wavelength obtained from the known dominant wavelength coordinates [24], as shown in Figure 3 and Appendix A, Table A1. An equation for obtaining the dominant wavelength (symbol: DWL) is created from θ. The obtained sixth-order approximation expression (R 2 = 0.98) is shown in Equation (7). DWL = 2.631 × 10 −11 θ 6 − 1.299 × 10 −8 θ 5 + 3.068 × 10 −8 θ 4 + 9.3879 × 10 −4 θ 3 − 0.1806 × θ 2 + 12.557 × θ+ 200.53 (7)

Satellite Data Used
GCOM-C is an earth observation satellite launched by Japan in December 201 satellite has 9 bands of 380 nm, 412 nm, 443 nm, 490 nm, 530 nm, 565 nm, 674 nm, 7 and 869 nm in the visible/near-infrared region. All are equipped with SGLI sens can observe with a resolution of 250 m. This study used Level-2 data of "atmo corrected attenuation," which can easily analyze the contact area between land a The data used were from JAXA (Japan Aerospace Exploration Agency) EORC (Ear data from 7 April 2018 (immediately before the eruption) to 31 March 2019, shown ble 1, were obtained from the G-Portal site provided by the Observation Research Figure 4a,b shows the RGB color image of SGLI acquired on the same day as the S 2 color image. The SGLI reflectance image obtained has a resolution of 49 × 49 around Anak Krakatau. In addition, the land/water flag of the QA (quality assuran of SGLI's vegetation index (VGI) was used to mask the land information. Here, mask was created from the data on 9 January 2019 (Figure 4c), which was able to ca  The conversion equation from the chromaticity coordinates (x, y) to θ obtained from the satellite data using Equations (1)-(6) is expressed by the following equations in the calculation format of MS Excel:

Satellite Data Used
GCOM-C is an earth observation satellite launched by Japan in December 2017. This satellite has 9 bands of 380 nm, 412 nm, 443 nm, 490 nm, 530 nm, 565 nm, 674 nm, 763 nm, and 869 nm in the visible/near-infrared region. All are equipped with SGLI sensors that can observe with a resolution of 250 m. This study used Level-2 data of "atmospheric corrected attenuation", which can easily analyze the contact area between land and sea. The data used were from JAXA (Japan Aerospace Exploration Agency) EORC (Earth). The data from 7 April 2018 (immediately before the eruption) to 31 March 2019, shown in Table 1, were obtained from the G-Portal site provided by the Observation Research Center. Figure 4a,b shows the RGB color image of SGLI acquired on the same day as the Sentinel-2 color image. The SGLI reflectance image obtained has a resolution of 49 × 49 pixels around Anak Krakatau. In addition, the land/water flag of the QA (quality assurance) flag of SGLI's vegetation index (VGI) was used to mask the land information. Here, a land mask was created from the data on 9 January 2019 (Figure 4c), which was able to carry out the cleanest land-sea separation without the influence of clouds. The reflectance data in each pixel were first converted into X, Y, and Z according to Equations (1)-(3). In particular, as shown in Figure 2a, the reflectance of the nine bands obtained from the SGLI data was linearly interpolated in 5 nm steps and then multiplied by a 5 nm weight factor (JIS Z 8781-1) and converted to chromaticity coordinates X, Y, and Z. These coordinates were converted into x and y using Equations (4) and (5). Furthermore, the principal wavelength was calculated from x and y using Equations (7)- (9). The red squares in Figure 4c are the five stations (west, north, east, south, and south-west) acquired to investigate the tendency of the sea color in the waters around Anak Krakatau. Of these, the south-east station was set as the area closest to where the collapse of the mountain [5] occurred. The size of each pixel is 3 × 3. Figure 4d is an SGLI image of 20 December 2018, just before the eruption. lar, as shown in Figure 2a, the reflectance of the nine bands obtained from the SGLI da was linearly interpolated in 5 nm steps and then multiplied by a 5 nm weight factor (J Z 8781-1) and converted to chromaticity coordinates X, Y, and Z. These coordinates we converted into x and y using Equations (4) and (5). Furthermore, the principal waveleng was calculated from x and y using Equations (7)- (9). The red squares in Figure 4c are th five stations (west, north, east, south, and south-west) acquired to investigate the te dency of the sea color in the waters around Anak Krakatau. Of these, the south-east statio was set as the area closest to where the collapse of the mountain [5] occurred. The size each pixel is 3 × 3. Figure 4d is an SGLI image of 20 December 2018, just before the eruptio   Figure 3c is the discolored seawater area where the chromaticity judgment of SGLI was performed.

Color Characteristics of Discolored Water
We used SGLI data to characterize the dominant wavelengths of seawater around this island from April 2018 to March 2019. Figure 5 is a chromaticity diagram of the sea color at the stations around the island (west, north, east, south, and south-west) estimated from SGLI. However, data loss and data from 1 October 2018, 20 November 2018, 11 January 2019, and 3 February 2019, which deviated significantly from the chromaticity diagram, were excluded. Table 2 shows the chromaticity (x, y) and dominant wavelength statistics at each station. From this, the x and y values of the sea color changed in the range of about 0.24 to 0.38 for x and about 0.27 to 0.38 for y, and the average ± standard deviation of the entire dominant wavelength was 497 nm ± 2 nm before the eruption and 515 nm ± 35 nm after the eruption. In addition, most of the data are blue (the dominant wavelength is about 480 nm), extending from the white point W to the lower left. Eighty percent of all data have a dominant wavelength of 500 nm or less (blue to green). Apart from this, a relatively high-purity yellow-green sea color (the dominant wavelength is 560 to 580 nm) was also confirmed. Figure 5 also shows three lines showing the color characteristics of the discolored water before and after the eruption of Nishinoshima Island, a submarine volcano in Japan, in 2020 using the same method [16]. These lines indicate that the preeruptive baseline at Nishinoshima Island was about 475 nm, and the range of discolored water was from 535 nm to 615 nm. The sea color of Krakatau Island in this study is also within the range of these lines. Looking at the characteristics at each station (Table 2), the mean ± standard deviation of the dominant wavelength in the south-west direction after the eruption was 539 ± 42 nm, which was particularly high compared to other points. On the other hand, the dominant wavelengths at the north and east points hardly changed before and after the eruption.  Figure 3c is the discolored seawater area where the chromaticity judgment of SGLI was performed.

Color Characteristics of Discolored Water
We used SGLI data to characterize the dominant wavelengths of seawater around this island from April 2018 to March 2019. Figure 5 is a chromaticity diagram of the sea color at the stations around the island (west, north, east, south, and south-west) estimated from SGLI. However, data loss and data from 1 October 2018, 20 November 2018, 11 January 2019, and 3 February 2019, which deviated significantly from the chromaticity diagram, were excluded. Table 2 shows the chromaticity (x, y) and dominant wavelength statistics at each station. From this, the x and y values of the sea color changed in the range of about 0.24 to 0.38 for x and about 0.27 to 0.38 for y, and the average ± standard deviation of the entire dominant wavelength was 497 nm ± 2 nm before the eruption and 515 nm ± 35 nm after the eruption. In addition, most of the data are blue (the dominant wavelength is about 480 nm), extending from the white point W to the lower left. Eighty percent of all data have a dominant wavelength of 500 nm or less (blue to green). Apart from this, a relatively high-purity yellow-green sea color (the dominant wavelength is 560 to 580 nm) was also confirmed. Figure 5 also shows three lines showing the color characteristics of the discolored water before and after the eruption of Nishinoshima Island, a submarine volcano in Japan, in 2020 using the same method [16]. These lines indicate that the preeruptive baseline at Nishinoshima Island was about 475 nm, and the range of discolored water was from 535 nm to 615 nm. The sea color of Krakatau Island in this study is also within the range of these lines. Looking at the characteristics at each station (Table 2), the mean ± standard deviation of the dominant wavelength in the south-west direction after the eruption was 539 ± 42 nm, which was particularly high compared to other points. On the other hand, the dominant wavelengths at the north and east points hardly changed before and after the eruption.

Distribution Characteristics of Discolored Water
In Section 3.1, the dominant wavelength characteristics of the partially discoloredwater area near Anak Krakatau were shown. Next, we calculated the dominant wavelength distribution for each day and evaluated the distribution area quantitatively. Figure 6 is an example of the dominant wavelength distribution map calculated using SGLI data (as of 8 January 2019). This figure is roughly divided into a blue region (background water), a red region showing a relatively long dominant wavelength, and a green-to-yellow region located between blue and red. As shown in Figure 6, the boundaries of these regions almost coincided with the 500 nm and 560 nm contour lines. Figure 7 shows the results of applying the same treatment to the SGLI data 10 days after the eruption. Each day is represented by RGB color images (left) and a dominant wavelength image (right). From this, the data of each period are mainly divided into three color regions (Figure 6), and the water area indicated by the red boundary line of 560 nm is clearly detectable. However, the data on February 11 showed a highly complex pattern. Since such a peculiar pattern may significantly influence (error) the interpretation when quantifying the color change range, a more stable quantification of discolored water is needed.

Quantification of the Discolored Water Area
As explained in Section 3.2, it can be easier to analyze the spatial change of discolored water in one image by extracting the contour line of 500 nm or 560 nm. Here, all the contour lines of discolored seawater with a dominant wavelength of 560 nm or more (hereafter referred to as the "yellow region") are shown in Figure 8. In the water area near Anak Krakatau (area X in the figure), the distribution of the yellow area is expanded or contracted at almost the same position. As shown in Figure 8, the discolored-water area extending from the island to the south-west can be read as about 0.03 • and 0.04 • in the latitudinal and longitudinal directions, respectively. Assuming that the distance of 1 • is about 111 km, it is estimated that the yellow region extended to approximately 5.6 km in the south-west direction. At the end of March, we could qualitatively read that this yellow area was shrinking. Therefore, to quantitatively express the size of the yellow region, changes in the size of the yellow region were investigated only in area X. Figure 9 shows the relationship between the total data from April 2018 to March 2019 and the areas more than 500 nm and more than 560 nm. These areas shown here were calculated by multiplying the number of pixels in these regions by the square of the spatial resolution of SGLI (250 m). As a result, the size of these regions changed in a complicated manner within the range of 0 to 35 km 2 . Immediately after the eruptive activity on 22 December 2018, the area of discolored water expanded rapidly. In addition, the fact that the area of the dominant wavelength of 500 nm or more slightly increased just before this eruption is noteworthy from the viewpoint of eruption forecasting.

Quantification of the Discolored Water Area
As explained in Section 3.2, it can be easier to analyze the spatial change of discolored water in one image by extracting the contour line of 500 nm or 560 nm. Here, all the contour lines of discolored seawater with a dominant wavelength of 560 nm or more (hereafter referred to as the "yellow region") are shown in Figure 8. In the water area near Anak Krakatau (area X in the figure), the distribution of the yellow area is expanded or contracted at almost the same position. As shown in Figure 8, the discolored-water area extending from the island to the south-west can be read as about 0.03° and 0.04° in the latitudinal and longitudinal directions, respectively. Assuming that the distance of 1° is about 111 km, it is estimated that the yellow region extended to approximately 5.6 km in the south-west direction. At the end of March, we could qualitatively read that this yellow area was shrinking. Therefore, to quantitatively express the size of the yellow region, changes in the size of the yellow region were investigated only in area X. Figure 9 shows the relationship between the total data from April 2018 to March 2019 and the areas more than 500 nm and more than 560 nm. These areas shown here were calculated by multiplying the number of pixels in these regions by the square of the spatial resolution of SGLI (250 m). As a result, the size of these regions changed in a complicated manner within the range of 0 to 35 km 2 . Immediately after the eruptive activity on 22 December 2018, the area of discolored water expanded rapidly. In addition, the fact that the area of the dominant wavelength of 500 nm or more slightly increased just before this eruption is noteworthy from the viewpoint of eruption forecasting.

Discussion
In this paper, an attempt was made to quantify discolored seawater originating fro submarine volcanoes using the satellite GCOM-C SGLI sensor. Figures 5 and 6 show th discolored water can be used with a simple numerical value of one element by using t dominant wavelength index instead of the three elements such as the RGB color of t satellite. Conventionally, satellite-based methods for quantifying discolored seawa have often been discussed in terms of the distribution of chlorophyll-a and turbidity pro ucts [9,10,[25][26][27]. These parameters are often confused with the origin of phytoplankt reproduction and the runoff of turbid water from rain. For example, Whiteside et al. [2 pointed out that an increase in surface chlorophyll-a concentration after a volcanic eru tion could be associated with the basalt-andesitic ash material expelled from the volca and entrained into the ocean. Therefore, apart from these methods, quantifying the ori nal color of discolored seawater is also considered useful for monitoring volcanic activi The numerical value of this dominant wavelength will be discussed first.
The average ± standard deviation of the dominant wavelength obtained from SG was 497 nm ± 2 nm before the eruption (normal condition) and 515 nm ± 35 nm after t eruption (discolored condition), as shown in Figure 5 and Table 2. In Nishinoshima Islan where the same analysis was performed, the range of the discolored water area was abo 535-615 nm [16], so it was found that this time, the dominant wavelength distribution w within a very narrow range compared to Nishinoshima. It has been considered that su a change in the dominant wavelength is due to the chemical composition of seawater a the accompanying shift in pH. For example, from the chemical analysis of hot spring w ter, Ohsawa et al. [12] pointed out that Si affects the blue region near the dominant wav

Discussion
In this paper, an attempt was made to quantify discolored seawater originating from submarine volcanoes using the satellite GCOM-C SGLI sensor. Figures 5 and 6 show that discolored water can be used with a simple numerical value of one element by using the dominant wavelength index instead of the three elements such as the RGB color of the satellite. Conventionally, satellite-based methods for quantifying discolored seawater have often been discussed in terms of the distribution of chlorophyll-a and turbidity products [9,10,[25][26][27]. These parameters are often confused with the origin of phytoplankton reproduction and the runoff of turbid water from rain. For example, Whiteside et al. [28] pointed out that an increase in surface chlorophyll-a concentration after a volcanic eruption could be associated with the basalt-andesitic ash material expelled from the volcano and entrained into the ocean. Therefore, apart from these methods, quantifying the original color of discolored seawater is also considered useful for monitoring volcanic activity. The numerical value of this dominant wavelength will be discussed first.
The average ± standard deviation of the dominant wavelength obtained from SGLI was 497 nm ± 2 nm before the eruption (normal condition) and 515 nm ± 35 nm after the eruption (discolored condition), as shown in Figure 5 and Table 2. In Nishinoshima Island, where the same analysis was performed, the range of the discolored water area was about 535-615 nm [16], so it was found that this time, the dominant wavelength distribution was within a very narrow range compared to Nishinoshima. It has been considered that such a change in the dominant wavelength is due to the chemical composition of seawater and the accompanying shift in pH. For example, from the chemical analysis of hot spring water, Ohsawa et al. [12] pointed out that Si affects the blue region near the dominant wavelength of 480 nm. Al affects Si and Al in the region near 490 nm. From the chemical analysis of a crater lake, Onda et al. [13] also explained the green coloration near the dominant wavelength of 535 nm as being due to the effect of Fe 2+ . The study of Satsuma-Iojima Island [7] does not mention the dominant wavelength. However, the water is transparent-to-milky-white at a pH of around 2, yellowish brown at 3-5, and again white at higher pH levels. Since the seawater of Anak Krakatau also shows the yellow color of the RGB images in Figures 1 and 7, the pH is estimated to be about 3-5. Assuming that the discoloration is due to the influence of chemical components, the yellow-brown color at the dominant wavelength means that there is a large amount of iron outflow from Krakatau, not aluminum or silicon. However, this time, data verifying such a chemical composition and pH value could not be obtained, which remains a topic for the future. On the other hand, the color of this seawater is not only the color of sediments formed by hydrothermal water and gas discharged from submarine volcanoes reacting with seawater, as mentioned above, but also sediments brought from land by a volcanic collapse [5,29]; the color of suspended matter in the atmosphere and the color of clouds containing volcanic gas and volcanic ash in the atmosphere may also be detected [11,30], so caution is required.
Next, we consider the viewpoint of discolored water distribution. As shown in Figures 7 and 8, the discolored water distribution grew to about 5.6 km in the south-west direction of the island from January to February 2019 but shrank to about 0.5 km in late March 2019. According to Novellino et al. [20], volcanic activity was present two months after the mountain's collapse on 22 December 2018, and the area of the island expanded, after which the volcanic activity subsided. The cause of the change in the direction of the dominant wavelength seen in Figure 5 and Table 2 is still under investigation, but it is thought to be caused by the bathymetry and submarine geology around the island. See related references [5,[29][30][31][32] for this information.
Finally, we consider the limits of using SGLI. This sensor contains many bands in the visible region of 380 to 780 nm and is highly effective in determining detailed changes in ocean color. However, it must be recognized that the value includes an error because the wavelength resolution is not sufficient to correspond to the overlay coefficient of 5 nm. Additionally, as shown in Figure 4a,b, the 250 m resolution does not provide a detailed discolored water distribution pattern compared to a 10 m resolution sensor such as Sentinel-2. For these reasons, research on data fusion that combines high-resolution and low-resolution satellites will be necessary in the future.

Conclusions
The purpose of this study was to quantify the discolored seawater in the area around the Indonesian submarine volcano "Anak Krakatau" before and after its eruption in December 2018, from the viewpoint of the "dominant wavelength". As a result, the following three main items were found. First, the average ± standard deviation of the dominant wavelength obtained from SGLI was 497 nm ± 2 nm before the eruption (normal condition) and 515 nm ± 35 nm after the eruption (discolored condition). Second, the average ± standard deviation of the dominant wavelength at the south-west station closest to the crater was 541 nm ± 43 nm, the longest wavelength. The discolored seawater region around the island derived from SGLI was clearly detected from the contour line, with a dominant wavelength of 500 nm or 560 nm. Third, the water area with a dominant wavelength of 500 nm or more fluctuated significantly within the range of 0 to 35 km 2 . Additionally, the area of the dominant wavelength of 500 nm or more slightly increased just before the eruption; this fact may be used for eruption forecasting.
It is necessary to further verify the effectiveness of this proposed method in the future. In particular, it is essential to elucidate the relationship between the main wavelength and the chemical composition. However, field surveys of active submarine volcanoes are hazardous and enormously costly. Therefore, this method will be verified in hot spring water and caldera lakes, which are relatively safe and have sufficient compositional data. Finally, we will perform a similar analysis on submarine volcanoes distributed around the world to help in the estimation of submarine volcanic activity. Acknowledgments: The Sentinel-2 product used in this paper was supplied by the Earth Explorer System (https://earthexplorer.usgs.gov/ (accessed on 28 March 2023)) of USGS.

Conflicts of Interest:
The authors declare no conflict of interest.
Appendix A Table A1. Approximate values of chromaticity coordinates [24] and θ at representative wavelengths.