1 INTRODUCTION

Dissolved organic carbon (DOC) is an important carbon reservoir in the ocean, and colored dissolved organic matter (CDOM) is a part of the pool of DOC in seawater. Understanding of the distribution characteristics and laws of CDOM and its optical properties is not only especially significant in the rapid assessment of DOC flux in the marginal sea, but also an important parameter to estimate offshore carbon sinks (Rochelle-Newall and Fisher, 2002; Guo et al., 2007; Bowers et al., 2013; Ma et al., 2021; Zhang et al., 2021b). CDOM is an optically active part of dissolved organic matter in water; CDOM is a type of soluble organic matter containing humus, fulvic acid, and aromatic polymers and plays an important role in biogeochemical processes (Green and Blough, 1994; Coble, 2007). In addition, CDOM is an important part of dissolved organic carbon (DOC), which is the largest organic carbon pool in aquatic ecosystems (Carlson et al., 1994; Stedmon et al., 2003). The absorption of CDOM protects aquatic ecosystems from harmful UV exposure (Stedmon et al., 2000). Therefore, monitoring the spatiotemporal distribution of CDOM is very important for carbon cycle research and aquatic ecosystem protection.

Due to the complex composition of CDOM, its concentration cannot be directly measured, and its concentration is usually represented by absorption coefficients at representative wavelengths, such as 254, 280, 355, 375, 400, and 440 nm (D'Sa et al., 1999; Del Castillo and Coble, 2000; Zhang et al., 2005; Bai et al., 2013; Xu et al., 2018; De Stefano et al., 2022). Remote sensing inversion studies of CDOM in water bodies have focused on various aspects, such as spectral absorption characteristics and the correlation between water quality parameters and CDOM. The relationship between the CDOM optical properties of different water types and their remote sensing reflectance is the basis of constructing inversion models. A wide variety of methods concerning remote sensing have been developed and mainly include empirical methods and physics-based methods to quantify water quality parameters and classify water quality levels using hyperspectral data. Empirical models mainly analyze the correlation between the CDOM concentration and remote sensing reflectance to establish a statistical model. It has gradually become a more widely used statistical model. Based on Sentinel-2 images, Chen et al. (2017) used the empirical band ratio model to invert the a_g(440) (absorption coefficient at 440 nm) of Lake Huron, utilized the cross-validation method to calibrate and verify the model, and obtained the best CDOM retrieval algorithm with a B3/B5 model. Xu et al. (2018) established a band ratio model for the absorption coefficient of CDOM at 355 nm using the measured reflectance spectrum, and the results showed that the inversion effects of B4/B2 or B5/B2 and B7/B8 or B7/B8A based on the Sentinel-2 band ratio were the best for CDOM in the clear and turbid waters of Poyang Lake, respectively, indicating that the band ratio model was suitable for continuous monitoring in specific areas. Niroumand-Jadidi et al. (2019) introduced novel types of spectra-derived features for the estimation of in-water constituents and sought to identify band combinations that result in the strongest correlation of features obtained using a regression analysis with the content of the target object, which resulted in a relatively high R² over 0.7 for some water quality parameters, including Chl a, suspended solids, and CDOM. In general, empirical methods are built upon statistical relations between spectra-derived features and measured concentrations of water constituents. Physics-based inversion models have evolved to utilize semianalytical methods that can incorporate water column properties and the benthic substratum composition (Campbell et al., 2011; Li et al., 2018). However, each parameter of the semianalytical model has a clear physical significance. The algorithm must accurately measure the inherent optical properties of water, and the optical components of coastal water are complex, which increases the difficulty of inversion to some extent, whereas the empirical methods are capable of retrieving the constituents without prior knowledge about inherent optical properties, and they have proven to be less affected by atmospheric effects.

At the same time, the spectral slope (S_g) of the CDOM absorption spectrum usually indicates the composition and source of CDOM, which has become a scientific issue of widespread concern in industry. The sources of CDOM in aquatic ecosystems are mainly divided into terrestrial and marine authigenic sources. The terrestrial sources are mainly the inputs of soil, forest, or animal and plant residues and organic matter caused by human activities in the basin and are characterized by protein-like substances (Miller and McKnight, 2010). Marine authigenic sources are mainly the degradation and secretion of submerged plants, algae, bacteria, and microorganisms and are mainly composed of protein-like substances (Zhang et al., 2009). A large S_g value indicates mainly photochemical and microbial degradation of internal CDOM sources in the study area. In contrast, if the S_g value is small, the CDOM in the study area is mainly terrestrial dissolved organic matter (Helms et al., 2008). The characteristic band ratio M (E250꞉E365) represents the relative molecular size of CDOM, and the larger the S_g value, the smaller the M value (Peuravuori and Pihlaja, 1997). Due to the diversity of spectral slope estimation methods, researchers have used different wavelength intervals to estimate the spectral slope and obtain the best fit (Twardowski et al., 2004; Helms et al., 2008). Studies of S_g, in addition to the selection of wavelength spacing, depend on whether its estimation method is linear or nonlinear. Blough and Del Vecchio (2002) and Del Vecchio and Blough (2004) proved that nonlinear regression fitting better estimates the spectral slope by weighting the intense absorption region of CDOM.

The research described above indicates that the most common problem of remote sensing inversion of CDOM is the accuracy and universality of the model due to the different regional characteristics of different offshore seawater environments. The remote sensing inversion of spectral slope S_g must be based on the accuracy of the CDOM absorption spectrum fitting model, and the CDOM inversion algorithm developed for specific research areas is usually not directly applicable to other water environments (Zhu et al., 2013). In this paper, a remote sensing empirical inversion model of CDOM and its S_g in the sea area around the Leizhou Peninsula in spring and autumn is constructed using large-scale observation data and Sentinel-3A Ocean and Land Color Instrument (OLCI) data.

The aims of this article are as follows: 1) to preliminarily explore the spatiotemporal characteristics and main sources of CDOM content in the sea area around the Leizhou Peninsula; 2) to found the model with the highest fitting accuracy of the CDOM absorption spectrum based on the exponential model, hyperbolic model, and the combined hyperbolic-exponential model; 3) to build a remote sensing inversion model of CDOM and its spectral slope around the Leizhou Peninsula in spring and autumn based on the improvement of fitting accuracy of the model of the CDOM absorption spectrum; and 4) to propose the most suitable sensitive spectral band range for inversion of spectral slope in spring and autumn of the Leizhou Peninsula.

2 MATERIAL AND METHOD 2.1 Study area and sample collection

The Leizhou Peninsula is located at the southernmost tip of the Chinese mainland, northwest of the South China Sea, northeast of the Beibu Gulf to the west, and north of the South China Sea to the east (Fig. 1). The study area analyzed in this paper (19.8°N–22.0°N, 108.8°E–111.3°E) is located in the coastal waters around the Leizhou Peninsula. In recent years, with the development of coastal industry and aquaculture, severe human activities and external interference have led to a significant decrease in the water quality of the aquatic environment near the Leizhou Peninsula and a gradual increase in environmental pressure. In addition, due to the complex coastline of the Leizhou Peninsula with numerous bays and islands, the pollution of areas is affected by different factors. The water quality and ecological environmental factors in the coastal zone of the Leizhou Peninsula are complex and changeable due to the effects of coastal runoff and meteorological conditions in the South China Sea.

The CDOM data used in this study were collected during two cruises around the Leizhou Peninsula in the autumn of 2020 and the spring of 2021. In this study, only surface water data were used. Water samples were collected in 5-L acid-washed plastic bottles. The samples were sent to the laboratory for filtration immediately after collection and stored in a refrigerator at 4 ℃. The number of surface seawater samples collected in this study was 91, which included 49 stations in September 2020 and 42 stations in April 2021.

2.2 Water surface spectra determination

For spectral measurements, the measurement method above the water surface was adopted, and the zenith angle and azimuth angle were 45° and 135°, respectively; this method avoids the effect of direct solar reflection and has relatively small inherent differences within the profile observations (Tang et al., 2004). The collected spectral range is 318–950 nm. Multiple parallel spectral data were measured in the sampling periods at each site, and the mean value was calculated after eliminating abnormal spectra. The water remote sensing reflectance (R_rs) was derived using the following equation (Mobley, 1999; Fargion and Mueller, 2000):

where L_w is the off-water radiance, L_sky is the sky radiance, E_d(0+) (E_d represents the irradiance incident at the sea surface, that is, the irradiance downwards at the sea surface, and d represents the downward direction) is the total incident irradiance on the water surface, and r is the reflectivity of the air-water interface, which is 0.022.

2.3 CDOM spectral absorption determination

Water samples were processed in the laboratory within 6 h of their arrival to measure CDOM absorption. The first step was to filter the water sample with glass microfiber (GF/F) filters (0.20 μm). These filtered samples were then pipetted into 10-cm diameter cuvettes and placed in a Shimadzu UV-2600 spectrophotometer to quantify CDOM absorption. Milli-Q water was used as a blank. Then, the absorption coefficient a_g (λ) was calculated via Eq.2:

where A(λ) is the optical absorbance of CDOM measured using the Shimadzu UV-2600 spectrophotometer, and L represents the cuvette path length in meters (0.1 m in this study). Since the absorption coefficient of CDOM in the sea area around the Leizhou Peninsula is low and the absorbance signal at 400 nm or 440 nm is small, making it easy to engender considerable errors and hard to show the trend of distribution, the absorption coefficient at 355 nm, namely, a_g(355), is used as the proxy of the CDOM concentration in this paper.

2.4 Improvement in the CDOM absorption spectrum fitting model

The inversion of the CDOM compositions depends on the refinement of CDOM absorption spectrum fitting. The premise of accurately simulating the CDOM absorption spectrum is to understand the absorption characteristics of CDOM. Since the absorption spectra of CDOM decrease exponentially, the exponential model can be used to simulate the changes (Bricaud et al., 1981; Markager and Vincent, 2000; Stedmon et al., 2000):

where a_g(λ) is the absorption coefficient at wavelength λ, a_g(λ₀) is the absorption coefficient at reference wavelength λ₀, S_g is the slope of the absorption spectrum, and the background parameter Δ explains the baseline offset or attenuation caused by factors other than CDOM. Although this model has a highly precise fit for the absorption spectrum curve, S_g is highly dependent on the wavelength range, and a complete description of the CDOM spectral characteristics is difficult to obtain. Twardowski et al. (2004) used six empirical statistical models to fit and improve the band absorption coefficients at nine wavelengths, indicating that the hyperbolic model fits the CDOM spectrum better. The equation is as follows:

The hyperbolic model depends only on the hyperbolic slope h, which is generally 6.92 (dimensionless), and its constant slope does not adequately explain the CDOM absorption variability in large-scale waters. In addition, the spectral characteristics of CDOM absorption in the ultraviolet band are very important, but the model does not fit the ultraviolet band (Twardowski et al., 2004; Shanmugam, 2011). We intend to use the two-parameter model to better describe the CDOM spectral characteristics and to overcome the shortcomings of the aforementioned models, as follows:

where h₀ is an additional parameter that considers different types of water bodies and is independent of S_g; h₀ is obtained using following calculation (Shanmugam, 2011):

The optimized two-parameter model (7) is obtained by merging model (5) and model (6). This model can adapt to a wider range of water bodies, and to a certain extent, it reduces the excessive dependence of the single-exponential model on the wavelength range and the band universality of the hyperbolic model.

2.5 Sentinel-3A OLCI image data acquisition and preprocessing

The remote sensing data in this article are obtained from the Sentinel-3A OLCI sensor and can be downloaded free of charge from the European Space Agency (ESA) Copernicus Open Access Hub website (https://scihub.copernicus.eu). Over land, Sentinel-3A OLCI sensors can be used to monitor fires and land-use changes and to measure lake and river heights; over the ocean, information such as seawater temperature, sea color, sea level height, and sea ice thickness can be measured, and marine pollution and climate change can be monitored. The spatial resolution of the sensor is 300 m, and the sensor provides 21 bands of high signal-to-noise ratio data (Table 1). Based on the continuation of 15 spectral segments of the Medium Resolution Imaging Spectrometer (MERIS), 6 spectral segments are added to provide a method to improve the inversion of water color elements. Therefore, the Sentinel-3 OLCI is particularly suitable for studying complex coastal waters and has potential application value in the research and management of coastal ecological environments.

The criteria for remote sensing images selection include low cloud coverage and images captured during the same season as the research period. Figure 2 shows the remote sensing images used in this study. Remote sensing images of the sea area obtained around the Leizhou Peninsula on November 7, 2020, and May 22, 2021, were preprocessed primarily using radiometric calibration, atmospheric correction, and mask cloud processing. A time difference between the selected date of the remote sensing image and the actual sampling date was noted. Due to the close correlation between the CDOM absorption coefficient and sea surface salinity (SSS) (Nieke et al., 1997; Del Castillo and Miller, 2008; Das et al., 2016; Keith et al., 2016), the SSS was compared with the date of remote sensing images and the actual sampling data. The SSS data were obtained from the Global Ocean Data Assimilation System (GODAS) of the National Centers for Environmental Prediction (NCEP) to ensure consistency of data sources. Table 2 shows little difference between the actual sampling time and the remote sensing image selection time of SSS, indicating the feasibility of inversion research in these two different periods.

The ESA provides Sentinel Application Platform (SNAP) software for processing Sentinel-3A data, in which the Case 2 Regional/Coast Colour (C2RCC) algorithm based on neural network (NN) technology is integrated and effectively extracts the water color information of coastal waters and inland waters from Sentinel-3A OLCI images (Doerffer and Schiller, 2007). Therefore, the C2RCC algorithm is used in the present study to conduct atmospheric correction on the L1b level data of the obtained remote sensing images.

Considering the nature of CDOM and the measured spectral range of the sea area around the Leizhou Peninsula, B1–B11 are selected as the research bands in this paper. The measured remote sensing reflectance is converted into the equivalent band, and the B1 (400 nm)–B11 (709 nm) bands of the Sentinel-3A OLCI sensor are simulated and combined with the spectral response function. The equation used to calculate equivalent band is as follows (Trigg and Flasse, 2000):

where R_b(i) is the equivalent band reflectance of Sentinel-3A; λ is the wavelength; R_rs(λ) is the measured remote sensing reflectance at the corresponding wavelength; λ_min and λ_max are the starting and ending wavelengths of band i, respectively; and SRF(λ) is the spectral response of band i at wavelength λ.

Empirical techniques are the most popular methods that have long been leveraged in numerous coastal/inland studies to estimate in-water constituents (Gitelson et al., 1993; Han and Jordan, 2005; Kutser et al., 2005; Niroumand-Jadidi et al., 2019). Based on the B1–B11 equivalent bands simulated by the measured R_rs data, the Python algorithm was used to traverse 11 bands of spring and autumn season images and establish single band, mutual band sum, band difference, band ratio, and multiband combinations to ensure that the selection of combinations of all bands was more comprehensive. Let B be an optical image with N spectral bands; in this paper, N is 11. Combined and referring to the classification of band combination features by Niroumand-Jadidi et al. (2019), this article thoroughly examines both standard feature types (SFTs) and derived feature types (DFTs). Among them, SFTs included single band S, band addition and subtraction A, band ratio R, spectral derivative D, and normalized difference index NDI. The equations can be applied to any possible band combination.

where B_i, B_j, and B_k are generic spectral bands, and λ_i and λ_j are the generic wavelengths of the N-band image B.

Three types of derived spectral features are used in this article: 1) DFT1: color space transformation; 2) DFT2: the transformation of the coordinate system; and 3) DFT3: directional cosines (Niroumand-Jadidi et al., 2019). The specific transformation extensions to all band combinations are as follows:

where B_i, B_j, and B_k are generic spectral bands. This equation is derived based on a transformation of the spectral feature space to hue-saturation-intensity (HSI)-inspired feature space. For the HSI color model, hue H, saturation S, and intensity I are composed of three different bands.

where B_i, B_j, and B_k are generic spectral bands. The equation is mainly based on the principle of Cartesian to spherical coordinate system transformation to derive informative features for water quality retrieval. The azimuth (φ), elevation (θ), and radius (ρ) are computed using every possible combination of three bands.

where B_i, B_j, and B_k are generic spectral bands. This equation is the direction of cosines in 3D spaces formed by spectral bands. Cosine α, β, and γ in the direction of the X-, Y-, and Z-axes can be computed using every possible combination of three bands.

2.6 Method for evaluating accuracy

The parameters evaluated using the model described in this paper are the practical parameter (F), root mean square error (RMSE), and mean relative percentage error (MAPE). The CDOM absorption spectrum fitting model uses the F value of variance analysis, which is the practical parameter standard of the model, to evaluate the advantages and disadvantages of the model. The following equation is used to calculate the F value:

where R² is the correlation coefficient obtained by least-squares fitting; D_m is the degree of freedom of the model; and D_e is the degree of freedom of model parameter error. If the number of model parameters is p and the number of wavelengths used to fit the model is n, then D_m=p–1 and D_e=n–p.

As methods to evaluate the accuracy of the inversion model, the RMSE and MAPE are introduced to test the correlation and error between the inversion value of the model and the measured value. The equations used to calculate the RMSE and MAPE are as follows:

where X_obs is the measured CDOM absorption coefficient, X_mod is the model inversion value, and n is the number of sample points.

3 CONSTRUCTION OF THE INVERSION MODEL 3.1 Validation of atmospheric correction

After a preliminary atmospheric correction, the atmospheric correction results of the Sentinel-3A remote sensing images in the B1 (400 nm)–B11 (709 nm) bands are obtained. Figure 3 shows that although the remote sensing reflectance of the Sentinel-3A image after atmospheric correction is somewhat overestimated or underestimated compared with the measured remote sensing reflectance, the overall atmospheric correction results are ideal, and thus the subsequent inversion model can be constructed. Figure 3 shows also the results of the comparison between the remote sensing reflectance of images corresponding to different bands at the satellite-ground matching points in spring and autumn and the measured remote sensing reflectance.

3.2 Construction of the CDOM inversion model

Due to the different overall levels of CDOM in spring and autumn, this paper used the band ratio method in the empirical model to construct the corresponding CDOM inversion models in spring and autumn. Based on a certain interval, 28 sites were evenly selected from 42 sites in spring for model construction, and 14 sites were used to verify the accuracy. Similarly, 34 sites were evenly selected from 49 sites in autumn for model construction according to a certain interval, and 15 sites were used to verify the accuracy.

Different inversion models were constructed, including linear models, quadratic polynomial models, cubic polynomial models, and exponential models. The relationship between a_g(355) and the measured remote sensing reflectance in the two seasons was analyzed, and the CDOM inversion model of Sentinel 3A-OLCI was established by selecting the bands with the highest correlation among SFTs and DFTs in the band combinations. The band combinations with a fitting determination coefficient greater than 0.70 and their inversion models are listed in Table 3.

Table 3 shows that the inversion model of the multiband combination has the best inversion effect overall. Among the bands, the most sensitive band combination to a_g(355) in spring was (B4+ B11)/B3, and the highest fitting determination coefficient with a_g(355) was 0.751, and lowest RMSE was 0.047. The most sensitive band combination to a_g(355) in autumn was (B7–B1)/ B6; the highest fitting determination coefficient with a_g(355) was 0.754, and lowest RMSE was 0.151. Therefore, this paper chose the inversion model of the CDOM in spring and autumn as shown in Eqs.20 & 21:

3.3 Correlation analysis of S_g and a_g(355)

When the CDOM absorption coefficient is parameterized, the use of only one S_g value to parameterize the whole band is not ideal. CDOM has high absorption in the range of 250–500 nm and relatively weak absorption after 500 nm. Therefore, 275 nm, 295 nm, 355 nm, 412 nm, and 440 nm were selected as the critical points to divide the CDOM absorption spectra in the range of 250–500 nm. Since the characteristic CDOM absorption wavelength in this paper is 355 nm and the band combination between 412 nm and 500 nm is not sufficient to constitute the fitting relationship, 18 band combinations were analyzed in both seasons after screening. Combined with Eq.7 of the CDOM absorption spectrum fitting curve obtained in Section 4.1, the S_g values of 28 inversion samples in spring and 34 inversion samples in autumn were calculated, and the remaining samples were used to verify the accuracy of the subsequent S_g inversion model. The S_g was obtained by fitting different band combination ranges to identify the band range with the strongest correlation with a_g(355) for inversion model construction. The correlation between a_g(355) in the two seasons and S_g fitted by different bands is shown in Fig. 4.

Figure 4 shows that the fitted S_g values in different band ranges are negatively correlated with a_g(355). In spring, S_g(275–295) has the strongest correlation with a_g(355) (R=-0.836), and S_g(355– 412) has the weakest correlation with a_g(355) (R= -0.307); in autumn, S_g(250–295) displays the strongest correlation with a_g(355) (R=-0.906), and S_g(295–500) exhibits the weakest correlation with a_g(355) (R=-0.449). Overall, the shortwave range of the CDOM absorption spectrum is more sensitive than the longwave range, and the correlation between S_g and a_g(355) in autumn is higher than that in spring. As shown in Fig. 4, substantial differences are observed in the fitted S_g in different band ranges at different times, even in the same water area.

3.4 Remote sensing estimation of S_g

Based on the inherent optical relationship between the S_g value and a_g(355), S_g(275–295), and S_g(250–295) are selected to indicate the structure of the CDOM composition in spring and autumn, and the corresponding estimation model of S_g is established according to the band range (Table 4).

In the estimation models of a_g(355) and S_g in spring and autumn, the R² values of the quadratic polynomial model are higher, i.e., 0.712 and 0.822, respectively. Therefore, the model equation with the best fitting relationship and lowest RMSE is selected as the model to estimate S_g based on a_g(355). Combined with the CDOM inversion Eqs. 20 & 21, the remote sensing inversion of the CDOM compositions in spring and autumn in the coastal waters of the Leizhou Peninsula can be achieved. Equation 22 is the inversion model of spring S_g, and Eq.23 is the inversion model of autumn S_g.

4 RESULT 4.1 Distribution of field data

According to the measured CDOM absorbance data from 91 stations around the Leizhou Peninsula in the autumn of 2020 and spring of 2021, the distribution maps of the a_g(355) and its spectral slope were plotted (Figs. 5 & 6).

The a_g(355) values in spring and autumn were high inshore and low offshore (Fig. 5). The a_g(355) in autumn was higher than that in spring. The field observation data statistics of a_g(355) are presented in Table 5. In spring, the a_g(355) values ranged from 0.092 to 0.553/m, with an overall average of 0.249/m. The average value of a_g(355) on the east coast of the Leizhou Peninsula was 0.286/m, the average value of a_g(355) on the Qiongzhou Strait was 0.241/m, and the average value of a_g(355) on the west coast was 0.222/m, showing the following spatial distribution: east coast of the Leizhou Peninsula > Qiongzhou Strait > west coast of the Leizhou Peninsula. The lowest value of a_g(355) appeared to the northeast of Hainan Island (B52). The highest value appeared in the estuary of Zhanjiang Bay (B3). In autumn, a_g(355) ranged from 0.115 to 1.067/m, with an overall average of 0.609/m. The average value of a_g(355) on the east coast of the Leizhou Peninsula was 0.658/m, the average value of a_g(355) in the Qiongzhou Strait was 0.763/m, and the average value of a_g(355) on the west coast was 0.495/m, showing the following spatial distribution: Qiongzhou Strait > eastern coast of the Leizhou Peninsula > western coast of the Leizhou Peninsula. The lowest value of a_g(355) appeared in the central Beibu Gulf of Guangxi (S35), and the highest value appeared at the entrance of Zhanjiang Bay (S10). Based on the a_g(355) data measured during the spring and autumn voyages, the average a_g(355) of the east coast of the Leizhou Peninsula was 0.503/m, the average a_g(355) of the Qiongzhou Strait was 0.502/m, and the average a_g(355) of the west coast was 0.365/m. The overall a_g(355) showed the following spatial distribution: eastern coast of the Leizhou Peninsula > Qiongzhou Strait > western coast of the Leizhou Peninsula.

The S_g values in spring and autumn were low nearshore and high far from the shore, and the S_g in autumn was lower than that in spring (Fig. 6). The statistics of field observation data for S_g are presented in Table 6. In spring, the range of S_g(275–295) was 0.009–0.034/nm, and the overall average value was 0.026/nm. The average value of S_g(275–295) on the east coast of the Leizhou Peninsula was 0.024/nm, the average value of S_g(275–295) in the Qiongzhou Strait was 0.027/nm, and the average value of S_g(275–295) on the west coast was 0.028/nm. S_g(275–295) presented the following spatial distribution: western coast of the Leizhou Peninsula > Qiongzhou Strait > eastern coast of the Leizhou Peninsula. The lowest value of S_g(275–295) appeared in the estuaries on the southeast corner of Donghai Island (B55), and the highest value appeared in the offshore area of the northeast Leizhou Peninsula(B11). In autumn, the range of S_g(250–295) values was 0.009–0.028/nm, and the overall average was 0.018/m. The average S_g(250–295) on the east coast of the Leizhou Peninsula was 0.017/nm, that on the Qiongzhou Strait was 0.016/nm, and that on the west coast was 0.021/nm. S_g(250–295) presented the following spatial distribution: western coast of the Leizhou Peninsula > eastern coast of the Leizhou Peninsula > Qiongzhou Strait. The minimum value of S_g(250–295) was observed in the estuary of Zhanjiang Bay (S10), and the maximum value was observed in the central part of the Guangxi Beibu Gulf (S40). According to the measured S_g values of spring and autumn voyages, the average S_g off the east coast of the Leizhou Peninsula was 0.02/nm, that off the Qiongzhou Strait was 0.021/nm, and that off the west coast was 0.024/nm. The overall S_g presented the following spatial distribution: west coast of the Leizhou Peninsula > Qiongzhou Strait > east coast of the Leizhou Peninsula.

4.2 Evaluation of the accuracy of the inversion model

The accuracy of the inversion model for a_g(355) and its spectral slope constructed in this paper was verified using the verified measured dataset. Figure 7 shows the scatter plot comparing between the measured and inversion values of a_g(355) based on the verification data collected in spring and autumn. In spring, the inversion value of the verification dataset was relatively concentrated in the range of 0.1–0.3/m and had a small deviation from the 1꞉1 line; the RMSE was 0.052/m, and the MAPE was 18.56%. The station number with a relatively large deviation was located close to the central part of the Beibu Gulf. The MAPE of the measured value and the simulated value of a_g(355) was 55.88%, which was higher than that of the whole verification dataset. Therefore, the relatively large deviation of this point is caused by the inaccuracy of CDOM inversion. In autumn, the inversion value of the validation dataset was overestimated, the RMSE was 0.127/m, and the MAPE was 14.31%. The MAPE of the CDOM inversion model in the two seasons was less than 30%, and the RMSE was small. The overall a_g(355) inversion results are reasonable.

Figure 8 shows the scatter plot comparing between the measured value and the inversion value of S_g based on the verification data collected in spring and autumn. Since the inversion of S_g is an indirect inversion based on a_g(355), it is affected by the error of the CDOM inversion model. The spring S_g validation data were evenly distributed on both sides of the 1꞉1 line, and the inversion values were concentrated in the range of (0.025–0.035)/nm. The RMSE was 0.003/nm, the MAPE was 8.89%, and the model inversion effect was relatively good. The inversion values of the autumn S_g validation dataset were mostly concentrated in the range of (0.01– 0.02)/nm, and the overall S_g was lower than that in spring; the RMSE was 0.002/nm, and the MAPE was 13.66%. The inversion effect of the model was not as good as that in spring, but it also exhibited a reasonable deviation range.

4.3 Evaluation of the accuracy of the CDOM absorption spectrum fitting model

The mean CDOM absorption coefficients in spring and autumn are shown in Fig. 9. The dotted line represents the CDOM absorption coefficient at the characteristic wavelength of 355 nm. In this paper, the hyperbolic-exponential model is used to fit the absorption spectrum curve of CDOM. The purpose is to reduce the dependence of the exponential model on the wavelength range and improve the band universality of the hyperbolic model.

The three CDOM absorption spectrum fitting models are described in Table 7. According to the average absorption coefficient of CDOM, the S_g values of different bands in different seasons were obtained using the three models, as shown in Fig. 10. The three models showed that the overall S_g value in spring was higher than that in autumn, indicating that the hyperbolic-exponential slope model can identifies the difference in CDOM components, the spatiotemporal distribution, and the difference in S_g values in different bands.

The F value and fitting coefficient of determination (R²) were calculated to evaluate the accuracy of the three CDOM absorption spectrum models, and the statistical parameters of the three models (Table 8) were obtained. Table 8 shows that the hyperbolic-exponential model is the optimal statistical model for fitting the CDOM absorption spectrum curve from the F and R² values; this model not only has a high fitting coefficient of determination but also a relatively high practical parameter.

4.4 Inversion result

The optimal multiband ratio model obtained in this paper was applied to Sentinel-3A OLCI images captured on November 7, 2020, and May 22, 2021, to obtain the inversion distribution of a_g(355) and S_g around the Leizhou Peninsula in spring and autumn. Figure 11 shows that the a_g(355) values in spring and autumn had a distribution of higher values nearshore and lower values far from the shore, and the value of a_g(355) on the east coast of the Leizhou Peninsula was higher than that on the west coast. In spring, the range of a_g(355) was 0.05–0.8/m; the range of a_g(355) in autumn was 0.15–1.2/m, indicating higher values in autumn than in spring. The a_g(355) high-value area in spring was mainly located in Zhanjiang Bay to the northeast of the Leizhou Peninsula, Leizhou Bay, Wailuo Port in the southeast, and Beibu Gulf in Guangxi. The high-value area of a_g(355) in autumn was mainly located on the east coast of the Leizhou Peninsula along East Island in the southeast corner of the Wailuomen channel, along the Qiongzhou Strait, Liusha Bay, and along the coast of Lianzhou Bay in Guangxi.

The remote sensing inversion estimation of S_g in the coastal waters of the Leizhou Peninsula was performed (Fig. 12). According to the inversion results, S_g generally decreased from nearshore to offshore, and S_g in spring was higher than that in autumn. In spring, the range of S_g was 0.015–0.04/nm, and in autumn, it was 0.01–0.03/nm. The range of S_g in spring was higher than that in autumn. In spring, the low-value area of S_g was mainly located in Zhanjiang Bay to the northeast of the Leizhou Peninsula and along the coast of Leizhou Bay, Wailuo Port in the southeast, and Beibu Gulf of Guangxi; the low-value area of S_g in autumn was mainly located along the east and west coasts of the Leizhou Peninsula and along the coast of Lianzhou Bay in Guangxi.

5 DISCUSSION 5.1 Analysis of the spatial distribution characteristics of a_g(355) and S_g

Combined with the measured data and inversion results, the a_g(355) values in spring and autumn gradually decreased from the nearshore area to far from the shore. On the one hand, surface runoff inputs a large amount of exogenous dissolved organic matter, perhaps from domestic sewage from the upstream urban area and wastewater discharge from energy-consuming industrial enterprises (Zhang et al., 2021a). On the other hand, due to the continuous dilution of seawater and the effects of offshore wind and waves, the influence of rivers entering the sea gradually decreases far from the shore, and thus a_g(355) far from the shore was low.

In the spring and autumn, the spatial distributions of S_g and a_g(355) showed an inverse distribution, and the overall S_g of the East Bank was lower than that of the West Bank. The low S_g values were mainly concentrated in Leizhou Bay on the east coast of the Leizhou Peninsula, along the Wailuomen channel in the southeast corner, and near the Beibu Gulf of Guangxi. The values at these locations were mainly due to the concentrated distribution of a large number of shellfish and shrimp aquaculture areas on the east coast of the Leizhou Peninsula, the diversity of water habitats, the complexity of biological flora, and the serious nitrogen and phosphorus pollution. Zhanjiang Bay to the north of Donghai Island is the marine area where shoal reclamation and aquaculture are concentrated, and it is also the outlet of urban polluted water (Cheng et al., 2009; Fu et al., 2020; Wang et al., 2021); this water carries a large amount of terrestrial CDOM into the bay and is restricted by topography, rendering semienclosed bay aquatic ecosystems more vulnerable. The water exchange capacity in the Lianzhou Bay in Guangxi is weak, and many offshore vessels are present. The sewage from many ports and vessels easily flows down, and many rivers empty into the sea, such as the Nanliu River and the Dafeng River, which are distributed along the coast. Intensive human activities and external interference lead to the decrease in the water quality in the aquatic environment (Lai et al., 2014); thus, the proportion of humus in these waters is relatively high, and S_g is low. In addition, from the nearshore to the far shore, the S_g values in the water gradually increase, and the a_g(355) far from the shore is always high. This high level is because the source of CDOM far from the sea is mainly the internal degradation of phytoplankton, the fulvic acid content is high, and S_g is always high.

5.2 Analysis of the seasonal distribution characteristics of a_g(355) and S_g

In spring, high a_g(355) values were observed in various estuaries along the coast of the Leizhou Peninsula. This distribution occurred because phytoplankton had not started to proliferate in large quantities due to enhanced of photosynthesis. Endogenous degradation was not the main source of CDOM; terrestrial inputs might also exist (Qiao et al., 2014; Fu et al., 2020; Zhou et al., 2020; Zhang et al., 2021a). High a_g(355) values are not present in the middle of the Qiongzhou Strait, potentially because the organic matter produced by terrigenous factors is substantially reduced in the middle sea area due to dilution by seawater diffusion and tidal and current mixing (Wu et al., 2016). In autumn, a_g(355) was generally higher than the value in spring. In offshore and estuarine environments, phytoplankton do not directly produce CDOM, but the DOM released and degraded by phytoplankton indirectly produce CDOM through microbial action (Steinberg et al., 2004). The large amount of degraded organic matter generated by CDOM, combined with perennial pollution input from land runoff and pollutants from coastal aquaculture zones brought by wind and waves, leads to a large range of high a_g(355) values (Lü et al., 2012; Zhang et al., 2018).

Due to the different hydrological conditions in different periods near the Leizhou Peninsula, the source of CDOM was different in different seasons. The overall S_g in autumn was lower than that in spring, indicating that the a_g(355) level in autumn was substantially influenced by terrestrial sources. In spring, the minimum S_g values along the east coast of the Leizhou Peninsula from Donghai Island to the southeast corner of Wailuomen Channel, southwest corner of Liusha Bay, coast of Tieshan Port and coast of Lianzhou Bay all appeared, which was related to the high humus content in CDOM along the coast. Water exchange in the Qiongzhou Strait is frequent and complex and is influenced by water transport from east to the west year-round (Shi et al., 2002; Wang et al., 2018; Chen et al., 2019). Given water flow with the appropriate intensity, plant plankton makes use of nutrients, thus promoting the growth and reproduction of algae (Huang et al., 2016). Therefore, the S_g value in the middle part of the strait was higher. In autumn, the input of perennial seawater cage culture pollution led to the local accumulation of terrestrial pollutants in the bay with high values, the coastal runoff decreased, and large floats and gatherings of algae led to a higher proportion of phytoplankton degradation in autumn compared to spring; the proportion of humus in CDOM increased significantly, and S_g values were low.

6 CONCLUSION

Based on the band settings of Sentinel-3A OLCI images, the optical characteristics and sensitive bands of CDOM were analyzed in this paper, and a remote sensing estimation model for the absorption coefficient and composition of CDOM in the nearshore Leizhou Peninsula suitable for OLCI images was constructed. The main conclusions are described below.

1) The a_g(355) values of the CDOM concentration in the sea area around the Leizhou Peninsula decreased from the nearshore to the open sea, showing the following spatial distribution pattern: eastern coast > Qiongzhou Strait > western coast. Their average values were 0.503/m, 0.502/m, and 0.365/m, respectively. The a_g(355) values were (0.05 – 0.8)/m in spring and (0.15–1.2)/m in autumn, and overall, the values were higher in autumn than in spring.

2) The multiband ratio method was used to invert a_g(355). The combined study of the B1–B11 bands revealed that the inversion effect of CDOM was the best in spring (B4+B11)/B3 and autumn (B7–B1)/ B6, with determination coefficients of 0.751 and 0.754, respectively. The RMSEs of the verification points were 0.052 and 0.127, and the MAPEs were 18.56% and 14.31%, respectively. The RMSEs were all less than 0.2/m, and the MAPEs were all less than 20%.

3) The hyperbolic-exponential model was improved based on the exponential and hyperbolic models to obtain a more accurate spectral slope of CDOM band fitting. Compared with the exponential and curve models, the hyperbolic-exponential model improves the accuracy to a certain extent, according to the practical parameter (F) and fitting determination coefficient (R²) of the model.

4) The critical points of 275 nm, 295 nm, 355 nm, 412 nm, and 440 nm were selected to divide the 250– 500 nm CDOM absorption spectrum. The S_g and a_g(355) values of different fitting band ranges showed a negative correlation. Among them, the correlation between S_g(275–295) and a_g(355) was the greatest in spring, and the correlation between S_g(250–295) and a_g(355) was the greatest in autumn. Therefore, these two bands were selected to construct the inversion estimation model of S_g, and the RMSE verification points were 0.002/m and 0.003/m, respectively. The MAPEs were 8.89% and 13.66%, respectively, and they were both less than 15%.

Combined with the measured and inversion results, the S_g and CDOM concentrations are approximately opposite to the spatiotemporal distribution of the CDOM absorption coefficient; these values are high mainly in Zhanjiang Bay, Leizhou Bay, Qiongzhou Strait, Liusha Bay, Tieshan Harbor, and Lianzhou Bay. The terrestrial organic matter carried by the coastal aquaculture zone and runoff into the sea are the main sources of CDOM in the sea area around the Leizhou Peninsula.

7 DATA AVAILABILITY STATEMENT

The data that support the findings of this study are available from the corresponding author upon reasonable request.