Assessment of Atmospheric Correction Algorithms for Correcting Sunglint Effects in Sentinel-2 MSI Imagery: A Case Study in Clean Lakes

Abstract

The Sentinel-2 Multi-Spectral Instrument (MSI) is characterized by short revisit times (5 days), red-edge spectral bands (665 nm and 705 nm), and a high spatial resolution (10 m), making it highly suitable for monitoring water quality in both inland and coastal waters. Unlike SeaWiFS, which can adjust its viewing angles to minimize sunglint, the Sentinel-2 MSI operates with fixed near-nadir angles, which makes it more susceptible to sunglint. Additionally, the complex optical properties of water pose challenges in accurately determining its water-leaving reflectance. Therefore, we compared the effectiveness of six atmospheric correction (AC) algorithms (POLYMER, MUMM, DSF, C2RCC, BP, and GRS) in correcting sunglint using two typical lakes in Xinjiang, China, as examples. The results indicated that POLYMER achieved the highest overall evaluation score (1.61), followed by MUMM (1.21), while BP exhibited the lowest performance (0.62). Specifically, POLYMER showed robust performance at the 665 nm band with RMSE = 0.0012 sr⁻¹, R² = 0.74, and MAPE = 30.68%, as well as at the 705 nm band with RMSE = 0.0014 sr⁻¹, R² = 0.42, and MAPE = 38.44%. At the 443, 490, and 560 nm bands, MUMM showed better performance (RMSE ≤ 0.0026 sr⁻¹, R² ≥ 0.86, MAPE ≤ 28.20%). In terms of band ratios, POLYMER exhibited the highest accuracy (RMSE ≤ 0.093 and MAPE ≤ 22.2%), particularly for the ratio R_rs (490)/R_rs (560) (R² = 0.71). In general, POLYMER is the best choice for the sunglint correction of Xinjiang’s clean lakes. This study assessed the capability of different AC algorithms for sunglint correction and enhanced the monitoring capability of MSI data in clean waters.

1. Introduction

Remote sensing plays a critical role in evaluating water quality [1,2]. Instruments like MODIS and the Landsat series are extensively utilized for monitoring inland waters [3,4,5]. However, challenges persist regarding spatial, temporal, and spectral resolutions, complicating the effective monitoring of inland waters, particularly smaller bodies of water [6]. Leveraging advanced technology, such as a wide field of view and high sampling rate, the MSI features high spatial resolution ranging from 10 to 60 meters [7] and revisits every five days (or every 2 to 3 days for mid–low latitude regions) [8]. Compared to the TM, ETM+, and OLI sensors of the Landsat series, the MSI includes red-edge bands (665 and 705 nm), making it more suitable for monitoring water quality (Table S1) [6,9]. These advantages make MSI an ideal tool for monitoring inland waters, and it is widely used for monitoring water quality in both inland and coastal waters [10,11].

Atmospheric correction (AC) is essential for water color remote sensing [12,13]. The intricate optical characteristics of inland waters and the complex nature of atmospheric aerosols pose significant challenges in achieving accurate remote sensing reflectance [14,15,16]. Several AC algorithms, including Management Unit Mathematics Models (MUMMs) and Dark Spectrum Fitting (DSF), have been developed for inland waters [16,17]. These algorithms have demonstrated effective results on the Sentinel-2 MSI, with numerous studies evaluating their performances in inland waters [18,19,20]. Nevertheless, these studies often overlook the evaluation of the sunglint correction performance of AC algorithms.

Sunglint, the direct reflection of sunlight from the water surface, disrupts remote sensing signals and presents a significant challenge to water color remote sensing [21,22]. Therefore, mitigating or removing sunglint effects is a critical step in water color remote sensing. Unfortunately, the Sentinel-2 MSI operates with fixed near-nadir angles, making it more susceptible to sunglint [23]. In some clean lakes and reservoirs with low water reflectance, sunglint interference is highly significant and may dominate the total satellite signal. Currently, sunglint processing primarily involves masking or correction through various sunglint correction algorithms. Sunglint correction algorithms can be categorized into three primary types [24]. The first type is based on statistical models related to sea surface features [25]. The second type utilizes methods based on the relationships among the spectral bands of the image [22,26]. The third type employs polynomial models to estimate the contributions of the atmosphere and sunglint to spectral reflectance, thereby enabling corrections [27].

The Cox and Munk model links wind speed to sea surface roughness by utilizing the probability density functions of sea surface slopes and observational geometry to forecast areas affected by sunglint [25,28]. This model is effective for medium-to-low resolutions (approximately 300 to 1000 m). However, it is unsuitable for high-resolution images, as it cannot accurately describe the complex structures and local variations in the sea surface on a small scale [29]. Methods for sunglint correction based on inter-band relationships exploit the strong absorption properties of water in the near-infrared (NIR) bands. These methods remove the sunglint component based on the physical relationships between NIR bands and other bands [26,30,31]. However, in shallow or turbid waters, the NIR bands generally do not approach zero, which affects the effectiveness of sunglint correction. Glint Removal for Sentinel-2 (GRS) estimates the bidirectional reflectance distribution function (BRDF) of the rough air–water interface using the short-wave infrared (SWIR) band [22]. The sunglint signal obtained in the SWlR band is then propagated to the NIR and visible bands. The polynomial-based algorithm applied to MERIS (POLYMER) employs a spectral matching method, using a polynomial model to integrate data across all visible spectral bands, simulating the contributions of the atmosphere and sunglint to the spectral reflectance [27]. By iteratively optimizing the coefficients of the polynomial model, this algorithm minimizes the error between observed and predicted data, effectively recovering the true spectral information of waters under high sunglint conditions.

Considering the sunglint effects, this study systematically assessed the applicability of six AC algorithms for sunglint corrections of Sentinel-2 MSI data: POLYMER, Management Unit Mathematics Models (MUMMs), Dark Spectrum Fitting (DSF), Case 2 Regional Coast Colour processor (C2RCC), Black Pixel (BP), and GRS in clean waters (i.e., Bosten Lake and Ulungur Lake in Xinjiang Province) [16,17,22,27,32,33]. This study enhances the monitoring capabilities of MSI data by broadening their potential applications in clean waters.

2. Data and Methods

2.1. Study Area

Bosten Lake (41°49′N–42°08′N, 86°42′E–87°26′E) and Ulungur Lake (46°50′N–47°25′N, 86°59′E–87°33′E) are located in the northwestern inland region of China (Figure 1), which is characterized by a temperate continental climate. Bosten Lake and Ulungur Lake, the two largest freshwater lakes in Xinjiang Province, are vital to the local economy and ecosystem. Bosten Lake covers approximately 1000 km² and is situated at the southern foothills of the Tianshan Mountains. Its primary water sources are the Kaidu River, rainfall, and groundwater recharge, while the Kongque River serves as its outflow. The annual average water level variation in Bosten Lake ranges from 1 to 2 m and is significantly influenced by seasonal rainfall and melting snow. The average yearly temperature is approximately 8.6 °C, with annual precipitation ranging from 80 to 200 mm and an evaporation rate between 2000 and 3000 mm [34]. Ulungur Lake, located at an elevation below 1000 m and covering approximately 800 km², mainly receives water through surface runoff, with the Irtysh River and the Ulungur River being its primary inflows. The lake has an average annual evaporation of 1844.4 mm, receiving 116.5 mm of precipitation yearly, and an average annual temperature of 3.4 °C [35].

2.2. Field Measurements

The in situ data used in this study were collected through field surveys conducted in 2021 and 2022. The data include suspended particulate matter (SPM), Secchi disk depth (SDD), chlorophyll-a (Chla), and remote sensing reflectance (R_rs) from both Bosten Lake and Ulungur Lake. Field sampling was scheduled based on the transit times of the Sentinel-2 satellite, ensuring clear and cloud-free conditions. Sampling routes and sites were determined based on the shapes of the lakes, with distances between adjacent sampling sites exceeding 1 km. The coordinates of predefined sampling points were entered into handheld global positioning system (GPS) devices in advance. Local boats were used for sampling and guided to designated points by GPS coordinates. Sampling commenced upon securing the ship and recording the coordinates for subsequent site correlation. Water samples were collected in 1 L high-density polyethylene (HDPE) bottles from a depth of 0.50 m, totaling 5 L per site. The samples were temporarily stored at 4 °C in a portable refrigerator, filtered within 24 h, and transported to the laboratory for analysis. Before use, each bottle was acid-cleaned and then rinsed with distilled water.

Clear and cloudless weather conditions were needed to minimize the impact of direct sunlight and shadows from vessels on the light field. Using the FieldSpec Pro and following NASA’s guidelines, R_rs was measured above the water surface across a wavelength range of 350 to 1050 nm [36,37]. The calculation of R_rs was performed using the following equation:

$$R_{rs}=\left[L_{sw}(\lambda )-{\gamma L}_{sk}(\lambda )\right]{\rho }_p(\lambda )/{\mathsf{\pi }L}_p(\lambda )$$

(1)

where $L_{sw}$, $L_{sk}(\lambda )$, and $L_p(\lambda )$ represent the measured water surface, the radiance values of the sky, and the standard grayboard, respectively. $\mathsf{\gamma }$ is the air–water interface reflectance, which is 0.022 for calm water conditions. ${\rho }_p(\lambda )$ represents the reflectance of the standard grayboard.

The concentration of Chla was determined via acetone extraction. Cells were lysed by repeated freeze–thaw cycles, and Chla was extracted with a 90% acetone solution. Following centrifugation, the supernatant was collected, and absorbance values were measured at 630, 645, 663, and 750 nm using a Shimadzu UV-2600 spectrophotometer to calculate the concentration of Chla [38,39].

The SDD was measured by submerging the disk parallel to the water surface on the backlit side of the vessel until the colors on the disk were no longer visible, at which point the depth was recorded. Subsequently, the disk was lowered until it completely disappeared and was then slowly raised until the white surface reappeared, at which point the depth was recorded again. The average of these two depths represents the SDD. To minimize errors due to differences in visual acuity among experimenters, the same individual conducted all measurements throughout the field process [40].

The concentration of SPM was measured using the weight difference method. First, water samples were filtered through 0.47 μm Whatman GF/F membranes that had been baked at 450 °C. The filtered membranes were then placed in an oven at 103 °C to 105 °C and baked for 4 h, after which they were weighed using a balance with an accuracy of 0.0001 g. The total suspended matter concentration for each water sample was determined by the weight difference before and after filtration [41].

2.3. Satellite Data and Data Matching

Level-1C data of Sentinel-2 MSI (

Table 1. The match-up dates of in situ measurement and MSI data acquisition over Bosten Lake and Ulungur Lake.

Lake	MSI Image	Date	Number	Sunglint
Bosten	MSIL1C_20210917T045701T45TVG	2021.9.17	11	No
	MSIL1C_20210917T045701T45TWG	2021.9.17	14	Yes
	MSIL1C_20220612T050659T45TVG	2022.6.12	26	Yes
Ulungur	MSIL1C_20210526T051651T45TWN	2021.5.26	21	Yes

) were obtained from the European Space Agency (ESA) (https://dataspace.copernicus.eu/, accessed on 2 April 2023). The Sentinel-2 mission includes two satellites, Sentinel-2A (S2A) and Sentinel-2B (S2B), providing a revisit time of 5 days (2–3 days for mid–low latitude regions) [8]. S2A and S2B are equipped with MSI, which is capable of capturing data from 13 spectral bands, including red (665 nm), green (560 nm), blue (490 nm), and NIR (835 nm), with resolutions up to 10 m (Table S1). MSI also includes red-edge spectral bands (665 nm and 705 nm), which are particularly suitable for water color remote sensing [10,18].

The satellite data were restricted to within ±3 h of in situ data collection [42,43]. The spatial variability coefficient within a 3 × 3 pixel window was also below 15% [44]. After atmospheric correction, pixels with null or negative values in certain bands were identified as correction failures. These failed correction data were subsequently excluded during the matching of satellite-to-ground synchronous data. Based on these criteria, 72 satellite–ground synchronous data points were selected for this study (Table 1). Among these data points, 51 were from Bosten Lake, and 21 were from Ulungur Lake.

2.4. Atmospheric Correction Algorithms

Six AC algorithms were assessed, namely DSF, C2RCC, POLYMER, MUMM, BP, and GRS (

Table 2. Descriptions of AC algorithms.

Algorithms	Algorithm Principles
DSF (Acolite20211124)	Rayleigh LUT	6SV [52]
	Aerosol	Dark target approach (area-based)
	Sunglint	It estimates sunglint using estimations at a reference band (assuming zero ρw) reflectance and extrapolates it to other spectral bands.
C2RCC (SNAP 9.0)	Rayleigh LUT	NA
	Aerosol	SOS atmospheric parameters, O3, WV, NO2, O2, etc.
	Sunglint	NA
POLYMER (v4.16)	Rayleigh LUT	SOS [53]
	Aerosol	Polynomial fitting (per-pixel)
	Sunglint	The atmospheric component of this algorithm is a polynomial function used to derive the spectral reflectance of the atmosphere and sunglint.
MUMM (l2gen 9.5.1-V2021.1)	Rayleigh LUT	Ahmad and Fraser 1982 [54]
	Aerosol	NIR-SWIR band ratio (per-pixel)
	Sunglint	According to the Cox and Munk model, sunglint is predicted using wind speed data and subtracted from radiance when it falls between two thresholds.
BP (l2gen 9.5.1-V2021.1)	Rayleigh LUT	Ahmad and Fraser 1982 [54]
	Aerosol	NIR-SWIR band ratio (per-pixel)
	Sunglint	According to the Cox and Munk model, sunglint is predicted using wind speed data and subtracted from radiance when it falls between two thresholds.
GRS (V2.1)	Rayleigh LUT	OSOAA [55]
	Aerosol	Fitted to CAMS (area-based)
	Sunglint	It estimates the bidirectional reflectance distribution function (BRDF) of the rough air–water interface from the SWIR bands (i.e., around 1610 and 2200 nm). The sunglint signal obtained in the SWIR is then propagated toward the NIR and visible bands.

). The BP algorithm operates based on the “dark pixel” assumption in the NIR and SWIR bands [45,46,47]. The aerosol scattering ratio in the NIR or SWIR bands was calculated. The optimal model was determined based on aerosol model lookup tables (LUTs) and extrapolated aerosol parameters to the visible light bands. The MUMM proposed by Ruddick et al. [16] is an improvement over the GW94 algorithm [48]. Building on the standard algorithm, MUMM replaces the “dark pixel assumption” with the assumption that the ratio of water-leaving reflectance between two NIR bands (ρw (783)/ρw (865)) is a constant, referred to as MUMM_alpha. MUMM_epsilon, the aerosol reflectance ratio between 865 and 783 nm, was also considered. In this study, MUMM_alpha and MUMM_epsilon were set at 1.817 and 1.0, respectively. This substitution allowed for separating aerosol scattering in the NIR spectral range. Subsequently, the optimal aerosol model was determined based on aerosol LUT models, and aerosol parameters were extrapolated to the visible spectral range [49]. BP and MUMM algorithms were conducted under SeaDAS l2gen 9.5.1-V2021.1 [48,50,51]. In SeaDAS, the Cox and Munk model was adopted for sunglint correction. This model established a relationship between wind speed and sea surface roughness through the probability density function of the sea surface slope and the observational geometry to predict areas affected by sunglint. [25,28].

The DSF, developed by Vanhellemont and Ruddick [17], dynamically selects a “dark target” in the bands by searching for the darkest pixels in the entire image and performing a least squares regression on the lowest reflectance of the first 1000 pixels. The regression intercept represents the best reflectance estimate of the darkest target for the correction bands. The aerosol’s optical thickness and model for subsequent AC were obtained using the darkest pixel from the LUTs. Secondly, the sunglint reflection in other bands was calculated using the atmospheric transmittance and the ratio of Fresnel reflection on the water surface. In this study, the DSF algorithm was run under the ACOLITE_20211124, with the sunglint correction option activated.

The C2RCC algorithm utilizes an extensive training database derived from radiative transfer simulations to train an artificial neural network (ANN) model. This model integrates atmospheric correction and water color remote sensing inversion as a whole, simultaneously retrieving aerosol optical depth (AOD), water-leaving reflectance, and water quality parameter concentrations [33]. This study was conducted using C2RCC under SNAP 9.0. C2RCC does not support sunglint correction.

POLYMER is an AC algorithm [27] that mitigates sunglint contamination. This method employs a spectral matching approach with a polynomial fitting model for atmospheric scattering and sunglint alongside a bio-optical model for seawater reflectance. By establishing a coupled ocean–atmosphere bio-optical model, POLYMER enables hypotheses stating that the reflectance of aerosols and sunglint can effectively be modeled using polynomials. Through iterative processes utilizing spectral matching optimization methods, POLYMER seeks to iteratively determine the water-leaving reflectance. In this study, the version of POLYMER used was V4.16.

Harmel et al. [22] introduced the GRS algorithm as a comprehensive method for atmospheric and sunglint correction. This algorithm addresses molecular scattering, gas absorption, and radiation attributed to weakly absorbing aerosols, in addition to the direct reflection of light on the rough air–water interface. The core principle of sunglint correction involves estimating the bidirectional reflectance distribution function (BRDF) of the rough air–water interface using data from the SWIR band. The sunglint estimated in the SWIR band was subsequently extrapolated to the NIR and visible bands. In this study, GRS version V2.1 was used.

2.5. Sunglint Image Statistics and Angle Information

Sunglint occurs when sunlight is directly reflected off the water surface into the sensor, resulting in higher radiance signals than normal waters and appearing as white pollution in true color images (Figure S1). Based on this characteristic, sunglint can be visually identified from the white pollution in true color images and their radiance differences with the surrounding waters [21,22]. To further explore the impact of sunglint on the two lakes, this study employed visual interpretation to tally the number of images affected by sunglint and the number of normal images without clouds or sunglint from 2015 to 2022. Without considering the effect of wind and assuming that the water surface is a smooth plane, the angle ${\theta }_m$ represents the theoretical position of specular reflection relative to the satellite sensor’s viewing direction for a specific observation geometry (Figure S2) [56]. The angle ${\theta }_m$ is calculated as follows:

$$\mathit{cos}{\theta }_m=\mathit{cos}{\theta }_s\mathit{cos}{\theta }_v-\mathit{sin}{\theta }_s\mathit{sin}{\theta }_v\mathit{cos}∆\phi$$

(2)

where ${\theta }_m$ reflects the probability of sunglint occurrence to some extent, ${\theta }_v$ represents the sensor zenith angle, $∆\phi$ represents the relative azimuth angle (i.e., the difference between the solar azimuth angle and the sensor azimuth angle), and ${\theta }_s$ represents the solar zenith angle. However, it is important to note that in addition to observation geometry, wind is also a significant factor influencing sunglint formation. Wind causes fluctuations on the water surface, creating numerous irregular facets that alter the direction of light propagation, thereby affecting the formation of sunglint.

2.6. Classification of Water Types

To understand the optical water types (OWTs) in the study area, OWTs were classified according to the standards set by Spyrakos et al. [57]. This study followed the method outlined by Liu et al. [58], employing the spectral angle [59] as a measure to evaluate the similarity between the recorded spectra and the reference OWT spectra:

$$\alpha ={\mathit{cos}}^{-1}{\displaystyle \frac{\sum _{i=1}^n{p}_i{r}_i}{\sqrt{\sum _{i=1}^n{p}_i^2}\sqrt{\sum _{i=1}^n{r}_i^2}}}$$

(3)

$$S_{OWT}=1-{\displaystyle \raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$\pi $}\right.}$$

(4)

where $p_i$ is the reflectance of the measured spectrum in band i; $\alpha$ is the spectral angle between the measured spectrum and the reference spectrum, expressed in radians; and $r_i$ is the reflectance of the reference spectrum in band i. The calculated $S_{OWT}$ ranges from 0 to 1, with 1 indicating identical spectral shapes.

2.7. Accuracy Assessment

2.7.1. Statistical Metrics

The accuracy of the six AC algorithms was evaluated using various statistical metrics: the root mean square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R²). R² quantifies the correlation between the actual measured values and the corrected R_rs values. RMSE quantifies the root mean square difference between the corrected R_rs values from each algorithm and the actual measured values, indicating the average deviation. MAPE measures the average percentage error between the R_rs values corrected by each algorithm and the actual measured values.

$$R^2={\displaystyle \frac{{\left(\sum \left(X_i-\overline{X}\right)\left(Y_i-\overline{Y}\right)\right)}^2}{\sum {\left(X_i-\overline{X}\right)}^2\sum {\left(Y_i-\overline{Y}\right)}^2}}$$

(5)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{(Y_i-X_i)}^2}$$

(6)

$$MAPE={\displaystyle \frac{1}{n}}\sum _{i=1}^n\left|{\displaystyle \frac{Y_i-X_i}{X_i}}\right|\times 100\%$$

(7)

where Y represents the remotely sensed reflectance values after atmospheric correction, and X represents the measured hyperspectral values. $\overline{X}$ and $\overline{Y}$ represent the mean of the measured hyperspectral values and the remotely sensed reflectance values after AC.

2.7.2. Ranking Scores

The overall performances of the six AC algorithms were ranked using the comprehensive evaluation process proposed by Qin et al. [60] and Müller et al. [61]. This evaluation involved ranking the statistical parameters (RMSE, MAPE, R^2, and N).

The specific scoring criteria were as follows: (1) If RMSE and MAPE exceeded their respective 90% confidence interval means, the score was 0; if they fell within the interval, the score was 1; and if they were below the interval, the score was 2. (2) If R² was below the 90% confidence interval mean, the score was 0; if it fell within the interval, the score was 1; and if it exceeded the interval, the score was 2. (3) (3) If “N” was below the 90% confidence interval mean, the score was 0; if it fell within the interval, the score was 1; and if it exceeded the interval, the score was 2.

Subsequently, the total score for each AC algorithm was calculated. The total score for each algorithm was divided by the number of bands evaluated to obtain the algorithm’s score. The average score for all algorithms was calculated. Finally, the score for each algorithm was obtained by dividing the score of each atmospheric correction algorithm by the average score of all algorithms. A score greater than 1 indicates better correction performance, while a score less than 1 indicates poorer performance [60,61].

3. Results

3.1. Bio-Optical Characteristics of Study Areas

The spectral curve shapes of both lakes were similar; however, the measured remote sensing reflectance of Ulungur Lake typically exceeded that of Bosten Lake. The reflectance began to rise at 400 nm, peaked at around 550 nm, and then sharply decreased, approaching zero after 750 nm (Figure 2a). According to the classification results for each lake’s OWTs, compared to the 13 types of inland waters, except for BST08 on 17 September 2021 and BST06 on 12 June 2022, the remaining measured spectral data closely aligned with OWT3 (defined as clean water by Spyrakos et al. [57]) (Figure 2b,c). This suggested that the waters in the study area were primarily classified as clean water. However, the second-highest membership was of OWT9, indicating some characteristics of case water. In terms of substance concentrations, the SDDs and standard deviations for Bosten Lake and Ulungur Lake were 3.38 ± 1.22 m and 1.49 ± 0.21 m, respectively. The Chla concentrations were 2.88 ± 2.08 μg/L and 1.26 ± 0.73 μg/L, respectively. The SPM concentrations were 2.30 ± 1.12 mg/L and 5.33 ± 2.65 mg/L, respectively (

Table 3. Variations in the bio-optical properties of Bosten Lake and Ulungur Lake.

Lake	Number	SDD (m)		Chla (μg/L)		SPM (mg/L)
		Min–Max	Mean ± Std	Min–Max	Mean ± Std	Min–Max	Mean ± Std
Bosten	51	1.50–6.80	3.38 ± 1.22	0.54–8.06	2.88 ± 2.08	0.20–5.20	2.30 ± 1.12
Ulungur	21	0.95–1.90	1.49 ± 0.21	0.24–3.73	1.26 ± 0.73	4.21–10.31	5.33 ± 2.65

).

3.2. Assessment of the Atmospheric Correction Algorithms

3.2.1. Single Bands

Generally, the six AC algorithms demonstrated the highest accuracy at the 490 and 560 nm bands (RMSE ≤ 0.0061 sr⁻¹, MAPE ≤ 38.47%, R² ≥ 0.67), followed by the 443 nm band, and they performed the poorest in the red and NIR bands (Figure 3 and

Table 4. Statistics of evaluation indicators for six AC algorithms (bold means the best statistical value).

Algorithm	Band	R2	RMSE (sr−1)	MAPE (%)	N	Algorithm	Band	R2	RMSE (sr−1)	MAPE (%)	N
DSF	443	0.57	0.0069	41.82	69	MUMM	443	0.86	0.0026	28.20	72
	490	0.76	0.0057	28.35	72		490	0.94	0.0024	16.32	72
	560	0.83	0.0046	19.91	72		560	0.94	0.0024	14.50	72
	665	0.46	0.0019	48.62	72		665	0.65	0.0013	45.56	72
	705	0.20	0.0016	61.48	70		705	0.17	0.0016	62.32	67
C2RCC	443	0.61	0.0069	42.59	72	BP	443	0.30	0.0034	51.02	62
	490	0.79	0.0069	34.74	72		490	0.67	0.0061	38.47	72
	560	0.85	0.0054	23.12	72		560	0.79	0.0044	20.73	72
	665	0.64	0.0018	36.82	72		665	0.31	0.0024	47.12	58
	705	0.47	0.0014	38.52	72		705	0.32	0.0016	48.43	48
POLYMER	443	0.86	0.0032	22.78	72	GRS	443	0.47	0.0057	72.68	72
	490	0.91	0.0035	18.61	72		490	0.72	0.0050	42.19	72
	560	0.91	0.0038	15.81	72		560	0.80	0.0044	24.23	72
	665	0.74	0.0012	30.68	72		665	0.44	0.0021	71.94	70
	705	0.42	0.0014	38.44	72		705	0.19	0.0019	93.07	69

). Some algorithms failed to correct certain pixels in specific bands (Table 4). C2RCC and POLYMER successfully matched all 72 sample points, followed by GRS (N = 69 at 705 nm), with the BP algorithm matching the fewest (N = 48 at 705 nm).

Among the six AC algorithms, the POLYMER and MUMM algorithms demonstrated similar performance at the 443 nm band (POLYMER: MAPE = 22.78%, RMSE = 0.0032 sr⁻¹, R² = 0.86; MUMM: MAPE = 28.20%, RMSE = 0.0026 sr⁻¹, R² = 0.86) (Table 4). At the 490 and 560 nm bands, the MUMM algorithm demonstrated superior correction performance, exhibiting the lowest RMSE and MAPE and the highest R² (490 nm band: MAPE = 16.32%, RMSE = 0.0024 sr⁻¹, and R² = 0.94; 560 nm band, MAPE = 14.50%, RMSE = 0.0024 sr⁻¹, and R² = 0.94) (Table 4). At the 665 nm band, the POLYMER algorithm performed the best, exhibiting the lowest RMSE and MAPE with a high R² (MAPE = 30.68%, RMSE = 0.0012 sr⁻¹, and R² = 0.74). At the 705 nm band, C2RCC and POLYMER exhibited similar performances with comparable RMSE, MAPE, and R² values (C2RCC: MAPE = 38.52%, RMSE = 0.0014 sr⁻¹, R² = 0.47; POLYMER: MAPE = 38.44%, RMSE = 0.0014 sr⁻¹, R² = 0.42).

3.2.2. Band Ratios

Band ratio algorithms are widely used in remote sensing applications, particularly for retrieving water bio-geochemical parameters. These algorithms are crucial for mitigating systematic retrieval errors that may arise from atmospheric corrections [12,62,63,64]. This study evaluated the performances of band ratio algorithms under various AC algorithms, including R_rs (443)/R_rs (560), R_rs (490)/R_rs (560), R_rs (665)/R_rs (490), and R_rs (665)/R_rs (560). The DSF and BP algorithms demonstrated significant underestimation, while both underestimation and overestimation were observed for the C2RCC and GRS algorithms (Figure 4). In contrast, scatter plots depicting band ratios for the POLYMER and MUMM algorithms closely approximated the 1:1 line, with the POLYMER algorithm exhibiting a more concentrated distribution of data points (Figure 4).

Compared to other band ratios, all six AC algorithms demonstrated relatively high R² values in the R_rs (490)/R_rs (560) ratio (Figure 4 and

Table 5. Band ratio errors between in situ R_rs and MSI R_rs were obtained for the six AC algorithms (bold means the best statistical value).

Algorithm	Ratio	R2	RMSE	MAPE (%)	Algorithm	Ratio	R2	RMSE	MAPE (%)
DSF	443/560	0.01	0.342	40.8	MUMM	443/560	0.01	0.132	20.5
	490/560	0.21	0.174	15.0		490/560	0.44	0.098	9.4
	665/490	0.11	0.094	31.4		665/490	0.02	0.088	26.5
	665/560	0.03	0.081	35.4		665/560	0.05	0.076	32.4
C2RCC	443/560	0.32	0.219	35.9	BP	443/560	0.31	0.256	37.1
	490/560	0.33	0.217	26.8		490/560	0.65	0.222	25.4
	665/490	0.02	0.061	18.3		665/490	0.08	0.107	33.9
	665/560	0.12	0.056	25.5		665/560	0.07	0.087	35.7
POLYMER	443/560	0.46	0.093	14.4	GRS	443/560	0.28	0.266	43.4
	490/560	0.71	0.080	9.0		490/560	0.02	0.144	16.9
	665/490	0.08	0.052	17.0		665/490	0.01	0.097	29.6
	665/560	0.05	0.049	22.2		665/560	0.10	0.101	45.3

), commonly used for water quality parameter inversion in clean lake waters like those in Bosten Lake and Ulungur Lake. Among them, POLYMER exhibited the highest accuracy (R² = 0.71, RMSE = 0.080, and MAPE = 9.0%). Among these six AC algorithms, POLYMER had the smallest RMSE and MAPE across all band ratios (Table 5). POLYMER performed the best in band ratio comparisons, surpassing other algorithms, while the GRS algorithm exhibited the poorest performance.

3.2.3. Ranking

According to the proposed ranking algorithm, POLYMER obtained the highest score of 1.61, demonstrating the best atmospheric correction ability in Xinjiang lakes. MUMM and C2RCC scored above 1, indicating relatively good overall performance. BP obtained the lowest score of 0.62, indicating poor performance (Figure 5). In general, POLYMER performed the best overall when considering both single bands and band ratios. However, it should be noted that while MUMM aligned closely with the 1:1 line in single-band evaluations, POLYMER exhibited the best performance in band ratios.

3.3. Capability of Sunglint Correction

3.3.1. Sunglint Image Statistics

This study conducted a statistical analysis of the solar zenith angles, sensor zenith angles, and relative azimuth angles observed in Bosten Lake and Ulungur Lake in 2022. The statistical results indicated that the solar zenith angle varied significantly between months, typically reaching its minimum from April to August. The sensor zenith angle of the MSI was relatively small, ranging from 0 to 12°. The relative azimuth angles between the sun and the sensor varied considerably but tended to be smallest from June to August. The ${\theta }_m$ first decreased, reached its minimum from April to August, and then increased throughout the year (Figure 6 and Figure 7).

In addition to observation geometry, wind is an important factor influencing the formation of sunglint. Wind causes fluctuations on the water surface, altering its roughness and creating various geometric patterns, which in turn affect the propagation direction of sunlight. In this study, daily wind data for 2022 were obtained from the fifth-generation European Centre for Medium-Range Weather Forecasts (ECMWFs)-based reanalysis of the global climate (ERA5, https://cds.climate.copernicus.eu/). The results show that wind speed at Bosten Lake is mainly concentrated in the range of 1–4 m/s. During the summer, southeasterly winds prevail, while in winter, northeasterly winds dominate (Figure 6e). Ulungur Lake is primarily affected by northwesterly winds in winter and southeasterly winds in summer, with significantly higher wind speeds in summer compared to winter (Figure 7e).

This study also tallied the number of images affected by sunglint for the two lakes. The statistical results indicated that after excluding suboptimal observations (i.e., cloud, ice, etc.), MSI image statistics from 2015 to 2022 showed that both lakes were affected by sunglint. Out of 307 images of Bosten Lake, 57 were affected by sunglint; out of 265 images of Ulungur Lake, 63 were affected by sunglint. The occurrences of sunglint were predominantly concentrated between April and August (Figure 6f and Figure 7f).

3.3.2. Performance of Sunglint Correction

The optical properties of aquatic organisms in adjacent areas were expected to be similar and exhibit the same spectral curves. Based on this hypothesis, we analyzed the spectral curves of adjacent-sunglint (white areas in the true color images) and no-sunglint areas (Figure 8). The results indicated that DSF and GRS exhibited significantly higher R_rs values for all bands in the sunglint area compared to the no-sunglint area (Figure 8b,g,i,n). Conversely, the C2RCC, MUMM, and BP algorithms had higher R_rs values in the no-sunglint areas compared to the sunglint areas. This inconsistency with the expected high reflectance in the sunglint areas indicates excessive correction in these regions (Figure 8c,e,f,j,l,m). The spectral curves of adjacent-sunglint and no-sunglint areas in the POLYMER algorithm were more consistent, demonstrating the most robust corrective performance in sunglint areas (Figure 8d,k).

The images of TOA reflectance and atmospherically corrected R_rs at 490 nm for Bosten Lake and Ulungur Lake, processed by different algorithms, were compared (Figure 9). The white areas of TOA reflectance indicate waters affected by sunglint (Figure 9a,h). For the C2RCC, MUMM, and BP algorithms, the failure to identify sunglint has led to the overcorrection of aerosol, resulting in higher R_rs in the no-sunglint areas (Figure 9). After applying the GRS correction, no significant changes were observed in the sunglint regions. The DSF algorithm exhibited insufficient sunglint correction, resulting in significantly higher R_rs values in the sunglint areas after correction compared to the no-sunglint areas. In contrast, the POLYMER algorithm showed consistent R_rs values between the sunglint and no-sunglint areas, indicating excellent sunglint correction ability.

To enhance the assessment of atmospheric and sunglint correction performance, this study categorized the sample points into two groups based on visual interpretation: areas affected by sunglint and areas not affected by sunglint. We evaluated the correction performance of each algorithm separately for each area. Within the sunglint-affected area, the AC algorithms demonstrated higher correction accuracy in the first three bands (443, 490, and 560 nm) compared to the last two bands (665 and 705 nm), with the lowest accuracy at 705 nm. In single band comparisons, the POLYMER algorithm consistently showed the highest R², while the MUMM algorithm had the lowest RMSE and MAPE. DSF and C2RCC exhibited similar performances, whereas the BP algorithm had the poorest correction performance (Table S2). After band ratios, the POLYMER algorithm showed the highest accuracy with lower RMSE and MAPE and higher R², whereas the BP algorithm had the worst performance (Table S3). In areas without sunglint, the various algorithms demonstrated different correction accuracies compared to the sunglint-affected areas, with the BP algorithm significantly improving and achieving the highest R² at 705 nm (Table S4). In single-band comparisons, the MUMM algorithm had higher R² and lower RMSE, while the POLYMER algorithm had lower MAPE (Table S4). BP, DSF, and C2RCC had similar correction performances. After band ratios, the POLYMER algorithm showed the highest correction performance (Table S5).

4. Discussion

4.1. Applicability of Atmospheric Correction Algorithms

Achieving high-precision R_rs for inland waters is a significant challenge due to the combined effects of complex atmospheric and aerosol optical properties, as well as sunglint [12]. We evaluated the suitability of six AC algorithms for lakes in Xinjiang Province, China. The essence of atmospheric correction lies in the removal of aerosol scattering using various assumptions or specific parameters. However, compared to in situ measured R_rs, certain methods exhibited suboptimal accuracy due to erroneous assumptions or incorrect parameterization.

The GRS algorithm is a sunglint correction algorithm specifically developed for MSI images affected by sunglint. Although it demonstrated high precision in other regions, its correction accuracy was low in this study due to the influence of aerosols [22,23]. The BP algorithm assumes that the NIR or SWIR reflectance of water bodies is zero. While the BP algorithm performs well under optimal observation conditions [65], it encounters calibration failures under non-ideal conditions, such as sunglint [29]. In regions like Xinjiang’s lakes, where sunglint has a significant impact, the “dark pixel” assumption no longer holds. This leads to the overestimation of aerosol signals, thereby reducing accuracy.

The core of the MUMM algorithm is the accuracy of the MUMM_alpha coefficient, which directly determines the precision of the MUMM algorithm’s results [48]. In this study, the MUMM algorithm demonstrated high precision in single-band comparisons but lower accuracy in band ratios. This was attributed to underestimation at the 443 nm and 490 nm bands and overestimation at the 560 nm band by the MUMM algorithm. These errors became evident after calculating band ratios, revealing the discrepancies.

The DSF algorithm operates on the assumption of land–water dark pixel selection. It also dynamically selects a specific spectral band for a given pixel, thus replacing the global aerosol model with a regional aerosol model. The aerosol model employed in the DSF algorithm primarily relies on the non-absorbing and weakly absorbing aerosol models of the Second Simulation of Satellite Signal in the Solar Spectrum (6S) [15]. However, this model exhibits limitations in terms of Rayleigh scattering and single or multiple scattering corrections [17]. Additionally, the DSF algorithm uses the SWIR band to estimate sunglint and extrapolate it to other spectral bands. Although it can reduce the impact of sunglint to some extent, it does not completely eliminate it.

While the C2RCC algorithm has demonstrated commendable calibration accuracy in other research domains [19], its performance in our specific study area was suboptimal. This algorithm relies on a neural network trained with a substantial database primarily derived from European oceanic waters, which does not encompass a global scope [66]. The training data significantly influenced the correction results [18,67]. The effects of sunglint exacerbate the deficiencies of the training model, leading to unsatisfactory calibration accuracy in Xinjiang lakes.

The POLYMER algorithm for reflectance retrieval, which is iteratively solved through spectral matching optimization, demonstrates superior accuracy. The algorithm uses a per-pixel spectral matching approach based on a simple polynomial reflectance model. The parameters of these models are continuously adjusted during the iteration process to fit the measurement data [27], allowing the POLYMER to mitigate sunglint effects and improve data usability. It is worth noting that the algorithm exhibits a systematic low bias in single-band comparisons, but this effect is effectively removed through band ratios, leading to higher accuracy. With the advancement of computer technology, machine learning methods are increasingly used to retrieve inland water quality parameters. These data-driven algorithms can implicitly correct systematic biases in atmospheric correction to some extent [68]. Therefore, the POLYMER algorithm represents an ideal correction algorithm for MSI data susceptible to sunglint effects.

4.2. Implications for MSI Sunglint Correction

The MSI sensor onboard the Sentinel-2 satellite acquires ground information from a fixed observation angle, unlike sensors such as SeaWiFS, OCTS, and CZCS, which can tilt up to 20° to reduce the impact of sunglint [29,69,70]. This study analyzed the effects of sunglint on 12 lakes with different optical properties across various regions of China (Figure 10 and Figure 11). Following Spyrakos et al. [57], the results showed that clean lakes and turbid lakes were affected differently by sunglint (Figure 11). Clean lakes, such as Bosten Lake, Ulungur Lake, Qinghai Lake, Namtso Lake, Fuxian Lake, Daxi Reservoir, and Songhua Lake, experienced significant impacts from sunglint. In contrast, turbid lakes, such as Dianchi Lake, Chaohu Lake, Taihu Lake, Chagan Lake, and Hulun Lake, were less affected (Figure 11). Numerically, excluding suboptimal observations (i.e., cloud, ice, etc.), 27% of the images for the seven clean lakes were affected by sunglint, being as high as 41% between April and August. In contrast, only 5% of the images for the five turbid lakes were affected by sunglint. In clean waters, the water-leaving reflectance is lower, resulting in a higher proportion of sunglint signals and a more significant impact. In contrast, for turbid waters, the presence of a substantial amount of Chla, SPM, and other substances in the water leads to a marked increase in the water-leaving reflectance, resulting in a lower proportion of sunglint signals and a less noticeable impact [71].

Given the significant impact of sunglint on high-resolution satellite imagery, it is essential to minimize these influences to enhance data utility. The Cox and Munk model, developed through statistical methods, has demonstrated suitable identification and prediction results [25,28]. Originally intended for moderate spatial resolution, the Cox and Munk model faces challenges when applied to high-spatial-resolution imagery due to scale effects in optical remote sensing [72]. This limitation arises from the fact that while wind-generated ocean waves are discernible in high-resolution optical imagery, they remain invisible in coarse spatial resolution optical imagery [73]. For high-resolution satellite imagery, Hedley et al. [26] established a linear relationship between the NIR band and other bands by selecting designated regions of interest (ROIs), enabling sunglint correction. Additionally, this study employs POLYMER and GRS algorithms. The GRS algorithm utilizes SWIR band information to estimate the impact of sunglint, which is subsequently extrapolated to NIR and visible spectral bands for sunglint correction due to the high variability in sunglint and its coupling with aerosols and Rayleigh scattering. Another consideration is the complexity of aerosol properties in the Xinjiang region, where the GRS correction failed. The POLYMER algorithm can accurately remove sunglint primarily due to its distinctive spectral optimization method. This algorithm uses a polynomial model to represent the spectral reflectance of atmospheric scattering and sunglint. Unlike traditional algorithms that only use the NIR band, POLYMER utilizes the entire spectral range from blue to NIR bands, providing broader spectral information to accurately estimate and correct for atmospheric and sunglint effects. By iteratively optimizing the parameters of the atmospheric and ocean water reflectance models, the algorithm can best fit the observed data. Additionally, POLYMER employs a polynomial fitting method to integrally model the residual sunglint, aerosol scattering, and coupling terms, thereby simplifying calculations and enhancing correction accuracy. Therefore, the POLYMER algorithm achieved the highest correction accuracy and most effective sunglint removal [27].

5. Conclusions

The satellite sensor receives over 90% of the total radiation from atmospheric scattering and sunglint reflection, while the water-leaving signal constitutes less than 10%. Therefore, atmospheric correction is crucial in water color remote sensing. In this study, we assessed six AC algorithms for MSI imagery in Xinjiang lakes. The algorithms assessed were DSF, C2RCC, POLYMER, MUMM, BP, and GRS. According to the overall performance ranking scheme, POLYMER achieved the highest score of 1.61, demonstrating superior accuracy compared to the other AC algorithms. Both the MUMM and POLYMER algorithms demonstrated high accuracy in single bands. POLYMER exhibited the highest accuracy in band ratios. Notably, the POLYMER algorithm can correct for sunglint effects and effectively enhance data utility for MSI data in clean lakes. This study assessed the ability of different AC algorithms to correct sunglint and helped to improve the monitoring capabilities of MSI data in inland waters, especially enhancing its application potential in clear waters.