Performance Assessment of Landsat-9 Atmospheric Correction Methods in Global Aquatic Systems

Abstract

The latest satellite in the Landsat series, Landsat-9, was successfully launched on 27 September 2021, equipped with the Operational Land Imager-2 (OLI-2) sensor, continuing the legacy of OLI/Landsat-8. To evaluate the uncertainties in water surface reflectance derived from OLI-2, this study conducts a comprehensive performance assessment of six atmospheric correction (AC) methods—DSF, C2RCC, iCOR, L2gen (NIR-SWIR1), L2gen (NIR-SWIR2), and Polymer—using in-situ measurements from 14 global sites, including 13 AERONET-OC stations and 1 MOBY station, collected between 2021 and 2023. Error analysis shows that L2gen (NIR-SWIR1) (RMSE ≤ 0.0017 sr⁻¹, SA = 6.33°) and L2gen (NIR-SWIR2) (RMSE ≤ 0.0019 sr⁻¹, SA = 6.38°) provide the best results across four visible bands, demonstrating stable performance across different optical water types (OWTs) ranging from clear to turbid water. Following these are C2RCC (RMSE ≤ 0.0030 sr⁻¹, SA = 5.74°) and Polymer (RMSE ≤ 0.0027 sr⁻¹, SA = 7.76°), with DSF (RMSE ≤ 0.0058 sr⁻¹, SA = 11.33°) and iCOR (RMSE ≤ 0.0051 sr⁻¹, SA = 12.96°) showing the poorest results. By comparing the uncertainty and consistency of Landsat-9 (OLI-2) with Sentinel-2A/B (MSI) and S-NPP/NOAA20 (VIIRS), results show that OLI-2 has similar uncertainties to MSI and VIIRS in the blue, blue-green, and green bands, with RMSE differences within 0.0002 sr⁻¹. In the red band, the OLI-2 uncertainties are lower than those of MSI but higher than those of VIIRS, with an RMSE difference of about 0.0004 sr⁻¹. Overall, OLI-2 data processed using L2gen provide reliable surface reflectance and show high consistency with MSI and VIIRS, making it suitable for integrating multi-satellite observations to enhance global coastal water color monitoring.

1. Introduction

Since the successful launch of Landsat-1 on 23 July 1972 [1], the Landsat program has provided a half-century-long record of Earth observations [2,3], making a significant contribution to the advancement of Earth sciences [4]. Although Landsat series satellites were initially designed for terrestrial observations, they have also been widely used in aquatic ecosystem observations, including inland lakes [5,6,7,8], rivers [9,10,11], and coastal water [12,13,14,15] monitoring. Especially after the launch of Landsat-8 in 2013, its onboard Operational Land Imager (OLI) not only enhanced the signal-to-noise ratio but also increased one spectral band centered at 443 nm to improve the radiometric quality over water [2,16]. Landsat-9, as a continuation of the Landsat program, was successfully launched on 21 September 2021, carrying an Operational Land Imager-2 (OLI-2) with the same spatial resolution (30 m) and swath as OLI. Compared with OLI/Landsat-8, OLI-2/Landsat-9 increases the radiometric resolution from 12-bit to 14-bit and improves the signal-to-noise ratio (SNR) by 7–30% in all bands, implying that the quality of OLI-2/Landsat-9 products in aquatic ecosystems is expected to catch up with or exceed that of OLI [2,17], which makes it full of potential in coastal zone, inland lake, and river applications.

The prerequisite for obtaining high-quality water color products is to obtain accurate remote sensing reflectance ($R_{rs}$) over water, which requires not only a satellite sensor with good performance but also excellent atmospheric correction (AC) methods. The atmospheric contribution occupies most of the signals received by water color satellite sensors at the top of atmosphere (TOA), accounting for up to 90% of the total signal [18]. To obtain accurate water-leaving reflectance information, the atmospheric contribution should be estimated and subtracted from the total TOA signal measured by the sensor. This process is called AC [19], and the AC process is one of the main sources of uncertainties in water color products. Currently, the “black pixel” AC method proposed by Gordon and Wang [20] is primarily utilized for oceanic (Case I) water, which assumes the ocean in the near-infrared (NIR) band is black, namely, the water-leaving reflectance ${\rho }_w$ is zero, due to strong water absorption in the NIR. Although the black pixel AC method performs well in Case I waters and has been used by the National Aeronautics and Space Administration (NASA) as an official AC method [21], it fails in coastal (Case II) waters with strong particulate scattering, where the non-negligible ${\rho }_w$ of the NIR band invalidates the black pixel assumption.

Fortunately, numerous AC methods have been developed and used in Case II water environments such as coastal zones, inland lakes, and rivers. Popular approaches include bio-optical model-based algorithms like Level 2 generator (L2gen) [22], dark spectral fitted algorithms (DSF) [23], and the machine learning-based AC algorithms Case 2 Regional Coast Color (C2RCC) [24], spectral matching algorithms like the Polynomial-based algorithms (Polymer) [25], image-based algorithms like cloud shadow algorithms [26] and image correction for atmospheric effects (iCOR) [27], etc. In addition, two commonly used generalized algorithms, ARCSI [28] and LaSRC [29], designed for landscape, have also been used in a few coastal monitoring cases.

The performance of different AC methods has been evaluated by researchers in various regions. For example, Pahlevan et al. (2017) [30] evaluated three band combinations of L2gen applied to Landsat-8, NIR–SWIR1, NIR–SWIR2, and SWIR1–SWIR2, using in-situ measurements from the Aerosol Robotic Network-Ocean Color (AERONET-OC) (for Landsat-8/9, the NIR, SWIR1, and SWIR2 bands correspond to wavelengths of 865 nm, 1609 nm, and 2201 nm, respectively). The evaluation showed that the NIR–SWIR1 combination had the lowest uncertainty, followed by the NIR–SWIR2 combination, with both having RMSE ≤ 0.0010 sr⁻¹. The SWIR1–SWIR2 combination had the highest uncertainty, with RMSE ≤ 0.0032 sr⁻¹. Wei et al. (2018) [31] analyzed the performance of DSF, L2gen (NIR–SWIR1), and cloud shadow approaches using Landsat-8 data in coral reef and coastal turbid waters. They found that L2gen (NIR–SWIR1) and the cloud shadow approaches produced highly consistent results with the in-situ measurements in shallow coral reefs and optically deep waters. Pahlevan et al. (2018, 2019) [32,33] used OLI/Landsat-8 data processed by L2gen, together with AERONET-OC in-situ measurements, to evaluate the uncertainty of ETM+/Landsat-7 and TM/Landsat-5, and made adjustments to their calibration gains. Ilori et al. (2019) [32] evaluated the performance of four AC methods (ARCSI, LaSRC, DSF, and L2gen (NIR–SWIR1)) for Landsat-8 data using in-situ measurements provided by AERONET-OC in coastal waters. Their findings confirm that the two general AC methods, ARCSI and LaSRC, perform significantly worse in coastal environments compared to the two AC methods (DSF and L2gen (NIR–SWIR1)) specifically designed for water, and the L2gen produces $R_{rs}$ products with the lowest uncertainty. Additionally, Yan et al. (2023) [34] conducted a global assessment of five AC methods (DSF, C2RCC, iCOR, L2gen (NIR–SWIR1), and Polymer) applicable to Landsat-8 data using in-situ measurements from AERONET-OC, Marine Optical Buoy (MOBY), and SeaWiFS Bio-optical Archive and Storage System (SeaBASS). They assessed the performance of these AC methods by classifying optical water types (OWTs) based on spectral similarity. Their results indicate that L2gen (NIR–SWIR1) has the highest accuracy, with $R^2\ge 0.74$ and RMSE ≤ 0.0018 sr⁻¹, across four visible bands, and it produces the most accurate $R_{rs}$ in five different OWTs, ranging from clear to turbid water. Van et al. (2023) [35] proposed a machine learning atmospheric correction method, AC-Net, which can be applied to tropical inland water bodies, achieving an RMSE of 0.0039 sr⁻¹ and a SA of 19.5°. Kabir et al. (2023) [2] conducted a comparative analysis of the top-of-atmosphere reflectance (${\rho }_t$) from OLI/Landsat-8 and OLI-2/Landsat-9, as well as ${\rho }_w$ processed using L2gen. The results show that the ${\rho }_t$ difference between the two sensors is within 0.8% in the visible-near-infrared bands and around 2% in the SWIR1 and SWIR2 bands. In the visible range, the median difference in ${\rho }_w$ is between 1.5% and 2.5%, indicating high consistency between OLI-2/Landsat-9 and OLI/Landsat-8 in aquatic ecosystem monitoring. Based on previous studies, it can be concluded that there is still a lack of assessing uncertainties in various AC methods for Landsat-9 data in global water types, which can provide recommendations for the suitability of different AC methods and help improve AC methods, reducing unnecessary errors and ensuring the quality of OLI-2/Landsat-9 data in coastal and inland water research and applications [2].

Considering the long revisit period of one single high-spatial-resolution satellite (approximately 16 days for the Landsat series) [36] and the significant limited amount of effective data due to clouds and haze [37], the joint use of multiple on-orbit spaceborne sensors becomes crucial in dynamic coastal areas, which not only improves the temporal resolution but also improves the spatial coverage of the valid data pixels. Li et al. (2020) [38] demonstrated that after the deployment of OLI-2/Landsat-9, combined with OLI/Landsat-8 and MultiSpectral Instrument (MSI)/Sentinel-2A/B, the revisit period can be reduced to 2.3 days, greatly enhancing the continuity of coastal water quality monitoring. This places high demands on the consistency between Sentinel-2A/B and Landsat-8/9. In fact, many efforts have been made to ensure consistency between the Landsat and Sentinel series, such as the similar design of the MSI and OLI sensors. However, differences in satellite orbits, illumination conditions, and sensor viewing angles pose challenges to this consistency. Studies [39,40] have focused on evaluating the consistency between Landsat and Sentinel data. For example, Trevisiol et al. (2024) [40] proposed harmonization coefficients for the European continent, which were used to align Landsat-9 with Landsat-8/Sentinel-2 and cross-validate the consistency of surface reflectance and four derived vegetation indices. The results showed a very high similarity between Landsat-9 and Landsat-8, as well as good interoperability between Landsat-9 and Sentinel-2. However, there is currently a lack of research assessing the differences in suitability between Landsat-9 and other commonly used medium-to-high spatial resolution satellite remote sensing sensors for coastal water quality inversion, such as MSI/Sentinel-2A/B, Visible Infrared Imaging Radiometer Suite (VIIRS)/S-NPP, and NOAA-20, in coastal water environments [41,42,43].

Therefore, to assess the uncertainty of Landsat-9 in global coastal and inland waters, determine the optimal AC method for Landsat-9, and evaluate the consistency differences between Landsat-9 and operational satellites such as Sentinel-2A/B, S-NPP, and NOAA-20, this study utilized global in-situ datasets from AERONET-OC and MOBY to evaluate the six most widely validated and proven effective AC methods (DSF, C2RCC, iCOR, L2gen (NIR-SWIR1), L2gen (NIR-SWIR2), and Polymer) for OLI-2/Landsat-9 data in ocean color remote sensing. The in-situ measurements were also categorized into different OWTs based on measured $R_{rs}$ to explore the performance of AC methods in various optical water environments. Additionally, the study compared the consistency and uncertainty differences between OLI-2/Landsat-9 and two on-orbit spaceborne sensors of MSI/Sentinel-2A/B and VIIRS/S-NPP/NOAA-20, providing insights into the uncertainty levels of Landsat-9 data, and its assessment of consistency differences among Landsat-9, Sentinel-2, S-NPP, and NOAA-20 can facilitate data integration and enhance interoperability.

2. Materials and Methods

2.1. Satellite Data

Satellite remote sensing data acquired by the OLI-2 sensor aboard Landsat-9, MSI sensors on Sentinel-2A and Sentinel-2B, and VIIRS sensors on S-NPP and NOAA-20 were utilized in this study.

Landsat-9, as the ninth satellite in the NASA and United States Geological Survey (USGS) joint Landsat satellite remote sensing program, was successfully launched on 27 September 2021. It has a revisit period of 16 days, and carries the OLI-2 sensor, which is an improved version of OLI onboard Landsat-8. The OLI-2 has similar spectral bands and spatial resolution as OLI (see

Table 1. Comparison of similar bands for the OLI-2, MSI, and VIIRS, with SR denoting spatial resolution in meters.

OLI-2	Wavelength (μm)	SR (m)	MSI	Wavelength (μm)	SR (m)	VIIRS	Wavelength (μm)	SR (m)
B1	0.430–0.450	30	B1	0.433–0.453	60	M2	0.436–0.454	750
B2	0.450–0.510	30	B2	0.458–0.523	10	M3	0.478–0.498	750
B3	0.533–0.590	30	B3	0.543–0.578	10	M4	0.545–0.565	750
B4	0.636–0.673	30	B4	0.650–0.680	10	M5	0.662–0.682	750

), and the radiometric resolution of OLI-2 (14-bit) is higher than OLI (12-bit), which further enhances the application potential of OLI-2 in coastal water bodies [3]. In this study, a total of 102 scenes of Landsat-9 Level 1 data from 2021 to 2023 were downloaded from the USGS website (https://earthexplorer.usgs.gov/ (accessed on 15 June 2024)). The OLI-2/Landsat-9 data used in this study are official reprocessed products with adjustments to reduce calibration differences with OLI (https://www.usgs.gov/landsat-missions/landsat-mission-headlines (accessed on 15 June 2024)).

Sentinel-2A and Sentinel-2B are two satellites launched by the European Space Agency (ESA) under the Copernicus program in 2015 and 2017, respectively [44]. Both are equipped with the MSI sensor, which has a 12-bit radiometric resolution and 13 spectral bands with ground resolutions of 10 m, 20 m, and 60 m. In this study, the MSI data with four visible bands similar to those of OLI-2 were used and analyzed, and the spectral ranges and ground resolutions are shown in Table 1. All top-of-atmosphere radiance data from the four MSI bands were resampled to a ground resolution of 60 m. Warren et al. (2019) [45] analyzed the MSI data processed using 6 AC methods, including DSF, C2RCC, iCOR, L2gen, Polymer, and Sen2Cor in European nearshore waters, and concluded that Polymer is the most effective one. A similar conclusion was also reached by SòRIA et al. (2022) [46]. Thus, Polymer was chosen in the atmospheric correction process of Sentinel-2 data in this study.

S-NPP was launched jointly by NOAA and NASA in 2011, while NOAA-20 was launched by NOAA in 2017, and both are equipped with the VIIRS sensor. The VIIRS sensor has a 12-bit radiometric resolution and 22 spectral bands, including one panchromatic diurnal band, 16 bands with a spatial resolution of 750 m, and six bands at a resolution of 375 m. This study selected four visible bands of VIIRS that closely match OLI-2 for comparative analysis, and the details are provided in Table 1. The VIIRS Level 2 data used in this study were downloaded from website (https://oceancolor.gsfc.nasa.gov (accessed on 20 June 2024)). The data were atmospherically corrected using the L2gen method, which has been widely evaluated and proven to be accurate and reliable [47,48].

2.2. In-Situ Data

In-situ measurements from AERONET-OC and MOBY were used in this study. The AERONET program, established by NASA and PHOTONS (PHOtométrie pour le Traitement Opérationnel de Normalisation Satellitaire; Univ. of Lille 1, CNES, and CNRS-INSU), has been operational for over 25 years. It is a global aerosol monitoring network supported by national agencies, institutes, universities, individual scientists, and partners. The program provides standardized, publicly accessible field data for research, satellite validation, and other applications. AERONET-OC, a component of the AERONET program, measures water-leaving reflectance using sun photometers installed on offshore platforms [49,50]. The reliability and accuracy of AERONET-OC data have been well validated, and the data have been widely used in assessing the uncertainties of spaceborne remote sensing data [34,51,52].

MOBY is a mooring system operated by NOAA near the coast of Lanai Island, Hawaii. It has operated since 1997 and provides a continuous time series of normalized water-leaving reflectance (${\rho }_{wn}$). MOBY has been used to calibrate multiple satellite sensors, including Sea-viewing Wide Field of View Sensor (SeaWiFS), MODIS, Medium Resolution Imaging Spectrometer (MERIS), VIIRS, and Ocean and Land Colour Instrument (OLCI) [53,54,55].

In-situ data from a total of 14 stations from AERONET-OC and MOBY spanning from 2021 to 2023 were used in this study. The locations of the stations are shown in Figure 1, and detailed information is presented in

Table 2. The latitude and longitude information and the Principal Investigators (PIs) for 14 stations used in this study, as well as the number of matchup data points (N).

No.	Station Name	Latitude	Longitude	PI	N
1	ARIAKE_TOWER	33.104N	130.272E	Joji Ishizaka/Kohei Arai	5
2	Bahia Blanca	39.148S	61.722W	Hubert Loisel/Paula Pratolongo/Robert Frouin	4
3	Chesapeake Bay	39.124N	76.349W	Dirk Aurin	19
4	Galata Platform	43.045N	28.193E	Frederic Melin	5
5	Gustav Dalen Tower	58.594N	17.467E	Frederic Melin	7
6	Kemigawa Offshore	35.611N	140.023E	Hiroto Higa	6
7	Lake Erie	41.826N	83.194W	Tim Moore/Steve Ruberg/Menghua Wang	2
8	MOBY	20.4613N	157.1101W	NOAA/SJSU	3
9	Palgrunden	58.755N	13.152E	Susanne Kratzer	2
10	San Marco Platform	2.942S	40.215E	Barbara Bulgarelli	1
11	Section-7 Platform	44.546N	29.447E	Barbara Bulgarelli	10
12	South Greenbay	44.596N	87.951W	Nima Pahlevan	3
13	USC SEAPRISM	33.564N	118.118W	Burton Jones/Matthew Ragan	12
14	Venise	45.314N	12.508E	Barbara Bulgarelli	13

. For the AERONET-OC data categorized into three quality levels, the highest quality Level 2.0 data were used in this study. For MOBY data classified into four levels, the “Good” quality data were chosen. Following Pahlevan et al. (2021) [51], the ${\rho }_{wn}$ provided by AERONET-OC and MOBY was divided by the top-of-atmosphere solar irradiance ($F_o$) [56] to obtain the $R_{rs}$ as shown in Equation (1), where $\lambda$ denotes the wavelength:

$$R_{rs}(\lambda )=\frac{{\rho }_{wn}\left(\lambda \right)}{F_o\left(\lambda \right)}$$

(1)

2.3. Atmospheric Correction Methods

The top-of-atmosphere reflectance (${\rho }_t$) received by spaceborne ocean color sensors at the top of the atmosphere primarily consists of contributions from Rayleigh scattering by atmospheric molecules (${\rho }_r$), aerosol scattering (${\rho }_a$), and water-leaving reflectance (${\rho }_w$) [20,57] as shown in the following equation:

$${\rho }_t={\rho }_r+{\rho }_a+t{\rho }_w$$

(2)

where t is the atmospheric diffuse transmittance. The atmospheric correction process involves removing the atmospheric contributions from the total top-of-atmosphere reflectance received by the sensor, thereby isolating the ${\rho }_w$. Dividing ${\rho }_w$ by $\pi$ gives the $R_{rs}$. During the atmospheric correction procedure, the contribution of Rayleigh scattering can be estimated accurately [19]. However, the diverse composition of atmospheric aerosols makes it challenging to accurately estimate aerosol contributions, which could account for up to 90% of the total reflectance over water [18].

Various AC methods estimating aerosol contributions over water bodies have been developed. The commonly used methods of DSF, C2RCC, iCOR, L2gen, and Polymer applicable for Landsat-9 data were analyzed in this study. A brief introduction to these atmospheric correction methods is provided in

Table 3. Brief description of atmospheric correction methods used in this study.

	DSF	C2RCC	iCOR	L2gen	Polymer
Platform	Acolite 2023.10.23	SNAP 9.0.0	VITO 3.0	SeaDAS 8.3.0	Polymer v4.17beta2
Rayleigh correction method	LUT built using 6SV	Machine learning method	LUT built using MODTRAN 5 [58]	LUT built using Ahmad and Fraser (1982) [59]	LUT built using SOS
Aerosol model	Continental/ Maritime aerosols	Aerosols based on AERONET-OC data	MODTRAN rural models	Aerosols based on AERONET-OC data	NA
Aerosol correction method	Dark spectrum fitting [60,61]	Machine learning [24]	Dark target and AOT multi-parameter inversion [27]	Iterative bio-optical estimation model with band ratios of NIR/SWIR [30,62]	Spectral matching [25,63]

.

These atmospheric correction methods can be classified into two categories: two-step and one-step methods. The two-step methods include DSF, iCOR, L2gen, and Polymer, where Rayleigh scattering and gas absorption are removed first, followed by the aerosol contributions. The one-step method is C2RCC, which is based on a machine learning approach that takes the top-of-atmosphere reflectance as input and performs atmospheric correction through a pre-trained neural network, directly outputting $R_{rs}$ [51]. Among these methods, iCOR and Polymer outputs ${\rho }_w$, which is then divided by $\pi$ to obtain $R_{rs}$, while the other methods directly output $R_{rs}$.

In terms of aerosol correction methods, the DSF method automatically selects the lowest spectral reflectance within one scene to determine the atmospheric path reflectance by assuming that the atmosphere is homogeneous and that black pixels definitely exist [30,62]. C2RCC uses a neural network that has been well trained with a dataset of surface water reflectance and top-of-atmosphere radiance obtained through radiative transfer simulations [24]. The iCOR algorithm commonly utilizes land pixels to perform the dark target method and multi-parameter inversion of aerosol optical thickness, employing the MODTRAN radiative transfer model for atmospheric modeling to correct for atmospheric scattering and absorption in satellite imagery [27]. In the L2gen method, an iterative method based on a bio-optical model, is used to estimate aerosol reflectance in the NIR or SWIR bands, which is then further extrapolated to the visible spectrum by selecting the appropriate aerosol models from pre-defined aerosol look-up tables [57,63]. Polymer is a spectral matching algorithm based on two models: one is a polynomial model that simulates atmospheric contributions and sun glint, and the other is a water-leaving reflectance model that simulates water reflectance through chlorophyll-a concentration and backscattering coefficients. According to the spectral similarity proposed by Ruddick et al. (2006) [64], the model is extended to the NIR bands to ensure its applicability in turbid waters. Through iterative adjustments of the parameters in both models, Polymer ensures optimal spectral fitting [25,65].

Additionally, L2gen combines an iterative bio-optical model with the NIR/SWIR atmospheric correction method, which requires the reflectance ratio between two NIR or SWIR bands to retrieve aerosol contributions. It has been demonstrated that combinations of the NIR–SWIR1 or NIR–SWIR2 bands work effectively for Landsat-8 data [30]. Since both Landsat-9 and Landsat-8 have similar spectral band configurations, these two different band combinations were also respectively used with L2gen to verify their performance for Landsat-9 data in this study, and they are referred to as L2gen (NIR–SWIR1) and L2gen (NIR–SWIR2) hereafter.

2.4. Procedure for Comparing Satellite and In-Situ Measurements

In this study, in-situ measurements were first utilized to evaluate uncertainties in water surface reflectance obtained from OLI-2/Landsat-9 processed by six atmospheric correction methods, including DSF, C2RCC, iCOR, L2gen (NIR–SWIR1), L2gen (NIR–SWIR2), and Polymer. Following this, a comparison of the consistency and uncertainty differences between OLI-2/Landsat-9 and two on-orbit sensors, MSI/Sentinel-2A/B and VIIRS/S-NPP/NOAA-20, was conducted. The flowchart of this study is illustrated in Figure 2.

When matching satellite data with in-situ measurements, the Landsat-9 data pixels flagged by clouds, land, stray light, and sun glint were masked out, and the median of valid data pixels within a $5\times 5$ spatial window and $\pm 3$ h temporal window was used. If the number of valid pixels within the $5\times 5$ window exceeded half (namely greater than 12 in this study), the matchup data were retained; otherwise, they were discarded. The same procedure was also applied to MSI and VIIRS data.

2.5. Evaluation Indicators

To assess the performance of atmospheric correction methods for Landsat-9 data over water bodies, evaluation metrics including Root Mean Square Error (RMSE), Absolute Error (AE), Bias, Relative Percentage Difference (RPD), Correlation Coefficient ($R^2$), and spectral angle (SA) were used. Among these, the SA reflects the consistency of the spectral shape between satellite and in-situ measurements [65], and SA is an indicator commonly used in atmospheric correction for its insensitivity to amplitude variations. It has been widely applied in the evaluation of atmospheric correction methods for satellites such as Landsat-8 (OLI), Sentinel-3 (OLCI), and HY-1C (CZI, Coastal Zone Imager) [34,41,66]. The evaluation indicators are defined as follows:

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^N{(R_{E_i}-R_{M_i})}^2}{N}}}$$

(3)

$$\mathrm{AE}={\displaystyle \frac{1}{N}}\sum _{i=1}^N|R_{E_i}-R_{M_i}|$$

(4)

$$\mathrm{Bias}={\displaystyle \frac{1}{N}}\sum _{i=1}^N(R_{E_i}-R_{M_i})$$

(5)

$$\mathrm{RPD}=100\times {\displaystyle \frac{1}{N}}\sum _{i=1}^N{\displaystyle \frac{|R_{E_i}-R_{M_i}|}{R_{M_i}}}$$

(6)

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^N{(R_{M_i}-R_{E_i})}^2}{{\sum }_{i=1}^N{(R_{M_i}-{\overline{R}}_M)}^2}}$$

(7)

$$\mathrm{SA}={cos}^{-1}\left({\displaystyle \frac{{\sum }_{j=1}^n(R_{E_j}·R_{M_j})}{\sqrt{{\sum }_{j=1}^n{R}_{E_j}^2}\sqrt{{\sum }_{j=1}^n{R}_{M_j}^2}}}\right)$$

(8)

In the above equations, $R_{E_i}$ represents the remote sensing reflectance obtained from satellite data after atmospheric correction, $R_{M_i}$ represents the in-situ measured $R_{rs}$, N is the number of matchup data, i denotes an individual data point, n represents the total number of spectral bands, and j indicates a single band.

3. Results

3.1. Error Statistical Analysis of Different AC Methods

Figure 3 shows the scatter plots comparing the $R_{rs}$ values at 443 nm, 482 nm, 561 nm, and 655 nm bands derived from OLI-2/Landsat-9 data using six AC methods (DSF, C2RCC, iCOR, L2gen (NIR-SWIR1), L2gen (NIR-SWIR2), and Polymer) with in-situ measurements. Figure 4 presents the variations in error metrics ($R^2$, AE, RMSE, and Bias) of the six atmospheric correction methods with wavelength.

Table 4. Statistical numbers of OLI-2 $R_{rs}$ derived using six AC methods (DSF, C2RCC, iCOR, L2gen (NIR-SWIR1), L2gen (NIR-SWIR2)), and Polymer compared to in-situ data in the visible bands. The statistical metrics include the Correlation Coefficient ($R^2$), slope and intercept of the regression line, Root Mean Square Error (RMSE), Absolute Error (AE), Bias, spectral angle (SA), and the number of matchups (N). The values indicating the best performance are highlighted in bold.

AC	Band (nm)	${\mathit{R}}^2$	Slope	Intercept	RMSE (sr−1)	AE (sr−1)	Bias (sr−1)	SA (°)	N
DSF	443 nm	0.57	0.94	0.0054	0.0058	0.0052	0.0052	11.33	77
	482 nm	0.77	1.03	0.0047	0.0053	0.0048	0.0048
	561 nm	0.91	1.04	0.0032	0.0039	0.0034	0.0034
	655 nm	0.91	1.10	0.0024	0.0031	0.0027	0.0027
C2RCC	443 nm	0.40	0.77	0.0016	0.0030	0.0017	0.0008	5.74	93
	482 nm	0.57	0.87	0.0015	0.0029	0.0017	0.0009
	561 nm	0.89	0.97	0.0008	0.0019	0.0012	0.0006
	655 nm	0.94	0.98	0.0004	0.0010	0.0006	0.0004
iCOR	443 nm	0.18	0.59	0.0048	0.0051	0.0037	0.0032	12.96	93
	482 nm	0.39	0.80	0.0042	0.0050	0.0036	0.0033
	561 nm	0.63	1.05	0.0026	0.0051	0.0035	0.0029
	655 nm	0.51	1.16	0.0025	0.0054	0.0033	0.0030
L2gen (NIR−SWIR1)	443 nm	0.84	1.15	0.0001	0.0017	0.0013	0.0007	6.33	82
	482 nm	0.91	1.15	0.0001	0.0016	0.0012	0.0008
	561 nm	0.96	1.11	−0.0003	0.0014	0.0009	0.0004
	655 nm	0.96	1.14	0.0000	0.0012	0.0007	0.0004
L2gen (NIR−SWIR2)	443 nm	0.79	1.14	−0.0001	0.0019	0.0014	0.0004	6.38	82
	482 nm	0.89	1.15	−0.0001	0.0017	0.0012	0.0006
	561 nm	0.96	1.12	−0.0004	0.0015	0.0010	0.0003
	655 nm	0.95	1.14	−0.0001	0.0012	0.0007	0.0003
Polymer	443 nm	0.34	0.49	0.0028	0.0027	0.0021	0.0009	7.76	93
	482 nm	0.49	0.52	0.0029	0.0027	0.0021	0.0007
	561 nm	0.88	0.63	0.0017	0.0024	0.0013	−0.0006
	655 nm	0.92	0.69	0.0003	0.0015	0.0007	−0.0005

lists values of the error metrics for the six AC methods.

It is evident that the number of matchup points between satellite and in-situ measurements varies across the different AC methods. The C2RCC, iCOR, and Polymer have the highest number of matching points of 93, L2gen has 82, and DSF has the fewest of 77. The number of valid matchup data points between field measurements and Landsat-9 data varies with different atmospheric correction methods, which is mainly related to the effectiveness of AC methods and cloud thresholds used by different AC methods [64].

Analyzing results from Figure 3 and Figure 4, and Table 4, it is clear that the L2gen (NIR-SWIR1) and L2gen (NIR-SWIR2) methods perform best with the smallest errors. As shown in Figure 3 and Table 4, for the L2gen (NIR-SWIR1) method, the $R^2$ values range from 0.84 to 0.96, and the RMSE values are between $0.0012$ and $0.0017{\mathrm{sr}}^{-1}$. For the L2gen (NIR-SWIR2) method, the $R^2$ values range from 0.79 to 0.96, and the RMSE values are between $0.0012$ and $0.0019{\mathrm{sr}}^{-1}$. These two methods exhibit similar accuracy and generally have lower errors than the other four methods. Figure 4 further clearly illustrates that the L2gen (NIR-SWIR1) method has relatively higher $R^2$ values and lower RMSE and AE values, indicating slightly better performance than the L2gen (NIR-SWIR2) method. However, it is worth noting that, as shown in Figure 3, both the L2gen (NIR-SWIR1) and L2gen (NIR-SWIR2) methods tend to overestimate $R_{rs}$ values when $R_{rs}>0.01{\mathrm{sr}}^{-1}$, and this overestimation becomes more pronounced as the $R_{rs}$ value increases. Compared to DSF and iCOR, the C2RCC and Polymer methods have relatively smaller errors. The $R^2$ values range from 0.40 to 0.94 for the C2RCC method, and from 0.34 to 0.92 for the Polymer method. The RMSE values are between $0.0015$ and $0.0027{\mathrm{sr}}^{-1}$ for C2RCC, and between $0.0010$ and $0.0030{\mathrm{sr}}^{-1}$ for Polymer. Although the error statistics between these two methods seem similar, C2RCC generally performs slightly better than Polymer as shown in Figure 4. Additionally, Figure 3 shows that Polymer tends to underestimate when $R_{rs}>0.01{\mathrm{sr}}^{-1}$, while the C2RCC method does not show such a significant deviation. Therefore, based on the statistical results of the matchup data in this study, C2RCC generally outperforms Polymer for OLI-2/Landsat-9 data. DSF and iCOR exhibit the highest errors among the atmospheric correction methods, with DSF recording $R^2$ values from 0.57 to 0.91 and RMSE values ranging from $0.0031$ to $0.0058{\mathrm{sr}}^{-1}$. The iCOR results have $R^2$ values between 0.18 and 0.63 and RMSE values from $0.005$ to $0.0054{\mathrm{sr}}^{-1}$. These errors are significantly larger compared to the other four atmospheric correction methods. Additionally, both methods demonstrate notable overestimations across all spectral bands from 443 nm to 655 nm.

In addition, it is shown in Figure 4 that the six AC methods examined in this study perform differently across visible spectral bands for OLI-2/Landsat-9 data. Among them, the performance difference across varying spectral bands is relatively larger for C2RCC, Polymer, and DSF, and smaller for iCOR, L2gen (NIR-SWIR1), and L2gen (NIR-SWIR2). Their statistical errors of RMSE, AE, and Bias increase with the varying wavelength from red to blue, and errors in the blue-green bands (443 nm, 482 nm) are significantly larger than those in the yellow-red ones (561 nm, 655 nm). Similar results were also demonstrated in evaluating Sentinel-2 and Landsat-8 data by Pahlevan et al. (2021) [51]. This could be attributed to errors introduced by misusing an aerosol type different from the actual one when extrapolating aerosol contributions from the NIR/SWIR, to visible spectral bands during the atmospheric correction procedure [67].

Considering that the errors of results processed by the six AC methods vary with wavelength, SA, which can reflect the similarity in spectral shapes between the satellite-derived and in-situ $R_{rs}$, was further calculated and compared in this study. The smaller the SA value, the higher the similarity in the spectral shape of the satellite-derived and in-situ $R_{rs}$.

Figure 5 shows the SA of the results processed by the six AC methods used in this study. Significant differences in SA can be observed among different AC methods. The C2RCC and L2gen exhibit the smallest median SA values, with C2RCC at $5.74°$ and L2gen showing $6.33°$ and $6.38°$ for its two spectral combinations, reflecting a more concentrated SA distribution with a relatively narrow interquartile range. This is followed by Polymer, with median SA values of $7.76°$, then comes DSF with a median SA of $11.33°$. The iCOR has the largest median SA of $12.96°$, with the longest box plot indicating poor stability.

To sum up, among the six AC methods used in this study, the L2gen method using two spectral band combinations of NIR–SWIR1 and NIR–SWIR2 performs better than the others across the four spectral bands for Landsat-9 data. L2gen (NIR-SWIR1) achieves the highest $R^2$, lowest RMSE, AE, and a relatively small SA across all four visible bands. L2gen (NIR–SWIR2) exhibits the smallest Bias. Overall, L2gen (NIR–SWIR1) and L2gen (NIR–SWIR2) demonstrate similar superior performance, with L2gen (NIR–SWIR1) slightly outperforming L2gen (NIR–SWIR2). This is consistent with the findings of Yan et al. (2023) using Landsat-8 data [34].

Following the L2gen methods, the C2RCC and Polymer methods also demonstrate similar performance for Landsat-9 data. Compared to L2gen, C2RCC and Polymer show slightly worse precision in the yellow-red spectral bands (561 nm, 655 nm), while at blue-green wavelengths (443 nm, 482 nm), their performance deteriorates significantly, with noticeably lower $R^2$ values and significantly higher RMSE, AE, and Bias [34,45]. By comparison, C2RCC performs slightly better than Polymer.

Finally, the iCOR and DSF methods demonstrate the poorest performance across all four visible spectral bands for Landsat-9 data, consistently overestimating $R_{rs}$. This aligns with previous evaluation studies for Landsat-8 [34] and Sentinel-2 [68] data.

Figure 6 displays the Landsat-9 482 nm images processed by various AC methods. The two L2gen combinations along with C2RCC and Polymer yield similar images. The results indicate that the DSF method produces higher $R_{rs}$ values, while iCOR shows substantial differences compared to the other methods, aligning with the error analysis presented earlier. Except L2gen and DSF, images processed by the three other methods exhibit striping and spatial non-uniformity on the eastern edge. This striping on the eastern edge is also observed in Landsat-8 imagery [39].

3.2. Performance Variations in AC Methods in Different OWTs

The performance of AC methods usually varies with OWTs [51]. In this section, to evaluate the performance of the six AC methods in different OWTs, the water bodies of matchup data in this study were further classified into four OWTs, including both clear and turbid waters, based on in-situ measured $R_{rs}$ spectra following the optical water classification method of Wei et al. (2016) [69]. The performance of the six AC methods over different OWTs is then demonstrated.

To eliminate the magnitude differences in the original $R_{rs}$ data while preserving their spectral shape characteristics, the in-situ measured $R_{rs}$ spectra were first normalized to obtain $n{R}_{rs}$ according to Equation (9), $n{R}_{rs}$ represents the normalized $R_{rs}$ spectrum, n denotes the total number of wavelengths, and ${\lambda }_i$ represents the individual wavelengths of 443 nm, 482 nm, 561 nm, and 655 nm. Then, an unsupervised clustering method of Kmeans++ was applied to classify the normalized spectra into different OWTs. The in-situ data in this study were categorized into four OWTs (OWT1 to OWT4), corresponding to water types 4, 8, 15, and 17 from the 23 global water types derived by Wei et al. (2016). As shown in Figure 7, it can be seen that the four OWTs in this study cover both clear and turbid waters:

$$n{R}_{rs}=\frac{R_{rs}}{\sqrt{{\sum }_{i=1}^n{R}_{rs}{({\lambda }_i)}^2}}$$

(9)

Figure 8 presents scatter plots comparing in-situ $R_{rs}$ with OLI-2/Landsat-9 data processed by six AC methods over four OWTs. The accuracy of the six AC methods across four OWTs is further ranked in Figure 9 based on RPD values, which are also listed in

Table 5. The Relative Percentage Difference (RPD), median spectral angle (SA), and the number of matches (N) of Landsat-9 data processed by six atmospheric correction methods in four OWTs and wavelengths.

AC Methods	OWTs	443 nm	482 nm	561 nm	655 nm	SA (°)	N
DSF	OWT1	135	89	150	815	8.23	16
	OWT2	203	123	94	483	11.29	20
	OWT3	430	199	90	249	17.26	25
	OWT4	173	92	40	64	10.86	16
C2RCC	OWT1	43	33	43	53	4.33	17
	OWT2	85	56	32	64	8.47	26
	OWT3	91	47	20	44	7.79	26
	OWT4	25	20	12	21	4.55	24
iCOR	OWT1	98	75	167	1494	11.06	16
	OWT2	114	80	88	572	13.37	27
	OWT3	230	103	48	138	15.73	26
	OWT4	242	131	64	121	11.90	24
L2gen (NIR-SWIR1)	OWT1	29	19	35	122	6.44	17
	OWT2	42	23	17	54	6.35	21
	OWT3	80	32	13	39	9.43	26
	OWT4	34	19	12	19	3.70	18
L2gen (NIR-SWIR2)	OWT1	37	23	38	133	6.47	17
	OWT2	42	24	21	78	7.44	21
	OWT3	75	30	13	39	9.47	26
	OWT4	37	21	12	19	3.59	18
Polymer	OWT1	61	39	40	52	4.75	17
	OWT2	80	44	16	34	9.89	26
	OWT3	146	67	16	25	16.43	26
	OWT4	37	31	22	24	5.99	24

. The larger the RPD value, the higher the uncertainty, resulting in a lower ranking. Figure 10 demonstrates the median $R_{rs}$ derived from OLI-2/Landsat-9 processed by six AC methods in four OWTs, and the corresponding median in-situ measurements are also plotted as references. The SA between satellite data and field measurements is also given in Table 5.

For the Polymer method, the matchup data points scatter close to the 1:1 line in OWT1 and OWT2. However, in OWT3 and OWT4, significant underestimations occur when $R_{rs}>0.01{\mathrm{sr}}^{-1}$. On the other hand, the C2RCC method results generally agree well with field data across the four OWTs, except for some outliers in OWT2 in Figure 8. This results in C2RCC performing slightly better than Polymer as shown in Section 3.1 of this study. Notably, Figure 9 and Figure 10, and Table 5 show that C2RCC performs best in turbid waters of OWT4 in the spectral range from 443 nm to 561 nm among the six AC methods. This might be attributed to the large number of turbid water cases included in the C2RCC training dataset [21]. DSF and iCOR show significantly higher uncertainty than the other four AC methods, both across different bands and OWTs. Additionally, DSF is more suited to turbid waters than to clear water bodies, aligning with the previous findings for Sentinel-2 and Sentinel-3 [68,70].

From Figure 8, Figure 9 and Figure 10, and Table 5, L2gen (NIR-SWIR1) and L2gen (NIR-SWIR2) consistently rank in the top two across four spectral bands in OWT1, OWT2, and OWT3. However, in turbid waters of OWT4, a slight overestimation for $R_{rs}$ at 561 nm and 655 nm can be observed in Figure 8 and Figure 10. The L2gen (NIR-SWIR1) slightly outperforms L2gen (NIR-SWIR2) in OWT1, OWT2, and OWT4, while L2gen (NIR-SWIR2) shows a smaller RPD in the moderately turbid water of OWT3. This is consistent with the findings of Pahlevan et al. (2017) [39] that L2gen (NIR-SWIR2) produces more robust $R_{rs}$ in moderately turbid waters.

Overall, compared with the other four AC methods, L2gen performs more stably and consistently across four OWTs and four visible bands for Landsat-9 data, despite a slight overestimation for $R_{rs}$ at 561 nm and 655 nm in OWT4. Both Polymer and C2RCC can be used in clear waters (OWT1, OWT2, and OWT3), but they exhibit more uncertainties compared to L2gen. C2RCC is particularly suited for more turbid waters like OWT4 in this study. Both DSF and iCOR exhibit significant overestimation of $R_{rs}$ and higher uncertainty across all four OWTs compared to the four other AC methods.

From Figure 11, it is evident that Landsat-9 data processed using L2gen (NIR-SWIR1) exhibit high consistency with in-situ measurements across various OWTs, demonstrating Landsat-9’s robust capability to accurately capture spectral characteristics. However, it is also worth noting that relatively higher uncertainty exhibits at the blue band, which should be taken into consideration when interpreting results in this spectral region.

4. Discussion

4.1. Uncertainties of Matchup Analysis

This study evaluates the performance of six commonly used AC methods for OLI-2/Landsat-9 data with in-situ measurements from AERONET-OC and MOBY. In terms of satellite-derived surface reflectance, apart from errors caused by the AC procedure, uncertainties might also be introduced by the spatial and temporal window sizes in the matchup process.

Given the scale of the satellite observations, adopting an $n\times n$ box in the matching experiments helps mitigate potential navigation errors in the satellite data, reduces the impact of small-scale spatial variability, and increases the number of successful matches [71]. However, although spaceborne sensors with extensive coverage can effectively average geophysical variability within a pixel, in-situ stations such as AERONET-OC and MOBY may not fully capture these variations, thereby introducing some uncertainty [64,72]. There is currently no consensus on the optimal selection of box size. Bailey et al. (2006) used SeaWiFS as an example to calculate the minimum sample size required to obtain reliable results, finding that a $7\times 7$ box was reasonable while also noting that a $5\times 5$ box did not significantly affect the results. Considering that a larger box might introduce geophysical variations that could affect the outcomes, a $5\times 5$ box was ultimately recommended.

In addition, instead of using the coefficient of variation (CV) threshold for data validity assessment, this study opted for the median error to mitigate the influence of outliers. Recent research by Barnes et al. (2019) [47], which examined the impact of CV thresholds and other data screening techniques using VIIRS and MODIS, found that these techniques did not substantially enhance validation statistics and could lead to unnecessary data loss. Given the relatively scarce data availability from Landsat-9, which has a 16-day revisit cycle and was launched just over two years prior to the study, the CV threshold was not employed for spatial uniformity testing, and median error was used instead. A time window of $\pm 3$ h, which is commonly recommended in evaluating the ocean color remote sensing data [15,21], was used during the matching process. However, most of the in-situ measurements used in this study come from coastal waters as shown in Figure 1. Previous studies have demonstrated that factors such as rainfall, wind, tides, river plumes, or human activities can lead to rapid changes in the optical properties of coastal waters [73,74,75]. It was also observed that $R_{rs}$ values measured at the AERONET-OC Venise site could vary up to 15% within 3 h [52].

To ensure the quality of the experiment, this study only used quality-controlled AERONET-OC Level 2 data and MOBY “Good” level data, which resulted in a loss of some matched data points. This study strongly recommends expanding the network of stations to increase the amount of in-situ data, ensuring broad geographic coverage and enabling evaluation of sensor performance in complex optical waters, particularly in rapidly changing environments such as estuaries, optically shallow waters, and eutrophic waters. Additionally, increasing the amount of data would also facilitate the use of smaller time windows, thereby reducing uncertainties in the matching process. In addition to increasing the number of in-situ measurements, efforts should be made to enhance data sharing. Existing platforms like AERONET and SeaBASS [55] provide excellent examples, and the recently established WISPstation network has also expanded the range of available data [76]. It is important to note that data formats and quality often differ across platforms, requiring significant time for users to standardize formats and select appropriate data. Therefore, strengthening international collaboration, establishing standardized data collection processes and processing protocols, and unifying data storage formats would greatly benefit the evaluation of uncertainties in both historical and future remote sensing sensor data, and improve retrieval performance.

4.2. Analysis of Error Sources of Different AC Methods

It is shown in this study that the L2gen AC methods with two NIR-SWIR band combinations (NIR-SWIR1 and NIR-SWIR2) achieve the best performance. Since both methods share the same underlying atmospheric correction procedure and use the same 865 nm NIR band combined with different SWIR bands, they produce very similar outcomes. The superior performance of L2gen may be attributed to the following reasons: (1) Besides a strict data pre-filtering excluding pixels potentially affected by clouds or sun glint, the aerosol model used in L2gen is built based on extensive in-situ aerosol optical properties from AERONET, and the in-situ measurements used in this evaluation are primarily from AERONET-OC sites. (2) Using the NIR and SWIR bands of 865 nm, 1609 nm, and 2201 nm with high SNR in atmospheric correction, the band combinations between NIR and SWIR can satisfy the black pixel assumption for most cases in coastal water. As shown in this study, the NIR-SWIR1 combination performs better than the NIR-SWIR2 in OWT1 and OWT2, while the latter produces more robust $R_{rs}$ in moderately turbid water of OWT3, which is consistent with previous studies [39]. However, in highly turbid water of OWT4, the L2gen with both NIR-SWIR band combinations tends to slightly overestimate as the $R_{rs}$ values increase over 0.01 sr⁻¹.

The C2RCC ranks second after the L2gen in performance. It filters out fewer data pixels, resulting in the highest number of matchups. However, it shows higher uncertainties in the 443 nm and 482 nm bands compared to L2gen, while its performance improves in the 561 nm and 655 nm bands. Notably, C2RCC achieves the lowest uncertainty in turbid water (OWT4) but ranks third to fourth in the other three water types (OWT1 to OWT3). This might be due to the fact that the training dataset for C2RCC does not cover all actual atmospheric aerosol types and includes sufficient training for sediment-rich waters but insufficient training for other OWTs, as machine learning methods such as C2RCC strongly depend on the datasets in their training process [21].

Polymer ranks fourth overall among the six AC methods in this study. It also filters out fewer data pixels like C2RCC, resulting in a high number of matchups. Its performance in longer wavelengths is significantly better than in shorter ones. However, unlike C2RCC, Polymer is not suitable for sediment-rich waters, ranking fourth in OWT4, which is consistent with Liu et al.’s (2022) [21] findings. The relatively poorer performance of Polymer may be due to the following reasons: (1) It assumes an Angstrom coefficient of 1.0 for aerosol spectral optical properties, while the actual range is 0.5–1.3 [64], and strong absorbing aerosols near coasts or inland may also lead to biases, particularly in these environments [21]. (2) Its bio-optical water reflectance model, which estimates the water-leaving reflectance based on the chlorophyll-a concentration and backscattering coefficients, is effective in clear waters (OWT1 and OWT2) where phytoplankton dominates. However, in turbid waters, the presence of large amounts of sediments can make the model’s applicability challenging. It has been addressed in work by Wang et al. (2020) [77] that treating the aerosol scattering exponent as a variable instead of a fixed value and using IOP (Inherent Optical Property)-based surface water reflectance models can improve the performance of Polymer in turbid waters.

The DSF ranks poorly due to its reliance on the black pixel assumption, which presumes atmospheric homogeneity and depends on the presence of non-reflective land pixels in the image. This assumption often fails in coastal areas where such pixels are scarce, leading to systematic overestimations of $R_{rs}$ and high SA values, indicating poor spectral fidelity [45]. However, the performance of DSF improves in turbid waters, likely due to the increased presence of reflective sediments and closer proximity to land, which align with its design assumptions. Furthermore, the lack of adjacency correction in DSF may result in the contamination of water pixels by adjacent land, exacerbating errors in processed images [34].

The iCOR algorithm often overestimates reflectance due to its reliance on land pixels for aerosol estimation. In coastal satellite imagery, where these land pixels are frequently sparse, iCOR struggles to accurately utilize them to estimate aerosol optical thickness (AOT), often resorting to default AOT values that do not represent actual atmospheric conditions accurately [45]. The strength of iCOR lies in its unique consideration of adjacency effects, which effectively reduces land pixel contamination in inland water bodies such as rivers and lakes. Moreover, because it does not require an in-depth understanding of radiative transfer or absolute sensor calibration, it is easier to implement [27].

L2gen(NIR-SWIR1) is identified as the best-performing method for Landsat-9, with the RMSE ≤ 0.0017 sr⁻¹. Yan et al. (2023) [34] compared DSF, C2RCC, iCOR, L2gen(NIR-SWIR2), and Polymer, concluding that L2gen(NIR-SWIR2) performs the best with the RMSE ≤ 0.0018 sr⁻¹. Similarly, Ilori et al. (2019) [32] evaluated DSF, L2gen(NIR-SWIR1), LaSRC, and ARCSI, recommending L2gen(NIR-SWIR1) as the most reliable method with an RMSE of ≤0.0015 sr⁻¹. These consistent findings underscore the robustness of L2gen for both Landsat-8 and Landsat-9.

4.3. Consistency Analysis of OLI-2/Landsat-9 with Other On-Orbit Remote Sensing Sensors

The long revisit period of approximately 16 days for the Landsat-9 data limits its applications in dynamic coastal areas; therefore, a joint use of multiple on-orbit spaceborne sensors, such as MSI/Sentinel-2 or VIIRS/S-NPP/NOAA-20, is usually necessary [40]. The uncertainty of MSI data has been assessed multiple times [39,45,51]. For VIIRS, as the successor to MODIS, the uncertainty and consistency of its $R_{rs}$ products have also been validated and evaluated by the scientific community several times since it was launched in 2012 [47,48]. Notably, Pardo et al. (2023) [48] used datasets in the Atlantic Ocean to compare VIIRS data with Sentinel-3 and MODIS. However, there is still a lack of consistency assessments between MSI, VIIRS, and OLI-2 data in aquatic systems.

In this study, a time window of ±3 h was chosen to match the MSI, VIIRS, and OLI-2 data, as well as the in-situ measurements from AERONET-OC. Note that, with the long revisit period of 16 days for the OLI-2/Landsat-9 data, it is difficult to obtain concurrent matchups for MSI, VIIRS, and OLI-2 data on the same day. Thus, the OLI-2 data were matched up with MSI and VIIRS, respectively. Since VIIRS has a revisit period of about one day, 52 valid matchups were obtained between OLI-2 and VIIRS. MSI, with a revisit period of six days, resulted in only 23 matchups with OLI-2. Figure 12 presents the statistics of the overpass time differences of OLI-2 versus MSI and VIIRS matchup points obtained in this study. It can be seen that the matchup data between MSI and OLI-2 are nearly simultaneous within 30 min, while the time differences between VIIRS and OLI-2 are greater, with a median average of 2.4 h.

Figure 13 demonstrates the scatter plots between satellite data (MSI, VIIRS, and OLI-2) and in-situ measured $R_{rs}$. Results show that the performance of OLI-2 is generally comparable to MSI and VIIRS. The RMSE errors in

Table 6. Error statistics of RMSE (sr⁻¹) for OLI-2, MSI, and VIIRS versus in-situ data.

Sensor	443 nm	482 nm	561 nm	655 nm	N
MSI	0.0016	0.0014	0.0013	0.0012	23
OLI-2	0.0016	0.0015	0.0013	0.0008
VIIRS	0.0016	0.0011	0.0010	0.0004	52
OLI-2	0.0014	0.0012	0.0011	0.0008

further support this observation. Specifically, in the first three visible bands of 443 nm, 482 nm, and 561 nm, the RMSE values of OLI-2, MSI, and VIIRS are very close, with a difference of less than 0.0002 sr⁻¹. However, at 655 nm, the uncertainty of the OLI-2 data is lower than that of MSI but higher than that of VIIRS, with a difference of approximately 0.0004 sr⁻¹ between them.

These differences could be partly attributed to spatial coverage and time differences between the satellite and in-situ data, which lead to variations in water optical properties, and partly to the use of different atmospheric correction methods—Polymer for MSI data and L2gen for VIIRS and OLI-2. Nevertheless, the RMSE differences between the three sensors are much smaller than those observed in the previous evaluation experiment between L2gen and other AC methods such as DSF, C2RCC, and Polymer using Landsat-9 data. For these three sensors on board different satellites, the uncertainty differences are within an acceptable range, suggesting that OLI-2 data have the potential to be effectively combined with MSI and VIIRS data for comprehensive applications.

The spatial distributions of $R_{rs}$ data at four visible spectral bands from OLI-2/Landsat-9, MSI/Sentinel-2B, and VIIRS/S-NPP for the Venise station (2 February 2022) and Section-7 station (12 May 2022), as well as the corresponding frequency distributions, demonstrate general consistency among the three sensors, with similar spatial patterns and closely matching frequency distributions shown in Figure 14 and Figure 15. However, the OLI-2 (30 m) and MSI (60 m) data show finer details compared to VIIRS (750 m), with the latter displaying small jagged edges along image boundaries. Moreover, the $R_{rs}$ values at 561 nm and 655 nm from the three sensors exhibit rather similar spatial patterns of variation in coastal waters, while at 443 nm and 482 nm, the OLI-2 $R_{rs}$ values are slightly higher than those of VIIRS. We speculate that the differences are caused by the use of different band combinations in estimating aerosol contributions despite using the same L2gen atmospheric correction procedure.

It is also worth noting that the overpass time difference is over two hours, during which the varying water optical properties could contribute to the observed differences. We observe that the discrepancies in lakes (marked in a red rectangle) are more significant than those in coastal waters, which we speculate could also result from the variable water optical properties in the lake, where the impact of multiple land activities is more pronounced. The noticeable cloud displacement within the red rectangle could also lead to inconsistencies in the frequency distributions. Additionally, as indicated by the red arrow in Figure 14, the MSI data suffer from pronounced striping effects at 443 nm and 482 nm, which could potentially be improved by utilizing the concurrent, smoother OLI-2 data.

5. Conclusions

The performance of the latest Landsat-9, launched in 2021, is highly anticipated for global inland and coastal aquatic ecosystem monitoring, and its application depends on reliable atmospheric correction processing. In this study, the performance of six atmospheric correction methods (DSF, C2RCC, iCOR, L2gen(NIR-SWIR1), L2gen(NIR-SWIR2), and Polymer) available for Landsat-9 data was evaluated and compared using global in-situ data from AERONET-OC and MOBY. The results show that L2gen(NIR-SWIR1) demonstrates the lowest uncertainty (RMSE ≤ 0.0017 sr⁻¹, SA = 6.33°) across the four optical water types. L2gen (NIR-SWIR2) follows closely (RMSE ≤ 0.0019 sr⁻¹, SA = 6.38°), followed by C2RCC (RMSE ≤ 0.0030 sr⁻¹, SA = 5.74°) and Polymer (RMSE ≤ 0.0027 sr⁻¹, SA = 7.76°). Finally, iCOR (RMSE ≤ 0.0051 sr⁻¹, SA = 12.96°) and DSF (RMSE ≤ 0.0058 sr⁻¹, SA = 11.33°) exhibit relatively high uncertainties. This provides a reference for selecting optimal atmospheric correction methods for Landsat-9 data applications in aquatic systems.

Additionally, the uncertainty and consistency of OLI-2/Landsat-9 in the visible bands were compared with concurrent on-orbit sensors MSI/Sentinel-2A/B and VIIRS/S-NPP/NOAA-20. The results suggest that they exhibit relatively high consistency, making it possible to form a multi-satellite observation system. This enables researchers to track and analyze dynamic changes in the inland and coastal water environment conveniently, providing timely decision-making tools and guidance for addressing ecological issues such as algal blooms and pollution diffusion.