Deep Learning-Based Spectral Reconstruction Technology for Water Color Remote Sensing and Error Analysis

Abstract

Land observation multispectral satellites (e.g., Landsat-8/9 and Sentinel-2) offer high spatial resolution but have limited spectral bands for water color observation and insufficient spectral resolution. This study proposes a spectral reconstruction model based on a residual neural network (Deep Spectral Reconstruction Learning Network, DSR-Net) to provide additional spectral bands support for nearshore water observations. The model is trained on 60 million pairs of quasi-synchronous reflectance data, and achieves stable reconstruction of 15 water color channels of the surface level reflectance for water pixels (ρ_w) from visible to near-infrared bands, considering sensor noise and atmospheric correction errors. Validation results based on AERONET-OC data show that the root mean square error of reconstructed ρ_w by DSR-Net ranges from 4.09 to 5.18 × 10⁻³, representing a reduction of 25% to 43% compared to original atmospheric correction results. The reconstruction accuracy reaches the observation level of the Sentinel-3/OLCI water color sensor and is universally applicable to different water categories, effectively supporting nearshore water color observation tasks such as colored dissolved organic matter inversion and cyanobacteria monitoring. The errors in the multispectral reflectance-based ρ_w primarily arise from sensor noise and atmospheric correction errors. After DSR-Net reconstruction, approximately 59% of the uncertainty caused by sensor noise and 38% of that caused by atmospheric correction errors are reduced. In summary, the spectral reconstruction products generated by DSR-Net not only significantly enhance the water color observation capabilities of current satellite sensors but also provide critical technical support for marine environmental monitoring and the design of next-generation sensors.

1. Introduction

The enhanced capabilities of land observation remote sensing sensors have facilitated their progressive application in coastal and inland water monitoring, enabling acquisition of observational data with improved spatial resolution. Recent studies demonstrate that land observation sensors (LOSs) can effectively quantify spatiotemporal variations in suspended particulate matter and chlorophyll-a concentrations in marine environments, with measurement accuracy reaching operational thresholds [1,2,3,4,5]. Nevertheless, inherent limitations persist compared to dedicated water color sensors (WCSs). Most LOSs prioritize spectral bands exhibiting strong atmospheric transmissivity (green, red, and near-infrared regions), while lacking dedicated spectral configurations for critical aquatic parameters such as colored dissolved organic matter (CDOM), phytoplankton pigment absorption characteristics (e.g., chlorophyll-a and phycocyanin), and fluorescence emission peaks. These spectral constraints not only reduce the robustness of water constituent retrieval algorithms but also limit their applicability for comprehensive aquatic environmental monitoring [6,7,8].

Spectral reconstruction techniques provide an effective solution to address spectral band limitations in water color observations and enhance the coastal monitoring capabilities of multispectral sensors. Studies have demonstrated that broadband spectral observations exhibit significant redundancy characteristics [9,10,11]. For instance, the panchromatic (PAN) band of Landsat-8, covering the 500–680 nm spectral range, partially overlaps with the red and green bands. After separating the overlapping regions, the PAN band provides additional spectral information not captured by the red and green bands. On the other hand, signals from adjacent spaced bands (Δλ ≤ 20 nm) display spectral redundancy, characterized by high inter-band correlations [12]. This property allows for complete spectral reconstruction in both pelagic and nearshore waters using a limited number of optimally selected bands (typically 5–15), achieving an optimal balance between signal-to-noise ratio (SNR) and data storage efficiency [12,13,14,15,16]. In summary, the core of spectral reconstruction techniques lies in leveraging the redundancy inherent in broadband signals along with the continuous nature of spectral curves to isolate or derive reflectance values for specific bands from known spectral information.

Building on these principles, spectral reconstruction approaches are broadly categorized into multivariate regressor models and intelligent learning models. Regressor models require a high correlation between the reconstructed band and the known bands. For example, Castagna et al. [17] and Niroumand-Jadidi and Bovolo [10] established a linear regression model calibrated for Landsat-8 that links the orange band (613 nm) with the PAN, green, and red bands. Reconstructed orange bands achieve accuracy comparable to that of the original red band, enabling applications in water color studies such as cyanobacterial bloom detection. Paulino et al. [18] developed a synthetic band generation method that tested three multivariate regression models on Sentinel-2 and Sentinel-3 image pairs to reconstruct eight visible bands, where linear regression achieved the highest accuracy with 28% bias relative to in situ observations. However, in Case-2 waters, the complexity of water color constituents (e.g., phytoplankton, CDOM, and non-algal particles) reduces inter-band correlations, increasing the challenge for regression. Recent breakthroughs in intelligent learning technologies for data mining and predictive modeling have provided novel pathways to fully exploit spectral continuity and redundancy. Niroumand-Jadidi and Bovolo [10] developed Deep OrAnge Band Learning Network (DOABLE-Net) trained on simulated hyperspectral data, successfully constructing a phycocyanin absorption band (620 nm) for Sentinel-2 sensors lacking PAN capability, thereby enabling reliable dynamic monitoring of cyanobacterial blooms. Banerjee et al. [9] utilized Hyperspectral Imager for the Coastal Ocean (HICO) data to establish hyperspectral-to-multispectral mapping relationships, reconstructing 76 bands (440–865 nm) for Sentinel-2, thereby providing cost-effective hyperspectral capabilities for water quality monitoring and algal bloom detection. Wang et al. [19] extended the spectral coverage of WCSs into near-blue ultraviolet (nbUV, 360–400 nm) through neural network modeling of correlations between visible and nbUV bands, subsequently deriving global distributions of the diffuse attenuation coefficients for downwelling irradiance (K_d, m⁻¹) using reconstructed nbUV spectral data. While neural networks demonstrate superior multispectral reconstruction performance in optically complex Case-2 waters, critical limitations persist. First, model training remains contingent on the representativeness of simulated spectral datasets, which often fail to capture the full variability of in situ bio-optical conditions. Second, sensor-specific radiometric noise patterns and residual atmospheric correction errors, which are rarely quantified or integrated into the training process, introduce systematic biases. These error sources propagate cumulatively through subsequent processing stages, amplifying uncertainties in derived biogeochemical parameters.

This study employs the surface level reflectance for water pixels (ρ_w) as training data to establish nonlinear mapping relationships between spectral bands of LOSs and WCSs through a Deep learning-based Spectral Reconstruction Network (DSR-Net). The training dataset integrates quasi-synchronized observations from LOSs and WCSs, with rigorous quality control applied across spatial, temporal, and spectral dimensions, yielding approximately 60 million high-quality matched spectral pairs. Leveraging this dataset, DSR-Net achieves robust LOS-to-WCS spectral reconstruction while partially addressing sensor noise and residual atmospheric correction errors. Furthermore, this study systematically evaluates the reconstruction accuracy of DSR-Net across spectral bands, its operational applicability for nearshore water quality monitoring, and its comparative advantages over conventional reconstruction models. The investigation also elucidates error propagation mechanisms inherent in spectral reconstruction processes and identifies key factors influencing reconstruction fidelity through sensitivity analyses.

2. Data

2.1. Remote Sensing Data

This study employs high quality (cloud cover < 5%) remote sensing data from Landsat-8 (since 2013), Landsat-9 (since 2021), Sentinel-2 (since 2015) and Sentinel-3 (since 2016) acquired from their respective launch dates through 2023. The Operational Land Imager (OLI) on Landsat-8 and its successor (OLI-2) on Landsat-9 share close spectral configurations, forming a dual-satellite system (hereafter Landsat-8&9/OLI) that enhances temporal resolution through coordinated acquisitions. Notably, while their spectral bands are similar, the radiometric resolution differs: Landsat-9/OLI-2 provides 14-bit quantization, whereas Landsat-8/OLI provides 12-bit. Landsat-8&9/OLI comprises eight multispectral bands and a PAN band spanning the visible to shortwave infrared (SWIR) range. The visible and near-infrared (VNIR) bands have bandwidths of 20–75 nm and a SNR of approximately 110, while the PAN band integrates green, orange, and red signals across 500–680 nm. The Multispectral Imager (MSI) on Sentinel-2 features 13 spectral bands covering the visible to SWIR regions. In addition to VNIR bands, MSI incorporates four red-edge bands optimized for vegetation characterization. Sentinel-2/MSI VNIR bands exhibit bandwidths of 15–65 nm and a SNR of approximately 130.

In comparison, the Ocean and Land Color Imager (OLCI) onboard Sentinel-3 is characterized by narrow spectral bands (2.5–10 nm bandwidth in visible regions), enhanced SNRs (peak value > 1800), and high radiometric resolution. Beyond red, green, and blue bands that overlap with Landsat-8&9/OLI and Sentinel-2/MSI, OLCI includes specialized bands for phytoplankton fluorescence at 680 nm and phycocyanin absorption at 620 nm.

Regarding data accessibility, Level-1 products for Landsat-8&9/OLI, including top-of-atmosphere (TOA) reflectance as well as solar and satellite zenith and azimuth angles, are distributed by the United States Geological Survey (USGS) via EarthExplorer (https://earthexplorer.usgs.gov, accessed on 1 January 2025). Level-1 products for Sentinel-2/MSI and Sentinel-3/OLCI, including TOA reflectance as well as solar and satellite zenith and azimuth angles, are distributed by the Copernicus Data Space Ecosystem (https://dataspace.copernicus.eu, accessed on 1 January 2025).

2.2. In Situ Data

The AErosol RObotic NETwork—Ocean Color (AERONET-OC) system provides critical support for water color data calibration and quality assurance. Each station employs modified CIMEL radiometers measuring water color wavelengths (e.g., 412, 443, 488, 510, 551, 667, 870, and 1020 nm with about 10 nm bandwidth) to acquire key parameters: water-leaving radiance (L_w), normalized water-leaving radiance (L_wn), and aerosol optical thickness (τ_a). AERONET-OC data products are classified into three tiers: Level 1.0 (unscreened data), Level 1.5 (cloud cleared and quality-controlled data), and Level 2.0 (quality assured data) [20]. All tiers are publicly accessible through the AERONET portal (http://aeronet.gsfc.nasa.gov/, accessed on 1 January 2025). The f/Q-corrected products (L_wn_f/Q) were excluded from validation and analysis procedures due to concerns that chlorophyll concentration-based f/Q corrections, while effective for high-reflectance waters, may inadequately perform in turbid aquatic environments [20] and induce spectral overcorrection in suspended particulate matter-dominated systems [3]. To ensure maximum reliability and objectivity, this study utilizes Level 2.0 L_wn_IOP products [21]. ρ_w is calculated as L_wn/F₀ × π, where F₀ is the solar irradiance following Thuillier et al. [22]. For accuracy assessment, satellite observations were matched to AERONET-OC measurements within ±30 min of the overpass. When multiple AERONET-OC data met this criterion, linear interpolation was applied to the two spectra bracketing the overpass time. The eight AERONET-OC stations presented in Figure 1 were selected based on comprehensive criteria, including the requirement for a sufficient number of high-quality matchups with satellite observations [23,24] and the need for representation across diverse aquatic environments, specifically encompassing both coastal and offshore waters. This selection yielded a dataset comprising over 800 spectral observations spanning turbid waters, phytoplankton-dominant waters, algal bloom waters, inland waters, and open ocean waters to evaluate multi-source remote sensing data quality and reconstruction accuracy. Measuring periods of the selected stations and the number of matchups are provided in

Table 1. The measuring periods and the number of matchups by multi-source remote sensing data at AERONET-OC stations.

Stations	Measuring Periods	Matchups
		Landsat-8&9	Sentinel-2	Sentinel-3	Total
ARIAKE_TOWER	2018–2023	17	42	76	135
MVCO	2004–2018, 2020, 2022–2025	14	1	5	20
WaveCIS_site_CSI_6	2010–2024	14	64	105	183
Helsinki_Lighthouse	2006–2017, 2019	6	16	68	90
Pålgrunden	2008–2025	17	57	204	278
Ieodo	2013–2014, 2016–2019	1	-	-	1
Zeebrugge-MOW1	2014–2017, 2019, 2021, 2022	6	9	17	32
Thornton_C-power	2015–2018, 2023, 2025	13	16	59	88

.

3. Methods

3.1. Preprocess

ACOLITE v20231023 was employed to preprocess Landsat-8&9/OLI, Sentinel-2/MSI, and Sentinel-3/OLCI data, encompassing radiometric calibration, glint correction, atmospheric correction, and reprojection. Atmospheric correction utilized the dark spectrum fitting (DSF) method [3], which demonstrates robust performance across clear waters, terrestrial regions, and high-turbidity or highly productive Case-2 waters [3,25,26,27]. SWIR-based glint correction was applied to Landsat-8&9/OLI and Sentinel-2/MSI to mitigate sun glint contamination and ensure nadir-view reflectance accuracy [3,28]. Atmospherically corrected reflectance products were reprojected and resampled to a uniform 300 m spatial resolution using averaging over corresponding source pixels, aligning them with the Sentinel-3/OLCI observations.

3.2. Spatiotemporal–Spectral Data Matching

Discrepancies in overpass timing, spectral configurations, and atmospheric correction methodologies may undermine cross-sensor data coherence in multi-source remote sensing observations, particularly in dynamic coastal waters. The quasi-synchronous spectral dataset (its data sources are given in Supplementary File Tables S1–S3) requires comprehensive validation of spatiotemporal and spectral alignment prior to model training to ensure that LOS and WCS observations correspond to the identical target.

This study systematically analyzed spatiotemporal discrepancies in multi-source remote sensing data. In high-dynamic coastal waters (e.g., sediment front), bio-optical properties can exhibit rapid temporal variability, with remote sensing products showing pronounced spectral variability from water mass advection and dispersion. To ensure temporal consistency, a ±30-min synchronization threshold was implemented. For spatial alignment, the cross-correlation coefficient (Rc) served as the primary validation metric, calculated for co-located observation windows in multi-source imagery as defined in Equation (1):

$$Rc={\displaystyle \frac{{\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^m(x(i,j)-\overline{x})}\cdot (y(i,j)-\overline{y})}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^m{(x(i,j)-\overline{x})}^2}}}\cdot \sqrt{{\displaystyle {\sum }_{i=1}^n{\displaystyle {\sum }_{j=1}^m{(y(i,j)-\overline{y})}^2}}}}}.$$

(1)

In Equation (1), x and y represent the pixel matrices of the windows in LOS and WCS observation windows, respectively, where i and j denote row and column indices within the windows. $\overline{x}$ and $\overline{y}$ represent the mean pixel values of x and y, respectively. The window dimensions n and m were fixed at 25 pixels × 25 pixels, corresponding to a 7.5 km × 7.5 km observational footprint. Principal component analysis (PCA) was applied to the LOS and WCS imagery, with the first principal component selected as the feature-matching layer. A sliding-window search was performed within a ±0.9 km range centered on the WCS window’s geographic coordinates to compute Rc for each candidate window in the LOS imagery. This spatial buffer accommodated potential displacements from maximum 30-min temporal offsets at assumed 1.8 km/h current velocities. Observation windows were validated as spatially consistent when the maximum Rc exceeded 0.8. Both datasets were decomposed into 25 × 25-pixel windows to facilitate subsequent spectral angle calculations and model input processing.

Spectral angle (θ_SAM) [29] was adopted as an evaluation metric to assess spectral similarity between corresponding LOS and WCS bands. Its formulation is given by Equation (2):

$${\theta }_{SAM}={\cos }^{-1}({\displaystyle \frac{y^{T}x}{‖x‖‖y‖}}).$$

(2)

In Equation (2), x and y are equal-length one-dimensional vectors containing the spatially averaged reflectance values per spectral band from corresponding LOS and WCS observation windows. These vectors preserve the shared spectral bands between sensors while collapsing spatial information through averaging. A θ_SAM threshold less than 10° was applied to synchronized observations to account for inherent variability from atmospheric correction errors, overpass timing discrepancies, and spatial resolution differences, while effectively filtering spectral anomalies caused by short-term hydrodynamic disturbances.

In addition to spatiotemporal–spectral consistency validation, the training dataset compilation integrated supplementary quality control criteria to ensure spectral coherence between LOS and WCS observations. Key metrics included the τ_a difference threshold at 550 nm (Δτ_a(550) < 0.5) for quasi-synchronized acquisitions and land cover classification restricted to the ocean. Using these constraints, the study systematically assembled quality-controlled quasi-synchronized reflectance data and τ_a(550), establishing a spatiotemporally consistent LOS-WCS spectral dataset. The integrated workflow from data filtering to product generation is schematically summarized in Figure 2.

3.3. Construction and Refinement of the Training Dataset

The accuracy of spectral reconstruction is heavily relied on in the quality of the quasi-synchronous dataset. The error sources primarily originate from sensor noise and atmospheric correction. The error magnitude is modulated by atmospheric and surface conditions, solar and satellite geometries, spectral band configurations, and atmospheric correction methods [17].

Given the inherent error characteristics of LOS-WCS datasets, rigorous analysis of error propagation mechanisms is critical when utilizing these data for model training. To enhance reconstruction accuracy, Sentinel-3/OLCI spectra (as the reference output) were stringently controlled to minimize error contamination. When atmospheric correction refinements plateaued, bio-optical model-based filtering of corrected reflectance values proved effective for enhancing dataset quality. This study integrated multiple bio-optical frameworks [30,31] (detailed in Appendix A) to generate a 150,000-entry simulated spectral dataset spanning five water types: clear waters, phytoplankton-dominated waters, algal bloom waters, turbid waters, and extreme turbidity waters (≥25,000 spectra per class). Sentinel-3/OLCI spectra were validated by calculating θ_SAM against each simulated spectrum, and spectra exhibiting a minimum θ_SAM > 2° were classified as low-quality and excluded from the training dataset.

The training dataset was derived from the LOS-WCS dataset after bio-optical filtering. Subsequently, a training dataset comprising 60 million quasi-simultaneous spectra pairs was constructed. The WCS spectra originated from Sentinel-3/OLCI imagery, while the corresponding LOS spectra originated from Sentinel-2/MSI (26 million spectra) and Landsat-8&9/OLI (34 million spectra) imagery.

3.4. DSR-Net Model

The DSR-Net model utilized input parameters including the eight spectral bands of Landsat-8&9/OLI or eleven bands of Sentinel-2/MSI, solar and satellite geometries (solar zenith angle, satellite zenith angle, and relative azimuth angle), and τ_a(550) derived from ACOLITE. Fifteen VNIR bands from Sentinel-3/OLCI served as output targets, excluding bands with gas transmittance < 0.75, significant water absorption features, or limited relevance to water color applications. The spectral configurations of input and output bands are detailed in Figure 3.

The DSR-Net is designed and trained under three foundational assumptions: (1) input LOS reflectance inherently contains uncertainties arising from atmospheric correction error, atmospheric variability, solar and satellite geometries, sensor noise, adjacency effects, and so on; (2) bio-optically filtered Sentinel-3/OLCI reflectance aligns with natural aquatic spectral signatures, exhibiting minimal residual uncertainties from sun glint and adjacency effects; (3) nonlinear relationships exist between atmospheric correction errors and solar and satellite geometries, sensor wavelengths, ρ_w and τ_a(550).

Residual blocks mitigate gradient vanishing and are thus widely employed for complex spectral reconstruction problems [32,33,34]. DSR-Net employs a residual neural network architecture comprising 32 stacked residual convolutional blocks (Figure 4). Each block integrates two convolutional layers with ReLU activation functions and output scaling (×0.1), supplemented by residual skip connections to preserve gradient flow. This architecture addresses vanishing gradient challenges while optimizing feature reuse efficiency. The framework adapts channel dimensions to accommodate multi-source LOS data inputs, resolves nonlinear spectral mapping relationships between LOS and WCS bands, and achieves robust reconstruction through end-to-end training.

3.5. Uncertainty Quantification

3.5.1. Sensor Noise Quantification

The uncertainty in TOA reflectance induced by sensor noise (σ_noise) can be estimated using the SNR, calculated as:

$$\begin{array}{c}{\sigma }_{\mathrm{noise}}=\end{array}{\displaystyle \frac{\pi \cdot L_{\mathrm{ref}}}{{\mathrm{F}}_0\cdot SNR}}.$$

(3)

where L_ref represents the reference radiance and F₀ represents the solar irradiance at the TOA. Values of L_ref and SNR were obtained from the World Meteorological Organization (https://space.oscar.wmo.int/, accessed on 1 January 2025), while L_ref was extracted from sensor metadata. The corresponding spectral band parameters are compiled in

Table 2. L_ref, SNR and F₀ across sensors.

Wavelength (nm)	Lref (W m−2 sr−1 μm−1)/SNR/F0 (W m−2 μm−1)
	Landsat-8&9			Sentinel-2			Sentinel-3
400							63	2188	1485
412							74	2061	1711
443	40	130	1896	129	129	1874	66	1811	1865
490	40	130	2004	128	154	1960	51	1541	1934
510							44	1488	1923
560	30	100	1821	128	168	1825	31	1280	1799
620							21	997	1650
667	22	90	1549	108	142	1513	16	883	1531
779				67	105	1291	9	812	1176
865	14	90	952	52	72	1041	6	666	959

, with complete σ_noise analysis presented in Section 4.3.1.

3.5.2. Atmospheric Correction Error Simulation

Building upon the 6SV radiative transfer model [35,36] that underpins ACOLITE’s DSF lookup tables, this study employs 6SV simulations to evaluate both bio-optical filtering performance and noise impacts on ρ_w.

For bio-optical filtering validation, the TOA reflectance, spectral band configurations, solar and satellite geometries (obtained from Sentinel-3/OLCI products), as well as the atmospheric and aerosol condition (inferred from the acquisition date and underlying surface conditions) are treated as known quantities, while τ_a(550) is input as a random variable into the 6SV radiative transfer model. Subsequent spectral validation against AERONET-OC measurements confirmed the filter’s capability to constrain uncertainties, with detailed analysis presented in Section 4.3.1.

In addition, the 6SV radiative transfer model was employed to rigorously evaluate the DSR-Net’s capacity to suppress atmospheric correction errors and sensor noise while elucidating error propagation dynamics. Isolated perturbations were introduced through two controlled scenarios: (1) sensor noise amplification through random noises (1.06 × 10⁻³) in TOA reflectance, doubling LOS noise and halving SNR, to quantify ρ_w uncertainties under degraded conditions; and (2) atmospheric correction uncertainty elevation via random τ_a(550) noise (3.6 × 10⁻²) to assess DSR-Net’s robustness against amplified atmospheric errors. Both scenarios were benchmarked against AERONET-OC measurement, enabling systematic quantification of error sources and their suppression, thereby validating DSR-Net’s efficacy in mitigating spectral reconstruction inaccuracies across diverse water and atmospheric conditions. Comprehensive analysis appears in Section 4.3.2.

3.6. Accuracy Assessment

The coefficient of determination (R²), root mean square error (RMSE), and percentage difference (PD) were employed to evaluate discrepancies between atmospheric corrected reflectance, reconstructed reflectance, and in situ measurements, thereby quantitatively assessing spectral quality and reconstruction performance. The computational formulations of these metrics are provided in Equations (4)–(6):

$${\mathrm{R}}^2={[{\displaystyle \frac{{\displaystyle {\sum }_{i=1}^N[(y_i-{\overline{y}}_i)(x_i-{\overline{x}}_i)]}}{\sqrt{{\displaystyle {\sum }_{i=1}^N{(y_i-{\overline{y}}_i)}^2}{\displaystyle {\sum }_{i=1}^N{(x_i-{\overline{x}}_i)}^2}}}}]}^2$$

(4)

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

(5)

$$\mathrm{PD}={\displaystyle \frac{1}{N}}{\displaystyle {\sum }_{i=1}^N\frac{y_i-x_i}{x_i}}$$

(6)

where x_i represents in situ measured ρ_w, and y_i represents either atmospheric corrected or model-reconstructed ρ_w. R² quantifies the agreement between x_i and y_i, RMSE characterizes their absolute discrepancy, and the PD indicates their relative deviation. A positive PD value indicates overestimation in corrected or reconstructed reflectance, while a negative value indicates underestimation.

4. Results

4.1. Accuracy Assessment of the ACOLITE Products

This study conducted accuracy assessments of ρ_w products from Landsat-8&9/OLI, Sentinel-2/MSI, and Sentinel-3/OLCI utilizing AERONET-OC site data, yielding 88, 205, and 534 valid matchups, respectively. Sentinel-3/OLCI data underwent additional spectral filtering via bio-optical models (hereafter denoted as Sentinel-3*/OLCI) to remove outliers affected by sun glint, adjacency effects, and atmospheric correction error, retaining 396 high-quality ρ_w. The spectral matchup quantities and ρ_w product accuracy metrics for each sensor are summarized in

Table 3. Accuracy metrics of ρ_w products from Landsat-8&9/OLI, Sentinel-2/MSI, Sentinel-3/OLCI, and bio-optically filtered Sentinel-3/OLCI data. N denotes the number of matched site observations.

Wavelength (nm)	R2/RMSE (×10−3)/PD
	Landsat-8&9 (N = 88)			Sentinel-2 (N = 205)			Sentinel-3 (N = 534)			Sentinel-3 * (N = 396)
400							0.47	12.64	8.69	0.49	7.00	8.01
412							0.38	8.41	2.10	0.46	4.94	1.12
443	0.66	13.31	1.50	0.53	7.89	0.89	0.59	8.06	1.25	0.70	5.15	0.88
490	0.83	10.19	0.65	0.84	5.20	0.20	0.84	5.40	0.36	0.89	3.66	0.21
510							0.88	5.07	0.27	0.91	2.92	0.15
560	0.94	6.31	0.18	0.94	4.11	−0.01	0.93	4.25	0.09	0.94	3.51	0.04
620							0.88	3.53	0.11	0.88	2.45	0.02
667	0.89	6.29	0.64	0.86	3.41	0.10	0.87	2.49	0.15	0.89	1.92	0.04
779				0.56	1.51	0.71	0.38	1.93	1.77	0.22	1.25	1.44
865	0.25	3.05	3.67	0.00	1.63	−2.23	0.18	1.07	3.65	0.17	0.82	2.53
Total	0.86	8.60	1.33	0.88	4.75	−0.15	0.79	6.03	1.62	0.87	3.75	1.15

* Sentinel-3/OLCI data underwent additional spectral filtering via bio-optical models.

.

Comparative analysis demonstrated that Sentinel-3/OLCI and Sentinel-2/MSI achieve superior overall accuracy, with RMSE of 6.03 × 10⁻³ and 4.75 × 10⁻³, respectively, while Landsat-8&9/OLI exhibits a RMSE of 8.60 × 10⁻³. Systematic overestimation in blue spectral bands was observed across all sensors, consistent with land adjacency effects at coastal AERONET-OC stations as reported by Vanhellemont [3]. Following bio-optical spectral filtering, the total RMSE of the Sentinel-3 */OLCI dataset decreased to 3.75 × 10⁻³, demonstrating substantial accuracy improvement. While filtering partially mitigated blue-band overestimation in Sentinel-3/OLCI data, residual biases persist due to ambiguities in distinguishing blue-band signal variations caused by adjacency effects versus water component changes (e.g., reduced CDOM absorption). Future refinements in the atmospheric correction process may resolve these signal attribution challenges, though such advancements lie beyond the scope of this study.

4.2. Accuracy Assessment of the Reconstruction

The DSR-Net model was implemented using PyTorch (version 2.2.2) and trained on an NVIDIA GeForce RTX 4070 Ti GPU. After 5000 iterations (about 72 h), the L1 Loss [37] stabilized at 1.2 × 10⁻⁴, indicating that the DSR-Net model achieved full convergence.

Table 4. Reconstruction accuracy for Landsat-8&9/OLI and Sentinel-2/MSI data. N denotes the number of matched site observations.

Wavelength (nm)	R2/RMSE (×10−3)/PD
	Landsat-8&9 (N = 88)			Sentinel-2 (N = 205)
400	0.60	6.94	−1.93	0.73	7.07	4.13
412	0.72	6.44	1.86	0.68	5.04	1.01
443	0.86	6.69	1.02	0.79	5.29	0.67
490	0.92	5.23	0.30	0.89	4.17	0.13
510	0.91	5.03	0.08	0.91	4.22	0.02
560	0.95	5.22	0.11	0.96	3.61	0.05
620	0.84	5.52	−0.06	0.90	4.16	−0.01
667	0.92	4.13	0.33	0.91	2.84	0.09
779	0.48	2.15	1.08	0.69	1.64	0.85
865	0.36	1.72	2.26	0.52	0.90	−0.89
Total	0.91	4.09	0.39	0.91	5.18	0.78

shows the accuracy assessment of spectral reconstruction results for Landsat-8&9/OLI and Sentinel-2/MSI data.

As demonstrated in Table 4, DSR-Net not only expands the usable spectral range of LOS data but also significantly enhances spectral accuracy across bands. This improvement is evidenced by elevated R² values, reduced PD, and RMSE reductions of 25–43% compared to ACOLITE products. For Landsat-8&9/OLI, the total RMSE decreased by 4.51 × 10⁻³, accompanied by a PD reduction of 0.94, effectively mitigating systematic blue-band overestimation and achieving reconstruction accuracy comparable to the Sentinel-3/OLCI dataset. Sentinel-2/MSI exhibited substantial accuracy enhancements across all bands except 779 nm, with RMSE reductions ranging from 0.5 to 2.6 × 10⁻³. The marginal error increase at 779 nm post-reconstruction remains acceptable given Sentinel-3/OLCI’s inherent lower observational accuracy at this wavelength compared to Sentinel-2/MSI. Collectively, the reconstructed Sentinel-2/MSI spectral products surpass the quality of the original Sentinel-3/OLCI dataset and approach the performance of the bio-optically filtered Sentinel-3 */OLCI reference data.

To further evaluate DSR-Net’s applicability to complex Case-2 waters, four categories were extracted from the synchronized spectral dataset based on chlorophyll concentration (Chl, derived from the OC3S algorithm [38]), suspended particulate matter concentration (SPM, derived from the semi-empirical radiative transfer model [39,40,41]), and CDOM absorption at 443 nm (a_g(443), derived from the quasi-analytical algorithm QAA_v6 [42,43]):

• Clear water: Chl < 2 μg/L, SPM < 5 mg/L and a_g(443) < 1 m⁻¹;
• Phytoplankton-dominated water: Chl ≥ 10 μg/L, SPM < 25 mg/L and a_g(443) < 1.2 m⁻¹;
• Turbid water: Chl < 10 μg/L, SPM ≥ 25 mg/L and a_g(443) < 1.2 m⁻¹;
• Mixed Case-2 waters: 2 μg/L ≤ Chl < 10 μg/L, 5 mg/L ≤ SPM < 25 mg/L and 0.6 m⁻¹ ≤ a_g(443) < 1.2 m⁻¹.

This classification scheme, adapted from Banerjee et al. [9], was optimized based on the distribution of in situ matchups and prevailing marine conditions. Modifications included the following: (1) removing categories for algal bloom waters and extremely turbid waters lacking supporting measurements from AERONET-OC stations; (2) merging Case-2 waters with non-prominent optical components into the mixed Case-2 water category; and (3) slightly adjusting the concentration ranges for phytoplankton-dominated and turbid waters based on a literature review of coastal waters [44,45]. The reconstruction accuracy of DSR-Net was then systematically accessed across four water categories under diverse bio-optical conditions.

Table 5. Reconstruction accuracy of DSR-Net for different water categories. N denotes the number of matched site observations.

Wavelength (nm)	R2/RMSE (×10−3)/PD
	Clear Water (N = 5 *)			Phytoplankton- Dominated (N = 42)			Turbid Water (N = 69)			Mixed Water (N = 151)
400				0.59	7.63	5.15	0.11	6.52	0.39	0.46	7.05	4.16
412	0.96	9.16	1.46	0.47	4.52	1.38	0.58	4.73	0.07	0.44	5.58	1.19
443	0.94	9.48	1.47	0.56	4.96	0.96	0.76	5.22	0.10	0.55	5.78	0.78
490	0.79	6.20	0.68	0.60	3.51	0.25	0.85	5.77	−0.04	0.68	3.92	0.19
510				0.84	2.57	0.10	0.47	5.70	−0.06	0.82	3.04	0.07
560	0.19	5.46	0.60	0.92	1.89	0.02	0.88	6.25	−0.01	0.80	3.36	0.09
620				0.94	1.30	−0.02	0.52	6.25	−0.01	0.76	2.69	−0.07
667	0.21	3.59	2.90	0.78	1.65	0.07	0.81	5.90	0.02	0.51	1.83	0.16
779				0.46	1.04	1.09	0.40	2.41	0.64	0.38	0.82	1.06
865	0.00	2.25	22.99	0.05	1.16	2.82	0.47	1.55	1.22	0.00	1.05	−2.35
Total	0.78	6.58	5.02	0.78	3.52	1.09	0.92	5.25	0.23	0.78	4.00	0.13

* Partial evaluation gaps for specific bands in the clear water category were observed due to limited spectral coverage at certain stations (e.g., absence of the 620 nm band at Zeebrugge-MOW1 and Thornton_C-power stations).

summarizes the reconstruction accuracy of DSR-Net across four water categories. Overall, the DSR-Net model demonstrates strong robustness and generalization capability, with comprehensive R² values exceeding 0.78 and RMSE remaining below 7.0 × 10⁻³, and with turbid waters exhibiting optimal performance (R² = 0.92, RMSE = 5.25 × 10⁻³). Band-specific error analysis reveals distinct mechanisms: blue-band discrepancies primarily arise from reflectance overestimation due to land adjacency effects, while near-infrared band errors stem from weak water-leaving signals where sensor noise and atmospheric correction errors disproportionately obscure true hydrological signatures. In contrast, green bands demonstrate exceptional stability, particularly in phytoplankton-dominated waters, achieving R² up to 0.92 in phytoplankton-dominated waters.

4.3. Error Sources and Control

4.3.1. Error Sources

Given that the ρ_w from LOS data input to the DSR-Net model inherently contain uncertainties, this study quantitatively characterizes their sources and investigates error propagation mechanisms during spectral reconstruction. Following Castagna et al. [17], these uncertainties primarily originate from sensor noise and atmospheric correction error. While Table 3 summarizes the total errors across spectral bands, the analysis further categorizes these uncertainties as follows:

1.

Sensor noise

The σ_noise across spectral bands for different sensors are presented in

Table 6. σ_noise across sensors.

Wavelength (nm)	Landsat-8&9	Sentinel-2	Sentinel-3
400			6.09 × 10−5
412			6.60 × 10−5
443	5.10 × 10−4	1.68 × 10−3	6.10 × 10−5
490	4.82 × 10−4	1.33 × 10−3	5.40 × 10−5
510			4.87 × 10−5
560	5.18 × 10−4	1.31 × 10−3	4.30 × 10−5
620			4.04 × 10−5
667	4.96 × 10−4	1.58 × 10−3	3.81 × 10−5
779		1.55 × 10−3	3.02 × 10−5
865	5.13 × 10−4	2.20 × 10−3	3.04 × 10−5
Total	5.04 × 10−4	1.61 × 10−3	4.73 × 10−5

. Sentinel-3 exhibits superior SNR characteristics, maintaining σ_noise generally below 7.0 × 10⁻⁵. In contrast, LOS imagery demonstrates lower SNR performance, with σ_noise ranging from 4.8 × 10⁻⁴ to 2.2 × 10⁻³.

2.

Atmospheric correction errors

Spectral statistics (Table 3) indicate that approximately 26% of Sentinel-3/OLCI reflectance were rejected by bio-optical plausibility filtering, primarily attributed to overestimations of τ_a(550) inducing negative reflectance retrievals. Bio-optical filtering (as detailed in Section 3.3) is then performed on the 6SV simulation results (${\hat{\rho }}_w$). As shown in Figure 5, comparisons between ${\hat{\rho }}_w$ and AERONET-OC in situ measurements yield a RMSE of 3.97 × 10⁻³, marginally surpassing the observational accuracy of the Sentinel-3 */OLCI dataset.

To further investigate the distribution patterns of atmospheric correction errors across water categories, four representative water categories were analyzed. As shown in Figure 6, ρ_w products of ACOLITE exhibit strong agreement with in situ measurements for all four water categories, except for systematic overestimations in the blue bands. Simulated ρ_w values gradually decrease as τ_a(550) increases, eventually being flagged as implausible by bio-optical models. Notably, while bio-optical constraints ensure the physical plausibility of ρ_w, they do not ensure absolute accuracy, particularly in blue bands where reflectance enhancements may ambiguously originate from reduced CDOM absorption or amplified adjacency effects. This critical uncertainty diminishes DSR-Net’s reconstruction fidelity in nearshore environments. Validation across the four water classes demonstrates that bio-optical data control methods remain effective under diverse water and aerosol conditions, successfully suppressing both over- and underestimation of τ_a(550) and improving ρ_w observational precision.

4.3.2. Error Propagation and Controls

Leveraging the isolated controlled variables detailed in Section 3.5.2, the error propagation and accuracy enhancement of the DSR-Net were systematically evaluated under amplified sensor noise and atmospheric correction error scenarios (

Table 7. Uncertainty in ρ_w and reconstruction results after introducing random errors (up to 1.06 × 10⁻³) to TOA reflectance.

Wavelength (nm)	R2/RMSE (×10−3)/PD
	ρw			Reconstructed ρw
443	0.56	32.82	1.14	0.79	15.94	0.64
490	0.71	33.66	0.57	0.89	12.92	0.11
560	0.94	14.73	0.02	0.96	10.91	0.04
667	0.67	29.21	0.91	0.93	7.97	0.08
779	0.57	4.64	0.70	0.72	4.73	0.83
865	0.00	17.67	−9.28	0.54	2.74	−1.23
Total	0.78	26.15	−1.23	0.94	10.74	−0.01

and

Table 8. Uncertainty in ρ_w and reconstruction results after introducing random errors (up to 3.6 × 10⁻²) to τ_a(550).

Wavelength (nm)	R2/RMSE (×10−3)/PD
	ρw			Reconstructed ρw
443	0.53	32.28	1.03	0.79	18.34	0.74
490	0.78	23.86	0.31	0.88	15.11	0.17
560	0.92	17.18	0.04	0.95	13.47	0.06
667	0.83	15.42	0.21	0.91	10.27	0.09
779	0.23	9.05	0.60	0.45	6.59	0.79
865	0.07	9.26	−2.41	0.31	4.40	−1.28
Total	0.84	20.69	−0.13	0.93	12.87	0.01

). In sensor noise amplification, the DSR-Net demonstrated significant performance improvements, elevating the R² from 0.78 to 0.94 while achieving a 59% reduction in RMSE. In atmospheric correction error amplification, comparable enhancements were observed with R² increasing from 0.84 to 0.93 while achieving a 38% reduction in RMSE, thereby validating the model’s robust error suppression capacity. Spectral band analysis revealed wavelength-dependent efficacy, where shorter wavelengths (e.g., 443 nm) exhibited marked improvements (R² increased from 0.56 to 0.79, RMSE reduced by 51%) compared to limited gains in longer bands (e.g., 865 nm), attributable to weak water-leaving signals. These findings highlight the comparable and non-negligible impacts of sensor noise and atmospheric correction errors, emphasizing the necessity to rigorously account for error propagation mechanisms and their cascading effects during spectral reconstruction.

To systematically evaluate the reconstruction accuracy and robustness of DSR-Net across diverse water categories, Figure 7 illustrates the ρ_w for four water categories after introducing τ_a(550) noise of 3.6 × 10⁻² and TOA reflectance noise of 1.06 × 10⁻³ during processing, alongside the corresponding DSR-Net spectral reconstruction results.

Following the amplified errors, the average RMSE across all water categories in Figure 7 increased to 2.27 × 10⁻³. After spectral reconstruction, spectral errors were significantly reduced across all wavelengths, with spectral shapes aligning more closely with in situ measurements and partial suppression of adjacency effects (e.g., Figure 7b), yielding a reduced average RMSE of 1.31 × 10⁻³. DSR-Net’s reconstructions further revealed observational accuracy variations in Sentinel-3/OLCI products across water categories: for mildly turbid or chlorophyll-dominated waters (Figure 7a,b), reflectance uncertainties were concentrated in blue and NIR bands, with error magnitudes substantially higher than those in red and green bands. In contrast, turbid waters (Figure 7d) exhibited predominant green band uncertainties, likely attributable to sensor limitations (band saturation) or inherent atmospheric correction model errors.

4.4. Application: Observation of CDOM and Cyanobacteria Blooms

To validate the reliability of DSR-Net reconstructed data and its observational advantages over LOSs, this study applied the reconstructed products to retrieve phycocyanin concentrations and CDOM absorption. Phycocyanin retrieval utilized the Phycocyanin Index (PCI), which exploits the absorption feature near 620 nm correlated with phycocyanin concentration to map spatiotemporal distributions of cyanobacterial blooms [46]. Previously, this algorithm could not be implemented for Sentinel-2 or Landsat-8&9 due to the absence of critical orange bands (e.g., 620 nm). Figure 8 illustrates the spatial distribution of a cyanobacterial bloom near the Helsinki Lighthouse station via PCI. DSR-Net achieved high-precision reconstruction of VNIR bands, with PCI retrievals (Figure 8d) showing strong consistency with Sentinel-3 products (Figure 8b) and in situ measurements (Figure 8c). Additionally, the DSR-Net partially mitigated reflectance overestimation caused by adjacency effects, though minor systematic overestimation persists in blue bands due to limitations in training data accuracy.

Another innovative contribution of DSR-Net lies in its ability to support the QAA_v6 through spectral reconstruction, enabling the estimation of CDOM absorption. QAA_v6 evolved from the QAA framework [47], which derives inherent optical properties (IOPs) from L_wn. In the QAA_v6, total water absorption is decomposed into contributions from pure seawater, phytoplankton pigments, detritus and minerals, and gelbstoff (e.g., CDOM). Consequently, QAA_v6 implementations require multiple water color bands (e.g., 443, 490, 555, and 670 nm) to resolve these absorption features. To address the limited spectral bands available on LOS, some researchers have developed simplified QAA variants with reduced band requirements [48]. This study proposes an alternative solution by leveraging DSR-Net-reconstructed spectra to fulfill QAA_v6’s spectral prerequisites. Figure 9 presents a synchronized a_g(443) distribution derived from Sentinel-3/OLCI and reconstructed spectral data. The DSR-Net-based a_g(443) product exhibits spatial consistency with Sentinel-3/OLCI outputs while demonstrating superior SNR and enhanced textural clarity in low-CDOM regions, underscoring the model’s potential for complex aquatic optical scenarios.

5. Discussion

5.1. Reconstruction of Orange Band

LOS have become pivotal tools for coastal environmental monitoring due to their high-spatial-resolution capabilities. With the expanding applications of aquatic remote sensing, various spectral reconstruction techniques have emerged. The orange band, critical for water color observations, holds significant value in phycocyanin retrieval and related domains. This study conducts a cross comparison of orange band reconstruction methodologies, quantifying the performance of DSR-Net against existing models [10,17].

Figure 10 compares orange band reconstruction results from DSR-Net (a) with PAN-based methods (b and c). DSR-Net-reconstructed spectra exhibit strong agreement with in situ measurements, with only two outliers identified through comparison. Both points occur in hydrodynamically dynamic sediment frontal zones, likely due to temporal mismatches between field sampling and satellite overpass. Panels b and c shows the PAN-based results [10,17] and exhibit comparable predictive accuracy, with RMSE values of 9.21 × 10⁻³ and 1.04 × 10⁻². The study demonstrates that DSR-Net achieves superior reconstruction accuracy compared to PAN-based methods, as its neural network architecture effectively addresses the impacts of sensor noise and atmospheric correction errors. In contrast, the performance of PAN-based methods remains heavily dependent on atmospheric correction precision. While additive noise can be partially mitigated through band arithmetic operations, multiplicative noise (e.g., adjacency effects) and significant atmospheric correction residuals undermine their robustness, particularly in optically complex environments such as turbid coastal zones or sediment-laden waters.

5.2. Limitations and Improvements

The training dataset for spectral reconstruction may originate from in situ spectral measurements, bio-optical model simulations, or satellite observations. While in situ measurements (e.g., AERONET-OC) exhibit high credibility, their limited sample size and restricted coverage of water types hinder their ability to meet the large-scale dataset requirements of neural network training. Simulated reflectance from bio-optical models addresses data volume limitations but fails to account for sensor noise and atmospheric correction errors, reducing the generalization capability and robustness of trained models. Integrating considerations of data reliability, sample diversity, and model applicability, the use of quasi-synchronized LOS-WCS data as the DSR-NET training dataset is optimal. However, this approach faces the following limitations:

The spectral reconstruction process faces significant data imbalance across water categories, with approximately 50% of spectral data excluded during spatial feature matching due to insufficient coherence. Rejected samples predominantly originate from nearshore zones with strong vertical mixing, cloud/shadow-affected areas, and homogeneous open oceans lacking textural variation. The quasi-synchronized LOS-WCS dataset comprises 26% turbidity waters, 16% phytoplankton-dominated waters, and over 50% mixed Case-2 waters. Notably, algal bloom waters and extreme turbidity waters constitute a limited proportion of natural aquatic environments. The scarcity of spectral training samples for these optically extreme conditions, combined with the limited applicability of existing bio-optical models and atmospheric correction methods under high particle loads or algal biomass, significantly degrades DSR-Net’s accuracy in such environments. To enhance the generalizability and robustness of the DSR-Net model, it is necessary to expand the spectral sample library for extreme water color scenarios and develop new atmospheric correction methods with broad adaptability.

The precision of atmospheric correction critically determines DSR-Net accuracy, as atmospheric correction uncertainty dominates spectral reconstruction error budgets. Taking spectral band saturation and adjacency effects as examples, the former alters spectral shapes, increases spatial matching complexity, and leads to underestimation of reconstructed band reflectance; the latter systematically causes overestimation of blue-band reflectance in nearshore waters. Consequently, DSR-Net exhibits weaker performance in blue-band reconstruction, with a RMSE of approximately 7.01 × 10⁻³, significantly higher than those of red and green bands. Recent advances in mitigating land adjacency effects for Landsat-8/OLI and Sentinel-2/MSI atmospheric correction [49,50] offer promising pathways for future accuracy improvements. Additionally, sensor noise of LOS, comparable in magnitude to atmospheric correction errors, further exacerbates error accumulation. Although Section 4.3 has elucidated the propagation mechanisms of sensor noise and atmospheric correction errors, unresolved biases persist due to spatiotemporal mismatches, scale disparities (point vs. pixel observations), and divergent solar and satellite geometries between in situ and satellite datasets.

In summary, owing to the support of massive spectral datasets, DSR-Net’s spectral reconstruction no longer relies on spectral overlap, with accuracy primarily determined by the quality and scale of the quasi-synchronized spectral dataset. Even without a PAN band in Sentinel-2/MSI, the DSR-Net achieves band reconstruction at 620 nm, demonstrating accuracy comparable to Landsat-8&9/OLI. However, the black-box nature of neural networks currently limits the ability to systematically resolve the relationships among band quantity, observational precision, and reconstruction errors.

6. Conclusions

This study proposes DSR-Net, a deep residual neural network model for spectral reconstruction, aimed at addressing the limited spectral resolution of LOS in water monitoring. Results show that DSR-Net robustly reconstructs water color bands, increasing the number of reconstructed bands and improving reflectance accuracy.

A filtering method combining temporal threshold constraints and maximum cross-correlation analysis, along with bio-optical model-driven refinement, ensured spatiotemporal consistency in LOS-WCS datasets. This approach enhanced spectral quality, reducing errors in Sentinel-3 */OLCI products by 38% and lowering RMSE from 6.03 × 10⁻³ to 3.75 × 10⁻³. The resulting 60 million quasi-simultaneous spectra pairs provided a strong basis for model training in optically complex water environments.

The 32-layer residual convolutional architecture of DSR-Net accurately models nonlinear relationships between LOS and WCS bands. It achieves a 25–43% reduction in average RMSE after reconstruction, while effectively suppressing uncertainties from multiple error sources, including a 59% decrease in sensor noise-induced errors and a 38% reduction in atmospheric correction-related errors. Error analysis further indicates that most residual uncertainties in ρ_w originate from sensor noise and atmospheric correction, confirming the importance of comprehensive error handling. The model demonstrates stable reconstruction performance in various water environments, from turbid waters to phytoplankton-dominated systems, and consistently delivers spectral quality on par with or exceeding Sentinel-3/OLCI observations.

DSR-Net enables high-precision reconstruction of missing water color bands for Sentinel-2/MSI and Landsat-8&9/OLI, enhancing both accuracy and spectral dimensionality to meet the needs of advanced water color remote sensing applications such as cyanobacteria monitoring and CDOM inversion. Blue-band overestimation remains to be resolved through improved atmospheric correction. Future work should expand dataset diversity, integrate physical models with deep learning, and develop dynamic error compensation. Overall, DSR-Net provides a practical and innovative approach to LOS spectral reconstruction, supporting operational satellite applications and informing next-generation sensor design.