Advances in Dissolved Organic Carbon Remote Sensing Inversion in Inland Waters: Methodologies, Challenges, and Future Directions

Abstract

Inland waters, serving as crucial carbon sinks and pivotal conduits within the global carbon cycle, are essential targets for carbon assessment under global warming and carbon neutrality initiatives. However, the extensive spatial distribution and inherent sampling challenges pose fundamental difficulties for monitoring dissolved organic carbon (DOC) in these systems. Since 2010, remote sensing has catalyzed a technological revolution in inland water DOC monitoring, leveraging its advantages for rapid, cost-effective long-term observation. In this critical review, we systematically evaluate research progress over the past two decades to assess the performance of remote sensing products and existing methodologies in DOC retrieval. We provide a detailed examination of diverse remote sensing data sources, outlining their application characteristics and limitations. By tracing uncertainties in retrieval outcomes, we identify atmospheric correction, spatial heterogeneity, and model and data deficiencies as primary sources of uncertainty. Current retrieval approaches—direct, indirect, and machine learning (ML) methods—are thoroughly scrutinized for their features, effectiveness, and application contexts. While ML offers novel solutions, its application remains nascent, constrained by limited waterbody-specific samples and model constraints. Furthermore, we discuss current challenges and future directions, focusing on data optimization, feature engineering, and model refinement. We propose that future research should (1) employ integrated satellite–air–ground observations and develop tailored atmospheric correction for inland waters to reduce data noise; (2) develop deep learning architectures with branch networks to extract DOC’s intrinsic shortwave absorption and longwave anti-interference features; and (3) incorporate dynamic biogeochemical processes within study regions to refine retrieval frameworks using biogeochemical indicators. We also advocate for multi-algorithm collaborative prediction to overcome the spectral paradox and unphysical solutions arising from the single data-driven paradigm of traditional ML, thereby enhancing retrieval reliability and interpretability.

1. Introduction

Under the background of global carbon neutrality goals, dissolved organic carbon (DOC) in inland waters has become an important research subject for carbon assessment and carbon emissions. DOC in inland waters plays a critical role in global carbon cycling and global climate change. Approximately 40% of organic carbon is stored annually in inland reservoirs [1], with concentrations equivalent to 6–13% of marine organic carbon [2]. Inland rivers transport up to 400 million metric tons of organic carbon each year [3]. Statistical data indicate [4,5] that 25% to 44% of carbon in inland water bodies dominated by rivers, lakes, and reservoirs is emitted into the atmosphere as greenhouse gases. Under microbial and photochemical processes, DOC in water bodies becomes a net source of atmospheric carbon dioxide [6,7], and high DOC concentrations accelerate global warming. In turn, the positive feedback cycle of global warming further promotes biological and physicochemical changes in inland waters [8,9,10,11], altering DOC fate pathways and intensifying greenhouse gas emissions.

The DOC concentrations in inland waters directly affect drinking-water risks and water resource management difficulty [12,13,14]. When river water with high DOC concentrations recharges groundwater, oxidation products generated by bacterial oxidative processes significantly influence groundwater pH levels [15]. Particularly during drinking-water treatment, high DOC concentrations react with chlorine to produce substantial disinfection byproducts, increasing cancer risks [16]. Additionally, DOC in inland water bodies alters lake food web structures, exerting profound impacts on ecosystem functions and biodiversity [17].

The traditional approach for monitoring DOC in inland waters involves manual fixed-point sampling of water bodies followed by laboratory analysis. However, the distribution of inland waters is relatively scattered with extensive coverage, resulting in high sampling difficulty and prolonged sampling cycles. The dynamic processes of biogeochemical cycles persistently act upon inland water bodies, inducing spatiotemporally uncertain dynamic variations in DOC [18,19]. Traditional sampling methods are insufficient to accommodate the requirements of large-scale and long-term monitoring. Therefore, adopting advanced technologies to achieve accurate and high-frequency monitoring and assessment of inland water DOC concentrations constitutes a current imperative demand.

The variations in DOC concentration within water bodies influence the optical characteristics of dissolved organic matter, which provides a technical possibility for retrieving DOC through the responses of aquatic optical properties. However, the light absorption by DOC is relatively complex, with absorption spectra lacking characteristic peaks, resulting in often suboptimal practical application effectiveness. Colored dissolved organic matter (CDOM), the optically active component of DOC also termed “yellow substance” [20], exhibits strong absorption in ultraviolet and blue light spectral regions, demonstrating more sensitive aquatic optical responses. CDOM has emerged as an effective optical characteristic proxy for DOC inversion in specific rivers [21], lakes [22,23], and estuarine/coastal waters [24].

Remote sensing technology is a crucial method for measuring and analyzing the optical properties of water bodies. Its ability to rapidly acquire large-scale water quality data has made it a significant tool for studying DOC in inland waters, overcoming the limitations inherent in traditional ground-based monitoring methods [25,26,27,28,29]. This review analyzed the remote sensing literature on DOC in inland waters indexed in SCI-EXPANDED from 1 January 2005 to January 2025 through Web of Science. After deduplication and screening, the final dataset comprised 227 articles contributed by 1120 authors affiliated with 478 organizations across 47 countries. The top three productive nations were the United States (83 articles, 36.56%), China (70 articles, 30.84%), and Canada (33 articles, 14.54%). Global-scale research patterns and international collaborations are visualized in Figure 1, revealing distinct geographical distributions and cooperative networks within this scientific domain.

Among journals publishing more than five articles on the topic (

Table 1. Journals with more than 5 articles.

Source	Documents	Citation	Average Citation
Remote sensing	25	730	29.20
Remote Sensing of Environment	18	1332	74
Biogeosciences	11	380	34.54
Water Research	9	326	36.22
Science of the Total Environment	8	246	30.75
Journal of Geophysical Research: Biogeosciences	6	184	30.66
Water	6	114	19
International Journal of Applied Earth Observation and Geoinformation	5	84	16.8

), Remote Sensing ranked first in output (25 articles, 11.1% of total publications), followed by Remote Sensing of Environment (18 articles, 7.9%), both emphasizing satellite-based remote sensing for biogeochemical studies in inland waters and iterative advancements in DOC retrieval models. Keyword co-occurrence mapping (Figure 2) further reveals that remote sensing technology has emerged as a pivotal tool for DOC research in inland aquatic systems over the past decade, with thematic clusters highlighting its critical role in monitoring carbon cycling, water quality, and climate feedback mechanisms.

Although significant progress has been made in remote sensing technology for DOC monitoring, multiple technical bottlenecks persist in the accurate inversion of CDOM in inland waters. Inland water bodies exhibit more complex optical characteristics, where their radiative transfer processes are strongly influenced by total suspended matter (TSM) and phytoplankton [30,31]. As an important optically active constituent, the spectral signals contributed by CDOM are often obscured by the scattering noise from TSM and absorption signals from phytoplankton, rendering traditional water-color remote sensing methods constructed for Case I waters inapplicable for direct implementation [32,33,34]. Furthermore, regional variations in DOC sources and composition pose additional challenges to the generalizability of inversion methods [24]. The current remote sensing inversion of inland water DOC reveals several critical research gaps that urgently need to be addressed:

• How can the application effectiveness of remote sensing data in DOC inversion for inland waters be improved?
• How can robust DOC/CDOM remote sensing inversion methods suitable for inland waters with complex optical properties be developed?
• How can the professional efficacy of traditional machine learning in water quality inversion be specifically enhanced?

Consequently, conducting in-depth discussions to address these challenges and explore more transferable inversion methods with optimization strategies is crucial. This review synthesizes recent advances in remote sensing retrieval approaches for DOC in inland waters, systematically examines persisting technical challenges across methodological implementations, and critically discusses limitations and future priorities in current inversion frameworks. By integrating empirical findings and theoretical refinements, the analysis aims to offer guidance for next-generation DOC monitoring protocols while contributing actionable insights to advance evidence-based water resource governance and ecological conservation strategies.

2. Integration of Multi-Source Data and Uncertainty Provenance Analysis

Early ocean-color satellites prioritized sensors optimized for systematic monitoring of vast Case 1 waters, employing wide-swath scanning to achieve global coverage. Owing to lower concentrations of suspended particulates and dissolved organics, marine optical signals exhibit spectral simplicity, substantially reducing the complexity of water constituent retrieval and enabling standardized model development. The 1978 launch of the U.S. coastal zone color scanner (CZCS), the first dedicated ocean-color satellite, enabled the systematic mapping of global marine chlorophyll concentrations, culminating in the inaugural global ocean primary productivity atlas. Subsequent missions, including India’s IRS-P3 (1996), Japan’s ADEOS-1 (1996), and others with enhanced swath-width capabilities, further advanced observational frameworks (

Table 2. The world’s leading water-color remote sensing satellites [35,36,37,38].

Source	Satellite	Sensor	Number of Bands	Band Range (nm)	Spatial Resolution (m)	Temporal Resolution (Day)
Ocean-Color Sensors	Nimbus-7	CZCS	6	433–12,500	825	1–2
	IRS-P3	MOS	18	408–1600	500	5
	ADEOS-I	OCTS	12	402–125,00	700	41
	Terra (EOS AMI)	MODIS Terra	36	405–14,385	1000	1–2
	KOMPSAT-I	OSMI	6	400–900	850	28
	HY-1A	COCTS	10:04	402–12,500	1100:250	3
	HY-1A	CZI	10:04	420–890	1100:250	3
	ENVISAT	MERIS	15	412–1050	300/1200	3
	Myriade Series	PARASOL	9	443–1020	6000	16
	Oceansat	OCM-II	12	400–900	350/4000	2
	Sentinel-3A/B	OLCI	16	400–1040	300	2
	Himawari-9	AHI	16	450–13,400	500–2000	10 min
	NOAA-20	VIIRS	22	412–2250	375, 750	0.5
	HY-1C/1D	COCTS	10	402–12,500	1100	1
	GK-2B	GOCI-II	13	380–865	500	1 h
	EOS-06	OCM-3	13	400–1010	360	2
	PACE	OCI	200	340–890	1000	2
Inland/Coastal Water Sensors	Sentinel-2	MSI	13	443–2190	10, 20, 60	5
	HJ-1A/B	CCD	4	430–900	30	4
	Landsat-8, 9	OLI	11	433–12,510	15, 30, 100	16
	Planet	PlanetScope-2	8	455–860	3	1
	Trra, Aqua	MODIS	36	402–965 3660–14,338.5	250, 500, 1000	1–2
	SPOT-6/7	HRVIR	5	450–680	10, 20	26
	GF-5	AHSI	330	400–2500	30, 60	5–16

).

The late 20th-century emergence of global warming and carbon cycle research propelled ocean-color remote sensing into a pivotal role in quantifying marine carbon sinks. Long-term datasets from platforms such as NASA’s Terra/EOS AM-1 (1999), Korea’s KOMPSAT-I (1999), China’s HY-1A (2002), Argentina’s SAC-C (2000), ESA’s ENVISAT (2002), and France’s Myriade Series (2004) became indispensable for modeling marine primary productivity and carbon flux dynamics. Post-2000, the global carbon neutrality imperative shifted scientific attention to inland aquatic carbon sinks. However, kilometer-scale resolutions of traditional ocean-color satellites prove inherently incompatible with the fine-grained spatial heterogeneity of inland systems (e.g., rivers) [39,40]. This spatial-scale discordance—compounded by complex inland optical properties—has prompted the deployment of land/coastal sensors with enhanced spatial resolution (e.g., 10–30 m) and spectrally tailored radiometric capabilities for inland water monitoring.

2.1. Satellite–Air–Ground Synergistic Observation

High-resolution land-focused satellites (e.g., Landsat OLI, Sentinel-2 MSI) with 10–30 m spatial resolution enable the spatial differentiation of dissolved organic carbon (DOC) in medium-sized lakes [41,42,43,44,45,46,47,48]. However, their utility in high-frequency continuous monitoring is constrained by extended revisit cycles (5–16 days) and persistent cloud interference—for instance, data availability for Sentinel-2 in southern China falls below 20% [49]. High-frequency satellites like Terra/Aqua MODIS (1–2-day revisit) partially offset temporal resolution limitations, but their coarse spatial resolution and broad spectral bandwidths necessitate the integration of boundary-bandwidth correction models for radiometric optimization [50,51]. While HJ-1A/B CCD satellites offer high spatiotemporal resolution suitable for small-lake CDOM monitoring [52], their limited spectral resolution risks feature loss, requiring ground-truth data for spectral interpretation [53,54]. Commercial platforms (e.g., Planet, 3 m resolution), driven by market forces, prioritize high spatial and temporal resolution imagery as their core competitive edge. While this endows them with exceptional spatial identification capabilities for small-scale river monitoring, the inherent trade-off between spectral and spatial resolution necessitates substantial compromise in spectral resolution to maintain adequate image signal-to-noise ratios. As a result, critical UV absorption peaks (200–400 nm) from aromatic compounds and conjugated double-bond organics in DOC remain undetectable due to the limited spectral resolution of commercial systems, leading to the loss of key spectral fingerprints for DOC characterization [34].

A comprehensive analysis of inland/coastal-water-satellite-based studies concerning inland waters CDMO/DOC, spanning records from the inception of the Web of Science through 2025, was undertaken (articles failing retrieval criteria were manually screened out), as shown in Figure 3.

The Landsat 8/9 and Sentinel-2 satellites exhibit the most widespread application, attributable to their quantitatively superior numbers of spectral bands and broader band ranges. The Terra and Aqua satellites, constrained by their lower spatial resolutions, are primarily suitable for large-scale estuarine and extensive lacustrine studies. The very coarse spatial resolution of Planet satellites significantly increases computational complexity when applied to large estuaries, though they remain appropriate for river and lake investigations [55].

Table 3. Typical application cases of remote sensing data sources in inland waters.

Case	Study Area	Overview
[56]	River basins and coastal areas from the Rajang River	Using Landsat-8 data to construct band ratio combinations, perform regression based on in situ DOC, validate the model with three verification methods (simple grouping, K-fold analysis, and bootstrap), and estimate the DOC flux from April 2013 to December 2018 by using the constructed regression model (R2 = 0.88, MAPE = 5.71%) and river discharge.
[57]	Erhai Lake	A CDOM prediction model was constructed using empirical methods based on Aqua satellite imagery and insitu measured data. The model was then used to invert the CDOM changes across the entire lake from 2013 to 2019.
[43]	Small water surface reservoirs in the Brazilian semiarid region	Based on Landsat-8 imagery and RapidEye commercial satellite imagery, a CDOM model was constructed. The results showed that the green band of Landsat-8 performed better (R2 = 0.69 vs. RapidEye: R2 = 0.25), especially for non-perennial reservoirs with high CDOM concentrations and without optical interference from phytoplankton.
[41]	Ganh Hao River	The MLR model developed from Sentinel-2 data demonstrated stable performance (comprehensive error value = 0.66, 0.53) across both water body types (Class 1: low aCDOM (412), Class 2: medium to high aCDOM (412)), while the Landsat-8-based MLR model achieved the highest accuracy (value = 0.15) in Class 1 but showed significant performance degradation in Class 2 (value = 0.46).

presents typical application cases of remote sensing data sources in inland waters.

The spatial, temporal, and spectral configurations of sensors impose significant constraints on inland water research. Particularly with the growing demand for high-frequency dynamic monitoring in turbid, optically complex waters, the limitations of single-platform systems in terms of observation continuity and data utility have become increasingly apparent, highlighting the urgent need to develop an integrated multi-source data framework.

To overcome single-sensor constraints, satellite–air–ground synergistic frameworks are emerging as a paradigm [58,59,60]. Spatially, drone-borne hyperspectral systems (decimeter-scale resolution) resolve DOC concentration gradients in rivers [61,62,63], circumventing the pixel-mixing artifacts endemic to satellite data [64,65,66]. Temporally, when short-term extreme rainfall or snowmelt events flush terrestrial organic matter (e.g., litter, livestock manure, fertilizer residues) into water bodies as dissolved organic carbon (DOC), traditional single-platform sampling frequencies often fail to capture these event-driven DOC pulses. Models built without such high-frequency data cannot accurately reflect real conditions, compromising subsequent analytical results. Therefore, implementing sub-second sampling with near-surface hyperspectral imagers enables the effective capture of DOC fluctuations following ultra-short-term events [67]. This provides critical data support for optimizing sampling frequencies and algorithm design, making monitoring and analytical methods more adaptable to complex and dynamic environmental conditions. Simultaneously, this approach allows for the effective monitoring and management of explosive “black water “ events to avoid ecological catastrophes [68].

The benefits of this synergistic framework rely on a range of advanced technologies. For instance, Sentinel-2 MSI’s enhanced radiometric sensitivity (e.g., Band 1 at 443 nm) successfully retrieves blue-violet signals in high-CDOM waters [69]. Spatiotemporal fusion algorithms (e.g., STARFM) harmonize multi-resolution datasets to achieve continuous coverage [70,71], complemented by tri-level validation networks (satellite-UAV-ground spectrometers) on the Google Earth Engine (GEE) platform for automated data matching and consistency assessment [60,72].

2.2. Uncertainty Provenance

Uncertainty in DOC remote sensing retrieval arises from coupled errors across the processing chain [73,74], with atmospheric correction being the dominant factor for inland waters [75,76]. The optical complexity of these systems—shaped by anthropogenic activities (e.g., industrial discharge, agricultural runoff, shipping disturbances) and heterogeneous topography (e.g., mountainous closed basins, estuarine deltas)—generates terrestrial aerosol-dominated atmospheres (enriched with organic carbon and minerals) [77]. These aerosols, compounded by strong absorption from waterborne CDOM and non-algal particles (NAP, e.g., sediments, humus) in near-infrared (NIR) bands [78], invalidate core assumptions of marine-oriented atmospheric correction models (e.g., FLAASH). For instance, post-correction blue-violet band reflectance in highly turbid, CDOM-rich inland waters often falls ≤ 0 [79,80], highlighting systemic model failures.

Targeted atmospheric correction strategies are, thus, critical for inland aquatic systems [79,81,82]. While some studies bypass correction by directly modeling raw imagery [80], such approaches lack universality due to regional environmental dependencies. Pioneering work by Fan et al. [83] demonstrated the efficacy of multilayer neural networks in correcting turbid water atmospheres, offering a scalable framework for inland applications [75,84]. Hardware advancements, such as Sentinel-2 MSI’s enhanced radiative sensitivity and signal-to-noise ratio, further mitigate detection challenges for blue-violet band water-leaving radiance [69].

Spatial heterogeneity exacerbates uncertainty. Low-resolution sensors (e.g., MODIS) underestimate DOC biogeochemical gradients in inland waters due to scale mismatch [40]. For small-scale features (e.g., river meanders, lake margins), dynamic resolution selection and linear spectral mixture analysis (LSMA) are essential to disentangle land-water mixed signals [85].

Data and model structural limitations compound errors [86,87]. SPOT HRVIR’s high inter-band correlation (R² = 0.92–0.99) reduces sensitivity to inland reservoir DOC variability [88]. GF-5’s hyperspectral capability remains underutilized due to limited historical data (launched 9 May 2018), restricting its application to pilot studies [89,90]. To enhance reliability, recent efforts focus on model architecture innovation. This review systematically categorizes existing models’ developmental trajectories, technical merits, and constraints (summarized in

Table 4. Comparison of sources of uncertainty.

Error Source	Atmospheric Correction	Spatial Heterogeneity	Model/Data Deficiencies
Impact Nature	Fundamental, systemic errors	Regional, scale-dependent errors	Algorithmic or structural limitations
Correctability	Requires ground validation + advanced algorithms	High-resolution data + spectral unmixing	Model optimization + data fusion
Directness on DOC Retrieval	Directly determines spectral fidelity	Indirectly affects pixel purity	Dependent on input data quality + model architecture

), providing a roadmap for next-generation high-fidelity DOC retrieval frameworks.

3. Optical Principles and Methods of DOC Remote Sensing Retrieval

3.1. Optical Foundations of DOC Remote Sensing Retrieval

The principle of DOC remote sensing inversion is primarily grounded in the coupling relationship between aquatic optical properties and radiative transfer mechanisms (Figure 4).

Specifically, the water-leaving radiance formed through solar radiation undergoing surface reflection, in-water scattering/absorption, and transmission processes penetrates the atmosphere to be captured by spaceborne sensors. The DOC remote sensing inversion is achieved through the extraction and processing of remote sensing information. The complete inversion workflow comprises three core stages: First, radiometric calibration converts raw digital number values into absolute radiance quantities; subsequently, regionally applicable atmospheric correction algorithms for inland waters are employed to isolate water-leaving radiance; and ultimately, based on corrected water surface reflectance spectra, regression models or bio-optical models incorporating DOC concentration or absorption characteristics are established to achieve the spatiotemporal inversion of DOC concentrations.

3.2. Validation and Evaluation

In model validation and evaluation, methods such as independent sample validation, K-fold cross-validation, and leave-one-out cross-validation are commonly employed [43,56,57]. For machine learning models, training and test sets are partitioned according to industry conventions like 7:3 or 8:2 [91]. Under the premise of ensuring the training set covers sufficient spectral features, an independent test set is utilized to quantify the model’s generalization error. During cross-sensor validation, band matching is accomplished through the spectral response function (SRF): Measured hyperspectral data are convolved with the target sensor’s SRF, converted into the corresponding satellite band reflectance characteristics, and then input into the inversion models to verify cross-platform applicability. The spectral response function (SRF) is given by Equation (1).

$${\mathrm{B}\mathrm{a}\mathrm{n}\mathrm{d}}_{\mathrm{i}}={\displaystyle \frac{{\int }_{{\mathsf{\lambda }}_{\mathrm{m}\mathrm{i}\mathrm{n}}}^{{\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}}\mathrm{S}\mathrm{R}\mathrm{F}\left(\mathsf{\lambda }\right){\mathrm{R}}_{\mathrm{r}\mathrm{s}}\mathrm{d}\mathsf{\lambda }}{{\int }_{{\mathsf{\lambda }}_{\mathrm{m}\mathrm{i}\mathrm{n}}}^{{\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}}\mathrm{S}\mathrm{R}\mathrm{F}\left(\mathsf{\lambda }\right)\mathrm{d}\mathsf{\lambda }}}$$

(1)

${\mathrm{B}\mathrm{a}\mathrm{n}\mathrm{d}}_{\mathrm{i}}$ represents the equivalent band of the remote sensing satellite, where ${\mathsf{\lambda }}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ and ${\mathsf{\lambda }}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ are the boundary wavelengths of band i, and $\mathrm{S}\mathrm{R}\mathrm{F}\left(\mathsf{\lambda }\right)$ is the spectral response of the i-th band of the sensor at wavelength $\mathsf{\lambda }$.

The performance evaluation of remote sensing inversion models is typically based on metrics such as R², MAE, RMSE, and bias. Here, R² reflects the model’s explanatory power for the variance in DOC concentration, MAE quantifies the average deviation of the retrieved values, RMSE is sensitive to errors from extreme values, and bias reveals the model’s systematic tendency towards overestimation or underestimation. The commonly used performance evaluation metrics for remote sensing inversion models and their corresponding model explanatory power are presented in the

Table 5. Main performance metrics and model explanatory power for remote sensing DOC inversion.

Evaluation Metrics	Formula	Correlation with Error
R2	$1-{\displaystyle \frac{{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{y}}_{\mathrm{i}}-{\tilde{\mathrm{y}}}_{\mathrm{i}})}^2}{{{\sum }_{\mathrm{i}=1}^{\mathrm{n}}({\mathrm{y}}_{\mathrm{i}}-{\overline{\mathrm{y}}}_{\mathrm{i}})}^2}}$	A higher R2 value indicates a smaller sum of squared deviations between predicted and measured values relative to the total variance, reflecting a lower overall error level of the model.
MAE	${\displaystyle \frac{1}{\mathrm{n}}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}}\left|{\mathrm{y}}_{\mathrm{i}}-{\tilde{\mathrm{y}}}_{\mathrm{i}}\right|$	The smaller the MAE, the smaller the average absolute error of the retrieved values, indicating better prediction stability of the model in regions with gradual water gradients.
RMSE	$\sqrt{{{\displaystyle \frac{1}{\mathrm{n}}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}}({\mathrm{y}}_{\mathrm{i}}-{\tilde{\mathrm{y}}}_{\mathrm{i}})}^2}$	A larger RMSE indicates poorer model performance in handling extreme values or anomalous scenarios, where retrieved results potentially exhibit greater variability, and it is effective for identifying extreme scenarios such as estuaries and algal bloom areas.
Bias	${\displaystyle \frac{1}{\mathrm{n}}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}}({\mathrm{y}}_{\mathrm{i}}-{\tilde{\mathrm{y}}}_{\mathrm{i}})$	A large absolute bias value may result from the model’s omission of atmospheric correction or radiative transfer losses, inducing systematic deviations in retrieved results; this can be addressed by refining the model with physical priors.
MAPE	${\displaystyle \frac{100\%}{\mathrm{n}}}{\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{n}}}\left|{\displaystyle \frac{{\mathrm{y}}_{\mathrm{i}}-{\tilde{\mathrm{y}}}_{\mathrm{i}}}{{\mathrm{y}}_{\mathrm{i}}}}\right|$	A MAPE of 0% indicates a perfect model. The smaller the MAPE value, the better the accuracy of the prediction model.

note: $y_i$ is the measured value for sample i; ${\tilde{y}}_i$ is the retrieved value of the model; ${\overline{y}}_i$ is the mean of measured samples.

.

3.3. Direct Inversion Methods for Remote Sensing of DOC and Physical Drivers of Their Accuracy

3.3.1. Direct Retrieval Method for DOC Remote Sensing: Spectral Matching and Concentration Quantification

The technical framework of the direct inversion method comprises three core procedures: (1) collecting spatially representative DOC in situ measurement data; (2) synchronously acquiring remote sensing imagery and extracting spectral characteristics of target water bodies (e.g., band reflectance, band ratios, or spectral indices); and (3) developing inversion equations through correlation analysis and regression modeling. As one of the earliest methodological frameworks in DOC remote sensing, Chen and Shi (2001) [92] pioneered a multivariate linear model (Equation (2)) leveraging 130 simulated spectral datasets to invert DOC concentrations from optimal band combinations of reflectance.

$$\mathrm{l}\mathrm{o}\mathrm{g}\left(\mathrm{D}\mathrm{O}\mathrm{C}\right)=1.2419\mathrm{l}\mathrm{o}\mathrm{g}(\mathrm{R}670/\mathrm{R}412)-0.2614$$

(2)

Hirtle and Rencz [80] employed Landsat ETM+ Band 2 to establish a logarithmic model for DOC (log(DOC)) in Nova Scotia lakes (${\mathrm{R}}^2=0.72$), but it was not applicable to Finnish lakes with high DOC concentrations (>18.3 mg/L) [93], revealing the regional dependency limitation of the model. Recently, Chunhock et al. [56], through conducting a comparative analysis of 24 river DOC inversion models, identified that the exponential function model utilizing the Landsat-8 OLI B4/B3 band combination (Equation (3)) demonstrated optimal accuracy, though its applicability remains constrained to low-turbidity river systems.

$$\mathrm{D}\mathrm{O}\mathrm{C}=89.86{\mathrm{e}}^{\mathrm{B}4/\mathrm{B}3}$$

(3)

3.3.2. Physically Driven Factors Governing the Accuracy of Direct Inversion Methods

While direct methods demonstrate operational simplicity, their inversion accuracy faces inherent limitations. CDOM, constituting 10–90% of DOC [94,95,96], dominates spectral signals through its ultraviolet-visible absorption characteristics. However, non-chromophoric constituents such as carbohydrates and amino acids remain spectrally undetectable due to optical inertness, resulting in scale decoupling between spectral signatures and DOC concentrations as remote sensing signals only capture partial DOC components. This decoupling is partially mitigated in estuarine and coastal waters under single-salinity-driven mixing regimes, manifesting dual conservative mixing behavior through coupled “DOC-salinity” and “CDOM-salinity” relationships. As a hydrological tracer of river-ocean mixing, salinity-mediated dual conservation reflects characteristic conservative mixing patterns between terrestrial and marine water masses [97,98,99]. In major Arctic and subarctic rivers, including the Ob, Yenisei, and Yukon, CDOM and DOC exhibit robust, high-correlation relationships [99]. This strong covariation arises from their proximity to polar regions, where runoff and precipitation drive substantial inputs of terrestrial carbon from organic-rich soils [100], sustaining tightly coupled CDOM–DOC dynamics with minimal influence from biogeochemical alterations [101,102].

Table 6. Regional robust relationship and R² between CDOM and DOC.

Number	CDOM–DOC	R2	Reference
1	$\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}=0.6054+0.4939·\mathrm{D}\mathrm{O}\mathrm{C}$	0.86	[103]
2	$\ln \mathrm{D}\mathrm{O}\mathrm{C}=\mathsf{\alpha }+\mathsf{\beta }\ln \mathrm{a}\mathrm{g}\left(275\right)+\mathsf{\gamma }\ln \mathrm{a}\mathrm{g}\left(295\right)$	/	[104]
3	$\mathrm{D}\mathrm{O}\mathrm{C}=55+357·{\mathrm{a}}_{\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}}\left(443\right)$	/	[105]
4	$\mathrm{D}\mathrm{O}\mathrm{C}=245+171·{\mathrm{a}}_{\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}}\left(443\right)$	/	[106]
5	${\mathrm{a}}_{\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}}\left(440\right)=0.5·\mathrm{D}\mathrm{O}\mathrm{C}-1.52$	0.95	[107]
6	$$\begin{gathered} \mathrm{D}\mathrm{O}\mathrm{C}=32.942·{\mathrm{a}}_{\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}}\left(412\right)+95.587 \\ \mathrm{D}\mathrm{O}\mathrm{C}=95.519·{\mathrm{a}}_{\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}}\left(412\right)+78.795 \\ \mathrm{D}\mathrm{O}\mathrm{C}=213.34·{\mathrm{a}}_{\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}}\left(412\right)+38.044 \end{gathered}$$	0.78 0.81 0.72	[108]
7	DOC = 2.13 + 1.24 × (CDOM)	0.84	[109]
8	$\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}=1.593\mathrm{D}\mathrm{O}\mathrm{C}-2.453$	0.88	[46]
9	$\mathrm{D}\mathrm{O}\mathrm{C}=1.268{\mathrm{a}}_{\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}}\left(440\right)+3.623$	0.76	[44]
10	$\mathrm{D}\mathrm{O}\mathrm{C}=2.351+92.515{\mathrm{c}}_{\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}}$	0.873	[110]
11	${\mathrm{c}}_{\mathrm{D}\mathrm{O}\mathrm{C}}=\mathsf{\alpha }+\mathsf{\beta }·{\mathrm{a}}_{250}+\mathsf{\gamma }·{\mathrm{a}}_{365}$	/	[111]
12	${\mathrm{c}}_{\mathrm{D}\mathrm{O}\mathrm{C}}=59.1{\mathrm{c}}_{\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}}$	0.74	[112]
13	$\mathrm{D}\mathrm{O}\mathrm{C}=1.89+0.78{\mathrm{a}}_{\mathrm{C}\mathrm{D}\mathrm{O}\mathrm{M}}\left(443\right)$	0.73	[113]

compiles representative CDOM–DOC relationships with associated R² values observed across these river and other water systems.

However, in the vast majority of rivers and inland water bodies, DOC–CDOM relationships exhibit diminished conservatism due to complex interactions involving photochemical degradation, heterogeneous terrestrial inputs, and microbial transformations [99]. For instance, subtropical rivers draining intensively managed agricultural watersheds (e.g., the Pearl River) display pronounced seasonal DOC–CDOM decoupling driven by accelerated microbial processing under high-temperature, high-humidity conditions [114,115,116,117], with variability exceeding that observed in temperate systems like the Yangtze River [118]. The high organic matter load of anthropogenic origin in the Nile River in Africa leads to the highest DOC concentration in autumn [119]. The Mississippi River demonstrates disrupted correlations due to autochthonous CDOM production from active phytoplankton blooms [120,121]. As a lowland river, the Murray is perennially influenced by floods. Following flood inundation, substantial phytoplankton and carbon are delivered to the Murray River, resulting in an extremely unstable correlation between CDOM and DOC [122,123]. Tidal modulation further complicates estuarine DOC dynamics, where concentrations may exhibit positive or negative correlations with tidal height depending on upstream terrestrial inputs [124] or hydraulic retention time [125]. While river discharge generally governs DOC dilution/transport, producing discharge–concentration correlations [126,127], these relationships become statistically insignificant under complex hydrological regimes [128]. Notably, DOC accumulation in mesohaline zones has been documented in nutrient-enriched inland waters [129]. Such multifaceted nonlinear behaviors collectively undermine CDOM–DOC correlations, representing a pervasive challenge across inland aquatic systems.

3.4. DOC Remote Sensing Indirect Inversion Method: Cross-Media Inference via Robust CDOM–DOC Relationships

Indirect DOC retrieval hinges on establishing cross-media predictive relationships between DOC and CDOM by leveraging the latter’s optical activity, contingent upon their statistically robust correlation (Table 3). Fichot and Benner (2011) [104] developed a multiple linear regression (MLR) model using CDOM absorption coefficients at 275 nm and 295 nm across diverse global water bodies, achieving a minimal DOC retrieval error of 4.2%. However, Asmala et al. [130] identified multicollinearity among predictors (VIF > 10) in this model during validation in three Finnish rivers, proposing, instead, a simple linear regression (SLR) model based solely on 355 nm absorption to enhance robustness. Optimizing regression architecture is critical for cross-media inference accuracy. In Eutrophic Lake Ebinur (China), comparative analyses of linear, quadratic, exponential, and logarithmic models revealed the superior performance of linear regression (R² > 0.74 vs. R² < 0.72 for nonlinear models) [112], likely attributable to the salinity-mediated enhancement of linear CDOM–DOC coupling.

3.4.1. Semi-Empirical Method for CDOM: From Spectra to CDOM

CDOM retrieval from remote sensing reflectance (Rrs) predominantly employs empirical methods supplemented by semi-analytical optical parameterizations. A standard workflow is as follows: Based on the spectral absorption curve, the combination of sensitive multispectral satellite bands is selected to establish a statistical model of a_CDOM (the absorption coefficient of CDOM, which is often used to characterize CDOM concentration). For instance, the Kolyma River study [103] employed Landsat TM/ETM+ band ratios (Band 3 and Band 2/Band 1) to construct a linear regression model, yet the maximum accuracy reached only R² = 0.7832, which exposes the insufficient spectral resolution of broadband sensors in resolving characteristic absorption peaks of CDOM. Lai et al. [94] used Landsat B1/B3 ratios for CDOM estimation (R² = 0.82), subsequently deriving DOC concentrations via CDOM–DOC correlations with RMSE = 0.65 m⁻¹ and MSE = 10.9%. Its performance is constrained by two critical bottlenecks:

• Model rigidity: Traditional least squares regression relying on static parameters (e.g., fixed band weights) struggles to adapt to spatiotemporal heterogeneity of water inherent optical properties (IOPs) [30,103,131].
• Error propagation: The “two-step” indirect inversion pathway (Rrs → a_CDOM → C_DOC) induces nonlinear amplification of errors. In the Kolyma River case [103], DOC inversion standard errors increased from ±0.92 mg L⁻¹ at the CDOM stage to ±1.68 mg L⁻¹, representing an 82.6% error escalation.

While empirical frameworks partially incorporate IOPs, their reliance on heuristic band ratios neglects the explicit modeling of IOP component interactions (e.g., phytoplankton vs. non-algal particle absorption-scattering coupling), fundamentally limiting model generalizability.

3.4.2. Analytical Method: From Spectra to CDOM

Analytical methods offer broader applicability compared to empirical frameworks. Rooted in radiative transfer theory, these methods derive absorption and backscattering coefficients through rigorous analytical solutions. However, practical implementation remains challenging due to multiple scattering and optical heterogeneity in natural waters [132]. Semi-analytical methods bridge this gap by coupling radiative transfer equations with empirical parameterizations, preserving physical interpretability while ensuring computational feasibility. These approaches demonstrate superior parameter retrieval accuracy and generalizability over traditional empirical models [133,134]. Current mainstream semi-analytical algorithms include the quasi-analytical algorithm (QAA) [135]; the Garver–Siegel–Maritorena (GSM) algorithm [136,137]; and the generalized inherent optical Properties (GIOP) algorithm [138,139].

The widely used QAA_v6 [140] and QAA_CDOM [133,141] algorithms excel in ocean-color applications but exhibit limitations in turbid inland waters. High suspended sediment loads induce multiple scattering and terrestrial signal interference, leading to significant errors in inherent optical property (IOP) retrievals [142]. For instance, Pan et al. [143] reported an RMSE = 1.39 m⁻¹, when applying QAA to hypereutrophic Lake Taihu. Recent advancements focus on algorithm customization: Wang et al. [144] recalibrated QAA empirical equations using in situ data, developing the QAA_cj variant for highly turbid estuaries (RMSE < 1.12 m⁻¹). Le et al. [145] proposed a phytoplankton absorption coefficient separation algorithm for Taihu Lake water bodies, successfully decoupling chlorophyll and CDOM absorption signals (similarity coefficient S = 0.97 between separated and measured spectra). However, spectral aliasing effects between CDOM and suspended particulate matter (SPM) in the blue spectral region (400–500 nm) still lead to residual spectral confounding errors (RMSE) in inversion. Notably, recent research in China’s Yangtze River Estuary [146] introduced machine learning techniques, utilizing a backpropagation neural network to establish a nonlinear mapping model between the backscattering coefficient of suspended particles (b_bp) and the hybrid absorption coefficient a_p (sum of phytoplankton absorption coefficient a_ph and non-algal particle absorption coefficient a_dg). This data-driven approach effectively enhances the physical consistency of CDOM concentration retrieval.

Critical improvements for QAA in inland waters involve (1) the localized calibration of empirical parameters and sub-equations within QAA architectures [140,147,148,149,150,151,152], and (2) reference wavelength optimization [153]. The standard optical assumptions at default reference wavelengths (e.g., 670 nm) in QAA_v6 and QAA_CDOM algorithms mismatch actual inland water conditions dominated by elevated CDOM absorption and SPM scattering. This discrepancy necessitates dynamic wavelength adjustments tailored to site-specific water composition and constituent gradients. Empirical studies demonstrate that shifting reference wavelengths from the conventional 670 nm to 740 nm (e.g., turbid inland waters in Northeast China) [154] or near-infrared bands (e.g., Lake Taihu [155] and Chinese turbid inland lakes [156]) enhances water column penetration depth and mitigates suspended particulate interference, thereby significantly improving QAA’s retrieval stability in eutrophic waters.

The GSM and GIOP frameworks employ distinct mathematical approaches for deriving CDOM absorption coefficients: GSM utilizes nonlinear equations, while GIOP relies on eigen-based matrix inversion techniques. Since GSM uses nonlinear equations to derive optical parameters such as the absorption coefficients of substances in water bodies, it is highly dependent on prior spectral libraries. It needs to rely on laboratory and in-situ measurement differences to construct accurate and comprehensive spectra covering CDOM, phytoplankton, and suspended particulate matter, so as to enable the GSM model to have better adaptability in different types of water bodies (such as oceans, lakes, and rivers). In applied research, Matsuoka et al. [157] successfully applied the GSM model to estimate CDOM absorption in coastal waters, achieving DOC retrieval through robust CDOM–DOC correlations (R² = 0.97). However, its efficacy in inland DOC estimation remains unvalidated due to complex optical interference. Salama et al. [158] modified the GSM model while obtaining the spectral dependence of inland waters, addressing the limitation that GSM is limited to the ocean. Both GSM and QAA exhibit significant performance degradation at high solar zenith angles [159], necessitating enhanced atmospheric correction protocols. To mitigate this, Xu et al. [160] developed a spherical-shell atmospheric vector radiative transfer model using Monte Carlo simulations, explicitly accounting for Earth curvature effects under extreme illumination conditions.

GIOP offers superior flexibility through a dynamic selection of phytoplankton absorption models (e.g., Bricaud’s formulation vs. exponential decay) and region-specific parameter optimization [135,139,161,162]. Despite this adaptability, GIOP generally underperforms in retrieval accuracy compared to QAA and GSM. A comparative study in eastern New Caledonia lagoons revealed GIOP’s inferior precision [142], relegating it to niche applications despite its theoretical versatility.

Table 7. Comparative advantages and constraints of QAA, GSM, and GIOP.

Model	Core Advantages	Applicable Inland Water Types	Operational Constraints
QAA	Lowest computational complexity, extremely fast processing speed Fully transparent and traceable inversion process (no optimization black box)	Clean lakes Low-to-moderate turbidity reservoirs Low-flow rivers	Low-to-medium SZA (sensitive to angle changes) Multispectral bands Low computational resource demand
GSM	Capable of rapid estimation in highly turbid waters	Estuarine mixing zones High-sediment rivers Eutrophic shallow lakes	Low-to-medium SZA Multispectral bands Iterative computation required, high computational resource demand
GIOP	Multi-component IOPs spectral resolution capability Customizable parameterization schemes with high flexibility for complex optical properties	Urban polluted waters Heavily eutrophic lakes Algal bloom-dominated waters	Medium-to-high SZA Hyperspectral data High-iteration computation, high computational resource demand

summarizes the core advantages and application limitations of QAA, GSM, and GIOP.

Although analytical methods have explicitly modeled IOPs compared to empirical frameworks, the generalization capabilities of algorithms such as QAA, GSM, and GIOP across water bodies are still constrained by drastic fluctuations in substance concentrations across different water areas. Introducing mass-specific inherent optical properties (MSIOPs) can mitigate the interference of substance concentration fluctuations on optical signals. For example, a*_CDOM quantifies the CDOM absorption capacity per unit mass of DOC, while b*_bbp uniformly characterizes the specific scattering efficiency of particulate matter. De Stefano et al. [163] discovered through Gaussian decomposition that there is a strong nonlinear relationship between the a₂₇₀:a₃₂₀ ratio and DOC-specific absorption coefficient a*₃₅₅ (a(355)/DOC) and a*₄₄₀ (a(440)/DOC). The constructed model achieved favorable results in both deep and shallow lakes (with high R² and MAPD < 16%).

3.5. Enhanced Strategies for Nonstationary CDOM–DOC Relationships

In aquatic systems, CDOM and chlorophyll-a concentrations typically exhibit a weak correlation [164,165]. In contrast, DOC (dissolved organic carbon) demonstrates significant sensitivity to phytoplankton dynamics [166] and increases markedly with algal proliferation during eutrophication [167]. When chlorophyll-a concentration exceeds 0.8 μg/L, biological processes—such as algal growth and mortality—dominate DOC gradient variations. The extracellular products secreted (EPS) during vigorous algal growth and photosynthetic byproducts are predominantly low-molecular-weight colorless compounds. This causes an imbalance between the proportion of DOC components released by algae and CDOM, disrupting the DOC–CDOM correlation typically formed in natural waters from similar sources (e.g., terrestrial input and microbial metabolism). Conversely, when chlorophyll-a concentration falls below this threshold, abiotic processes dominate, and the DOC–CDOM correlation reemerges. To address this biological decoupling phenomenon, Liu et al. [99] developed a dual-mode inversion framework. This framework employs a “conservative mixing” model to describe the linear relationship between DOC and CDOM under low chlorophyll-a conditions and utilizes a “biological disturbance” model to quantify the impact of biological processes on DOC variability during algal blooms. This approach adaptively resolves the challenge of DOC dynamics across different trophic states.

Beyond biological disturbances, photochemical processes additionally impair CDOM’s capacity as a DOC proxy. Photodegradation (photobleaching), defined as the photochemical mineralization of dissolved organic matter under solar radiation, intensifies substantially in highly irradiated shallow inland waters. Within these systems, aromatic conjugated structures in CDOM experience accelerated cleavage through direct photolysis or indirect photo-oxidation mechanisms. Simultaneously, macromolecular humic substances decompose into low-molecular-weight organic acids, fundamentally restructuring their optical characteristics and critically compromising CDOM’s reliability for DOC estimation.

Furthermore, given photodegradation’s minimal influence on visible band absorption (>380 nm), retrieval models dependent on this spectral range cannot detect photolytic alterations in CDOM, thereby introducing systematic biases. Conversely, CDOM’s ultraviolet-band optical properties demonstrate heightened sensitivity to photodegradation. Specifically, the attenuation rate of a_CDOM(380) (indicative of conjugated double-bond systems) significantly exceeds that of a_CDOM(275) (representing phenolic structures). This differential degradation elevates the spectral slope S_275–295, enabling its application as an optical tracer for monitoring CDOM compositional transformation. The Yangtze River Estuary model [168] incorporated the spectral slope S_275–295 as a characteristic parameter into the CDOM–DOC derivation methods, resolving non-conservative mixing issues between CDOM and DOC, with the correlation coefficient increased to R² = 0.746. Danhiez et al. [169] achieved enhanced DOC retrieval accuracy by synergistically integrating S_275–295 and S_320–412 into inversion models. Monsoon-driven observations reveal distinct CDOM dynamics: elevated high-molecular-weight fractions with lower S_280–500 during monsoon seasons, contrasting sharply with post-monsoon dominance of low-molecular-weight CDOM and higher S_280–500 [170]. In regions where stable statistical correlations between DOC and CDOM are lacking, integrating biogeochemical process indicators into remote sensing inversion frameworks offers a promising pathway to enhance model robustness.

3.6. Machine Learning-Driven DOC Retrieval

Recent advances in machine learning (ML) techniques—including neural networks, support vector machines, random forests, and deep learning—have demonstrated significant potential for DOC estimation by leveraging their capacity to model nonlinear relationships and fuse multisource data. Unlike conventional empirical approaches, ML models dynamically synthesize multispectral imagery, meteorological parameters, and environmental variables, autonomously extracting complex feature associations to map spatiotemporal DOC distributions (Figure 5). Key strengths lie in automated data processing, adaptive model optimization, and the resolution of nonlinear interactions.

Early applications focused on CDOM estimation, with backpropagation (BP) neural networks outperforming traditional band-ratio models through multidimensional inputs and robust fitting [171]. Random forest (RF) algorithms addressed single-model biases by aggregating decision trees, achieving reliable CDOM retrievals in Chinese inland lakes [172]. XGBoost further advanced robustness by integrating regularization to mitigate overfitting, demonstrating superior performance in the Songhua River $({\mathrm{R}}^2=0.89,\mathrm{t}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{d}\mathrm{a}\mathrm{t} {\mathrm{R}}^2=0.85)$ [113], Lake Chao (spanning 40-year CDOM dynamics, ${\mathrm{R}}^2=0.955$, RF: ${\mathrm{R}}^2=0.924$) [91], and Pearl River Estuary (${\mathrm{R}}^2=0.90$) [173]. Figure 6 shows a comparative demonstration of the application performance of new ML technologies in inland waters for some typical cases, including [174,175]. Particularly for Chaohu Lake, the study cited empirical models proposed by Xu et al. [176] (2018), Olmanson et al. [177] (2020), Chen & Zhu [178] (2022), and Siswanto et al. [179] (2011). Evaluation showed that all four models had determination coefficients (R²) below 0.01, with the MAE ranging from 0.136 to 1.71, the RMSE ranging from 0.164 to 0.219, and a maximum bias of 1.248, indicating significant estimation deviations. Similarly, when three empirical models proposed by Sun et al. [180] were validated with data from the Pearl River Estuary, the R² values only ranged from 0.53 to 0.57, and the MAPE was between 23.27% and 46.87%, significantly underperforming compared to ML models. These results highlight the application advantages of ML in retrieving DOC in inland waters. Emerging studies highlight ML’s unique ability to abstract features and control error propagation, particularly in optically complex inland waters where empirical models oversimplify biogeochemical processes and indirect retrievals suffer accuracy loss [18,180,181,182,183,184,185,186,187,188,189]. This advantage has been validated by extensive data: After testing ML, traditional empirical models, and the QAA algorithm using 1097 samples from multiple countries including Australia and New Zealand, Pahlevan et al. [190] found that ML maintains prediction stability across three orders of magnitude of a_CDOM (from 10⁻² to 10¹ m⁻¹), whereas traditional models and QAA are only reliable at the 10⁰ absorption coefficient level. Additionally, ML exhibits superior estimation bias (slope = 0.752, RMSLD = 0.693) and uncertainty compared to empirical models (slope = 0.586, RMSLD = 1.108) and QAA (slope = 0.607, RMSLD = 1.149).

Remote sensing inversion methods for DOC have evolved from empirical–statistical approaches to physics-informed paradigms and, more recently, artificial intelligence-driven frameworks. However, critical technical bottlenecks persist (

Table 8. Comparison of various remote sensing inversion methods.

Method/Step				Advantages	Disadvantages	Limitations	Applicability
Direct Inversion Methods				Simple model; Fast computation; Low data requirements.	High regional dependency; Ignores optical mechanisms; Poor generalization.	Only suitable for optically stable waters; Low long-term monitoring reliability.	Short-term monitoring of single water body (e.g., clear rivers).
Indirect Inversion Method	From Spectra to CDOM	Semi-Empirical Method		Relatively strong physical relevance; Moderate data needs.	Affected by CDOM sources and seasonal variations.	Effective for high CDOM waters; Large errors in low CDOM waters.	CDOM dominated eutrophic lakes/rivers.
		Semi-Analytical Method	QAA	Clear physical mechanisms; Compatible with multi-spectral satellite data.	Relies on atmospheric correction accuracy; Large errors in deep water/highly turbid waters.	Requires accurate separation of CDOM from other absorbers (e.g., phytoplankton).	Moderately turbid shallow lakes.
			GSM	Low complexity, strong global applicability; Robust for highly turbid waters.	Requires prior spectral library support.	CDOM absorption easily confounded with particulate matter in turbid waters.	Large turbid lakes/estuaries; High suspended sediment waters.
			GIOP	Highly customizable; Flexible; Adapts to complex optical properties.	Difficult parameter optimization; High result uncertainty.	Requires extensive validation data for sub-model integration.	Urban waters or eutrophic lakes with complex optical properties.
	From CDOM to DOC	Robust CDOM–DOC Relationships		Sensitive to high CDOM concentrations, captures seasonal DOC variations; Simple implementation.	Demands extensive field sampling for CDOM absorption and DOC data.	CDOM:DOC ratio affected by sources (terrestrial/autochthonous), seasonality (e.g., snowmelt), and photodegradation may cause model failure.	CDOM-dominated waters; Terrestrial input regions; Short-term monitoring needs.
ML Method				Strong high-dimensional data processing; Integrates multi-source data (spectral + environmental factors); Superior nonlinear modeling.	Requires large labeled datasets; Poor model interpretability; High computational resources.	Weak generalization in data-scarce regions.	Complex waters with hyperspectral data support; Long-term temporal monitoring.

). Direct retrieval methods remain constrained by stringent water quality requirements and limited generalizability. While deep learning architectures show potential to mitigate error propagation in indirect approaches, current efforts largely repurpose generic machine learning models rather than developing DOC-specific solutions. Such general-purpose ML approaches are subject to dual constraints arising from both data limitations and inherent model characteristics.

First, the efficacy of general models is often constrained by the data-driven paradigm: ML relies on large-scale annotated datasets for end-to-end training. However, acquiring in situ measurements of DOC in aquatic remote sensing is costly, and samples are often spatially heterogeneous. When sample sizes are insufficient, the data struggle to comprehensively capture the seasonal variations, estuarine mixing processes, algal bloom dynamics, and periodic anthropogenic activities (e.g., fishing, agricultural runoff within watersheds) within the study area. This data scarcity significantly compromises the applicability of model inversion results in complex scenarios. Furthermore, the spectral characteristics of CDOM exhibit nonlinear distributions across diverse water bodies, which limited samples fail to fully represent within the feature space. For water areas with limited samples, strategies like transfer learning and domain adaptation can be employed. This involves initial training using marine models or samples from inland water areas with abundant data, followed by fine-tuning with a small number of samples from the target region. Domain adaptation techniques reduce the distribution discrepancy between the source domain (water areas with large samples) and the target domain (small-sample target area) through feature alignment or adversarial learning, facilitating rapid model adaptation to new scenarios. Concurrently, data augmentation techniques can be leveraged, such as using generative adversarial networks (GANs) to generate more training data from limited samples, thus enhancing data diversity.

Second, the interaction between small sample sizes and ML models further exacerbates errors: (1) Models struggle to distinguish effective signals from noise during training, easily overfitting to random fluctuations in the data, and (2) insufficient samples amplify parameter estimation errors, leading to substantially degraded generalization capability. These deficiencies are particularly pronounced in highly heterogeneous waters or lakes with strong seasonality, potentially causing biases in inversion results to exceed acceptable thresholds for practical applications. In this regard, a machine learning model can be trained based on in situ data, and a high signal-to-noise ratio model can be constructed by using the high accuracy of in situ measurement data [191,192].

Furthermore, the inherent properties of ML models impose fundamental constraints on DOC inversion accuracy. BP neural networks, optimized via gradient descent, are prone to converging to local minima within non-convex loss functions. This is especially problematic when DOC spectral features overlap with those of suspended particulate matter and chlorophyll-a, potentially causing the model to misattribute spectral signals from high-chlorophyll regions to DOC, resulting in systematic overestimation errors in algal bloom-dominated waters. For tree-based models like XGBoost, dependence on tree-depth parameters increases markedly in waters with complex compositions. Excessive tree depth induces overfitting, causing significant divergence between training and test set accuracy, particularly in optically complex zones such as estuarine mixing areas. Regarding CNNs, while pooling operations confer translational invariance, they inevitably discard fine-grained spatial location information. This leads to structural errors in inversions for small water bodies or inland lakes with steep water quality gradients. More critically, while CNNs automatically extract spectral features, they—like other deep learning approaches [193,194]—struggle to explicitly incorporate physicochemical priors, such as radiative transfer theory in water or the fluorescence properties of organic matter. This results in a lack of interpretability in the translation of spectral features to biogeochemical parameters.

4. Optimizing DOC Retrieval: From Feature Engineering to Algorithmic Synergy

4.1. Synergistic Global Exploration of Domain-Specific Hyperparameter Space via Intelligent Optimization Algorithms

The direct transplantation of generic machine learning models inherently constrains their efficacy in domain-specific applications, particularly for DOC retrieval in optically complex aquatic systems. Employing optimization algorithms as “couplers” between ML methods and domain-specific knowledge can address the limitations of general-purpose ML systems. By establishing a parameter optimization framework under multi-objective constraints, hydrogeographic principles and the Beer–Lambert law can be transformed into mathematical constraints, thereby directing model architectures toward domain-optimal and physically reasonable solutions. Concurrently, initializing parameter weights through prior knowledge (correlation relationships) accelerates convergence while avoiding local optima and counterintuitive solutions. For instance, Abdollahi et al. [195] effectively mitigated the defect of gradient descent methods being prone to becoming trapped in local optima by introducing genetic algorithms (GA) into the parameter optimization process of backpropagation (BP) neural networks. Furthermore, Chen et al. [196] innovatively integrated GA’s global exploration capability with XGBoost’s regularization constraints to construct a GA-XGBoost joint optimization framework, which significantly enhanced the inversion accuracy of water quality parameters in urban rivers.

4.2. Data Optimization—Feature Engineering

Within theoretical frameworks of model fusion and optimization, advanced feature engineering is imperative to construct and enhance optical relevance in data inputs. Based on the exponential decay characteristics of CDOM in the ultraviolet-visible spectral range (e.g., contributing 50% of the absorption at 443 nm [197]), shortwave band combinations have been extensively employed for DOC inversion. Based on systematic analyses of the literature [93,94,103,110,145,172,173,176,189,198,199,200,201,202,203,204] (statistical results shown in Figure 7), in inland waters with high CDOM concentrations, water bodies exhibit larger absorption coefficients in blue and violet spectral regions [205]. The “red-blue”, “green-blue”, and “red-violet” bands demonstrate enhanced applicability. This advantage may manifest through synergistic effects in spectral response mechanisms: The blue-violet bands predominantly reflect intrinsic CDOM absorption characteristics, while the red bands, being less influenced by components like chlorophyll, effectively decouple mixed spectral signals, thereby improving the robustness of DOC inversion methods. When CDOM concentrations decrease, the red-green spectral proportions in absorption characteristics increase [22]. In such scenarios, red-green bands exhibit better performance in inland waters with non-extremely low concentrations, which aligns with the findings reported by Zhu et al. [107].

However, the inherent optical heterogeneity of inland waters [206,207] and spectral interference from complex water quality parameters [107,208] fundamentally undermine the applicability of traditional characteristic bands. This interference originates from the deep coupling of absorption signals among CDOM, NAP, and phytoplankton. By integrating in situ measurements from multiple global regions [208,209,210,211,212,213,214,215,216,217,218,219,220,221] (Argentina, Portugal, Brazil, Canada, New York State-USA, Southern Finland, Southeastern/Northeastern China, Scotland-UK, and Southwestern Sweden), a ternary diagram of non-water absorption (Figure 8e) and typical absorption spectra (Figure 8a–d) of inland waters at the characteristic wavelength of CDOM (~440 nm) were plotted. The figure reveals that the absorption of the three components forms a “mixed fingerprint” effect.

In high-turbidity rivers, NAP dominates (mean absorption contribution: 67.19%), severely masking CDOM signals; lakes exhibit CDOM predominance (67.12%) with balanced contributions from NAP (19.74%) and Ph (18.13%); whereas reservoirs display the strongest three-component spectral mixing (CDOM: 42.69%, Ph: 31.33%, NAP: 25.97%). Scattered data points in ternary diagrams further confirm no absolute dominance of any single optical component, with spatial heterogeneity in Ph-NAP compositional ratios driving waterbody-specific CDOM interference mechanisms—exemplified by reservoirs where CDOM contribution ranges from 6.9% to 93.56% (n = 300), highlighting the challenge in selecting optical decoupling features for inland waters.

From the perspective of current research, current methodologies for retrieving DOC predominantly prioritize the selection of short-wavelength spectral bands (blue and green regions), while demonstrating limited utilization of long-wavelength bands (yellow and infrared regions). While this strategy reduces model complexity, it simultaneously sacrifices the detailed representation of CDOM characteristics in long-wavelength spectra. Experimental results from Zhu et al. further substantiate that incorporating spectral bands exceeding 600 nm can effectively enhance CDOM inversion accuracy, particularly in complex inland freshwater systems [48,107,205,222,223]. Although the incorporation of long-wavelength bands can enhance inversion accuracy, traditional band ratio processing approaches struggle to resolve their nonlinear interactions [18,224,225]. Feature optimization methods such as filter-based approaches (PCA [226], the Pearson correlation coefficient [227], the chi-square test, the distance correlation coefficient [228]), wrapper-based approaches (recursive feature elimination [229], greedy algorithms [230], and exhaustive search), and embedded approaches [231] (penalty term-based feature selection and learning model-based feature ranking) can yield highly expressive model input information. However, these methods rely on the manual construction of the feature database and fail to autonomously uncover cross-scale spectral correlations.

In comparison, large-scale deep learning models (e.g., transformer-based architectures and CNN) generally exhibit superior feature learning capabilities. Future research on DOC remote sensing inversion could leverage these large models to construct multi-scale feature fusion deep learning frameworks. A dual-branch network architecture could be designed: The shortwave branch (400–600 nm) would employ ResNet-18 to extract intrinsic absorption characteristics of CDOM, with the ResNet-18 architecture having been proven to excel in monitoring the vertical distribution of algal blooms in inland reservoirs [232], thanks to its robust feature extraction capabilities and stable training process. The longwave branch (600–900 nm) would utilize the convolution block attention module (CBAM) to decouple interference from turbid water bodies, where the CBAM mechanism has verified its effectiveness in decoupling chlorophyll content in bay waters [233], with its attention mechanism extendable to spectral signal separation tasks in turbid inland waters. However, the shortwave and longwave designs require high spatial and temporal resolution data support [234] for application in complex inland waters, further highlighting the necessity of the satellite–air–ground synergistic data collaboration discussed in Section 2.1. Ultimately, a feature pyramid could be implemented to achieve cross-band synergistic interpretation of spectral information.

5. Conclusions and Prospects

Since 2010, emerging remote sensing paradigms have fundamentally revolutionized inland water DOC monitoring, transitioning from discrete in situ sampling to remote sensing-based quantification—a transformation closely aligned with the global carbon neutrality imperative. While current inversion frameworks exhibit limitations in spatiotemporal resolution, atmospheric correction accuracy, and methodological generalizability, six convergent pathways emerge to advance this field:

• Land-observing satellites (e.g., Landsat-8 and Sentinel-2) have proven to be effective and advantageous in replacing ocean-color remote sensing for monitoring small-scale inland water bodies. However, their standalone application remains constrained by insufficient spectral granularity and temporal coverage, necessitating synergistic integration with near-surface and UAV-mounted hyperspectral platforms.
• Uncertainty mitigation requires rethinking atmospheric correction paradigms. Legacy marine-oriented models (FLAASH, 6S) prove inadequate for optically complex inland waters. While neural networks show potential, bespoke atmospheric correction protocols tailored to terrestrial sensors and regional biogeochemical variability should be developed alongside next-generation sensors with enhanced radiometric sensitivity.
• Indirect DOC inversion via CDOM proxies remains viable in systems governed by salinity gradients or terrestrial carbon export via unidirectional runoff. However, the decoupling mechanism caused by the complex effects of biogeochemistry needs to be addressed using a framework of local driver optimization.
• Methodological evolution hinges on transcending the empirical–analytical dichotomy. Semi-analytical approaches coupling radiative transfer models with bio-optical mechanisms exhibit superior generalizability over their empirical counterparts, yet their inland water adaptations (QAA, GSM, and GIOP) require substantial refinement. Hybrid models integrating mechanistic constraints with data-driven calibration represent a critical frontier.
• Machine learning’s nonlinear mapping capacity offers promise in circumventing error propagation in traditional methods, but its black-box nature and data dependency necessitate physics-informed architectures. Future research may employ optimization algorithms as a coupling mechanism between ML methods and domain knowledge to resolve the single data-driven paradigm of general ML.
• Advancing spectral feature engineering demands transcending heuristic feature selection. Deep learning architectures with dual-branch networks could disentangle shortwave-longwave spectral interactions, enabling cross-band synergistic analysis while suppressing sensor-specific noise.