Performance Evaluation of Inherent Optical Property Algorithms and Identification of Potential Water Quality Indicators Using GCOM-C Data in Eutrophic Lake Kasumigaura, Japan

Abstract

Lake Kasumigaura, one of Japan’s largest lakes, presents significant challenges for remote sensing due to its eutrophic conditions and complex optical properties. Although the Global Change Observation Mission-Climate (GCOM-C)/Second-generation Global Imager (SGLI)-derived inherent optical properties (IOPs) offer water quality monitoring potential, their performance in such turbid inland waters remains inadequately validated. This study evaluated five established IOP retrieval algorithms, including the quasi-analytical algorithm (QAA_V6), Garver–Siegel–Maritorena (GSM), generalized IOP (GIOP-DC), Plymouth Marine Laboratory (PML), and linear matrix inversion (LMI), using measured remote sensing reflectance (Rrs) and corresponding IOPs between 2017–2018. The results demonstrated that the QAA had the highest performance for retrieving absorption of particles (a_p) with a Pearson correlation (r) = 0.98, phytoplankton (a_ph) with r = 0.97, and non-algal particles (a_nap) with r = 0.85. In contrast, the GSM algorithm exhibited the best accuracy for estimating absorption by colored dissolved organic matter (a_CDOM), with r = 0.87, along with the lowest mean absolute percentage error (MAPE) and root mean square error (RMSE). Additionally, a strong correlation (r = 0.81) was observed between SGLI satellite-derived remote-sensing reflectance (R_rs) and in situ measurements. Notably, a high correlation was observed between the a_ph (443 nm) and the chlorophyll a (Chl-a) concentration (r = 0.84), as well as between the backscattering coefficient (b_bp) at 443 nm and inorganic suspended solids (r = 0.64), confirming that IOPs are reliable water quality assessment indicators. Furthermore, the use of IOPs as variables for estimating water quality parameters such as Chl-a and suspended solids showed better performance compared to empirical methods.

1. Introduction

The uneven distribution of lakes and marshes as inland water bodies across the globe leads to notable regional variations in water availability, biodiversity, aquatic ecosystems, and biogeochemical properties [1,2]. These water bodies play a vital role by contributing to biodiversity, nutrient cycling, environmental stability, supplying drinking water, supporting aquaculture, enabling recreational activities, and offering other vital benefits that contribute to human well-being and the health of global ecosystems [3,4]. However, in environments where primary production is high and water exchange is limited, problems such as organic pollution and eutrophication occur, emphasizing the need for sustainable monitoring and management of water systems to preserve ecological balance [5]. Additionally, numerous studies have highlighted the effects of recent climate change on lake ecosystems [6,7]. Therefore, it is crucial to consistently monitor ecosystem trends and changes in water quality [8,9,10].

Ocean color remote sensing by satellites provides the means for sustainable environmental monitoring with low labor and cost [11,12]. In recent years, high-resolution spatiotemporal observations by satellites such as the Global Change Observation Mission-Climate (GCOM-C)/Second-generation Global Imager (SGLI), Sentinel-3/Ocean and Land Color Imager (OLCI), and GEO-KOMPSAT-2B/Geostationary Ocean Color Imager-II (GOCI-II) have been realized, enabling detailed spatiotemporal water quality observations even for water bodies such as lakes, which have smaller spatial scales compared to those of marine areas [13,14,15,16]. However, as pointed out in many previous studies, optically complex water bodies such as lakes present several challenges, including atmospheric correction and water quality estimation errors [17,18,19]. These challenges are due to the diverse optical properties of lakes, which are influenced by factors such as depth, types of suspended matter, and the presence of various types of organic and inorganic materials. This has led to extensive research on the development and verification of various atmospheric correction models and water quality estimation models to enhance accuracy and reliability [20,21]. The complexity of lake environments requires specific algorithms that can accurately separate the contributions of different water constituents from the overall optical signal detected by satellites.

The effectiveness of inherent optical properties (IOPs) depends on using well-validated algorithms, particularly in environments such as highly eutrophic and optically complex waters [22]. These algorithms come in various forms and are designed to generate a wide range of optical data products, each serving different purposes [10,23]. Semi-analytical algorithms (SAAs) are essential for deriving IOPs from ocean color data, with widely used methods including the QAA in its various versions (QAA_v5, QAA_v6, QAA710, QAA716, and QAA750E), which employ spectral decomposition to retrieve absorption and backscattering coefficients [10,18,24,25]. GIOP, particularly GIOP-DC, offers a modular framework with customizable parameterizations [10,26,27], improving flexibility but requiring careful sub-model selection [23]. The GSM algorithm uses nonlinear optimization for simultaneous IOP retrieval [28], performing well in open ocean waters but requiring constraints for complex environments [10,27,29]. The PML algorithm is regionally optimized for coastal waters [30], balancing accuracy in moderately turbid conditions. Additionally, linear matrix inversion (LMI) methods provide an alternative by solving radiative transfer equations directly [31,32], offering transparency in IOP separation but being sensitive to noise and initial assumptions. Each algorithm exhibits unique advantages and limitations in satellite-based water quality monitoring, with performance varying significantly across different water types [10,27,29]. Ensuring these IOP algorithms are validated is crucial for generating accurate, reliable, and actionable data and minimizing uncertainty, which supports water quality monitoring, ecosystem management, and the assessment of biogeochemical characteristics [21,23,33]. Accurate in situ IOP measurements are essential for ensuring reliable remote sensing validation, which enhances the ability to estimate critical water quality parameters such as chlorophyll a, suspended solids, and dissolved organic matter. However, optically complex waters, often rich in phytoplankton, organic material, and non-algal particles, introduce unique challenges for optical measurements [34,35]. By developing and refining strong algorithms, we can significantly improve remote sensing capabilities. This includes tracking harmful algal blooms, monitoring ecosystem health, and adapting tools to fit a wide range of aquatic environments. Ultimately, these developments offer dependable, high-quality data that facilitate informed decision-making and promote sustainable water resource management [36,37].

Many studies on water quality estimations using satellite data have focused on chlorophyll a (Chl-a), suspended particulate matter, and other parameters, while others have focused on estimating IOPs. It has been reported that the IOP approach is effective for understanding biogeochemical dynamics and characterizing the water quality of target water bodies [12,38,39]. The estimation of IOPs from satellite data would make it possible not only to understand the light environment in water bodies, but also to determine optical properties related to particulate and dissolved organic matter (DOM) and particulate inorganic matter [39,40]. This would allow the simultaneous acquisition of multiple water quality parameters from satellite data, contributing to meaningful environmental monitoring. However, IOP estimation is sensitive to atmospheric correction errors since it uses multiple wavelengths of remote sensing reflectance (R_rs) captured by satellites, leading to uncertainties in the spatial representation of IOPs [33,41,42,43,44]. Additionally, although many IOP estimation algorithms have been proposed, they are often based on empirical methods, semi-analytical inversion methods, and machine learning models, leaving many unknowns regarding their applicability to optically complex water bodies [11,25,26,28,30,32,45]. IOPs provide insights into the absorption and scattering properties of water, which are influenced by substances such as phytoplankton. In the assessment of water quality, they can reveal biogeochemical components such as Chl-a, particulate organic nitrogen (PON), particulate organic carbon (POC), and suspended solids (SS) [46,47]. Chl-a is a key pigment in phytoplankton. It influences the color of water [16,48,49], enabling the estimation of algal biomass and the monitoring of eutrophication through specific wavelength absorption. PON and POC, indicative of organic matter in water, affect both scattering and absorption, providing insights into biogeochemical cycles and nutrient availability [50,51,52,53,54]. SS contribute to increased turbidity, leading to the attenuation of light transmission through the water column and the intensification of backscattering effects. This is primarily caused by the enhanced scattering and absorption of photons by the elevated concentration of particulate matter [55,56,57,58].

Remote sensing has been used to explore the optical properties of water bodies across various regions and a wide range of aquatic environments [5,35,41]. Remote sensing provides unparalleled capabilities for synoptic spatial coverage, high temporal resolution, and large-scale applicability in water quality monitoring [59,60], overcoming the inherent limitations of in situ sampling methods. Satellite-derived IOPs offer critical insights into spatial heterogeneity and seasonal dynamics of aquatic ecosystems. This study examines the case of Lake Kasumigaura, the second-largest lake in Japan, which is a vital component of the region’s ecosystem, economy, and water resource management system [61]. However, similarly to many freshwater bodies worldwide, it faces significant environmental challenges, including eutrophication, pollution, and water quality deterioration, driven by both anthropogenic activities and natural processes [62]. Furthermore, climatic variations and seasonal hydrodynamics exacerbate water quality issues, complicating management and restoration efforts. Previous research has developed various methods to assess water quality in Lake Kasumigaura, focusing on the application of machine learning and algorithms to predict Chl-a and suspended solids using remote sensing data [16,63,64,65]. However, addressing these intricate challenges requires extensive water quality parameters to understand the drivers of water quality changes and to develop effective mitigation strategies for sustainable lake management [66,67].

The aim of this study was to identify suitable IOP algorithms and the key IOP indicators for enhanced water quality monitoring in eutrophic aquatic environments, assuring higher accuracy and minimal errors. Specifically, the study evaluates the performance of five IOP algorithms, each developed with distinct characteristics of optical properties, and to explore the relationship between IOPs and water quality parameters. The research builds on further understanding the light environment in aquatic systems through IOPs and evaluating their potential for estimating water quality parameters. Using measured R_rs and IOP data from Lake Kasumigaura, the accuracy of the five IOP algorithms was validated. The study also examined the precision of atmospheric correction and IOP estimation using GCOM-C satellite data. Lastly, the relationship between the estimated IOPs and water quality metrics was analyzed to assess the viability of IOP-based monitoring for water quality evaluation.

2. Materials and Methods

2.1. Study Area

Lake Kasumigaura, the second-largest lake in Japan, is located northeast of Tokyo and has a surface area of 167.63 km² (Figure 1). The surrounding area largely consists of natural landscapes and agricultural lands. The lake has experienced notable shifts in phytoplankton communities, nutrient ratios, and water temperature [68,69] and is used for fishing, irrigation, tourism, and recreation [70]. Since 1977, the National Institute for Environmental Studies (NIES) has been conducting regular monthly observations at ten monitoring stations, as shown in Figure 1.

2.2. Data Collection

2.2.1. Field Observations

Between 2017 and 2018, in situ observations were conducted at ten spatially distributed stations (Figure 1). Sampling was conducted during the optimal season (primarily summer to autumn) to ensure favorable conditions, avoiding periods of extreme weather such as heavy rain or strong winds that could affect lake water sampling and measurements. Due to this temporal constraint, the validation results may not fully encompass the complete range of seasonal R_rs and IOP variations. Optical measurements, including the upward radiance and downward irradiance, were performed at 2 nm intervals using the hyperspectral radiometers TRIOS RAMSES-ARC for radiance and RAMSES-ACC for irradiance [71]. For the measurement of backscattering (b_b), HOBI Labs HydroScat was used to measure the total b_b by applying a σ correction to correct for the effect of light dissipation at the optical path length between the sensors (HOBI-Labs_Inc., Tucson, AZ, USA) [72,73]. For the measurement of optical absorption coefficients, collected surface water was used and filtered through a Whatman Nuclepore membrane (pore size: 0.4 µm). The filtrate was placed in a 10 cm quartz cell, and absorption of colored dissolved organic matter (a_y) was measured using a Shimadzu MPS-2400 spectrophotometer (Shimadzu Corporation, Kyoto, Japan) [74]. In situ optical ground data were obtained by collecting lake water samples from designated stations, filtering them through 25 mm glass microfiber filters (Whatman glass microfiber filters grade GF/F: 0.7 µm), and mounting them on a spectrophotometer (Shimadzu UV-2400). The optical absorption coefficient (a_p) of the particles was measured using a spectrophotometer (Shimadzu MPS-2400) equipped with an end-on photomultiplier for detecting light intensity across a specified wavelength range, allowing for precise quantification of particle absorption and scattering properties [75]. The optical absorption coefficient of tryptone (detritus + inorganic suspended matter) was then measured by immersing the filtered Whatman glass microfiber filters in ethanol on a filter funnel to confirm that the phytoplankton pigment had been removed, and then the optical absorption coefficient was measured again; a_ph was then calculated by subtracting the optical absorption coefficient of tryptone from the a_p [76,77]. The IOPs, namely, the a_p(λ), a_dg(λ), a_ph(λ), and b_bp(λ), were also derived using the IOP algorithm. According to Yamashita [78], the a_dg(λ) component, which integrates a_CDOM(λ) and a_NAP(λ), can be separated using coefficients derived from least squares regression with the measured a_CDOM(λ) and derived a_dg(λ).

2.2.2. Water Quality Dataset by the NIES

The NIES initiated a monitoring project at Lake Kasumigaura in 1977. Since then, it has consistently tracked the lake’s water quality and biological characteristics at ten monitoring stations [16,61,66,79,80]. The in–situ water quality data collected by the NIES at Lake Kasumigaura were obtained from monitoring database (accessible at: https://db.cger.nies.go.jp/gem/moni-e/inter/GEMS/database/kasumi/data/water/wq_data.zip; accessed on 2 September 2024). The water quality parameters employed in this study were Chl-a, POC, PON, DON, and SS for the period from 2018 to 2022 [81]. SS collected by the NIES include organic and inorganic SS. To understand the relationship between IOPs and SS, the separation of organic and inorganic SS is important since the ecological role SS play in water bodies depends on whether they are mostly organic or inorganic compounds [82,83]. Organic SS are directly related to the nitrogen content in phytoplankton. Organic and inorganic SS were separated based on the Redfield ratio [84]. The Redfield ratio is the C:N:P ratio of the elemental composition (CH₂O)_x(NH₃)_y(H₃PO₄)_z of marine phytoplankton, which is approximately 106:16:1 [85]. The correlation of IOPs with both organic and inorganic SS was evaluated. The differentiation between organic SS and inorganic SS was critical to accurately assess their respective biological influences on IOPs. The separation of organic SS and inorganic SS enables a more precise evaluation of their individual contributions to light absorption and scattering processes [86].

2.2.3. GCOM-C Satellite Imagery

GCOM-C/SGLI provides multispectral and multi-polarization imagery over a wide range of wavelengths (ultraviolet to infrared). For this study, we acquired GCOM-C/SGLI satellite imagery with a spatial resolution of 250 m, focusing on normalized water-leaving radiance, to estimate R_rs over various aquatic systems for the period from 2018 to 2022. R_rs serves as the fundamental optical parameter that relates water-leaving radiance to the IOPs of aquatic systems. R_rs can be acquired through either in situ measurements or satellite remote sensing [87]. The spectral distribution of R_rs(λ) is determined by radiometrically measuring the upwelling radiance and downwelling irradiance above the water surface [87,88]. The R_rs is defined by the following equation:

$$R_{rs}\left(\mathsf{\lambda }, {\theta }_0, \theta , ∆\varnothing \right)\equiv {\displaystyle \frac{L_w\left(\mathsf{\lambda }, {\theta }_0, \theta , ∆\varnothing \right)}{E_d(0^{+}, \mathsf{\lambda }, {\theta }_0)}}\left[{sr}^{-1}\right]$$

(1)

where R_rs is the remote sensing reflectance; L_w represents the radiance exiting the water under idealized conditions normalized for the mean Earth–Sun distance, with the Sun at zenith and no atmospheric attenuation; and E_d at 0⁺ is the actual solar irradiance reaching the sea surface after accounting for atmospheric absorption and scattering from the top of the atmosphere [89]. Data acquisition involved accessing the Japan Aerospace Exploration Agency’s (JAXA) G-Portal system (https://gportal.jaxa.jp/gpr/), where processed level 2 products relevant to water quality monitoring were selected based on our study area’s location and acquisition time.

This study utilized level 2 SGLI products with version 3 atmospheric correction processed through an algorithm developed based on the SeaWiFS and MODIS (Gordon and Wang, 1994) approaches [89,90], while incorporating developments from Japanese ocean color satellites ADEOS/OCTS [91] and ADEOS2/GLI [92]. The algorithm implements a sequential correction approach, first removing Rayleigh-scattered radiance from top-of-atmosphere reflectance before addressing the more complex aerosol reflectance component [19,93]. A critical innovation involves the use of dual near-infrared bands coupled with the linear combination index method, which significantly improves water-leaving reflectance estimation in turbid waters by focusing on the NIR band analysis [89]. Further refinements include improved atmospheric transmittance calculations derived directly from these simulations, sophisticated sun glint correction incorporating inter-band parallax compensation, and an automated quality control mechanism that prevents negative water-leaving reflectance through iterative aerosol model reselection [93,94]. This study utilized data from the visible and near-infrared radiometer (SGLI-VNR) and the non-polarization channels, as detailed in

Table 1. Center wavelengths and bandwidths of the GCOM-C/SGLI.

Channel	Center Wavelength (nm)	Bandwidth (nm)
VN1	380	10
VN2	412	10
VN3	443	10
VN4	490	10
VN5	530	20
VN6	565	20
VN7	673.5	20
VN8	673.5	20
VN9	763	12
VN10	868.5	20
VN11	868.5	20

.

2.3. Study Design

The study was structured into two phases to achieve its objectives (Figure 2). In the first phase, the performance of various IOP algorithms was evaluated to identify the best-performing algorithm for each IOP, utilizing measured IOPs (dashed box in Figure 2). In the second phase, the focus was on identifying the key water quality indicators by analyzing the correlation matrix, with an emphasis on parameters showing strong correlations.

2.4. Semi-Analytical IOP Algorithms

In this study, five IOP algorithms were examined, namely, the quasi-analytical algorithm (QAA), the Graver–Siegel–Maritorena (GSM) algorithm, the generalized IOP (GIOP) algorithm, linear matrix inversion (LMI), and the Plymouth Marine Laboratory (PML) algorithm (Figure 2). Several methods have been developed to retrieve IOPs. Gordon et al. [95] derived the relationship between inherent and apparent optical properties through an analysis of the radiance transfer theory. Hoge and Lyon [32] obtained IOPs using the LMI of oceanic radiance models, with a focus on the analysis of errors from both the model and radiance measurements. The LMI approach utilizes a matrix equation for accurately obtaining IOPs and provides a comprehensive framework for water quality assessment based on R_rs [96,97]. The updated MATLAB code for linear matrix inversion, found on the University of Maine website, was downloaded from the IOCCG working group website (http://www.ioccg.org/groups/Software_OCA/Chapter_08_insitu.zip) and modified for SGLI-observed wavelengths before applying IOP inversion. This study applied both in situ data inversion for IOP validation and synthetic data inversion for GCOM-C satellite images. PML IOP inversion models use field-measured data and R_rs from satellite images. The PML IOP algorithm’s Python code, provided by the IOCCG working group (http://www.ioccg.org/groups/Software_OCA/PML.zip), was modified to apply to the GCOM-C/SGLI satellite images for IOP inversion. The PML algorithm was developed based on the Graver and Siegel nonlinear statistical method based on the ratio between upwelling and downwelling radiance to water reflectance [30]. In this study, the commonly applied techniques included the utilization of Python (version 3.12) scripts, MATLAB (Release R2023b, Version 23.2) code, and the sea-viewing data analysis system (SeaDAS) software package. SeaDAS version 8.4 was downloaded from the NASA Ocean Color website (https://seadas.gsfc.nasa.gov) and applied to derive IOPs using in situ as well as satellite imagery [12]. Semi-analytical algorithms (SAA) have been developed based on empiricism and the radiative transfer theory [98]. The SeaDAS software, which incorporates semi-analytical algorithms such as the QAA, GIOP algorithm, and GSM algorithm, is commonly used for analyzing marine IOPs derived from ocean color data acquired via satellites [99,100]. In SeaDAS, parameter configurations for IOP retrieval algorithms were were performed by choosing the IOP algorithm version (QAA_v6, GSM, GIOP-DC), defining reference wavelengths, and setting initial constraints for absorption (a_ph, a_dg) and backscattering (b_bp). For QAA_v6, the backscattering slope (η) was raised to 1.0–1.3 to better model high particle loads, while GSM requires modified initial guesses, including an a_dg slope (S_dg) of 0.0206 nm⁻¹ (up from 0.018 nm⁻¹) and a particulate backscattering ratio increased to 1.5 paired with nonlinear optimization. GIOP enables the configuration of spectral constraints and initial estimates for phytoplankton, CDOM, and detritus absorption [26,27]. These settings allow flexible tuning of phytoplankton absorption, CDOM (S_dg adjustable from 0.015 to 0.018 nm⁻¹), and backscattering slope (η elevated to 1.2 in eutrophic cases), ensuring accurate retrievals in complex scattering environments. SeaDAS enables the dynamic creation of various semi-analytical algorithms, allowing for the assessment of specific modeling assumptions and the customization of semi-analytical algorithms for given applications [45]. Moreover, the software supports ensemble inversion modeling, which aids in extracting detailed information on absorption and backscattering coefficients derived from ocean color data acquired via satellites [21].

2.5. Accuracy Assessment of Inherent Optical Property Algorithms Using In Situ and Remote Sensing Data

Assessing the accuracy of prediction models is crucial for evaluating their performance [101]. The metrics used in this study are the mean absolute percentage error (MAPE), root mean square error (RMSE), and the sample Pearson correlation coefficient (r). The MAPE and RMSE assess the magnitude of prediction errors, and the sample Pearson correlation coefficient assesses the linear relationship between the predicted and actual values [102].

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

(2)

$$\mathrm{RMSE}=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{\mathrm{i}=1}^n{\left({\mathrm{x}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}\right)}^2}r$$

(3)

$$r={\displaystyle \frac{{\sum }_{\mathrm{i}=1}^n\left({\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)\left({\mathrm{Y}}_{\mathrm{i}}-\bar{\mathrm{Y}}\right)}{\sqrt{{\sum }_{\mathrm{i}=1}^n{\left({\mathrm{X}}_{\mathrm{i}}-\overline{\mathrm{x}}\right)}^2}{\sum }_{\mathrm{i}=1}^n{\left({\mathrm{Y}}_{\mathrm{i}}-\bar{\mathrm{Y}}\right)}^2}}$$

(4)

where n is the number of observations, x_i represents the in situ measured IOPs of the n^th observation, and y_i represents the derived IOP value of the i^th observation. $\overline{\mathrm{x}}$ and Ȳ are the means of the in situ measured values and the derived values, respectively. The correlation coefficient was used to understand the relationship of IOPs and the measured water quality parameters using a correlation matrix (heat map) generated for graphical representation [103].

The consistency and dispersion of the comparison between datasets of a_p(λ), a_ph(λ), and a_dg(λ) derived using the QAA, GIOP, GSM, PML, and LMI IOP algorithms with the measured IOPs (Table 2) were compared using Taylor diagrams. Taylor diagrams are used to characterize the potential of an algorithm in estimating IOPs in terms of the correlation coefficient, normalized standard deviation, and normalized unit root mean square deviation (uRMSD). In this diagram, a model performs better if the obtained IOPs are closer to the in situ data [104], where in the ideal case, r is equal to one, the normalized uRMSD is zero, and the normalized standard deviation is one [29,105]. The following equation was used to calculate the uRMSD:

$$\mathrm{u}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{D}=\sqrt{{\displaystyle \frac{1}{n}}\sum _{\mathrm{i}=1}^n{\left({\mathrm{X}}_{\mathrm{i}}-{\mathrm{Y}}_{\mathrm{i}}\right)}^2-{\mathrm{B}\mathrm{i}\mathrm{a}\mathrm{s}}^2}$$

(5)

where X_i represents the in situ measured IOP values, Y_i represents the derived IOP values, n is the number of observations, and Bias is the average difference between the derived and in situ measured values.

$$\mathrm{F}={\displaystyle \frac{\mathrm{M}\mathrm{e}\mathrm{a}\mathrm{n} \mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e} \mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n} \left(\mathrm{M}\mathrm{S}\mathrm{B}\right)}{\mathrm{M}\mathrm{e}\mathrm{a}\mathrm{n} \mathrm{s}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{r}\mathrm{e} \mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{i}\mathrm{n} \left(\mathrm{M}\mathrm{S}\mathrm{W}\right)}}$$

(6)

$$\mathrm{M}\mathrm{S}\mathrm{B}={\displaystyle \frac{\mathrm{S}\mathrm{S}\mathrm{B}}{{\mathrm{d}\mathrm{f}}_{\mathrm{b}\mathrm{e}\mathrm{t}\mathrm{w}\mathrm{e}\mathrm{e}\mathrm{n}}}}$$

(7)

$$\mathrm{M}\mathrm{S}\mathrm{B}={\displaystyle \frac{\mathrm{S}\mathrm{S}\mathrm{W}}{{\mathrm{d}\mathrm{f}}_{\mathrm{w}\mathrm{i}\mathrm{t}\mathrm{h}\mathrm{i}\mathrm{n}}}}$$

(8)

$$p-\mathrm{value}=\mathrm{P} ({\mathrm{F}}_{\mathrm{calculated}}\ge {\mathrm{F}}_{\mathrm{critical}}|{\mathrm{d}}_{f1},{\mathrm{d}}_{f2})$$

(9)

The F-statistic (F_calculated) compares the variation between groups (SSB) to the variation within groups (SSW). The degrees of freedom for the numerator (d_f1) are k − 1, for the denominator (d_f2)—N − k. The F_critical value from the F-distribution at the significance level (α) determines if the F-statistic is significant.

Table 2. Descriptive statistics of the measured IOPs a_p(λ), a_ph(λ), a_NAP(λ), and a_CDOM(λ) of the observed SGLI wavelengths in Lake Kasumigaura [unit: m⁻¹]. SD denotes standard deviation.

Measured IOP	Sample Size	Min	Max	Mean	Median	SD
ap (412 nm)	24	0.93	1.97	1.63	1.69	0.34
ap (443 nm)	24	0.76	1.90	1.30	1.25	0.30
ap (490 nm)	24	0.41	1.14	0.74	0.71	0.19
ap (530 nm)	24	0.23	0.58	0.41	0.40	0.09
ap (565 nm)	24	0.16	0.40	0.28	0.27	0.06
ap (670 nm)	24	0.22	0.73	0.39	0.33	0.15
aph (412 nm)	24	0.28	0.99	0.57	0.51	0.23
aph (443 nm)	24	0.26	1.25	0.57	0.48	0.29
aph (490 nm)	24	0.12	0.69	0.31	0.25	0.19
aph (530 nm)	24	0.04	0.37	0.14	0.11	0.09
aph (565 nm)	24	0.01	0.24	0.08	0.06	0.06
aph (670 nm)	24	0.16	0.63	0.30	0.25	0.14
aNAP (412 nm)	24	0.075	2.164	1.180	1.512	0.793
aNAP (443 nm)	24	0.049	1.489	0.796	1.036	0.533
aNAP (490 nm)	24	0.031	0.967	0.506	0.637	0.342
aNAP (530 nm)	24	0.018	0.798	0.385	0.457	0.273
aNAP (565 nm)	24	0.013	0.729	0.309	0.345	0.230
aNAP (670 nm)	24	0.0002	0.606	0.203	0.215	0.173
aCDOM (412 nm)	24	0.593	1.548	1.088	1.114	0.288
aCDOM (443 nm)	24	0.429	1.109	0.757	0.785	0.192
aCDOM (490 nm)	24	0.255	0.621	0.442	0.462	0.111
aCDOM (530 nm)	24	0.165	0.377	0.279	0.293	0.067
aCDOM (565 nm)	24	0.121	0.282	0.195	0.204	0.045
aCDOM (670 nm)	24	0.049	0.204	0.083	0.080	0.031

Table 2. Descriptive statistics of the measured IOPs a_p(λ), a_ph(λ), a_NAP(λ), and a_CDOM(λ) of the observed SGLI wavelengths in Lake Kasumigaura [unit: m⁻¹]. SD denotes standard deviation.

Measured IOP	Sample Size	Min	Max	Mean	Median	SD
ap (412 nm)	24	0.93	1.97	1.63	1.69	0.34
ap (443 nm)	24	0.76	1.90	1.30	1.25	0.30
ap (490 nm)	24	0.41	1.14	0.74	0.71	0.19
ap (530 nm)	24	0.23	0.58	0.41	0.40	0.09
ap (565 nm)	24	0.16	0.40	0.28	0.27	0.06
ap (670 nm)	24	0.22	0.73	0.39	0.33	0.15
aph (412 nm)	24	0.28	0.99	0.57	0.51	0.23
aph (443 nm)	24	0.26	1.25	0.57	0.48	0.29
aph (490 nm)	24	0.12	0.69	0.31	0.25	0.19
aph (530 nm)	24	0.04	0.37	0.14	0.11	0.09
aph (565 nm)	24	0.01	0.24	0.08	0.06	0.06
aph (670 nm)	24	0.16	0.63	0.30	0.25	0.14
aNAP (412 nm)	24	0.075	2.164	1.180	1.512	0.793
aNAP (443 nm)	24	0.049	1.489	0.796	1.036	0.533
aNAP (490 nm)	24	0.031	0.967	0.506	0.637	0.342
aNAP (530 nm)	24	0.018	0.798	0.385	0.457	0.273
aNAP (565 nm)	24	0.013	0.729	0.309	0.345	0.230
aNAP (670 nm)	24	0.0002	0.606	0.203	0.215	0.173
aCDOM (412 nm)	24	0.593	1.548	1.088	1.114	0.288
aCDOM (443 nm)	24	0.429	1.109	0.757	0.785	0.192
aCDOM (490 nm)	24	0.255	0.621	0.442	0.462	0.111
aCDOM (530 nm)	24	0.165	0.377	0.279	0.293	0.067
aCDOM (565 nm)	24	0.121	0.282	0.195	0.204	0.045
aCDOM (670 nm)	24	0.049	0.204	0.083	0.080	0.031

3. Results

3.1. Comparative Analysis of IOP Algorithms

To assess the performance of the IOP algorithms and determine the most suitable algorithm for Lake Kasumigaura, the correlation between the derived and measured IOPs was analyzed across six wavelength bands (412, 443, 490, 530, 565, and 670 nm). These wavelengths were chosen due to their availability in remote sensing satellite imagery and their compatibility with commonly used ocean color sensors (see

Table 3. Accuracy assessment results for QAA, PML, LMI, GSM, and GIOP algorithms using in situ measured a_p(λ), a_ph(λ), a_NAP(λ), and a_CDOM(λ).

IOP Algorithm	Error Metrics	QAA	PML	LMI	GSM	GIOP
ap (λ)	MAPE	0.31	0.35	0.36	0.54	0.29
	RMSE	0.29	0.31	0.42	0.57	0.33
	r	0.98	0.96	0.95	0.94	0.95
	F	180.95	139.17	259.35	318.18	169.11
	p-value	8.9 × 10−59	4.2 × 10−52	2.6 × 10−68	6.9 × 10−74	4.9 × 10−57
	% between ±30% to 1:1	91.81	85.83	79.31	75.04	85.97
aph (λ)	MAPE	0.23	0.60	0.56	0.90	0.40
	RMSE	0.08	0.24	0.17	0.21	0.14
	r	0.97	0.69	0.83	0.75	0.88
	F	43.84	30.59	47.49	61.19	37.06
	p-value	6.8 × 10−27	7.6 × 10−21	2.3 × 10−28	2.4 × 10−33	6.0 × 10−24
	% between ±30% to 1:1	89.17	56.11	63.89	65.83	75.17
aNAP (λ)	MAPE	2.18	3.10	1.29	0.98	4.02
	RMSE	0.31	0.35	0.34	0.30	0.38
	r	0.85	0.74	0.73	0.84	0.73
	F	103.75	85.76	95.52	147.51	70.39
	p-value	5.5 × 10−45	1.3 × 10−40	4.7 × 10−43	1.5 × 10−53	2.9 × 10−36
	% between ±30% to 1:1	74.19	69.58	61.25	75.53	62.03
aCDOM (λ)	MAPE	0.70	0.10	0.52	0.46	0.76
	RMSE	0.23	0.31	0.25	0.21	0.27
	r	0.85	0.65	0.83	0.87	0.79
	F	117.65	60.61	96.28	128.01	84.23
	p-value	5.6 × 10−48	3.8 × 10−33	3.1 × 10−43	4.9 × 10−50	3.4 × 10−40
	% between ±30% to 1:1	71.25	52.50	66.67	73.33	59.56

) [29].

A one-way ANOVA test was conducted to evaluate the performance of five different IOP algorithms, using a sample size of 144 from six bands for each IOP. At a 95% confidence level (α = 0.05), the F-critical value, based on the degrees of freedom (4, 138), was approximately 3.89. All the IOP algorithms demonstrated statistically significant differences because their F-values exceeded the F-critical value, with the corresponding p-values below 0.0001. In addition to the ANOVA test, correlation coefficients and error metrics were calculated to assess the relationship between the measured and derived IOPs. The results revealed variability in both correlation and error metrics, indicating substantial differences in IOP inversion across the algorithms.

The QAA demonstrated superior performance, with consistently high r indicating a strong correlation between the derived and measured values. For a_p(λ), it achieved the highest correlation (r = 0.98), the lowest errors (MAPE = 0.31, RMSE = 0.29), and an outstanding 91.81% of the values were within ±30% of the 1:1 line. The F-statistic for the QAA was the highest (F = 180.95), reinforcing its robust performance and statistical significance, with a p-value of 8.9 × 10⁻⁵⁹. Similarly, for a_ph(λ), the QAA maintained its top performance with r = 0.97, MAPE = 0.23, and RMSE = 0.08. It also achieved a high F-statistic (F = 43.84) and a p-value of 6.8 × 10⁻²⁷, signifying strong statistical significance. In terms of accuracy, it was highly reliable, with 89.17% of values within ±30% of the 1:1 line. For a_NAP(λ), the QAA’s performance remained solid with r = 0.85 and an F-statistic of 103.75, highlighting its reliability in this parameter. For a_CDOM(λ), GSM emerged as the best algorithm, achieving the highest correlation (r = 0.87) and an F-statistic of 128.01. It demonstrated the lowest errors (MAPE = 0.46, RMSE = 0.21), and 73.33% of values were within ±30% of the 1:1 line. The statistical significance of GSM was notable, with a p-value of 4.9 × 10⁻⁵⁰, making it particularly effective for environments dominated by dissolved organic matter. Previous research has shown that the QAA and GSM work well in waters with varying aquatic environmental conditions [10,27].

The GIOP, LMI, and PML algorithms exhibited moderate-to-lower performances across most IOPs. For a_p(λ), GIOP achieved r = 0.95 with a reasonable accuracy, though its F-statistic (F = 169.11) and p-value (4.9 × 10⁻⁵⁷) suggested a moderate correlation, still statistically significant but not as strong as the QAA’s. For a_ph(λ), GIOP showed a balanced performance with r = 0.88, MAPE = 0.40, and RMSE = 0.14, but its F-statistic (F = 37.06) indicated a less optimal fit compared to the QAA. GSM performed moderately for most IOPs but excelled in a_CDOM(λ), reinforcing its performance for dissolved organic matter analysis. The LMI and PML algorithms demonstrated inconsistent and moderate performance results across the IOPs; LMI exhibited moderate-to-high correlations (r = 0.73 to 0.83), but its overall performance remained lower compared to the QAA and GSM. In contrast, the PML algorithm consistently exhibited the lowest performance across the parameters. For a_ph(λ), PML had the weakest correlation (r = 0.69) and the highest errors (MAPE = 0.60, RMSE = 0.24), with only 56.11% of values within ±30% of the 1:1 line. Its F-statistic of 85.76 and p-value of 1.3 × 10⁻⁴⁰ further highlighted its limitations. Similarly, for a_CDOM(λ), PML’s r = 0.65, along with higher errors (MAPE = 1.10, RMSE = 0.31), suggested its limited applicability for accurate IOP inversion in complex aquatic environments, despite its potential use in simpler cases.

The evaluation of the IOP algorithm performance (Table 3 and Figure 3) for total absorption indicates that the QAA had the highest accuracy, followed by the GIOP algorithm. The LMI algorithm showed moderate reliability, whereas the GSM and PML algorithms had low effectiveness, with the PML algorithm having the worst performance. For a_ph, the algorithm performance followed the order QAA > GIOP > LMI > GSM > PML. The QAA had the highest accuracy, with the GIOP algorithm closely trailing. The LMI algorithm outperformed the GSM and PML algorithms, which showed the lowest effectiveness for this parameter. Regarding a_NAP, the ranking was QAA > GSM > PML > LMI > GIOP. The QAA had the best performance, followed by the GSM algorithm. The PML algorithm outperformed the LMI and GIOP algorithms, which ranked the lowest in this category. For a_CDOM, the ranking was GSM > QAA > LMI > GIOP > PML. The GSM algorithm had the best performance, followed by the QAA. However, the QAA had consistently low errors for a_CDOM and across all wavelengths, comparable to those of the GSM algorithm. Notably, the LMI algorithm outperformed both the GIOP and PML algorithms, which exhibited the lowest accuracy. Overall, the QAA was the most reliable algorithm, with higher correlation coefficients across all wavelengths for a_p(λ), a_ph(λ), and a_NAP(λ) and low MAPE and RMSE values for a_CDOM. For a_CDOM, GSM had the highest correlation, followed by the QAA. The QAA and the GSM algorithms were the most reliable algorithms for IOP estimation at Lake Kasumigaura, offering robust and consistent results with minimal errors across all wavelengths and IOPs. The GIOP algorithm performed well but was slightly less effective. The LMI algorithm exhibited variable performance, often surpassing the PML algorithm, which generally showed lower accuracy.

The variability in algorithm performance across wavelengths and IOPs highlights the sensitivity of IOP algorithms (Figure 3 and Figure 4). The Taylor diagram results reveal distinct spectral and algorithmic dependencies in the performance of IOP retrievals (Figure 4). The QAA demonstrated strong consistency across most wavelengths (412–670 nm), effectively retrieving a_p, a_ph, and a_CDOM at shorter wavelengths (412–443 nm), with a shift to a_NAP at longer wavelengths (490–670 nm). PML exhibited variable performance, excelling in a_ph and a_NAP retrievals at mid-range wavelengths (443–565 nm), while GSM and LMI showed selective accuracy in a_CDOM retrievals (490 nm for GSM; 530 nm for LMI). In contrast, GIOP consistently underperformed for a_NAP (412 nm) and a_CDOM (565 nm), and LMI displayed limitations in a_CDOM retrieval at 443 nm and 670 nm. These patterns underscore wavelength-specific algorithm biases, with the QAA exhibiting the broadest spectral versatility, while specialized algorithms (GSM, LMI) performed well only for specific IOPs within narrow spectral ranges. At 670 nm, the smaller deviations suggest measurements that were more consistent, with non-algal particles dominating absorption. Correlation coefficients r ≥ 0.79 show moderate-to-strong alignment between the predicted and observed values, especially for the QAA. However, the lower correlation values at 530 and 565 nm suggest that these wavelengths were more challenging for the models, likely due to the interplay of particles and absorption phenomena. The QAA performed reliably at 412 to 565 nm, especially in capturing a_ph. The GIOP and LMI algorithms had the lowest correlation at 412 and 490 nm for a_NAP, and the QAA showed a moderate performance at 670 nm for a_CDOM, with r = 0.81 and RMSE = 0.32. The performance of the PML and LMI algorithms generally showed more variability across different types of absorption and wavelengths, with neither method consistently outperforming the others in all scenarios. The low standard deviation of the PML algorithm at 530 nm for a_ph(λ) suggests low variability in its estimates and indicates a reliable performance. The discrepancies between algorithms at various wavelengths indicate that some are better suited for IOPs, necessitating careful selection based on the intended application. Selecting an algorithm that matches the environmental conditions and optical complexities of the water body under study is essential.

3.2. Accuracy Assessment of the GCOM-C/SGLI Satellite Imagery and In Situ Remote Sensing Reflectance

This study conducted an accuracy assessment by acquiring in situ R_rs data at ten stations. R_rs values were extracted from the level 2 GCOM-C/SGLI satellite images at these locations. The subsequent analysis aimed to evaluate the spectral shape and accuracy of satellite-derived R_rs data to determine their applicability for assessing IOPs.

The R_rs results in Figure 5a,b exhibited a spectral shape characteristic of organically polluted waters, with prominent light absorption in the blue region. R_rs values increased progressively from the blue (443 nm) to green (565 nm) wavelengths, followed by a decrease into the red spectral region (670 nm). The measured R_rs spectra demonstrated greater consistency, whereas satellite-derived R_rs displayed variability across stations. This pattern aligns with the R_rs observations reported by Salem et al. [106].

Comparing the in situ measured R_rs and the SGLI satellite-derived R_rs across the observed wavelengths of the SGLI provides insights into the reliability of satellite observations. Figure 5a,b demonstrates that the spectral shapes of R_rs were generally consistent between the two datasets, while Figure 6 further quantified this agreement through a scatter plot comparison of R_rs values at each observation wavelength. The correlation coefficients were relatively high across all wavelengths, ranging from 0.81 to 0.91, indicating strong relationships in the R_rs spectra. The SGLI-derived R_rs exhibited strong spectral agreement with in situ measurements, showing significantly higher correlation coefficients at 490 nm (r = 0.91) and 530 nm (r = 0.89) compared to shorter wavelengths. The MAPE values showed more variation, ranging from 22.4% to 55.0%. The SGLI-derived R_rs at 412 nm and 443 nm exhibited a slight overestimation, with MAPE of 50.7% and 55.0%, respectively, indicating moderate deviations from in situ R_rs.

3.3. Correlation Between the Algorithm-Derived IOPs and the Measured Water Quality Parameters

The correlation of IOPs and the monitoring of biogeochemical properties have the potential to further our understanding of aquatic environments [107]. The correlation between these IOPs and biogeochemical parameters was analyzed using Pearson correlation heatmaps (Figure 7). To elucidate the specific characteristics of IOPs and their relationships with biogeochemical properties, it is essential to differentiate between the various IOP components. The study found distinct patterns in the correlation of IOPs, derived from the QAA, with measured water quality parameters (i.e., Chl-a, POC, PON, DON, and SS) across various wavelengths of IOPs. These findings underscore the effectiveness of a_p(λ), a_ph(λ), and a_NAP(λ) derived using the QAA and a_CDOM(λ) derived using the GSM algorithm in identifying correlations between IOPs and in situ biogeochemical parameters.

Parameter a_p(λ), derived using the QAA, showed associations with various biogeochemical parameters, with significant correlations across different wavelengths. The particle absorption correlation coefficient at 443 nm had a strong correlation with Chl-a, with a coefficient of 0.7, and positive correlations across wavelengths, ranging from 0.35 to 0.70. Phytoplankton cells contain pigments, including Chl-a, that absorb light at specific wavelengths, contributing to the overall particle absorption [108]. The particle absorption at 565 nm correlated well with POC, showing a correlation of 0.63, with consistent correlations (0.25 to 0.63) across wavelengths. Similarly, the correlation with PON at 565 nm was 0.66, with a positive correlation (0.29 to 0.66) across wavelengths. POC and PON are components of organic matter associated with particles, such as phytoplankton, detritus, and other suspended organic materials [47,109]. Light absorption by these particles is thus influenced by the concentration of organic matter, particularly pigments and light-absorbing organic matter [110]. The correlation with DON was weaker, peaking at 0.32 and generally being weak across wavelengths. For organic SS, a correlation of 0.66 was observed at 565 nm, with high correlations (0.27 to 0.66) across wavelengths. Organic SS are a major contributor to particle absorption as they include a variety of organic particles, such as detritus, microorganisms, and aggregated organic matter [111]. In contrast, inorganic SS exhibited negative-to-weak correlations with a_p(λ).

The correlation analysis of the QAA-derived a_ph at selected wavelengths with different water quality parameters revealed a range of relationships, underscoring the complex interactions within aquatic ecosystems. Chl-a exhibited a strong positive correlation with a_ph, particularly at 443 nm (r = 0.73), because it is a primary pigment in phytoplankton and directly responsible for light absorption in the blue spectrum; phytoplankton absorption is thus closely linked to Chl-a concentration [108]. However, a_ph at 412 nm showed weak correlations with most water quality parameters. Positive correlations were observed between a_ph and POC (r = 0.15 to 0.5) and PON (r = 0.18 to 0.54). The correlation of particulate organic materials is associated with phytoplankton, which contributes to the overall absorption properties of the water [47]. DON was generally low and had a negative correlation with a_ph. Organic SS had a moderate correlation with a_ph (r = 0.15 to 0.52) because they often originate from decomposing phytoplankton and other organic matter, contributing to light absorption. In contrast, inorganic SS generally show low correlations with phytoplankton absorption. This is likely due to inorganic SS primarily scattering light rather than absorbing light.

Parameter a_CDOM(λ) derived from using the GSM algorithm was examined in relation to various biogeochemical parameters, revealing correlations across wavelengths. The correlation of a_CDOM with dissolved nutrients allows for the determination of DON concentrations [112]. Absorption by colored DON is influenced by the mass of dissolved matter and organic SS in water [113,114]. The a_CDOM at 443 nm had a moderate correlation with Chl-a, with a coefficient of 0.46, and showed positive correlations across wavelengths. As phytoplankton (which contains Chl-a) grows and decomposes, it releases organic materials, including a_CDOM [108]. Parameter a_CDOM at 565 nm showed a moderate correlation with POC and PON, with a correlation of 0.53 and 0.51, demonstrating positive correlations across wavelengths. The correlation with DON was high, reaching 0.60, with positive correlations (0.49 to 0.60) across wavelengths. This suggests that a_CDOM is a useful indicator for assessing DON concentrations [115,116]. Since both DON and a_CDOM are derived from the breakdown of organic matter, their concentrations are correlated [117]. The correlation with organic SS was also high (0.59 at 565 nm); it showed a positive correlation across all wavelengths. The strength of this correlation depends on environmental conditions, sources of organic matter, and the characteristics of the given aquatic environment [34]. Inorganic SS, however, displayed negative-to-weak correlations with a_CDOM(λ).

The relationship between the QAA-derived a_NAP(λ) and various biogeochemical parameters was investigated. Several key correlations were found across different wavelengths. The NAP absorption coefficient at 565 nm exhibited a moderate correlation with Chl-a, with a coefficient of 0.46, and had positive correlations across wavelengths, ranging from 0.35 to 0.46. Higher Chl-a leads to an increase in the production of organic detritus, which contributes to the pool of non-algal particles as phytoplankton cells die and break down. The absorption at 565 and 670 nm showed strong correlations with POC, with a correlation of 0.55, and maintained high correlations (0.43 to 0.55) across wavelengths. Similarly, the correlation with PON at 565 and 670 nm was 0.58, showing moderate-to-high correlations (0.46 to 0.58) across wavelengths. The correlation of a_NAP with POC and PON depends on the composition of the particulate matter in the water and the specific environmental conditions [109]. A positive correlation was observed between a_NAP and particulate organic matter. The correlation with DOM was 0.54 at 443 and 530 nm, with positive correlations across wavelengths, ranging from 0.24 to 0.54. The correlation with organic SS peaked at 0.6 at 670 nm, showing the best correlations (0.5 and 0.6) across wavelengths. In contrast, inorganic SS exhibited negative-to-weak correlations with a_NAP(λ).

The correlation analysis of the QAA-derived b_bp at different wavelengths with various water quality parameters revealed significant relationships with the optical properties of the water body. The correlation between b_bp and Chl-a was generally low, with values around 0.28 across different wavelengths. This is likely because Chl-a, primarily associated with light absorption, contributes less to the particulate matter that influences backscattering. In contrast, b_bp showed moderate-to-substantial positive correlations with POC and PON, ranging from 0.40 to 0.45. This indicates that particulate organic materials likely contribute to the backscattering properties, enhancing the light scattering by particles in the water [118,119]. On the other hand, b_bp exhibited a weak positive correlation with organic SS (around 0.38), reflecting the role of organic SS in light scattering. Notably, b_bp had strong correlations with inorganic SS, with a consistent value of 0.64 across all wavelengths, highlighting the significant impact of inorganic particles on light backscattering.

4. Discussion

4.1. Performance Evaluation of IOP Algorithms and Validation of R_rs

The performance of the IOP retrieval algorithms across IOPs and wavelengths highlights significant differences in accuracy and reliability. The QAA consistently outperformed other algorithms, demonstrating the lowest error metrics and the highest correlation coefficients for most parameters. For a_p(λ) and a_ph(λ), the QAA achieved the highest accuracy with low MAPE and RMSE and high correlation coefficients. This performance is corroborated by previous studies [10,27,29] that emphasized the QAA’s ability to provide precise absorption estimates. The QAA outperforms other IOP retrieval algorithms in eutrophic lakes due to its semi-analytical, spectrally adaptive approach, which effectively decouples absorption and backscattering even in eutrophic waters [10]. In contrast, the GSM algorithm, while achieving a reasonable correlation for a_p(λ), exhibited higher MAPE and RMSE, indicating greater variability in its estimations [105]. The PML and LMI algorithms showed weaker performance, with lower r values and higher error metrics. The GIOP algorithm followed with reasonable error metrics, supporting its competitive accuracy as noted by Jorge et al. [27] and Werdell et al. [26].

The GSM algorithm exhibited a slightly better performance for estimating both a_NAP(λ) and a_CDOM(λ), highlighting its robustness and potential for deriving a_dg(λ) [11]. This makes it a valuable tool for applications in aquatic optics, particularly in environments where precise separation of absorption components is critical. However, the QAA performed slightly better, with a higher correlation coefficient. For a_CDOM(λ), the GSM algorithm achieved the highest correlation, with lower errors, aligning with the results obtained by Betancur-Turizo et al. [11] and Lewis and Arrigo [106]. GSM’s robustness in retrieving CDOM-dominated absorption is attributed to its semi-empirical parameterization of a_CDOM spectral slopes [28]. The GIOP algorithm had moderate accuracy, while the PML algorithm showed the weakest performance, with the lowest correlation and the highest MAPE and RMSE values.

The GIOP algorithm demonstrated a competitive performance for a_ph(λ) and a_NAP(λ), although it was not as consistently accurate as the QAA or GSM algorithms [27,29]. In eutrophic environments, both the QAA and GIOP algorithms show potential for accurately deriving absorption coefficients. Specifically, GIOP outperformed the PML and LMI algorithms for estimating a_ph(λ), achieving better correlation coefficients. Additionally, GIOP demonstrated lower error metrics, suggesting its suitability for use with further fine-tuning [10]. These results highlight the robustness of GIOP in eutrophic conditions, making it a promising tool for deriving absorption properties in complex aquatic environments. For a_NAP(λ), GIOP’s performance was similar to that of LMI and PML, with slightly higher error metrics. These findings suggest that while GIOP is not the most robust algorithm, additional parameterizations are needed for highly eutrophic environments [27], but its competitive performance in specific scenarios positions it as a viable alternative, particularly when optimized for specific optical conditions [10,120].

The performance of IOP algorithms depends on the optical water class and underlying equations used in their development, which can significantly influence their accuracy and effectiveness [11,27]. The PML and LMI algorithms exhibited a weaker performance, as evidenced by their higher error metrics and lower correlation coefficients across most IOPs. For a_CDOM(λ), the PML algorithm showed the highest MAPE and RMSE among all algorithms, with a significantly lower correlation coefficient, indicating its limited accuracy in retrieving a_CDOM. Similarly, for a_ph(λ), PML’s performance was poor, reflecting its inability to accurately handle phytoplankton absorption. The LMI algorithm demonstrated a similarly inconsistent performance, with moderate error metrics for a_CDOM(λ) and a_ph(λ) but a lower correlation coefficient [120]. These weaknesses underline the limitations of PML and LMI in accurately retrieving IOPs compared to the more robust QAA and GSM algorithms.

For shorter wavelengths, the error metrics were higher for algorithms such as the GSM algorithm, indicating potential issues with signal attenuation or noise [29]. Despite the variability observed for the GSM algorithm at lower wavelengths, there were notable similarities between the results of the GIOP and GSM algorithms, both of which utilize the Levenberg–Marquardt algorithm for solving unconstrained nonlinear least-squares problems [11]. The QAA and the GSM algorithm have the best accuracy, with consistent low error metrics and high correlation coefficients across various conditions [27]. The GIOP algorithm has potential but requires further tuning and optimization to improve its accuracy and reduce its variability [120]. Given the limitations of shorter wavelengths in complex hydrodynamic conditions within aquatic environments, longer wavelengths are increasingly being recognized for their enhanced utility in characterizing the optical properties of water [10].

The accuracy assessment of R_rs shows that there is a generally strong correlation between GCOM-C/SGLI satellite imagery and in situ data, particularly at higher wavelengths. Improvements in satellite data processing, atmospheric correction algorithms, and calibration/validation procedures could enhance the accuracy of satellite-estimated R_rs across all wavelengths [19,26,29,121]. Despite the challenges posed by the highly eutrophic conditions of Lake Kasumigaura, remote sensing reflectance-based water quality indicators have been successfully applied to estimate key parameters such as Chl-a and SS, demonstrating their utility in reducing uncertainty in optically complex waters [16,122,123,124]. Moreover, integrating satellite data with in situ measurements and advanced modeling techniques may improve the reliability and application of satellite-based water quality assessments [125,126]. Atmospheric correction improves retrieval of IOPs by minimizing aerosol overestimation in high-turbidity regimes, and these improvements preserve the spectral integrity of subsurface optical properties, which is critical for deriving aph, a_NAP, a_CDOM, and b_bp in chlorophyll-rich waters [26]. Aerosol models and sun glint parallax correction further reduce uncertainties in coastal and inland waters, where complex aerosol mixtures and surface glare often obscure the water-leaving signal needed for accurate IOP inversion [124,127].

The correlation analysis of water optical properties with various water quality parameters revealed that relationships varied based on the characteristics of the water components and their effects on light absorption and scattering. The QAA-derived a_p at 443 and 530 nm exhibited a strong correlation with Chl-a and had a moderate correlation with POC, PON, and organic suspended solids. This moderate-to-strong relationship reflects the combined contributions of phytoplankton pigments, particulate organic matter, detritus, and non-algal particles to the total particle absorption [47]. The QAA-derived a_ph at 443 and 530 nm showed high correlations with Chl-a (r = 0.69 and r = 0.73), Supporting studies indicating QAA-derived IOPs (especially a_ph) as effective Chl-a proxies [41,46,128,129]. GSM-derived a_CDOM at 443 nm exhibited positive correlations (r = 0.54) with DON, indicating that a_CDOM has the potential to serve as a proxy for detecting dissolved organic matter. [130]. The QAA-derived a_NAP at 443, 530, and 670 nm exhibited positive correlations with POC, PON, and organic suspended solids, underscoring the significant role of organic components in water optical properties by contributing to light absorption [46,47,131]. Conversely, inorganic SS showed strong positive correlations with b_bp (r = 0.64), reflecting the substantial influence of inorganic particles on light scattering, which is crucial for understanding water clarity and particle concentration [132]. The high interrelationship among backscattering coefficients across different wavelengths, particularly with inorganic SS, emphasizes how these particles dominate light scattering in water [133]. These findings highlight the importance of specific wavelengths in monitoring water quality, with different optical properties providing valuable insights into the presence and concentration of both organic and inorganic matter in aquatic environments.

This study evaluated the performance of commonly applied IOP algorithms for water quality monitoring in highly eutrophic lakes, incorporating validation with in situ measurements and satellite data. A key limitation arises from the inherent optical complexity of such environments, which can significantly impair the accuracy of IOP retrievals [134]. High variability in water constituents, including dissolved organic matter, suspended sediments, and phytoplankton, introduces challenges in isolating distinct optical signatures [21,135]. Furthermore, atmospheric interference, particularly due to light scattering and absorption, introduces additional uncertainties in remote sensing data, affecting water quality assessments [20,59,124]. Given the high sensitivity of IOP algorithms to minor perturbations [27], these environmental and atmospheric factors may reduce the reliability of derived biogeochemical parameters.

4.2. Comparison of Phytoplankton Absorption and Chlorophyll a

Understanding Chl-a and phytoplankton absorption is crucial for monitoring aquatic environments and evaluating the impact of environmental changes on primary production and nutrient dynamics [136,137]. Standard GCOM-C/SGLI algorithms have been developed through empirical approaches to enable cross-sensor compatibility for chlorophyll a (Chl-a) estimation [138].

The correlation between Chl-a and a_ph (443 nm) indicated good accuracy, with a linear correlation of r = 0.73 (Figure 7b) and a polynomial correlation of r = 0.84 (Figure 8a,b). A polynomial function was subsequently developed to derive Chl-a using a_ph (443 nm), reflecting this enhanced relationship.

$$\mathrm{C}\mathrm{h}\mathrm{l}-\mathrm{a}=-236.43\times {a_{ph}(443 \mathrm{n}\mathrm{m})}^2+336.76\times a_{ph }(443 \mathrm{n}\mathrm{m})-12.89$$

(10)

From the comparison of the correlation between the Chl-a concentration and a_ph at different wavelengths, alongside the derived Chl-a values, the correlation coefficient for Chl-a measured against a_ph at 443 nm was 0.84, and the RMSE value was 13.26 μg/L, indicating a good relationship between the Chl-a concentration and phytoplankton absorption at this wavelength due to the dominant absorption characteristics of photosynthetic pigments in the blue spectral region [139]. This relationship forms the basis for many bio-optical algorithms that estimate Chl-a from remote sensing reflectance, particularly in open ocean waters where phytoplankton pigments dominate the optical signature [140]. This result is due to the varying absorption efficiency of phytoplankton pigments, which absorb more strongly in the blue region and less in other regions, thereby affecting the relationship with Chl-a. In contrast, the Chl-a values that Murakami [138] derived had a correlation coefficient of 0.56 and RMSE values of 36.51 μg/L, and the Chl-a estimated based on a_ph (443 nm) had a correlation coefficient of 0.84 and the RMSE value of 13.26 μg/L, respectively. The Chl-a values estimated based on a_ph (443 nm) had a better correlation, which indicates that absorption by phytoplankton is a good indicator of Chl-a in Lake Kasumigaura. However, the strength of the correlation and potential estimation errors must be considered. This method outperformed remote sensing reflectance-based Chl-a estimations, which achieved a validation r of 0.65 [16]. Spectral decomposition analysis (SDA) has exhibited comparative performance at Lake Kasumigaura [64,65]. To assess the Chl-a concentration, the right combination of a_ph can be used based on phytoplankton biomass in water quality assessments [141,142]. This indicates that IOP-based algorithms can be applied for water quality estimation [18].

4.3. Comparison of the Correlation Between Backscattering of Particles and Suspended Solids

High particle concentrations significantly affect light backscattering in water by altering backscattering coefficients and spectral properties. Studies have shown that the measured backscatter intensity can be used to estimate SS based on particle size distributions and concentrations [57,58]. Additionally, particle backscattering is crucial for estimating SS in highly turbid coastal waters, underscoring the importance of understanding the interactions between backscattering coefficients and suspended particles [55,56]. The increase in turbidity at Lake Kasumigaura is likely attributable to sediment suspension and higher inorganic SS [122].

The analysis of water optical properties, particularly the relationship between SS and backscattering at 443 nm, reveals important distinctions between organic and inorganic suspended particles. The correlation between organic SS and water optical properties (Figure 9a), specifically backscattering at 443 nm, was weak (r = 0.38 and RMSE = 0.24 mg/L) because other optically active substances in organic SS, such as phytoplankton, non-algal particles, and DOM, have absorption properties. The complex nature of particulate organic matter, which predominantly absorbs light rather than scattering it, limits the contribution of organic matter to backscattering signals. For inorganic SS, the correlation with b_bp (443 nm) (Figure 9b) was high (r = 0.64 and RMSE = 25.05 mg/L). The backscattering of particles at 443 nm provides good insight into inorganic suspended particles [47]. The correlation of suspended solids and backscattering indicates distinct optical properties, where organic and inorganic components interact differently with light. The backscattering at 443 nm is a good indicator for assessing inorganic suspended particles, offering valuable insights into water quality and particle composition [46,131]. The b_bp-based estimation of inorganic SS has significant potential to be accurate, especially if refined methodologies are employed or additional parameters are considered.

5. Conclusions

In this study, the performance of the QAA, PML, LMI, GIOP, and GSM IOP algorithms at Lake Kasumigaura, Japan, were investigated. A comparison of the IOP algorithms across different wavelengths and IOPs was conducted based on the key metrics, including the correlation coefficient. Notably, the QAA demonstrated a consistently superior performance for a_p(λ), a_ph(λ), and a_NAP(λ), as indicated by its low MAPE and RMSE values (0.23 m⁻¹ and 0.08 m⁻¹) and a high correlation coefficient (0.85 to 0.98). The GSM algorithm had the highest correlation for a_CDOM(λ), indicating its reliability across a spectrum of conditions at Lake Kasumigaura. The PML and LMI algorithms showed relatively high error rates, particularly at shorter wavelengths, indicating potential discrepancies in their estimations and limitations in their application at these specific spectral bands. Based on the comparative analysis of the IOP algorithms, the QAA and the GSM algorithms were chosen for the analysis of the implications of IOPs on water quality due to their higher correlation coefficients, lower MAPE and RMSE, and strong consistency.

The accuracy assessment of the level 2 GCOM-C/SGLI satellite-derived R_rs compared with the in situ measured R_rs showed a strong correlation at mid-to-longer wavelengths and a moderate correlation at shorter wavelengths. Reliability of satellite-derived R_rs is crucial for the effective application of IOP algorithms. Studies have highlighted the critical need for improved atmospheric correction techniques, particularly at lower wavelengths, to enhance the accuracy and reliability of remote sensing data across various applications. The correlation analysis of the QAA-derived IOPs with the measured water quality parameters showed a significant correlation in that a_ph at 443 nm correlated well with the Chl-a concentration (r = 0.84, RMSE = 13.26 μg/L) and that b_bp at 443 nm correlated well with inorganic SS (r = 0.64, RMSE = 25.05 mg/L). These findings highlight that the different levels of correlation of IOPs serve as indicators of Chl-a, POC, PON, DON, and both organic and inorganic SS at Lake Kasumigaura. Improving the predictive accuracy of water quality by employing advanced methods and incorporating additional environmental factors can enhance long-term water quality monitoring in eutrophic lakes, particularly by using IOPs alongside satellite remote sensing data.