Analysis of the Influence of Input Conditions on the Diffuse Attenuation Coefficient for Downwelling Irradiance Based on the Radiative Transfer Model

Abstract

The diffuse attenuation coefficient for downwelling irradiance (K_d)representsthe exponential decrease of light with depth due to scattering and absorption in seawater, and is one of the key products for describing ocean optical properties. To estimate K_d over broad oceanic regions, semi-analytical models utilizing remote-sensing reflectance (R_rs) and inherent optical properties (IOPs) derived from satellite observations are commonly employed. Among these, K_d models based on radiative transfer simulations often consider only the solar zenith angle (SZA) among various atmospheric and water quality variables, which can lead to discrepancies between estimated and actual values. In this study, we investigate the effects of four atmospheric variables-SZA, wind speed, aerosol type, and aerosol optical depth (AOD)-on K_d using radiative transfer simulations. To reflect varying water quality, simulations were conducted for three water types: clear, intermediate, and turbid. By analyzing the change in K_d values as each environmental variable was changed from its minimum to maximum condition, we found that SZA had the greatest impact, followed by AOD. In contrast, wind speed and aerosol type showed minimal influence and may be excluded from future algorithm improvement considerations. When analyzing K_d estimated from the semi-analytical model, SZA-induced errors reached up to 28.17% in turbid waters, and AOD-related errors were as high as 17.93%. Although the semi-analytical model theoretically accounts for SZA, significant discrepancies were still observed, especially under turbid conditions. Therefore, to improve the accuracy of K_d estimation, the influence of SZA should be prioritized, and additional corrections for AOD and turbidity should also be incorporated into the K_d model development. This study identifies key environmental variables affecting K_d retrieval and suggests directions for improving the model, contributing to the development of more accurate K_d algorithms applicable under diverse marine conditions.

1. Introduction

Ocean color remote sensing is a technology that estimates the optical and biological characteristics of the ocean by observing the spectral signals reflected from the sea surface. These signals result from the absorption, scattering, and attenuation of sunlight by various optically active constituents in seawater, and are observed using satellite or airborne sensors. The diffuse attenuation coefficient for downwelling irradiance (K_d) is an exponential function that represents the degree to which the downward diffuse irradiance (E_d) in the vertical direction is attenuated by various optical processes, as shown in Eq. (1). It is one of the key parameters representing the optical properties of the ocean (Lee et al., 2018). Eq. (1) can be rearranged into an equation for K_d, as shown in Eq. (2).

E_d(z, λ) = E_d(0^-, λ)e^-K_d(λ)z       (1)

\(\begin{align}K_{d}(z, \lambda)=z^{-1} \ln \frac{E_{d}\left(0^{-}, \lambda\right)}{E_{d}(z, \lambda)}=-\frac{\left(d \ln E_{d}(z, \lambda)\right.}{d z}\end{align}\)       (2)

Here, z represents the depth from the water surface. In reality, the K_d distribution varies depending on z, but it is difficult to measure Ed for all z. Therefore, K_d just below the water surface in the surface layer (z =0^-, d →0) can be used as a representative value, and in this case, z can be omitted and simplified to K_d(λ). K_d plays an important role in deriving information related to the marine ecosystem, such as the depth of the euphotic layer, which is used to estimate heat transfer or primary productivity in the upper ocean (Lewis et al., 1990; Marra et al., 1995; Zhao et al., 2013), and can be used to classify clear waters (Case 1) and optically complex turbid waters (Case 2) (Jerlov, 1976). Satellite-based remote sensing technology is essential to derive K_d for a wide ocean area. Empirical and semi-analytical algorithms are mainly used to estimate K_d, and two approaches are utilized for the empirical algorithm (Min et al., 2007). The first method estimates K_d at 490 nm using the blue-green wavelength ratio of remote-sensing reflectance (R_rs) or water-leaving radiance (L_w), and then extends it to the entire wavelength range using a regression equation (Austin and Petzold, 1981; Mueller, 2000).

The second method derives chlorophyll concentration using the ratio of R_rs, and then estimates K_d based on this (Morel, 1988). Empirical algorithms are simple to calculate and easy to apply to satellite data, but they have limitations in reflecting diverse and complex marine environments. To overcome these limitations, a semi-analytical model using remote sensing technology based on a radiative transfer model was proposed (Lee et al., 2005a). This method consists of a K_d model that calculates K_d by using the absorption coefficient(a) and backscattering coefficient(b_b), which are inherent optical properties (IOPs) from R_rs. Lee et al. (2005b) proposed a K_d model using a radiative transfer model, but it had problems such as excluding the ultraviolet range below 400 nm and underestimating the effect of short-wavelength molecular scattering. To address these issues, they proposed a more recent K_d model(Lee et al., 2013). However, the sea surface affects the light incident on the ocean depending on atmospheric conditions, which affects the calculation of K_d, and these external environmental variables cause errors in K_d estimation. Atmospheric environmental variables, such as solar zenith angle (SZA), wind speed, and aerosol, directly affect the distribution of light entering the sea surface; therefore, an analysis of their influence is necessary.

Therefore, this study aims to compare and analyze K_d estimation errors according to major environmental variables and quantitatively evaluate the relative influence of each variable by utilizing the HydroLight radiative transfer model (Mobley, 1994; Lee et al., 2005b), which can obtain various numerical model information about the ocean. In particular, by considering not only atmospheric conditions but also turbidity, a water quality condition, we aim to establish the foundation for a precise K_d calculation technique applicable to various marine conditions. The results of this study are expected to improve the accuracy of satellite-based K_d calculation algorithms and serve as practical basic data for enhancing the reliability of ocean color data and further enhancing the algorithm in the future.

2. Materials and Methods

2.1. HydroLight Simulation

Because the acquisition of large amounts of ocean color information through field observations is limited, many studies utilize HydroLight simulation to generate analysis data. HydroLight simulation is a program that numerically radiative transfer model, calculating the radiance and irradiance distributions by considering the optical properties of seawater and environmental conditions. To perform the simulation, common input IOPs for pure water, as well as IOPs for chlorophyll, colored dissolved organic matter (CDOM), and inorganic particles, are required regardless of environmental conditions. The absorption coefficient of pure water (aw) and scattering coefficient of pure water (b_w) were used as data presented in Pope and Fry (1997) and Smith and Baker (1981) in the range of 200-1,000 nm in 5 nm increments, respectively. The IOPs for chlorophyll and CDOM were calculated using the default models and coefficients set in HydroLight Simulation (Mobley and Sundman, 2012a, 2012b). Absorption coefficient of non-algal particles (a_nap) and scattering coefficient of non-algal particles (b_nap) used the information provided by Ahn (1990) in the range of 300-1,000 nm in 5 nm increments. Because the high absorption of water in the near-infrared region tends to prevent light from reaching deep into the water, resulting in very high K_d, we set it to the range of 400-700 nm, which is mainly used to analyze K_d(λ) from satellites (Mobley, 1994; Prasetyo et al., 2018).

2.2. Setting Conditions for Environment Variables

To analyze the influence of environmental variables on K_d, simulation scenarios were constructed using a set of predefined conditions. In this study, we aimed to examine the influence of four factors that can affect the amount of light entering the sea surface: SZA, wind speed, aerosol type, and aerosol optical depth (AOD). To evaluate the maximum change and error range of K_d that may occur due to changes in environmental variables, we set minimum and maximum values for each variable and distinguished cases (Table 1).

Table 1. Minimum and maximum conditions for environmental variables applied in the HydroLight simulation

Considering that SZA values above 70° are associated with high uncertainty and low reliability depending on season and latitude, and that the development of ocean color satellite-based algorithms has an effect (Li et al., 2017), the minimum was set to 0° and the maximum was set to 60°. Considering that the influence of surface gravity waves is significant in the range of wind speeds up to 10 m/s and that the waveform reaches saturation when it exceeds 10 m/s, resulting in little change in sea surface structure, the minimum was set to 0 m/s and the maximum was set to 10 m/s (Melville and Fedorov, 2015). The aerosol types were defined as marine aerosol (Type 1) and continental aerosol (Type 10) as the minimum and maximum, respectively, utilizing the range provided by the HydroLight simulation. Type 1 is characterized by dominant forward scattering caused by relatively large atmospheric particles, with comparatively low absorption, resulting in a higher irradiance reaching the sea surface (Gathman et al., 1983). In this case, since the propagation direction of light does not change significantly, the angular distribution is anisotropic, leading to higher underwater transmittance and generally lower estimated K_d. However, it should be noted that under conditions of very low solar altitude, the longer atmospheric path length increases scattering and absorption, which can in turn reduce transmittance. AOD was calculated using the extended version (RADTRAN-X) of the atmospheric propagation model RADTRAN, originally developed by Gregg and Carder (1990), which covers the spectral range from 300 to 1,000 nm (Mobley and Sundman, 2012b). RADTRAN is designed to rapidly and accurately predict the spectral irradiance of direct solar radiation and diffuse skylight reaching the sea surface under given atmospheric conditions, such as aerosol type, water vapor, and ozone concentrations, and solar altitude, with an accuracy within 6.6%. In this study, AOD was calculated using input parameters such as aerosol type and average horizontal visibility. The minimum is set to 0.13 when the visibility is 30 km, and the maximum is set to 3.91 when the visibility is 1 km.

In addition to the input conditions, to examine the influence of water quality conditions on K_d, we analyzed the effects by setting the combination of total suspended matter (TSM), chlorophyll concentration, and CDOM extinction coefficient into three cases: clear, intermediate, and turbid waters (Table 2). The input data for each case, according to turbidity, was based on the dataset proposed by Ahn and Park (2020), which is based on the range of field observation data observed in the waters around the Korean Peninsula. The TSM concentration is set to increase in logarithmic intervals of 0.0625 from 0.3160 g/m³. Although turbidity concentrations exceeding 500 g/m³ have been observed in domestic coastal waters with high turbidity, the maximum value was set to 177.8280 g/m³ to ensure that the influence of turbidity does not overwhelm the influence of the established environmental variables (Choi and Park, 1998). The TSM for intermediate turbidity was set to 17.7828 g/m³, which corresponds to the middle of the logarithmic interval. The chlorophyll concentration and CDOM absorption coefficient values were set according to the TSM concentrations set for clear and turbid waters, as shown in Table 2, and for intermediate turbidity, the values corresponding to the middle of the log scale interval were also applied.

Table 2. Input conditions by turbidity level in the HydroLight simulation

2.3. Research Methods

In this study, the K_d of the simulation derived according to the input conditions is regarded as the true value and is defined as Ture_K_d (Fig. 1). In order to analyze the effect of environmental variables changing from the minimum to the maximum, the change in Ture_K_d was calculated by fixing all variables except the target variable to be analyzed. The variation in Ture_K_d was plotted according to wavelength to analyze the spectral distribution according to the change in the target variable, and among them, the distribution of change by environmental variable was visualized for comparison for 490 nm, which is representatively used in K_d analysis.

Fig. 1. Flowchart of K_d sensitivity analysis to environmental variable changes using HydroLight simulation.

To estimate K_d based on satellite data, the IOPs values derived from R_rs must be used to calculate K_d using a semi-analytical algorithm. In this study, we applied the K_d model proposed by Lee et al. (2013), and the K_d calculated through this was defined as Model_K_d (Fig. 1). The applied K_d model is based on the radiative transfer model, using a and b_b as input data, and includes a correction for SZA, which has the greatest influence, as presented in Eq. (3).

K_d(λ) = m₀a(λ) + (1 - γ × ηw(λ)) × m₁ × (1 - m₂e^-m3a(λ)) x b_b(λ)       (3)

Here, m₀ ≈ 1 + 0.005θ_a is expressed as θ_a, and m₁, m₂, and m₃ are applied as 4.18, 0.52, and 10.8 derived from the radiative transfer model. γ is 0.265, and η_w(λ) is applied by calculating b_bw(λ)/b_b(λ). The difference between Model_K_d calculated through the K_d model and True_K_d of the same input conditions was calculated to analyze the error by the K_d model. True_K_d and Model_K_d when the input conditions of the environmental variables are minimum and maximum were plotted graphically to compare the error by the K_d model and the amount of change by the environmental variables.

The percentage error from the K_d model was calculated and compared by dividing by True_K_d. Furthermore, the root mean square error (RMSE) and the coefficient of determination (R²) were calculated for quantitative analysis. In addition, since very small values can result in disproportionately large percentage errors due to small changes, the symmetric mean absolute percentage error (SMAPE) was calculated and compared to allow for a stable comparison of relative errors even at small values. When comparing data, smaller RMSE and SMAPE values indicate greater accuracy, while R² values closer to 1 indicate similar values.

To compare the effects of turbidity when analyzing errors from True_K_d analysis or the K_d model, the levels were categorized into low TSM environments (representing clear waters), middle TSM environments (representing slightly turbid waters), and high TSM environments (representing very turbid waters). These were then compared.

3. Results

3.1. Analysis of the Impact of K_d on Environmental Variable Changes

In order to compare which environmental variable has the greatest influence when the environmental variables affecting K_d are set to the minimum and maximum values, a graph was plotted according to turbidity classification, as in Fig. 2. First, K_d, when all environmental variables are set to the minimum value (SZA: 0°, wind speed: 0 m/s, aerosol type: 1, AOD: 0.31), is represented by a black dotted line as the Minimum condition, and the K_d data changed to the maximum value for each environmental variable are represented by solid lines. When the wavelength distribution of True_K_d was compared according to turbidity conditions, it tended to be low in short wavelengths in clear sea areas and increased significantly in the wavelength range above 600 nm. However, in turbid sea areas with high TSM concentrations, K_d values were high at short wavelengths and tended to decrease rapidly around 580 nm. This is because light scattering and absorption by suspended particles in turbid waters are strong, and a and b_b have large values at short wavelengths(Morel and Prieur, 1997). This confirms the presence of an effect due to turbidity.

Fig. 2. True_K_d distribution by environmental variable changes across turbidity level. (a) Low TSM data. (b) Middle TSM data. (c) High TSM data.

Although the distribution of True_K_d differed depending on the turbidity classification, the differences caused by changes in environmental variables were similar. In Low TSM, it was confirmed that the change in True_K_d became greater as SZA and AOD changed above 600 nm. This is because the absorption in pure water increases as the wavelength increases, and as the absorption increases above 600 nm, the attenuation effect, according to the change in SZA, reacts much more sensitively, resulting in a larger change range. On the contrary, in High TSM, the change in True_K_d becomes smaller as the wavelength increases, because in turbid waters, a decreases with longer wavelengths, so the effect of SZA is less reflected. Among the four variables, the difference in True_K_d due to the change in SZA was the largest, and the difference due to the change in AOD was the second largest. In addition, the K_d distribution according to the change in aerosol type showed almost no difference before and after, and the graph confirmed that the K_d distribution of wind speed was different compared to the aerosol type.

For the average difference in True_K_d according to the change in each variable was calculated. In Low TSM, the differences were 0.0585 m^-1, 0.0021 m^-1, 0.0002 m^-1, and 0.0244 m^-1 for SZA, wind speed, aerosol type, and AOD, in that order. In High TSM, the differences were 2.8048 m^-1, 0.1173 m^-1, 0.0123 m^-1, and 1.1643 m^-1. These results indicate that SZA has the strongest influence, being approximately twice as influential as AOD. As for wind speed and aerosol type, the difference is approximately 24 times and 228 times, respectively, in the High TSM environment compared to the influence of SZA. It is relatively very small, so it was judged that they can be excluded from the environmental variables that should be given priority when improving the K_d algorithm.

If we previously looked at the effect of K_d over the entire wavelength range, we wanted to compare the effects of environmental variable changes on 490 nm, which is typically used in K_d analysis. For one target variable, the change in K_d(∆(True_K_d)) was calculated as it changed from the minimum to the maximum, and the changes were expressed through a box plot (Fig. 3). Regardless of turbidity, the change due to SZA was calculated to be the largest, with an average change of 2.82 m^-1 in High TSM. The changes for the remaining variables excluding the target variable were distributed in a wide range, from 1.73 to 3.94 m^-1. In the case of AOD, the average change was 0.69 m^-1 in High TSM, which was relatively smaller than the effect due to SZA, but the range of changes was 0.10 to 1.70 m^-1, which meant that the effect of AOD could vary depending on different environmental conditions. The variation of K_d by aerosol type was confirmed to have a very small effect, with an average variation of 0.01 m^-1 in High TSM, close to 0. In the case of wind speed, an average variation of 0.44 m^-1 was confirmed in High TSM, but it was judged that the influence was not as large as that of SZA or AOD. Therefore, among the major environmental variables, SZA, wind speed, aerosol type, and AOD, we aimed to focus on analyzing the variation of K_d caused by SZA and AOD.

Fig. 3. Impacts of input variables on True_K_d at 490 nm (max-min) across turbidity level. (a) Low TSM data. (b) Middle TSM data. (c) High TSM data.

3.2. Error Analysis Using the K_d Model according to Changes in Environmental Variables

3.2.1. K_d Error Analysis according to SZA Change

In order to calculate K_d using IOPs, a semi-analytical K_d model must be applied, and errors may occur in this process. Since the influence of SZA and AOD is important through True_K_d analysis, the difference between True_K_d and Model_K_d as SZA and AOD change from minimum to maximum is represented in a graph as in Fig. 4 to compare visually. By comparing either the solid lines or the dotted lines on the graph, the error caused by the K_d model under the same SZA and turbidity conditions can be identified. Comparing either the True_K_d lines or the Model_K_d lines allows assessment of the differences resulting from the change in SZA from 0° to 60°. In Low TSM, when SZA is 0°, the average error by the K_d model was 0.0077 m^-1, and as it increased to 60°, the average error by the K_d model increased to 0.0508 m^-1. On the other hand, Middle TSM and High TSM showed different results from Low TSM. In Middle TSM, the average errors by the K_d model for cases where SZA was 0° and 60° were 0.2671 m^-1 and 0.0524 m^-1, respectively, and in High TSM, they were 2.3548 m^-1 and 0.4162 m^-1, respectively. This confirmed that there is a limitation that the error is about 5 times larger, even when SZA is small, because the proportion of particle scattering increases in turbid waters, and the K_d model cannot completely reflect this. The change in Model_K_d due to changes in SZA converged to almost 0 in Low TSM, but showed an average difference of 0.0339 m^-1 in High TSM. This is because SZA, a, and b_b are input data for the K_d model, and since the same a and b_b derived from the simulation are applied, only a slight difference occurs due to changes in SZA.

Fig. 4. Distribution of True_K_d and Model_K_d at minimum and maximum SZA across turbidity level. (a) Low TSM data. (b) Middle TSM data. (c) High TSM data. The Model_K_d values at SZA = 0° and 60° show only a slight difference.

To quantitatively assess the error of the True_K_d model, defined as the difference between True_K_d and Model_K_d, several metrics were calculated: percentage error, RMSE, R², and SMAPE(Table 3). As shown in Fig. 4, under Low TSM conditions at SZA 0°, the percentage error was as low as 6.91%, and R² was close to 1, indicating high model accuracy. However, in the case of Middle TSM and High TSM, the percentage error for 60° was 5.10% and 9.59%, which were 4 to 5 times different from the case of 0°, and R² was also 0.93 or higher, showing high accuracy compared to the true value. However, as the SZA changed, the percentage error changed by 28.17% in High TSM, indicating that it was greatly affected by the SZA. Through qualitative and quantitative analysis results, it was confirmed that the error by the K_d model due to changes in SZA varied depending on the turbidity of the seawater, and that the percentage error due to SZA was greater in turbid sea areas, indicating the need for correction for turbidity.

Table 3. Quantitative evaluation of SZA changes according to turbidity level

3.2.2. K_d Error Analysis according to AOD Change

To evaluate how the difference between True_K_d and Model_K_d varies with changes in AOD from minimum to maximum, which has the second largest influence after SZA, as shown in Fig. 5. In Low TSM, the average error of Model_K_d with AOD of 3.91 was 0.0167 m^-1, and when AOD was 0.13, the average error was 0.0077 m^-1, showing that the error was about twice as high when AOD was high. The fact that there was a relatively small difference compared to the influence of SZA shows that the influence of SZA is more dominant. In Middle TSM and High TSM, when AOD was 0.13, the values were 0.2671 m^-1 and 2.3548 m^-1, respectively, and when AOD was 3.91, they were 0.1316 m^-1 and 1.1905 m^-1, respectively, confirming that the case with low AOD had an error that was about twice as large. This is because the case with AOD of 3.91 reflects the case where there are excessive particles in the atmosphere, and because, unlike SZA, the K_d model does not consider the atmospheric environment, such as AOD, so the error effect is analyzed to be greater.

Fig. 5. Distribution of True_K_d and Model_K_d at minimum and maximum AOD across turbidity level. (a) Low TSM data. (b) Middle TSM data. (c) High TSM data. The Model_K_d values at AOD = 0.13 and AOD = 3.91 are identical.

Table 4. Quantitative evaluation of AOD changes according to turbidity level

As a result of quantitatively analyzing the error of Model_K_d according to the change in AOD, in Low TSM, the percentage error was low at less than 7% for both cases where AOD was 0.13 and 3.91, and R² showed high accuracy at over 0.97. This shows that the influence of AOD is somewhat small in optically clear waters. In Middle and High TSM, when AOD is as large as 3.91, the percentage error and SMAPE range from 12.74 to 19.83%, which is higher than the percentage error when SZA is 60°. However, as AOD changed from the maximum to the minimum, the percentage error increased by 17.93%, which was lower than the change in percentage error according to the change in SZA, confirming again that the effect of AOD change on the Model_K_d error was relatively small. Therefore, to improve the accuracy of the K_d model, SZA should be prioritized and given greater weight than AOD. Furthermore, while changes in atmospheric environmental variables such as SZA and AOD are important, the impact on K_d can vary depending on the level of seawater turbidity. Therefore, additional turbidity-dependent applications should also be considered.

4. Discussion and Conclusions

This study identified key environmental variables that affect the estimation of K_d using radiative transfer model-based simulations. It examined how variations in these variables influence K_d and contribute to errors in the K_d model. Environmental variables included atmosphere-related factors such as SZA, wind speed, aerosol type, and AOD. Furthermore, water quality conditions that could influence K_d were analyzed by dividing the water into three cases, from clear to turbid, based on TSM concentration. The analysis revealed that SZA had the greatest impact under allturbidity conditions. In particular, in turbid waters, the percentage error of K_d increased by 28.17% as SZA varied from 0° to 60°, significantly impacting the accuracy of the K_d model. AOD showed relatively minor errors in clear waters, but a 17.93% change in percentage error in turbid waters. However, its impact was found to be less significant than that of SZA across all turbidity conditions and was considered secondary in terms of algorithm improvement. Changes in wind speed and aerosol type had minimal effects on K_d, suggesting that they can be excluded from consideration when improving the algorithm.

While the impact of these environmental variable changes was confirmed, we found that even under the same environmental conditions, the distribution and error varied in a complex manner depending on the level of seawater turbidity. In particular, as SZA and AOD changed from minimum to maximum, the percentage error increased in clear waters, but in turbid waters, the percentage error was greater at the minimum value and decreased at the maximum value. This can be explained by the fact that increasing SZA and AOD enhance atmospheric scattering, while higher turbidity further intensifies scattering within the water column. These processes lead to a more uniform angular distribution of light, thereby reducing the sensitivity of the K_d model to angular variations (Cui et al., 2014). Consequently, in turbid waters, higher SZA and AOD values were associated with smaller K_d model errors. This finding highlights the complex interactions among SZA, AOD, and turbidity, but the K_d model adopted in this study does not explicitly account for turbidity effects. Therefore, when refining the K_d model, priority should be given to SZA correction, while additional adjustments for AOD and turbidity conditions should also be incorporated.

In this study, to determine the maximum impact of environmental variable changes on K_d, simulations were performed by specifying the minimum and maximum values of each variable, and the results were analyzed. However, it was found that seawater turbidity not only changes the K_d distribution characteristics but also reduces the percentage error due to environmental variables, exerting a complex influence. These results suggest that it is necessary to refine the environmental variables used as simulation input conditions further and analyze the data under various combinations of conditions. Additionally, this study analyzed the individual effects of SZA and AOD under different turbidity conditions, but their interaction effects were not considered. Future work should investigate the interaction between SZA and AOD by testing a wider range of values to identify trends. Such analyses could contribute to the improvement of K_d algorithms by allowing for the subdivision of environmental conditions and the application of different models, or by enabling the design of more refined correction schemes.

Recently, satellite-based K_d products have been widely utilized to monitor broad oceanic regions regularly. For example, South Korea operates the Geostationary Ocean Color Imager-II (GOCI-II) onboard the GEO-KOMPSAT-2B satellite, which provides K_d products for the East Asia region at hourly intervals with a spatial resolution of 250 m (Huh and Jin, 2022). Currently, the satellite-derived K_d estimation applies an IOPs-based K_d model, as used in this study, but only SZA correction has been applied (Korea Hydrographic and Oceanographic Agency, 2021). To further improve the accuracy of satellite-based K_d products, it is necessary to develop correction algorithms that incorporate not only SZA but also the effects of AOD and turbidity, based on the findings of this study and in conjunction with in-situ observations. This improved K_d algorithm could be extended beyond the East Asian region to various marine environments worldwide and is expected to be incorporated into future satellite missions. Such advancements will enable more accurate monitoring of climate change and environmental variability in ocean optical properties.

In conclusion, to improve the accuracy of future satellite-based K_d retrieval algorithms, it is essential to obtain extensive simulation data that reflect diverse atmospheric and water-quality conditions, refine the SZA correction function included in existing K_d models, and conduct continuous research to incorporate additional correction terms for AOD and turbidity.

Author Contributions

Conceptualization: Lee HB, Min JE, Ahn JH; Data curation: Lee HB; Methodology, Formal analysis, Validation: Lee HB, Min JE, Ahn JH; Project administration: Min JE, Kim KL; Funding acquisition: Kim TH; Resources: Ahn JH; Supervision: Min JE, Ahn JH; Writing-original draft: Lee HB; Writing-review & editing: All authors.

Conflicts of Interest

No potential conflict of interest relevant to this article was reported.

Funding

This research was supported by the Korea Institute of Marine Science & Technology Promotion (KIMST), funded by the Ministry of Oceans and Fisheries (RS-2022-KS221660).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.