2.1.

Study Area

In this study, the East Sea, Yellow Sea, and South Sea, and the waters around Jeju Island were included in the analyses. To accurately represent the diverse marine environmental characteristics of the three seas surrounding the Korean Peninsula and generate optimal machine learning data along with credible depth estimation results, we selected Samcheok (East Sea), Hallim (South Sea), and Cheonsuman Bay (West Sea) as our training areas (Fig. 1 and Table 1). Specifically, Hallim was selected as an area representative of the South Sea based on the general characteristics of the South Sea coastal waters and the coexistence of sandy and basaltic seabed materials.

Fig. 1

Geographic location of training areas. Sentinel-2A/B RGB images of (a) Cheonsuman, (b) Hallim, and (c) Samcheok. The blue boxes indicate three additional test areas, different from the training areas. Deokjeok in Yellow Sea, Seongsan in South Sea, and Sokcho in East Sea.

Table 1

Geographic coordinates of training areas.

2.2.

Materials

2.2.2.

Bathymetric data

The depth data provided by KHOA were water depth values used for the latest nautical chart (echo-sounding in 2020), extracted and edited based on echo-sounder data, with the referenced depths based on the datum level (DL) (Fig. 2). Considering that a vector format was used for bathymetric data, they were resampled to align with the 10-m resolution of the satellite imagery grid. Drawing on prior research regarding the limitations of light penetration depth, our study focused solely on areas with depths $<20\mathrm{m}$.^3,5,14 We employed tidal values from the corresponding timestamps for model training and result test to adjust for the datum.

Fig. 2

Real-depth in situ echo-sounding bathymetry data from the KHOA of (a) Cheonsuman, (b) Hallim, and (c) Samcheok.

2.2.3.

Tidal data

To obtain tidal data, we employed the NAO99.Jb tidal model provided by the National Astronomical Observatory of Japan.³⁵ The NAO99.Jb tidal model with a spatial resolution of 1/12 deg (about 1 km) was designed for use in the Northwest Pacific region.³⁶

To ascertain the precision of the NAO99.Jb model, its outputs were systematically compared to observation data. The detailed analysis was performed on three positions in Yellow Sea (Incheon, Pyeongtaek, and Anheung) with high tidal range [Fig. 3(a)]. The tidal amplitudes obtained from the tide stations at these locations were compared to the predicted results provided from the model. The error at all stations was calculated to be $<5\mathrm{cm}$ (Table 4). These findings suggest that the NAO99.Jb model can be effectively utilized as tidal calibration data.

Fig. 3

(a) A map showing the locations of Incheon (37.4519° N, 126.5922° E), Pyeong-taek (37.1366° N, 126.5408° E), and Anheung (37.6747° N, 126.1294° E). (b) A time-series graph comparing values between the observation (black) and NAO99.Jb (red) from July 1, 2020, to July 3, 2020. The $x$ axis is time and $y$ axis is sea surface height.

Table 4

The amplitude of observed values from the three regions was compared with the amplitude of values from the NAO99.Jb model.

Amplitude (cm)	Incheon	Pyeongtaek	Anheung
Observation (①)	464.0	465.4	354.7
NAO99.Jb (②)	463.3	465.0	358.4
Difference (①-②)	0.7	0.5	−3.7

2.3.

Satellite-Derived Bathymetry Mechanism

2.3.1.

Beer–Lambert law

The total upwelling radiance ($L_t$) observed from the satellite was defined as the sum of atmospheric path radiance ($L_p$), specular radiance ($L_s$), subsurface volumetric radiance ($L_v$), and bottom radiance ($L_b$), as expressed by Eq. (1) (Fig. 4):

Eq. (1)

$$L_t=L_p+L_s+L_v+L_b.$$

Fig. 4

SDB mechanism for various sediment types.

In Eq. (1), $L_p$ can be removed through atmospheric correction and $L_s$ and $L_v$ can be removed through sun-glint and deep-water corrections, respectively, leaving only $L_b$, defined by the Beer–Lambert law as per Eq. (2):

Eq. (2)

$$L_b={\int }_{\lambda }^{\lambda +\mathrm{\Delta }\lambda }[\rho (\lambda )L_{\lambda }{e}^{-(\sec \theta +\sec Ø)\alpha (\lambda )Z}]\mathrm{d}\lambda ,$$

where $\lambda$ is the wavelength, $\rho (\lambda )$ is the bottom reflectance, $\alpha (\lambda )$ is the water’s attenuation coefficient, $\theta$ is the viewing angle (from the nadir), $\mathrm{\Phi }$ is the solar-illumination angle (from the vertical), and $Z$ is the water depth. Equation (2) indicates that reflectance decreases exponentially as the water depth increases; this decrease is more pronounced for longer wavelengths.

2.4.

Preprocessing of Satellite Images

2.4.1.

Sun-glint correction

Sun-glint is observed in satellite images when sunlight reflects directly into the sensor due to a tilted surface. This can arise from various factors, including the sea surface, sun’s position, sensor’s viewing angle, and wind. To enhance the accuracy of water reflectance results, sun-glint correction was applied.³⁷ This correction typically involves establishing a linear relationship between the NIR band and other bands, followed by adjustments for outlier pixels.^38,39 This procedure was conducted using the Sentinel Application Platform offered by the European Space Agency (Fig. 5).

Fig. 5

(a) Sentinel-2 red-green-blue (RGB) image of Cheonsuman in the Yellow Sea, (b) RGB image before sun-glint correction, and (c) RGB image after land masking and sun-glint correction.

2.5.

Depth Estimation Using a Machine Learning Model

2.5.1.

Depth estimation model based on random forest

We constructed a model to estimate water depth using Sentinel-2A/B satellite images, electronic nautical chart data, and the tidal model (Fig. 6). The input data for the machine learning model were extracted from the Sentinel-2A/B images of the training areas, followed by sun-glint correction and land masking. Subsequently, we employed a mean filter to mitigate noise in satellite images by replacing the value of target pixels with the mean of their $3\times 3$ pixels surroundings. Our model used depth data from the electronic nautical chart, corrected based on tidal height values extracted while capturing satellite images. We then matched the preprocessed satellite imagery of five bands with the reference depth data corrected through tidal model data. A dataset was created using matched data corresponding to the number of multi-temporal images. We grouped the band values and depth values for every pixel where band values of each image were present. Finally, the dataset was composed by creating a random sample from the data. This dataset was used as training material for the machine learning model. For depth estimation, we used the RF method, which involves training multiple decision trees. This algorithm facilitates easy variable modification and demands high dataset accuracy for training.⁵ We constructed the RF-based SDB model using the ensemble package in Python’s scikit-learn tool [Fig. 6(a)]. The trained model was then applied to independently observed satellite images to estimate water depths in the training and test area. Depths estimated from the satellite imagery were adjusted to the DL standard for comparison with the nautical chart data [Fig. 6(b)].

Fig. 6

Flowchart of the SDB model. (a) Training and (b) predicting processes. The red box is the SDB model created during the training process and used for predicting.

3.1.

Depth Estimation Based on Satellite Imagery

The model accuracy was validated using 20% of the learning dataset, corresponding to 3000 randomly selected data points per depth segment (totaling 12,000). As measured by RMSE, the errors were 5.0526, 4.6616, and 2.0749 m for Cheonsuman, Hallim, and Samcheok, respectively. Samcheok demonstrated a higher $r$ of 0.9152 than the other locations (Table 6). A previous study on waters with clarity similar to Samcheok, specifically in areas where the annual average chlorophyll-a concentration is less $1.0\mathrm{mg}/{\mathrm{m}}^3$, reported similar RMSE values between 1.77 and 1.97 m.⁵

Table 6

Validation results of three SDB models trained with Sentinel-2.

3.2.

Quantitative Evaluation

To compare the performance of the SDB model across the three training areas, a quantitative evaluation was conducted on the model using statistical analyses. For objective testing, data points were randomly extracted at 5-m depth intervals from satellite images that were not used during the depth estimation model training process. These evaluation results were then compared with depths from electronic nautical charts (Table 7). Significant variances were observed among the training areas: Samcheok exhibited the highest estimation accuracy ($r=0.9$, $\mathrm{RMSE}=2.5861$), followed by Hallim ($r=0.52$, $\mathrm{RMSE}=5.4863$) and Cheonsuman ($r=-0.05$, RMSE = 6.4603). The shallow water estimations for Samcheok were precise estimations, with accuracy diminishing linearly as depth increased. Interestingly, the RMSE for depths between 15 and 20 m was lower than that for depths between 5 and 15 m.

Table 7

Sentinel-2 data used as evaluation data.

3.3.

Qualitative Evaluation

Independent satellite images were used for the evaluation dataset, similar to the quantitative evaluation. To investigate the cause, we conducted a density scatter plot analysis, which allows for the visualization of data distribution and patterns. A density scatter plot was generated to visually compare the real and estimated depths across the three training areas, with the $x$ and $y$ axes representing the real and estimated depths, respectively [Fig. 7]. In the density scatter plot, the higher the proportion of red indicates a higher density of points, which can be interpreted as being influenced by certain factors. A plot closer to the 1:1 line indicated that the model better represented the real values. For Cheonsuman, the estimated depth values predominantly clustered within the 5- to 12-m range irrespective of the variations in actual depth [Fig. 7(a)]. Meanwhile, higher accuracy was achieved at depths of 10 to 20 m in Hallim. Nevertheless, regions with high-density scatter points appeared in the 0- to 7.5-m depth range [Fig. 7(b)]. Conversely, the data for Samcheok exhibited high prediction accuracy in shallow waters. However, this accuracy decreased with increasing depth [Fig. 7(c)].

Fig. 7

Density scatter plot analysis between the real and estimated depths. (a) Cheonsuman, (b) Hallim, and (c) Samcheok.

Maps were generated for the three training areas showing the estimated depths [Figs. 8(a), 8(d), and 8(g)], 2020 nautical chart depths [Figs. 8(b), 8(e), and 8(h)], and differences between the two [Figs. 8(c), 8(f), and 8(i)]. These maps were utilized to identify regions with significant discrepancies. The smallest error between the real and estimated depths was observed for Samcheok (RMSE = 2.5861 m). A general tendency of overestimation was observed across the entire area, with localized underestimations along the coastal regions [Fig. 8(i)]. In Hallim, results centered around Biyangdo indicated an RMSE of 5.4863 m. Notably, the coastal areas close to Biyangdo exhibited overestimation in the northwest direction and underestimation in the offshore direction [Fig. 8(f)]. The southeastern waters exhibited relatively low error, with certain areas indicating overestimation. Cheonsuman had the highest RMSE value at 6.4603 m. The northern region of this training area saw alternating patterns of over- and underestimations, while the southern region predominantly showed an overestimation trend [Fig. 8(c)]. The causes behind the errors observed in both Hallim and Cheonsuman are discussed in Sec. 4.

Fig. 8

Water depth and differences for (a)–(c) Cheonsuman, (d)–(f) Hallim, and (g)–(i) Samcheok, respectively. (a), (d), (g) Real depth maps and (b), (e), (h) SDB model result maps of the training areas. (c), (f), and (i) Differences in water depth between that obtained from the SDB model results and excluding the real depth. Red and blue in (c), (f), and (i) indicate overestimated and underestimated SDB model results, respectively.

4.1.

Evaluation of SDB Results and Accuracy Affected by Turbidity

In water bodies, such as the Yellow Sea, that are significantly affected by tides and predominantly distributed with fine-grained sediment, the seabed sediments are readily resuspended due to strong and recurring tidal currents, thus, increasing the seawater turbidity.³⁸ This scattering often leads to shallower depth estimates than the actual depths. Cheonsuman, embodying the marine environmental characteristics typical of the Yellow Sea, exhibited a depth estimation accuracy lower than that in the East Sea.

The density scatter plot and correlation coefficient also failed to align with the actual depth value distributions. In areas with high turbidity, shallow depths are overestimated, and deep depths are underestimated, leading to errors.³³ This was observed in Cheonsu Bay. In regions deeper than 10 m, an inversion phenomenon was observed, where the estimated depth decreased as the actual depth increased. In areas with heightened turbidity, underwater suspended matter typically scatters light, resulting in a higher reflectance than in clearer waters.

To address these issues, we conducted an additional analysis using the normalized difference turbidity index (NDTI) to assess the impact of turbidity on the depth estimation model. The NDTI method measures the concentrations of soil sediments, microalgae, and other suspended materials that contribute to water turbidity, utilizing the green (B3) and red band (B4), as defined in Eq. (7).⁴³ NDTI values range from $-1$ to 1, with those nearing $-1$ indicating less turbidity and clear waters:

We calculated the NDTI using the reflectance of pixels from the depth estimation test across the three areas (Fig. 9). Cheonsuman displayed a mid-level NDTI value without correlating to the depth estimation results [Fig. 9(a)]. In contrast, for Hallim and Samcheok, regions with relatively low turbidity indices, higher accuracy was achieved for the in-depth estimation [Figs. 9(b) and 9(c)]. However, varied NDTI values were observed in the shallow waters of Hallim at 0 to 7.5 m depth [Fig. 9(b)].

Fig. 9

Scatter plot analysis based on NDTI levels for (a) Cheonsuman, (b) Hallim, and (c) Samcheok.

Upon the addition of NDTI values to the training data, the correlation and accuracy of the results improved compared to those yielded by the original SDB model, with Cheonsuman showing the most significant change. The correlation shifted from an originally non-existent correlation ($r=-0.05$) to a low correlation ($r=0.3272$), and the RMSE decreased by 1.1 m. However, in the 0 to 5 m depth range of Cheonsuman, the RMSE increased. Meanwhile, in the deeper waters (15 to 20 m) of Hallim and Samcheok, the RMSE increased by 0.20 and 0.56 m, respectively, whereas in the shallow waters (0 to 5 m), the RMSE improved slightly, decreasing by 0.20 and 0.08 m, respectively. These results indicate that if turbidity is not taken into consideration when developing satellite image-based depth estimation models, it can lead to significant errors due to the influence of turbidity. Therefore, it suggests that only by considering turbidity can the accuracy for turbid waters be improved (Fig. 10).

Fig. 10

Results of the SDB model with additional NDTI data. Note: The number under the r and RMSE values indicates the change from the existing SDB model. Blue and red indicate positively and negatively altered main results, respectively.

4.2.

Impact of Seabed Sediment on the SDB Model

Coastal areas with tides typically experience resuspension of fine sedimentary particles due to recurring tidal currents, which affects underwater turbidity. Despite the partial removal of the turbidity effect in Hallim at 0 to 10 m depth, which caused an approximate 0.2 m reduction in the RMSE, a relatively high error was still observed in the range of 5.7102 to 7.5959 m. To discern the cause of this discrepancy, depth profiles were plotted for the overestimated depth range and areas with relatively low deviation, and a depth trend analysis was conducted (Fig. 11).

Fig. 11

(a)–(c) Water depth on the ①–③ transect lines in (d), respectively. Black and red in (a)–(c) indicate real and SDB model depths, respectively. The location of 0 m in (a)–(c) implies a point close to the coastline in (d).

Figures 11(a) and 11(b) show that the depths estimated by the machine learning model were $\sim 10\mathrm{m}$ deeper than the actual depths, although the patterns of depth changes aligned well. As verified through Sec. 2.2.3, the error was within 5 cm, and considering the tidal range in this region is $<4.5\mathrm{m}$, such a 10 m discrepancy cannot be attributed solely to tidal influences.

To determine the cause of this overestimation, we created a scatter plot of reflectivity by depth [Fig. 12(a)]. According to the Beer–Lambert law, we distinguished area where reflectivity showed an exponential decrease with depth (blue), and those where reflectivity increased with depth (red). This characteristic was observed in all bands, although there were differences in slope. Although reflectivity decreases exponentially in most sea areas in clear waters,¹ results for Hallim showed a different characteristic, implying the involvement of other factors.

Fig. 12

(a) Scatter plot of the Hallim area results with the actual depth as the $x$-axis and band-2 as the $y$-axis. Black dots express all points in the area, among which blue dots indicate that the difference between the actual and predicted depths is $\le 3\mathrm{m}$; red dots indicate that the difference between the actual and predicted depths is $>3\mathrm{m}$. (b) Depths within 10 m classified based on (a).

The locations were confirmed by marking them according to their characteristics [Fig. 12(b)], and visual readings were obtained using WorldView-3 satellite R (MS2, 630 nm)-G (MS3, 545 nm)-B (MS4, 480 nm) images (with a spatial resolution of 1.2 m) (Fig. 13). As observed in Figs. 13(a)①, 13(a)②, and 13(b)③ areas where the model overestimated the depth displayed a noticeably darker seabed than their surroundings. In conducting on-site investigations of these regions, we identified a basaltic seabed interspersed with patches of white sand (Fig. 14).

Fig. 13

WorldView-3 RGB image of Hallim 2018-11-15 11:43(KST). (a) Areas where depth was overestimated, and (b) areas where depth was well estimated. The red box in (b) shows the in-situ area in Fig. 14(a).

Fig. 14

Sites where on-site investigations were conducted at (a) Hallim (yellow circles indicate points where pictures were taken), (b) 33.39376° N, 126.23653° E, (c) 33.39381° N, 126.23635° E, and (d) 33.3941° N, 126.23776° E.

In shallow waters, the seabed color could influence SR. Remote reflectance was affected by the color of the seabed materials. That is, areas with dark seabed materials had low reflectance and are overestimated than their actual depth. For Hallim Harbor, the overestimation in shallow areas can likely be attributed to the basaltic nature of the seabed. Indeed, we found that reflectance characteristics varied based on seabed materials. Thus, if we incorporate additional seabed spatial data into the training dataset in the future, we anticipate enhancements in model performance. The sediment distribution map, created from airborne hyperspectral imaging, is scheduled to be provided by KHOA.

4.3.

Application of the SDB Model in Test Area

To assess whether the results of this study could represent different marine environments, we applied the three SDB models to regions with marine characteristics similar to those of the training areas. For this purpose, we selected Deokjeok, Seongsan, and Sokcho, all within 100 km and where the latest nautical chart data exist (Table 8). To determine the appropriateness of applying the SDB model in regions with similar coastal characteristics, we compared predictions for Seongsan using two different SDB models (Fig. 15).

Table 8

Information on regions with characteristics similar to the study area.

Fig. 15

Results of Evaluation Seongsan using a different SDB model. (a) Real depth maps and (b), (d) SDB model result maps. (c), (e) Density scatter plot analysis between the real and estimated depths. (b), (c) Results of using the SDB model of Hallim. (d), (e) Results of using the SDB model of Samcheok.

The results from the SDB model of Hallim showed $r=0.69$ and RMSE = 4.7903 m, which were more accurate than the results from the SDB model of Samcheok, $r=0.40$ and RMSE = 5.4924 m (Fig. 15). Despite the higher validation of the SDB model of Samcheok, the more accurate evaluations using the SDB model of Hallim indicate the effectiveness of applying SDB models trained on area with similar characteristics (Table 6).

When predictions were made using the SDB model with similar oceanic environmental characteristics for three area, the results were also similar to those in Sec. 3 (Fig. 16). As measured by RMSE, the prediction accuracies were 5.8292, 4.7903, and 3.0220 m for Deokjeok, Seongsan, and Sokcho, respectively. Sokcho demonstrated a higher correlation coefficient ($r$) of 0.8848 than the other locations (Table 9).

Fig. 16

Evaluation results of test area. (a)–(c) Deokjeok, (d)–(f) Seongsan, and (g)–(i) Sokcho. (a), (d), (g) Real depth maps and (b), (e), (h) SDB model result maps. (c), (f), (i) Density scatter plot analysis between the real and estimated depths.

Table 9

Evaluation results of a test area using the SDB model.

Analysis of the depth map and density scatter plot results also revealed similarities to those in Sec. 3. Significantly, the data distribution patterns in the density scatter plots were alike. In Seongsan, the results were similar to those in Hallim, with accurate predictions in shallow depths (0 to 5 m) and some overestimations [Fig. 16(f)]. Sokcho’s results showed an inverse proportional pattern, akin to those in Samcheok [Fig. 16(i)]. The results for Deokjeok were similar to those in Cheonsu, overestimating in shallow depths and underestimating in deeper waters [Fig. 16(c)]. Therefore, it is inferred that the predictions for regions not included in the SDB model’s training process yielded similar results, indicating that these outcomes may be characteristic of specific coastal environments.

Most studies on SDB models are limited by their application to only shallow water depths of 0 to 20 m; depth estimates are affected by external factors that affect the reflectivity of the sea surface and the depth, such as sunlight, waves, and tides. Therefore, it is important to determine how accurately external factors can be compensated for through the mean filter, sunglint correction, etc.

Furthermore, since the quality of the ground truth data determines the model’s accuracy, it is necessary to calibrate the estimated depth using accurate composition information for each sea area. The bathymetry data used as the ground truth data must comprise up-to-date data surveyed at approximately the same time as the satellite image acquisition.