Nearshore Bathymetry from ICESat-2 LiDAR and Sentinel-2 Imagery Datasets Using Deep Learning Approach

: Accurate bathymetric data is crucial for marine and coastal ecosystems. A lot of studies have been carried out for nearshore bathymetry using satellite data. The approach adopted extensively in shallow water depths estimation has recently been one of empirical models. However, the linear empirical model is simple and only takes limited band information at each bathymetric point into consideration. It may be not suitable for complex environments. In this paper, a deep learning framework was proposed for nearshore bathymetry (DL-NB) from ICESat-2 LiDAR and Sentinel-2 Imagery datasets. The bathymetric points from the spaceborne ICESat-2 LiDAR were extracted instead of in situ measurements. By virtue of the two-dimensional convolutional neural network (2D CNN), DL-NB can make full use of the initial multi-spectral information of Sentinel-2 at each bathymetric point and its adjacent areas during the training. Based on the trained model, the bathymetric maps of several study areas were produced including the Appalachian Bay (AB), Virgin Islands (VI), and Cat Island (CI) of the United States. The performance of DL-NB was evaluated by empirical method, machine learning method and multilayer perceptron (MLP). The results indicate that the accuracy of the DL-NB is better than comparative methods can in nearshore bathymetry. After quantitative analysis, the RMSE of DL-NB could achieve 1.01 m, 1.80 m and 0.28 m in AB, VI and CI respectively. Given the same data conditions, the proposed method can be applied for high precise global scale and multitemporal nearshore bathymetric maps generation, which are beneﬁcial to marine environmental change assessment and conservation.


Introduction
The nearshore areas are vital to both humans and ecology. They provide an important resource for human productive life; hence, they are valued by the military forces of all countries. Accurate bathymetric maps are of economic value and importance to human activities such as sailing navigation, fishing, coastal planning, etc. The commonly used methods of bathymetry include passive and active bathymetry [1].
Light Detection and Ranging (LiDAR) is an active method extensively used for bathymetry. It can actively detect the spatial information of underwater features and then display the underwater environment in three dimensions through laser point clouds with very low error in the vertical direction. Traditional airborne LiDAR and shipborne LiDAR are highly accurate, high-density and short-period marine mapping technology recognized by mankind. Traditional airborne LiDAR and shipborne LiDAR would be unable to perform measurements due to the complex topography and harsh environment of the near-shore waters, as well as the inaccessibility of some of the shallower waters that are in dispute [2,3]. In situ measurements make airborne and shipborne bathymetry limited in certain areas. To break through this limitation, scholars have tried to use satellite-based LiDAR to obtain water depth information. A lot of studies have proved that satellite-based LiDAR can also obtain bathymetric points with enough accuracy through processing [4]. Consequently, this method is gradually becoming an alternative to in situ measurements 1.
The spatial resolution of 13 bands, including band 2 (blue), band 3 (green), band 4 (red), and band 8 (near-infrared) can reach 10 m, which provides the detailed characteristics of coastal areas where the seabed depth may be highly uneven. 2.
The 10 spectral bands selected in the study cover the range of 490-2190 nm, including the optical properties, depth, and spectral information of the bottom substrate (visible domain). 3.
L2A data is the surface reflectance data product obtained by the official atmospheric correction based on L1C. There is no need for other preprocessing. The cloud content of remote sensing images selected for water depth inversion is less than 1%, so there is no need for cloud removal.
The Appalachian Bay (AB), Virgin Islands (VI), and Cat Island (CI) of the United States were selected as the study areas. Table 1 lists the multispectral remote sensing image information of each study area. True color images of these three areas, which represent benthic types (coral reefs, seagrasses, and sand), are shown in Figure 1, providing a completely independent evaluation of the models developed for the study.
bathymetry (DL-NB) from ICESat-2 LiDARand Sentinel-2 Imagery datasets. First, the bathymetric points from the spaceborne ICESat-2 LiDAR were extracted instead of in situ measurements. Then, the DL-NB made full use of the initial regional multi-spectral information of Sentinel-2 at each bathymetric point to train the model. Finally, based on the trained model, the bathymetric maps of selected study areas were produced including the Appalachian Bay (AB), Virgin Islands (VI), and Cat Island (CI) of the United States. To Evaluate the bathymetry accuracy of the proposed method, the traditional linear method [34], machine learning method [26] and multilayer perceptron (MLP) [35] were selected as the baseline.

Sentinel-2 Data
There are abundant remote sensing image data sources for optical depth inversion; however, the sentinel-2 L2A data was selected as its following characteristics.
1. The spatial resolution of 13 bands, including band 2 (blue), band 3 (green), band 4 (red), and band 8 (near-infrared) can reach 10 m, which provides the detailed characteristics of coastal areas where the seabed depth may be highly uneven. 2. The 10 spectral bands selected in the study cover the range of 490-2190 nm, including the optical properties, depth, and spectral information of the bottom substrate (visible domain). 3. L2A data is the surface reflectance data product obtained by the official atmospheric correction based on L1C. There is no need for other preprocessing. The cloud content of remote sensing images selected for water depth inversion is less than 1%, so there is no need for cloud removal.
The Appalachian Bay (AB), Virgin Islands (VI), and Cat Island (CI) of the United States were selected as the study areas. Table 1 lists the multispectral remote sensing image information of each study area. True color images of these three areas, which represent benthic types (coral reefs, seagrasses, and sand), are shown in Figure 1, providing a completely independent evaluation of the models developed for the study.

Bathymetric Data
Both ICESat-2 and NOAA NGS Topobathy Lidar data were used in the study. The water depth points extracted from ICESat-2 were used as a priori data for network training. NOAA bathymetric points were used as the reference bathymetric points for accuracy assessment. ICESat-2 satellite-based LiDAR satellite provides us with an active remote sensing detection technology that uses 531 nm photon-counting LiDAR [36] with higher agility and underwater penetration capability. A diameter of 17 m per pulse and a spacing of 0.7 m along the track represent the spatial resolution of ICESat-2. After calibrating the bathymetric error and other errors, the spaceborne photon-counting LiDAR have a potential to achieve the bathymetric accuracy in shallow and clean water areas [6], and are capable of quantitatively obtaining shallow water depths. The bathymetric points of the nearshore were extracted from ICESat-2 for the model training. The Advanced Topographic Laser Altimeter System (ATLAS) [37] ATL03 disciplines information, and NOAA NGS Topobathy Lidar information used in this article were described in Table 2. Each ATLAS ATL03 data contains three groups (6 pieces) of ground track data: gt1l, gt1r, gt2l, gt2r, gt3l, and gt3r. Each group of data contains a strong information track and a weak information track. In this study, we only select strong information track data of each group to extract water depth.
Topographic and bathymetric LiDAR data from the U.S. coastal islands provided by the NOAA Office of Coastal Management [38] was employed as verification bathymetric points. This LiDAR bathymetric data has the following characteristics: 1.
The vertical accuracy of the LiDAR in measuring shallow water areas can reach ((0.25 2 ) + (0.0075 × d) 2 ) m under 95% confidence level (d is water depth); the vertical accuracy of the LiDAR in measuring deep water areas can reach ((0.30 2 ) + (0.013 × d) 2 ) m under a 95% confidence level.

2.
The horizontal accuracy of the LiDAR can reach (3.5 + 0.05 × d) m at a 95% confidence level.

3.
The LiDAR data can be obtained free of charge and processed conveniently. The verification bathymetric points of AB vary from 0 m to greater than 20 m. The verification bathymetric points of VI vary from 0 m to 35 m. Concurrently, the verification bathymetric points of CI range from 0 to 5 m.

Method Overview
The proposed method mainly includes the following steps. Firstly, bathymetric points were extracted from ICESat-2 ATLAS ATL03 data as the prior data. Then, the feature tensors were extracted from the registered Sentinel-2 images with a certain window size at each prior water depth point. Subsequently, the feature tensors were input into the depth learning framework (DL-NB) designed in this paper for model training. The airborne LiDAR data was used as validation data for performance evaluation. Finally, the large-scale bathymetric maps were generated. At the same time, a comparative analysis with baselines was performed.

Bathymetry from ICESat-2 ATL03
The bathymetric points were extracted from ICESat-2 ATL03 data instead of in situ measurements. The processing mainly consists of four steps:

1.
It is necessary to convert the point cloud from WGS84 ellipsoidal height to orthogonal height; this is because even though the length of the laser track in our study area is short, there is a tilt of the sea level in the ellipsoidal height.

2.
Noise filtering is implemented based on a two-dimensional window filter, with each point as the center, setting the window size and the point density threshold within the window to filter out discrete noise points. In most cases, the manual process is necessary.

3.
Sea level and seafloor determination are important to depth calculation. The sea level was determined based on histogram statistics at each points segment near the sea level, referring to two rules: 1. the points density of sea level is relatively high near the surface; 2. sea level is higher than seafloor.

4.
Refraction correction is performed on the seafloor points according to the algorithm proposed by Parrish et al. [6].
A schematic diagram of the ICESat-2 point cloud before and after processing is shown in Figure 2.
As can be seen from the above figure, after processing, the bathymetry value is calculated by differentiating the sea level and the refraction-corrected seafloor point clouds.
Assuming negligible changes in ocean bathymetry within a short period, the Sentinel-2 optical remote sensing images and airborne LiDAR data need to be matched in time. The tidal correction of the corresponding time on the Sentinel-2 optical remote sensing images should be considered [42,43], and the bathymetry values can be expressed as: where H image is the image inversion bathymetry value, H Lidar is the water depth after tidal correction by LiDAR, tide ICESat-2 is the tidal height at the acquisition time of satellite-based LiDAR data (available in the .h5 file), tide Sentinel-2 is the tidal height at the acquisition time of Sentinel-2 optical remote sensing image, and the tide information of the corresponding tide stations in the study area can be viewed through the National Ocean Data Center for correction [44].
level, referring to two rules: 1. the points density of sea level is relatively high near the surface; 2. sea level is higher than seafloor. 4. Refraction correction is performed on the seafloor points according to the algorithm proposed by Parrish et al. [6].
A schematic diagram of the ICESat-2 point cloud before and after processing is shown in Figure 2.

Deep Learning Architecture
CNN has shown its advantages in image recognition and classification, as well as regression analysis. In this paper, a 2D CNN-based deep learning framework was designed for bathymetric inversion. Its potential ability for bathymetric data estimation was evaluated. To train the model, the bathymetric point extracted from ICESat-2 should be registered with the pixel value in the sentinel-2 images. The pixel can be regarded as weighted averages of nearby known pixels. Hence, the method took into account the impact of adjacent pixels on water depth retrieval through 2D CNN. Figure 3 shows the structure of the DL-NB. The role of the convolutional kernel of the CNN is to expand the feature, and the role of pooling is to reduce the width and height of the input image to make the model deeper. ReLU is the activation function, and the expression is shown as follows: where x is the input-independent variable and f (x) is the function value. The neurons are adjusted nonlinearly after linear transformation, that is to say, the input vector from the previous layer of the neural network is transformed by w T x + b and then output by max 0, w T x + b transformation. Using the ReLU function can be more efficient than retrograde gradient descent and backward propagation, avoiding the problems of gradient explosion and gradient disappearance. The ReLU function is not affected by the complex activation function like the exponential function. The dispersion of activity can also reduce the overall computational cost of the neural network, which in turn simplifies the whole computational process [45]. In this paper, the most basic CNN was used, and the input layer was 10 neurons. We used the water depth points extracted from ICESat-2 as the a priori bathymetric points. At the same time, we extracted a 7 × 7 subimage on the Sentinel-2 image (10 bands used in the study) with the a priori bathymetric point as the center. Feature tensors of size 10 × 7 × 7 (bands × width × height) were input into the network, whereas the depths of the priori bathymetric points were input into the network as labels for model training. The 2D CNN has a total of 5 layers, containing 64, 128, 256, 256, 512 neurons respectively. The output of each neuron was transferred to the input of the next neuron by the nonlinear activation function, and the activation functions of the hidden layers all adopted the ReLU function, which largely reduces the gradient disappearance. At last, the water depth was predicted by the linear activation function. reduces the gradient disappearance. At last, the water depth was predicted by the linear activation function. Backpropagation is the process used along with optimization methods to train the network [46], in which the weights in the network are updated according to the learning rate (α = 0.001) by calculating the gradient of the loss function and then using gradient descent for adaptive moment estimation (Adam, β1 = 0.9, β2 = 0.99), iterating continuously. When the iteration (epoch = 1000) stops and when the loss function converges at the same time the training of the model is completed.

Accuracy Assessment
To evaluate the performance of our trained model (DL-NB), several classic methods were employed as the baseline, including linear regression, MLP and Random Forest. The root means square error (RMSE) was calculated as an absolute metric. The smaller the RMSE, the higher the accuracy of the model. The RMSE expression is shown in formula 3.
Moreover, the coefficient of determination (R 2 ) was employed to describe the model fitting effect; the value of R 2 is in the range of [0, 1]; the larger the value, the better the model fitting effect. The expression is shown in formula 4.
N in the above equations denotes the sample size of test, is the estimated water depth, indicates the mean value of the estimated depth and is the corresponding depth from the NOAA airborne LiDAR data.

Convolution Window Size Tuning
The convolution window size is important to the 2D CNN as well as the inversion accuracy. Considering the learning efficiency of the model, different window sizes were employed in Table 3. The result shows that the model (DL-NB) can achieve relatively high Backpropagation is the process used along with optimization methods to train the network [46], in which the weights in the network are updated according to the learning rate (α = 0.001) by calculating the gradient of the loss function and then using gradient descent for adaptive moment estimation (Adam, β1 = 0.9, β2 = 0.99), iterating continuously. When the iteration (epoch = 1000) stops and when the loss function converges at the same time the training of the model is completed.

Accuracy Assessment
To evaluate the performance of our trained model (DL-NB), several classic methods were employed as the baseline, including linear regression, MLP and Random Forest. The root means square error (RMSE) was calculated as an absolute metric. The smaller the RMSE, the higher the accuracy of the model. The RMSE expression is shown in formula 3.
Moreover, the coefficient of determination (R 2 ) was employed to describe the model fitting effect; the value of R 2 is in the range of [0, 1]; the larger the value, the better the model fitting effect. The expression is shown in formula 4.
N in the above equations denotes the sample size of test, H estimated is the estimated water depth, H estimated indicates the mean value of the estimated depth and H truth is the corresponding depth from the NOAA airborne LiDAR data.

Convolution Window Size Tuning
The convolution window size is important to the 2D CNN as well as the inversion accuracy. Considering the learning efficiency of the model, different window sizes were employed in Table 3. The result shows that the model (DL-NB) can achieve relatively high accuracy using the window size of 7 × 7 pixels. A window size too small or too large is not suitable for the model. Hence, the 7 × 7 window size was selected in our experiment.

Bathymetry Maps of Models
Using the trained model and the pre-processed Sentinel-2 images, the nearshore bathymetric maps of three study areas were generated in Figure 4. accuracy using the window size of 7 × 7 pixels. A window size too small or too large is not suitable for the model. Hence, the 7 × 7 window size was selected in our experiment.

Bathymetry Maps of Models
Using the trained model and the pre-processed Sentinel-2 images, the nearshore bathymetric maps of three study areas were generated in Figure 4.

Accuracy Analysis of Bathymetric Estimates
The correlation between the satellite-derived bathymetry (SDB) and in situ bathymetric points captured by the airborne LiDAR system was illustrated by scatter plots in each study area. As shown in Figure 5, the red line is the y = x line. Although the validate points are not evenly distributed, generally there is a strong correlation between the SDB and the in situ data. To further evaluate the performance of the DL-NB, R 2 and RMSE between the retrieved water depths and in situ depths in three study areas were calculated and a comparison of accuracy with baselines were summarized in Table 4.

Accuracy Analysis of Bathymetric Estimates
The correlation between the satellite-derived bathymetry (SDB) and in situ bathymetric points captured by the airborne LiDAR system was illustrated by scatter plots in each study area. As shown in Figure 5, the red line is the y = x line. Although the validate points are not evenly distributed, generally there is a strong correlation between the SDB and the in situ data. To further evaluate the performance of the DL-NB, R 2 and RMSE between the retrieved water depths and in situ depths in three study areas were calculated and a comparison of accuracy with baselines were summarized in Table 4.

Accuracy Analysis of Bathymetric Estimates
The correlation between the satellite-derived bathymetry (SDB) and in situ bathymetric points captured by the airborne LiDAR system was illustrated by scatter plots in each study area. As shown in Figure 5, the red line is the y = x line. Although the validate points are not evenly distributed, generally there is a strong correlation between the SDB and the in situ data. To further evaluate the performance of the DL-NB, R 2 and RMSE between the retrieved water depths and in situ depths in three study areas were calculated and a comparison of accuracy with baselines were summarized in Table 4.   As shown in Table 4, the DL-NB can significantly outperform the baselines especially, in the Appalachian Bay and Virgin Islands. The RMSE of the Appalachian Bay improved by 173% overusing the MLP and the R 2 improves from 67% to 93%. Similarly, the RMSE for the Virgin Islands improved by 202% overusing the MLP, and the R 2 improved from 57% to 84%. Bathymetric inversions using the MLP had the worst accuracy in both the Appalachian Bay and the Virgin Islands. The LR and RF can achieve comparable performance.  As shown in Table 4, the DL-NB can significantly outperform the baselines especially, in the Appalachian Bay and Virgin Islands. The RMSE of the Appalachian Bay improved by 173% overusing the MLP and the R 2 improves from 67% to 93%. Similarly, the RMSE for the Virgin Islands improved by 202% overusing the MLP, and the R 2 improved from 57% to 84%. Bathymetric inversions using the MLP had the worst accuracy in both the Appalachian Bay and the Virgin Islands. The LR and RF can achieve comparable performance.

Error Analysis of SDB
The error of SDB in this paper mainly comes from Sentinel-2 image, the a priori water depth points extracted by ICESat-2, and in situ data provided by NOAA. Firstly, although the ICESat-2 ATL03 datasets were preprocessed to eliminate most of the errors during the prior water depth points extraction, the estimated refractive index of the water column will still lead to errors [47]. Besides, as shown in Figure 2, the filtered sea floor point cloud has a certain thickness, likely due to the noise or multi-path effect, which brings errors too. Secondly, atmospheric correction of Sentinel-2 images is essential for SDB; yet, sun glint and cloud may still persist after the correction and cause error [48]. Apart from that, the water quality, underwater topography and cover type in the study areas may affect the inversion accuracy of water depth as well [9,[49][50][51]. Thirdly, it is difficult to maintain temporal synchronization for in situ data and other remote sensing data. Although the in situ data was employed as validation data, the accuracy of in situ data is affected by many factors such as geographical location, sea tidal and acquisition process [9].

Comparative Analysis of the Results of the Study Area
As can be seen from Table 4, the depth inversion accuracy of the DL-NB model is higher than the other three methods in each study area. Notably, another finding is that Cat Island has the highest accuracy, which is much higher than Virgin Islands. This may be explained by several reasons. One potential reason is that deeper water makes the water column more complex, and the inversion accuracy of the DL-NB model decreases with the increase of water depth. In addition, the water quality, underwater topography and cover types in different study areas are different. The underwater terrain of the Appalachian Bay is relatively flat, and the underwater cover of the Virgin Islands is more complex, which may affect the results of depth inversion as well.

Spatial Distribution of the Error
In order to deeply investigate the inversion methods, the error spatial distribution maps were generated by retrieved bathymetric maps and in situ DEM. As shown in Figure 6. Figure 6a-l correspond with the spatial distribution of bathymetric estimates error by different methods. Generally, there is no distinct rule in the error distribution. For DL-NB, the overestimation often happened in the shallow area of Appalachian Bay, and the underestimation always occurred in the deep area of Appalachian Bay. However, the error distribution was opposite in the Virgin Islands with the same method. By comparison, the results of DL-NB had the smallest differences in each study area, while the other three models tended to largely deviate from the in situ data. In particular, the MLP had the largest deviation in the Virgin Islands, which was over 6.6 m in deep areas.

Error Analysis of SDB
The error of SDB in this paper mainly comes from Sentinel-2 image, the a priori water depth points extracted by ICESat-2, and in situ data provided by NOAA. Firstly, although the ICESat-2 ATL03 datasets were preprocessed to eliminate most of the errors during the prior water depth points extraction, the estimated refractive index of the water column will still lead to errors [47]. Besides, as shown in Figure 2, the filtered sea floor point cloud has a certain thickness, likely due to the noise or multi-path effect, which brings errors too. Secondly, atmospheric correction of Sentinel-2 images is essential for SDB; yet, sun glint and cloud may still persist after the correction and cause error [48]. Apart from that, the water quality, underwater topography and cover type in the study areas may affect the inversion accuracy of water depth as well [9,[49][50][51]. Thirdly, it is difficult to maintain temporal synchronization for in situ data and other remote sensing data. Although the in situ data was employed as validation data, the accuracy of in situ data is affected by many factors such as geographical location, sea tidal and acquisition process [9].

Comparative Analysis of the Results of the Study Area
As can be seen from Table 4, the depth inversion accuracy of the DL-NB model is higher than the other three methods in each study area. Notably, another finding is that Cat Island has the highest accuracy, which is much higher than Virgin Islands. This may be explained by several reasons. One potential reason is that deeper water makes the water column more complex, and the inversion accuracy of the DL-NB model decreases with the increase of water depth. In addition, the water quality, underwater topography and cover types in different study areas are different. The underwater terrain of the Appalachian Bay is relatively flat, and the underwater cover of the Virgin Islands is more complex, which may affect the results of depth inversion as well.

Spatial Distribution of the Error
In order to deeply investigate the inversion methods, the error spatial distribution maps were generated by retrieved bathymetric maps and in situ DEM. As shown in Figure  6. Figure 6a-l correspond with the spatial distribution of bathymetric estimates error by different methods. Generally, there is no distinct rule in the error distribution. For DL-NB, the overestimation often happened in the shallow area of Appalachian Bay, and the underestimation always occurred in the deep area of Appalachian Bay. However, the error distribution was opposite in the Virgin Islands with the same method. By comparison, the results of DL-NB had the smallest differences in each study area, while the other three models tended to largely deviate from the in situ data. In particular, the MLP had the largest deviation in the Virgin Islands, which was over 6.6 m in deep areas.

Model Portability
The data pre-processing is important to obtain a more accurate bathymetric map. Besides, there are many other factors affecting bathymetric results, including seawater turbidity, water column conditions and bottom type, etc. It makes sense to check the portability of the model in different environments. Based on the DL-NB, cross-validation was performed between the Virgin Islands and the Appalachian Bay. The DL-NB model was trained in one area and used in another. The validation result is shown in Table 5 indicates that the portability of the DL-NB model is poor. A possible reason is that there is great diversity in underwater terrain and coverage types among these areas, which will be reflected in the pixel values of remote sensing images. Figure 7 illustrates the average band value curves of 5 m and 10 m water depth in the same period of the US Appalachian Bay and the US Virgin Islands. There are great differences in the band values curve at a certain water depth in different study areas. Therefore, it is difficult to apply the trained model in one area to another different area for bathymetry.

Model Portability
The data pre-processing is important to obtain a more accurate bathymetric map. Besides, there are many other factors affecting bathymetric results, including seawater turbidity, water column conditions and bottom type, etc. It makes sense to check the portability of the model in different environments. Based on the DL-NB, cross-validation was performed between the Virgin Islands and the Appalachian Bay. The DL-NB model was trained in one area and used in another. The validation result is shown in Table 5 indicates that the portability of the DL-NB model is poor. A possible reason is that there is great diversity in underwater terrain and coverage types among these areas, which will be reflected in the pixel values of remote sensing images. Figure 7 illustrates the average band value curves of 5 m and 10 m water depth in the same period of the US Appalachian Bay and the US Virgin Islands. There are great differences in the band values curve at a certain water depth in different study areas. Therefore, it is difficult to apply the trained model in one area to another different area for bathymetry.

Conclusions
In this study, a CNN-based deep learning framework was proposed for nearshore bathymetry (DL-NB). The bathymetric points from the spaceborne ICESat-2 lidar were extracted as the a priori measurement to train the DL-NB model with pre-processed sentinel-2 Images in selected study areas. Three classic methods were employed as baselines. The bathymetric maps, retrieved by different methods, show that the DL-NB model has richer details and better continuity visually.
To validate the performance of the proposed method, the inversion results were compared with in situ airborne LiDAR data from NOAA. The comparison suggested that the DL-NB model can outperform all the baselines, with the RMSE of 1.01, 1.8, 0.28 and the R 2 of 0.93, 0.94, 0.82 in the three study areas respectively. RF can obtain a relatively higher accuracy than LR, and the performance of MLP was relatively poor. The results from different study areas also indicated that the uncertainty of accuracy increases with

Conclusions
In this study, a CNN-based deep learning framework was proposed for nearshore bathymetry (DL-NB). The bathymetric points from the spaceborne ICESat-2 lidar were extracted as the a priori measurement to train the DL-NB model with pre-processed sentinel-2 Images in selected study areas. Three classic methods were employed as baselines. The bathymetric maps, retrieved by different methods, show that the DL-NB model has richer details and better continuity visually.
To validate the performance of the proposed method, the inversion results were compared with in situ airborne LiDAR data from NOAA. The comparison suggested that the DL-NB model can outperform all the baselines, with the RMSE of 1.01, 1.8, 0.28 and the R 2 of 0.93, 0.94, 0.82 in the three study areas respectively. RF can obtain a relatively higher accuracy than LR, and the performance of MLP was relatively poor. The results from different study areas also indicated that the uncertainty of accuracy increases with depth. Moreover, the spatial distribution of error was analyzed between the bathymetric maps and in situ data. It was found that, although there is no distinct rule in the error distribution, DL-NB had the smallest differences in each study area.
Finally, cross-validation was performed between different study areas to check the portability of DL-NB. The result indicate that the portability of the DL-NB model was poor in the study. It can be concluded that the diversity of environmental factors may limit the portability.
In the future, the proposed method can be tested by different remote sensing data and applied for high-precision global scale and multitemporal nearshore bathymetric map generation. These maps would be beneficial to marine environmental change assessment and conservation.