**3. Results**

*3.1. DDM*

#### 3.1.1. Correction of ICESat-2 Dataset

The ICESat-2 gt1l transect from the 2020 dataset corresponds to the strong beam and presents some variability in the depth range. The results obtained in this study, after removing the noise photons and correcting the signal for refraction bias, are presented in Figure 6. For comparison, the official signal detection and classification provided with the downloaded L2 ATL03 dataset were presented in Figure 2.

**Figure 6.** Point clouds of the ICESat-2 signal acquired on 14 May 2020. The signal was processed to remove the noise, correct for refraction, and identify the seafloor. Uncorrected seafloor photons appear in red, while corrected photons are in green.

In Figure 6, photon positions (latitude and longitude) were projected onto a local geographic plane. Therefore, the horizontal axis corresponds to the along track distance. The origin point corresponds to the northernmost location of the trajectory. For the current study, the analysis indicates that (1) points from the seabed detected in this study are following the bottom topography, distinguishable on the satellite imagery; (2) while the ATL03 data classified with a high and medium confidence level (corresponding to the blue and green points in Figure 2) are located at or close to the surface, our bathymetry algorithm correctly identifies the bottom topography from low and buffer confidence points, a much smaller portion of the returned signal; and finally (3) the ATL03 dataset removed only a small fraction of the noise photons in comparison to the results generated with the DBSCAN.

The DBSCAN algorithm was configured based on an empirical approach with the value = 0.65 m. This value, valid for our study area, allowed us to retrieve a majority of the seabed signal while eliminating most of the noise photons. The remaining noise points can be manually removed during the validation phase.

#### 3.1.2. Validation of ICESat-2 Data

The comparison between ICESat-2 ellipsoidal heights and the Litto3D® ellipsoidal heights is presented in Figure 7.

**Figure 7.** Point clouds of Litto3D® dataset (blue), and ICESat-2 raw (yellow) and corrected (red) seabed photons.

Figure 7 highlights the importance of correcting for the refraction bias, as a vertical bias is clearly visible between the corrected (red) and non-corrected (yellow) data. The error generated by refraction alone can reach up to 2 m in shallower waters and 5 m for deeper waters with a RMSE of 0.89 m and a MAE of 0.73 m. A vertical bias of about 1 m is visible on Figure 7 between the reference dataset and the corrected ICESat-2 data close to the surface.

#### 3.1.3. Digital Depth Model

ICESat-2 corrected and validated data were used to calibrate the relative DDM. The calibration required the identification of a good model to bound the ICESat-2 dataset to the relative water depth values from the 0.5 m MS imagery.

Scaled pixel values were extracted from the relative water depth map derived from the 0.5 m MS imagery at the same location than ICESat-2 bathymetric points using QGIS 3.18.3 (open-source geographic information system). Several regression models were tested, and the corresponding equations and their performance (in terms of the RMSE) are presented in Figure A1 (Appendix A). The regression chosen is a 2nd degree polynomial (Equation (6)). The expression of the latter is simple and performs well, with a RMSE of 0.895 m (see Figure 8).

$$\mathbf{y} = -45.87\mathbf{x}^2 + 74.567\mathbf{x} - 31.581\tag{6}$$

Figure 9 shows the final DDM obtained using ENVI through the application of the model to the relative DDM. The hatched areas correspond to depths greater than the maximum calibration depth.

(**a**) (**b**)

**Figure 8.** (**a**) Relative DDM with superposition of ICESat-2 bathymetric points; (**b**) 2nd degree polynomial regression.

**Figure 9.** Digital depth model at the acquisition time of Pleiades-1A, calibrated with the ICESat-2 dataset.

3.1.4. Digital Depth Model Validation

The reliability of the DDM was quantified by comparing the estimated bathymetry to the Litto3D® reference dataset. Points from the bathymetric LiDAR point clouds were extracted, along the path of ICESat-2, from the DDM. The predicted RMSE was 0.895 m and the observed RMSE was 0.874 m along the ICESat-2 path. The predicted R2 coefficient was 0.931 and the observed R<sup>2</sup> coefficient was 0.97. In addition, we report a MAE of 0.701 m.

#### *3.2. Benthic Habitat Classification*

Results from the four classifiers tested using different combinations of predictors are summarized in Figure 10, presenting both the overall accuracy and the kappa coefficient values.

**Figure 10.** Performances of the different classifiers using different geomorphological predictors. (**a**) Overall accuracy; (**b**) Kappa coefficient.

The NN algorithm configured with three hidden neurons for one layer systematically provided the lowest accuracy and the lowest kappa score with an overall accuracy which does not exceed 33.33% and kappa coefficient values that are all null. The neural network using only one hidden neuron produced better, yet inconclusive results, except for the combination of predictors "2".

The ML and the SVM algorithms generally produced the best classification results. The ML algorithm allows for a global accuracy of 96.62% and a kappa coefficient of 0.94 when using two spectral bands (Green and Blue) and with the addition of the three geomorphic predictors.

The SVM results were not as affected by the absence of the red spectral band. The results are constant and reached an overall accuracy of 96.50% and a kappa coefficient of 0.95 when using a DAM with three spectral bands and the slope as the only geomorphic predictor.

Maps of the benthic habitats with the best classification results for each depth range, are presented in Figure 11.

These results, compared to the 0.5 m MS imagery and the DAM, are consistent with the classification presented in Figure 5, except for a bias in the classification of corals and algae, appearing in Figure 11a. The green band on the right of the image is an error in the classification process.

**Figure 11.** Maps of benthic habitats in the study area. (**a**) Classification map generated using the SVM with the slope geomorphic predictor. This map corresponds to depths shallower than 3.8 m and is based on all three spectral bands (R, G, and B); (**b**) classification map generated with the ML classifier and the three geomorphic predictors. This map corresponds to depths in the range of 3.8–15 m and is based on two spectral bands (G and B).

#### **4. Discussion**

#### *4.1. Bathymetric Errors*

RMSE values comparing the DDM to the Litto3D® dataset were obtained along the ICESat-2 ground track, thus at the same place used for the calibration. Here, we discuss the impact of both the depth values and the location of the validation transect on the results.

Figure 12 shows the DDM from the Litto3D® dataset. While the DDM produced in our study reaches 33 m depth, the Litto3D® survey of this area indicated depths reaching at least 82 m.

The map of the differences between the Litto3D® and the DDM calibrated with ICESat-2 dataset is shown in Figure 13. The extrapolation works very well over the range of depths used in the calibration. However, the error increases at deeper depths. Once again, in this figure, the hatched areas correspond to depths greater than the maximum calibration depth of the model.

Large error values seem to appear in deeper waters (over 15 m depth), probably due to the fact that the bathymetry was calibrated with a limited depth range (the ICESat-2 dataset does not exceed a depth of 15 m). On the other hand, the fact data sampling was restricted to the ICESat-2 track is not ideal for the calibration. Most of the soundings represent a depth lower than 5 m (this concerns nearly 85% of the total amount of points for the 2020 dataset). The dataset only has a few points representing higher depth values. This was confirmed by the study of three other transects, taken at different places over the area (a transect along the ICESat-2 swath, a transect perpendicular to the swath, and a transect extracted far from the swath). The results of those tests are visible in Figures A2–A4 (Appendix B), showing that depth strongly affects the quality of the bathymetry. Consequently, errors increase for depth exceeding around 15 m. However, for shallower depth values, the results are similar, regardless of the transect location.

**Figure 12.** Digital depth model generated from the Litto3D® dataset acquired over Mayotte and centered on the study site. The land area is masked.

**Figure 13.** Map of the differences between the DDM derived from the Litto3D® and the ICESat-2/Pleiades-1 fusion.

The 10-year difference in the time of acquisition between Litto3D® and ICESat-2 could also induce a systematic error, due to a change in the bottom topography caused, for instance, by erosion or a change in the mean sea level (MSL), although those changes are likely to be well beyond the vertical accuracy provided by the method.

Mayotte has been prone to a succession of earthquakes since May 2018. The origin of these earthquakes is located to the east of the island. There are four permanent GPS stations in Mayotte and their rigorous monitoring has allowed experts to observe a displacement of all the stations by several centimeters towards the East and a subsidence of several centimeters since the beginning of the events [54–56].

In addition, the conversion of datums, using CIRCE software, could be a source of error. The grid used for the calculation is the GGM04V1 and the resulting vertical accuracy is estimated by the software at 10/20 cm.

On the other hand, during the correction of the refraction effect, n**<sup>1</sup>** and n**<sup>2</sup>** refractive indices were assumed and could therefore contribute to a small bias.

The method used to retrieve the map of the relative water depth could be improved to obtain more accurate DDM by implementing more recent and innovative approaches, such as IMBR, OBRA, MODPA or SMART-SDB [11,24,57–59].

#### *4.2. Impact of the Spatial Resolution of the Multispectral Imagery*

In this study, the DDM was generated at the VHR of 0.5 m. However, other studies used sensors providing a spatial resolution of 10 m (Sentinel-2) or 30 m (Landsat-8) [17,39,60]. The spatial resolution drawn from the Pleiades-1A sensor was degraded in order to compare the RMSE. This process was done in ENVI with the "Resize Data" tool. The pixel size of the output was set according to the desired spatial resolution. The results are presented in Figure 14 and Table 4.

**Figure 14.** Performances of the DDMs obtained from different spatial resolutions of Pleiades-1A and calibrated with ICESat-2.


**Table 4.** Accuracy using the original image resolution and lower spatial resolution.

Figure 14 highlights the importance of the imagery spatial resolution on the accuracy of the bathymetry. RMSE remained under 1 m when the spatial resolution remained below 5 m, but increased rapidly after.

In other studies, the RMSE reached between 1.5 and 2 m for the Yongle atoll, located in South China [17]. It was 1.2 m on average in the Acklins islands in the Bahamas based on the Sentinel-2 MS satellite with a 10 m spatial resolution [17]. The RMSE was 0.96 m with the MS satellite Sentinel-2B (10 m spatial resolution) and 1.54 m using the Landsat-8 satellite (30 m spatial resolution) in the Virgin Islands [33]. Moreover, these study areas had a diffuse attenuation coefficient (*Kd*) similar to the Mayotte study area.

One of these studies obtained different results using Sentinel-2 observations and ICESat-2 observations from multiple swaths [60]. The DDM was produced with an extrapolation process conducted over the entire area with a RMSE of 3.36 m. However, when the study area was constrained between the two ICESat-2 swaths, the RMSE decreased to 0.35 m. This study area had a higher turbidity of *Kd* = 1.68 m−<sup>1</sup> [60].

During the acquisition time of some of these studies, meteorological events such as hurricanes occurred and could have impacted the topography of the bottom and affected the results. However, the evaluation of possible episodic events was not reported for this study or investigated.
