# Improved Filtering of ICESat-2 Lidar Data for Nearshore Bathymetry Estimation Using Sentinel-2 Imagery

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## Abstract

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## 1. Introduction

## 2. Study Areas and Data Sources

#### 2.1. Study Areas

^{2}[37]. The geographical location of this area is between 18.26°~18.43°N and 64.80°~65.0°W. The Continuously Updated Digital Elevation Model (CUDEM) obtained in December 2014 for the US coast developed by NCEI, was used as in situ data to verify the performance of our bathymetric method in St. Thomas [38]. The second study region, as Figure 1b shows, was the surrounding waters around Acklins Island and Long Cay in Southeastern Bahamas. The geographical location of this area is between 22.10°~22.60°N and 73.90°~74.40°W. There is a lagoon between Acklins Island and Long Cay. The bottom is mainly reef, sand, and stone. The third study region, as Figure 1c shows, was the Huaguang Reef. Huaguang Reef is one of the main reefs of Xisha Islands in the northwestern South China Sea, about 330 km away from Hainan Island. The geographical location of this area is between 16.13°~16.28°N and 111.52°~111.86°E. There are several coral reefs in the region. In all three sites, the in situ bathymetric data are not easy to access to evaluate the empirical SDB model; therefore, we applied ICESat-2 bathymetric photons to evaluate bathymetric maps based on SDB-AP. A total of 80% of the ICESat-2 bathymetric points were used to train the empirical model, and the remaining 20% were used to verify the SDB-AP bathymetric result. In addition, we discuss Chen’s method [32] along with our method; thus, we chose two sites (Shanhu Island and Nan Island) and the corresponding ICESat-2 tracks (see Table 1). According to Chen’s definition, the photon density of ICESat-2 track data on 2 February 2019, 24 May 2019, and 19 August 2019 are low, medium, and high, respectively. Three types of ICESat-2 data with different density distributions of photons can help to validate the accuracy of these DBSCAN algorithms.

#### 2.2. ICESat-2 Lidar Datasets

#### 2.3. Sentinel-2 Satellite Imagery

## 3. SDB-AP Method

#### 3.1. Adaptive DBSCAN for ICESat-2 Signal Photon Detection

#### 3.2. Bathymetric Correction for Detected Seafloor Photons

#### 3.3. Outlier Removal for Corrected Seafloor Photons

- I.
- Wavelet filteringA hard threshold was optimally set according to the noise level estimation of each layer of the wavelet decomposition.
- II.
- K-medoids classificationThe data were divided into three categories by the K-medoids algorithm [47]. In the K-medoids algorithm, such a point would be selected from the current cluster—the minimum sum of the distances from it to all other points (in the current cluster)—as the center point, which allows the cluster size not to vary greatly.
- III.
- Outlier removal along the geographic axisThe data $A$ were sorted along the ICESat-2 along-track first. For each category, the outliers were detected and eliminated using scaled mean absolute difference MAD, and these outliers were eliminated with a window size of 50. The outliers were defined as the elements that differ from the median by more than three scaled$MAD$ from the median in the window. $MAD$ could be expressed as follows:$$MAD=c\times \mathrm{median}(\mathrm{abs}\left(A-\mathrm{median}\left(A\right)\right)$$
- IV.
- Outlier removal along the depth axisThe remaining data were then processed. The outliers were defined as the elements more than three scaled $MAD$ in data with the window size of 100, and the recognized outliers were removed.

#### 3.4. Matching ICESat-2 Data to Sentinel-2 Images with Different Spatial Resolution

#### 3.5. SDB Retrieval by Merging the Sentinel-2 Data with ICESat-2 Data

#### 3.5.1. Atmosphere Correction

#### 3.5.2. Spatial Operation

#### 3.5.3. Clouds, Whitecaps, and Land Pixels Mask

#### 3.5.4. Empirical SDB Retrieval

## 4. Results

#### 4.1. Bathymetric Retrieval by ICESat-2 Data

#### 4.2. Bathymetric Retrieval by the SDB-AP

#### 4.3. Validation

^{2}, and RMSE details are also shown in the figures.

^{2}= 0.9951 and a low standard Root Mean Squared Error (RMSE) at 0.68 m, which proves that our adaptive DBSCAN and outlier-removal algorithm are effective. For SDB-AP-estimated depths and the in situ data over St. Thomas, R

^{2}was 0.93, and the RMSE was 1.91 m, as shown in Figure 8. Compared with the ICESat-2-derived bathymetric depths, the bathymetric accuracy of SDB-AP estimated depth decreases due to the error accumulation effects, including the ICESat-2 inversion error, the spatial matching error between ICESat-2 and Sentinel data, the Sentinel image process error, the empirical SDB model error, etc. Among them, the empirical SDB model error is the main error source; generally, the error for the empirical SDB model is about 2 m [15,17,18,20]. Figure 6d–f shows the performance of SDB-AP estimated depths when the ICESat-2-derived bathymetric points were used as testing data in the three study areas. The R

^{2}in St. Thomas site reached the top (R

^{2}= 0.96), followed by that in the Huaguang Reef site and Acklins Island site, 0.94 and 0.91, respectively. All RMSEs in the St. Thomas site, Acklins Island site, and Huaguang Reef site were less than 10% of the maximum depths, and the smallest RMSE was in the Acklins Island site with the value of 0.27 m.

^{2}fell, which revealed that there were large errors in deep water (>20 m) and that the SDB is more feasible for shallow water within a depth of 10 m.

#### 4.4. Comparison between Adaptive DBSCAN and Standard DBSCAN

^{2}was 0.96 and that the RMSE was 1.14 m, indicating that our algorithm is consistent with the in situ data. However, for the results derived by the standard DBSCAN algorithm, the R

^{2}was 0.94, and the RMSE was 1.94 m.

## 5. Discussion

#### 5.1. Impact of Outlier Removal on Bathymetry Accuracy

#### 5.2. Stability of SDB-AP

^{2}of 0.94 and an RMSE of 1.88 m, while the result on 1 March 2016 was relatively the worst, with an R

^{2}of 0.91 and an RMSE of 2.06 m. It should be noted that the deviation between different dates may be caused by many reasons, such as satellite remote-sensing reflection difference or the tide [52,53,54]. For each date, the R

^{2}and RMSEs were also calculated and shown in the top-left corners. The mean R

^{2}was 0.93, and the mean RMSE was 2.00 m, which is less than 10% of the maximum depth. These key regression equation parameters mean great temporal consistency of SDB-AP over different dates.

#### 5.3. Comparison with an Adaptive Variable Ellipse Filtering Bathymetric Method

#### 5.4. Comparison with Different Methods Deriving Bathymetry from Sentinel-2

^{2}. The reason for this may be that the location of points for the error analysis corresponds to the location of points used to train the network. In terms of the RMSE, the deep-learning method had a worse accuracy at 0–10 m, and the reason may be that there were insufficient training points. However, it had better performance in the water depth range of 10 to 30 m. In future research, the deep-learning method is superior for deep-water bathymetry.

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

- Compute the Euclidean distance matrix $Dis{t}_{N\times N}$ from $i$ to $j$ for all points in dataset $D$.$$Dis{t}_{N\times N}=\left\{\mathrm{dist}\left(i,j\right)\mid 1\u2a7di\u2a7dN,1\u2a7dj\u2a7dN\right\}$$
- Sort each row element in the distance matrix $Dis{t}_{n\times n}$ in ascending order.The first column of matrix $Dis{t}_{N\times N}$ represents the distance from the object to itself and the elements in column $k$ constitute the K-nearest neighbor distance vector ${D}_{K}$ of all points.
- Calculate the vector ${D}_{k}$ mean value $\overline{{D}_{k}}$. Calculate all $k\left(k=1,2,\dots ,N\right)$to obtain candidate radius dataset ${D}_{\epsilon}$, which is expressed as follows:$${D}_{\epsilon}=\left\{{\epsilon}_{k}=\overline{{D}_{k}}\mid 1\le k\le N\right\}$$The values of the candidate $\epsilon $ dataset less than 0.4 would be eliminated.

**Figure A1.**Sentinel-2 bathymetric maps over the St. Thomas site: (

**a**) our adaptive DBSCAN, (

**b**) standard DBSCAN, (

**c**) in situ. The dark grey line corresponds to the trajectory of ICESat-2 on 13 December 2020.

**Figure A2.**Error scatter plots near the St. Thomas sites: (

**a**) adaptive DBSCAN; (

**b**) standard DBSCAN. The red line is the 1:1 line, while the blue line represents the regression line. $N$ is the number of the training gridded bathymetric points from ICESat-2, and the regression equation details are shown in the top-left corner.

**Figure A3.**Bathymetric maps over the St. Thomas site: (

**a**) Sentinel-2 inversion result without outlier removal, (

**b**) Sentinel-2 inversion result with SDB-AP method, (

**c**) in situ data.

**Figure A4.**Error scatter plots for different bathymetry estimation methods over St. Thomas without using the outlier-removal method: (

**a**) ICESat-2 bathymetric estimated depths vs. in situ depths, (

**b**) SDB-AP estimated depths vs. in situ depths, (

**c**) SDB-AP estimated depths vs. ICESat-2 bathymetric estimated depths. The red line is the 1:1 line, while the blue line represents the regression line. $N$ is the number of the training gridded bathymetric points from ICESat-2, and the regression equation details are shown in the lower-right corner.

**Figure A5.**Error scatter plots on different dates over St. Thomas: (

**a**) 1 March 2016, (

**b**) 21 November 2016, (

**c**) 21 March 2019, (

**d**) 12 September 2019, (

**e**) 4 April 2020, (

**f**) 3 May 2021.

**Figure A6.**Comparison of the detected ICESat-2 signal photons based on our method, AVEBM, and the standard DBSCAN method on different dates: (

**a**,

**d**,

**g**) adaptive DBSCAN on 22 February 2019, 24 May 2019, and 19 August 2019, respectively; (

**b**,

**e**,

**h**) AVEBM on 22 February 2019, 24 May 2019, and 19 August 2019, respectively; and (

**c**,

**f**,

**i**) standard DBSCAN with fixed $\text{}\epsilon =1\text{}\mathrm{m}$ and $Minpts=5$ on 22 February 2019, 24 May 2019, and 19 August 2019, respectively.

**Figure A7.**Bathymetric maps derived from Sentinel-2 using different methods: (

**a**) linear model and (

**b**) deep-learning method.

**Table A1.**Error analysis in different depth ranges: Linear model bathymetric depths vs. in situ depths.

Depth (m) | N | R^{2} | RMSE (m) | Bias (m) | MAE (m) |
---|---|---|---|---|---|

0–10 | 244 | 0.8935 | 1.0700 | −0.1171 | 0.5233 |

10–20 | 452 | 0.8125 | 2.6690 | −1.6661 | 2.3869 |

20–30 | 541 | 0.4132 | 2.2092 | −0.4535 | 1.8305 |

0–30 | 1237 | 0.9225 | 2.0187 | −0.3298 | 1.9875 |

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**Figure 1.**Overviews of three study areas: (

**a**) Saint Thomas, US Virgin Islands—the background satellite image belongs to Sentinel-2 acquired on 15 January 2019. All red lines correspond to the laser trajectories of ICESat-2 on 22 November 2018, 10 February 2019, and 13 December 2020, respectively. A total of 80% of the ICESat-2 bathymetric points were randomly used to train the empirical model, and the remaining 20% as well as in situ data were used to verify the SDB-AP bathymetric result. (

**b**) Acklins Island—the satellite image in the background belongs to Sentinel-2 acquired on 27 January 2020. All red lines correspond to the laser trajectories of ICESat-2 on 12 November 2018, 11 February 2019, 12 March 2019, 3 June 2019, and 2 September 2019. 80% of the ICESat-2 bathymetric points were used to train the empirical model, while the remaining 20% were used to verify the SDB-AP bathymetric result. (

**c**) Huaguang Reef—the satellite image in the background belongs to Sentinel-2 acquired on 13 August 2019. All red lines correspond to the laser trajectories of the ICESat-2 on 22 October 2018, 22 February 2019, 21 April 2019, 19 April 2020, 19 July 2020, and 20 August 2020. 80% of the ICESat-2 bathymetric points were used to train the empirical model, while the remaining 20% were used to verify the SDB-AP bathymetric result.

**Figure 3.**Outlier-removal result based on our method with the noise photons (light blue) and the outlier-removal signal photons (red): (

**a**) St. Thomas site, (

**b**) Acklins Island site, and (

**c**) Huaguang Reef site.

**Figure 5.**Enlarged satellite images and profiles of geolocated photon returns over three study sites: (

**a**,

**b**) St. Thomas on 21 February 2019; (

**c**,

**d**) Acklins Island on 3 June 2019; (

**e**,

**f**) Huaguang Reef on 22 February 2019; bathymetric retrieval by ICESat-2 data over the St. Thomas site with the detected seafloor signal photons (red), the corrected seafloor photons from our detected result photons(orange), the detected sea surface (dark blue), and the noise photons (light blue).

**Figure 6.**SDB-AP derived-bathymetric maps and error scatter plots of SDB-AP estimated depths vs. ICESat-2 bathymetric depths: (

**a**) derived bathymetric maps in the St. Thomas site, (

**b**) derived bathymetric maps in the Acklins Island site, (

**c**) derived bathymetric maps in the Huaguang Reef site, (

**d**) error scatter plots in St. Thomas site, (

**e**) error scatter plots in the Acklins Island site, and (

**f**) error scatter plots in the Huaguang Reef site. The red line is the 1:1 line, while the blue line represents the regression line. $N$ is the number of the training gridded bathymetric points from ICESat-2, and the regression equation details are shown in the top-left corner.

**Figure 7.**Error scatter plot: ICESat-2 bathymetric depths vs. in situ depths over St. Thomas. The red line is the 1:1 line, while the blue line represents the regression line.$N$ is the number of the training gridded bathymetric points from ICESat-2, and the regression equation details are shown in the top-left corner.

**Figure 8.**Error scatter plot: SDB-AP estimated depths vs. in situ depths over St. Thomas. The red line is the 1:1 line, while the blue line represents the regression line. N is the number of training gridded bathymetric points from in situ data, and the regression equation details are shown in the top-left corner.

**Figure 9.**Error scatter plots in different depth ranges over St. Thomas: (

**a**–

**c**) ICESat-2 bathymetric depths vs. in situ depths; (

**d**–

**f**) SDB-AP depths vs. ICESat-2 bathymetric depths.

**Figure 10.**Comparison of the detected ICESat-2 signal photons based on our method and standard DBSCAN method on 12 December 2020: (

**a**) adaptive DBSCAN; (

**b**) standard DBSCAN with fixed $\epsilon $ and $Minpts$.

**Figure 11.**Outlier removal results over St. Thomas site: the bottom return photons (light blue), the outlier-removal signal photons (red). (

**a**) adaptive DBSCAN; (

**b**) standard DBSCAN with fixed $\epsilon $ and $minpts$ detection results.

Site | St. Thomas | Acklins Island | Huaguang Reef | Shanhu Island | Nan Island | |
---|---|---|---|---|---|---|

Location | 18.26°~18.43°N 64.80°~65.07°W | 22.10°~22.60°N 73.90°~74.40°W | 16.13°~16.28°N 111.52°~111.86°E | 111.617°~111.618°N 16.534°~16.548°E | 111.612°~111.614°N 16.529°~16.55°E | 112.202°~112.333°N 16.956°~16.933°E |

ICESat-2 Tracks-beam | 22 November 2018-GT1/2/3R 10 February 2019-GT1/2/3L 13 November 2020-GT1L | 12 November 2018-GT1/2L 11 February 2019-GT1/2/3R 12 March 2019-GT1/2/3R 3 June 2019-GT1/2/3L 2 September 2019-GT2/3R | 22 October 2018-GT1/2/3R 22 February 2019-GT1/2/3L 21 April 2019-GT1/2/3L 19 April 2020-GT1/2/3R 19 July 2020-GT1/2/3L 20 August 2020-GT1/2L | 22 February 2019-GT3L | 24 May 2019-GT2L | 19 August 2019-GT1L |

Sentinel-2 | 15 January 2019 1 March 2016 21 November 2018 21 March 2019 12 September 2019 4 April 2020 3 May 2021 | 27 January 2020 | 13 August 2019 | \ | \ | \ |

In situ Data | 9 December 2014 CUDEM | \ | \ | \ | \ | \ |

Depth (m) | N | R^{2} | RMSE (m) | Bias (m) | MAE (m) |
---|---|---|---|---|---|

0–10 | 382 | 0.9035 | 0.9548 | 0.1039 | 0.5397 |

10–20 | 246 | 0.7951 | 2.2463 | −1.0138 | 1.9493 |

20–30 | 420 | 0.4281 | 2.5499 | −0.8490 | 2.2155 |

Depth (m) | N | R^{2} | RMSE (m) | Bias (m) | MAE (m) |
---|---|---|---|---|---|

0–10 | 199 | 0.82516 | 1.2259 | 0.3846 | 1.0195 |

10–20 | 331 | 0.8260 | 1.8768 | −0.8994 | 1.6265 |

20–30 | 461 | 0.4697 | 2.4056 | −0.7402 | 2.08725 |

**Table 4.**Error analysis in different depth ranges: deep learning bathymetric depths vs. in situ depths.

Depth (m) | N | R^{2} | RMSE (m) | Bias (m) | MAE (m) |
---|---|---|---|---|---|

0–10 | 289 | 0.8073 | 1.3980 | 0.4948 | 1.1408 |

10–20 | 377 | 0.8293 | 1.6895 | 1.1531 | 1.4291 |

20–30 | 461 | 0.4406 | 2.1800 | 0.5675 | 1.8222 |

0–30 | 1127 | 0.9425 | 2.0068 | 0.8560 | 1.6428 |

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## Share and Cite

**MDPI and ACS Style**

Xie, C.; Chen, P.; Pan, D.; Zhong, C.; Zhang, Z.
Improved Filtering of ICESat-2 Lidar Data for Nearshore Bathymetry Estimation Using Sentinel-2 Imagery. *Remote Sens.* **2021**, *13*, 4303.
https://doi.org/10.3390/rs13214303

**AMA Style**

Xie C, Chen P, Pan D, Zhong C, Zhang Z.
Improved Filtering of ICESat-2 Lidar Data for Nearshore Bathymetry Estimation Using Sentinel-2 Imagery. *Remote Sensing*. 2021; 13(21):4303.
https://doi.org/10.3390/rs13214303

**Chicago/Turabian Style**

Xie, Congshuang, Peng Chen, Delu Pan, Chunyi Zhong, and Zhenhua Zhang.
2021. "Improved Filtering of ICESat-2 Lidar Data for Nearshore Bathymetry Estimation Using Sentinel-2 Imagery" *Remote Sensing* 13, no. 21: 4303.
https://doi.org/10.3390/rs13214303