# Intertidal Bathymetry Extraction with Multispectral Images: A Logistic Regression Approach

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data Set

#### 2.1. Study Areas

^{2}. The Tagus estuarine surface is characterized by extensive tidal flats, salt marsh vegetation and mudflats, where 40% of the estuarine area is intertidal [2,5,36] (Figure 1). The depths in the Tagus estuary vary between 2 m in the northern part that includes most mudflats, the middle part with average depths of 7 m, and 46 m in the downstream sections at the main navigation channel [5,36]. The Tagus estuary is mesotidal (tidal range between 2 and 4 m) with a maximum amplitude of 3.9 m and has a semidiurnal tide regime [32,36].

^{2}belonging to the Bijagós archipelago area is intertidal zone [38] (Figure 2). Bijagós has a semidiurnal tide regime and is also meso-tidal, with maximum amplitudes of 4.3 m [32,36].

#### 2.2. Satellite Images

#### 2.3. Tide Data

#### 2.4. In Situ Data for Validation

## 3. Methods

#### 3.1. Preprocessing

#### 3.2. Intertidal Zone Pixels’ Selection

#### 3.3. Logistic Regression

**a**and

**k**, where the steepness is correlated with the parameter

**a**. The function will increase if

**a**is positive and will decrease with tidal height (${h}_{i}$), when

**a**is negative. The logistic function superior asymptote is correlated with the

**k**value. The shape of the logistic function is tuned by these parameters, and they are estimated through adjustment with each pixel reflectance. The LowLim in Equation (3), related to the lower asymptote, could be a third parameter to characterize the logistic function. However, this parameter is not related with the shape of the sigmoid and will be neglected in the following analysis. In fact, the correlation between the tide height and the time variable reflectance is described only by the other two parameters. The sigmoid function is shown in Figure 6a for a range of steepness values. According to our experience, the steepness parameter

**a**must be in the range −10 m

^{−1}to −2 m

^{−1}.

**a**and

**k**and predict the surface elevation (${h}_{t}$). The

**a**parameter can be defined through the tide regime and topography, reducing the number of parameters to be estimated. As the function is not linear, the terrain height ${h}_{t}$ and the parameter

**k**are obtained by searching in the bi-dimensional space of the minimum solution of the cost function:

**k**is the maximum reflectance. Hence, the pixel’s height is predicted by searching in the one-dimensional space (local tide range) of the minimum solution of the cost function. The cost function for a range of steepness values is shown in Figure 6b. We observe that the steepness value is not relevant for the predicted height. In fact, the predicted height range is 2.51 to 2.60 m, changing the steepness value from −2 m

^{−1}to −10 m

^{−1}, and the cost function minimum ranges from 0.012 to 0.04 (reflectance).

#### 3.4. Derivation of the Bathymetric Model

#### 3.5. Log-Transformed Ratio Bands Bathymetric Models

## 4. Results

#### 4.1. Pre-Processing

#### 4.2. Intertidal Model Estimation

#### 4.3. Logarithm Ratio Model Estimation

^{th}of August 2018 (3.55 m tide height) and on the 6

^{th}of December 2017 (4.08 m tide height) were used in the Tagus estuary and Bijagós, respectively. The model was calibrated with 507 and 78 depth values in both sites, selected from hydrographic survey in the Tagus estuary [53] and from a nautical chart in Bijagós [54]. Further details concerning the bathymetric model derivation with the ratio-transformed methodology [30,43,51] are presented in the Appendix A (Annex A). We confined the range of the calibration depths between 0 and 10 m (Figure A2) because the selected ratio bands presented best results in shallow waters [30,43,51,52].

#### 4.4. Validation of the Models

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**ANNEX-A—Logarithm ratio model estimation**

^{2}= 0.79). For the Bijagós archipelago, the correlation between the data sets was lower (R

^{2}= 0.54), but the data used in this case for the calibration has not been updated since the 1960’s [54,55], and this could be a large source of error. Perhaps, the sample of depths used in this study for calibration (N = 500 for Tagus estuary and N = 307 for Bijagós) could be considered exaggerated. In fact, some authors defend that few calibration points were needed to calibrate the model, 5 to 10 [51] or 10 control points [43], because the model had only two parameters (${m}_{1}$ and ${m}_{0}$) that required tuning.

**Figure A1.**Linear regression graphics between in situ measurements (depths in meters) and the logarithm ratio. (

**a**) Tagus estuary—13AUG18 S2A L2A image. (

**b**) Bijagós archipelago—25APR18 S2B L2A image. (Red dashed line: linear regression best fit; red rectangle: correlation coefficient (R

^{2}) between data sets and Equation (7) solution).

**Figure A2.**Bathymetric model for the Tagus estuary achieved through the logarithm ratio band algorithm. S2A L2A 08AUG2018 image.

**Figure A3.**Bathymetric model for the Bijagós archipelago achieved through the logarithm ratio band algorithm. S2A L2A 06DEC2017 image.

## References

- Brito, A.C.; Moita, T.; Gameiro, C.; Silva, T.; Anselmo, T.; Brotas, V. Changes in the Phytoplankton Composition in a Temperate Estuarine System (1960 to 2010). Estuar. Coasts
**2015**, 38, 1678–1691. [Google Scholar] [CrossRef] - Taborda, R.; Freire, P.; Silva, A.; Andrade, C.; Freitas, M.C. Origin and evolution of Tagus estuarine beaches. J. Coast. Res.
**2009**, 56, 213–217. [Google Scholar] - Gameiro, C.; Cartaxana, P.; Brotas, V. Environmental drivers of phytoplankton distribution and composition in Tagus Estuary, Portugal. Estuar. Coast. Shelf Sci.
**2007**, 75, 21–34. [Google Scholar] [CrossRef] - Wright, L.D.; Syvitski, J.P.; Nichols, C.R. Chapter 5: Coastal Morphodynamics and Ecosystem Dynamics. In Tomorrow’s Coasts: Complex and Impermanent; Wright, L.D., Nichols, C.R., Eds.; Springer: New York, NY, USA, 2019; pp. 69–84. [Google Scholar] [CrossRef]
- Guerreiro, M.; Fortunato, A.B.; Freira, P.; Rilo, A.; Taborda, R.; Freitas, A.C.; Andrade, C.; Silva, T.A.; Rodrigues, M.; Bertin, X.A.; et al. Evolution of the hydrodynamics of the Tagus estuary (Portugal) in the 21st century. J. Integr. Coast. Zone Manag.
**2015**, 15, 65–80. [Google Scholar] [CrossRef] - Silva, A.N.; Taborda, R.; Antunes, C.; Catalão, J. Understanding the coastal variability at Norte beach, Portugal. J. Coast. Res.
**2013**, 65, 2173–2178. [Google Scholar] [CrossRef] - Nerem, R.S.; Beckley, B.D.; Fasulto, J.T.; Hamlington, B.D.; Masters, D.; Mitchum, G.T. Climate-change–driven accelerated sea-level rise detected in the altimeter era. In Proceedings of the National Academy of Sciences, Toulouse, France, 25 February 2018; pp. 2022–2025. [Google Scholar] [CrossRef][Green Version]
- Schuerch, M.; Spencer, T.; Temmerman, S.; Kirwan, M.L.; Wolff, C.; Lincke, D.; McOwen, C.J.; Pickering, M.D.; Reef, R.; Vafeidis, A.T.; et al. Future response of global coastal wetlands to sea-level rise. Nature
**2018**, 561, 231–234. [Google Scholar] [CrossRef] - Bastos, A.P.; Ponte Lira, C.; Calvão, J.; Catalão, J.; Andrade, C.; Pereira, A.J.; Taborda, R.; Rato, D.; Pinho, P.; Correia, O. UAV Derived Information Applied to the Morphological Study of Slow changing Dune Systems. J. Coast. Res.
**2018**, 85, 226–230. [Google Scholar] [CrossRef] - Silva, A.; Taborda, R.; Catalão, J.; Freire, P. DTM extraction using video monitoring techniques: Application to a fetch limited beach. J. Coast. Res.
**2009**, 56, 203–207. [Google Scholar] - Bird, C.O.; Bell, P.S.; Plater, A.J. Application of marine radar to monitoring seasonal and event-based changes in intertidal morphology. Geomorphology
**2017**, 285, 1–15. [Google Scholar] [CrossRef][Green Version] - Chénier, R.; Faucher, M.; Ahola, R. Satellite-Derived Bathymetry for Improving Canadian Hydrographic Service Charts. ISPRS Int. J. Geo. Inf.
**2018**, 7, 306. [Google Scholar] [CrossRef][Green Version] - Dierssen, H.M.; Theberge, J.A.E. Bathymetry: Assessing Methods. Volume II Water and Air. Encyc. Nat. Res.
**2014**. [Google Scholar] [CrossRef] - Quadros, N.D.; Collier, P.A. A New Approach to Delineating the Littoral Zone for an Australian Marine Cadastre. J. Coast. Res.
**2008**, 24, 780–789. [Google Scholar] [CrossRef] - Wozencraft, J.; Millar, D. Airborne Lidar and integrated technologies for coastal mapping and nautical charting. Mar. Techno. Soc. J.
**2005**, 39, 27–35. [Google Scholar] [CrossRef] - Jawak, S.D.; Vadlamani, S.S.; Luis, A.J. A Synoptic review on deriving bathymetry information using Remote Sensing Technologies: Models and Comparisons. Adv. Remote Sens.
**2015**, 4, 147–162. [Google Scholar] [CrossRef][Green Version] - Chénier, R.; Ahola, R.; Sagram, M.; Faucher, M.; Shelat, Y. Consideration of Level of Confidence within Multi-Approach Satellite-Derived Bathymetry. ISPRS Int. J. Geo-Inf.
**2019**, 8, 48. [Google Scholar] [CrossRef] - Mason, D.C.; Davenport, I. Accurate and Efficient Determination of the Shoreline in ERS-1 SAR images. IEEE Trans. Geosci. Remote Sens.
**1996**, 34, 1243–1253. [Google Scholar] [CrossRef] - Catalão, J.; Nico, G. Multitemporal backscattering logistic analysis for intertidal bathymetry. IEEE Trans. Geosci. Remote Sens.
**2016**, 55, 1066–1073. [Google Scholar] [CrossRef] - Pacheco, A.; Horta, J.; Loureiro, C.; Ferreira, Ó. Retrieval of nearshore bathymetry from Landsat 8 images: A tool for coastal monitoring in shallow waters. Remote Sens. Environ.
**2015**, 159, 102–116. [Google Scholar] [CrossRef][Green Version] - Niedermeier, A.; Hoja, D.; Lehner, S. Topography and morphodynamics in the German Bight using SAR and optical remote sensing data. Ocean Dyn.
**2005**, 55, 100–109. [Google Scholar] [CrossRef] - Schwäbisch, M.; Lehner, S.; Norbert, W. Coastline extraction using ERS SAR interferometry. In Proceedings of the 3rd ERS Symposium, Florence, Italy, 14–21 March 1997; pp. 1049–1053, Space Service Environment, ESA SP-414. [Google Scholar]
- Sagar, S.; Roberts, D.; Bala, B.; Lymburner, L. Extracting the intertidal extent and topography of the Australian coastline from a 28-year time series of Landsat observations. Remote Sens. Environ.
**2017**, 195, 153–169. [Google Scholar] [CrossRef] - Bishop, -T.R.; Sagar, S.; Lymburner, L.; Beaman, R. Between the tides: Modelling the elevation of Australia’s exposed intertidal zone at continental scale. Estuar. Coast. Shelf Sci.
**2019**, 223, 115–128. [Google Scholar] [CrossRef] - Pahlevan, N.; Sarkar, S.; Franz, B.A.; Balasubramanian, S.V.; He, J. Sentinel-2 MultiSpectral Instrument (MSI) data processing for aquatic science applications: Demonstrations and validations. Remote Sens. Environ.
**2017**, 201, 47–56. [Google Scholar] [CrossRef] - Said, R.; Mahmud, M.R.; Hasan, R.C. Evaluating satellite-derived bathymetry accuracy from Sentinel-2A high-resolution multispectral imageries for shallow water hydrographic mapping. Available online: https://iopscience.iop.org/article/10.1088/1755-1315/169/1/012069/pdf (accessed on 24 April 2019).
- Lyzenga, D. Passive Remote-Sensing techniques for mapping water depth and bottom features. App. Opt.
**1978**, 17, 379–383. [Google Scholar] [CrossRef] - Lyzenga, D.R. Shallow-water bathymetry using combined lidar and passive multispectral scanner data. Int. J. Remote Sens.
**1985**, 6, 115–125. [Google Scholar] [CrossRef] - Lyzenga, D.R.; Malinas, N.P.; Tanis, F.J. Multispectral Bathymetry using a Simple Physically Based Algorithm. IEEE Trans. Geosci. Remote Sens.
**2006**, 44, 2251–2259. [Google Scholar] [CrossRef] - Stumpf, R.P.; Holderied, K.; Sinclair, M. Determination of water depth with high-resolution satellite imagery over variable bottom types. Limnol. Oceanogr.
**2003**, 48, 547–556. [Google Scholar] [CrossRef] - Bell, P.S.; Bird, C.O.; Plater, A.J. A temporal waterline approach to mapping intertidal areas using X-band marine radar. Coast. Engin.
**2016**, 107, 84–101. [Google Scholar] [CrossRef][Green Version] - Instituto Hidrográfico. Tabelas de Marés; Vol II Países Africanos de Língua Oficial Portuguesa e Macau; Instituto Hidrográfico: Lisbon, Portugal, 2018. [Google Scholar]
- Liu, Y.; Li, M.; Zhou, M.; Yang, K.; Mao, L. Quantitative Analysis of the Waterline method for Topographical Mapping of Tidal Flats: A case study in the Dongsha Sandbank, China. Remote Sens.
**2013**, 5, 6138–6158. [Google Scholar] [CrossRef][Green Version] - Ryu, J.-H.; Won, J.S.; Min, K.D. Waterline extraction from Landsat TM data in a tidal flat. A case study in Gomso Bay, Korea. Remote Sens. Environ.
**2002**, 83, 442–456. [Google Scholar] [CrossRef] - Ryu, J.-H.; Kim, C.-H.; Lee, Y.-K.; Won, J.-S.; Chun, S.-S.; Lee, S. Detecting the intertidal morphologic change using satellite data. Estuar. Coast. Shelf Sci.
**2008**, 78, 623–632. [Google Scholar] [CrossRef] - Neves, F. Dynamics and Hydrology of the TAGUS Estuary: Results from in Situ Observations. Ph.D. Thesis, Faculdade de Ciências da Universidade de Lisboa, Lisbon, Portugal, 2010. [Google Scholar]
- GUINÉ-BISSAU. A Reserva de Biosfera do Arquipélago dos Bijagós: Um Património a Preserver; Ministerio de Agricultura, Alimentación y Medio Ambiente de España, Administração da Guiné-Bissau: Bissau, Guiné-Bissau, 2012; p. 211. [Google Scholar]
- Carvalho, L.; Figueira, P.; Monteiro, R.; Reis, A.; Almeida, J.; Catry, T.; Lourenço, P.; Catry, P.; Barbosa, C.; Catry, I.; et al. Major, minor, trace and rare earth elements in sediments of the Bijagós archipelago, Guinea-Bissau. Mar. Pollut. Bull.
**2018**, 829–834. [Google Scholar] [CrossRef] - Sentinel’s Scientific Data Hub. Available online: https://scihub.copernicus.eu/ (accessed on 8 March 2019).
- European Space Agency. Sentinel-2 User Handbook; ESA Standard Document; ESA: Paris, France, 2015; Available online: https://sentinel.esa.int/documents/247904/685211/Sentinel-2_User_Handbook (accessed on 12 June 2019).
- European Space Agency. Sentinel-2 MSI Technical Guide. 2017. Available online: https://earth.esa.int/web/sentinel/technical-guides/sentinel-2-msi (accessed on 18 June 2019).
- Casal, G.; Monteys, X.; Hedley, J.; Harris, P.; Cahalane, C.; McCarthy, T. Assessment of empirical algorithms for bathymetry extraction using Sentinel-2 data. Int. J. Remote Sens.
**2019**, 40, 2855–2879. [Google Scholar] [CrossRef] - Caballero, I.; Stumpf, R.P. Towards routine mapping shallow bathymetry in environments with variable turbidity: Contribution of Sentinel-2A/B satellites mission. Remote Sens.
**2020**, 12, 451. [Google Scholar] [CrossRef][Green Version] - Vanhellemont, Q.; Ruddick, K. Atmospheric correction of metre-scale optical satellite data for inland and coastal water applications. Remote Sens. Environ.
**2018**, 216, 586–597. [Google Scholar] [CrossRef] - Hedley, J.D.; Roelfsema, C.; Brando, V.; Giardino, C.; Kutser, T.; Phinn, S.; Mumby, P.; Barrilero, O.; Laporte, J.; Koetzh, B. Coral reef applications of Sentinel-2: Coverage, characteristics, bathymetry and benthic mapping with comparison to Landsat 8. Remote Sens. Environ.
**2018**, 216, 598–614. [Google Scholar] [CrossRef] - Royal Belgium Institute of Natural Sciences. ACOLITE Python User Manual. 2019. Available online: https://odnature.naturalsciences.be/remsem/software-and-data/acolite (accessed on 27 January 2020).
- Vanhellemont, Q.; Ruddick, K. Turbid wakes associated with offshore wind turbines observed with Landsat 8. Remote Sens. Environ.
**2014**, 145, 105–115. [Google Scholar] [CrossRef][Green Version] - Vanhellemont, Q.; Ruddick, K. Advantages of high quality SWIR bands for ocean colour processing: Examples from Landsat-8. Remote Sens. Environ.
**2015**, 161, 89–106. [Google Scholar] [CrossRef][Green Version] - Vanhellemont, Q.; Ruddick, K. Acolite for Sentinel-2: Aquatic Applications of MSI Imagery. In Proceedings of the ESA Living Planet Symposium, Prague, Chez Republic, 9–13 May 2016. [Google Scholar]
- Ruddick, K.; Vanhellemont, Q.; Dogliotti, A.; Nechad, B.; Pringle, N.; Van der Zande, D. New Opportunities and Challenges for High Resolution Remote Sensing of Water Colour. In Proceedings of the Ocean Optics XXIII, Victoria, BC, Canada, 7 October 2016. [Google Scholar]
- Caballero, I.; Stump, P.R.; Meredith, A. Preliminary assessment of turbidity and chlorophyll impact on bathymetry derived from Sentinel-2A and Sentinel-3A satellites in South Florida. Remote Sens.
**2019**, 11, 645. [Google Scholar] [CrossRef][Green Version] - Caballero, I.; Stumpf, R.P. Retrieval of nearshore bathymetry from Sentinel-2A and 2B satellites in South Florida coastal waters. Estuar. Coast. Shelf Sci.
**2019**, 226, 106277. [Google Scholar] [CrossRef] - Instituto Hidrográfico. Levantamento Hidrográfico Instalações Navais da Azinheira (Estuário do Tejo); Instituto Hidrográfico: Lisbon, Portugal, 2018. [Google Scholar]
- Instituto Hidrográfico. Cartas Náuticas do Arquipélago dos Bijagós Guiné-Bissau (223); Instituto Hidrográfico: Lisbon, Portugal, 1969. [Google Scholar]
- International Hydrographic Organization. IHO C-55 Publication Status of Hydrographic Surveying and Charting Worldwide, 2020, Monaco. Available online: https://iho.int/uploads/user/pubs/cb/c-55/c55.pdf (accessed on 17 February 2020).
- McFeeters, S.K. The use of the Normalized Difference Water Index (NDWI) in the delineation of open water features. Int. J. Remote Sens.
**1996**, 17, 1425–1432. [Google Scholar] [CrossRef] - Legleiter, C.J.; Roberts, A.A.; Lawrence, R.L. Spectrally based remote sensing of river bathymetry. Earth Surf. Proc. Landf.
**2009**, 1787. [Google Scholar] [CrossRef] - Niroumand-Jadidi, M.; Vitti, A.; Lyzenga, D. Multiple Optimal Depth Predictors Analysis (MODPA) for river bathymetry: Findings from spectro radiometry, simulations, and satellite imagery. Remote Sens. Environ.
**2018**, 218, 132–147. [Google Scholar] [CrossRef] - Hamylton, S.M.; Hedley, J.D.; Beaman, R.J. Derivation of high-resolution bathymetry from multispectral satellite imagery: A comparison of empirical and optimization methods through geographical error analysis. Remote Sens.
**2015**, 7, 16257–16273. [Google Scholar] [CrossRef][Green Version] - Hedley, J.D.; Harborne, A.R.; Mumby, P.J. Simple and robust removal of sun glint for mapping shallow-water benthos. Int. J. Environ.
**2005**, 113, 2107–2112. [Google Scholar] [CrossRef] - Mason, D.C.; Davenport, I.J.; Flather, R.A.; Gurney, C.; Robinson, G.J.; Smith, J.A. A sensitivity analysis of the waterline method of constructing a digital elevation model for intertidal areas in ERS SAR scene of eastern England. Estuar. Coast. Shelf Sci.
**2001**, 53, 759–778. [Google Scholar] [CrossRef] - Bué, I.; Catalão, J.; Semedo, A. Intertidal Topo-bathymetry extraction from SAR and Multispectral images. In Proceedings of the Living Planet Symposium, Milan, Italy, 13–17 May 2019. [Google Scholar]

**Figure 1.**Tagus estuary in Lisbon. Red-green-blue (RGB) composite after atmospheric correction of Sentinel-2B imagery on 13 August 2018. The two orange rectangles identify specific intertidal areas at the Tagus estuary (top right—Alcochete and lower left—Seixal and Azinheira).

**Figure 2.**The Bijagós archipelago in Guinea-Bissau. RGB composite after atmospheric correction of Sentinel-2B imagery on 25 April 2018.

**Figure 3.**Tidal height variation: (

**a**) Tide height at Tagus estuary from March to October 2018 and (

**b**) Tide height at Bijagós archipelago from December 2017 to May 2018. The red dots represent the Sentinel-2 images dataset (time—11:21 UTC).

**Figure 4.**Bathymetric model acquired by hydrographic survey in Tagus estuary—Azinheira area (red: 3.1 m above chart datum and green: 7.2 m below chart datum).

**Figure 5.**Guinea-Bissau status of hydrographic surveying in accordance with International Hydrographic Organization (IHO) information (adapted from IHO [55] (p 215)).

**Figure 6.**(

**a**) NIR reflectance time series as a function of the tide height (red circles) and adjusted sigmoid function for a range of steepness parameters (from −2 to −10) and (

**b**) cost function for a range of steepness values.

**Figure 7.**Normalized Difference Water Index (NDWI) temporal variability: (

**a**) Alcochete area in Tagus estuary and (

**b**) Formosa, Maio, and Ponta islands at Bijagós archipelagos.

**Figure 8.**NDWI temporal variability of the three classes: water (blue), intertidal (green), and land (red); (

**a**) Tagus estuary and (

**b**) Bijagós archipelago.

**Figure 9.**(

**a**) Tagus estuary intertidal model estimated using the logistic regression method and 18 S2 images (red: 3.1 m and dark blue: 0.7 m). The two blue rectangles highlight specific intertidal areas at the Tagus estuary (bottom left—Seixal and Azinheira; top right—Alcochete), (

**b**) zoom on the intertidal model estimated for the Tagus estuary—Seixal and Azinheira areas, and (

**c**) zoom on the intertidal model estimated for the Tagus estuary—Alcochete area.

**Figure 10.**(

**a**) Bijagós intertidal model estimated from 19 S2 images (red: 4.2 m and dark blue: 1.3 m). The two yellow rectangles highlight different intertidal areas; (

**b**) zoom on the intertidal model estimated for the Bijagós (top right rectangle in (

**a**)—sandy beaches); and (

**c**) zoom on the intertidal model (bottom left rectangle in (

**a**)—mostly mangroves and mudflats [37,38]).

**Figure 11.**Comparison between derived intertidal model in Tagus estuary and cartographic intertidal area shown in white. Greatest differences are observed along the navigation channel due to intense maritime traffic in the area.

**Table 1.**List of Sentinel-2 A&B images used in this study for intertidal bathymetry extraction. Tide height (m) corresponding to image acquisition time (11:21 UTC). (a) Tagus estuary and (b) Bijagós archipelago.

Number | Date | Sensor | Tide Height (m) |
---|---|---|---|

(a) | |||

1 | 21 March 2018 | S2A | 0.72 |

2 | 26 March 2018 | S2B | 2.95 |

3 | 05 May 2018 | S2B | 1.40 |

4 | 10 May 2018 | S2A | 2.97 |

5 | 15 May 2018 | S2B | 1.92 |

6 | 19 June 2018 | S2A | 1.68 |

7 | 24 June 2018 | S2B | 3.15 |

8 | 29 July 2018 | S2A | 1.43 |

9 | 03 August 2018 | S2B | 1.58 |

10 | 08 August 2018 | S2A | 3.35 |

11 | 13 August 2018 | S2B | 0.89 |

12 | 18 August 2018 | S2A | 2.19 |

13 | 23 August 2018 | S2B | 2.89 |

14 | 22 September 2018 | S2B | 2.84 |

15 | 27 September 2018 | S2A | 1.17 |

16 | 07 October 2018 | S2A | 3.02 |

17 | 22 October 2018 | S2B | 2.86 |

18 | 27 October 2018 | S2A | 0.99 |

(b) | |||

1 | 01 December 2017 | S2A | 2.19 |

2 | 06 December 2017 | S2B | 4.08 |

3 | 26 December 2017 | S2B | 1.90 |

4 | 10 January 2018 | S2A | 1.39 |

5 | 15 January 2018 | S2B | 2.90 |

6 | 20 January 2018 | S2A | 3.88 |

7 | 25 January 2018 | S2B | 1.36 |

8 | 30 January 2018 | S2A | 3.07 |

9 | 09 February 2018 | S2A | 1.52 |

10 | 19 February 2018 | S2A | 3.97 |

11 | 01 March 2018 | S2A | 3.68 |

12 | 06 March 2018 | S2B | 3.59 |

13 | 21 March 2018 | S2A | 4.01 |

14 | 31 March 2018 | S2A | 4.04 |

15 | 05 April 2018 | S2B | 3.35 |

16 | 15 April 2018 | S2B | 3.75 |

17 | 25 April 2018 | S2B | 1.34 |

18 | 10 May 2018 | S2A | 1.46 |

19 | 20 May 2018 | S2A | 4.16 |

**Table 2.**Number of intertidal candidate pixels for the logistic regression versus application of threshold and saturation index. (a) Tagus estuary and (b) Bijagós archipelago. Red circles: threshold and saturation index selected to generate the intertidal models. Red rectangles: standard deviation of the intertidal model created after the logistic regression and the comparison with the bathymetric survey in the Tagus estuary and depths extracted from a nautical chart in the Bijagós archipelago.

(a) | ||||

Candidate pixels | Standard Deviation (m) | |||

Threshold | sat = 0.2 | sat = 0.3 | ||

0.15 | 1130556 | 0.3463 | 0.3456 | 0.3438 |

1029078 | 0.3413 | 0.3407 | ||

0.17 | 945951 | 0.3468 | 0.3449 | 0.3436 |

0.18 | 873121 | 0.3557 | 0.3536 | 0.3508 |

(b) | ||||

Candidate pixels | Standard Deviation (m) | |||

Threshold | sat = 0.2 | sat = 0.4 | ||

0.10 | 4445416 | 0.7164 | 0.7172 | 0.7179 |

4131866 | 0.7177 | 0.7043 | ||

0.12 | 3895423 | 0.7310 | 0.7157 | 0.7066 |

0.13 | 3664775 | 0.7153 | 0.7155 | 0.7158 |

**Table 3.**Statistical analysis of the differences between the hydrographic survey at Tagus basin (Azinheira) and the satellite-derived bathymetry (Logarithm Ratio and Logistic Regression). N is the number of samples.

Algorithm | Sentinel 2 (Images) | N | Bias (m) | STD (m) | RMSE (m) | Max (m) | Min (m) |
---|---|---|---|---|---|---|---|

Logarithm Ratio | 08AUG18 (3.35 m tide height) | 507 | 1.81 | 1.31 | 2.23 | 3.74 | −6.98 |

Logistic Regression | 18 images (Table 1a) | 508 | −0.51 | 0.34 | 0.61 | 2.18 | −1.20 |

**Table 4.**Statistical analysis of differences between chart depths in the Bijagós archipelago and the satellite-derived bathymetry (Logarithm Ratio and Logistic Regression). N is the number of samples.

Algorithm | Sentinel 2 (Images) | N | Bias (m) | STD (m) | RMSE (m) | Max (m) | Min (m) |
---|---|---|---|---|---|---|---|

Logarithm Ratio | 06DEC2017 (4.08 m tide height) | 78 | 4.84 | 1.26 | 5.00 | −2.21 | −7.54 |

Logistic Regression | 19 images (Table 1b) | 66 | −0.46 | 0.70 | 0.90 | 1.70 | −1.50 |

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**MDPI and ACS Style**

Bué, I.; Catalão, J.; Semedo, Á.
Intertidal Bathymetry Extraction with Multispectral Images: A Logistic Regression Approach. *Remote Sens.* **2020**, *12*, 1311.
https://doi.org/10.3390/rs12081311

**AMA Style**

Bué I, Catalão J, Semedo Á.
Intertidal Bathymetry Extraction with Multispectral Images: A Logistic Regression Approach. *Remote Sensing*. 2020; 12(8):1311.
https://doi.org/10.3390/rs12081311

**Chicago/Turabian Style**

Bué, Isabel, João Catalão, and Álvaro Semedo.
2020. "Intertidal Bathymetry Extraction with Multispectral Images: A Logistic Regression Approach" *Remote Sensing* 12, no. 8: 1311.
https://doi.org/10.3390/rs12081311