# An Approach for the Automatic Characterization of Underwater Dunes in Fluviomarine Context

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Underwater Dunes

#### 2.1. Formation of the Underwater Dunes

#### 2.2. Morphological Descriptors of the Dunes

## 3. Underwater Dunes Characterization from a DBM

- The dune orientation is computed using the segment joining the starting and ending pixel of the crest line. We considered the direction facing the lee side of the dune. The segment orientation angle is measured from the north (O
_{m}). - The depth (P
_{C}) of a dune is computed using the depth of each pixel of the crest line, as illustrated in Figure 11A. The minimum value among these pixels (i.e., closest to the water surface) is considered as the dune depth, since this information is valuable to detect dunes representing a risk for safe navigation. - The width (W
_{D}) is defined as the horizontal distance between the dune lee and stoss troughs. To compute this measure, we considered the stoss and lee trough pixels matched with each crest line pixel. Therefore, a width value is computed for each pixel composing the crest line, as illustrated in Figure 11B. The median value among all crest line pixels is considered as the dune width. - The height of a dune (H
_{C}) also considers the matching between the pixels of the crest line and the troughs. A height value is computed for each crest line pixel as the distance between the crest line pixel and the line joining the stoss and lee troughs (see Figure 4C). The median value among all the crest line pixels is considered as the height of the dune. - The stoss and lee angles (α
_{S}and α_{L}), as well as stoss and lee widths (W_{S}and W_{L}), are computed in a similar fashion as the measures related to the crest line. The median values computed are considered as the stoss and lee angles, as well as stoss and lee widths of the dune. - The sinuosity index ($S{i}_{d}$) is computed considering (3). The geodetic distance (${D}_{C}$) is calculated as illustrated in Figure 7. Please note that the length of the crest line (${L}_{c}$) is not computed as the number of pixels composing the crest line. Instead, the geometric distance between the centers of the pixels is used to increase accuracy given the variability of the crest line sinuosity.
- The steepness and symmetry indexes are computed for each dune object considering the values previously estimated for the width (W
_{D}, W_{S}, and W_{L}) and height (H_{C}), as defined in (1) and (2).

- The spacing between two consecutive dunes in a field is computed considering the distances between the crest lines of each dune. The computation of the spacing requires a direction. Therefore, the median value of the dune orientation of the objects located on the field is considered here. The spacing is computed for each pixel of the crest lines, as illustrated in Figure 12. Then, the mean value is considered as the spacing (λ
_{S}) of the dunes of a field. - The standard deviation of the spacing (${\sigma}_{\lambda s}$) is computed considering all the spacing values of the dunes on a field. This descriptor is useful to characterize the dunes dispersion on the seafloor surface.
- The dunes density (${f}_{D}$) is computed using the ratio between the surface of the field covered by dunes (${A}_{CD}$) and the total surface of the field (${A}_{field}$), as described in (4). ${f}_{D}$ is a third-order descriptor mentioned by the authors of [24], therein also called fullbeddedness or fraction of the seafloor covered by dunes.

_{S}) is more variable in Figure 12B than in Figure 12A. Consequently, the standard deviation (${\sigma}_{\lambda s}$) is expected to be higher for isolated dunes (Figure 12B) than adjacent dunes (Figure 12A). In addition, the fraction of the seafloor covered by dunes (${f}_{D}$) shall be higher in the field with adjacent dunes (Figure 12A) than in the field with isolated dunes (Figure 12B).

## 4. Characterization of the Dunes of the Northern Traverse of the Saint Lawrence River

#### 4.1. The Northern Traverse of the Saint Lawrence River

#### 4.2. Morphological Descriptors of the Dunes of the Northern Traverse

_{D}, W

_{S}, and W

_{L}). On the contrary, in such context, the angular descriptors each side of the dune can be reliably estimated. The angular symmetry index ranges from 0.20 to 14.2, with a median value of 1.27, as illustrated in Figure 15B. The value of the symmetry index based on the width ranges from 0.2 to 10.5, with a median value of 1.21 (Figure 15A). The reason for having values lower than 1 is due to the imperfect identification of the stoss and lee troughs in the segmentation approach, as previously mentioned. Therefore, in the proposed method, the angular symmetry index is used to characterize the dune objects. The sinuosity index, as illustrated in Figure 15C, ranges from 1.01 to 6.32, with a median value of 1.11. The steepness index ranges from 0.0025 to 0.1197, with a median value of 0.0398 (Figure 15D).

_{S}, ${\sigma}_{\lambda S}$, ${f}_{D}$) are also calculated for the nine sectors of the Northern Traverse, as presented in Table 2.

## 5. Analysis and Discussion

_{S}, ${\sigma}_{\lambda S}$, ${f}_{D}$) are illustrated in Figure 18.

_{S}) and standard deviation (${\sigma}_{\lambda S}$) share similar values in the southern sectors (i.e., G04–G10), as illustrated in Figure 18. However, in the northern sectors (i.e., G11–G15), the value of ${\sigma}_{\lambda S}$ is remarkably lower than the value of λ

_{S}. Thereby, it shows that the dunes on the southern sectors are more spatially dispersed than the dunes on the northern sectors. This conclusion is supported by the fraction of the seafloor covered by dunes (${f}_{D}$), as illustrated in Figure 18. The southern fields have less than 50% of their surface covered by dunes. On the contrary, the northern fields have more than 50% of the seafloor covered by dunes. By analyzing these three descriptors (i.e., λ

_{S}, ${\sigma}_{\lambda S}$, ${f}_{D}$), one can state that the dunes on the northern fields are adjacent to each other, while the southern sectors consist of isolated dunes. This is consistent with the expert knowledge expressed by the professionals responsible for the maintenance of the Northern Traverse. Therefore, this demonstrated that the morphological descriptors, automatically extracted by the proposed method, adequately characterize the dune fields of the navigation channel. Furthermore, such morphological descriptors may be useful to better understand the relationship between the dunes and their hydrodynamic factors. As an example, Figure 19 illustrates the relationship between dunes and the flow current.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Correlation between the flow velocity, grain size sediment, and the sedimentary structure formed (adapted from [4]).

**Figure 3.**Isolated dunes (

**A**) and adjacent dunes (

**B**) on the seafloor. The red lines represent the troughs and the magenta lines represent the crest line of the dunes.

**Figure 4.**Descriptors estimated for the crest line of the dunes. The crest line is displayed in magenta and the troughs in red. X

_{S}and X

_{E}represents, respectively, the starting and ending points of the crest line. In (

**A**,

**B**), L

_{C}represent the length of the crest line. The migration direction of the dune relative to the north (O

_{m}) is presented in (

**A**). The orientation angle (O

_{C}) of the crest line of the dune, usually perpendicular to the current, is presented in (

**B**). The height (H

_{C}) and depth (P

_{C}) of the dune are illustrated in (

**C**).

**Figure 5.**Width and spacing of the dunes. In (

**A**), the width is represented by the distance between the dune stoss and lee troughs (W

_{T}). In (

**B**), the width is represented by the horizontal distance between the dune lee and stoss troughs (W

_{D}). In (

**C**), the width is represented by the spacing measured between two consecutive dunes at their crest lines (λ

_{D}).

**Figure 6.**Measurements for dune stoss and lee sides. W

_{S}, W

_{L}, α

_{S}, and α

_{L}represent, respectively, the width of the stoss side, the width of the lee side, the angle of the stoss side, and the angle of the lee side (adapted from [18]).

**Figure 7.**Measurements considered in the computation of the sinuosity index. ${L}_{c}$ represents the length of the crest line and ${X}_{S}$, ${X}_{E}$ the starting and ending point of the crest line, respectively. ${D}_{c}$ represents the geodetic distance between the crest line extremities (adapted from [29]).

**Figure 8.**Proposed method for automatic extraction of dune morphological descriptors and field of dunes morphological descriptors.

**Figure 9.**The dune object identified using its salient features and components. In (

**A**), the dune object on the seafloor is schematized. In (

**B**), the dune object is schematized as identified on the DBM grid. The crest line is in magenta, the trough lines are in red, the stoss sides are displayed in green, and the lee sides are displayed in blue.

**Figure 10.**Data and results for the dune segmentation approach proposed by [17] for the sector G14 of the Northern Traverse. (

**A**,

**B**) illustrate, respectively, the DBM and the salient features of the dunes identified in Phase I; the crest lines are displayed in red and the troughs in blue. In (

**C**), the dune objects segmented in Phase II are presented. Please note that each segmented dune illustrated in (

**C**) are represented with a different color.

**Figure 11.**(

**A**) schematized the extraction of the depth associated with each pixel of the crest line. (

**B**) illustrates the estimation of the width for each cell of the crest line of the dune. The crest lines are in magenta, the trough lines are in red, the stoss sides are displayed in green, and the lee sides are displayed in blue. As previously mentioned, we can observe that for each crest line pixel, our extraction method matched a stoss trough pixel and a lee trough pixel in the morphological descriptors computation.

**Figure 12.**Spacing between the crest lines of two consecutive dune objects. The crest lines are in magenta, the trough lines are in red, the stoss sides are displayed in green, and the lee sides are displayed in blue. λ

_{S}represents the spacing between dunes while $s$ and $e$ represents, respectively, the starting and ending point of the crest lines. (

**A**) presents adjacent dunes in a field and (

**B**) presents isolated dunes on a field. The dunes in A are more equally spaced than in (

**B**), considering the spacing (λ

_{S}) between these objects calculated for each pixel of the crest lines.

**Figure 13.**Considered sectors of the Northern Traverse of the Saint Lawrence River as well as 3D representations of some DBMs and segmented dunes (colored objects superimposing the DBM surfaces). To better observe the dunes on the seafloor, a vertical exaggeration of 5 is used in the 3D representations.

**Figure 14.**Histograms of the morphological descriptor values. Please note that in (

**A**–

**D**) the descriptors of the dunes are in blue. In (

**E**,

**F**), the stoss descriptors are in blue and the lee descriptors are in red. The additional color (i.e., orange) results from the superposition of the red and blue colors.

**Figure 15.**Histograms of the symmetry indexes. (

**A**): the symmetry index calculated with the width of the stoss and lee sides of the dunes. (

**B**): the angular symmetry index calculated with the angles of the stoss and lee sides. (

**C**): the sinuosity. (

**D**): the steepness values of the dunes.

**Figure 16.**Median-depth of the dunes per sector. Please note that consecutive sectors are equally spaced. Since sectors G05, G06, and G07 are not considered, sectors G04 and G08 are more distant than the other consecutive sectors.

**Figure 18.**In the left, the spacing (λ

_{S}) between the dunes and the standard deviation (${\sigma}_{\lambda S}$) per sector. In the right, the fraction of the seafloor covered by dunes (${f}_{D}$ ) per sector.

**Table 1.**Morphological descriptors of the fields of the Northern Traverse sectors. O

_{m}is the median orientation, Pc the minimum depth of the crest line, Hc is the median height, W

_{D}is the median width of the dunes, $S{i}_{d}$ is the sinuosity of the dune, and $S{y}_{a}$ is the angular symmetry of the dunes.

Sector | O_{m} (°) | P_{C} (m) | H_{C} (m) | W_{D} (m) | $\mathit{S}{\mathit{i}}_{\mathit{d}}$ | $\mathit{S}{\mathit{y}}_{\mathit{a}}$ |
---|---|---|---|---|---|---|

G04 | 57.18 | 13.52 | 0.60 | 16.97 | 1.16 | 1.49 |

G08 | 33.69 | 13.71 | 0.43 | 20.81 | 1.11 | 1.43 |

G09 | 21.92 | 13.94 | 0.54 | 8.49 | 1.10 | 1.34 |

G10 | 20.22 | 14.25 | 0.48 | 12.00 | 1.10 | 1.10 |

G11 | 21.80 | 14.03 | 0.78 | 23.42 | 1.10 | 1.16 |

G12 | 23.33 | 16.47 | 0.84 | 21.00 | 1.11 | 1.52 |

G13 | 27.21 | 14.94 | 2.45 | 34.00 | 1.09 | 1.25 |

G14 | 36.19 | 14.42 | 2.64 | 36.00 | 1.09 | 1.24 |

G15 | 201.48 | 15.15 | 1.66 | 28.00 | 1.10 | 1.54 |

**Table 2.**Spacing between the dune objects (λ

_{S}), standard deviation (${\sigma}_{\lambda S}$), and fullbeddedness (${f}_{D}$) for the nine dunes fields of the Northern Traverse.

Sector | λ_{S} (m) | ${\mathit{\sigma}}_{\mathit{\lambda}\mathit{S}}\text{}\left(\mathbf{m}\right)$ | ${\mathit{f}}_{\mathit{D}}\text{}(\%)$ |
---|---|---|---|

G04 | 70.95 | 66.66 | 29 |

G08 | 39.47 | 35.16 | 17 |

G09 | 48.35 | 48.80 | 18 |

G10 | 38.78 | 41.58 | 46 |

G11 | 38.47 | 28.42 | 61 |

G12 | 46.29 | 29.29 | 51 |

G13 | 47.13 | 28.35 | 76 |

G14 | 48.51 | 23.55 | 86 |

G15 | 52.72 | 26.41 | 62 |

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**MDPI and ACS Style**

Cassol, W.N.; Daniel, S.; Guilbert, É.
An Approach for the Automatic Characterization of Underwater Dunes in Fluviomarine Context. *Geosciences* **2022**, *12*, 89.
https://doi.org/10.3390/geosciences12020089

**AMA Style**

Cassol WN, Daniel S, Guilbert É.
An Approach for the Automatic Characterization of Underwater Dunes in Fluviomarine Context. *Geosciences*. 2022; 12(2):89.
https://doi.org/10.3390/geosciences12020089

**Chicago/Turabian Style**

Cassol, Willian Ney, Sylvie Daniel, and Éric Guilbert.
2022. "An Approach for the Automatic Characterization of Underwater Dunes in Fluviomarine Context" *Geosciences* 12, no. 2: 89.
https://doi.org/10.3390/geosciences12020089