# Surface Characterisation of Kolk-Boils within Tidal Stream Environments Using UAV Imagery

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

**Figure 2.**A schematic detailing kolk-boil formation at the sea surface [20].

## 2. Materials and Methods

#### 2.1. Study Site

#### 2.2. Data Collection

#### 2.3. Data Processing

^{2}(Figure A1), i.e., >15% of an image) it was possible to quickly identify if no kolk-boils were present and the user could move to the next image if that was the case. If the same kolk-boil was present across multiple images, it was noted what number (identifier) that boil had in the previous image and was recorded as part of the classification process. Once started, a survey was processed in one operation, by the same user, to maintain consistency and avoid between-user bias.

#### 2.4. Post-Processing

^{2}), kolk-boil classification (type and confidence), kolk-boil presence, telemetry data, and relevant explanatory variables taken from the central point of each image (current velocity (m/s), current direction (degrees), tidal phase (assigned based on the average current velocity and direction), depth (m), seabed roughness (m), slope angle (degrees) and aspect (degrees)). Kolk-boils deemed to be visually poorly defined (≤40 confidence score) were excluded due to significant uncertainty around whether they were kolk-boils.

#### 2.5. Data Analysis

_{1}, f

_{3}, f

_{4}and f

_{6}) were used for current velocity (k = 8), seabed slope angle (k = 5), depth (k = 5) and seabed roughness (k = 5). Cyclic cubic regression splines (f

_{2}and f

_{5}) were applied when modelling seabed slope aspect (k = 5) and current direction (k = 5) as for both variables 0° must match 360°. Two anisotropic tensor products (f

_{7}to f

_{8}), henceforth referred to as “interaction” included current velocity and seabed slope angle (k = 5 and 5), as well as current direction and seabed slope aspect (k = 5 and 5) in the model. The first interaction used thin plate splines for both variables while the second utilised cyclic cubic regression splines. The model included tidal phase (α

_{0}to α

_{4}) as the only parametric variable. This included declining ebb (

_{DE}), declining flood (

_{DF}), fast ebb (

_{FE}), fast flood (

_{FF}) and increasing flood (

_{IF}) phases. To avoid the issue of complete separation, and the Hauck–Donner effect, within the binomial model the increasing ebb phase (

_{IE}) data, due to having minimal effect on the overall model fit, were removed from analysis. The numeric classification given to each individual flight ϛ(FlightID

_{i}) was incorporated into the final model as a random effect variable to account for temporal autocorrelation.

_{i})

_{i}) = α0TidalPhase

_{DE,i}+ α1TidalPhase

_{DF,i}+ α2TidalPhase

_{FE,i}+ α

_{3}TidalPhase

_{FF,}i + α

_{4}TidalPhase

_{IF,i}+ f

_{1}(Current Velocity

_{i}) + f

_{2}(Seabed Slope Angle

_{i}) + f

_{3}(Depth

_{i}) + f

_{4}(Seabed Roughness

_{i}) + f

_{5}(Current Direction

_{i}) + f

_{6}(Seabed Slope Aspect

_{i}) + f

_{7}(Current Velocity

_{i}, Seabed Slope Angle

_{i}) + f

_{8}(Current Direction

_{i},Seabed Slope Aspect

_{i}) + ϛ(FlightID

_{i})

## 3. Results

#### 3.1. Kolk-Boil Distribution

#### 3.2. Kolk-Boil Presence

## 4. Discussion

#### 4.1. Kolk-Boil Characterisation

#### 4.1.1. Distribution

#### 4.1.2. Presence

#### 4.2. Implications for Tidal Energy Developments

^{2}(Figure A1).

#### 4.3. Future Work

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**(

**A**) The effect of current speed on formed boil area; (

**B**) The effect of depth on formed boil area; (

**C**) The effect of current direction on formed boil area; (

**D**) The effect of tidal phase on formed boil area; (

**E**) The effect of seabed slope angle on formed boil area; (

**F**) The effect of seabed roughness on formed boil area; (

**G**) The effect of seabed slope aspect on formed boil area.

**Figure A2.**(

**A**–

**C**) The effect of tidal phase, current velocity and seabed slope angle on kolk-boils area respec-tively; (

**D**–

**F**) The effect of seabed slope aspect, depth and seabed roughness on kolk-boils area re-spectively; (

**G**) The effect of current direction on kolk-boils area; (

**H**) The effect current velocity on seabed slope angle; (

**I**) The effect of current direction on seabed slope aspect.

**Figure A3.**QQ and residual vs. fitted plots for kolk-boil presence model detailing a binomial distribution fits well and that there is no clear pattern in residuals.

**Figure A4.**Over-dispersion plot for kolk-boil presence model. Given the fitted model (red line) is within the simulated values there was no dispersion.

**Figure A5.**Residual vs. time and autocorrelation function (ACF) plots for kolk-boil presence. No temporal correlation is observed.

**Figure A6.**QQ and residual vs. fitted plots for kolk-boil area model detailing a gaussian distribution fits well and that there is no clear pattern in residuals.

**Figure A7.**Over-dispersion plot for kolk-boil area model. Given the fitted model (red line) is within the simulated values there was no dispersion.

**Figure A8.**Residual vs. time and autocorrelation function (ACF) plots for kolk-boil area. No temporal correlation is observed.

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**Figure 4.**UAV coverage, over ground, of surveys split across (

**a**) ebb and (

**b**) flood tidal phases for 2016 and 2018 combined.

**Figure 5.**Example kolk-boils from UAV imagery and the difference between “formed” and un-formed” categorisations, with the red line indicating the visible part of the boil perimeter.

**Figure 6.**The distribution of formed kolk-boils, based on tidal phase, within the Inner Sound from 2016 and 2018 combined. Flood tidal flow is in an easterly direction, ebb flow in a westerly direction. Grey shaded area represents UAV coverage over ground, with black dots highlighting tidal turbine positions.

**Figure 7.**Cumulative counts of kolk-boil presence (an image with a kolk-boil in it) and absence (an image without a kolk-boil in it) in relation to tidal phase (

**A**), current velocity (

**B**), current direction (

**C**), depth (

**D**), seabed slope angle (

**E**), seabed slope aspect (

**F**) and seabed roughness (

**G**). Bars for kolk-boil presence (green) and absence (grey) are stacked.

**Figure 8.**GAM relationships for kolk-boil presence are shown. (

**A**–

**E**) show the effect of current velocity, depth, seabed slope angle, current direction and tidal phase on the predicted probability of kolk-boil presence, whereas this is coloured in (

**F**,

**G**) highlighting the two-way interaction effect of current velocity with seabed slope angle, and current direction with seabed slope aspect. The dashed lines in (E) and shaded areas of (

**A**–

**D**) represent the 95% confidence intervals. In all plots data are represented by the rug tick marks.

UAV and Camera Specifications | 2016 | 2018 |
---|---|---|

UAV | SwellPro SplashDrone 3+ | DJI Phantom 4 Advanced V2.0 |

Camera | GoPro HERO4 Black (12 MP) | 1-inch CMOS Sensor (20 MP) |

Aspect Ratio | 4:3 (4000 × 3000 pixels) | 3:2 (5472 × 3648 pixels) |

Average Relative Altitude Flown (m) | 46 | 70 |

Image Type Taken | JPEG | Simultaneous pairs of RAW and JPEG |

Sampling Interval between Images/Image Pairs (Seconds) | 1 (subsampled to match 2018 data) | 5 |

Average Image Area (m^{2}) | 5119.56 | 11,577.52 |

**Table 2.**Variables included in the final kolk-boil presence model (excluding those penalised) identified using GAMs with a significance level of p < 0.05. For parametric coefficients, which are presented on the logit scale, estimate, standard error (Std. error), z-values (z), and p-values (p) are shown. For smooth terms, the estimated degrees of freedom (EDF), chi-squared (Chi.sq) and p-values (p) are shown.

Parametric Coefficients: | Model Summary: |
---|---|

Tidal Phase: Decreasing Ebb (Intercept, α_{0}) | Estimate = −1.627 |

Std. Error = 1.425 | |

z = −1.141 | |

p = 0.254 | |

Tidal Phase: Decreasing Flood (α_{1}) | Estimate = −0.747 |

Std. Error = 1.715 | |

z = −0.435 | |

p = 0.663 | |

Tidal Phase: Fast Ebb (α_{2}) | Estimate = −2.410 |

Std. Error = 1.586 | |

z = −1.519 | |

p = 0.129 | |

Tidal Phase: Fast Flood (α_{3})Tidal Phase: Increasing Flood (α _{4}) | Estimate = −3.113 |

Std. Error = 1.560 | |

z = −1.996 | |

p = 0.046 | |

Estimate = −3.808 | |

Std. Error = 2.529 | |

z = −1.506 | |

p = 0.132 | |

Smooth Terms: | |

Current Velocity (${f}_{1}$) | EDF = 6.093 |

Chi.sq = 24,747.999 | |

p ≤ 0.001 | |

Seabed Slope Angle (${f}_{2}$) | EDF = 7.567 × 10^{−1} |

Chi.sq = 3.903 | |

p = 0.039 | |

Depth (${f}_{3}$) | EDF = 1.878 |

Chi.sq = 142.214 | |

p = 0.003 | |

Current Direction (${f}_{5}$) | EDF = 5.887 × 10^{−1} |

Chi.sq = 5.611 | |

p = 0.221 | |

Current Velocity/ Seabed Slope Angle (${f}_{7}$) | EDF = 1.633 |

Chi.sq = 13.378 | |

p = 0.002 | |

Current Direction/ Seabed Slope Aspect (${f}_{8}$) | EDF = 2.119 |

Chi.sq = 5.878 | |

p = 0.042 | |

R^{2} (adj.) = 0.203 Deviance explained = 30.2% | |

n = 7236 |

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**MDPI and ACS Style**

Slingsby, J.; Scott, B.E.; Kregting, L.; McIlvenny, J.; Wilson, J.; Couto, A.; Roos, D.; Yanez, M.; Williamson, B.J.
Surface Characterisation of Kolk-Boils within Tidal Stream Environments Using UAV Imagery. *J. Mar. Sci. Eng.* **2021**, *9*, 484.
https://doi.org/10.3390/jmse9050484

**AMA Style**

Slingsby J, Scott BE, Kregting L, McIlvenny J, Wilson J, Couto A, Roos D, Yanez M, Williamson BJ.
Surface Characterisation of Kolk-Boils within Tidal Stream Environments Using UAV Imagery. *Journal of Marine Science and Engineering*. 2021; 9(5):484.
https://doi.org/10.3390/jmse9050484

**Chicago/Turabian Style**

Slingsby, James, Beth E. Scott, Louise Kregting, Jason McIlvenny, Jared Wilson, Ana Couto, Deon Roos, Marion Yanez, and Benjamin J. Williamson.
2021. "Surface Characterisation of Kolk-Boils within Tidal Stream Environments Using UAV Imagery" *Journal of Marine Science and Engineering* 9, no. 5: 484.
https://doi.org/10.3390/jmse9050484