# A Spatially Explicit Comparison of Quantitative and Categorical Modelling Approaches for Mapping Seabed Sediments Using Random Forest

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Environmental Data

#### 2.3. Ground-Truth

#### 2.4. Statistical Modelling

_{sm}and ALR

_{gm}are the additive log-ratios of sand to mud and gravel to mud and M, S, and G are the proportions of mud, sand, and gravel size fractions measured in a grab sample, respectively. Note that the results are unaffected by the choice of size fraction to serve as the denominator [53]. Model predictions were then back-transformed to a compositional scale bound between 0 and 1, corresponding to the relative percentage of each size fraction and summing to 1 for each sample [54]:

#### 2.5. Explanatory Variables

#### 2.6. Evaluating Model Performance

#### 2.7. Map Prediction

## 3. Results

#### 3.1. Grain Size Data

#### 3.2. Spatial Autocorrelation

#### 3.3. Variable Selection

_{sm}, ALR

_{gm}, grain size classes, and the presence of coarse substrates (Table 2 and Table 3). Backscatter range was commonly correlated with the backscatter standard deviation (SD) (ρ ≥ 0.70) and only one of these two variables was generally selected, except in the classification model where the correlation between backscatter range at 250 m scale and backscatter SD at 100 m scale was below this threshold. The different curvature measures were often correlated at similar scales and also to RDMV. Total curvature was correlated with one of these variables at every scale tested and consistently had a weaker relationship with the response—it was therefore removed from all models. The two measures of complexity, SA:PA and VRM, were also correlated at similar scales.

#### 3.4. Grain Size Model Evaluation and Comparison

#### 3.5. Coarse Model Assessment

#### 3.6. Combined Map and Model Tuning

## 4. Discussion

#### 4.1. Model Comparison

#### 4.2. Spatial Assessment

#### 4.3. Spatial Prediction

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

#### Multibeam Echosounder Data Processing

## Appendix B

#### Variable Scale Selection

_{sm}and ALR

_{gm}) to test for non-parametric monotonic relationships. We attempted to determine up to two appropriate scales (i.e., “intrinsic scales”; [78]) for each predictor by identifying local peaks in the plot of correlation versus variable scale. Because calculating correlation coefficients between a multi-level categorical response (viz., grain size classes) and quantitative predictors is not as straightforward, we used univariate multinomial logistic regressions to test the ability of each predictor at each scale to explain the grain size sediment class. The residual deviance of the univariate models was plotted against variable scale and up to two local minima were identified in each graph as intrinsic scales. All correlation scores and multinomial logistic regressions were calculated in R using the cor() and multinom() functions within the “stats” and “nnet” packages [79,80].

## Appendix C

#### Variogram Analysis

**Figure A1.**Mud fraction variogram circular model with 250 m lags; nugget = 0.0069, partial sill = 0.0162, major range = 1496.63 m.

**Figure A2.**Sand fraction variogram circular model with 250 m lags; nugget = 0.0050, partial sill = 0.0152, major range = 1210.05 m.

**Figure A4.**Coarse substrate variogram circular model with 360 m lags; nugget = 0.0603, partial sill = 0.0786, major range = 199.12 m.

## Appendix D

#### Error Matrices

Observed | ||||||||
---|---|---|---|---|---|---|---|---|

(g)mS | (g)sM | gmS | gS | M | mS | sM | ||

Predicted | (g)mS | 10 | 4 | 0 | 0 | 0 | 2 | 2 |

(g)sM | 9 | 43 | 1 | 0 | 1 | 0 | 29 | |

gmS | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |

gS | 0 | 0 | 0 | 2 | 0 | 0 | 0 | |

M | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |

mS | 1 | 0 | 0 | 0 | 0 | 4 | 2 | |

sM | 5 | 30 | 2 | 0 | 0 | 3 | 39 |

Observed | ||||||||
---|---|---|---|---|---|---|---|---|

(g)mS | (g)sM | gmS | gS | M | mS | sM | ||

Predicted | (g)mS | 0 | 1 | 0 | 2 | 0 | 0 | 2 |

(g)sM | 18 | 46 | 0 | 0 | 0 | 7 | 23 | |

gmS | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |

gS | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |

M | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |

mS | 0 | 1 | 0 | 0 | 0 | 0 | 0 | |

sM | 7 | 29 | 3 | 0 | 1 | 2 | 46 |

Observed | |||||||
---|---|---|---|---|---|---|---|

(g)mS | (g)sM | gmS | gS | mS | sM | ||

Predicted | (g)mS | 4 | 3 | 0 | 0 | 0 | 0 |

(g)sM | 16 | 56 | 2 | 0 | 4 | 37 | |

gmS | 2 | 0 | 0 | 2 | 0 | 0 | |

gS | 0 | 0 | 0 | 0 | 0 | 0 | |

mS | 2 | 0 | 0 | 0 | 2 | 0 | |

sM | 1 | 19 | 1 | 0 | 0 | 18 |

Observed | |||||||
---|---|---|---|---|---|---|---|

(g)mS | (g)sM | gmS | gS | mS | sM | ||

Predicted | (g)mS | 0 | 1 | 0 | 2 | 0 | 0 |

(g)sM | 21 | 66 | 3 | 0 | 6 | 39 | |

gmS | 1 | 0 | 0 | 0 | 0 | 0 | |

gS | 0 | 0 | 0 | 0 | 0 | 0 | |

mS | 0 | 0 | 0 | 0 | 0 | 0 | |

sM | 3 | 11 | 0 | 0 | 0 | 16 |

Observed | ||||||
---|---|---|---|---|---|---|

gmS | gS | M | mS | sM | ||

Predicted | gmS | 0 | 0 | 0 | 0 | 0 |

gS | 0 | 2 | 0 | 0 | 0 | |

M | 0 | 0 | 0 | 0 | 0 | |

mS | 0 | 0 | 0 | 18 | 7 | |

sM | 3 | 0 | 1 | 16 | 142 |

Observed | ||||||
---|---|---|---|---|---|---|

gmS | gS | M | mS | sM | ||

Predicted | gmS | 0 | 0 | 0 | 0 | 0 |

gS | 0 | 0 | 0 | 0 | 0 | |

M | 0 | 0 | 0 | 0 | 0 | |

mS | 0 | 2 | 0 | 1 | 2 | |

sM | 3 | 0 | 1 | 33 | 147 |

Observed | |||||
---|---|---|---|---|---|

gmS | gS | mS | sM | ||

Predicted | gmS | 0 | 2 | 2 | 0 |

gS | 0 | 0 | 0 | 0 | |

mS | 0 | 0 | 8 | 3 | |

sM | 3 | 0 | 21 | 130 |

Observed | |||||
---|---|---|---|---|---|

gmS | gS | mS | sM | ||

Predicted | gmS | 0 | 0 | 1 | 0 |

gS | 0 | 0 | 0 | 0 | |

mS | 0 | 2 | 0 | 1 | |

sM | 3 | 0 | 30 | 132 |

Predicted | Observed | ||

Muddy | Sandy | ||

Muddy | 142 | 19 | |

Sandy | 8 | 20 |

Predicted | Observed | ||

Muddy | Sandy | ||

Muddy | 145 | 36 | |

Sandy | 5 | 3 |

Predicted | Observed | ||

Muddy | Sandy | ||

Muddy | 131 | 24 | |

Sandy | 2 | 12 |

Predicted | Observed | ||

Muddy | Sandy | ||

Muddy | 132 | 33 | |

Sandy | 1 | 3 |

Observed | |||
---|---|---|---|

Predicted | Present | Absent | |

Present | 30 | 47 | |

Absent | 9 | 103 |

Observed | |||
---|---|---|---|

Predicted | Present | Absent | |

Present | 44 | 57 | |

Absent | 15 | 176 |

## Appendix E

#### Continuous Quantitative Model Performance

**Table A15.**Accuracies of unclassified quantitative grain size predictions using spatial and non-spatial cross-validations.

LOO CV | S-LOO CV (1500 m) | ||
---|---|---|---|

Mud | %VE | 60.96 | −6.42 |

MAE (%) | 8.28 | 13.51 | |

Pearson | 0.78 | 0.13 | |

Spearman | 0.68 | 0.06 | |

Sand | %VE | 60.05 | −10.99 |

MAE (%) | 8.01 | 12.91 | |

Pearson | 0.78 | 0.06 | |

Spearman | 0.67 | 0.03 | |

Gravel | %VE | 29.66 | −2.06 |

MAE (%) | 1.13 | 1.58 | |

Pearson | 0.61 | 0.13 | |

Spearman | 0.40 | 0.32 |

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**Figure 1.**Ternary diagrams with (

**a**) Folk, (

**b**) simplified Folk and (

**c**) European nature information system (EUNIS) classes.

**Figure 4.**Inner Frobisher Bay multibeam echosounder (MBES) bathymetry contoured at 50 m with shaded terrain and sample sites.

**Figure 8.**Predicted Folk grain size classes for (

**a**) categorical and (

**b**) quantitative models, with (

**c**) agreement between predictions.

**Figure 9.**Predicted simplified Folk grain size classes for (

**a**) categorical and (

**b**) quantitative models, with (

**c**) agreement between predictions.

**Figure 10.**Predicted “muddy/sandy” grain size classes for (

**a**) categorical and (

**b**) quantitative Random Forest models, with (

**c**) agreement between predictions.

**Figure 11.**Predicted probability of coarse substrates using the spatially resampled leave-one-out cross validation (SR-LOO CV) (200 m) model.

Coarse Substrates | Raster Cells |
---|---|

Present | 65 |

Absent | 259 |

ALR_{sm} | ALR_{gm} | Classification | |||
---|---|---|---|---|---|

Variable | Spatial Scale (m) | Variable | Spatial Scale (m) | Variable | Spatial Scale (m) |

Backscatter | - | Bathymetry | - | Bathymetry | - |

Bathymetry | - | Backscatter | - | Backscatter | - |

Distance from coast | - | Distance from coast | - | Distance from coast | - |

Backscatter range | 200 | Backscatter SD | 100 | Backscatter range | 250 |

Eastness | 50 | Eastness | 100 | Backscatter SD | 100 |

Eastness | 500 | Eastness | 400 | Eastness | 10 |

Northness | 10 | Northness | 250 | Eastness | 450 |

Plan curvature | 50 | Plan curvature | 50 | Northness | 10 |

Plan curvature | 350 | Plan curvature | 300 | Plan curvature | 150 |

Profile curvature | 450 | Profile curvature | 300 | Plan curvature | 300 |

RDMV | 300 | Profile curvature | 450 | Profile curvature | 300 |

SA:PA | 10 | Slope | 10 | RDMV | 200 |

Slope | 10 | Slope | 450 | RDMV | 350 |

Slope | 500 | VRM | 200 | Slope | 10 |

VRM | 400 | VRM | 400 | Slope | 450 |

VRM | 10 |

Coarse Substrates | |
---|---|

Variable | Scale (m) |

Bathymetry | - |

Backscatter | - |

Distance from coast | - |

Backscatter SD | 100 |

Eastness | 100 |

Eastness | 500 |

Northness | 250 |

Plan curvature | 100 |

Plan curvature | 350 |

Profile curvature | 10 |

RDMV | 100 |

RDMV | 300 |

Slope | 200 |

VRM | 100 |

VRM | 350 |

**Table 4.**Performance of quantitative and categorical grain size predictions using three schemes with spatial and non-spatial cross-validations.

LOO CV | S-LOO CV (1500 m) | ||||
---|---|---|---|---|---|

Categorical | Quantitative | Categorical | Quantitative | ||

Folk | % correctly classified | 54.64 | 48.46 | 46.72 | 48.58 |

Kappa | 0.25 | 0.14 | 0.12 | 0.10 | |

Simplified Folk | % correctly classified | 85.50 | 82.25 | 78.79 | 78.11 |

Kappa | 0.52 | 0.34 | 0.05 | 0.04 | |

Muddy/Sandy | % correctly classified | 86.29 | 84.62 | 78.36 | 79.88 |

Kappa | 0.53 | 0.41 | 0.06 | 0.11 |

**Table 5.**Threshold-independent accuracy of coarse substrate model using spatial and non-spatial cross validation (CV) approaches and with spatially independent training data.

LOO CV | S-LOO CV (200 m) | SR-LOO CV (200 m) | |
---|---|---|---|

AUC | 0.86 | 0.67 | 0.76 |

Max kappa | 0.62 | 0.24 | 0.40 |

**Table 6.**Accuracies of grain size and coarse substrate components of combined seabed sediment predictions.

Muddy/Sandy (Variables Reduced) | Coarse Presence-Absence | |
---|---|---|

% correctly classified | 70.37 | 75.64 |

Kappa | 0.34 | 0.40 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Misiuk, B.; Diesing, M.; Aitken, A.; Brown, C.J.; Edinger, E.N.; Bell, T. A Spatially Explicit Comparison of Quantitative and Categorical Modelling Approaches for Mapping Seabed Sediments Using Random Forest. *Geosciences* **2019**, *9*, 254.
https://doi.org/10.3390/geosciences9060254

**AMA Style**

Misiuk B, Diesing M, Aitken A, Brown CJ, Edinger EN, Bell T. A Spatially Explicit Comparison of Quantitative and Categorical Modelling Approaches for Mapping Seabed Sediments Using Random Forest. *Geosciences*. 2019; 9(6):254.
https://doi.org/10.3390/geosciences9060254

**Chicago/Turabian Style**

Misiuk, Benjamin, Markus Diesing, Alec Aitken, Craig J. Brown, Evan N. Edinger, and Trevor Bell. 2019. "A Spatially Explicit Comparison of Quantitative and Categorical Modelling Approaches for Mapping Seabed Sediments Using Random Forest" *Geosciences* 9, no. 6: 254.
https://doi.org/10.3390/geosciences9060254