# Unified Geomorphological Analysis Workflows with Benthic Terrain Modeler

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## Abstract

**:**

**Data Set License:**CC-BY

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Marine Geomorphometry Algorithms

#### 2.1.1. Surface Gradients

**Geodesic slope**: In 2017, ArcGIS added support for computing slope on a geodesic. Instead of computing the results in a Cartesian plane, the geodesic method computes directly on the ellipsoid [30]. It retains the use of a $3\times 3$ neighborhood, but improves on the planar method by measuring the angle between the surface and the geodetic datum for each of the 8 adjacent cells, and is fitted with least squares described in Figure 1. This produces more accurate results, particularly when used in conjunction with new high resolution bathymetry sensors with low positional uncertainty [10]. For typical sonar and lidar applications, the positional uncertainty of the observations and the effects of creating a DEM surface will be primary determinants in the accuracy of the slope calculation.

**Aspect**: Aspect measures surface direction. In ArcGIS, it ranges from 0 to 359.9 degrees, measured clockwise from north, and −1 for locations of no slope, based on the same Horn [18] method. BTM augments this with an additional aspect calculation, which converts aspect into two variables: Northerness ${A}_{N}$, due south to due north, and easterness ${A}_{E}$, due west to due east [19,20].

#### 2.1.2. Curvature/Relative Position

**Curvature**: Curvature is the second derivative of the bathymetric surface, or the first derivative of slope, computed in ArcGIS using the method of Zevenbergen et al. [37]. Curvature is evaluated by first calculating the second derivative for each cell in the surface using a moving $3\times 3$ window, and then fitting a fourth order polynomial to the values within the window (see Figure 1). Curvature evaluated only parallel to the slope (profile curvature) can describe the acceleration or deceleration of benthic flow, while curvature evaluated perpendicular to slope (planiform curvature) can help describe convergence or divergence of flow.

**Bathymetric Position Index**: BPI is a marine focused version of the Topographic position index (TPI) [38] which classifies landscape structure (e.g., valleys, plains, hill tops) based on the change in slope position over two scales. BPI quantifies where a location on a bathymetric surface is relative to the overall seascape [12]. For each cell in a surface, BPI is evaluated by finding the difference between the elevation value of the cell and the mean elevation of all cells in an annulus (a ring shape bounded by two concentric circles) surrounding the location. The use of an annulus allows for the exclusion of immediately adjacent cells when measuring mean surrounding elevation. The resulting values are positive near crests and ridges, and negative near cliff bases and valley bottoms.

**Relative difference to the mean**: Relative difference to the mean measures relative position of a location using the mean of a continuous neighborhood of cells rather than an annulus. Similar to BPI, it is evaluated by finding the difference between the mean elevation of all cells in the neighborhood and the elevation of the focal cell. This difference is divided by the range of the focal neighborhood, where range is the difference between the maximum and minimum elevations in the neighborhood.

#### 2.1.3. Rugosity/Surface Roughness

**Surface Area to Planar Area**,

**Vector Ruggedness Measure**, and

**Arc-Chord Ratio**.

**Surface Area to Planar Area**: Following the work of Jeff Jenness [23], BTM has implemented the

**Surface Area to Planar Area (SAPA)**tool since its release.

**SAPA**evaluates rugosity using a $3\times 3$ neighborhood, by drawing a line from the center of each cell in the window to the center of the central cell in three dimensions. The result is a network of eight triangles in the central cell which approximates the contoured surface at the cell location. The sum area of these triangles is divided by the two dimensional cell area to obtain a measure of rugosity. Because of its calculation method,

**SAPA**is tightly coupled with slope, and is surpassed by the other methods in BTM for computing rugosity.

**Vector Ruggedness Measure**: Sappington at al. [22] describe a measure of surface roughness titled Vector Ruggedness Measure (VRM) that is also calculated using a moving $3\times 3$ window, based on an earlier method proposed by Hobson [43]. For each cell in the window, a unit vector orthogonal to the cell is decomposed using the three dimensional location of the cell center, the local slope, and the local aspect. A resultant vector for the window is evaluated and divided by the number of cells in the moving window. The magnitude of this standardized resultant vector is subtracted from 1 to obtain a dimensionless value that ranges from 0 (no variation) to 1 (complete variation). Typical values are small (≤0.4) in natural data.

**Arc-Chord Ratio**: The Arc-Chord Ratio (ACR) was introduced in DuPreez [24]. Similar to Friedman et al. [42], ACR evaluates surface ruggedness using a ratio of contoured area (surface area) to the area of a plane of best fit (POBF), where the POBF is a function of the boundary data. By using a POBF rather than a horizontal plane to determine planar area, rugosity is decoupled from slope at the scale of the surface, and is being adopted as an improved measure of surface roughness [44]. DuPreez [44] provides two three dimensional methods of deriving ACR that are independent of data dimensionality and scale; both are supported by BTM.

**Arc-Chord Ratio**tool, and calculates a single ACR value for an area of interest (AOI) rather than creating a surface of local ACR values. This AOI is chosen by the user based on the context and scale of the analysis, as well as the resolution of the data. The depth surface is converted to a triangulated irregular network (TIN) and clipped to the AOI. Contoured area is determined by summing the triangle areas within the TIN. Planar area is determined by fitting a POBF to the elevation values along the boundary of the AOI, using the Global Polynomial Interpolation tool in ArcGIS to obtain the fitted plane, and as shown in Figure 4. The result is a single ratio representing global ACR rugosity for the area of interest.

**Surface Area to Planar Area (Slope-corrected)**: The second method of calculating the Arc-Chord Ratio is exposed through the

**Surface Area to Planar Area**tool described above. By selecting the “Correct Planar Area for Slope” option, the tool will divide the contoured area by the cell area as projected onto the plane of the local slope. The result is a surface where each cell represents the local ACR rugosity.

#### 2.1.4. Distribution Moments

**Calculate Metrics (Depth Statistics)**tool.

**Calculate Metrics (Depth Statistics)**exposes summary statistics currently available in ArcGIS with the

**Focal Statistics**tool, as well as several statistics that have not yet been implemented in ArcGIS.

#### 2.1.5. Multiscale Analysis

**Compare Scales of Analysis**tool samples a user-selected $200\times 200$ neighborhood of cells in a bathymetry surface and calculates a user-specified statistic. The statistic is then computed at 20 neighborhood sizes within a specified range, and the 20 result grids are presented in a single image for visual comparison, as shown in Figure 5. This image can help users qualitatively understand which scales of analysis identify benthic features and processes of interest. Focal statistics available to use for comparison include median, minimum, maximum, and percentile, which require a percentile value used for filtering to be specified.

**Slope**,

**Aspect**,

**SAPA**and

**SAPA**(

**Slope-corrected**), but the balance of the tools provide an opportunity to explore the impact of scale on the results. While the

**Compare Scales of Analysis**tool offers a generalized comparison of scales, the

**Calculate Metrics at Multiple Scales**tool generates grids of one or more of the following at any number of scales: mean, standard deviation, variance, kurtosis, interquartile range, and VRM. This provides an automated solution to generating full grids of distribution moments and rugosity across multiple scales for use in a multiscale model, or simply for the purpose of investigating the impact of scale on the results.

#### 2.2. Software Architecture

#### 2.3. Example Study Site

## 3. Results

#### 3.1. Classified Benthnic Zone Mapping

**Classify Benthic Terrain**tool, in which a classification dictionary was manually created to generate a map of benthic zones for the study area, or stored as XML. The newest release of BTM includes the

**Run All Model Steps**tool, which condenses this workflow into a single step, and accepts both CSV and Excel files as classification dictionaries.

**Run All Model Steps**tool. The original dataset was clipped to obtain a smaller study area that highlights the benthic structures immediately surrounding Buck Island.

- Scale and resolution of the input data
- Scale of focal operations used to calculate BPI and slope
- Previous studies of the area of interest
- Typical values observed for the benthic zone of interest
- The range of values in each classification artifact

#### 3.2. Integrating R Statistical Analysis

**arcgisbinding**, which provides functions for reading, writing, converting, and manipulating spatial data between ArcGIS and R. The advantages of the

**arcgisbinding**package compared to packages like

**rgdal**are most noticeable when considering the breath of data that can be transferred and when coordinated data manipulation is needed. For example, the package can read and write to any data source that exists within ArcGIS. This includes vector data stored in formats such as shapefiles, file geodatabase, or a URL for a feature service, and any supported raster data types, including complex types like mosaic datasets. Additionally, in the

**arcgisbinding**package, the same functions used to read in data, can also be used to perform actions like creating custom subsets and selections, reprojecting both vector and raster data on the fly, and resampling and adjusting the extent of raster data. All of the above mentioned functionality is contained in the functions arc.open or arc.select if working with vector data, as shown, or arc.open and arc.raster if working with raster data.

# Load library containing R-ArcGIS bridge functionality library(arcgisbinding) # Check connection between R and ArcGIS has been established arc.check_product() input_gdb <- “C:/ArcGIS/Projects/BTM/BTM.gdb” feature_class <- “Field_AAData_ClassifiedLocations” # Establish pointer to desired data’s stored location arc_locations <- arc.open(file.path(input_gdb, feature_class)) # Convert from an ArcGIS data type to an R data frame object df_locations <- arc.select(arc_locations) # Convert from an R data frame object to a spatial data frame object # from the R package sp spdf_locations <- arc.data2sp(df_locations) |

# Remove NAs df_locations <- na.omit(df_locations) # Creation of training/testing datasets smp_size <- floor(0.80 * nrow(df_locations)) # Randomly select observation numbers to ensure sample is randomly selected train_ind <- sample(seq_len(nrow(df_locations)), size = smp_size) # Subset the original data based on the randomly selected observation # numbers to make the training data set df_locations_train <- df_locations[train_ind, ] # Subset the original data on the remaining observations to make the # testing data set df_locations_test <- df_locations[-train_ind, ] # Make predictor variable into a factor df_locations_train$D_STRUCT <- as.factor(df_locations_train$D_STRUCT) # Separate response from the covariates btm.train_covariates <- df_locations_train[, 2:17] btm.train_response <- df_locations_train[, 1] # Apply Principal Component Analysis btm.train_pca <- prcomp(btm.train_covariates, center = TRUE, scale. = TRUE) |

#### 3.3. Terrain Attribute Relationships

#### 3.3.1. Slope

#### 3.3.2. Covariate Selection

#### 3.3.3. Remarks

## 4. Discussion

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

AOI | Area of interest |

BIRNM | Buck Island Reef National Monument |

BPI | Bathymetric Position Index |

BTM | Benthic Terrain Modeler |

DTM | Digital terrain model |

GIS | Geographic information system |

IQR | Interquartile range |

LiDAR | Light Detection and Ranging |

MBES | Multibeam Ecosounder |

NOAA | National Oceanic and Atmospheric Administration |

POBF | Plane of best fit |

SAPA | Surface area to planar area |

TIN | Triangulated irregular network |

VRM | Vector ruggedness measure |

## Appendix A.

#### Appendix A.1. Derived Parameters

- k denotes the position of the current raster cell;
- Z is the value of the cell;
- i and j are the two rasters being compared;
- $\mu $ is the mean of the raster;
- N is the total number of cells.

Layer | Environmental Covariate |
---|---|

1 | Aspect easterness |

2 | Aspect northerness |

3 | Broad scale BPI standardized (60–80) |

4 | Fine scale BPI standardized (10–15) |

5 | Interquartile range (IQR) |

6 | Bathymetry (LiDAR) |

7 | Kurtosis (Pearson) |

8 | Mean |

9 | Relative difference to mean |

10 | Standard deviation |

11 | Reflectance (LiDAR) |

12 | Slope (planar) |

13 | Slope of the slope (max $\Delta $ in slope) |

14 | Rugosity (ACR) |

15 | Rugosity (SAPA) |

16 | Rugosity (VRM) |

Layer | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | −0.001505 | −0.000064 | −0.000070 | −0.000074 | −0.001187 | −0.000116 | −0.001187 | −0.000151 | −0.000113 | 0.000753 | −0.000293 | −0.001150 | −0.000004 | −0.000014 | −0.000005 | |

2 | −0.02035 | −0.000174 | −0.000018 | 0.000274 | −0.005216 | −0.000269 | −0.005231 | 0.000012 | 0.000360 | 0.002170 | 0.000938 | 0.003334 | 0.000013 | 0.000045 | 0.000013 | |

3 | −0.00781 | −0.02005 | 0.000123 | 0.000072 | 0.000495 | −0.000025 | 0.000460 | 0.000110 | 0.000102 | −0.000443 | 0.000236 | 0.000704 | 0.000010 | 0.000036 | 0.000022 | |

4 | −0.01952 | −0.00471 | 0.29382 | 0.000070 | −0.000161 | −0.000008 | −0.000159 | 0.000063 | 0.000099 | −0.000181 | 0.000223 | 0.000489 | 0.000016 | 0.000040 | 0.000031 | |

5 | −0.02094 | 0.0727 | 0.17456 | 0.38188 | −0.000080 | −0.000094 | −0.000078 | 0.000012 | 0.000235 | −0.000157 | 0.000551 | 0.001311 | 0.000020 | 0.000083 | 0.000033 | |

6 | −0.0371 | −0.15321 | 0.13208 | −0.09758 | −0.04917 | −0.000071 | 0.014664 | −0.000356 | −0.000091 | −0.005869 | −0.000263 | −0.001478 | −0.000001 | 0.000015 | 0.000014 | |

7 | −0.01123 | −0.02448 | −0.02069 | −0.0156 | −0.17901 | −0.01488 | −0.000068 | −0.000030 | −0.000077 | −0.000073 | −0.000219 | 0.000277 | 0.000003 | −0.000013 | 0.000002 | |

8 | −0.03705 | −0.15354 | 0.12279 | −0.09619 | −0.0476 | 0.99459 | −0.0142 | −0.000357 | −0.000091 | −0.005891 | −0.000261 | −0.001482 | −0.000001 | 0.000015 | 0.000014 | |

9 | −0.01078 | 0.00082 | 0.06726 | 0.0872 | 0.01686 | −0.05514 | −0.01445 | −0.05526 | 0.000016 | −0.000172 | 0.000040 | −0.000146 | 0.000002 | 0.000005 | 0.000004 | |

10 | −0.02384 | 0.07124 | 0.18349 | 0.40352 | 0.96982 | −0.0415 | −0.10875 | −0.04173 | 0.01651 | −0.000540 | −0.002241 | −0.000031 | −0.000086 | −0.000055 | 0.000048 | |

11 | 0.03378 | 0.0915 | −0.16976 | −0.15727 | −0.13822 | −0.57182 | −0.02204 | −0.57346 | −0.0384 | −0.15457 | −0.000540 | −0.002241 | −0.000031 | −0.000086 | −0.000055 | |

12 | −0.02606 | 0.0785 | 0.17926 | 0.38571 | 0.96182 | −0.05086 | −0.1308 | −0.0505 | 0.01777 | 0.99042 | −0.14996 | 0.004609 | 0.000066 | 0.000245 | 0.000106 | |

13 | −0.02568 | 0.06997 | 0.13414 | 0.21164 | 0.57397 | −0.07169 | 0.04158 | −0.0718 | −0.0162 | 0.61259 | −0.15597 | 0.63653 | 0.000182 | 0.000415 | 0.000301 | |

14 | −0.0055 | 0.01546 | 0.10146 | 0.38474 | 0.48963 | −0.00152 | 0.02906 | −0.00171 | 0.00986 | 0.54408 | −0.11896 | 0.50955 | 0.35024 | 0.000012 | 0.000013 | |

15 | −0.00734 | 0.02177 | 0.16034 | 0.40183 | 0.83457 | 0.01642 | −0.04372 | 0.01634 | 0.01338 | 0.85408 | −0.13833 | 0.78137 | 0.33215 | 0.54067 | 0.000020 | |

16 | −0.00395 | 0.0102 | 0.15266 | 0.48178 | 0.51791 | 0.02527 | 0.0124 | 0.02513 | 0.01487 | 0.5628 | −0.13889 | 0.52841 | 0.37625 | 0.89434 | 0.5639 |

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**Figure 1.**Least squares fitting of the curvature calculations, including that used by the geodesic slope computation. The pink curve is a polynomial fit against the cells in each $3\times 3$ neighborhood, here labeled ${Z}_{1}$ to ${Z}_{9}$ where ${Z}_{5}$ is the origin cell.

**Figure 2.**Buck Island Reef National Monument LiDAR depth data Section 2.3, and the surface gradients of planar slope, northerness and easterness. Upper left: planar slope, displayed with the perceptually uniform color map viridis [33], in degrees, values normalized by the standard deviation ($\sigma =4.05$). Center left: Northerness of aspect, from due north to due south (1 to −1), linear ramp. Lower left: Easterness of aspect, from due east to due west (1 to −1), linear ramp. Inset maps: (

**A**) is east of island, with large depth variation along a reef edge; (

**B**) is along the bank in the northeast corner of the region.

**Figure 3.**The tape-chain rugosity measurement is an in-situ method of evaluating terrain heterogeneity. The ratio of the chain length (${L}_{chain}$) to profile length (${D}_{chain}$) describes the rugosity of the two dimensional profile. Used under Creative Commons Attribution license (CC BY) from Friedman et al. [42].

**Figure 4.**Components required to calculate Arc-Chord Ratio (ACR) (a) for a bathymetric surface using a moving $3\times 3$ window, and (b) for an area of interest using a triangulated irregular network. Reprinted by permission from Cherisse Du Preez: Springer Nature Landscape Ecology, 2015 [24].

**Figure 5.**Output from

**Compare Scales of Analysis**tool, with Median calculated for focal neighborhoods ranging from $3\times 3$ to $60\times 60$. Fine scale detail is lost by the $21\times 21$ neighborhood, and only broad trends remain at the $48\times 48$ scale.

**Figure 6.**The BTM Python Add-in, which provides a simple graphical interface for accessing the analytical tools provided.

**Figure 8.**A habitat classification map created for a subregion of Buck Island National Marine Reserve using the Run All Model Steps tool. The white zone represents terrain above sea level.

**Figure 9.**Output from the summary() function on the results from the principal component analysis to explain the proportion of variance explained by each selected covariate.

**Figure 10.**Output from the plot() function on the results from the principal component analysis which show the components that explain 95 percent of the variance.

**Figure 11.**Left: planar slope, ${S}_{p}$, in degrees. Center: geodesic slope, ${S}_{g}$, in degrees. Right: Slope differences, (${S}_{g}-{S}_{p}$), with the displayed range of (1 to -1). Most areas show very small changes in the values, but locations with high rugosity, and steep slopes show localized larger differences. Same inset locations described in Figure 2.

Name | Algorithm | Notes | References |
---|---|---|---|

Slope | $\mathrm{arctan}\sqrt{({\frac{dz}{dx}}^{2}+{\frac{dz}{dy}}^{2})}$ | Computed over a $3\times 3$ neighborhood | [18] |

Statistical Aspect | $57.29578\times \mathrm{arctan}2(\frac{dz}{dy}+\frac{dz}{dx})$ | Generates Easterness and Northerness | [19,20] |

Mean Depth | $\frac{{\sum}_{i=x-(n+1)/2}^{x+(n+1)/2}{\sum}_{j=y-(n+1)/2}^{y+(n+1)/2}{z}_{ij}}{{n}^{2}}$ | n is the size of a square neighborhood of cells | |

Standard Deviation | $\sqrt{\frac{{\sum}_{i=x-(n+1)/2}^{x+(n+1)/2}{\sum}_{j=y-(n+1)/2}^{y+(n+1)/2}{({z}_{ij}-\overline{z})}^{2}}{{n}^{2}}}$ | $\overline{z}$ is the mean elevation of cells within the analysis neighborhood | |

Variance | ${\sigma}^{2}$ | $\sigma $ is the standard deviation of a neighborhood of cells | |

Interquartile Range | $CD{F}^{-1}(0.75)-CD{F}^{-1}(0.25)$ | $CDF$ is the cumulative distribution function of all cells in the analysis neighborhood | [21] |

Kurtosis | $\frac{{\mu}_{4}}{{\sigma}^{4}}$ | ${\mu}_{4}$ is the fourth central moment and $\sigma $ is the standard deviation of all cells in the analysis neighborhood | [21] |

BPI | ${z}_{xy}-{\overline{z}}_{annulus}$ | ${\overline{z}}_{annulus}$ is the mean elevation value of all cells within an annulus-shaped neighborhood | [12] |

VRM | see Section 2.1.3 | [22] | |

SAPA | see Section 2.1.3 | [23] | |

SAPA (Slope-corrected) | see Section 2.1.3 | Decoupled from slope as per ACR | [24] |

ACR | see Section 2.1.3 | [24] |

Interface | Role |
---|---|

Graphical menu | Direct interaction (see Figure 6) |

Python toolbox | Direct and scripted interaction |

Command-line | Reproducible, scalable, programmatic |

Jupyter Notebooks | Teaching and exploration |

**Table 3.**Classification table used for creation of Figure 8. Missing values indicate that the bound is not applicable to the benthic zone.

Class | Zone | Broad BPI (Lower) | Broad BPI (Upper) | Fine BPI (Lower) | Fine BPI (Upper) | Slope (Lower) | Slope (Upper) | Depth (Lower) | Depth (Upper) |
---|---|---|---|---|---|---|---|---|---|

1 | Reef Crest | −87 | 541 | −907 | 2229 | 11 | −2 | ||

2 | Back Reef | −87 | 541 | −459 | 885 | 52 | −6 | ||

3 | Bank or Shelf | −402 | 699 | −1355 | 4469 | 74 | −18 | ||

4 | Reef Flat | −9 | 541 | −459 | 1333 | 67 | −8 | ||

5 | Channel | −323 | 384 | −907 | 1333 | 53 | −12 | −1 | |

6 | Fore Reef | −323 | 541 | −1355 | 2229 | 61 | −14 | ||

7 | Lagoon | −166 | 463 | −459 | 1333 | 49 | −7 | ||

8 | Salt Pond | −9 | −9 | −11 | −11 | 53 | −7 | ||

9 | Shoreline Intertidal | −9 | 384 | −11 | 436 | 19 | −2 |

Parameter | Value |
---|---|

Bathymetry Raster: | LiDAR bathymetry (clipped) |

Broad-scale BPI Inner Radius: | 25 |

Broad-scale BPI Outer Radius: | 250 |

Fine-scale BPI Inner Radius: | 5 |

Fine-scale BPI Outer Radius: | 25 |

Classification Dictionary: | See Table 3 |

© 2018 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**

Walbridge, S.; Slocum, N.; Pobuda, M.; Wright, D.J.
Unified Geomorphological Analysis Workflows with Benthic Terrain Modeler. *Geosciences* **2018**, *8*, 94.
https://doi.org/10.3390/geosciences8030094

**AMA Style**

Walbridge S, Slocum N, Pobuda M, Wright DJ.
Unified Geomorphological Analysis Workflows with Benthic Terrain Modeler. *Geosciences*. 2018; 8(3):94.
https://doi.org/10.3390/geosciences8030094

**Chicago/Turabian Style**

Walbridge, Shaun, Noah Slocum, Marjean Pobuda, and Dawn J. Wright.
2018. "Unified Geomorphological Analysis Workflows with Benthic Terrain Modeler" *Geosciences* 8, no. 3: 94.
https://doi.org/10.3390/geosciences8030094