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Marine Geodesy
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Evaluating the Suitability of Multi-Scale Terrain
Attribute Calculation Approaches for Seabed
Mapping Applications
Benjamin Misiuk, V. Lecours, M. F. J. Dolan & K. Robert
To cite this article: Benjamin Misiuk, V. Lecours, M. F. J. Dolan & K. Robert (2021): Evaluating
the Suitability of Multi-Scale Terrain Attribute Calculation Approaches for Seabed Mapping
Applications, Marine Geodesy, DOI: 10.1080/01490419.2021.1925789
To link to this article: https://doi.org/10.1080/01490419.2021.1925789
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Group
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Evaluating the Suitability of Multi-Scale Terrain
Attribute Calculation Approaches for Seabed Mapping
Applications
Benjamin Misiuk
a,d
, V. Lecours
b
, M. F. J. Dolan
c
, and K. Robert
d
a
Department of Oceanography, Dalhousie University, Halifax, Canada;
b
School of Forest, Fisheries,
and Geomatics Sciences, University of Florida, Gainesville, FL, USA;
c
Marine Geology, Geological
Survey of Norway, Trondheim, Norway;
d
School of Ocean Technology, Fisheries and Marine
Institute of Memorial, University of Newfoundland, St. John’s, Canada
ABSTRACT
The scale dependence of benthic terrain attributes is well-
accepted, and multi-scale methods are increasingly applied for
benthic habitat mapping. There are, however, multiple ways to
calculate terrain attributes at multiple scales, and the suitability
of these approaches depends on the purpose of the analysis
and data characteristics. There are currently few guidelines
establishing the appropriateness of multi-scale raster calculation
approaches for specific benthic habitat mapping applications.
First, we identify three common purposes for calculating terrain
attributes at multiple scales for benthic habitat mapping: (i)
characterizing scale-specific terrain features, (ii) reducing data
artefacts and errors, and (iii) reducing the mischaracterization of
ground-truth data due to inaccurate sample positioning. We
then define criteria that calculation approaches should fulfill to
address these purposes. At two study sites, five raster terrain
attributes, including measures of orientation, relative position,
terrain variability, slope, and rugosity were calculated at mul-
tiple scales using four approaches to compare the suitability of
the approaches for these three purposes. Results suggested
that specific calculation approaches were better suited to cer-
tain tasks. A transferable parameter, termed the ‘analysis dis-
tance’, was necessary to compare attributes calculated using
different approaches, and we emphasize the utility of such a
parameter for facilitating the generalized comparison of terrain
attributes across methods, sites, and scales.
ARTICLE HISTORY
Received 2 December 2020
Accepted 20 April 2021
KEYWORDS
benthic habitat mapping;
geomorphometry; multi-
beam echosounder; scale;
seabed mapping;
terrain analysis
Introduction
Benthic habitat mapping approaches often seek to relate continuous-cover-
age environmental variables to discrete observations of seabed habitats,
CONTACT Benjamin Misiuk ben.misiuk@dal.ca Department of Oceanography, Dalhousie University,
Halifax, Canada.
Supplemental data for this article can be accessed online at https://doi.org/10.1080/01490419.2021.1925789.
This article has been republished with minor changes. These changes do not impact the academic content of the article.
ß2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group
This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives
License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction
in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way.
MARINE GEODESY
https://doi.org/10.1080/01490419.2021.1925789
termed “ground-truth”observations, to predict habitat distributions over
broader extents. Environmental variables may span one or multiple
domains, each partly describing the environmental characteristics that
determine suitable habitat for benthic organisms. These domains often
include sediment properties and dynamics, physical and chemical oceanog-
raphy, inter-species (i.e., community) interactions, and seabed morphology.
Terrain attributes derived from bathymetric data are highly useful for
describing seabed morphology, and their use has become commonplace for
benthic habitat mapping. Terrain attribute calculation is a part of the field
of geomorphometry, which is the science of quantitative land-surface ana-
lysis (Pike, Evans, and Hengl 2009). Given their potential utility as surro-
gates for ecological patterns such as biodiversity (McArthur et al. 2009,
2010; Harris 2012), surface characteristics describing the slope, orientation,
relative position, and variability of the seafloor (Wilson et al. 2007; Bouchet
et al. 2015) are routinely applied to predict distributions of species (e.g.,
Galparsoro et al. 2009;Bu
cas et al. 2013) and broader habitats or
‘benthoscapes’(e.g., Brown, Sameoto, and Smith 2012; Calvert et al. 2015;
Ierodiaconou et al. 2018). A high potential for surrogacy, combined with
the increasing availability of high-resolution bathymetric data and user-
friendly tools, has facilitated the widespread adoption of terrestrial geomor-
phometric techniques for marine applications over the past two decades
(Lecours et al. 2016b). The calculation of raster terrain attributes from
bathymetric data to describe seabed morphology can be considered part of
the current quantitative predictive benthic mapping paradigm (Harris and
Baker 2012; Bouchet et al. 2015).
Following several key studies on seabed morphometry (e.g., Lundblad et al.
2006;Wilsonetal.2007), and efforts to provide guidelines on marine geo-
morphometry (e.g., Lecours et al. 2015b; Lecours et al. 2016b; Lucieer,
Lecours, and Dolan 2018), there has been progress towards establishing stand-
ards for the use of digital terrain models (DTMs) and terrain attributes for
benthic habitat mapping. Fundamental concepts from terrestrial geomorph-
ometry are now being explored in a marine context, such as spatial scale and
scale-dependence of terrain attributes (e.g., Dolan and Lucieer 2014;Giusti,
Innocenti, and Canese 2014;Lecoursetal.2015a;Miyamotoetal.2017;
Misiuk, Lecours, and Bell 2018), and the selection of variables and algorithms
(e.g., Dolan and Lucieer 2014;Bouchetetal.2015;Lecoursetal.2016a). The
field of marine geomorphometry is further distinguished by marine-specific
terrain attributes, segmentation, and classification approaches (e.g., Lundblad
et al. 2006; Du Preez 2015; Di Stefano and Mayer 2018;Diesingand
Thorsnes 2018;Masetti,Mayer,andWard2018; Walbridge et al. 2018),
advances in the production of digital bathymetric models (Calder 2003;
Linklater et al. 2018), and effects of DTM error and uncertainty on terrain
2 B. MISIUK ET AL.
attributes and habitat maps (e.g., Lucieer, Huang, and Siwabessy 2016;
Lecours et al. 2017a; Lecours et al. 2017b). The study of these marine-specific
terrain attribute characteristics has spurred the development of marine geo-
morphometry as a sub-discipline of geomorphometry (Lecours et al. 2018).
This topic has gained traction, as highlighted by the publication of 18 articles
from a special issue on marine geomorphometry in the international journal
Geosciences (Lucieer, Dolan, and Lecours 2019). Its application to benthic
habitatmappinghasrecentlybeenhighlightedbySmithMenandroand
Bastos (2020), who found that ‘geomorphometry’was one of the most used
keywords for seabed mapping articles in the last decade.
Spatial scale is a fundamental concept in geomorphometry. It is well
established that terrain attributes are scale-dependent –that the attributes
themselves depend on the scale at which they are calculated (i.e., the scale
of analysis; Woodcock and Strahler 1987; Wood 1996). The scale of terrain
analysis is intrinsically linked to the source data resolution, and the highest
attainable bathymetric resolution is ultimately constrained by the quality,
resolution, and geometry of the raw sounding data (Hughes Clarke 2018).
The finest achievable scale is not necessarily the most appropriate for every
analysis though, and the calculation of seabed terrain attributes at multiple
scales is increasingly common (e.g., Rengstorf et al. 2012,2013; Giusti,
Innocenti, and Canese 2014; Miyamoto et al. 2017; Misiuk, Lecours, and
Bell 2018; Porskamp et al. 2018; Pearman et al. 2020; Trzcinska et al. 2020;
Zelada Leon et al. 2020). Despite the increased implementation of multi-
scale analyses, there is still little guidance on the appropriateness of multi-
scale approaches for specific benthic habitat mapping applications. Here,
we note that ‘multi-scale’refers broadly to methods and analyses that con-
sider multiple different spatial scales (Dolan and Lucieer 2014).
Using seabed slope as an example, Dolan and Lucieer (2014) compared
five methods of multi-scale terrain attribute calculations and concluded
that each method produces different results. They highlighted the chal-
lenges of determining best practices for calculating terrain attributes at
variable scales, since the suitability of calculation approaches depends on
the purpose of analysis and qualities of the data. Three of the multi-scale
approaches (1–3inTable 1) rely on various combinations of terrain attri-
bute calculation using a 3 3 focal window and aggregating over broader
spatial extents, which are simple operations in most GIS software packages.
The ‘kk-window’method (4 in Table 1; a.k.a. ‘roving window’) differs by
varying the size of the focal analysis window used to calculate the terrain
attributes, which is not always straightforward to perform. There is a large
potential for methodological variation since calculations differ depending
on the attribute, algorithms used, and the number of cells within the kxk
window to which they are applied. Options for ‘kk-window’calculations
MARINE GEODESY 3
are not supported for many attributes in commercial software packages.
Finally, several approaches have been proposed for calculating multi-scale
attributes that simultaneously integrate information from multiple spatial
scales in one or several layers (Method 5 in Table 1; e.g., Gallant and
Dowling 2003; Schmidt and Andrew 2005;Dr
agut¸, Eisank, et al. 2009;
Dr
agut¸, Schauppenlehner, et al. 2009; Wood 2009; Gorini and Mota 2011;
Lindsay and Newman 2018; Shang et al. 2021). Many of these integrated
methods differ fundamentally from the first four in Table 1 and are outside
of the scope of this article.
Several studies have investigated the use and effects of multi-scale calcu-
lation methods on specific terrain attributes (e.g., Dolan and Lucieer 2014;
Lecours et al. 2017b; Moudr
y et al. 2019), but there remains a lack of gen-
eral guidelines on the appropriateness of multi-scale methods for common
benthic habitat mapping applications. The goal of this paper is therefore to
investigate the appropriateness of multi-scale raster calculation methods for
specific scale manipulation applications, and to provide recommendations
on their use. First, we identify three common purposes for manipulating
the scale of terrain attributes in a benthic habitat mapping context and dis-
cuss criteria for determining the suitability of multi-scale raster calculation
methods for each purpose. These purposes are then explored using several
benthic terrain attributes at two study sites. The suitability of the multi-
scale methods for each purpose is evaluated, and the findings are discussed
to provide recommendations on their use.
Scale manipulation purpose, criteria, and methods
Purpose and criteria
There are a variety of potential reasons for manipulating the spatial scale of
terrain attributes for benthic habitat mapping –here we focus on three of
the most common, which are relevant to many habitat mapping studies:
Table 1. Five multi-scale approaches for calculating terrain attributes (Dolan and Lucieer
2014). Asterisks denote marine examples.
# Method Abbreviated name Published examples
1 Resample DTM then
calculate attribute
Resample-calculate Rengstorf et al. (2012), Gottschalk et al. (2011)
2 Average DTM then
calculate attribute
Average-calculate Giusti, Innocenti, and Canese (2014)
3 Calculate attribute
then average
Calculate-average Misiuk, Lecours, and Bell (2018)
4 Calculate attribute
using variable
kkwindow
kk-window Bargain et al. (2017), Porskamp et al. 2018),
Trzcinska et al. (2020)
5 Multiple integrated
spatial scales
Integrated-multiscale Gorini and Mota (2011), Lindsay and Newman (2018),
Lecours and Espriella (2020), Shang et al. (2021)
4 B. MISIUK ET AL.
1. Characterizing scale-specific terrain features. The scale of analysis may
be purposefully adjusted to measure specific seabed features (e.g., dunes,
reefs, pockmarks) that are poorly captured using default calculation
parameters and source resolution, or to test or target scales expected to
influence ecological processes of interest (e.g., Giusti, Innocenti, and
Canese 2014; Gafeira, Dolan, and Monteys 2018; Porskamp et al. 2018;
Zelada Leon et al. 2020). In such cases, it may be desirable to employ a
method that allows the user to explicitly target terrain features at par-
ticular scales and avoid conflation with seabed features and characteris-
tics at other scales.
2. Reducing data errors and artefacts. The scale at which terrain attrib-
utes are calculated may be adjusted (either knowingly or unknow-
ingly) when attempting to reduce the effects of noise and acquisition
artefacts in elevation or depth data (e.g., Albani et al. 2004;Gafeira,
Dolan, and Monteys 2018,Buhl-Mortensenetal.2020;Florinskyand
Filippov 2021). Focal filters and resampling are used for this purpose,
but they can affect the scale of analysis for measuring seabed features
via terrain attributes. Naturally, these approaches aim to reduce the
influence of data outliers or errors on the terrain attribute calculation,
but it may also be useful, and necessary for downstream analyses, to
understand the effects that filtering operations have on the scale of
the attributes.
3. Matching the positional accuracy of ground-truth data. The scale of ter-
rain attributes may be manipulated when attempting to match the pos-
itional accuracy of ground-truth data. The uncertainty of seabed sample
locations can be on the order of meters or tens of meters when geore-
ferenced from a surface platform, yet the horizontal resolution and pos-
itional accuracy of sonar data are generally much higher (Strong 2020).
Where discrepancies exist between measured and actual sample loca-
tions, there is potential to mis-characterize the benthic environment by
assigning incorrect terrain attribute values to ground-truth samples. The
scale of terrain analysis should therefore be broader than the positional
uncertainty of the ground-truth samples to avoid a spatial mismatch
between terrain characterization and ground-truth information (Lecours
and Devillers 2015). Terrain attributes can be generalized spatially to
represent the seabed over a broader area in order to reduce the impacts
of incorrect spatial matching (Sillero and Barbosa 2021), yet this may
affect the scale of analysis at which the terrain is quantified. A suitable
method for characterizing spatially uncertain ground-truth samples
should reduce the error of terrain attribute values between measured
and actual ground-truth locations with the least amount of generaliza-
tion to the terrain attribute.
MARINE GEODESY 5
The suitability of the four multi-scale terrain attribute calculation meth-
ods selected (Methods 1–4, Table 1) is explored for these three purposes at
two study sites of finer (km) and broader (100 s km) scales using five com-
mon benthic terrain attributes.
Datasets
D’Argent Bay
Multibeam echosounder survey of D’Argent Bay, Newfoundland and
Labrador (NL), Canada, was conducted on December 4–7, 2018 and
February 19–23, 2019 to provide data for benthic habitat mapping in
Placentia Bay –an area designated as an Ecologically and Biologically
Significant Area by Fisheries and Oceans Canada (Templeman 2007;Figure
1A). Drop camera observations at this site suggested a heterogeneous sea-
bed primarily comprising gravel and boulder, with patches of soft sediment
near the coast (Shang et al. 2021). Approximately 43 km
2
were mapped
using a Kongsberg EM2040p (400 kHz) with differential GPS (Fugro 3610
DGNSS) aboard the research vessel D. Cartwright. Twenty-five sound vel-
ocity profiles of the water column were acquired using an AML Base X
profiler for sound speed corrections. The raw multibeam data were
imported to the bathymetric processing software Qimera (QPS) for post-
processing. Sound velocity and tidal corrections were applied, and the data
were cleaned and gridded at 5 m resolution. The 5 m raster was projected
to UTM Zone 21 N to obtain metric map units for terrain attribute calcula-
tions. These data are typical of high-resolution coastal mapping surveys,
and are ideal for investigating the effects of terrain attribute scale manipu-
lation over fine spatial extents (10 s-100s of m).
Bjørnøya slide
The General Bathymetric Chart of the Oceans (GEBCO) is the most com-
prehensive global bathymetric data source. Since the 2019 release, GEBCO
grids have been developed through the Nippon Foundation-GEBCO Seabed
2030 Project (Mayer et al. 2018). The GEBCO dataset comprises bathym-
etry from multiple sources, compiled at 15 arc-second intervals. The
bathymetry data, together with information on the data source, are freely
available for download and are increasingly accessed as a trusted source of
regional-global scale bathymetry data. Here, GEBCO_2019 bathymetry data
from an example area on the Norwegian continental margin were down-
loaded as a broad scale case study (GEBCO Bathymetric Compilation
Group 2019). The Norwegian Mapping Authority Hydrographic Service
conducted multibeam surveys of the continental shelf and slope in this area
during 2007–2008 as part of the national offshore mapping programme
6 B. MISIUK ET AL.
MAREANO. These data are incorporated in the GEBCO compilation,
which also includes multibeam data (including transit lines) from various
surveys in the area, together with background interpolated data. The other-
wise smooth continental slope that dips westwards into the Norwegian Sea
is incised within the study area by the 200,000- to 300,000-year-old
Bjørnøya (Bear Island) slide (Laberg and Vorren 1993), which spans several
tens of kilometers (Figure 1B). To the south of the slide, the upper slope
includes extensive sandwave fields investigated by King et al. (2014) and
Bøe et al. (2015), who also provided further details on the geological his-
tory of the area. The presence of morphological features spanning a range
of scales, along with multibeam acquisition-related artefacts and distinct
differences in the quality and resolution of the source bathymetric datasets,
Figure 1. Locations of study sites at (A) D’Argent Bay, Newfoundland and Labrador, Canada, and
(B) the Bjørnøya slide and surrounding area on the Norwegian continental margin. Source: Author,
country borders were obtained from the ESRI Countries WGS84 layer.
MARINE GEODESY 7
make this a relevant area to explore the consequences of multi-scale terrain
analysis performed on a regional compiled dataset. The 15 arc-second
GEBCO_2019 floating-point grid was projected to UTM Zone 33 N in
ArcGIS Pro using bilinear interpolation to achieve square raster cells at
250 m resolution for terrain attribute calculation.
Terrain attribute calculation
The following five common terrain attributes were selected for analysis to
broadly represent different classes (orientation, relative position, terrain
variability, slope, rugosity, respectively; Wilson et al. 2007):
1. the eastness (sine) component of aspect,
2. relative difference to the mean value (RDMV),
3. the local standard deviation of bathymetry (SD),
4. seabed slope, and
5. vector ruggedness measure (VRM).
Each terrain attribute is readily calculated using each of the multi-scale
approaches (1–4; Table 1). The effects of multi-scale calculation method are
expected to be very similar for some attributes of the same class (e.g., east-
ness and northness components of aspect; measures of ruggedness), and
redundant variables were therefore not included.
Slope and eastness were both calculated using the eight-neighbor ‘Queen’s
case’according to Horn (1981), with a custom R function to enable calcula-
tion at multiple kkfocal windows (Supplementary Material). Several con-
figurations could be used for the slope calculation (e.g., Rook’s case
according to Ritter 1987), but the Queen’s case is standard and well-accepted,
generally providing a superior representation of the surface through the
incorporation of elevation or depth data from the diagonals (i.e., NE, NW,
SE, SW; Dolan and Lucieer 2014). RDMV and SD were calculated using the
Terrain Attribute Selection for Spatial Ecology toolbox (TASSE v.1.1) for
ArcGIS (Lecours 2017a), and VRM was calculated using the Benthic Terrain
Modeller (BTM) toolbox (Sappington, Longshore, and Thompson 2007;
Walbridge et al. 2018), both of which allow for calculation over multiple
focal window sizes. Equations for all terrain attribute calculations used in
this study are provided in the Appendices.
Multi-scale implementation
The ‘resample-calculate’method for calculating terrain attributes at mul-
tiple scales (Method 1 in Table 1) was implemented using a mean aggrega-
tion within the ‘raster’package (Hijmans 2019) in R 3.6.3 (R Core Team
8 B. MISIUK ET AL.
2019). Equal weights were applied to all cells within a square aggregation
window of size jjfor j¼1, 3, 5, …, 19 to achieve a coarser bathymetric
raster for each scale of analysis. Terrain attributes were then calculated
using a 3 3 focal window on the coarsened raster grids. The ‘average-cal-
culate’method (Method 2 in Table 1) was implemented by passing mean
filters of dimensions jjfor j¼1, 3, 5, …, 19 over the bathymetric layers
using the focal() function within the ‘raster’package, then calculating ter-
rain variables within a 3 3 focal window using the smoothed bathymetric
rasters. The inverse was performed for the ‘calculate-average’method
(Method 3 in Table 1)–terrain attributes were calculated from the bathy-
metric rasters at their native resolution using a 3 3 focal window, then
were smoothed using mean filters of size jjfor j¼1, 3, 5, …, 19.
The approaches used to calculate terrain attributes using these first three
methods all rely on a combination of calculating the attribute within a
33 focal window and manipulating the aggregation window size j; the
‘kk-window’method (Method 4 in Table 1) varies the size of the focal
window kused to calculate each attribute at its native resolution, and its
implementation differs depending on the attribute. Eastness and slope were
calculated using methods from Horn (1981), but the kkwindows were
manipulated using focal weights matrices via the focal() function within the
‘raster’package in R. Depth values were extracted from the outer eight
neighbors perpendicular to, and diagonal from, the focal cell of the kk
window using the weights matrices, then were used to calculate x- and y-
components of the gradient according to Horn (i.e., using half weight at
the diagonals). Note that this is a simple method of calculating slope using
the ‘Queen’s case’for kkwindows larger than 3 3, and more intricate
methods might incorporate depth information from intermediate extents of
the focal window. RDMV and SD are calculable based on summary statis-
tics of the cells within a focal window, which can therefore be expanded to
any size using the TASSE toolbox. VRM is a measurement of the variability
of orthogonal vectors from the raster cells within a focal window –it can
also be scaled up to multiple window sizes within the BTM toolbox
(Walbridge et al. 2018).
Scale manipulation parameters
It is necessary to define parameters by which the multi-scale terrain attri-
bute methods (Table 1) can be characterized to facilitate comparison.
1. The ‘aggregation window size’,j, is the number of cells in the x and y
directions over which values are aggregated for a given method. Here,
aggregation refers to any generalization of terrain attribute values over a
MARINE GEODESY 9
broader scale, and can therefore include any averaging or resampling of
bathymetric or terrain attribute data.
2. The ‘focal window size’,k, is the number of cells in the x and y direc-
tions of the window used to calculate the terrain attribute value at the
focal cell.
3. The ‘cell length’,l
c
(i.e., the ‘cell size’), is the length of the cell in map
units, which, for the calculation of focal terrain attributes, is normally
set equal in x and y directions using an appropriate carto-
graphic projection.
4. The ‘cell neighborhood size’,m
c
, is the maximum number of cells in the
x and y directions over which the value of the terrain attribute at the
focal cell is affected. It can be determined by considering k, but also
depends on the number of additional cells in the x or y directions that
may have affected calculation at the focal cell due to other operations
(e.g., aggregation; Figure 2).
5. The ‘attribute calculation distance’,D
i
, is the width of the area, in map
units, over which elevation (or depth) information is incorporated at
the attribute calculation step –it is unique because it depends on the
order of operations in the calculation and aggregation of the attribute
(e.g., whether aggregation is performed before or after calculating the
terrain attribute).
6. The total ‘analysis distance’,D
t
, is the maximum x and y distance in
map units over which the value of the terrain attribute at the focal cell
is affected. D
t
is the product of the cell length and cell neighborhood
size, l
c
m
c
, which we note has previously been referred to as ‘scale
factor’(e.g., Lundblad et al. 2006).
These parameters are all descriptive of the different calculation meth-
ods, but the attribute calculation distance, D
i
, and analysis distance, D
t
,
are transferable parameters that facilitate the comparison of methods. D
i
describes over what distance the terrain attribute was originally calcu-
lated, or the scale of features that were quantified at the step where the
attribute was calculated. If elevation or depth information is aggregated
prior to calculating the attribute, or not at all, the attribute calculation
distance is equal to the analysis distance (D
i
¼D
t
). D
t
is the total dis-
tance over which the calculation of a raster terrain attribute is affected.
Each multi-scale method relies on manipulating the other parameters (j,
k,l
c
,m
c
)inordertochangeD
t
, which can, in turn, be used to organize
attributes into comparable classes (e.g., Table 2).Forexample,resam-
pling bathymetry then calculating the attribute adjusts D
t
by manipulat-
ing the bathymetric cell length l
c
over an area jj,andthisproducesa
greater rate of change for D
t
than by maintaining a constant cell length
10 B. MISIUK ET AL.
but changing the jjwindow using another method (e.g., averaging).
Conversely, calculating an attribute over kkwindow sizes requires a
larger value of kto achieve comparable units of analysis distance as the
methods that manipulate j–a source of potential confusion since both
the focal and aggregation window sizes are sometimes referenced to
describe the magnitude of terrain attribute rescaling, depending on the
method (Moudr
yetal.2019). These parameters are not necessarily inter-
changeable, as demonstrated in Table 2. The total ‘analysis distance’(D
t
)
Figure 2. Calculating raster terrain attributes at analysis distance D
t
¼45 m using four different
multi-scale methods: (A) ‘resample-calculate’, (B) ‘average-calculate’, (C) ‘calculate-average’, and
(D) ‘kk-window’. Parameters at the bottom of each pane describe the aggregation window
size (j), focal window size (k), cell length (l
c
), cell neighborhood size (m
c
), and attribute calcula-
tion distance (D
i
). Solid borders represent the focal cell; bold borders represent D
i
. Note that for
(B) and (C), the analysis distance (D
t
) of calculations at the focal cell is extended to 45 m by the
aggregation windows of each neighboring cell within the 33 focal window.
MARINE GEODESY 11
is therefore a useful metric to ensure comparability between different
methods and avoid ambiguity; it is used to reference the scale of terrain
attributesfortheremainderofthispaper.
Comparison and statistics
Terrain attributes were compared to determine the suitability of the four
multi-scale calculation methods for the three common applications and cri-
teria addressed here. All terrain attributes were mapped at each site, and
two-dimensional terrain profiles were used to visualize the change in attri-
bute values at features of interest. The characterization of scale-specific ter-
rain features was relevant at both sites, but the effects of calculation
method on data artefacts were explored primarily at the Bjørnøya slide.
Matching the positional accuracy of ground-truth sampling generally con-
cerns high resolution datasets; this was investigated at D’Argent Bay. Select
terrain attribute profiles are provided in the text, and all remaining profiles
are provided in the Appendices.
Table 2. Example of scale manipulation parameters over ten analysis distances (D
t
) based on
multi-scale calculation method, applied to a 5 m resolution input dataset. An example with a
250 m resolution input dataset is provided in the Appendix. Note how D
i
and D
t
vary relative
to the other parameters and each other.
Resample bathymetry, calculate attribute (‘resample-calculate’)
Agg. window size j(cells) 1 3 5 7 9 11 13 15 17 19
Focal window size k(cells) 3 3 3 3 3 3 3 3 3 3
Cell length l
c
(m) 5152535455565758595
Cell neighborhood size m
c
(cells) 3 3 3 3 3 3 3 3 3 3
Attr. calculation distance D
i
(m) 15 45 75 105 135 165 195 225 255 285
Analysis distance D
t
(m) 15 45 75 105 135 165 195 225 255 285
Average bathymetry, calculate attribute (‘average-calculate’)
Agg. window size j(cells) 1 3 5 7 9 11 13 15 17 19
Focal window size k(cells) 3 3 3 3 3 3 3 3 3 3
Cell length l
c
(m) 5555555555
Cell neighborhood size m
c
(cells) 3 5 7 9 11 13 15 17 19 21
Attr. calculation distance D
i
(m) 15 25 35 45 55 65 75 85 95 105
Analysis distance D
t
(m) 15 25 35 45 55 65 75 85 95 105
Calculate attribute, average attribute (‘calculate-average’)
Agg. window size j(cells) 1 3 5 7 9 11 13 15 17 19
Focal window size k(cells) 3 3 3 3 3 3 3 3 3 3
Cell length l
c
(m) 5555555555
Cell neighborhood size m
c
(cells) 3 5 7 9 11 13 15 17 19 21
Attr. calculation distance D
i
(m) 15 15 15 15 15 15 15 15 15 15
Analysis distance D
t
(m) 15 25 35 45 55 65 75 85 95 105
Calculate attribute over kkwindow (‘kk-window’)
Agg. window size j(cells) 1 1 1 1 1 1 1 1 1 1
Focal window size k(cells) 3 5 7 9 11 13 15 17 19 21
Cell length l
c
(m) 5555555555
Cell neighborhood size m
c
(cells) 3 5 7 9 11 13 15 17 19 21
Attr. calculation distance D
i
(m) 15 25 35 45 55 65 75 85 95 105
Analysis distance D
t
(m) 15 25 35 45 55 65 75 85 95 105
12 B. MISIUK ET AL.
Characterizing scale-specific terrain features
Identifying the most appropriate scale(s) at which to capture geomorpho-
logical features and ecological patterns has long been a goal of geomorph-
ometry and habitat mapping, but has proven challenging in practice
(Dr
agut¸, Eisank, et al. 2009; Lechner et al. 2012; Dove et al. 2020). A suit-
able method for manipulating attribute scale to match the scale of terrain
features should allow for the representation of meaningful information
explicitly from a given scale, and ideally, avoid conflation with terrain fea-
tures at other scales.
The similarity and information content of terrain attribute values were
compared to the finest analysis distance at both study sites to determine
the suitability of the multi-scale methods for targeting specific scale-
dependent terrain features. Pearson’s coefficient of correlation describes the
linear relationship between variable pairs (i.e., similarity). It was computed
between each of the nine analysis distances and the finest one for each of
the five attributes to compare the redundancy of different attribute scales.
Shannon’s(1948) entropy has been described as ‘a measure of the amount
of information required on the average to describe the random variable’
(Cover and Thomas 2006). Entropy was calculated for each analysis dis-
tance of each attribute to compare the amounts of information retained
when using the four multi-scale approaches. The entropy HðXÞof a dis-
crete random variable Xis defined by:
HX
ðÞ
¼X
x
px
ðÞlogpx
ðÞ (1)
where px
ðÞis the probability of observing a given data value. Given a suffi-
cient number of observations, a continuous random variable can be quan-
tized into bins to estimate the probability density function (Optican and
Richmond 1987), which can be used to calculate the entropy (Hall and
Morton 1993; Cover and Thomas 2006). Here, sample values (n0.4
and 1.4 million, respectively) of all scales of a given attribute for a given
method were quantized into 1,000 bins of equal width, spanning the full
range of data values to estimate the entropy. The number of bins was
selected to roughly accommodate sample sizes at both study sites by bal-
ancing the bias and variance of information that is retained from the ori-
ginal data based on recommendations in the literature ( ffiffiffi
n
p;Meyer 2008).
Additional bin configurations were also tested, and results were generally
invariant. Quantization and entropy calculations were performed using the
R package ‘infotheo’(Meyer 2014).
Entropy values were standardized to the finest scale separately for each
attribute to compare relative changes in information resulting from the dif-
ferent multi-scale calculation methods. A value of 1 represents the same
amount of information as the finest scale; values less than or greater than 1
MARINE GEODESY 13
represent less or more entropy than the finest scale, respectively. Given the
criteria for a multi-scale method that targets terrain attributes at specific,
dominant scales, it would be ideal to select a method that produces attributes
having low correlation with the finest scale(s) and also high information con-
tent (entropy). A low correlation with the finest scale(s) but also low entropy
suggests that the attribute is not redundant, but also that it contains less
information, whereby correlation may have been reduced at the cost of infor-
mation content. A high correlation and high entropy suggest that the attri-
bute is similar to the finest scale but still retains information content.
Reducing data errors and artefacts
DTM artefacts can significantly affect terrain attribute calculations (Lecours
et al. 2017b) and habitat maps that are produced using affected terrain attrib-
utes (Lecours et al. 2017a). DTMs and terrain attributes are thus commonly
filtered to reduce the influence of data error or artefacts on downstream map
products (e.g., Novaczek, Devillers, and Edinger 2019), yet the effects of these
operations on the scale of analysis are not necessarily explicit. Common
DTM errors include acquisition artefacts resulting from an improper com-
pensation of platform motion or sound velocity during acoustic surveys,
artefacts caused by the imperfect integration or fusion of data from different
sources (e.g., combining singlebeam echosounder data with lead line meas-
urements and radar altimetry data), and interpolation artefacts that may
introduce a gridding pattern in the data (Lecours et al. 2016b).
The effectiveness of each multi-scale calculation method was compared
for reducing the effects of data errors and compilation artefacts at the
Bjørnøya slide. Although it is difficult to measure the magnitude of data
artefact reduction statistically, prominent compilation artefacts are often
apparent from terrain attribute maps. Their locations can also be referenced
using the GEBCO type identifier (TID) grid to determine where different
datasets were integrated, and what methods were used for data collection –
though exact data origins can be difficult to determine (e.g., data labelled
as “pre-generated grid”). Terrain profiles at a distinct slide feature and a
data compilation boundary were used to explore the effects of the different
calculation methods on apparent errors and known compilation artefacts.
Values of terrain attributes at the profiles were plotted for the ten analysis
distances to observe the effects of the multi-scale methods on the influence
of data errors for terrain attribute calculations.
Matching the positional accuracy of ground-truth data
The disparity between positional accuracy of sonar data and ground-truth
samples can be problematic when using terrain attributes to characterize
14 B. MISIUK ET AL.
the benthic environment, and may introduce error that negatively impacts
downstream habitat maps (G
abor et al. 2020; Strong 2020). While the pos-
itional accuracy of sonar soundings is constrained primarily by the posi-
tioning, synchronization, and motion compensation systems of the
acquisition platform, positional uncertainty of ground-truth data can be
influenced by additional sources such as equipment drift from the vessel.
Methods and technologies exist to increase the positional accuracy of ben-
thic ground-truth data (e.g., line out calculation, ultra-short baseline), yet it
may not always be possible to match the accuracy of sonar-derived terrain
data given the acquisition platform, sampling equipment, and water depth
(Lecours and Devillers 2015). Ground-truth data from global databases like
the Ocean Biogeographic Information System (OBIS) can also have very
low positional accuracy (Moudr
y and Devillers 2020) compared to bathy-
metric data. As a result, error in ground-truth data positioning can cause
mischaracterization of the benthic environment, wherein ground-truth
observations are assigned incorrect terrain attribute values based on the
measured sample position, which differs from the actual position, which is
not known. The effect may become more severe when characterizing the
terrain at finer scales (G
abor et al. 2020).
One method for mitigating such mischaracterization is to coarsen, or
generalize, the terrain attributes to reflect the spatial uncertainty associated
with the ground-truth samples. Such operations will generally also affect
the scale of terrain attributes though, and this should be carefully consid-
ered in the context of the analysis. For example, in cases where it is desir-
able to quantify the terrain at fine scales, it is important to seek a method
for reducing spatial precision of terrain variables that maintains a fine scale
of analysis. Such cases may motivate an efficient reduction in spatial preci-
sion, which impacts the scale of analysis minimally.
Spatially uncertain benthic sampling was simulated at the D’Argent
Bay site to investigate the efficiency with which the spatial precision of
terrain attributes can be reduced to avoid ground-truth mischaracteriza-
tion. First, 1,000 sample points simulating the ‘actual’locations of
ground-truth samples were randomly generated within the area of multi-
beam coverage at D’Argent Bay. Each sample point was assigned a spatial
buffer of 20 m radius, within which a second point was randomly gener-
ated, representing the ‘measured’sample location, which differs from the
‘actual’by a horizontal error of up to 20 m. Values of all five terrain
attributes were extracted at both points across the ten analysis distances
(D
t
), as calculated using each of the four multi-scale methods. The differ-
ence between terrain attribute values for each sample pair (‘actual’–
‘measured’) was calculated to represent the potential error for each sam-
ple, given maximum hypothetical positional errors of 0–20 m. Errors
MARINE GEODESY 15
between the four multi-scale calculation methods were compared at each
analysis distance.
Case study results
Characterizing scale-specific terrain features
Features at a variety of spatial scales can be resolved from the D’Argent
Bay dataset. At the finest scale, topographic complexity can be captured
from only a few neighboring cells at 5 m resolution (Figure 3). A terrain
profile illustrates how these are superimposed on broader topographic fea-
tures that span tens to hundreds of meters (Figure 3A). At the broadest
scales, features can be observed that span hundreds or thousands of meters
–almost the length of the entire study site.
The four terrain attribute calculation methods tested produced different
results for this dataset. The topographic position of the mounds, trenches,
and the features they contain can be characterized using RDMV. Using the
‘average-calculate’and ‘calculate-average’methods, fine-scale features are
smoothed out at analysis distances greater than 15 m (Figure 4). Of these
two methods, the former retains some information at moderate analysis
distances (e.g., D
t
¼45 to 75 m), suggesting general topographic highs and
lows, while the latter has smoothed out nearly all detail. RDMV calculated
using the variable ‘kk-window’method enables identification of the two
50–75 m high points on the mound identified in Figure 3B, which, import-
antly, are separated by a topographically negative feature. Similarly, the
‘resample-calculate’method enables the identification of features at distinct
scales, albeit at a decreased horizontal resolution (i.e., greater cell length).
From this terrain profile, it appears that both ‘resample-calculate’and
‘kk-window’methods are effective at identifying topographic position at
distinct scales using RDMV. However, we note that none of the layers in
Figure 4 are at broad enough scales to identify the entire mound as a topo-
graphic high. The analysis distance, D
t
, enables comparison of the max-
imum horizontal extent of the RDMV layer (D
t
¼105 m) with that of the
mound (width 200 m). A broader analysis distance would therefore be
required to describe this feature.
Though subtler than with RDMV, the slopes of features along the profile
in Figure 3 also exhibit different values when calculated at multiple scales
using the four methods (Figure 5). One important difference is that the
‘calculate-average’method fails to characterize flat sections of topographic
highs and lows –instead averaging the slope value across the entire feature.
This is apparent from the slope map, where flat areas are poorly defined at
16 B. MISIUK ET AL.
the 65 m analysis distance compared to the ‘kk-window’method
(Figure 6).
All methods produced attributes of decreasing correlation with the finest
scale, yet entropy values of the ‘resample-calculate’and ‘kk-window’
attributes exceeded those of the finest scale, on average (Figure 7). Entropy
values were generally invariant to increases in analysis distance with the
‘calculate-average’method. Although ‘average-calculate’attributes had the
lowest correlation scores of any method, entropy values decreased markedly
with increasing analysis distance, suggesting a loss of information. This
conforms with observations of terrain attributes along the profile (e.g.,
Figure 4), which show that the variability of attributes was often greatly
Figure 3. Hillshaded 5 m resolution bathymetry at D’Argent Bay. A terrain profile from West to
East (A) shows topographic features at several scales. Finer-scale features are superimposed on
broader ones (B).
MARINE GEODESY 17
reduced at broad scales. Similar findings were observed at the Bjørnøya
slide (Appendices), yet we note that correlation and entropy statistics at
both sites were variable between attributes. All correlation and entropy sta-
tistics for the individual attributes and methods are provided in the
Supplementary Material.
Figure 4. Relative difference to the mean value (RDMV) at the transect in Figure 3A across ten
analysis distances (D
t
) using four different multi-scale calculation methods at D’Argent Bay.
Values at the finest scale (red) describe correspondingly small topographic features; values at
moderate (green) and broad (purple) scales differ substantially between methods. Dashed lines
indicate the extent of the feature indicated in Figure 3B.
18 B. MISIUK ET AL.
Reducing data errors and artefacts
The Bjørnøya slide dataset contains features at a variety of scales, but also
artefacts resulting from multisource data compilation. These include linear
artefacts remaining from multibeam data processing and surface generation,
Figure 5. Slope at the transect in Figure 3 calculated across ten analysis distances (D
t
) using
four different multi-scale calculation methods at D’Argent Bay. Slope details and flat areas are
averaged out using the ‘calculate-average’method. Dashed lines indicate the extent of the fea-
ture indicated in Figure 3B.
MARINE GEODESY 19
boundary discrepancies between datasets of different sources, and combina-
tions of data of variable source resolutions –for example, multibeam data
overlaying broader interpolation (Figure 8). Focal filters may be used to
mitigate the influence of such artefacts, yet the incorporation of depth
information from surrounding raster cells affects the scale of subsequent
terrain attribute calculations. The ‘average-calculate’method, for example,
can be conceptualized as a focal filter followed by terrain attribute calcula-
tion, and it is informative to examine this operation in the context of the
other multi-scale calculation methods.
At the finest analysis distance (D
t
¼750 m), compilation artefacts are
apparent in the RDMV layer over much of the study area, or are
Figure 6. Hillshaded slope at D’Argent Bay. The magnified area shows features along the ter-
rain profile. At analysis distance D
t
¼15 m (A), an arrow indicates the feature discussed in the
text and annotated in Figure 3. The scale of the slope layers is increased to D
t
¼65 m using
(B) ‘calculate-average’and (C) ‘kk-window’methods. The color ramp is clipped to a maximum
of 20to facilitate comparison between maps.
20 B. MISIUK ET AL.
indistinguishable from bathymetric features (Figure 9B). Although the
‘resample-calculate’method effectively highlights extensive topographic fea-
tures at broader scales, compilation artefacts are obvious at many locations
(Figure 9C). Perhaps more nefarious than obvious artefacts, though, is the
confusion between artefacts and physical features, which can severely
impact downstream mapping applications (e.g., species/habitat distribution
models, benthoscape maps). The ‘kk-window’method also performed
well at characterizing broader topographic features, yet compilation arte-
facts have been propagated to broader scales (Figure 9F). The other two
methods –‘average-calculate’and ‘calculate-average’–contrast with the
former two. RDMV maps demonstrate a loss of detail at broader scales,
affecting both the terrain representation and compilation artefacts (Figure
9D, E). This is corroborated by terrain profiles and results from section
“Characterizing scale-specific terrain features”, which suggested a loss of
information resulting from these two approaches (Appendices).
Figure 7. Average correlation and entropy statistics of terrain attributes compared to the finest
scale using each multi-scale calculation method at D’Argent Bay. Error bars show the standard
deviations of all variables at each analysis distance.
MARINE GEODESY 21
The eastness at the finest analysis distance (D
t
¼750 m) also appears to
be substantially impacted by the various data compilation artefacts at the
slide location (Figure 9G). At coarser scales, these effects manifest differ-
ently depending on the multi-scale calculation method, but at all scales,
data compilation artefacts are easily confused with actual features. At
Figure 8. Hillshaded 250 m resolution GEBCO bathymetry (left) and data source identified via
type identifier (TID) grid (right) at the Bjørnøya slide. A terrain profile from North to South (A;
bottom) crosses what appears to be a dataset compilation boundary (at B) near the crown of
the slide. Note that the pre-generated grid sections contain multiple data sources and are not
necessarily of uniform quality/resolution. The pre-generated grid data south of B comprise full-
coverage multibeam bathymetry from which more consistent terrain attributes are expected.
22 B. MISIUK ET AL.
analysis distance D
t
¼3,750 m, ‘resample-calculate’,‘average-calculate’, and
‘kk-window’maps all look similar, unlike those of RDMV. The maps
produced using these methods also suggest that, in addition to smoothing
Figure 9. Effects of terrain attribute calculation methods on multisource data compilation (A)
artefacts at the Bjørnøya slide. Relative difference to the mean value (RDMV) and eastness at
analysis distance D
t
¼750 m (B, G) are increased to D
t
¼3,750 using ‘resample-calculate’(C,
H), ‘average-calculate’(D, I), ‘calculate-average’(E, J), and ‘kk-window’(F, K) methods. The
data compilation boundary identified in Figure 8 is indicated by the dashed red line in (A).
MARINE GEODESY 23
out data artefacts, the eastness of broader terrain features is now being
quantified. The ‘calculate-average’layer is the most distinct (Figure 9J);
fine-scale variability and acquisition line artefacts are still apparent north of
the slide and broader features are not quantified. The finer-scale features
and artefacts have been averaged with surrounding data to suggest a less
easterly orientation than indicated by the other methods north of the slide.
For eastness, the attribute calculation distance (D
i
), which describes over
what distance the terrain attribute is initially quantified, appears to pro-
foundly affect how the terrain is represented at broader scales. ‘Calculate-
average’is the only method here in which D
i
is not equal to the total ana-
lysis distance, D
t
, and it is apparent that broad-scale terrain features are
less distinct compared to the other methods (Figure 9; Appendices). The
terrain profile at the top of the slide that crosses the boundary of two data-
sets –potentially of different source resolutions –shows that averaging the
values of the more variable northern section obscures the broader-scale
changes in aspect that are apparent from the other layers (Figure 10). In
essence, by calculating the attribute before aggregating it, the ‘calculate-
average’method takes a local consensus of what the value of the attribute
is at the finest scale. The profile suggests that the ‘resample-calculate’and
‘average-calculate’methods quantify broader-scale terrain features while
smoothing the variability in the northern section of the dataset, while the
‘kk-window’method quantifies broader-scale terrain features but does a
poor job at smoothing the data.
These observations generally hold for the other attributes that aim to
measure some aspect of terrain variability (i.e., SD, VRM). ‘Resample-calcu-
late’and ‘kk-window’methods retained a higher level of information
describing both terrain detail and compilation artefacts. The ‘average-calcu-
late’method consistently produced a decrease in detail (both of terrain and
artefacts) at broader scales. The terrain detail and artefacts of attributes
resulting from the ‘calculate-average’method were inconsistent depending
on the attribute, likely as a result of the variable effect that the artefacts
have on the different attribute calculations (since the calculation is per-
formed prior to the smoothing operation –i.e., averaging or aggregating).
All terrain attribute maps and profiles at both study sites are provided in
the Appendices.
Matching the positional accuracy of ground-truth data
The ‘calculate-average’method was consistently efficient at reducing errors
caused by sample location uncertainty. Figure 11 demonstrates that even
with a modest increase in analysis distance (e.g., from 15 to 45 m), the
mean error between ‘actual’and ‘measured’terrain attribute values can be
24 B. MISIUK ET AL.
reduced to levels comparable to those achieved at the coarsest scales using
‘kk-window’and ‘resample-calculate’methods. The ‘kk-window’
method performed comparatively poorly at reducing positionally induced
errors, with both higher and more variable errors than the other methods.
Results from the ‘resample-calculate’method are more nuanced; although
box plots show that this method effectively reduced much of the error
Figure 10. Eastness from North to South (left to right) at the profile in Figures 8 and 9calcu-
lated across ten analysis distances (D
t
) using four different multi-scale calculation methods at
the Bjørnøya slide. Vertical dashed lines show approximate locations of the slide crown (black)
and dataset compilation boundary (red).
MARINE GEODESY 25
caused by spatially inaccurate sampling as measured by the median, the
means of the absolute error suggest the influence of extreme outliers. This
discrepancy is suspected to be caused by an increasing proportion of sam-
ple pairs (‘actual’and ‘measured’) occurring in the same raster cell with
increasing cell size, which reduces the error between them to zero.
However, if sample pairs occur across cell borders, there is a large error
between the ‘measured’and ‘actual’terrain attribute values. The magnitude
of this discrepancy appears to increase with scale (Figure 11). In contrast,
the more gradational methods (i.e., ‘average-calculate’,‘calculate-average’)
are accommodating to locational error reduction across a range of scales,
with a more consistent relationship between the mean of the absolute error
and the remainder of the error distribution.
Discussion and recommendations
The analysis of seabed morphology is an important component to charac-
terizing benthic habitat, and there is a strong need to better resolve the
effects of terrain attribute rescaling operations that are commonly applied
in that context. Previous research has demonstrated the disparity between
results from different multi-scale calculation methods (Dolan and Lucieer
Figure 11. Scaled (0-1) absolute error between all terrain attribute values at ‘actual’and
‘measured’sample sites for multiple analysis distances at D’Argent Bay. Box plots show the
error distributions at analysis distances that can be achieved using all multi-scale calculation
methods (i.e., including ‘resample-calculate’), with means at all scales displayed as circles.
26 B. MISIUK ET AL.
2014), and the importance of spatial scale in benthic habitat mapping is
generally recognized (Lecours et al. 2015a). There has also been increased
interest in methods for testing and implementing terrain attributes at mul-
tiple scales for benthic habitat mapping (e.g., Rengstorf et al. 2012; Giusti,
Innocenti, and Canese 2014; Miyamoto et al. 2017; Misiuk, Lecours, and
Bell 2018; Porskamp et al. 2018). Given the increased uptake of these meth-
ods, and lack of existing guidelines, the goal of this paper was to investigate
the appropriateness of multi-scale calculation approaches for three common
habitat mapping applications.
The fitness-for-use or fitness-for-purpose of these approaches ultimately
depends on a combination of the terrain attribute, data quality, and project goals
(Devillers et al. 2007; Dolan and Lucieer 2014;P
^
oc¸as et al. 2014), yet we note
qualities, based on these results, that may help to distinguish the relative suitabil-
ities of these approaches (Table 3). Generally, the ‘resample-calculate’and ‘kk-
window’methods performed similarly for the three applications. The ‘average-
calculate’and ‘calculate-average’methods also performed similarly to each other.
The ‘resample-calculate’and ‘kk-window’methods were both effective
at characterizing specific scale-dependent features at both sites in this
study. Correlation and entropy statistics demonstrated that these methods
effectively provided new information that was not represented at the native
analysis distance, and this was corroborated by observations of the attribute
maps and terrain profiles. An interesting characteristic linking ‘resample-
calculate’and ‘kk-window’methods is that once the cell length has been
adjusted for ‘resample-calculate’, the size of the focal window k, in map
Table 3. Comparison of relative suitability of multi-scale calculation methods for the three
purposes identified in this study.
Purpose Criteria Multi-scale method performance Comments
Resample-
calculate
Average-
calculate
Calculate-
average
kk-
window
Characterize
specific
features or
processes.
Maximize new
and unique
information
at the
target scale.
Good Poor Poor Good ‘kk’and
‘resample-calculate’
methods were
effective. Selection
depends on the
desired resolution.
Reduce data
compilation
artefacts.
Minimize influence of
artefacts on the
terrain attribute.
Mixed Mixed Mixed Poor ‘Average-calculate’
reduced the
magnitude
of artefacts, but
also reduced terrain
information.
Match
positional
accuracy of
ground-truth.
Minimize error
between
terrain attribute
values
at ‘measured’and
‘actual’sample
locations.
Poor Good Good Poor ‘Calculate-average’
provided the
greatest reduction
in sample
locational error.
MARINE GEODESY 27
units, is equal to that of the ‘kk-window’method at a given analysis dis-
tance (e.g., Figure 2). It is likely that using an attribute calculation distance
(D
i
) equal to the total analysis distance (D
t
) is important in this context,
which allows for the integration of depth information at the full analysis
extent. We recommend that either of these approaches be selected for the
purpose of characterizing scale-specific features –selection between the two
may be determined by the desired cell length.
Differences in the effectiveness at reducing data noise and artefacts
between these methods were less straightforward to interpret. The ‘kk-
window’method appeared to perform poorly at reducing data artefacts in
nearly all cases. Results between the other three methods were mixed –
largely depending on the variable in question. The ‘average-calculate’
method appeared to reduce the magnitude of errors consistently, but this
almost always corresponded to a loss of morphological detail. It is unclear
whether the artefact reduction, relative to the amount of detail loss, was
superior to the other methods. It is therefore difficult to recommend any of
these approaches generally for artefact reduction, though they may be
effective for specific variables and datasets. We suggest that generally, other
purpose-built methods such as median, low-pass, or Fourier filtering may
be preferable for consistent and general-purpose artefact reduction (e.g.,
Wilken et al. 2012).
The methods most useful for describing features at specific scales were
less effective at matching positionally-uncertain ground-truth samples
simulated in this study, and vice-versa. Implicit in the goal of describing
scale-specific features is that new information must be captured from dif-
ferent spatial extents. This goal is essentially counter to that of matching
the positional uncertainty of ground-truth, which is to generalize terrain
attribute values at a given measured location so that any seabed sample
proximal to that location will not be mischaracterized. The ‘calculate-aver-
age’method performed best for matching positionally uncertain ground-
truth, relying exclusively on localized information for the terrain attribute
calculation, which is subsequently generalized. Results suggested that, all
else being equal, this method was the most efficient at minimizing the error
between the measured terrain attribute values and the actual, given a spatial
discrepancy of up to 20 m.
The link between spatial precision and the terrain attribute scale should
be considered even when manipulating the scale of analysis is not the pri-
mary goal of the operation. It is possible, for example, to reduce spatial
precision by simply characterizing broader-scale features –thereby increas-
ing the likelihood that actual ground-truth locations occur on the same ter-
rain features as measured from the erroneous sample geolocation. However,
it may be preferable to quantify features at the native scale then generalize
28 B. MISIUK ET AL.
(i.e., ‘smooth’) values over a broader area if a finer scale of analysis is
desired. The difference between these approaches can be understood from
the attribute calculation distance (D
i
) and analysis distance (D
t
) parame-
ters. If precision is to be reduced by characterizing broader-scale features,
then an increase in analysis distance can be attained using any method in
which D
t
and D
i
are equal (e.g., ‘resample-calculate’,‘average-calculate’,
‘kk-window’), meaning that the terrain attribute calculation is per-
formed using elevation information from a broader area. Results here sug-
gest that the ‘average-calculate’method may be a suitable approach,
whereas variable ‘kk-windows’may be a poor choice (Figure 11). If
maintaining a fine attribute scale is desirable though, the calculation dis-
tance, D
i
, can be fixed, followed by manipulation of D
t
(e.g., the
‘calculate-average’method), wherein only local elevation information is
used at the calculation step.
This concept highlights the importance of the order of operations in
multi-step terrain attribute calculations, emphasizing the difference, for
example, between ‘calculate-average’and ‘average-calculate’methods. The
order in which the aggregation and calculation are performed dictates the
distance over which attributes are initially calculated (D
i
). The subsequent
generalization of the attribute values to a broader analysis distance does
not affect the distance at which they were initially derived, which has
implications for the application of the calculated attributes. For example,
slope calculated from 5 m cells using a 3 3 focal window, which is then
averaged over a 7 7 aggregation window, produces an analysis distance
D
t
¼45 m, but does not represent the slope of the full 45 m area (e.g.,
Figure 2). The slope of this area can be measured using any method
wherein depth information from the 45 m area is incorporated in the slope
calculation –in other words, where the calculation distance (D
i
) is equal to
the analysis distance (D
t
) of the attribute (‘average-calculate’,‘resample-cal-
culate, ‘kk-window’methods). This aligns with the apparent usefulness
of the ‘resample-calculate and ‘kk-window’methods for characterizing
scale-specific terrain features found in this study.
In addition to facilitating comparison of different multi-scale terrain
calculation methods, transferable parameters such as analysis distance
(D
t
) are useful for determining the appropriate attribute scale for describ-
ing specific terrain features. For example, structurally complex environ-
ments may support elevated levels of biodiversity by providing
attachmentsurfacesforepifaunaandshelterforotherorganisms(Ross
et al. 2007; Buhl-Mortensen et al. 2010;McArthuretal.2010). If the scale
of structural features such as rocky outcrop, boulder, or coral mounds is
known –for example, through direct observation or high-resolution sur-
veying (Diesing and Thorsnes 2018)–the analysis distance can be set
MARINE GEODESY 29
appropriately to match the feature scale. Although seabed mapping stud-
ies that employ multi-scale terrain characterization commonly state the
focal (kk) or aggregation (jj) window sizes used for the calculations,
this does a comparatively poor job of describing at what spatial scale fea-
tures are being quantified. The analysis distance (D
t
)describesthedis-
tance over which terrain attribute values are affected in map units, and
depends on an interplay between cell length (l
c
), aggregation window size
(j), and focal window size (k).
Only a few configurations of the scale parameters used to calculate ana-
lysis distance are presented here (Table 2), yet the complexity of tracking
these can be increased depending on the treatment of the bathymetric data
or the selection of alternative raster calculation approaches. For example,
depth data might initially be aggregated (using one of many focal filters or
resampling techniques) and then used to calculate attributes over variable
kk-windows, complicating the tracking of D
i
and D
t
. Additionally, all
terrain attribute calculations here are assumed to use square aggregation
and focal windows (jj;kk), while these can actually assume different
shapes (e.g., circle, donut), which may even be asymmetric (e.g., oval, rect-
angle), potentially affecting the determination of the parameters or causing
them to vary with direction. Using asymmetric cases, scale parameters may
be anisotropic, and can be calculated in multiple directions if necessary.
Common cases are considered here to focus on the implications of multi-
scale calculation methods. While these additional possibilities may frustrate
the tracking of multi-scale terrain attribute calculation parameters in some
instances, it may be highly advisable for applications such as matching
ground-truth uncertainty while maintaining a certain analysis distance. We
also note other alternatives to multi-scale terrain attribute calculation meth-
ods that differ fundamentally from those presented here, such as quadratic
surface estimation (Evans 1972; Wood 1996). The analysis distance is still
attainable in such cases –though it may vary with location (Shang
et al. 2021).
A diverse set of terrain attributes were calculated to investigate the three
scale manipulation purposes identified in this paper, yet it is important to
note that while these findings (Table 3) may be transferable to similar
applications, they also may vary given different goals and dataset character-
istics. For other applications, or even other terrain attributes, it is import-
ant to reassess the purpose of scale manipulation in that context. For
similar applications though, findings here may be highly relevant –even
for terrestrial analogs such as selecting appropriate predictor scale and bal-
ancing the scale of analysis with DTM error (e.g., Florinsky and Kuryakova
2000; Albani et al. 2004; Bradter et al. 2013), or handling sources of sample
location uncertainty (G
abor et al. 2019). Furthermore, the manipulation of
30 B. MISIUK ET AL.
scale is not limited to terrain characterization. Methods for characterizing
benthic substrates from acoustic backscatter features have also implemented
multi-scale approaches, (Blondel and G
omez Sichi 2009; Robert, Jones, and
Huvenne 2014; Janowski et al. 2018; Zelada Leon et al. 2020), and Malik
(2019) has demonstrated the importance of slope scale on acoustic back-
scatter estimation. Regardless of the application, the appropriateness of
multi-scale methods must be carefully assessed given the context and data
characteristics.
‘Integrated-multiscale’terrain attribute calculation methods (Method 5 in
Table 1) have not been discussed here in detail, yet they may offer several
advantages over fixed-scale approaches for benthic habitat mapping. By
incorporating terrain information from multiple spatial scales simultan-
eously, redundancies may be avoided that may otherwise hinder the use of
terrain attributes at multiple separate scales for statistical modelling and
classification (e.g., multicollinearity, multi-dimensionality, variable inter-
pretability). ‘Integrated-multiscale’methods may also help to maximize the
amount of relevant terrain information for predictive models, simultan-
eously avoiding subjective scale selection and potentially simplifying the
variable selection process. An outstanding difficulty on the generalized
application of such approaches for seabed mapping, though, is an expansive
methodological variation between specific attributes and software imple-
mentations. It is currently unclear whether any given approach can be
applied universally to different terrain attributes, and whether any such
generalizable approach is preferable to others for specific benthic habitat
mapping applications (e.g., benthoscape mapping, habitat distribution mod-
elling, unsupervised classification) or geomorphological characterisation.
These topics warrant future research.
Conclusions
Implicit in any comparison of terrain attribute scale is that the parameters
used to perform the attribute calculations are transferable across different
calculation methods. We stress the importance of using a generalized par-
ameter for such comparisons, and propose the analysis distance (D
t
)asa
straightforward, interpretable metric that relates directly to the scale of ana-
lysis in map units. We encourage the use of D
t
as a terrain attribute
descriptor to increase the transferability and interpretability of mapping
results that utilize multi-scale terrain analysis methods.
Having organized terrain attributes calculated using different multi-
scale methods according to analysis distance, results suggest important
differences between methods that help to define their suitability for three
common habitat mapping applications. The ‘kk-window’and
MARINE GEODESY 31
‘resample-calculate’methods were generally successful at targeting distinct
seabed terrain features at variable scales. In contrast, the ‘average-calcu-
late’method was most consistent at reducing data artefacts, but we note
that this comes at the cost of reducing the information content of the ter-
rain attribute. Simulations also suggested that the latter method was
effective at reducing ground-truth characterization error due to inaccurate
positioning, as was the ‘calculate-average’method, which produced the
greatestreductioninerror.Thecalculationof“analysis distance”for these
attributes allows for their direct comparison and facilitates understanding
of the effects of different methods on the scale of terrain feature
characterization.
Acknowledgements
Thank you to the Fisheries and Marine Institute’s School of Ocean Technology and Centre
for Applied Ocean Technology for access to the boat and technical personnel and to Kirk
Regular and Eugene Antle for D’Argent Bay data collection. Thank you to Alexandre
Schimel for comments and suggestions on the manuscript.
Disclosure statement
The authors declare no competing interests.
Funding
This work was partly supported by Fisheries and Oceans Canada’s Coastal Environmental
Baseline Program and by a Canada Research Chair program through a chair in Ocean
Mapping to KR. BM was partially supported by the Fisheries and Marine Institute’s School
of Ocean Technology, and by an International Postdoctoral Fellowship awarded through
the Ocean Frontier Institute/Canada First Research Excellence Fund. Funds allocated to VL
by the University of Florida Senior Vice President for Agriculture and Natural Resources
were used to support collaboration with BM at the University of Florida School of Forest,
Fisheries, and Geomatics Sciences.
ORCID
Benjamin Misiuk http://orcid.org/0000-0001-5822-4574
Data availability statement
The GEBCO_2019 bathymetry data supporting the findings in this study are available for
free from the GEBCO data portal: https://www.gebco.net/data_and_products/gridded_
bathymetry_data/gebco_2019/gebco_2019_info.html. Access to the D’Argent Bay multibeam
data will be considered upon request by the authors.
32 B. MISIUK ET AL.
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Appendices
Appendix 1: terrain attribute equations
Eastness
The aspect of the focal cell is defined by
a¼atan2 dz
dy,dz
dx
180
p(A1)
where dz
dyand dz
dxare rates of depth change in the y and x directions, respectively. These
were determined here using eight weighted neighbors at the outer extents of the focal win-
dow (Horn 1981). Aspect is then converted to compass direction using the rules
ac¼90a,a90
450a,a>90
(A2)
and eastness is given by the sine of the aspect in radians:
eastness ¼sin acp
180
:(A3)
RDMV
The relative difference to the mean value (RDMV) is a unitless measure of topographic
position of the focal cell within the focal window. It is defined by
RDMV ¼zzc
ðÞ
zmax zmin
(A4)
where zis the mean depth of cells in the focal window, zcis the depth of the focal cell,
and zmax and zmin are the maximum and minimum depth values within the focal window,
respectively. Positive RDMV values, therefore, indicate locally elevated cells and negative
values indicate local depressions.
Standard deviation
The bathymetric standard deviation is calculated by
SD ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pziz
ðÞ
2
k2
s(A5)
where ziare depth values of each cell within the focal window, zis the mean depth of cells
in the focal window, and kis the focal window size.
Slope
Slope in degrees is defined by
slope ¼180
parctan ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
dz
dx
2
þdz
dy
2
s
0
@1
A(A6)
where dz
dxand dz
dyare rates of depth change in the x and y directions, respectively. These
MARINE GEODESY 39
were determined using eight weighted neighbors at the outer extents of the focal window
(Horn 1981).
VRM
The vector ruggedness measure (VRM) calculation is described in detail by Sappington,
Longshore, and Thompson (2007). The entire land (or seabed) surface is first decomposed
into unit vectors orthogonal to each grid cell, using the slope and aspect:
xyi¼sin ai
ðÞ
, (A7)
xi¼xyisin bi
ðÞ
, (A8)
yi¼xyicos bi
ðÞ
, (A9)
and
zi¼cos ai
ðÞ (A10)
where aiand bare the slope and aspect at each grid cell. The VRM for a given focal win-
dow is then defined by
VRM ¼1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Pxi
ðÞ
2þPyi
2þPzi
ðÞ
2
qk2(A11)
where kis the size of the focal window.
40 B. MISIUK ET AL.
Appendix 2: Bjørnøya slide scale parameters
Table A1. Example of scale manipulation parameters over ten analysis distances (D
t
) based on
multi-scale calculation method, applied to a 250 m resolution input dataset.
Resample bathymetry, calculate attribute (‘resample-calculate’)
Agg. window size j(cells) 1 3 5 7 9 11 13 15 17 19
Focal window size k(cells) 3 3 3 3 3 3 3 3 3 3
Cell length l
c
(m) 250 750 1250 1750 2250 2750 3250 3750 4250 4750
Cell neighborhood size m
c
(cells) 3 3 3 3 3 3 3 3 3 3
Attr. calculation distance D
i
(m) 750 2250 3750 5250 6750 8250 9750 11250 12750 14250
Analysis distance D
t
(m) 750 2250 3750 5250 6750 8250 9750 11250 12750 14250
Average bathymetry, calculate attribute (‘average-calculate’)
Agg. window size j(cells) 1 3 5 7 9 11 13 15 17 19
Focal window size k(cells) 3 3 3 3 3 3 3 3 3 3
Cell length l
c
(m) 250 250 250 250 250 250 250 250 250 250
Cell neighborhood size m
c
(cells) 3 5 7 9 11 13 15 17 19 21
Attr. calculation distance D
i
(m) 750 1250 1750 2250 2750 3250 3750 4250 4750 5250
Analysis distance D
t
(m) 750 1250 1750 2250 2750 3250 3750 4250 4750 5250
Calculate attribute, average attribute (‘calculate-average’)
Agg. window size j(cells) 1 3 5 7 9 11 13 15 17 19
Focal window size k(cells) 3 3 3 3 3 3 3 3 3 3
Cell length l
c
(m) 250 250 250 250 250 250 250 250 250 250
Cell neighborhood size m
c
(cells) 3 5 7 9 11 13 15 17 19 21
Attr. calculation distance D
i
(m) 750 750 750 750 750 750 750 750 750 750
Analysis distance D
t
(m) 750 1250 1750 2250 2750 3250 3750 4250 4750 5250
Calculate attribute over kkwindow (‘kk-window’)
Agg. window size j(cells) 1 1 1 1 1 1 1 1 1 1
Focal window size k(cells) 3 5 7 9 11 13 15 17 19 21
Cell length l
c
(m) 250 250 250 250 250 250 250 250 250 250
Cell neighborhood size m
c
(cells) 3 5 7 9 11 13 15 17 19 21
Attr. calculation distance D
i
(m) 750 1250 1750 2250 2750 3250 3750 4250 4750 5250
Analysis distance D
t
(m) 750 1250 1750 2250 2750 3250 3750 4250 4750 5250
MARINE GEODESY 41
Appendix 3: Bjørnøya slide correlation and entropy statistics
Figure A1. Average correlation and entropy statistics of terrain attributes compared to the fin-
est scale using each multi-scale calculation method at the Bjørnøya slide. Standard deviations
are shown by the error bars.
42 B. MISIUK ET AL.
Appendix 4: D’Argent Bay terrain attribute maps
Figure A2. Eastness at D’Argent Bay at analysis distance D
t
¼15 m (A) is increased to D
t
¼
65 m using (B) ‘resample-calculate’, (C) ‘average-calculate’, (D) ‘calculate-average’, and (E) ‘kk-
window’methods.
MARINE GEODESY 43
Figure A3. Relative difference to the mean value (RDMV) at D’Argent Bay at analysis distance
D
t
¼15 m (A) is increased to D
t
¼65 m using (B) ‘resample-calculate’, (C) ‘average-calculate’,
(D) ‘calculate-average’, and (E) ‘kk-window’methods.
44 B. MISIUK ET AL.
Figure A4. Bathymetric standard deviation at D’Argent Bay at analysis distance D
t
¼15 m (A)
is increased to D
t
¼65 m using (B) ‘resample-calculate’, (C) ‘average-calculate’,(D)‘calculate-
average’, and (E) ‘kk-window’methods.
MARINE GEODESY 45
Figure A5. Slope at D’Argent Bay at analysis distance D
t
¼15 m (A) is increased to D
t
¼65 m
using (B) ‘resample-calculate’, (C) ‘average-calculate’,(D)‘calculate-average’, and (E) ‘kk-win-
dow’methods.
46 B. MISIUK ET AL.
Figure A6. Vector ruggedness measure (VRM) at D’Argent Bay at analysis distance D
t
¼15 m
(A) is increased to D
t
¼65 m using (B) ‘resample-calculate’, (C) ‘average-calculate’, (D)
‘calculate-average’, and (E) ‘kk-window’methods.
MARINE GEODESY 47
Appenidx 6: Bjørnøya slide terrain attribute maps
Figure A10. Eastness at the Bjørnøya slide at analysis distance D
t
¼750 m (A) is increased to
D
t
¼3,750 m using (B) ‘resample-calculate’, (C) ‘average-calculate’,(D)‘calculate-average’, and
(E) ‘kk-window’methods.
MARINE GEODESY 51
Figure A11. Relative difference to the mean value (RDMV) at the Bjørnøya slide at analysis dis-
tance D
t
¼750 m (A) is increased to D
t
¼3,750 m using (B) ‘resample-calculate’, (C) ‘average-
calculate’, (D) ‘calculate-average’, and (E) ‘kk-window’methods.
52 B. MISIUK ET AL.
Figure A12. Bathymetric standard deviation at the Bjørnøya slide at analysis distance D
t
¼
750 m (A) is increased to D
t
¼3,750 m using (B) ‘resample-calculate’, (C) ‘average-calculate’, (D)
‘calculate-average’, and (E) ‘kk-window’methods.
MARINE GEODESY 53
Figure A13. Slope at the Bjørnøya slide at analysis distance D
t
¼750 m (A) is increased to D
t
¼3,750 m using (B) ‘resample-calculate’, (C) ‘average-calculate’, (D) ‘calculate-average’, and (E)
‘kk-window’methods.
54 B. MISIUK ET AL.
Figure A14. Vector ruggedness measure (VRM) at the Bjørnøya slide at analysis distance D
t
¼
750 m (A) is increased to D
t
¼3,750 m using (B) ‘resample-calculate’, (C) ‘average-calculate’, (D)
‘calculate-average’, and (E) ‘kk-window’methods.
MARINE GEODESY 55
Appendix 7: Bjørnøya slide terrain attribute profiles
Figure A15. Relative difference to the mean value (RDMV) from North to South (left to right)
at the profile in Figure 8 calculated across 10 analysis distances (D
t
) using four different multi-
scale methods at the Bjørnøya slide. Vertical dashed lines show approximate locations of the
slide crown (black) and dataset compilation boundary (red).
56 B. MISIUK ET AL.
Figure A16. Bathymetric standard deviation from North to South (left to right) at the profile in
Figure 8 calculated across 10 analysis distances (D
t
) using four different multi-scale methods at
the Bjørnøya slide. Vertical dashed lines show approximate locations of the slide crown (black)
and dataset compilation boundary (red).
MARINE GEODESY 57
Figure A17. Slope from North to South (left to right) at the profile in Figure 8 calculated across
10 analysis distances (D
t
) using four different multi-scale methods at the Bjørnøya slide. Vertical
dashed lines show approximate locations of the slide crown (black) and dataset compilation
boundary (red).
58 B. MISIUK ET AL.
Figure A18. Vector ruggedness measure (VRM) from North to South (left to right) at the profile
in Figure 8 calculated across 10 analysis distances (D
t
) using four different multi-scale methods
at the Bjørnøya slide. Vertical dashed lines show approximate locations of the slide crown
(black) and dataset compilation boundary (red).
MARINE GEODESY 59
