Appendix 3. ArcGIS® systematic instructions: how to measure the arc-chord ratio (ACR)
rugosity index of a three-dimensional surface
Note: Step numbers correspond to workflow illustrated in Fig. 1.
1) Open ArcGIS® ArcMap™ (instructions written for version 10.2).
2) Activate the necessary extensions. To do this, navigate to: Customize/Extensions. Check
the boxes beside 3D Analyst, Geostatistical Analyst, and Spatial Analyst.
3) Import the elevation (or bathymetric) raster and the surface feature/s (defined spatial
subset/s to be analysed) using Add data. Note: if you intend on analysing the entire raster
(and not a subset) use the Raster Domain tool (ArcToolbox 3D Analyst Tools/
Conversion/From Raster/Raster Domain) to create a boundary (polygon) with the same
dimensions as the raster.
4) Multiple features within a single feature class can be analysed simultaneously.
5) Start by calculating the contoured area (numerator of rugosity equation). To convert the
raster into a triangular irregular network (TIN), navigate to: ArcToolbox/3D Analyst
Tools/Conversion/From Raster/Raster to TIN.
Fig 1. The derived surfaces and workflow (grey arrows) of arc-chord ratio (ACR) method for
calculating rugosity of a three-dimensional surface (elevation raster). The example is a 2 km
radius surface from the plateau at Learmonth Bank, British Columbia
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6) In the “Raster to TIN” dialog box, insert your references for the following parameters:
a. In Raster: insert the name of the elevation raster.
b. Output TIN: name and specify the location to store the resulting TIN.
c. Leave the other parameters blank or at the default settings (optional).
d. Click Okay. The new elevation TIN will appear in the Table of Contents.
7) To clip a TIN surface, navigate to: ArcToolbox/3D Analyst Tools/Data Management
Tools/TIN/Edit TIN.
8) In the “Edit TIN” dialog box, insert your references for the following parameters:
a. Input TIN: insert the name of the elevation TIN.
b. Input Feature Class: from the dropdown menu select the surface feature to be
clipped. The selected feature will appear in the table below.
c. In the table change: the “Height Field” to “<None>” and change the “SF Type” to
“Hard_Clip”.
d. Leave the other parameters blank or at the default settings.
e. Click Okay. This tool edits the original TIN so it will be listed under the same
name and in the same location in the Table of Contents.
9) To calculate the contoured area, navigate to: ArcToolbox/3D Analyst Tools/Triangulated
Surface/Polygon Volume.
10) In the “Polygon Volume” dialog box, inset your references for the following parameters:
a. Input Surface: insert the name of your (contoured) elevation TIN.
b. Input Feature Class: insert the name of your surface feature.
c. Height Field: from the dropdown menu select <None>.
d. Surface Area Field: insert the name of the new table field that will store the
contoured area value (suggestion: “contoured”).
e. Leave the other parameters blank or at the default settings.
f. Click Okay. The contoured area value will appear in the Attribute Table of the
surface feature.
11) To view the contoured area value: in the Table of Contents right click the original surface
feature file, select Open Attribute Table, and scroll to the end of the table.
12) To calculate the planar area, we first need to identify and then isolate the boundary data.
13) To define the boundary, navigate to: ArcToolbox/Analysis Tools/Proximity/Buffer.
14) In the “Buffer” dialog box, inset your references for the following parameters:
a. Input Feature: insert the name of your surface feature.
b. Output Feature Class: name and specify the location to store the resulting buffer
polygon.
c. Linear unit: enter the cell length (cell size available from raster metadata; units are
in meters by default).
d. Side Type (optional): change to OUTSIDE_ONLY.
e. Leave the other parameters at the default settings.
f. Click Okay. The boundary buffer polygon file will appear in the Table of
Contents.
15) To isolate the boundary data use the clip tool, navigate to: ArcToolbox/Data Management
Tools/Raster/Raster Processing/Clip.
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16) In the “Clip” dialog box, insert your references for the following parameters:
a. In Raster: insert the name of your elevation raster.
b. Output Extent: insert the name of the buffer (from step 14).
c. Check the box beside Use Input Features for Clipping Geometry.
d. Output Raster Dataset: name and specify the location to store the resulting
boundary raster.
e. Leave the other parameters blank or at the default settings.
f. Click Okay. The new boundary raster will appear in the Table of Contents.
17) To covert the raster to point data, navigate to: ArcToolbox/Conversion Tools/From
Raster/Raster to Point.
18) In the “Raster to Point” dialog box, insert your references for the following parameters:
a. Input raster: insert the name of the boundary raster (from step 16).
b. Leave the other parameters at the default settings.
c. Output point features: name and specify the location to store the resulting
boundary point features.
d. Click Okay. The new boundary point features will appear in the Table of
Contents.
19) To interpolate the plane of best fit (POBF), open the Geostatistical Wizard in
Geostatistical Analyst.
20) In the “Geostatistical Wizard” dialog box, insert your references for the following
parameters:
a. Methods: select Global Polynomial Interpolation
b. Input Data, Source Dataset: insert the name of the boundary point features (from
step 18).
c. Input Data, Data Field: change to “GRID_CODE”.
d. Click Next.
e. Leave the other parameters at the default settings. Check that Order of
polynomial: 1.
f. Click Finish.
g. Note the name and stored location of the resulting Global Polynomial
Interpolation POBF polygon.
h. Click OK. The new planar polygon file will appear in the Table of Contents.
21) In the Table of Contents, right click the Global Polynomial Interpolation POBF polygon
file, select Data, and then select Export to Raster.
22) In the “GA Layer to Grid” dialog box, insert your references for the following
parameters:
a. Input geostaticical layer: insert the name of the Global Polynomial Interpolation
file (POBF polygon).
b. Output Raster Dataset: name and specify the location to store the resulting POBF
raster.
c. Output cell size (optional): change to the cell size of the original raster.
d. Leave the other parameters at the default settings.
e. Click Okay. The new planar raster will appear in the Table of Contents.
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23) To convert the raster into a triangular irregular network (TIN), navigate to to Raster to
TIN again (see step 5).
24) In the “Raster to TIN” dialog box, insert your references for the following parameters:
a. In Raster: insert the name of the POBF raster (from step 22).
b. Output TIN: name and specify the location to store the resulting TIN.
c. Leave the other parameters blank or at the default settings (optional).
d. Click Okay. The new POBF TIN will appear in the Table of Contents.
25) Note the POBF polygon is an enveloping polygon, and therefore so is the POBF raster
and TIN. To clip the POBF TIN to the appropriate surface dimensions, navigate back to
Edit TIN (see step 7).
26) In the “Edit TIN” dialog box, insert your references for the following parameters:
a. Input TIN: insert the name of the POBF TIN.
b. Input Feature Class: from the dropdown menu select the surface feature to be
clipped. The selected feature will appear in the table below.
c. In the table change: the “Height Field” to “<None>” and change the “SF Type” to
“Hard_Clip”.
d. Leave the other parameters blank or at the default settings.
e. Click Okay. This tool edits the original POBF TIN so it will be listed under the
same name and in the same location in the Table of Contents.
27) To calculate the planar area, navigate to the Polygon Volume tool again (see step 9).
28) In the “Polygon Volume” dialog box, inset your references for the following parameters:
a. Input Surface: insert the name of your POBF TIN.
b. Input Feature Class: insert the name of your surface feature.
c. Height Field: from the dropdown menu select <None>.
d. Surface Area Field: insert the name of the new table field that will store the
minimal area value (suggestion: “planar”).
e. Leave the other parameters blank or at the default settings.
f. Click Okay. The planar area value will appear in the Attribute Table of the surface
feature.
29) To view the planar area value: in the Table of Contents right click the original surface
feature file, select Open Attribute Table, and scroll to the end of the table.
30) Before calculating the arc-chord ratio (ACR) rugosity index navigate to:
ArcToolbox/Data Management Tools/Fields/Add Field.
31) In the “Add Field” dialog box, write the equation and insert the references into the space
provided:
a. Input Table: insert the name of your surface feature.
b. Field Name: insert the name of the new table field that will store the ACR
rugosity value (suggestion: “rugosity”).
c. Field Type: from the dropdown menu select DOUBLE.
d. Leave the other parameters blank or at the default settings.
e. Click Okay. The new field will appear in the Attribute Table of the surface
feature.
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32) To calculate the ACR rugosity index, navigate to: ArcToolbox/Data Management
Tools/Fields/Calculate Field.
33) In the “Calculate Field” dialog box, write the rugosity equation and insert the references
into the space provided:
a. Input Table: insert the name of your surface feature.
b. Field Name: insert the name of your ACR rugosity field.
c. Expression: click on the calculator symbol.
d. In the “Field Calculator” dialog box, insert the references into the space provided
and solve for the ACR rugosity index using the rugosity equation (Equation 1 in
paper):
contoured area
rugosity = planar area
The text should be entered in the space provided as:
[contoured area value]/([planar area value]
or for example: [contour] / [planar]
e. Click Okay. The ACR rugosity index value will appear in the rugosity field in the
Attribute Table of the surface feature.
34) To view the ACR rugosity value: in the Table of Contents right click the original surface
feature file, select Open Attribute Table, and scroll to the end of the table.
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