Landscape Ecology

, Volume 30, Issue 1, pp 181–192 | Cite as

A new arc–chord ratio (ACR) rugosity index for quantifying three-dimensional landscape structural complexity

  • Cherisse Du Preez
Research Article



Rugosity is an index of surface roughness that is widely used as a measure of landscape structural complexity in studies investigating spatially explicit ecological patterns and processes. This paper identifies and demonstrates significant issues with how we presently measure rugosity and, by building on recent advances, proposes a novel rugosity index that overcomes these issues.


The new arc-chord ratio (ACR) rugosity index is defined as the contoured area of the surface divided by the area of the surface orthogonally projected onto a plane of best fit (POBF), where the POBF is a function (interpolation) of the boundary data only. The ACR method is described in general, so that it may be applied to a range of rugosity analyses, and its application is detailed for three common analyses: (a) measuring the rugosity of a two-dimensional profile, (b) generating a rugosity raster from an elevation raster (a three-dimensional analysis), and (c) measuring the rugosity of a three-dimensional surface.

Case studies and results

Two case studies are used to compare the ACR rugosity index with the rugosity index most commonly used (i.e. surface ratio rugosity), demonstrating the advantages of the ACR index.

Discussion and conclusions

The ACR method for quantifying rugosity is simple, accurate, extremely versatile, and consistent in its principles independent of data dimensionality (2-D or 3-D), scale and analysis software used. It overcomes significant issues presented by traditional rugosity indices (e.g. decouples rugosity from slope) and is a promising new landscape metric. To further increase ease of use I provide multiple ArcGIS® resources in the electronic supplementary materials (e.g. Online Appendix 1: a downloadable ArcToolbox containing two ACR rugosity geoprocessing model tools).


Rugosity Arc–chord ratio Slope Structural complexity Topographic heterogeneity Landscape ecology Roughness ArcGIS 



My thanks to V. Tunnicliffe (supervisor and mentor) for her invaluable support and advice and R. Canessa for introducing me to GIS; both provided valuable comments on the manuscript. I also thank my colleagues J. Rose, and E. Edinger for their helpful ideas. Learmonth Bank multibeam bathymetry was collected by the Canadian Hydrographic Service and personnel of the Canadian Coast Guard Ship (CCGS) Vector, and provided by J. Vaughn Barrie (Geological Survey of Canada). Research was sponsored by the Natural Sciences and Engineering Research Council (NSERC) through the Canadian Healthy Oceans Network, a university-government partnership dedicated to biodiversity science for the sustainability of Canada’s three oceans. Additional support was provided by a University of Victoria Fellowship and a NSERC postgraduate scholarship.

Supplementary material (463 kb)
Appendix 1 ArcTool box (ArcGIS® geoprocessing model tools and example data in a zipped folder) (ZIP 463 kb)
10980_2014_118_MOESM2_ESM.docx (300 kb)
Appendix 2 ArcGIS® systematic instructions: how to generate an arc-chord ratio (ACR) rugosity raster from an elevation raster (word document) (DOCX 300 kb)
10980_2014_118_MOESM3_ESM.docx (440 kb)
Appendix 3 ArcGIS® systematic instructions: how to measure the arc-chord ratio (ACR) rugosity index of a three-dimensional surface (word document) (DOCX 440 kb)


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of BiologyUniversity of VictoriaVictoriaCanada

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