A new arc–chord ratio (ACR) rugosity index for quantifying three-dimensional landscape structural complexity
- 1k Downloads
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).
KeywordsRugosity 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.
- Ahsan N (2010) Predictive habitat models from AUV-based multibeam and optical imagery. In: OCEANS 2010 MTS/IEEE Seattle, IEEE, SeattleGoogle Scholar
- Ardron J (2005) Protecting British Columbia’s coral and sponges. Living oceans society report (v. 1.0), Sointula, BCGoogle Scholar
- Barrie JV, Conway KW (2002) Contrasting glacial sedimentation processes and sea-level changes in two adjacent basins on the Pacific margin of Canada. In: Dowdeswell J, O’Cofaigh C (eds) Glacier-influenced sedimentation on high-latitude continental margins. Geological Society, London 203:181–194Google Scholar
- ESRI (2013) ArcGIS Desktop 10.2. Environmental Systems Resource Institute, Redlands, CaliforniaGoogle Scholar
- Friedman A, Pizarro O, Williams SB, Johnson-Roberson M (2012) Multi-scale measures of rugosity, slope and aspect from benthic stereo image reconstructions. PLoS One 7(12):1–14Google Scholar
- Gray DH (1997) Canada’s unresolved maritime boundaries. Boundary Secur Bull 5(3):61–71Google Scholar
- Hill J, Wilkinson C (2004) Methods for ecological monitoring of coral reefs. Australian Institute of Marine Science, TownsvilleGoogle Scholar
- Hobson RD (1972) Surface roughness in topography: quantitative approach. In: Chorley RJ (ed) Spatial analysis in gemorphology. Harper and Row, New York, pp 221–245Google Scholar
- Jenness J (2006) Topographic position index (TPI) v. 1.2 [Electronic manual]. Jenness Enterprises, Flagstaff. http://www.jennessent.com/downloads/TPI_Documentation_online.pdf
- Jenness J (2013) DEM surface tools for ArcGIS [Electronic manual]. Jenness Enterprises, Flagstaff. http://www.jennessent.com/downloads/DEM%20Surface%20Tools%20for%20ArcGIS_A4.pdf
- Larkin D, Vivian-Smith G, Zedler JB (2006) Topographic heterogeneity theory and ecological restoration. In: Donald A, Falk MP, Zedler J (eds) Foundations of restoration ecology. Island Press, Washington, pp 142–152Google Scholar
- McGarigal K, Cushman SA, Ene E (2012). FRAGSTATS v4: spatial pattern analysis program for categorical and continuous maps. Computer software program produced by the authors at the University of Massachusetts, Amherst. http://www.umass.edu/landeco/research/fragstats/fragstats.html
- Milner PR (2008) Final field report: CCGS Vector, North Coast and Queen Charlotte Island Surveys, July 25–September 8, 2008. Institute of Ocean Sciences, Department of Fisheries and Oceans, SydneyGoogle Scholar
- Risser PG, Karr JR, Forman RTT (1984) Landscape ecology: directions and approaches. Illinois Natural History Survey Special Publ. 2, ChampaignGoogle Scholar
- Sinclair AF, Conway KW, Crawford WR (2005) Associations between bathymetric, geologic and oceanographic features and the distribution of the British Columbia bottom trawl fishery. ICES CM 2005/L:25:1–31Google Scholar
- SPIP™ The scanning probe image processor. Image metrology APS, Lyngby. http://www.imagemet.com/
- Wright DJ, Pendleton M, Boulware J, Walbridge S, Gerlt B, Eslinger D, Sampson D, Huntley E (2012) ArcGIS Benthic Terrain Modeler (BTM), v. 3.0, Environmental Systems Research Institute, NOAA Coastal Services Center, Massachusetts Office of Coastal Zone Management. http://www.esriurl.com/5754