Skip to main content
SpringerLink
Log in

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

  • Research Article
  • Published:
Landscape Ecology Aims and scope Submit manuscript

Abstract

Introduction

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.

Methods

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).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Ahsan N (2010) Predictive habitat models from AUV-based multibeam and optical imagery. In: OCEANS 2010 MTS/IEEE Seattle, IEEE, Seattle

  • Ardron J (2005) Protecting British Columbia’s coral and sponges. Living oceans society report (v. 1.0), Sointula, BC

  • Ballantyne VA, Foreman MGG, Crawford WR, Jacques R (1996) Three-dimensional model simulations for the north coast of British Columbia. Cont Shelf Res 16:1655–1682

    Article  Google Scholar 

  • Barrie JV, Conway KW (1999) Late quaternary glaciation and postglacial stratigraphy of the Northern Pacific margin of Canada. Quart Res 51:113–123. doi:10.1006/qres.1998.2021

    Article  Google 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 203:181–194

  • Barsimantov JA (2010) Vicious and virtuous cycles and the role of external non-government actors in community forestry in Oaxaca and Michoacán, Mexico. Hum Ecol 38(1):49–63

    Article  Google Scholar 

  • Beatty SW (1984) Influence of microtopography and canopy species on spatial patterns of forest understory plants. Ecology 65:1406–1419. doi:10.2307/1939121

    Article  Google Scholar 

  • Beck MW (1998) Comparison of the measurement and effects of habitat structure on gastropods in rocky intertidal and mangrove habitats. Mar Ecol Prog Ser 169:165–178

    Article  Google Scholar 

  • Bornhold BD, Barrie JV (1991) Surficial sediments on the western Canadian continental shelf. Cont Shelf Res 11:685–699. doi:10.1016/0278-4343(91)90074-G

    Article  Google Scholar 

  • Bridge TCL, Done TJ, Beaman RJ, Friedman A, Williams SB, Pizarro O, Webster JM (2010) Topography, substratum and benthic macrofaunal relationships on a tropical mesophotic shelf margin, central Great Barrier Reef, Australia. Coral Reefs 30:143–153

    Article  Google Scholar 

  • Chave J (2013) The problem of pattern and scale in ecology: what have we learned in 20 years? Ecol Lett. doi:10.1111/ele.12048

    PubMed  Google Scholar 

  • Crawford RW, Greisman P (1987) Investigation of permanent eddies in Dixon Entrance, British Columbia. Cont Shelf Res 7:851–870

    Article  Google Scholar 

  • Cusson M, Bourget E (1997) Influence of topographic heterogeneity and spatial scales on the structure of the neighbouring intertidal endobenthic macrofaunal community. Mar Ecol Prog Ser 150:181–193

    Article  Google Scholar 

  • Dahl AL (1973) Surface area in ecological analysis: quantification of benthic coral-reef algae. Mar Biol 23:239–249

    Article  Google Scholar 

  • Du Preez C, Tunnicliffe V (2011) Shortspine thornyhead and rockfish (Scorpaenidae) distribution in response to substratum, biogenic structures and trawling. Mar Ecol Prog Ser 425:217–231

    Article  Google Scholar 

  • Du Preez C, Tunnicliffe V (2012) A new video survey method of microtopographic laser scanning (MiLS) to measure small-scale seafloor bottom roughness. Limnol Oceanogr Method 10:899–909

    Article  Google Scholar 

  • Dufour A, Gadallah F, Wagner HH, Guisan A, Buttler A (2006) Plant species richness and environmental heterogeneity in a mountain landscape: effects of variability and spatial configuration. Ecography 29:573–584

    Article  Google Scholar 

  • Dunn DC, Halpin PN (2009) Rugosity-based regional modeling of hard-bottom habitat. Mar Ecol Prog Ser 377:1–11

    Article  Google Scholar 

  • ESRI (2013) ArcGIS Desktop 10.2. Environmental Systems Resource Institute, Redlands, California

  • 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):1–14

    Google Scholar 

  • Galparsoro I, Borja Á, Bald J, Liria P, Chust G (2009) Predicting suitable habitat for the European lobster (Homarus gammarus), on the Basque continental shelf (Bay of Biscay), using Ecological-Niche Factor analysis. Ecol Model 220:556–567

    Article  Google Scholar 

  • Gratwicke B, Speight MR (2005) The relationship between fish species richness, abundance and habitat complexity in a range of shallow tropical marine habitats. J Fish Biol 66:650–667. doi:10.1111/j.1095-8649.2005.00629.x

    Article  Google Scholar 

  • Gray DH (1997) Canada’s unresolved maritime boundaries. Boundary Secur Bull 5(3):61–71

    Google Scholar 

  • Henry L-A, Navas JM, Hennige SJ, Wicks LC, Vad J, Roberts JM (2013) Cold-water coral reef habitats benefit recreationally valuable sharks. Biol Conserv 161:67–70

    Article  Google Scholar 

  • Hill J, Wilkinson C (2004) Methods for ecological monitoring of coral reefs. Australian Institute of Marine Science, Townsville

    Google Scholar 

  • Hobson RD (1972) Surface roughness in topography: quantitative approach. In: Chorley RJ (ed) Spatial analysis in gemorphology. Harper and Row, New York, pp 221–245

    Google Scholar 

  • Hoechstetter S, Walz U, Dang LH, Thinh NX (2008) Effects of topography and surface roughness in analyses of landscape structure: a proposal to modify the existing set of landscape metrics. Landscape Online 3:1–14. doi:10.3097/LO.200803

    Google Scholar 

  • Huston M (1979) A general hypothesis of species diversity. Am Nat 113(1):81–101

    Article  Google Scholar 

  • Ierodiaconou D, Laurenson L, Burq S, Reston M (2007) Marine benthic habitat mapping using multibeam data, georeferenced video and image classification techniques in Victoria, Australia. J Spat Sci 52(1):93–104

    Article  Google 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 142–152

    Google Scholar 

  • Levin SA (1974) Dispersion and population interactions. Am Nat 108:207–228

    Article  Google Scholar 

  • Levin SA (1992) The problem of pattern and scale in ecology. Ecology 73:1943–1967

    Article  Google Scholar 

  • Levin LA, Etter RJ, Rex MA, Gooday AJ, Smith CR, Pineda J, Stuart CT, Hessler RR, Pawson D (2001) Environmental influences on regional deep-sea species diversity. Annu Rev Ecol Syst 32:51–93

    Article  Google Scholar 

  • Lundblad ER, Wright DJ, Miller J, Larkin EM, Rinehart R, Naar DF, Donahue BT, Anderson SM, Battista T (2006) A benthic terrain classification scheme for American Samoa. Mar Geod 29:89–111

    Article  Google Scholar 

  • McArthur MA, Brooke BP, Przeslawski R, Ryan DA, Lucieer VL, Nichol S, McCallum AW, Mellin C, Cresswell ID, Radke LC (2010) On the use of abiotic surrogates to describe marine benthic biodiversity. Estuar Coast Shelf Sci 88:21–32

    Article  Google Scholar 

  • McCormick MI (1994) Comparison of field methods for measuring surface topography and their associations with a tropical reef fish assemblage. Mar Ecol Prog Ser 112:87–96

    Article  Google Scholar 

  • McGarigal K, Tagil S, Cushman SA (2009) Surface metrics: an alternative to patch metrics for the quantification of landscape structure. Landscape Ecol 24:433–450

    Article  Google 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, Sydney

  • Moser K, Ahn C, Noe G (2007) Characterization of microtopography and its influence on vegetation patterns in created wetlands. Wetlands 27:1081–1097

    Article  Google Scholar 

  • Neves BM, Du Preez C, Edinger E (2014) Mapping coral and sponge habitats on a shelf-depth environment using multibeam sonar and ROV video observations: Learmonth Bank, northern British Columbia, Canada. Deep-Sea Res Pt II 99:169–183

    Article  Google Scholar 

  • Nowell ARM, Jumars PA (1982) Flow environments of aquatic benthos. Annu Rev Ecol Syst 15:303–328

    Article  Google Scholar 

  • Risk MJ (1972) Fish diversity on a coral reef in the Virgin Islands. Atoll Res Bull 193:1–6

    Article  Google Scholar 

  • Risser PG, Karr JR, Forman RTT (1984) Landscape ecology: directions and approaches. Illinois Natural History Survey Special Publ. 2, Champaign

    Google Scholar 

  • Roberts CM, Ormond RF (1987) Habitat complexity and coral reef fish diversity and abundance on Red Sea fringing reefs. Mar Ecol Prog Ser 41:1–8

    Article  CAS  Google Scholar 

  • Sappington JM, Longshore KM, Thompson DB (2007) Quantifying landscape ruggedness for animal habitat analysis: a case study using Bighorn Sheep in the Mojave Desert. J Wildl Manag 71:1419–1426

    Article  Google Scholar 

  • Schlacher TA, Schlacher-Hoenlinger MA, Williams A, Althaus F, Hooper JNA, Kloser R (2007) Richness and distribution of sponge megabenthos in continental margin canyons off southeastern Australia. Mar Ecol Prog Ser 340:73–88

    Article  Google Scholar 

  • Shumway CA, Hofmann HA, Dobberfuhl AP (2007) Quantifying habitat complexity in aquatic ecosystems. Freshwater Biol 52(6):1065–1076. doi:10.1111/j.1365-2427.2007.01754.x

    Article  Google 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:25:1–31

  • SPIP™ The scanning probe image processor. Image metrology APS, Lyngby. http://www.imagemet.com/

  • Stahl WR (1962) Similarity and dimensional methods in biology. Science 137:205–212

    Article  CAS  PubMed  Google Scholar 

  • Stambaugh MC, Guyette RP (2008) Predicting spatio-temporal variability in fire return intervals using a topographic roughness index. For Ecol Manag 254(3):463–473

    Article  Google Scholar 

  • Swanson FJ, Kratz TK, Caine N, Woodmansee RG (1988) Landform effects on ecosystem patterns and processes. Bioscience 38:92–98

    Article  Google Scholar 

  • Walker BK, Jordan LKB, Spieler RE (2009) Relationship of reef fish assemblages and topographic complexity on southeastern Florida coral reef habitats. J Coast Res 53:39–48

    Article  Google Scholar 

  • Wedding LM, Friedlander AM, McGranaghan M, Yost RS, Monaco ME (2008) Using bathymetric lidar to define nearshore benthic habitat complexity: implications for management of reef fish assemblages in Hawaii. Remote Sens Environ 112(11):4159–4165

    Article  Google Scholar 

  • Wilson MFJ, O’Connell B, Brown C, Guinan HC, Grehan AJ (2007) Multiscale terrain analysis of multibeam bathymetry data for habitat mapping on the continental slope. Mar Geod 30:3–35

    Article  Google Scholar 

  • Woodby D, Carlile D, Hulbert L (2009) Predictive modeling of coral distribution in the Central Aleutian Islands, USA. Mar Ecol Prog Ser 397:227–240

    Article  Google Scholar 

  • Wright DJ, Heyman WD (2008) Introduction to the special issue: marine and coastal GIS for geomorphology, habitat mapping, and marine reserves. Mar Geod 31:223–230

    Article  Google Scholar 

  • 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

  • Wu J (2004) Effects of changing scale on landscape pattern analysis: scaling relations. Landscape Ecol 19:125–138

    Article  Google Scholar 

  • Wu J (2013) Key concepts and research topics in landscape ecology revisited: 30 years after the Allerton Park workshop. Landscape Ecol 28:1–11

    Article  CAS  Google Scholar 

Download references

Acknowledgments

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.

Author information

Authors and Affiliations

  1. Department of Biology, University of Victoria, PO Box 3080, Victoria, BC, V8W 3N5, Canada

    Cherisse Du Preez

Authors
  1. Cherisse Du Preez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cherisse Du Preez.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Appendix 1

ArcTool box (ArcGIS® geoprocessing model tools and example data in a zipped folder) (ZIP 463 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)

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)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Du Preez, C. A new arc–chord ratio (ACR) rugosity index for quantifying three-dimensional landscape structural complexity. Landscape Ecol 30, 181–192 (2015). https://doi.org/10.1007/s10980-014-0118-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10980-014-0118-8

Keywords

Search

Navigation