The role of topography in promoting fractal patchiness in a carbonate shelf landscape

Sam Purkis, K. E. Kohler

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Satellite remote sensing has shown numerous aspects of coral reef seascapes to be fractal. That is, they display characteristics of scale-invariance and complexity. To date, an understanding of why reefscapes adopt this curious scaling has been lacking. This property was investigated using high-resolution terrain models built using bathymetric LiDAR soundings of the shallow Puerto Rico insular shelf. A computer-simulation model constructed using simple random processes was adequate to describe many of the intricacies of actual coral reef terrain. This model, based on fractional Brownian motion (fBm), produced surfaces that were visually and statistically indistinguishable from natural seabeds, at spatial scales of 0.001-25 km2. The conformity between model and nature allowed us to ascertain the importance of topography as a driver for the fractal patchiness that has been shown to occur in plan-view maps of reefscapes (e.g. Purkis et al. J Sediment Res 75:861-876, 2005, J Geol 115:493-508, 2007). For the considered Puerto Rican shelf, the necessary Brownian-like seabed topography likely arose through karst erosion overprinted by several episodes of reef development.

Original languageEnglish (US)
Pages (from-to)977-989
Number of pages13
JournalCoral Reefs
Volume27
Issue number4
DOIs
StatePublished - Dec 1 2008
Externally publishedYes

Fingerprint

patchiness
carbonates
topography
carbonate
coral reefs
coral reef
Puerto Rico
computer simulation
karsts
Brownian motion
remote sensing
reefs
simulation models
karst
sediments
reef
erosion
sediment

Keywords

  • Fractal
  • Fractional Brownian motion
  • LiDAR
  • Remote sensing
  • Topography

ASJC Scopus subject areas

  • Aquatic Science

Cite this

The role of topography in promoting fractal patchiness in a carbonate shelf landscape. / Purkis, Sam; Kohler, K. E.

In: Coral Reefs, Vol. 27, No. 4, 01.12.2008, p. 977-989.

Research output: Contribution to journalArticle

@article{543810a3192b4a54b72e0bdda0ee5c71,
title = "The role of topography in promoting fractal patchiness in a carbonate shelf landscape",
abstract = "Satellite remote sensing has shown numerous aspects of coral reef seascapes to be fractal. That is, they display characteristics of scale-invariance and complexity. To date, an understanding of why reefscapes adopt this curious scaling has been lacking. This property was investigated using high-resolution terrain models built using bathymetric LiDAR soundings of the shallow Puerto Rico insular shelf. A computer-simulation model constructed using simple random processes was adequate to describe many of the intricacies of actual coral reef terrain. This model, based on fractional Brownian motion (fBm), produced surfaces that were visually and statistically indistinguishable from natural seabeds, at spatial scales of 0.001-25 km2. The conformity between model and nature allowed us to ascertain the importance of topography as a driver for the fractal patchiness that has been shown to occur in plan-view maps of reefscapes (e.g. Purkis et al. J Sediment Res 75:861-876, 2005, J Geol 115:493-508, 2007). For the considered Puerto Rican shelf, the necessary Brownian-like seabed topography likely arose through karst erosion overprinted by several episodes of reef development.",
keywords = "Fractal, Fractional Brownian motion, LiDAR, Remote sensing, Topography",
author = "Sam Purkis and Kohler, {K. E.}",
year = "2008",
month = "12",
day = "1",
doi = "10.1007/s00338-008-0404-5",
language = "English (US)",
volume = "27",
pages = "977--989",
journal = "Coral Reefs",
issn = "0722-4028",
publisher = "Springer Verlag",
number = "4",

}

TY - JOUR

T1 - The role of topography in promoting fractal patchiness in a carbonate shelf landscape

AU - Purkis, Sam

AU - Kohler, K. E.

PY - 2008/12/1

Y1 - 2008/12/1

N2 - Satellite remote sensing has shown numerous aspects of coral reef seascapes to be fractal. That is, they display characteristics of scale-invariance and complexity. To date, an understanding of why reefscapes adopt this curious scaling has been lacking. This property was investigated using high-resolution terrain models built using bathymetric LiDAR soundings of the shallow Puerto Rico insular shelf. A computer-simulation model constructed using simple random processes was adequate to describe many of the intricacies of actual coral reef terrain. This model, based on fractional Brownian motion (fBm), produced surfaces that were visually and statistically indistinguishable from natural seabeds, at spatial scales of 0.001-25 km2. The conformity between model and nature allowed us to ascertain the importance of topography as a driver for the fractal patchiness that has been shown to occur in plan-view maps of reefscapes (e.g. Purkis et al. J Sediment Res 75:861-876, 2005, J Geol 115:493-508, 2007). For the considered Puerto Rican shelf, the necessary Brownian-like seabed topography likely arose through karst erosion overprinted by several episodes of reef development.

AB - Satellite remote sensing has shown numerous aspects of coral reef seascapes to be fractal. That is, they display characteristics of scale-invariance and complexity. To date, an understanding of why reefscapes adopt this curious scaling has been lacking. This property was investigated using high-resolution terrain models built using bathymetric LiDAR soundings of the shallow Puerto Rico insular shelf. A computer-simulation model constructed using simple random processes was adequate to describe many of the intricacies of actual coral reef terrain. This model, based on fractional Brownian motion (fBm), produced surfaces that were visually and statistically indistinguishable from natural seabeds, at spatial scales of 0.001-25 km2. The conformity between model and nature allowed us to ascertain the importance of topography as a driver for the fractal patchiness that has been shown to occur in plan-view maps of reefscapes (e.g. Purkis et al. J Sediment Res 75:861-876, 2005, J Geol 115:493-508, 2007). For the considered Puerto Rican shelf, the necessary Brownian-like seabed topography likely arose through karst erosion overprinted by several episodes of reef development.

KW - Fractal

KW - Fractional Brownian motion

KW - LiDAR

KW - Remote sensing

KW - Topography

UR - http://www.scopus.com/inward/record.url?scp=55349136548&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=55349136548&partnerID=8YFLogxK

U2 - 10.1007/s00338-008-0404-5

DO - 10.1007/s00338-008-0404-5

M3 - Article

AN - SCOPUS:55349136548

VL - 27

SP - 977

EP - 989

JO - Coral Reefs

JF - Coral Reefs

SN - 0722-4028

IS - 4

ER -