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

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.