Scaling analysis of coral reef systems: an approach to problems of scale

Dimensional analysis and scaling are related, semi-formal procedures for capturing the essential process(es) controlling the behaviour of a complex system, and for describing the functional relationships between them. The techniques involve the parameterization of natural processes, the identification of the temporal and spatial scales of variation of processes, and the evaluation of potential interactions between processes referenced to those scales using non-dimensional (scaled) parameters. Scaling approaches are increasingly being applied to a broad range of marine ecological problems, with the aims of assessing the relative importance of physical and biological parameters in controlling variation in process rates, and placing limits on the ability of one process to affect another. The value of the approach to coral reef research lies in the conceptualization of relationships between discipline-specific processes, and the evaluation of scale-dependent processes across the large range of spatial and temporal scales which pertain to coral reefs. Characteristic scales of physical, geological and biological processes exhibit different patterns of distribution along the temporal dimension. Scaling arguments based on examples from reef systems indicate that a large group of biological and biogeochemical processes are strongly influenced by hydrodynamic processe occuring at similar time scales within the range from about on hour to one year. We argue that scaling approaches to process-related problems are pre-requisite to interdisciplinary research on coral reefs.