Describing scales of features in river channels using fractal geometry concepts

Quantitative description of spatial patterns is often at the heart of ecological research in aquatic systems, particularly for investigations of how biota respond to physical habitat. A common first step for approximating a river channel is tessellation, or the discretization of the channel into cells of approximately uniform size, and assigning each cell a representative value for velocity or other characteristics. More innovative methods may use the fractal dimension to characterize patterns of features in spatially complex geological structures, such as channel bed forms. Unfortunately, these methods lose information because they either force continuous data into a grid framework or assume that complexity is constant over a range of scales. The current understanding of aquatic processes would improve if information about the scale of channel features could be preserved throughout the analysis instead of being discarded in the first step because simplifying assumptions were used. New methods are presented that characterize complex spatial data sets with minimal use of assumptions or simplifying approximations. The new methods identify dominant features in a set of coordinate data, locate the positions of such features in the cross section, describe how kinetic energy is distributed in these features, and quantify how features of different scales relate to one another. The effectiveness of this technique on mathematical constructs having known characteristics is demonstrated. The methods are then used to describe a Missouri River cross section before and after river regulation to illustrate how the methods can be used to quantify changes in physical habitat patterns that may not be apparent using other methods. Improved description of complex shapes in aquatic environments may lead to increased understanding of aquatic processes in general, and in particular, the way aquatic organisms relate to physical habitat. Copyright © 2000 John Wiley & Sons, Ltd.