Fractal dimensions of individual flocs and floc populations in streams

摘要

The fractal dimension of an individual floc is a measure of the complexity of its external shape. Fractal dimensions can also be used to characterize floc populations, in which case the fractal dimension indicates how the shape of the smaller flocs relates to that of the larger flocs. The objective of this study is to compare the fractal dimensions of floc populations with those of individual flocs, and to evaluate how well both indicate contributions of sediment sources and reflect the nature and extent of flocculation in streams.Suspended solids were collected prior to and during snowmelt at upstream and downstream sites in two southern Ontario streams with contrasting riparian zones. An image analysis system was used to determine area, longest axis and perimeter of flocs. The area–perimeter relationship was used to calculate the fractal dimension, , that characterizes the floc population. For each sample, the fractal dimension, , of the 28 to 30 largest individual flocs was determined from the perimeter–step-length relationship. Prior to snowmelt, the mean value of ranged from 1·19 (Cedar Creek, downstream) to 1·22 (Strawberry Creek, upstream and downstream). A comparison of the means using -tests indicates that most samples on this day had comparable mean values of . During snowmelt, there was no significant change in the mean value of at the Cedar Creek sites. In contrast, for Strawberry Creek the mean value of at both sites increased significantly, from 1·22 prior to snowmelt to 1·34 during snowmelt. This increase reflects the contribution of sediment-laden overland flow to the sediment load. At three of the sampling sites, the increase in fractal dimensions was accompanied by a decreases in effective particle size, which can be explained by an increase in bed shear stress. A comparison of fractal dimensions of individual flocs in a sample with the fractal dimensions of the floc populations indicates that both fractal dimensions provide similar information about the temporal changes in sediment source contributions, about the contrasting effectiveness of the riparian buffer zones in the two basins, and about the hydraulic conditions in the streams. Nevertheless, determining the individual fractal dimensions of a set of large flocs in a sample is very time consuming. Using fractal dimensions of floc populations is therefore the preferred method to characterize suspended matter. Copyright © 2000 John Wiley & Sons, Ltd.