Fractal dimensions of individual flocs and floc populations in streams

Abstract

Abstract:The fractal dimension of an individual¯oc is a measure of the complexity of its external shape. Fractal dimensions can also be used to characterize¯oc populations, in which case the fractal dimension indicates how the shape of the smaller¯ocs relates to that of the larger¯ocs. The objective of this study is to compare the fractal dimensions of¯oc populations with those of individual¯ocs, and to evaluate how well both indicate contributions of sediment sources and re¯ect the nature and extent of¯occulation 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¯ocs. The area±perimeter relationship was used to calculate the fractal dimension, D, that characterizes the¯oc population. For each sample, the fractal dimension, D i , of the 28 to 30 largest individual¯ocs was determined from the perimeter±step-length relationship. Prior to snowmelt, the mean value of D i ranged from 1 . 19 (Cedar Creek, downstream) to 1 . 22 (Strawberry Creek, upstream and downstream). A comparison of the means using t-tests indicates that most samples on this day had comparable mean values of D i . During snowmelt, there was no signi®cant change in the mean value of D i at the Cedar Creek sites. In contrast, for Strawberry Creek the mean value of D i at both sites increased signi®cantly, from 1 . 22 prior to snowmelt to 1 . 34 during snowmelt. This increase re¯ects the contribution of sediment-laden overland¯ow to the sediment load. At three of the sampling sites, the increase in fractal dimensions was accompanied by a decreases in eective particle size, which can be explained by an increase in bed shear stress. A comparison of fractal dimensions of individual¯ocs in a sample with the fractal dimensions of the¯oc populations indicates that both fractal dimensions provide similar information about the temporal changes in sediment source contributions, about the contrasting eectiveness of the riparian buer zones in the two basins, and about the hydraulic conditions in the streams. Nevertheless, determining the individual fractal dimensions of a set of large¯ocs in a sample is very time consuming. Using fractal dimensions of¯oc populations is therefore the preferred method to characterize suspended matter.

The effect of shear-dependent flocculation on the multimodality of effective particle size distributions in a gravel-bed river during high flows

“…In the present study, higher relative volumes of the macrofloc class and lower relative volumes of the flocculi and microfloc classes were measured downstream compared to the upstream sites. Similar observations showing higher occurrence of macroflocs in downstream reaches have been reported elsewhere (Gibbs et al 1989;de Boer et al 2000;Stone et al 2021).…”

Bacteria‐sediment associations in an alpine, freshwater environment and their effects on particle size, density and settling velocity

“…As bacterial concentrations increase, individual bacterium may join the margins of existing flocculated material to produce increasingly elaborate composite particles and therefore coincide with an overall decrease in effective density (i.e. an increase in fractal dimension; de De Boer et al ; Hodder ). While the concentration of bacteria may affect other aspects of the floc, such as shape, we expect that these parameters would have less of an impact on settling velocity than changes in effective density for particles within a given size class.…”

Investigation of Flocculation Characteristics in the Yangtze Estuary

“…It showed that N f generally increased as G increased, and the mean N f under freshwater and salinity of 7 PSU increased by nearly 37% and 28%, respectively, from around 1.89 and 1.88 at G =10s À1 to about 2.58 and 2.41 at G = 65 s À1 . A larger fractal dimension for a given size will lead to increased floc effective density and settling velocity because flocs become more stable and dense as the fractal dimension rises [27,44,[51][52][53]. This may shed light on why the median floc size peaked at moderate G but the median floc settling velocity increased with G (see Figures 8 and 9).…”