Dirk H. De Boer

Hierarchies and spatial scale in process geomorphology: a review

Abstract The form and functioning of a geomorphic system is the end product of a set of interacting processes which operate at a large variety of spatial and temporal scales. An appreciation of the nested, hierarchical structure of geomorphic systems offers insight into the effect of scale in process geomorphology. A literature review led to the formulation of a series of propositions concerning the spatial scale problem in process geomorphology. These propositions are presented in a theoretical framework indicating their association. Central to the spatial scale problem in process geomorphology is that a geomorphic system must be viewed in its complex, hierarchicl context: every geomorphic system consists of an array of ever smaller, lower-level systems, and is at the same time part of a sequence of ever larger, higher-level system. In a geomorphic system there exists a similarity between the scales of process and form. Furthermore, within a geomorphic system there is a similarity between spatial and temporal scales so that the timespan to present system behaviour and morphology increases with system size. In a geomorphic system, differences occur in the sensitivity of morphology to changing process conditions. Depending on the time elapsed since a change in process conditions, morphology in a geomorphic system may be either polygenetic, when only partial adjustment of the morphology (i.e. only at smaller scales) has occurred, or characteristic of the process domain, when all aspects of morphology (i.e. at all scales) are adjusted to present process conditions. In the latter case, dominance of landscape evolution by high-frequency, low-magnitude process results in a smooth landscape having small-scale irregularities, whereas dominance by low-frequency, high-magnitude processes produces an irregular landscape having large-scale irregularities. When spatial scale is held constant, the model of evolution of a geomorphic system varies with the timescale of interest. Conversely, when temporal scale is held constant, the model of evolution varies with the spatial scale of interest. In both cases, the canon (fixed rules) and options of a geomorphic system vary with the scale, temporal or spatial, of interest. The linkages between spatial and temporal scale and between the scales of form and process of geomorphic systems lead to four additional points. First, whether or not an event is catastrophic depends on the hierarchical level of the geomorphic system. Second, because of increased travel time and a larger variety of possible pathways, differences between the temporal patterns and material properties of input and output increase with the hiirarchical level and scale of a geomorphic system. Third, frequent, small-scale processes may cause infrequent, large-scale events when viewed at the same hierarchical level. Fourth and last, differences between geomorphic systems at the same level are controlled by variables varying over distances equal to or smaller than the distance between the system, but equal to or larger than the spatial dimensions of the systems.

Changing Contributions of Suspended Sediment Sources in Small Basins Resulting from European Settlement on the Canadian Prairies

Lake sediments provide an integrated record of the sediment yields and sources in the contributing basin. In the research area on the prairies of western Canada, the earliest sediments deposited in the larger lakes predate European settlement, allowing direct evaluation of basin response to settlement. Lake sediment cores were collected from an unnamed lake in the Stony Creek drainage basin in the aspen parkland region of eastern Saskatchewan. Pre- and post-settlement sediments in a central core were separated on the basis of an increase in Populus pollen associated with the southward advance of the aspen parkland ecotone caused by fire suppression following settlement. A wet chemical extraction procedure was used to separate the operationally defined organic fraction, the acid-soluble authigenic fraction, and biogenic silica from the clastic, non-carbonate, allogenic fraction of the lake sediment. Changes in the mineralogy and geochemistry of the clastic, allogenic fraction indicate that settlement resulted in an increased contribution of topsoil to the sediment load of Stony Creek. Elemental ratios, however, show that topsoil did contribute to the allogenic lake sediment fraction prior to settlement. Post-settlement changes in deposition rates of the allogenic fraction resulted from changes in land use rather than from climatic variability. Allogenic deposition rates reached a maximum in the 1950s and 1960s owing to an increase in the area under field crops and the increased use of high-powered agricultural machinery. Allogenic deposition rates decreased in more recent years because of a more extensive application of soil conservation measures. Post-settlement changes in deposition rates of individual elements within the allogenic fraction indicate that various sediment sources respond differently to changes in land use. Over the most recent 100 years, since the onset of European settlement, the erosional response of the basin appears to be controlled by land use changes rather than by climatic variability.

Fractal dimensions of individual flocs and floc populations in streams

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, D, that characterizes the floc population. For each sample, the fractal dimension, Di , of the 28 to 30 largest individual flocs was determined from the perimeter–step-length relationship. Prior to snowmelt, the mean value of Di 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 Di . During snowmelt, there was no significant change in the mean value of Di at the Cedar Creek sites. In contrast, for Strawberry Creek the mean value of Di 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

Self-organization in fluvial landscapes: sediment dynamics as an emergent property

Erosion and deposition by flowing water generally follow simple rules relating the rates of erosion and deposition to slope angle and other variables. When these rules are applied at small scales, the resulting landscape has large-scale properties which are apparent in its morphological attributes, e.g., drainage network configuration, and in its functional attributes, e.g., sediment dynamics. These emergent properties are not part of the basic, small-scale rules but, instead, result from repeated application of these rules and the ensuing self-organization of the landscape. This paper discusses a cellular model of long-term evolution of a fluvial landscape. The model is started by applying rainfall to a square group of cells of random size and at a random location within a grid. Erosion takes place as the water moves from each cell to its lowest neighbor. Sediment is routed downslope according to a transport equation with the transport rate dependent on the elevation difference between two adjacent cells. The model allows both erosion and deposition of sediment, depending on the difference between sediment input and output of a cell. When all runoff has been routed across the edge of the grid, a new rainstorm with a random area is applied at a random location and the whole process is repeated. Starting with a block-faulted landscape, over time a drainage network evolves. Sediment yield records of the drainage basins display a complex behavior, even though there are no external factors that would explain the variations in sediment yield. The complexity of sediment dynamics in the model arises from self-organization within the modeled system itself. This study is a first step towards separating the impact of this aspect of complexity on the sediment yield and depositional record from the impact of external factors associated with global change.

An evaluation of fractal dimensions to quantify changes in the morphology of fluvial suspended sediment particles during baseflow conditions

The morphology of suspended sediment particles reflects the origin of the suspended load and any modifying processes that may have occurred during transport and storage in the aquatic system. The objective of this study was to evaluate the use of four fractal dimensions to quantify visually observed changes in the morphology of fluvial suspended sediment particles during baseflow conditions. Samples were collected during summer low flow in a small stream on the Canadian Prairies. Particle morphology data were obtained with a transmitted light microscope, a CCD camera and an image analysis system. The morphology of the particle population was characterized using four fractal dimensions (D, DK, D1 and D2). D was derived from the area–perimeter relationship and showed an increase from 1·26±0·02 on 30 June, to 1·34±0·02 on 4 July, to 1·42±0·01 on 7 July. Visually, the increase in D represented the formation of large particles with intricate shapes and increased perimeters. DK was determined from the area–rank relationship and varied from 1·86±0·01 on 30 June, to 1·90±0·00 on 4 July, to 1·74±0·00 on 7 July. The decrease in DK between 4 July and 7 July would indicate a greater concentration of the particle area over a small number of large particles. Although the decrease in DK is consistent with observed changes in the particle size distributions, DK should be used with the considerable caution because DK varied more than one standard error between replicates. D1 and D2 were determined from the length–perimeter and length–area relationships, respectively. D1 proved to be of little value for quantifying changes in particle morphology as it showed little change with time, despite considerable visual changes. D2 however, was useful, despite some variation between replicates. Over the sampling period, D2 for the composite data sets showed a steady decrease from 1·74±0·02 on 30 June, to 1·68±0·02 on 4 July, to 1·60±0·01 on 7 July. This change in D2 indicates that, through time, the larger particles became longer and thinner relative to the smaller ones. This study shows that temporal changes in D, DK and D2 were consistent with, and allow quantification of, observed changes in particle morphology. D1 did not reflect observed morphological changes, and is therefore of little value for this type of study. The changes in particle morphology coincided with an increase in primary production in the form of algae.

Evaluating the potential of SEM/EDS analysis for fingerprinting suspended sediment derived from two contrasting topsoils

Sediment source fingerprinting can provide information on the contribution of various sediment sources to the suspended load of a stream. This study was conducted to evaluate the potential of SEM/EDS analysis (scanning electron microscopy/energy dispersive spectrometry) to fingerprint two types of topsoil in a research basin: a black, chernozemic, farmland soil and a grey, podzolic, forest soil. Simulated suspended sediment samples were prepared from each of the two soils, and SEM/EDS analysis of these samples provided information about the size distribution, mineralogy, and morphology of the particles. The two simulated suspended sediment samples were similar in particle size distribution, mineralogy, and total chemistry, so that these characteristics did not provide a distinctive fingerprint for the two topsoils. An important difference between the two simulated suspended sediment samples was the morphology of the CLAY class particles, consisting of water-stable clay aggregates. CLAY class particles derived from the grey forest soil were irregular whereas those derived from the black farmland soil were rounded. This difference in particle morphology can be explained by the difference in land use, and may provide a distinct fingerprint for each topsoil.

Fractal dimensions of suspended solids in streams: comparison of sampling and analysis techniques

Fluvial suspended sediment typically consists of a variety of complex, composite particles referred to as flocs. Floc characteristics are determined by factors such as the source, size and geochemical properties of the primary particles, chemical and biological coagulation processes in the water column and shear stress and turbulence levels in the stream. Studies of floc morphology have used two contrasting methods of sampling and analysis. In the first method, particles settle on a microscope slide and are observed from below using an inverted microscope. The second method uses filtration at no or low vacuum and particles deposited on the filter are observed with a microscope. Floc morphology can be quantified using fractal dimensions. The aims of the present study were to examine the effect of the two sampling methods on the fractal dimensions of particle populations, and to evaluate for each method how well the fractal dimensions at the various sampling sites reflect basin conditions. Suspended solids were collected in triplicate on inverted microscope slides and on 0·45 μm Millipore HA filters in two southern Ontario streams with contrasting riparian zones during a minor runoff event resulting from the melt of a freshly fallen snowpack. An image analysis system was used to determine area, longest axis and perimeter of particles. The morphology of the particle population of each sample was characterized using four fractal dimensions (D, D1, D2 and DK). Systematic differences in fractal dimensions obtained with the two methods were observed. For the settling method, outlines of larger particles were frequently blurred because of the distance between the focal plane (the top of the inverted microscope slides) and the plane of the particle outline. In this method, the blurring of large particles can cause an increase in the projected area and length of the particle. The effect on the particle perimeter is unpredictable because it depends on the amount of detail lost through blurring and its effect on the apparent increase in particle size. Because of blurring, D and D1 tend to be systematically lower for the settling method, whereas the net effect on D2 is unpredictable. Particle size distributions derived from settling are typically coarser because small, low density particles may remain in the water column and all particles may not deposit on the slides. This loss of fines results in systematically lower DK values for the settling method compared with the filtration method. Fractal dimensions and particle size distributions obtained with the filtration method were sensitive to and clearly indicated differences between drainage basins and between sites within each basin. These differences were explained by basin characteristics and conditions. Fractal dimensions and particle size distributions obtained with the settling method were less sensitive to drainage basin characteristics and conditions, which limits their usefulness as process indicators. Copyright

Constraints on spatial transference of rainfall-runoff relationships in semiarid basins drained by ephemeral streams

Abstract Field data on drainage basin response have a characteristic scale which is determined by the size of the basin investigated. As a rule, information obtained at one particular scale can be extrapolated over a limited scale range only. This study identifies the nature of constraints on spatial scale transference in a series of semiarid badland drainage basins ranging in area from < 1 to 202 260 m2. Research focussed on the rainfall-runoff relationship during a single rainstorm so that the temporal scale was kept constant. Spatial scale transference between systems of differing scale was restricted by morphological and functional constraints. Morphological constraints are caused by morphological elements present in large scale systems but absent in small scale ones. Functional constraints arise solely from the characteristics of the matter and energy flows in the systems of interest. Limits imposed upon spatial scale transferences by morphological and functional constraints are fuzzy rather than sha...

A DEVICE FOR MEASURING GULLY HEADWALL MORPHOLOGY

This paper describes a low-cost device for measuring the three-dimensional morphology of a gully headwall. The device was designed to operate in a gully system with the following characteristics: overhanging banks caused by a thick, dense root mat; retreat of the underlying unconsolidated sediments through small slab failures, leading to a considerable variation in retreat rate at each point on the headwall; and changes in the orientation of the headwall owing to changes in sediment properties and the topographical and hydrological controls of gully growth. The device is used to measure a series of closely spaced vertical profiles of the headwall, and the collected data are combined to draw a contour map showing the distance from the plane of the instrument to the headwall. Comparing maps for sequential times enables retreat rates for the diffferent proportions of the headwall to be quantified.