Water Resources Research Center, University of Minnesota
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It has long been recognized that catchment geomorphology relationships can be used as predictors of catchment flood characteristics. These geomorphologic relationships can be determined for river networks which have been automatically extracted from digital elevation data. If scaling properties exist in a catchment or river network then laws which hold at one scale (for example, basins with horizontal length scale of 1 kilometer) can be extrapolated with appropriate scaling to other scales (such as basins with horizontal length scales of tens of kilometers). This research has examined several basins for the purpose of (1) differentiating between the hillslope and channel scales from digital elevation data, and (2) identifying the presence of scaling in river networks and estimating the scaling laws. The ultimate goal of such research is to relate the findings about scaling in river networks to measures of hydrologic response of the river basin.
There is evidence that river networks are fractals which means that small basins, such as sub basins of a larger basin, have statistically similar structure with larger basins. Two methods were used to estimate the fractal dimensions of the terrain surface and the river networks: (1) the variation method, and (2) the box-counting method. Artificial river networks were generated from Iterated Function Systems (IFS) for verification of the box-counting results. Neither of the two methods for determining the fractal dimension of a surface were capable of predicting the breakpoint between the hillslope and channel scales, at least from the resolution at which the digital elevation data were available for this study.
The fractal dimension of the branching structure of a river network can be expressed as log RB /log RL (where RB and RL are Horton'8 bifurcation and length ratios) which is equivalent to the fractal dimension of the river network when individual streams have a fractal dimension of unity. In this research we investigated the reliability of estimating the fractal dimension of river networks based on Horton's ratios RB and RL as opposed to estimation from indirect methods such as the box-counting method. It was found that Horton's ratios can be difficult to estimate, and that they remain constant when the threshold area defining the network sources is varied and when the resolution of the digital elevation data is varied. For the two river networks studied (the fractal dimensions of individual streams in both networks were unity) the boxcounting method was shown to be in agreement with the fractal dimension of the branching structure estimated from Horton's ratios.
Future research should address the following two problems: (1) Determination of the hillslope scale from morphometric properties of the river network based on the assumption that threshold area does not remain constant over the basin but changes with local slope, and (2) Exploration of Diffusion Limited Aggregation (DLA) models for studying the evolution and structure of river networks and their hydrologic response.
Foufoula-Georgiou, Efi. Helmlinger, Keith R. 1992. Geomorphologic Study of River Basins and Hydrologic Response. Water Resources Research Center.
Water Resources Research Center
Foufoula-Georgiou, Efi; Helmlinger, Keith R..
Geomorphologic Study of River Basins and Hydrologic Response.
Water Resources Research Center, University of Minnesota.
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