16 research outputs found
Scaling Laws for River Networks
No full textSeemingly unrelated empirical hydrologic laws and several experimental facts related to the fractal geometry of the river basin are shown to find a natural explanation into a simple finite-size scaling ansatz for the power laws exhibited by cumulative distributions of river basins areas. Our theoretical prediction suggest that the exponent of the power law is directly related to a suitable fractal dimension of the bondaries, to the elongation of the basin, and to the scaling exponent of mainstream lengths. Observational evidence from digital elevation maps of natural basins and numerical simulations for optimal channel networks are found to be in good agreement with the theoretical predictions. Analytical results for Scheidegger's trees are exactly reproduced
On Hack’s law
No full textAbstract. Hack’s law is reviewed, emphasizing its implications for the elongation of river basins as well as its connections with their fractal characteristics. The relation between Hack’s law and the internal structure of river basins is investigated experimentally through digital elevation models. It is found that Hack’s exponent, elongation, and some relevant fractal characters are closely related. The self-affine character of basin boundaries is shown to be connected to the power law decay of the probability of total contributing areas at any link and to Hack’s law. An explanation for Hack’s law is derived from scaling arguments. From the results we suggest that a statistical framework referring to the scaling invariance of the entire basin structure should be used in the interpretation of Hack’s law
Randomly pinned landscape evolution
No full textA simple scheme for the evolution of a fluvial landscape in heterogeneous environments is critically examined to capture the essential mechanism responsible for the recurrent scale-free landforms in the river basin. It is shown that, regardless of boundary and initial conditions, geomorphological constraints in the form of quenched randomly pinned regions play a key role in the robust emergence of aggregation patterns with a scaling behavior in agreement with that of real river basins
On Landscape Self-Organization
No full textA new quantitative characterization of landscape-forming processes in the general framework of self-organized criticality and of fractal analyses is proposed. The coupled processes considered are threshold-independent hillslope evolutions and threshold-dependent fluvial transport phenomena. From a body of experimental and theoretical evidence we argue that geomorphological thresholds, principles of minimum energy expenditure and concepts of self-organized criticality are of crucial importance for the understanding of the basic general mechanisms which govern landscape evolution. This paper considerably extends both the theoretical framework and the empirical evidence for a recently developed theory which incorporates the above general principles. The modeling of landscape evolution by principles of self-organization is accomplished through the introduction of diffusion processes operating mainly on the hillslopes and the coupling of these processes with the fluvial evolution of the network previously studied through principles of self-organized criticality. The effects of spatial variability of surface erodibility are investigated under the general framework of random space functions with a correlation structure. Finally, a fractal analysis of the characteristics of the resulting landscape is performed and compared with recent results from real landforms to suggest the relationship of landscape fractal dimensions with the underlying landscape-forming processes.ECH
Planetary stewardship in an urbanizing world: beyond city limits
No full textCities are rapidly increasing in importance as a major factor shaping the Earth system, and as such must take corresponding responsibility. With currently over half of the world population, cities are supported by resources originating from primarily rural regions that are often located around the world far distant from the urban loci of use. The multiple and complex environmental and social challenges the world faces require interconnected solutions and a coordinated governance approach to planetary stewardship. There is a new opportunity to conceptualize a key component of planetary stewardship as a global system of cities that develop sustainable processes and policies in concert with its non-urban areas. The potential for cities to cooperate as a system and with rural connectivity could not only increase their capacity to effect change and foster stewardship at the planetary scale but also increase their resource security
Can One Gauge the Shape of a Basin
No full textThis paper investigates the effects of geometrical factors characterizing the shape of a river basin on the features of its hydrologic response. In particular, we wonder if by measuring the hydrologic response (i.e., gauging) the salient geomorphic features of the basin can be recovered. We argue that the basic structure of the channel network tends, in ideal conditions, to yield some universal characters of the width function W(x) defining the relative proportion of a contributing area at a distance x from the outlet. W(x) exhibits low-frequency features, which are geometry-dominated, and high-frequency features determined by recurrent aggregation patterns. It is suggested that given the shape of the basin one can indeed forecast in a rational manner the main characters of the hydrologic response which are imprinted in reproducible width functions. However, the inverse problem (i.e., the determination of the shape from the measure of the hydrologic response) is less solidly defined because of the possible loss of irretrievable information induced by the dynamics of runoff processes. Therefore the question posed in the title cannot be solved in general, although many elements for a general theory are seemingly established.ECH
Geomorphological Width Functions and the Random Cascade
No full textWe examine the geomorphological width functions of several river basins through the formalism of conservative (microcanonical) random cascades and we compare the results with those of more conventional fractal and multifractal analyses. We suggest that the spatial patterns of aggregation described by the width functions analyzed show common recurrent characters and that the implications of the robust identification of the singularity spectra via Legendre transforms are supported also by random cascade rationale.ECH
Are River Basins Optimal Channel Networks
No full textDrainage networks generated with a simulation model based on the scaling relationship between slopes and areas were found to have total energy expenditure values very near the minimum value of optimal channel networks. Using this model to grow networks inside the boundaries of real basins, it is shown that the drainage networks identified with the aid of digital elevation maps in such basins tend to organize themselves in configurations that minimize total energy expenditure. The role of perturbations in the search for configurations with lower energy and the existence of unstable equilibrium landscapes are also examined.ECH
Self-Organized Fractal River Networks
No full textOptimal channel networks (OCN's) obtained by minimizing the local and global rates of energy expenditure evolve automatically from arbitrary initial conditions to network configurations exhibiting fractal and multifractal statistics indistinguishable from those observed in nature. It is suggested that OCN's are spatial models of self-organized criticality and that natural fractal structures like river networks may arise as a joint consequence of optimality and randomness.ECH
Geomorphological Signatures of Varying Climate
No full textA LONGSTANDING question in geomorphology(1,2) is whether the topography of a particular landscape is in balance with current climate-driven processes, or contains relict signatures of past climates. For the glaciated landscapes of the Northern Hemisphere, the latter obviously applies but the situation is far from clear in regions where climate-driven processes have changed only in intensity, rather than character. We have addressed this question using a mathematical model of landscape evolution(3,4) and find that both cases-contemporary balance and relict features-are possible. For a sinusoidal climate fluctuation, we find that all climate states (wet and dry) leave geomorphological signatures only when there is no active uplift. With active uplift and the associated increase in erosion, the topography tracks the current climate and any relict features are likely to reflect only the wettest conditions previously experienced by the landscape. In both cases, the temporal evolution of the landscape in response to cyclic climate forcing is complex, and leads to the unexpected result that valley density is largest during periods dominated by slow downslope movement of sediment, rather than during times of strong fluvial incision, as would be anticipated from steady-state models(5-7).ECH
