Eco-geomorphology and vegetation patterns in arid and semi-arid regions

International audienceThe interaction between vegetation and hydrologic processes is particularly tight in water-limited environments where a positive-feedback links water redistribution and vegetation. The vegetation of these systems is commonly patterned, that is, arranged in a two phase mosaic composed of patches with high biomass cover interspersed within a low-cover or bare soil component. These patterns are strongly linked to the redistribution of runoff and resources from source areas (bare patches) to sink areas (vegetation patches) and play an important role in controlling erosion. In this paper a new modeling framework that couples landform evolution and dynamic vegetation for water-limited ecosystems is presented. The model explicitly accounts for the dynamics of runon-runoff areas that controls the evolution of vegetation and erosion/deposition patterns in water limited ecosystems. The analysis presented here focuses on the interaction between vegetation patterns, flow dynamics and sediment redistribution for areas with mild slopes where sheet flow occurs and banded vegetation patterns emerge. Model results successfully reproduce the dynamics of both migrating and stationary banded vegetation patterns (commonly known as tiger bush). Modeling results show strong feedbacks effects between vegetation patterns, runoff redistribution and geomorphic changes. The success at generating not only the observed patterns of vegetation but also patterns of runoff and erosion redistribution, which gives rise to modeled microtopography similar to that observed in several field sites, suggests that the hydrologic and erosion mechanisms represented in the model are correctly capturing the essential processes driving these ecosystems

Eco-geomorphology of banded vegetation patterns in arid and semi-arid regions

This study utilizes Robert Putnam’s “Two Level Game Theory” to understand whether public opinion influenced President Obama\u27s first-term administration when confronted with foreign policy decisions. Some scholars argue that there is an overall lack in understanding of how public opinion affects American foreign policy because the public is disengaged and uneducated on foreign issues and that the role of media influences the public’s attitude towards a certain issue. Accordingly, it is hypothesized here that public opinion was not a factor in this process. To test this proposition, the study evaluates three cases: the “closing” of Guantanamo Bay, the United States’ intervention in Libya, and the continuation of the drone program. Throughout each case, multiple variables are examined including: public opinion of the citizens and the political elite, President Obama’s political communication, and international diplomatic actions. Findings indicate that public opinion did not play any major role in President Obama’s foreign policy decision-making process; therefore, President Obama’s policies did not meet Robert Putnam’s criteria of domestic influence in the two level game theory

An Analytical and Numerical Study of Optimal Channel Networks

We analyze the Optimal Channel Network model for river networks using both analytical and numerical approaches. This is a lattice model in which a functional describing the dissipated energy is introduced and minimized in order to find the optimal configurations. The fractal character of river networks is reflected in the power law behaviour of various quantities characterising the morphology of the basin. In the context of a finite size scaling Ansatz, the exponents describing the power law behaviour are calculated exactly and show mean field behaviour, except for two limiting values of a parameter characterizing the dissipated energy, for which the system belongs to different universality classes. Two modified versions of the model, incorporating quenched disorder are considered: the first simulates heterogeneities in the local properties of the soil, the second considers the effects of a non-uniform rainfall. In the region of mean field behaviour, the model is shown to be robust to both kinds of perturbations. In the two limiting cases the random rainfall is still irrelevant, whereas the heterogeneity in the soil properties leads to new universality classes. Results of a numerical analysis of the model are reported that confirm and complement the theoretical analysis of the global minimum. The statistics of the local minima are found to more strongly resemble observational data on real rivers.Comment: 27 pages, ps-file, 11 Postscript figure

Unified View of Scaling Laws for River Networks

Scaling laws that describe the structure of river networks are shown to follow from three simple assumptions. These assumptions are: (1) river networks are structurally self-similar, (2) single channels are self-affine, and (3) overland flow into channels occurs over a characteristic distance (drainage density is uniform). We obtain a complete set of scaling relations connecting the exponents of these scaling laws and find that only two of these exponents are independent. We further demonstrate that the two predominant descriptions of network structure (Tokunaga's law and Horton's laws) are equivalent in the case of landscapes with uniform drainage density. The results are tested with data from both real landscapes and a special class of random networks.Comment: 14 pages, 9 figures, 4 tables (converted to Revtex4, PRE ref added

Mathematical analysis of a model of river channel formation.

The study of overland flow of water over an erodible sediment leads to a coupled model describing the evolution of the topographic elevation and the depth of the overland water film. The spatially uniform solution of this model is unstable, and this instability corresponds to the formation of rills, which in reality then grow and coalesce to form large-scale river channels. In this paper we consider the deduction and mathematical analysis of a deterministic model describing river channel formation and the evolution of its depth. The model involves a degenerate nonlinear parabolic equation (satisfied on the interior of the support of the solution) with a super-linear source term and a prescribed constant mass. We propose here a global formulation of the problem (formulated in the whole space, beyond the support of the solution) which allows us to show the existence of a solution and leads to a suitable numerical scheme for its approximation. A particular novelty of the model is that the evolving channel self-determines its own width, without the need to pose any extra conditions at the channel margin

Cellular Models for River Networks

A cellular model introduced for the evolution of the fluvial landscape is revisited using extensive numerical and scaling analyses. The basic network shapes and their recurrence especially in the aggregation structure are then addressed. The roles of boundary and initial conditions are carefully analyzed as well as the key effect of quenched disorder embedded in random pinning of the landscape surface. It is found that the above features strongly affect the scaling behavior of key morphological quantities. In particular, we conclude that randomly pinned regions (whose structural disorder bears much physical meaning mimicking uneven landscape-forming rainfall events, geological diversity or heterogeneity in surficial properties like vegetation, soil cover or type) play a key role for the robust emergence of aggregation patterns bearing much resemblance to real river networks.Comment: 7 pages, revtex style, 14 figure

Basins of attraction on random topography

We investigate the consequences of fluid flowing on a continuous surface upon the geometric and statistical distribution of the flow. We find that the ability of a surface to collect water by its mere geometrical shape is proportional to the curvature of the contour line divided by the local slope. Consequently, rivers tend to lie in locations of high curvature and flat slopes. Gaussian surfaces are introduced as a model of random topography. For Gaussian surfaces the relation between convergence and slope is obtained analytically. The convergence of flow lines correlates positively with drainage area, so that lower slopes are associated with larger basins. As a consequence, we explain the observed relation between the local slope of a landscape and the area of the drainage basin geometrically. To some extent, the slope-area relation comes about not because of fluvial erosion of the landscape, but because of the way rivers choose their path. Our results are supported by numerically generated surfaces as well as by real landscapes

A qualitative and quantitative evaluation of experimental model catchment evolution

Due to the geological time scales required for observation of catchment evolution, surrogates or analogues of field data are necessary to understand long-term processes. To investigate long-term catchment behaviour, two experimental model catchments that developed without rigid boundaries under controlled conditions are examined and a qualitative and quantitative analysis of their evolution is presented. Qualitatively, the experimental catchments have the visual appearance of field scale data. Observation demonstrates that changes in catchment shape and network form are conservative. Quantitative analysis suggests that the catchments reach an equilibrium form while a reduction in the channel network occurs. While the catchments are laboratory scale models, the results provide insights into field scale behaviour

An experimental and computer simulation study of erosion on a mine tailings dam wall

Mine tailings dams pose a significant risk to the environment if not correctly designed, built and maintained. The effect of erosion on a back-filled and capped earthen dam wall was examined by construction of an analogue in an experimental model landscape simulator. The ability of a computer-based erosion model to simulate erosion processes on the experimental structure was examined. The experimental landscape simulator uses a rainfall simulator to create overland flow and erode an artificial soil. At the commencement of rainfall, erosion occurred rapidly with deep gullies developing on the dam wall batter. The gullies developed by downcutting, with consequent bank collapse and slumping, and followed flow lines towards their source. A physically based erosion model (SIBERIA) was used to simulate erosion on the experimental dam wall. Erosion and consequent development of the experimental structure were modelled by SIBERIA. The ability of SIBERIA to model incision and landscape development in the experimental setting was further examined by use of a simple one-dimensional experimental catchment. The laboratory experiment and computer simulations demonstrated that erosion on the tailings dam is driven by concentrated runoff and that runoff control is crucial to the long-term stability of such structures. The study demonstrates that computer-based erosion models can be used to predict how erosion occurs on the experimental landscapes examined, thus providing confidence in their use and application