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

Using paleoclimate reconstructions to analyse hydrological epochs associated with Pacific decadal variability

The duration of dry or wet hydrological epochs (run lengths) associated with positive or negative Inter-decadal Pacific Oscillation (IPO) or Pacific Decadal Oscillation (PDO) phases, termed Pacific decadal variability (PDV), is an essential statistical property for understanding, assessing and managing hydroclimatic risk. Numerous IPO and PDO paleoclimate reconstructions provide a valuable opportunity to study the statistical signatures of PDV, including run lengths. However, disparities exist between these reconstructions, making it problematic to determine which reconstruction(s) to use to investigate pre-instrumental PDV and run length. Variability and persistence on centennial scales are also present in some millennium-long reconstructions, making consistent run length extraction difficult. Thus, a robust method to extract meaningful and consistent run lengths from multiple reconstructions is required. In this study, a dynamic threshold framework to account for centennial trends in PDV reconstructions is proposed. The dynamic threshold framework is shown to extract meaningful run length information from multiple reconstructions. Two hydrologically important aspects of the statistical signatures associated with the PDV are explored: (i) whether persistence (i.e. run lengths) during positive epochs is different to persistence during negative epochs and (ii) whether the reconstructed run lengths have been stationary during the past millennium. Results suggest that there is no significant difference between run lengths in positive and negative phases of PDV and that it is more likely than not that the PDV run length has been non-stationary in the past millennium. This raises concerns about whether variability seen in the instrumental record (the last ∼100 years), or even in the shorter 300–400-year paleoclimate reconstructions, is representative of the full range of variability.</p

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

Testing fluvial erosion models using the transient response of bedrock rivers to tectonic forcing in the Apennines, Italy

The transient response of bedrock rivers to a drop in base level can be used to discriminate between competing fluvial erosion models. However, some recent studies of bedrock erosion conclude that transient river long profiles can be approximately characterized by a transport‐limited erosion model, while other authors suggest that a detachment‐limited model best explains their field data. The difference is thought to be due to the relative volume of sediment being fluxed through the fluvial system. Using a pragmatic approach, we address this debate by testing the ability of end‐member fluvial erosion models to reproduce the well‐documented evolution of three catchments in the central Apennines (Italy) which have been perturbed to various extents by an independently constrained increase in relative uplift rate. The transport‐limited model is unable to account for the catchments’response to the increase in uplift rate, consistent with the observed low rates of sediment supply to the channels. Instead, a detachment‐limited model with a threshold corresponding to the field‐derived median grain size of the sediment plus a slope‐dependent channel width satisfactorily reproduces the overall convex long profiles along the studied rivers. Importantly, we find that the prefactor in the hydraulic scaling relationship is uplift dependent, leading to landscapes responding faster the higher the uplift rate, consistent with field observations. We conclude that a slope‐ dependent channel width and an entrainment/erosion threshold are necessary ingredients when modeling landscape evolution or mapping the distribution of fluvial erosion rates in areas where the rate of sediment supply to channels is low