Models of Fractal River Basins

Two distinct models for self-similar and self-affine river basins are numerically investigated. They yield fractal aggregation patterns following non-trivial power laws in experimentally relevant distributions. Previous numerical estimates on the critical exponents, when existing, are confirmed and superseded. A physical motivation for both models in the present framework is also discussed.Comment: 16 pages, latex, 9 figures included using uufiles command (for any problem: [email protected]), to be publishes in J. Stat. Phys. (1998

Balancing water resources conservation and food security in China

China’s economic growth is expected to continue into the next decades, accompanied by sustained urbanization and industrialization. The associated increase in demand for land, water resources, and rich foods will deepen the challenge of sustainably feeding the population and balancing agricultural and environmental policies. We combine a hydrologic model with an economic model to project China’s future food trade patterns and embedded water resources by 2030 and to analyze the effects of targeted irrigation reductions on this system, notably on national agricultural water consumption and food self-sufficiency. We simulate interprovincial and international food trade with a general equilibrium welfare model and a linear programming optimization, and we obtain province-level estimates of commodities’ virtual water content with a hydrologic model. We find that reducing irrigated land in regions highly dependent on scarce river flow and nonrenewable groundwater resources, such as Inner Mongolia and the greater Beijing area, can improve the efficiency of agriculture and trade regarding water resources. It can also avoid significant consumption of irrigation water across China (up to 14.8 km3/y, reduction by 14%), while incurring relatively small decreases in national food self-sufficiency (e.g., by 3% for wheat). Other researchers found that a national, rather than local, water policy would have similar effects on food production but would only reduce irrigation water consumption by 5%

Geomorphic controls on elevational gradients of species richness

Elevational gradients of biodiversity have been widely investigated, and yet a clear interpretation of the biotic and abiotic factors that determine how species richness varies with elevation is still elusive. In mountainous landscapes, habitats at different elevations are characterized by different areal extent and connectivity properties, key drivers of biodiversity, as predicted by metacommunity theory. However, most previous studies directly correlated species richness to elevational gradients of potential drivers, thus neglecting the interplay between such gradients and the environmental matrix. Here, we investigate the role of geomorphology in shaping patterns of species richness. We develop a spatially explicit zero-sum metacommunity model where species have an elevation-dependent fitness and otherwise neutral traits. Results show that ecological dynamics over complex terrains lead to the null expectation of a hump-shaped elevational gradient of species richness, a pattern widely observed empirically. Local species richness is found to be related to the landscape elevational connectivity, as quantified by a newly proposed metric that applies tools of complex network theory to measure the closeness of a site to others with similar habitat. Our theoretical results suggest clear geomorphic controls on elevational gradients of species richness and support the use of the landscape elevational connectivity as a null model for the analysis of the distribution of biodiversity

On Hack\u27s Law

Hack\u27s 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\u27s law and the internal structure of river basins is investigated experimentally through digital elevation models. It is found that Hack\u27s 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\u27s law. An explanation for Hack\u27s 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\u27s law

Metapopulation capacity of evolving fluvial landscapes

The form of fluvial landscapes is known to attain stationary network configurations that settle in dynamically accessible minima of total energy dissipation by landscape-forming discharges. Recent studies have highlighted the role of the dendritic structure of river networks in controlling population dynamics of the species they host and large-scale biodiversity patterns. Here, we systematically investigate the relation between energy dissipation, the physical driver for the evolution of river networks, and the ecological dynamics of their embedded biota. To that end, we use the concept of metapopulation capacity, a measure to link landscape structures with the population dynamics they host. Technically, metapopulation capacity is the leading eigenvalue (M) of an appropriate landscape matrix subsuming whether a given species is predicted to persist in the long run. (M) can conveniently be used to rank different landscapes in terms of their capacity to support viable metapopulations. We study how (M) changes in response to the evolving network configurations of spanning trees. Such sequence of configurations is theoretically known to relate network selection to general landscape evolution equations through imperfect searches for dynamically accessible states frustrated by the vagaries of Nature. Results show that the process shaping the metric and the topological properties of river networks, prescribed by physical constraints, leads to a progressive increase in the corresponding metapopulation capacity and therefore on the landscape capacity to support metapopulationswith implications on biodiversity in fluvial ecosystems

Scaling properties of tidal networks

A new methodology is developed to extract tidal network from hydrodynamic conditions, and use data derived from numerical modeling or field observations to test the hypothesis that tidal networks are characterized by scale-invariant properties. Different tidal network configurations have been obtained from long-term numerical simulations in an idealized basin. These simulations show the influence of hydrodynamic conditions (tidal range, TR) and sediment (grain size sediment, D50) on the final configuration of the network. One of the signatures of scale-invariant behavior is related to the presence of a power law relationship in the probability distribution of geometrical characteristics. For each model configuration and field site, the probability distribution of drainage area and the drainage volume has been calculated, and in both cases tidal networks show scale-invariant characteristics. After assessing the sensitivity of the results, an energy expenditure analysis shows that tidal basins evolve toward a state with less morphodynamic activity, with a lower energy expenditure compare with the initial state

Generalized reproduction numbers and the prediction of patterns in waterborne disease

Understanding, predicting, and controlling outbreaks of waterborne diseases are crucial goals of public health policies, but pose challenging problems because infection patterns are influenced by spatial structure and temporal asynchrony. Although explicit spatial modeling is made possible by widespread data mapping of hydrology, transportation infrastructure, population distribution, and sanitation, the precise condition underwhich awaterborne disease epidemic can start in a spatially explicit setting is still lacking. Here we show that the requirement that all the local reproduction numbers R 0 be larger than unity is neither necessary nor sufficient for outbreaks to occur when local settlements are connected by networks of primary and secondary infection mechanisms. To determine onset conditions, we derive general analytical expressions for a reproduction matrix G0, explicitly accounting for spatial distributions of human settlements and pathogen transmission via hydrological and human mobility networks. At disease onset, a generalized reproduction number Λ0 (the dominant eigenvalue of G0) must be larger than unity.We also show that geographical outbreak patterns in complex environments are linked to the dominant eigenvector and to spectral properties of G0. Tests against data and computations for the 2010 Haiti and 2000 KwaZulu-Natal cholera outbreaks, as well as against computations for metapopulation networks, demonstrate that eigenvectors of G0 provide a synthetic and effective tool for predicting the disease course in space and time. Networked connectivity models, describing the interplay between hydrology, epidemiology, and social behavior sustaining human mobility, thus prove to be key tools for emergency management of waterborne infections