Geometry of River Networks I: Scaling, Fluctuations, and Deviations

This article is the first in a series of three papers investigating the detailed geometry of river networks. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, we report here a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the scaling of the length of sub-basin's dominant stream with its area, a characterization of basin shape known as Hack's law. We generalize this relationship to a joint probability density and show that fluctuations about scaling are substantial. We find strong deviations from scaling at small scales which can be explained by the existence of linear network structure. At intermediate scales, we find slow drifts in exponent values indicating that scaling is only approximately obeyed and that universality remains indeterminate. At large scales, we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape. The extent of approximate scaling is significantly restricted by these deviations and will not be improved by increases in network resolution.Comment: 16 pages, 13 figures, Revtex4, submitted to PR

The Lotic Intersite Nitrogen Experiments: an example of successful ecological research collaboration

Collaboration is an essential skill for modern ecologists because it brings together diverse expertise, viewpoints, and study systems. The Lotic Intersite Nitrogen eXperiments (LINX I and II), a 17-y research endeavor involving scores of early- to late-career stream ecologists, is an example of the benefits, challenges, and approaches of successful collaborative research in ecology. The scientific success of LINX reflected tangible attributes including clear scientific goals (hypothesis-driven research), coordinated research methods, a team of cooperative scientists, excellent leadership, extensive communication, and a philosophy of respect for input from all collaborators. Intangible aspects of the collaboration included camaraderie and strong team chemistry. LINX further benefited from being part of a discipline in which collaboration is a tradition, clear data-sharing and authorship guidelines, an approach that melded field experiments and modeling, and a shared collaborative goal in the form of a universal commitment to see the project and resulting data products through to completion

Geometry of River Networks II: Distributions of Component Size and Number

The structure of a river network may be seen as a discrete set of nested sub-networks built out of individual stream segments. These network components are assigned an integral stream order via a hierarchical and discrete ordering method. Exponential relationships, known as Horton's laws, between stream order and ensemble-averaged quantities pertaining to network components are observed. We extend these observations to incorporate fluctuations and all higher moments by developing functional relationships between distributions. The relationships determined are drawn from a combination of theoretical analysis, analysis of real river networks including the Mississippi, Amazon and Nile, and numerical simulations on a model of directed, random networks. Underlying distributions of stream segment lengths are identified as exponential. Combinations of these distributions form single-humped distributions with exponential tails, the sums of which are in turn shown to give power law distributions of stream lengths. Distributions of basin area and stream segment frequency are also addressed. The calculations identify a single length-scale as a measure of size fluctuations in network components. This article is the second in a series of three addressing the geometry of river networks.Comment: 16 pages, 13 figures, 4 tables, Revtex4, submitted to PR

Uncertainties, sensitivities and robustness of simulated water erosion in an EPIC-based global gridded crop model

Water erosion on arable land can reduce soil fertility and agricultural productivity. Despite the impact of water erosion on crops, it is typically neglected in global crop yield projections. Furthermore, previous efforts to quantify global water erosion have paid little attention to the effects of field management on the magnitude of water erosion. In this study, we analyse the robustness of simulated water erosion estimates in maize and wheat fields between the years 1980 and 2010 based on daily model outputs from a global gridded version of the Environmental Policy Integrated Climate (EPIC) crop model. By using the MUSS water erosion equation and country-specific and environmental indicators determining different intensities in tillage, residue handling and cover crops, we obtained the global median water erosion rates of 7 t ha-1 a-1 in maize fields and 5 t ha-1 a-1 in wheat fields. A comparison of our simulation results with field data demonstrates an overlap of simulated and measured water erosion values for the majority of global cropland. Slope inclination and daily precipitation are key factors in determining the agreement between simulated and measured erosion values and are the most critical input parameters controlling all water erosion equations included in EPIC. The many differences between field management methods worldwide, the varying water erosion estimates from different equations and the complex distribution of cropland in mountainous regions add uncertainty to the simulation results. To reduce the uncertainties in global water erosion estimates, it is necessary to gather more data on global farming techniques to reduce the uncertainty in global land-use maps and to collect more data on soil erosion rates representing the diversity of environmental conditions where crops are grown

Uncertainties, sensitivities and robustness of simulated water erosion in an EPIC-based global gridded crop model

Water erosion on arable land can reduce soil fertility and agricultural productivity. Despite the impact of water erosion on crops, it is typically neglected in global crop yield projections. Furthermore, previous efforts to quantify global water erosion have paid little attention to the effects of field management on the magnitude of water erosion. In this study, we analyse the robustness of simulated water erosion estimates in maize and wheat fields between the years 1980 and 2010 based on daily model outputs from a global gridded version of the Environmental Policy Integrated Climate (EPIC) crop model. By using the MUSS water erosion equation and country-specific and environmental indicators determining different intensities in tillage, residue handling and cover crops, we obtained the global median water erosion rates of 7 t ha−1 a−1 in maize fields and 5 t ha−1 a−1 in wheat fields. A comparison of our simulation results with field data demonstrates an overlap of simulated and measured water erosion values for the majority of global cropland. Slope inclination and daily precipitation are key factors in determining the agreement between simulated and measured erosion values and are the most critical input parameters controlling all water erosion equations included in EPIC. The many differences between field management methods worldwide, the varying water erosion estimates from different equations and the complex distribution of cropland in mountainous regions add uncertainty to the simulation results. To reduce the uncertainties in global water erosion estimates, it is necessary to gather more data on global farming techniques to reduce the uncertainty in global land-use maps and to collect more data on soil erosion rates representing the diversity of environmental conditions where crops are grown

Positivity of the English language

Over the last million years, human language has emerged and evolved as a fundamental instrument of social communication and semiotic representation. People use language in part to convey emotional information, leading to the central and contingent questions: (1) What is the emotional spectrum of natural language? and (2) Are natural languages neutrally, positively, or negatively biased? Here, we report that the human-perceived positivity of over 10,000 of the most frequently used English words exhibits a clear positive bias. More deeply, we characterize and quantify distributions of word positivity for four large and distinct corpora, demonstrating that their form is broadly invariant with respect to frequency of word use.Comment: Manuscript: 9 pages, 3 tables, 5 figures; Supplementary Information: 12 pages, 3 tables, 8 figure

Drivers of success in implementing sustainable tourism policies in urban areas

The existing literature in the field of sustainable tourism highlights a number of barriers that impede the implementation of policies in this area. Yet, not many studies have so far considered the factors that would contribute to putting this concept into practice, and few address the case of urban areas. The concept of sustainability has only received limited attention in urban tourism research, even though large cities are recognised as one of the most important tourist destinations that attract vast numbers of visitors. Adopting a case study approach, this paper discusses a number of drivers of success identified by policy-makers in London to contribute to the implementation of sustainable tourisms policies at the local level, and briefly looks at the relationship between these drivers and the constraints perceived by the respondents to hinder the implementation of such policies in practice. These findings may help policy-makers in other large cities to successfully develop and implement policies towards sustainable development of tourism in their area

Stochastic analysis of surface roughness

For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method was applied to different road surface profiles which were measured with high resolution. Evidence of Markov properties is shown. Estimations for the parameters of the Fokker-Planck equation are based on pure, parameter free data analysis

Comment: Cultural eutrophication of natural lakes in the United States is real and widespread

This is the published version