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

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

A Landscapeâ Based Classification of Fish Assemblages in Sampled and Unsampled Lakes

We related fish species patterns and landscapeâ scale environmental data from 216 Michigan lakes to identify repeatable types of fish assemblages, identify environmental factors related to assemblage types, and classify fish assemblages in unsampled lakes. Multivariate regression tree modeling of fish species abundances identified six assemblage types that were explained by degreeâ days during the iceâ free period, lake surface area, and mean lake surface temperature. Warmwater species dominated southern lakes, while coolwater and coldwater species had higher abundances in northern lakes. Coolwater species were present in large southern lakes, whereas warmwater species were excluded from northern lakes that had low mean surface temperatures or low degreeâ days. These results suggest that patterns of lake fish assemblages are shaped by differences in climate as well as lakeâ specific differences in surface temperature regimes and in vertical availability of coldwater and coolwater habitats. Because we related fish patterns to readily available landscapeâ level data, our approach can be used to characterize fish assemblages in all lakes across broad geographic extents.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142256/1/tafs0414.pd

Remotely sensed albedo allows the identification of two ecosystem states along aridity gradients in Africa

Empirical verification of multiple states in drylands is scarce, impeding the design of indicators to anticipate the onset of desertification. Remote sensing‐derived indicators of ecosystem states are gaining new ground due to the possibilities they bring to be applied inexpensively over large areas. Remotely sensed albedo has been often used to monitor drylands due to its close relationship with ecosystem status and climate. Here, we used a space‐for‐time‐substitution approach to evaluate whether albedo (averaged from 2000 to 2016) can identify multiple ecosystem states in African drylands spanning from the Saharan desert to tropical Africa. By using latent class analysis, we found that albedo showed two states (low and high; the cut‐off level was 0.22 at the shortwave band). Potential analysis revealed that albedo exhibited an abrupt and discontinuous increase with increased aridity (1 − [precipitation/potential evapotranspiration]). The two albedo states co‐occurred along aridity values ranging from 0.72 to 0.78, during which vegetation cover exhibited a rapid, continuous decrease from ~90% to ~50%. At aridity values of 0.75, the low albedo state started to exhibit less attraction than the high albedo state. Low albedo areas beyond this aridity value were considered as vulnerable regions where abrupt shifts in albedo may occur if aridity increases, as forecasted by current climate change models. Our findings indicate that remotely sensed albedo can identify two ecosystem states in African drylands. They support the suitability of albedo indices to inform us about discontinuous responses to aridity experienced by drylands, which can be linked to the onset of land degradation.This work was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant XDA19030500), the National Key Research and Development Program of China (Grant 2016YFC0503302), the European Research Council (BIODESERT project, ERC Grant Agreement 647038), the Joint PhD, Training Program of the University of Chinese Academy of Sciences, and the Research Foundation of Henan University of Technology (Grant 31401178)

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

A Multimetric Assessment of Stream Condition in the Northern Lakes and Forests Ecoregion Using Spatially Explicit Statistical Modeling and Regional Normalization

We sampled fish communities, water temperature, water chemistry, physical habitat, and catchment characteristics for 94 stream sites selected randomly throughout the Northern Lakes and Forests ecoregion and used those data to explicitly model reference conditions and assess ecological stream condition at each site via a regional normalization framework. The streams we sampled were first order through fourth order, and the catchments ranged from 0.9 to 458 km2. We developed multiple linear regression (MLR) models that predicted fish community metrics, water chemistry characteristics, and local physical habitat from catchment characteristics; we used these models to compare existing conditions with the conditions that would be expected based on the regression models. Our results indicated that the fish communities were relatively unimpaired because the catchment variables associated with human‐induced land use change were important in only 1 of the 10 fish metric models. Agricultural land use was a significant variable in the MLR equation for species of Lepomis (sunfish). Agricultural land use and urban land use were both significant variables in all of the MLR models predicting water chemistry variables; urban land use was a significant variable in the MLR model predicting the percent coverage of all instream cover types. Regional normalization indicated that none of the sites were impaired based on fish community attributes. However, our analysis based on water chemistry metrics indicated that 22– 35% of the sites were impaired and that, based on physical habitat, 6–14% of the sites were impaired. A comparison with other published studies of the ecoregion suggested that the regional normalization process correctly characterized stream condition.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/141590/1/tafs0697.pd

Search for non-relativistic Magnetic Monopoles with IceCube

The IceCube Neutrino Observatory is a large Cherenkov detector instrumenting $1\,\mathrm{km}^3$ of Antarctic ice. The detector can be used to search for signatures of particle physics beyond the Standard Model. Here, we describe the search for non-relativistic, magnetic monopoles as remnants of the GUT (Grand Unified Theory) era shortly after the Big Bang. These monopoles may catalyze the decay of nucleons via the Rubakov-Callan effect with a cross section suggested to be in the range of $10^{-27}\,\mathrm{cm^2}$ to $10^{-21}\,\mathrm{cm^2}$. In IceCube, the Cherenkov light from nucleon decays along the monopole trajectory would produce a characteristic hit pattern. This paper presents the results of an analysis of first data taken from May 2011 until May 2012 with a dedicated slow-particle trigger for DeepCore, a subdetector of IceCube. A second analysis provides better sensitivity for the brightest non-relativistic monopoles using data taken from May 2009 until May 2010. In both analyses no monopole signal was observed. For catalysis cross sections of $10^{-22}\,(10^{-24})\,\mathrm{cm^2}$ the flux of non-relativistic GUT monopoles is constrained up to a level of $\Phi_{90} \le 10^{-18}\,(10^{-17})\,\mathrm{cm^{-2}s^{-1}sr^{-1}}$ at a 90% confidence level, which is three orders of magnitude below the Parker bound. The limits assume a dominant decay of the proton into a positron and a neutral pion. These results improve the current best experimental limits by one to two orders of magnitude, for a wide range of assumed speeds and catalysis cross sections.Comment: 20 pages, 20 figure

Flavor Ratio of Astrophysical Neutrinos above 35 TeV in IceCube

A diffuse flux of astrophysical neutrinos above $100\,\mathrm{TeV}$ has been observed at the IceCube Neutrino Observatory. Here we extend this analysis to probe the astrophysical flux down to $35\,\mathrm{TeV}$ and analyze its flavor composition by classifying events as showers or tracks. Taking advantage of lower atmospheric backgrounds for shower-like events, we obtain a shower-biased sample containing 129 showers and 8 tracks collected in three years from 2010 to 2013. We demonstrate consistency with the $(f_e:f_{\mu}:f_\tau)_\oplus\approx(1:1:1)_\oplus$ flavor ratio at Earth commonly expected from the averaged oscillations of neutrinos produced by pion decay in distant astrophysical sources. Limits are placed on non-standard flavor compositions that cannot be produced by averaged neutrino oscillations but could arise in exotic physics scenarios. A maximally track-like composition of $(0:1:0)_\oplus$ is excluded at $3.3\sigma$, and a purely shower-like composition of $(1:0:0)_\oplus$ is excluded at $2.3\sigma$.Comment: 8 pages, 3 figures. Submitted to PR

Characterization of the Atmospheric Muon Flux in IceCube

Muons produced in atmospheric cosmic ray showers account for the by far dominant part of the event yield in large-volume underground particle detectors. The IceCube detector, with an instrumented volume of about a cubic kilometer, has the potential to conduct unique investigations on atmospheric muons by exploiting the large collection area and the possibility to track particles over a long distance. Through detailed reconstruction of energy deposition along the tracks, the characteristics of muon bundles can be quantified, and individual particles of exceptionally high energy identified. The data can then be used to constrain the cosmic ray primary flux and the contribution to atmospheric lepton fluxes from prompt decays of short-lived hadrons. In this paper, techniques for the extraction of physical measurements from atmospheric muon events are described and first results are presented. The multiplicity spectrum of TeV muons in cosmic ray air showers for primaries in the energy range from the knee to the ankle is derived and found to be consistent with recent results from surface detectors. The single muon energy spectrum is determined up to PeV energies and shows a clear indication for the emergence of a distinct spectral component from prompt decays of short-lived hadrons. The magnitude of the prompt flux, which should include a substantial contribution from light vector meson di-muon decays, is consistent with current theoretical predictions.Comment: 36 pages, 39 figure

Calibration and Characterization of the IceCube Photomultiplier Tube

Over 5,000 PMTs are being deployed at the South Pole to compose the IceCube neutrino observatory. Many are placed deep in the ice to detect Cherenkov light emitted by the products of high-energy neutrino interactions, and others are frozen into tanks on the surface to detect particles from atmospheric cosmic ray showers. IceCube is using the 10-inch diameter R7081-02 made by Hamamatsu Photonics. This paper describes the laboratory characterization and calibration of these PMTs before deployment. PMTs were illuminated with pulses ranging from single photons to saturation level. Parameterizations are given for the single photoelectron charge spectrum and the saturation behavior. Time resolution, late pulses and afterpulses are characterized. Because the PMTs are relatively large, the cathode sensitivity uniformity was measured. The absolute photon detection efficiency was calibrated using Rayleigh-scattered photons from a nitrogen laser. Measured characteristics are discussed in the context of their relevance to IceCube event reconstruction and simulation efforts.Comment: 40 pages, 12 figure