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  1. Abstract

    The multilayer network framework has served to describe and uncover a number of novel and unforeseen physical behaviors and regimes in interacting complex systems. However, the majority of existing studies are built on undirected multilayer networks while most complex systems in nature exhibit directed interactions. Here, we propose a framework to analyze diffusive dynamics on multilayer networks consisting of at least one directed layer. We rigorously demonstrate that directionality in multilayer networks can fundamentally change the behavior of diffusive dynamics: from monotonic (in undirected systems) to non-monotonic diffusion with respect to the interlayer coupling strength. Moreover, for certain multilayer network configurations, the directionality can induce a unique superdiffusion regime for intermediate values of the interlayer coupling, wherein the diffusion is even faster than that corresponding to the theoretical limit for undirected systems, i.e. the diffusion in the integrated network obtained from the aggregation of each layer. We theoretically and numerically show that the existence of superdiffusion is fully determined by the directionality of each layer and the topological overlap between layers. We further provide a formulation of multilayer networks displaying superdiffusion. Our results highlight the significance of incorporating the interacting directionality in multilevel networked systems and provide a frameworkmore »to analyze dynamical processes on interconnected complex systems with directionality.

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  2. Abstract

    A long‐standing question in geomorphology concerns the extent that statistical models of terrain elevations have adequate characteristics with respect to the known scaling properties of landscapes. In previous work, it has been challenging to ascribe statistical significance to metrics adopted to measure landscape properties. Here, we use a recently developed surrogate data algorithm to generate synthetic surfaces with identical elevation values to the source data set, while also preserving the value of the Hölder exponent at any point (the underpinning characteristic of a multifractal surface). Our primary source data are from a laboratory experiment on landscape evolution. This allows us to examine how the statistical properties of the surfaces evolve through time and the extent to which they depart from the simple (multi)fractal formalisms. We show that there is a strong departure that is driven by the diffusive processes in operation. The number of sub‐basins of a given channel order (for orders sufficiently small relative to the basin order) exhibits a clear increase in complexity after a steady‐state for sediment flux is established. We also study elevation data from Florida and Washington States, where the relative departure from simple multifractality is even more strongly expressed but is similar formore »two very different locations. Our results show that at the very least, the minimum complexity for a stochastic model for terrain statistics with appropriate geomorphic scalings needs to incorporate a conditioning between the pointwise Hölder exponents and elevation.

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  3. Abstract

    To date, there is no consensus on the probability distribution of particle velocities during bedload transport, with some studies suggesting an exponential‐like distribution while others a Gaussian‐like distribution. Yet, the form of this distribution is key for the determination of sediment flux and the dispersion characteristics of tracers in rivers. Combining theoretical analysis of the Fokker‐Planck equation for particle motions, numerical simulations of the corresponding Langevin equation, and measurements of motion in high‐speed imagery from particle‐tracking experiments, we examine the statistics of bedload particle trajectories, revealing a two‐regime distance‐time (LTp) scaling for the particle hops (measured from start to stop). We show that particles of short hop distances scale asL~giving rise to the Weibull‐like front of the hop distance distribution, while particles of long hop distances transition to a different scaling regime ofL~Tpleading to the exponential‐like tail of the hop distance distribution. By demonstrating that the predominance of mostly long hop particles results in a Gaussian‐like velocity distribution, while a mixture of both short and long hop distance particles leads to an exponential‐like velocity distribution, we argue that the form of the probability distribution of particle velocities can depend on the physical environment within which particle transportmore »occurs, explaining and unifying disparate views on particle velocity statistics reported in the literature.

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  4. Abstract

    The abundant lakes dotting arctic deltas are hotspots of methane emissions and biogeochemical activity, but seasonal variability in lake extents introduces uncertainty in estimates of lacustrine carbon emissions, typically performed at annual or longer time scales. To characterize variability in lake extents, we analyzed summertime lake area loss (i.e., shrinkage) on two deltas over the past 20 years, using Landsat‐derived water masks. We find that monthly shrinkage rates have a pronounced structured variability around the channel network with the shrinkage rate systematically decreasing farther away from the channels. This pattern of shrinkage is predominantly attributed to a deeper active layer enhancing near‐surface connectivity and storage and greater vegetation density closer to the channels leading to increased evapotranspiration rates. This shrinkage signal, easily extracted from remote sensing observations, may offer the means to constrain estimates of lacustrine methane emissions and to develop process‐based estimates of depth to permafrost on arctic deltas.

  5. Abstract

    The effective characterization of topographic surfaces is a central tenet of geomorphology. Differences in land surface properties reveal variations in structural controls and the nature and efficacy of Earth‐shaping processes. In this paper, we employ the Hölder exponents,α, characterizing the local scaling behavior of topography and commonly used in the study of the (multi)fractal properties of landscapes and show that the joint probability distribution of the area of the terrain with a given elevation andαcontains a wealth of information on topographic structure. The conditional distributions of the hypsometric integrals as a function ofα, that is,Ihyp|α, are shown to capture this structure. A multivariate analysis reveals three metrics that summarize these conditional distributions: Strahler's original hypsometric integral, the standard deviation of theIhyp|α, and the nature of any trend of theIhyp|αagainstα. An analysis of five digital elevation models (DEMs) from different regions of the United States shows that only one is truly described by the hypsometric integral (Mettman Ridge from central Oregon). In the other cases, the new metrics clearly discriminate between instances where topographic roughness is more clearly a function of elevation, as captured by the conditional variables. In a final example, we artificially sharpen the ridges and valleys ofmore »one DEM to show that while the hypsometric integral and standard deviation ofIhyp|αare invariant to the change, the trend ofIhyp|αagainstαcaptures the changes in topography.

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  6. Bedload particle hops are defined as successive motions of a particle from start to stop, characterizing one of the most fundamental processes of bedload sediment transport in rivers. Although two transport regimes have been recently identified for short and long hops, respectively, there is still the lack of a theory explaining the mean hop distance–travel time scaling for particles performing short hops, which dominate the transport and may cover over 80 % of the total hop events. In this paper, we propose a velocity-variation-based formulation, the governing equation of which is intrinsically identical to that of Taylor dispersion for solute transport within shear flows. The key parameter, namely the diffusion coefficient, can be determined by hop distances and travel times, which are easier to measure and more accurate than particle accelerations. For the first time, we obtain an analytical solution for the mean hop distance–travel time relation valid for the entire range of travel times, which agrees well with the measured data. Regarding travel times, we identify three distinct regimes in terms of different scaling exponents: respectively, $\sim$ 1.5 for the initial regime and $\sim$ 5/3 for the transition regime, which define the short hops, and 1 for the Taylor dispersionmore »regime defining long hops. The corresponding distribution of the hop distance is analytically obtained and experimentally verified. We also show that the conventionally used exponential distribution, as proposed by Einstein, is solely for long hops. Further validation of the present formulation is provided by comparing the simulated accelerations with measurements.« less
  7. Abstract. The abundance of global, remotely sensed surface water observations has accelerated efforts toward characterizing and modeling how water moves across the Earth's surface through complex channel networks. In particular, deltas and braided river channel networks may contain thousands of links that route water, sediment, and nutrients across landscapes. In order to model flows through channel networks and characterize network structure, the direction of flow for each link within the network must be known. In this work, we propose a rapid, automatic, and objective method to identify flow directions for all links of a channel network using only remotely sensed imagery and knowledge of the network's inlet and outletlocations. We designed a suite of direction-predicting algorithms (DPAs),each of which exploits a particular morphologic characteristic of thechannel network to provide a prediction of a link's flow direction. DPAswere chained together to create “recipes”, or algorithms that set all theflow directions of a channel network. Separate recipes were built for deltasand braided rivers and applied to seven delta and two braided river channelnetworks. Across all nine channel networks, the recipe-predicted flowdirections agreed with expert judgement for 97 % of all tested links, andmost disagreements were attributed to unusual channel network topologiesthat can easily bemore »accounted for by pre-seeding critical links with knownflow directions. Our results highlight the (non)universality ofprocess–form relationships across deltas and braided rivers.« less