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Abstract Due to its importance for water availability in the tropics and subtropics, efficient tracking of the seasonal and long‐term shifts of the intertropical convergence zone (ITCZ) is of great value. Current approaches, which are based on tracking changes in the annual mean of single variables, ignore the intra‐annual dynamics, while more sophisticated methods are computationally intensive. Here we propose a new probabilistic framework to track the ITCZ, which is based on tracking the location of maximum precipitation and minimum outgoing longwave radiation in overlapping longitudinal windows. Our framework is seasonally and longitudinally explicit, allows for joint consideration of multiple variables to define the ITCZ, and is flexible in its implementation, thus, it can be used in analyses of different scales and scopes. We apply our framework to analyze the recent climatology of the ITCZ and report a southward trend in its location over central Pacific in the late twentieth century. 

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,I_hyp|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 theI_hyp|α, and the nature of any trend of theI_hyp|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 of one DEM to show that while the hypsometric integral and standard deviation ofI_hyp|αare invariant to the change, the trend ofI_hyp|αagainstαcaptures the changes in topography. 

Abstract Accounting for the burial of tracer particles during bedload transport is an important component in the formulation of tracer dispersal in rivers. Herein we propose a modified active layer formulation, which accounts for the effect of burial and admits analytical solutions, enabling insightful exploration of the phenomenon of superdiffusion of bedload tracers at the intermediate timescale. This phenomenon has been observed in recent numerical results using the 2‐D Exner‐Based Master Equation. By assuming that tracers in the active layer can exchange with nontracer particles in the substrate layer to preserve mass, and that tracers entering the substrate layer get permanently trapped during the timescale of analysis, we are able to deduce governing equations for the tracer concentration in both layers. The active layer tracer concentration is shown to be governed by an advection‐diffusion equation with a sink term, and the increase of tracers in the substrate layer is driven by a corresponding source term. The solution for the variance of tracer population is analytically determined and can be approximated by the sum of a diffusion‐induced scaling (∝t¹) and an advection‐induced scaling (∝t³) terms at the intermediate timescale, which explains the phenomenon of superdiffusion. The proposed formulation is shown to be able to capture the key characteristics of tracer transport as inferred by comparison with available results of numerical simulations.