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Observing Rivers With Varying Spatial Scales.

ABSTRACT: The National Aeronautics and Space Administration/Centre national d'études spatiales Surface Water and Ocean Topography (SWOT) mission will estimate global river discharge using remote sensing. Synoptic remote sensing data extend in situ point measurements but, at any given point, are generally less accurate. We address two questions: (1)What are the scales at which river dynamics can be observed, given spatial sampling and measurement noise characteristics? (2) Is there an equation whose variables are the averaged hydraulic quantities obtained by remote sensing and which describes the dynamics of spatially averaged rivers? We use calibrated hydraulic models to examine the power spectra of the different terms in the momentum equation and conclude that the measurement of river slope sets the scale at which rivers can be observed. We introduce the reach-averaged Saint Venant equations that involve only observable hydraulic variations and which parametrize within-reach variability with a variability index that multiplies the friction coefficient and leads to an increased "effective" friction coefficient. An exact expression is derived for the increase in the effective friction coefficient, and we propose an approximation that requires only estimates of the hydraulic parameter variances. We validate the results using a large set of hydraulic models and find that the approximated variability index is most faithful when the river parameters obey lognormal statistics. The effective friction coefficient, which can vary from a few percent to more than 50% of the point friction coefficient, is proportional to the riverbed elevation variance and inversely proportional to the depth. This has significant implications for estimating discharge from SWOT data.

SUBMITTER: Rodriguez E

PROVIDER: S-EPMC7540328 | biostudies-literature | 2020 Sep

REPOSITORIES: biostudies-literature

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Observing Rivers With Varying Spatial Scales.

Rodríguez Ernesto E Durand Michael M Frasson Renato Prata de Moraes RPM

Water resources research 20200914 9

The National Aeronautics and Space Administration/Centre national d'études spatiales Surface Water and Ocean Topography (SWOT) mission will estimate global river discharge using remote sensing. Synoptic remote sensing data extend in situ point measurements but, at any given point, are generally less accurate. We address two questions: <i>(1)What are the scales at which river dynamics can be observed, given spatial sampling and measurement noise characteristics? (2) Is there an equation whose var ...[more]

PMID: 33041381

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Project description:The concepts, theoretical behavior and experimental applications of temporal diffusion spectroscopy are reviewed and illustrated. Temporal diffusion spectra are obtained using oscillating-gradient waveforms in diffusion-weighted measurements, and represent the manner in which various spectral components of molecular velocity correlations vary in different geometrical structures that restrict or hinder free movements. Measurements made at different gradient frequencies reveal information on the scale of restrictions or hindrances to free diffusion, and the shape of a spectrum reveals the relative contributions of spatial restrictions at different distance scales. Such spectra differ from other so-called diffusion spectra which depict spatial frequencies and are defined at a fixed diffusion time. Experimentally, oscillating gradients at moderate frequency are more feasible for exploring restrictions at very short distances which, in tissues, correspond to structures smaller than cells. We describe the underlying concepts of temporal diffusion spectra and provide analytical expressions for the behavior of the diffusion coefficient as a function of gradient frequency in simple geometries with different dimensions. Diffusion in more complex model media that mimic tissues has been simulated using numerical methods. Experimental measurements of diffusion spectra have been obtained in suspensions of particles and cells, as well as in vivo in intact animals. An observation of particular interest is the increased contrast and heterogeneity observed in tumors using oscillating gradients at moderate frequency compared with conventional pulse gradient methods, and the potential for detecting changes in tumors early in their response to treatment. Computer simulations suggest that diffusion spectral measurements may be sensitive to intracellular structures, such as nuclear size, and that changes in tissue diffusion properties may be measured before there are changes in cell density.

Dataset Information

Observing Rivers With Varying Spatial Scales.

Publications

Observing Rivers With Varying Spatial Scales.

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