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.

中文翻译：

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观察不同空间尺度的河流


摘要 美国国家航空航天局/国家空间研究中心地表水和海洋地形 (SWOT) 任务将利用遥感技术估算全球河流流量。天气遥感数据扩展了原位点测量，但在任何给定点，通常不太准确。我们解决两个问题：（1）在给定空间采样和测量噪声特征的情况下，可以在什么尺度上观察河流动态？ (2)是否存在一个以遥感获得的平均水力量为变量、描述空间平均河流动态的方程？我们使用校准的水力模型来检查动量方程中不同项的功率谱，并得出结论：河流坡度的测量设置了可以观察河流的尺度。我们引入了平均圣维南方程，该方程仅涉及可观察到的水力变化，并且通过乘以摩擦系数并导致“有效”摩擦系数增加的变化指数来参数化范围内的变化。推导了有效摩擦系数增加的精确表达式，并且我们提出了仅需要估计水力参数方差的近似值。我们使用大量水力模型验证了结果，并发现当河流参数服从对数正态统计时，近似的变异指数是最忠实的。有效摩擦系数可以从点摩擦系数的百分之几到50%以上变化，与河床高程变化成正比，与深度成反比。这对于根据 SWOT 数据估算排放量具有重要意义。