Remote sensing has the potential to dramatically advance river discharge monitoring globally, but precision of primary data (water surface elevation (WSE) and river width) remains a limiting factor. WSE can be measured from altimeters, and river width from imagers, but the measurements historically have not been made concurrently from space. This is changing with the advent of the Surface Water and Ocean Topography (SWOT) mission and is anticipated by the combination of high-resolution commercial imagery and DEMs from ArcticDEM. WSE and width respond to changing flow conditions as modulated by the three-dimensional structure of the river channel bed and banks. The relationship between WSE and width thus increases monotonically and is essentially the hypsometric curve of the river. In this study, we explore how simultaneous measurements of WSE and width, combined with the monotonic nature of the river hypsometric curve, can be used to improve measurements of river discharge. First, we present an algorithm to compute the river hypsometric curve from noisy measurements of WSE and width. Second, we demonstrate a method to compute estimates of WSE and width constrained to the river hypsometric curve, and we analyze the probability distribution function of the hypsometrically constrained WSE and width estimates. Specifically, we show that the variance of width and WSE is reduced by invoking a hypsometric constraint, at the cost of an induced correlation between the WSE and width errors. Third, we show that river discharge estimated with the hypsometrically constrained WSE and width is more precise than that without hypsometric constraint, and we predict the expected reduction in discharge error. Fourth, we look at six example river reaches measured by ArcticDEM. The WSE root mean square error had a median across the six reaches of 39.3 cm, which was improved to 33.4 cm across the six reaches using the hypsometric constraint. The discharge predictions were similarly improved: the constrained height and width produce more accurate discharge estimates for five of the six reaches and show reduced variation among flow laws. With the launch of SWOT, river hypsometry constraints applied to simultaneous measurement of WSE and width will support new discharge estimates globally.

中文翻译：

---

利用河流螺旋测量技术改进河流流量遥感


遥感有可能极大地推动全球河流流量监测，但原始数据（水面高程 （WSE） 和河流宽度）的精度仍然是一个限制因素。WSE 可以用高度计测量，河流宽度可以用成像仪测量，但历史上这些测量不是从太空同时进行的。随着地表水和海洋地形 （SWOT） 任务的出现，这种情况正在发生变化，并且高分辨率商业影像与 ArcticDEM 的 DEM 相结合可以预示这一情况。WSE 和宽度响应由河道床和河岸的三维结构调制的变化水流条件。因此，WSE 和宽度之间的关系单调增加，本质上是河流的螺旋曲线。在这项研究中，我们探讨了如何同时测量 WSE 和宽度，结合河流高度曲线的单调性质，来改进河流流量的测量。首先，我们提出了一种算法，根据 WSE 和宽度的噪声测量来计算河流高度测温曲线。其次，我们演示了一种计算受河流高度测距曲线约束的 WSE 和宽度估计值的方法，并分析了受高度测振约束的 WSE 和宽度估计值的概率分布函数。具体来说，我们表明，通过调用螺旋测距约束来减小宽度和 WSE 的方差，但代价是 WSE 和宽度误差之间的诱导相关性。第三，我们表明使用高度计量约束的 WSE 和宽度估计的河流流量比没有高度参数约束的河流流量更精确，并且我们预测了流量误差的预期减少。第四，我们查看了 ArcticDEM 测量的六个示例河流范围。 WSE 均方根误差在六个范围中的中位数为 39.3 cm，使用高度计约束在六个范围中提高到 33.4 cm。流量预测也得到了类似的改进：约束的高度和宽度为 6 个河段中的 5 个河段产生了更准确的流量估计，并且流律之间的变化较小。随着 SWOT 的推出，应用于同时测量 WSE 和宽度的河流螺旋测量约束将支持全球新的流量估计。