Using river hypsometry to improve remote sensing of river discharge

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.