A Curve‐Fitting Method for Estimating Bathymetry From Water Surface Height and Width

Abstract River discharge estimation requires knowledge of bathymetry. However, aside from a few locations where surveys have been conducted, bathymetric data are unavailable, even for major rivers. It has been suggested that water surface elevation and flow width measurements from the upcoming Surface Water and Ocean Topography (SWOT) satellite mission (planned launch 2021) may be used to infer the submerged channel geometry; however, the full potential of these measurements for inferring bathymetry has yet to be explored. We apply four different techniques, with varying assumptions about height‐width relationships, to predict unknown bathymetry. We call these “curve‐fitting methods” the linear, slope break, nonlinear, and nonlinear slope break (NLSB) methods. The linear and slope break methods are based on a linear height‐width relationship, while the nonlinear and NLSB methods are based on a height‐width relationship derived from hydraulic geometry equations. We generate SWOT‐like observations of height and width based on 5‐m gridded Upper Mississippi River data and evaluate the performance of each curve‐fitting method given the SWOT‐like observations. The NLSB method predicts bed elevation and low flow area with the least error, although the nonlinear method may be preferred in low data conditions. Additionally, we show that our method outperforms previously suggested methods, and we propose an NLSB‐based bathymetry prior for Bayesian discharge estimation algorithms.