The Surface Water and Ocean Topography (SWOT) satellite mission planned for launch in 2020 will map river elevations and inundated area globally for rivers >100 m wide. In advance of this launch, we here evaluated the possibility of estimating discharge in ungauged rivers using synthetic, daily “remote sensing” measurements derived from hydraulic models corrupted with minimal observational errors. Five discharge algorithms were evaluated, as well as the median of the five, for 19 rivers spanning a range of hydraulic and geomorphic conditions. Reliance upon a priori information, and thus applicability to truly ungauged reaches, varied among algorithms: one algorithm employed only global limits on velocity and depth, while the other algorithms relied on globally available prior estimates of discharge. We found at least one algorithm able to estimate instantaneous discharge to within 35% relative root‐mean‐squared error (RRMSE) on 14/16 nonbraided rivers despite out‐of‐bank flows, multichannel planforms, and backwater effects. Moreover, we found RRMSE was often dominated by bias; the median standard deviation of relative residuals across the 16 nonbraided rivers was only 12.5%. SWOT discharge algorithm progress is therefore encouraging, yet future efforts should consider incorporating ancillary data or multialgorithm synergy to improve results.

The forthcoming Surface Water and Ocean Topography (SWOT) satellite mission will provide global measurements of the free surface of large rivers, providing new opportunities for remote sensing‐derived estimates of river discharge in gaged and ungaged basins. SWOT discharge algorithms have been developed and benchmarked using synthetic data but remain untested on real‐world swath altimetry observations. We present the first discharge estimates from AirSWOT, a SWOT‐like airborne Ka‐band radar, using 6 days of measurements over a 40‐km segment of the Willamette River in Oregon, USA. The three evaluated discharge algorithms estimated discharge with normalized root‐mean‐square errors of 10–31% when compared with in situ gage data but were sensitive to an initial estimate of mean annual discharge. Our results show that these discharge algorithms provide reliable discharge estimates on remotely sensed data at SWOT‐like spatial scales while highlighting the need for further algorithm sensitivity tests.

An inverse method to estimate the discharge of rivers observed by satellite altimetry is developed and assessed. The flow model relies on the Saint-Venant equations combined with a dedicated algebraic system. The resulting hierarchical flow model combined with variational data assimilation enables estimation of the key unknown flow features: the discharge Q(x,t), an effective bathymetry b(x) and friction coefficients K(x). Numerical results are analyzed for three rivers in two different observation contexts (corresponding to the SWOT Cal-Val orbit and to the SWOT nominal orbit) and three different scenarios of prior information availability. These investigations cover numerous realistic worldwide applications. It is shown that the space-time variations of the river discharge Q(x, t) and the bathymetry profile b(x) can be accurately inferred. However the inferred values of Q may be obtained at a multiplicative factor only (a bias). This bias vanishes as soon as an accurate mean value or one reference value of one of the three inferred field is provided. Once the assimilation of the satellite measurements has been done during a sufficiently long time period representing enough flow variability (one year), the low complexity algebraic flow model provides discharge estimations in real computational time from newly acquired measurements.