The water surface slope (WSS), hydraulic gradient, or flow gradient of a river is the slope of the hydraulic grade line, that is, the change of the pressure head per distance unit (Gliński et al., 2011;Herrmann & Bucksch, 2014;Julien, 2018b). It is typically defined positive for an decreasing water surface elevation (WSE) in downstream direction (Julien, 2018b). WSS is not stationary but changes over time and space. Especially in natural rivers that are non-uniform and unsteady, the WSS is variable over time because of morphological changes of the river bed and flood waves (Julien, 2018a). Locally, WSS may differ from larger-scale averages and change with every reach because of local characteristics like cascades, pools, or tributary estuaries (Rhoads, 2020;Schumm, 2005). While the WSS of an alluvial river is gradual, bedrock causes natural discontinuities in semi-alluvial rivers (Julien, 2018b). In hydrology, WSS is a critical parameter required to calculate flow velocity and discharge (Manning, 1891;Rhoads, 2020). The flow velocity derived from WSS is also essential for densifying spatial or temporal low-resolution water level measurements from non-repeating satellite altimetry missions such as Cryosat-2 (Tourian et al., 2016). Generally, the WSS can be used to correct any satellite altimetry mission to compensate for the satellites' ground track variability when calculating long-term water level time series at fixed locations, so-called virtual stations (VS). WSE measurements of the "Shuttle Radar Topography Mission" (SRTM) are regularly used to derive WSS (