The ICESat-2 and SWOT satellite earth observation missions provide highly accurate water surface slope (WSS) observations in global rivers for the first time. While water surface slope is expected to remain constant in time for approximately uniform flow conditions, we observe time varying water surface slope in many river reaches around the globe in the ICESat-2 record. Here, we investigate the causes of time variability of WSS using simplified river hydraulic models based on the theory of steady, gradually varied flow. We identify bed slope or cross section shape changes, river confluences, flood waves and backwater effects from lakes, reservoirs, or the ocean as the main hydraulic phenomena causing time changes of WSS in rivers. We illustrate these phenomena at selected prototypical river sites around the world. These sites show that WSS observations can provide new insights into river hydraulics and can enable estimation of river discharge from water level observations at sites with complex hydraulic characteristics.