Several research groups have been developing algorithms to calculate river discharges using satellite measurements only. However, the use of ground measurements is useful to greatly reduce the uncertainties. We have developed and tested an original Bayesian method to estimate streamflow at hydrometric stations using satellite measurements of water surface elevation (stage), width and slope as input data. The tests were conducted using an existing set of synthetic data defined in the context of the future SWOT satellite mission for a range of rivers. Typical sets of ground discharge measurements (1-24 gaugings) were created by sampling these synthetic data and adding measurement errors. We found that the reach-averaged cross-sectional geometry of each site can usually be approximated by a single rectangular, trapezoidal, parabolic or triangular shape, or a combination of two shapes for low and high flows. Based on such cross-sectional shapes, simple stage-width-slope-discharge models can be derived based on the Manning equation for fairly steady and uniform flows. A few gaugings in each flow segment of the model are necessary to estimate the parameters and produce discharge records with acceptable uncertainty. Our results show that it is possible to apply methods used for ground hydrometric stations to virtual stations created by satellite remote sensing throughout large river networks. Fewer ground discharge measurements are required because the satellite provides the water surface width and slope in addition to the stage. The proposed Bayesian approach bridges the gap between traditional ground-based hydrometry and river hydraulics remote sensing, and observational strategy can be optimized based on uncertainty quantification. Figure: Estimates of a parameter of the model: the mean elevation h0 of the Sacramento River bed using 2-24 gaugings. Boxplots show 95% probability intervals and the medians. Prior distribution is shown in white (0 gauging).