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The NASA Surface Water Ocean Topography (SWOT) mission and ESA Sentinel-1, inter-alia, propose to monitor inland waters from satellites. The radar altimeter and the microwave radiometer can be used to monitor water surface level and assess the cross-sectional mean flow velocity, respectively. However, for most river sites bathymetric data are lacking, preventing the direct computation of discharge. In this context, a new methodology for simulating the bathymetry and estimating the discharge is proposed. The approach is based on entropy theory and can be applied using ground and satellite observations. Four parameters are needed and include channel roughness, water surface slope, channel bottom elevation, and an entropy parameter of flow depth. These parameters are estimated using a genetic algorithm by minimizing the error in the observed maximum surface velocity. Parameter uncertainty is considered through 1,000 random realizations based on different initial values. Eighteen streamflow measurements recorded from three different gauged river sites are used to benchmark the ground observations. The method included ENVISAT altimetry and Moderate Resolution Imaging Spectroradiometer (MODIS) data (2002-2010) at one river site. Relative to ground measurements, the method provides good results with an error in channel area and discharge that, on average, does not exceed 10% on the 50th percentile. Relative to satellite measurements, channel area is well simulated with an error, on average, lower than 9%; discharge is less well simulated and represented by an error greater than 30% on the 50th percentile.