River Extraction under Bankfull Discharge Conditions Based on Sentinel-2 Imagery and DEM Data

River discharge and width, as essential hydraulic variables and hydrological data, play a vital role in influencing the water cycle, driving the resulting river topography and supporting ecological functioning. Insights into bankfull river discharge and bankfull width at fine spatial resolutions are essential. In this study, 10-m Sentinel-2 multispectral instrument (MSI) imagery and digital elevation model (DEM) data, as well as in situ discharge and sediment data, are fused to extract bankfull river widths on the upper Yellow River. Using in situ cross-section morphology data and flood frequency estimations to calculate the bankfull discharge of 22 hydrological stations, the one-to-one correspondence relationship between the bankfull discharge data and the image cover data was determined. The machine learning (ML) method is used to extract water bodies from the Sentinel-2 images in the Google Earth Engine (GEE). The mean overall accuracy was above 0.87, and the mean kappa value was above 0.75. The research results show that (1) for rivers with high suspended sediment concentrations, the water quality index (SRMIR-Red) constitutes a higher contribution; the infrared band performs better in areas with greater amounts of vegetation coverage; and for rivers in general, the water indices perform best. (2) The effective river width of the extracted connected rivers is 30 m, which is 3 times the image resolution. The R², root mean square error (RMSE), and mean bias error (MBE) of the estimated river width values are 0.991, 7.455 m, and −0.232 m, respectively. (3) The average river widths of the single-thread sections show linear increases along the main stream, and the R² value is 0.801. The river width has a power function relationship with bankfull discharge and the contributing area, i.e., the downstream hydraulic geometry, with R² values of 0.782 and 0.630, respectively. More importantly, the extracted river widths provide basic data to analyze the spatial distribution of bankfull widths along river networks and other applications in hydrology, fluvial geomorphology, and stream ecology.