We present an improvement to a previously presented algorithm that used a Bayesian Markov Chain Monte Carlo method for estimating river discharge from remotely sensed observations of river height, width, and slope. We also present an error budget for discharge calculations from the algorithm. The algorithm may be utilized by the upcoming Surface Water and Ocean Topography (SWOT) mission. We present a detailed evaluation of the method using synthetic SWOT-like observations (i.e., SWOT and AirSWOT, an airborne version of SWOT). The algorithm is evaluated using simulated AirSWOT observations over the Sacramento and Garonne Rivers that have differing hydraulic characteristics. The algorithm is also explored using SWOT observations over the Sacramento River. SWOT and AirSWOT height, width, and slope observations are simulated by corrupting the ‘‘true’’ hydraulic modeling results with instrument error. Algorithm discharge root mean square error (RMSE) was 9% for the Sacramento River and 15% for the Garonne River for the AirSWOT case using expected observation error. The discharge uncertainty calculated from Manning’s equation was 16.2% and 17.1%, respectively. For the SWOT scenario, the RMSE and uncertainty of the discharge estimate for the Sacramento River were 15% and 16.2%, respectively. A method based on the Kalman filter to correct errors of discharge estimates was shown to improve algorithm performance. From the error budget, the primary source of uncertainty was the a priori uncertainty of bathymetry and roughness parameters. Sensitivity to measurement errors was found to be a function of river characteristics. For example, Steeper Garonne River is less sensitive to slope errors than the flatter Sacramento River.