The Amazon, the world's largest rainforest, faces a severe historic drought. The Rio Negro River, one of the major Amazon River tributaries, reaches its lowest level in a century in October 2023. Here, we used a U-net deep learning model to map water surfaces in the Rio Negro River basin every 12 days in 2022 and 2023 using 10 m spatial resolution Sentinel-1 satellite radar images. The accuracy of the water surface model was high with an F1-score of 0.93. The 12 days mosaic time series of water surface was generated from the Sentinel-1 prediction. The water surface mask demonstrated relatively consistent agreement with the Global Surface Water (GSW) product from Joint Research Centre (F1-score: 0.708) and with the Brazilian Mapbiomas Water initiative (F1-score: 0.686). The main errors of the map were omission errors in flooded woodland, in flooded shrub and because of clouds. Rio Negro water surfaces reached their lowest level around the 25th of November 2023 and were reduced to 68.1\% (9,559.9 km$^2$) of the maximum water surfaces observed in the period 2022-2023 (14,036.3 km$^2$). Synthetic Aperture Radar (SAR) data, in conjunction with deep learning techniques, can significantly improve near real-time mapping of water surface in tropical regions.