Deployment of Sentinel-1 (S1) satellite constellation carrying a C-band synthetic aperture radar (SAR) enables regular and timely monitoring of floods from their onset until returning to nonflooded (NF) conditions. The major constraint on using SAR for near-real-time (NRT) flood mapping has been the inability to rapidly process the obtained imagery into reliable flood maps. This study evaluates the efficacy of S1 time series for quantifying and characterizing inundation extents in vegetated environments. A novel algorithm based on statistical time-series modeling of flooded (F) and NF pixels is proposed for NRT flood monitoring. For each new available S1 image, the probability of temporarily F conditions is tested against that of NF conditions by means of likelihood ratio tests. The likelihoods for the two conditions are derived from early acquisitions in the time series. The algorithm calibration consists of adjusting two likelihood ratio thresholds to match the reference F area extent during a single flood season. The proposed algorithm is applied to the Caprivi region, the resulting maps were compared to cloud-free Landsat-8 (LS8) derived maps captured during two flood events. A good spatial agreement (85-87%) between LS8 and S1 flood maps was observed during the flood peak in both 2017 and 2018 seasons. Significant discrepancies were noted during the flood expansion and recession phases, mainly due to different sensitivities of the data sources to the emerging vegetation. Overall, the analysis shows that S1 can stand as an effective standalone or gap-filling alternative to optical imagery during a flood event.