Three synthetic aperture radar (SAR) data classification methodologies were used to assess the ability of single-polarization and dual-polarization TerraSAR-X (TSX) data to classify surface water, including open water, ice, and flooded vegetation. Multi-polarization SAR observations contain more information than single-polarization SAR, but the availability of multi-polarization data is much lower, which limits the temporal monitoring capabilities. The study area is a principally natural landscape centered on a seasonally flooding river, in which four TSX dual-co-polarized images were acquired between the months of April and June 2016. Previous studies have shown that single-polarization SAR is useful for analyzing surface water extent and change using grey-level thresholding. The H-Alpha-Wishart decomposition, adapted to dual-polarization data, and the Kennaugh Element Framework were used to classify areas of water and flooded vegetation. Although grey-level thresholding was able to identify areas of water and non-water, the percentage of seasonal change was limited, indicating an increase in water area from 8% to 10%, which is in disagreement with seasonal trends. The dual-polarization methods show a decrease in water over the season and indicate a decrease in flooded vegetation, which agrees with expected seasonal variations. When comparing the two dual-polarization methods, a clear benefit of the Kennaugh Elements Framework is the ability to classify change in the transition zones of ice to open water, open water to marsh, and flooded vegetation to land, using the differential Kennaugh technique. The H-Alpha-Wishart classifier was not able to classify ice, and misclassified fields and ice as water. Although single-polarization SAR was effective in classifying open water, the findings of this study confirm the advantages of dual-polarization observations, with the Kennaugh Element Framework being the best performing classification framework.