The European Space Agency provides unprecedented monitoring of Earth's oceans through a network of Synthetic Aperture Radar (SAR) satellites called Sentinel-1. Imagery from these satellites captures a variety of atmosphere and ocean surface phenomena including waves, atmospheric turbulence, ocean fronts, and marine biology. Computer vision methods have been used to process the large number of acquired images, but the use of machine learning methods has been severely limited by sparsely labeled data. Consequently, we apply a self-supervised learning method, SwAV, to three years of Sentinel-1 satellite observations (3 million images) to learn an unsupervised embedding for SAR images, then fine-tune the model to detect wind streaks and mesoscale convection cells through supervised learning. Our results demonstrate detection performance improvement over the previous state-of-the-art model but suggest that self-supervised training has marginal improvements over a more standard approach of transfer learning from a model trained on natural images.