The Tibetan Plateau, known as the Asian Water Tower, faces significant water security challenges due to its high sensitivity to climate change. Advancing Earth observation for sustainable water monitoring is thus essential for building climate resilience in this region. This study proposes a two-stage transfer learning strategy using the SegFormer model to overcome domain shift and data scarcit--key barriers in developing robust AI for climate-sensitive applications. After pre-training on a diverse source domain, our model was fine-tuned for the arid Zhada Tulin area. Experimental results show a substantial performance boost: the Intersection over Union (IoU) for water body segmentation surged from 25.50% (direct transfer) to 64.84%. This AI-driven accuracy is crucial for disaster risk reduction, particularly in monitoring flash flood-prone systems. More importantly, the high-precision map reveals a highly concentrated spatial distribution of water, with over 80% of the water area confined to less than 20% of the river channel length. This quantitative finding provides crucial evidence for understanding hydrological processes and designing targeted water management and climate adaptation strategies. Our work thus demonstrates an effective technical solution for monitoring arid plateau regions and contributes to advancing AI-powered Earth observation for disaster preparedness in critical transboundary river headwaters.