The escalating impacts of climate change necessitate enhanced monitoring techniques for debris covered glaciers (DCG) , a critical yet challenging subject in environmental studies. This urgency underscores the importance of developing advanced methodologies that improve precision in satellite imagery analysis. Our study introduces the Physics-Informed cascaded Swin-Unet (PICSw-UNet) model, a substantial upgrade over traditional segmentation methods such as UNet-ResNet34. By integrating domain-specific physical knowledge with deep learning, our model refines segmentation tasks effectively. Leveraging the architecture of Swin-UNet cascades, this hybrid approach incorporates physical constraints into the training process, guiding the learning algorithm towards more realistic and accurate predictions. Experimental results demonstrate the superiority of our model with improvements in key performance metrics, including Intersection over Union (IoU) and Area Under the Curve (AUC). Specifically, the Physics-Informed cascaded Swin-Unet (PICSw-UNet) achieved an IoU of 91.65\% and an AUC of 96.4\%, compared to 81.24\% and 87.6\%, respectively, for the UNet-ResNet34. Moreover, our model also shows enhanced efficiency with a reduced inference time (IT) of 0.2795 seconds. These advancements indicate promising implications for future remote sensing applications and glaciological studies, offering a promising direction for advancing image analysis methodologies.