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Increase in the global mean temperature is extensively affecting ice sheets and reducing them. Assessment of this reduction and its causes is required to project its global climatic impact. A usual way of analyzing the reduction is by calculating the change in annual snow accumulation over these ice sheets. This can be done with the help of images from the Snow Radar sensor, an airborne sensor which captures the snow profile of different years. In this paper, we use deep learning to uniquely identify the position of each annual snow layer in the Snow Radar images taken across different regions over the Greenland ice sheet. We train with more than 15,000 images and estimate the thickness of each snow layer within a mean absolute error of 0.54 to 7.28 pixels, depending on year. A highly precise snow layer thickness can help study the ablation and accumulation of snow through time and thus support glaciological studies. Such a well-trained deep learning model can be used with ever-growing datasets to aid in the accurate assessment of snow accumulation on the dynamically changing ice sheets.