Global warming is rapidly reducing glaciers and ice sheets across the world. Real time assessment of this reduction is required so as to monitor its global climatic impact. In this paper, we introduce a novel way of estimating the thickness of each internal ice layer using Snow Radar images and Fully Convolutional Networks. The estimated thickness can be analysed to understand snow accumulation each year. To understand the depth and structure of each internal ice layer, we carry out a set of image processing techniques and perform semantic segmentation on the radar images. After detecting each ice layer uniquely, we calculate its thickness and compare it with the available ground truth. Through this procedure we were able to estimate the ice layer thicknesses within a Mean Absolute Error of approximately 3.6 pixels. Such a Deep Learning based method can be used with ever-increasing datasets to make accurate assessments for cryospheric studies.