HoughLines should be a perfect function for pencils on paper, but melting ice will produce curves, not strict edges. Nevertheless you can start with this function, and switch later to tracking with Optical Flow or something. You can put several dozens of points to the every edge, and then track how they move down. But you should constrain the Optical Flow in a way so it searches for new points' positions in the vertical direction only. If the ice is melting slowly, you can even implement your own search with a block-matching-like technique.
HoughLines should be a perfect function for pencils on paper, but melting ice will produce curves, not strict edges. Nevertheless you can start with this function, and switch later to tracking with Optical Flow or something. You can put several dozens of points to the every edge, and then track how they move down. But you should constrain the Optical Flow in a way so it searches for new points' positions in the vertical direction only. If the ice is melting slowly, you can even implement your own search with a block-matching-like technique.