Scientists are studying past changes in sea level in order to make accurate future predictions of this consequence of climate change, and they're looking down to Earth's core to do so. "In order to fully understand the sea-level change that has occurred in the past century, we need to understand the dynamics of the flow in Earth's core" says Mathieu Dumberry, a professor in physics at the University of Alberta.
The connection is through the change in the speed of Earth's rotation. Melt water from glaciers not only causes sea-level rise, but also shifts mass from the pole to the equator, which slows down the rotation. (Picture the Earth as a spinning figure skater. The skater moves his or her arms in to spin more quickly or out to slow down.) The gravity pull from the Moon also contributes to the slow down, acting a little like a leaver break. However, the combination of these effects is not enough to explain the observations of the slowing down of Earth's rotation: a contribution from Earth's core must be added.