## (Solution document) The negative topography ("hole") left by the rapid melting of a large ice sheet relaxes exponentially in time back to normal ("flat") topography.

1.    The negative topography ("hole") left by the rapid melting of a large ice sheet relaxes exponentially in time back to normal ("flat") topography. This process can be represented by u(t) = u0 exp (-t/tao), where u is the (negative) topographic displacement of the surface, t is time, and  is the characteristic relaxation time.

(a)  Given that at any time after the ice sheet melts the force driving topographic relaxation, and hence the rate of rebound of the underlying mantle and crust, is proportional to the remaining negative topography, explain mathematically via a simple differential equation why this relaxation process is exponential in time.

(b) If the relaxation time, , for the removal of the Ice Age Fennoscandian ice sheet has been estimated from 14C-dated uplift of paleo-shorelines to be about 5000 years, and the ice sheet is known to have melted about 9000 years ago, leaving an initial "hole" about 200 meters deep, how much remaining postglacial uplift, or "rebound," can be expected to occur in the future (unless, of course, the ice sheet starts growing again)? (10 points)

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