  A new method is proposed to recover the water-wave surface elevation from
pressure data obtained at the bottom of the fluid. The new method requires the
numerical solution of a nonlocal nonlinear equation relating the pressure and
the surface elevation which is obtained from the Euler formulation of the
water-wave problem without approximation. From this new equation, a variety of
different asymptotic formulas are derived. The nonlocal equation and the
asymptotic formulas are compared with both numerical data and physical
experiments. The solvability properties of the nonlocal equation are rigorously
analyzed using the Implicit Function Theorem.
