  We propose higher-order approximation formulae recovering the surface
elevation from the pressure at the bed and the background shear flow for
small-amplitude Stokes and solitary water waves. They offer improvements over
the pressure transfer function and the hydrostatic approximation. The formulae
compare reasonably well with asymptotic approximations of the exact relation
between the pressure at the bed and the surface wave in the zero vorticity
case, but they incorporate the effects of vorticity through solutions of the
Rayleigh equation. Several examples are discussed.
