In this letter, we present a method to reconstruct the surface elevation of an inviscid traveling gravity wave in two dimensions using the pressure measured at any depth. In order to achieve this reconstruction, we derive a map from the pressure at an arbitrary depth   p(x,z 0 )     p   (  x  ,    z    0    )         to the horizontal velocity at the bottom of the fluid domain. Once this map is established, we use the result presented in Oliveras et al. (2012) to find the free-surface   η     η       . In addition to the fully nonlinear relationship, we present a “heuristic” asymptotic formula that does not involve the wave speed   c     c       .
['Vishal Vasan', 'Katie Oliveras']
Water-wave profiles from pressure measurements: Extensions