  The physics of air-water interfaces plays a central role in modern theories
of the hydrophobic effect. Implementing these theories, however, has been
hampered by the difficulty of addressing fluctuations in the shape of such soft
interfaces. We show that this challenge is a fundamental consequence of mapping
long wavelength density variations onto discrete degrees of freedom. Drawing
from studies of surface roughness in lattice models, we account for the
resulting nonlinearities simply but accurately. Simulations show that this
approach captures complex solvation behaviors quantitatively.
