  Employing smart Monte Carlo sampling techniques within the grand canonical
ensemble, we investigate the properties of water at a model hydrophobic
substrate. By reducing the strength of substrate-water attraction we find that
fluctuations in the local number density, quantified by a rigorous definition
of the local compressibility $\chi(z)$, increase rapidly for distances $z$
within $1$ or $2$ molecular diameters from the substrate as the degree of
hydrophobicity, measured by the macroscopic contact angle $\theta$, increases.
Our simulations provide evidence for a continuous (critical) drying transition
as the substrate-water interaction becomes very weak: $\cos(\theta)\to -1$. We
speculate that the existence of such a transition might account for earlier
simulation observations of strongly enhanced density fluctuations.
