  We investigate density fluctuations in a liquid close to a solvophobic
substrate at which a surface critical drying transition occurs. Using classical
density functional theory, we determine three measures of the spatial extent
and strength of the fluctuations, i.e., the local compressibility
$\chi_{\mu}(z)$, the local thermal susceptibility $\chi_T(z)$ and the reduced
density $\chi_*(z)$; $z$ is the distance from the substrate. Whilst the first
measure is frequently used, the second and third were introduced very recently
by Eckert et.al., Phys. Rev. Lett. 125, 268004 (2020). For state points in the
critical drying regime, all three measures, each scaled by its bulk value,
exhibit very similar forms and the ratio of $\chi_T(z)$ to $\chi_{\mu}(z)$, for
fixed $z$ in the vapour-liquid transition region, is constant. Using a scaling
treatment of surface thermodynamics we show that such behaviour is to be
expected on general grounds.
