  We present a new velocity-resolved survey of 2.9 $\mu$m spectra of hot H$_2$O
and OH gas emission from protoplanetary disks, obtained with CRIRES at the VLT
($\Delta v \sim$ 3 km s$^{-1}$). With the addition of archival Spitzer-IRS
spectra, this is the most comprehensive spectral dataset of water vapor
emission from disks ever assembled. We provide line fluxes at 2.9-33 $\mu$m
that probe from disk radii of $\sim0.05$ au out to the region across the water
snow line. With a combined dataset for 55 disks, we find a new correlation
between H$_2$O line fluxes and the radius of CO gas emission as measured in
velocity-resolved 4.7 $\mu$m spectra (R$_{\rm co}$), which probes molecular
gaps in inner disks. We find that H$_2$O emission disappears from 2.9 $\mu$m
(hotter water) to 33 $\mu$m (colder water) as R$_{\rm co}$ increases and
expands out to the snow line radius. These results suggest that the infrared
water spectrum is a tracer of inside-out water depletion within the snow line.
It also helps clarifying an unsolved discrepancy between water observations and
models, by finding that disks around stars of M$_{\star}>1.5$ M$_\odot$
generally have inner gaps with depleted molecular gas content. We measure
radial trends in H$_2$O, OH, and CO line fluxes that can be used as benchmarks
for models to study the chemical composition and evolution of planet-forming
disk regions at 0.05-20 au. We propose that JWST spectroscopy of molecular gas
may be used as a probe of inner disk gas depletion, complementary to the larger
gaps and holes detected by direct imaging and by ALMA.

Earth and Planetary Astrophysics