  Previous analyses of mid-infrared water spectra from young protoplanetary
disks observed with the Spitzer-IRS found an anti-correlation between water
luminosity and the millimeter dust disk radius observed with ALMA. This trend
was suggested to be evidence for a fundamental process of inner disk water
enrichment, used to explain properties of the Solar System 40 years ago, in
which icy pebbles drift inward from the outer disk and sublimate after crossing
the snowline. Previous analyses of IRS water spectra, however, were uncertain
due to the low spectral resolution that blended lines together. We present new
JWST-MIRI spectra of four disks, two compact and two large with multiple radial
gaps, selected to test the scenario that water vapor inside the snowline is
regulated by pebble drift. The higher spectral resolving power of MIRI-MRS now
yields water spectra that separate individual lines, tracing upper level
energies from 900 K to 10,000 K. These spectra clearly reveal excess emission
in the low-energy lines in compact disks, compared to the large disks,
demonstrating an enhanced cool component with $T \approx$ 170-400 K and
equivalent emitting radius $R_{\rm{eq}}\approx$ 1-10 au. We interpret the cool
water emission as ice sublimation and vapor diffusion near the snowline,
suggesting that there is indeed a higher inwards mass flux of icy pebbles in
compact disks. Observation of this process opens up multiple exciting prospects
to study planet formation chemistry in inner disks with JWST.
