  We study the evolution of dynamic fluctuations averaged over different space
lengths and time scales to characterize spatially and temporally heterogeneous
behavior of TIP4P/2005 water in liquid and supercooled states. Analysing a
million particle simulated system we provide evidence of the existence, upon
supercooling, of a significant enhancement of spatially localized dynamic
fluctuations stemming from regions of correlated mobile molecules. We show that
both the magnitude of the departure from the value expected for the system-size
dependence of an uncorrelated system and the molecular size at which such
trivial regime is finally recovered clearly increase upon supercooling. This
provides a means to estimate an upper limit to the maximum length scale of
influence of the regions of correlated mobile molecules. Notably, such upper
limit grows two orders of magnitude on cooling, reaching a value corresponding
to a few thousand molecules at the lowest investigated temperature.
