  Studies of water thermodynamics have long been tied to the identification of
two distinct families of local structures, whose competition could explain the
origin of the many thermodynamic anomalies and of the hypothesized
liquid-liquid critical point in water. Despite the many successes and insights
gained, the structural indicators proposed throughout the years were not able
to unequivocally identify these two families over a wide range of conditions.
We show that a recently introduced indicator, $\Psi$, which exploits
information on the HB network connectivity, can reliably identify these two
distinct local environments over a wide range of thermodynamic conditions (188
to 300 K and 0 to 13 kbar), and that close to the liquid-liquid critical point
the spatial correlations of density fluctuations are identical to those of the
$\Psi$ indicator. Our results strongly support the idea that water
thermodynamic properties arise from the competition between two distinct and
identifiable local environments.
