A wide
range of geometric order parameters have been suggested
to characterize the local structure of liquid water and its tetrahedral
arrangement, but their respective merits have remained elusive. Here,
we consider a series of popular order parameters and analyze molecular
dynamics simulations of water, in the bulk and in the hydration shell
of a hydrophobic solute, at 298 and 260 K. We show that these parameters
are weakly correlated and probe different distortions, for example
the angular versus radial disorders. We first combine these complementary
descriptions to analyze the structural rearrangements leading to the
density maximum in liquid water. Our results reveal no sign of a heterogeneous
mixture and show that the density maximum arises from the depletion
in interstitial water molecules upon cooling. In the hydration shell
of the hydrophobic moiety of propanol, the order parameters suggest
that the water local structure is similar to that in the bulk, with
only a very weak depletion in ordered configurations, thus confirming
the absence of any iceberg-type structure. Finally, we show that the
main structural fluctuations that affect water reorientation dynamics
in the bulk are angular distortions, which we explain by the jump
hydrogen-bond exchange mechanism