  We introduce the spatial correlation function $C_Q(r)$ and temporal
autocorrelation function $C_Q(t)$ of the local tetrahedral order parameter
$Q\equiv Q(r,t)$. Using computer simulations of the TIP5P model of water, we
investigate $C_Q(r)$ in a broad region of the phase diagram. First we show that
$C_Q(r)$ displays anticorrelation at $r\approx 0.32$nm at high temperatures
$T>T_W\approx 250$ K, which changes to positive correlation below the Widom
line $T_W$. Further we find that at low temperatures $C_Q(t)$ exhibits a
two-step temporal decay similar to the self intermediate scattering function,
and that the corresponding correlation time $\tau_Q$ displays a dynamic
crossover from non-Arrhenius behavior for $T>T_W$ to Arrhenius behavior for
$T<T_W$. Finally, we define an orientational entropy $S_Q$ associated with the
{\it local} orientational order of water molecules, and show that $\tau_Q$ can
be extracted from $S_Q$ using an analog of the Adam-Gibbs relation.
