  We investigate structural order in glassy water by performing classical
molecular dynamics simulations using the extended simple point charge (SPC/E)
model of water. We perform isochoric cooling simulations across the glass
transition temperature at different cooling rates and densities. We quantify
structural order by orientational and translational order metrics. Upon cooling
the liquid into the glassy state, both the orientational order parameter $Q$
and translational order parameter $\tau$ increase. At T=0 K, the glasses fall
on a line in the $Q$-$\tau$ plane or {\it order map}.
  The position of this line depends only on density and coincides with the
location in the order map of the inherent structures (IS) sampled upon cooling.
We evaluate the energy of the IS, $e_{IS}(T)$, and find that both order
parameters for the IS are proportional to $e_{IS}$. We also study the
structural order during the transformation of low-density amorphous ice (LDA)
to high-density amorphous ice (HDA) upon isothermal compression and are able to
identify distinct regions in the order map corresponding to these glasses.
Comparison of the order parameters for LDA and HDA with those obtained upon
isochoric cooling indicates major structural differences between glasses
obtained by cooling and glasses obtained by compression. These structural
differences are only weakly reflected in the pair correlation function. We also
characterize the evolution of structural order upon isobaric annealing, leading
at high pressure to very-high density amorphous ice (VHDA).
