The evolution of the structure of water from the stable high temperature liquid to its glass, low-density amorphous ice (LDA), is studied through large-scale molecular dynamics simulations with the mW model [J. Phys. Chem. B 113, 4008 (2009)]. We characterize the density, translational, and orientational ordering of liquid water from the high temperature stable liquid to the low-density glass LDA at the critical cooling rate for vitrification. A continuous transition to a tetrahedrally ordered low-density liquid is observed at 50 K below the temperature of maximum density and 25 K above a temperature of minimum density. The structures of the low-density liquid and glass are consistent with that of a continuous random tetrahedral network. The liquid-liquid transformation temperature T(LL), defined by the maximum isobaric expansivity, coincides with the maximum rate of change in the local structure of water. Long-range structural fluctuations of patches of four-coordinated molecules form in the liquid. The correlation length of the four-coordinated patches in the liquid increases according to a power law in the range 300 K to T(LL)+10 K; a maximum is predicted at T(LL). To the best of our knowledge this is the first direct estimation of the Widom line of supercooled water through the analysis of structural correlations.