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The x-ray absorption spectra of water and ice are calculated with a many-body approach for electron-hole excitations. The experimental features, including the effects of temperature change in the liquid, are reproduced from configurations generated by ab initio molecular dynamics. The spectral difference between the solid and the liquid is due to two major short-range order effects. One, due to breaking of hydrogen bonds, enhances the pre-edge intensity in the liquid. The other, due to a nonbonded molecular fraction in the first coordination shell, affects the main spectral edge in the conversion of ice to water. This effect may not involve hydrogen bond breaking as shown by experiment in high-density amorphous ice.