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H_2O submillimeter emission is a powerful diagnostic of the molecular interstellar medium in a variety of sources, including low- and high-mass star forming regions of the Milky Way, and from local to high redshift galaxies. However, the excitation mechanism of these lines in galaxies has been debated, preventing a basic consensus on the physical information that H_2O provides. Both radiative pumping due to H_2O absorption of far-infrared photons emitted by dust and collisional excitation in dense shocked gas have been proposed to explain the H_2O emission. Here we propose two basic diagnostics to distinguish between the two mechanisms: 1) in shock excited regions, the ortho-H_2O 3_{21}-2_{12} 75um and the para-H_2O 2_{20}-1_{11} 101um rotational lines are expected to be in emission while, if radiative pumping dominates, both far-infrared lines are expected to be in absorption; 2) based on statistical equilibrium of H_2O level populations, the radiative pumping scenario predicts that the apparent isotropic net rate of far-infrared absorption in the 3_{21}-2_{12} (75um) and 2_{20}-1_{11} (101um) lines should be higher than or equal to the apparent isotropic net rate of submillimeter emission in the 3_{21}-3_{12} (1163 GHz) and 2_20-2_{11} (1229 GHz) lines, respectively. Applying both criteria to all 16 galaxies and several galactic high-mass star-forming regions where the H_2O 75um and submillimeter lines have been observed with Herschel/PACS and SPIRE, we show that in most (extra)galactic sources the H_2O submillimeter line excitation is dominated by far-infrared pumping, with collisional excitation of the low-excitation levels in some of them. Based on this finding, we revisit the interpretation of the correlation between the luminosity of the H_2O 988 GHz line and the source luminosity in the combined galactic and extragalactic sample.