We present a systematic survey of multiple velocity-resolved H$_2$O spectra using Herschel/HIFI towards nine nearby actively star forming galaxies. The ground-state and low-excitation lines (E$_{rm up},le 130,{rm K}$) show profiles with emission and absorption blended together, while absorption-free medium-excitation lines ($130,{rm K}, le, E_{rm up},le,350,{rm K}$) typically display line shapes similar to CO. We analyze the HIFI observation together with archival SPIRE/PACS H$_2$O data using a state-of-the-art 3D radiative transfer code which includes the interaction between continuum and line emission. The water excitation models are combined with information on the dust- and CO spectral line energy distribution to determine the physical structure of the interstellar medium (ISM). We identify two ISM components that are common to all galaxies: A warm ($T_{rm dust},sim,40-70,{rm K}$), dense ($n({rm H}),sim,10^5-10^6,{rm cm^{-3}}$) phase which dominates the emission of medium-excitation H$_2$O lines. This gas phase also dominates the FIR emission and the CO intensities for $J_{rm up} > 8$. In addition a cold ($T_{rm dust},sim,20-30,{rm K}$), dense ($n({rm H})sim,10^4- 10^5,{rm cm^{-3}}$) more extended phase is present. It outputs the emission in the low-excitation H$_2$O lines and typically also produces the prominent line absorption features. For the two ULIRGs in our sample (Arp 220 and Mrk 231) an even hotter and more compact (R$_s,le,100$ pc) region is present which is possibly linked to AGN activity. We find that collisions dominate the water excitation in the cold gas and for lines with $E_{rm up}le300,{rm K}$ and $E_{rm up}le800,{rm K}$ in the warm and hot component, respectively. Higher energy levels are mainly excited by IR pumping.
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