Line profiles of the o-H₂O fundamental line at 557 GHz towards 29 Class 0 and Class 1 low-mass protostars as observed with Herschel/HIFI (in black, from Kristensen et al. (2012)), superimposed with the closest matching line profile from our grid of 48 models (red = X0 model, pink = S0, green = X1, blue = S1). Predicted profiles were calculated for the specific distance and rest velocity of each source without any arbitrary intensity rescaling. The model parameters (source model, , and i) are written in the top right corner of each panel, and are summarized in Table 3. The plotted model is of the same evolutionary Class as that attributed by Kristensen et al. (2012) on the basis of T_bol, except for three borderline sources denoted “Class 0/1” (see text). In Ser MM4, two different models are shown for the blue and red wings (X0 and S0, respectively).