Context :

Aims : As part of the WISH ( Water In Star-forming regions with Herschel ) key project , systematic observations of H _ { 2 } O transitions in young outflows are being carried out , with the aim of understanding the role of water in shock chemistry and its physical and dynamical properties .

In this paper , we report on the observations of several ortho- and para-H _ { 2 } O lines performed with the HIFI instrument towards two bright shock spots ( R4 and B2 ) along the outflow driven by the L1448 low-mass proto-stellar system , located in the Perseus cloud .
These data are used to identify the physical conditions giving rise to the H _ { 2 } O emission and infer any dependence with velocity .

Methods : We used a large velocity gradient ( LVG ) analysis to derive the main physical parameters of the emitting regions , namely n ( H _ { 2 } ) , T _ { kin } , N ( H _ { 2 } O ) and emitting-region size .
Comparison has been made with other main shock tracers , such as CO , SiO and H _ { 2 } and with shock models available in the literature .

Results : These observations provide evidence that the observed water lines probe a warm ( T _ { kin } \sim 400-600 K ) and very dense ( n \sim 10 ^ { 6 } -10 ^ { 7 } cm ^ { -3 } ) gas , not traced by other molecules , such as low- J CO and SiO , but rather traced by mid-IR H _ { 2 } emission .
In particular , H _ { 2 } O shows strong differences with SiO in the excitation conditions and in the line profiles in the two observed shocked positions , pointing to chemical variations across the various velocity regimes and chemical evolution in the different shock spots .
Physical and kinematical differences can be seen at the two shocked positions .
At the R4 position , two velocity components with different excitation can be distinguished , with the component at higher velocity ( R4-HV ) being less extended and less dense than the low velocity component ( R4-LV ) .
H _ { 2 } O column densities of about 2 10 ^ { 13 } and 4 10 ^ { 14 } cm ^ { -2 } have been derived for the R4-LV and the R4-HV components , respectively .
The conditions inferred for the B2 position are similar to those of the R4-HV component , with H _ { 2 } O column density in the range 10 ^ { 14 } -5 10 ^ { 14 } cm ^ { -2 } , corresponding to H _ { 2 } O/H _ { 2 } abundances in the range 0.5 - 1 10 ^ { -5 } .
The observed line ratios and the derived physical conditions seem to be more consistent with excitation in a low velocity J-type shock with large compression rather than in a stationary C-shock , although none of these stationary models seems able to reproduce all the characteristics of the observed emission .

Conclusions :