As outlined in our paper, we developed a model which is able to explain all recorded THz pump-probe data at 12.3 THz in the static water cell as well as in the liquid jet. The model includes an instantaneous temperature-dependent response by an acoustic phonon, an inherent non-linear response of water, and a slower thermal response. The order of magnitude of the non-linear contributions agrees with previous experimental results by us² and other groups (see ref. 32, 33 and 35 in ref. 1) as well as with simulations², which predict an enhanced non-linear response of water in the frequency range of the libration.