Probabilities for several rovibrational (de-)excitation of H₂O. The colour code is the same as in Figs. 5 and 6. Circles of the same colour refer to the excitation process while solid or dashed lines the opposite. Note: P^eff (v′ ← v) is only weakly dependent on x (i.e. temperature). It is used to obtain a cubic polynomial fit P(v' ← v) in Eq. (10) for each transition v' ← v. For convenience, the vertical dashed line at x = 0 gives the coefficient value of a₀ at 300 K, evaluated by the analytical fit as ${10}^{a_0}$; see Eq. (8).