Parameter space distribution of the H₂O far-infrared pumping excitation modelling with observed para-H₂O 2₀₂–1₁₁ or 2₁₁–2₀₂and ortho-H₂O(3₂₁–3₁₂)in each panel. ±1σ contours are shown for each plot. Different colours with different line styles represent different temperature components of the warm dust as shown in the legend. The explored warm dust temperature range is from 35 K to 115 K. The temperature contours that are unable to fit the data are not shown in this figure. From the figure, we are able to constrain the τ₁₀₀, T_warm and N_H2O /ΔV for the five sources. However, there are strong degeneracies. Thus, we need additional information, such as the velocity-integrated flux densities of J ≥ 4 H₂O lines, to better constrain the physical parameters.