a)F₆/F₄ (oH₂O 3₂₁−3₁₂-to-pH₂O 2₂₀−2₁₁) and b) F₆/F₂ (oH₂O 3₂₁−3₁₂-to-pH₂O 2₀₂−1₁₁) line flux ratios as a function of the 75-to-100 μm far-IR color. Blue symbols: N_H2O/ΔV = 10¹⁵cm^-2/ (km s^-1) and τ₁₀₀ ≤ 0.1; black: N_H2O/ΔV = 5 × 10¹⁵cm^-2/ (km s^-1) and τ₁₀₀ ≤ 0.1; red: N_H2O/ΔV = 5 × 10¹⁵cm^-2/ (km s^-1) and τ₁₀₀ = 1.0; green: N_H2O/ΔV = 10¹⁵cm^-2/ (km s^-1) and τ₁₀₀ = 1.0; magenta: same as blue symbols but with collisional excitation included with T_gas = 150 K and n_H2 = 3 × 10⁵ cm^-3. The small numbers close to the symbols indicate the value of T_dust . The observed averaged ratios for strong-AGN and HII+mild-AGN sources (Y13) are indicated with dashed horizontal lines, and indicate that the regions probed by the H₂O submm emission are characterized by warm dust (T_dust ≳ 45 K).