Experimental validation of empirical formulas incorporating vertical soil temperature dynamics for phreatic evaporation

Phreatic evaporation is a critical link in the vertical interactions between surface water and groundwater; accurate quantification is essential for assessing shallow groundwater resources in the Huaibei Plain. This study analyzes the influence of soil temperature at different water table depths on phreatic evaporation using meteorological observations and data collected by large-scale lysimeter arrays at the Wudaogou experimental station between 2010 and 2019. A temperature coefficient is proposed to account for the relative difference between soil temperature at the surface and at water table depth. It is incorporated into three empirical formulas for phreatic evaporation to account for vertical soil temperature dynamics. Phreatic evaporation estimates derived from the original (E₀) and improved (E_i) formulas are compared with observations (E_obs). Results indicate that: ① Agreement between E_i and E_obs is higher than that between E₀ and E_obs. Relative to E₀, E_i improves overall accuracy by 5.89%—7.00% and reduces the relative error by 9.55%—10.13%. ② Among the improved formulas, the power function outperforms the modified Averianov and Ye Shuiting formulas. Accuracy improvement is the largest for a water table depth of 0.6 m. ③ Total-order and first-order sensitivity indices reveal that, in the improved formulas, the sensitivity of H is the highest, while the sensitivity of E₀ is the lowest, further confirming the necessity of incorporating soil temperature effects into phreatic evaporation calculations.