Modelling the Impact of Initial Water Content on Sorptivity and β Parameters of the Cumulative Infiltration Curve

Cumulative infiltration is a key factor for the accurate determination of the soil water balance. The 1D QEI model, which incorporates the hydraulic conductivity, K , for initial ( θ i ) and saturated ( θ s ) volumetric water contents the sorptivity, S , and the β parameter, has become a popular formulation to simulate the cumulative infiltration curve. However, given the complexity of estimating S and β for variable values of the hydrological studies tend to rely on infiltration measurements conducted under dry initial soil conditions, often overlooking how initial water content affects the shape of the infiltration curve. To address this issue, this work proposes two simple empirical functions (PTF) relating both S and β to Δ θ . These PTF, which were developed based on the corresponding analytical solutions for S and β , were applied to different values of Δ θ and six synthetic soils with textures ranging from loamy sand to clay. Keeping θ s constant, increasing values of θ i , from the residual water content, θ r , to θ s , were evaluated. The numerical consistency of the new models was evaluated by comparing the cumulative infiltration curves generated by applying the analytical solutions and the proposed PTFs to the QEI function for different soil textural characteristics and Δ θ values against the corresponding simulations performed with HYDRUS‐1D. The results demonstrated that θ i significantly influences the cumulative infiltration curve. While linear relationships passing through the origin ( R 2 = 0.99; p < 0.001) were observed between S 2 and Δ θ , asymptotic growth functions characterized the relationships between β and Δ θ ( R 2 = 0.99, p < 0.001). Excellent fits were also found between the HYDRUS‐1D simulations for increasing values of Δ θ and those generated with the QEI model using both the analytical solutions and the proposed PTF approaches. The results suggest that θ i must be considered in infiltration models to ensure the accuracy of hydrological studies. Unsaturated S and β values can be accurately estimated from data easily obtained through disc infiltration experiments.