Investigation and parameterization of the ponding height effect on dynamic suction head estimation in the Green-Ampt model

The Green-Ampt model (GAM) is a widely used infiltration model, which assumes a sharp wetting front with a static effective suction head. Studies have shown that the suction head is related to the infiltration rate (i.e., the dynamic effective suction head, S). A power law relationship describing S∝-αCaβ, where Ca is the capillary number, and α and β are fitting parameters, has been used to modify the GAM and improves the simulation of the infiltration, especially during the early stage. However, studies also have pointed out that ponding height affects the optimization of the effective suction head in the classical GAM. To clarify and quantify the ponding height effect on the dynamic effective suction head of the modified GAM, we conducted one-dimensional vertical infiltration experiments by maintaining a ponding water on the top of the sand columns (including 80 constant ponding height experiments and 13 falling ponding height experiments). The results show that the power law relationship can be simplified to S∝-αCa (β=1) for all experiments, and the optimized equilibrium suction is independent of the ponding height. On the other hand, decreases in the initial ponding height for the falling ponding height experiments or in the fixed ponding height for the constant ponding height experiments result in increases in optimized α. To eliminate the effect of ponding height on the parameter optimization, we successfully derived a new formula for the dynamic effective suction head with ponding height-independent parameters.