Philip’s infiltration equation for variable-head ponded infiltration

Abstract

Summary Often the Philips infiltration equation has been applied as a fitting equation or as the subsurface component in run-off models. Many a time, the theoretical assumptions for the theory have not been fulfilled. Originally Philip showed that the power series solution can be applied for a constant-head boundary condition at the soil surface. It has later been showed that the power series solution can be applied for falling head infiltration. More general, it is here shown that the power series solution can be applied for variable-head ponded infiltration when the ponding depth is described as a power series in t n 2 , n = 0,1,2, ⋯ . It is shown that the sorptivity only is dependent on the initial ponding depth and not the ponding depth for t > 0. Results obtained using the power series theory and other solution methods of Richard’s equation are finally compared.