An analytical approximation method for the linear source soil infiltrability measurement and its application

SummarySoil infiltrability is the fundamental feature for soil infiltration. There exist many soil infiltration rate measurement methods. In this paper, an analytical approximation solution to the mathematic model for soil infiltrability estimation with the linear source method (Mao et al., 2008) is presented, based on the mass-balance principle, which, when the supplied flow rate is constant, produces a cumulative infiltration equivalent to the Lewis–Milne equation by ignoring water ponding at the soil surface (Lewis and Milne, 1938). Both the wetted area-time function and the infiltrability-time function in the analytical solution were assumed as the forms of exponential functions. Laboratory recorded data in the linear source experiments were used to estimate the wetted area-time function. Mass balance principle was used to estimate the infiltration-time function, as related to the wetted area-time function. The results calculated with the analytical solution and those estimated with the numerical solution and “direct” and “inverse” methods proposed by Philip and Farrell (1964) based on the Kostiakov and Philip infiltration models were compared. The precisions of these four methods were estimated based on the mass/water balance principle, by comparing the recovered water volume from the soil infiltrability-time functions and the actually supplied water. The analytical solution produced the lowest errors of 6.5%, as compared with 6.6–10.8% errors of the other three methods. The steady infiltration rate estimated with the analytical solution of the linear source method is 50.37 mm/h while the numerical solution underestimated the steady infiltration rate by 24.9% as 37.81 mm/h. The most important meaning of this analytical solution is that both the soil infiltrability and the cumulative infiltration can be expressed in analytical function and calculated from the determined continuous infiltration formula as well. This study provides a good alternative tool for relevant research studies, such as rainfall–runoff process prediction, hydrologic models and irrigation system design and management.

► A new analytical solution to the linear source method was developed.
► The limitation of the numerical solution was overcome.
► The precision of the new solution is the highest compared with other six methods.