One-dimensional nonlinear steady infiltration

An approximate solution of the one-dimensional nonlinear steady infiltration with arbitrary plant withdrawal functions is presented. The solution is derived using perturbation expansion methods and is applicable for homogeneous soils for which the hydraulic conductivity function is of the rational power form. The soil domain is either a semi-infinite flow medium or a finite-depth medium overlying a shallow water table. The boundary condition at the surface of the soil is taken as the steady constant flux, and the bottom boundary condition is a prescribed head at a depth. The water extraction functions used herein include the uniform, the piecewise constant, and the exponential uptake. The perturbation solution showed very good agreement with the exact implicit solutions for various soil types and surface flux conditions. The approximate solution provided a basis on which explicit algebraic equations for parameter estimation can be derived. Numerical results show the effects of the soil type, surface flux, and rooting depths on the pressure distribution in the soil.