Abstract

Analytical solutions to Richards' equation have been derived to describe the distribution of pressure head, water content, and fluid flow for rooted, homogeneous soils with varying surface fluxes. The solutions assume that (i) the constitutive relations for the hydraulic conductivity and water content as function of the pressure head are exponential, (ii) the initial water content distribution is a steady-state distribution, and (iii) the root water uptake is a function of depth. Three simple forms of root water uptake are considered, that is, uniform, stepwise, and exponential functional forms. The lower boundary of the rooted soil profile studied is a water table, while at the upper boundary time-dependent surface fluxes are specified, either infiltration or evaporation. Application of the Kirchhoff transformation allows us to linearize Richards' equation and derive exact solutions. The steady-state solution is given in a closed form and the transient solution has the form of an infinite series. The solutions are used to simulate the hydraulic behavior of the rooted soils under different conditions of root uptake and surface flux. The restricted assumptions for the solutions may limit the applicability, but the solutions are relatively flexible and easy to implement compared to other analytical and numerical schemes. The analytical solutions provide a reliable and convenient means for evaluating the accuracy of various numerical schemes, which usually require sophisticated algorithms to overcome convergence and mass balance problems.

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