An Exact Solution to the Linearized Richards Equation for Layered Media With Flexible Initial Condition

Abstract

AbstractSrivastava and Yeh (1991, https://doi.org/10.1029/90WR02772) derived an exact solution to the linearized Richards equation (LRE) for two‐layer medium infiltration using the Laplace transform (LT) method with a particular initial condition assumed, making the most pioneering contribution to the derivation of exact solutions to the layered‐medium LRE (i.e., ES‐LMLREs). However, the LT method is unsuitable for deriving an ES‐LMLRE that considers either an arbitrary initial condition or an arbitrary number of layers, or both, preventing further progress in developing ES‐LMLREs. Adopting a new solution strategy, namely a conjunctive use of the variable separation method and the transfer matrix method, we develop a novel exact layered‐medium‐LRE infiltration solution, overcoming the above difficulties. First, the proposed solution is successfully validated against the Srivastava‐Yeh solution. As a feature‐demonstration example, a layered‐medium water absorption process is simulated, and our solution well captures how the heterogeneity of hydraulic parameters affects the dynamics of this process. Moreover, the proposed solution is a valuable benchmark for related numerical models.