Frequency domain-based analytical solutions for one-dimensional soil water flow in layered soils

Solutions of the linearized Richardson-Richards Equation (RRE) for one-dimensional soil water flow in layered soils with sinusoidal flux in the frequency domain are derived. We evaluate the accuracy of our analytical and other analytical solutions by comparing them with results from a standard numerical model. Our analytical solution agrees with the numerical solution under multi-layered heterogeneous soil, while others disagree. We also demonstrate the capability of the proposed solution to simulate soil moisture dynamics under a realistic, multi-frequency flux case. The procedure described in the paper is valid for any series of arbitrary periodic flux superpositions for layered heterogeneous Ks${{K}_s}$. Moreover, our solution is efficient in the calculation compared with numerical solutions, especially when dealing with long-time series soil moisture, which can provide a validation of numerical models. Analytical solution to Richardson-Richards equation is derived for layered heterogeneous soil under periodic boundary. Steady and fluctuating components can be directly estimated under layered heterogeneous soils. Analytical solution has advantages in accuracy and efficiency for validation of numerical models.