Finite water-content vadose zone flow method
The finite water-content vadose zone flux method[1][2] represents a one-dimensional alternative to the numerical solution of Richards' equation[3] for simulating the movement of water in unsaturated soils.
The Richards equation is difficult to approximate in general because it does not have a closed-form analytical solution except in a few cases.
[4] The finite water-content method, is perhaps the first generic replacement for the numerical solution of the Richards' equation.
First, as an ordinary differential equation it is explicit, guaranteed to converge [5] and computationally inexpensive to solve.
The finite water content method readily simulates sharp wetting fronts, something that the Richards solution struggles with.
[6] The main limiting assumption required to use the finite water-content method is that the soil be homogeneous in layers.
However, the derivation employs a hodograph transformation[7] to produce an advection solution that does not include soil water diffusivity, wherein
These three ODEs represent the dynamics of infiltrating water, falling slugs, and capillary groundwater, respectively.
Furthermore, because the finite water-content method does not explicitly include soil water diffusivity, it necessitates a separate capillary relaxation step.
With reference to Figure 1, water infiltrating the land surface can flow through the pore space between
In the context of the method of lines, the partial derivative terms are replaced with: Given that any ponded depth of water on the land surface is
, the Green and Ampt (1911)[12] assumption is employed, represents the capillary head gradient that is driving the flow.
Therefore in the context of the method of lines: and, which yields: The performance of this equation was verified for cases where the groundwater table velocity was less than 0.92
[14] Results of that validation showed that the finite water-content vadose zone flux calculation method performed comparably to the numerical solution of Richards' equation.
The paper describing this method [2] was selected by the Early Career Hydrogeologists Network of the International Association of Hydrogeologists to receive the "Coolest paper Published in 2015" award in recognition of the potential impact of the publication on the future of hydrogeology.
