Summary of the Article on Soil Water:

## Soil Water Modeling

The article discusses the modeling of soil water in a multi-layer system, where the vertical soil moisture transport is governed by various processes, including infiltration, surface and subsurface runoff, gradient diffusion, gravity, and canopy transpiration through root extraction.

### Conservation of Mass

The conservation of mass for one-dimensional vertical water flow in soils is described by the equation:

∂θ/∂t = -∂q/∂z - e

where θ is the volumetric soil water content, t is time, z is height in the soil column, q is the soil water flux, and e is a soil moisture sink term representing evapotranspiration loss.

### Darcy's Law and the Richards Equation

The soil water flux, q, is described by Darcy's law:

q = -k (∂ψ_h/∂z)

where k is the hydraulic conductivity, and ψ_h is the hydraulic potential, consisting of the soil matric potential (ψ_m) and the gravitational potential (ψ_z).

Substituting Darcy's law into the conservation of mass equation yields the Richards equation:

∂θ/∂t = ∂/∂z [k(∂ψ/∂z + 1)]

This equation is numerically solved to predict changes in soil water content, as described in the section on the numerical solution (Section 2.7.3.2).