Calculating changes in the volumetric moisture content profile as a function of time is the

critical step in determining the state of the ground. This is in part due to the highly

nonlinear nature of the parameters associated with soil moisture.

The flow of water (ν) through a porous media is governed by Darcy's Law, which states

that

∂*h*

(5.1)

∂*z*

the surface, and *h *(*m*) the total head equals the elevation head, or depth, (*z*) minus the

pressure head (ψ), i.e., *h *= *z *cos ϕ - Ψ = *z *cos ϕ - *P*f / ρw g , *P*f (*Pa*) is pressure, ρw (*kg/m*3)

is the density of water, ϕ is the surface slope, and *g *(*m*2/s) is gravity. If the soil is

unsaturated, ψ < 0 and *h *> *zcos*ϕ. For saturated soils ψ ≥ 0, requiring that *h *≤ *z*ecosϕ.

Also governing the flow of moisture through a soil is the conservation of mass, which

states that the time rate of change of the moisture content in a given volume equals the

net gain/loss of fluid in the volume, i.e.,

∂θw

∂*v * ρ ∂θi

=- - i

+ *sources *- *losses*

(5.2)

∂*z * ρw ∂*t*

∂*t*

where θw (*cm*3/cm3) is the volumetric moisture content, θi (*cm*3/cm3) is the volumetric ice

content, ρi (*kg/m*3) is the density of ice, and *t *(*sec*) is time. Equation (5.2) assumes that

changes with respect to time in the soil porosity and water density are negligible

compared to changes in the soil moisture and total head. Further discussion on the change

in ice content is found in Chapter 6. The source and loss terms in this equation account

for occurrences such as runoff and plant root uptake. The latter is for future development.

Equation (5.2) is subject to the following flow boundary conditions at the surface and at

the bottom of the soil column:

@*z*=0

(5.3)

@ *z *= *z*bot

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