Green-Ampt Infiltration Model

There are two basic assumptions should be made before derivating the Green-Ampt infiltration model : one is the soil texture is uniform, the other is the soil above the wetting front is saturated.

Acoording to Darcy's law：

Because surface flux q is defined as positive up, and infiltration rate f is defined as positive down, we can draw:

in which,

H = the depth of ponding(cm),

K_s = saturated hydraulicconductivity (cm/s),

q = flux at the surface (cm/h), i.e. the infiltration rate,

ψ_f = suction at wetting front (negative pressure head),

Z_f =depth of the wetting front(cm).

Z_f can be related to the cummulative amount of infiltrated water, F[cm], by:

where,

θ_i = initial moisture content(dimensionless) ,

θ_s = saturated moisture content(dimensionless).

So, the relation between F and f can be written as:

When ponding, infiltration rate f is considered to be equal to rainfall intensity P, and H=0, then:

Time of ponding is given by 

Recognizing that f=dF/dt, H is considered to be very small, so

Separate variables in the differential equation above:

Use u substitution to integrate.

we get:

Integrate the previous equation

Substitute the original variables back into integrated equation, let Δθ=(θ_s-θi),we can draw:

Usually, the cumulative infiltration is given by the following equation: