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),

Ks = saturated hydraulicconductivity (cm/s),

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

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

Zf =depth
of the wetting front(cm).

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



where,

θi = initial moisture content(dimensionless) ,

θs = 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=(θs-θi),we can draw:



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