Green Ampt Infiltration

Soil composition. Subscripts s, w, a stand for...

Green-Ampt

Named for two men; Green and Ampt. The Green-Ampt^[1] method of infiltration estimation accounts for many variables that other methods, such as Darcy's law, do not. It is a function of the soil suction head, porosity, hydraulic conductivity and time.

$\int_0^{F(t)} {1-\psi\,\Delta\theta\over F+\psi\,\Delta\theta}\, dF = \int_0^t K\,dt$

where

ψ

is wetting front soil suction head;

θ

is water content;

K

is Hydraulic conductivity;

F

is the total volume already infiltrated.

Once integrated, one can easily choose to solve for either volume of infiltration or instantaneous infiltration rate:

$F(t)=Kt+\psi \, \Delta\theta \ln \left[1+{F(t)\over \psi \, \Delta\theta}\right].$

Using this model one can find the volume easily by solving for $F (t)$ . However the variable being solved for is in the equation itself so when solving for this one must set the variable in question to converge on zero, or another appropriate constant. A good first guess for $F$ is $K t$ . The only note on using this formula is that one must assume that $h 0$ , the water head or the depth of ponded water above the surface, is negligible. Using the infiltration volume from this equation one may then substitute $F$ into the corresponding infiltration rate equation below to find the instantaneous infiltration rate at the time, $t$ , $F$ was measured.

$f(t)=K\left[{\psi \, \Delta\theta\over F(t)}+1\right].$

1. Water Resources Engineering, 2005 Edition, John Wiley & Sons, Inc, 2005.

Pre 2014 Blogs

Green Ampt Infiltration

Green-Ampt

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