Green & Ampt equation

At any time, , the penetration of the infiltrating wetting front will be . Darcy's law can be stated as follows:

K_sI(t)$ is the cumulative infiltration at time , and is equal to .

Using this relation for to eliminate and performing the integration yields,

\begin{table}

\centering
\begin{tabular}{ l l l l }

with & & infiltration amount &

& $K_s$ & hydr. conductivity & $[cm/h]$ \\
& $h_f$ & wetting front pressure head (negative) & $cm$ \\
& $h_s$ & water pressure at surface (ponding) & $cm$ \\
& $\theta_s$ & moisture content at saturation & $-$ \\
& $\theta_0$ & antecedent moisture & $-$ \\

\end{tabular} \end{table} I(t)$ to one side of the equation:

$$

The R-program to calculate infiltration amounts with Green & Ampt looks like this:

<<GreenAmpt, fig=TRUE, height=4.0, echo=FALSE>>= I <- seq(0,100,by=1.0) t0 <- 0.05 ts <- 0.25 hs <- 0.0 # cm hf <- -12.0 # cm Ks <- 8.0 # cm/hour t <- 1/Ks*((I-(hf-hs)*(ts-t0))*log(1-(I/((hf-hs)*(ts-t0))))) # hours plot(t,I,xlim=c(0,6),ylim=c(0,25),xlab="t [hour]", ylab="I in [cm]")