*3.3. Green–Ampt Model*

This model represents infiltration into homogeneous soils under the conditions of continuously saturated soil surface and uniform initial soil moisture as:

$$f\_{\mathfrak{c}} = K\_{\mathfrak{s}} \left[ 1 - \frac{\psi\_{av}(\theta\_{\mathfrak{s}} - \theta\_{\mathfrak{l}})}{F} \right],\tag{15}$$

where *F* the cumulative depth of infiltrated water. To express the infiltration as a function of time, this equation can be solved after the substitution *fc* = *dF*/*dt*. The resulting equation [45] is:

$$F\_{\parallel} = K\_s t - \psi\_{av} (\theta\_s - \theta\_i) \ln \left[ 1 - \frac{F}{\psi\_{av} (\theta\_s - \theta\_i)} \right]. \tag{16}$$

Equation (16) assumes immediate ponding and an infinite supply of water at the surface. Under more general conditions, with a constant rainfall rate *r* > *Ks*, that begins at the time *t* = 0, surface saturation is reached at a time *tp* > 0. For *t* ≤ *tp*, the infiltration rate *q*0 is equal to *r* and later to the infiltration capacity. Mein and Larson [104] formulated this process through Equation (15) as:

$$r - K\_s = -\frac{K\_s \psi\_{a\upsilon} (\theta\_s - \theta\_i)}{\int\_0^{t\_p} r \, dt} \,\, \,\tag{17}$$

which leads to the determination of *tp* as:

$$t\_p = -\frac{K\_s \psi\_{dv} (\theta\_s - \theta\_i)}{r(r - K\_s)}.\tag{18}$$

Furthermore, for *t* > *tp*, Equation (16) becomes:

$$F = F\_p - \psi\_{av} (\theta\_s - \theta\_i) \ln \left[ \frac{F - \psi\_{av} (\theta\_s - \theta\_i)}{F\_p - \psi\_{av} (\theta\_s - \theta\_i)} \right] + K\_s (t - t\_p) \tag{19}$$

Equation (19) can be solved at each time, for example, by successive substitutions of *F* which is then substituted into Equation (15) to obtain the corresponding value of *fc*.
