Soil Water Flow - Transport in the Atmosphere-Vegetation-Soil Continuum - page 160

h f h 0 0 θ i θ θ t

s f

s

At time t 1

At time t 2 > t 1
Figure 4.24 Green and Ampt model of iniltration: θ and h proiles at two times.

the iniltration rate will be at a maximum. When the wetting front moves away from
the soil surface, the inluence of the matrix head will decrease and also the iniltration
rate will decrease. The Green-Ampt iniltration model followed this reasoning and
adopted the following assumptions ( Figure 4.24 ):

1. Throughout the wetted zone, the volume fraction of water, θ t , is uniform and constant
with time.
2. The change of θ i to θ t at the wetting front takes place in a layer of negligible thickness.
3. The pressure head at the wetting front, h f , has a constant value, independent of the posi-
tion of the wetting front, s f .

These assumptions are quite realistic for iniltration into coarse-textured soils with
low initial water content, as wetting fronts are generally very sharp under those condi-
tions. From the irst assumption it follows that throughout the transmission zone the
hydraulic conductivity, k t , has a constant value. Besides, the lux density is the same
everywhere in the transmission zone.
Assuming negligible thickness of the water layer on the soil surface, h = 0 at s = 0,
and using the second and third assumption, Darcy's law for Green-Ampt iniltration
can be written as:


 


 

==− ∂

∂ =− ∂

H
s ∂ + ∂

h
s

z
s

h
s


 



Iq k k

  =− −

k

f

1 (4.28)

t

∂

f

The cumulative iniltration is:

∞
∫ θθ θθ
0

− ( ) = ( )

I = d s s (4.29)

cum t i t i f

s =