Soil Water Flow - Transport in the Atmosphere-Vegetation-Soil Continuum - page 159

Rate

Infiltration rate
according to Horton

End of
shower

Start of
runoff

Rainfall rate

Runoff

Saturated conductivity

Time

Figure 4.23 Use of the equation of Horton to determine amounts of iniltration and
runoff.

=+ −

I I

 

− β t

 

I I t

0 f

1 − e (4.27)

cumf

β

Figure 4.23 shows how the amount of runoff can be determined with Horton's model.
Runoff starts when the iniltration rate is equal to the rainfall rate. Before this time
all rainfall did iniltrate. The iniltration in the runoff period follows from Eq. ( 4.27 ):
take the difference between I cum at the end of the shower and at the start of runoff.
The cumulative runoff follows from the difference between total rainfall and total
iniltration.

Question 4.11: Runoff occurs during an intensive rain shower with a mean intensity of
25 mm h -1 and duration of 2 hours. We use the Horton iniltration equation to calculate
the amount of runoff. The Horton soil parameters are: I 0 = 70 mm h -1 , I f = 8 mm h -1 and
β = 1.5 h -1 .
a) At which time starts the runoff?
b) How much water has iniltrated at this time?
c) How much rain water iniltrates between the start of the runoff and the end of the
shower?
d) How much is the total runoff during this rain shower?

4.8.2 Green-Ampt Iniltration Model
Because iniltration causes the soil to become wetter with time, water at the front
edge of the wetting pattern advances under the inluence of matrix head gradients as
well as gravity. During the early stages of iniltration when the wetting front is near
the surface, the matrix head gradients predominate over the gravitational head, and