Figure 7.4.2 (p. 235)
(a) Cross-section through an unsaturated porous medium; (b)
Control volume for development of the continuity equation in
an unsaturated porous medium (from Chow et al. (1988)).
Porous media definitions
[Note: Many are analogous to snow properties.]
Soil matrix properties:
 particle density
m 
m ass of m ineral grains
Mm

volum e of m ineral grains
Vm
;
typically  m  2650 kg m
 bulk density
b 
m ass of m ineral grains

Mm
volum e of soil
Vs
 porosity
  n  s 
volum e of voids

volum e of soil
V void

  1
Vs
Water content variables: (only relevant for unsaturated zone)
 volumetric water content
 
volum e of w ater
volum e of soil
 relative saturation
s

s
;
0  s 1

Vw
Vs
;
0    s
b
m
-3
[Note: Soil type/texture is used to identify soil hydraulic
properties via tabulated relationships.]
“Brooks-Corey” or “Clapp-Hornberger” Soil
Hydraulic Parameters (based on soil type)
porosity
Sat.
hydraulic
conductivity
(Ks)
Sat. matric
head (|ψs|)
Table 7.4.1 (p. 241)
Green-Ampt Infiltration Parameters for Various Soil Classes
Figure 7.4.3 (p. 237)
Moisture zones during infiltration (from Chow et al. (1988)).
Figure 7.4.4 (p. 237)
Moisture profile as a function of time for water added to the soil
surface.
Figure 7.4.5 (p. 238)
Rainfall infiltration rate and cumulative infiltration. The
rainfall hyetograph illustrates the rainfall pattern as a
function of time. The cumulative infiltration at time t is Ft or
F(t) and at time t + Δt is Ft + Δt or F(t + Δt) is computed
using equation 7.4.15. The increase in cumulative infiltration
from time t to t + Δt is Ft + Δt – Ft or F(t + Δt) – F(t) as shown
in the figure. Rainfall excess is defined in Chapter 8 as that rainfall
that is neither retained on the land surface nor infiltrated into the
soil.
Figure 7.4.6 (p. 238)
Variables in the Green-Ampt infiltration model. The
vertical axis is the distance from the soil surface, the
horizontal axis is the moisture content of the soil (from
Chow et al. (1988)).
Figure 7.4.8 (p. 243)
Ponding time. This figure illustrates the concept of ponding
time for a constant intensity rainfall. Ponding time is the
elapsed time between the time rainfall begins and the time
water begins to pond on the soil surface.
Modeling Actual Infiltration using the timecompression approximation (TCA)
Actual infiltration model:

P , t0  t  t p

f (t )  
 f c (t  t c ) , t p  t  t r
TCA condition #1:
f c (t  t c ) t  t  f c (t p  t c )  P
p
TCA condition #2:
t p  tc

0
f c (t ) dt  P  t p
Depending on the particular infiltration
capacity model chosen (Philip or GreenAmpt), the two TCA conditions (equations)
can be solved explicitly for the two unknowns
(time to ponding and compression time) to get
an explicit expression for the actual
infiltration: f(t).
See supplementary TCA notes for more
details…
From actual infiltration model, can compute
cumulative infiltration and/or infiltration
excess runoff:
tp
tr
F 

f (t ) dt 
0
tr
Q 
P
0
tr
 P dt
0


f c (t  t c ) dt
tp
tr
f (t ) dt 
P
tp
f c (t  t c ) dt  P t r  F