Outline
• Announcements
• More tension infiltrometers
• More infiltration
Soil Physics 2010
Announcements
• One more review session in G217
Agronomy, today, noon – 2:00 pm.
• Homework 5 due Wednesday after
Spring Break
• Homework 5 is now posted. There is
a pdf file, and an Excel file.
Soil Physics 2010
Tension infiltrometer
(developed in part here at ISU;
patent held by Ankeny, Horton,
& Kaspar)
Water is applied to
the soil surface at a
negative pressure
Soil Physics 2010
Steady infiltration at
a given tension y
gives estimate of K(y)
Reservoir
Measuring infiltration
Bubble
tower
How do you supply water under tension?
Air inlet
Mariotte
bottle
Dh
Soil Physics 2010
Pulling air down
is like
pulling water up
Air coming out of
this hose has a
suction Dh:
That’s what is needed
to pull air down, and
bubbles out of the
inlet tube.
Air outlet
Mariotte bottle, part 2
Air inlet
This supplies water at a
constant tension – as
used in the hydraulic
diffusivity experiment.
Dh
q
B
Soil Physics 2010
Mariotte
bottle
Mariotte bottle, part 3
Air inlet
This is a useful
way to supply
water at a
constant head…
or to maintain
water at a
constant height.
Dh
Soil Physics 2010
Mariotte
bottle
Mariotte bottle, part 4
Change h by
moving end
of tube up or
down.
Dh1
Water exits
tube at
h = –Dh1 + Dh2
Dh2
Soil Physics 2010
Supply
Mariotte
Control
Tension infiltrometer
Reservoir
Mariotte control bottle (“bubble tower”)
and supply bottle (“reservoir”)
in a single portable unit.
Soil Physics 2010
Big reservoir, small Dh control
Fewer holes in big reservoir
Bubble
tower
Reservoir
The point of the tension infiltrometer
Soil Physics 2010
The tension infiltrometer allows
field measurement of a few points
on the K(h) curve, near saturation
where it changes fastest.
Bubble
tower
Why is the wetting front sharp?
q
L
2) If it weren’t, it would
become sharp.
z
K(q)
1) Need less gradient
when q is near qs.
Need big gradient at
low q.
3) At the front, capillary
forces dominate.
Behind the front,
gravity rules.
qi
Soil Physics 2010
q
Why is the wetting front sharp?
q
3) At the front, capillary
forces dominate. Behind
the front, gravity rules.
Behind the front, ym near zero.
Water in large pores can stay
in large pores → high K.
z
qi
Soil Physics 2010
At the front, ym is strong.
Water in large pores is pulled
into smaller pores → K drops.
More about infiltration
Specifically the Green & Ampt model
q
ym = 0 at saturation
L
Potential difference
z
from surface to wetting front:
qi
Distance
from surface to wetting front:
Gradient
L + ym
L
ym initial condition
Soil Physics 2010
Green & Ampt model i t   i 
c
q
b
I t  
I t 
i t   K s 
L
 i t  dt
b
 it 
t
20
L + ym
z
qi
L
As I (Sinfiltration)
increases, gradient
decreases.
Soil Physics 2010
infiltration rate, cm/hr
Gradient
15
soil-limited
soil and rain-limited
10
5
0
0
1
2
3
time, hrs.
4
5
Green & Ampt model
q
z
antecedent volume wetness:
Suction at wetting front:
porosity
Ksat
time step
precipitation rate
available porosity
20
infiltration rate, cm/hr
qi
rain-limited
mean time, cumulative distance to
15
hr
precip
wetting
soil-limitedfront
hydraulic
gradient
0.23
433 cm
0.47
0.1 cm/hr
0.025
5 cm/hr
0.24
Instantaneous rate
soilrain and soil
limited
limited
cumulative
infilt
infilt
infiltration
soil and rain-limited
10
5
0.025
0.050
0.075
0.100
0.125
0.250
0.375
0.500
0.104
0.208
0.313
0.417
4157.80
2079.40
1386.60
1040.20
0
0
Soil Physics 2010
1
2
3
time, hrs.
4
5
415.780
207.940
138.660
104.020
5.000
5.000
5.000
5.000
0.125
0.250
0.375
0.500
Philips model
Recall that horizontal infiltration can be
modeled as a diffusion process, with x(t)  t½
But for vertical infiltration, the gradient is
always at least 1, so x(t) → Ks at large t.
So for vertical infiltration, the short-time
infiltration rate is i(t)  t½ , but the long-term
behavior is more like i(t)  t.
Soil Physics 2010
J. R. Philips on infiltration
Infinite series solution, with the first 2 terms
dominating:
i t  
s
2 t
i t  
s
2 t
  A2  K 0  t 
0
K
I t  
3 A3 t
2
 i t  dt
 2 A4 t  ...
 s t  Kt
Early time: diffusion term dominates
Late time: constant term dominates
Soil Physics 2010
– conceptually like Green & Ampt