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Soil Physics 2010
Outline
• Announcements
• More tension infiltrometers
• More infiltration
Soil Physics 2010
• 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.
Announcements
Measuring infiltration
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
Steady infiltration at a given tension gives estimate of K()
Res
ervo
ir
Bubble tower
Soil Physics 2010
Soil Physics 2010
Mariotte bottle
How do you supply water under tension?
h
Air coming out of this hose has a suction h:That’s what is needed to pull air down, and bubbles out of the inlet tube.
Air inlet
Air outlet
Pulling air down is like
pulling water up
Soil Physics 2010
Mariotte bottle
Mariotte bottle, part 2Air inlet
This supplies water at a constant tension – as used in the hydraulic diffusivity experiment.
B
h
Soil Physics 2010
Mariotte bottle
Mariotte bottle, part 3
h
Air inlet
This is a useful way to supply water at a constant head…
or to maintain water at a constant height.
Soil Physics 2010
Mariotte bottle, part 4
h1
Water exits tube at
h = –h1 + h2
Control Mariotte
Supply Mariotte
h2
Change h by moving end of tube up or down.
Res
ervo
ir
Bubble tower
Soil Physics 2010
Tension infiltrometerMariotte control bottle (“bubble tower”)
and supply bottle (“reservoir”) in a single portable unit.
Big reservoir, small h controlFewer holes in big reservoir
Res
ervo
ir
Bubble tower
Soil Physics 2010
The point of the tension infiltrometer
The tension infiltrometer allows field measurement of a few points
on the K(h) curve, near saturation where it changes
fastest.
i
Soil Physics 2010
Why is the wetting front sharp?
z
L
K(
)
1) Need less gradient when is near s. Need big gradient at low .
2) If it weren’t, it would become sharp.
3) At the front, capillary forces dominate. Behind the front, gravity rules.
Soil Physics 2010
Why is the wetting front sharp?
i
z
3) At the front, capillary
forces dominate. Behind the front, gravity rules.
Behind the front, m near zero. Water in large pores can stay in large pores → high K.
At the front, m is strong. Water in large pores is pulled into smaller pores → K drops.
i
Soil Physics 2010
More about infiltrationSpecifically the Green & Ampt model
z
m initial condition
m = 0 at saturation
L
Potential difference from surface to wetting front:
Distancefrom surface to wetting front:
L + m
L
Gradient
Soil Physics 2010
Green & Ampt model
i
z
L
L + m
L
Gradient
As I (infiltration) increases, gradient decreases.
0
5
10
15
20
0 1 2 3 4 5
infi
ltra
tio
n r
ate,
cm
/hr
time, hrs.
soil-limited
soil and rain-limited
tIb
iti c
t
s ti
bKti
dttitI
Soil Physics 2010
Green & Ampt model
i
z
0
5
10
15
20
0 1 2 3 4 5
infi
ltra
tio
n r
ate,
cm
/hr
time, hrs.
soil-limited
soil and rain-limited
antecedent volume wetness: 0.23Suction at wetting front: 433 cmporosity 0.47Ksat 0.1 cm/hrtime step 0.025precipitation rate 5 cm/hravailable porosity 0.24
Instantaneous raterain-limited soil- rain and soil
mean time, cumulative distance to hydraulic limited limited cumulativehr precip wetting front gradient infilt infilt infiltration
0.025 0.125 0.104 4157.80 415.780 5.000 0.1250.050 0.250 0.208 2079.40 207.940 5.000 0.2500.075 0.375 0.313 1386.60 138.660 5.000 0.3750.100 0.500 0.417 1040.20 104.020 5.000 0.500
Soil Physics 2010
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:
...22
3
24
3002 tA
tAtKA
t
sti
Kt
sti
2 KttsdttitI
Early time: diffusion term dominatesLate time: constant term dominates
– conceptually like Green & Ampt