Water Flow in the Field

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Water Flow in the Field
Infiltration Rate (i) The volume flux of water
flowing into the soil profile per unit area the
maximum rate at which soil in a given condition
at a given time can absorb water. Cumulative
Infiltration (I) The cumulative amount of
infiltration over a given time period. Infiltrabil
ity Combined terminology to characterize the
infiltration properties of a soil.
2
If the application rate R is lt imax water will
infiltrate as fast as it is applied and is flux
controlled. If the application rate is gtimax
water infiltration is instead profile controlled.
3
The infiltration rate into a dry soil is
characteristically very rapid initially, the
decreases with time to a relatively constant or
final value.
What is the dominant driving force initially?
ii
What is the dominant long term driving force?
i
if Ks
t
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Typical moisture distribution characteristics
during ponded infiltration
?
saturated
transition
z
transmission
wetting front
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Typical moisture distribution characteristics
during ponded infiltration
?
saturated
t1
transition
z
t2
transmission
t3
wetting front
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?H
t1
z
t2
?H 1
t3
Why does the hydraulic gradient approach unity
over time?
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Effect of initial water content on infiltration
?3gt?2gt?1
?1
?1
i
I
?2
?2
?3
?3
t
t
8
t
?1
z
?2
?3
?3gt?2gt?1
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Truckee Meadows Water Conservation Program
Peak Summer ET 5.0 cm/week Average Water
Year Irrigate 2 times/week Drought Water
Year Irrigate 1 time/week Justification Conserve
water and develop a healthier and more deeply
rooted lawn.
Will this approach work based on what you now
know about the properties and characteristics of
infiltration and water flow in fine, medium, and
coarse textured soils?
10
Consider first that the irrigation objective is
to replace stored soil moisture i.e., no
long-term moisture deficit. Consider next what
happens when you have a coarse textured soil,
then a fine textured soil. What kind of a water
management program would likely be more effective
and why?
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Infiltration into a layered soil condition.
Coarse over fine
i
Fine over coarse
t
Layer interface
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Rain-Pond Infiltration
If rainfall intensity (R) is less than the
initial infiltration rate, water will infiltrate
under unsaturated flow. Hence, at long intervals
of time ?H approaches unity and the flux is equal
to the application rate which is equal to
K(?). The lower the supply rate, the lower the
degree of saturation thus non-ponding and
pre-ponding infiltration rates are supply
controlled.
14
On the other hand, if water supply to the surface
is greater than the soils infiltration rate,
free water begins to accumulate (rain-pond),
taking the form of water pockets until the
surface storage capacity is satisfied. Rain-pond
infiltration, as is ponded infiltration, is
therefore profile controlled. Once the surface
storage capacity has been satisfied, runoff
begins.
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Consider an event of variable intensities and
duration
i (cm/min)
Given Event 1 hour in duration at an intensity
of 0.06 cm/min
1.0
.08
.06
Cumulative Runoff
.04
.02
Runoff begins about 0.25 hr after the start of
the event
0.2
0.4
0.6
0.8
1.0
t (hr)
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Theoretical Considerations

• We can apply the General Flow Equation to the
  infiltration process by assuming the appropriate
  boundary conditions.
• GFE ??/?t ?/?z D(?)??/?z ?K(?)/?z
• ?i is constant through the soil profile
• At tgt0, water entry at the face is maintained at
  some higher water content ?o, where ?ogt?i
• D(?) is known or assumed and
• The rate of advance of ? over distance is
  proportional to t1/2.

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Green-Ampt (1911)
This model characterizes infiltration into an
infinite medium of some initial water content ?i,
where the surface at tgt0 is held at a constant
?0. i ic b/I where ic is the asymptotic
steady infiltration flux reached when t and I
become very large. Since at t 0, I also is
zero, the equation predicts an initially infinite
infiltration rate that decreases steeply at
first, then more moderately as it tends towards
its final value.
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• The assumptions for application are
• that the entire wetted region is at the same ?0
  and that the wetting front is infinitely sharp
• K(?) and D(?) are constant
• and h at the wetting front is constant.
• The application is empirical since the final h
  must be determined experimentally. This model can
  be applied to both horizontal and vertical
  infiltration.

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Through the application of Darcys Law (see
example 4.1 in Jury Horton) I ??
(2D0t)1/2 where D0 soil water diffusivity of
the wet soil region K0(?h/d?), and dI/dt i
?? (D0/2t)1/2 NOTE The infiltration rate is
proportional to t-1/2.
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Kostiakov (1932)
An empirical model that also provides for an
infinite I, but implies that as t increases
I approaches zero rather than some non-zero
constant. i ßt-n where ß and n are
constants. Commonly used by engineers, but is
relevant only to horizontal infiltration where
there is no gravity gradient.
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Horton (1940)
This model provides I as an explicit function of
t. I ict (i0 ic)/k 1 e-kt dI/dt i
ic (io ic)e-kt where ic, i0, and k are the
defining constants. At t 0, i is not infinite
but takes on some finite value i0, and the
constant k determines how quickly i will decrease
from i0 to ic. Difficult to apply because it
contains 3 constants, all of which must be
evaluated experimentally.
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Philip (1957)
Characterizes infiltration into an infinitely
deep (or long) homogeneous porous medium of an
initially uniform water content (?i) that has as
the inflow boundary a higher water content ? gt
?i. Horizontal Infiltration I St1/2 dI/dt i
S/2t1/2 where S is the characterizing
constant known as sorptivitiy.
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Vertical Infiltration I St1/2 At .. dI/dt
i S/2t1/2 A where A is considered
analogous to ic at some K(?). Sorptivitiy (S) is
a function of the water content boundary
conditions, increases as the difference between ?
and ?i increases, and is measured as the slope of
the I vs. t1/2 relationship.
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Philips Model Example for Rain Pond
Infiltration Jury Horton
Assume that the ponded infiltration rate (maximum
possible) into a soil can be characterized using
the Philips infiltration model. Calculate 1)
the time at which the ponded infiltration rate P
equals the rainfall rate R and 2) the amount of
time required for a process with a constant
rainfall rate R to add the same total amount of
infiltration (I) water to the soil as in the
ponded process.
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Given Ponding will not occur under constant
rainfall input until some time at which the
applied rate exceeds the value of the maximum
infiltration rate under continual ponding. Also,
more water will enter the soil prior to ponding
when the rainfall rate is lower than when it is
higher. Solution i P S/2t1/2 A (2(P-A))/S
1/t1/2 t1/2 S/(2(P-A)) t S2/(4)(P-A)2
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In this first scenario, P is the maximum final
infiltration rate and t is the minimum time
required to initiate ponding. In the second
scenario, cumulative infiltration under ponding
is equal to the cumulative rainfall over a given
time interval (Pt). Hence, I Pt St1/2
At t(P-A)/S t1/2 t1/2 S/(P-A) t S2/(P-A)2
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Example Calculation
Given Horizontal and Vertical Infiltration ?i
0.10 ?s 0.50 Depth to wetting front 10
cm t 16 min K(?s) 10-2 cm/min Find the
approximate value for S and determine I for 10,
100, 1000, 10000, and 100000 min.
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First consider horizontal infiltration I St1/2
??d S ??d/t1/2 S (0.50 0.10)(10
cm)/(16)1/2 1.0 cm/min1/2 Hence, at t 10
min, I 3.16 cm
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