d infiltration
TRANSCRIPT
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SURFACE WATER HYDROLOGY (CE547)
Definition of terms used to describe water movement in the
unsaturated zone
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SURFACE WATER HYDROLOGY (CE547)
DEFINITIONS
Infiltration: the movement of water from soil surface into
the soil
Redistribution: the subsequent movement of infiltrated
water in the unsaturated zone of soil
Exfiltration: evaporation from the upper layer of the soil
Capillary Rise: the movement from the saturated zone
upward into the unsaturated zone due to surface tension
Recharge: the movement of percolating water from the
unsaturated zone to the subjacent saturated flow
Percolation: downward flow in the unsaturated zone
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SURFACE WATER HYDROLOGY (CE547)
Material Properties of Soil
Pore size and its distribution indicated by grain size distribution
(accumulative frequency plot of grain diameter (log scale) Vs Weight
fraction of grains with smaller diameter
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SURFACE WATER HYDROLOGY (CE547)
Material Properties of Soil (contd)
Particle Density (m) is the weighted average density of
the mineral grains up a soil
Bulk Density (b) is the dry density of the soil
Porosity,, is the proportion of pore spaces in a volume
of soil
m
mmV
m m
bs a w m
M M
V V V V
1 b
m
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SURFACE WATER HYDROLOGY (CE547)
SOIL-WATER STORAGE
Volumetric water content (or simply water content), , is
the ratio of water volume to soil volume
Measurement: The representative soil sample of known
volume is first weighed, then at 105oC the sample is dried
in oven, reweighed and calculated as
m
s
VV
are the weights before and after drying, respectively
swet sdry
w s
swet sdry
M M
V
Here M and M
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SURFACE WATER HYDROLOGY (CE547)
SOIL-WATER STORAGE (contd)
Degree of Saturation or Wetness, S, is the proportion of
pores that contain water
Total Soil-Water storage is expressed as a depth [L]
(volume per unit area), which is the product of the
volumetric water content times the thickness of the layer
w
a w
VS
V V
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SURFACE WATER HYDROLOGY (CE547)
Ranges of porosities, field capacities, and permanent wilting
points for soils of various textures.
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SURFACE WATER HYDROLOGY (CE547)
SOIL-WATER FLOW
Darcys Law:
x
-1
, q is the volumetric flow rate in the x-direction per unit
cross sectional area of medium (LT ),
z is the elevation above an arbitrary datum (L)
p is the water p
x h
h
d z pq K
dx
d pdzK
dx dx
where
-2
-1
h
ressure (FL )
K is the hydraulic conductivity of the medium LT
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SURFACE WATER HYDROLOGY (CE547)
SOIL-WATER FLOW (contd)
Pressure Head,
Darcys Law for vertical unsaturated flow
The relations between pressure and water content [()] and
between hydraulic conductivity and water content [Kh()] are
crucial determinants of unsaturated flow in soils
has dimensions Lw
p
1
z h
h
d zq K
dz
dK
dz
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SURFACE WATER HYDROLOGY (CE547)
Hydraulic Conductivity, Kh[LT-1], is the rate (volume per
unit time per unit area) at which water moves through a
porous medium under a unit potential-energy gradient.
Hydraulic-Conductivity-Water-Content Relations: For a
given soil, unsaturated hydraulic conductivity is very low
at low to moderate water contents; it increases
nonlinearly to its saturated value, Kh*, as the water
content increases to saturation.
SOIL-WATER FLOW (contd)
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SURFACE WATER HYDROLOGY (CE547)
Soil-Water Pressure:
The water table is the surface at which pressure (p) is
equal to zero (at atmospheric pressure)
Negative pressure is often called tension or suction and
is called tension head, matric potential, or martic suctionwhen p
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SURFACE WATER HYDROLOGY (CE547)
Pressure-Water-Content Relations Moisture-Characteristics curve is the relation between pressure
head,, (often plotted on a logarithmic scale) and water content,,
for a given soil
SOIL-WATER FLOW (contd)
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SURFACE WATER HYDROLOGY (CE547)
Analytical Approximations ofand KhRelations
SOIL-WATER FLOW (contd)
*
*
ae
b
b
ae
c
h h
c
h h
S S
K S K S
K K
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SURFACE WATER HYDROLOGY (CE547)
Hysteresis in the ()
relation for Rubicon sandy
loam
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SURFACE WATER HYDROLOGY (CE547)
Soil Water pressure (tension), , Vs. degree of saturation, S, for soils
of three different textures
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SURFACE WATER HYDROLOGY (CE547)
Representative Values of parameters
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SURFACE WATER HYDROLOGY (CE547)
Factors Affecting Infiltration
Gravity:The greater the depth of water over the
surface, the greater is the hydrostatic head orthe gravitational force.
Existing Soil Moisture: Dry Soil: Creates a strong capillary potential in the
capillary size pores between soil grains. The capillary
force is strongest just under the dry ground surface. Wet Soil: Wetness in the soil creates resistance to
infiltration
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SURFACE WATER HYDROLOGY (CE547)
Soils at surface: A loosened soil in a newly ploughedfield will infiltrate rainfall rapidly, but as the rain continues,
the soil is compacted and the infiltration rate is reduced.
Inwash of Fine Material: reduces the size of pore
openings, reducing infiltration.
Compaction by man and animals: Reduction ininfiltration results.
Natural processes:Burrowing by animals and insects,
provides additional openings for water to penetrate the soil.
Factors Affecting Infiltration (contd...)
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SURFACE WATER HYDROLOGY (CE547)
Vegetative Cover: provides protection for the
soil from compaction by rain mixed effect!!
Temperature: Viscosity of water increases with
decrease in temperature decrease in infiltration
Measurement Error: may occur due to the
entrapped air in the soil.
Factors Affecting Infiltration (contd...)
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SURFACE WATER HYDROLOGY (CE547)
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SURFACE WATER HYDROLOGY (CE547)
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SURFACE WATER HYDROLOGY (CE547)
Designation of hydrologic soil-profile horizons. Note that this figure is idealized
and that one or more of these horizons may be absent in a given situation
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SURFACE WATER HYDROLOGY (CE547)
Hydrologic Horizons: For describing water
movement in soils, a set of horizons are definedbased on the range of water contents and the soil-
water pressure. The depths of loaction and thethicknesses of these hydrologic horizons vary both
in space and time
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SURFACE WATER HYDROLOGY (CE547)
Groundwater Zone (Phreatic Zone):
Saturated, Pressure head in positive
If no groundwater flow, only hydrostatic pressure
Water table is at atmospheric pressure.
The level at which water would stand in a well
Fluctuations of water table seasonal climatic
variations
Recharge due to individual storm events is possible
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SURFACE WATER HYDROLOGY (CE547)
Tension-saturated zone (capillary fringe):
Entire zone of negative pressures (tension) above the
water table is known as vadose zone
Lowest portion of this Vadose zone is nearlysaturated, due to capillary effect. Surface tension
forces draw the water into the spaces above the
water table, creating the tension-saturated zone orcapillary fringe.
Here, the pressure is hydrostatic
Pressure at the top of this zone is ae= height of thecapillary rise in the soil
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SURFACE WATER HYDROLOGY (CE547)
Intermediate zone:
Enters through percolation from above and leaves by gravity
drainage.
Tension in this zone depends on soil texture, water content.
Most of the soil profile is occupied by this zone Root Zone (soil moisture zone):
Zone from which plant roots can extract water during
transpiration
Its upper boundary is the soil surface, while its lower boundary is
indefinite and irregular
Water enters by infiltration and leaves by transpiration,
evaporation and gravity drainage. Water content is usually above
PWP
May approach saturation following intense infiltration events, but
would be below field capacity most of the times, between events.
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SURFACE WATER HYDROLOGY (CE547)
Typical moisture profile development with a constant rainfall rate
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SURFACE WATER HYDROLOGY (CE547)
Infiltration rate versus time for a given rainfall intensity
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SURFACE WATER HYDROLOGY (CE547)
Infiltration curves for several rainfall intensities
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SURFACE WATER HYDROLOGY (CE547)
Quantitative Modeling of Infiltration at a Point
Analysis applies to representative soil volumes that are
large relative to the typical pore size
Water is assumed to move only in the liquid state and its
movement is not significantly affected by the flow of air in
the soil pores or by temperature or by osmotic gradients
Water is assumed to move vertically through inter-
connected inter-grain pores that are randomly distributed
throughout a quasi-homogeneous soil
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SURFACE WATER HYDROLOGY (CE547)
Richards Equation
Darcy's law for vertical unsaturated flow is combined with
conservation of mass to obtain the Richards equation, which
is the basic theoretical equation for infiltration into a homogeneous
porous medium.
h
Non-linear, No closed form anlytical solutions, except for highly
simplified - and K relations and boundary conditions.
Ri h d E ti ( td )
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SURFACE WATER HYDROLOGY (CE547)
The Richards equation can be used as a basis for numerical
modeling of infiltration, exfiltration, redistribution, by specifying
appropriate boundary conditions and initial conditions, dividing
the soil into thin layes, and applying the equation to each layer
sequentially at small increments of time.
The predictions from the numerical models are found to have
reasonably good agreement with laboratory and field measurement.
Richards Equation (contd...)
Richards Equation (contd )
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SURFACE WATER HYDROLOGY (CE547)
However, numerical solutions may not be directly useful in providing
conceptual overview of the ways in which various factors influence
infiltration
They are generally too computationally intensive for inclusion in
operational hydrologic models.
Thus there have been a number of attempts to develop approximate
analytical solutions to the Richards equation, for situations such as
infiltration.
Richards Equation (contd...)
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SURFACE WATER HYDROLOGY (CE547)
Soil Water Diffusivity
h
h h
KD K
2L T
b
ae
C
h hK K
3 2b bh ae hD b K
0 0ae hand D
Since
and
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SURFACE WATER HYDROLOGY (CE547)
Richards Equation
Recall
Darcys Law
Total head
So Darcy becomes
Continuity becomes
z
h
Kqz
zh
z
zq K
z
K Kz
D K
z
D K
Soil water diffusivity
Kz
Dzz
q
t
zq K Kz
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SURFACE WATER HYDROLOGY (CE547)
Infiltration
General Process of water
penetrating from groundinto soil
Factors affecting
Condition of soil surface,vegetative cover, soilproperties, hydraulicconductivity, antecedentsoil moisture
Four zones
Saturated, transmission,wetting, and wetting front
depth
Wetting Zone
Transmission
Zone
Transition Zone
Saturation Zone
Wetting Front
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SURFACE WATER HYDROLOGY (CE547)
Infiltration
Infiltration rate
Rate at which water enters the soil at the surface (in/hr or
cm/hr)
Cumulative infiltration
Accumulated depth of water infiltrating during given time
period
t
dftF0
)()(
)(tf
dt
tdFtf
)()(
Eq. 1
Eq. 2
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SURFACE WATER HYDROLOGY (CE547)
Hortonian Infiltration
Recall Richards Equation
Assume K and D are
constants, not a function oforz
Solve for moisture diffusion
at surface
Kz
Dzt
z
K
zDt
2
2
02
2
zD
t
ktcc effftf
)()( 0
f0initial infiltration rate, f
cis constant rate and k is decay constant
Eq. 3
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SURFACE WATER HYDROLOGY (CE547)
Hortons Infiltration curve and hyetograph
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SURFACE WATER HYDROLOGY (CE547)
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SURFACE WATER HYDROLOGY (CE547)
Hortonian Infiltration
0
0.5
1
1.5
2
2.5
3
3.5
0 0.5 1 1.5 2
Time
Infiltra
tion
rate,
k1
k3
k2
k1 < k2 < k3
fc
f0
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SURFACE WATER HYDROLOGY (CE547)
Green-Ampt Model
Physically based
Original proposition in 1911 by Green and Ampt
Subsequent development: Mein and Larson (1973)
Applies Darcys law and principle of conservation of
mass
In a finite difference formulation that allows view of the
infiltration process.
Good performance when compared with numerical
solutions of the Richards equation.
Idealized Conditions
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SURFACE WATER HYDROLOGY (CE547)
Idealized Conditions
Z : vertical axis (upward)
Z` : downward direction along the z-axis
f(t) : infiltration time at t [LT-1]
F(t): total amount of water infiltrated upto time t [L]
Consider a block of soil homogeneous to an infinite depth
Horizontal surface at which there is no ET
Initial water contentois invariant and
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SURFACE WATER HYDROLOGY (CE547)
Green Ampt Infiltration
Wetted Zone
Wetting Front
Ponded Water
Ground Surface
Dry Soil
0h
L
i
z
LLtF i )()(
dt
dL
dt
dFf
zh
Kz
Kf
fz
hKqz
MoistureSoilInitial
FrontWettingtoDepth
i
L
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SURFACE WATER HYDROLOGY (CE547)
Green Ampt Infiltration
(Cont.)
Apply finite difference to thederivative, between
Ground surface
Wetting front
Kz
Kf
Wetted Zone
Wetting Front
Ground Surface
Dry Soil
L
i
z0,0 z
fLz ,
KL
KKz
KKz
Kf f
0
0
FL
LtF )(
1
FKf
f
Kz
Kf
Eq. 4
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SURFACE WATER HYDROLOGY (CE547)
1
LK
dt
dL f
1
FKf
f
dt
dLf
Green Ampt Infiltration
(Cont.)
LtF )(
Wetted Zone
Wetting Front
Ground Surface
Dry Soil
L
i
z
L
dLdLdt
K
f
f
CLLtK
ff )ln(
Integrate
Evaluate the constant of integration
)ln( ffC
0@0 tL
)ln(L
LKtf
ff
Eq. 5
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SURFACE WATER HYDROLOGY (CE547)
Green Ampt Infiltration (Cont.)
)ln(
L
LKt
f
ff
)1ln(f
fF
KtF
1
FKf f
Wetted Zone
Wetting Front
Ground Surface
Dry Soil
L
i
z
See: htt ://www.ce.utexas.edu/ rof/mckinne /ce311k/Lab/Lab8/Lab8.html
Eq. 6
Eq. 7
Given K, t, ,and , a trial value of F is substituted on the right-hand side (agood trial value is F=Kt), and a new value of F calculated on the left-hand side,
which is substituted as a trail value on the right-hand side, and so on, until the
calculated values of F converge to a constant. The final value of cumulative
infiltration F is substituted into Eq. 7 to determine the corresponding potential
infiltration ratef.
Iterative solution
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SURFACE WATER HYDROLOGY (CE547)
Soil Parameters
Green-Ampt model requires
Hydraulic conductivity, Porosity, Wetting Front Suction
Head
Brooks and Corey
Soil Class Porosity Effective
Porosity
Wetting
Front
Suction
Head
Hydraulic
Conductivity
n e K(cm) (cm/h)
Sand 0.437 0.417 4.95 11.78
Loam 0.463 0.434 9.89 0.34
Clay 0.475 0.385 31.63 0.03
e r
(1 )i e es
e
res
Effective saturation
Effective porosity
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SURFACE WATER HYDROLOGY (CE547)
Ponding time
Elapsed time between the time rainfall begins
and the time water begins to pond on the soilsurface (tp)
Ponding Time
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SURFACE WATER HYDROLOGY (CE547)
Ponding Time
Up to the time of ponding, all rainfall hasinfiltrated (i= rainfall rate)
if ptiF *
1F
Kf f
1
* p
f
ti
Ki
)( KiiKt
fp
Potential
Infiltration
Actual Infiltration
Rainfall
Accumulated
RainfallInfiltration
Time
Time
In
filtrationrate,
f
Cumulative
Infiltration,
F
i
pt
pp tiF *
Eq. 8
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SURFACE WATER HYDROLOGY (CE547)
ln fP f pf P
FF F K t t
F
Eq. 9
Eq. 9 can be used to calculate the depth of infiltration after ponding, and
then Eq. 7 can be used to obtain the infiltration ratef.
Actual Infiltration Rate
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SURFACE WATER HYDROLOGY (CE547)
Example
Silty-Loam soil, 30%
effective saturation,
rainfall 5 cm/hr intensity
30.0
/65.0
7.16
486.0
e
e
s
hrcmK
cm
340.0)486.0)(3.01()1( ees 340.0*7.16
hr17.0
))(65.00.5(0.5
68.565.0
)(
KiKii
Kt f
p