Infiltration
ERS 482/682
Small Watershed Hydrology
ERS 482/682 (Fall 2002)
Lecture 7 - 1
Definitions
• infiltration:
– process by which water enters the soil surface
• infiltration rate, f(t): [L T-1]
– rate at which water enters the soil surface
• water-input rate, w(t): [L T-1]
– rate at which water arrives at the soil surface
• infiltration capacity, f*(t): [L T-1]
– maximum rate at which infiltration can occur
• depth of ponding, H(t): [L]
– depth of water standing on the surface
ERS 482/682 (Fall 2002)
Lecture 7 - 2
Definitions
• percolation
– downward movement of water through the soil
• hydraulic conductivity, Kh: [L T-1]
– rate at which water moves through a porous medium
under a unit potential-energy gradient
• sorptivity, Sp: [L T-1/2]
– rate at which water will be drawn into an unsaturated soil
in the absence of gravity forces
• soil-water pressure or matric potential, : [L]
– water pressure (tension) head in a soil
• air-entry tension, ae:
[L]
– pressure head when significant volumes of air begin to
appear in soil pores; occurs at the capillary fringe (i.e.,
height of the tension-saturated zone)
ERS 482/682 (Fall 2002)
Lecture 7 - 3
Why is infiltration important?
ERS 482/682 (Fall 2002)
Lecture 7 - 4
Why is infiltration important?
• Determines availability of water for
overland flow
– Flood prediction
ERS 482/682 (Fall 2002)
Lecture 7 - 5
Why is infiltration important?
• Determines availability of water for
overland flow
– Flood prediction
– Irrigation plans
ERS 482/682 (Fall 2002)
Lecture 7 - 6
Why is infiltration important?
• Determines availability of water for
overland flow
– Flood prediction
– Irrigation plans
– Runoff pollution
• Determines how much water goes into the
soil
– Groundwater estimates
– Water availability for plants
ERS 482/682 (Fall 2002)
Lecture 7 - 7
Infiltration conditions
wt 
• No ponding: H t   0
f t   wt   f * t 
Soil column
ERS 482/682 (Fall 2002)
Lecture 7 - 8
Infiltration conditions
wt 
• No ponding: H t   0
f t   wt   f * t 
• Saturation from above:
H t   0
f t   f * t   wt 
Soil column
ERS 482/682 (Fall 2002)
Lecture 7 - 9
Infiltration conditions
wt 
• No ponding: H t   0
f t   wt   f * t 
• Saturation from above:
H t   0
f t   f * t   wt 
• Saturation from below:
H t   0
f t   0
ERS 482/682 (Fall 2002)
Soil column
Lecture 7 - 10
• Capillarity:
– Sorptivity
– Matric potential
Figure 5.2: Manning (1987)
• Gravity:
– Percolation
– Hydraulic conductivity
ERS 482/682 (Fall 2002)
Lecture 7 - 11
What are models?
Models are representations of the real world
A model is a conceptualization of a system
that retains the essential characteristics of
that system for a specific purpose.
ERS 482/682 (Fall 2002)
Lecture 7 - 12
Assumptions for most infiltration
models
•
•
•
•
•
Water moves vertically
Homogeneous soil
Soil volume > pore size
Moving water is liquid only
Water movement not affected by
– Airflow in soil pores
– Temperature
– Osmotic gradients
ERS 482/682 (Fall 2002)
Lecture 7 - 13
Infiltration models
•
•
•
•
•
Horton
Kostiakov
Green-Ampt
Philip
Others
ERS 482/682 (Fall 2002)
Lecture 7 - 14
Infiltration rate, f(t)
What we want to quantify…
w
tsat
ERS 482/682 (Fall 2002)
Time, t
Lecture 7 - 15
Infiltration rate, f(t)
What we want to quantify…
w
K*h
tsat
ERS 482/682 (Fall 2002)
Time, t
Lecture 7 - 16
Infiltration rate, f(t)
What we want to quantify…
f(t)=f*(t)
f(t)<f*(t)
Runoff
K*h
tsat,3
ERS 482/682 (Fall 2002)
tsat,1
tsat,2
Time, t
Lecture 7 - 17
What we want to quantify…
Figure 4.2: Brooks et al. (1991)
ERS 482/682 (Fall 2002)
Lecture 7 - 18
Horton model
• Infiltration rate resembles a decreasing
exponential function:
Exponential function:
f x   e x
f(x)=ex
where e = 2.71828…
 
d ex
 ex
dx
x
ERS 482/682 (Fall 2002)
Lecture 7 - 19
Infiltration rate, f(t)
Horton model
f0
f(t) = fc + (f0 – fc)e-kt
x
x
x
x
x
fc
x
x
x
Time, t
ERS 482/682 (Fall 2002)
Lecture 7 - 20
Infiltration rate, f(t)
Kostiakov model
f(t) = Kkt-
Time , t
ERS 482/682 (Fall 2002)
Lecture 7 - 21
Green-Ampt model
• Based on
– Darcy’s law (Eq. 6-8b)
H(t)
Water
zf(t)
Wet soil
=
wetting
front
d  z  p 
w

qz   K h
dz
Capillary suction
at wetting front
f t   K
*
h
H t   z t   
ERS 482/682 (Fall 2002)
f
z f t 
f
Dry soil
 = 0
Soil column
Lecture 7 - 22
Green-Ampt model

zf(t)
Figure 8.10: Hornberger et al.(1998)
ERS 482/682 (Fall 2002)
Lecture 7 - 23
Green-Ampt model
• Initially (before rain)
 = 0, H(t) = 0, f = 0
H t   z f t   f 
*
f t   K h
z f t 
Dry soil
 = 0
f t   K h  0 
ERS 482/682 (Fall 2002)
Soil column
Lecture 7 - 24
Green-Ampt model
• If w < K*h:
H(t) = 0

w = rainfall rate
Storage 
 > 0
Kh()
f t   w
until t = tw
time when rain stops
ERS 482/682 (Fall 2002)
Dry soil
 = 0
Soil column
Lecture 7 - 25
Green-Ampt model
• If w > K*h:
H(t) = 0

Storage 
 =
Kh() up to K*h
f t   w
until t=tp
time when ponding starts
ERS 482/682 (Fall 2002)
Dry soil
 = 0
Soil column
Lecture 7 - 26
Green-Ampt model
• If w > K*h:
for t>tp
f t   K
*
h
H t   z t   
f
z f t 
 H t    f
f t   K 1 
z f t 

*
h
=
f



Dry soil
 = 0
Soil column
Equation 6-40 (error in book)
ERS 482/682 (Fall 2002)
Lecture 7 - 27
Green-Ampt model
• If w > K*h:
for t>tp
Change in
water content
zf(t)
•Volume infiltrated
F t   z f t    0 
•H(t) ~ 0
•rate
  f    0 
f t   K 1 



F
t


*
h
Equation 6-42
ERS 482/682 (Fall 2002)
=
Dry soil
 = 0
Soil column
Lecture 7 - 28
Green-Ampt model
• Difficulties with model
– Need to know
•
•
•
•
Table 6-1
Porosity, 
measure
Initial water content, 0
Table 6-1
K*h
f
Equation 6-46 with Table 6-1
• See Examples 6-6 and 6-7
ERS 482/682 (Fall 2002)
Lecture 7 - 29
Philip model
• For t>tp
•Volume infiltrated
=
F t   S pt1 2  K pt
where t = time since ponding began
Sp = sorptivity
Kp = hydraulic conductivity
 S p  1 2
f t    t  K p
 2 
ERS 482/682 (Fall 2002)
Dry soil
 = 0
Soil column
Lecture 7 - 30
Philip model
• Works after ponding only
• Used for characterizing
spatial variability of
infiltrometer measurements
=
Dry soil
 = 0
Soil column
ERS 482/682 (Fall 2002)
Lecture 7 - 31
Other models
• Richard’s equation
– Physically-based
– Numerically intensive
• Morel-Seytoux and Khanji model
– Includes viscous resistance
• Smith-Parlange model
– Account for different rates of changing
hydraulic conductivity with water content
ERS 482/682 (Fall 2002)
Lecture 7 - 32
Measuring infiltration
• Flooding (ring)
infiltrometers
– Single ring
– Double ring
• Rainfallrunoff plot
infiltrometers
ERS 482/682 (Fall 2002)
Lecture 7 - 33
Ring infiltrometers
Bouwer (1986)
Cylinder infiltration
True infiltration
Water-entry pressure head  0.5ae
ERS 482/682 (Fall 2002)
Lecture 7 - 34
Estimating infiltration parameters
Time, t
(hr)
f(t)
(cm hr-1)
0.485
0.64
0.79
0.94
1.09
1.24
1.39
1.55
1.70
1.84
2.00
5.00
4.38
4.05
3.83
3.67
3.55
3.46
3.38
3.31
3.26
3.21
ERS 482/682 (Fall 2002)
Box 6-2 and Example 6-9
Data from Example 6-8
ponding begins; determined in Example 6-7
Lecture 7 - 35
Estimating infiltration parameters
Box 6-2 and Example 6-9
Time, t
(hr)
t’
(hr)
f(t)
(cm hr-1)
0.485
0.64
0.79
0.94
1.09
1.24
1.39
1.55
1.70
1.84
2.00
0.00
0.155
0.305
0.455
0.605
0.755
0.905
1.065
1.215
1.365
1.515
5.00
4.38
4.05
3.83
3.67
3.55
3.46
3.38
3.31
3.26
3.21
ERS 482/682 (Fall 2002)
Lecture 7 - 36
Estimating infiltration parameters
Box 6-2 and Example 6-9
Time, t
(hr)
t’
(hr)
f(t)
(cm hr-1)
0.485
0.64
0.79
0.94
1.09
1.24
1.39
1.55
1.70
1.84
2.00
0.00
0.155
0.305
0.455
0.605
0.755
0.905
1.065
1.215
1.365
1.515
5.00
4.38
4.05
3.83
3.67
3.55
3.46
3.38
3.31
3.26
3.21
ERS 482/682 (Fall 2002)
Least squares approach:
Find the parameters that
provide the ‘best fit’ of the
model to the observed data
‘best fit’ occurs when sum of
the squared differences
between measured and
modeled values is minimized
Lecture 7 - 37
Estimating infiltration parameters
Box 6-2 and Example 6-9
Time, t
(hr)
t’
(hr)
f(t)
(cm hr-1)
0.485
0.64
0.79
0.94
1.09
1.24
1.39
1.55
1.70
1.84
2.00
0.00
0.155
0.305
0.455
0.605
0.755
0.905
1.065
1.215
1.365
1.515
5.00
4.38
4.05
3.83
3.67
3.55
3.46
3.38
3.31
3.26
3.21
ERS 482/682 (Fall 2002)
Equations 6B2-8 and 6B2-9
 f ti  
 1 
2 N   1 2   2 f ti   1 2 
ti 
ti 


Sp 
2
 1    1 
N       1 2 
 ti    ti 
 1 
2 f ti   S p   1 2  note error
ti 

in book!
Kp 
2N
Lecture 7 - 38
Estimating infiltration parameters
Time, t
(hr)
t’
(hr)
0.485
0.64
0.79
0.94
1.09
1.24
1.39
1.55
1.70
1.84
2.00
0.00
0.155
0.305
0.455
0.605
0.755
0.905
1.065
1.215
1.365
1.515
ERS 482/682 (Fall 2002)
Box 6-2 and Example 6-9
f ti 
1
1
f(t)
(cm hr-1)
ti1 2
ti1 2
ti
5.00
4.38
4.05
3.83
3.67
3.55
3.46
3.38
3.31
3.26
3.21
sum
sum
sum
sum
Lecture 7 - 39
Variability of infiltration
• Factors that affect infiltration rate
– Water-input rate or depth of ponding
– Hydraulic conductivity at the surface
•
•
•
•
•
Organic surface layers
Frost
Swelling-drying
Inwashing of fine sediment
Anthropogenic modification
ERS 482/682 (Fall 2002)
Lecture 7 - 40
Variability of infiltration
• Factors that affect infiltration rate
– Water-input rate or depth of ponding
– Hydraulic conductivity at the surface
•
•
•
•
•
Organic surface layers
Frost
Swelling-drying
Inwashing of fine sediment
Anthropogenic modification
ERS 482/682 (Fall 2002)
Lecture 7 - 41
Variability of infiltration
• Factors that affect infiltration rate
– Water content of surface pores
– Surface slope and roughness
– Chemical characteristics of soil
• hydrophobicity
– Physical/chemical properties of water
ERS 482/682 (Fall 2002)
Lecture 7 - 42
Figure 4.5: Brooks et al. (1991)
Point  watershed???
Infiltration capacity
• Manley (1977) approach
w2
q
2 K h*
Rainfall rate
K*+h
w
Infiltration
0
0.5
1.0
Fraction of watershed area
ERS 482/682 (Fall 2002)
Lecture 7 - 43
Point  watershed???
• Areal-weighted averages
f t  
Philip equation:
Sp
2
t 1 2  K p
•Measure at several locations
•Calculate area-weighted
average of Sp and Kp
E f t  
 t
E Sp
2
1 2
 
 E Kp
Areal-weighted average of infiltration
ERS 482/682 (Fall 2002)
Lecture 7 - 44
Point  watershed???
• Divide watershed into subareas
– Soil properties
– Initial conditions
– Etc.
• Calculate areally-weighted infiltration
E f t  
ERS 482/682 (Fall 2002)
 t
E Sp
2
1 2
 
 E Kp
Lecture 7 - 45
Example: Incline Creek Watershed
Sullivan et al. 1996
• Objective: determine which data
collection techniques are best for
quantifying spatial variations in surface
infiltration
– Used Philip equation
ERS 482/682 (Fall 2002)
Lecture 7 - 46
Watershed size:
7.2 km2
ERS 482/682 (Fall 2002)
Lecture 7 - 47
•Performed 50 tests
with disk permeameter
ERS 482/682 (Fall 2002)
Lecture 7 - 48
•Performed 50 tests
with disk permeameter
•Sites were selected based on:
Accessibility
Minimal surface disturbance
Macropores were absent
•Tried to pick sites that
represented different soil
types and vegetative cover
ERS 482/682 (Fall 2002)
Lecture 7 - 49
•Created GIS coverages
Soil types
Vegetative groupings
•Used field method to determine
average areal % of vegetation
classification per diskpermeameter test
•Calculated weighted values for
Ks based on average areal %
vegetation cover
ERS 482/682 (Fall 2002)
Lecture 7 - 50
The infiltration
rates were used to
estimate time to
ponding and runoff
potential
ERS 482/682 (Fall 2002)
Lecture 7 - 51