CE 343
I NFILTRATION AND R UNOFF G ENERATION
Riddhi Singh
Email: riddhi@civil.iitb.ac.in
This module covers
Infiltration: the physical basis
Infiltration: models
Runoff generation:
conceptualization
Estimating rainfall excess
2
INFILTRATION
THE PHYSICAL BASIS
3
Surface water is water stored or flowing on the earth’s surface. It continually
interacts with the atmospheric and subsurface water systems.
Retention: storage held for long time depleted by evaporation
Detention: short term storage depleted by flow
Image: http://ceephotos.karcor.com/wordpress/wp-content/uploads/20110623-kjans-Small-Open-Channel-Flow-Ann-Arbor-MI.jpg (top)
http://www.hydrosconsult.eu/s/cc_images/cache_5828534.jpg (middle)
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Interception: precipitation held by vegetation
Interception: precipitation caught by
the canopy
Throughfall: intercepted water
falling straight to ground
Stemflow: intercepted water running
along leaves and branches and down
the stem to reach the ground
Roth, B.E., Slatton, K.C. and Cohen, M.J., 2007. On the potential for high‐resolution lidar to improve rainfall
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interception estimates in forest ecosystems. Frontiers in Ecology and the Environment, 5(8), pp.421-428.
Interception loss may account for 10-20% of total rainfall
Depends upon the species composition of vegetation, its density and
storm characteristics
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Depression storage
Frei, S. and Fleckenstein, J.H., 2014. Representing effects of micro-topography on runoff generation and
sub-surface flow patterns by using superficial rill/depression storage height variations. EMS, 52, 5-18.
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Subsurface water flows beneath the land surface
Soil moisture
unsaturated flow
Subsurface outflow
Groundwater
outflow
Saturated flow
Schematic showing subsurface water zones and flow
processes.
Today, we will focus only on those subsurface processes that lead to generation of surface
runoff (we ignore groundwater flow)
Based on Figure 4.1.1 in Chow et al. (2010)
Image: http://www.sfu.ca/geog355fall01/awhall/runoff_paths.jpg
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Capillary forces saturate the porous medium for a short distance
in the capillary fringe
Schematic showing subsurface water zones and flow
processes.
Based on Figure 4.1.1 in Chow et al. (2010)
Image: http://www.sfu.ca/geog355fall01/awhall/runoff_paths.jpg (left)
http://www.amiadini.com/NewsletterArchive/141007-NL176/envEnl-176_clip_image008.jpg (right)
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Factors affecting infiltration capacity
• Characteristics of soil
– Type: sand, silt, clay
– Texture, structure, permeability
– Underdrainage conditions
– Dry or wet
• Surface of entry
– Land use
– Raindrops displace fines in the soil and clog pore spaces in
upper layers
• Fluid characteristics
– Turbidity: clay and colloid content
– Temperature affects viscosity
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Measuring infiltration capacity: Double ring
infiltrometer
Water is filled in both concentric rings and the rate at which it is lost is noted as a
function of time, experiment continues till a constant rate is attained
Issues: 1) spot measurement, 2) raindrop impact is not simulated, 3) setup
disturbs original structure of soil, 4) results depend upon size of the device
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Rainfall simulator
Controlled experiments
with various combinations
of intensity and duration of
rainfall, surface runoff
rates and volumes are
measured.
Water-budget method is
used to estimate
infiltration rate.
Note: infiltration capacity
will be obtained when
rainfall intensity is higher
than the infiltration rate.s
Liu, W., Feng, Q., Deo, R.C., Yao, L. and Wei, W., 2020. Experimental study on the
rainfall-runoff responses of typical urban surfaces and two green infrastructures
using scale-based models. Environmental management, 66, pp.683-693.
12
Flow in unsaturated porous medium: porosity and soil moisture
content
Water
Air filled voids
Solid particles
Control surface
Cross section through an unsaturated porous medium
volume of voids
=
total volume
Based on Figure 4.1.2 in Chow et al. (2010)
volume of water
=
total volume
Image: https://www.soils.org/images/publications/sssaj/67/3/703f11.jpeg
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Continuity equation for flow in an unsaturated porous medium
q+
dy
z
q
dz
z
dx
dz
x
y
q
Control volume for development of continuity equation in an unsaturated porous
medium
Based on Figure 4.1.3 in Chow et al. (2010)
Image: http://seit.unsw.adfa.edu.au/research/images/icinpm2011-1.jpg
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Continuity equation for flow in an unsaturated porous medium
dy
q=Q/ A
Vwater ,C .V =  dxdydz
q
q + dz
z
z
dx
B = mass of soil water
dB
dB
=
= 1,
=0
dm
dt
dz
0=
x
y
d
 w d  +   w V.dA

dt C .V .
C .S
RTT
1st term:
d
d


d

=


dxdydz
=

dxdydz
( w
) w
w
dt 
dt
t
C .V .
2nd term:
 w V.dA = w  q +
q
C .S
Equating both terms:
q 
+
=0
z t


q 
dz  dxdy −  w qdzdxdy
z 
Image: http://seit.unsw.adfa.edu.au/research/images/icinpm2011-1.jpg
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Forces acting on an element in unsaturated flow: gravity, friction
and suction
Suction head : 
Total head =  + z ( gravity head )
Suction head is the part of the total energy possessed by the fluid due to the soil
suction forces. Capillary forces (surface tension), adhesive forces (electrostatic), etc.
together contribute towards the suction head.
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Richards equation: the governing equation for unsteady
unsaturated flow in a porous medium
-Saturated unconfined flow:
gravity and friction
(saturated, unconfined flow)
-Unsaturated flow: also
consider suction force
h
q = −K
z
Forces to consider
Darcy’s law
Henry Darcy
Experimental setup
Now using continuity:
q 
+
=0
z t
 
h  
→  −K  +
=0
z 
z  t
 ( + z )  
 

→  −K
+
=
0,
D
=
K

z 
z

 t
Photo not
available
Lorenzo A. Richards
→
   

= D
+K
t z  z

Image: http://en.wikipedia.org/wiki/Henry_Darcy (left)
http://biosystems.okstate.edu/darcy/LaLoi/figure2.jpg (right)
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The soil suction head and hydraulic conductivity are
themselves a function of soil moisture content
Soil suction head (cm)

K
Hydraulic conductivity, K (cm/day)

Soil moisture content 
Based on Figure 4.1.4 in Chow et al. (2010)
Image: http://uregina.ca/~sauchyn/geog327/moisture.gif
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In Class Exercise
Calculate the soil moisture flux q (cm/ day) between depths 0.8 m and 1.8 m in
the soil at Deep Dean. The data for total head at these depths are given at
weekly time intervals in columns 2 and 3 of the table below. For this soil, the
relationship between hydraulic conductivity (cm/day) and soil suction head (cm)
is: 𝐾 = 250 −𝜓 −2.11
Week
Total head (𝒉𝟏 ) at 0.8 m (cm)
Total head (𝒉𝟐 ) at 1.8 m (cm)
1
-145
-230
2
-165
-235
3
-130
-240
4
-140
-240
5
-125
-240
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INFILTRATION
MODELS
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The real world is heterogeneous, a typical conceptualization
of infiltration is shown below:
0 Moisture content
Depth
Saturation zone
Transition
zone
Transmission
zone
Wetting
zone
Wetting front
Infiltration rate, f (LT-1) is the
rate at which water enters the
soil at the surface. Is equal to
its maximum possible value,
infiltration capacity, if rate
exceeds rainfall intensity.
Cumulative infiltration, F (L) is
the accumulated depth of
water infiltrated during a given
time period.
t
F (t ) =  f ( )d
0
Based on Figure 4.2.1 in Chow et al. (2010)
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Infiltration model I: the simplest one was proposed by Horton (1933, 1939)
who observed that infiltration begins at some rate fo and exponentially
decreases until it reaches a constant rate fc.
𝑘: 𝑑𝑒𝑐𝑎𝑦 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡(𝑇
)
𝑓: infiltration capacity at time 𝑡 from start of
the rainfall
𝑓𝑐 : final steady state infiltration capacity
occurring at 𝑡 = 𝑡𝑐
𝑓𝑜 : initial infiltration capacity at 𝑡 = 0
𝑘: Horton’s decay coefficient (soil and
vegetation), ℎ−1
All infiltration rates in mm/h
Based on Figure 4.2.2(b) in Chow et al. (2010)
Horton’s equation can be derived
from Richards equation by assuming
that K and D are constants
independent of the moisture content
of the soil.
𝜕𝜃
𝜕2𝜃
𝜕𝑡
Infiltration rate f, and
cumulative infiltration F
𝑓(𝑡) = 𝑓𝑐 + (𝑓𝑜 − 𝑓𝑐 )𝑒 −𝑘𝑡
−1
=𝐷
𝜕𝑧 2
fo
F
f
fc
Time
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Infiltration model II: Philip (1957, 1969) solved Richards equation by assuming
that K and D can vary with moisture content (he employed the Boltzmann
transformation to convert Richards equation to an O.D.E)
Suction head
Gravity head
F (t ) = St1/2 + Kt
1 −1/2
f (t ) = St + K
2
S: a parameter called sorptivity, which is a function of
the soil suction potential.
As t approaches infinity, f(t) tends to ?
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In Class Exercise
The infiltration capacity of soil in a small watershed was found to
be 6 cm/h before a rainfall event. It was found to be 1.2 cm/h at
the end of 8 hours of storm. If the total infiltration during the 8
hours period of storm was 15 cm, estimate the value of the
decay coefficient in Horton’s infiltration equation.
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Infiltration model III:I Green and Ampt (1911) proposed an alternative
approximate conceptualization of the infiltration process, this is the GreenAmpt model for infiltration
At any time t since infiltration begun:
Continuity:
F (t ) = L( − i ) = L
dh
dz
Darcy:
 +L
→ f =K
L
 + F
f =K
F
dF
 + F
→
=
K
Combining:
dt
F
 F (t ) 
→ F (t ) − ln 1 +
 = Kt





q = − f = −K
 

f (t ) = K 
+ 1
 F (t ) 
Image: http://api.ning.com/files/0PKyB0rYTqqMxCFs*7HJEnA7AGv4M*YWs7HvzIC0GLDUoUcq9vzKVpQatRNsWehOLM09ZgNpVfqkmPsJ4hdM5Tu8MmSnGIoi/1058531748.png
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Green-Ampt parameters
Rawls, W.J., Brakensiek, D.L. and Miller,
N., 1983. Green-Ampt infiltration
parameters from soils data. Journal of
hydraulic engineering, 109(1), pp.6270.
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In class exercise: Estimating infiltration
Compute the infiltration rate, f and cumulative infiltration, F after
one hour of infiltration into a silt loam soil that initially had an
effective saturation of 30 percent.
Assume water is ponded to a small but negligible depth on the
surface.
For silt loam, use :
effective porosity ,  e = 0.486
 = 16.7 cm
K = 0.65 cm / h
 = (1 − se )  e
Example 4.3.1 in Chow et al. (2010)
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Ponding time: is the elapsed time between the time rainfall begins and the
time water begins to pond at the surface
Saturated
0
Depth
Soil moisture
content
t<tp
t>tp
t=tp
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Three assumptions posed by Mein and Larson (1973) lead to the derivation of
an expression of ponding time:
0
Saturated
Soil moisture
content
Depth
t<tp
t>tp
Infiltration rate, f
t=tp
i
Potential
infiltration
Rainfall
1. Prior to the time ponding occurs, all the rainfall
is infiltrated
2. The potential infiltration rate f is a function of
the cumulative infiltration, F
3. Ponding occurs when the potential infiltration
rate is less than or equal to the rainfall intensity
 

f (t ) = K 
+ 1
 F (t ) 
 

→i = K
+ 1
 it

 p

Actual infiltration
tp
Time
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RUNOFF GENERATION
CONCEPTUALIZATION
There are many flow paths through which water may reach the river channel.
Generally runoff generation is conceptualized using two models: Hortonian
Overland Flow model and Saturation Overland Flow model
Image: http://www.hydrosconsult.eu/s/cc_images/cache_5828534.jpg
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Hortonian overland flow occurs when rainfall intensity (i) exceeds the
infiltration capacity (f) of the soil.
i>f
i-f
Applicable to:
1. Impervious surfaces in urban areas
2. Natural surfaces with thin soil
layers and low infiltration capacity
in semiarid and arid areas.
3. Entire catchment
f
Rainfall excess = i − f
Horton considered surface runoff to take the form of a sheet flow whose depth might be
measured in fractions of an inch.
Image: http://geography.unt.edu/~williams/geog_3350/examreviews/exam2images/hydrol1.gif
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Saturation overland flow is produced when subsurface flow saturates the soil
near the bottom of a slope and overland flow then occurs as rain falls onto
the saturated soil.
Applicable to:
1. Vegetated surfaces in humid
regions
2. Bottom of hill slopes and near
stream banks
Variable source areas are the area of the watershed actually contributing to the stream at any
time. It expands during rainfall and contracts thereafter.
Image: http://ks.water.usgs.gov/pubs/reports/wrir.99-4242.fig02.gif (left)
http://soilandwater.bee.cornell.edu/research/VSA/processes/im_fig2.jpg (right)
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A streamflow hydrograph is a graph showing the flow rate as a
function of time at a given location on a stream
A hydrograph is an integral expression of the physiographic and climatic characteristics that
govern the relations between rainfall and runoff of a particular drainage basin (Chow, 1959)
Image: http://www.xmswiki.com/w/images/2/2a/GSDAImage077.png (left)
http://blackpoolsixthasgeography.pbworks.com/f/1265744759/Storm%20Hydrograph.png (right)
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Hydrographs tell the story of the catchment…
Image: http://www.xmswiki.com/w/images/2/2a/GSDAImage077.png (left)
http://water.usgs.gov/edu/graphics/wcsnowmeltchart.gif (right)
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Baseflow separation: the separation of the direct runoff from
baseflow
Inflection point
N
A. Straight line method
B. Fixed base length method
C. Variable slope method
Image: http://www.engineeringexcelspreadsheets.com/wp-content/uploads/2011/03/Hydrograph-Example.jpg
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RUNOFF GENERATION
RAINFALL EXCESS
Excess rainfall or effective rainfall is that rainfall which is neither retained on
the land surface nor infiltrated into the soil. After flowing across the
watershed, excel rainfall becomes direct runoff.
The graph of excess rainfall vs. time is called the excess rainfall hyetograph (ERH).
The difference between observed total rainfall and excess rainfall is termed abstractions or losses.
Image: http://upload.wikimedia.org/wikipedia/commons/5/52/Saturated_ground_due_heavy_rainfall_in_Wagga_Wagga.jpg
38
Losses = infiltration + interception + surface storage + evaporation
Assessing rainfall excess is the first step towards estimating streamflow.
Image: http://echo2.epfl.ch/VICAIRE/mod_1a/chapt_1/pictures/fig1.3.gif
39
Depending on whether streamflow data is available or not,
rainfall excess can be estimated in two ways:
1. Streamflow is available: Φ index method
2. Streamflow is not available: infiltration equations, or by SCS method
Image: http://faculty.ksu.edu.sa/saleh-alhassoun/CE4251/chapter1.files/image004.gif
40
1. The Φ index is that constant rate of abstractions that will yield an
excess rainfall hyetograph (ERH) with a total depth equal to the depth
of the direct runoff over the watershed.
Rainfall [in]
Initial
abstraction
Rainfall excess
Φ index
Losses
M
rd =  ( Rm − t )
m =1
1.
2.
3.
4.
Pick a time interval, Δt
Judge the number of intervals, M of rainfall that actually contribute to direct runoff
Subtract ΦΔt from the observed rainfall in each interval
Adjust the values of Φ and M as necessary so that the depths of direct runoff and
excess rainfall are equal (equation above)
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2a. Abstraction using infiltration equations: is estimated by
determining the ponding time and infiltration under a variable
intensity rainfall
Rainfall [in]
Initial
abstraction
Continuing
abstraction
Rainfall excess
Φ index
Derivation are based on the following principles:
1. In absence of ponding, cumulative infiltration is calculated from cumulative rainfall
2. The potential infiltration rate at a given time is calculated from cumulative infiltration
at that time
3. Ponding has occurred when the potential infiltration rate is less than or equal to
rainfall intensity
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2b. SCS method for estimating abstractions: developed by the Soil
Conservation Service (1972) for determining rainfall excess using information
of soil type, vegetation, and antecedent moisture conditions
Actual
Precipitation rate
Fa
Pe
=
S P − Ia
Potential
Pe
Ia
Fa
Time
Fa is the water retained
S is the maximum retention potential
Pe is the excess precipitation
P is the total precipitation
Ia is the initial abstraction
P = Pe + I a + Fa
( P − Ia )
→P =
e
2
P − Ia + S
I a = 0.2 S
( P − 0.2S )
Pe =
P + 0.8S
2
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Through experiments, the data for P and Pe was plotted for many watersheds
and the SCS curves were found. To standardize the curves, a dimensionless
curve number CN is defined such as:
1000
S=
− 10
CN
Curve number lie between 0 and 100
Curve number of 100 for impervious surfaces
For each soil type (A,B,C, and D) and land use type, a different
curve number exists
Image: http://www.professorpatel.com/uploads/7/6/5/6/7656897/7766438.jpg?606
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Corrections can be made for antecedent moisture conditions: for dry (AMC I)
or wet (AMC III) conditions, equivalent curve numbers are calculated by:
AMC group
Total 5 –day antecedent rainfall (in)
Dormant Season
Growing Season
I
Less than 0.5
Less than 1.4
II
0.5 to 1.1
1.4 to 2.1
III
Over 1.1
Over 2.1
4.2CN ( II )
10 − 0.058CN ( II )
23CN ( II )
CN (II I ) =
10 + 0.13CN ( II )
CN ( I ) =
Table 5.5.1 in Chow et al. (2010)
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Curve numbers depend on soil type
Soil type
A
High infiltration rates. Deep sand, deep
loess, aggregated soils
B
Moderate infiltration rates. Shallow loess,
sandy loam
C
Slow infiltration rates. Clay loams, shallow
sandy loam, soils low in organic content,
and soils usually high in clay.
D
Very slow infiltration rates. Soils that swell
significantly when wet, heavy plastic clays,
and certain saline soils
Increasing curve numbers
Group
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And land use…
Table 5.5.2 in Chow et al. (2010)
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Reading assignment:
Travel time
Stream networks
From Chow/ Subramanya
WATERSHED CONCEPTS
TRAVEL TIME, STREAM NETWORKS
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