Abstractions From Precipitation.pptx

1
Abstraction from
precipitation
By- J. Tripura

Interception
• Interception refers to precipitation that does not reach the soil, but is instead intercepted by the
leaves, branches of plants and the forest floor, buildings, and other objects above ground
surface. It mainly occurs in the canopy and in the forest floor.
• Three Main Components of Interception:
1. Interception Loss : The water that is retained by vegetation surfaces that is later evaporated into the
atmosphere, or absorbed by the plant. Interception loss prevents water from reaching the ground surface and is
regarded as a primary water loss.
2. Throughfall: The water which falls through spaces in the vegetation canopy, or which drips from the leaves,
twigs and stems and falls to the ground.
3. Stemflow: The water which trickles along the stems and branches and down the main stem or trunk to the
ground surface.
• The interception storage capacities of the vegetation vary with the type and structure of the
vegetation and with meteorological factors.
Abstraction from precipitation
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Contd. Interception
• Interception losses are described by the following equation:
𝑰𝑳 = 𝑺 + 𝑲 × 𝑬 × 𝒕 (1)
Where, 𝐼𝐿 = total volume of water intercepted (mm), S =interception storage whose value varies
from 0.25 to 1.25 mm depending on the nature of vegetation, E = rate of evaporation in mm/hr, t
= duration of rainfall in hrs, K =ratio of vegetal surface area to its projected area.
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• The interception loss is large for a small rainfall
and levels off to a constant value for larger storms
(see fig. aside).
• In hydrological studies dealing with floods
interception loss is less significant and is not
separately considered.

Depression Storage
• Depression storage is the term applied to water that is lost because it becomes trapped in
the numerous small depressions that are characteristic of any natural surface
or
• Depression storage refers to small low points in undulating terrain that can store
precipitation.
• Depression storage exists on pervious and impervious surface.
• The volume water in depression storage at any time during precipitation is given by
(Linsley 1982):
𝑽 = 𝑺𝒅 (𝟏 − 𝒆−𝒌𝑷𝒆) (2)
• Where, V = Volume of water in depression storage, 𝑺𝒅 = Maximum storage capacity, 𝑃𝑒 =
Rainfall excess, K = constant equal to 1/𝑆𝑑.
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Contd. Depression Storage
• Typical values for depression storage range from 1 to 8 mm (0.04 to 0.3 in) with some
values as high as 15 mm (0.6 in) per event.
• Factors Affecting Depression Storage
(1) Nature of terrain; (2) Slope (3) Type of soil surface
(4) Land use (5) Antecedent rainfall (6) Time
• Empirical Estimates of Depression Storage (for storms)
Sand 0.20 inches
Loam 0.15 inches
Clay 0.10 inches
Impervious areas 0.062 inches
Pervious urban 0.25 inches
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Evaporation
• Evaporation is the process by which the precipitation that falls on the earths surface is
returned to the atmosphere as vapour.
Evaporation (and Transpiration) are small for a runoff event and can be neglected.
The bulk of these abstractions take place during the time between runoff events, which is usually long.
Hence, these are more important during this time interval.
• Factors Affecting Evaporation:
1. Wind: When wind speed is high it assists evaporation.
2. Heat: Evaporation is more in summer as compared to winter.
3. Exposed surface area: For instance, a wet cloth spread out dries faster than when folded.
4. Humidity: Dryness assists evaporation; for instance, clothes dry faster in summer than
during the monsoon when the air is humid.
5. Quality of water: under identical condition evaporation from sea water is about 2-3%
less that from fresh water.
6. Atmospheric pressure: A decrease in the barometric pressure, as in high altitudes,
increases evaporation.
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Contd. Evaporation
7. Vapour pressure: Vapour pressures at the water surface and air above: the rate of evaporation
is proportional to the difference between the saturation vapour pressure at the water surface
(Dalton’s law)
𝑬𝑳 = 𝑪 (𝒆𝒘 – 𝒆𝒂) (3)
Where, 𝐸𝐿 : rate of evaporation (mm/day); C : a coefficient depend on wind velocity, atmospheric
pressure and other factors; 𝑒𝑤 : the saturation vapour pressure at the water surface (mm of
mercury); 𝑒𝑎: the actual vapour pressure of air (mm of mercury)
• Evaporation continues till 𝑒𝑤 = 𝑒𝑎
Measurement and Estimation of Evaporation
 The amount of water evaporated from a water surface is estimated by the following methods:
A) Mass Transfer Method
B) Actual Observations
C) Data collected from evaporimeters (Pan observations)
1. U.S. Weather Bureau Class A Pan
2. Standard IS Land Evaporation Pan
3. Sunken Colorado Evaporation Pan
4. Floating Evaporation Pan
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In most design problems, evaporation is measured by
evaporation pans which are called evaporimeters. A
evaporimeters or evaporometers are water circular pans
made of galvanized iron, zinc or copper.

Contd. Measurement and Estimation of Evaporation
D) Empirical evaporation equation
1) Meyer’s Formula
2) USBR Formula
3) Horton’s Formula
4) Thornthwaite Formula
E) Analytical Methods
1) Water Budget method
2) Energy Budget method
A. Mass Transfer Method
• This method is based on turbulent mass transfer in the boundary layer to calculate the mass of
water vapour transferred from surface to the surrounding atmosphere.
• The evaporation is expressed as-
𝑬 =
𝟒𝟔.𝟎𝟖 𝒆𝟏−𝒆𝟐 𝒗𝟐−𝒗𝟏
𝑻+𝟐𝟕𝟑 𝒍𝒏
𝒛𝟏
𝒛𝟐
(4)
• Where E = Evaporation in mm/h, z1 & z2 = Arbitrary levels above water surface, e1 & e2 =
Vapour pressure at z1 & z2 in km/h, v1 & v2 = wind velocity at z1 & z2 in km/h, T = Average
temperature in C between z1 & z2.
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B. Method of Actual Observations
• Here, Atmometers are provided with special surface which are kept wet from where the
evaporation takes place.
 There is continuous supply of water to the surface for measuring the evaporation.
 A variety of Atmometers are used in the world. The most frequently used one are Piche and Bellani
Atmometer.
 The different types of atmometers indicate different amount of evaporation under different meteorological
conditions
 However, they are not common because of their small size.
C.1 U.S. Weather Bureau Class A Pan
 In most design problems, evaporation is measured by evaporation pans which are called evaporimeters.
 The most commonly used evaporimeters in India is US Weather Bureau Class A Pan.
 A pan is a metal container (square or circular) with diameter varying from 300 – 1500 mm.
 It is filled water at depth in pan is maintained 180 mm to 200 mm.
 The water loss is measured in a specified period (Normally twice daily at 8:30 am and 5:30 pm).
 The rate of evaporation is then correlated to the evaporation from a reservoir.
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Piche Atmometer
Bellani Atmometer
U.S. Weather
Bureau Class A Pan

C.2 Standard IS Land Evaporation Pan
The IS 5973-1970 standard evaporation pan (Class A pan) has diameter of 1220 mm and depth of
255 mm.
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ISI Evaporation Pan

C.3 Sunken Colorado Evaporation Pan
The sunken Colorado pan is a square shape of 920 mm (3 ft.) side and 460 mm (18 in.) deep and
made of unpainted galvanized iron sheet. As the name suggests, it is buried in the ground in such
a way that about 100 mm of the top projects above the ground surface.
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Sunken Colorado pan

C.4 Floating Evaporation Pan
The floating pan is of 900 mm diameter and 450 mm deep, and is supported on the raft floating
in water.
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Evaporation Tank or pan
Stilling well: This is an instrument to determine the
water level in the evaporation pan. The stilling well
is installed in the evaporation pan and leveled with
the adjustable leveling foot screw. By using the
suspension measuring rod (hook gauge) suspended in
the smoothing pipe (stilling well) the variation of
water level can be measured very accurately by using
the micrometer scale on the measuing rod. Daily the
result of evaporation and precipitation is measured
within the still well, by means of a high quality
evaporation micrometer with a measuring range of
01 mm and an accuracy of 0.02 mm.

Pan Evaporation Observations
• Advantages:
1. Cost of installation is reasonably low.
2. It is easy for measurement.
• Disadvantages:
1. The pan gives higher rate of evaporation than that of large free water surface.
2. Effects of wind and radiation are more which overestimate the evaporation rate.
Empirical Formulae
• Various empirical formulae have been developed by different investigators to estimate the evaporation.
• Most of them are dependent on wind velocity, temperature and atmospheric pressure.
1. Meyer’s equation (1915):
𝐸 = 𝐶 ( 1 + 𝑉 / 16 ) ( 𝑒𝑠 − 𝑒𝑎) (5)
• Where, E = Evaporation from water body in mm/day, 𝑒𝑎 = Actual vapour pressure of
overlying air mm of Hg; 𝑒𝑠 = Vapour pressure at water surface in mm of Hg, C = Coefficient
varying from 0.36 to 0.50.
2. Fitzgerald’s equation (1886):
𝐸 = ( 0.4 + 0.124 𝑉 ) (𝑒𝑠 − 𝑒𝑎) (6)
• V = Mean monthly Wind velocity at the water surface in km/hrs. Hg
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Contd. Empirical Formulae
3. Horton’s equation (1917):
𝐸 = 0.635 [(𝜃. 𝑣𝑤) – 𝑣] (7)
• Where, E = Evaporation in mm/day, θ = Wind factor 𝑣𝑤 = Maximum Vapour pressure at water
surface in mm of mercury, v = Actual Vapour pressure in air in mm of mercury
4. Thornthwaite Formula (1948):
𝐸 = 16 [(10𝑇)/𝐼]^𝑎 (8)
• Where, E = Evaporation in mm/month, T = Monthly Mean Temperature, a = Function of I,
𝐼 = ∑ (𝑇/𝑆)^1.51
• USBR Equation:
𝐸 = 4.57 𝑇 + 43.3 (9)
• Where, E = Annual Evaporation of the water body in cm, T = Annual mean temperature in ̊C.
5. Rower's Formula (1931):
𝐸 = 0.771( 1.465 − 0.000732𝑝𝑎)(0.44 + 0.0733𝑢0) 𝑒𝑠 − 𝑒𝑎 (10)
• Where, 𝑝𝑎= mean barometric reading in mm of mercury, u0 = mean wind velocity in km/hr at
ground level, which can be taken to be the velocity at 0.6 m height above ground.
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Analytical Method
1. Water Budget Equation (i.e. Conservation of mass)
• The Law of Conservation of Mass dates from Antoine Lavoisier's 1789 discovery that mass
is neither created nor destroyed.
• It is the simplest analytical method.
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(11)

Contd. Analytical Method
2. Energy Budget Equation (i.e. Conservation of energy)
• The law of conservation of energy states that energy can neither be created nor destroyed.
According to principle of physics the energy in a closed system remains constant.
• It is the most accurate method.
• A heat balance following the principle of the conservation of energy is evaluated from
incoming, outgoing and stored energy as follows:
𝑯𝒏 = 𝑯𝒂 + 𝑯𝒆 + 𝑯𝒈 + 𝑯𝒔 + 𝑯𝒊 (12)
• Where, Hn = Net heat energy received in the water body, Ha = Sensible heat transfer from
water body to air, He = Heat energy consumed in evaporation process =𝜌𝐿𝐸𝐿 (where 𝜌=density
of water, L=latent heat of evaporation and 𝐸𝐿=evaporation), Hg = Heat flux to the ground, Hs =
Heat stored in the water surface, Hi = Heat going out of system by flow of water.
• If the time periods are short, the terms Hs and Hi can be neglected as negligibly small.
• All the terms except Ha can either be measured or evaluated indirectly.
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All the energy are calculated in calories per square mm per day

𝑯𝒏 = 𝑯𝒄 𝟏 − 𝒓 − 𝑯𝒃 (13)
Where, 𝐻𝑐 1 − 𝑟 = incoming solar radiation into a surface of
reflection coefficient (albeido or reflectivity) r.
• The sensible heat term Ha which cannot be readily
measured is estimated using Bowen’s Ratio
(𝛽) given by the expression-
𝜷 =
𝑯𝒂
𝝆𝑳𝑬𝑳
= 𝟔. 𝟏 × 𝟏𝟎−𝟒
× 𝑷𝒂
𝑻𝒘−𝑻𝒂
𝒆𝒘−𝒆𝒂
(14)
Where, 𝑃𝑎 = atmospheric pressure in mm of mercury, 𝒆𝒘 =
saturated vapour pressure in mm of mercury, 𝒆𝒂 = actual
vapour pressure of air in mm of mercury, 𝑻𝒘= temperature of
water surface in °C and 𝑻𝒂= temperature of air in °C.
• From Eqs (12) and (14) 𝑬𝑳 , can be evaluated as
𝐸𝐿 =
𝐻𝑛−𝐻𝑔 − 𝐻𝑠 − 𝐻𝑖
𝜌𝐿(1+𝛽)
(15)
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Energy balance in a water body

Methods of Reducing Evaporation From Soil, Lake Or Reservoirs
 By Keeping Free Water Surface Area Minimum
 By spreading certain chemical films on the reservoirs and lakes surface.
o Eg. cethyl alcohol (hexadecanol) and steary alcohol ( octadecanol)
 By Suitable Wind Breakers
 Mechanical Covers
o Eg. Permanent or temporary roofs over the reservoir, and floating roofs
o These measures are limited to very small water bodies such as ponds. etc.
 By Providing Mulch (cover) on the Land Surfaces.
 By removing or cleaning weeds and water loving plants, etc.
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Transpiration and its Measurement
 Transpiration is the process of water
movement through a plant and its
evaporation from aerial parts, such as
leaves, stems and flowers. Water is
necessary for plants but only a small
amount of water taken up by the roots is
used for growth and metabolism.
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Contd. Transpiration and its Measurement
 Environmental factors that affect the rate of transpiration
1. Light
Plants transpire more rapidly in the light than in the dark. This is largely because light stimulates the opening of
the stomata (mechanism). Light also speeds up transpiration by warming the leaf.
2. Temperature
Plants transpire more rapidly at higher temperatures because water evaporates more rapidly as the temperature
rises. At 30°C, a leaf may transpire three times as fast as it does at 20°C.
3. Humidity
At high humidity (moist air), the stomata tends to close and thus limit the exit of water
vapour from the plant. In addition, at high humidity the atmosphere contains more water and
has low atmospheric demand, meaning that it has limited capacity to absorb more water.
4. Wind
When there is no breeze, the air surrounding a leaf becomes increasingly humid thus
reducing the rate of transpiration. When a breeze is present, the humid air is carried away and
replaced by drier air.
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Contd. Transpiration and its Measurement
 Environmental factors that affect the rate of transpiration
5. Soil water
A plant cannot continue to transpire rapidly if its water loss is not made up by replacement
from the soil. This immediately reduces the rate of transpiration (as well as of photosynthesis).
6. Stage of plant development
Transpiration depends upon plant growth as the water requirement is different at different
stage of its growth.
 Measurement of Transpiration
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Various methods of measurement of transpiration, the most
common method is by the ‘Phytometer’.
𝑊𝑇 = 𝑊𝐼 + 𝑊𝐴 – 𝑊𝐹 (16)
Where, WT = Water loss due to transpiration, WI = Initial weight of
apparatus in the beginning, WF = Final weight of apparatus at end of
experiment, WA = Water added during plant growth.

Evapotranspiration
 It is the quantity of water transpired by the plant during their growth (or retained in plant
tissue), plus the moisture evaporated from the soil and the vegetation (Michael, 1978).
 It accounts for the movement of water from sources such as soil, canopy interception and
water bodies.
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 Evapotranspiration or consumptive use of water is the depth of
water consumed by evaporation and transpiration during crop
growth, including water consumed by accompanying weed growth.
 Consumptive use of water includes the water deposited by rainfall
and subsequently evaporating without entering the plant system.
 Its study is important in the design of reservoir, irrigation canals,
water balance on earth surface and projects relating to water.
 The value of consumptive use of water varies from crop to crop and
also for the same crop it varies with time as well as place.

Contd. Evapotranspiration
 Potential evaporation or potential evapotranspiration (PET) is defined as the amount of
evaporation that would occur if a sufficient water source were available.
 Actual evapotranspiration (AET) is the amount of water that is actually removed from the
surface by evaporation and transpiration.
 If the water supply to the plant is adequate, soil moisture will be at the field capacity and AET
will be equal to PET.
 If the water supply is less than PET, the soil dries out and the ratio AET/PET would then be
less than unity (eg. Clayey soil).
 Except in a few specialized studies, all applied studies in hydrology use PET (not AET) as a
basic parameter in various estimations related to water utilizations connected with ET process.
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Factors Affecting Evapotranspiration
 Meteorological factors:
 It increases with the increase in temperature, sunshine and wind velocity but decreases with humidity.
 Plant and soil factors:
o Greater the density of vegetation, greater is the evapotranspiration.
o When the vegetative surface becomes dry and the soil moisture decreases, the evaporation decreases.
o Evapotranspiration depends upon the stage of the plant growth.
Measurement/Estimation of ET (or Consumptive use): The various methods adopted are
broadly classified into:
 a) Direct measurement of consumptive use of water.
o Lysimeter Method
o Field Experimental Method
o Integration Method
 b) Empirical formula
o Blaney-Cridddle Equation
o Christiansen Equation

1.Lysimeter Method
• Lysimeter is an evapotransporimeter, which is a circular tank
with pervious bottom whose diameter may be extended to 5m.
• Tanks are watertight cylindrical containers open at one end and
are set into ground with their rim flush with the surface.
• Consumptive use is determined by the difference of the total
water applied to the tank and that draining through the
pervious bottom and collected in a pan.
• This method is time consuming and expensive.
• It can be defined mathematically as-
𝑬𝑻 = 𝑹𝑾 + 𝑰𝑾 – 𝑸𝑫 + 𝜹𝑺 (17)
Where, ET = Evapo-transpiration QD = Quantity of water drained
RW = Rainfall water, IW = Irrigation water
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2. Field Experimental Plots Method
• In this method the irrigation water is applied to the selected field experimental plots.
• In the plot, all the elements of water budget are measured in a known time interval and the
evapotranspiration is determined as:
Evapotranspiration = Precipitation + Irrigation input – Runoff – Increase in soil storage –
Groundwater loss
• Since it is difficult to determine the ground water loss due to deep percolation so it can be
neglected by maintaining the moisture condition in the plot at the field capacity.
3. Integration Method
• In this method the consumptive use of water is determined by the summation of the products
of-
• i. Consumptive use of water for each crop times its area.
• ii. Consumptive use of water for natural vegetation time its area.
• iii. Evaporation from water surface times water surface area.
• iv. Evaporation from bare land times its area.
Note: It is necessary to know the division of total area under irrigation crops, natural vegetation, water surface area and
bare land area.
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Contd. Evapotranspiration: Empirical Method
1. Blaney-Cridddle Equation
• It is based on the data collected from the arid Western Zone of the United States.
• It is based on the assumption that evapotranspiration depends only on the potential mean
monthly temperature and the monthly daylight hours.
𝑬𝑻 𝒐𝒓 𝑷𝑬𝑻 = ∑
𝒌𝒑 𝟒.𝟔𝟏𝒕+𝟖𝟏.𝟑
𝟏𝟎𝟎
(18)
Where, ET = evapotranspiration (cm), t = mean monthly temperature (°C), p = monthly
percentage of hours of bright day, k = monthly consumptive use coefficient for the crop.
2. Christiansen Equation
• The Christiansen equation for estimation of potential evaporation is as below:
𝑬𝑻 = 𝟎. 𝟒𝟕𝟑 𝑸𝟎 𝑪 (19)
Where, 𝑄0 = Solar radiation at the top of the atmosphere converted to mm of equivalent
evaporation, C = Coefficient derived from series of climatic measurements like temperature,
humidity, wind, sunshine, elevation etc.
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Infiltration
• Infiltration is the process by which surface water on the ground surface enters into the soil
mass, through the pores of soil. (or It is defined as the flow of water from above ground into
the subsurface).
• It is commonly used in both hydrology and soil Mechanics.
• Percolation on the other hand is the passage of water within the soil.
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Infiltration Capacity (𝑓𝑝)
• It is the maximum rate at which water can be
absorbed by a given soil per unit area under given
conditions (expressed in cm/hour).
• Actual rate of infiltration (𝑓𝑎) can be defined as-
𝑓𝑎 = 𝒇𝒑 when 𝒊 ≥ 𝒇𝒑 (20)
𝑓𝑎 = 𝒊 when i < 𝒇𝒑 (21)
• Where 𝑓𝑝 = infiltration capacity (cm/hr); i = intensity of
rainfall (cm/hr); 𝑓𝑎 = actual rate of infiltration (cm/hr)

Factors affecting Infiltration
A. Slope of the land:- The steeper the slope (gradient), the less the infiltration or seepage.
B. Degree of saturation:- The more saturated the loose Earth materials are, the less the infiltration.
C. Porosity:- Porosity is the percentage of open space (pores and cracks) in a earth surface. The greater the
porosity, the greater the amount of infiltration.
D. Compaction:- The clay surfaced soils are compacted even by the impact of rain drops which reduce
infiltration. This effect is negligible in sandy soils
E. Surface Cover Condition:-
A. Vegetation:- Grasses, trees and other plant types capture falling precipitation on leaves and branches,
keeping that water from being absorbed into the Earth & take more time to reach in to the ground.
B. Land Use:- Roads, parking lots, and buildings create surfaces that are not longer permeable. Thus
infiltration is less.
F. Temperature – At high temperature viscosity decreases and infiltration increases
A. Summer – Infiltration increases
B. Winter – Infiltration decreases
G. Other Factors – a) Entrapped air in pores- Entrapped air can greatly affect the hydraulic conductivity at or
near saturation b) Quality of water -Turbidity by colloidal water c) Freezing - Freezing in winter may lock
pores. d) Annual & seasonal changes –According to change in land use pattern. Except for Massive
deforestation & agriculture.
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Measurement of Infiltration rate
A. By Infiltrometers (known as Flooding type infiltrometers)
o Single ring infiltrometers (or Simple tube type infiltrometers)
o Double ring infiltrometers
B. By Rainfall Simulators
C. By Hydrograph Analysis
1. Single ring Infiltrometer
Material of ring  Metal cylinder, Ring diameter  25-30 cm, Ring length 50-60 cm with
both ends open. Thus, length of cylinder= ( 2 x diameter).
It is driven into a level ground such that about 10 cm of cylinder is above the ground.
Water is poured into the top part to a depth of 5 cm & pointer is set inside the ring to indicate
the water level to be maintained.
The volume of water added during different time intervals, and the plot of the infiltration
capacity vs time is obtained.
Uniform Infiltration is obtained after 2-3 hrs.
• Main drawback- infiltrated water spreads at the bottom of ring. Thus the tube is not truly
representing the area through which infiltration is taking place.
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Contd. Measurement of Infiltration rate
o The single ring involves driving a ring into the soil and supplying water in the ring either at
constant head or falling head condition.
o Constant head refers to condition where the amount of water in the ring is always held constant means the
rate of water supplied corresponds to the infiltration capacity.
o Falling head refers to condition where water is supplied in the ring, and the water is allowed to drop with
time. The operator records how much water goes into the soil for a given time period.
2. Double ring Infiltrometer
 This is the most commonly used flooding type infiltrometer. It consists of two concentric
rings driven into soil uniformly without disturbing the soil.
 The second bigger ring around inner ring help to control the flow of water spread through the
first ring.
 Material of ring  Metal cylinder, Ring diameter  30 cm & 60 cm, Ring length  25 cm,
Ring driven into soil  15 cm, Water level maintain  5 cm
 The water in both the rings should be kept the same during the observation period.
 Measurement is taken only from the inner tube.
 Water is supplied either with a constant or falling head condition, and the operator records
how much water infiltrates from the inner ring into the soil over a given time period.
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B. Rainfall simulator
o In this a small plot of land of about 2 m x 4 m site is
provided with a series of nozzles on the longer side with
arrangement and collect and measure the surface runoff
rate.
o The specially designed nozzles produce raindrops falling
from a height of 2 m and are capable of producing
various intensities of rainfall.
o Experiments are conducted under controlled conditions
with various combinations of intensities and durations
and the surface runoff rates and volumes are measured
in each case.
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o Using the water budget equation involving the volume of rainfall, infiltration and runoff, the
infiltration rate and its variation with time are estimated.
o If the rainfall intensity is higher than the infiltration rate, infiltration capacity values are obtained.
o Rainfall simulator type infiltrometers give lower values than flooding type infiltrometers. This is due
to effect of the rainfall impact and turbidity of the surface water present in the former.

C. Hydrograph Analysis
o In this infiltration capacity of a small
watershed is obtained by analysing measured
runoff hydrograph and corr. rainfall
records.
o A fairly homogenous measured runoff
hydrograph and corr. rainfall records of an
isolated storm, if available; water budget
equation is applicable to estimate the
abstraction (means removal/separation) by
infiltration.
o In this the evapotranspiration losses are
estimated by knowing the land cover/use of
the watershed.
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ESITMATION OF INFILTRATION
o The infiltration rate 𝒇 𝒕 is the velocity or speed at which water enters into the soil.
o It is usually measured by the depth (mm) of the water layer that can enter the soil in one
hour (Or rate at which water enters the soil at the surface).
o Cumulative Infiltration 𝑭 𝒕 denotes the accumulated depth of water infiltrating during
given time period. Thus,
𝐹 𝑡 = 0
𝑡
𝑓 𝑡 𝑑𝑡 and 𝑓 𝑡 =
𝑑𝐹
𝑑𝑡
(22)
o Infiltration Capacity Rate Curve as obtained from infiltrometer is essentially observed to be
decaying curve (max to min). Some mathematical expressions to describe the shape of curve,
given by various investigators are :-
o a) Horton’s equation
o b) Phillips equation
o c) Kostiakov equation
o d) Green–Ampt equation
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a) Horton’s equation
o Horton expressed the decay of infiltration capacity with time as an exponential decay given
by-
𝑓(𝑡) = 𝑓𝑐 + 𝑓𝑜 − 𝑓𝑐 𝑒𝑘𝑡 (23)
o 𝑓(𝑡) = infiltration capacity at any time t from the start of the rainfall, 𝑓𝑜= initial infiltration
capacity at t = 0, 𝑓𝑐 final steady state infiltration capacity (constant rate or ultimate infiltration
capacity) occurring at t= 𝑡𝑐, k = Horton's decay coefficient (depends upon soil characteristics
and vegetation cover).
o The difficulty of determining the variation of the three parameters𝑓(𝑡), 𝑓𝑐𝑎𝑛𝑑𝑓𝑜with soil
characteristics and antecedence moisture conditions preclude the general use of Horton’s
equation.
b). Philip's equation (1957)
o Philip's two term model relates 𝐹 𝑡 as-
𝐹 𝑡 = 𝐾𝑡 + 𝑠𝑡0.5
(24)
Where, s = a function of soil suction potential called as sorptivity, K = Darcy's hydraulic
conductivity
37

o The infiltration capacity by eq. 22 can be expressed as-
𝑓 𝑡 = 𝐾 +
1
2
𝑠𝑡−0.5 (25)
c). Kostiakov Equation ( 1932)
𝐹 𝑡 = 𝑎𝑡𝑏 (26)
The infiltration capacity by eq. 22 can be expressed as-
𝑓 𝑡 = (𝑎𝑏)𝑡(𝑏−1)
(27)
Where a and b are local parameters (or constants depends on soil moisture & vegetable cover)
with a> 0 and 0 < b < 1.
d). Green–Ampt equation (1911)
o Green and Ampt proposed a model for infiltration capacity based on Darcy's law as-
𝑓 𝑡 = 𝐾(1 +
𝜂𝑆𝑐
𝐹𝑝
) (28)
Where, 𝜂 = porosity of the soil, S =capillary suction at the wetting front and K = Darcy's
hydraulic conductivity..
38

o For consistency in hydrological calculations, a constant value of infiltration rate for the entire
storm duration is adopted. The average infiltration rate is called the INFILTRATION
INDEX.
o The two commonly used infiltration indices are the following:
(i) φ – index (ii) W – index.
o They are extremely used for the analysis of major floods when the soil is wet and the
infiltration rate becomes constant.
o The indices are mathematically expressed as
𝝓 − 𝑖𝑛𝑑𝑒𝑥 = (𝑃 − 𝑅)/𝑡𝐸 (29)
𝑾 − 𝑖𝑛𝑑𝑒𝑥 = (𝑃 − 𝑅 − 𝐼𝑎)/𝑡𝐸 (30)
Where, P=total storm precipitation (cm), R=total surface runoff (cm), 𝐼𝑎 =Initial losses i.e.
depression and interception losses (cm), tE= elapsed time period or Time period of runoff (in
hours)
Infiltration Indices
39

o This is defined as the rate of infiltration above which rainfall volume = runoff
volume(saturation).
o The shaded area below the horizontal line is assumed that all losses are due to infiltration
only.
o For determination of Φ - index, a horizontal line is drawn on the hyetograph such that the
unshaded area above that line is equal to the volume of surface runoff.
𝝓−𝑖𝑛𝑑𝑒𝑥
40

o For the soil conditions in India for flood producing storms C.W.C has found following
relationship
𝝓 = (𝐼 − 𝑅)/24 and 𝐑 = 𝛼 × 𝐼1.2 (31)
Where, R = Runoff in cm from a 24 hr rainfall of intensity I (cm/hr), α = Coefficient depends
upon soil type.
o In estimating maximum flood for design purpose, in absence of any other data, a Φ- index
value of 0.10 cm/hr can be assumed.
o Φ – Index for a catchment, during a storm depends on
o Soil type
o Vegetation cover
o Initial moisture condition
𝝓−𝑖𝑛𝑑𝑒𝑥
41

o This is the average infiltration rate during the time when the rainfall intensity>infiltration
rate.
o Refer Eq. 30 for W-index.
Note: The w-index is more accurate than the Φ-index because it subtracts initial losses
(depression and interception losses).
Example Problem: A 12-hour storm rainfall with the following depths in cm occurred over a
basin:
2.0, 2.5, 7.6, 3.8, 10.6, 5.0, 7.0, 10.0, 6.4, 3.8, 1.4 and 1.4 cm. The surface runoff resulting from
the above storm is equivalent to 25.5 cm of depth over the basin. (i). Determine the average
infiltration index (Φ-index) for the basin (ii) find avg. infiltration rate for central 8 hours.
o Soln.-
Total rainfall in 12 hours = 61.5 cm; Total runoff in 12 hours = 25.5 cm; Total infiltration in 12
hours = 36 cm; Average infiltration = 3.0 cm/hr;
Average rate of infiltration during the central 8 hours: 8 Φ +2.0+2.5+1.4+1.4 = 36
Therefore, Φ = 3.6cm/hr
W−𝑖𝑛𝑑𝑒𝑥
42

Infiltration capacity curve
43

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