Hydrology
(CE 424)
CHAPTER 4
Abstractions From Precipitation
Instructor:
Dr. Saleh AlHassoun
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
LOSSES FROM PRECIPITATION
- Evaporation and transpiration are transferred to the
atmosphere as water vapor. In engineering hydrology,
runoff is the prime subject of study and evaporation and
transpiration phases are treated as "losses “.
- Before the rainfall reaches the outlet of a basin as runoff,
certain demands of the catchment such as interception,
depression storage and infiltration have to be met. If
the precipitation is not available for surface runoff is
defined as "loss"
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Evaporation Process
Is the process in which a liquid changes to the gaseous
state(water vapor) at the free surface below the boiling
point through the transfer of heat energy.
*When some molecules possess sufficient kinetic energy,
they may cross over the water surface. The net escape of
water molecules from the liquid state to the gaseous state
constitutes evaporation.
•Evaporation occurs from :
1. Water bodies such as …..,
2. Soil : saturated, bare, vegetation
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Influencing Factors
1. Vapor pressures at the water surface(es) and air above(e) :
the rate of evaporation is proportional to the difference between
the saturation vapor pressure at the water surface.
2. Air and water temperature(t ; tw) : the rate of evaporation
increases with an increase in the water temperature.
3. Wind : the rate of evaporation increases with the wind speed up to
critical speed beyond which any further increase in the wind
speed has no influence on the evaporation rate
4. Atmospheric pressure: a decrease in the barometric pressure ( as in
high altitudes), increases evaporation.
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5. Quality of water: under identical conditions evaporation from sea
water is about 2-3% less than from fresh water.
6. Size of water body : E ^ as A ^
Methods of Estimating Evaporation
 1. Water budget( storage equation) method :
( P+ I ) - ( O + E ) = ΔS
so
E = I – O – ΔS + P
 2. Energy budget method
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3. Aerodynamic method :
Dalton’s law
E = C (es – e)
E : rate of evaporation (mm/day)
es : the saturation vapor pressure at the water surface;
(milibar or mm of mercury) (mb or mm Hg)
e : the actual vapor pressure of air (mb or mm Hg)
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C : a coefficient depends on wind speed, atmospheric
pressure and other factors,
C= a+ bu
a , b are constants ;
u : wind speed (m/s) ; ( u2 : wind speed at height 2m.)
Values of constants for different empirical methods
Method
Lake
Hefner
Meyer
Harbeek
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u
E
a
b
u
Units of
0
0.122
u4
m/s
mm/day
3.6
0.064
u8
m/s
mm/day
0
0.29A^-0.05
u2
m/s
mm/day
Unit of
Example :
If
E = f(u) (es – e)
Given : C = f(u) = 0.14 u
and : Δe = es - e = 5.6 mb.
, u = 30 km/hr.
What is daily E from lake ?
Solution :
Since C = a + bu so: a = 0 ; b = 0.14
u= 30 km/hr = 8.33 m/sec.
E = 0.14(8.33)(5.6) = 6.53 mm/day or daily E = 6.53 mm.
For lake Hefner method : a= 0 , b= 0.122 , u4 = 9.24 m/s.
Then
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E = 0.122(9.24) (5.6) = 6.3 mm/day .
Evaporation Measurement
1.
EVAPORIMETER
CLASS A Evaporation Pan
-
-
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The most widely used method of
measuring or monitoring the
water body evaporation.
The standard National Weather
Bureau Class A pan :
( 1.21 m diameter, 25.5 cm depth,
it is placed on a wooden structure
of 15 cm height).
Pan Coefficient : Cp
The actual evaporation from a nearby leak is
less than that of pan evaporation
Why ?
- The sides of the pan is exposed to the sun.
- The temperature over the pan is higher that over
the lake.
Lake evaporation = Cp pan evaporation
E
= Cp Ep
Cp = pan coefficient = 0.7 for Class A Pan.
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Evaporation Estimations
Empirical Evaporation Equation
Most of empirical formulae are based on the Dalton-type
equation:
E = Kf(u) (ew - ea)
E = lake evaporation in mm / day,
es = saturated vapor pressure at the water-surface temperature;
e = actual vapor pressure of overlying air at a specified height;
f(u) = wind-speed correction function and
K = a coefficient.
The term e is measured at the same height at which wind speed
in measured.
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Evaporation Estimations
Meyer's Formula (1915):
E = KM (es - e) ( I + u8/16 )
u8 = monthly mean wind velocity about 8 m above ground
KM = coefficient of 0.36 for large deep waters and 0.50 for small,
shallow waters
The limitations of the formula that at best be
expected to give an approximate magnitude
of the evaporation.
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Evaporation Measurement
1.
Analytical methods
The analytical methods for the determination of lake
evaporation can be broadly classified into three
categories as :
I. Water-budget method,
2. energy-balance method, and
3. mass-transfer method
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I. Water-budget method,
It involves writing the hydrological continuity equation for the lake and
determining the evaporation from a knowledge or estimation of other
variables.
Thus considering the daily average values for a lake, the continuity
equation is written as:
EL = P + (Vis-Vos) + (Vig-Vog) – TL – Δ S
All quantities are in units of volume (m3) or depth (mm) over a reference
Area. p,.Vis,Vos and Δ S can be measured. However, it is not possible
to measure Vig,Vog and TL and therefore these quantities can only be
estimated.
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If the unit of time is kept large, say weeks or months, better accuracy in
the estimate of EL is possible. In view of the various uncertainties in the
estimated values and the possibilities of errors in measured variables,
the water-budget method cannot be expected to give very accurate
results.
EVAPOTRANSPIRATION
TRANSPIRATION
Transpiration is the process by which water leaves the body of a living
plant and reaches the atmosphere as water vapor. The water is taken up
by the plant-root system and escapes through the leaves.
The important factors affecting transpiration are :
- atmospheric vapor pressure,
- temperature,
- wind, light intensity and
-characteristics of the plant, such as the root and leaf systems.
Measurement of T :
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Phytometer
EVAPOTRANSPIRATION
Evapotranspiration
takes place at the land where plants exist ;
also lose moisture by the evaporation of water from
soil and water bodies.
In hydrology and irrigation practice, it is found that
evaporation and transpiration processes can be
considered advantageously under one term as
Evapotranspiration.
The term consumptive use is also used to denote
this loss by evapotranspiration.
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EVAPOTRANSPIRATION Equations
Penman’s Equation
Is based on sound theoretical reasoning and is
obtained by a combination of energy-balance and
mass-transfer approach.
E = Δ/(Δ + γ) Qn + γ /(Δ + γ) Ea
Measurement of ET :
•Tanks
•Lysimeters
•Field Plots
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Interception
It is the segment of precipitation that is prevented to reach the
ground by vegetation and subsequently evaporates
rainfall
Interception = Rainfall – stemflow – throughfall
throughfall
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stemflow
Influencing Factors
1. Storm characteristics : rainfall intensity, duration,
wind …etc
2.
The vegetation : species, age, density of plants and trees
3.
Season of the year: time of plant growing
It is estimated of that : of the total rainfall in area during
plant-growing season, the interception loss is 10-20 %.
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% Rainfall
Interception loss as
Influencing Factors
100
80
60
40
20
5
10 15 20 30
Rainfall (mm)
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
Estimation of interception can be significant in annual or
long-term models

For heavy rainfalls during individual storm events
interception is neglected
Estimation of Interception
Most interception loss develops during the initial storm
period and the rate of interception rapidly approach to
zero.
Horton:
Ii = Si + KEt
Ii
SI
Ki
E
t
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Li = 0.015+ 0.23 P (ash trees)
Li = 0.03+ 0.22 P (oak trees)
= the volume of water intercepted (mm)
= the interception storage whose values varies from 0.25
to 1.5 depending on the nature of vegetation
= ration of vegetal surface area to its projected area
= Evaporation rate in (mm/h) during the precipitation
= duration of rainfall in hours
Depression Storage
When the precipitation of a storm reaches the ground,
it must fill up all depressions before it can flow over the
surface
The volume of water trapped in these
depressions called depression storage
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Influencing Factors
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1.
Type of soil : 0.50 cm for sand, 0.25 cm fro clay;
2.
The condition of the surface : amount and nature of
depression ;
3.
The slope of Catchment ;
4.
The soil moisture
Infiltration
Is the process by which precipitation moves down through the surface
of the earth and replenishes soil moisture recharge aquifers, and
ultimately support runoff quantities.
Soil water zone – max depth
from which water can be
returned to surface
through capillary action
or ET.
Gravitational water – flow
direction is vertical
due to gravity.
(unsaturated zone or
zone of aeration)
Capillary zone, less
than
atmospheric
pressure
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Groundwater, saturation at
atmospheric pressure
Unsaturated zone
Transmission zone,
uniform
moisture
content, not
saturated
Wetting Front
Infiltration Capacity
Infiltration capacity (Ic): The maximum rate at which a given soil at
a given time can a absorb water (cm/h)
The actual rate of infiltration f can be expressed as :
I = Ic when i ≥ Ic
I = i when i < Ic
Where i = the intensity of rainfall
The infiltration capacity of a soil is high at the beginning of a
storm and has and extensional decay at the time elapses.
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Measurement of Infiltration
There are two kinds of infiltrometers :
1. Flooding-type infiltrometer, and
This is, a simple instrument consisting essentially of a metal cylinder, 30
cm diameter and 60 cm long, open at both ends. This cylinder is driven
into the ground to a depth. Water is poured into the top part to a depth of
5 cm and a pointer is set to mark the water level.
As infiltration proceeds, the volume is made up by adding water from
from a burette to keep the water level at the tip of the pointer.
Knowing the volume of water added at different time intervals, the
plot of the infiltration capacity vs time is obtained
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Horton’s Infiltration Model
- If the rainfall supply exceeds the infiltration capacity, the
infiltration tends to decrease in exponential manner
I t  I f  ( I o  I f )e  kh t
Where :
fct : the infiltration capacity (depth/time)
at any time t from the start of the rainfall
ffc: a final or equilibrium capacity
fco: the initial infiltration capacity
Kh: a constant representing the rate of decrease in f capacity
td: duration of the rainfall
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 -INDEX
-
 index is determined for a single storm and not
applicable to other storm and
-
Large storm on wet soil and
Infiltration rate may be assumed to be relatively uniform
-
Volume losses includes the interception, depression storage
and infiltration
Runoff volume

Intensity
Volume Losses
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Time
Example 3.5

A storm with 10.0 cm precipitation produce a direct
runoff of 5.8 cm given the time distribution of the storm
as below, estimate the - INDEX of the storm?
Time from start (h)
Incremental rainfall in
each hour (cm)
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1
2
3
4
5
6
7
8
0.4
0.9
1.5
2.3
1.8
1.6
1.0
0.5
Solution:
Total infiltration = 10.0-5.8 = 4.2 cm
Assume the time of rainfall excess = 8 hr (for the first trail)
Then Ф = 4.2/8 = 0.525 cm/h
This value makes the rainfall of the first hour and eight hour ineffective as their magnitude is
less than 5.25 cm/h.
Assume the time of rainfall excess = 6 hr (for the second trail)
Infiltration = 10-0.4-0.5-5.8 = 3.3 cm
Then Ф = 3.3/6 = 0.55 cm/h and by calculating the rainfall excesses
Time from start (h)
1
Rainfall excesses (cm)
0
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2
3
4
5
6
7
0.9-0.55 = 0.35 0.95 1.75 1.25 1.05 0.45
then total rainfall excesses= 5.8 cm. = total runoff
8
0