CHAPTER THREEAbstraction From Precipitation

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Engineering Hydrology (ECIV 4323)

Instructor:

Dr. Yunes Mogheir

φ

LOSSES FROM PRECIPITATION

- Evaporation and transpiration are transferred to the atmosphere as water vapour. 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 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

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Influencing Factors

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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)

Where EL = C (ew – ea)

EL : rate of evaporation (mm/day)C : a coefficient depend on wind velocity, atmospheric pressure and

other factorsew : the saturation vapour pressure at the water surface (mm of

mercury)ea : the actual vapour pressure of air (mm of mercury)

Influencing Factors

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2. Air and water temperature: 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.Atmosphere pressure: a decrease in the barometric pressure ( as in high altitudes), increases evaporation.

5. Quality of water: under identical condition evaporation from sea water is about 2-3% less that from fresh water.

6. Size of water body

Evaporation Measurement

1. EVAPORIMETER

CLASS A Evaporation Pan

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- The most widely used method of finding 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 x pan evaporation

Cp = pan coefficient and equal 0.7 for Class A land Pan.

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Evaporation Estimations Empirical Evaporation Equation

Most of empirical formulae are based on the Dalton-type equation:

EL = Kf(u) (ew - ea)

EL = lake evaporation in mm / day, ew = saturated vapour pressure at the water-surface temperature in

mm of mercury, ea = actual vapour pressure of over-lying air at a specified height in

mm of mercury, f(u) = wind-speed correction function and

K = a coefficient.

The term ea is measured at the same height at which wind speed in measured. -٨

Evaporation Estimations Meyer's Formula (1915):

EL = KM (ew - ea) ( I + u9/16 )

u9 = monthly mean wind velocity about 9 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

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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, and3. mass-transfer method

It involves writing the hydrological continuity equation for the lake anddetermining the evaporation from a knowledge or estimation of othervariables.

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 referenceArea. p,. Vis, Vos and Δ S can be measured. However, it is not possibleto measure Vig, Vog and TL and therefore these quantities can only beestimated.

If the unit of time is kept large, say weeks or months, better accuracy inthe estimate of EL is possible. In view of the various uncertainties in theestimated values and the possibilities of errors in measured variables,the water-budget method cannot be expected to give very accurateresults. -١١

I. Water-budget method,

EVAPOTRANSPIRATION

TRANSPIRATION

Transpiration is the process by which water leaves the body of a living plant and and reaches the atmosphere as water vapour. The water is taken up by the plant-root system and escapes through the leaves.

The important factors affecting transpiration is - atmospheric vapour pressure, - temperature, - wind, light intensity and - characteristics of the plant, such as the root and leaf systems

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EVAPOTRANSPIRATION

Evapotranspiration takes place, the land area in which plants stand 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 head 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.

Equation 3.13

Equation 3.14

Tables 3.3, 3.4 and 3.5

-١٤Example 3.2

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It is the segment of precipitation that is prevented to reach the ground by vegetation and subsequently evaporates

Interception

rainfall

throughfall

stemflow

Interception = Rainfall – stemflow – throughfall

Route of interception

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1. Interception loss : rain water retained by the vegetation as surface storage >>>> evaporate

2. Througfall : rain water can drip off the plant leaves to join the ground surface or the surface flow

3. Stem flow: the rain water may run along the leaves and braches and down the stem to reach the ground surface

Influencing Factors

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1. Storm characteristics : rainfall intensity, duration, wind …etc

2. The vegetation : species, age, density of plants and trees3. 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 %.

Influencing Factors

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ó Estimation of interception can be significant in annual or long-term models

ó For heavy rainfalls during individual storm events interception is neglected

Rainfall (mm)

Inte

rcep

tion

loss

as

% R

ainf

all

5 10 15 20 30

20

4060

80100 Beech trees

Estimation of Interception

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Most interception loss develops during the initial storm period and the rate of interception rapidly approach to zero.

Ii = Si + KEt

Ii = the volume of water intercepted (mm)SI = the interception storage whose values varies from 0.25 to 1.5

depending on the nature of vegetationKi = ration of vegetal surface area to its projected areaE = Evaporation rate in (mm/h) during the precipitationt = duration of rainfall in hours

Horton:Li = 0.015+ 0.23 P (ash trees)Li = 0.03+ 0.22 P (oak trees)

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When the precipitation of a storm reaches the ground, it must fill up all depressions before it can flow over the surface

Depression Storage

The volume of water trapped in these depressions called depression storage

Influencing Factors

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1. Type of soil : 0.50 cm for sand, 0.25 cm fro clay2. The condition of the surface : amonut and nature of depression 3. The slope of Catchment 4. The soil moisture

Infiltration

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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.

Unsaturated zone

Gravitational water – flow direction is vertical due to gravity. (unsaturated zone or zone of aeration)

Transmission zone, uniform moisture content, not saturated

Capillary zone, less than atmospheric pressure

Groundwater, saturation at atmospheric pressure

Wetting Front

Infiltration Capacity

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Infiltration capacity (fc): 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 :

f = fc when i ≥ fc

f = i when i < fc

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.

Infiltration Capacity

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Measurement of Infiltration

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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

- If the rainfall supply exceeds the infiltration capacity, the infiltration tends to decrease in exponential manner

Where :

fct : the infiltration capacity (depth/time) at any time t from the start of the rainfallffc: a final or equilibrium capacityfco: the initial infiltration capacityKh: a constant representing the rate of decrease in f capacitytd: duration of the rainfall

tkcfoccfct

heffff −−+= )(

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Horton’s Infiltration Model

- φ 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

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φ -INDEX

Intensity φ

Time

Volume Losses

Runoff volume

Example 3.5

ó 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 φ-

INDEX of the storm?

Time from start (h) 1 2 3 4 5 6 7 8

Incremental rainfall in each hour (cm)

0.4 0.9 1.5 2.3 1.8 1.6 1.0 0.5

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Solution:Total infiltration = 10.0-5.8 = 4.2 cmAssume 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

then total rainfall excesses= 5.8 = total runoff

Time from start (h) 1 2 3 4 5 6 7 8Rainfall excesses (cm) 0 0.9-0.55 = 0.35 0.95 1.75 1.25 1.05 0.45 0

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WH3

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ó 3.2ó 3.4ó 3.9ó 3.13