KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY,

KUMASI, GHANA

COLLEGE OF ENGINEERING

DEPARTMENT OF GEOLOGICAL ENGINEERING

LECTURE NOTES FOR

GED 357: BASIC HYDROLOGY

Prepared by:

E. K. Appiah-Adjei

August, 2009

COURSE OUTLINE – FIRST SEMESTER, 2009

WEEK ACTIVITY

1 REGISTRATION

2-3 INTRODUCTION: Hydrologic Cycle Practical Values (and Failures) of Hydrology

3-5 WEATHER AND HYDROLOGY: Temperature, Humidity and Precipitation Types and Variations of Precipitation Measurement of Precipitation Analysis of Precipitation Data

6-7 EVAPORATION (+ EVAPOTRANSPIRATION): Factors affecting evaporation from free water surface Seasonal and Ariel Variations of Evapotranspiration Measurement and Estimation of Evaporation.

8-9 INFILTRATION: Factors affecting infiltration Methods of determining infiltration Storage and movement of infiltration

10-12 RUNOFF: Sources and components of runoff Factors affecting total volume and distribution of runoff Measurement, estimation and prediction of runoff Hydrograph Analysis Drainage Patterns

13-16 EXAMINATION

REFERENCES Wilson, E. M. (1983). Engineering Hydrology. Macmillan Education Ltd., London, 309pp.

Shaw, E. M. (1988). Hydrology in Practice. Chapman and Hall, UK, 569pp.

Ward, R. C & Robinson, M. (1990). Principles of Hydrology. McGraw-Hill Co., London, 365pp.

Linsley, R. K., Kohler, M. A. & Paulhus, J. H. (1982). Hydrology for Engineers. McGraw-Hill

Co., USA, 508pp.

Reddy, P. J. R. (2007). A Textbook of Hydrology. Laxmi Publications (P) Ltd., New Delhi,

530pp.

Chow, T. V., Maidment, R. D. & Mays, W. L. (1988). Applied Hydrology. McGraw-Hill Co.,

572pp.

ii

1.0 INTRODUCTIONThe word hydrology is derived from the Greek words hydor and logos, which means water and

science respectively. Thus it is, broadly, defined as the study of the origin, movement, distribution,

and quality of water on and over the surface of the earth. Basically, hydrology deals with all the

waters (i.e., rainfall, snow, surface water, groundwater, etc), on the earth and their usefulness to life,

and embraces the concept of the hydrologic cycle, which is the transportation of water through the

air, over the ground surface and through the strata of the earth.

Due to the several applications of hydrology in many branches of engineering like hydraulics, water

resources, irrigation, etc., the term engineering hydrology is often used. Engineering hydrology

deals with segments of the very broad field of hydrology pertinent to the design and operation of

engineering projects for the control and use of water. In this course, a basic understanding and

application of the principles of hydrology to solving engineering problems will be treated.

1.1 THE HYDROLOGICAL CYCLE

The hydrologic cycle (Fig. 1) describes the continuous movement of water on, above and below the

surface of the earth. The cycle has no exact beginning or ending point, but may be conveniently

assumed to start with evaporation of water from the oceans since most of the water on earth is in the

oceans. Solar radiation from the sun evaporates water in oceans (or surface water) into water vapour.

Moving air masses transport the vapour from the ocean surface and then into the atmosphere by

rising air currents where they condense to form clouds under right conditions. The clouds move in

the atmosphere until under suitable conditions when they condense and form water droplets. These

droplets may then fall as precipitation (i.e. rainfall, snow and hail) to the oceans, streams, land

surface, etc., or may re-vaporize while still aloft. The precipitation that falls directly into streams is

known as channel precipitation. Portions of the precipitation falling on the land surface may be

intercepted by trees and vegetation, and eventually evaporated back to the atmosphere whereas the

rest of it reaches the ground. The precipitation that reaches the ground surface is known as

throughfall.

Precipitation falling on the land surface may be stored temporarily as snow and ice or as water in

puddles known as depression storage. Some of the precipitation -rain and melting ice or snow- will

drain across the land surface as overland flow to stream channels. The total flow in a stream is

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known as runoff. Portions of the precipitation will also seep through the surface soil by a process

called infiltration, and then move vertically downwards by gravity (in a process known as

percolation) into the saturated ground zone beneath the water table. Water stored in the saturated

zone beneath the water table is known as groundwater. Some of the infiltrated water, sometimes,

stays close to the land surface and may flow back into surface water bodies in a process known as

interflow. More so, groundwater may, under favourable conditions, seep directly as baseflow into

surface water and vice versa. A spring is produced when the water table is intercepted by

topography and water gushes out from the land surface. Infiltrated water can also be transpired by

plants and evaporated from the plants into the atmosphere in a process known as

evapotranspiration.

Figure 1: The Hydrological Cycle (after Shaw, 1996)

It should be appreciated that the description of the hydrological cycle in Fig.1 is very much over

simplified. For example, some of the water, which enters the surface streams, may percolate to the

groundwater system while in other cases groundwater becomes the source of surface stream flows

(i.e. effluent and influent streams). Also, some precipitation may remain on the ground as snow for

several months, and in some cases years, before melting releases the water to streams or groundwater

system. It should be noted, generally, that:

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The cycle may be short-circuited at several stages, e.g. precipitation may be trapped by

vegetation and re-vaporize back to the atmosphere;

There is no uniformity in the time a cycle is completed;

The intensity and frequency of the cycle depends on geography and climate, which varies

according to latitude and season of the year;

Man can exercise control on certain parts of the cycle, e.g. runoff can be directed to a

preferred storage place instead of it flowing naturally to a stream or groundwater system.

The movement of water in the cycle on earth spans from an average depth of 1 km in the lithosphere

to a height of about 15 km in the atmosphere (Reddy, 2007). The hydrologic cycle also serves to

emphasize the four basic phases of interest to the hydrologist (i.e., precipitation, evapotranspiration,

surface stream flow, and groundwater). The movement of water through the various phases of the

cycle is very erratic, both in time and area. On occasions, torrential rains may flood surface channels

whilst at other times precipitation and stream flow may appear to have stopped completely leading to

droughts. In adjacent areas the variations in the cycle may be quite distinct. It is precisely these

extremes of floods and droughts that are often of most interest to the engineering hydrologist since

many of the hydraulic engineering projects are designed to protect against the ill effects of extreme

events.

The science of meteorology may explain the reasons for these climatic extremes, and the hydrologist

should understand it at least in broad detail. However, the engineer must be able to deal

quantitatively with the interrelations between the extremes and the various phases of the cycle so as

to be able to predict their influence on man-made structures (quite) accurately. Also of concern is the

frequency with which the various extremes of the cycle may occur since it is the basis of economic

analysis, which is, or should be, the final determinant for all structures. Quantitatively, the

hydrological cycle is evaluated using the general water balance equation expressed as:

Inflow = outflow ± changes in storage

This relation is based on the law of conservation of mass and can be applied to systems of any size

(e.g. an area, a reservoir, a lake, etc.). The equation is time-dependent; hence the elements of inflow

must be measured over the same time period as the outflow. For example, a simple water balance

equation of a region may be represented as:

P = SR + ET + S(streams, lakes, seas, etc.) + G(groundwater),

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where P is precipitation, SR is surface runoff, ET is evapotranspiration, S is change in surface water

storage and G is change in groundwater storage.

The hydrologic cycle reaches the atmosphere and traverses the domain of hydrometeorology and

climatology. In the hydrosphere (i.e., all the water surrounding the earth), it embodies the domain of

potamology (the study of surface streams), limnology (the study of lakes, lagoons, etc), cryology

(study of snow and ice), and glaciology (the study of glaciers). Table 1 presents an estimate of

word’s water in the hydrological cycle.

Table 1: Estimate of the world’s water resource (Source: UNESCO, 1971)

Parameter Volume (km3) Equivalent

Depth1 (m)

Average Residence

Time2

Oceans and Seas 1 370 x 106 2500 4000+ yrs

Freshwater Lakes and Reservoirs 125 000 0.25 ~ 10 yrs

Swamps 3 600 0.007 1 – 10 yrs

River Channels 1 700 0.003 ~ 2 weeks

Moisture in Soil and Unsaturated Zone 65 000 0.13 2 wks – 1 yr

Groundwater 4 x 106 to 60 x 106 8 – 120 2 wks – 10000 yrs

Ice Caps and Glaciers 30 x 106 60 10’s – 1000’s of yrs

Atmospheric Water 13 000 0.025 8 – 10 days

Biological Water 700 0.001 ~ 1 week

In the lithosphere, the hydrologic cycle relates to agronomy, hydrogeology and geomorphology.

Since water affects both plant and animal lives, the hydrologic cycle extends to plant ecology,

silviculture, biohydrology, and hydrobiology. The cycle has its important influence in agriculture,

forestry, geography, watershed management, political science, economics, sociology, etc. Other

areas of practical importance of the hydrological cycle include structural design, wastewater

disposal, water supply and/or treatment, irrigation, drainage, hydropower, flood control, navigation,

erosion and sediment control, salinity control, pollution abatement, recreational use, fish and

wildlife, insect control, and coastal works.

1 Equivalent depth is estimated as though the storage were uniformly distributed over the entire earth surface2 Residence Time is the average duration for water to pass through a water molecule to pass through a subsystem of the hydrological cycle

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In recent years, there has been considerable attention paid to the world water balance –e.g. Nace,

1971; Lvovitch, 1970; Sutcliffe, 1970- and most recent estimates of these data emphasize the

ubiquitous nature of groundwater. A critical study of some of the water resources data (e.g., in Table

1) would show the relative importance of groundwater over the other components of the hydrological

cycle. Ignoring the over 90% of the earth’s water that rests in the oceans and seas at high levels of

salinity, groundwater accounts for about two-thirds (2/3) of the fresh water resources of the world.

However, if one limits the consideration to only the utilisable fresh water reserves, then groundwater

almost accounts for the total body of fresh water. However, the volumetric superiority of

groundwater is tempered by its average residence times. Considering only the most active

groundwater regimes estimated at about 4 x 106 km3 (Lvovitch, 1970), rather than the 60 x 106 km3,

the fresh water breakdown comes to approximately:

Soil Moisture 1.5%

Surface Waters (rivers, reservoirs, swamps, etc.) 3.5%

Groundwater 95%

1.2 HYDROLOGY IN ENGINEERING

As stated in previous section, the engineer basically applies the principles of hydrology in the

designing, building and operation of engineering projects for the control and use of water. Thus the

engineer often needs to have a good idea of the main processes within the hydrological cycle and be

able to estimate the quantity of water (as well as the distribution, time of occurrence and frequency

of occurrence of water) to be expected at the project site. The engineer can be able to do this by

analysing and interpreting data on the processes in the cycle and effectively applying them.

Some of the practical applications of hydrology in engineering are in the estimation of:

the flood flows to be expected at a spillway, highway culvert or in a city drainage system;

the reservoir capacity required to assure adequate water for irrigation, water supply or

hydroelectric power generation;

the effects reservoirs, levees, and other control works will exert on flood flows in a stream;

the water budget of a region;

the contaminant transport risk and establishing environmental policy guidelines; etc.

Depending on their scale of operations, certain organisations may employ their own specialist

hydrologist to analyse their problems whilst others will not need fulltime hydrologists.

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1.3 SCOPE AND LIMITATIONS OF HYDROLOGY

Hydrology deals with many topics, which for convenience may be classified into two phases,

namely; i. data collection, and ii. methods of analysis and application.

The complex features of natural processes involved in hydrologic phenomena make it difficult to

treat many hydrologic processes by rigorous deductive reasoning. It is not always possible to start

with basic physical law and from it determines the hydrologic result to be expected. Rather, it is

necessary to begin with a mass of observed facts, statistically analyse these, and from the analyses

establish a system pattern that govern these events. The hydrologist is thus, in a difficult position

without adequate historical data for the particular area. The collection of hydrologic data has

therefore been the life work of many hydrologists, and is a primary function of many geological

survey departments, weather bureaux, and other related units. It is therefore important to learn how

these data are collected and published and the limitations of their accuracy, and the proper methods

of interpretation and adjustments.

Generally, each hydrologic problem is unique in that it deals with a distinct set of physical conditions

within a specific river basin. Hence, the quantitative conclusions of one analysis are often not

directly transferable to another problem. However, the general solution for most problems can be

developed from application of few relatively standard procedures.

1.4 SOURCES OF INFORMATION

The main source of meteorological data in Ghana is in the Meteorological Services Department

(MSD), which has offices in all regions. Other sources of information include the Ministry of

Agriculture, Ghana Water Company Limited (GWCL), Civil Aviation Authority (CAA), Volta River

Authority (VRA), and Irrigation Development Authority (IDA). Other sources include private

organisations such as the Universities and other research organisations like CSIR. MSD has a

number of publications available for sale at their Accra office.

2.0 WEATHER AND HYDROLOGYThe hydrological characteristics of an area or a region depend primarily on its climate, and then on

the geology and topography. The topography influence precipitation and the occurrence of lakes,

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marshland and flow rates of runoff whilst the rocks in the earth (i.e., geology) sometimes serve as

water reservoirs (i.e., groundwater) and source of water supply to rivers and lakes; the geology also

has an influence on the nature of the topography.

Climate is the average weather3 pattern in an area or a region over a long period of time; usually 30

years by WMO standard. The climate of a region depends on its geographic position on the earth

surface. The climatic factors that establish the hydrologic features of a region are the amount and

distribution of precipitation, the occurrence of snow and ice, and the effects of wind, temperature,

and humidity on evaporation and snow melt. To obtain these parameters, daily weather

measurements have to be made over a long time periods. Hence, the design and operation of

hydraulic projects involve meteorological considerations. Hydrologic problems in which

meteorology plays an important role include the determination of the possible maximum

precipitation for an area. It is, therefore, important for the hydrologist to have some understanding of

the meteorological processes that determines a regional climate. As a result, hydrometeorology has

evolved as a specialized branch of hydrology linking the fundamental knowledge of meteorology4

with the needs of the hydrologist. Hydrometeorology basically studies the atmospheric processes

which affect water resources.

2.1 STRUCTURE OF THE ATMOSPHERE

The atmosphere forms a distinctive protective layer of gases of about 100 km thick around the earth.

Its chemical composition is made up of Nitrogen (78%), Oxygen (21%), Argon (0.9%), Carbon

Dioxide (0.03%), Water Vapour (0 - 4%), and Trace amounts of other gases. These trace gases may

include small proportions of inert gases, ozone, hydrocarbons, ammonia, nitrates, man-made gaseous

contaminants from industries, radioactive isotopes from nuclear explosions, etc., which may exist

temporarily in the atmosphere. Majority of the ozone is concentrated in the stratosphere where it

protects life on earth by absorbing ultra-violet radiations from the sun and thus reducing global

warming. On other hand, increasing release of high amounts of carbon dioxide into atmosphere by

activities of man will strengthen greenhouse effect and thereby contribute to global warming.

In the atmosphere, temperature varies in an irregular but characteristic way with increasing altitude

whilst both air pressure and density continuously decreases with increasing altitude. The irregular 3 Weather is a mix of events that happen each day in the atmosphere in terms of temperature, rainfall, humidity, etc. It’s recorded daily and predicted worldwide by meteorologists.4 Meteorology is the study of the changes in temperature, air pressure, moisture, and wind direction in the atmosphere.

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variation of temperature divides the atmosphere into layers known as spheres, as shown in Fig. 2.

The layers may mainly be divided into an upper and lower atmosphere, the demarcation being about

50 km above sea level. The upper atmosphere plays a secondary role in climatic changes, while the

lower atmosphere is where most of the critical mass and energy transfer occur. The lower

atmosphere is also divided into two parts –Stratosphere and Troposphere.

Figure 2: Structure of the atmosphere (after Shaw, 1996)

The troposphere is the lowest layer in the atmosphere where almost all the dust and moisture of the

atmosphere is concentrated. The temperature in this layer decreases with increasing altitude at an

average rate of 6.5 oC/km; this is known as lapse rate. The top of the troposphere, the dividing line

between the troposphere and stratosphere, is called the tropopause. The average height of the

tropopause is about 11 km (see Fig. 3) but ranges from 8 km at the Poles to 16 km at the Equator.

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This seasonal variation of the tropopause may be caused by changes in air temperature and pressure

in the atmosphere; generally when the surface temperatures are high and pressure is high at sea level,

there is the tendency for the tropopause to be at a higher level

The stratosphere is above the tropopause, contains very little moisture and dust but a major portion

of ozone. After a general decrease in temperature through the troposphere, the rise in temperature

from heights of 20 to 50 km is caused by a layer of ozone, which absorbs short wave solar radiation

and so releasing some of the energy as heat. The stratopause, located at about 50 km above the

earth’s surface is the upper limit of the stratosphere. Above the stratopause are the mesosphere and

then the thermosphere, which together forms the upper atmosphere.

To the hydrologist, the troposphere is the most important layer because it contains about 75 % of the

weight of the atmosphere and virtually all its moisture. This is also the area in which atmospheric

processes which affect water resources mostly takes place. However, meteorologists are becoming

increasingly interested in the stratosphere and mesosphere since it is in these outer regions that some

of the disturbances affecting the troposphere and the earth’s surface have their origin. Some of the

characteristics/variables in the atmosphere pertinent to hydrology include temperature, pressure,

humidity, cloudiness and wind.

a) Temperature: Temperature is a measure of the coldness or hotness of a body. It is measured

with a thermometer in units of oC or K {K = 273 + oC; oC = 1.8 (oF – 32)}. A continuous automatic

recording of temperature with time can be done with an instrument called thermograph. Globally,

temperature is generally warmer in regions near the equator than at the poles. However, the effects of

specific heat of the earth and water, patterns of oceanic and atmospheric currents, the seasons of the

year, topography, vegetation and altitude tend to vary this rule. The variation of temperature with

altitude in the atmosphere is as explained in fig. 3 and the section above. Within a day, temperature

varies from a minimum around sunrise to a maximum after the sun has reached its zenith before it

begins to fall through the night till sunrise again; the daily average temperature for the day is taken as

the average of the maximum and minimum temperatures for the day. The mean monthly temperature

is the arithmetic average of the mean daily temperatures of all days in the month. Similarly, the mean

annual temperature is the arithmetic average of all the mean monthly temperatures in a year

b) Atmospheric Pressure and Density: Atmospheric pressure is defined as the weight of a

column of air of unit cross-sectional area from the level of measurement to the top of the atmosphere.

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It may be considered to be the downward force on a unit horizontal area resulting from the action of

gravity (g) on mass (m) vertically above it. Pressure is usually measured with a barometer in bars or

mm height of a column of mercury. At sea level the average atmospheric pressure (p) is 1 bar (≈ 100

kPa ≈ 100 kN/m2 ≈ 760 mmHg = 1013.25 mb = 1 atm). Pressure can be estimated by using the ideal

gas law given by the expression:

P = ρRT ...................................................... (Eqn. 1)

where ρ is air density; R is the specific gas constant (= 2.87 X 10-3 mb cm3g-1K-1 for dry air); and T is

air temperature in Kelvin.

c) Water Vapour: Humidity is the amount of water vapour -the most important constituent in the

atmosphere to the hydrologist- in the atmosphere. It is usually measured as vapour pressure in

millibars. The distribution of water vapour varies over the earth’s surface according to temperature;

it is highest at the equatorial regions and lowest at the poles. In any given area, warmer air would

have more water vapour than cold air.

The amount of water vapour in the air is directly related to the temperature, and thus although lighter

than air, water vapour is restricted to the lower layers of the atmosphere. Water vapour movement

and phases are crucial to the earth-wide heat and mass balance. Upon evaporation and condensation

of water vapour, heat is absorbed and released respectively. Since the two processes rarely occur at

the same location, the vapour is the carrier of mass and energy from one part of the globe to another.

It is the liquid and solid precipitation of vapour that ultimately controls the land based hydrological

processes. Humidity can be measured with a hygrometer. Some of the recognized physical

parameters used in determining water vapour in the atmosphere are described below:

1) Saturated Vapour Pressure: Air is said to be saturated when it contains the maximum

amount of water vapour it can hold at its prevailing temperature. The pressure exerted by water

vapour molecules in this state is known as saturated vapour pressure (SVP) at that particular

temperature. SVP values vary with air temperature as shown in Figure 3; at any temperature (T)

saturation occurs at a corresponding vapour pressure, еs. Saturated air may take up even more water

vapour and become supersaturated if it is in contact with liquid water in a sufficiently finely divided

state (e.g. very small water droplets in clouds); this supersaturated air mass will lie above the svp

curve in fig. 3. However, unsaturated atmospheric air mass will be below the svp curve as indicated

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with point Y on fig. 3. The relation between saturated vapour pressure and temperature can be

approximated by the equations:

es=2.7489× 108 exp .( −4278.6T d+242.79 ) ……………….. (Eqn. 2)

es=6.11exp .( 17.27 T237.3+T ) ………………. (Eqn. 3)

where temperature is in oC and еs is mb; the relation is used to estimate vapour pressure e at any air

temperature T.

2) Dew Point: This is the temperature at which a mass of unsaturated air becomes saturated

when cooled at constant pressure and water content (i.e., no change in humidity of the air) before

condensation starts. If the unsaturated atmospheric air mass at Y (T, e) is cooled without any change

in humidity (Fig. 4), then Y would move horizontally until it intersects the curve at Y* (Td, e) to

become saturated. The temperature, Td, at this point of intersection is the dew point and e is the

vapour pressure of the air mass.

Figure 4: Saturation vapour pressure curve of water vapour in air

3) Saturation Deficit: If more water vapour is added to the unsaturated air mass at Y while

temperature is kept constant, the vapour pressure of the air mass will increase vertically up until it

intersect the curve at Ys (T, es) where the air mass becomes saturated. The difference between the

saturation vapour pressure (еs) and the actual vapour pressure of the air mass at that specific air

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Y*

Ys

Y

temperature is known as saturation deficit (also known as vapour pressure deficit. This deficit

represents the extra amount of water vapour the air can hold at temperature T before becoming

saturated. For example, in fig. 3, еs and е are 17 mmHg and 7 mmHg respectively, which imply that

the:

Saturation deficit = еs – е = 17 – 7 = 10 mmHg

If evaporation is allowed to take place in the unsaturated air mass Y, thereby increasing humidity and

vapour pressure, without controlling temperature, then the air mass will move diagonally until it

reaches saturation at point Yw (Tw, ew). The temperature Tw is called the wet-bulb temperature and it

is the temperature to which the original air can be cooled by evaporating water into it; this can be

found by using the wet bulb thermometer.

4) Relative Humidity: This is the relative measure of the amount of moisture in the air to the

amount needed to saturate the air at the same temperature (usually expressed in percentage). It is in

fact the amount of water vapour in a given volume of air expressed as a ratio of the maximum

possible amount of water vapour that the same volume of air can hold at the same temperature. From

fig. 3:

Relative Humidity = е/еs x 100% = 7/17 x 100% = 41.18 %.

Relative humidity is usually measured with a psychrometer. This instrument consist of two glass

thermometers –viz. wet bulb thermometer and dry bulb thermometer- ventilated by a fan, which are

used to measure the wet bulb temperature and ambient air temperature respectively. The wet bulb

thermometer has it mercury bulb wrapped with a wick with the other end of wick submerged in

distilled water to ensure continuous moisture supply to the bulb; its measured values are always less

than the dry bulb ones. The difference between the two temperatures (T - Tw), known as wet bulb

depression, is proportional to relative humidity. The measured values of temperature from the

psychrometer and atmospheric pressure are related by:

e = ew – γ (T - Tw) .............................. (Eqn. 3)

where e (mb) is vapour pressure at dry bulb temperature T (oC); ew (mb) is saturated vapour pressure

corresponding to wet bulb temperature Tw (oC); and γ is the psychrometer constant (γ = 0.66 mb/oC if

e is in mb; γ = 0.485 if e is in mmHg)

5) Absolute Humidity: This is equivalent to water vapour density (ρw), and in simple terms

may be defined as the amount of water vapour contained in a given volume of air. Vapour density is

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generally expressed as the mass of water vapour per unit volume of air at a given temperature. Thus

if a volume V m3 of air contains mw g of water vapour, then:

Absolute humidity = (mass of vapour, g)/(volume of air, m3) = mw/V (gm-3)

6) Specific Humidity (q): It is defined as the mass of water vapour in a unit of moist air. This

relates the mass of water vapour mw (g) to mass of moist air (kg) in a given volume. It is given by the

relation:

q = (mass of water vapour, g)/(mass of moist air, kg)

q = mw (g)/(mw + md) (kg) ......................................... (Eqn. 4)

q = ρw/ρm (gkg-1)

From ideal gas law (Eqn. 1), the density of dry air (ρd) and water vapour (ρw) are given by:

ρd=Pd

Rd T= P−e

Rd T ;

ρw= eRwT

=0.622 eRd T

, (since Rw = Rd/0.622)

Therefore, the density of moist and specific humidity can be obtained from the relations:

ρm=ρd+ ρw=P−0.378 e

RdT ....................................... (Eqn. 5)

q=ρw

ρm= 0.622 e

P−0.378 e ........................................ (Eqn. 6)

where md is the mass of dry air in kg; ρw is the density of water; and ρm is the density of moist air; e

is the water vapour pressure; and P is total air pressure (i.e., combination of vapour pressure and dry

air pressure)

7) Precipitable Water: It is the total amount of water vapour in a column of air expressed as

the depth of liquid water in mm over the base area of the column. The precipitable water gives an

estimate of the maximum possible rainfall under the unreal assumption of total condensation.

In a column of water vapour of unit cross-sectional area (Fig. 5), a small thickness, dz, of the moist

air contains a mass of water given by:

dmw = ρwdz

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Thus in a column of air from heights z1 and z2, corresponding to pressures p1 and p2, the total mass of

water would be given by:

But dp is related to height as: ,

This implies:

Thus: But

Figure 5: A column of water vapour

Converting to height of water (W) in mm (NB: ρw = 1 g/cm3, area of column = 1 cm2) gives:

where p is in mb, q in g/kg, and g = 9.81 m/s2.

In practice, q is not known to be a function of p. Hence, W is evaluated by summing the

contributions for a sequence of layers in the troposphere from series of measurements of specific

humidity, q, at different heights, and using the average specific humidity q over each layer with the

appropriate pressure difference:

........................................ (Eqn. 7)

Sample Calculation

From a radiosonde (balloon) ascent, the pairs of measurements of pressure and specific humidity

shown in Table 2 were obtained. Calculate the precipitable water in the column of air up to the 250

mb level (g = 9.81 m/s2).

Pressure (mb) 1005 850 750 700 620 600 500 400 250

Specific Humidity g/kg 14.2 12.4 9.5 7.0 6.3 5.6 3.8 1.7 0.2

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Pn – Pn+1 = 155 100 50 80 20 100 100 150

Mean q = 13.30 10.95 8.25 6.65 5.95 4.70 2.75 0.95

2061.5 1095 412.5 532 119 470 275 142.5

This implies,

Hence, the precipitable water up to the 250 mb level:

TRIAL QUESTIONS

1. At a weather station, the air pressure is measured to be 101.1 kPa, the air temperature is 22 oC and

the dew point temperature is 18 oC. Calculate the corresponding:

(a) saturated vapour pressure; (b) actual vapour pressure (c) relative humidity; (d) specific

humidity; (e) air density.

[Ans.:

2. An air mass is at a temperature of 28 oC with relative humidity of 70 %. Determine:

(a) saturation vapour pressure; (b) saturation deficit; (c) actual vapour pressure in mb and in mm

Hg; (d) dew point; and (e) wet-bulb temperature.

[Ans.: (a) 28.32 mm Hg; (b) 8.5 mm Hg; (c) 19.82 mm Hg or 26.36 mb; (d) 22 oC; (e) 23.7 oC]

3. A psychrometer recorded the dry bulb and wet-bulb temperatures of 41 oC and 27 oC respectively

when the atmospheric pressure was 1001 mb. Determine:

(a) actual vapour pressure; (b) saturation vapour pressure; (c) relative humidity; (d) dew point

[Ans.: (a) 26.4 mb; (b) 77.8 mb; (c) 33.9 %; (d) 22 oC]

15

3.0 PRECIPITATIONThe water in the atmosphere, although forming one of the smallest storages of the earth’s water, is

the most vital source of fresh water for mankind and life on earth. Water is present in the air in its

gaseous, liquid and solid states as water vapour, cloud droplets and ice crystals respectively. The

formation of precipitation from water vapour, as it exists in the air, is a complex and delicately

balanced process. If air is pure, condensation of water vapour to water droplets will occur only when

the air becomes greatly supersaturated. However, the presence of small airborne particles called

aerosols, or in this case condensation nuclei, provide the nuclei around which water vapour in normal

saturated air can condense. The condensed water droplets fuse or collide together to form large

droplets (i.e. coalescence), which with time overcome air resistance in the atmosphere and fall as

precipitation.

There are two main types of condensation nuclei; the distinction is due to Aitkin (Mason, 1975):

i. hygroscopic particles having affinity for water vapour on which condensation begins before

the air becomes saturated; these are commonly salt particles from the ocean, and

ii. non hygroscopic particles needing some degree of super-saturation, depending on their size,

before attracting condensation –e.g. natural dust and grits, soot and ash particles.

Condensation nuclei range in size from radius of 10-3µm for small ions to about 10µm for large salt

particles. The condensation of aerosols in time and space varies considerably; the number of particles

in a given volume depends on the size of the particles. A typical number for the smallest particle is

about 40,000 per cc whilst for giant nuclei of more than 1µm radius, there may be only 1 per cc.

Large hygroscopic salt nuclei are normally confined to maritime regions, but the tiny ones called

Aitkin nuclei can travel across continents and even circumnavigate the earth. Although condensation

nuclei are essential for widespread condensation of water vapour, only a small fraction of the nuclei

present take part in cloud droplet formation at any one time.

Before precipitation can occur at any time, moist air must first be cooled to near dew point. This can

be brought about in three (3) ways, namely:

i. By adiabatic expansion of rising air: A volume of air may be forced to rise by a mountain

range; the reduction in pressure causes a lowering of temperature without any transfer of

16

heat, which will lead to cooling of the air to condense at dew point. The type of precipitation

arising from this air lifting process is termed as orographic precipitation.

ii. By a meeting of two different air masses (i.e.): For example when a warm mass of air

converges with a cold mass, the warm air is by convection forced to rise over the cold air to

cool to dew point; this leads to convective precipitation. Also, any mixing of contrasting

masses of air will lower the overall temperature, thereby leading to condensation and

subsequent precipitation.

iii. By contact between a warm moist air mass and a cold object such as the ground. This may

cause the air to cool to dew point. This process is termed frontal activity and often leads to

frontal precipitation.

3.1 MEASUREMENT OF PRECIPITATION

In the measurement of precipitation, three basic rules must be observed viz.

i. All measurements must be comparable and consistent;

ii. Standard instruments must be installed uniformly in representative areas; and

iii. Regular observational procedures –e.g. daily, weekly, or monthly- must be adopted.

(NB: Daily reading is the most reliable since it enables every change that occurs to be measured)

Precipitation is usually measured at a point using collectors of very simple construction. Essentially,

the collectors should be of standardised dimension for quality control checks and serve the purpose

of estimating the volume of precipitation per unit area. Rainfall, which is the most common form of

precipitation in Ghana, is measured with rain gauge. Snow fall may be measured with a rain gauge

fitted with a heating system or using a graduated stick to determine snow thickness and densities at

depth for estimating the equivalent amount of water in a unit of snow. Rain gauges may be broadly

classified under two main headings, namely: recording and non-recording gauges.

3.1.1 Non-Recording GaugesIn this type of rain gauge, the amount of rainfall intercepted by a gauge is measured by an observer at

regular intervals, usually every 24 hours but it could be weekly or monthly. The collecting funnel is

17

exactly 5 inches in diameter and 4 inches deep. The rain is led into the glass or polythene via the

funnel, and then read later by the observer. In exceptionally heavy rains, this may overflow into an

inner glass can, and in very rare cases these two may overflow into the outer casing of the gauge.

The outer and inner casings do not allow evaporation to take place.

3.1.2 Recording Gauges

Recording gauges automatically measure and record, continuously, the amount and time of a rainfall

event. There are two basic types of recording gauges, namely: the tilting siphon and the tipping

bucket types.

a) Tilting Siphon Gauge: The tilting siphon is classified under float gauges. The principle of all

float gauges is that rainfall is collected into a funnel and transferred into a float chamber. The

vertical movement of the float as the water rises in the chamber is transmitted by means of a pulley

and pen arm to a revolving chart.

In the tilting siphon, the float chamber is counter balanced by a weight so that when 5 mm (or 0.2”)

of rain has been collected the chamber tilts forward filling the siphon tube and suddenly starting the

siphon action. Water flows out of the chamber until the level has fallen to that of the exit hole when

siphoning ceases and the lightened float chamber resumes its upright position. Normally, a daily

plug and chart are fitted such that the chart revolves at speed of 0.45 inch per hour. Other gauges

have been fitted with electrical strip chart mechanism whereby the time scale is magnified.

b) Tipping Bucket Gauge: In this system, rain is transferred from the collecting funnel into one of

the two compartments of the tipping bucket system, and when a definite small amount has been

collected the bucket tips over. This action allows the falling rain to be collected into the other

compartment while at the same time emptying the other. Each movement of the bucket is

transmitted, mechanically or electrically, to a moving strip chart so that the rainfall record consists of

stages representing the small amount of rain (e.g. 0.01 mm).

In relation to the tilting siphon, the main disadvantages of the tipping bucket gauge are that:

i. rainfall of less than the capacity of the bucket of the compartments are not recorded, and

ii. if rain ceases before the bucket tips, the surface area from which evaporation may take place

is large.

18

It advantages are that it is:

i. mechanically much simpler,

ii. able to record electrically at a distance, and

iii. it is less likely to be damaged by frost than the enclosed chamber of the tilting siphon type.

3.2 SITING OF RAIN GAUGES

The choice of a suitable site for a rain gauge is a professional job; it must be decided with

competence. The amount measured by the gauge should be representative of the rainfall in the

surrounding area. What is actually caught as a sample is the amount that falls over the orifice area of

the gauge (i.e. 150 cm2). Therefore, it is best to find some level ground, if possible, but definitely

avoiding steep hillsides especially those sloping down towards the prevailing wind. This means it is

important to know the prevailing wind direction of the country or the town in which the siting is

required. A sheltered, but not over sheltered, site is ideal.

A modification of the site will have effects on the readings –e.g. new structures, collapsing of

existing buildings, or vegetation growth can affect the readings. Structures of height, h, around the

gauge should be at distance not less than 2h from the gauge. For areas where there is no vegetation –

e.g. Accra plains, and some parts of the Northern and Upper regions- the area is over-exposed. Under

such circumstances, turf wall may be required to provide the needed shelter. The outer face of the

turf wall is made to slope (streamlining) in order to reduce the generation of eddy currents around as

would be experienced with vertical walls. The area must, also, be properly drained to prevent

flooding and possible submergence of the gauge.

3.3 ANALYSIS OF PRECIPITATION

Rainfall (or, in more general term, precipitation) data obtained from a single gauge station over a

long period of time can be presented in the form chronological charts or bar graphs e.g., moving

average (or time series) curve, mass curve, hyetograph, etc. Hyetograph is a graph showing the

variation of rainfall intensity with time whereas a mass curve is a graph of cumulative depth of

rainfall against time. In analysing point rainfall data, these types of graphs are often used. If one

needs to determine the trend or pattern in a data more clearly, then the moving curve average means

of analyzing data is appropriate since it smoothens out extreme variations in the data.

19

One of the basic requirements in the hydrological study of a catchment area is an accurate evaluation

of the average precipitation over the entire area per year, month, or the duration of an individual

storm. Several methods may be used to determine the areal precipitation of a catchment; the standard

ones include the:

(i) Arithmetic Mean, (ii) Thiessen Polygon, and (iii) Isohyetal Maps

3.3.1 Arithmetic Mean Method

The simplest objective method is to calculate the arithmetic mean of all the rain gauge measurements

of the area under study. This technique may give adequate results if:

i. there is an even distribution of gauges, as for example in grid system, and

ii. the area has no marked diversity in topography, so that the range in altitude is small and

hence variation in rainfall amount is minimal.

The mean rainfall under this method is given by:

Mean Rainfall, R=∑i=1

n Ri

n.......................... (Eqn. 8)

where n is the number of rain gauges, and Ri is the rainfall of a particular station.

If a long-term average for the catchment area is available, then the method may be improved by

using the arithmetic mean of the station values, expressed as the percentages of their averages for the

same long period, and applying the resultant mean percentage to the areal average rainfall. If

accurate values of the areal rainfall are first obtained from a large number of gauge stations, then it

may be found that measurements from a small number of stations may give equal satisfaction. For

example, in the Thames Basin (9981 km2) of England, it was found that the annual areal rainfall

could be determined by taking the arithmetic mean of 24 well-distributed and representative gauges,

to within +2% of the value determined from a more elaborate method using 225 stations (IWE,

1937). In many areas, especially in mountainous areas, where rain gauge sites may be

unrepresentative and/or unevenly distributed, the results obtained from the arithmetic mean method

may have substantial errors.

20

3.3.2 The Thiessen Polygon

The Thiessen method (Thiessen, 1911) is, also, an objective method in which the rainfall amounts at

individual stations are weighted by the fractions of the catchment area represented by the gauges and

then summed. The rain gauge stations are plotted on a map and the catchment area is divided into

polygons by lines that are equidistant between pairs of adjacent gauges. The procedure may be

summarised into the following steps:

i. Connect adjacent stations with straight lines to form triangles with the stations as the apexes.

ii. Draw perpendicular bisectors to all lines in (i).

iii. Use the points of intersection of the bisectors in (ii) to draw polygons, which will have the

stations as their centres on a one-to-one basis.

iv. Determine the area of each polygon or part therefore and associate it with the respective

stations.

v. Sum up the product of the areas (ai) and gauge readings (Ri) to obtain the mean areal rainfall,

which is given by:

Mean Rainfall, R=∑i=1

n Ri ai

A ........................... (Eqn. 9)

where A is the total area; ai is the individual polygon area; the ratio ai/A is dimensionless and it is

known as the Thiessen coefficient.

The use of the Thiessen polygon makes allowance for the uneven distribution of gauges in the area,

and also enables data from adjacent outside stations to be incorporated into the mean. Such stations

may be more influential to segment of the study area than the nearest station inside the study area.

The polygons are usually drawn once and may be used for the analysis of subsequent readings so

long as the stations are unchanged.

3.3.3 Isohyetal Method

Isohyets are contours linking points of equal rainfall. The Isohyetal method is considered one of the

most accurate methods, but it is subjective and dependent on skilled, experienced analysts having a

good knowledge of the rainfall characteristics of the region containing the catchment area. This

method also uses values from external stations, where available, in its estimations.

21

Isohyets are drawn at chosen intervals across the catchment by interpolating between the gauge

measurements. The areas between the isohyets and the watershed are measured (e.g. with a

planimeter). The areal rainfall is calculated from the product of the inter-isohyetal areas (ai) and the

corresponding mean rainfall between the isohyets (ri) divided by the total catchment area (A). It is

given by:

Mean Rainfall, R=∑i=1

n air i

A .......................... (Eqn. 10)

In drawing the isohyets for monthly or annual rainfall over a catchment, topographical effects on the

rainfall distribution are incorporated. The isohyets are drawn between the gauges over a contour base

map taking into account exposure and orientation of both gauges and the catchment surface. It is in

this subjective drawing of the isohyets that experience and knowledge of the area are essential for

good results. The isohyetal method is generally used for analysing storm rainfalls, since these are

usually localised over small areas with a large range of rainfall amounts being recorded over short

distances.

3.3.4 Missing Data Estimation

Missing data is simply unrecorded data or breaks in data from a particular gauge station in a given

time. The causes of these may be as a result of instrumental failure, disaster, sickness or death of

attendant, laziness or drunkenness of attendant, industrial action, etc. In analyses of data from such

stations, it is better to estimate the missing records and fill the data gaps rather than doing the

analyses with the gaps. The missing records may be estimated from gauge readings surrounding the

gauge of concern are:

1. Interpolation of the missing record from isohyetal maps that cover area of concern

2. The station average method given by the relation: Pm=∑j=1

N P j

N............. (Eqn. 11)

where Pm = the missing station value, Pj = rainfall at known stations around the missing gauge,

and N = number of stations of known rainfall.

3. The normal ratio method given by the relation: Pm=PA (m)

N ∑j=1

N P j

PA ( j) ........ (Eqn. 12)

where PA(m) = average rainfall at missing station; PA(j) = average rainfall at the known stations.

22

4.0 EVAPORATIONWater is brought into the air as vapour by evaporation. It is a physical process by which water

vapour escapes from a free wet surface like land, roofs, road, oceans, streams, etc., at a temperature

below the boiling point of water. In addition to loss of water by evaporation from soil, water is also

lost by transpiration from plants covering the soil or water surface. The water mainly passes through

the roots to the stem or trunk and is lost to the atmosphere through the pores, i.e. stomata, in the leafy

parts of the plants. The combined loss by evaporation and transpiration is known as

evapotranspiration. Water vapour is the principal participant in the way energy changes in the

atmosphere; the energy changes are responsible for the weather phenomenon, which serves as an

important link between the various phases of the hydrological cycle.

However, evaporation is one of the most difficult parameters in the hydrological cycle to quantify.

Even though it is difficult to define the unseen amounts of water stored or moving underground,

above the ground surface the great complexities of evaporation make it an even more elusive

quantity to define. Evaporation may account for large differences that occur between incoming

precipitation and water available in rivers, and varies seasonally. In hot climates with seasonal

rainfall, evaporation causes rivers to dry up and river flows are dependent on excessive heavy rainfall

in the wet season. In temperate climates, if annual totals are considered, evaporation would appear to

deprive many areas of all its rainfall; surplus surface water feeds the rivers in the winter.

Measurements of evaporation and transpiration are important to many scientific fields. It is

indispensable in the solution of many water management problems. Reliable evaporation data is

required for planning, designing and operating reservoirs, ponds, shipping canal, irrigation and

drainage systems. Estimating evaporation is especially very important in arid zones where water

must be used in the most efficient way. Knowledge of the water requirements of crops depends

partly on accurate determination of the loss of water by evaporation.

4.1 FACTORS AFFECTING EVAPORATION

The physical processes in the change of state from liquid to vapour operates in both evaporation and

transpiration, and thus the general physical conditions influencing evaporation rates are common to

both. These include:

23

(i) Latent heat: is the energy required to break the bonds that hold water molecules together and

bring them to vapour state without temperature change; this energy is provided by sun (i.e. solar

radiation). It affects evaporation amounts over the surface of the earth according to latitude and

season.

(ii) Temperature: Water molecules in a system are always in motion. When the temperature is

increased, the water molecules gain more energy, move faster and break away from the surface into

the atmosphere as water vapour; this increases the rate of evaporation. Also, the higher the air

temperature, the more water vapour it can hold; thus the faster the evaporation rate.

(iii) Humidity: When humidity is high, the ability of air to absorb more water vapour decreases and

the rate of evaporation decreases.

(iv) Wind: When water vaporizes into the atmosphere, the boundary layer between the evaporating

surface and air becomes saturated. This layer must be removed and continually replaced by drier air

if evaporation is to proceed. The vapour removal process depends on wind and air turbulence, hence

making wind speed very important. Higher wind speed increases evaporation rate and vice versa.

However, if the wind speed is great enough to remove all the vapour as it is formed, then any further

increase in wind speed would not increase evaporation appreciably.

(v) Weather Pattern: Damp unsettled weather -mainly along coastal regions- usually has its air

content saturated with water vapour and is not conducive to aid in evaporation. However, more

evaporation occurs when the air in the atmosphere is dry and warm (e.g. in inland areas).

(vi) Nature of Evaporating Surface: Increase in size of an area increases the area’s exposure to solar

radiation and, therefore, increase evaporation amounts but the depth of evaporation decreases.

Evaporation rate also varies with the colour and reflective properties of the surface (i.e. albedo).

Irregular surfaces have the tendency to cause wind turbulence and enhance evaporation. However,

wind passing over smooth even surfaces yields little turbulence and does not influence evaporation.

(vii) Quality of Water: The presence of solute (or any impurity) in water reduces evaporation since

more energy would then be needed to cause evaporation than water in its pure form e.g., evaporation

from sea water is less than that of pure water.

24

4.2 DEFINITION OF COMMON TERMS

a) Transpiration: It is the loss of water to the atmosphere in the form of water vapour through

the stomatal pores of plants. The factors influencing this process may be grouped into three, namely:

1. Plant type – i.e. extent and efficiency of the roots in absorption of moisture, stage of growth,

leaf area, and stomata openings.

2. Properties of the soil – i.e. water holding capacity; available water, and depth of soil.

3. Meteorological factors – includes solar radiation, temperature, humidity, and wind

speed.

b) Potential Evaporation: It is the quantity of water vapour that can be lost by a surface of pure

water per unit area per unit time under the existing atmospheric conditions such as wind, pressure,

temperature and humidity.

c) Potential Evapotranspiration: It is the maximum amount of water capable of being lost as

water vapour in a given climate by a continuous stretch of vegetation covering the whole area/ground

when the soil is kept saturated. Simply, it is a measure of the ability of atmosphere to remove water

from a surface assuming there is no limitation on water supply. This includes evaporation from soil

and transpiration from vegetation from a specified region for a given time interval.

d) Actual Evapotranspiration: It is the amount of water vapour evaporated by the soil and

transported by plants under existing conditions.

e) Bowen’s Ratio: At an evaporation surface the loss of upward energy flux as sensitive heat to

the energy used in the evaporation is the Bowen’s Ratio

f) Albedo: It is the amount of incident light reflected from a surface or an indication of a body’s

diffuse reflectivity. It is a dimensionless constant, and is defined as the ratio of reflected to incident

electromagnetic radiation

25

4.3 MEASUREMENT OF EVAPORATION

Direct measurement of evaporation can be made with an evaporation pan whenever possible. The

pans are of standard dimension, e.g. B.S. 183 mm square and 610 mm deep, filled with water to a

depth of 550 mm and set in the ground so that the rim of the pan is 76 mm from the surrounding

ground. Observations of the water level are made at regular time intervals to determine the

evaporation.

Pan evaporation measurements are usually too high, due to the relatively small capacities and

shallow depths of the pans, in comparison to evaporation from lakes and other evaporative surfaces.

Hence, a pan coefficient (depending on the dimensions and siting of the pan) has to be applied to the

measured values to reduce the disparities [i.e., Eactual = Epan x K; where K is pan coefficient]. The

application of coefficients to relate pan measurements to large bodies of open water involves some

difficulties; thus it must be done with care.

Another device used in measuring direct evaporation is known as the Atmometer. The device is

made up of a water supply system connected to a porous surface and the amount of evaporation for a

given time period is given by change in the water storage. The device is simple, inexpensive and

easy to operate, but care must be taken to ensure that the porous surface for evaporation is kept clean.

Two types of this device available are the Piche atmometer and Bellani atmometer.

Evapotranspiration, on the other hand, can be measured using a lysimeter. It consists of a circular

tank of about 60 to 90 cm in diameter and 180 cm deep, filled with soil and natural vegetation of the

area where evapotranspiration is require, and then buried to ground level. The set up in the tank is

designed in such a way that it accurately reproduces the soil type and profile, moisture content, and

type and size of vegetation of the surrounding area. Measurement of precipitation in (or water added)

and drainage out, and/or weighing the tank to get the moisture retained in the soil is used in

determining evapotranspiration (i.e. by simple water budget calculation). It is a time consuming

method and very expensive.

4.4 ESTIMATION OF EVAPORATION

The major methods used in the estimation of evaporation, Eo, from open waters include:

26

i. Mass transfer (Aerodynamic method),

ii. Water Budget Method,

iii. Energy Budget Method,

iv. Energy Flux Method, and

v. Penman’s Formula (a combination of mass transfer and energy balance methods)

4.4.1 Mass Transfer (aerodynamic method)

The most straight forward method used to estimate evaporation from open water surface, Eo, is the

bulk aerodynamics equation originating with Dalton, and is given as:

Eo = f(u).(es – ed) ................................... (Eqn. 13)

where f(u) is a function of wind speed, and (es – ed) is the saturation deficit.

f(u) takes two forms: f(u) = a(b + u) and f(u) = Nu, where a, b, and N are empirical mass transfer

coefficients. Thus evaporation is related to wind speed and is proportional to the vapour pressure

deficit. Detailed studies by Penman (1948) using the first form resulted in the commonly used, Eo,

expression given as:

Eo = a(b + u).(es – ed)

Eo = 0.35 (0.5 + u/100).(es – ed) ................................... (Eqn. 14)

The Eqn. 14 is for air measurements made at 2 m above the surface with vapour pressure in mm of

Hg, wind speed in miles/day and Eo in mm/day. The other form of the equation is given as:

Eo = Nu. (es – ed) .................................. (Eqn. 15)

The value of the mass transfer coefficient, N, is dependent on the height and units of air

measurements of the evaporating surface. From a study of numerous sizes of reservoirs, Harbeck

(1962) incorporated a further factor of the surface area into Eqn. 15 to determine evaporation loss

from a reservoir as:

Eo = 0.291 A-0.05 u (es – ed) mm/day, .................................... (Eqn. 16)

where A is in m2, u is in m/s at height 2 m, and es and ed are in mb.

27

4.4.2 Water Budget Method

This method consists of accounting for all the water entering and leaving a particular catchment or

drainage basin. Regular and systematic measurements of rainfall over the whole area would lead to a

close approximation of the amount of water arriving from the atmosphere. Again, stream gauging of

the channels draining the area and accurately prepared flow rating curves would indicate the water

leaving the area by surface routes. The difference between the two, i.e. water entering and leaving

the catchment area, can be accounted for only in three ways, by:

i. a change in the storage within the catchment either in surface lakes and depressions or in

underground aquifers;

ii. the difference in underground flow into and out of the catchment; and

iii. evaporation and transpiration.

The first and second can “easily” be evaluated and the difference accounts for the third. The general

water balance equation for such a situation is, therefore, given as:

E = P + I ± U – O ± S ..................................... (Eqn. 17)

where E is evapotranspiration, P is total precipitation, I is surface inflow, U is underground flow, O

is surface outflow, and S is change in storage both surface and subsurface.

If observations are made over a sufficiently long time, the significance of S, which is not cumulative,

will decrease and can be ignored if the starting and finishing points are chosen to coincide as nearly

as possible with the same seasonal conditions. The significance of U cannot be generalized but in

many cases can be assigned a second order of importance for known geological conditions that

predict large underground flows. In such cases, a good estimation of evaporation becomes possible

and the method becomes the means of arriving at a first approximation.

4.4.3 Energy Budget Method

Similar to the water budget approach, this method involves accounting for all thermal energy

involved in effecting evaporation from a surface. Evaporation from a lake or reservoir may be

28

calculated on a weekly or monthly basis by taking into consideration the energy required to effect the

evaporation. A heat balance following the principle of the conservation of energy is evaluated from

incoming, outgoing, and stored energy. The elements of the heat energy are shown in Fig. 5. In the

diagram, Qs is the short wave solar radiation, Qrs is the reflected short wave radiation, Q1 is the long

wave radiation from the water body, Qc is sensible heat transfer to the air, Qg is the change in stored

energy, and Qv is the energy transfer between water and bed. The energy, QEo, required for

evaporation, can be calculated as follows:

QEo = Qs – Qrs – Ql – Qc ± Qg ± Qv .................................. (Eqn. 18)

Care must be taken to ensure that all the terms have the same energy units, W/m 2. The evaporation

from open water, Eo, is given by:

Eo = QEo/λ mms-1 .................................. (Eqn. 19)

where λ is the latent heat of vaporisation of water (J/kg).

Some energy equations include a separate term for incoming long wave radiation but this contributes

comparatively small amounts of energy. This approach involves a great deal of instrumentation and

the data processing involved is consequently extensive and time consuming. However, the method is

reliable and can be used over a suitable period of time for a specific reservoir until satisfactory mass

transfer coefficient have been determined (Shaw, 1988).

Figure 5: Energy Budget Measurement

29

4.4.4 Vapour Flux Method

The vapour flux method uses air measurements at fairly close levels above the water surface and

considers the turbulent transfer of water vapour through the small height difference. The equation

due to Thornthwaite and Holzmann (1939) takes the form:

cm/s ......................... (Eqn. 20)

where the wind speeds are in cm/s at heights z1 and z2 (cm), vapour pressure in mb, p is atmospheric

pressure in mb, is air density (g/cm3) and k is Von Korman’s constant (= 0.41).

The above equation is valid for normal conditions when the vapour transfer is by frictional

turbulence. With greater heating of the ground and increased lapse rate, the vapour flow is affected

by the wind speed and the relationship with the height used in Eqn. (20) does not hold.

4.4.5 Penman’s Theory

Penman (1948) presented a theory and a formula for the estimation of evaporation from weather

data; viz. mean air temperature, relative humidity, wind velocity at a standard height, and hours of

sunshine. The theory is based on two conditions, which must be met, if continuous evaporation is to

occur, and these are that there must be:

i. a supply of energy to provide latent heat of vaporisation; and

ii. a mechanism for removing the vapour once produced.

The Penman’s formula for open water evaporation is given by:

, .................................... (Eqn. 21)

where Ea = 0.35 (0.5 + u/100).(ea – ed) and H = RI(1 – r) – RO

H is the availability heat; is the hygrometric constant (= 0.27 mm of Hg/oF); ∆ is the slope of

saturated vapour pressure curve; RI and RO are incoming and outgoing solar radiation, respectively,

dependent on sunshine hours, temperature and humidity; r is the albedo; Ea is evaporation for a

hypothetical case of equal temperatures of air and water.

30

5.0 INFILTRATIONIn any part of this world, a portion of the precipitation that falls as rain and/or snow on pervious land

surface first wet the vegetation or bare soil and then infiltrates into the subsurface soil and rock

formations. Some of the water that infiltrates will remain in the shallow soil layers as soil water.

Other portions of the infiltrated water gradually move vertically and/or horizontally through the soil

and subsurface material and may eventually seep into streams or recharge groundwater aquifers. If

the aquifers are porous enough to allow water to move freely through it, people can drill wells into

the aquifer to tap the water. Water may travel long distances or remain in groundwater storage for

long periods before returning to the surface or seeping into water bodies like streams, oceans etc..

How much water infiltrates depends greatly on the ability of the soil to absorb falling precipitation;

surface pores largely control the rate at which infiltration occurs. The maximum rate at which water

can enter a soil at any given condition is the infiltration capacity. The infiltration capacity varies

from soil to soil and is also different for the same soil type in dry and moist conditions; it decreases

as the soil becomes saturated. Investigations (Horton, 1940; etc.) have shown that for any soil under

constant rainfall, the infiltration rate is described by the relation:

ft = fc + (fo − fc)e − kt ………………………. (Eqn. 22)

where ft is the infiltration capacity (L/T) at time t;

fc is the constant or equilibrium infiltration capacity (L/T) after the soil has been saturation;

fo is the initial infiltration capacity; k is a constant for a specific soil and surface texture (T-1).

The k-value is small if vegetation is present whilst a smoother surface texture like bare soil will yield

large values of k. Also, fc and fo are functions of soil type and cover. For example, bare sandy or

gravelly soils will have high fc and fo values while bare clayey soils have low values; but fc and fo

will increase for both soils if they are turfed.

5.1 FACTORS AFFECTING INFILTRATION

The factors that influence infiltration rate include the following:

(i) Precipitation: The greatest factor controlling infiltration is the amount and characteristics

(intensity, duration, etc.) of precipitation that falls as rain or snow. If the arrival of rainfall at the soil

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surface is less than the infiltration capacity, all of the water will infiltrate. However, if rainfall

intensity at the soil surface exceeds the infiltration capacity, some of the water will remain on the

land surface and lead to runoff once depression storage is filled. Large drops of rain may sometimes

render bare soils impermeable, by their compacting action and tendency to wash fine particles into

the voids, and lower infiltration rate.

(ii) Soil type and characteristics: The surface soil pores, mineralogical composition and water content

largely control the infiltration rate. For example, coarse-grained sandy soils have large spaces

between each grain and allow water to infiltrate quickly while clayey soils resist infiltration (since

the clay minerals absorb water, expand and reduce porosity) leading to more overland flow into

streams. Also, soil already saturated from previous rainfall can't absorb much more water and thus

less rainfall will become infiltrated.

(iii) Vegetation cover: Dense vegetation cover -like forest or grass- tend to make soils more porous

when the root systems, layers of organic debris, burrowing animals and insects open up the soil and

serves as preferential paths for infiltrating water. Also, vegetation cover and top layer of non-

decomposed leaf litter can protect the soil from pounding rainfall and help infiltration process. The

vegetation cover can also slow the movement of runoff, allowing more time for it to seep into the

ground. This is why forested areas have the highest infiltration rates of any vegetative types.

(iv) Land use practices like man/animals treading on land surfaces, vehicular movements and

construction of roads, parking lots, buildings, etc., often leads to compaction of land surfaces and can

severely reduce infiltration.

(v) Slope of land surface: Water that falls on steeply-sloping land areas will run off the surface more

quickly and infiltrate less than water than falls on flat land.

5.2 METHODS OF DETERMINING INFILTRATION

Some of the ways of determining the rate of infiltration include the following:

(a) Infiltrometer: The infiltrometer can be used to measure the rate at which water infiltrate into

soils. The commonest type of this instrument, known as double ring infiltrometer, consists of inner

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and outer tubes (or rings), inserted vertically into the ground and supplied with a constant head of

water from Marriot bottle (or a graduated burette ). Water draining from the inner ring is measured

by addition of water to maintain the constant head, at regular time intervals, and then used in

determining the infiltration rate. The water that drains from the outer ring contributes to lateral flow

and prevent lateral seepage from the central core. Some of the drawbacks of the double ring

infiltrometer are:

i. it is very time consuming, requiring trial and error to get equal water levels in the rings,

ii. the rings are extremely heavy to move and therefore reduce the practicality of the

instrument,

iii. and it also requires a flat undisturbed surface, which is sometimes not available.

(b) Water Budget Method: Infiltration is one of the components of the hydrological cycle, hence

the general mass balance hydrologic equation, described in previous sections, can be used to

determine it rate or volume. Given all the other variables with infiltration (in volume or depth per

unit time) as the only unknown, simple algebra solves infiltration as:

IF = BI + P − ET − S − R − IA ................................... (Eqn. 23)

where BI is the boundary input i.e. output from adjacent directly connected impervious areas;

P is precipitation; ET is evapotranspiration; R is surface runoff; and S is the storage through

depressions or detention areas;

(c) Infiltration Equations: The rate of infiltration can also be estimated using infiltration equations

like the Horton’s formula (Eqn. 22) or the Philip’s equation (1960) given as:

ft = 0.5At – 1/2 + B …………………… (Eqn. 24)

where A and B are related to soil properties and to the physical considerations of the soil water

movement.

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6.0 RUNOFFRunoff is a term used to describe the total flow from a basin collected at the basin outlet into a

stream, river or drain. Overland flow or surface runoff (a component of runoff) is used to describe

water that flows on land surface after precipitation either before it enters a watercourse, after it

leaves a watercourse as flood water, or after it rises to the surface naturally from subsurface. It is a

major component of the hydrological cycle and is easily observed if the flow is down a driveway to a

curb and into culverts. However, it is harder to notice if flowing overland in a natural setting.

During heavy rains, runoff may be noticed as small rivulets of water flowing downhill along

channels into creeks, streams, and rivers. These surface water bodies serve as a tributary to a large

river somewhere downstream, which will eventually flow into a lake and then an ocean. Thus runoff

serves as source of replenishment for most streams, rivers, lakes, oceans and other water bodies. On

the other hand, runoff may be diverted by humans for their own uses. Generally, runoff may be

generated from precipitation in three main ways, namely:

(i) Infiltration excess overland flow: This type of runoff occurs when the rate of precipitation on a

land surface exceeds the rate at which water can infiltrate the ground, and any depression storage on

the surface is already filled. Thus the excess rate of precipitation would end up as runoff. This is also

known as Hortonian overland flow (after Robert E. Horton) or unsaturated overland flow, and

commonly occurs in arid and semi-arid regions where rainfall intensities are high and the soil

infiltration capacity is reduced because of surface sealing, or in paved areas.

(ii) Saturation excess overland flow: This source of runoff takes place when the surface soil is

saturated and all depression storages are filled and rain continues to fall to immediately produce

surface runoff. This runoff is also referred to as saturated overland flow.

(iii) Subsurface return flow: After precipitation has infiltrated through the soil, especially on an up-

slope portion of a hill, the water may flow laterally through the soil and flow out of the soil (i.e.,

interflow) along the sloping sides of the hill to contribute to the runoff. On other occasions,

groundwater may seep out at locations where the topography intercepts the water table at the sloping

sides of land areas to contribute to runoff. This source of runoff is known as the subsurface return

flow.

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5.1 FACTORS AFFECTING RUNOFF

As with all aspects of the hydrological cycle, the interaction between precipitation and surface runoff

varies according to time and geography. Thus, similar storms occurring at locations with different

geological and topographic features will produce different surface runoff effects or amounts. The

surface runoff for any given watershed or catchment is affected by meteorological factors, the

physical characteristics of the land surface and land use practices.

The meteorological factors include the type of precipitation (i.e., rain, snow, sleet, etc.), rainfall

characteristics (i.e., intensity, size of rain drops, duration, etc.), and evapotranspiration factors like

temperature, relative humidity, wind speed, etc. as discussed in previous sections. It should be noted

that runoff will, generally, decrease as infiltration and evapotranspiration increases, and vice versa.

Hence the various factors (discussed in previous sections) that influence evapotranspiration and

infiltration also influence runoff rate and volume.

The physical characteristics of a land surface are mainly defined by its geology, topography and

vegetation. The soil characteristics, slope and type of vegetation cover, as well as the presence of

ponds and other surface water reservoirs in a drainage basin will either ease or hinder runoff rates

and volume. For example, the presence of many surface water reservoirs (e.g. ponds, puddles, etc)

would prevent or delay runoff from continuing downstream until their storage is full.

As more people inhabit an area, more development and urbanization occur leading to more of the

natural landscape being replaced by impervious surfaces like roads, houses, parking lots, markets,

etc., that reduce infiltration of water into the ground and accelerate runoff to ditches, culverts and

streams. In addition to increasing imperviousness, removal of vegetation and soil, grazing the land

surface, constructing drainage networks and certain agricultural practices (e.g. tilling and leaving

farmlands bare) increase runoff volumes and shorten runoff time into streams from rainfall (and

snowmelt, in places with snow falls). As a result, the peak discharge, volume, and frequency of

floods may increase in nearby streams.

5.2 METHODS OF ESTIMATING RUNOFF

Several approaches can be used in estimating runoff volume or rate. Some of which include:

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1. Water Budget Method: Similar to the approaches discussed in previous sections, it involves

accounting for all the water entering and leaving a catchment area with runoff as the unknown,

which can subsequently be estimated from a water balance equation of the area.

2. Discharge Formulae: Runoff from a catchment into streams or open channels can be calculated

by using empirical flow open channel flow equations derived by Manning and Chezy below. The

equations apply to steady uniform flow condition; this condition means within the reach of the

channel under consideration, the velocity (v), the cross-sectional area (A) and bed slope (S) of the

channel are everywhere constant and do not change with time.

Chezy formula: v = C√ RS ……………………………… (a)

Manning equation: v = 1n

R2 /3 S1/2 ………………………..... (b)

Where v is average flow velocity, C is Chezy coefficient, R is hydraulic radius (=A/P), A is cross-

sectional area of channel, P is wetted perimeter, S is channel bed slope, n is Manning coefficient

3. Velocity-Area Method: This is a direct method of obtaining a discharge value to correspond with

a stage measurement in which the flow velocities are measured at selected verticals of known depth

across a measured river section (which is referred to as a river gauging station). At the river cross-

section, mean velocities for small sub-areas of the cross-section (v i) obtained from point velocity

measurements at selected sampling verticals across the river multiplied by the corresponding sub-

areas ( ) and the products are summed to give total discharge, Q, given by:

Q=∑i=1

n

vi ai ………………… (Eqn. 25)

where n = the number of sub-areas.

The river flow velocities at the selected sampling verticals across the river cross-section are

measured with a current meter. The average velocity of flow across the vertical (strip) is

determined in two ways: (i) velocity at 0.6 depth, and (ii) mean of velocity measurements at 0.2 and

0.8 depths below the water surface.

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From the velocity and depth measurements across a river cross-section (or gauge station), discharge

may be estimated in two ways (Fig. 7), namely:

(i) Mean Section Method – in this method, the averages of the mean velocities in the verticals and

of the depths at the boundaries of a section sub-division are taken and multiplied by the width of the

sub-division, or segment:

where bi is the distance of the measuring point (i) from the bank datum and there are n sub-areas.

(ii) Mid-Section Method – here, the mean velocity and depth measured at a subdivision point are

multiplied by the segment width measured between the mid-points of the neighbouring segments

with n being the number of measured verticals and sub-areas. In calculating flow under this method,

the first and last verticals should be sited as near as possible to the banks to make flows at the edges

very negligible since they are not considered in the estimation. The total flow is given by:

Figure 7: Calculating discharge from velocity and depth measurements on a cross-section.

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.................................... (Eqn. 26)

.................................... (Eqn. 27)

4. Dilution Gauging: This method involve adding a chemical solution or tracer of known

concentration into a stream and measuring the dilution of the tracer downstream after it has

completely mixed with the stream water. The method is very suitable in measuring discharge in

small turbulent flowing streams with steep gradients where current metering is not practicable and

the use of flow-structures would be unnecessary expensive. The tracer (of concentration Ct and flow

rate qt) can be added either by constant-rate injection until the sampling downstream reveals a

constant concentration level or administered in a single dose as quickly as possible, known as gulp

injection. The discharge, Q, of stream flow with background concentration (Co) in each case can be

obtained from sampling point concentration (Cs) and flow rate (qt) by:

(i) Constant-Rate Injection: …………... (Eqn. 28)

(ii) Gulp Injection: ……........... (Eqn. 29)

The conditions for dilution gauging are:

i. At the point of measurement or sampling, the chemical tracer should be completely mixed

with the stream (i.e. the flow before dropping the tracer should be turbulent)

ii. The chemical should have high solubility and be stable (not reactive) in water

iii. The chemical should be non-toxic to fish and other aquatic life.

iv. The background concentration of chemical of interest should be low.

v. The chemical should be capable of accurate quantitative analysis in very dilute solutions.

vi. The chemical should be cheap and readily available.

5. Flow Rating Curve: A rating curve is a graph that shows the connection between the water level

elevation, or stage of a river channel at certain cross-section, and the corresponding distance at that

section (e.g. Fig 6). The curve is obtained from measurement of discharge and stage readings at the

river section over a long period of time to establish their relationship at that section. This would

enable future discharges (runoff) to be estimated from stage readings alone. Aside the rating curve, a

rating equation and rating table of a river cross-section can also be used to establish a stage-discharge

relationship. The stage readings are measured with a staff. River discharge measurements at the

cross-section can be made using velocity-area methods, flow-measuring structures (e.g. weirs,

flumes, etc.), dilution gauging, etc.

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Figure 6: Flow rating curve

5. Flow Rating Curve: A hydrograph is a plot of the discharge (or stage) against time at a location

along the river. It includes the integrated contributions from surface runoff, groundwater seepage,

drainage and direct precipitation. The shape of a hydrograph of a single storm occurring over a

catchment area follows a general pattern as shown in fig. 7. This pattern shows a period of rise that

culminates in a peak, followed by a period of decreasing discharge (called recession) which may, or

may not, decrease to zero discharge, depending on the amount of groundwater flow.

Figure 7a: Components of a hydrograph Figure 7b: Hydrograph with bank storage

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The hydrograph has two main components, a broad band near the time axis representing baseflow

contributed from groundwater, and the remaining area above the baseflow, the surface runoff (or

direct runoff), which is produced by the storm. In the beginning of the rainfall, the river discharge is

low and a period time elapses before the river begins to rise. During this period the rainfall is

intercepted by vegetation or soaks into the ground to make up the soil moisture deficit. The length of

the delay before the river rises depends on the wetness of the catchment before the storm and on the

intensity of the rainfall.

When the rainfall has made up the catchment deficits and when surfaces and soils are saturated, the

rain begins to contribute to the stream flow. The proportion of rainfall that finds its way to the river

is known as effective rainfall; the rest is “lost” in evaporation, detention on the surface or detention

in the soil. As the storm proceeds, the proportion of effective rainfall increases and that of lost

rainfall decreases, resulting in a strongly rising limb. The peak of the hydrograph usually occurs after

the effective rainfall has reached its maximum. The time from the beginning of the rainfall to the

peak of the hydrograph is generally called the ‘time to peak’. The time between the centre of gravity

of the effective precipitation and the centre of gravity of the direct runoff is called lag or lag time.

Time is required for the surface runoff to reach the station where the hydrograph is observed. First

the area closest to the station contributes to the surface runoff, followed by the areas further

upstream. This means that in a small catchment, for a given uniformly distributed rainfall, the time to

peak, and also the lag time, will be shorter than in a large catchment. In fact, the shape of the

hydrograph is influenced by climate, topography and geology of the catchment; climate and

topography influence the rising limb whilst geology influences the recession (de Laat & Svanije,

2006)

The boundary between surface runoff and baseflow is usually difficult to define. However, if this

boundary is ably defined, for a hydrograph, make it possible to determine the runoff from a

catchment arising from a rainfall event. Two approaches used in defining the boundary are by:

i. use of the empirical relationship N = 0.827A0.2; where N is time in days from peak to end

and A is the catchment in km2, and

ii. determining a master depletion curve for a particular guage station and applying it to a

given storm to determine the baseflow.

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