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:

Ing. Dr. E. K. Appiah-Adjei

September, 2018

ii

COURSE OUTLINE – FIRST SEMESTER, 2018/2019

WEEK ACTIVITY

1 REGISTRATION

2 – 3

INTRODUCTION:

• Definitions, History, and the Hydrological Cycle

• Applications of Hydrology in Engineering

4 – 5

WEATHER AND HYDROLOGY:

• Structure of the Atmosphere

• Temperature (Analyses of Temperature Data)

• Atmospheric Pressure, Air Density and Water Vapour

6 – 7

PRECIPITATION:

• Formation of Precipitation

• Measurement of Precipitation

• Analysis of Rainfall Data

8

INFILTRATION:

• Definitions and Factors Affecting Infiltration

• Measurement and Estimation of Infiltration

9 MID-SEMESTER EXAMINATIONS

10

EVAPORATION (+ EVAPOTRANSPIRATION):

• Definitions and Factors Affecting Evaporation (+ Evapotranspiration)

• Measurement and Estimation of Evaporation (+Evapotranspiration)

11 – 12

RUNOFF:

• Sources and Components of Runoff

• Factors Affecting Runoff

• Catchment Characteristics and Drainage Patterns

• Measurement and Estimation of Runoff

13 REVISION

14 – 16 EXAMINATION

RECOMMENDED LITERATURE

• 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.

iii

TABLE OF CONTENTS

COURSE OUTLINE – FIRST SEMESTER, 2016/2017 ...................................................................... ii

RECOMMENDED LITERATURE....................................................................................................... ii

TABLE OF CONTENTS ..................................................................................................................... iii

1. INTRODUCTION ......................................................................................................................... 1

1.1 The Hydrological Cycle .......................................................................................................... 2

1.2 Applications of Hydrology in Engineering ............................................................................. 6

1.3 Scope and Limitations of Hydrology ...................................................................................... 6

1.4 Sources of Hydrological Information ...................................................................................... 7

2. WEATHER AND HYDROLOGY ................................................................................................ 8

2.1 Structure of the Atmosphere ................................................................................................... 8

2.1.1 Temperature ................................................................................................................... 10

2.1.2 Atmospheric Pressure and Density ................................................................................ 11

2.1.3 Water Vapour ................................................................................................................. 11

2.1.4 Sample Calculation ........................................................................................................ 16

2.2 Trial Questions ...................................................................................................................... 16

3. PRECIPITATION ........................................................................................................................ 17

3.1 Siting of Rain Gauges ........................................................................................................... 19

3.2 Measurement of Precipitation ............................................................................................... 19

3.2.1 Non-Recording Gauges .................................................................................................. 20

3.2.2 Recording Gauges .......................................................................................................... 21

3.3 Analysis of Rainfall ............................................................................................................... 22

3.3.1 Arithmetic Mean Method ............................................................................................... 23

3.3.2 The Thiessen Polygon .................................................................................................... 23

3.3.3 Isohyetal Method ........................................................................................................... 24

3.3.4 Missing Data Estimation ................................................................................................ 25

4. INFILTRATION .......................................................................................................................... 26

4.1 Factors Affecting Infiltration ................................................................................................ 26

4.2 Measurement and Estimation of Infiltration ......................................................................... 27

5. EVAPORATION ......................................................................................................................... 29

5.1 Factors Affecting Evaporation .............................................................................................. 29

5.2 Definition of Common Terms ............................................................................................... 30

5.3 Measurement of Evaporation ................................................................................................ 31

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5.4 Estimation of Evaporation ..................................................................................................... 32

5.4.1 Mass Transfer (aerodynamic method) ........................................................................... 32

5.4.2 Water Budget Method .................................................................................................... 33

5.4.3 Energy Budget Method .................................................................................................. 34

5.4.4 Vapour Flux Method ...................................................................................................... 35

5.4.5 Penman’s Theory ........................................................................................................... 35

5.5 Estimation of Evapotranspiration .......................................................................................... 36

6. RUNOFF ...................................................................................................................................... 38

6.1 Catchment Characteristics ..................................................................................................... 39

6.1.1 Drainage Pattern............................................................................................................. 40

6.2 Factors Affecting Runoff ...................................................................................................... 40

6.3 Measurement and Estimation of Runoff ............................................................................... 41

1

1. INTRODUCTION

The word hydrology is derived from the Greek words hydor and logos, which means water and science

respectively. Hydrology is, broadly, defined as the study of the origin, movement, distribution, and

quality of water in and over the surface of the earth. Basically, it deals with all the waters (i.e., rainfall,

snow, surface water, groundwater, etc.) on earth and their usefulness to life. Due to its applications in

many branches of engineering (like hydraulics, water resources, irrigation, etc.), the term engineering

hydrology may sometimes be used instead. However, 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.

The history of the evolution and development of hydrology as a multi-disciplinary subject has been

presented by Biswas (1970) and dates back to the times of great civilizations in China, the Middle

East, Greece and Rome. The Greek philosophers are believed to be the first serious students of

hydrology, after which other scholars came in to advance their understanding of separate phases of

water in the natural environment. However, it was not until the 17th century that the work of a

Frenchman, Perrault through measurements of rainfall and stream flow in the catchment of the upper

Seine River provided convincing evidence of the form of the currently accepted hydrological cycle

(Dooge, 1959). The eighteenth century saw advances in hydraulics and mechanics of water movement

by Bernoulli, Chezy, and many others while the nineteenth century saw experimental work on water

flow by people like Darcy and Manning, which are familiar works in groundwater and surface-water

movement. In the 1940s and onwards, hydrology became established in institutions of higher education

as an academic subject. As its importance in the assessment, development, utilisation and management

of the water resources became increasingly realised at all levels, the United Nations proclaimed the

period 1965-1974 as the International Hydrological Decade. During that period, intensive efforts in

hydrologic education research, development of analytical techniques and collection of hydrological

information on a global basis, were promoted in Universities, Research Institutions, and Government

Organisations. The promotion of hydrology continued afterwards and has become the norm over the

years till today.

In this course, a basic understanding and application of the principles of hydrology for solving

engineering problems are treated. This would involve an examination of the basic hydrologic processes

and their practical applications for engineering projects, especially in water resources management,

and will deal with the different phases of the hydrologic cycle.

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1.1 THE HYDROLOGICAL CYCLE

The hydrologic cycle (Fig. 1.1) 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 assumed to start

conveniently 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 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, hail, etc.) to the oceans, streams, land

surface, etc., or may re-vaporize while still aloft.

The precipitation that falls directly into the 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, whilst the rest may reach the ground surface. The precipitation that

reaches the ground surface is known as throughfall.

Figure 1.1: The Hydrological Cycle (after Shaw, 1996)

3

Precipitation that falls 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 (i.e. the 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

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, laterally, 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 may, also, be transpired by plants and

evaporated subsequently to the atmosphere in a process known as evapotranspiration.

It should be appreciated that the description of the hydrological cycle in Fig. 1.1 is over simplified

because some of the water that enters the surface streams may percolate to the groundwater system

while, in other cases, the 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. More so, it

should be noted, generally, that:

• 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). Four important phases of the cycle of

great interest to the engineering hydrologist are precipitation, evaporation (evapotranspiration), runoff,

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. More so,

4

the variations in the cycle may be quite distinct in adjacent areas. It is, precisely, these extremes of

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

engineering projects are designed to protect the ill effects of extreme events.

The science of meteorology may explain the reasons for the climatic extremes. However, the engineer

has to understand it, at least, in broad detail and be able to deal quantitatively with the interrelations

between the extremes and the various phases of the cycle in order to predict their influence on man-

made structures (quite) accurately. Also, the frequency with which the various extremes of the cycle

occur need to be of great concern to the engineer because those form 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 or hydrologic

equation expressed as:

Inflow – Outflow = Change in Storage (1.1)

This equation simply states that the change in water storage in an area is equal to the difference between

the total water inflow into the area and total water outflow from the same area. The relation is based

on the law of conservation of mass and can be applied to an area, catchment or reservoir of any size.

A catchment (synonymous with drainage basin or watershed) is defined as an area of land with

topographic divide that collects all surface runoff in the area and discharges most of this water to a

stream, river or a water body in the area. The equation is time-dependent; hence the elements of the

inflow must be measured over the same time period as the outflow and storage. For example, a simple

water balance equation of a catchment may be represented as:

S(catchment) = P − SR − ET ± G (1.2)

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

storage of the catchment and G is net groundwater flow.

The study of the hydrologic cycle is very important in many disciplines since the cycle traverses the

lithosphere through the hydrosphere to the atmosphere where it is related to 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). In the lithosphere, however, the cycle

5

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 important influence in agriculture, forestry, geography, watershed management, political

science, economics, and sociology. 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.

Table 1.1 presents an estimate of world’s water resource distribution in the hydrological cycle and

indicates the relative importance of groundwater over the other components of the cycle. Ignoring the

over 90% of the earth’s water that rests in 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 utilizable 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 1.5% for soil moisture, 3.5% for surface water (i.e., rivers, reservoirs, swamps, etc.),

and 95% for groundwater.

Table 1.1: 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

1 Equivalent depth is estimated as though water storage were uniformly distributed over the entire earth surface 2 Residence time is the average duration for a water molecule to pass through a subsystem of the hydrological cycle

6

1.2 APPLICATIONS OF HYDROLOGY IN ENGINEERING

As stated earlier, the engineer basically applies the principles of hydrology in the design, 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 (as well as distribution, time of occurrence and frequency) 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 applying them effectively.

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

• Estimation of the flood flows to be expected at a spillway, highway culvert or in a city

drainage system;

• Estimation of the reservoir capacity required to assure adequate water for irrigation, water

supply or hydroelectric power generation;

• Determining the effect reservoirs, levees, and other control works will exert on flood flows in

a stream;

• Estimation of the water budget of a catchment or region;

• Evaluating 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 for them whilst others will not need fulltime hydrologists.

1.3 SCOPE AND LIMITATIONS OF HYDROLOGY

Hydrology deals with many topics, which may be classified conveniently into two phases, namely;

i. data collection, and ii. methods of analyses 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 a

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

to begin with a mass of observed facts, statistically analyse them and, from the analyses, establish a

systematic pattern that govern the events. The hydrologist is, thus, in a difficult position if adequate

historical data for a particular area of interest is not available. The collection of hydrologic data has,

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

7

Services Departments, Weather Bureaux, and other related units. Hence, it is important to learn how

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

interpretation and adjustments. The basic hydrological data required in most projects include

meteorological data (like temperature, wind velocity, humidity, etc.); precipitation data; evaporation

data; stream flow data; data on groundwater conditions; data on cropping patterns, crops and their

consumptive use; water quality data on surface streams and groundwater; and geomorphology.

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

within a specific 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 HYDROLOGICAL INFORMATION

The main source of hydrologic data in Ghana is from the Meteorological Services Department (MSD),

which has offices in all the regions. Other sources of information can be obtained from the

Hydrological Services Department, Ministry of Food and Agriculture, Civil Aviation Authority, Ghana

Water Company Limited, Volta River Authority, Bui Dam Authority, Irrigation Development

Authority, CSIR, and other research institutions like the Universities. MSD has a number of

publications available for sale at their Accra office where some data may be obtained.

8

2. WEATHER AND HYDROLOGY

The hydrological characteristics of an area or a region depend, primarily, on its climate, and on the

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

marshland and flow rates of runoff whereas geology has an influence on the nature of topography and,

sometimes, serve as water reservoirs (i.e., groundwater storage) and source of water supply to rivers

and lakes.

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

years by the World Meteorological Organisation 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 estimate these parameters, daily

weather measurements have to be made over a long time period.

Although, in practice, the hydrologist will usually rely on the services of a professional meteorologist

for weather data and forecasts, it is essential for the hydrologist to have some understanding of the

atmospheric processes that defines a regional climate in order to “appreciate the complexities of the

atmosphere and the difficulties that the meteorologist often has in providing answers to questions of

quantities and timing” (Shaw, 1988). 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 is, basically, the study of atmospheric processes that affect water

resources.

2.1 STRUCTURE OF THE ATMOSPHERE

The atmosphere is a distinctive protective layer of air, water vapour and other gases of about 100 km

thick around the earth and has the structure shown in Fig. 2.1. The chemical composition of the layer

comprises 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

3 Weather is a mix of events that happen each day in the atmosphere in terms of temperature, rainfall, humidity, etc. It is

recorded daily and predicted worldwide by meteorologists. 4 Meteorology is the study of the changes in temperature, air pressure, moisture, wind direction, etc. in the atmosphere.

9

gases, ozone, hydrocarbons, ammonia, nitrates, man-made gaseous contaminants from industries,

radioactive isotopes from nuclear explosions, etc., which may exist temporarily in the atmosphere.

Figure 2.1: Structure of the atmosphere (after Shaw, 1996)

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

whilst both air pressure and density continuously decrease with increasing altitude. The irregular

variation of temperature divides the atmosphere into layers known as spheres (as shown in Fig. 2.1).

These may, mainly, be divided into upper and lower atmospheres with the demarcation at 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

10

divided into two as Stratosphere and Troposphere while the Mesosphere and Thermosphere

together forms the upper atmosphere.

Almost all the dust and moisture in the atmosphere is concentrated in the troposphere. Also, the

temperature in the troposphere decreases with increasing altitude at 6.5 oC/km average rate and is

known as lapse rate. The top of the troposphere, i.e. the dividing line between the troposphere and

stratosphere, is called the tropopause and has an average height of about 11 km (see Fig. 2.1), but

ranges from 8 km at the Poles to 16 km at the Equator. This variation of the tropopause is caused by

changes in air temperature and pressure in the atmosphere. Generally, when surface temperatures are

high and pressure is high at sea level, there is the tendency for the tropopause to be at a higher level.

After a general decrease in temperature through the troposphere, the rise in temperature from heights

of 20 to 50 km above the tropopause (i.e. in the stratosphere) is caused by a layer of ozone, which

absorbs short wave solar radiation and releases some of the energy as heat. The stratosphere contains

very little moisture and dust, but has a major portion of the ozone.

The troposphere is the most important layer to the hydrologists because it contains about 75 % of the

weight of the atmosphere and, virtually, all its moisture. Also, the atmospheric processes, which affect

water resources, mostly, take place in the troposphere. 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

parameters in the atmosphere pertinent to hydrology include temperature, pressure, humidity, and wind

speed.

2.1.1 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 shown in Fig. 2.1 and was explained

in the previous section. Within a day, temperature varies from a minimum value at around sunrise to a

11

maximum value, after the sun has reached its zenith, before it begins to fall through the night till sunrise

again. The average temperature for a 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 in the month. Similarly, the mean annual temperature is the arithmetic average of all the

mean monthly temperatures in a year

2.1.2 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. It may be considered to be the downward force on

a unit horizontal area resulting from the action of gravity (g) on a mass (m) vertically above it. The

pressure is, usually, measured with a barometer in bars or mm height of a column of mercury. In the

atmosphere, both the pressure and air density decrease with increasing altitude, however, the air

density decrease is more rapid (Fig. 2.1).

At sea level, the average atmospheric pressure (p) is 1 bar (≈ 100 kPa ≈ 100 kN/m2 ≈ 760 mmHg =

1013.25 mb = 1 atm). The pressure can be estimated using the ideal gas law expression given by:

P = ρRT (2.1)

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.

2.1.3 Water Vapour

Humidity is the amount of water vapour in the atmosphere. Water vapour is the most important

constituent in the atmosphere to the hydrologist and is usually measured as vapour pressure in millibars

(mb). The distribution of water vapour varies over the earth’s surface according to temperature; i.e. 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. Thus, although water

vapour is lighter than air, it 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

12

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

and solid precipitation of this 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:

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 2.2. 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. 2.2, but an

unsaturated atmospheric air mass will be below the svp curve as indicated with point Y on Fig. 2.2.

Figure 2.2: Saturation vapour pressure curve of water vapour in air

The relation between saturated vapour pressure and temperature can be approximated by the equations

(2.2) and (2.3):

𝑒𝑠 = 2.7489 × 108 exp. (−4278.6

𝑇+242.79) (2.2)

𝑒𝑠 = 6.11 exp. (17.27 𝑇

237.3 + 𝑇) (2.3)

0

5

10

15

20

25

30

35

-10 -5 0 5 10 15 20 25 30 35

Sa

tura

tio

n V

ap

ou

r P

ress

ure

(m

mH

g)

Temperature (oC)

es

Td

YY*

Ys

Yw

13

where temperature is in oC and еs is mb with T representing air temperature. These relations are used

to estimate saturated vapour pressure, es, 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. For example, if the unsaturated atmospheric air mass at Y (T, e) is cooled without

any change in humidity (Fig. 2.2), 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.

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

intersects 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

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 the example in Figure 2.2, 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 at which the original air can be cooled by evaporating water into it. This can be

measured 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 Figure 2.2:

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

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

thermometers (viz. wet bulb thermometer and dry bulb thermometer), which are ventilated by a fan

14

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

thermometer has its mercury bulb wrapped with a wick with one end of wick submerged in distilled

water to ensure continuous moisture supply to the bulb. The measured values from the wet bulb

thermometer 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) (2.4)

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 may be defined, in simple

terms, as the amount of water vapour contained in a given volume of air. Vapour density is, 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) (2.5)

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 relations:

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

q = mw (g)/(mw + md) (kg) (2.6)

q = ρw/ρm (gkg-1) (2.7)

From ideal gas law in Eqn. (2.1), the density of dry air (ρd) and water vapour (ρw) can be given as:

𝜌𝑑 =𝑃𝑑

𝑅𝑑𝑇=

𝑃 − 𝑒

𝑅𝑑𝑇, and 𝜌𝑤 =

𝑒

𝑅𝑤𝑇=

0.622𝑒

𝑅𝑑𝑇 (since Rw = Rd/0.622).

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

𝜌𝑚 = 𝜌𝑑 + 𝜌𝑤 = 𝑃 − 0.378𝑒

𝑅𝑑𝑇, (2.8)

𝑞 =𝜌𝑤

𝜌𝑚=

0.622𝑒

𝑃 − 0.378𝑒 (2.9)

15

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

water vapour pressure; P is total air pressure (i.e., vapour pressure plus dry air pressure); Rd is dry air

gas constant; and Rw is the wet air gas constant.

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. In simple terms, precipitable water gives an

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

In a column of water vapour of unit cross-sectional area (Fig. 2.3), a small thickness, dz, of the moist

air contains a mass of water given by:

dmw = ρwdz

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

Hence,

Figure 2.3: 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. This is given as:

(2.10)

dz

z

Z1

Z2

16

2.1.4 Sample Calculation

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

shown in Table 2.1 were obtained. Calculate the precipitable water in the column of air up to the 250

mb level (g = 9.81 m/s2).

Table 2.1: Measurements from radiosonde

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

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:

2.2 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; and (d) air density.

[Ans.: (a) 26.40 mb; (b) 20.60 mb; (c) 78 %; (d) 1.2 kg/m3]

2. Air mass is at a temperature of 28 oC with relative humidity of 70 %. Using Figure 2.2, determine:

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

deficit; and (d) dew point.

[Ans.: (a) 28 mm Hg; (b) 19.6 mm Hg; (c) 8.4 mm Hg; (d) 21.5 oC]

3. A psychrometer recorded 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; and (d) dew point

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

17

3. PRECIPITATION

Moisture in the atmosphere, although forming one of the smallest storages of the earth’s water

resource, is the most vital source of fresh water for mankind and life on earth. In the air, water is

present in its gaseous, liquid and solid states as water vapour, cloud droplets and ice crystals

respectively. The processes involved in the formation of precipitation can be summarized in the

following steps:

1. Supply of warm moist air (i.e., water vapour) to the atmosphere

2. Cooling of the warm moist air to its dew point

3. Condensation

4. Growth of particles (i.e., coalescence)

Basically, the moisture is supplied to the atmosphere through evaporation from wet surfaces (i.e.,

rivers, lakes, seas, etc.) and transpiration from vegetation. The warm moist air is then forced to rise to

its dew point through:

i. Orographic Lifting (i.e., adiabatic expansion of rising air): occurs when a volume of air is

forced to rise by a mountain range. The lifting of the air will reduce the pressure and cause a

lowering in temperature without any transfer of heat, which will lead to cooling of the air to

condense at dew point. The type of precipitation arising from this air lifting or adiabatic process

is termed as orographic precipitation.

ii. Convection (i.e., meeting of two different air masses): 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, which leads to convective precipitation. Also, any mixing of contrasting

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

subsequent precipitation. Convective rainfall is common in tropical regions and, usually,

appears as a thunderstorm in temperate climates during the summer period. Rainfall

intensities of convective storms can be very high locally; however, the duration is generally

short.

iii. Frontal Lifting: This occurs when a warm moist air mass comes into contact with a cold object

such as the ground or when a colder air mass intrude a slightly warm one and causes it to rise

and lose temperature to its dew point. This leads to frontal precipitation.

18

iv. Convergence: This occurs in a tropical region (i.e. Inter-Tropical Convergence Zone) where

the air masses originating from the Tropics of Cancer and Capricorn converge and is lifted.

The position of the ITCZ governs the occurrence of wet and dry seasons in the tropics and

determines the main rain-bringing mechanism, which is also called monsoon. In July, the ITCZ

lies to the North of the equator and in January it lies to the South. In certain places near the

equator, such as on the coast of Nigeria, the ITCZ passes two times per year, causing two wet

seasons; near the Tropics of Capricorn and Cancer (e.g. in the Sahel). However, there is

generally only one dry and one wet season.

When the cooled air mass reaches dew point, condensation then begins. If the cooled air mass is pure,

condensation of the 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, in the atmosphere provide the nuclei around which water vapour in normal

saturated air can condense. The condensed water droplets fuse or come 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 (according to Aitkin (Mason, 1975)), viz.:

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.

19

3.1 SITING OF RAIN GAUGES

The choice of a suitable site for a rain gauge is a professional job. It must be decided with competence

since 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, steep hillsides

especially those sloping down towards the prevailing wind must be avoided. 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.

In the case of an existing site, a modification of its surroundings like building of new structures,

collapsing of existing buildings, or vegetation growth can affect the readings. Usually, structures of

height, h, around the gauge should be at distance not less than 2h from the gauge. For over-exposed

areas where there is not much vegetation, like Accra plains and some parts of the Northern and Upper

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

should be 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. Rain gauge density refers to the number of rain gauges

erected in a given area. Commonly in most developed countries, one rain gauge station is erected in

every 100 km2. However, these may vary depending on topographic and other considerations.

3.2 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 followed.

(NB: Daily reading is the most reliable since it enables every change 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. The different forms of precipitation available

include:

20

i. Rain: is a liquid precipitation of drop size greater than 0.5mm to a maximum size of 6mm.

ii. Drizzle: is a fine sprinkle of rain with a diameter of 0.1 to 0.5mm and intensity <1 mm/hr.

iii. Dew: is moisture condensed from atmosphere in small drops on surfaces due to cooling at

night.

iv. Glaze: is freezing of drizzle or rain when they come into contact with cold objects.

v. Sleet: is, simply, frozen rain or rain drops that get frozen while falling through air at

subfreezing temperature.

vi. Snow: is precipitation in the form of small ice crystals (i.e., water vapour condenses to ice).

The fusing together of the ice crystals form snowflakes (i.e. the equivalent of rain).

vii. Hail: is a small spherical lump of ice (>5 mm in diameter) composed of concentric layers.

viii. Frost: is a feathery deposit of ice formed on the ground or on the surface of exposed objects

by dew or water vapour that has frozen.

ix. Graupel: are pellets of ice 2 – 5mm in diameter formed by collisions of snow crystals and

raindrops when the temperature of the cloud is near freezing.

x. Fog: is a thin cloud of varying size formed at the surface of the earth by condensation of

atmospheric vapour (interfering with visibility). Mist is a very thin fog

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.

3.2.1 Non-Recording Gauges

In 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 size of the gauge

varies between countries, but is usually standardized within each country. Its collecting funnel is

usually 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. Normally, the gauge is set into the ground with its rim level 12

inches (300 mm) above the ground surface, which should ideally be covered with short grass,

chippings, or gravel to prevent in splash of water during heavy rains. In exceptionally heavy rains, the

water may overflow into the 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.

21

3.2.2 Recording Gauges

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

event. The rainfalls collected by these gauges are usually recorded cumulatively (i.e., in a mass curve)

from which a hyetograph (i.e., plot of rainfall intensity with time) or depth of rainfall in a given time

can be derived. There are three basic types of recording gauges, namely: tilting siphon, tipping bucket

and weighing gauge 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 to, suddenly, start 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 float 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. When a definite small amount has been collected,

the bucket tips over to allow the falling rain to be collected into the other compartment while at the

same time emptying the earlier filled bucket. Each movement of the bucket is transmitted,

mechanically or electronically, to a moving strip chart to record the rainfall in stages representing the

small amount of rain (e.g. 0.01 mm per stage).

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.

On the other hand, the tipping bucket is:

i. mechanically much simpler,

22

ii. able to record electronically at a distance, and

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

b) Weighing Type Gauge: In this type of rain gauge, when a certain weight of rainfall (or snow) is

collected in a tank, which rests on a spring-lever balance, it triggers a pen to move on chart wrapped

around a clock driven drum to record the weight of the rain. The rotation of the drum sets the time

scale while the vertical motion of the pen records the cumulative precipitation.

Aside the above gauges, signals from radars and satellite images can also be used to determine the

magnitude, areal distribution and movement of rainfalls or storms. The radar works on the basis of the

reflection of an energy pulse transmitted by the radar, which can be elaborated into maps that give the

location and the height of storms. The data from these methods are, particularly, useful in remote

areas or areas where increased spatial or time resolution is required. However, they are usually used to

supplement data from a network of rain gauges.

3.3 ANALYSIS OF RAINFALL

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 of 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 (or depth) with time whereas a mass curve is a graph of the 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 averages curve approach of

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

Generally, the important parameters that define any rainfall are the:

1. Depth of rainfall expressed as the thickness of a water layer on the surface in mm or inches,

2. Intensity or rate of the rainfall (i.e. depth of water per unit of time e.g. mm/s, mm/min, etc.),

3. Duration of the rainfall in seconds, minutes or hours,

4. Areal extent of the rainfall in km2, and

5. Frequency of occurrence, which is usually expressed by the 'return period' e.g. once in 10 years.

23

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

of the average rainfall over the entire area per year, month, or the duration of an individual storm.

Several methods may be used to determine the areal rainfall of a catchment. However, the basic

standard ones in use are the Arithmetic Mean, Thiessen Polygon, and Isohyetal Map methods.

3.3.1 Arithmetic Mean Method

This is the simplest method of estimation and involves the calculation of the arithmetic mean of all the

rain gauge measurements in the area under study. The 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 (i.e. the range in altitude is small; thus, the

variation in rainfall amount is minimal).

The mean rainfall under this method is given by:

Mean Rainfall, 𝑅 = ∑𝑅𝑖

𝑛

𝑛𝑖=1 (3.1)

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

Shaw (1988) indicates that if accurate values of the areal rainfall are first obtained from a large number

of gauge stations for a basin, then measurements from a small number of stations may give equal

satisfaction for the same basin. This was demonstrated for the Thames Basin (9981 km2) of England

where 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.

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:

24

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 = ∑𝑅𝑖𝑎𝑖

𝐴

𝑛𝑖=1 (3.2)

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

known as the Thiessen Coefficient.

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

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

be more influential to segments 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.

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). Then 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 = ∑𝑎𝑖𝑟𝑖

𝐴

𝑛𝑖=1 (3.3)

25

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 consideration the 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 localized over small areas with a range of rainfall amounts 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 as follows:

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

2. The station average method given by the relation:

𝑃𝑚 = ∑𝑃𝑗

𝑁

𝑁𝑗=1 (3.4)

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

N = number of stations of known rainfall; and

3. The normal ratio method given by the relation:

𝑃𝑚 = 𝑃𝐴(𝑚)

𝑁∑

𝑃𝑗

𝑃𝐴(𝑗)

𝑁𝑗=1 (3.5)

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

26

4. INFILTRATION

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

surface first wets the vegetation or bare soil and then infiltrates into the subsurface formation. 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 may eventually

seep into streams or recharge groundwater aquifers. The 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 depend greatly on the ability of the soil to absorb the falling precipitation.

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

a soil in any given condition can absorb water is known as the infiltration capacity. The infiltration

capacity varies from soil to soil. It is also different for the same soil type in dry and moist conditions;

i.e. decreases as the soil becomes saturated. Studies (Horton, 1940; etc.) have shown that for any soil

under constant rainfall, the infiltration rate can be described by the relation:

ft = fc + (fo − fc)e − kt (4.1)

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 value of k is small if vegetation is present on the soil 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. The equation (4.1) applies for the situation of

ponded infiltration, i.e. when there is standing water on the surface, for instance when using

infiltrometer rings.

4.1 FACTORS AFFECTING INFILTRATION

The factors that influence infiltration include the following:

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

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

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

27

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 hinder 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 cannot absorb much more water and,

thus, less rainfall will be infiltrated.

(iii) Vegetation cover: Dense vegetation cover –like forest or grass– tends 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 the reason forested areas have the higher infiltration rates than other vegetation types.

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

construction of roads, parking lots, buildings, etc., often lead 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.

4.2 MEASUREMENT AND ESTIMATION OF INFILTRATION

Some of the methods for measuring or estimating 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 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

28

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, thus, 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 its

rate or volume. Given all the other variables with infiltration (in volume or depth per unit time) as the

only unknown, simple algebra can be used to determine the infiltration as:

IF = BI + P − ET − S − R − IA (4.2)

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) Sprinkling Tests: This also known as artificial rainfall simulation. Sprinklers are used in simulating

a known intensity of rainfall i, which is greater than the infiltration capacity (i > ft). This is carried

out on a well-defined slightly sloping plot of a few tens of square meters in size and the water that

runs off over the surface (i - fp) is collected in a gutter and continuously measured. After a long time,

the surface runoff becomes approximately constant, indicating that ft is approaching a constant value

fc. The sprinkling is then terminated and the runoff monitored until it has ceased. The sprinkling tests

infiltration values are, normally, about half those obtained from the flooding-type infiltrometers

because of the dynamic action of falling water drops.

29

5. EVAPORATION

This 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 vegetation 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 water loss by evaporation

and transpiration is known as evapotranspiration. Water vapour is the principal participant in the way

energy changes in the atmosphere and the energy changes are responsible for the weather phenomenon,

which serves as an important link between the various phases of the hydrological cycle.

5.1 FACTORS AFFECTING EVAPORATION

The physical processes that aid in the change of state from liquid to vapour operate in both evaporation

and transpiration. Thus, the general physical factors that influence evaporation rates are common to

transpiration as well. These factors include:

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

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

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

season of year.

(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, which 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. Likewise, when humidity is low, more water vapour can be absorbed

into the atmosphere and, thus, increase evaporation rate.

(iv) Wind Speed: 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

30

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 exposure of the area 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.

5.2 DEFINITION OF COMMON TERMS

a) Transpiration 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:

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

leaf area, and stomata openings.

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

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

b) Potential Evaporation 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 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

31

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 in a specified region for a given time interval.

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

by plants under existing conditions.

e) Bowen’s Ratio is the ratio of the loss of upward energy flux as sensitive heat to the energy used in

the evaporation at an evaporation surface.

f) Albedo 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 solar

radiation.

5.3 MEASUREMENT OF EVAPORATION

Measurements of evaporation (and transpiration) are important to many scientific fields, although they

are among the most difficult parameters in the hydrological cycle to quantify. Evaporation data is,

actually, indispensable in the solution of many water management problems. For example, 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. Also, knowledge of the water requirements of

crops depends partly on accurate determination of the loss of water by 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 × K; where K is pan coefficient].

32

Another device used in measuring direct evaporation is known as the Atmometer. This 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. However, 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 required, and then buried to ground level. The set up in the tank is designed

to accurately reproduce the soil type and profile, moisture content, and type and size of vegetation of

the surrounding area. Measurements of precipitation into the tank, drainage out of the tank and weight

of moisture retained in the soil are used in determining the evapotranspiration by simple water budget

approach. This method is time consuming and very expensive.

Another indirect way of measuring evapotranspiration from large areas is through remote sensing using

satellites or airplanes. The images obtained from this method give information on the type of crop and surface

temperatures of the crop, which are used in combination with a soil moisture simulation model (e.g.

Nieuwenhuis et al., 1985) to determine evapotranspiration.

5.4 ESTIMATION OF EVAPORATION

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

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)

5.4.1 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, which is given as:

Eo = f(u).(es – ed) (5.1)

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

33

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) (5.2)

The Eqn. (4.2) 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) (5.3)

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. (5.3) to determine evaporation loss from a reservoir as:

Eo = 0.291 A-0.05 u (es – ed) mm/day, (5.4)

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

5.4.2 Water Budget Method

This method involves 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 in only three ways by:

i. the 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 losses.

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 (5.5)

34

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 both surface and subsurface storage.

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 can, in

many cases, 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.

5.4.3 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 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. 5.1. In the Fig. 5.1, 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 (5.6)

Care must be taken to ensure that all the terms have the same energy units, W/m2. The evaporation

from open water, Eo, is given by:

Eo = QEo/λ mms-1 (5.7)

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

This approach involves a great deal of instrumentation and the data processing involved is very

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).

35

Figure 5.1: Energy budget measurements

5.4.4 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 (5.8)

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. (5.8) does not hold.

5.4.5 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.

36

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

, (5.9)

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.

5.5 ESTIMATION OF EVAPOTRANSPIRATION

Empirical methods are often used to estimate potential evapotranspiration (ETo) for most hydrological

modelling and irrigation planning studies. Over the past decades, a large number of empirical methods

have been developed for the calculation of ETo from climate data. These methods vary from simple

relationships (e.g. Blaney and Criddle (1962), USDA SCS (1970), Doorenbos and Pruitt (1977),

Hargreaves and Samani (1985), etc.) to complex methods based on physical processes (e.g. Allen et

al. (1998), Walter et al. (2000), etc.). The choice of any of the methods for use depends on the location,

climate of the location, and availability of input data.

Commonly, the FAO56 Penman-Monteith (i.e. Allen et al., 1998) and, sometimes, the standardized

ASCE Penman-Monteith (i.e., Walter et al., 2000) equations are accepted and used as standards for

estimating potential evapotranspiration (Itenfisu et al., 2003). These methods, however, require

extensive meteorological data, which is not always available in most locations especially in the

developing world. Therefore, the simple and accurate methods are relied upon under such

circumstances. One of such simple methods is the Hargreaves method (Hargreaves and Samani, 19825;

19856), which is amongst the most accurate of the simple methods, requires very minimum data and

does not dependent on any local calibration. The method estimates ETo based on mean temperature,

5 G. Hargreaves and Z. Samani (1982). Estimating potential evapotranspiration. Journal of Irrigation and Drainage

Engineering-ASCE, 108(3): 224–230. 6 G. Hargreaves and Z. Samani (1985). Reference crop evapotranspiration from temperature. Applied Engineering in

Agriculture, 1(2): 96–99.

37

temperature difference and regression of global radiation (Rs measured at the Earth’s surface) that

takes account of regression of extra-terrestrial irradiance (Ra) and is given by:

05.0)8.17(0023.0 TDTRET ao += (5.10)

Where ETo = potential evapotranspiration in mm/day,

Ra = extra-terrestrial radiation in mm/day,

T = mean daily temperature in oC, and

TD = difference between maximum and minimum daily temperatures in oC.

38

6. RUNOFF

Runoff is a term used to describe the total flow from a basin collected at its outlet to a stream, river or

reservoir. It, generally, comprises direct runoff and baseflow. The direct runoff is the sum of surface

runoff and interflow. The term surface runoff (or overland flow) is used to describe water that flows

on the land surface after precipitation either before it enters a watercourse or after it leaves a

watercourse as flood water. 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, surface runoff may be noticed as small rivulets of water flowing downhill along

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

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

generally, serves as the 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 usage.

Generally, surface runoff may be generated from precipitation in three main ways; namely:

i. Infiltration excess overland flow: This 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. It, 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 paving of areas.

ii. Saturation excess overland flow: This takes place when the surface soil is saturated, 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 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. These sources of runoff are known as subsurface

return flow.

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6.1 CATCHMENT CHARACTERISTICS

A land area whose runoff drains toward a common point or through a single stream is called drainage

basin (watershed or catchment area). The boundary line, along a topographic ridge, separating two

adjacent drainage basins is called drainage divide. A point or location at which all surface runoff from

a basin comes together or concentrates as outflow from the basin is called concentration point or

measuring point (i.e. since the stream outflow is usually measured at this point). The time required

for rain falling at the most distant point in a drainage area (i.e., on the boundary of a basin) to reach

the concentration point is called the concentration time. This is a very important variable because

only rainfalls of duration greater than the time of concentration are able to produce runoff from the

entire catchment area and cause high intensity floods.

The characteristics of a drainage basin may be, physically, described by: (i) the number of streams, (ii)

the length of streams, (iii) stream density expressed as the number of streams per the area of the basin,

and (iv) drainage density expressed as the total length of all stream channels (perennial and

intermittent) per unit area of the basin. The drainage density varies inversely as the length of overland

flow and indicates the drainage efficiency of the basin. A high value indicates a well-developed

network with great potential for causing intense floods while a low value indicates moderate runoff

with high terrain permeability.

A stream within a catchment may be classified as: (i) Influent Stream when its bed is above the

groundwater table and seepage from the stream feeds the groundwater resulting in a buildup of water

mound; (ii) Effluent Stream when its surface water elevation is below the groundwater table and,

thus, the groundwater feeds the stream; (iii) Ephemeral Stream if the stream will, usually, dry up

completely in rainless periods; and (iv) Perennial Stream if the stream flows throughout the year,

even in the most severe drought situations. Perennial streams are, mostly, associated with effluent

streams while ephemeral conditions are, usually, with influent streams. There is also a situation where

the groundwater table will be above the bed of the stream during the wet season, but drop below the

bed during the dry season. Hence, the stream flows during wet season (due to surface runoff and

groundwater contribution) but becomes dry during dry seasons. Such a stream is called an intermittent

stream.

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6.1.1 Drainage Pattern

The arrangement and disposition of streams, which a drainage system etches into the land surface, and

which may reflect the sum total of the factors influencing the number, size, and frequency of streams

in a particular area is called a drainage pattern. These patterns develop when surface runoff is

enhanced and earth materials provide the least resistance to erosion. Their shapes or patterns are,

generally, influenced by:

i. Initial slope,

ii. Lithology and lithological variations,

iii. Structure (in its broadest sense),

iv. Geological and geomorphological history of the area, and

v. Climate and rainfall regime of the area.

The three main available drainage patterns are:

i. Dendritic drainage pattern, which is the most common form and looks like the branching pattern

of tree roots. This is developed in regions underlain by homogeneous material, i.e. where the

subsurface geology has a similar resistance to weathering; hence there is no apparent control over

the direction of the tributaries. It is characterized by tributaries joining larger streams at acute

angle.

ii. Trellis drainage pattern is similar to common garden trellis, but this develops in structurally

controlled topographic environment. It is characterized by short tributary streams that join a main

stream at nearly right angles.

iii. Radial drainage pattern develops around a central elevated point like round uplifted land areas. It

is characterized by tributary streams extending outward to a well-defined point.

6.2 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, physical

characteristics of the land surface and land use practices.

41

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.

6.3 MEASUREMENT AND ESTIMATION OF RUNOFF

Several approaches can be used to estimate runoff volume or rate. Some of these approaches are:

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. This

unknown term can, subsequently, be estimated using a water balance equation of the area. To

effectively apply this method, the catchment under consideration needs to be appropriately defined.

This can be done by catchment delineation, mostly, from a topographic map. The delineation of a

catchment involves the following steps:

i. Locate the river, lake, stream, wetland or water bodies of interest on a topographic map(s).

42

ii. Trace the watercourse from its source to its mouth, including the tributaries, to help determine the

general beginning and ending boundaries.

iii. Examine the contour lines on the topographic map that are near the watercourse and use their

intervals to determine the final elevation of your location. Normally, contour lines spaced far

apart indicate a landscape that is more level and gently sloping (i.e., flat areas) while contour

lines with much closed spacing indicate dramatic rise or fall in elevation over a short distance

(i.e., steep areas).

iv. Check the slope of the landscape by locating two adjacent contour lines and determining their

respective elevations. The slope is calculated as the change in elevation, along a straight line,

divided by the distance between the endpoints of that line. Usually, a depressed area (e.g. valley)

on the map is represented by a series of contour lines “pointing” towards the highest elevation

while a higher area (e.g. ridge, hill, etc.) is represented by a series of contour lines “pointing”

towards the lowest elevation.

v. Determine the direction of drainage in the area of the water body by drawing arrows perpendicular

to a series of contour lines that decrease in elevation. Runoff seeks the path of least resistance as

it travels downslope; this path is the shortest distance between contours, hence a perpendicular

route.

vi. Mark the break points surrounding the water body. The “break points” are the highest elevations

where half of the runoff would drain towards one body of water, and the other half would drain

towards another body of water.

vii. Identify the break points and connect the break points with a line following the highest elevations

in the area; this completed line represents the boundary of the watershed.

viii. Once the watershed boundary on the map has been outlined, imagine a drop of rain flowing down

the slopes at different points on the watershed boundaries to the nearest stream that flows to the

water body of interest to verify that the boundaries are correct.

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

using the empirical open channel flow equations (6.1) and (6.2) derived by Chezy and Manning

respectively. The equations apply to steady uniform flow condition. This condition means that within

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

slope (S) are constant and do not change with time.

Chezy formula: v = C√𝑅𝑆 (6.1)

43

Manning equation: v = 1

𝑛R2/3S1/2 (6.2)

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, and n is Manning coefficient.

The velocities obtained from equations (6.1) and (6.2) are multiplied by the channel cross-sectional

areas to obtain the runoff (or discharge).

3. Rational Method: The rational approach uses equation (6.3) to obtain the yield (or runoff) of a

catchment by assuming a suitable runoff coefficient. This yield of the catchment is the net quantity of

water available for storage, after all losses, for the purposes of water resources utilisation and planning,

like irrigation, water supply, etc.

Runoff = C x A x R (6.3)

Where A is the catchment area, P is the precipitation and C is the runoff coefficient. The value of C

varies depending on the soil type, vegetation, geology, etc. and is available in literature.

4. Velocity-Area Method: 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. This section of a river is referred to as a river gauging station. At the river

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

measurements at selected verticals across the river are multiplied by the corresponding sub-areas ( )

and their products summed to give total discharge, Q, given by:

𝑄 = ∑ �̅�𝑖𝑛𝑖=1 𝑎𝑖 (6.4)

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.

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

may be estimated in two ways (Fig. 6.1), namely:

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

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 n is number of sub-areas.

(ii) Mid-Section Method – Under this method, 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 6.1: Using mean section and mid-section methods to calculate discharge from velocity and

depth measurements for a cross-section.

5. Dilution Gauging: The method involves 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-

(6.5)

(6.6)

45

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: (6.7)

(ii) Gulp Injection: (6.8)

The tracer or chemical that can be used in this method must meet the following requirements:

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 should be low in the flowing water.

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

vi. The chemical should be cheap and readily available.

6. 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 discharge at that

section (e.g. Fig. 6.2). 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 the section. This enable future

discharges (runoff) to be estimated from the 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, usually, 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 6.2: Flow rating curve for a stream section

7. Hydrograph Analysis: 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 the general pattern shown in Fig. 6.3. 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 seepage.

Figure 6.3a: Components of a hydrograph Figure 6.3b: Hydrograph with bank storage

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

baseflow contribution from groundwater, and the remaining area above the baseflow representing the

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surface runoff (or direct runoff) produced by a storm. At the beginning of rainfall, river discharge is

low and a period of 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 ‘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 and is followed by the other 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. The climate and

topography influence the rising limb whilst geology influences the recession (de Laat and Svanije,

2006)

The boundary between surface runoff and baseflow is usually difficult to define. However, if this

boundary is ably defined, for a hydrograph, makes it possible to determine the runoff from a catchment

arising from a rainfall event. Two approaches used in defining the boundary are by:

i. 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 gauge station and applying it to a given

storm to determine the baseflow.