WATER RESOURCES DEVELOPMENT - CiteSeerX

ADDIS ABABA UNIVERSITY FACULTY OF TECHNOLOGY

DEPARTMENT OF CIVIL ENGINEERING

WATER RESOURCES DEVELOPMENT Course Material

Prepared By:

Abdulkarim H. Seid Shimelis B. Dessu

Addis Ababa

Ethiopia

May 2006.

Water Resources Development (CE )

May 2006

Objective

This course provides a broad understanding of the basics of Water Resources Development. The emphasis is on importance, assessment, project

conception, planning and operation principles and procedures, evaluation and implementation of water resource development projects. Computer

applications included.

Course Outline

Reference: - Water Resources Engineering, by R. K. Linsely and J.B. Franzini

- Water Resources Planning, By Neil S. Grigg

- Environmental Impact of Water Resources Projects. By Larry W. Canter

Student Assessment

Assignment 10 %

Project 10%

Mid Exam 30 %

Final Exam 50 %

Total 100 %

Inst.. E-mail:

Tel.

Unit 1 Introduction

Basic problems

Basin as the unit

for planning

Water Budget

Characteristics of a

Basin

Unit 2 Assessment of Water

Resources

Introduction

Demand for Water

Types of WR

information

Data requiremtn of

WRP

Regional analysis

Time series

Analysis

Unit 3 Planning and

Operation Tools

Introduction

Optimization

LP

Introduction to DP

Economics for WR

Systems

Unit 4 River Basin

Development plan

General

Components of

RBD

Phases of RB

master plan study

Unit 5 Planning for WRD

Hydrologic estimates

required for

Reservoir project

Non reservoir project

Basin wide planning

Unit 6 Elements of WR

project Formulation

Stages of WRP

Project formulation

Project appraisal

Civil Engineering Dept., AAU WATER RESOURCES DEVELOPMENT

May, 2006 ii

Table of Content

1 Introduction ...................................................................................................................................... 1

1.1 Some basic concepts ......................................................................................................... 1

1.2 The basic problem: uneven distribution of water ............................................................. 2

1.3 The basin as the unit for planning .................................................................................... 4

1.4 The water budget of a basin ............................................................................................. 6

1.5 Major characteristics of a basin ........................................................................................ 8

1.5.1 General setting of the basin ...................................................................................... 8

1.5.2 Socio-economic setting of the basin ......................................................................... 8

1.5.3 Physical environment ............................................................................................... 9

2 Assessment of Water Resources ................................................................................................. 11

2.1 Introduction .................................................................................................................... 11

2.2 Types of water resources information ............................................................................ 12

2.3 Classification and Data requirements of water Resources Development projects ......... 14

2.4 Regional analysis for the generation of missing data ..................................................... 15

2.5 Reestablishment of natural flows ................................................................................... 16

2.6 Regional Analysis ........................................................................................................... 17

2.6.1 Correlation and Regression .................................................................................... 17

2.7 Time Series Analysis and Monte Carlo Simulation ....................................................... 20

2.8 Decomposing a time series into its components ............................................................ 22

2.9 Statistical properties of time series ................................................................................. 24

2.10 Hydrologic Models ......................................................................................................... 25

2.11 SCS model for estimating runoff volume and peak flood .............................................. 26

2.11.1 Runoff Volume ....................................................................................................... 26

2.11.2 Runoff curve Numbers for selected Agricultural, suburban and urban land uses .. 27

2.11.3 Peak discharge and flood hydrograph .................................................................... 29

2.12 Demand for water ........................................................................................................... 30

2.12.1 Introduction ............................................................................................................ 30

2.12.2 Category of Demand .............................................................................................. 30

2.12.3 Demand Projections and Policy Formulation ......................................................... 31

2.12.4 Water Demand for Human Settlements .................................................................. 34

2.12.5 Industrial Demand .................................................................................................. 35

2.12.6 Electric Power Demand .......................................................................................... 37

2.12.7 Agricultural Demand .............................................................................................. 37

2.12.8 Navigation, waterways and Recreation .................................................................. 38

3 Planning and Operation Tools ...................................................................................................... 40

3.1 The system approach to water resources development .................................................. 40

3.1.1 Systems Engineering .............................................................................................. 40

3.1.2 Terminologies and definitions ................................................................................ 41

3.1.3 Basic water accounting modeling concepts ............................................................ 42

3.2 Feasibility Tests .............................................................................................................. 44

3.3 Optimization ................................................................................................................... 45

3.4 Linear programming ....................................................................................................... 46

3.2.1 Forms of Linear Programming ............................................................................... 48

3.2.2 Solution algorithms for LP problems ..................................................................... 49


May, 2006 iii

3.5 Dynamic Programming (DP) .......................................................................................... 53

3.6 Economics for WR Systems ........................................................................................... 56

3.6.1 General ................................................................................................................... 56

3.6.2 Formulating the Analysis ....................................................................................... 56

3.6.3 Defining the Alternatives ....................................................................................... 56

3.6.4 Physical consequences -Benefits and Costs ........................................................... 57

3.6.5 Benefit-Cost Analysis (BCA) ................................................................................. 60

3.6.6 Methods of Economic Appraisal (Discounting Techniques) ................................. 62

3.7 Environmental Considerations in Planning .................................................................... 66

4 River Basin Development (Master) Plan ...................................................................................... 70

4.1 General ........................................................................................................................... 70

4.2 Components of a River Basin Development Master Plan .............................................. 70

4.3 Phases of a Master Plan Study ....................................................................................... 72

5 Planning for Water Resources Development .............................................................................. 73

5.1 Introduction .................................................................................................................... 73

5.2 Hydrologic estimates required for reservoir projects ..................................................... 77

5.3 Hydrologic Estimates Required For Non-reservoir Projects .......................................... 79

5.4 Hydrologic Estimates Required For Basin-wide Long-term Planning for Integrated

Development of Water Resources .............................................................................................. 82

6 Elements of (WR) Project Formulation ......................................................................................... 84

6.1 Stages of WR project ...................................................................................................... 84

First Stage: Preliminary (or Reconnaissance) Report ............................................................ 84

Second Stage: Feasibility Report ........................................................................................... 84

Third Stage: Final Design and Preparation of Contract Documents ...................................... 85

Fourth Stage: Construction ..................................................................................................... 85

Fifth Stage: Operation ............................................................................................................ 85

6.2 Formulation of a single engineering project ................................................................... 85

6.3 Project Appraisal ............................................................................................................ 87

Reference..................................................................................................................................................... 88

Sample Exam Questions and Partial Solutions/Answers ........................................................................ 89


May, 2006 1

1 Introduction

1.1 Some basic concepts

The concepts of river as a watercourse, of natural drainage network consisting of a main water course and

its tributaries and of river basin as a geographically defined area that is drained by drainage network are

certainly quite intuitive and have already been understood for long time. Less intuitive, since not seen

from the Earth surface, are the concepts of aquifer as a water carry geological stratum or strata and of

underground storage as a volume of water stored in geology strata located under the surface. The

understanding that such entities are parts but not the totality of a system which incorporates other

components or factors affected by or affecting water resource physical, biological, human society and its

activities as well as all their complex mechanics of interdependence is a relatively new and unfortunately

not always well digested concept in the area of water resources.

Undoubtedly river basins (regional, inter-regional, national, international according to a geographic and

political point of view) or their subdivisions have played and will continue to play very relevant role,

being clearly identifiable as conceptual units in which a strong interaction of factors important to human

society may be expected. It has however to be understood that along the line of the system concept for

which the river basin is a component part, many involved factors can be limited to the exclusive

consideration of the boundaries represented by water divides or the internal physical or socio-political sub

divisions. Their areas of influence and dependence may by far extrapolate the basin’s geographical

boundaries. Typical examples are for instance cases when two adjacent basins are physically connected by

underground aquifers or when the use of water resources has far reaching consequences for human

communities not only regionally but also at global, national or international level.

A further important concept, water resources development may be interpreted as being the endeavour or

activities aimed at improving the beneficial use of water for human society. In this definition, all possible

uses such as consumptive (e.g. water supply, irrigation) or non consumptive (eg. Hydropower, navigation),

as well as all aspects related to the considered resource (quantity, time distribution, quality) are involved.

The concept of water resources development intends to integrate the different views and perceptions of

individuals or society affected by the availability of water as portrayed below:

To people in arid zones:- drought relief, irrigation, food, employment

To people in wet zones:- flood protection, hydropower, navigation

To the hydraulic engineer:- dam, reservoir, river training, water treatment plants, pumping stations, power

plants

To the environmentalist:- habitat deterioration, pollution, deforestation, destruction of wetland

To the lawyer:- water rights, legislation, institutional questions

To the economist:- economic growth, alleviation of poverty, generation or opportunities

Water resource development projects have often- as a concept- been used to represent the engineering

works or systems such as dams, canals, hydropower stations, etc. designed to develop a specific water

potential. In a broader sense such definitions does not appear sufficient or even entirely consistent with the

systems approach. An improved definition results when the project is considered as being a set of policies,

allocation of means and actions required to achieve specific water resources development objectives

within a pre-established time horizon.

Following the same line of ideas a water resources development plan would then represent an articulate set

of projects located in the region, sub-basin, a basin or any other geographic or administrative unit that

might be defined. In the virtue of their articulation the ideal geographic units or the establishment of a

water resources development plan are the river basins (or their sub-basins)


May, 2006 2

1.2 The basic problem - uneven distribution of water

Water is one of the essential prerequisites of life. A country's water resources include all the water in

rivers, lakes, seas, and groundwater. The distribution of water in nature in space and time, however, is

such that it is scarce at some locations and at particular times and excess at other locations (and at another

time at same location). Rainfall, which is the main water input to our ecosystem, is variable in space and

time. This is then reflected, for instance, in river flow, groundwater and lake-levels. Some areas get more

or less uniform and good amount of rainfall most of the year (like areas in Southwest Ethiopia), whereas

other places get their rainfall concentrated in few months (the wet season). Still there are places that get

very scanty rainfall. On the other hand the society's demand is not in general synchronised with the

availability of water. In fact, some needs, such as irrigation water requirements are high during periods of

no, or less rainfall. Hence man is faced with the task of developing the available water resources to meet

his needs.

With water needs for domestic use and that for food production being the basic requirements, water needs

of a society, both in quantity and quality depend upon its level of development. Water is needed for energy

production (hydropower), industrial use, recreation, and navigation (waterways), to mention the most

common and traditional ones. Thus projects are designed and implemented to meet all or some of these

needs.

The very water that is essential for life may also threaten life. Floods cause from time to time great losses

to human life and property. Thus settlements and developments on banks of rivers should be protected

from occurring floods, high flows in streams should not cause damage to bridges, etc., for instance by

building dykes, In such cases the water has to be controlled so that its harmful consequences are

minimised, if not totally prevented.

Consumptive and non-consumptive uses of water: Some of the uses of water, such as hydropower

generation and recreation do not actually 'use up' the water. That is the water is still available after it is

'used'. For instance in a hydropower plant, once the water hits the turbine blades it is still available

downstream with its quantity and quality not materially affected. On the other hand, water use for

irrigation of crops is a consumptive use. The water that is applied on the fields is taken up by the plants,

which is then to a greater extent transpired into the atmosphere. Hence most of the water applied is

consumed and no more available downstream. Depending up on the method of water application,

however, some of the excess water is returned into the stream (or any other water source), or into the

groundwater aquifer.

Part of the water that is used for domestic and industrial purposes may be returned into the hydrologic

system in the form of used-up water, or sewage (industrial and domestic). This if not properly treated

before it is injected into the water bodies of a basin (streams, lakes or groundwater) seriously affects the

quality of the water in hydrologic system, which in turn damages the quality of the environment we live

in. Polluted water can not support life, particularly the aquatic one. Thus one has to cope with not only

quantity of water but also quality of the water resources.

Structural and non-structural measures: Water resources development deals with projects that are

implemented for the proper utilisation and control of water. A (WR) project consists of constructed

facilities and other measures that control, utilize or limit the use of water. All measures that involve

constructed facilities are called structural measures. These could involve the building of an impoundment

behind a dam, for irrigation, water supply, or hydropower development purposes, the construction of

dykes, culverts and other drainage structures, or restricting the use of flood plains only to uses that are not

damaged by flooding (an example of a non-structural measure for flood mitigation), or the rehabilitation

of stream courses to cope with problems of environmental degradation and water quality. Measures that do

not involve constructed facilities but make use of other management tools to achieve some specified goals

are known as non-structural. Examples of such measures include, rules (regulations) to limit or control

water and land use (e.g., flood warning systems, restrictive zoning on flood plains). A project may consist

of one or more structural or non-structural measures.


May, 2006 3

The planning and design of all these measures needs then answers to such questions as how much water

is needed for the specific project in question?, how much water is expected at a particular site in a

basin?, and what are the legal constraints?, i.e. who may use the water, how economical is a given

project?, what are the impacts of the project(s) on the society and the environment?, etc. The water

resources engineer deals mainly with such questions. As society's needs grow more and more issues have

to be addressed in the planning and implementation of water resources projects.

Water resources development is a multi-phase process, which starts from inception of a given project, be it

water supply, irrigation, or a basin master plan. This might come from different bodies, depending upon

the type and size of the project and the type of economic and administrative set-up of a country. For

example, the local community, or a regional administration can initiate a project to provide safe drinking

water for a selected settlements (towns) within the region, whereas projects like water master plan for a

basin are beyond scopes of regional administrations and hence are tasks of the central government.

Once a project is initiated and it is taken for further follow-up, the planning phase begins. Depending upon

the size of the project this can involve in itself various people and stages. The outcome of this phase could

be appropriate alternative(s) (or scenarios) for the implementation, for instance source of water (surface or

groundwater), type of scheme single- or multi-purpose, etc. The alternative which is taken as the most

appropriate (?) is then designed and implemented (constructed if a structural measure).

After a project is implemented (constructed) there is a need for the proper operation of the implemented

scheme so that the benefits for the implantation of the project can be derived. For instance, if the project

involves an irrigation scheme, water application to the fields should follow according to the needs (in

space and time). A scheme that is not properly operated not only adversely affects the success of the

project but also brings about undesirable consequences such as environmental problems.

Once a project is implemented then follow the operation of the constructed schemes and the monitoring of

the overall performance.


May, 2006 4

Figure 1-1 Steps in Water Resources Development

1.3 The basin as the unit for planning

A drainage basin is an area that is tributary to a point on a stream. It is separated from neighbouring basins

by the drainage divide, which is formed by the mountain ridges. Thus all surface water derived from

rainfall received in the basin leaves the basin through the lowest point on the ridge. The concept can also

be applied to groundwater although the boundaries of surface water and groundwater basins may not

necessarily coincide. In practice, however, it is frequently assumed that the two coincide. Thus it is

Inception of WS project

Planning

Criteria Evaluation

Detailed design

Alternative 1 Alternative n Alternative 2 …

Best alternative

Implementation

Operation

Political Initiative

- Society’s WS need - Environmental challenge

- Regional development, etc.

- Professionals - Technology

- Man’s demands - Nature’s constraint - Natural system

Hydrological & Ecological - Social system Legal, Administrative, etc

Tools (eg. Models)

Key

Input

Flow of

activities


May, 2006 5

common to speak about water resources of a basin, which include both surface waters within the basin's

watershed and the underground water resources that are physically interconnected into one system of

water.

Obvious even to the particular user is the impact his use may have when he is diverting water for a

consumptive use or into another basin. The water is, of course, not ordinarily "consumed". It is, for

example, spread out on the land or discharged into a flume, canal or cistern. Evaporation and transpiration

eventually return high percentage to the atmosphere, resulting in a sizable net loss to the available surface

supply. That portion of the water that joins the groundwater by percolation may eventually be recoverable

downstream or locally, but the quality of the groundwater may be affected in the process and surface water

availability will be diminished. For example decreased flow, for example, may bring about increased salt-

water intrusion into the groundwater system.

In other words, man's and nature's works within the basin effect alterations, directly or indirectly, in the

water's quantity, quality or rate and timing of flow. These changes in the behaviour of the hydrosystem

may be felt at distant points in the basin.

Traditionally water resources development has been largely project based without due regard to the overall

basin development. Projects are initiated in response to some pressing needs. This could be a flood

damage, soil erosion, food or power shortage, etc. Schemes were planned and implemented for single or

multiple objectives. A single purpose project is designed and implemented to serve one purpose, which

could be energy production, i.e. hydropower scheme. If the scheme involves storage of water, then the

regulated flow that is used for energy production can be used further downstream for irrigation, in which

case the project serves two purposes, namely energy production and irrigation. The reservoir can still be

used for retaining high flows during wet season thereby serving as flood control reservoir. Such

multipurpose projects need, however, good operating procedures so that all the objectives are met to

some acceptable degree. For instance, to maximise power generation in this example the reservoir level

should be high always, whereas for flood control, at the beginning of the wet season the reservoir should

have more space (less water), so that it can accommodate more of the incoming floods. This means the

two uses, i.e. power generation and flood control, look contradictory and hence a compromise should be

reached to maximise both benefits. The benefits from a flood control scheme can be estimated by the

amount of damage that could be averted (both life and property) if a certain proportion of the high flow is

retained in the reservoir. In the past the benefits derived from water resources projects have been thought

in monetary terms, i.e. projects were considered for implementation based on their benefit cost (B/C)

ratios. This is, however, changing as more emphasis is being given to the preservation of the environment.

Thus environmental objectives are nowadays almost always part of any project.

As mentioned above, the water resources of a river basin are interrelated. Water flows in a basin from the

drainage divide towards the outlet point. Thus projects located upstream are better situated than those near

the downstream end of the basin, in terms of quantity and quality of water. Thus the proper utilisation of

the water resources of a basin calls for the integrated approach in the planning and implementation of the

projects so that the overall benefit, as seen basin wide, is maximised. Development of other resources such

as land and minerals poses some demand of water supply, hence the same can not be treated alone without

considering it in the plan for water resources development.

Recognising this, contemporary basin development plans are prepared taking into account all the resources

(human, water, land, mineral, etc) of the basin. Projects are then identified in the basin-wide plan and their

combined effects studied and different scenarios of development produced. This approach, which in

contrast to the traditional project-based one considers the entire basin as a unit of planning, is known as

Integrated River Basin Development. In this regard the comprehensive water resources development

plan that is developed for the entire basin and which serves as the reference based on which projects are

initiated is called the Master Plan for the development of water resources of the basin. The trend today is

that master plans encompass 'all' available resources of the basin and are called Integrated River Basin

Development Master Plan.


May, 2006 6

Figure 1-2 The drainage basin with some human interventions

As mentioned above the development of the basin's water resources can not be separately treated from the

development of other resources of the basin. For example, the availability of large area of arable land

indicates the need for irrigation water, if the rainfall is not sufficient, etc. Hence in studying a given basin,

a multitude of factors are used to characterise it, which have some bearing on the development of its

resources.

1.4 The water budget of a basin

The water budget of a basin is a concept used to express quantitatively the components of the hydrologic

cycle. A schematic illustration of the water budget of a basin is shown in Figure 1-3:

The general hydrologic equation of water budget can be written in the form

P - R - G - ET = S,

Where P = precipitation received at the ground level. Precipitation is one of the most frequently measured

hydrologic variables. Estimated aerial values of precipitation are used in the equation.

R = surface runoff (i.e. excess water that has left the region in the form of stream flow). This can

be estimated from hydrometric measurements at the outlet of the study area.

G = amount of water that moves from or to the basin as deep seepage. It is very difficult to

estimate this component although, however, its magnitude is in general very small.

ET = evapotranspiration, i.e. the sum of evaporation and transpiration. Point estimates can be made

using instruments like Pans or using ET equations based on some meteorological variables.

Areal estimates of ET are made either using the hydrologic equation above, or by correlating

point estimates with some influencing factors, like temperature or altitude.

S = is change in storage both in unsaturated soil moisture and the saturated (groundwater) zones.

The hydrologic (water budget) equation can be applied to an entire basin, some part of it or isolated water

bodies, such as lakes. It can be applied over any period of time of interest. To use the equation in a

meaningful way one has to determine the components of the hydrologic cycle in the equation.


May, 2006 7

Figure 1-3 A schematic illustration of the water budget of a basin

Q

t

Streamflow (hydrograph)

Interception

Depression

storage

Infiltration

Overland

flow

Interflow

Percolation

(to GW)

Deep

groundwater

Channel

input

Channel

input

Channel

input

E

E

T

E

T

i

t

Precipitation input

(heytograph)

ET


May, 2006 8

Surface water in Ethiopia amount to 110 BM3, much of which leaves the country through its

transboundary rivers. Groundwater availability is estimated as 2.6 BM3. The highest surplus water is to be

found in the Abay basin (52.62 BM3) followed by Ghibe-Omo (17.96 BM

3).

Table 1-1 Water Resources Development in Ethiopia

No Uses Coverage

1

Water supply (total)

rural

urban

Livestock watering

17 % (population)

15 %

31 %

Negligible

2 Sanitation (total)

rural

Urban

8 % (population)

1 %

60 %

3 Irrigation 3 % of potential

4 Hydropower 1.5 % of potential

5 Aquatic Resources (fisheries) < 10 % of potential

6 Inland Water Transport Negligible

1.5 Major characteristics of a basin

1.5.1 General setting of the basin

This refers to the physical size of the basin, which is commonly given in km2, the orientation, and its

location. The size of a basin can be an indication of the significance the basin may have on the national

economy, in terms of available water, human and other resources. Depending upon whether a basin finds

itself within the boundaries of a country or not the basin can be classified as either a national or

international one. A basin whose entire area lies within one country is a national basin, whereas an

international basin has its area distributed over at least two countries. The development of an international

basin is more complicated than a national one while the issue of water sharing among the riparian

countries (those that share the basin, also known as basin states) is often difficult to deal with. A good

example of such an international basin is the Abay basin, which together with that of the White Nile

extends over ten countries. Thus development of the water resources of an international basin should

address issues that can not be solved at the national level. In such cases the legal constraint is the most

difficult one to overcome.

1.5.2 Socio-economic setting of the basin

Important elements of the socio-economic setting are the administrative setup, the economy, land tenure

system, settlements and the extent of urbanisation, and the population characteristics. The administrative

setup plays an important role in the implementation of the overall plan for a basin. The responsibilities of

the regional and federal (central) government should complement each other for a better coordination of

development activities. A basin in a predominantly urban area is expected to have more problem of water

quality, as domestic and industrial outflows are frequently discharged into the river system of the basin

with no or inadequate treatment. A typical drainage basin in Ethiopia is the Awash. The size of population

(per unit area) is also an indication of the stress the basin is exposed to. This could be expressed, for

instance, in terms of the average size of land a family owns. Higher population density would mean more


May, 2006 9

intensive use of the land resources, which could lead to land degradation. A good performing economy is

an important ground for development. Recurrent famine and war often distract the growth of the national

economy and hence also adversely affect the development of the resources of the river basin.

1.5.3 Physical environment

The physical environment consists mainly of the topography, climate, the water resources, mineral

resources, and the soils of the basin. These factors substantially determine the potentials and constraints of

the basin, particularly in a predominantly agricultural economy. The topography to a great extent

determines the mirco-climate of the basin, which leads to the different Agro-climatic zones. Moreover, the

prevalence of steep slopes would indicate soil erosion risks, and possible land degradation. Rainfall is

certainly the most important climatic variable affecting the water resources of the basin. The moisture

input to the basin is in the form of rainfall, which varies in space and time. The water resources of a basin

are all the waters in the surface water bodies and underground water. The assessment of the water

resources of a basin is the first step in the overall planning for development. The various steps and

methods involved in this procedure are discussed in section 2 and a review of the hydrologic cycle is given

in Figure 1-4 below:

Figure 1-4 The Hydrologic Cycle with yearly flow volumes based on annual surface precipitation on earth,

~119,000 km3/year.

The hydrologic cycle describes the path followed by water in its continuous transformation from oceans to

the atmosphere, to the land and back to the sea. Powered by solar radiation, water evaporates from oceanic

surfaces and joins the atmospheric moisture. This is then transported inland by means of winds, where it

gains elevation as a result of which it condenses. The clouds so formed become the very source of

moisture to the river basin. The water that reaches the ground in the form of precipitation (rainfall and

snowfall) partly gets into the ground while the remaining to a large extent flows overland and reaches the


May, 2006 10

stream networks. Streams join to make large rivers, which drain the basin and eventually the water reaches

the seas and oceans thus completing the cycle. The water that infiltrates into the ground partly stays

temporarily in the soil formation, thus becoming soil moisture, and the rest may percolate deep into the

groundwater system, which flows towards seas and oceans.

The different components of the hydrologic cycle can be grouped together into subsystems or broken

down into new sub-processes, depending on the level of detail in the analysis and purpose of the analysis.

A hydrologic system can be defined as a structure or volume in space, surrounded by a boundary that

accepts water and other inputs, operates on them internally and produces and output.

The objective of hydrological system analysis is to study the system operation and predict its internal

states and output. A hydrological system model is an approximation of the actual system. Its inputs and

outputs are measurable hydrological variables and the model’s structure is a set of equations linking input

to output. Central to model structure is the concept of system transformation. The input and output can be

expressed as functions of time I(t) and O(t) respectively. A system performs a transformation of the input

into output represented by transformation operator or equation.

Example: A watershed

The watershed can be looked upon as an operator transforming the moisture input, I(t): precipitation, into

output, O(t): runoff, evaporation and transpirataion.


May, 2006 11

2 Assessment of Water Resources

2.1 Introduction

Water resources can be neither developed nor managed rationally without an assessment of the quantity

and quality of water available. A basic water resources assessment activity involves the collection and

processing of hydrological, meterological, and hydrogeological data, plus the auxiliary data required for

their areal interpolation, in order to permit a preliminary assessment to be made of available water

resources on which to found national or regional long-term plans for overall water resources development.

The information is particularly required for the purpose of:

assessing a country's water resources (quantity, quality, distribution in time and space), the

potential for water-related development, and the ability of the supply to meet actual and

foreseeable demand,

planning, designing and operating water projects, such as water supply, irrigation and hydropower

projects,

assessing the environmental, economic and social impacts of water management practices,

existing and proposed, and planning sound management strategies,

assessing of the response of water resources to other, non-water sector activities, such as

urbanization or forest harvesting,

providing security for people and property against water-related hazards, particularly floods and

droughts

Thus a WRA program in its broad sense comprises of the following:

the institutional framework and the manpower involved in the collection, maintenance and

dissemination of the hydrological, hydro-geological, and physiographic data

a network of measurement stations where the hydrological and hydrogeological data are collected

the set of techniques, procedures and software that are used in the processing, interpreting and

final dissemination of the collected data

The entire activity is illustrated in the block diagram shown below (source: WRA Activities - Handbook

for National Evaluation, UNESCO/WMO 1988).


May, 2006 12

Figure 2-1 Component of Activities involved in water resources assessment program

2.2 Types of water resources information

The diversity of possible uses of water resources information implies that there is a considerable range of

types of data. Conventional water resources information comprises that statistics of a variety of

meteorological and hydrological elements. These elements include:

precipitation (rainfall, snow)

river levels and flows, and lake or reservoir levels

groundwater levels,

evapotranspiration

sediment concentrations and loads in rivers

Water quality (bacteriological, chemical and physical) of surface water and groundwater.

The primary data collected should then be converted into useful information on the water resources.

Collection of Hydrological

Data (components of the

hydrologic cycle- including

quantity and quality of

surface and groundwater)

Collection of

Physiographic Data

(topography, soils,

geology)

Techniques of Areal Assessment

of Water Resources

(regionalization techniques)

Education and

Training Basic and Applied

Research

Water resources information (data banks, maps)

Users

(planning, design and

operation of water

resources facilities)


May, 2006 13

Frequently needed pieces of information include:

mean annual, monthly, or seasonal values,

maxima and minima, and selected percentiles,

measures of variability, such as standard deviation,

Continuous records in the form, for example, of river flow hydrographs.

There is a requirement for both historical and real-time data, to cater for the full range of needs, from

project design through to flood warning. For planning purpose one may do well with monthly data (of

stream flow, for example), whereas for design and operation data of higher time resolution are needed.

The information needed usually depends upon the type of project under consideration, whether single

(multi) purpose projects, or basin wide master plans.

The raw data collected as part of the routine measurement procedures have to be processed in order to

obtain the information required for a specific application. For instance sediment measurements could be

used to assess the accumulation of sediment behind a proposed dam, which in turn is used to estimate the

dead storage space.

In the processing of the primary data to get the information needed for a specific application, however,

there are frequent problems that have to be dealt with. These are:

1. There are gaps in the series of observed data

2. The observation period is too short

3. Data are not available at the site of interest but in neighbouring region.

In addition, the need to investigate the response of the scheme to be designed, for instance an irrigation

development, requires the estimation of extreme events (floods and low flows). In the study of reliability

of the system in meeting its objectives there is a need for the generation of synthetic data (streamflow, for

example). There are hydrologic techniques that are applied to solve the above problems. These techniques

are briefly discussed below, which are then presented in detail later in this chapter.

In addition, the data collected as part of the routine measurement procedures may need further treatment

before it can be used for the specific purpose it is needed. Two of the typical cases are:

the data collected may not be directly from the same area as the location of the intended project,

there could be gaps and interruptions in the records due to several reasons, such as instrument

breakup, security problems, etc.

The processing of hydrometeorological data for engineering purposes is the subject matter of engineering

hydrology, hence will not be dealt with here [Students are advised to review hydrology lessons]. However,

a few selected topics shall be included in this discussion, which are not commonly treated but are useful in

the practice.


May, 2006 14

2.3 Classification and Data requirements of water Resources Development projects

Water projects defer on their need for data on the hydrology of the site where they are implemented. A

description of the various water projects is given in Table 2-1 below:

Table 2-1 Project purposes, their objectives and their associated structural measures

Project purpose Objectives Structural measures

Flood Control Flood-damage prevention or

reduction, protection of life and

economic development

Dams, storage reservoirs, levees, floodwalls,

channel improvements, floodways, pumping

stations, flood warning systems, diversions and

other flow retarding measures

Hydroelectric

power generation

Provision of electric power for

economic development and improving

living standards

Dams (weirs), storage reservoirs, penstocks,

power plants

Municipal and

industrial water

supply

Provision of water for municipal and

industrial uses

Dams, reservoirs, wells, conduits, pumping

plants, intake works, water treatment plants,

saline-water conversion, distribution systems

Irrigation Increase and stabilization of

agricultural production

Dams, storage reservoirs, wells, canals, pumping

stations, weed control and desilting works,

distribution systems

Drainage Increase and stabilization of

agricultural production, urban

development, protection of public

health

Ditches, tile drains, pumping stations, sluices

Navigation Transportation of goods and

passengers

Dams, storage reservoirs, canals, locks, channel

improvements, harbor works

Water quality

control

Protection or improvement of water

supplies for municipal, industrial and

agricultural uses, protection of fish

and wildlife, development of

commercial fishing

Waste treatment facilities, reservoir storage for

low-flow augmentation, waste-water collection

systems

Recreation enhancement of recreation and sport

opportunities

Storage reservoirs, facilities for recreational use,

pollution control works

Fish and wildlife

enhancement

Improvement of habitat for fish and

wildlife, reduction or prevention of

fish and wildlife losses associated with

men's activities, provision for

expansion of commercial fishing

fish hatcheries, fish ladders and screens,

reservoir storage, pollution control works

Sediment control Reduction and control of silt load in

streams and protection of reservoirs

Desilting works, channel and revetment works,

band stabilization, special dam construction


May, 2006 15

Table 2-2 summarizes data needs of the various water resource projects. Detailed steps involved in making

hydrologic estimates for the projects are presented subsequently.

Table 2-2 Water Resource Projects and their respective Data need.

Water projects

water levels

river flow

sediment

water quality

time

series

max

min

time

series

max

min

time

series

max min time

series

max min

redistribution of

water (diversions,

intakes, canals)

M

M

M

H

H

H

H

M

M

H

M

M

redistribution of

water in time

(reservoirs)

M

M

M

H

H

H

M

M

M

H

M

M

energy production

(hydropower)

H

M

M

H

M

H

H

M

M

M

M

M

water confiners

(dams, floodbanks)

H

H

M

M

H

M

M

M

M

M

M

M

water relievers

(spillways)

M

H

M

H

H

M

M

quality

improvements

(water and sewage

treatment)

H

M

H

M

M

M

H

H

H

flow and level

forecasts

(flood control,

reservoir operation)

H

H

H

H

H

H

H = high level or priority, M = medium level of priority

2.4 Regional analysis for the generation of missing data

Regional analysis is needed when hydrological data, in particular streamflow series, are either nonexistent

of too short for solving major problems in a given river basin. The technique is based on a comparison of

watershed characteristics between the one with unknown or short streamflow series and neighboring

watersheds for which these series are available. Among the principal characteristics upon which the

comparison is based are the sizes of the watersheds, the topography, soils and land cover, precipitation and

other meteorological factors (if available). When the homogeneity among watersheds is established, cross

correlation between records can be evaluated. If this correlation is acceptable, the time series can be

extended mostly by linear regression models. If no flow records are available in the problem area, runoff

can be estimated using the known watershed data by simple proportion with drainage area ratios and /or

rainfall ratios when they exist.

Regional analysis is applicable to problems in which historical series are needed, for instance for reservoir

sizing and nonreservoir structures for flood control, irrigation and water supply, determination of flooding

potential, and for integrated river basin planning.


May, 2006 16

2.5 Reestablishment of natural flows

Most historical streamflow records reflect upstream extractions for various useful purposes. The flow

values measured at these gaging stations must be corrected in order to obtain natural flows which are

necessary for several hydrological analyses, such as statistical analyses, water budgets, establishment of

prior water rights (legal aspects) and benefits and costs with and without proposed or existing structures.

The correction method would seem very simple, namely eliminating the effects of man-made structures

such as dams. However, in many cases, information about these effects is not available and must be

estimated. The problem is further complicated by the return flows from extractions that occur upstream of

the gaging station and for which only rough estimates can be made. Streamflow routing procedures are

often required to determine natural flows.

Analysis of flow variability

The annual flow distribution shows long-term variations in mean flow. In particular, the data on dry and

wet periods and trends are needed. Variations can also result from changes in land use pattern. Time

series analysis can be applied to long historical records to obtain flow distributions.

Low-flow frequency analysis is also based on historical records and, in some cases, is used for

determining the required conservation storage of a reservoir, a system of reservoirs, or a complete water

supply system in a region. These analyses are useful for showing the necessity for low-flow augmentation.

Frequency curves of reservoir storage are used to evaluate the probability of failure to meet demands when

a reservoir runs dry, or to estimate power production potential or recreational benefits. The latter are based

upon the frequency with which a reservoir is filled over a given level at certain time periods. Modern

techniques such as queuing theory and simulation can be used to develop these storage frequency curves.

For analysis of flood protection measures, several flood characteristics are required. These include the

design flood peak discharge and its corresponding recurrence interval and shape, total flood volume and

time-to-peak. With the knowledge of these characteristics, the storage for flood control and the design of

other structural or nonsturctural measures to prevent flooding of valuable areas can be estimated for a

given probability of failure. Reservoir and channel routing techniques are used to determine inundated

areas.

Hydrologic Modelling

The planning and management of water resources system are dependent upon information relating to the

spatial and temporal distribution of hydrologic phenomena. In a country like Ethiopia, hydro

meteorological data base is insufficient, scarce or unavailable. As a result, planning and management

decisions are subject to hydrologic uncertainties in addition to uncertainties of the non hydrologic nature.

More precise information can be extracted from more extensive data bases: however, it is often difficult to

justify delay in decision making pending the acquisition of additional data because resulting benefits

would have to be forgone. A more feasible course of action is to use mathematical models of hydrologic

processes in order to extrapolate and interpolate information over time and space.

When historical flood data do not exist or are insufficient, the unit hydrograph or other rainfall-runoff

modelling techniques can be used to estimate them using meteorological data. Rainfall-runoff models are

valuable to develop long records of flows which are needed for several of the analyses mentioned above.

Their inputs are generally rainfall and temperature (if snowmelt is relevant), evapotranspiration and soil

moisture data and the watershed characteristics. This method is applied when, as often occurs,

hydrological data series are short compared to the meteorological series. Another important application of

these models is the short-term prediction of flows and flood forecasting. A reliable flood forecasting

model linked with a warning system may provide a valuable nonstructural flood protection system. With

these warning systems, larger damages can be prevented through evacuation of the flood prone areas or

regulation of reservoirs.

Stochastic hydrology may be used to develop a number of flow records of any given length which have

about the same statistical parameters as the historical record. These records are used mainly in simulation

analysis to determine reservoir capacity and operation policies. In applying this technique, several series


May, 2006 17

of equal length should be generated and used in the simulation to obtain reliable statistical evaluations of

the system's performance.

The most widely used method of reservoir storage requirements is simulation. For flood control purposes,

a short-term simulation is needed, in which the time step is much smaller than the usual monthly routings

for other project purposes. Usually short interval flood studies are made for each major historical flood by

simulating the operation of the reservoir projects. Regardless of the purpose of the dam, reservoir routing

procedures are needed to test the ability of the spillways to evacuate the flood. For conservation purposes,

such as water supply, irrigation and hydroelectric power production, a monthly simulation analysis will

also be required. For single purpose conservation reservoirs, Rippl-diagram analysis can sometimes

provide sufficient accuracy.

Advanced mathematical techniques, such as optimization and simulation, are applied, in particular for

integrated river basin planning. They may also be useful for analysis of reservoir operation problems.

The objective of all these techniques is directly or indirectly an optimization of the system's parameters.

Therefore, a quantitative measure of benefits and costs of each alternative design or operation must be

developed. The characteristics of this system, namely mass balances, power productions, hydrologic

inputs, water quality and several water demands should be developed as constraints in mathematical form.

This constitutes the set of constraints under which the system's parameters to be optimized can be varied.

Mathematical models may also be used on a real-time basis to determine optimal operation of an existing

reservoir or reservoir system. Such applications require the existence of a reliable flood forecasting

system.

Other Hydrologic Techniques

In addition to the above, other types of information are needed in the design and operation of water

projects. Sediment reserve storage is generally estimated separately. Sediment transport is calculated on

the basis of direct measurement of bed load and suspended sediment at the reservoir site. When no data is

available at the site of interest indirect methods, based on discharge, river slope, soil cover and other

parameters, may have to be applied. They have, however, limited accuracy.

Water surface profiles are needed to establish the height of levees for flood protection. They are based on

backwater calculations or on stage-discharge curves such as available for river gaging stations.

Water requirements for fish and wildlife protection are estimated separately and included in storage

capacity and operation studies as constraints. For this purpose, interdisciplinary teamwork among

engineers, biologists, ecologists, etc. is necessary.

2.6 Regional Analysis

2.6.1 Correlation and Regression

Among the techniques used in the regional analysis of hydrologic variables, correlation and regression are

the most frequently used techniques. The main objectives of this analysis are the transfer of information

between points at which the same variable is observed, or between two among several variables observed

simultaneously. This includes the completion of missing data in hydrologic series, and the prediction of a

variable from the observed one or several other variables.

Correlation is a mathematical description of the relationship between two variables. Regression represents

a mathematical equation expressing one random variable as being correlatively related to another random

variable, or to several random variables. The regression equation may be any function that can be fitted to

a set of points of observed variables. Determining mathematical models of correlative association to two

or more variables, so that the best prediction of one variable can be obtained from the other variables, is

referred to as regression analysis, and the models are called regression functions.

The case of two random variables is referred to as bivariate (or bivariable) distribution and the relation

between these two variables is called the simple or bivariate correlative association, and the simple or

bivariate regression. The case of a random variable related to several (more than one) random variables is


May, 2006 18

referred to as the multiple correlative association and the multiple regression. The linear equation of

relations represents the simple linear and the multiple linear correlation and regression, which depends on

whether two or more variables are involved. The opposite cases are the simple nonlinear and multiple

nonlinear correlation and regression.

Steps in the regression analysis: whether a simple or multiple correlation or regression analysis is

performed, the five steps are necessary for complete information about this association:

1. Selecting a function of correlative relation, simple or multiple of linear or any nonlinear type;

2. Estimating parameters (statistics) that measure the degree or correlative association;

3. Testing the significance of statistics that measure the correlative association;

4. Estimating parameters of regression equation, and

5. Testing the significance of regression parameters, or drawing the confidence limits about the fitted

regression function.

The following two types of regressions are current in hydrology:

a) Cause-effect based relations, where a random variable, y, is correlatively related to causal factors,

xI, which produce or affect the outcomes of y. Typical examples are a runoff-rainfall relation,

because the rain is the basic causal factor of runoff, with river geometric, soil, moisture and

climatic factors affecting the basic cause-effect relation.

b) relations or random variables, which have the same causative factors, such as the correlative

association of the runoff of a river tot he runoff of an adjacent river, or the association of rainfall

variables at the adjacent precipitation stations , and similar. Both cases are similarly treated in

correlative association.

In fitting a linear regression model, the linear association of the random variables should be checked first.

This can be done, for example, by testing the correlation coefficient for significance, or by making a

scatter plot of the variables. Important observations should be made if the relationship of the two variables

appear linear, and if the variance of the dependent variable is constant over a range of values of the

independent variable. A relationship where the variance is constant is called homoscedastic. If the original

data do not exhibit linear relationship, some transformations (particularly the log transformation) may

render them linear.

The correlation coefficient is also used to measure the linear association between the variables. Its

magnitude determines the strength of the linear association, whereas the sign indicates whether one of the

variables increases when the other decreases.

Estimation of the correlation coefficient: assume that N simultaneous observations of the random variables

x and y are available. The ith pair of observations is denoted by (xi, yi), i = 1, …, N. The sample estimate, r,

of the population correlation coefficient, r is given by

N

i

iy

N

i

ix

yx

N

i

ii

yx

xy

yNyS

xNxS

SS

yxNyx

SS

Sr

1

22

1

22

1

in which Sxy is the estimate of the covariance, xy , x, and y are the estimates of the population means of x

and y, respectively, and sx and sy are estimates of the variance of x and y.

Once the correlation coefficient is computed a statistical test of significance is performed to check if the

population correlation coefficient is different from zero. To make the test of significance, compute the

statistic


May, 2006 19

21

2

r

Nrt

The null hypothesis (that = 0) is rejected, hence the value of r computed above is taken as significant, if

/t/ > tcrit, where tcrit is the point on the Student's t distribution with n-2 degrees of freedom that has a

probability of exceedence of /2. If the correlation between the variables is found significant, estimate the

parameters of the regression model as outline below.

The linear regression model to be used is

Nixy iioi ,...,2,11

where: yI = ith observation of the response (or dependent) variable

xI = ith observation of the explanatory variable

o =intercept

1 = slope

= random error or residual for the ith observation

It is assumed that I is a (normally distributed) random variable which is independent of xi and has a mean

of zero and a constant variance 2, which does not depend on x.

The sample estimates of the slope and the intercept of the linear regression model are given by

lyrespectivexandyofmeansthearexandywhere

xbyb

and

xxn

yxxynb

o

,

,

)(

1

221

The above is an example if a simple linear regression, which is used with one explanatory variable. Some

hydrologic variables, such as the stream flow, are functions of several other variables, for example, basin

area, mean altitude of the basin, percentage of basin forested, average slope, etc. In such cases the used of

multiple regression gives better results.

Application to hydrology

As described in the previous sections, the method of linear regression can be used to extend a short record

using a longer record, between which there exists a significant, correlation, fill in missing data, again

using data from adjacent stations, extend short records by using other climatic and basin characteristics,

such as the use of rainfall with (or without) basin characteristics.

In all the above cases either linear or multiple regression can be used to establish the relationship between

the dependent and the independent variable(s). For instance, if x and y represent hydrologic variables

measured at two neighboring stations with y being of shorter duration than x, then a regression equation

between y and x can be used to predict values of y from x values.

Regional Flood Frequency Analysis: Correlation and regression of hydrologic and related variables on a

regional basis are frequently used to extend short records, fill in gaps in records, and estimate flow at

ungauged sites. Regional analysis of hydrologic data is also applied to produce regional (rainfall)

Intensity-Depth-Frequency curves, regional flow-duration curves, regional flood and low-flow frequency

curves, and regional values of other relevant hydrologic variables. An outline of the regional flood

frequency analysis method, is given below.

Hydrologic records at most gauged sites are usually too short to justify the type of extrapolations made in

estimating floods of low frequency. Commonly one estimates a flood of a 100 years return period based

on a record length of 25 years. Given that sufficient data will seldom be available at the site of interest, it


May, 2006 20

makes sense to climatic and hydrologic data from nearby and similar locations. A successful example of

regionalisation is the index flood method.

The concept underlying the index flood method is that the distribution of floods at different sites in a

region are the same except for a scale or index-flood parameter which reflects the size, rainfall, and runoff

characteristics of each watershed. Generally the mean is taken as the index flood. The steps in the

application of the index flood method are summarized below:

a) Prepare single-station flood-frequency curves for each station within the homogeneous region

b) Compute the ratio of flood discharges taken from the curves at various frequencies to the mean

annual flood from the same station

c) Compile ratios for all stations and find the median ratio for each frequency

d) Plot the median ratios against recurrence interval to produce a regional frequency curve.

Hence, to estimate the T-year flood for any site within the homogeneous region,

estimate mean annual flood (the index flood, a flood with a return period of 2.33 years) for the site

read the ratio from the regional frequency curve for the given recurrence interval

estimate the T-year flood as the product of the mean annual flood and the ratio from the regional

frequency curve.

Application to ungauged basins: Regional frequency curves are most useful to estimate floods in

ungauged basins. Since the regional curves show the relation between the flood of any recurrence interval

and the mean annual flow, an estimate of the mean annual flood is sufficient to estimate the flood for the

required recurrence interval. The mean annual flood is usually estimated by applying regression analysis

with the factors that affect the flood, such as the drainage area. The flood of any given recurrence interval

for the ungauged basin is estimated by determining the corresponding flood ratio from the regional-

frequency curve for the region of which the ungauged basin is a part and multiplying it by the estimated

mean annual flood of the ungauged basin.

2.6.2 Time Series Analysis and Monte Carlo Simulation

In the design and operation of water resources systems, engineers have always recognized the variability

and uncertainty of the hydrologic inputs. Rainfall, streamflow, evapotranspiration and groundwater flow

are all more or less unpredictable processes. A sequence of hydrologic events will rarely repeats itself.

Operational, or synthetic hydrology is used to solve the limitation of historical hydrologic inputs.

Recognizing that streamflows and other hydrologic time series are random processes, operational

hydrology attempts to generate sequences with the correct probability behavior. These sequences can then

be used in a series of Monte Carlo experiments directed toward defining the probabilistic behavior of the

output.


May, 2006 21

Figure 2-2 Concept of Monte Carlo Simulation

Time Series: observed realizations of a random process are usually called time series, i.e. time series is in

short the sequence of records of a hydrologic process in time, such as streamflow. Time series analysis is

the exercise of estimating the properties of the underlying process that lead to the observed time series.

Operational, or synthetic, hydrology utilizes the results of time-series analysis to hypothesize

mathematical models capable of producing realizations that would be statistically indistinguishable form

the observed hydrologic series. The sequences generated using these models are commonly known as

synthetic sequences to distinguish them from the historic ones. Synthetic streamflows are used in problems

of reservoir design and operation of river-basin water resources-systems.

Single and multiple time series: a single time series (or univariate series) is simply a time series of one

hydrologic variable at a given site. In contrast, a multiple time series (multivariate series) is a set of two or

more time series.

Uncorrelated and correlated time series: given a time series X, if the x's at time t depend on those at

some time t-k, then the series is said to be autocorrelated, serially correlated, or correlated in time. An

uncorrelated series is also called independent. For two series X and Y, if the y's at time t are dependent on

the x's at some time t-k, for k = 0, 1, 2, …., then the series are called cross-correlated. The individual

series could be autocorrelated or independent but cross-correlated.

Stationary and nonstationary time series: A hydrologic time series is stationary if it is free from trends,

shifts, or periodicity (cyclicity). This implies that the statistical parameters of the series, such as the mean

and variance, remain constant through time. Otherwise, the time series is nonstationary. Generally,

hydrologic time series defined on an annual time scales are stationary, although this assumption may be

incorrect as a result of large-scale climatic variability, etc. Hydrologic time series defined at time scales

smaller than a year, such as monthly series, are typically nonstationary, mainly because of the annual

cycle.

.

.

.

.

.

.

Deterministic

Model

(i.e. Basin

Model)

.

.

.

Input distribution Sample input realizations range of otputs


May, 2006 22

2.7 Decomposing a time series into its components

Attributes of a time series such as trend, shift and seasonality are called its components. In fitting

stationary time series models, it is necessary to reduce the time series to stationarity. This is effected by

removing any trends, shifts and periodicity from the series.

Trends and shifts: a trend is a gradual change in sample statistics of a time series, such as the mean and

variance, whereas a shift is a sudden change in these parameters. There could be both linear and nonlinear

trends in a time series.

Removing trends: A linear trend in a time series yt in the mean can be removed by subtracting the mean

from the series, whereas the trend in the variance, if any, can be removed by dividing the difference (yt -

ymean) by the standard deviation of the series.

Removing shifts: Shifts in the mean are removed by deducting the mean and shift in the variance is

removed by dividing the difference by the appropriate standard deviation.

Seasonality: Hydrologic series defined at time intervals smaller than a year (such as monthly series)

generally exhibit distinct seasonal (or periodic) patterns. These result from the annual revolution of the

earth around the sun which produces the annual cycle in most hydrologic processes. Generally seasonal or

periodic variations in the mean, variance, covariance and skewness are of interest.

Removing seasonality in the mean and variance: removing the seasonality in the mean is accomplished by

taking the difference yt- yt, where yt is the monthly mean for January, February, …, if t is a monthly index.

The seasonality in variance can then be removed by dividing the difference by the standard deviation of

the respective months. This operation is called seasonal standardization (or deseasonalizing) of the

original series.

Apart from the seasonality in the mean and variance, the seasonality in the autocorrelation coefficient is of

interest. But this is not readily apparent from the time series plot. Hence a special plot is made to see the

seasonality in the autocorrelation coefficient. This is done by computing the correlation coefficient, for

instance for monthly series, between the February flow (for all years) with those of January, to obtain r1,2,

similarly for other months to obtain r1,1, . . . . , r1,12 and, in general, rk,1, . . . , rk,12. The plot of rk,t for k > 0,

may, depending on the hydrologic series under consideration, exhibit a seasonal or periodic pattern. In

contrast, for annual series, the correlation coefficient rk is assumed to remain constant.


May, 2006 23

t

yt

yt

t

yt

yt

y1

y2

yt-yt

t

yt-yt

t

t

st

constant s

st

s1

s2

t

t

(yt - yt)/s

t

(yt - yt)/s

Removing trends Removing shifts


May, 2006 24

2.8 Statistical properties of time series

Table 2-3 Overall sample statistics

Statistical Measure Formula

Mean

Variance

Skewness coefficient

Sample autocorrelation coefficient

where N = sample size. Cv = s/y, is the coefficient of variation.

Table 2-4 Statistical Measures for assessment of simulation result

Statistical Measure Formula

Correlation Coefficient

Root mean square

n

t

tt SOn

rms1

2)(1

Mean absolute error

Maximum absolute error

Bias from the mean

Nash and Sutcliff coefficient

where Ot = Observed or historical data, St = Simulated result

The overall sample statistics computed above are normally used for annual series. Seasonal hydrologic

time series, such as monthly flows, may be better described by considering statistics on a seasonal basis.

Let the seasonal time series yv,t, in which v = year; v = 1, . . . N; and t = 1, . . . w, with N and w denoting

N

t

t yyN

s1

22 )()1

1(

3

1

3

)2)(1(

)(

sNN

yyN

g

N

t

t

kN

t

tktk

kk

kyyyyN

c

c

cr

1

0

0),)((1

so

n

t

tt SSOO1

))((

n

t

tt SOn

mae1

1

ttnt

SOae1maxmax

n

t

tt SOn

mde1

)(1

n

t

t

n

t

tt

OO

SO

R

1

2

1

2

2

)(

)(

1

N

t

tyN

y1

)1

(


May, 2006 25

the number of years of record and the number of seasons per year, respectively. The seasonal mean is

obtained as

Similar concept is applied to determine the seasonal variance. Furthermore, the season-to-season

coefficient of correlation, rk,t is determined by

For instance, for monthly stream-flow time series, r1,3 represents the correlation between the flows January

and March.

2.9 Hydrologic Models

The problems of decision making in both the design and operation of water resources systems, such as

flood control reservoirs, canals, water supply systems and irrigation schemes have resulted in a need for

mathematical approaches such as simulation and synthesis to investigate the different scenarios of project

implementation and operation.

Simulation is defined as the mathematical description (imitation) of the response of a hydrologic water

resources system to a series of events during the selected period of time. It could mean, for example, the

calculation of reservoir levels for different draw off levels, or the computation of the catchment runoff for

different land use patterns in the drainage basin, etc. Simulation requires an abstraction of the real life

system, a component of it, in some form, i.e. model. Hence the model 'reproduces' some desired response

of the catchment behaviour, such as the daily runoff.

Models can be classified as Physical or mathematical, continuous or discrete (time), lumped or distributed

parameter, black-box or structure-imitating, stochastic or deterministic, event-based or continuous models.

wtyN

yN

vtvt ,1)

1(

1,

,

1/ 2

0, 0,

, , ,

1

2

0, ,

1

2

0, ,

1

( )

1( )( ), 0

1( ) , 0

1( ) , 0

k t

k

t t k

N

k t v t t v t k t k

v

N

t v t t

v

N

t k v t k t k

v

cr

c c

c y y y y kN

c y y kN

c y y kN


May, 2006 26

2.10 SCS model for estimating runoff volume and peak flood

2.10.1 Runoff Volume

The US Soil Conservation Service model (SCS, 1972) is widely used for estimating floods on small to

medium-sized ungauged drainage basins. It was the product of more than 20 years of studies involving

rainfall-runoff relationships from small rural watersheds across the U.S. The model was developed to

provide a consistent basis for estimating the amounts of runoff under varying land use and soil types.

Together with the SCS triangular unit hydrograph, the method can be used to estimate peak floods from a

known rainfall hyetograph. According to this method, the volume of direct runoff resulting from a rainfall

of P is given by

Where Ia is the initial abstraction, and S is the potential retention in the basin, which equals the initial

abstraction Ia plus the cumulative infiltration, F. No runoff occurs until rainfall equals an initial abstraction

Ia is satisfied. After allowing for Ia the depth of runoff Q is the residual after subtracting F. Commonly the

initial abstraction, Ia, is taken that the initial abstraction is about 20 % of the potential retention in any

storm, i.e. Ia = 0.2S, hence,

The potential retention is expressed in terms of a dimensionless curve number CN, which depends on soil

type and land use/cover in the drainage basin.

Where CN is in English units and S is in inches.

The value of CN depends on the soil, cover, and hydrologic conditions of the land surface. Accordingly,

soils may be put into one of the four groups, A, B, C, and D; or one of three dual classes, A/D, B/D and

C/D. Definition of the classes are:

A: (Low runoff potential) The soils have a high infiltration rate and low runoff even when thoroughly

wetted. They chiefly consist of deep, well drained to excessively drained sands or gravels. They

have a high rate of water transmission as for deep sand or loess, aggregated silts.

B: The soils have a moderate infiltration rate when thoroughly wetted, as for moderately fine to

moderately coarse-textured soils such as sandy loam. They have a moderate rate of water

transmission.

C: The soils have a slow infiltration rate when thoroughly wetted, as for fine-textured soils such as

clay loam, shallow sandy loam, soils low in organic content. They chiefly have a layer that impedes

downward movement of water or have moderately fine to fine texture. They have a slow rate of

water transmission.

D: (High runoff potential).The soils have a very slow infiltration rate when thoroughly wetted, such as

swelling and plastic clays, and clay pan. They have a very slow rate of water transmission.

Dual hydrologic groups are given for certain wet soils that can be adequately drained. The first letter

applies to the drained condition, the second to the undrained. Only soils that are rated D in their natural

condition are assigned to dual classes.

SIP

IPQ

a

a

2)(

SP

SPQ

8.0

)2.0( 2

SCN

10

1000


May, 2006 27

Cover: relates to various types of vegetation and crops, land treatments and crop practices, paving and

urbanization.

2.10.2 Runoff curve Numbers for selected Agricultural, suburban and urban land uses

____Table 2-5 Runoff Curve Numbers for AMC II______________________ ______

Hydrologic Soil Group

Land use description A B C D

Cultivated land

Without conservation treatment 72 81 88 91

With conservation treatment 62 71 78 81

Pasture or range land:

Poor condition 68 79 86 89

Good condition 39 61 74 78

Meadow: Good condition 30 58 71 78

Wood or forest land:

Thin stand, poor cover, no mulch 45 66 77 83

Good cover 25 55 70 78

Open spaces, lawns, parks, etc:

Good condition: grass cover on 75 % or more

of the area 39 61 74 80

Fair condition: grass cover on 50 to 75 %

of the area 49 69 79 84

Commercial and business area (85 % impervious) 89 92 94 95

Industrial districts (72 %) 81 88 91 93

Streets and roads:

Paved with curbs and storm sewers 98 98 98 98

Gravel 76 85 89 91

Dirt 72 82 87 89

Arid and semi-arid range areas

Herbaceaou- mixture of grass, weeds, and low-growing

brush, with brush the minor element (poor) 80 87 93

(fair) 71 87 89

(good) 62 74 85

Desert shrub - major plants include saltbush (poor) 63 77 85 88

greasewood, creosotebush, blackbrush, brusage 55 72 81 86

ple verde, mesquite, and cactus (good) 49 68 79 84


May, 2006 28

Hydrologic condition: refers to the condition whether the vegetation is dense and in good condition, and

whether the soil is rich in organic matter and has a well-aggregated structure, resulting in high infiltration

and low runoff.

CN also depends on the antecedent moisture condition of the drainage basin (wetness), and three classes of

antecedent moisture condition (AMC) are defined, AMC I - dry(wilting point), AMC II - average, and

AMC III - wet(field capacity). The values of CN listed in the table (above) are standard values

corresponding to AMC II. For the other two cases (AMC I and III) the following table can be used.

___ Table 2-6 Runoff Curve Numbers for AMC I and AMC III _______

Corresponding CNs

CN for AMC II AMC I AMC III

100 100 100

95 87 98

90 78 96

85 70 94

80 63 91

75 57 88

70 51 85

65 45 82

60 40 78

55 35 74

50 31 70

45 26 65

40 22 60

35 18 55

30 15 50

25 12 43

20 9 37

15 6 30

10 4 22

5 2 13


May, 2006 29

2.10.3 Peak discharge and flood hydrograph

A triangular (SCS) approximation to the unit hydrograph is used to estimate the peak flood from the

effective rainfall determined above. This triangular unit hydrograph is shown below:

The time to peak flow,

Tp = 0.5D + 00.6tc, where tc is the time of concentration.

The peak flow is given by,

qp = 0.208 A/Tp, where a is km2, and Tp is in h, and qp in m

3/s.

The time of concentration is estimated using a number of empirical formulae in the literature. The one

most commonly used is the Kirpich formula, which in English units has the form

tc = 0.0078L0.77

S-0.385

,

Where L is the length of channel from headwater to outlet,

ft, and S is the average slope of the watershed, ft/ft, and

tc is in minutes.

In metric units,

tc = L0.77

S-0.385

/3000,

Where L is in meters and tc in hours.

Tb =2.67Tp

1.67Tp Tp D

D/2

La

qp


May, 2006 30

2.11 Demand for water

2.11.1 Introduction

Water use can be divided in to two categories, consumptive use, in which water is an end to itself, and

nonconsumptive use, in which water is a means to an end. Consumptive use includes municipal,

agriculture, industry and mining. Nonconsumptive use includes instream uses such as hydropower,

transportation and recreation. From an economic viewpoint, we have the greatest ability to model

consumptive uses. Consumptive uses are modelled using consumptive functions and nonconsumptive uses

are modelled using production functions. Water use refers to the amount of water applied to achieve

various ends so that it is a descriptive concept. Water demand is the scheduling of quantities that

consumers use per unit of time for particular prices of water, which is an analytical concept.

A forecast is an estimate of the future state of a parameter that has four dimensions: quantity, quality, time

and space. In the context of water-demand forecasting, the parameter of interest could be the daily average

use, daily maximum use, and others. In water project design and planning, the major factors determining

the project cost are the quantity of water that must be supplied, treated, distributed, and of waste water to

be collected , treated, and disposed of each year. The character, size, and timing-of engineering works for

water facilities in the future largely depend on the future-water use which must be forecasted. Therefore,

the ability to manage and operate existing water supply facilities and then to plan and design new water

supply facilities is directly tied to the ability to describe both present and future water use.

Future in forecasting could refer to hours, days, weeks, months or years, depending upon the particular

problem. Because of the size and capital intensiveness of most water projects, the time scale in water

demand forecasting generally is years with 15-25 years for medium-range forecasting and 50 years for

long-range forecasting. Forecasting can not strictly be a scientific procedure, since the future, properly

speaking, does not exist. Water demand is defined in economic terms that are related to its price. It differ

form the concept of water requirement used in engineering analysis. Forecast of water demand should also

reflect technological changes in production processes, product outputs, raw materials, water handling and

waste treatment methods, social taste, and public policies with respect to water use and development.

Explicit inclusion of these factors is important in medium and long-range forecasts. Otherwise, forecast

results would be of limited value to decision-makers. Therefore, simplistic methods such as linear

extrapolation of past water demand (called projection) are generally not appropriate for long-term

forecasting. However, the methods remain appropriate to assist in managing water during a crisis period,

during which the forecast-time horizon is short.

Due to the ever changing nature of social, economic and political environments in a region, there exist

numerous uncertainties in any forecast, Errors in water use forecasts may arise form inappropriate or

unintended assumptions made in determining the parameters of forecast. These include future population,

industry mix, and relationships between the values of model parameters and level of water use. Whatever

the causes, errors in forecasting produce excess economic and environmental costs; such costs may be

avoided through the use of improved forecasting approaches. In addition, improved methodologies for

forecasting water demands are needed to account for:

(1) Growing number of conflicts among water uses and water users;

(2) Increasing realization of interrelationships among the different outputs from water resource systems

(3) Increasing scope and scale of water resources development.

2.11.2 Category of Demand

The principal components of water demands are usually grouped as municipal and rural, agricultural,

industrial and infrastructural demand as indicated on the left side of Table 2-7, but there is no standardized

procedure for this subdivision. This scheme also indicates that, beyond the above mentioned four major

categories. Water demands arise in other fields of regional and national planning, Such as transportation,


May, 2006 31

recreation, preservation or extension of swamp and wetland habitat and conservation or utilization of

estuaries.

On the right hand side in Table 2-7, water demands are grouped according to their effect on the sources of

water supply such as withdrawal, in-stream and on-site uses (U.N.,1976)

Table 2-7 Principal categories of water demand (U.N. 1976)

Municipal & rural demand M M Drinking W W Withdrawal

Agricultural demand A M Domestic uses W N Instream use

Industry I M Public uses in settlements W O Onsite use

Infrastructure F A,M Livestock W

A Fish and wildlife

M,A,F Flood loss management N,O,W

M,A Drainage O,W

A Swamp and wetland habitat O,W

A Utilization of estuaries N,O

A Soil moisture conservation O

F Navigation N

F Hydropower N

A,M Irrigation W

I Mining W

I,M Steam power W

I,M Cooling W

I,M Processing W

I,M Boiling W

M,I,A Waste disposal N

M,F Recreation N

M,F Water sports N

M,F Aesthetic enjoyment N

2.11.3 Demand Projections and Policy Formulation

Water demand projection is required at each of the four levels of planning, Viz. (i) project level (ii)

regional level, (iii) national level, and (iv)international level. The planning at these levels is interrelated

and iterative. Correspondingly, water demands have to be derived interactively. Furthermore, since water

demand and development are embedded and circularly related with economic development and

demographic change, alternative scenarios of development have to be projected and water demand

estimated interactively.


May, 2006 32

Water demand estimates over a long period, say about 50 years, should be the first study in any national or

regional planning process. This unfortunately, has been generally neglected.

The flow chart of a regional demand projection as based on alternative scenarios is given in Figure 2-3. It

will be noted that the demand estimate is closely linked with general developmental planning and project-

oriented supply planning.

Even if detailed models of water demand interlinked with economic development through input-output

analysis and demographic projections as discussed above are not developed, advancement can be made by

improving the simple projections on the following basis. First the storage cost data and storage-yield

relationships may be based on detailed regional data. Second, the alternative water supply standards and

water reliability could be explicitly costed. Third, alternative programmers of water development may be

developed for each region.


May, 2006 33

3(c)

3(c)

3(b)

3(a)

3(a)3(c)

3(b)

3(a)

3(b)

Water shortage

occure in the region

as a whole

Available supplies

cover demands in each

of the subsystems

Water shortage may

occure in some of the

subsystems

Development of new sources of water supply

International water grid

Regional water grid

Design of water supply systems (

including development of resources)

Analysis of water use technologies and

iterative revisions of the preliminary

projections of water demands

Regrouping of the demand against the

potential source of supply

22

Priliminary projecteion on

water demands and

comparison with local water

availabilities based on

alternative future scenarios

44

Formulation of policies and programmes

for managing and developing water

resources; integration with other studies

55

Periodic comparison of the the projected

scenarios with the actual one and revision

of the demand projection

77

Periodic revision of the economic and

social base study leading to new or

modified scenarios

11

Economic and social base study;

preliminary formulation of alternative

scenarios

66

Projection on other resources and services

(land, labour, capital, minerals, energy,

transport, etc.)

Figure 2-3 Flow chart of regional water demand projection based on alternative scenarios (U.N. 1976)


May, 2006 34

2.11.4 Water Demand for Human Settlements

This category covers the usual categories expressed under domestic and municipal use for urban and rural

settlements. The major categories covered under urban water demands, in addition to domestic uses, are

public facilities and services (street cleaning, fire-fighting, parks, schools, hospitals, etc) commercial units

(stores, apartment house, laundries, etc.) and industrials establishments Rural settlements need water for

livestock in addition to domestic uses.

The daily water demand of a human being varies between 1.5 and 20 liters, depending mainly on climate

and on physical activity. Daily per capita in-house water uses average about 15 to 20 liters in rural areas

and about 100 to 150 liters in residential districts of urban areas. The household and other urban water

demands depend upon the economic levels of community, climate conditions, cultural practices, pricing

policies and economics of supply and demand. There is a distinct difference between the developed and

the developing countries. In the former, the basic aim of planning is to arrive at the desired level of water

supply at minimum cost. In developing countries, the aim of planning has been to determine the allocation

of the available scarce capital to achieve a social minimum of adequate water supply.

The raw demands shall be converted in to economic demands by evaluating the elasticity of demand in

various categories as supply water is going to be more and more expansive in future.

The project requirements for different categories of use has to be corrected for non primary benefits and

conveyance losses (Figure 2-4) The latter average roughly to about 15 per cent of demand. It must also

be adjusted for the ratio of other benefits to direct primary benefit as shown in Figure 2-4. The other

benefit represents attraction of new developments in view of better water supply. Correspondingly,

marginal cost curves for supplying increasing demand can be worked out. From these two studies the

economic demands and corresponding unit cost can be obtained. Thus economic demand over a period of

time and optimum capacities to be installed in due time can be determined.

Demand curve adjusted for

conveyance losses

GI=GH / (1-Lf)

Adjusted demand curve

FD=(1-Lf) FE

Water requirement adjusted for losses in the system

AC=AB/1-Lf (Where Lf = function of water loss)

Raw demand curve

PR

ICE

OF

WA

TE

R (

doll

ars/

ha

m)

DEMAND FOR WATER (ha-m/ha)E

D

EFIHG

CBA

Figure 2-4 Adjusted demand curve for all losses

Although there are difficulties in quantifying the above procedure, even a conceptual appreciation will

mean improvement over the present insensitiveness to issues. In view of the above it has been suggested

that the forecasts should take in to account (1) regulation (ii) pricing policy, (iii) education campaign,

(iv)housing trend (v) supply cost, and (vi) change in technology. Since these changes are uncertain,

probabilistic future forecasts may be worked out. The approach can also be extended to agricultural

demands.


May, 2006 35

In developing countries, according to World Health Organization (WHO) study, 77 percent of the

population were not adequately served with community water supply, and this percentage was estimated to

increase to 83 percent by 1980, in view of rapid population increase and slow rate of water supply

provision (Wollman, 1972). The central problem is scarcity of funds and organization. A three stage

development has accordingly been proposed by WHO. In the primary stage a rudimentary system to

provide minimum amount of water, mainly through public stand posts with only a limited number (up to

10 percent) of the consumers receiving water services in their houses or premises is proposed (U.N., 1976

). In addition to quantity figures, quality specifications are also important.

2.11.5 Industrial Demand

Industrial water demand varies considerably with the type of industry and even for the same industry

depending upon the age of the technology used. This makes demand estimation difficult. However, only

few industries account for most of the demand. Excluding the steam electric plants, which require the

maximum amount of water, the major users are the steel industry, petroleum refining and wood and pulp

production.

The major groups of water use in industry are (a) cooling; (b) Processing; (c) boiler water: and (d) general

use (drinking water; air-conditioning; cleaning, etc.) About three fourths of industrial water is used for

cooling. To give an idea, estimated withdrawal demand according to categorized grouping of industries is

given in Table 2-8.

Table 2-8 Water requirements for selected industries

S. No. Product

Unit

Water required per

unit (Litres)

1 Bread USA per tonne 2,100 - 4,200

2

Canned foods, average for fruits,

vegetables and juices 1965, USA, per tonne 24,000

3 Meat Packaging USA per tonne 23,000

4 Canned fish Canada, per tonne 58,000

5 Chicken per bird, USA 25

6 Milk USA per litres 3,000

7 Sugar [from sugar beet] USA, avg. per tonne 6,000

8 Beer USA, kilolitres 15,000

9 Pulp and paper USA, avg. per tonne 236,000

10 Gasoline USA, kilolitres 7,000 - 10,000

11 Synthetic gasoline USA, per kilolitres 377,000

12 Oil refinery

Sweden, per tonne

of crude Petrolium 10,000

13 Synthetic fuel

From coal USA, per kilolitres 265,500

From shale USA, per kilolitres 20,800


May, 2006 36

14

Sulphuric acid [contact process]

(100% H2SO4) USA, per tonne 2,700 - 20,300

15 Textiles [steeping and dressing flax] per tonne 30,000 - 40,000

16 Textiles [bleaching] per tonne 80,000 (?)

17 Textiles [dying and finishing] per tonne 60,000 - 100,000

18 Textiles mills [synthetic fibers] per tonne 2,000,000

19 Iron and steel mills per tonne 86,000

20 Automobiles per vehicle 38,000

Note: These values are dependent on technology and are indicatives based on figures given by Leeden, 1975.

Since the cost of water as a proportion of the finished product is very small (usually below 1 percent),

there is little possibility of reduction in demand. While the industry gets the water almost free, socially the

water is very expensive.

Figure 2-5 suggests a definition format for important aspects of industrial water uses. In fact, the three

parameters which represent the minimum for each industrial water use are (i) Gross water requirement

(G); (ii) consumption use (U); and (iii) waste load in the wastewater discharge (WD) Usually in kg of

biological oxygen demand .Regarding the other elements of the scheme amount of gross water use might

be provided in a wide variety of combinations of re-circulated water (R) and intake water (I). Similarly,

the waste load in the final effluent (WE) can largely differ from that in the water discharge leaving the

production as a result of treatments within the subsequent phases. In other words, the water demands of an

industrial unit can not be defined in terms of intake water and effluent waste loads unless the degree of in-

plant recirculation and treatments are also specified.

In projecting the water requirements for industry, the first problem, is to estimate what will be produced.

For developing countries, investments in manufacturing facilities are likely to be relatively discrete events

that can be identified, placed in their foreseeable locations and given a probable scale of output.

Production units that are small in size and relatively numerous can be projected as a function of GNP or

population, based upon present conditions. New plants are likely to use the best technologies available at

the time of their construction unless some restriction on choice of technology is imposed by local

conditions.

ED

R

GIWE

UD

UR

WD

Up

Production process

Lagoon, spray irrigation

system, and/or

underground disposal

Water treatment

facility other than

lagoon, etc.

Water

treatment facility

Figure 2-5 Definition of terms relating to Industrial water demand (U.N. 1976)

I = Water intake

R = Water re-circulated

G = Gross water applied for all in-plant uses


May, 2006 37

U = Consumptive use or net depletion of water

= UP + UD + UR where: Up = Consumptive use in the production process; UD = Consumptive use in

the waste water disposal system; and UR = Consumptive use in the recirculation system

D = Waste water discharge from the production process

E = Final effluent from the production unit (available for reuse). Where a lagoon or spray irrigation

systems is involved, the final effluent, if any, consists of lagoon overflow, seepage and/or surface

runoff

WD = Waste load in the waste water discharge, for example, kg of Biochemical oxygen demand

(BOD)

WE = Waste load in the final effluent, i.e., kg of BOD, Degree of recirculation = R/G x 100 percent.

The rate of water use for a new industry may, therefore, be different from that found in a country in which

plants are old. There are considerable options for reducing the water intake by industry and improving the

quality of effluents. Long-term forecasts are dependent on policy and technology and the procedure

adopted by Whitford (1972) for municipal demand may be followed effectively for industrial forecasts as

well (Collins and plummer, 1974).

In addition to water demand, it is also necessary to estimate the waste load.

2.11.6 Electric Power Demand

Water is a factor in the production of all electric power from thermal and hydro-electric plants. No

permanent withdrawals are involved in hydro plants.

Power Demand Curves

Power Demand curves for power within a given service area could be established by projecting usage at

the base price and correcting for elasticity of demand in the manner described previosly.

Power Market survey

A power market survey is a study to predict power use within a selected geographical area for a series of

dates in to the future. The projection utilizes per capita usages based on the existing price structure,

anticipated technological changes, and projected population.

For estimation of future water use for power generation the future projection of power requirements is

needed which is complicated on the account of several factors. One is the usual interaction of supply and

demand for a mix of demand of varying elasticities and a mix of supply possibilities. The second is the

cyclic interrelation of supply of power and growth of economy as power is one of the essential inputs for

all sectors. Further, technology is changing rapidly.

2.11.7 Agricultural Demand

Water is on of the most important input factors of agricultural production. In humid regions rainfall

usually supplies water in adequate quantities and agriculture is an on-site water use having significant

effects on the amount of quality of run-off available for other water uses in the downstream areas. In arid

regions virtually all the water required for agricultural production is to be provided from outside, i.e. from

neighbouring rivers or groundwater through water supply or irrigation systems. Within intermediate (semi-

arid, temperate and semi-humid climatic conditions, agricultural water demands are frequently satisfied by

a combination of on-site and external supplies.

Irrigation, already accounting for the major proportion of water use is expected to become a key issue of

water resources development on a world-wide scale and in a long range perspective (U.N., 1976). This

conclusion follows from the need to increase food production for the increasing population, the fact that

irrigation is essentially off-line consumption use, and finally because large scale irrigation schemes and

their supply system have a significant impact on the local environment with potential long-term effect on

regions far from the sites of irrigation schemes.


May, 2006 38

Agricultural water requirements vary from country to country and in different parts of the country

depending upon agro-climatic, hydrologic, economic, social, institutional and political factors, all of which

are circularly related.

Agricultural water demands are estimated on three levels:

(a) the end-product level, where total agricultural production and its combinations are analyzed;

(b) the input-factor level, where desirable combinations of production factors (seeds, fertilizers, water,

equipment, human and institutional resources) are analyzed for a given level of total agricultural

production; and

(c) level of the water supply system where structural and managerial alternatives (in terms of gross water

demands) are analyzed for the given water demand.

Water demand in levels (a) and (b) largely depends on its overall availability and the specific cost of water

supplies within the region concerned. In humid regions, conditions of adequate and inexpensive water

supply can mostly be taken for-granted. As soon as the need for external water resources (irrigation

demand) emerges the need to decrease the cost of water supply requires extensive studies on level (c) and

their results may influence decisions on level (b) Under conditions of severe aridity, irrigation water

becomes one of the decisive input factors for consideration on level (b) and may have a significant role

also in decisions for level (a). Therefore, a reasonable combination and substitution possibilities among

the various production sectors are to be carefully spelt out for each specific set of conditions. The

projection of water demands for irrigation and the construction or a water supply system will lead to

desired results on the end-product level only if planning and development are multidimensional.

Agricultural demand planning also involves decisions on several hierarchical levels. At the national level

decisions have to be made about the development and cropping pattern several agro-climatic, hydrologic

and administrative regions. At the regional level decisions have to be made about water resources

development level, cropping pattern and unit of water supplies. At the farm level the issue is about

technology of irrigation, water management and choice of crop. All these decisions are interrelated.

2.11.8 Navigation, waterways and Recreation

Water demands for navigation can be estimated either arbitrarily by determining when navigation can be

supported of by ascertaining the relative merits of different forms of transportation on the basis of

projected tonnage movement between various points. Since the latter requires a cost benefit analysis, the

estimated costs of maintaining waterways to various depths will have to be made available at least in

rough form.

The use of barriers and locks reduces navigation water requirements as compared to what is needed in a

free flowing stream. Thus, for a given increase in carrying capacity, the choice will lie between diverting

water for other uses or a capital investment designed to reduce the use of water. The water-resource

planner may be able to conclude that a designated number of navigable waterways constitute an inviolate

minimum, but even this knowledge will not be enough to support minimum water requirements unless

physical circumstances prohibit barriers and locks. The planners and transportation specialists may not be

able to do more than reach an informed, albeit arbitrary, judgement once they have estimate the probable

volume and movement of freight and size of vessels. Whether navigation flows appear explicitly in the

projected demand will depend upon their magnitude and seasonality as compared with other flows over

the navigable reaches of the river.

The recreational uses of streams are likely to imply requirements that coincide with those implicit in the

maintenance of high environmental quality. It may be possible, therefore, for the demands of

environmentalists to be analyzed first of all in terms of the comparative merits of alternative economic

activities, e.g tourism versus industry, before attempting to measure the intangibles, i.e aesthetic

satisfaction not reflected in the money measurement of the national bill of goods. One recreational use of

water, boating itself is a polluting activity, but is partly controlled by regulations regarding the disposition

of wastes; escaping oil and gasoline may also be a problem. These sources of pollution, except for special

cases, are still minor compared with municipal and industrial wastes.


May, 2006 39

Evaluation of the recreational uses of water is relatively difficult because water perse does not usually

figure in the price system. This means that either the prices of complementary goods-boats, flippers and

fishing rods have absorbed the economic rents that would otherwise be inputed to water or, as is more

likely in view of the relatively competitive nature of the markets for recreational commodities, the value of

water in recreational usage perse escapes from the accounting system. In a study on the values of water in

alternative uses, the recreational value of water was five times its value in agriculture and only 1/14 of its

value in industry;

Participation in water-based recreation activities is a function of many variables. Time is an especially

important variable not only in terms of changes in the aggregate, i.e. increased personal income, increased

leisure time and changing social tastes, but also with respect to the recreational behaviour of a single

family group. Of particular importance is the determination of typical patterns of participation in mixes of

water based recreation activities. This problem is in addition to that of determining whether or not positive

enjoyment is derived from a journey to and form the location of the recreation. Except for fervent white-

water canoeists, fishermen and scuba divers, the typical receptionist probably has a bundle of activities as

his objective.

The demands for water-based recreation are sometimes expressed by required per capital length of shore-

lines and area of water surface. An are indicative value of 0.2 meter per capita of lake shore and 0.05

hectare per capital of water surface was applied in recent regional planning in Hungary ( U.N., 1976).


May, 2006 40

3 Planning and Operation Tools

3.1 The system approach to water resources development

3.1.1 Systems Engineering

Systems Engineering (Hall and Dracup): systems engineering may be defined as the art and science of

selecting from a large number of feasible alternatives, involving substantial engineering content, that

particular set of actions which will best accomplish the overall engineering objectives of decision makers,

within the constraints of law, morality, economics, resources, political and social pressures, and laws

governing the physical, life and other natural resources.

Water resources Engineers and Planners should develop a number of reasonable alternatives for public

officials to consider; they should also evaluate the economic, environmental, political, and social impacts

(consequences) that might result from each alternative.

Tools and methodologies are required for defining and evaluating the alternatives for managing the water

resources system (Optimization, model development and simulation).

However, use of these tools can not guarantee development of optimal plans for water resources

development and management; objectives and priorities of different interest groups, that somehow

influence the decision making process and are stake holders, are competing each other and change with

time.

What systems methodology can do:

Help define and evaluate, in a rather detailed manner, numerous alternatives that represent various

possible compromises among conflicting groups (or purposes), values, and management objectives.

In particular, a rigorous and objective analysis should help to identify possible trade-offs between

quantifiable objectives so that further debate and analysis can be more informed.

The system concept:

A system may be defined as a set of objects which interact in a regular, interdependent manner. Such a

system can be characterized by

A rule which determines whether any particular object is to be considered as part of the

system or of the environment (i.e. definition of the system boundary)

A statement of the input and output interactions with the environment,

A statement of the interrelationships between the elements of the system, the inputs and the

outputs, including any external interactions between output and input (feedback)

Figure 3-1 Representation of the system concept


May, 2006 41

Usual objectives: to modify the controllable and partially controllable inputs so as to maximize the

desirable outputs and to minimize the undesirable outputs.

3.1.2 Terminologies and definitions

Decision variables: these are the controllable and partially controllable variables, which could be varied to

attain optimality of some ‘objective function’. For example, in a reservoir operation study, the amount of

release in any time period, such as a month, can be fixed in accordance to some pre-set rule, thus it is a

decision variable. Obviously, there are limits which the release can not violate. For instance, at any time,

the total volume of water to be released can not exceed the amount of water available. Thus, in deciding

the value of the release, one has to know the possible values the release can attain without violating some

constraints, volume available in the reservoir in this particular case.

In general, there are quite many constraints that limit the values the decision variables can assume. Hence

the question of feasibility of the set of values assigned to a set of decision variables is an important one.

The set of decision variables that do not violate any of the constraints for the particular problem at hand is

called a feasible solution, or feasible policy, where the policy refers to the set of values the decision

variable have been assigned.

The subset of all possible feasible policies (sets of values of the decision variables) is called the policy

space.

State variables: are those variables that describe the status of the system in terms of some quantifiable

entities. For instance, for a storage reservoir, the amount of water available in it at any time is a state

variable relevant in reservoir operation studies. In general, if V and Q denote the magnitude and quality of

water in a given system, which are functions of space (location) and time, then the state of the system can

be described by

S = [V(x,y,z,t), Q(x,y,z,t)] ; where: V and Q are examples of state variables.

Thus, Water resources development is aimed at altering the current state of the system in accordance to

‘optimal’ policy, i.e. set of values of decision variables.

System Parameters: these are similar to state variables in that they describe some attributes of the system

but are less variable (less time-variant) than the state variables. For instance, in a reservoir operation study,

the capacity of the reservoir, which is fixed by the normal pool level, is an example of a system parameter.

It is constraint on the state variable in that the state variable can not assume values greater that the active

storage capacity (of course, neglecting the surcharge storage).

State Transition or System Equation: these are equations that compute the output state of a system given

the value of the current state variable and the value of the decision variables.

Objective/Performance Measures: these are quantitative measures of the performance of a specific aspect

of a system. Often the phrase ‘Objective function(s)’ is used to refer to the mathematical form of the

formulation of the performance measure. The general objective can be, for instance, stated as

‘maximization of net profit’, or ‘minimization of cost’, etc. These objectives are then put in mathematical

form by using the decision variables and other relevant parameters.

Simulation: this is an iterative process of running a mathematical model with various feasible values of

the decision variables until the user decides that best solution has been found to achieve a specific

performance measure.

Optimization: this is similar to simulation, except that a mathematical procedure is used to control the

iterative process and adjust the decision variables until the procedure determines it has found the best

solution.


May, 2006 42

Decision Support System (DSS): an integrated computing framework consisting of a database, model base

and user interface/dialogue facility that facilitates the development and evaluation of alternative courses of

action. It is used to transform data to information to support the decision process.

Mathematical Model: conceptualization of a system that retains the essential characteristics of that system

for a specific purpose.

In water resources engineering models:

Can represent important interdependencies and interaction among the various control

structures and users of water resources systems.

Permit an evaluation of the economic and physical consequences of alternative engineering

structures, of various operating and allocating policies, and of different assumptions

regarding future flows, technology, costs and social and legal requirements.

However, models have inherent limitations in representing the real world and hence results based on

simulation models should adequately be checked before it is mapped to the real world.

3.1.3 Basic water accounting modeling concepts

Consider the schematic diagram shown below

a b c

Figure 3-2 Schematic diagram of water accounting modeling

This schematic diagram is actually a basic underlying concept of water accounting modelling. A schematic

diagram represents the spatial relationship of features in a water resources system (upstream to

downstream) although it does not represent the actual spatial scale.

Suppose you were asked to determine how much water to release from the reservoir to meet the

downstream demand of the city, irrigation area, and the environmentally sensitive wetland area. You could

not simply add up the individual requirement because there are other loses and gains in the system, some

of which depend upon the amount of water in the river. Rather you would decide upon a value for release

and perform a water balance as the water moved from point to point downstream. This is where a

mathematical model is useful; it allows one to try different options on the computer, rather than in the

‘field’ in the hope of finding a reasonable approximation of the desired value.

This section of river could be modelled for a variety of purposes. We might need hydraulic model to

compute stages and velocities in some reaches, water quality model to predict quality conditions in the

river, ecological models to predict species survivability, etc. While all these models have their uses, often

the problem at hand is more basic, i.e. the question is how much water is required to meet the demand in


May, 2006 43

the system. Water accounting models can answer this question and in fact, they are probably the most used

type of model in water resources.

To develop an accounting model, we begin by converting the schematic diagram to a node-link diagram as

seen in Figure 3-2c.

The links represent the river reaches and the nodes represent computation points for a model. This

computation points could be reservoirs, confluence points, diversions, inflow points, etc. For each node we

want to solve the equation

OIdt

dV

Where: V is the volume, I the inflow and O the outflow from the node.

This equation represents the basic principle of conservation of mass. Since water does not compress, this

is equivalent to conservation of volume, which can be termed a volume balance. Since we are dealing with

water, this is often called a water balance or water accounting equation. The time scales of interest in

managing water resources often vary from hours to days to weeks to months. Therefore, we convert the

differential equation into a difference equation:

OIt

V ; rearranging terms yields: V = (I-O) t = I t - O t

Since V is volume then I t must be in volume units, implying that I (and also O) is a rate (volume/unit

time). If a node has either no storage (non-storage node) or constant storage then,

V = 0 = I t - O t I t = O t

or the outputs from a node must equal the inputs to the node.

We can expand this equation to account for multiple inputs and outputs by

n

k

k

n

j

j tOtI11

Since we solve the above equation at each node, this implies an order of computation from upstream to

downstream. The outputs from an upstream node become an input for the next downstream node. This

also suggests a strategy of guessing a value of water input (reservoir release) at the most upstream node

and computing the water balance downstream to the final node. If all demands are not met, the input to the

most upstream node is too small. Likewise if all demands are met and excess water is available at the most

downstream node, then the input to the most upstream node is too large.

We can extend this analysis over time, by repeating the water balance calculations from upstream to

downstream for each time period of interest (for example, monthly).

Model Errors:

Formulation error: this occur when the basic mathematical and logical formulation of the model are

incorrect. This could be due to inadequate process description, incorrect model components, etc.

Implementation: these occur when the implementation computer coding is incorrect.

Application: these occur when the model is applied to a situation that does not match what the model is

intended to represent; the wrong model for the intended use.

Model testing:

Calibration: this is a process that might be considered as a part of verification. It consists of determining

the most appropriate values of model parameters, such that the model adequately reproduces observed

conditions. Attempting to minimize the difference between computed and observed condition is a common

measure used in calibration effort.

Verification: this is a process of determining that the model is “doing things right.” It involves testing the

model under various conditions to determine if it has formulation and implementation errors.


May, 2006 44

Validation: this is a process of determining that the model is “doing the right things.” It involves testing

the model under situation for which it was designed and determining if the results seem reasonable. It is

focused on finding application errors. A common approach is to split the data on observed conditions into

one part used for verification and calibration and the other part is used to test the quality of the computed

answers as a validation effort.

Deterministic analysis: this involves using limited sets of input data considered to be representative for a

problem. The model output is interpreted as representative for the input conditions.

Stochastic analysis: this involves using either many sets of input data or a statistical characterization of

the input data representative of a broad range of input possibilities. The model output is statistically

analyzed to determine expectations and ranges of uncertainty.

Expert systems: these are models that represent the logic of evaluating a specific situation in the form of

symbolic “If-then” rules. They are often used to model procedural, heuristic knowledge.

3.2 Feasibility Tests

Project planners must select from a myriad of proposed projects. Each proposal must pass five feasibility

tests.

The test of engineering feasibility: is passed if the proposed project is physically capable of performing

its intended function. The point is not that almost any desired water resources project could be built if

expense were no object. A specific proposal consists of a specific physical system which may not work

satisfactorily.

The test of economic feasibility: is passed if the total benefits that result from the project exceed those

which would accrue without the project by an amount in excess of the project cost. It is important that the

comparison be with and without rather than before and after because many of the after affects may even

occur without the project and can thus not properly be used in project justification. Economic feasibility is

contingent on engineering feasibility because a project incapable of producing the desired output is not

going to produce the benefits needed for its justification.

The test of financial feasibility: is passed if sufficient funds can be raised to pay for project installation

and operation. While financial feasibility should always be contingent on engineering feasibility, projects

have been constructed which simply do not work. A project may be economically feasible but financially

infeasible because the benefits are insufficiently concrete for the beneficiaries to appreciate their true

value or are distributed among too many people for payment to be practical. A project may be

economically infeasible but financially feasible because someone is willing to pay for the fulfilment of

non-economic goals. Financial feasibility also depends on local interests believing estimated economic

benefit to the degree that they are willing to raise their portion of the required funds.

The test of political feasibility: is passed if the required political approval can be secured. Ordinarily

political support follows proof of economic and engineering feasibility.

Political pressure for project construction may even be quite strong despite proof of economic

infeasibility. On the other hand, groups which feel they are adversely affected often oppose project

installation. For example, a humid region may oppose water export to an arid region. Almost every project

harms someone, and if enough people are harmed or if those who are harmed are sufficiently vocal, they

may be able to use political processes to prevent project construction.

The test of social feasibility: is passed if the potential users will respond favourably to project

construction. Project success depends on the users of project output being motivated to shift to irrigated

agriculture, to utilize electrical equipment, or to do whatever else is needed to realize potential project

benefits. The more drastic the changes are that the project requires in the lives of the beneficiaries, the

greater is the inertia that can be expected from those slow to change their way of living. The infusion of

productive capital will not automatically transform a tradition-bound society. Some projects, such as

recirculation of municipal waste water after treatment, may encounter increased inertia because of

psychological connotations or cultural unacceptability.


May, 2006 45

3.3 Optimization

The major types of problems that must be solved for various types of WR systems are:

determining the optimal scale of development of the project

determining the optimal dimensions of the various components of the system; and

determination of the optimal operation of the system.

Let the solutions to these problems be denoted by X1, X2, and X3, and then the benefit associated with

these solutions is

B = f(X1, X2, and X3)

The determination of X1, X2, and X3 involves maximisation of the benefit function, which in this case is

the objective function. Thus, in many WR projects the problems can be formulated as

Maximise B = f(X1, X2, and X3)

In most cases, there are several constraints under which the maximisation has to be achieved, such as

technological, economic (or budgetary), etc.

Conventional procedures for deign and analysis are basically iterative trial-and-error procedures. The

effectiveness of conventional procedures is dependent upon an engineer’s intuition, experience, skill and

knowledge of the WR system. Conventional procedures are typically based upon using simulation models

in a trial-and-error process.

Optimisation eliminates the trial-and-error process of changing a design and re-simulating with each new

design change. Instead, an optimisation model automatically changes the design parameters. An

optimisation procedure has mathematical expressions that describe the system and its response to the

system inputs for various design parameters.

An optimisation problem in WR may be formulated in a general framework in terms of the decision

variables (x) with an objective function to

Optimise f(x)

Subject to constraints

G(x) = 0

And bound constraints on the decision variables

xl < x <xu

Where x is a vector of n decision variables (x1, x2, . . . ,xn), g(x) is a vector of m equations called

constraints and xl and xu represent the lower and upper bounds, respectively, on the decision variables. The

sets of variables that describe the system (the project or the set of management plans or operating rules)

are known as decision variables, in the terminology of mathematical models. Thus, selecting the decision

variables for a particular plan means defining the plan completely.

Every optimisation problem has two essential parts: the objective function and the set of constraints. The

objective function describes the performance criteria of the system. Constraints describe the system or

process that is being designed or analysed and cab of two forms: equality constraints and inequality

constraints. A feasible solution of the optimisation problems is a set of values of the decision variables that

simultaneously satisfy the constraints. An optimal solution is a set of values of the decision variables that

satisfy the constraints and provides an optimal value of the objective function.

Depending upon the nature of the objective function and the constraints, an optimisation problem can be

classified as: (a) linear vs. nonlinear, (b) deterministic vs. probabilistic; (c) static vs. dynamic; (d)

continuous vs. discrete; and (e) lumped parameter vs. distributed parameter. Linear programming

problems consist of both a linear objective function and all constraints are linear.


May, 2006 46

3.4 Linear programming

This technique is used when the objective function as well as all constraint equations are linear. Unlike

most optimization techniques, linear programming software packages are available and this has made the

method more attractive. If the planning problem involves only two decision variables (i.e. two-

dimensional problem) then it can be solved using a simple graphical approach (see examples below). For

more complex problems one resorts to analytical means using the linear programming algorithm or use is

made of software packages.

The general form of an LP model can be expressed as

n

j

jjo xcxMinorMax1

)(

subject to

njforx

miforbxa

j

n

j

ijij

,,2,10

,,2,11

where cj is the objective function coefficients, aij is the technological coefficients and bi is the right-hand

side (RHS) coefficient.

Formulation example 1 [Lucks, Water Resources Systems Planning and Analysis]

Two types of crops can be grown in a particular irrigation area each year. Each unit quantity of crop A can

be sold for a price of PA and requires WA units of water, LA units of land, FA units of fertilizer and HA units

of labor. Similarly crop B can be sold for a price of PB and requires WB, LB, FB and HB units of water,

land, fertilizer and labor, respectively, per unit of crop. If the available quantities of water, land, fertilizer

and labor are W, L, F, and H, respectively,

Formulate a linear programming model for estimating the quantities of each of the two crops that should

be produced in order to maximize the total income.

Formulation Example 2 [Mays and Tung, Hydrosystems Engineering and Management]

Consider a system composed of a manufacturing factory and a waste treatment plant owned by a

manufacturer. The manufacturing plant produces finished goods that sell for a unit price of B 10 K.

However, the finished goods cost B 3 K per unit to produce. In the manufacturing process two units of

waste are generated for each unit of finished goods produced. In addition to deciding how many units of

goods to produce, the plant manager must also decide how much waste will be discharged without

treatment so that the total net benefit to the company can be maximised and the water quality requirement

of the watercourse is met.

The treatment plant has a maximum capacity of treating 10 units of waste with 80 percent waste removal

efficiency at a treatment cost of B 0.6 k per unit of waste. There is also an effluent tax imposed on the

waste discharged to the receiving water body (B 2 k for each unit of waste discharged). The water

pollution control authority has set an upper limit of four units on the amount of waste any manufacturer

may discharge. Formulate an LP model for this problem.

Formulation:

Treatment plant capacity KT

Amount of product X1

Waste discharged directly to river X2

Treatment plant efficiency ( ) = 80%

2X1 – X2 KT


May, 2006 47

2X1 – X2 0

X1 0

X2 0

X2 + (1- )(2X1 – X2) 4

Money

Sell 10X1

Cost 3X1 Production cost

2[X2 + (1- )(2X1 – X2)] Tax

0.6[X2 + (1- )(2X1 – X2)] Treatment cost

The objective is maximizing the benefit.

Benefit = [Sell – Cost] - 2.6[X2 + (1- )(2X1 – X2)]

= 10X1 - 3X1 - 2.6[X2 + (1- )(2X1 – X2)]

= -6.6X1 + 2.6X2

Formulation Example 3 [H.A. Wagner, Principles of Operations Research]

The Haut Dam Water System is comprised of several dams, reservoirs, and river tributaries. One of these,

the Gaul Dam Reservoir, is used for recreation (swimming, water sking, canoeing). It is important to keep

the average depth of this reservoir within the prescribed limits, which vary from one month to the next.

The section chief in the State’s waterways department is responsible for monthly decision on how much

water to release from the Haut Dam into the Gaul Dam. The engineers in the department have estimated a

rapid rate of seepage and evaporation at Gaul Dam, gt, and Et; since rainfall is negligible, Gaul Dam must

be maintained by spillage from Haut Dam.

Suppose that the chief’s department plans ahead for 20 months. During month t, let St denote the average

depth of the reservoir prior to augmenting with Haut Dam water; S1 = 20 for month 1. Let yt be the

number of meters the chief decides to add to the average depth in month t, i.e. a positive value for yt

indicates a decision to augment the reservoir with dam water. Let Lt and Ut represent the lower and upper

prescribed limits, respectively, of the average reservoir depth after augmentation of dam water in month t.

River RiverGaul Dam

Reservoir

River

Haut Dam

Reservoir

River

a. Suppose that the cost of augmenting the reservoir is ct per meter in month t, formulate an

appropriate optimization model.

b. Suppose that the cost of augmenting the reservoir is ct per meter in month t, provided that the

augmentation amount does not exceed 1.5 meters. Any augmentation in excess of 1.5 meters incurs

a cost of dt per meter per month t, revise your answer in part a) to reflect this cost structure.

Formulation:

yt – Decision Variable [release in depth from Haut Dam]

20

1

cost

tt yct

River

(1- )(2X1- X2)X2

2X1- X2

2X1

T.Plant

Plant


May, 2006 48

Constraints:

St+1 = St + yt – Et -gt

St Ut

St Lt

3.2.1 Forms of Linear Programming

The two types of LP model formulations used are known as the standard form and the canonical form.

The standard form is used for solving the LP model algebraically. An LP model is said to be in the

standard form if the following are satisfied:

all constraints are equality except for the nonnegativity constraints associated with the decision

variables which remain inequality of the type;

all RHS coefficients of the constraint equations are nonnegative;

all decision variables are nonnegative; and

the objective function can either be maximised or minimised.

An LP model expressed in the standard form takes the following form:

n

j

jjo xcxMinorMax1

)(

njforx

miforb

miforbxa

j

i

n

j

ijij

,,2,10

,,2,10

,,2,11

An LP model expressed in the canonical form has the following characteristics:

all decision variables are nonnegative;

all constraints are of the type

the objective function is of the maximisation type.

n

j

jjo xcxMax1

njforx

miforbxa

j

n

j

ijij

,,2,10

,,2,11

Frequently, the LP model originally constructed does not satisfy the characteristics of a standard form or a

canonical form. The following elementary operations can be used to transform the LP model into any

desired form.

1. Maximisation of a function f(x) is equal to the minimisation of its negative counterpart,

2. constraints of the type can be converted to the type by multiplying by -1 on both side of the

inequality

3. Equality can be replaced by two inequalities of the opposite sign. For example, an equation g(x) =

b can be substituted by g(x) b and g(x) b.

4. An inequality involving an absolute expression can be replaced by two inequalities without an

absolute sign. For example, /g(x)/ b can be replaced by g(x) b and g(x) -b.


May, 2006 49

5. If a decision variable x is unrestricted in sign (i.e. it can be positive, zero or negative), then it can

be replaced by the difference of two nonnegative decision variables; x = x+- x-, where x+ 0, and

x- 0.

6. To transform an inequality into an equation, a nonnegative variable can be added or subtracted.

Convexity: if two points P1(x11,x12) and P2(x21,x22) are within the feasible space, these spce is convex, if all

points on the straight line joining P1 and P2 are feasible solutions.

3.2.2 Solution algorithms for LP problems

1. Graphical method

The procedure in this method consists of defining the feasible region (or space) graphically and

determining the maximum (or minimum) value of the objective function in the region. It is, however,

limited to cases where there are at most two decision variables. For all LP problems, if the optimum

solution exists, then it always falls on the boundary of the feasible space (more specifically, at one of the

corner points along the boundary. Such points are called feasible extreme points).

The following are the three important properties of feasible extreme points in an LP problem:

Property 1a: if there is only one optimal solution to an LP model, then it must be a feasible extreme point.

Property 1b: If there are multiple optimal solutions, then at lease two must be adjacent feasible extreme

points.

Property 2: there are only finite number of feasible extreme points.

Property 3: If a feasible extreme point is better (measured with respect to xo) than all its adjacent feasible

points, then it is better than all other feasible extreme points, i.e. it is a global optimum.

Example

An irrigation project is to be developed. There is 1800 ha-m of water available annually. Two high value

speciality crops, A and B, are considered for which water consumption requirements are 3 ha-m and 2 ha-

m per hectare, respectively. It has also been determined that the planting of more than 400 ha crop A or

600 ha crop B would cause an adverse effect on the market for these special crops. It has been estimated

that each hectare devoted to crop A will result in Birr 300 profit, while a hectare of crop B will net Birr

500. Develop an LP model and solve for the maximum benefit from the project.

Solution:

From the description, the decision variables will be the hectare of crop A, Xa, and the hectare of crop B,

Xb, and the objective function may be formulated as

Max Z = 300Xa + 500Xb

Subjected to

Xa 400

Xb 600

3Xa + 2Xb 1800 Water availability.

Xa 0, Xb 0

Evaluate Z based on Feasibility and optimality conditions.

Xa = 200

Xb = 600

Z = 360,000

3Xa + 2X

b= 1800

Xa

= 4

00

Xb = 600

0Xa

800600400200

Xb

1000

800

600

400

200


May, 2006 50

Example 2

Two types of crops can be grown in a particular irrigation area each year. Each unit quantity of crop A can

be sold for a price of PA and requires WA units of water, LA units of land, FA units of fertilizer and HA units

of labor. Similarly crop B can be sold for a price of PB and requires WB, LB, FB and HB units of water,

land, fertilizer and labor, respectively, per unit of crop. If the available quantities of water, land, fertilizer

and labor are W, L, F, and H, respectively,

a) Formulate a linear programming model for estimating the quantities of each of the two crops that

should be produced in order to maximize the total income

b) What quantity of each crop should be produced to gain maximum income. Use the data given in

the table below:

Requirements per unit of crop and available resources

No Resource Crop A Crop B Maximum available resource

1. Water 2 3 60

2. Land 5 2 80

3. Fertilizer 3 2 60

4. Labour 1 2 40

Unit price 30 25

The objective function can be written as

F = 30X1 + 25X2

Subjected to

5X1 + 3X2 60

5X1 + 2X2 80

3X1 + 2X2 60

X1 + 2X2 40

X1 0, X2 0

Solve Formulation example 3 (above) using the graphical method.

2. The Simplex Method

The simplex method is a very well-known and most commonly used algorithm for solving LP problems

algebraically. It can be applied to solve problems involving thousands of decision variables. In practice,

computer codes (programs) are available that employ this method and seldom is the solution sought

manually.

Summary of the Simplex Method (refer also to examples given below)

From the descriptions of the simplex algorithm for solving an LP problem, the solution procedure follows

two basic conditions, that is, the optimality condition and the feasibility condition. More specifically on

the algebraic operations, these two conditions can be phrased as follows.

3Xa + 2X

b= 60

2Xa + 3X

b= 60

Xa + 2X

b= 40

5Xa +

2Xb=

80

40

30

20

10

Xb

3010 20 400XaXa

800


May, 2006 51

The optimality condition dictates the selection of an entering variable which has the potential to further

improve that value of the current objective function. Given the xo row re-expressed in terms of the non-

basic variables only, one selects the entering variable in maximization (minimization) from the non-basic

variables having the most negative (most positive) coefficient in the xo row. When all the LHS coefficients

of the xo row in the simplex tableau are nonnegative (non-positive), the optimum solution to the problem

is reached.

The feasibility condition dictates the selection of a leaving variable so that solutions obtained during

simplex iterations always remain feasible. The leaving variable is the basic variable corresponding to the:

smallest positive ratio of the current value of the basic variables to the positive constraint coefficients of

the entering variable regardless of whether the problem is a maximization or minimization type.

The following steps summarize the simplex method for maximization:

Step 0: Express the problem in standard form with a starting basic feasible solution and then develop the

tableau format. The initial tableau must always contain a basic feasible solution (check for an identity

matrix).

Step 1: Scan the Xo row; if all elements are nonnegative, stop; the optimal solution has been found;

otherwise, go to step 2.

Step 2: Select the entering variable as the one corresponding to the most negative Xo coefficient. This

identifies the pivot column or the key column.

Step 3: Scan the pivot (key) column coefficient; if all are non-positive, stop; the solution is unbounded. If

at least one element is positive, go to step 4.

Step 4: Calculate

0/ ikikii aallforab

Where aik is the ith element of the pivot column. Then find ( )min(

_

i .The variable defined in step 2

replaces the variable of the pivot row in the next solution.

Step 5: To get the next tableau divide the pivot row by the pivot element. Now use this row to perform

row operations (addition of multiples of this row) on the other rows to get all zeros in the rest of the pivot

column (including the xo row).

Return to step 1.

Pivot equation:

New pivot equation = old pivot equation / pivot element

Other equations = old equation – (its entering column coefficient)*(new pivot equation)

Example

Consider Example 2 of the Graphical Method

The objective function can be written as

F = 30X1 + 25X2

Subjected to

5X1 + 3X2 60

5X1 + 2X2 80

3X1 + 2X2 60

X1 + 2X2 40

X1 0, X2 0

Standardize

Max F = 30X1 + 25X2 F - 30X1 - 25X2 = 0


May, 2006 52

Subject to

5X1 + 3X2 + X3 = 60

5X1 + 2X2 + X4 = 80

3X1 + 2X2 + X5 = 60

X1 + 2X2 + X6 = 40

Select set of m (no. of constraint equations) variables that yield feasible trial solution and set the n-m

(where n is the number of unknown) variables to zero, then solve the m equations for the selected m

variables to obtain a solution. Such a solution is called a basic solution. The selected variables are called

the basic solution variables or simply the basis. The variables set equal to zero are the outside variables or

nonbasic variables.

X1 = X2 = 0 ; hence nonbasic solution.

Reading Assignment

Shadow price

Degenerecy

crop

Variables

Basic V f x1 x2 x3 x4 x5 x6 b b/a

f 1 -30 -25 0 0 0 0 0

x3 0 2 3 1 0 0 0 60 30

x4 0 5 2 0 1 0 0 80 16

0 1 0.4 0 0.2 0 0 16

x5 0 1 2 0 0 1 0 40 40

x6 0 3 2 0 0 0 1 60 20

f 1 0 -13 0 6 0 0 480

x3 0 0 2.2 1 -0.4 0 0 28 12.72727

0 0 1 0.4545 -0.18182 0 0 12.73

x1 0 1 0.4 0 0.2 0 0 16 40

x5 0 0 1.6 0 -0.2 1 0 24 15

x6 0 0 0.8 0 -0.6 0 1 12 15

f 1 0 0 5.9091 3.636364 0 0 645.5

x2 0 0 1 0.4545 -0.18182 0 0 12.73

x1 0 1 0 -0.182 0.272727 0 0 10.91

x5 0 0 1 0 -0.125 0.625 0 15

x6 0 0 0 -0.364 -0.45455 0 1 1.8182


May, 2006 53

3.5 Dynamic Programming (DP)

Dynamic programming (DP) is a mathematical procedure designed primarily to improve the

computational efficiency of solving selected mathematical programming problems by decomposing them

into smaller, and hence computationally simpler, subprograms. Dynamic programming typically solves the

problem in stages, with each stage involving exactly one optimizing variable.

DP transforms a complicated n-variable decision process into a series of n-stages with a single decision at

each stage. For instance, take the case of maximizing a monthly (variable) yield for a reservoir of known

capacity. Assume further that there are n-months of historic (or synthetic, for that matter) flow records.

Typically this is an optimization problem in which the n-months’ releases are to be optimized. In an LP

formulation, the optimization algorithm attempts to maximize the releases by formulating an appropriate

objective function that involves the releases of all the months. DP, on the other hand, approaches the

problem from a different angle. The optimization problem is transformed as a sequence of n decision

processes, or stages, at which the single monthly release at, say month i, is “optimally” selected to

maximize the total release over the entire length of record. Thus, decision is made at each stage; in the

present example, at each month. This sequential decision process can be shown as in the following figure:

Figure 3-3 Basic elements and terminologies:

Stages: are the points, in time or space, where decision are made.

Decision Variables (di) : are courses of action to be taken for each stage. In the example discussed above,

the release to be made at each stage (i.e. month) is an example of a decision variable.

State variables (Si): are variables that describe the state of the system at any stage i. In the example above,

for instance, the amount of water available in the reservoir at the end of each stage is a state variable.

Stage return (ri): is a scalar measure of the effectiveness of the decision making at each stage. This can be

viewed as a component of the objective function in the context of LP optimization. The stage return is a

function of the input state, the output state, and very importantly, the value of the decision variable at that

stage.

Stage transformation or state transition (tn): is a single-valued transformation which expresses the

relationships between the input state, the output state, and the decision. The state transition is used to

estimate feasible states in the next stage, given the state at the end of the current stage.

Consider the following example (to be discussed in the class): suppose there is a volume Q of water to be

allocated to 3 users and let X1, X2, and X3 be the quantities allocated to the three users and R1(x1), R2(x2)

and R3(x3) denote the corresponding benefits realized from these allocations. It is desired to allocate the Q

amount of water to the three users so that the total revenue is to be maximized. The problem can be

formulated as a sequential decision process and then solved using DP.

S1 S2

r1

1

d1

r2

S3

1

d2

i

di

ri

Si Si+1

N-1

dN-1

N

dN

rN-1 rN


May, 2006 54

The allocation made to the first user affects the subsequent allocations to be made to the remaining two

users as water that is allocated to user 1 is no more available for downstream uses. Thus, the allocations to

made to any of the users should be made in such a way as to maximize the total benefit. The feasible space

for the decision variables x1, x2, and x3 also are not the same. Because of the locations of the users,

allocation to the first user can be made from the total mount of water available, Q, while that for the

second user can be made only from the amount S2 = Q – X1. Similarly, X3 can take values between zero,

no allocation, and a maximum of S3 = Q – X1 – X2 = S2 – X2.

Let f1(Q) be the maximum possible net benefits from allocations x1, x2, and x3, for a given quantity of

water, Q. Then

)x(R)x(R)x(R)Q(f maxmaxmaxxxx

\

3322111

321

(1)

where

2133

122

1

0

0

0

XXQSX

XQSX

QX

by the same reasoning, if f2(S2) is the maximum possible net benefit from allocations made after the first

stage, i.e. x2, and x3, then

)x(R)x(R)S(f maxmaxxx

\

332222

32

(2)

From the above two equations,

)S(f)x(R)Q(f maxx

22111

1

, but since S2 = Q – X1,

Q = S1

Stage 1: (User 1)

Benefit R1 Stage 2: (User 2)

Benefit R2

Stage 3: (User 3)

Benefit R3

X1

X2 X3

S2 = S1-X1 S3 = S2-X2

S4 = S3-X3


May, 2006 55

)XQ(f)x(R)Q(f maxx

12111

1

(3)

Where QX10

The solution to the above problem is recursive, since, to solve (3), the value of f2(Q-X1) must be known.

On the other hand, f2(Q-X1) can be evaluated if f3(Q-X1-X2) is known. The above is what is known as

backward formulation of the DP solution procedure. The problem could also be formulated as a forward

problem, in which solution starts from the first stage.

Recursive computation is a feature of DP; the computations at the current stage utilize a summary

information of the cumulative optimal values of the objective (revenues in the above example) of all the

stages previously considered. The forward and backward recursive equations for a general case depicted in

the above picture are given below:

)S(f)d,S(r)S(f

)S(f)d,S(r)S(f

i

*

iiii

d

i

*

i

i

*

iiii

d

i

*

i

opt

opt

i

i

11

11

DP solution procedure is based on a principle forwarded by Bellman: No matter in what state of what

stage one may be, in order for a policy to be optimal one must proceed from that state and stage in an

optimal matter; this is known as Bellman’s principle of optimality.

Multiple state variables

The problem discussed involved the optimal allocation of a single variable, i.e. water, and as such involves

only one state variable. There are, however, cases where two or more state variables are involved, such as

the case of finding optimal operation of two interconnected reservoirs. In such cases, for each stage, the

decision has to be made on the values of the releases from both reservoirs. Such cases where multiple state

variables are involved increase the required computational effort. In general, the total number of discrete

states that have to be considered increases exponentially as the number of state variables increases, a

phenomenon terms “curse of dimensionality” of multiple-state-variable dynamic programming problems.


May, 2006 56

3.6 Economics for WR Systems

3.6.1 General

The task of water resources planners can be broadly summarised as

identification or development of alternative water resource design (or management) plans

and the evaluation of the economic, ecological, environmental and social impacts of these

alternative plans

select (or advise on the selection of ) most appropriate alternative plan

Among the various criteria that are used for the comparison of alternative plans the economic one is the

most frequently used and quantifiable criterion. It involves basically the computation of the benefits and

costs a plan would entail should it be implemented, i.e. Benefit Cost Analysis (BCA).

Below are listed some steps (from Linsley) that could be followed in an economy study for WR planning:

1. Each alternative that seems promising should be identified and clearly defined in physical terms

2. Insofar as practicable, the physical estimates for each alternative should be translated into money

estimates

3. Usually the money estimates need to be placed on a comparable basis by appropriate conversion

that make use of the mathematics of compound interest.

4. A choice (or recommendation for a choice) among the alternatives must be made. This choice is

properly influenced both by the comparison in terms of money units and by other matters that it

has not been practicable to reduce to money terms (so-called "irreducibles" or "intangibles").

3.6.2 Formulating the Analysis

Economic analysis is performed in a series of steps. Each alternative must be explicitly defined and the

resulting physical consequences must be predicted. A monetary value must be placed on each physical

consequence. A discount rate must be selected and applied to convert the predicted time stream of

monetary values into an equivalent single number. Only then can the alternatives be directly compared.

Each step is developed as follows.

3.6.3 Defining the Alternatives

An engineering alternative is a course of action physically capable of achieving the design objective.

Structural alternatives (a dam, for example) characteristically involve a large first cost for project

construction to produce benefits throughout the project life. Nonstructural alternatives (flood-plain zoning,

for example) involve benefits and costs which are both fairly well distributed over project life. A properly

defined alternative must be specified by the engineer with sufficient clarity for its economic and intangible

consequences to be evaluated and its nature understood by those responsible for the final selection.

Properly defined alternatives are an evidence of clear thinking and a necessity for adequate consequence

prediction. A properly formulated set of engineering alternatives includes all possibilities for action

(including taking no action at all) which have a realistic chance of proving optimum. Special care is

necessary to include nonstructural alternatives with which engineers may be less familiar. The alternatives

are called mutually exclusive if only one of a set can be selected. Alternatives may be mutually exclusive

because of conflicting space requirements, limited financial resources, limited resource inputs (water, for

example), or limited demand or need for resulting output. At other times, it may be practical to implement

two or more of the alternatives.


May, 2006 57

3.6.4 Physical consequences - Benefits and Costs

Definition

Benefits and costs can only be measured with respect to a goal. Each alternative course of action requires

the commitment of resources. Benefits measure the effectiveness of the action in achieving the goal. The

resources once committed cannot be used elsewhere. Their commitment has the opportunity cost of other

uses sacrificed. Costs measure the effectiveness of the sacrificed action in achieving the goal.

Theoretically, benefits and costs may be based on any desired goal. Ideally, the goal would be an

unambiguous and unanimously accepted social welfare function. Practically, the goal becomes the second-

order efficiency objective of economic efficiency or maximum national income. However, numerical

estimates of benefits and costs with respect to other goals are sometimes also included. Strictly speaking,

such effects cannot be measured in the same units as efficiency benefits or efficiency costs. Combining the

two requires a value judgement on the relative merits of the goals.

The effectiveness of alternative courses of action in reaching the efficiency goal is measured with

reference to the pure-competition model. Even though planning from the public viewpoint is based on a

market model, the analysis differs from that which would be made by a private firm. The primary

differences are:

1. The public viewpoint incorporates all costs and all benefits to whomsoever they may accrue.

External economies and diseconomies need to be evaluated.

2. The discount rate may be lower than that used by private firms because of the substitution of

collective time preference for the financial const of borrowed money.

3. When market prices lose their normative significance because of deviation from the pure

competition model, the government planner, rather than continue to use them as does the private

planner, should attempt to evaluate the true economic worth of each input and output.

4. When analyzing projects producing products or outputs which are not marketable, the government

planner must derive an equivalent market value through demand analysis.

Benefit – Cost Categories

Project consequences fall into four main classes:

1. Tangible (Market) benefits

2. Intangible (Extra market) benefits,

3. Project construction associated/induced costs, and

4. Project installation cost.

1. Tangible (Market) benefits: result from the consequences to private parties which can be assigned a

monetary value. Many consequences are evaluated in the market place but consequences are still

considered tangible even though they must be established by a more elaborate deductive process. The

decision of how abstract a consequence must be before it can no longer be assigned a meaningful

monetary value is essentially a value judgement, and hence some agencies set numerical values on

consequences which other agencies consider intangibles. Benefit as used in the following discussion is a

net value incorporating both adverse and favourable consequences and may on occasion be negative.

a) Primary benefits denote the value obtained fro project-produced goods and services. The benefits

accrue from physical effects of the project on the user as contrasted with effects transmitted through

market transactions.

(i) Direct benefits accrue to those who put project output to its intended use. By project purpose,

they may consist of a reduction in physical damage to items coming in contact with flood-water,

increase in farm income resulting from application of irrigation water, the value the consumer


May, 2006 58

received from the use of electric power, the savings in transportation cost for goods moved by

navigation, or the satisfaction the re-creationist derives fro this experience.

(ii) Indirect benefits result as individuals realize the economic consequences of technological

external effects. The effects may result either from the production of project output or from its use

by others. Output intended for one purpose (low-flow augmentation for water quality control) may

also achieve other beneficial effects (navigation). Flood control projects may benefit users of

transportation and communication systems by reducing interruptions and reduce the wages lost by

workers or crop losses by farmers when industrial or food-processing plants are closed by flooding,

Irrigation may reduce dust storms.

(iii) Land-enhancement benefits result when a more productive land use is made possible by the

project and are distinguished from direct benefits to the land use, which would prevail without the

project. For example, a flood control project may enable farmers to shift from a lower- to a higher-

value crop by reducing flooding. Land-enhancement benefits equal the net crop income from the

higher-value crop with flood protection less the net crop income from the lower-value crop with

flood protection. The direct benefits are the net gain in crop income from the lower-value crop

which results because of the prevention of flood losses. Sometimes flood protection causes

agriculture to be replaced by urban development, and the increase in land productivity is considered

a land-enhancement benefit. Agricultural land-enhancement benefit is not distinguished from other

primary benefits in irrigation projects where the crop pattern radically changes with the arrival of

irrigation water. However, the enhancement of land value within urban areas surrounded by newly

irrigated land is a benefit which may be properly attributed to project construction.

b) Secondary benefits denote value added to activities influenced by the project through economic rather

than technological linkages. They result from pecuniary external effects.

i. Secondary benefits (“steming-from” benefits) may result from forward production linkages that

increase the net income of those who process project output. Cotton production by an irrigation

project must be processed a number of times before it is sold as clothing, and each intermediate

processor may profit from the increased business. The net stemming-from benefit is the income

from processing project output net of the sum of the income which would be obtained from

processing output displaced by the project and output which would result were the money spent on

the project devoted to an alternative investment.

ii. Secondary benefits ("induced-by" benefits) may result from backward production linkages which

increase the net income of those who provide goods and services to the project area. Cotton

produced by an irrigation project will require the purchase of farm machinery, fertilizer, and other

materials and thus initiate a chain reaction profiting all these businesses and all those who in turn

supply them. Again, the net induced-by benefit would be the increased income of those serving the

project area less the loss in income of those who would otherwise provide input for the alternate and

the displaced investments.

c) Employment benefits: denote the economic-value gained from the increased employment opportunity

from new jobs created to construct, maintain, or operate the project. A related effect is the increased

employment opportunity induced by production of project output. Irrigation projects attract those

living elsewhere on a marginal income to a new productive rural enterprise. Project output may also

stimulate investment opportunity on the farms and within the communities where it is used.

d) Public benefits: are realized in achievement of goals other than economic efficiency and thus can be

evaluated in efficiency dollars only by means of a value judgment on the relative desirability of the

second goal. Specific recognition is most often given economic stabilization, income redistribution,

regional development, and environmental quality.

2) Intangible (extra market) benefits: describe consequences which cannot be assigned a monetary

value but which should be considered when deciding whether or not to build a project. Examples are the

saving of life or improvement of health, improved environmental aesthetics, and the preservation of areas

of unique natural beauty and scenic, historical, or scientific interest.


May, 2006 59

3) Project construction: requires private parties to bear costs as well as realize benefits. These costs are

subtracted from the benefits to calculate a net benefit realized.

(a) Associated costs: include private investment to produce or utilize project output. An example is

the farm costs required to prepare the land for irrigation, convert to a new cropping pattern, and

purchase the machinery required by the new crops. Whenever secondary benefits are counted for

project justification their associated costs should also be counted. Sometimes non-sponsoring public

agencies may be required to pay the cost of such items as schools and better roads to serve the more

intensive land use.

(b) Induced costs: evaluate adverse consequences of project construction and should be evaluated

whether or not the sponsoring agency has a legal financial obligation to pay damages. Examples are

the cost of downstream flood control measures necessitated by upstream land drainage, the

increased cost of transportation required for the discharge of the excess flow, and the cost of

drainage system to remove excess irrigation water.

4) The cost of project installation: is placed in the denominator of the benefit-cost ratio. The initial cost

includes construction cost, engineering and administration cost, right-of-way cost, the cost of relocating

facilities, and other minor costs. Construction cost is the amount paid to the contractor for completing the

work outlined in the plans and specifications. Engineering and administration cost is the expense of

preparing the necessary plans and specifications, inspecting construction work, providing technical review

of engineering details, conducting special investigations such as hydraulic-model studies or geologic

exploration, and completing the incidental administrative paper work. Right-of-way cost is the opportunity

cost of using the land required for project installation and maintenance. Lands which may still be used by

the original owner such as lands along a reservoir periphery, inundated only during exceedingly rare

floods, or lands under overhead power lines or over underground pipelines may be secured by easements.

The cost of relocating facilities is the amount required to move or to modify bridges, roads, railroads,

pipelines, and power lines located on the project right-of-way. Other costs include state dam filing fees or

payments for water-rights acquisition.

After installation, the project has continuing costs of operation, maintenance, and replacement. Operation

includes the opening and closing of gates, overseeing hydroelectric plants, purchasing power for pumping,

and other activities required to produce project output on a continuing basis. Maintenance includes

preventive maintenance to reduce anticipated breakdowns and repairs to the project production

mechanism. Weeds must be cleaned out of channels and erosion damage repaired. Machinery must be

serviced. Recreational areas must be kept clean and attractive. Trash blocking flow through culverts must

be removed. Major repairs may be needed after large floods. Replacement includes installing at periodic

intervals new pumps, well casings, or machinery whose useful life is less than that of the project as a

whole.


May, 2006 60

3.6.5 Benefit-Cost Analysis (BCA)

General

Having identified the physical consequences of each alternative, it is necessary to decide which ones are

relevant to the analysis. Some may not be because of the viewpoint taken in the study, a neutral effect

which is neither desirable nor undesirable, a tenuous connection to the project, their small magnitude, or

some other reason. Other consequences may be dropped from further evaluation because they are identical

for each alternative and an economic study is concerned only with differences (incremental costs). The

relevant consequences can be separated into two groups. Some can be assigned a reasonable monetary

value. The others may have some monetary value but also require supplemental determination of the

intangible factors.

Essentially BCA offers a way of comparing benefits and costs of a given alternative plan. The basic

problem associated with such procedure is, however, the fact that the different alternatives considered may

involve components that may have different design life. Moreover, the costs and benefits may occur at

different times. In most of the cases a major portion of the total cost of a project occurs at the beginning.

For example, a hydropower development involving the construction of a dam requires that the dam and all

the other necessary structures (conveyance, turbines, etc) be built at the beginning. The benefits in the

form of revenue from sale of electrical energy come over an extended period of time. Hence the costs and

benefits should be reduced to some common time to be compared. This is usually done making use of the

"time value of money".

To do this, estimated lives of elements are needed in the computation of annual benefits and costs of

projects. The table below is taken from US experience and the values given should serve as guide. Actual

local data should preferably be used whenever available. The life of a component of a project (say

reservoir) is governed by many other factors than the actual deterioration of the involved hydraulic

structures. In addition to the useful lives of the elements a project one has to select the rate at which the

discounting is going to be done, i.e. fix discount rate. Values used depend on the economy of the country,

and whether the project is implemented by a private enterprise or is part of public work.

Cash flow diagram

The graphic presentation of each value plotted by time is called a cash flow diagram. The standard

representation for a cash flow diagram is that receipts (benefits) are represented by arrows pointing

upward, while costs are represented by arrows pointing downward. Arrows pointing toward the centerline

indicate cash flows which may be taken either way in a general diagram. The length of the arrow is made

proportional to the cost or benefit. The horizontal axis denotes time. For convenience in analysis and with

little loss in accuracy for long-lived projects, all cash flows during a year are by convention combined into

lump sums occurring at the end of the year. Figure 3-4 is a cash flow diagram which might be predicted

for our hypothetical irrigation project.

Time

Envelope curves

Annual operation and maintainance cost

with periodic larger replacement cost

Large expenditure during period of initial

project construction

Additional benefit as

irrigation extends to

new land

Benefit from average crop production


May, 2006 61

Figure 3-4 Cash flow diagram for a hypothetical irrigation project

Annual benefits and costs will not in fact be constant every year but will vary around average values in an

almost random fashion with crop production and maintenance needs. However, only expected average

values are normally predicted in advance, even though the random component could conceivably be

introduced through simulation. Drawing of the cash flow diagram can be greatly simplified by use of

envelope curves as a substitute for the many arrows.

Discounting factors

There are discounting formulae that are used to worth of money at different times. The forms of payment

considered could either be single payment at some time (say at the beginning) or a stream (or series) of

payments. The problem could be to find the present worth of series of payments in the future, or a single

amount at some time in the future, or to find the equivalent stream of payments for a given present value,

etc. The six basic formulae are given below:

1. Single-payment compound amount factor

F = P(1+ i)n

2. Single-payment present worth factor

P = F/(1+ i)n

3. Sinking fund factor

4. Capital recovery factor

5. Uniform series compound amount factor

6. Uniform series present worth factor

n

n

ii

iAP

)1(

1)1(

Where F = a future sum of money

P = present sum of money

A= an end-of-period payment (say annual, or monthly)

i = interest (discount) rate

1)1( ni

iFA

1)1(

)1(n

n

i

iiPA

i

iAF

n 1)1(


May, 2006 62

Table 3-1Lives (in years) for some elements of hydraulic projects (Linsley)

Item Years Item Years

Canals and ditches

Coagulating basins

Construction equipment

Dams:

Crib

Earthen, concrete, or masonry

Loose rock

Steel

Filters

Flumes:

Concrete or masonry

Steel

Wood

Fossil-fuel power plants

Generators:

above 3000 kva

1000 - 3000 kva

50 hp - 1000 kva

below 50 hp

Hydrants

Marine construction equipment

Meters, water

Nuclear power plants

Penstocks

75

50

5

25

150

60

40

50

75

50

25

28

28

25

17-25

14-17

50

12

30

20

50

Pipes:

Cast-iron

2 - 4 in.

4 - 6 in.

8 - 10 in.

12 in. and above

Concrete

Steel

Under 4 in.

over 4 in.

Transmission lines

Tugs

Wood-stave

14 in. and larger

3 - 12 in.

Pumps

Reservoirs

Standpipes

Tanks:

Concrete

Steel

Wood

Tunnels

Turbines, hydraulic

Wells

50

65

75

100

20

30

40

30

12

33

20

18-25

75

50

50

40

20

100

35

40-50

3.6.6 Methods of Economic Appraisal (Discounting Techniques)

Once the lives of elements of a project and the discount rate are fixed the BCA can be made in one of the

following ways:

I. Present worth Method (PW)

In the present worth method a project is selected as best if it results in largest present worth (PW) of the

discounted algebraic sum of benefits and costs over the project’s lifetime.

n

t

tt CBtiF

PPW

1

(%),,

Where Ct is the cost and Bt the benefit with the subscripted year, n is the period of analysis in years, and i

is the discount rate. When the annual net benefits B = Bt -Ct are constant over the project life except for

the initial first cost K the formula may be simplified to:


May, 2006 63

niF

PKPW (%),,B

When the net benefits vary according to some regular gradient, the appropriate gradient factor should be

used. Calculation of present worth from a cash flow diagram is a purely mechanical process. However,

certain rules must be followed in comparing the calculated present worth to make correct choices.

RULE 1: Figure all present worths to the same time base. Whether or not alternatives are to be initiated at

the same time, each present worth must be discounted to the same base year because sums of

money at different times are different economic goods.

RULE 2: Figure all present worths by using the same discount rate. Whether or not alternatives are to be

financed from the same funds, each must be discounted at the same rate if the result is to be an

index of intrinsic project merit.

RULE 3: Base all present worths on the same period of analysis. Whether or not alternatives have a

common economic life, the comparison must be based on a service provided over a common

period of time. This may be done either by evaluating the- cost of extending the service past the

termination of the shorter-lived alternatives or by calculating the value of the unused life of the

longer-lived alternatives.

RULE 4: Calculate the present worth of each alternative. Choose all alternatives having a positive present

worth. Reject the rest. This ends the procedure if no sets of mutually exc1usive a1tematives are

involved. The choice among alternatives in such a set is made by Rule 5.

RULE 5: Choose the alternative in a set of mutually exclusive alternatives having the greatest present

worth.

RULE 6: If the alternatives in the set of mutually exclusive alternatives have benefits which cannot be

quantified but are approximately equal, choose the alternative having least cost.

Example

A single example based on the two mutually exclusive alternative water supply projects described in Table

shown below will be used to illustrate all four discounting techniques. Project A provides an initial

investment large enough to meet the demands for water for 40 years, and project B uses investment in two

stages to meet the same demand. The present worths are calculated to be

No Item Project A Project B A - B

1 Construction cost

$40,000,000 $25,000,000 1st stage $ 15,000,000

$30,000,000 2nd stage $ -30,000,000

2

O and M (per year)

$160,000 for 40 years

$100,000 1st 20 years $ 60,000

$220,000 2nd 20 years $ - 60,000

3 Economic life (years) 40 40 for each stage

4 Period of analysis (Years) 40 40

5 Annual benefits $2,500,000 $2,500,000

6 Discount rate 5% 5%

For Project A

PW of Benefits = 2,500,000[P/A, 5%, 40] = 42,900,000

PW of Cost = 40,000,000 + 160,000[P/A, 5%, 40] = 42,740,000

PW of A = PW of Benefits - PW of Cost

= 2,500,000[P/A, 5%, 40] - 40,000,000 – 160,000[P/A, 5%, 40] = 153,000

For project B

PW of Benefits = 2,500,000[P/A, 5%, 40] = 42,900,000


May, 2006 64

PW of costs = 25,000,000 + 30,000,000[P/F, 5%, 20] + 100,000[P/A, 5%, 20] + 220,000[P/A, 5%, 20]

[P/F, 5%, 20] = 38,590,000

PW of B = 42,900,000 – 38,590,000 = 4,308,000

Therefore we should choose project B since its present worth is greater. If the role of analyzing only

differences were strictly applied, the equal annual benefits could be deleted from the evaluation of each

alternative to provide the same conclusion with less work.

II. Benefit-Cost-Ratio Method (BCR)

Benefit cost ratio method computes the BCR to select the most promising project among alternative

projects. The BCR is defined as the ratio of present worth of benefits (PWb) and present worth of costs

(PWc).

c

b

PW

PWBCR

n

i

c

n

i

b

CniF

PPW

BniF

PPW

1

1

(%),,

(%),,

Annual values can alternatively be used without affecting the ratio. Series discounting factors may be used

in either summation as appropriate.

The decision on whether particular cash flows should be considered costs or negative benefits is

sometimes arbitrary and affects the benefit-cost ratio. While it does not affect project selection by the

procedure described below, it is important to recognize that the best project has the greatest net benefits,

not the largest benefit-cost ratio. Several authors have suggested that the benefit-cost ratio method leads to

different decisions than the other techniques do. However, this conflict only occurs when the incremental-

cost principle of Rule 4 is neglected.

Four rules must he followed to apply the method correctly.

RULE 1 Figure all benefit-cost ratios by using the same discount rate.

RULE 2 Compare all alternatives over the same period of analysis.

RULE 3 Calculate the benefit-cost ratio for each alternative. Choose all alternatives having a benefit-cost

ratio exceeding unity; Reject the rest. If sets of mutually exclusive alternatives are involved,

proceed to Rule 4.

RULE 4 Rank the alternatives in the set of mutually exclusive alternatives in order of increasing cost.

Calculate the benefit-cost ratio by using the incremental cost and incremental benefit of the next

alternative above the least costly alternatives. Choose the more costly alternative if the

incremental benefit-cost ratio exceeds unity. Otherwise, choose the less costly alternative.

Continue the analysis by considering the alternatives in order of increased costliness, the

alternative on the less costly side of each increment being the most costly project chosen thus far.

Example:

Project A and B considered before are mutually exclusive.

Project Benefit Cost B C B/ C

B 42,900,000 38,590,000 0 4,150,000 0

A 42,900,000 42,740,000

B/ C = 0 << 1 hence Project B shall be selected based on the Benefit cost ratio method of analysis.

III. Rate-of-Return Method (ROR)

The rate of return is defined as the discount rate at which the present worth equals zero and is found by

trial and error. The project with highest rate of return is selected from alternative projects.


May, 2006 65

RULE 1 Compare all alternatives over the same period of analysis. Rates of return over different

economic lives can not be meaningfully compared because investment opportunity for the returns

from the shorter-lived alternatives must be considered in determining whether capital should

remain committed to the longer-lived alternative.

RULE 2 Calculate the rate of return for each alternative. Choose all alternatives having a rate of return

exceeding the minimum acceptable value. Reject the rest. If sets of mutually exclusive alternatives

are involved, proceed to Rule 3.

RULE 3 Rank the alternatives in the set of mutually exclusive alternatives in order of increasing cost.

Calculate the rate of return on the incremental cost and incremental benefits of the next alternative

above the least costly alternative. Choose the more costly alternative if the incremental rate of

return exceeds the minimum acceptable discount rate. Otherwise choose the less costly alternative.

Continue the analysis by considering the alternatives in order of increased costliness, the

alternative on the less costly side of each increment being the most costly project chosen thus far.

The rate-of-return method will not lead to the same decisions as the present-worth method unless the

incremental analysis of Rule 3 is used in place of selecting the mutually exclusive alternative with the

highest rate of return. The rate-of-return method must be applied with caution because more than one rate

of return exists when annual costs exceed annual benefits in years after annual benefits first exceed annual

costs, but Heebink has shown that the rate-of-return method using Rule 3 still gives consistent answers

even when dual solutions exist. The water resources planner needs to be alert to this problem in comparing

stage construction or non-structural alternatives by the rate-of-return method.

Example:

Referring to the Table of the previous example

PW = PW of Benefits - PW of Cost = 0

PW of A = 2,500,000[P/A, i%, 40] - 40,000,000 – 160,000[P/A, i%, 40] =0

i = 5.03%

PW of B = 2,500,000[P/A, 5%, 40] - [ 25,000,000 + 30,000,000[P/F, 5%, 20] + 100,000[P/A, 5%, 20] +

220,000[P/A, 5%, 20] [P/F, 5%, 20]] = 0

i = 6.5%

Since both return values are greater than the minimum (5%) the rate of return for the increamental cost

and benefit shall be determined.

Rate of return by for selecting project A against B

15,000,000 – 30,000,000[P/F ,i% ,20] + 60[P/A ,i% ,20] - 60[P/A ,i% ,20] = 0

By trial and error i = 3.39% which is less than 5%

Hence project B is selected as its cost is less than that of project A

IV. Annual Cost Method (AC)

The annual cost method converts all benefits and costs into equivalent uniform annual figures and net

annual benefits are computed. Decision rules resemble those for the present-worth method because each

annual cost is a present worth times a constant capital recovery factor.

RULE 1 Figure all annual costs by using the same discount rate.

RULE 2 Base all annual costs on the same period of analysis.

RULE 3 Calculate the net annual benefit of each alternative. Choose all alternatives having a positive net

annual benefit. Reject the rest. If sets of mutually exclusive alternatives are involved, proceed to

Rule 4.

RULE 4 Choose the alternative in a set of mutually exclusive alternatives, having the greatest net annual

benefit.

RULE 5 If the alternatives in the set of mutually exclusive alternatives have benefits which can not be

quantified but are approximately equal, choose the alternative having the least annual cost.


May, 2006 66

A simple comparison of benefits and costs requires that one computes the present values (worth) of all

costs (initial as well as others) and benefits and compare the sums and compute the net benefit, i.e.

Benefits minus Costs. Alternatively the benefit-cost ratio can be computed based on the present worth of

the benefits and costs.

The (internal) rate of return (ROR) is that discount rate at which the present worth of benefits and costs

become equal.

3.7 Environmental Considerations in Planning

The growing environmental concern poses a dilemma for engineers faced at one extreme by demands that

all construction cease and at the other extreme by pressure to get on with building as rapidly as possible. A

new set of social values- moral, philosophic, and aesthetic- join technical standards and economic

evaluation as decision factors in the planning process. Although many planners were taken by surprise,

these changes were long overdue. The basic problem of population control will be met, either by man or

nature, but the water-resources planner of the future must give more thought to the environmental

problems.

Planners of the future must be innovative, broad-gaged, and more critical of evaluations of "need." They

cannot look to quantitative measures of beauty or ecology to develop their plans. They cannot rely solely

on a showing of economic benefits. Innovation may require such steps as devising ways to lower water

requirements, encouraging nonstructural solutions in flood mitigation, and finding better ways to treat

wastes and reclaim wastewater. A broad-gage view-point must recognize the interrelationships among

water pollution, air pollution, and solid-waste disposal; the role of water supply in population dispersion;

the consequences of water, project construction on local ecologic relationships, and the effect of projects

on water pollution. Most important of all, however, is the critical evaluation of the real need for a project

It is a reasonable assumption that public works necessary to maintain needed services will continue to be

constructed. Water projects needed to maintain public health and safety and the accepted amenities will be

included in these public works. Hydroelectric projects may be considered as essential replacements for

scarce fossil fuel. Irrigation projects which could be replaced by increased productions in humid regions,

flood mitigation projects which are substitutes for good land management, storage to modify pollution by

dilution when better treatment could serve more effectively, water supply projects to encourage growth of

major metropolitan areas, and recreation projects which compete with nearby projects or natural areas are

also nonessential. The planner will have to be more alert to alternatives than ever before.

Where projects seem to be essential, the planner will find it necessary to consider carefully the ecological

impact on the stream and adjacent areas and try to develop a plan which will have a minimum of

detrimental effects. In the architectural design of structures special thought must be given to appearance.

Special treatment of surfaces to avoid large expanses of concrete, colouring to blend with the

surroundings, planting of grass, shrubs, or trees to enhance visual feeling, and other similar measures

should be considered.

A partial list of environmental consequences of water-resource projects might include:

1. Degradation of downstream channel or coastal beaches by loss of sediment trapped in a reservoir

2. Loss of unique geological, historical, archaeological, or scenic sites flooded by a reservoir

3. Flooding of spawning beds for migratory fish preventing their reproduction or destruction of

spawning gravel by channel dredging or lining

4. Change in stream water temperature as a result of a reservoir leading to changes in aquatic species

in the stream

5. Release of reservoir bottom water which may be high in dissolved salts or low in oxygen resulting

in a change in aquatic species

6. Drainage of swamps, potholes, etc., decreasing the opportunity for survival of aquatic or

amphibious animals or waterfowl


May, 2006 67

7. Change in water quality as a result of drainage from an irrigation project which may encourage

growth of algae in the receiving water or lead to a change in aquatic species as salinity of the

receiving body increases

8. Creation of a barrier to normal migration routes of land animals by a reservoir

9. Altering aquatic species by increased turbidity from man-induced erosion or from dredging

operations

10. Damage to higher species by reason of toxic materials (pesticides, toxic metals, etc.) discharged to

a stream and concentrated in the food chain

11. Damage to fish by passage through pumps or turbines or over the spillways of high dams

12. Damage to stream-bank vegetation by alteration of flow patterns in a stream.

Many more items could be added to this list and there are probably subtle effects which have not yet been

identified. A clear distinction should be made between damage which is temporary (construction

operations, tree clearing, sanitary landfill, etc.) and effects which are long-term and irreversible.


May, 2006 68

Dams and Reservoirs

Potential Negative Impact Mitigating Measures

Direct

1. Negative environmental effects of construction:

Air and water pollution from construction and waste

disposal.

Soi1 erosion

Destruction of vegetation, sanitary and health problems from

construction camps

2. Dislocation of people living in inundation zone

3. Loss of land (agricultural, forest, range, wetlands) by inundation to

form reservoir.

4. Loss of Historic, cultural or aesthetic features by inundation

5. Loss of wild lands and wildlife habitat

6. Proliferation of aquatic weeds in reservoir and downstream impairing

dam discharge, irrigation systems, navigation and fisheries and

increasing water 1oss through transpiration.

7. Deterioration of water quality in reservoir

8. Sedimentation of reservoir and loss of storage capacity.

9. Formation of sediment deposits at reservoir entrance creating

backwater effect and flooding and water logging upstream

1. Measures to minimize impacts:

Air and water pollution control

Careful location of camps, buildings, burrow pits, quarries,

spoil and disposal sites

Precaution to minimize erosion

2. Relocation of people to suitable area, provision of compensation in kind

for resources lost, provision of adequate health services, infrastructure,

and employment opportunities.

3. Siting of darn to decrease losses; decrease size of dam and reservoir,

protect equal areas in region to offset losses.

4. Siting of dam or decrease of reservoir size to avoid loss; salvage or

Protection of cultural properties.

5. Siting of dam or decrease of reservoir size to avoid/minimize loss;

establishment of compensatory parks or reserved areas; animal rescue

and relocation.

6. Clearance of woody vegetation from inundation zone prior to flooding

(nutrient removal); provide weed control measures; harvest of weeds for

compost, fodder or biogas; regulation of water discharge and

manipulation of water levels to discourage weed growth.

7. Clearance of woody vegetation from inundation zone prior to flooding

Control for land uses, wastewater discharges, and agricultural

chemical use in watershed.

Limit retention time of water in reservoir.

Provision for multi-level releases to avoid discharge of anoxic water.

8. Control of land use in watershed (especial1y prevention of conversion

of forests to agriculture)

Reforestation and/or soil conservation activities in watersheds(1imited

effect)

Hydraulic removal of sediments (flushing, sluicing, release of density

currents)

9. Sediment flushing, sluicing


May, 2006 69

10. Scouring of river bed below dam.

11. Decrease in floodplain (recession) agriculture.

12. Salination of flood plain lands.

13. Salt water intrusion in estuary and upstream.

14. Disruption of riverine fisheries due to changes in flow, blocking of fish

migration and changes in water quality and liminology.

15. Snagging of water related diseases

16. Increase of water related diseases

17. Conflicting demands for water use.

18. Social disruption and decrease in standard of living of resettled people.

19. Environmental degradation from increased pressure on land.

20. Disruption/destruction of tribal/indigenous groups.

21. Increase in humidity and fog locally, creating favourable habitat for

insect disease vectors (mosquitoes, tsetses.).

10. Design of tap efficiency and sediment re1ease (e.g. sediment flushing,

sluicing) to increase salt content of released water

11. Regulation of dam releases to partially replicate natural flooding regime

12. Regulation of flow to minimize effect.

13. Maintenance of at least minimum flow to prevent intrusion.

14. Maintenance of at least minimum flow for fisheries, provision of fish

ladders) and other means of passage; provide protection of spawning

grounds; aquaculture and development of reservoir fisheries in

compensation.

15. Selective clearance of vegetation before flooding.

16. Design and operation of dam to decrease habitat for vector

Vector control

Disease prophylaxis and treatment

17. Planning and management of dam in context of regional development

plans; equitable allocation of water between large and small holders and

between geographic regions of valley.

18. Maintenance of standard of living by ensuring access to resources at

least equalling those lost, provision of health and social services.

19. Choice of resettlement site to avoid surpassing carrying capacity of land.

Increase of productivity or improve management of land (agricultural,

range, forestry improvements) to accommodate higher population.

20. Avoid dislocation of un-acculturated people; where not possible, relocate

in area allowing them to retain lifecyc1e and customs.

21. Vector control.

Indirect

22. Uncontrolled migration of people into the area, made possible by

access roads and transmission lines.

23. Environmental problems arising from development made possible by

dam - (irrigated agriculture, industries and municipal growth).

22. Limitation of access, provision of rural development and health services

to try to minimize impact.

23. Basin wide integrated planning to avoid overuse, misuse, and conflicting

of water and land resources.

External

24. Poor land use protection in catchment areas above reservoir resulting

in increased siltation and change in water quality.

24. Land use planning efforts which include watershed areas above dam


May, 2006 70

4 River Basin Development (Master) Plan

4.1 General

Master Plan (for the integrated development of resources): is a phased development plan formulated to

exploit the opportunities for single and multipurpose water resources projects in a defined geographic area

over a specific period of time. Often the development of other resources, such as land, mineral, etc, is also

considered in such studies. The terms ‘River Basin Development Plan’, or ‘Master Plan for the Integrated

Development of Resources’ are also used with more or less the same meaning.

The basic objectives of RB development master plans are:

The preparation of the river basin development master plan that will guide the development of

resources in the basin particularly with respect to the occurrence, distribution, quality and quantity

of water resources for a period of about 30 to 50 years,

The preparation of water allocation and utilisation plan(s) under alternative development scenarios

and to generate data, information and knowledge that will contribute to the future water allocation

negotiations with other co-riparian regions (or countries).

Regional plans of this type often include a schedule showing the phased development of programs,

sufficient information on the characteristics of each project to indicate clearly general physical

arrangements, scale, controlling parameters (such as dam elevation, capacities), and a schedule of

investment costs.

These plans are based on a review of previous reports on individual projects, on discussions with planners

in governmental agencies and other organisations, with private individuals, on the results of screening

studies; and on topographic, geological, hydrological and other information.

Integrated WR master planning can be classified as: single-jurisdiction, multi-jurisdiction, international (or

inter-state), and those involving inter-basin water transfer.

(Elaborate this, together with maps showing)

4.2 Components of a River Basin Development Master Plan

Most river basin development plans comprise of three basic components, namely, WR Planning, Regional

Planning and Landuse Planning.

Water Resources Planning: this unit addresses the development of water and associated resources within

the physical boundaries of the river basin. The activities under this component of the master plan include

the following tasks:

a) Assessment of water resources

Studies are conducted with the aim of assessing the WR potential of the basin. Below is a brief outline of

these studies and the results expected:

Hydrogeology: types, and extents of aquifers, hydraulic and other relevant parameters of the groundwater

aquifer, groundwater level maps, recharge rates, safe yields, etc. Inventory of existing groundwater

exploitation schemes such as boreholes, springs, long-term forecast of probable change in quantity and

quality of groundwater, etc.

Hydrology-Climatology: climatic and hydrometric variables required for other studies, such as land use

planning, hydrogeology, irrigation and drainage, dams and reservoirs. Such information include: design

floods for hydraulic structures, yield of catchments for selected storage sites, sediment yields, water

quality (such as for irrigation).

b) WR development studies (projects)

Irrigation and drainage: deals with existing irrigation development in the basin and

identification of future development sites and design of selected schemes.


May, 2006 71

o assessment of irrigation potentials of the basin (small, medium and large scale

development), identification of irrigation schemes that will be considered for further

analysis, collection and analysis of or related data, the preparation of technical data such

as evaluation of irrigation water requirement, and typical design criteria, typical designs

and quantities.

o Identification of possible problems of drainage, soils salinity, and proposal preparation to

deal with these problems, if they exist.

Dams and reservoirs: deals with assessment of possibilities for water storage for other uses (such

as irrigation, power production, etc). Moreover, preliminary designs are made and economic

analysis conducted to screen out the less suitable sites.

o Identification of possible storage sites,

o Preliminary design works and determination of dam sections, economic analysis of

selected dams and their viability assessed,

Hydropower development: deals with the identification and study of potential hydropower

development sites. In particular the following are carried out:

o Analysis of project natural conditions (topography, hydrology, geology, and geotechnics),

o Preliminary design of involved hydraulic structures,

o Preliminary cost estimate of the selected projects and prioritisation for future

development.

Water supply and sanitation/sewerage: is concerned with urban and rural community water

supply and sanitation, i.e. water supply for human consumption, livestock, industrial use, for

mining operations, etc. The following are main activities:

o Assessment of exiting water supply coverage in the basin, problems and identification of

gaps,

o Forecast of population and demand trends for the period of the master plan,

o Evaluation of the performances of community water supplies and identification of their

adequacy (in quality and quantity).

o Identify water supply and sanitation projects to be studied in more detail,

o Review and evaluation of existing and/or proposed policy, strategies, legislation and

institutions existing water tariffs and formulation of recommendations.

c) Water Resources Development Planning:

Deals with the formulation of alternative development scenarios. The various projects identified in the

different sectors, mainly under irrigation and drainage, hydropower development, is considered and

alternative scenarios are played to assess the response of the WR system.

Regional planning deals with development and spatial distribution of all human (economic) activity within

the basin.

Land use planning is concerned with the allocation and use of land between competing purposes.

Often the preparation of RB master plan involves large number of people organised in groups. The studies

may take, depending on size and complexity of basin, up to 3 to 4 years to complete. The grouping of

experts in a typical RB master plan study is shown below:

Natural Resources

Geology and Mineral Resources

Wildlife

Fishery

Energy

Forestry


May, 2006 72

Water Resources

climatology/hydrology

hydrogeology

irrigation and drainage

dams and hydropower

dam geology

WR development planning

Socio-Economy

Regional planning, economy and institutions

Urban development planning (and tourism)

Demography/sociology

Environment

environment

soil conservation

health

Agriculture

agriculture

livestock

land use planning/ agro economy

soils survey

Technical support groups

GIS

Surveying and Drafting

Laboratories (soils, water quality, etc)

4.3 Phases of a Master Plan Study

RB planning studies are conducted in three phases as outlined below:

Phase I: Reconnaissance level investigation and preparation of indicative master plan

Phase II: Data Collection, site investigation, survey and analysis,

Phase III: Preparation of final master plan (includes also feasibility-level study of selected projects).


May, 2006 73

5 Planning for Water Resources Development

5.1 Introduction

To meet the demands for the desired quantity and quality of water at particular locations and times,

engineers, economists, political scientists, lawyers, planners and conservationists often have to collaborate

in planning, designing, constructing, and operating structures and implementing non-structural measures

that will permit improved management of natural water supplies.

The incentive to plan for increased control of any water resource often follows a major disaster, such as a

flood, drought (which might bring about famine), intolerable water quality conditions, or a waterborne

disease epidemic. The need for a co-ordinated (or integrated) development of a basin's water resources and

thus mitigating the consequences of haphazard utilisation of the water resources also initiates planning for

the Basin Master Plan.

Planning involves the systematic and orderly study of a project right from its inception to the evaluation of

alternatives and then to the final selection of the preferred alternative. Thus planning also involves the

steps followed in the design of the alternatives considered for selection, except of course the detailed

design of any of the alternative candidates. Water resources engineers and planners should develop a

number of reasonable alternatives for public officials to consider; they should also evaluate the economic,

environmental, political and social impacts that might result from each alternative.

To engage in a successful water resources development study, the engineer must possess not only the

requisite mathematical and systems methodology skills, but also an understanding of the environmental

engineering, economic, legal, political, cultural and social aspects of water resources planning problems.

A reasonable knowledge of economic theory is just as important as an understanding of hydraulic,

hydrologic and environmental engineering disciplines. Economics has always had, and will continue to

have, a significant role in the planning of water resources investments. It is obvious that the results of most

water resources management decisions have a direct impact on people and their relationships. Hence

inputs from those having a knowledge of law, regional planning, and political science are also needed

during the comprehensive planning of water resources systems, especially during the development and

evaluation of the results various planning models. Politics has always played, will also play, the major role

in the final decision, hence the water resources engineer (planner) should always be aware of this fact.

Some knowledge of the politics of the day is then desirable.

Two definitions of planning are given below, one from a UN planning team and the other from the US

NWC.

Planning aims at the optional use of available resources. Water resources development planning involves

examination of short-term and long-term needs and ways to meet these needs. It involves the comparative

evaluation of alternative solutions with respect to their technical, economic and social merits. Planning

means looking into the future and looking from a broad spectrum of disciplines.

Planning is the creative and analytical process of : (1) hypothesising sets of possible goals. (2) assembling

needed information to develop and systematically analyse alternative courses of action for attainment of

such goals. (3) displaying the information and consequences of alternative actions in an authoritative

manner, (4) devising detailed procedures for carrying out the actions, and (5) recommending courses of

action as an aid to decision makers in deciding a set of goals and courses of action to pursue.

Thus, in short, planning for water resources development involves the systematic consideration of

alternatives to achieve some pre-set objectives. The alternatives have to be evaluated based on the degree

to which each alternative meets the objective(s) with the undesirable consequences being at acceptable

level. It is a multi-phase, multi-level process that draws the attention of politicians, engineers,

conservationists, economists, the public, lawyers, etc. Thus planning for water resources has political,

technical, legal, economic, environmental and financial aspects.

Advantages and disadvantages of planning (pros and contras): although planing for water resources

development might seem quite obvious, there are, however, some criticisms and, in some instances, even


May, 2006 74

objections to planning. If planning is viewed as a tool using which allocation of water resources for

various uses is done efficiently then there seems to be a strong argument for it. However, it is a common

observation that several development plans did not meet their objectives, i.e. have failed. Various reasons

could be cited for the failure, for instance:

lack of institutional support for the implementation of the plans

changing economic and political conditions and failure to update the plans when conditions

change, such as change of leadership

failure by the plans to consider all possible alternatives

inadequate evaluation of alternatives

inadequate information (knowledge) on the problems and boundary conditions during planning

The major argument against planning for such undertaking as regional (or basin-wide) resources

development is that the conditions that govern the selection of a particular alternative (or series of

alternatives) are not static but rather change continuously. This would mean that major factors such as

objectives, economic and political conditions, administrative set-ups, etc., change with time. This is in fact

a strong argument and should be taken seriously. Planning often involves the forecasting of future

conditions for some duration of time ahead. Hence, if the assumptions made about the future fail to hold to

the extent which could affect the decision-making procedure then such plans could not bring the desired

results. For instance, if the socio-economic situation in a country changes radically (like change of system

from planned economy to a market economy) within the planning horizon then such a plan should be

revisited. Hence a continuous reviewing and updating of plans are needed in order for the plans to be of

use even during the duration of time they apply.

Objectives: Identifying relevant planning objectives, and defining the relative importance of each of these

objectives, is one of the most difficult aspects of water resources planning. In fact planning is a problem

solving process. In the society's endeavour to develop (and strive for survival) quite a number of problems

have to be dealt with. Identifying a problem and committing oneself to deal with the problem leads to the

setting of the goals of development, hence the objective the planning exercise is fixed.

There are always many social groups (or individuals) that are influenced by the implementation of a

particular project to a greater or lesser extent. Moreover, these social groups can be involved in the

decision-making process and hence the overall fate of a particular alternative selected for consideration

may depend on the extent to which it fulfils the needs (objectives) of the social groups involved in the

process. In addition, the problem becomes more complex due to the fact that some of the objectives, such

as environmental quality for instance, may not be quantifiable in comparable units with the other

objectives, such as economic return from irrigated agriculture.

Water resources planning objectives can be either 'global' or specific. The former refers to the overall

objective, stated in broad terms, of developing a nation's (region's) water resources. These could be stated

as, for instance, national development and enhancement of environmental quality. Specific objectives

often pertain to projects and are more precise and limited in scope. They should, however, agree with the

'global' objectives.

In Ethiopia, the Federal Water Policy (FWP) incorporates the overall objectives of developing the

country's water resources. These objectives are:

Develop the water resources of the country for the benefits of the people, for strategic planning

and national well-being and for security on sustainable basis

Conserve, protect and enhance water resources and the overall aquatic environment of the country

and protect them from degradation, pollution, depletion, waste and misuse on sustainable basis.

Ensure the provision of basic necessities of water at the household level

Allocate and apportion water, based on comprehensive and integrated plans and optimum

allocation principles that incorporate efficiency of use, equity of access and sustainability of the

resource.


May, 2006 75

Manage and combat drought and famine as well as other associated slow on-set disasters through

efficient allocation, redistribution, transfer, storage and efficient use of measures

Maintain, improve regulate and monitor the quality of all water resources

Utilise, protect, and conserve the country's trans-boundary water resources for socio-economic

development of all the peoples of Ethiopia.

The following principles are adopted in drafting the FWP

Water is the common and indivisible natural endowment and asset of all the peoples of Ethiopia

Every Ethiopian citizen has the inalienable right to have access to sufficient water of acceptable

quality, to satisfy basic human needs

Water shall be recognised both as economic and social good and as well as a private and public

good for all-round, viable, fair and sustainable management (emphasis added)

Water resources development shall be under-pined on:

An integrated framework

Needs assessment (demand oriented)

Objective oriented and capacity based planning

Management of water resources shall recognise and incorporate social equity norms including

equity to access for water use

Economic efficiency in water resources management shall be insured

System reliability and sustainability shall form the basis of plans, programmes, projects,

infrastructures and schemes in water resources

Environmental integrity shall constitute a central part of water resources management.

Stakeholders' participation including community and women participation in the relevant aspects

of water resources management shall be promoted and ensured and the participatory approach,

involving users, decision and policy makers, planers, implementers, and donors shall be promoted.

The principle of "some for all and not all for some" shall be adopted and promoted.

Classification of plans: water resources development plans are conducted at different levels of

administration, at different stages and with different scopes. These pertain to the questions such as who,

for what purpose, and to what extent. Below is listed a descriptive structure of planning (source US-

NWC):

Planning Jurisdictions

Federal

Interstate regional

State

Intrastate regional

Local

Scope of planning programs

Multi-sectoral planning: co-ordinated planning for all sectors of public endeavour, such as land

use, housing, transportation, water resources, waste disposal, and energy supply

Sectorial planning: integrated planning for all functions within one sector, such as water resources

functional planning: planning to meet specific need within a sector, such as flood control or

preservation of wild life

Stages of planning

Policy planning: definition of overall goals and program objectives, policy development, overall

budget and priority analysis, dissemination of program guides, and evaluation results

Framework planning: identification of general problems and needs, outlining a range of possible

alternative futures, inventory of available resources and general opportunities, assessment of

overall adequacy of resources, determination of need for further specific investigations


May, 2006 76

General appraisal planning: broad evaluation of alternative measures for meeting hypothesised

goals and objectives, with recommendations for action plans and programs by specific agencies or

entities.

Implementation planning: investigations of a specific structural or non-structural measure, or

system of measures, in sufficient detail to determine whether it will serve intended purposes in a

manner consistent with established goals, objectives, and criteria and, if so, whether it is

physically possible to implement it within estimated costs and within limits of financial feasibility.

Some of the activities of the planning exercise for water resources are given below:

Examples of activities in:

Policy planning

o assess broad national needs

o hypothesise national goals and objectives

o identify problems and opportunities in achieving goals

o identify costs and benefits in achieving goals

o recommend goals and objectives

o co-ordinate national priorities

o review programs for achievement of goals

Framework planning: from viewpoint of broad region-wide totals and on "no-project" basis

o inventory and evaluate available data

o assess present and future water use and environmental needs

o assess available water and related land resources

o evaluate general regulation potential and identify water quality management approaches

o inventory present status of development

o inventory general means available to satisfy needs

o assess general alternatives to meet different goals

o identify problem areas that need priority attention

o recommend actions that can be taken at present and those that require further study

General appraisal planning: on the basis of local projects or measures, and over regional or watershed

areas:

o estimate present and future water use and environmental needs

o estimate available water and related land resources

o make preliminary evaluations of alternative water quality management approaches

o make preliminary estimates of costs, benefits and consequences of specific alternative

projects and measures

o compare alternative projects and measures

o devise alternative early action and future programs

o recommend specific early action and alternative future programs, including selection of

projects or measures for implementations study

Implementation planning: for specific projects or measures:

o evaluate specific water use and environmental needs

o evaluate available water and related land resources

o evaluate regulation potential for different degrees of storage

o evaluate degree of water quality control with different degrees of storage


May, 2006 77

o prepare conceptual designs and cost estimates

o make economic analyses of benefits and consequences

o make financial analyses to demonstrate payout

o recommend an alternative to be selected

o recommend concerning authorisation

5.2 Hydrologic estimates required for reservoir projects

General steps for all reservoirs

1. In the case of ungaged sites or sites with insufficient flow records, perform regional studies

utilizing data from nearby locations. Regionalized quantities may include average annual

precipitation, precipitation intensity-duration-frequency relations, unit hydrograph parameters,

annual runoff and extreme runoff-frequency relations

2. Determine natural flows at the reservoir and downstream damage centers

3. Determine reservoir characteristics such as area/capacity/elevation curves

4. Determine reservoir storage and pool elevation frequency curves from results of sequential

routings where reservoir is operated for all authorized project purposes

5. Determine design floods for establishing reservoir spillway capacity. Determine reservoir and

channel routing criteria

6. Determine maximum reservoir elevation by routing the spillway design flood

7. Determine reservoir freeboard requirements for wind and wave action

8. Determine water surface elevations throughout reservoir and tributaries for hypothetical dam

failures and for selected design floods

9. Determine quantity and distribution of sediment deposited in the reservoir (sediment storage) for

selected future time periods

10. Determine reservoir inactive storage, and minimum pool elevation to satisfy requirements for fish

and wildlife, recreation, etc.

11. Consider requirements for emergency evacuation of flood water in sizing outlet works

12. Determine reservoir operation rules

13. Determine the probability of failure of meeting the reservoir purpose

14. Determine effects of reservoir on streamflows, environmental quality (including temperature, DO,

BOD, etc.), sediment movement within the backwater reach and below the project, downstream

channel degradation, bank sloughing, evaporation, fish and wildlife, and groundwater regime, etc.

Complementary steps for reservoirs with flood control storage

1. Determine reservoir operating plan considering ability to forecast future flows during flood

emergency, including selection of downstream locations for which the reservoir should be

operated to reduce flood damages

2. Establish minimum foresight period of streamflow forecasts that can influence operation of

reservoirs and the corresponding average forecast accuracy for that length of forecasts (fore

example, a 20 per cent error for flows up to 12 hours in the future)

3. Determine flood control storage requirements and corresponding regulated flows for proposed

reservoir by performing sequential routing studies in which flooding at major damage centers is

minimized

4. Determine peak discharge-frequency curves for natural and regulated conditions at each major

damage centers below the proposed reservoir for a range of flood storage capacities

5. Determine outlet capacity requirements considering downstream channel capacities and desired

rate of evacuation (drawdown)


May, 2006 78

6. On the basis of stage-discharge-flood damage relationship and the peak average annual preproject

flood damages at each major flood damages frequency curve and average annual preproject flood

damages at each major flood damage center

7. Select range of feasible flood control storages and compute the associated mean annual costs

8. For each flood control alternatives, determine the modified flood damage frequency curve.

Estimate the expected value of mean annual flood losses averted (flood control benefits)

9. Develop functional relationship between mean annual costs of flood control (item 7) and expected

annual magnitude of flood losses averted (item 8)

10. Apply economic (cost-benefit analysis) and other criteria applicable in the given context (social,

ecological, etc) for selection of the most advisable flood control alternative. Whenever necessary,

the procedure should be based not only on the single valued flood discharge-flood loss

relationship but should also take into account seasonal and duration effects

Complementary steps for reservoirs with hydroelectric storage

1. Determine at-site energy demands, which the project must meet. For power systems, determine

system demands and the minimum project demands

2. Determine reservoir evaporation rates for normal and drought conditions

3. determine reservoir inflows to be used in sequential routings under project conditions on monthly,

10-day or weekly basis

4. Determine the reservoir power storage requirements and pool elevations which are necessary to

provide the annual firm energy

5. Determine the installed capacity for the project from the regionally selected marketable plant

factor and the annual firm energy

6. Determine the annual secondary energy and dependable capacity from long-term sequential

routings

7. Based on plant factor, power schedule, and channel characteristics, determine need for

reregulating structure and/or effect of tailwater fluctuations

Complementary steps for reservoirs with conservation storage

1. Determine demands on the reservoir for conservation purposes, such as municipal and irrigation

demands (generally monthly, 10-day or weekly schedules)

2. Determine reservoir evaporation rates for normal and drought conditions

3. determine reservoir inflows to be used in sequential routings under project conditions on a

monthly, 10-day or weekly basis

4. determine reservoir conservation storage required to meet the demands on the reservoir

Complementary steps for multipurpose reservoirs

1. Determine reservoir purposes and magnitude of demands corresponding to each purpose and their

variability; determine priorities among reservoir purposes

2. determine if water delivery will be direct from reservoir or if it will be diverted from a

downstream point which will allow release to go through turbines

3. Determine need, size and elevation of multiple level outlet capacity

4. Determine reservoir storage and corresponding pool elevations to accomplish multiple use of

storage as determined by sequential routings for all purposes

Complementary steps for mixes of reservoirs and other structural and nonstructural measures


May, 2006 79

1. Determine design floods for selected degrees of protection for reservoirs, levees, channel

improvements, diversions, relocations, flood-proofing, flood plain zoning, etc.

2. Determine selected combination of reservoir storage, levees, channels, diversions, relocations,

etc., which produce the best plan for the whole basin considering all pertinent hydrologic,

economic, and social criteria.

5.3 Hydrologic Estimates Required For Non-reservoir Projects

The following hydrologic estimates (procedural steps) refer to specific types of water projects, which do

not provide for flow control by means of storage reservoirs.

Irrigation Projects

1. Determine water requirements for various crops

2. Determine irrigation requirements (the amount of water that should be supplied to 1 hectare of a

field during the irrigation period to create conditions most favorable for the crop growth)

3. Determine water intake needs on the basis of irrigation requirements (with due consideration

given to their seasonal variability), irrigation area, crop rotation, and the efficiency of the future

irrigation system

4. On the basis of historical flow records (or maps of runoff isolines) compute long-term normal

flow which is to be used for determining irrigation capacity of the stream

5. Analyze intra-annual flow distribution. Identify critical flow values and critical season of the year.

6. perform flood flow analysis for determining the size of the flow control structures, storm water

inlets, mudflow channels, and flood gates in order to avoid destruction of hydraulic structures and

erosion of the irrigation network

7. Perform analysis of water level (stage) variability in order to determine location, type and size of

irrigation water intake structures

8. Compute water sediment concentration and its variability with respect to streamflow rate, stream

depth, width and length

9. Analyze chemical composition of irrigation water during different seasons of a year (high flows,

low flows, etc)

10. Perform water-balance computations based on the surface water measurements of inflow, outflow,

evaporation, groundwater regime, moisture dynamics in the aeration zone, meteorological

conditions, vegetation state and its growth

11. Estimate the volume of irrigation runoff, return flow and evapotranspiration losses; analyze the

possibilities of irrigation runoff reuse for other purposes

12. Assess the environmental impact of the contemplated irrigation project (soil salinization, water-

logging, water quality deterioration, streamflow reduction, etc)

Drainage projects

1. Carry out regional study of rivers in the regions future drainage of swamps and marsh-ridden areas

in order to estimate their water-carrying capacity during rainfall-flood period

2. Investigate areas to be drained and arrange for hydrologic data collection

3. Investigate river basins with existing drainage projects to obtain :

a. detailed description of drainage systems

b. present use of drained lands,

c. the state of drainage canals and rivers

d. the character of man's activity within the watershed, and

e. description of the state of lands adjacent to drainage systems within natural landscapes


May, 2006 80

4. Investigate hydrological regime of reclaimed areas in order to develop regional estimates for

hydrological computation of drainage systems, namely:

a. mean flow

b. maximum and minimum discharges during various seasons

c. local runoff

5. Investigate influence of reclamation works on water and (heat) regime, water resources and water

content of reclaimed and adjacent areas, including :

a. moisture exchange within the aeration zone

b. water level regime

c. flow regime

d. evaporation

e. infiltration of precipitation and waters for irrigation from reclamation systems

f. moisture content of soils and subsoils

g. regime of water use by different kinds of crops

h. water quality

6. Develop regional recommendations for purposeful management of water, air and feeding regimes

within the zone of active water exchange, and first of all of the active zone with roots layer, under

reclamation

7. Investigate the influence of reclamation on natural landscapes in different physiographical and

climatic conditions in order to evaluate the character of their change and change of biological

productivity

8. Organize collection of necessary observational data to provide hydrometeorological information

for reclamation systems in order to increase their efficiency and the productivity of drained lands

Municipal and industrial water supply projects

1. Forecast alternative levels of water demand by industry and municipalities

2. Perform regional studies to define location of potential sources of water supply (surface and

groundwater resources)

3. For each potential supply source, determine:

a. volume and quality of water available as related to different water supply reliability levels

b. time-distribution of available water resources, both in terms of their quantity and quality,

and

c. cost of resource development alternatives

4. Perform demand/supply analysis to select the most desirable (e.g. least costly) supply scheme

5. Determine design parameters of diversion and intake facilities (e.g. head-gates, pumps,

compensation reservoir)

6. Determine design parameters of water treatment (purification) plants, if necessary

7. Determine design parameters of the delivery system

8. Determine effects of proposed solution on basin-wide flows, water quality, sediment movement,

etc.

Water Quality Projects

1. Perform regional studies to locate all present and potential water uses that affect or are affected by

water quality. The major water uses of interest are:

a. municipal, including storm water runoff

b. industrial

c. agricultural


May, 2006 81

d. commercial fishing

e. water contact recreation

f. non-water contact recreation

2. For each of the present and potential water uses, determine:

a. intake water quality requirements

b. intake water treatment alternatives (technical and economic data)

c. wastewater discharge loads in relation to different water use technologies, and temporal

distribution of wastewater discharges, and

d. wastewater treatment alternatives (technical and economic data)

3. Perform hydrologic studies to determine design streamflow rates for further analysis of waste-

assimilative capacity of the river system. These studies should be concerned with:

a. duration of low-flow periods

b. possibility of occurrence of low flows of selected durations,

c. severity (e.g. total deficiency in water supply with respect to some reference flow and

some duration),

d. time of occurrence within the annual cycle and

e. areal extent of low-flow phenomena

4. Perform waste-assimilative studies for the given river system (including estimation of dispersion

and mixing zones), for different design (reference) and streamflow rates

5. Perform water quality management studies to determine the most desirable (e.g. least costly) way

of achieving specific water quality objectives

Flood control projects

6. Determine preproject peak discharge-frequency curves at each major flood damage center

7. In the case of ungaged sites or sites with insufficient flow records, perform regional studies

utilizing data from nearby stations

8. Determine natural flows at the reservoirs and at downstream damage centers

9. Determine design floods for nonreservoir structures

10. Determine freeboard requirements for wind and wave action for nonreservoir structures

11. Determine water surface elevations for length of channel or levee and beyond

12. Determine effects of changes on flows, environmental quality, etc.

13. Determine probability of failure during life of proposed structure

14. On the basis of stage-discharge-flood damage relationships and the peak discharge-frequency

curves, determine a preproject flood damage frequency curve and average annual preproject flood

damage at each major flood damage center

15. select range of feasible structural and nonstructural flood control alternatives and compute the

associated mean annual costs

16. For each flood control alternative, determine the modified flood damage frequency curve.

Estimate the expected value of mean annual flood losses averted (flood control benefits)

17. Develop functional relationship between mean annual costs of flood control (item 10) and

expected annual magnitude of flood losses averted (item 11)

18. Apply economic (cost-benefit analysis) and other criteria applicable in the given context (social,

ecological, etc.) for selection of the most advisable flood control alternative. Whenever possible,

the procedure should be based not only on the single valued flood discharge-flood loss

relationship but should also take into account seasonal and duration effects


May, 2006 82

5.4 Hydrologic Estimates Required For Basin-wide Long-term Planning for Integrated Development of Water Resources

There are nearly as many study procedures for integrated basin-wide development as there have been

basin projects. The following specification, basin on United Nations1, serves primarily as an illustrative

example and also as a checklist of the major steps in hydrologic investigations for basin-wide planning

concerning integrated development of water resources

1. Appraise the adequacy of available hydrometeorological data (e.g. precipitation, evaporation,

evapotranspiration, air temperature) and hydrological data (e.g. flow time series, flood

hydrographs, aquifer recharge characteristics, quality parameters, sediment transport parameters)

2. Select key control points in the river system taking into consideration location of stream-gaging

stations, major water users, present and planned flow control

3. Determine what additional data are required with consideration given to the purpose of the

investigations and the methods which are to be used for subsequent water management analysis

(e.g. classical balances, simulation, optimization)

4. Devise methods, standards, and schedules for acquiring additional data (e.g. extension of flow

records, application of rainfall-runoff models, regional analysis)

5. Arrange for acquisition of additional data

6. Analyze and organize the data for studying problems of

a. municipal, industrial, and agricultural water supply

b. flood control

c. water quality control

d. hydroelectric power generation

e. inland navigation

f. recreational use of water, and

g. nature conservation

7. Estimate annual flow variability and characteristics of intra-annual flow distribution

8. Estimate the amount of water which can be withdrawn from groundwater resources without

producing undesired results

9. Estimate the minimum flow requirements in the control profiles (i.e. flow which must be

maintained because of aesthetic, scenic, sanitary and/or biological reasons)

10. Determine available water resources and analyze potential peak storage alternatives

11. Estimate flood characteristics for selected profile (e.g. peak flow frequency curves for natural and

regulated flow, design flood flow, channel routing criteria)

12. Develop flood control alternatives (e.g. storage, flow retardation measures, levees, flood walls,

channel improvements, floodways)

13. Estimate low-flow characteristics for selected profiles (e.g. minimum flow frequency curves for

natural and regulated flow, design low flows)

14. Develop water quality control alternatives (e.g. low flow augmentation)

15. Estimate hydrologic characteristics for hydroelectric power generation studies

16. Develop hydroelectric power generation alternatives

17. Estimate hydrologic characteristics for irrigation studies

18. Develop irrigation alternatives

19. Estimate hydrologic characteristics for inland navigation studies (e.g. depth, width, current

velocity)

1 United Nations (1970). Integrated river basin development. New York, United Nations


May, 2006 83

20. Develop navigation development alternatives

21. Estimate hydrologic characteristics for recreational studies (e.g. depth, area of water surface,

water quality )

22. Develop alternatives for recreational use of water

23. Estimate hydrologic characteristics for fish and wildlife studies (e.g. water temperature, water

quality)

24. Develop alternatives of habitat improvements for fish and wildlife

25. Analyze the present and potential institutional arrangements for water resources management

26. Evaluate all alternatives and prepare a comprehensive long-term plan for the integrated

development of water resources in the river basin, including an assessment of impacts of projects

on the environment and hydrologic regime.


May, 2006 84

6 Elements of (WR) Project Formulation

6.1 Stages of WR project

This section outlines the process by which WR projects are identified, and formulated. It starts by

describing the levels of studies conducted in a typical study involving the evaluation and implementation

of a structural measure or non-structural measure to achieve a pre-set goal of WR development. The

following is a typical five-stage sequence of reports, documents, and actions for a (WR) project, including

the preliminary (or reconnaissance) report, the feasibility report, the contract documents, and activities

during construction and operation.

First Stage: Preliminary (or Reconnaissance) Report

This consists of office studies, field studies, and the preparation of a report. The report prepared as a result

of these studies should answer the following questions:

Is a feasible project likely?

What are approximate estimates of capacity and cost?

What additional studies are needed to confirm feasibility?

The investigation begins with office studies, using available information contained in previous reports,

maps, and data. Basic materials include maps and photographs (topographic maps, land surveys, county

and city tax maps, transportation maps, aerial photographs); geologic and soil surveys and data;

climatological data; stream flow and ground water records; water quality and sediment measurements;

information on ecological and environmental conditions; and data and forecasts pertinent to the specific

purpose of the project (e.g., projection of water supply requirements, or electric power demands;

characteristics of existing water supply, or electric generation and transmission systems; etc.).

Office studies may be adequate to make initial determinations of the general arrangement of the project

components, the capacity of the project or the services it can provide, and its cost. Better estimates can be

made by supplementing office studies by field reconnaissance and surveys. This work is needed to

confirm the estimates made in office studies, to suggest changes in them, and to obtain detailed

information concerning such matters as needed relocations in cases where the available maps are not

recent.

Topographic surveys, stream flow measurements, and geological and soils investigations may be needed,

but these should be kept to a minimum, consistent with the nature of the preliminary report. The personnel

involved in this work are normally engineers and geologists, but they may also include environmentalists

and other specialists.

Second Stage: Feasibility Report

If the project sponsor determines that additional studies are warranted based on the preliminary report and

other considerations, a feasibility report will be prepared. This report should contain enough information

to permit a decision on whether or not to implement the project. This implies technical studies more

detailed than those required for the preliminary report, financial and economic analyses, and a plan for

project implementation. The feasibility report should include the following:

a. Descriptions and analyses of the data

b. Confirmation of construction feasibility based on additional field and laboratory investigations,

studies of project arrangements and individual project features, and analysis of construction methods

(sources of construction materials, access to the project site, diversion of water during construction,

etc.)

c. Final recommendations for arrangement of project works, preliminary plans and other analyses to

determine the principal quantities of construction, a reliable cost estimate, and discussions of the

design criteria

d. Construction schedule showing the timing and costs of project features


May, 2006 85

e. Economic analyses of the project

f. Financial analyses projecting the year-by-year costs, revenues, and subsidies for the project

g. Plans for financing construction, and for managing the construction and operation of the project

h. Institutional and legal requirements

i. Assessments of the environmental and social impacts of construction and operation, and other

impact studies if required depending on the extent of detailed drawings and of analyses needed to

confirm construction feasibility and make reliable estimates of project cost, the work in this phase

consists of designs in addition to planning studies.

Third Stage: Final Design and Preparation of Contract Documents

Contract documents include plans and specifications which are sufficiently detailed to obtain tenders

(bids) from qualified construction and equipment contractors. The plans (drawings) and specifications are

based on additional studies of the details of project works, the logistics of construction, other aspects

related to temporary and permanent facilities, and the performance of contractors. The contract documents

also contain additional information on the responsibilities of the project sponsor and the contractor.

Various forms to be completed by the contractor provide information on the contractor's legal status and

financial capabilities, set forth the quantities and prices for construction and for equipment, and elaborate

on the construction methods proposed by the contractor.

The sponsor and engineers review the tenders made by contractors. A major factor is the prices offered by

a contractor, but other factors considered may include the reputation and previous experience of the

contractor, the specific working methods proposed to carry out the construction or manufacture of

equipment, and in the case of the latter, the operating efficiency of the equipment to be provided.

Contractors' tenders are usually ranked after weighting the factors, in order to determine which tenders are

in the sponsor's best interest, and awards are made accordingly.

Fourth Stage: Construction

Additional detailed drawings needed during construction are prepared by the sponsor's engineers and by

the contractors subject to the sponsor's approval. Payments to the contractors are usually made based on

measurements of work in progress or completed, in accordance with the terms of the contract documents.

Usually, a percentage of each payment is withheld by the sponsor and released only when the work is

entirely completed and accepted. Supervision of construction by the sponsor's engineers often includes

field layout of major works, approval of contractors' choices of working procedures and materials,

interpretation of the plans and specifications, approval of the contractors' drawings needed to supplement

the engineers' drawings, inspection of construction activities and of finished work to ensure conformance

with plans and specifications, measurement of quantities of construction, and certifications required as a

basis for payments to the contractors.

Fifth Stage: Operation

The sponsor may employ outside engineers and other consultants to assist in operation for a limited

period, train operators, prepare manuals for operation and maintenance, and monitor the performance of

the various features (structural, hydrologic, hydraulic, etc.). Studies of operating rules may continue as

experience develops.

6.2 Formulation of a single engineering project

The engineers (or the interdisciplinary team of specialists) that formulate a water resources project define

the arrangement of project components, and sufficient details concerning their sizes and functions so that

realistic cost estimates can be prepared.

Project formulation relates to stages 1 to 3, above; it begins in a rudimentary way in the reconnaissance

level work required for the preliminary report, is refined and elaborated in the feasibility report stage, and


May, 2006 86

undergoes additional changes and detailed definition in the preparation of the plans and specifications for

the contract documents.

During project formulation, the planner evaluates the available data and conceives a plan to utilize water

and related land resources to meet project needs. This work draws on scientific training, experience with

other projects of similar type or with similar components, and imagination and judgment to layout a

project that fits the available topographic, geologic, and soils conditions. Account is also taken of

information on water volumes and flow rates, nature and magnitude of project products and services that

are desired, and existing or potential constraints.

Constraints may include legal limitations on water or land involving quantities or uses; practical

limitations on relocations, land purchase, and easements permitted for buildings, roads, railroads, utilities

and other human-made features; or obvious unsuitability of a site for certain types of developments (e.g., a

type of dam may be unsuitable for certain topographic configurations, geology, or construction material

availabilities). In most cases more than one layout is possible. A good planner will eliminate the most

unsuitable alternatives while assessing the remaining alternatives fairly and comprehensively. With some

sites and service requirements, the planner may be able to proceed directly to the optimal solution. In the

more usual case, alternative layouts will need to be prepared and examined for cost, function, construction

suitability, and other factors.

The planner may approach a solution for a site starting with the perspective of a water need of a particular

type and magnitude (e.g., municipal and industrial water supply) and then consider the possibilities for

modifying the project to make it suitable for multipurpose operations (e.g., recreation, hydroelectric

power). Or, the planner may from the beginning examine a variety of plans that exploit the site for all the

opportunities for multipurpose development.

The formulation of a project as discussed above emphasizes structural details, costs, project services,

reliability, safety, and other engineering matters. It is necessary, however, to consider the impacts of a

project that are not primarily of an engineering or cost nature. If the formulation team is dominated by

engineers, it will be necessary to consult with or have formal assessments by other specialists at various

stages to ensure that environmental, sociological, institutional, and other factors are adequately taken into

account. Otherwise, projects may be proposed that cannot be implemented. At the early stages of planning,

impact analysis can be limited to identifying the most obvious problems, but studies at later stages need to

be more comprehensive.

As the work of formulation proceeds, the planner gains an improved understanding of site conditions,

advantages and disadvantages of alternative project arrangements, and possible opportunities for using the

site to produce more or different project services. The planner is, therefore, better able to communicate

with the sponsor of the project, and reconsideration of project objectives and purposes, scale, or other

aspects may result from such communication.

As an example of the formulation process, the process of considering and assessing alternatives for

protecting an urban riverside community against flood damage will be discussed here. Alternative projects

are to be evaluated utilizing possible methods of reducing flood damages to existing buildings and other

facilities and reducing flood risk to permit additional urban growth. Three principal approaches to

reducing flood damage may be considered: (1) management measures; (2) local protection facilities; and

(3) upstream flood control reservoirs.

The first approach is primarily a nonstructural solution. It includes some or all of the following

components: (a) zoning, to limit the types of land uses permitted to those which may not be severely

damaged by floods (e.g., agriculture, recreation, wild areas), and to specify the types of construction if

facilities are permitted; (b) protection of individual properties, by waterproofing the lower floors of

existing buildings; (c) flood warning system, to evacuate residents and to move valuables; and (d) flood

insurance, to recognize the risks of floods and to provide compensation when damages are not avoidable at

acceptable cost.

The second approach emphasizes the construction of levees or walls to prevent inundation from floods

below some specified design flood flow (often the highest flood of record). Additional works may include


May, 2006 87

drainage and pumping facilities for areas that are sealed off from precipitation runoff to the river by the

levees; and modifications to increase the hydraulic capacity or stability of the river, such as changes in

profile or direction, channelization, and paving.

The third approach is based on the construction of one or more reservoirs upstream from the community.

This implies the availability of site(s) that are suitable for a dam, spillway, and outlet works, and a large

enough reservoir to capture the volume of a design flood and release it at non-damaging rates. Alternative

sites as well as alternative layouts of works enter into this analysis. This approach to flood control lends

itself to consideration of multipurpose reservoir uses; these may typically be recreation, hydroelectric

energy generation, and water supply.

Depending on the risk that floods will occur which are larger than the design flood for local protection

works, or the design floods for upstream reservoirs, these second and third approaches should also include

management (nonstructural) elements such as those in the first approach.

6.3 Project Appraisal

Project appraisal is the process by which a reviewing authority determines whether a water resources

project meets appropriate criteria for authorization and/or funding, or whether a regional plan meets

appropriate standards for proceeding with implementation studies of one or more component projects.

Different governmental, lending and other agencies have, to some extent, varying criteria, which are used

to appraise projects, submitted for approval of funding.


May, 2006 88

Reference

1. Ray K. Linsley, Joseph B. Franzini, David L. Freyberg, George Tchobanoglous: “Water

Resources Engineering,” 4th

Edition, McGraw-Hill Inc, New York, 1992.

2. Neil S. Grigg, “Water Resources Planning,”

3. Larry W. Canter, “Environmental Impact of Water Resources Projects,”

4. Chow, Ven Te, Maidment, Daivd R. and Mays, Larry W., “Applied Hydrology”, McGraw-

Hill Publishing Company, New York, New York, 1998.

5. Maidment, David R., “Handbook of Hydrology”, McGraw-Hill Publishing Company, New

York, New York, 1993.


May, 2006 89

Sample Exam Questions and Partial Solutions/Answers

Instruction: Show all the necessary steps clearly.

Assume any missed data with justification.

1. Discuss briefly

a. the definition of Water Resources Development

b. Sustainability Criteria for design of Water Resources Development Project

c. Steps of planning in Water Resources Development and

d. What EIA is and the steps for carrying out EIA.

2. Find the maximum value of the following function

F(X1, X2, X3) = X1 + 2X3 + X2X3 – X12 – X2

2 – X3

2

3. Construct an optimization model for estimating the least-cost combination of active storage

capacities, K1 and K2, of two reservoirs located on a single stream, used to produce a constant

flow or yield downstream of the two reservoirs. Assume that the cost functions Cs(Ks) at each

reservoir site S are known and there is no dead storage and no evaporation. Assume that 10

years of monthly unregulated flows are available at site S. the system diagram is as shown in

Fig. 1.

Fig. 1. Two Reservoirs in series

Where Q1,t and Q2,t are the unregulated streamflows at sites 1, and 2, respectively. Q2,t – Q1,t is the

incremental inflow between site 1 and site 2, R1,t is the release from the upstream reservoir, and Y

is the constant yield from the downstream reservoir, S1,t and S2,t are the reservoir storages and K1

and K2 are the reservoir capacities.

Q1,t R1,t Y

S2,t S1,t

K1 K2

Q2,t – Q1,t


May, 2006 90

4. A city administration is planning for a flood control project. The goal being to protect parts of

the city against the 100-years flood. One of the alternatives under consideration is to use an

existing reservoir, which is currently the source of water for the city. Because the current

reservoir size is not sufficient to fulfill the flood-control objective, raising the dam height by

2m is being considered with the aim of using the additional storage thus obtained for flood

control purposes. the flood-damage costs can be approximated by the following:

For Q 25, D = 0

For 25 < Q 60, D = 0.06 + 0.0025 x (Q – 25)

For Q > 60, D = 0.12 + 0.340 x (Q – 60)

Where, Q = fow rate at flood risk zone in m3/sec,

D = Damage cost in Millions of Birr

The flood-frequency relationships for the two cases can ba approximated by the following

regression equations:

Case 1: Current situation

QT = 9.2833 + 29.293 x ln(T)

Case 2: With raised dam

QT = 3.4415 + 19.8683 x ln(T)

Where QT is flow at damage-risk zone in m3/sec for a return period T in years.

Considering return periods of 2, 5, 10, 20, 50 and 100 years

i. Determine the damage-frequency curves for both , i.e. current situation and with the

proposed measure,

ii. Determine the expected annual damages for both no-project case and the proposed

alternative,

iii. Taking the remaining useful life of the reservoir to be 50 years and with a discounting

rate of 5%, determine the present worth of the reduction in flood damage cost should

the proposed structural measure be implemented.

5. Consider the following LP Problem:

Maximize X0=3X1+5X2

Subject to

X1 < 4

X2 < 6

3X1 +2X2 < 18

a) Identify the feasible extreme points for the problem

b) Find the optimum feasible solution

c) Determine the amounts of reduction of the non-binding constraints without affecting the

feasibility of the current optimal solution.


May, 2006 91

6. A city administration is planning for a flood control project the goal being to protect parts of

the city against the 100-years flood. One of the alternatives under consideration is to use an

existing reservoir, which is currently the source of water for the city. Because the current

reservoir size is not sufficient to fulfill the flood-control objective, raising the dam height by 2

meters is being considered with the aim of using the additional storage thus obtained for flood

control purposes. The flood-damage costs can be approximated by the following.

7. A reservoir shown in figure 1, which is part of a hydroelectric power scheme, has lost about 40

percent of its capacity due to sedimentation. In order to maintain the power generating

capacity of the plant, it was proposed to use a (natural) lake as temporary storage of ‘kiremt’

flows, which could later be diverted to the reservoir. Records of stream flow are available for

a gauging station located on a river A upstream of the dam, for the streams that flow in to and

out of the lake, as well as records of the lake water level. There are also meteorological

stations nearby all then important sites, from which required climate data can be obtained. As

part of the study for the feasibility of the proposed scheme, it is proposed to carry out

simulation of the scheme.

River

River

River B

River M

River A

Proposed diversion site

El. 1800masl

Lake

El. 1400masl

Lake

El. 1600masl

Fig. 1. Schematic layout of the proposed scheme

i) List the major types of information /data required to carry out the proposed

simulation of the system?

ii) Write down the relevant equations for the reservoir, and the lake, you may neglect

losses in channels and river segments.

iii) What result would be expected from the simulation exercise?


May, 2006 92

8. Data: Water availability, Land Extension, Crop Productivity, Manpower, Specific Benefit

Problem: Determine the amount of each crop that maximizes the benefits

Resource/input Maximum

Availabel Input

Crop1 Crop 2

Land 50ha 2 ha/ton 3 ha/ton

Water 250 Mill. m3 20 mill m3 5 mill m3

Manpower 90 Man Months 6 MM/ton 4 MM/ton

Benefit Max? 180 Birr/ton 210 Birr/ton

9. Dynamic programming – Hydropower and reservoire

Reservoir Storage, Si

Reservoir Capacity, k

Return from Energy,

ri(xi)

Release Xi

i = stage(Season) 1,..,4

Inflow, Ii

Data

Season/stage i = 4 i = 3 i = 2 i = 1

Inflow, Ii 2 x 106 m

3 4 x 10

6 m

3 6 x 10

6 m

3 4 x 10

6 m

3

Release

xi x106 m

3

Return, ri (xi)

i = 4 i = 3 i = 2 i = 1

0 0 0 0 0

2 1.9 2.2 1.7 1.6

4 3.9 4.1 3.6 3.4

6 4.8 5.9 5.0 4.5

k = 8 x 106 m

3

xi x106 m

3 [Turbines]

Sin = Sfin = 6 x 106 m

3 [= keep some water in the reservoir]

Which are the seasonal releases that maximize the return?


May, 2006 93

10. Describe briefly: [5pts each]

a. the importance of economic analysis Water Resources Development project

i. Help planners with quantification of benefit and cost of alternative WR projects

ii. Involves basically the computation of the benefits and costs a plan would entail should

it be implemented,

iii. Helps to express each item and step in moneyary unit with the time value of money

iv. Reinforces the technical feasibility of projects

v. Help in budget allocation of the funding body, etc.

b. What do you understand by the terms “Integrated River Basin Development Master Plan”

Integrated River basin development master plan:

i. is a phased development plan formulated to exploit the opportunities for single and

multipurpose water resources projects

ii. is prepared in a defined geographic area over a specific period of time.

iii. Encompasses development of other resources such as human, land, minerals, etc.

iv. Identifies projects basin wide and investigates their combined effect basin wide.

v. Alternative scenarios for different projects

vi. Serves as a reference based on which projects can be initiated, etc.

c. The major river basins in Ethiopia.


May, 2006 94

11. a. Using illustrative examples and/or sketches discuss the major feasibility tests to be done

for a water resource development project. [7 pts]

Major feasibility tests:[Refer your hand out for the detail]

i. Technical feasibility

ii. Economic feasibility

iii. Financial feasibility

iv. Political feasibility

v. Social feasibility

b. Take one water resource development project that you are familiar with and enumerate

exhaustively the physical consequences with respect to cost and benefit related to its

implementation and operation.[8 pts]

Physical consequences with respect to cost and benefit:

i. Primary benefit: denote value added to activities influenced by the project through

technological linkages.

ii. Secondary benefit: denote value added to activities influenced by the project through

economic rather than technological linkages.

iii. Employment benefits: denote the economic-value gained from the increased employment

opportunity from new jobs created to construct, maintain, or operate the project.

iv. Public benefits: are realized in achievement of goals other than economic efficiency and

thus can be evaluated in efficiency dollars only by means of a value judgment on the

relative desirability of the second goal.

v. Intangible (extra market) benefits: describe consequences which cannot be assigned a

monetary value but which should be considered when deciding whether or not to build a

project.

12. Four alternative projects presented in Table 1 can be used for developing a water supply for a

community for the next 40 years. Use the benefit –cost ratio method to compare and select an

alternative. Use 6% interest rate.[15 pts]

Year Project I Project II Project III Project IV

Construction cost (Mill. Birr)

0 40 30 20 10

10 0 0 0 10

20 0 10 20 10

30 0 0 0 10

Operation and Maintenance cost (thousand Birr)

0 – 10 120 110 120 120

10 – 20 120 110 130 120

20 – 30 140 120 130 130

30 – 40 160 140 150 130

For Project I

PW of costs = 40,000,000 + 120,000[P/A, 6%, 20] + 140,000[P/A, 6%, 10] [P/F, 6%, 20] +

160,000[P/A, 6%, 10] [P/F, 6%, 30]

=40,000,000 + 1,376,391+321,287 + 205,035

=41,902,713


May, 2006 95

For Project II

PW of costs = 30,000,000 + 110,000[P/A, 6%, 20] + 10,000,000[P/F, 6%, 20] + 120,000[P/A, 6%, 10]

[P/F, 6%, 20] + 140,000[P/A, 6%, 10] [P/F, 6%, 30]

= 30,000,000 + 1,261,691 + 3,118,047 + 275,389 +227,061

= 34,882,189

For Project III

PW of costs = 20,000,000 + 110,000[P/A, 6%,10] + 130,000[P/A, 6%, 20] [P/F, 6%, 10] +

20,000,000[P/F, 6%, 20] + 150,000[P/A, 6%, 10] [P/F, 6%, 30]

=20,000,000 + 883,210 + 832,617 + 6,236,095 +192,220

=28,144,142

For Project IV

PW of costs = 10,000,000 + 120,000[P/A, 6%,20] + 10,000,000[P/F, 6%, 10] + 10,000,000[P/F, 6%, 20]

+ 130,000[P/A, 6%, 20] [P/F, 6%, 20] + 10,000,000[P/F, 6%, 30]

=10,000,000 + 1,376,391 + 5,583,948 + 3,118,047 +1,741,101 + 464,929 =22,284,439

Assigning equal benefit for all the four alternatives, the benefit cost ratio for Project IV will be

the highest and hence it will be the best alternative for implementation.

13. All the rivers crossing Addis Ababa are almost serving as a sewer line with regard to their waste

content. It is planned to launch a pilot study on the Banteyiketu river which flows through the center

of Addis Ababa. The Banteyiketu river is chosen as a pilot river for the recurrent flooding along the

river and the extent of pollution induced by the domestic and industrial waste disposed directly to the

river which finally joins the highly utilized Awash river. Existing challenges of urban centers includes

drainage, land scarcity, industrialization, increasing population, etc.. Water related natural hazard such

as flooding, low flow, destruction of the ecosystem, etc. go hand in hand with the aforementioned

urban problems. Taking the above challenges into account in the context of water resource

development,

a. list down the exhaustively the types of data required for the pilot study, [8.0 pts]

Required data list

i. Topography

1. Location of infrastructures,

2. River and drainage network

3. Contour map

4. Boundary of the catchment

5. Location of WR projects

ii. Meteorological data,

1. Rainfall: intensity, duration, frequency

2. Temperature

3. Humidity

4. Wind,

5. Evaporation, etc.

iii. Geology,

iv. Hydrologic:

1. runoff amount, and river stage,

2. Peak flow

3. Low flow

4. Average flow,


May, 2006 96

5. Ground water level, yield, etc.,

v. Socio-economic situation,

1. Population,

2. Population density and pattern,

3. Life standard,

4. Water supply coverage and drainage,

5. Education and health service coverage, etc.

vi. Previous hazard/damage record,

vii. Existing WR projects

1. Structures: dams, weirs, barrages,

2. Irrigation, water supply,

3. Drainage and sewerage, etc.

viii. Water quality; physical, chemical, bacteriological,

ix. Catchment characteristics,

1. Soil : texture, structure, infiltration rate, etc.

2. Slope: drainage area and channels/river,

3. Sediment yield and transport mechanism,

4. Land use and land cover, etc.

x. Environmental/ecosystem, etc.

b. Suggest methods of analysis and important consideration as a water resource engineer. [7.0 pts]

Statistical Analysis of data

Measures of tendencies

Regression analysis

Correlation

i. Check adequacy, consistency and reliability of collected data [statistical methods]

ii. Summarize the data as per the expected result of the WR project.

Socio-economic and environmental data shall be processed in accordance to make

sure that the recommended solutions will be effective and sustainable.

iii. Search for any relationship between the collected data [statistical methods]

iv. Select or develop a model that will help to simulate the processes in consideration

Proper model for population forecast

Due to the size of the catchment application of large watershed models will not be

feasible for Banteyiketu river. Hence, small scale models like the rational method and

the US-SCS (United States Soil Conservation Service) method were used to determine

the peak discharge flood protection works.

The dry period flow quantity will be analyzed for its capacity to carry the waste

disposed into the river and its suitability to keep the ecosystem along the river.

v. Check the model results through validation process

vi. Draw conclusions and Make recommendations based on the analysis, etc.


May, 2006 97

14. A flood control district can construct a number of alternative control works to alleviate the flood

pattern in the district. These alternatives include dam A, dam B, and a levee system C. The levee

system can be built alone or in combination with dam A or B. Both dams can not be built together but

either one can function alone. The life of each dam is 80 years and the life of the levee system is 60

years. The cost of capital is 6%. Information on total investment, operation and maintenance costs,

and average annual flood damage is given below. What form of flood control would be the most

economical? [15.0 pts]

Project Life

(Years)

Total investment

(Million $)

Annual O & M

(Thousand $)

Average annual Flood

damages (Million $)

A (dam) 80 6.2 93 1.10

B (dam) 80 5.3 89 1.40

C (levee) 60 6.7 110 0.80

AC 12.9 203 0.40

BC 12.0 199 0.50

Do Nothing 0 0 2.15

For A

PW of costs = 6,200,000 + 93,000[P/A, 6%, 80] + 110,000[P/A, 6%, 80]

=6,200,000 + 1,535,000 + 321,287 + 18,160,000

=25,895,000 [2.0 pts]

For B

PW of costs = 5,300,000 + 89,000[P/A, 6%, 80] + 1,400,000[P/F, 6%, 80]

= 5,300,000 + 1,469,000 + 23,113,000

= 29,882,000 [2.0 pts]

For C

PW of costs = 6,700,000 + 110,000[P/A, 6%, 60] + 80,000[P/A, 6%, 60] + 2,150,000[P/F, 6%, 60] [P/A,

6%, 20]

=6,700,000 + 1,778,000 + 12,929,000 + 740,000

=22,147,000 [2.0 pts]

For A and C

PW of costs = 12,900,000 + 93,000[P/A, 6%, 80] + 110,000[P/A, 6%, 60] + 400,000[P/A, 6%, 60] +

110,000[P/F, 6%, 60] [P/A, 6%, 20]

=12,900,000 + 1,535,000 + 1,778,000 + 6,464,000 + 379,000

=19,942,000 [2.0 pts]

For B and C

PW of costs = 12,000,000 + 89,000[P/A, 6%, 80] + 110,000[P/A, 6%, 60] + 500,000[P/A, 6%, 60] +

140,000[P/F, 6%, 60] [P/A, 6%, 20]

=12,000,000 + 1,469,000 + 1,778,000 + 8,081,000 + 482,000

=20,758,000 [2.0 pts]

Do Nothing

PW of costs = 2150,000[P/A, 6%, 80]

=35,494,000 [2.0 pts]

By the present worth method of analysis, the total cost for option AC (Dam A and Levee) is the

least among the six options; hence, best alternative for implementation. [3.0 pts]


May, 2006 98

15. Despite the name” The Water Tower of Africa” in recognition to the number of fresh water lakes,

inland rivers and cross boundary rivers including the Nile river, Ethiopia has paradoxically been

stricken by recurrent drought. Although, the annual total volume of water available [about 113 Bm3]

by far exceeds the total demand the country has remained unable to use its water resources potential. a. Discuss in brief the causes of this paradoxical challenge and [8.0 pts]

i. International water right policy on cross boundary rivers

ii. Lack of well defined WR development plan and strategy in national as well as regional

level

iii. Low economic capacity to implement WR projects

iv. Political instability of the country

1. Unstable economic and investment policy

2. Discourages investors

3. Consumes the budget

v. Lack of accountability of professionals, leaders, and beurocracy;

vi. Inadequate knowledge of the existing challenges in WR development

vii. Lack of institutional support for water resources assessment, development planning,

implementation and operation,

viii. Lack of data and information about the available water resource,

ix. Lack of proper communication mechanism for exchange of information (Database)

between professionals, researchers and decision/policy makers

x. Poor Technical capacity (Technology and human resource)

xi. Topography

1. Most rivers flow in deep gorges

2. Irrigable land is far from the water source,

3. Settlement of population is far from either the source or the utilizable land, etc.

xii. Traditional farming and deforestation,

xiii. Poor infrastructure: roads, power, communication facilities, etc.


May, 2006 99

b. its possible remedial measures in the context of Water Resources Development. [7.0 pts] i. Encourage Public participation in WR project planning and implementation,

ii. Encourage involvement of professionals on international water related decisions and

agreements

iii. National coordination in WR development with respect to;

1. preparation of National WR development plan and strategy

2. Development of Water right legislation

3. Information/data exchange,

4. Technological exchange and update,

5. Experience sharing, etc.

iv. Develop human resource capacity;

1. Produce professionals in WR related fields,

2. Produce skilled manpower through long term or short term trainings, etc.

v. Control of population overgrowth for optimum resource allocation

vi. Improved methods of farming (from rain fed agriculture to irrigation)

vii. Create Awareness of WR development projects for

1. Decision makers,

2. Politicians,

3. The society,

4. Concerned bodies and development partners, etc.

viii. Equitable distribution of resources

ix. Afforestaion

x. Encourage participation of private investors in WR development

xi. Use of local technologies and materials for WR development, etc.

16. Consider the following LP Problem:

Maximize X0=3X1+5X2

Subject to

X1 < 4

X2 < 6

3X1 +2X2 < 18

d) Identify the feasible extreme points for the problem

e) Find the optimum feasible solution

f) Determine the amounts of reduction of the non-binding constraints without affecting the

feasibility of the current optimal solution.

This is almost the same as the irrigation scheme

example discussed in class.

From the description, the decision variables will be X1 and

X2 and the objective function may be formulated as

Max X0 = 3X1 + 5X2

Subjected to

X1 4

X2 6

3 X1 + 2 X2 18

X1 0, X2 0


May, 2006 100

As there are only two decision variables a graphical technique can be employed for optimization

From the graph the feasible space is the shaded region and the feasible extreme points and their

respective output in the objective function is given in the following Table.

Point X1 X2 X0

A 0 0 0

B 0 6 30

C 2 6 36

D 4 3 27

E 0 4 20

Hence, the optimum feasible solution is X1 = 2 and X2 = 6 that produces X0 = 36

At the optimum feasible solution, only half of the available X1 is utilized whereas X2 is totally

consumed. Hence, the remaining half could be reduced without affecting the output.

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