A STRATEGY FOR DECISION MAKING IN WATER RESOURCES By Kwabena Oben-Nyarko

A STRATEGY FOR DECISION MAKING IN WATER RESOURCES By Kwabena Oben-Nyarko
A STRATEGY FOR DECISION MAKING IN WATER RESOURCES
PLANNING FOR DEVELOPING COUNTRIES
By
Kwabena Oben-Nyarko
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
WITH A MAJOR IN CIVIL ENGINEERING
In the Graduate College
THE UNIVERSITY OF ARIZONA
1979
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
I hereby recommend that this dissertation prepared under my direction
by
Kwabena
entitled
Oben-Nyarko
A Strategy for Decision Making in Water Resonrces
Planning for Developing
Countries
be accepted as fulfilling the dissertation requirement for the Degree
of Doctor of Philosophy
/07//979
Date
Dissertation Director
As members of the Final Examination Committee, we certify that we have
read this dissertation and agree that it may be presented for final
-
defers
:
Date
Date
Date
Date
72
/12;041
Date
Final approval and acceptance of this dissertation is contingent on the
candidate's adequate performance and defense thereof at the final oral
examination.
11/78
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment
of requirements for an advanced degree at The University of Arizona
and is deposited in the University Library to be made available to
borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without
special permission, provided that accurate acknowledgment of source
is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by
the head of the major department or the Dean of the Graduate College
when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission
must be obtained from the author.
SIGNED:
(
This is dedicated to my mom, Afua Amankwaa,
my late sister, Afua Oye (Ketewa),
my brother, Kwasi Addo-Nyarko,
and my daughter, Afua Oforiwaa.
iii
ACKNOWLEDGMENTS
I would like to thank the many people who helped to bring this
dissertation to completion. In particular, I am grateful to the dissertation director, Dr. Simon Ince, who was also my academic advisor throughout the duration of my graduate program, for his guidance and practical
advice in this work; Drs. Emmett Laursen, Donald R. Davis, Gerald
Matlock, Russell Gum and Jim DeCook, all members of the dissertation
committee, for reviewing the work and for their suggestions at various
stages of the work.
I would also like to thank the following heads of state agencies
in Ghana who provided assistance during the data-gathering phase of the
study: Mr. Nii Boi Ayibotele, head of the Water Resources Research Unit
(CSIR) in Ghana, for providing logistic support and advice; Mr. Sampson
Acheampong, head of the Hydrology Division of the Architectural and
Engineering Services Corporation, Ghana, for providing all the streamflow data, reports and advice, through our communications during the
period of study duration; Mr. Danquah of the Meteorological Services
Department of Ghana, for providing the rainfall and evaporation data;
Mr. Mensah, Senior Engineer of the Irrigation Department, Central Region,
for supplying information on the Nsuaem Project and other proposed irrigation projects in the Central Region; and Mr. Acquah and Mr. Gunaratnam,
iv
both of the Ghana Water and Sewage Corporation, for their discussions on
water resource developments in Ghana and advice. The staffs of these
agencies also deserve mention for their assistance during my visits to
them, especially those of the Water Resources Research Unit, with whom
I stayed during the entire period, for accepting me as one of them.
The graduate study program which culminated in this work would
not have been possible if the African-American Institute, New York, had
not provided financial assistance throughout my stay in the United
States. To Wilbur Jones and Heather Monroe, who were my program officers
for the duration of my stay, I am very grateful for the attention paid
to my problems, and wish that they continue their good work. To the
family of Dr. Ince, who was my host family, I am very grateful for their
kindness and encouragement. To Ernest Baafi, who provided computer programming assistance, and Erika Louie, who skillfully and patiently typed
the drafts and final copy of this work, I am grateful for their services.
Finally, to my family in Ghana who had to do without me in the
last year of stay in the United States, and to all those who in one way
or another contributed to the success of this study, I am grateful.
TABLE OF CONTENTS
LIST OF TABLES LIST OF ILLUSTRATIONS ABSTRACT CHAPTER
1.
Study Objectives
Motivation
The Importance of Hydrologic Data
1
3
4
7
8
11
16
19
20
Study Setting
Geography and Climate
Economy
Source of Data
Research Outline
2.
INTRODUCTION
STRATEGY FOR DECISION MAKING
Decision Making in Water Resources
Benefit-Cost Methodology
Cost-Effectiveness Methodology
Bayesian Decision Approach
The Strategy
Strategy Requirements
Strategy Components
Summary
21
22
23
27
29
31
32
33
41
42
42
44
45
51
56
57
3. HYDROLOGIC UNCERTAINTIES AND METHODOLOGY
Hydrologic Uncertainties
Natural Uncertainty
Data Acquisition Methods
Streamflow Synthesis Models
Informational Uncertainty
Bayesian Decision Analysis
vi
vii
TABLE OF CONTENTS, Continued
Page
Other Considerations
Economic Model
Summary
4.
THE STUDY PROJECT--THE AYENSU PROJECT
Historical Setting
Goals and Purposes
Decision Criteria
Cropping Pattern
Constraints
Water Constraint
Crop Constraints
Model Output
Project Alternatives
Alternative 1: The Existing Kwanyaku Reservoir
System Plus Power System
Alternative 2: Increased Kwanyaku Reservoir
Storage System
Alternative 3: Nsuaem-Kwanyaku System
Summary 5.
67
70
71
73
75
75
80
82
85
85
ALTERNATIVES' CAPABILITIES AND EVALUATION
102
102
107
110
116
119
126
128
129
134
141
148
148
151
156
88
88
101
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
Summary Conclusion
Recommendations
67
Design Objective
Release Computation
The Streamf low Model
Reservoir Releases
Simulation Procedure
The Bayesian Part
Worth of Transferred Data
Results
Simulation Results
Worth of Procedure
Power Addition Sensitivity Analysis
Alternative Selection
Summary 6.
62
64
66
159
159
164
165
viii
TABLE OF CONTENTS, Continued
Page
APPENDIX A: THE RESERVOIR OPERATION SIMULATION PROGRAM
"SIMUL" USERS GUIDE 167
APPENDIX B: CONVERSION FACTORS 195
REFERENCES 197
LIST OF TABLES
Table
4.1.
Page
Coefficients and constraints used in the linear
programming model 76
4.2.
Water supply for irrigation 78
4.3.
Parameters for computation of consumptive use 81
4.4.
Results of linear programming analysis
84
4.5.
Kwanyaku Water Work's Statistics
4.6.
Annual drafts from the Kwanyaku Reservoir 89
4.7.
Streamflow data recorded at Oketsew (cfs)
91
4.8.
Streamf low recorded at Swedru on Akora
4.9.
Recorded streamf low data at Nsuaem
4.10.
Oketsew data obtained by regression with Densu at Nsawam.
95
4.11.
Sources of streamflow data for correlation with data on
Ayensu at Oketsew 97
4.12.
Transferred data from Oketsew and Nsawam to Nsuaem
.
98
4.13.
The project features:
. .
99
5.1.
Monthly irrigation water requirements 118
5.2.
Parameters of the ARIMA models
131
5.3.
Cost and benefit parameters used in computation 133
5.4.
Economic parameters for the power system
135
5.5.
Expected net revenue from irrigation
5.6.
Cost statistics on establishing and maintaining a
stream gage in Ghana 87
92
94
Ayensu Irrigation Project
ix
137
142
X
LIST OF TABLES, Continued
Table
Page
5.7.
Expected net revenue from power
5.8.
The decision tableau for alternative selection
149
157
LIST OF ILLUSTRATIONS
Figure
1.1.
Page
Basin location (Ghana): location of Ayensu River
basin and project area 10
1.2.
Layout of Nsuaem Project
12
1.3.
Rainfall distribution in project area 1.4.
The Ayensu River Basin showing gaging stations
1.5.
Average rainfall distribution over Basin
2.1.
Sequences in strategy 34
2.2.
The decision tableau
40
3.1.
Adjusted range
3.2.
Confidence bands
4.1.
The Ayensu Project system 4.2.
Kwanyaku Reservoir characteristics
4.3.
Locations of Ayensu and Densu Basins
4.4.
Nsuaem Reservoir characteristics, Ayensu River
5.1.
Kolmogorov-Smirnov test 106
5.2
Plots of monthly streamflow series observed at Nsuaem .
111
5.3
The differenced series, Nsuaem on Ayensu River
113
5.4
Model identification
5.5
Flow chart for reservoir simulation 14
15
17
53
58
86
90
96
100
114
xi
120
xii
LIST OF ILLUSTRATIONS, Continued
Figure
Page
5.6.
Flow chart for operation rule 5.7.
Net benefit function for reservoir design (irrigation).
138
5.8.
Regression relationship between Nsuaem and Oketsew Data .
139
5.9.
Nsuaem Reservoir characteristics--extended
143
5.10.
Expected net benefit function from extended reservoir
characteristics 144
Standard deviation for irrigation net revenue
(10-year data set)
145
5.12.
Power plant capacity selection
150
5.13.
Effect of dam cost
5.14.
Effect of technological uncertainty 153
5.15.
Effect of deficiency penalty on irrigation benefits .
154
5.16.
Effect of worth of unit of water on irrigation
155
5.11.
124
152
ABSTRACT
Lack of adequate hydrologic information has been one of the major
reasons for postponement of many water resource developments in developing countries. Many of these decisions to postpone developments that
have been reviewed by the author have been found to be arbitrary and not
based on the extent of benefit that the additional information would contribute. Due to lack of understanding of the implications and natural
tendency towards risk aversion, the beneficiaries are deprived of goods
and services which the development would have produced.
In this dissertation a decision strategy which can guide decision
makers to determine if the additional information is essential, is
developed. The strategy is derived from the concepts of the three
currently used decision methodologies in water resources: namely, the
cost-effectiveness, benefit-cost and the Bayesian decision methodologies.
The concepts of these methodologies have been selected and combined for
their appropriateness to particular phases of the decision process.
Description of the analytical procedure in the use of the strategy is
given, and some analytical methods that can be used in the procedure
have also been suggested and discussed.
The applicability of the strategy is demonstrated by applying it
to a case study involving a decision that was taken to postpone a simple
irrigation project in Ghana. Three alternative plans for the irrigation
project were evaluated, based on selected decision criteria.
xiii
xiv
The results of the study indicated that the local hydrologic
factors in the project analyzed were not critical to the design decision,
and errors due to hydrologic uncertainties would be damped out in the
evaluation of the economic feasibility. The design decision proved to
be more sensitive to the economic and technological factors. The insensitivity of the design decision to the hydrologic factors was attributed
to a combination of climatic and topographical conditions existing in the
river basin.
Based on the results of the study, a rule was suggested to aid
decision makers to determine when a greater hydrologic base may be needed
for design and project viability decisions.
CHAPTER 1
INTRODUCTION
The purpose of developing water and related resources is to
improve the economic and social well-being (conditions) of a community.
In the planning of such developments, information on the water quantity,
quality and its distribution in time and space is needed to determine
their feasibility. However, in most cases in developing countries,
this information is either nonexistent or is limited. The developments,
if undertaken, are therefore based on a narrow data base, broad assumptions, empirical formulae or information transferred from similar
regions.
Although these are accepted procedures, and in many cases represent reasonable approaches, their adequacy for planning (and thus
decision making) is open to question. This is because there will be
some uncertainty on the outcome of the developments, and the implications on the area as a whole will not be known. Because of this uncertainty, developmenta are, in most case, postponed to collect more data.
It is generally accepted that more data is beneficial. But do
the increased benefits that result from additional data exceed those
lost due to the postponement of the development? How much more data is
adequate? Is the lack of adequate data a valid reason to postpone a
development project?
These are some of the questions which have faced many water
engineers all over the world. However, answers to these questions are
1
2
of more importance to developing countries than to the developed nations.
These developing countries, by their characteristics of having limited
financial resources, particularly foreign currency, limited skilled
labor, and scarce engineering personnel (Muiga and Reid, 1979), would
have to sacrifice a lot to obtain additional information. Apart from
the benefits foregone, they have to spend their scarce foreign currency
for importation of goods that would have been obtained from the project.
As it sometimes happens, the need for development may be so
urgent that the project has to be undertaken immediately. In such situations, engineers use the factor of safety as an insurance for the
uncertainties. But the question of how much safety factor is required
has been left to the judgment of the engineers who use their experience
in previous works as a guide. In some cases, the use of safety factors
may lead to conservative designs.
Also, because there is a scarcity of technical personnel, an
engineer is not only a planner and designer of projects, but also, if not
a decision maker himself, is at least an advisor to the decision maker.
Rarely does one find in the literature any studies which deal with all
of these stages in project development. The few attempts made so far
have emphasized some aspects of the project development process. For
instance, Chaemsaithong (1973) used the cost-effectiveness approach in
planning for the Mekong River projects. His emphasis was on the procedures in the methodology. In David and Duckstein's (1976), and Keeney
and Wood's (1977) work on the Tisza River Basin project in Hungary, the
emphasis was on illustration of the use of multiobjective decision-making
3
methods. Davis (1971), and Vicens, Rodriguez-Iturbe and Schaake (1974)
dealt with hydrologic uncertainties in project development and decisions
based on the effects of hydrologic data.
The need for a technique which combines all of the stages in
project development cannot be overemphasized because not only does it
serve as a guide for an engineer who finds himself in such a situation,
but it also shows the interconnection between the studies on the various phases in project development.
It is the purpose of this study, therefore, to develop a decision
strategy for water resources development which will incorporate all the
phases of project development. This study was planned with conditions
in rural communities of developing countries in mind; however, the
strategy, or parts of it, would be applicable elsewhere.
Study Objectives
A review of reports on some feasibility studies on water development projects in developing countries indicates that there is always
a recommendation for collection of more hydrologic data before the
design is undertaken. This recommendation does not necessarily come out
of evaluation of how much more benefit this additional data will add to
the project's original benefits, nor does it indicate how much more data
will be adequate. Therefore, the importance of the information on the
evaluation to decision making cannot be overlooked. This information
should be generated during the planning process. The objectives of this
study are, therefore:
4
1.
to develop a decision-making strategy for water resource
development in developing countries;
2.
to select methodologies for evaluation of the effects of hydrologic record length on the economic outcome of a project; and
3.
to use the strategy and methods selected to evaluate the decision
taken on a water resource development project in Ghana.
In satisfying these objectives, the emphasis will be on the
development and rationale of the decision strategy, and the evaluation
of the effect of inputs on a project's outcome. The analysis of the
decision on the Ghana project is used to illustrate the applicability of
the strategy.
Motivation
The term "developing country" has been used in the section above
without qualification. It is, therefore, appropriate at this stage to
define the term.
There is no general consensus on the definition of the term
"developing country." Unlike the developed countries, who possess a number of common characteristics by which they can be positively identified
(for example, industrialized production systems, relatively higher per
capita gross national product, relatively high adult literacy, high per
capita energy consumption, high per capita income, etc.), the developing
countries have diversified characteristics ranging from "undeveloped" to
"developed." Garcia (1971), for instance, defines a developing country
as a country whose annual per capita income is very low. The definition
5
is not applicable today because some of these countries which have been
described as "developing" may have a higher per capita income than the
developed ones. Two examples are Kuwait and Saudi Arabia.
However, there are some unique factors common to all of them by
which they can be identified. These are:
1.
A high proportion of population is involved in agriculture
(70-90 percent).
2.
Exports are mainly foodstuffs and raw materials (primary goods).
3.
Inadequate manpower resources, both in quality and quantity
(sometimes there is a lack of middle-class personnel).
4.
Inadequate infrastructure.
5. Dualism--existence of large metropolitan cities with modern civic
amenities on one hand, and poor, unhygienic and backward rural
areas on the other (Lemma, 1975).
Of these characteristics, the one which until recently was the
most neglected is "dualism," but it is the cause of many of the problems
in developing countries. Because of the disparity between urban and
rural areas, rural residents who are normally producers of the country's
foodstuffs and export goods, migrate to the cities to enjoy the amenities and better employment opportunities. The results of this migration
are: 1) production of food and export goods is reduced, i.e., the
country's foreign exchange earnings are reduced; 2) local currency and
foreign exchange is used for expansion of amenities in the urban areas
to meet the additional demands; 3) slums arise in the urban areas.
6
The problems caused by the rural-urban migration have caught
international attention. Donors of aid to developing countries are,
therefore, focusing their efforts on rural-level development (CortezComerer, 1977). In a recent address to the Board of Governors in
Nairobi, Kenya, Mr. Robert McNamara, President of the World Bank, called
for a worldwide reorganization of the development strategy which would
benefit the rural poor (Fisher, 1976). This call is receiving attention,
as exemplified by the efforts of agencies like the Food and Agriculture
Organization (FAO), United States Agency for International Development
(USAID), Canadian International Development Agency (CIDA), etc.
Some governments of the developing countries have realized that
without rural development there really can be no national development.
For instance, Julius Nyerere, President of Tanzania, is quoted as saying
"Others try to reach the moon, we try to reach the village" (CortezComerer, 1977, p. 66). The Ujamaa Project in Tanzania is an example of
the renewed efforts in rural community development.
The development of water resources is an essential prerequisite
for rural development. Besides being basic to the survival of human and
animal life, it is essential to the development of agriculture and
industry. The provision of good drinking water and sewage disposal
facilities would also promote good health and attract industries.
The planning of water resource development requires the use of
hydrologic information. However, because of lack of funds and personnel, and the general neglect of the rural areas, the collection of these
data might have been started only recently, or there may not be any data
7
at all for planning purposes. Sometimes decisions as to what to do when
faced with lack of or inadequacy of data in planning of development
projects are made intuitively, without considering their implications.
This research is addressed to the decision process in such undertakings.
It is hoped that this study will contribute to the efforts of those
engaged in developing the rural communities of developing countries.
The Importance of Hydrologic Data
The emphasis in this study will be on the effects of hydrologic
input on the project's outcome. It is, however, realized that water
resources development planning requires inputs of other variables like
economic, legal, social and political variables. This emphasis on
hydrology does not imply that the net returns from water resources projects are considered more sensitive to variations in hydrologic inputs.
On the contrary, James, Bower and Matalas (1969), testing for sensitiv-
ity of variables in the evaluation of the Potomac project, found that
the relative importance of the variables, in descending order, was:
1.
Economic development projection.
2.
Water quality objectives.
3.
Dissolved oxygen modeling.
4.
Hydrology
However, this does not detract from the importance of more hydrologic
information because even a small loss in net returns due to an error in
the hydrologic inputs can mean a considerable amount in terms of dollars;
for water resources projects typically involve large expenditures.
8
Hydrologic information is usually derived from hydrologic
data. The information is inversely related to the error of estimation of one or more hydrologic parameters. Nevertheless, the
engineer, planner or policy maker who is actually making decisions is
more interested in the integrated measure of the information--what impact
does the lack of hydrologic knowledge have on the decision? (Moss, 1978).
The integrated measure results from interaction of both hydrologic knowledge and the procedures that are used to incorporate the knowledge into
/
the decisions.
Hydrologic information is needed not only for planning and
design of water resources systems but also during their operation.
During planning, hydrologic information is needed to determine the
capabilities of various alternative solutions. In design, it is needed
to determine the size of components of the system, and during operation,
for the day-to-day decisions. Thus, it is obvious that hydrologic
information is indispensable in water resources project development.
In the remaining sections of this chapter, an introductory
description will be given of the Ayensu Project. This project was
postponed because it was felt that the planning and design were not
based on adequate hydrologic information. The project's rural setting
in a developing country will also be described.
Study Setting
The decision strategy to be developed will be used in evaluating
the decision taken on the proposed irrigation project in the Ayensu
9
River Basin in Ghana. The project, which was to be located in the
Central Region of Ghana, was to provide water supplies to irrigate a
27,000-acre area for food and cash crop production. The government, at
that time, was faced with increasing food imports and deplorable living
conditions in rural communities. This project, among others, was meant
to tackle these problems.
The feasibility study for the project was contracted to a
Japanese firm, Nippon Koei, who reported in 1967 that the project should
be given a priority over others because of its favorable location-between Accra and Cape Coast urban centers (Figure 1.1), and also because the soil and drainage conditions were favorable. However, this
report was based on only 8 months of streamflow data, collected at the
proposed reservoir site, and on data transferred from other areas.
Therefore, it was decided to collect more data to better assess the design before implementation. Ten more years of data have been collected
since the consultant's report. With the additional data, it is intended
here to evaluate the decision that was taken.
The selection of the Ayensu Project to illustrate this strategy
has been prompted by many reasons. Among them are the following:
1. Because of the project area's proximity to urban centers, the
rural-urban migration rate is high. This has led to some of the
villages registering negative growth in population (Census
Office, 1973). Economic activities are also dormant.
10
Figure 1.1. Basin Location (Ghana): Location of
Ayensu River Basin and Project Area.
11
2.
Since the consultant's report, the Ayensu Basin has become the
most densely gaged basin in Ghana. This report intends to
investigate the need for such a high-density network.
3.
The Ayensu River is one of the many rivers described in the Ghana
Water Year Book as a coastal river which flows across the
savanna areas of Southern Ghana. These savanna areas have been
underutilized because of their relatively semiarid conditions
(most farming in Ghana is rain-dependent).
It is hoped that results of this study might aid decisions on
implementation of developments along the other rivers in the savanna
zone.
Geography and Climate
The area earmarked for the irrigation project is located in the
southern portion of the Central Region near Winneba (Figure 1.1). As
shown in Figure 1.2 it stretches southward from the proposed dam site
near Nsuaem at its northern end to the junction of the Accra-Takoradi
and Winneba-Swedru roads, and then continues along the Accra-Takoradi
road to the left bank of the Brusheng River.
The area, which covers about 27,000 acres of savanna, is bounded
by a hill in the northwest end and declines with a modest slope towards
the Ayensu River in the east, and then towards the sea in the south.
In general, the topography varies from about level to gently-rolling.
Of the 27,000 acres, 12,000 acres have now been declared suitable for
the irrigation project (Aluja, 1977).
12
Figure 1.2. Layout of Nsuaem Project.
13
The climate in the project area is determined chiefly by movement
of the inter-tropical air mass which oscillates annually about the equator. Winds are generally southerly during the rainy season and northerly
during the dry season. Wind speeds are normally under 5 miles per hour;
however, thunderstorms with high gusts of wind are common. Clouds are
common except during the dry season, December to February. Temperatures
°
show only moderate variations, the daily temperatures varying from 15 C
°
°
to 37.6 C, with the mean around 26.6 C.
The area is generally humid with the relative humidity varying
from 65 percent in the mid-afternoon to 95 percent at night. The annual
rainfall is about 40 inches, most of this rain coming during the two
rainy seasons, April through mid-July and September through November.
The rest of the year is drier. The distribution of rainfall during the
year is shown in Figure 1.3.
The basin whose water resources will be used for this project
covers an area of 540 square miles, as measured at the proposed dam site
near Nsuaem. It is drained by the Ayensu River, along which there are
five gaging stations at Kofi Pare, Ayensuako, Oketsew, Nsuaem and
Okyereko. The Akora and Abuchen Rivers are the two principal tributaries, and they are gaged at Swedru and Asamankese, respectively. Most of
these gaging stations, shown in Figure 1.4, have been established only
recently.
The climatic conditions in the Basin are similar to that of the
project area. The Basin receives a slightly higher annual rainfall of
about 55 inches. Most of the rainfall is due to the orographic effect
14
MA MJJ AS ONDJ F
Months
Figure 1.3. Rainfall Distribution in Project Area.
15
Figure 1.4. The Ayensu River Basin Showing Gaging Stations.
16
caused by the Atewa Range (which rises to over 2,000 feet) along the
northern end of the Basin. The rainfall distribution over the year is
similar to that of the project area (Figure 1.5). The mean annual
evaporation rate, as measured near the existing reservoir at Kwanyaku,
is 55.2 inches.
Economy
The economy of the area is based on agriculture. However, its
description will not be complete without considering that of the whole
country since economic policies emanate from the central government. As
such, a brief description of the Ghana economy will be given to highlight
its similarities with those listed earlier for developing countries.
Much of the economic activity in Ghana is agricultural and rural.
Agriculture, broadly defined to include livestock, fishing and forestry,
accounts for more than 40 percent of the labor force, and accounts
annually for some 70 percent of total export earnings. One single crop,
cocoa, has had dominant influence on production, employment, foreign
exchange and government revenues. About three million acres of land are
currently under cocoa cultivation. Cocoa exports normally account for
60 percent of all export earnings.
Over the last decade and a half, the cocoa industry has declined,
due principally to low yield of trees because of old age, and the reduced
labor force on farms because of migration to the cities. During the same
period the population has been increasing at 2.7 percent per annum (population was estimated at 10 million in 1975). The reduced rate of growth
17
M A MjJ A S 0 N D J F
Months
Figure 1.5. Average Rainfall Distribution over Basin.
18
in output and high population growth rate have meant that the per capita
income has stagnated.
Until recently, when commercial farming of grains (notably rice
and industrial crops) began to be significant, farming was largely the
preserve of small-scale peasant farmers. Much peasant farming is traditional and for subsistence, so that no more than 50 percent of agricultural output enters the distribution system. In contrast to agriculture,
industry is dominated by modern enterprises. The structure of manufacturing activity, which was formerly dominated by wood products and basic
import substitutions, has turned to manufacture of consumer goods which
are highly dependent on imported inputs and equipment. In some cases,
as much as 80 percent of the raw material inputs come from outside the
country.
The failure of the economy to achieve sustainable growth during
the last decade and a half has been reflected in the increasing inability
of the economy to generate jobs. During this period investment was low,
and this, together with slow technical progress, has had an adverse
effect on employment opportunities.
Co-existent with urban unemployment has been a tendency for labor
shortages to develop in the agricultural sector. This has come about as
a result of rural-urban migration and low wages.
For the project area, apart from cocoa farming in the areas north
of Swedru, agricultural activities (including farming in other crops,
fishing and livestock raising) contribute only a small percentage to the
Basin's economy. The cocoa farms are found in the areas where annual
19
rainfall averages 60 inches and above. Agriculture in areas of less
rainfall has consisted mainly of cultivation of food crops for local
consumption like cassava and plantain. Sugar cane is the only cash crop
grown in the project area. Fishing is done only along the coast, principally in Winneba where there are presently over 400 fishing vessels
(the catch is about 40 tons per day). Large-scale livestock raising
has been recent, but potential for increase looks good. The Ministry
of Agriculture has established a cattle ranch and poultry farm at
Pomadze, with production of about 2,000 chicks per day for export and
local consumption. The government also intends to promote private
farming concerns when adequate water supply is available. Agriculture
provides employment for about 70 percent of the adult population, with
the rest holding government jobs.
Source of Data
The principal source of information for this study has been the
Hydrology Division of the State-owned Architectural and Engineering
Services Corporation (AESC). This division maintains and collects
streamflow data at the eight gaging stations within the Ayensu River
Basin. Data from the Densu Basin, which will be used in the study, was
also obtained from the same agency. Most of the stations in the Ayensu
Basin have been established within the last 12 years.
The meteorological data, mainly rainfall data, were obtained
from the Meteorological Services Department, also a Ghana Government
agency. Other information was obtained from reports on studies done by
foreign consulting firms for the Government of Ghana. The government's
20
water policy was deduced from the report on the government's Five-Year
Development Plan (1975-1980). Economic information was partly based on
the author's experience in the area and also on reports of committees
set up by the Ghana Government. In areas where the required data were
not available, data obtained in the United States have been modified for
use.
Research Outline
The research outline follows closely the sequence of the objectives as listed earlier. The next two chapters, i.e., Chapters 2 and 3,
will be devoted to the development of the decision-making methodology
and the theories underlying the methods which have been selected for
evaluating the effects of data inadequacy. Chapter 2 will be devoted
to review of the currently used decision methodologies and their combination to yield the technique to be used in this study. Chapter 3 will
cover discussion of methodologies that can be used in evaluation of the
effects of hydrologic information on the economic outcome of the project.
A brief discussion of various multiobjective decision-making methods
that can be used for project selection is also given.
Chapter 4 will take on the step-by-step approach of the strategy
for the project development, describing the goals of the project, measures of effectiveness, and alternatives considered. Chapter 5 takes
on the analysis of the effect of hydrologic uncertainties on the economic outcome of the project and also determines the capabilities of the
alternative plans. The evaluation of the decision on the Ayensu Project
is also discussed.
CHAPTER 2
STRATEGY FOR DECISION MAKING
The objective of this chapter is to develop a decision-making
strategy which can be used during the planning stage of water resource
development projects. Basically the strategy consists of a combination
of concepts of methodologies selected for their appropriateness to particular phases of the decision process. The major pcinciple underlying
this strategy is the adoption of concepts of already-proven methods
which are used as aids to decision making in water resources. This
approach has been selected because developing countries, by their characteristics, lack resources for research and development.
The term "adapt" rather than "copy" is used here because these
countries have resource endowments, cultural traditions and institutional
arrangements different from those countries where the methods were developed, and thus should use techniques that suit them.
The early sections of this chapter are used to discuss the currently used water resources decision-making methods and their deficiencies and relevance in the decision-making process. This is followed by
sections that describe the requirements which the strategy should meet.
The chapter is concluded with the listing and discussion of the various
steps in the strategy.
21
22
Decision Making in Water Resources
"Resource planning is ambivalent. We are told to look before we
leap, but we are also told that s(he) who hesitates is lost." These
words by Kaynor (1978, pg. 1302) amply describe the dilemma in which
resource planners often find themselves. This dilemma is caused by the
lack of information on which the planning is to be based.
In the case of most water resource development projects, substantial amounts of capital investment are involved, and undertakings
are usually irreversible if consequences prove undesirable. Thus, any
decisions taken should be based on sound, verifiable analysis.
The record of currently used methodologies in planning and
decision making in public utilities that are based on projected growth
and benefit-cost analysis, for example, does not look good. An example
is the airport capacity crisis in the United States, which has come
about as a result of the recent deregulation of air fares. Because of
cheaper fares caused by competition among airline companies, the number of air travelers has increased beyond the projected numbers.
It is not simply because these methodologies miss the mark, but
also because they fail to anticipate social changes which affect purposes
or goals. The meager information on which the planning is based introduces uncertainty--the unanticipated consequences which we known may
happen, but which we cannot predict with accuracy. Thus, the crux of
the planning issue is to find a means for handling uncertainty.
Many prescriptions have been suggested as a remedy for uncertainty. They range from feigning ignorance to elimination. Hirschman
23
(1967), for example, says that in some situations it is profitable to
ignore uncertainty, while Mack (1971) suggests that we can use it to our
advantage by building uncertainty into the planning process. All of
these prescriptions appear to have at least some theoretical merit
(Kaynor, 1978). However, reduction or elimination of uncertainty (if at
all possible) should not only be looked at from the point of view of
the pursuit of knowledge, but also in terms of benefits to be derived
in its application to development.
There are a number of decision-making approaches that are documented in the scientific literature. Those relevant to river basin
development include benefit-cost methodology (B-C), the cost-effeciveness
methodology (CEM), and the recent Bayesian decision theory (BDT). They
all have some deficiencies. In the following sections these approaches
will be reviewed and their deficiencies discussed. It is intended to
combine concepts of these methods in such a way that the deficiencies in
individual methods are catered for by the others. For historical
reasons, the benefit-cost methodology is discussed first and the Bayesian
decision methodology last.
Benefit-Cost Methodology
Benefit-cost methodology is widely used by governmental agencies
to determine the desirability of specific public works projects. In
general, the application of this technique indicates that a project
should be undertaken whenever benefits from a project (discounted at some
24
social rate of interest) is greater than the financial cost of the
project. Mathematically it takes the form:
B
R -
t
t = 1 (1 + i)
C
t
(2.1)
t
t = 1 (1 + i)
t
for the ratio, R; and for the difference, D:
TBC
t- t
D= E
t
t (1 + i)
where B
t
is the benefit at time t; C
(2.2)
t
is the cost at time t, which
includes the capital investment, operation and maintenance, and replacement; i is the discount rate; and T the economic life of the project.
The success or failure of this approach to policy issues and
decision making depends on the ability to correctly evaluate costs and
benefits. Since not all benefits or costs are easily quantifiable, the
rejection or approval of a project proposal could depend on how the
analyst interprets and quantifies those factors which are difficult to
quantify (the non-commensurate ones).
The use of benefit-cost analysis in public expenditures can be
traced back to the 1844 writings of J. Duprit in France. In the United
States, the Rivers and Harbors Act of 1902 stipulated that a board of
entineers report on the merits of river and harbor projects of the Army
Corps of Engineers. The reports were to include the amount of commerce
25
that would benefit with respect to the estimated cost. A later act
required a statement of local benefits to facilitate sharing of project
costs with local interests which would benefit from the project. Government participation in public projects was extended by the Flood
Control Act of 1936 which justified improvements to waterways for flood
control if the benefits to whomever they may accrue to are in excess of
the estimated costs. In the 1940s this principle was expanded to
justify other projects or programs for social welfare.
Despite its long history, there are still some problems to its
use. First there are the two most widely used criteria; namely, the
maximization of the benefit-cost ratio and maximization of net benefits.
These two criteria do not necessarily result in the selection of the
same project. Secondly, there are many fallacies in the use, some of
which are: 1) the single-criterion (economic) approach; 2) distribution
effects; and 3) the ratio fallacy.
In the real world, most, if not all problems, involve more than
one criterion; thus other criteria should be taken into consideration.
Also, as it often happens, the project's beneficial and negative effects
are seldom, if ever, spread over the population. In general, the
project's cost and negative effects are borne, at least in part, by
groups or areas different from those enjoying the benefits. An example
of this is the distribution of cost and benefits from Volta Lake in
Ghana. Volta Lake was created by the construction of the dam at
Akosombo. The resulting backwater stretches over 250 miles in length
and 50 miles at the widest part. The creation of the lake displaced
26
about 80,000 people, and villages which were originally far from the
river are now within the flood plains of the lake. These villages are
now periodically subjected to flooding, and their normally drinkable
streams have been fouled by waters from the lake. Malaria and other
water-borne diseases are common in these areas.
Whereas these villages lack good drinking water and electricity,
the hydropower generated and treated water from the lake are supplied to
inhabitants in urban areas like Accra and Tema which are 66 miles downstream from the dam.
Finally, the use of the ratio criterion tends to hide the magnitude of both cost and benefit.
In spite of the fallacies and criteria selection problem, the
methodology serves a useful purpose in many situations. Some advantages
in its use include: 1) the computational ease which it affords; and
2) it is considered to be devoid of human judgment at the final
decision stage. The latter is sometimes contested because even though
the final selection is devoid of human judgment once the criterion has
been selected, the prejudgment analysis is not. Further discussion of
the subject can be found in Kazanowski (1968), Howe (1971), Kneese
(1970), Hatry (1970), and Chaemsaithong (1973). The inability to
quantify all costs and benefits for decisions to reflect not only the
economics but other factors as well, set researchers looking for suitable methods. The cost-effectiveness methodology was one of the
results.
27
Cost-Effectiveness Methodology
The cost effectiveness methodology thrives on the deficiencies
-
of the benefit-cost methodology. Kazanowski (1972, P. 772)
describes it as possessing both "visceral and intellectual appeal."
Basically, it seeks to find significant differences in the costs or
resource requirements among the available alternatives for effecting
one or more goals, while also examining the benefical effects (English,
1968).
The history of the methodology can be traced to its use in
military and manned-space programs in the 1960s (Kazanowski, 1968;
Chaemsaithong, 1973). Since then, it has been used in almost every
field whenever planning is considered. Its use in water resources
began with de Neufville (1970) when he used it in the study of New
York City's water supply system. This was followed by a barrage of
literature based on this methodology. Only a few can be mentioned here.
Drobny, Qasim and Valentine (1970) used it in deciding which
waste water treatment and disposal alternative best served servicemen
in camps. They used the weighting method for the decision analyses.
de Neufville, Schaake and Stafford (1971) followed, on the New York
water supply with discussions by D. V. Smith (1972) and Duckstein and
Kisiel (1972); and Chaemsaithong (1973) used it for the multiobjective
planning for the Mekong River Basin in Thailand. Finally, the United
States Water Resources Council (1973) adopted the concepts in its
principles and standards for planning water and related land resources
so it became the basis for planning.
28
All of these users either followed the steps sugtested by
Kazanowski (1968) or modified them to suit their problems. The steps
proposed by Kazanowski are:
1.
Define the desired goals, objectives, or purposes that the
project is to fulfill.
2.
Translate the goals or objectives into sets of engineering,
economic, social, and environmental specifications.
3.
Establish project evaluation criteria or measures of effectiveness that relate project capabilities to the specifications.
4.
Consider if systems are to be designed on fixed cost or fixed
effectiveness.
5.
Develop alternative systems for the project.
6.
Determine the capabilities of the alternative system in terms of
the means of effectiveness.
7.
Generate an array of alternative systems versus measures of
effectiveness.
8.
Analyze the merits of systems by ranking the measures of
effectiveness.
9.
10.
Perform a sensitivity analysis on all of the above steps.
Document the hypotheses, rational model choice, data sources,
and analysis underlying the nine steps above.
Like the benefit-cost methodology, this approach is not faultless. Repeated application of the standardized approach has revealed
some difficulties in its application. These difficulties include:
29
1.
Fuzzy definitions of goals, especially those of societal
implications.
2.
The subjective nature of alternative selections.
3.
Uncertainties surrounding the input data.
4.
Problems of ranking or weighting alternatives.
Current studies in decision making in water resources seem to
view the uncertainty deficiency in the cost-effectiveness methodology as
the most important. This explains the mushrooming of literature in this
area in recent years.
Bayesian Decision Approach
Of the three decision approaches, the Bayesian decision methodology is the most recent. Jacobi (1975) credits Davis (1971) as being
the first to use it in hydrology. Davis used it to determine the worth
of additional data in a bridge design. Hitherto, the principle had been
used by others including McGilchrist, Chapman and Woodyer (1970), and
Shane and Gaver (1970). They used it, but in a different context, to
account for uncertainties for improved model parameter estimates.
Since Davis work, others have used his approach in various water
resource problems. To name a few of them, Jacobi and Richardson (1974)
and Duckstein, Szidarovszky and Yakowitz (1976) have used it to determine
the dead storage in the design of a reservoir subject to sedimentation;
Musy and Duckstein (1976) have used it for the tile drain designs in
irrigation; O'Hayre and Dowd (1978) used it to evaluate the impact of land
use and water resource management decisions on lake eutrophication; and
30
Lane, Davis and Nnaji (1978) used it to decide whether or not to continue
data collection in some experimental watersheds.
Basically, the Bayesian decision approach deals with risks and
uncertainties involved in decision making. Decision theory distinguishes
three kinds of decisions:
1.
Decision under certainty, which deals with decision problems
where there is a known deterministic connection between the acts
and outcomes because the variables involved are known with
certainty.
2.
Decision under risk--where the outcomes are not known with
certainty, but there is information available for their expression in a probabilistic manner.
3. Decision under uncertainty--where there is no deterministic
connection between acts and outcomes, and there is no data, or
the data available are unreliable to express the outcomes
probabilistically.
It is difficult to imagine situations in water resources in which
the decision maker has no information or any means to obtain them.
However, there are situations in which the decision maker does not have
precise knowledge of the probability distribution of possible outcomes.
English (1977, p. 16), describes the Bayesian approach as
the methodology that deals with conducting experiments designed
to collect, at least partial, information about the likelihood
of various outcomes and use that information in combination with
whatever prior information is available to generate probability
distributions for the outcomes . . . . With this new information
the decision is treated as one of decision-making under risk.
31
The Bayesian decision approach, like the others, has some faults.
First, it is used for single-objective problems. Secondly, it depends
on the ability of the analyst to quantify all variables involved.
Thirdly, it is predicated on the acceptability of the expected value
viewpoint in decision making. And finally, it requires multiple integrations with every source of uncertainty, thus adding a new dimension
to the problem and, therefore, increased cost for computation.
The fallacies and limitations of the methodologies listed above
indicate that no single methodology is good enough for decision making
which accounts for all factors. Thus the need for a technique that
overcomes some of these known limitations and fallacies is urgent.
The Strategy
The review of current usable methodologies above sets the stage
for the development of the strategy to be used in this study. It was
concluded in the last section that no single methodology will provide a
"faultless" methodology. Therefore, combination of the concepts of the
methodologies, selected for their appropriateness to particular phases
of the decision process, may be preferable. This is what this strategy
will attempt to do. In effect, the strategy will be a decision-making
methodology developed by adapting cost-effectiveness, benefit-cost and
Bayesian concepts to the needs and requirements of planning water
resource development in developing countries.
32
Strategy Requirements
Decisions which deal with the selection of a course of action or
with problems of "what to do?" are decisions about systems. These decisions are normally concerned with the planning, development, design, and
implementation of systems. In this study, the principal concern is the
decision making during the planning stage, which involves identifying,
describing, and producing an optimal system. Since planning is the first
stage in all development efforts, it is important that the right decision
be made at the stage.
In decision making, one is considering several ways to achieve
some desired results. The decision is normally based on what one
believes about the decision elements: namely, the alternatives, the
design variables, the outcome of the decision, and the desirability of
the outcomes. The belief, in turn, depends on the information available,
either through one's past experience, current analysis or communication
with other more-or-less knowledgeable people. At the time of the decision, it can only be based on information available. Since there may
not be sufficient information, the information used may include, in
various degrees and combinations, "explicit, hard, objective and quantitative data, and implicit, intuitive, subjective responses to gut
feelings" (Lifson, 1972, p. 19).
The sequence of activities which generate the information needed
for the decision is what is termed the "decision process." The input to
the decision process is information concerning the needs, resources, and
environments. The strategy developed here will, therefore, consist of
33
the identification of the stages in the decision process using the water
resource planning methods discussed above such that the right information
is generated to make the decision possible. The strategy should be such
that the decision resulting from it would be rational--i.e., expected to
yield the greatest degree of achievement of desired results. The other
requirement of this strategy would be its general applicability.
Rationality implies consistency in the processing of the information, realism in the models that are used to represent real-world
systems, and manageability of the resource available. Manageability
involves the general state of technology as well as the available
resource, at the time a decision is to be made. No attempt is made here
to develop a means to test for these requirements; however, it is
advised that users keep those in mind.
Strategy Components
From the point of view of this dissertation, a decision strategy
is a guide which defines the specific steps to be followed in order to
arrive at a good decision. The steps of the strategy, which have been
condensed from those of the cost-effectiveness methodology, include:
1.
Definition of the problem and selection of objectives for the
problem solution.
2.
Definition of decision criteria for alternative solutions.
3.
Proposition of alternative solutions.
4.
Analysis and evaluation--data requirements.
5. Selection of the best solution.
(Figure 2.1 shows the sequence and decisions at various steps.)
34
Problem Definition
and
Objective Selection
Decision Criteria
Effectiveness Cost (Benefits)
Schedule
1
Alternatives Proposition
Analysis and Evaluation
Decision Variable Selection
Information Analysis
and/or Gathering
I
Design Analysis, Decision
Function (Benefit-Cost)
Evaluation of Inputs-Hydrologic, Economic,
Technologic (uncertainty
analysis by Bayesian method)
Favorable
ir
Alternative Selection
End
Figure 2.1. Sequences in Strategy.
35
Specifically, the strategy will help guide the planning of the
resource development by assisting the decision maker(s) in answering such
interrelated questions as:
1.
Are the data available adequate for the planning?
2.
What should be done if the data is inadequate?
3.
What is the best alternative solution?
4.
What will be the effect of the development on the people?
Certainly not all of these questions will be answered to every-
body's satisfaction by the research effort reported here. In many cases
the research represents a preliminary analysis which can be further
studied and improved upon.
In the following sections, each of the steps listed above will
be discussed.
Step 1: Problem Definition and Selection of Objectives. A
project development is used as a means of achieving some set of human
needs and/or desires. As a first step of the strategy, it is expected
that these needs and desires be spelled out, and objectives to achieve
them be selected. In the case of rural communities in developing countries, the problem is lack of necessities for promotion of quality of
life. This may be translated into the following objectives:
1.
Economic efficiency (maximization of returns on investment).
2.
Distribution of newly-created income, say, by provision of
employment.
36
3. Fulfillment of social objectives, which may not be justified
on
economic grounds, but are deemed necessary and worthwhile by the
decision makers.
Not only should the statement of the problem be clear, but also
the objectives selected should be such that, if achieved, the problem
would be solved.
Step 2: Decision Criteria. To select the best solution to the
problem, there should be some criteria by which to make the choice.
Decision criteria, sometimes referred to as measures of effectiveness,
represent the relative achievement of objectives and provide the basis
of evaluating alternatives. They can be described as attributes which
represent fulfillment of needs and objectives. To satisfy the rationality requirement and reduce bias in the selection of alternatives, the
decision criteria should be specified early in the decision process.
In general there are three classes of criteria, namely:
1.
Effectiveness (benefit) criteria representing measures of needs
fulfillment.
2.
Resource criteria representing costs associated with levels of
effectiveness.
3. And sometimes the schedule criteria representing the time when
the system is to be required.
For example, in the Ayensu Project, the readily identifiable effectiveness criteria are net benefit from water available for irrigation, power
generated, and recreational facilities created. The cost criteria will
37
be the capital investment, land used and land inundated, and health
problems introduced. The only schedule criterion is the time of implementation.
From the above example, it is realized that the criteria can be
either quantitatively or qualitatively defined. To facilitate the selection of the best alternative plan, their relative importance to achievement of project objectives must also be specified.
Step 3: Proposition of Solutions. The third step of the
strategy is the proposition of alternative solutions for attainment of
objectives. This step is the most creative part of the strategy. It
is the formulation of plans representing a candidate solution.
It is realized that it is impossible to identify, describe, and
analyze the universe of all possible alternative solutions for the
attainment of objectives; however, attempts should be made to select
feasible and attractive alternatives.
In judging the feasibility of the selected alternatives, some of
the criteria proposed by Znotinas and Hipel (1979) can be used as a
guide:
1.
Economic feasibility (i.e., what are the capital costs?)
2.
Performance (does the project meet the objectives originally
defined?)
3. Technical feasibility (i.e., can the engineering aspects of the
alternative be fulfilled at reasonable cost and with the available resources?)
38
4. Social impacts (i.e., how will the alternative affect intended
and non-intended consumers?)
Each alternative plan should be able to stand on its own (i.e.,
not be dominated by others in the above criteria), or combinations of
some of them could be considered as separate. The alternatives must also
be acceptable to the set of criteria selected.
Sept 4: Analysis and Evaluation. After selection of the nondominated and feasible alternatives, analyses are performed in order to
obtain estimates of how each candidate solution will perform with respect
to the criteria and the constraints imposed by available resources.
Analysis involves exercising symbolic models to obtain estimates of the
systems' effectiveness, cost and schedule criteria. Evaluation, on the
other hand, involves the determination of the various inputs on the
systems' outcome(s).
This step in the strategy is very important, because it is at
this stage of the planning process that the effects of the available data
are analyzed and the decision to carry on with the project is taken.
The analytical and evaluation procedure consists of the following
steps:
1.
Identify the decision variables.
2.
Identify data and/or identify data acquisition methods for the
input variables.
3. Develop the decision function using the decision variables and
a decision criterion.
39
4.
Perform risk analysis over the decision function.
5.
Make a decision to either go on with the project
or collect more
information.
Since all variables involved in the design process are quantifiable, a decision methodology which has this characteristic will be
needed. This is where the benefit-cost methodology comes in. It is
used to select the decision variables that give the optimum benefits.
Since the data on the input variables are scanty, there will be
some uncertainty concerning the outcomes. The Bayesian decision methodology is used to evaluate the effect of the hydrologic uncertainty on
the project decision as to whether to go on with the planning process or
postpone because of inadequate data. The Bayesian approach not only
enables the quantification of degree of uncertainty, but also how long
to postpone the project for data collection, if it is necessary (Jacobi,
1975). If a favorable answer results from the evaluation procedure,
then the capabilities are displayed in the decision tableau (Figure 2.2).
Step 5: Alternative Selection. The decision tableau gives a
pictorial comparison of the capabilities and/or incapabilities of the
alternatives to aid the selection of the best alternative plan. Whereas
analysis and evaluation steps consist of rather mechanical processes in
the sense that the analyst follows already-tested procedures, the consideration of societal and environmental effects involved in selection
make it a matter of judgment and of value. The selection process
involves answering questions such as:
40
Criteria
C1
C2
..
..
..
..
al
Y 11
Y 12
Y 13
..
..
..
a2
Y 21
Alternative
..
"
a3
..
..
..
"
..
..
ak
Y ki
Y 44
..
..
..
..
..
..
3'k2
...
...
...
- an alternative plan
ci -
Yli
a decision criterion
y.-an outcome associated with c i for alternative a
ki
Figure 2.2. The Decision Tableau.
...
Yki
41
1.
Which alternative plan is the best solution to the problem?
2.
Is the best alternative good enough to justify the resource
investments involved? If not, should the development be dropped?
In the selection process, value judgments are applied to the
objectively deduced measures of effectiveness that were obtained as
results of the analysis. While many of the project outcomes will have
a specific market price, for some of the societal and environmental outcomes the assignment of monetary value will reflect subjective estimates of values. Much of the selection process, therefore, will center
on the definition of the relative utilities of the costs, benefits and
societal and environmental impacts of the various alternatives for the
basin development project.
Summary
It is observed that the steps of the strategy developed resemble
those of the cost-effectiveness methodology. However, the decision on
the effect of data inadequacy was performed using the combination of the
other two decision methods--benefit-cost and Bayesian decision. The
blending of these three decision methods has afforded the development
of this practical and useful methodology.
The practicality of the strategy will be tested on the evaluation of the decision taken on the proposed Ayensu project in Ghana.
Before that, the theoretical background of some of the methods to be
used will be given.
CHAPTER 3
HYDROLOGIC UNCERTAINTIES AND METHODOLOGY
The previous chapter reviewed the various decision methodologies
and developed a strategy for the decision-making process that will be
used in this study. This covered the first objective of the study.
This chapter deals mainly with the treatment of the second objective; namely, the evaluation of the effect of hydrologic information on
the economic outcome of the project. It will consist of a review of the
methods to be used for analyzing hydrologic uncertainty that is introduced by scanty information.
Hydrologic Uncertainties
There are two hypotheses in classification of uncertainty in
hydrology. The first considers all the uncertainties to be informational. Proponents of this hypothesis contend that if data on all
variables affecting a natural phenomenon are available, it will be possible to predict with certainty the future events involving that phenomenon. This hypothesis has not gained much support yet, because, to date,
it has not been possible to obtain adequate data on, even, the alreadyidentified variables.
The other hypothesis does not totally reject the lack of information as the main cause of uncertainty. However, it contends that it
is impossible to obtain information on all the variables involved, and
42
43
therefore probabilistic estimates should be used. It classifies the
hydrologic uncertainty into two categories: 1) natural uncertainty
caused by lack of control over the natural phenomena--the stochastic
property; and 2) the informational uncertainty due to lack of information on these phenomena.
The natural uncertainty is due to the many uncontrollable
effects and factors governing natural phenomenon. Thus, the realization
of a given natural event cannot be predicted in a deterministic way. An
example is the hydrological phenomenon of runoff. The magnitude of runoff depends on precipitation and the state of the drainage basin. These
two factors are highly random. The form, amount, and intensity of distribution of precipitation depend on a large number of meteorological
processes which are not yet susceptible to long-range forecasting. The
state of the drainage basin also changes, both in time and space. As a
consequence, the number of possible combination of events of precipitation and state of the basin which result in an unpredictable runoff event
are almost infinite.
In water resource planning, attempts are always made to predict
the magnitudes of these natural phenomenon for design of projects.
These attempts, more often than not, lead to development of a model, or
to selecting one of the familiar models to represent the process. However, there is seldom enough information available to select the correct
model. This introduces the other aspect of uncertainty--information
uncertainty.
44
There are two major types of this uncertainty. The first type
results when an incorrect representation of a fundamental process is
used. This is typified by use of an incorrect theoretical probability
distribution to describe the phenomenon. It is termed "model uncertainty." The second type, termed "sampling uncertainty," results when
the model of the basic process is known to be correct but the parameters
are not known with certainty because the data from which they are estimated may be scanty or unavailable.
If a wrong model is selected to predict the magnitudes of these
processes, decisions based on these magnitudes will be in error. Similarly, if the model is assumed correct but the parameter estimates are
in error, the resulting decision may also be wrong. Thus, the uncertainties introduced by incorrect selection of model and incorrect estimation of parameters are crucial to correct decision making.
It is generally accepted that there will always be a degree of
uncertainty in decision making, no matter how much we increase our knowledge and as long as perfect information is elusive. However, attempts
to deal with it are useful. The following sections, to be based on the
second hypothesis, will review some of the uncertainty reduction attempts
made so far and the theories behind them. This is done with the view of
adapting some of them for use in this study.
Natural Uncertainty
Until the beginning of this decade, natural uncertainty was the
only concern of researchers. However, to date, there is only one known
approach to reduce it; i.e., by obtaining more data. This additional
45
data may be obtained by: 1) postponing the intended project to collect
the data; 2) transfer of data from other basins with a longer record;
3) by creating the additional data--by relating the variable of concern
to other variables which affect the natural phenomenon; or 4) deducing
them from experience in the region.
There are other methods which, even though they do not reduce
natural uncertainty, make the analyst aware of the uncertainty. These
methods, generally termed synthetic data generation methods, utilize
the existing data to create other possible data which have characteristics similar to the original data. It is sometimes assumed that the
mean of the outcomes resulting from the use of these data series is
better than that from the original data, thus reducing the uncertainty.
This may not always be true; rather, the outcomes of the use of these
various possible sequences can help the analyst make a better decision.
In the following sections the methods currently in use for data
acquisition without postponing analysis, and synthetic data generation,
are discussed. The two approaches can be used, depending on the situation, either conjunctively or separately.
Data Acquisition Methods
There are three methods currently in use by engineers to acquire
more data. These are:
1.
the regional estimation technique;
2.
the statistical augmentation procedure; and
3. the engineer's experience.
46
The first two methods utilize regression analysis while the last one
utilizes the engineer's expertise, accumulated over the years of
his/her
study of various drainage basins.
Regional Estimation Technique. The regional estimation technique
uses the regression approach, involving the physiographical and meteorological characteristics such as basin area, slope, rainfall, vegetation
cover, drainage density and others. The regression method predicts values of the dependent variable (streamflow) from a linear equation of
independent variables (area, slope, rainfall, etc.). The set of coefficients of the linear equation is chosen so as to minimize the squared
difference between predicted and observed values.
A typical multiple regression model is the form:
y = b + E b. X.
o
•
1
1
(3.1)
where
y = the dependent variable
X.=the independent variable, i - 1, 2
b
o
= a constant
b,=the coefficient of the independent variable
n = the number of independent variables
Generally there are errors which will be normally distributed
due to the Central Limit theorem; but the assumption is not required in
order to perform the regression.
47
According to Ince (1974), the physiographic and meteorological
characteristics which affect annual streamflow in typical regions
include:
1.
basin area, A;
2.
vegetal cover, V;
3.
basin slope, S;
4.
drainage density, D; and
5. precipitation, P.
The effect of these characteristics upon the mean or variance of
the annual streamf low may occur in an additive manner or a multiplicative
manner. The former leads to the linear regression of the form:
y = b. + b A + b V + b S + b D + b P
i 2
3
4
5
6
(3.2)
and the latter to:
b b b b p
2 3 4 5 6
y =b AVSDP
1
(3.3)
which, on taking its logarithm, transforms to the linear form:
log Y = b1 + b 2 log A = b 3 Log V+ b
b
6
4
log S + b
5
log D+
log P
where the b's are the regression coefficients. There are computer
subroutines for the determination of these coefficients.
(3.4)
48
There are several well-known tests that are usually used to
evaluate these equations to select which one best describes the phenomenon. The tests include the t and F statistics and the R 2 (the correlation coefficient). The t statistic measures the probability that a
single regression coefficient could be at its observed level simply by
chance. Hence, the statement of 0.01 significance for a coefficient
means that such a value would occur because of sampling variability in
only 1 out of 100 cases. The F statistic is similar to the t, but it
measures the significance of all the coefficients in the equation simultaneously. The R
2
statistic indicates the explanatory power of the right-
hand variables in a regression. It ranges from 0 to 1. An R2 of 0.90
indicates that the right-hand variables explain 90 percent of the variability of the left-hand, or dependent variable.
Also, the independent variables which affect the dependent
variable can be selected by using the backward elimination procedure
(Draper and Smith, 1966). The procedure is a statistical technique that
eliminates variables, one by one, according to their statistical significance in explaining variation in the independent variable. The procedure continues to eliminate variables until those that are significant
at a predetermined level remain in the analysis. The significance level
that is traditionally used--and the one to be used in this study, if
necessary--is the 5-percent level.
Statistical Augmentation. The statistical augmentation approach
utilizes a relation among concurrent observations of a short and a long
sequence which corresponds to the observed events on the non-concurrent
portion of the long sequence. In this manner the short sequence is
49
lengthened and parameters can be estimated for use. Whether or not the
reliability of these estimates is greater than that of estimates of the
parameters based only on the observation, depends mainly upon the
strength of the relation between the concurrent observations for the
short and long sequences. Clarke (1973) gives the criterion for
increased reliability of the mean of the lengthened sequence as:
1
(n
1
- 2)
(3.5)
1/2
where p is the correlation coefficient of the lengthened sequence, and
n
1
is the length of the concurrent (short) sequence. For the variance,
Rosenblatt (1959) showed that the correlation coefficient must exceed
0.8 to prove that the new estimates have improved reliability.
Clarke gives the mean and variance, respectively, of the lengthened sequence as:
n
e
— s e /1 - 2
p
y 2
(3.6)
n + n
2
1
n1
— 2
1
(.- —)
E
s -
(Y - 17 ) +
Y[E 2 ]
y n l + n2 - 1 i=1 1j=n +1 Yj
1
(3.7)
2
—
—
2n
x ) +
b( x
--- Y +
Y
—
—
1 n
1
+ n
2
2
1
n
1
+ n
2
e
and
2
where
1
1
—
E (x. - x 1 )
y. (x . - x )/(
b = E 1
i=1
i=1
(3.8)
50
n
1
1
x =— E
1
1 i=1
X.
1
(3.9)
x denotes the longer sequence of length n , and y the shorter sequence
2
S
2
1
=
(n - 1)
Y 1
1
(Y 1 -
)
2
(3.10)
e. is a random normal variable with zero mean and unit variance.
O is introduced to facilitate comparisons of the case when noise is added
with the case when noise is not added. If e = 1, it means noise is
added; if noise is not added e
0. The term s e
y 2
- p
2
represents
noise.
n +n
1 2
1
e = — E
e.
2
n n +1
D
2 1
(3.11)
Matalas and Jacobs (1964) give the derivation of these equations. Other
statistical procedures for various objectives including that of Young,
Orlob and Roesner (1970) which can be used for filling missing gaps in
records, have also been published. Liongson (1976) gives details of
some of these procedures.
Engineer's Experience. The third (and the least used, except
when the other methods do not help) is the use of the engineer's experience. Engineers often use their engineering judgment to obtain
insights and assessments to parameters which are not readily obtained
by other means. This judgment may be used with a simple model to obtain
51
needed information. One instance in water resources planning where this
is used is given as follows:
The rainfall and runoff processes may be related by a simple
equation:
q = (1 - a) P
(3.12)
where
q = runoff amount
p = total rainfall
a = percentage of the rain which did not appear as runoff (lost)
Since there are almost always rainfall data available, and if
this model is suitable for the particular basin, then with the estimation of the loss fraction, a, an estimate of the runoff can be made. A
possible source of this estimate is the engineer's considerable expe-
ience over many years of studying river basins and analyzing their data.
In this case the engineer will be called upon to estimate loss fraction.
Streamflow Synthesis Models
The other technique for dealing with the inherent or natural
uncertainty in the use of a short hydrologic record is the synthetic
data generation method. This technique was first used by Thomas and
Feiring (1962). Unlike the augmentation procedures, it does not create
any new information but uses the statistical parameters of the available
data to generate some possible sequences. This allows the analyst to
52
appraise possible outcomes of a project at the planning stage. Duckstein
and Davis (1976, p. 11) describe this approach as: "a way of fully
utilizing the existing information in a statistically more sophisticated
manner to account for the natural uncertainty inherent in streamf low
process . . . .
It
The streamflow generation models commonly used at present are of
the short-memory type, i.e., models which do not exhibit long-term persistence. (Persistence is caused by the dependence of naturally occurring time series as exhibited in their serial correlation structure.)
The short-memory models are differentiated from the long-memory type by
the exponent in the Hurst relation of rescaled adjusted range, RN , to
the size of sample, N, given by:
R = (N/2)
N
K
(3.13)
The illustration shown in Figure 3.1 defines the variables. K is the
Hurst coefficient, and S
K
the storage capacity.
If the value of K is 0.5, which is the limiting value, the model
is said to have short memory. On the other hand, if it is greater than
0.73 it is described as having long memory. The discrepancy between
these two values is what is generally termed as the Hurst phenomenon.
The higher value, according to Hurst (1951), is due to persistence--the
tendency for high values to be followed by high values and low values
by low values.
A long-memory model known as the Fractional Gaussian Noise (FGN),
proposed by Mandelbrot (1971), was developed to explain the Hurst
53
R*
N
Figure 3.1. Adjusted Range.
54
phenomenon. However, it has not been used much in practice because of
its complexity; and also it is more expensive to operate than the shortmemory type. A conclusion reached by McLeod and Hipel (1978) in a study
of six different rivers concerning the choice of a generating model is
that, in many practical situations it may be unnecessary to employ the
FGN model in order to preserve the Hurst phenomenon. This is because
some short-memory models, particularly the Box and Jenkins (1970) autoregressive and moving average model (ARMA) preserves this characteristic.
With this background, the rest of the discussion on this topic will
be devoted to the ARIMA models.
ARIMA Models. Box and Jenkins (1970) describe a family of linear
stochastic models. These models are collectively referred to as the BoxJenkins models. However, if the process is stationary, the label
"autoregressive moving average" (ARMA) is employed. If differencing is
required to eliminate non-stationarity, the process is called an "autoregressive integrated moving average (ARIMA) model.
The general ARIMA model of order (p, d, p) is defined as:
d
(1)(B)(1-B) X
t
= 6(B)Z t
where
(1)(B) = 1 + 1;1) 1 B + . . . + (1) BP ;
e(B) -
1
- e,
B- . .. - 8 B q -
(3.14)
55
d, the order of differencing; Zt , the random process with mean zero and
2
variable CT , and:
6
BKX
t
= X
(3.15)
t-K
inwhichBisbackwardoperator.e.and (P k are the parameters of the
moving average and autoregressive processes, respectively.
To determine the correct model for a particular time series, it
is recommended to adhere to the identification, estimation and diagnostic
check stages of model development (Box and Jenkins, 1970; Box and Tiao,
1973; Hipel, McLeod and Lennox, 1977).
In the typical ARIMA modeling application, it is preferable that
there be a minimum of about 50 data points in order to get a reasonably
accurate maximum likelihood estimate for the parameters (Hipel et al.,
1977). Non-seasonal (annual) records of this length are hard to find in
developing countries. However, on a monthly basis the minimum data
requirement can be met, and seasonal effects can also be analyzed.
To cope with seasonality, the operator B in Equation 3.14 is
replaced by B s in order for the model to represent the same sub-series.
The seasonal model is therefore:
43, (B s ) v Dsyt(B s ) zt
D is the order of differencing.
(3.16)
56
Vy
t
= y
t
- y
t-1
= (1-B)
(3.17)
Yt
The error components Z
t themselves may be correlated; i.e., the
flow this month may depend on last month's flow. To allow for this
dependence, an error model of the form:
O(B)V d Z
t = O(B)Πt
(3.18)
is assumed, where now the sequence ia 1 is one of normally independent
t
distribution and 0(B) and
e(B) are polynomials of degree p and q,
respectively, in the operator B.
Subsituting for Z t in the equation (3.16) yields what Box and
Jenkins term the general multiplicative model:
cP(B)(1)(B 5 )V d V
s
DX
t
= 003)803)a t
(3.19)
of the order (p, d, q) x (P, D, Q) s
Informational Uncertainty
Over the last two decades, research efforts have produced techniques that deal explicitly with the problem of uncertainties present
in the design and planning of water resource projects. These successful
efforts have, until recently, mainly focused on the natural uncertainty
aspect of the whole range of uncertainties present in hydrologic problems. However, with the transfer of theories from other fields to
hydrology, the other aspects of the uncertainties are receiving increased
attention.
57
Information uncertainty, referred to in some literature as
sample uncertainty (Davis, Kisiel and Duckstein, 1972), is the uncertainty due to the shortness of data record from which the model parameters were estimated. For a long time engineers have been accounting
for this uncertainty by use of factors of safety, which is defined as a
measure of the resistance of a project over the loading. However, due
to the ever-increasing costs of construction, designing projects over
their loading may be uneconomical.
There are two procedures to deal with sample uncertainty: 1) by
use of confidence bands; and 2) by Bayesian decision theory. The former
approach recognizes that it is unrealistic, due to the sample uncertainty,
to specify a particular value as a true value. Rather, it estimates
bounds of this value based on some confidence limit. Figure 3.2 is an
illustration of this approach. The latter approach expresses the sample uncertainty affecting the decision through the probability density
function (pdfs) of the parameters. The pdfs can be updated with any
information which can be obtained via the Bayes rule. Since the concern here is on the decision, the second approach will be discussed.
Bayesian Decision Analysis
There are presently two approaches to the Bayesian decision
analysis. The first considers the sample uncertainty at the stage of
the use of the data in computing the decision variables. For example,
if the decision variable (R) is expressed in a form of a value function
f(R) which reflects the decision maker's preference for the outcomes,
then the expected value is given by:
58
0 Estimated values
• Unknown exact values
Upper bound
Lower bound
Decision Variable, Sm
Figure 3.2. Confidence Bands.
59
E[f(R)] = f f(R, q)f(q/I , Q)dg (3.20)
where q's are the uncertain inputs into the system and I Q is the prior
information about Q. f(q/ . . ) is the predictive distribution of Q.
Thus the optimal design is the decision variable which optimizes the
expected value function.
This approach is based on the assumption that once the uncertainty surrounding the inputs is taken care of an optimal decision can
be made. Vicens et al. (1974 and 1975) and Wood, Rodriguez-Iturbe and
Schaake (1974) have used this approach.
The second approach considers the uncertainty affecting the
decision to be made. This approach does not end when the optimal design
is made, as the first does. It goes on to check if decisions will be
improved by reducing the uncertainty. In effect, it determines the worth
of the information.
Whereas the second approach does more than the first, the computational burden is enormous. It takes two steps to arrive at the same
stage which the first approach reaches in only one step. That is,
Equation 3.18 is equivalent to:
E[f(R)/e] = folf(R,q)f(q/e)dci (3.21)
E[f(R)] = feE[f(R)/e]f(e/IR,Q)de (3.22)
and:
60
in the second approach,
e
is the parameter of the f(q/e), and f(e) is
the pdf of the parameter
Thus it is more expensive to use the second approach (Vicens et
al., 1977). However, for the purposes of this study as listed in the
objectives, it is more appropriate than the first approach. The next
section will be devoted to the details of the approach. Some users of
this two-step approach include Davis (1971), Musy and Duckstein (1976),
and Lane et al. (1978).
Bayesian Decision Procedure. The analytical procedure adopted
here is that of Davis (1971) which incorporates the natural uncertainty.
The steps include the following:
1.
Define the decision to be made and identify the alternatives.
2.
Define the goal function--select the state and decision
variables.
3.
Develop the stochastic properties of the knowledge of the state
variables as a probability density function (pdf).
If the decision is, say, selection of an alternative plan
which yields the maximum net benefits, then the goal function
g(a, e) is given by:
g(a,
e) =
iBF(a, x)f(x/e)dx
(3.23)
where a is the alternative, x is the state variable, and f(X/e)
is the pdf of x with parameter 0.
4.
Calculate the outcomes of the various alternatives and determine
the stochastic properties of the outcomes.
61
At this stage only the inherent uncertainty of the phenomenon (the stochastic nature) has been taken care of.
5.
Calculate the expectation of the goal function over the parameter.
O,
the uncertainty of which is expressed in terms of pdf,
g(e). The decision resulting from computations of expectation
of the goal function over e is termed the Bayes decision, and in
this case it is:
(3.24)
R(a*) = maxfg(a, 0)f(e)de
in which a* is the Bayes decision.
6.
Evaluate the decision using available data.
The Bayesian decision theory approach does not end at the
Bayes decision. It goes on to evaluate the decision. First,
it assumes that the true value of e is known, to which corresponds a certain decision, a t . If the decision a* is taken, the
opportunity loss resulting from this decision will be given by:
OL(a*, e t ) = g(a t ,
et)
— g (a*,
e t )
However in practice, the true value of
(3.25)
ace t )
is unknown; but
the prior pdf f(0) is available. Thus it is possible to compute
the expected opportunity loss:
XOL(a*, f) = fOL(a*, 0)F(e)de (3.26)
This expected opportunity loss (XOL) represents the expected
loss of not knowing the true value of e, given the decision
taken and the prior pdf. In effect, it evaluates the economic
62
worth of the available data by evaluating the decision that is
taken with respect to the theoretically optimal decision that
could be made. The prior pdf containing the information about
the parameters can be obtained using the data acquisition methods discussed earlier.
7. Evaluate worth of additional data.
If it is possible to obtain additional information by, say,
any of the augmentation methods discussed above, it will be possible to evaluate the worth of this additional information by
incorporating the new information with the old one via the Bayes
rule to obtain a new prior pdf (termed posterior pdf) and
repeating Steps 5 and 6. By expressing the added information
in terms of equivalent record length, it will be possible to
determine the optimum record length, if necessary.
In spite of the computational difficulties and expenses involved
in computer runs, the Bayes decision theory is considered the best
approach for hydrologic uncertainties (Dawdy, 1978). With computer
costs going down over time, due to technological advances, it can be a
useful tool.
Other Considerations
Even though the emphasis in this study is the hydrology, a
rational decision can only be made when all the other parameters affecting the decision are held at their optimized values. Apart from the
63
hydrologic parameters, the economic and technological parameters are also
important in the quantitative analysis of the strategy.
The economic parameters involved include those to be used in the
analysis of alternatives to be selected. They consist of cost and benefit parameters contained in the decision model used for the selection of
the size components to yield maximum benefits. Some of the parameters
can be obtained by analyzing the various purposes of the project.
Other parameters used in the decision process, apart from economic and hydrologic ones, include those that measure the level of performance of the system. For example, in the irrigation system, only
part of the water supplied will be available for plant growth because of
losses during transmission and from application. Also, in the power
system, the power generated will not be the full capacity of the plant
because of mechanical inefficiencies. These imperfections are due to
the level of technology. This group of parameters will, therefore, be
termed "technological parameters."
The inability to accurately measure these parameters introduces
a new dimension of uncertainty to the decision-making process. Economic
uncertainties can be the result of uncertainties due to variation of
construction cost, inflation, demand for certain commodities, and others.
Technological uncertainties may be due to the level of technology and
quality of the expertise of the people involved in the project.
Lack of time will limit the treatment of these uncertainties to
sensitivity analysis. The initial values for the parameters will, however, be based on the current state of affairs. In the case of the
64
economic parameters, it is suggested that an economic model be used to
compute their initial values.
Economic Model
The purpose of a model is to facilitate the study and understanding of the real system which would otherwise be too cumbersome and
intricate to handle. In economics, the model is usually a system of
equations representing a particular or composite aspect of some real (or
assumed) economic phenomena. By making use of such models, planners
explore the implications of a given objective and thus change their
rational choice in planning the long-term investment program as well as
avoiding potentially undesirable courses of action.
Many economic models such as Leontief's (1951) Input-Output model,
export base theory, and linear programming can be used for river basin
studies. However, the selection of one for use should be based on:
1.
The ability to simulate the pecularities of the region of
concern.
2.
Ease of calibrating the model.
3. The input data required for use.
Data for use of some of the models listed above will be difficult
to obtain in developing countries. However, for the purposes of this
study and the example project to be described in the next chapter, the
linear programming model will be discussed. In addition to the reasons
for model selection given above, the linear programming model is easier
to use because a number of computer routines are available.
65
Only a brief discussion of the linear programming model is
inserted here for completeness since literature on the subject abounds
in operations research books. Interested readers may check Hillier
and Lieberman (1974), Taha (1971) and Wagner (1975) for details.
Linear Programming Model. Hillier and Lieberman (1974) describe
linear programming as a model that deals with the problem of allocating
limited resources among competing activities in the "best" possible
way. "Best" used in this sense refers to optimality. Serving this
role, the model can be used also to determine the magnitude of such
activities.
In its basic form, a linear programming problem consists of
finding the appropriate non-negative values of decision variables, X.,
such that some linear function, F:
F =
E C.X.
i=1
11
for
i = 1, 2, 3 .m
(3.27)
is either minimized or maximized, subject to a set of constraints of the
form:
a, ,X. = b.
(3.28)
13
for
j
= 1, 2, 3 . .
.n
66
where
a,. = unit measure associated with variable
ij
X.,
the competing
activity
b. = the resource available
c.
1
the coefficient of variables in the objective functions.
Generally n m, and usually n > m.
Summary
In this chapter the methods of evaluating the effect of hydrologic
data on the outcome of a water resource project were considered. Sources
of uncertainties were identified and ways of dealing with them were discussed. How to decide if additional hydrologic data will be needed was
a major consideration. Uncertainties introduced by economic and technological parameters were also mentioned.
In the remaining chapters of this dissertation the applicability
of the strategy developed earlier will be tested, and methods discussed
in this chapter will be applied for the evaluation of the decision taken
on the proposed Ayensu Project in Ghana.
CHAPTER 4
THE STUDY PROJECT--THE AYENSU PROJECT
The strategy for decision making in water resources planning
which was developed in Chapter 2 is applied in this chapter to evaluate
the decision taken on the proposed Ayensu Basin Project in Ghana,
described in Chapter 1. This example application is undertaken to
demonstrate the utility of the strategy and to outline the procedures
used to arrive at a decision.
This chapter sets the stage for the analysis, in the next chapter, of the effects of the insufficient hydrologic information. Background information on the Ayensu River Basin and the proposed irrigation
project is presented; this information deals with the current usage of
the project area and with details of the irrigation project.
In order to formalize the nature of this study of the project,
the first three steps of the strategy are discussed here. First, the
goal and purposes of the project are defined. Second, the decision
criteria are defined, discussed and where possible, quantified. Finally,
the alternative solutions to the attainment of the defined goals are
described.
Historical Setting
With the exception of a small area which has been cultivated on
and off, the Ayensu Basin irrigation project area has been unutilized
67
68
for agriculture. The general location was shown in Figure 1.2. It
stretches from the north at Nsuaem Village to the south at Winneba,
spreading from Okyereko in the east to Mprumem, in the Brusheng River
Basin, in the west. The area is nationally known for the Efutu deer
hunting festival. It is also a favorite hunting ground for the grass
cutter hunters in the Central Region.
Though the potential of this area for irrigation has been known
since 1920 when the Winneba water supply project was first investigated
(M. Smith, 1969), serious consideration was not given to it until the
early 1960s when it was realized that a great proportion of the country's
foreign exchange earnings (nearly 25 percent) were being spent on importation of food items which could be grown locally (Lartey and Smith,
1968).
Until that time, the only purpose of water resource projects in
the country was for water supply for the "larger towns."
The first study of the project was done by Nippon Koei, a
Japanese consulting firm which, in addition to this project, studied
other potential irrigation sites in the country. The consultant's
report was presented in 1964, and it recommended that priority be given
to the Ayensu Project because of the following reasons:
1.
The project area has excellent soil conditions in comparison
with the others, being mainly composed of tropical black earth
which is suitable for production of paddy rice and other crops.
2.
The project area is located close to the main markets of AccraTema, Winneba, Swedru, Saltpond and Cape Coast.
69
3.
The project will be less troubled by drainage problems than the
others, because of the favorable topography.
4.
The project will find a cheap power source for the pumped irrigation because it will be located adjacent to the Winneba substation of the National Grid.
5. The project will be low in the unit construction cost in
comparison with the other projects.
However, due to some reasons, mainly that the streamflow information upon which the design was based was considered inadequate, the
recommendations were not implemented. Since then six more gaging stations have been established along the river.
In 1972, after six more years of hydrologic information had been
complied, Water Resources Consortium, a consortium of consultants from
the United States, reviewed the earlier preliminary report of Nippon
Koei. They also recommended that the project be given priority, but
that it should be implemented when more hydrologic data had been compiled.
Ten years after the first report, a local consultant of the
Ghana Government (Aluja, 1977) reviewed the two previous reports and
concluded that the components of the project as designed in earlier
studies were still valid and could be used for an area that is larger
(12,000 acres) than that suggested at first (8,600 acres).
It is to be noted that this project is not the only water
resource development project which has been postponed because of lack of
adequate data. Another example is the Kwanyaku Water Works which was
constructed to supply water for the Swedru District. Water Resources
70
Development International (1961, p. 2), reported
"Winneba District
Water Supply" based on a 15-year record, writing among other things,
that "Owing to insufficient data available for the river in its part
near Kwanyaku Reservoir, no clear forecasting can be made at present
as to the probable functioning of that reservoir."
Such statements are common in recommendations given by consultants on water projects in developing countries.
Goals and Purposes
In the Ayensu Project, the main goal is to utilize the water
resources of the Ayensu River for regional development. This goal is to
be met by: 1) introducing irrigated agriculture for production of food
crops for local consumption and export; and 2) the production of electric
energy for domestic and industrial use for processing the produce from
the irrigated farms.
It is believed that the two purposes of the project will create
employment opportunities for the local residents in order to curb the
migration to the urban areas in the country to look for jobs, and will
also improve the standard of living of the residents.
A study of reports on river basin studies and the Ghana Government's development plans, including the 1975-80 Five-Year Development
Plan, has enabled the following requirements to be established for this
project:
1. Water requirements: this goal involves satisfying the demand
for quantity and quality of water for irrigation.
71
2.
Power requirement: to satisfy the power
requirements for the
project and that of rural communities in the
region.
3.
Utilization of resources: the natural, social and
economic
resources needed to implement and operate the project should be
kept to a minimum. The resources considered in this study
include water, land, forest, and capital.
4. Flexibility: the proposed project should be flexible
enough to
meet a broad spectrum of future requirements, most of which
cannot be accurately foreseen at the present time.
The attainment of these goals may lead to further problems. For
example, the growth in irrigation and industrial development cannot be
divorced from a welter of societal aspects. These activities do not
only affect people living in the region but may stimulate immigration
into the region. Provision should, therefore, be made for the convenience of the new influx. The uncertainties involved in projecting these
societal problems are by themselves another research topic. In this
study these problems have been recognized; however, their analysis cannot be tackled for lack of time and information.
Decision Criteria
The second step in the strategy is the selection of the decision
criteria. As mentioned earlier, decision criteria constitute means by
which the suitability of a candidate solution to fulfill the desired
goals is judged or evaluated. In the case of the Ayensu Project, the
decision criteria are defined by relating them to the requirements of
the project.
72
The water requirements, for instance, is related to the yield
expected from the crops grown and the extent of area allocated to each
crop. It depends also on the water demands for domestic and industrial
uses. The types and extent of crops grown also determines the employment opportunities to be created.
The power requirement also is related to the type of processing
industries that are to be set up in the area. It therefore affects the
employment opportunities to be created. It may also determine the living
standard of the beneficiaries.
The resources utilized in such a project consist of capital, land,
people, water, and forest. In each case, the amount utilized may affect
other ongoing or future projects in the region or the nation as a whole.
Probability of water shortages is related to the flexibility of
the project to future requirements. This may be caused by uncertainty
in forecasting and technology.
Other criteria which are important but may not be directly
related to the requirements listed include health hazards and recreational opportunities. Of these criteria, the capital expended, water
used, land inundated and power produced are quantifiable. The rest are
not. In the case of the criteria which are difficult to quantify, their
relative importance to the goals will be rated either excellent, good,
fair or bad according to the outcomes of the alternatives to the goals.
To determine the magnitude of some of the quantitative criteria,
certain cost and benefit parameters will be needed. These parameters
are use-specific; therefore, they will be based on the outputs of the
73
projects. In the case of the power, the current energy
rates will be
used. For the water used for irrigation, its worth will be computed
using the linear programming model as discussed in the previous chapter.
The model determines the optimal crop-land allocations.
Cropping Pattern
Aluja (1977) lists the crops to be cultivated in this area as
consisting of rice, tobacco, vegetables, pasture green, maize, groundnuts (peanuts) and fruits. However, in view of the broadening of
emphasis, especially in terms of creation of job opportunities, certain
crops of commercial value are added in line with the policy underlying
the Five-Year Development Plan--namely to produce to feed not only the
people but the industries, also. The crops selected for this study will
consist of cotton, sugar cane, tobacco, pineapples, soya beans, and
groundnuts as the cash crops; corn, rice, and yams (cassava) as the
staple crops; and tomatoes, pepper, and okra as the vegetables.
To determine the cost and benefit parameters to be used in the
evaluation of the capabilities of alternative solutions, the linear
programming model was used to determine the cropping pattern and water
allocation which maximizes the net farm returns subject to available
resources. For this the objective function of the model can be put in
the form:
max NB =
E (P.
1
i=1
C.)X.
1 1
subject to the following constraints:
(4.1)
74
E x. < TIA
1 —
i=1
(4.2)
E a.X. < TW
—
i=1
(4.3)
E x. > TFC
1 —
i=1
(4.4)
E X. > TCC
1 —
i=1
(4.5)
E x. > XVEG
.
—
J-
(4.6)
where
NB = net benefits in cedis
(0)
X. = area for crop i (acres)
1
i = type of crop considered
P
i
= gross return of crop i per unit area (0/acre)
C. = cost of production of crop i per unit area (0/acre)
TIA = total irrigable area (acres)
TW = total water available (acre-feet)
TWC = total area allocated for food crops
TCC = total area allocated for cash crops
VEG = total area allocated for vegetables
a. = consumptive use of crop i
b = number of food crops
75
t = number of cash crops
= number of vegetable crops
Some constraints which could have been added are labor and
capacity of the water conveyance system. However, it is assumed that
the supply of labor is unlimited due to the unemployment
situation in
rural communities. Also, the water conveyance system is expected to be
designed to carry the amounts of water needed.
Table 4.1 shows the coefficients needed for the running of the
computer program. The cost and guarantee price values were obtained
from the Ministry of Agriculture of the Ghana Government (1976). The
unit crop prices used are based on the expected yield per acre for the
inputs (i.e., fertilizer, water and labor).
The method for determination of some of the technical coefficients and description of the constraints are discussed in the following
sections.
Since all the crops listed are important and are expected to be
grown, minimum constraints have been put on some of them.
Constraints
Water Constraint
The sources of water for the growing crops will be rainfall and
irrigation water. However, no one has knowledge of how much of the
rainfall is available for plant growth.
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Nippon Koei Co. (1967), in its report, used an empirical relationship to estimate the effective rainfall. The
relationship was given by:
ER = 0.75R -1
m
(4.7)
where ER is the effective rainfall and R the mean monthly rainfall,
m
both in inches. The monthly effective rainfalls computed using the above
relationship are listed in Table 4.2, with the mean monthly streamflows.
The two sources, along with moisture in the atmosphere, constitute the
water supply for plant growth. To determine if the water supply will
be adequate for the project, the plant water requirements for the entire
irrigable area were also computed.
Water Demand for Crops. The annual water demand for the various
crops depends upon the extent of the area allocated for them, their
consumptive uses, length of their growing seasons, and the total irrigation efficiency. An evaluation of the total irrigation efficiency
for the Ayensu Basin is rather difficult at this time; so for the
purpose of this study the demand is calculated for each crop based on
the acreage allocated, consumptive use, and length of the growing
season.
The consumptive use is the amount of water used by crops for
growth. Numerous empirical equations have been proposed for the estimation of consumptive use values for various crops (Hargreaves, 1968).
The simplest and the most commonly used is the Blaney-Criddle formula
(Viessman, Harbaugh and Knapp, 1972).
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U =
(4.8)
where
U = consumptive use of the crop in inches for the growing season
K = empirical consumptive-use crop coefficient for the growing
season (this coefficient varies with different crops being
irrigated)
F = sum of monthly consumptive use factors for the growing
season (sum of the products of mean monthly temperature and
monthly percentage of daylight hours of the year).
Values of K and F are obtainable from tables in Technical Release No.
21 of the Soil Conservation Service (SCS), United States Department of
Agriculture (USDA), 1970. Where these values were not found for particular crops in Technical Release No. 21, their consumptive use has been
determined using Hargreaves' (1966) equation:
(4.9)
U = K E
l p
1
where
(4.10)
E = 17.37dT (1-0.01 H )
n
E = potential evapotranspiration in mm
d = a monthly daytime coefficient;
H
n
12:00 P.M.
= mean monthly relative humidity at
in
T = average mean monthly temperature
° C.
80
Values of K
1
for various crops are also obtainable from
Hargreaves' work. The relative humidity data listed in Table 4.2
were
obtained from records kept at the Kwanyaku Water Works. Table 4.3 lists
the data used in estimating the consumptive use.
It is realized that using consumptive use instead of water-yield
relationship is a conservative approach. However, the water-yeild
relationships were not available for all the crops listed. Therefore,
for uniformity in the computation, the consumptive use, which could be
computed for all of them, was used.
Crop Constraints
Some crops have specific constraints due to either market capacity, the demand for them, soil quality, plant process capacity, etc.
There were no data on any of the criteria listed above. However, inferring from the Ghana Government's Five Year Plan report (1977), some minimum constraints can be put on the staple food crops and the crops serving
as raw materials for the industries.
Staple Food Crops. These crops, namely maize, rice and yam, are
basic in Ghanaian diets. Since the government policy is to reduce or
stop importation of these food crops, it is to be expected that any
irrigation project financed by the government should include them. However, there are no guidelines on how much of each should be grown.
Therefore, any estimates used here are based on population count and on
the experience of the author in this region.
Judging by the importance of these food crops in the Ghanaian
dishes, at least a third of the total irrigable area will be allocated
81
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82
for them. Of this acreage, at least 1,000 acres should be
for maize
which features prominently in the diets of the local residents.
Vegetables. The vegetables in the crop list are pepper and
tomatoes. The fruits of these crops are used alongside with the staple
food crops. These crops require a well-drained soil and can be grown
throughout the year. Also, due to lack of storage facilities, the
harvesting of these in large quantities at one time may outstrip the
demand by the local people and the available canning industries. As
such, the acreage allocated for them should not exceed a tenth of the
total crop.
Cash Crops. Cotton, sugarcane, soya beans, pineapples and
groundnuts (peanuts) are the cash crops to be cultivated. The extent
of cultivated acreage for these crops will determine the amount of
employment avenues to be created both during cultivating stage, processing into intermediate product, and final product stage. Since employment is one of the reasons for the project, and the government's policy
calls for production of raw materials to feed the existing industries,
not less than half of total acreage should be allocated for these
crops. All the crops listed are needed for the existing industries.
Therefore, each of them should be grown. The minimum allocation for
each crop is given in Table 4.1
Model Output
The program employed for solving this model is the LPGOGO
(Dallenbach and Bell, 1970). This program has a post-optimality analysis
feature which considers the range within which the resource may vary
83
without changing the basic (optimal) feasible
solution, showing the
shadow prices for those binding constraints. The
program also shows the
range of the objective function coefficients within which
changes are
permitted without altering the basic feasible solution.
The output of the program, shown in Table 4.4, lists the crop
pattern, the net revenue per crop and the total employment using the
estimated labor for each crop per acre. It is interesting to note that
the sugar cane featured prominently, taking nearly 50 percent of the
irrigable area. At present, this crop is the only cash crop grown by
residents in the irrigable area. The area allocations for the other
crops were also consistent with the constraints.
Water as a resource was a binding constraint in the program outputs. However, the annual supply is over and above the requirement for
irrigation. Less than 25 percent of the average stream flow at Nsuaem
will be needed. However, some of the periodic flows may not meet the
periodic requirement, and thus the need for a reservoir. Therefore, the
availability of water for irrigation will be constrained only by availability of sites for water storage for periods of drought. With the unit
costs and selling prices used, the water can be estimated to be worth
$41.20 per acre-foot; and for the land resource, $153.00 per acre.
The rather low value per unit resource can be attributed to
controls which the government exercises over the selling price of food
crops. As much as this can be commended for the consumers, it is a
disincentive to the farmers, who may want to optimize their returns from
the farm.
▪
84
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85
Project Alternatives
The next step in the strategy is the development of
project
alternatives. Various alternative projects can be developed for the
Ayensu project to meet the desired objectives. For irrigation water
storage and hydropower production a basic system, shown in Figure 4.1,
consisting of a reservoir, a powerhouse, and conveyance facilities is
predicated.
Among the various possible alternatives, three have been
selected for this study. They are:
1.
The existing Kwanyaku Reservoir plus power generating system.
2.
An increased reservoir capacity at the Kwanyaku works, with
power-generating system.
3. The proposed Nsuaem system plus the existing Kwanyaku Reservoir.
These are described in detail in the following subsections.
Alternative 1: The Existing Kwanyaku Reservoir
System Plus Power System
The existing Kwanyaku Reservoir system consists of a reservoir
with a capacity of 890 acre-feet formed by a 30-foot-high concrete overflow dam, a water treatment works, and a pipe distribution system from
the treatment works to the towns and villages in the basin. At the dam
site the catchment area is 370 square miles (Table 4.5 and Figure 4.2
list the statistics and the characteristics of the system).
The reservoir has been designed to meet the water demand at the
rate of 8.32 million gallons per day, even with zero river flow, for
three months. As of October 1976, the maximum monthly draft from the
86
87
Table 4.5. Kwanyaku Water Work's Statistics
Dam Type Mass Concrete Gravity Section
Catchment Area
317 square miles
Pond Surface at TWL
Spillway Length
Overall Dam Length
Height of Dam
140 acres
364 feet
416.5 feet
30 feet
88
reservoir was 75 million gallons (i.e., draft of 2.5 mgd), far below
the designed target. The yearly drafts since 1969 are as shown in
Table 4.6. It is speculated that the unused designed draft can be used
for irrigation purposes.
The power addition will utilize the present water head for
generation of hydropower.
Alternative 2: Increased Kwanyaku Reservoir Storage System
This alternative is being considered for increased storage and
head for power production at the Kwanyaku Reservoir site. The maximum
storage attainable at the site, as shown in Figure 4.2, is 3,682 acrefeet. This would demand an increase of 10 feet in dam height. The
streamf low data collected at Oketsew (just upstream of the dam) are
listed in Table 4.7 will be used for the analysis of this alternative.
Alternative 3: Nsuaem-Kwanyaku System
This combination system is being planned to take advantage of
the larger storage capacity at the Nsuaem site.
The Nsuaem site is located one mile upstream of the Nsuaem
village on the Ayensu River. The river flow at that section consists
Akora River,
of spill from the Kwanyaku Reservoir and contribution from
the major tributary of the Ayensu River.
At Swedru, where there is a gaging station, the Akora River
this river
covers an area of 175 square miles. The gaging station on
far (1976) are as
was established in 1970, and the recorded flows so
at Nsuaem dates
shown in Table 4.8. The streamf low record on the Ayensu
89
Table 4.6. Annual Drafts from the Kwanyaku Reservoir
Year
Draft (million gallons)
1969
121.08
1970
127.87
1971
151.31
1972
253.21
1973
369.54
1974
535.48
1975
604.27
90
170
160
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120
110
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200
400
600
800
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0
50
100
150
200
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1200
250
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Acres
Figure 4.2. Kwanyaku Reservoir Characteristics.
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93
back to 1960, of which only that from 1966 was actually recorded at
the
proposed dam site (Table 4.9). The record for the period 1960-1966 was
obtained by regression with the Oketsew record. Part of the Oketsew
record, shown in Table 4.10, was also obtained by regression with the
Nsawam record on the Densu River (Aluja, 1977). The locations of the
Ayensu and Densu Basins are shown in Figure 4.3. The available data at
Nsuaem that are taken into consideration in the regression ayalysis
were taken from sources as shown in Table 4.11 and from data listed in
Table 4.12.
From the above, it can be said that the first feasibility report
on the proposed Nsuaem project by Nippon Koei (1967) was based entirely
on transferred data obtained through regression. The report's recommendations, summarized in Table 4.13, consisted on a reservoir of capacity
of 20,000 acre-feet with an active storage of 10,500 acre-feet created
by a 41-foot earthen dam with a spillway discharge capacity of 8,500
cubic feet per second. The reservoir capacity was sufficient to irrigate 8,600 acres of land. The elevation-capacity curve provided by
Nippon Koei in its report is shown in Figure 4.4.
Ten years after Nippon Koei's report, Aluja (1977) reviewed the
project in light of ten more years of accumulated streamflow data.
With the exception of an increase in the irrigable area, from 8,600
acres to 12,000 acres, his recommendations agree with that of Nippon
Koei.
•
▪
▪
94
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96
Figure 4.3. Locations of Ayensu and Densu Basins.
(Source: Ayibotele, 1974)
97
Table 4.11. Sources of Streamflow Data for Correlation
with Data on Ayensu at Oketsew
Period
Source
September 1959 August 1966
Daily gages from Water
Supply Division at
Nsawam Bridge
August 1949 January 1959
Gage at the weir of
Nsawam Water Works
observed by Water
Supply Division for
Project Report of
Pakro Dam on Kuia River
Remark
The Nsawam weir was
equipped with timber
stop logs which were
dismantled from time
to time.
M/S Nippon Koei has
stated that it was not
clear what kind of method
was applied for discharge
rating under complicated
conditions, but the data
was assumed correct
January 1948 July 1949
GNCC* drawing
Runoff-Rainfall Relation
for the Densu River
Basin
* GNCC - Ghana National Construction Corporation.
▪
▪
98
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99
Table 4.13. The Project Features: Ayensu Irrigation Project
Irrigable Area
8,600 acres
Reservoir
High water level
Active storage capacity
Drawdown
elev. 80 feet
10,500 acre-feet
10 feet
Type
Height
Embankment volume
earth dam
41 feet
280,000 cubic yards
Dam
Pumping Station
Head
Installed capacity
68 feet
920 kW (460 kW @ 2 Nos.)
Main Canal
Length
26 miles
100
,
.
(tr
0
A
,
'4'
.
0
c
o
0
0
T
lic
o
C.0
1 9 0j
UT U OD 13A 0 I
101
In this combination system, the Kwanyaku Reservoir will be used
for water supply for domestic and industrial consumption, as it is used
now, while the Nsuaem one will be for power production and irrigation.
Summary
This chapter presented the goals and purposes of the Ayensu
Project and described the measures of effectiveness which were based on
both the economic and social objectives. An economic model--linear
programming--was used for the determination of some of the economic
parameters needed in evaluation of the alternatives described. These
parameters will be used in the next chapter.
With the historical background and data for evaluation given,
the stage is set to evaluate the various alternatives and determine the
effect of hydrologic information and method of data acquisition on the
capabilities of the alternatives.
CHAPTER 5
ALTERNATIVES' CAPABILITIES AND EVALUATION
The last chapter introduced the Ayensu Project by describing its
goals, the decision criteria to be used in the evaluation of the alternatives, and the alternatives themselves. This chapter deals with the
fourth step of the strategy's procedure: the analysis of the capabilities of the alternatives and the evaluation of the effect of adequacy or
inadequacy of information on the economic outcome of the project.
The analysis will include the selection of the reservoir and
power plant size in the three alternatives which meet the project objectives and at the same time maximize the resulting net benefits. The
analysis and results will be described using data on the Nsuaem alternative; however, the results on the other alternatives will be listed
also.
Design Objective
Using the difference criterion of the benefit-cost methodology,
the objective function for an optimal reservoir design procedure, considering possible over- or underdesign losses due to hydrologic uncertainties, could be stated as:
NB = max (B
R
- C )
T
(5.1)
102
103
in which the decision criterion, NB, is the net
benefits accruing from
the use of the water released from the reservoir;
B R , is the gross
benefits from use of reservoir releases for hydropower
and irrigation;
and, C , the total annualized capital cost, operation,
T
maintenance and
repair.
The gross benefit, B R , is represented by:
B
where B
R
irr
=B.
+B
irr
pow
and B
pow
(5.2)
are the gross proceeds from the irrigation and power
systems, respectively. C T , the total annualized cost is represented by:
C
where C
T
pow
= C+C.
+ OMR
pow
irr
(5.3)
and C.
are the annualized cost of power and irrigation
Irr
systems, respectively, and OMR is the operation, maintenance and repair
co s t.
The usual reservoir design approach has been to select a reservoir capacity and target release which will maximize the net benefits
of the project. This approach implies that the target release is
selected with respect to the reservoir capacity.
Whereas this approach may be adequate for some developed countries, it may not meet the needs of developing countries. There is a
hidden assumption that if the target release does not meet the demand
other sources can be used to supplement it. In the case of developing
countries, there may be no other source or it may not be affordable.
104
Therefore, they would rather approach the objective with the intent
of
meeting it.
The approach adopted for this study, therefore, is to
select a
reservoir size that meets a pre - determined target release such that
the
net benefits are maximized. This approach is based on
fixed effectiveness principle; i.e., for a particular resource investment, a predetermined level of effectiveness is expected to be achieved.
Using this design principle, the benefit function for the project
can be represented by:
aI
B.lrr
={
aI
R
- (3(I
R
- D)
2
I
I
R
R
> D
(5.4)
< D
R
for the irrigation purpose, and:
flT -(T--P) 2T
B
pow ={
flT - (P - T)
>
2
P
(5.5)
T<P
for the power.
In Equation 5.4, I R represents the release needed for irrigation
at a particular period; D is the available release; a is the unit benefit
from the use of I R ; and, 13. the penalty coefficient for inability to meet
the needed release. In equation 5.5, T is the energy capability of the
power plant installed, P is the energy producible by the water released,
n is the unit sale price of energy, 6 is the penalty coefficient for
overdesign and
that for underdesign.
105
A quadratic (or non-linear) function is used
for the penalty
terms to account for social and political aspects of the
problem (risk
aversion) (Musy and Duckstein, 1976). The underlying assumption is
that for maximum net benefit, the purpose requirement is equivalent to
the mean of the releases (Winkler, 1972). On the other hand, if the
penalty terms were described by a linear function instead of a non-linear
function, for maximum benefit, the median of the release must be equivalent to the target level.
In the preliminary analysis, it was realized that the releases
from the reservoir, by simulating the operation of the reservoir
(described later), were normally distributed (the normality assumption
was not rejected by Kolmogorov-Smirnov test at 95 percent confidence
limit as shown in Figure 5.1). However, in a normally distributed function the median and mean are aqual; therefore, for simplicity, the
penalty terms were substituted with linear functions (i.e., the square
indices were dropped).
The use of the penalty function to cater for underdesign and
overdesign also introduces a different kind of uncertainty. This uncertainty is due to the choice of penalty coefficients. For instance, one
may ask what compensation is adequate for the suffering due to poor crop
yield because of insufficient water for plant growth. How does one quantify the suffering due to loss of benefits from other developments which
could not be undertaken because the capital which could have been used
for them has been overinvested in the power plant which is not producing
power to its capacity?
106
1.0-
0.90.8-
ô
— 0.7-
• 0.4=
c
C
4 0.3-
0.20.1 -
.09
.001
.61
T
A
1
.05
.16
.50
.84
% of time less than indicated release
.95
Figure 5.1. Kolmogorov-Smirnov Test.
.99
t
.998 x 100
107
The uncertainties introduced by these
coefficients and others,
including the cost and benefit coefficients and overall
irrigation efficiency, will be investigated using sensitivity analysis in a later section.
The evaluation of the net benefit function requires the determination of the reservoir size, S m from which releases needed to meet the
annual requirements, I R , for the irrigation and T for the power, will be
made. The power P produced is related to the release D, by the following
expression:
P = HDye
(5.6)
where
H = net head created on the power plant
y
= unit weight of water
e = overall efficiency of the plant.
In the following sections, the procedure for determination of
releases and the simulation of reservoir operation will be described.
Release Computation
Releases from small reservoirs, of the kind that can be created
on the Ayensu River, are primarily dependent upon the inflows. Releases,
as defined here, include both spill and purpose requirement. The relation between the releases, D, and the inflows, Q, can be represented by
the continuity equation:
108
S. = S.
+ Q. - D .
1
1-1
(5.7)
where
S. = storage capacity of the reservoir at the end of
period i
=
storage capacity of the reservoir at the beginning of the
period
Qi =
inflow during the period i
D. = release during the period i
1
By this relationship, there is a hidden assumption that on the average,
the evaporation from the reservoir will be balanced by the direct rainfall on it. This assumption was justified by a pre-analytical check.
If it is further assumed that the storage at any period is dependent on the release, the following expression can be written:
S = f(D)
(5.8)
and the equation (5.8) can be arranged to yield:
D. = Q. + f(D.)
1
1
1
(5.9)
The function f(D) depends on the physical characteristics of the
site in terms of maximum storage possible and also the operation rule for
the reservoir use. Thus if the inflows can be predicted, the releases,
and therefore the benefits from its use, can be computed. The inflows
were predicted using a Box-Jenkins ARIMA model.
109
Since the inflows are random, so will be
the releases. Therefore, the net benefit would not be known with certainty,
and only its
expected value can be computed. The expected net
benefit can be expressed
as:
E[NB] = i DNB(D)f(D)dD
(5.10)
where
NB(D) = net benefit function
f(D) = probability distribution of the releases
For the decision evaluation purpose, two sets of ARIMA models
were developed. The first set of models were developed from the 10-year
record obtained after the Nippon Koei report in 1967. The second sets
were obtained using the 19-year record consisting of 7 years of transferred data from the Oketsew gaging station on the Ayensu River,
upstream of the Nsuaem Dam site, and 12-years transferred data from the
Nsawam gaging station on the Densu River via the Oketsew station. The
locations of the Ayensu and Densu River Basins were shown in Figure 4.3.
The two basins are known to have many hydrologic similarities (Ayibotele,
1974).
The reason for the two sets of models was to compare the designs
resulting from the two types of data sources. For the description of
model development, data from the 10-year record will be used.
110
The Streamf low Model
One of the Box and Jenkins ARIMA class of models was used
as the
forecasting model for streamflows used in the simulation process. This
model was found to be flexible and contains few parameters. The
recommended stages of identification, estimation and diagnostic check for the
model development were adhered to.
Due to the shortness of the streamf low record available and the
small size of reservoir likely to result, the monthly rather than the
annual streamflow forecasts were made. The monthly releases are later
combined into the annual releases to be used in the computation of annual
net benefits.
At the identification stage of the model, the 10-year streamflow
record (1967-1976) at Nsuaem were used. Plots of the raw data and its
logarithmic transformation (Figures 5.2a and 5.2b) showed that the
natural log-transformed one showed less non-stationarity and thus was
chosen for a further look. A first differencing of the transformed data
removed the seasonality (Figure 5.3). For the selection of class and
order of model, the autocorrelation and partial autocorrelation functions (used as tools for model identification) of the data shown in
Figures 5.4a and 5.4b, respectively, indicated that a first-order auto-
regressive model would be adequate. Thus a multiplicative ARIMA
(1, 0, 0) x (0, 1
W
t
= yhlri
'
t-1
0)
12
+ E
t
model was selected. The form of the model is:
+
o
(5.11a)
111
1.25
1.00-
0.75—
0.50-
0.25—
\
0.00
I
t
20
1
[
40
\-,
r
I
60
i
80
'
I
100
120
Time (months)
Figure 5.2. Plots of the Monthly Streamflow Series Observed
at Nsuaem. a) Raw Data Plot.
112
12
1
10-
20
40
I
60
80
1
100
Time (months)
Figure 5.2, Continued. Plots of the Monthly Streamf low
Series Observed at Nsuaem.
h) Natural Logarithm Plot.
120
113
4
vf\yfo
-8
1
20
40
1J
60
r
I
I
80
J
100
Time (months )
Figure 5.3. The Differenced Series, Nsuaem on
Ayensu River.
1
120
114
P
k
.5-
I
o
0
1
1
I
•
''
5
Ill
1
i
10
1
1
15
k , lags
a) The Autocorrelation Function.
1.0 —
4) kk
.5—
11n11.1
I
0
0
1ii
1
I
5
1
I
2a.
limits
I'f
(wt ,AR())
11
I
1
1
1
10
15
b) Partial Autocorrelation Function.
Figure 5.4. Model Identification.
k, logs
115
where
(5.11b)
and W
t
is the mean of the W
t series, which was nearly zero in all the
record sets considered. The other symbols are similar to those defined
in Chapter 3. This equation, when transferred to the data form,
reduces
to:
log Y
Y
1
t
= log y
1
t-12
1
+ (log y 1
- log y
) + E +
t-1
t-13
t
1
= Y + shift.
t
t
o
. (5.11c)
(5.11d)
The shift is defined as:
min ln (Y + shift) = 1.
Y
t
(5.11e)
are the monthly streamf low data.
Using Box and Jenkins (1970, Chapter 7) suggestion that the
approximate maximum likelihood estimates for the model parameter be
obtained by employing the unconditional sum of squares method, the
relationship:
(1) 1
=
(5.12)
was used as the initial parameter estimates in the optimization technique.
The final stage of the model development is the diagnostic check
which is concerned both with testing the adequacy of the model and indicating what might be wrong if inadequacies exist.
116
Two diagnostic checks were made.
First, by overfitting using a
second-order model, and then by checking if the
residuals are independent, normally distributed and homoscedatic.
For the overfitting test McLeod's (1974) likelihood ratio statistics test of:
n ln(aa
2
2
(K)/aa (r)) = X2 (r-k) (5.13)
was used to determine the significance of parameters
where
k = order of the original mode
r = order of the overfitted model
&a 2 (r) = residual variance estimate for the overfitted mode
2
X (r-k) = chi-square value with r-k degrees of freedom.
2
If X (r-k) from Equation 5.13 is greater than X 2 (r-k) from the tables
at 95 percent significance level, then a model with more parameters is
needed.
For the normality check, the residuals of a generated series
were tested and found to meet the assumptions.
Using the model (as given in Equation 5.11c), 10 sets of 50-year
monthly sequences were generated and these were used in the reservoir
operation simulation.
Reservoir Releases
The releases from the reservoir are not only dependent on the
inflow but also on other factors, including the operation rule. The
117
operation rule is some guideline by which releases are made to satisfy
demands. For the selection of the reservoir capacity that maximizes net
benefits, a very simple rule is adopted.
This rule does not make use of any outside information. Instead,
the release in each period (one month, in this case) is predicated solely
on the sum of amount impounded at the start of the period, and the amount
of inflow during the period. The rule can be summarized as follows:
First, a draft level, DL , is selected. This is the periodic (monthly)
release which must be met or else a penalty is assessed. In this project, the bigger of the water requirements for irrigation and power plant
capacity was chosen as the draft level. The draft level characterizes
the operating rule in the following manner:
if S.
+ Q. < D , release all water and leave reservoir
L
1
(R-1)
empty
> D , release DL , unless the remaining storage
if S.
L
1- 1 + Q.
exceeds the storage capacity, S m of the
reservoir. In that case, the release is
m
reservoir full.
, leaving the
(R-2)
applicable in some
This rather simple operating rule may not be
simplicity of
cases; however, its relevance here is underlined by the
the case, a check on requirethe project itself. If R-1 happens to be
The monthly
ments for the purposes is made to compute deficiencies.
irrigation requirements are shown in Table 5.1.
118
Table 5.1. Monthly Irrigation Water Requirements
Month
Water Required for Irrigation
(acre-feet)
January
3,200
February
1,760
March
0
April
1,632
May
6,445
June
0
July
3,064
August
0
September
2,584
October
8,192
November
9,595
December
9,280
Source:
Aluja (1977).
119
Simulation Procedure
A simple simulation procedure was developed to aid the determination of optimal design. The procedure consists of
simulating the
operation of the system and selecting the combination of the
components
(capacities) which yield the maximum expected net benefits. A computer
program, listed in Appendix A, was developed to perform the simulation.
There are two parts of the program. The first part develops the
streamflow model which simulates the historical data. This model is
used in the second part to forecast future flows into the reservoir. The
second part of the program simulates the operation of the reservoir and
calculates the yearly net benefits with respect to the capacities of the
components selected.
The following steps, which are illustrated in the flow chart
shown in Figures 5.5 and 5.6 describe the simulation procedure:
1.
Input the streamflow model parameters. This includes the Vs,
the white noise variance, and the seed needed for generation
of the random numbers.
2.
Input the reservoir characteristics--the elevation, storage-area
curve.
3.
Input the monthly irrigation requirements.
4.
Input the cost-benefit coefficients and the technological
parameters, including the overall efficiencies of power and
irrigation systems.
5.
Select a reservoir capacity, S.
6.
Select a turbine size, T.
120
START
Read reservoir characteristics-elevation, capability
V
Read cost, benefit, and technological
coefficients--e, (1, 13, 6, overall
irrigation efficiency, etc.
Read monthly irrigation water requirement,
WDIR; and residential water requirement, RWD
NSIM = number of simulations
JSIM = counter for NSIM
N = number of turbine sizes considered
I = month of year
L = number of reservoir capacities considered
IX = counter for number of reservoirs
M = total number of monthly series generated
Figure 5.5. Flow Chart for Reservoir Simulation.
121
2
, Ga , shift random number generator seed
Call RNORM to generate
Vs and shift; Call
2
GAMA to generate Ga
Call GENI to generate m
monthly streamflow series
IX < L
n< N
Select reservoir size,
Sm. IX
Select power plant size,
Ts. n
Figure 5.5. Flow Chart, Continued
122
Determine release using
operation rule for month
(Figure 5.6)
for month i
Determine head,
power plant
HH,
over
Compute Irrigation
Deficiencies
is
i = 12?
t..
Compute Irrigation and Power
Benefits for Year
BIR - BIR + XMa - yDEFIR
BP = rip
n
n=#
Test
vs. N
of plant sizes
selected
I
Figure 5.5. Flow Chart, Continued
123
Compute Mean and Standard
Deviation of Expected Net Benefits
[
Continued
Figure 5.5. Flow Chart,
124
Select Draft Level,
D
L
A. = D + S
1
m
=D
= S.
S.
1
1-1
+
I - D.
Determine Head Over
Power Plant
D. = Release for period i
S
S. = Storage at end of period
D
1
1
m
L
=
Size of reservoir
=
Draft level
Figure 5.6. Flow Chart for Operation Rule.
125
7.
Select the draft level, D L , for the period.
8.
Use the operation rule to compute the releases
and determine
deficiencies.
9.
Compute gross benefits and then net benefits for the life
of
the project.
10. Compute the mean and variance of net benefits.
11. Go to Step 6 and repeat Steps 6 through 10.
lia. Repeat Steps 5 through 10 until enough reservoir capacities
have been evaluated.
12.
Select the combination of reservoir and turbine sizes which
yield the maximum net benefits.
13. Perform sensitivity analysis using different values of cost,
benefit and technological parameters to evaluate their effects
on selected component sizes.
The simulation procedure up to this stage has taken into account
only the natural uncertainty, and the result is the expected net benefit.
This is where the conventional engineering analysis is normally concluded. However, the effect of the streamflow parameters has not been
investigated. Will the model parameters change if additional data is
included in the model development? How will this change, if any, affect
the decision taken above? Is the effect significant enough for decision change?
These are some of the questions' which will be answered in the
next section, where the effect of the information uncertainty on the
126
decision is analyzed. The Bayesian approach as proposed by Davis (1971)
will be used. However, the computational approach follows that of Moss
and Dawdy (1973).
The Bayesian Part
The conventional procedure, as listed in the flow chart, caters
only for the natural uncertainty. Since the streamf low record used for
the forecast model was short, it is assumed that the parameters' esti-
mates have uncertainty surrounding them and therefore the resulting
decisions may not be optimal.
With the W
W
t
t
series, the model used as given in Equation 5.11 was:
= (PW+ a +4)
t- 1
t
(5.14)
.
The more traditional one, as seen in hydrologic literature, is:
W
where V
eters W
t
t
t
- Tn = p(W
.
t-1
-) + U(1-p 2 ) 11 V
t
(5.15)
is a normal disturbance with mean 0 and variance 1. The param-
a2
and p are the mean, variance and serial correlation coeffi-
cient of the stationary series. Comparing equations 5.14 and 5.15, the
parameters can be equated as follows:
(5.16a)
=P
ciD o = W (1 — p) = 0
(5.16b)
-
2
G . aa - () )
a
(5.16c)
127
Beard (1965) disclosed that errors of estimate for the
serial correlation coefficient, p, and the variance are functions of
length of record
and of theoretical distributions. For all the data sets
considered, (I)
o
was always very small and therefore can be neglected.
According to Box and Jenkins (1970, page 254), for an autoregressive process of unit order the parameter (I) is distributed exactly
in
a student t-distribution with n-1 degrees of freedom and the parameters
of the distribution are given by:
= D
r
S, = L
12
/D
and
22
D
1 11
(n-1) D
D.
22
(5.17)
D
r
1 1
D
2
12
(5.18)
D
11 22
= D. = W.W, + w. w.
+ . . . w
.w
1 3
1+1 3+1
n+l=3 n+1-i
Ji
(5.19)
1
For n > 50, which is the case here, S, tends to {(1 - 2)/n}½
and the
normal approximation to the t-distribution is adequate (Box and Jenkins,
1970, p. 254; Davis and Patten, 1975).
With the pdfs and their parameters and parameters (q), s) a
new set (50 in this case) were generated using the Monte Carlo approach.
These new parameters are then used in the simulation procedures described
earlier. The average of the new set of expected net benefits is the
expected net benefit which takes into account, also, the sample uncertainty.
128
For the residuals, its variance is described by
the inverted
gamma 1 distribution with parameters given by Vicens
et al. (1975) as
2
1/2v and 1/2VS' , where:
2
lr
S =1E(W
t
-b
1
2,
- b W
) j
2 t-1
(5.20)
and
V = n - 2 .
Ew
(5.21)
t
b =V
(5.22)
Ew w
t -1t
and
Ew t
V
-1
=
1
2
Ew
Ew
t-1
t-1
-
(5.23)
Worth of Transferred Data
Due to the small size of the reservoir that can be created
because of topographical constraints, the data needed for use should be
either of monthly or one of less duration. Therefore only one of the
acquisition methods discussed, the data transfer method, can be used to
obtain prior information on the model parameters. The only other monthly
information on the parameter, apart from the observed data, is the transferred data.
129
This information was pooled with that of observed data
to obtain
the parameters of the distribution. Since the pdf of the model parameter is normal, its posterior distribution is also normal with
parameters:
1 1
11 nm + n m
- n + n 1
m
(5.24)
for the mean and
l
n
12
1
a
11
2
a
(5.25)
a2
for the variance. The letters with double prime represent the parameters
of the posterior distribution while those with single prime and no prime
represent those of the prior and observed data distributions, respectively. m is the mean; n, the length of sample data; and a 2 the variance.
With these new parameters, the Bayesian procedure is repeated.
The difference between the maximum expected net benefits of the observed
data above and of the pooled data represents the worth of the transferred
data.
Results
The objectives of this chapter, as stated in the beginning, were:
1) to determine the capabilities of the alternatives; and 2) to evaluate
the decision taken to postpone the Ayensu Project to collect more streamflow data. The earlier part of this chapter dealt with the description
130
of the analytical procedures used in the determination
of the capabilities. This part will describe and discuss the
results of the analyses
undertaken, and based on the results, evaluate the
decision.
To assist in the evaluation, two types of data sets are used:
1. The first type consists of the transferred
data sets which are:
a.
a 7-year streamflow data set transferred from the Oketsew
gaging station, upstream of the Nsuaem site on the Ayensu; and
b.
a 12-year data set transferred from the Nsawam gage on the
Densu River via Oketsew to Nsuaem.
2. The ten-year recorded data at the Nsuaem site. This recorded
data set is divided into two:
a.
using the first five years of data; and
b.
using the whole 10-year record.
The reasons for the selection of the two types of data sets were:
1.
To compare the results from the use of transferred data sets and
the recorded ones (this will enable the determination of the
worth of the transferred data).
2.
To compare results using a 5-year record and a 10-year record.
Also, with these data sets, two analytical procedures were compared. The
first, termed conventional, takes into consideration only the natural
uncertainty. The second procedure uses the Bayesian approach and considers both the natural and sample uncertainties.
Using these data sets plus a pooled data set of the 7- and 10year sets, five ARIMA models were developed, one from each data set.
The parameters of these models are listed in Table 5.2. Each of these
•
131
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132
models were used to generate 500-year monthly streamflow data which were
then used in the simulation of the reservoir operation to compute
the
benefits to be derived from the releases. The economic
and technological parameters used in the simulation procedure are listed
in Table 5.3.
Before discussing the results of the simulation, let us list the changes
which were made as a result of the preliminary runs of the program.
The first change was the criterion for the
determination of the
draft level, D . The draft level, as stated earlier, was to be
the
L
bigger of the requirement for the purpose, irrigation and power
production, of the project. The power requirement was the
water needed to
meet the capacity of the plant size selected. Since the power
requirement was always bigger, meeting it sometimes meant depleting the reservoir. This led to greater deficiencies in meeting the following irrigation requirements. Since the primary purpose of the project was
irrigation, it was felt that that requirement must be met first. Therefore, the draft level was set to the irrigation requirement
The second change was in power computation. Since the power
production is now a secondary purpose, imposing a penalty for not meeting the capacity would be defeating the purpose of setting the draft
level to the irrigation requirement. Therefore, the penalty portions
in the power benefit function were eliminated, leaving the benefit
function for the power purpose as:
P=
pow
(5.26)
133
Table 5.3. Cost and Benefit Parameters Used in Computation
Parameters Value 0
Power plant cost per KW capacity
1,045* ($909.00)
Price per KW-hour (residential)
0.21**
Penalty for overdesign (power)
0.00
Penalty for underdesign (power)
0.00
Worth of water to irrigation per acre-foot
41.20
Penalty for water deficiency per acre-foot
41.20
Canal cost per mile
43,000.00
Cost of dam per cubic yard:
Earth
Concrete
5.00
75.00
* Source: Chen (1978) "Economics of Low-Head Hydro, U. S. Case Studies."
**Adjusted from 1976 rate. Adjustment explained in text.
134
Also, the unit sale price of 3.3 pesawas
currently charged to
customers for power consumption (1976) was adjusted to reflect
the current unit cost of the power plant. Because power in use
now is produced from a plant which was built in 1965, and therefore cost
less, it
was found to be uneconomical to include the power addition if the same
unit price is to be charged for energy produced from a plant
whose cost
is nearly seven times as much as the old plant.
To reflect the present cost, a simple linear adjustment given by:
P
D
adj
P 1976
was used. P
C
1976'
adj
c
1976
(5.27)
1965
is the adjusted unit energy rate; P 1976 the 1976 rate;
the unit capacity plant cost as at 1976 (Chen, 1978) and C
that of 1965. The adjusted rate as computed by Equation 5.27 compares
6 '
well with figures quoted by Abudu (1976) and reproduced in Table 5.4.
With these changes made, the reservoir operation simulations were
performed.
Simulation Results
The objectives of this section are to present the results from
the simulation procedure, to discuss these results, and, based on the
discussion, to evaluate the decision taken to postpone the project.
Since the original decision was taken on the project for its irrigation
purpose alone, the discussion and the evaluation will, initially, be
135
Table 5.4. Economic Parameters for the Power System
System Akosombo*
(completed)
Kpong*
(under construction)
Bui*
(projected)
Nsuaem**
(proposed)
Capacity Index
Cost (U.S. $/kw)
Unit Energy (KWB)
Sale Price (pesewas)
144
2.1
1,030
14.9
1,165
18.0
909
21.0
* Source: Abudu (1976).
**Based on 1976 Akosombo unit energy sale price of 3.3 pesewas.
136
based on that purpose. The results from the power addition
will be
presented later. In the process of evaluation, some
questions raised
earlier will be answered.
The expected net benefits derived from the reservoir releases
for its use in irrigation, are presented in Table 5.5. Comparing
the
results, from the use of the various data sets as shown in Figure 5.7,
it is observed that, for all the various data sets, the maximum expected net benefits result from the reservoir size of 28,000 acre-feet,
the maximum possible capacity at the site. However, these net benefit
values do not differ much from those of the 20,000 acre-feet and 10,000
acre-feet reservoirs. The differences are in the order 1.9 and 4.3
percent between that of the 28,000 acre-foot one and those of 20,000 and
10,000 acre-foot, respectively.
It is also observed from Figure 5.7 that the net benefits from
the use of the transferred data were higher than those using the observed
data. For example, the 12-year transferred data set resulted in 12.3
percent higher net benefit estimates than the 10-year data set. The
higher net benefits with the transferred data sets can result only from
higher flow values, which meant that deficiencies were low. The higher
flows, in turn, can result if: 1) the period was wetter; and 2) the
flows were overestimated.
Figure 5.8 shows plots of regression lines used by the consultant (Nippon Koei, 1967) for data transfer from Oketsew to Nsuaem
(labeled "pre-report") and that computed with available observed data
(labeled "post-report), common to the two gaging stations. The prereport line (obtained from catchment area ratio method), undoubtedly,
137
Table 5.5. Expected Net Revenue from Irrigation
Data Set
Reservoir
Site
Reservoir
Size
3
x 10
(acre-feet)
Expected
Net Revenue
6
x 10
(0)
Standard
Deviation
of Revenue
5
x 10 (0)
5-year
Nsuaem
10.0
20.0
28.0
1.300
1.342
1.413
4.855
4.735
4.641
7-year
Nsuaem
10.0
20.0
28.0
1.531
1.536
1.545
3.477
2.953
2.347
10-year
Nsuaem
10.0
20.0
28.0
1.259
1.315
1.369
4.814
4.666
4.359
12-year
Nsuaem
10.0
20.0
28.0
1.533
1.543
1.562
2.986
2.401
1.765
10-year*
Nsuaem
10.0
20.0
28.0
1.191
1.263
1.331
4.258
4.078
3.787
Pooled*
Nsuaem
10.0
20.0
28.0
1.473
1.5117
1.547
2.777
2.320
1.755
17-year
Oketsew
1.093
1.102
1.130
4.617
4.603
4.547
0.89
1.72
3.68
138
1.6
12-year data set
7-year data set
"p oole d "
1.4
4.)
w
t2
V
0
1.0
Figure 5.7. Net Benefit Function for Reservoir
Design (Irrigation).
139
2000
o
1
0
[
f
200
400
I
j
600
Oketsew Flows
1f
800
I
f
1000
(cf s)
Figure 5.8. Regression Relationship between Nsuaem
and Oketsew Data.
1
1200
140
will yield higher flows than those of the post-report line.
Does it
mean that the flows used by the consultant
were overestimated?
To answer this question the 8-month streamflow data
collected
before the report was published were plotted
on Figure 5.8. The prereport line, computed by the catchment area ratio
method, slightly
underestimated these flows. This, in effect, means that the pre-report
flows were even higher than those used for the reservoir design. Also,
referring to Figure 5.2a, it is observed that flows after 1969 were
lower than those before. The post-1969 flows reflect the 5-year drought
which engulfed the whole of West Africa, resulting in massive food aid
programs to the region during that period.
Using the transferred data sets, the expected net benefit versus
reservoir size indicates that any reservoir sizes (up to the maximum
possible size of 28,000 acre-foot) will yield net benefits close to
that computed using the linear programming model (Table 4.4) less the
annual dam and canal construction costs. This means that deficiencies
were low. Therefore, the consultant did not err in selecting a reservoir size of 20,000 acre-feet.
However, the issue here is not the quality of information but
rather the integrated measure of the information--what impact does the
information have on the decision? Using the results from the 10-year
data set, it is computed that using a 20,000 acre-foot reservoir instead
of 28,000 acre-foot would result in annual loss in benefit of the order
of 3.1 percent. Postponing the project, on the other hand, has resulted
in a 100-percent loss in benefit from the 20,000 acre-foot reservoir, and
141
saddled the country with an annual bill of
01,034 (Table 5.6) for each
of the five gaging stations installed after
the publication of the con-
sultant's report.
If there was a site with larger capacity, i.e., assuming
the
reservoir characteristic curve could be extended as shown in Figure 5.9,
the resulting expected net benefit and its standard
deviation versus
reservoir capacity will be as shown in Figures 5.10 and 5.11. It is
observed that the benefit curve has nearly a flat crest. This indicates
that there can be a wide choice of reservoir sizes with very little difference between their resulting expected net benefit if the maximization
of net benefit is the decision criterion. In such a situation it may
be economically wise to base design decision on need rather than net
benefit maximization.
The flat crest also suggests that if one is uncertain about the
hydrologic information, a stagewise construction approach may be advisable. By this approach, the beneficiaries will not be deprived of services and goods from the development and revenues from the development
could be used to expand it when the need arises. This approach would
also permit more information to be collected and also advances in technology to be incorporated in the design decision of the subsequent
stages of the development.
Worth of Procedure
The integrated measure of information does not only result from
hydrologic knowledge but also from the procedures used to incorporate the
knowledge into the decision. Therefore, the importance of the procedures
should not be overlooked.
142
Table 5.6.
Cost Statistics on Establishing and
Maintaining a Stream Gage in Ghana
Cost of automatic gage recorder
0
1,000.00
Cost of materials for installation
450.00
Cost of labor for installation
390.00
Total cost for installation
1,840.00
Maintenance cost per gaging station per annum
400.00
Compensation for gage reader per annum*
360.00
Life of gage
10 years
Interest on gage cost
8 percent
Annual cost for gage installation
Total Annual Cost
274.00
0
1,034.00
Source: AESC (1978).
* Gage readers are volunteers compensated for time used.
•
143
so
6.0
otn
▪
5 . 0
90
4.0
..-1
m
•
x 3.0
30
o
o
2.0
20
40
60
20
100
Reservoir Capacity (acre-feet x 10 3 )
Figure 5.9. Nsuaem Reservoir Characteristics
Extended.
--
144
Set
v esx
1.5
1.1
io
40
6080ilOO
Reservoir Size (acre-feet) x 10
Figure
5.10.
3
Expected Net Benefit Function from
Extended Reservoir Characteristics.
145
Figure 5.11. Standard Deviation for Irrigation Net
Revenue (10-year Data Set).
146
The above discussion has been based on the
results from the use
of the conventional procedure which has an
underlying assumption that
the parameters of the streamflow process model and
process model itself
remain the same. From Table 5.2, it is observed that while
the streamflow process, from all the data sets, is modeled by an autoregressive
model of order one, after seasonality differencing the logarithmic transformed data series (ARIMA (1, 0, 0) x (0, 1, 0)
12
), the parameters do
change. The analysis was therefore repeated using the Bayesian procedure which takes into account, also, the variability of the model parameters.
The results of the Bayesian, using the 10-year data set, was a
2.8-percent lower net benefit, but with a reduced uncertainty, as indicated by the standard deviation (also shown in Table 5.5) than that of
the conventional procedure. This means that considering natural uncertainty alone may lead to overestimation of net benefit.
Using the 7-year data set as prior information on the parameters
of the 10-year data set, a higher net benefit value (11.8 percent) than
the 10-year set was obtained with a reduced uncertainty. This value is
only 1 percent below that of the transferred data sets. The closeness
of the results from the pooled set to that of the transferred data sets,
lends credence to the results of the transferred data set. It also
shows that the method of data transference was accurate. In all the
cases, the use of the 28,000 acre-foot reservoir yielded the maximum
net benefits.
147
From the previous section and this one,
it has been shown that
no matter what the type of information and the
analytical procedure
used, for the irrigation purpose, the size of reservoir for maximum
net benefits is 28,000 acre-feet. It can, therefore, be concluded that
for the reservoir size choice, the decision is insensitive to the
hydrologic factors.
One might ask why the design decision is not sensitive to the
hydrologic factors since they represent the information on extent of
the water resource.
A study of the four data sets used in this study reveals that
all the minimum flow volumes during the wet periods in the records
exceed the maximum capacity of the reservoir that can be created at the
site. From Table 5.1, it is found, also, that the draft requirement
during these periods is either zero or small, and therefore can be met
from the spill. The full capacity of the reservoir will, therefore,
be available for use in the drier periods.
If, however, the draft requirements during the drier periods
exceed the water stored and flows during those periods, then it is only
the reservoir with a higher capacity that would yield the higher net
benefit. From the results and the discussion above, a simple decision
rule can therefore be developed to serve as a guide to decision makers
in the developing countries as to when hydrologic factors may be crucial
to design decision. The design rule can be stated as follows:
148
if
draft requirement
maximum possible reservoir capacity
>1
and
minimum wet period flow volume
maximum possible reservoir capacity
>1
then design decision will not be sensitive to the local hydrologic factors and the reservoir size to yield the maximum net benefit is the
maximum possible capacity that can be created, other factors remaining
the same. This rule is found to be valid regardless of information
sources used.
Power Addition
The expected net benefits to be derived from the power addition
to the original project purpose are as presented in Table 5.7. From
this table it is observed that the power addition will not change the
reservoir design. Figure 5.12 shows that for the Nsuaem Project, a
power plant capacity of not less than 31,000 kilowatts will be needed.
Sensitivity Analysis
The decision strategy requires, as input, not only hydrologic
parameters but also others including the economic and technological
inputs. It is, therefore, appropriate that these inputs be also subjected to analysis to determine their influence on the decision.
Altogether, four inputs were evaluated for their effect on the
selection of reservoir size for the primary purpose of the project:
149
Table 5.7. Expected Net Revenue from Power
Data Set
Site
Reservoir
Size
(acre-feet)
Net Revenue
6
Z x 10
Plant Size
M.W.
5-year
Nsuaem
28,000
1.700508
31
7-year
Nsuaem
28,000
4.278099
53
10-year
Nsuaem
28,000
1.267283
29
12-year
Nsuaem
28,000
4.278958
53
10-year*
Nsuaem
28,000
1.209783
29
"Pooled"*
Nsuaem
28,000
2.782770
35
17-year
Oketsew
890
8.758130
20
17-year
Oketsew
3,682
1.208853
26
* From Bayesian procedure.
150
5.0
10-yeAr data set
30
50
Power Plant Capacity (MW)
Figure 5.12. Power Plant Capacity Selection.
151
1) the overall irrigation efficiency; 2)
construction costs; 3) the
magnitude of the penalty coefficient; 4) changes in prices of commodities produced from the project. The values of
these parameters, which
were held constant in the earlier analysis, were varied,
one at a time,
to determine their effect. The 10-year data set was used
for these
analyses.
Figures 5.13 through 5.16 show the results from these analyses.
It is observed that the effects of the construction cost and the overall
irrigation efficiency are similar in the sense that, as their values
increase the use of small reservoir size becomes economical. On the
other hand, the penalty coefficient indicates that if the suffering of
the intended beneficiaries is important then it will be economically
wise to invest in the bigger reservoir.
These two conflicting situations can be resolved by a compromise
analysis which might require that social and some other, non-quantifiable
factors be taken into account. This is the reason why the multiobjective
alternative selection approach is included in the strategy.
The fourth parameter, the worth of the water released on the
price of produce, had no effect on the reservoir size selection. These
analyses indicate that the uncertainties on the economic and technological inputs are more important than the hydrologic input in this project.
Alternative Selection
One might wonder why the consultants recommended the creation of
a new reservoir instead of using the existing Kwanyaku Reservoir if some
of the economic factors, especially the construction cost, indicated the
152
1.4
R1 = 15,000 acre-feet
P
2
= 20,000 acre-feet
R 3 = 28,000 acre-feet
1.0
4
6
a
Figure 5.13. Effect of Dam Cost.
153
1.7
III
0.5
IIIIIIIIIIIIIIIIIII
0.6
0.7
0.8
Irrigation Efficiency
Figure 5.14. Effect of Technological Uncertainty.
154
1.5
'
\
s
\
'
1.0
\
s
n
n \
n \
w
o
\,
n n
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14k
0
0.0
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R
1
R2
-0.5
R3
= 15,000 acre-feet
= 20,000 acre-feet
= 28,000 acre-feet
-1.0
11
III!
25
SO
1 1 111111111IFIIIIIIIIIIIIIIIIIIii
75
100
125
150
175
200
Penalty on Deficiency
Figure 5.15. Effect of Deficiency Penalty on Irrigation
Benefits.
225
Cedis
(0)
155
1.2
1.0—
R1 = 15,000 acre-feet
R2 = 20,000 acre-feet
R 3 = 28,000 acre-feet
0.0
iï
0
I
I
J
50
I
I
I
I
J
100
1
I
150
200
250
Cedis (Z)
Worth of Unit of Water (/acre-feet)
Figure 5.16. Effect of Worth of Unit of Water on
Irrigation.
156
use of a smaller reservoir. Table 5.8 displays
the capabilities of the
alternatives against the decision criteria selected earlier to aid
in
the evaluation of the alternatives.
It is obvious from the decision tableau that the Nsuaem-Kwanyaku
combination system dominates the other two alternatives; and
therefore,
there is no need to embark on a multiobjective decision analysis
as
recommended in Chapter 2. Apart from project cost and the land
inundated criteria, in all the other criteria the combination alternative
system either compares favorably or dominates the other alternatives.
At present, the Nsuaem site is not utilized and therefore it is
difficult to assess its value. However, the reservoir created on the
land would serve not only recreational purposes as listed in the criteria,
but also fishing, which might serve as a source of protein for the residents. As to the cost criterion, the benefit-cost ratio in the three
parameters compares faborably.
It is, therefore, concluded that the consultant did not err in
recommending the construction of the Nsuaem Reservoir.
Summary
This chapter dealt with the determination of the capabilities
of the alternatives selected. It dealt also with the evaluation of the
decision taken to postpone the Ayensu Project. It was found that among
the three alternatives, the Nsuaem-Kwanyaku combination system will
yield the highest maximum net benefits for all the decision criteria
considered.
•
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158
On the decision evaluation, it was realized that the hydrologic
factors upon which the decision to postpone was based, was not sensitive
to the design decision. All the four data sets considered resulted in
same design but slightly different net benefit estimates. It was also
realized that both the conventional and Bayesian analytical procedures
may yield the same design but the Bayesian indicates less uncertainty.
CHAPTER 6
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS
The sections here summarize the earlier chapters and list the
conclusions from the study. There is also a section which recommends
further work that has to be done in the use of the strategy developed.
Summary
Public-sector decision making generally involves a number of
complex quantitative and qualitative issues. Decision making in water
resource developments is no exception. It appears even more complex in
developing countires where the information upon which the decision is to
be based may either not be available, or is limited.
Because of these complexities in decision making, none of the
currently used decision methodologies in water resources, by themselves,
is adequate as an aide to decision making. Rather, a combination of
concepts of these methodologies, selected for their appropriateness to
particular phases of the decision-making process is considered more
adequate.
In this study, a decision strategy is developed by adapting
cost-effectiveness, benefit-cost and Bayesian concepts to the needs and
requirements of decision making in water resources developments in developing countries. In addition to the strategy itself, some methodologies
have been suggested which are designed to: 1) optimize the total problem
159
160
solving process rather than just the decision per se; 2) provide for
insufficiencies in data base as well as for uncertainties in causeeffect relationships; and 3) provide for human judgment, subjective
values and uncertainty which are essential elements in decision making.
Chapter 1 dealt with an introductory discussion of the situation
in developing countries, the motivation which led to the study, and the
objectives of the study which, in addition to the strategy development,
included the evaluation of a decision which had been taken to postpone
a water resource development project in Ghana. The background of the
project was given and the climatic, economic and social conditions in
the project area were also discussed.
Chapter 2 described the three decision methodologies whose concepts the strategy was derived from and discussed their merits and
demerits which make each one of them inadequate as a decision-making
methodology. The strategy was then introduced as a guide which defines
specific steps to be followed in arriving at a good decision. The steps
include:
1.
Problem definition and objectives selection.
2.
Definition of decision criteria.
3.
Alternative proposition.
4.
of data
Synthesis and analysis of alternatives, and evaluation
input adequacy.
decision criteria which
5. Best alternative selection based on
such areas.
reflect all factors affecting a decision in
161
Prior to the discussion of these steps, the requirements of
rationality and general applicability which the strategy was to meet
were described.
Chapter 3 summarized the methodologies that can be used to
acquire hydrologic data and augment an existing record without postponing the project. These methodologies were:
1.
The statistical methods, which were transfer of data from one
station to another within the same basin or from another basin,
via their physiographic characteristics, and augmenting an
existing record with a longer one from another station, if there
is a period common to the two records.
2.
Those based on the engineers experience of the climatic and
vegetal cover in the basin and the engineer's ability to synthesize data from information obtained from local residents.
It went on to describe uncertainties in hydrologic information
the
and how to deal with the natural and sample uncertainties using
hydroBayesian concepts. With regard to the uncertainties in the use of
the Box
logic data, it described the use of the short-memory models like
for the
and Jenkins ARIMA models and the Bayesian decision approach
determination of worth of additional data.
Chapters 4 and 5 contained the description of the use of the
in the evaluation of
strategy and some of the suggested methodologies
Chapter 4 described the
the decision taken on the project in Ghana.
decision criteria which
problems and goals of the development, the
included effectiveness (capabilities of the alternatives), cost,
162
schedule, social and environmental factors, and the three
alternatives
for the development. For the economic criteria, the
linear programming
model was used to compute cost and benefit coefficients which were
used in the decision function. The three alternatives considered
in the
study were:
1.
Using the existing Kwanyaku Reservoir for irrigation and power.
2.
Increasing the capacity of Kwanyaku Reservoir for both purposes.
3. Building a new reservoir at Nsuaem in addition to the existing
reservoir at Kwanyaku.
Chapter 5 took on the design of the alternatives using the
Nsuaem-Kwanyaku combination system as an illustration. In the design and
evaluation process some of the methodologies suggested in Chapter 3 were
used. The methodologies used included the data transfer from one station
to another within the same basin and from a station in another basin,
using the catchment area method. This method was selected over the other
augmenting and acquisition methods to enable the comparison of designs
as presented by consultants (i.e., without observed data) and that using
the recorded data. Since both data sets were short, ARIMA generating
models were developed from them to synthesize more data. The generated
monthly streamflow data were used in the reservoir operation simulation
and the expected net benefits were computed from the releases from the
reservoir for hydropower generation and irrigation.
The application of the strategy in the decision evaluation demonstrated the practicality and utility of the strategy and the methodologies in decision making. In determining the economic feasibility of the
163
project, it was realized that there was only a
small difference between
the expected net benefits using the transferred
data sets and the
observed data sets. In effect, it can be said that
the lack of or
the limited hydrologic data did not have much
influence in the project'
outcome, and as such, it is unprofitable to have
postponed the project
because of lack of hydrologic information.
The reasons for the small influence of the hydrologic information
on the design decision were deduced as being:
1.
The simple methods of data transfer and augmentation proved to
be accurate.
2.
The minimal annual flood volume is much greater than the reservoir size that can be created due to topographical limitations.
Because of this, only a small part of the flood waters can be
stored for use in drier perioas.
3. The environmental and social effects of the project are simple
and easily evaluated from the compiled hydrologic information.
The small influence of hydrologic uncertainties due to lack of
or limited hydrologic data was confirmed when the two uncertainty analytical procedures, conventional and Bayesian, yielded nearly the same
values as shown in Table 5.5. It was the economic and technological
inputs which had greater influence on the project's outcome, as shown by
the sensitivity analyses in Figures 5.10 - 5.13. Therefore, postponing
the project to collect more hydrologic data has deprived beneficiaries
of goods and services which the development would have provided.
164
Based on the results and the
reasons given above, a decision
rule was derived to guide decision makers as
to when to consider local
hydrologic inputs as crucial to decisions on simple
water resource developments. The rule, based on the climatology and
topographic conditions
in the basins, states that if the ratio of the
potential demand (draft
requirement) to the maximum possible storage capacity at
the site is
greater than unity and the ratio of the minimum annual flood volumes
to
the storage capacity is also greater than unity, then the local
hydrologic
inputs may not be crucial to the project's outcome.
It was observed that the expected net benefit versus reservoir
capacity curve (Figure 5.10) has nearly a flat crest and therefore the
differences in net benefits by the use of smaller or bigger reservoir
size were small. This suggested that the decision on reservoir capacity
may not be based on the benefit-cost decision criterion but rather on
need or requirement. As such, a stagewise development procedure can be
adopted so that as the need increases the development can be expanded.
Meanwhile more information could be collected to reduce uncertainty in
the decision making.
Conclusion
The case study analyzed here indicates that the strategy can be
used as a guide to decision making in water resources developments. It
showed how some concepts of the existing methodologies can be combined
to yield a useful methodology. It also showed how high the cost of postponement of a water resource development project because of lack of
adequate hydrologic information can be; and therefore, it may generally
165
not be profitable to postpone a development project. In
doing so, it
confirmed what earlier researchers like James et al. (1969) have shown-that hydrologic variables may not always be crucial
to decision making.
Under similar conditions, as described in the case study (i.e., topography, tropical wet and dry season climatology, and simple environmental
conditions), a water resource project can be undertaken with limited data
or no data at site as long as data transfer or augmentation are possible.
Also in simple water developments, the design decision may not
always depend on the benefit optimization criterion but on needs. Therefore, a stagewise development approach may be better. This approach
allows collection of more information and incorporation of advances in
technology in the decision making on subsequent stages of the development.
Recommendations
While there are many attractive features which make the strategy
developed in this study potentially useful for developing countries, its
demonstration here has emphasized only the economic and hydrologic factors of the decision-making process. This was because the other factors,
like the social and environmental, were predictable. However, the
strategy permits equally the treatment of these factors when they are
not easily predictable. A demonstration in a case study, in which all
factors affecting the decision are treated, will enhance the utility of
the strategy.
Secondly, even though the strategy is simple and easily understandable, the treatment of the hydrologic uncertainty as presented here
involves techniques from a branch of mathematical statistics which may
166
fall outside the educational curricula of the
professional engineer,
except those who have had the
opportunity to extend their knowledge at
post-graduate level. However, the approach as adopted here is
simple.
It is also an attempt to stress the usefulness of
such an approach in
decision making in developing countries.
As a final note, the reader is reminded that the objectives of
this study were to develop a decision strategy which can take factors in
developing countries into consideration in decision making in water
resource development and demonstrate its applicability. This dissertation has described how the study objectives have been met. The intention was not to introduce a new concept but to adapt existing concepts
for solution of problems in developing countries. In so doing, two
important issues have been proved:
1.
That the existing simple methodologies of data transfer and
augmentation are accurate.
2.
That these simple methods can be combined with the recently
introduced concepts like synthetic data generation and Bayesian
theory which are found mainly in research literature, to yield
a useful methodology that can be used in developing countries.
It is hoped that this study will be the beginning of an effort
to integrate the currently used and new concepts, and that the resulting
strategy developed here will contribute towards helping decision makers
in developing countries to better evaluate water resource developments.
APPENDIX A
THE RESERVOIR OPERATION SIMULATION PROGRAM "SIMUL"
USER'S GUIDE
167
168
The computer documentation contained in this appendix has been
prepared in conformity with the proposed ASCE
Standard for Engineering
Computer Program Documentation as submitted by the
Subcommittee on
Programs Documentation (1973).
Section 1: Program Identification
Program Title: Monthly Reservoir Operation for Irrigation and Hydropower
Production.
Program Code Name: SIMUL.
Program Writer: Kwabena Oben-Nyarko.
Program Documentation: Kwabena Oben-Nyarko.
Organization: Department of Civil Engineering
University of Arizona
Tucson, Arizona 85721.
Date: October 19, 1979.
Updates: None.
Source Language: Fortran IV. Cyber 74.
169
1.8 Abstract
Program SIMUL simulates the operation of a simple
reservoir for
hydropower production and irrigation, and computes
revenues from the sale
of: 1) the energy from the power system; and 2) the
yield of crops
obtained using the irrigation water. It uses a
monthly generated streamflow series to compute the releases from the
reservoir based on an operation rule (explained in the main text). Output from the
program consists of listings of inputs and revenues obtained from
the power and
irrigation system.
Section II: Engineering Documentation
Program SIMUL is the main program of a set of five programs
written to determine the economic feasibility of a water resource project. The other four programs, DIF, AUTO, SIMPS and MAXL are subprograms whose outputs are used as input to the SIMUL.
The starting point for the use of SIMUL is to determine a
streamflow-generating model which will generate a series to be routed
through the reservoir to determine releases. The synthetic generating
model used here is the Box and Jenkins autoregressive integrated moving
average model (ARIMA). The steps of identification, estimation of
paramaters and diagnostic check, as suggested by Box and Jenkins (1970),
are strictly adhered to.
The identification consists of determining the model which may
be either the autoregressive or moving average or a mixture of both,
and the order of the model. If the raw data input needs differencing
before stationarity is achieved, this is performed by DIF, using the
170
IMSL library program FTRDIF which, combined with FTAUTO (also
an IMSL
program), via AUTO, determines
the auto and partial auto-correlation
values to aid in determining the model and
its order. SIMP is used
with FTSIMP to give a first estimate of the parameters
and evaluate
the model based on a selected
confidence limit. MAXL uses FTMAXL to
determine the final parameters estimates
and the white noise variance.
These values are then input to the SIMUL which, with
the inputs of the
economic and technological parameters along with the operation rule
selected, computes the revenues from the various systems of the project.
Because AUTO, SIMPS and MAXL need the stationary series (i.e.,
output from DIF) as input, each of them is combined with DIF to avoid
punching of the stationary series data cards. Also, it is possible to
combine all of them, as was done here, to avoid punching outputs from
each of them to be used as inputs to others. This can be done only
when each of them has first been run individually.
Two procedures are possible with the SIMUL:
1.
Where the computed hydrologic parameters are assumed constant
and can be used to generate any number of streamflow series.
2.
Where the parameters are assumed also to be variables and
therefore are generated from their probability distribution
functions (pdfs).
The former is differentiated from the latter by the number of
simulations (NSIM) which is "one" when the former is used, or greater
than "one" when the latter is used.
171
Output from program SIMUL consists of:
1.
Listings of hydrologic parameters obtained from DIF-AUTO,
SIMPS and MAXL.
2. Listing of economic and technological inputs.
3. Results of economic feasibility computations, i.e., net revenues
from the systems.
Method of Solution
An understanding of the method of solution used in these programs
requires knowledge of linear models as developed by Box and Jenkins
(1970), the Bayesian decision theory as expoused by Davis (1971) and
basic hydraulics involving continuity equation, reservoir design and
reservoir operation. Chapters 3 and 5 of the text contain discussions
on some of the listed topics. The rest could be obtained from basic
hydraulics books.
The difference between the text and the program in terms of
computational procedure is that integrations are approximated by simulations, i.e.:
E[NB/e] =
Q
1 n
f(NG)f(Q)dQ = — E f(NB)
n
Q
i=l
f
and
E[NB] 2
= f f
f
0
Q
f(NB)f(Q)f(Q)dQde -
1
r n
r
r
f(NB)
rxn e=i t=1Q,e1
172
The variance is given by:
2
S =
1
2
() (NB ) 2- ( —
NB) )
n-1
The symbols are as defined in the main text.
Program Capabilities
Program SIMUL is dimensioned to handle ten different reservoir
sizes, 20 turbine sizes and 50 years of project life. However, these
can be modified to any number, depending on the system on which it is
run. With one simulation (i.e., the conventional) the cost is $1.45 per
runs needing a core memory of 120 K. For 50 simulations (i.e., Bayesian)
the cost is $7.63 per run on the University of Arizona's CYBER 74.
Program and Data Listing
Figure A-1 lists the main program and its subroutines for SIMUL.
Figure A-2 lists DIF-AUTO, SIMPS and MAXL and their data inputs.
Printed Output
Figures A-1 and A-2 list the outputs from SIMUL, DIF-AUTO and MAXL.
Program Options
There are only two program options:
1. Normality Test Option: If the INORM switch is on, the releases
DD are tested for normality by calling NORM where the histogram
and the cumulative distribution function are plotted.
173
2. Plotter Option: If IPUDTswitch is on, the plots of turbine
versus revenues and reservoir sizes versus revenues are plotted
using subroutine PLOTA. The subroutine PLOTA was obtained from
Oben-Nyarko (1976).
174
74/74
1
ORTRO TRACE FIN 4.6+428 10 1 22 1 79 19.0
PROGRAM 5IM01(INPOT,OUTPUTITAPE5RINPUT,TAPE6ROUTPUT,DEBOGROUTPLIT
PROGRAM SIMUL IS A
RESERVOIR MONTHLY OPERATION PROGRAM WHICH COMPUTES
REVENUES FROM THE PURPOSES TO WHICH RELEASES FROM THE PESERVOIF ARE
PUT. THE PUPOSES USED HER( APE POWER
IRRIGATION. THE RELEASES APE
BASED ON A SIMPLE OPERATION RULE WHICHANG
l'..i EXPLAINED IN THE ?AI
I TEXT.
INPUT TO THE PROGRAM COSISTS OF THE ECONOMIC,
TECHNOLOGICAL ANT
-YDROLnGIC PARAMETERS . THE ECONOMIC PARAMETERS CLINSIT
OF THE COST
AND BENEFIT COEFFICIENTS, THE TECHNOLOGICAL PARAMETERS CONSIST OF THE
EFFICIENCIES OF THE SYSTEMS USED ANo THE HITRAOLIC CONSIANTS.THE
-OLOGIC PARAMETERS CONSIST OF THE STREAmFLow huDEL
PARAMETERS.
THE HYDROLOGIC PARAMETERS ARE THUSE or THL 801-JENKINS
AR1MA MODEL
11,0,01*(0,1,0) WHICH IS USED TO GENERATE SYNTHETIC MONTLY STREAMFLOW
AS INPUT 10 THE RESERVOIR. RELEASES FROM
THE RESERVOIR ARE USEU FOR
HYDROPOWER GENERATION AND IRRIGATION.
OUTPUT OF SIMUL CONSISTS OF LISTINGS OF THEM ECONOMIC, TECHNOLOG
AND HYDROLOGIC INPUTS,AND 12T THE EXPECIED REVENUES
FROM THE
POWER AND IRRIGATION.
SIMUL IS CAPABLE OF VARYING THE HYDROLOGIC PARAMETERS BY GENERATIN
-G NEW PARAMETERS BASED ON THEIR por. A
SWITCH ( IF NSIM.GT.11 IS RUT
IN FOR THIS PROCEDURE (FIAYESIAN). IE(NIS/N .10. 1)144E CONVENTIONAL
PROCEDURE IS USED.
5
10
15C
20
C
25
30
C *********** ****** PROGRAM CARD
VARIABLE
1
ECONOMIC
INPUTS
0 4.* ******* 4.0*****Sis, *****
,
DEFINITION
FORMAT
35
40
C
45
C
CE---CONSTR. COST EARTH DAM
CC—CONSTR. COST CONCRETE DAM
PC---POWER PLAT COST /KW
CANC-TOTAL CANA COST
BR---UNIT WORTH OF n.ATLP FOR PRIG.
PP---uNIT SALE PRICE FOR ENERGY
PIP--PENALTY FOR II-FIG.
PEP--PENALTY FOR POKER
2
50
110.2
TECHNOLOGIC
F10.5
111--LGAG FACTOR
CEE--OVERALL IRRIG. EFFICIENCY
EFP--OVEEALL PENEE SYSTEM EFFICIENCY
XkW--CONVVF311.N FACTUR FIR HP TO KW
HP---HORSE POViflo (t, ,0)
(,AM--tN11
ICH1 Of WA1E.N.2.41
CINS T-PO4.Fk CLNVFF STUN CUNSTAf T 1?.
-
55
Figure A-1. Listing of SIMUL Program and Outputs.
175
3
60
C
65
C
70
C
HYDROLOGICAL
110.5
ARPS—AUIOPEGPESSIVE MODE( PARAMETEP
PMAS—MOVING AVIRAGF MOOFL PAPAM.
IP----NO. OF ARES PARAm
IQ ----NO. OF PEASPAPAM.
SHIFT—MODEL CONST.
EVWT--EXPECTED VALOr OF WI SERIES
NUIE VAPIANC1
PMAC---LIVERALL MOVIG AVERAGE
151E0—RANDOM NO. GENERATOR
WT IlL6INNINr, VALUES
ST GEN DATA 8EGINNING VALUES
WT STATIONARY SEPIES
CC
4
7:
C
80
C
OTHERS
110.5
xmnNS--NC.
OF NAYS IN MONTH( BFGINNI ,EG M/PCH
YIP—PERIODIC DRAFT LEVEL
SM RESERVOIR SIZE
VOL—VOLUME OF MATE PEALIN PAM
H
HEIGHT OF DA.
NOAT--- HL. Jr YLAN3ClSIPEAMFLOW DATA INPUT
CRF—CAPIIAL RECOVEFf FACTOR FOP 50 YP5(81C
85
COMMON /SV/SVAR(2,4)
COMMON /XD/SHIFT
COMMON1SL/IP,10,1W.ISEFO(5),APPS(2),PhAS(2).2(600).P1IAC,WNV,FT(5,
112/,SE5/
COMMON /77/Y(10,12),XMONS(12),NDAT
COMMON /TH/MTH
COMMON /SYS/IPT,IOUT
DIMENSION X1P(12),POW(10,3,50),EIPR(10,1,50 ) . 5 I 1-l8(10,3,50).TITL
1E161,VOLI101,Sm(10)0(10).WT(120)
DIMENSION 0(120 )
DIMENSION RWD(12)
DIMENSION TXPRI10),TYBP110I,XT5(10),CF(10 )
DATA IPT,IOUT/5,6/
90
95
MRS. 10
100
603
2
105C
MTH.12
XM.45752.
FORMAT(4110.4)
WRITE(IOUT.2)
FORMAT(1N1)
READ AND WRITE
TITIE OF R 7 nJEC1/STUDY
READEIPT,6bITITLE
WRITEEIOUT.5ITITEE
110
DEAD 01 HE1 INPUTS
READI111,901)YIP
READI ( PT,901)XMONS
901FORMAT) 1216.0)
Continued
Figure A-1. Listing of SIMUL Program,
176
115
READIIPT.902/CEF,XLF,CFP,UAMpXK.641P,CONST
READ ( IP 1,90 2)CRF.BR,P1P,PFP,CF,CL.PC,CANC,PP
READ(IPT , 902/SHIFT,EV.0,PNAC,WNV
902
FORMATI9F8.01
READIIPY,10/IP,10,LW
IF(IP.GT.0)READ(IPT.2015
READ(IPT,91)11SEFOM,J21,5)
NDAT210
READ(IPT. 4 00/1(Y(1,J1sJ21,121,I21,NOAT/
IF (IP.GT.0)READIIPT.20)1APPS11/.121,1P/
IF(IQ.GT.0)READ(IPT,20)1PMASI[1,121,101
WRITE(IUUT,4411ARPC(1),SNIFT,WNV,PMAC
441 FORMATI//T25,*P111 2 *,F6.3,/,725. 0 5HIFT 2SofF.2,/,125p*WHITE
IVARIANCE2*,F6.4,/.T25,*OVEP4LL M(JVING AVVRA(4 =2'06.4)
DO 330 I21,NDAT
00 331 J21pMTN
K2(I-11*MTH+J
331
0(K)2Y(I,J)*1.98*YMONSIJ/
330 CONTINUE
120
125
130
135C
0I Si
CONVERT INITIAL VALOUES TO AC—FT/CAY
DO 555 1.3,5
DU 556 J21,12
140
C
ST(I,J)2Y(1,J)*1.98*XM0NSIJ/
556 CONTINUE
555 CONTINUE
CCONSTANTS USED IN PROGRAM
145
C
150
C
NSIM2N0 • OF SIMULATIONS
NR2N0. OF ANNUAL STRANFLOWS GENLRATED
IP2LIFE OF PROJECT
NTS=NO. OF TUP11INES IPOWF4 PLANT SIZES) INVESTIGATED
FID52NO. UF RLSEPV0IF SIZES INVLSTIGATED
N4T2IINGTH OF STATIONAPY SFRILS
00 =BEGINNING POINT FOR PLOTTING
NN .MAX. Nn. OF POINTS 10 Pt PLOTTED
DIM =INTERVAL FOR PLOTTING Y—AYIS
155
160
165
170
RP
Figure
IPLOT21
NN225
0020.
DIM=10000.
NVAR22
NSIM=1
NP '5O
LP2NO
NTS23
NWT21013
NWT12NWT-1
XPP2LP*NSIM
XPI2XPP-1.
CANC21120000.
WPITEIIOUTPP2INSIM,NR
FOR(IAT(///25X,*NUMBFR UF SIMULATIOW.= 6 ,13,//,75Xv*IFNGTH UF '?A-CU).!)
A-1.
Listing of SIMUL Program, Continued
177
175
400
5
90
91
10
88
20
1..,I3/1//
FORMAT( 12F6 .0)
FORMATI30Y,8A10/////
FORMATI5F10.5,15/
FORMAT( 5I 10 )
FORMAT(8110)
FORMAT(PALO)
FORMATE8F10.1/
PERO.
DO 559 .1.1,NRS
180
559
CFCJI.O.
READ AND WRITE RESERVOIR CHAR4C1ERI5TICS
185
190
195
READ(IPT,700)1HID.121,NRS/
READEIPT.700/ISM(I),I=1,NRS/
PEADEIPTo7001(V01(1).1=1,NPS1
700 FORMAT(10F8.01
WRITEIIOUT,1121
FORMAT(/25Xp*FLEVATION *r7XfsEARAE11Y ,E,5X,*PAT. VOLUME*/)
112
DO 1 J=1,NPS
I
WPITE(1007,338/HIJ ) .SM(J),VOL(J)
FURMAT(25X.3)1 - 10.1,511/
338
DO 500 1.1INVAP
PEADIIPT,603/ISVAR(I.J),J=1,4)
500 CONTINUE
LIST THE INPUTS
200
205
210
WRITEIIOUT,111)PP,BR,PEPPRIR,CLFOLF
111 FURMA1(///725PEUNIT ENERGY PRICE ..E,F6.3,/7250WORTH OF UNI) WATER
1 TO IRRIGATION . ..,F6.3,/7250. PENALTY FUR PCNIR .*,f6.3t/125,*PENAL
1 1 Y FOR IRRIGATION ",E6.3,/T25.*OVEEAAL IRRIGATION EFFIC.
1,,T25,*LOA0 FACTOR .*.1- 6.31///
WRITE(IOUT,557)CE
557 FURMAT(///258p*COST OF DAM PER C)J-YD .*,F10.5/f/1
WRITEEIOUT#6/PC
FORMATI13F6.3/
444
FORMATI5X,* COST OF PLANT PER KW .*,E5.0///
6
INITIALIZE 1HE THREE-DIMENSIONAL ARRAY
DO 668 IX3=1,NRS
DO 667 115.1.NTS
DO 669 NSM.1.NSIM
215
FIRREIX3,115,NSM 1 .0.
POW(IX3o1V,NSM)=0.
STN8I1X3.LL5.NSMI= 0 .
220
669
667
668
CONTINUE
CONTINUE
CONTINUE
DO 501 JSIM=1,NSIM
IFINSIM.E0.1/60 TO IP 4
225
READ LIMITS OF GENFEATEE Mina EARAMETIPS
FUNCTI
GENERATE MUDEL RARtMETER_i DSIE,G MUNIE-EAPLU AFPRuACH NY
Continued
Figure A-1. Listing of SIMUL Program,
178
RNORM
230
DO 502 N.1.NVAR
VALUE.RNORMIN,JSEED)
IF ( N.E0.1)ARPS(1 ) .VALUE
IFIN.E0.2ISHIFT.-VALUE
235
502 CONTINUE
GENERATE WHITE MOIST VARIANCE 1WNV)
SS.O.
SSUM=0.
CALL DIF(NWT,WT)
DO 702 IW.2.NWT1
IW1.IW1
UT.WT(IW)-WI(IW1)*APPS(1)
SSUM=SSUM-FUT
SS.SS+UT*UT
702 CONTINUE
WV.SSUM/NWT1
VV.VIV*WV
240
245
250
COMPUTE RESIDUALS AND FIND THE WHITE NOISE
WNV.ISS- VV) /FLOATIN4T1 - 1/
255
COMPUTE OVERALL MOVING AVERAGEIPMAC/
260
701
PMAC.EVWT*11.-ARPS(I)/
WRITE(IOUT,701)ARPS(1),SHIFT,WNV,PMAC
FORMATI/25X.41E10. 4 .5X 11
SERIES BY EMSL
CALL SUBROUTINE GENI WHICH CUNVERIS GEN(PATED
SOPROTINE FIGEN1 TO MONTHLY GEVERATED DATA
265
124 CALL GENT
C********************* *** ***** ******************
BEGIN RESERVIJIR SIMULATION
270
SELECT RESERVOIR SIZE
DO 7 IX.1.NRS
CDC=CRE*(VOLTIX/4CE+CANC)
275
SELECT TURBINE 517E
TS.18000.
DO 100 L.1,NTS
IS.TS+2000.
PPE.TS*8760.*Y1F
CPS.TS*PC*CPE
280
rNFFGY GENFPATrO FfV. MLoiTH
TPM IS THE MAXI MUM PUSSIBLE
285
-
Figure A-1.
Listing of SIMUL Program, Continued
179
TPM.PPE/12.
NYY.O.
290
BP.O.
BIRO.
SO.SM(IX )
DO 601 NY.1,LP
NYY.NYY+1
POVER.O.
00.0.
DEFP.O.
DEFIR.O.
TPG.O.
DO 9 NM.10TH
JP.INTY-11*MTH+NM
WOIR.XtR(NM)/CEF
295
300
305
SELECT DRAFT LEVEL FOR PERIOD NM
DL.WDIR
USE OPERATION PULE TO COMPHTE RELEASES
310
72 WW.Z(JP)+SO
AA.DL+SMIIY/
IFIWW-AA/15,16,16
115
RELEASE D IF(WW.GT.AA)
16 D.WW-SM(IX)
320
COMPUTE POWER GI-NFRATED PG
325
330
335
340
PG.D*HIIX1*GAM*XWW*FFP*CCNST/HP
IF(PG-TPM)74,75,76
74 DEFP*DEFP+TPM-PG
GO TO 19
75 TPG.TPG+PG
GO TO 19
76 TPG.TPG+TPM
OVER.PG-TPM
POVER.POVER+OVER
GO TO 19
IFIWW-DL/17,1P,1 8
15
18 D.DL
PG.D*GAM*H(M*XKOIFF*COrST/HP
TFG=TPG+PG
DEFP=DEFP+TPM-PG
GO TO 19
17 D.WW
DEF1R=OFFIR+IWDIP - 01 4 CEF
31
Continued
Figure A-1. Listing of SIMUL Program,
180
19
SI.WW—D
SO.SI
IFISO.LT.0./S0.0.
OD•DD+D
9
CONTINUE
32
IFI1.E0.11WRITEIIOU1p32/CD,DEFP,DFFIP
FORMATI10X,3(E10.0,5X)/
345
C
350
COMPUTE Nt7 POWEP (YPS) AND IRVI.(XFIP) REVENUIS FOR EACH YEAP
'XPS.PP*TPG—PEP*POVER—CPS
XFIR.812#XM—PIR*OFFIR—CDC
XST.XPS+XFIR
355
SUM UP REVENUES FOP POWEP,9P,IPPIG,BIR
360
8P.E1P+XPS
BNB.BN8+XFIR*XEIR
365
601
CONTINUE
DETERMINE MEANS AND STANDARD DEVIATIONS
370
STN8(IXPL,JSIM).8N8
POW(IX,L,JSIM).BP/LP
FIRRIIX,1,JSIMIzBIR/1P
375
100
7
501
CONTINUE
CONTINUE
CONTINUE
DO 992 I.1.NRS
WRITE(IOUT,8)SM(I)
FORMAT(//1725,*RESERVOIR SIZE =*,F10.0i//)
TS.18000.
WRITE ( IOUT,661)
FORMATI//710,*NUMBFRÈ,8X,STURRINE SIZE*,5X,*POWEF BENS.98,*IPP RE
661
1N*,9X,*TOT. BEN. *,8X,*STAND. DFV.*/) •
AMAX.O.
DO 993 JvloNTS
T5.TS+2000.
XSD.O.
XSS=0.
XS=0.
DO 999 1.1,NSIM
XS*XS+POW(I,J,L)
XSD.XSD+STN8(I,J,1)
XSS.XSS+FIRP(I,J,1)
999
XBP*XS/NSIM
X8R=XSS/NSIN
XNE1.X8 ,'-fXRP
PST.(XSD—XPP*Y8R*X8P)/XPI
XSTD.SORTIPST/
8
380
385
390
395
Figure A-1. Listing of SIMUL Program, Continued
181
400
WRITE OUTPUTS
405
410
WRITEITOUT,80/J,TS,X1P,X0P,XNB,XCTO
IE(X8P.GT.AM4X) 60 TO 994
GO TO 993
994 AMAX.X8P
TSS.TS
80
FORMATI10X,15,5 ( 5X0:12.0))
993 CONTINUE
TX8P(1 ) .AMAX
XTS(I).TSS
TXBRII).X8R
415CPLOT
420
OUTPUT
IEI1PLOT.E0.1/CALL PLOTAIDTMINPS,TOP,CE,00,NN)
IMPIOT.E0.2)CALL PLOTA(PT,NTS,TXPP,CE,00,NN)
WRITE ( IOUT,81)
81 FORMATIM/1
992 CONTINUE
2000 STOP
END
Figure A-1. Listing of SIMUL Program, Continued
182
74 1 74
FUNCTION RNORM
OPT.° TPACF
rIN 4.64-428
10/72/79
19.07
1
FUNCTION RNORMIN.JSEED1
FUNCTION RNORM COMPUTES STOCHASTIC VALUES ACCORDING TO NoPMAL DIST.
5
COMMON /SV/SVARI2,41
SUMO.
DO 10 1.1,12
SUMRSUM+DRANDIJSEEDT
10
10 CONTINUE
VRSUM --6.
RNORMRV*SVAPIN041+SVARIN,11
IFIRNORM—SVARINs3/150,50,40
40 RNORMRSVARINO/
50 RETURN
15
END
FUNCTION DPAND
1
74/74
OPT.° TRACE
FIN 4.6+428
10/22/79
19.07
FUNCTION DRANDIJSEEDT
FUNCTION DPAND IS RANDOM NUMBER GENERATING ROUTINE. IT SHOULD BE
CHANGED WHEN DIFFERENT MACHINE fRUM O. Of A. CYBER 75 IS USED.
5
DRANDRRANFT0.01
RETURN
END
SUBROUTINE DIE 74/74
OPT.° TRACE
FIN 4.6+428
10/72/79
SUBROUTINE DIFILW.Z/
TO DIFFERENCE AN INLIq
5
FTRPIE
SUBROUTINE nu USES TPE IMSL SUBROLIIVE
ACHILVID. 10F STAIIONARY SER1ES
SERIFS 0111 1 1 STATTUNARITY 1 5
If THE COMPUTATION OF wNV
CALLED BACK Tn SIMUL TO BL USE(
COMMON /ZZ/Y110,121,XMONS1121,NDAT
COMMON /SYS/IPT,IOUT
10
15
20
DIMENSION 2I120T
READ1IPT.10TI 111 ,102,1P,IS,LZ
10 FORMAT(511O)
DO 12 IR1,NDAT
DO 13 JR1,12
KRII-11 4'12+J
Z(K)Y(
13
12 CONTINUE
FTPDIFIT01,102,IP,ISpLZ,Z,SHIET,LW,IERT
CALL
RETURN
END
Figure A-1. Listing of SIMUL Program, Continued
10.07.
183
SUBROUTINE GENI
1
5
10
74/74
OP1w0 TRACE
FIN 4.6442E
10/27/7q
SUBROUTINE GENT
C
C
C
C
C
C
C
SUBROUTINE
RANDOM NO.
SUBROUTINE
ANY NUMBER
OF MONTHLY
GENI USES ARIMA MODEL EARAMEILR5 APPS,RMAipPMAE,WNV AND
GENERATOR ISEED 10 GENERATE STATIONARY SERIES WT BY IMSL
FTGENI WHICH IS THEN CONVERTED TO STREAMFLUN SERIES.
OF DATA CAN BE GENERATED BY VARYING MOAT WHICH 15 THE NO.
SERIES GENERATED PER EACH 'SEED USED
COMMON ISL/IPpIC1,LW,ISEED151,ARPS(2),PMAS(2),Z(600).PNAC,WNVoST(5,
112),S(5)
COMMON /XD/SHIFT
COMMON /TH/MTH
COMMON /SYS/IPTpIOUT
DIMENSION 14(120),ZT(12),WA1900/
DATA MAXY,NDAT/5.120/
Jw1
DO 40 /Y=1,MAXY
15
20
CALL IMSL SUBROUTINE EISEN' TO GENERATE WI SERIES
25
CALL FTGEN 1 IARPS.PMAS1PMAC,SITY),WNV.ISEEDITY),IR,10,LW,W,WAT
CONVERT INITIAL VALUES TO LOG. E VALUES LESS SHIFT
30
DU 20 K.1,MTH
IT(K) ST(IY,K)+SHIFT
IF(ZTIK1.LT.I.I2T(K ).1.
ZTIK/wALOGIZT(K)1
,
35
20 CONTINUE
40
CONVERT NT SERIES TO GENERATED SERIES USING THE TRANSFORMED INITIAL
SERIES
C
DO 30 Lwl,NDAT
45
LI.MOD(L,MTH)
IFILI.E0.0/LI=MTH
2T(LI)22111.11+W(L)
Z(J) APE THE TRANSFORMED SERIES
50
55
ZIPmEXPIZTILITI—SHIFT
J=J+I
30 CONTINUE
40 CONTINUE
RETURN
END
Figure A-1. Listing of SIMUL Program, Continued
184
SUBROUTINE PLOTA
74/74
OPT.0
TRACE
FIN 4.6+428
SUBROUTINE PLOTA(DT.N0,0,05.000N)
DIMENSION OINN/p0S(NN)0(101),S(11)
DATA P/IHr/pC/1 )-4*/.0/1HO/pB/11.1 /
1
SU.00
DO 1 1•1,NO
UM.AMAX1(0(I)r0S(I)I
IF IUM.GT.SU/ SU.UM
5
1
CONTINUE
SL.ALOGIO(SU)
IF (SL.LTrOrN SL.SL-1
EM.INTi51.1+1
U.10.0**LM
02=0/2
U5=U/5
IF (5U.1F.U2) U.UP
IF (SU.LE.U5) U=U5
U=U/100
DO 2 1=1,11
SII).(I-1)*10*U
10
15
20
2
CONTINUE
PRINT 40
PRINT 41,S
DO 5 1.1,101
25
5
CONTINUE
3
CONTINUE
II*(I-1(*1041
X(II).P
JJ.0
K=INT(00/U+0.5).1
XK.Y(K)
X(K).0
PRINT 42,JJrX
X(10.)0(
DO 4 J.1040
PRINT 44rX
JJ.J*DT
L•INT((J(J)/U+0.5)+1
K.INT(0S(J)/U+0.5).1
XL.X(L)
Xl<=8(K)
811/.0
X(F).0
30
35
40
4 7 ,JJ,X
X(L)=YL
45
XIK)=XK
4
CONTINUE
PFINT 41,
50
55
40
41
42
43
44
S
PRINT 43
RETURN
FORMAT (20X,1814 * COMPUTED FLOW/20X,18H
FORMAT (148,11110.3)
FORMAT 1 TX, I7r 2X,61A1, 4041 )
FORMAT (DU)
FORMAT (20X,6181,40AI)
END
0
OBSLPIIED FLOW//1X)
Continued
Figure A-1. Listing of SIMUL Program,
10/22/79
185
**********4“, * asaw Aypisu Rivp pi,GJEcT
****44,444,044*m.4.4.4***
PHI
.57,
JHIFT
—783.00
WHIT. NOISE VAPIANCE.I.1849
OVERALL MOVING AVERAGE .—.0855
NUMBER OF SIMULATIONS.
1
LENGTH OF RECGRD. 50
ELEVATION
?1. ,I
CAPACITY
MAT. VGIUME
.1 ..1 vt) • v
11:/jUU.l.,
3 . ).(1
?..))00.
34.:,JODun .0
;!hr,1(,( ,r,
42.54000U.0
it,OOL I. .l
45.0
46.'.
5OUG0.0
ou";(70.6
39006C.(
4nofv.,
4'',OCA,.(,
47.5
48.5
49.4
50.0
70000.,,
60000.0
90000.0
100000.0
49,:i0u.,.c,
520000.0
5500u0.0
560000.0
UNIT ENERGY PRICE .
.210
WORTH OF UNIT wATER TO IPRIGATION .41.200
PENALTY FOR POWIR
0.000
PENALTY FOR IRRIGATION =41.200
OVERAAL IRRIGATION EFFIC. •
.400
LOAD FACTOR
.500
COST OF UAM PER CU—YD
5.00000
COST OF PLANT PER KW .1045.
RESERVOIR SIZE
10000.
Figure A-1. Listing of SIMUL Program, Continued
t***4**4,4,
186
RESERVOIR SIZE •
NUMBER
1
2
3
TURBINE SIZE
2
3
TURBINE
1
2
3
SIZE
SIZE
SIZE
20000.
22000.
24000.
.
1RR BEN
1441467.
1441467.
1441467.
TUT. BEN.
2905103.
2945820.
2824106.
STAND. DEV.
3R43R2.
364382.
384382.
60000.
POWER PEN
149097e.
1565421.
1560148.
20000.
22000.
24000.
TURBINE
1463636.
1504353.
1385639.
SIZE
RESERVOIR
NUMBER
POWER BEN
20000.
22000.
24000.
RESERVOIR
NUMBFP
50000.
188PEN
1461896.
1461296.
1461616.
TUT.
PLV.
PI-N.
2952876.
3C27319.
3022047.
3(5240.
3f5246.
1 65240.
70000.
POWER
BEN
1600695.
1613818.
1645337.
1PR
BEN
1474392.
1474392.
1474392.
TOT.
BEN.
3075088.
3082210.
311972 9 .
Program, Continued
Figure A-1. Listing of SIMUL
STAND.
DIV.
352347.
352347.
352147.
187
PROGRAM DIFAUT
OPT.0 TRACE
FTN 4.6+428
10/23/79
PROGRAM DIFAUT(INPUTpOUTPUT,PONCH.TAPE5.INPUT.TAPE6.0UTPUT.TAPE7.P
IUNCH)
1
5
14/74
C
C
DIMENSION ACV1201PAC(20).PACV(20).WKAREA(20)
DIMENSION Y(17.12),XMONS(12)
DIMENSION 2(204)
DATA X11014S/31.,30..31.P30.01.01..30.931.P30.01.01..28./
DATA IPTpIOUTpIAC/5,60/
10
15
C
20C
25
30
35
40
PROGRAM DIFAUT DIFFERENCES AND DETERMINES THE AUTU— AND PARTIAL
AUTOCORRELATION OF THE DIFFERENCE° TIME SERIES BY CALLING IMSL
SUBROUTINES FTRDIR AND FTAUTC
C
DEFINITION OF VARIABLES
ID1.0RDER OF NON—SEASONAL DIFFERENCE
IO2.0RDER OF SEASONAL DIFFERENCE
IP -TRANSFORMATION EXPONENT
0---LOGARITHMIC TRANSFORMATION'
J---AN EXPONENT TRANSFORMATION OF INDEX J
IS *LENGTH OF SEASONAL PERIOD
LZ .LENGTH OF VECTOR Z
ZUZIsTIME SERIES DATA AS INPUT AND OUTPUT
SHIFT-IF IP.0 IT IS NEGATIVE OF MIN OF 1+1 OTHERWISE IT IS ZERO
LW -OUTPUT TIME SERIES LENGTH
IER.ERROR PARAMETER(128+N)pN--1 INDICATES I01 AND/OR 102 LESS THAN
READ CONTROL CARDS.TITLE FIRST
C*********
NDAT.17
READ(IPT.10)ID1pID2p1PpISpLZ
10 FORMAT(5110)
READ TIME SERIES DATA ,INPUT FORMAT FIRST
C ***** ****
READ(IPTP11)((Y(I,J),J.1.12).1.1.NDAT )
FORMAT(8410)
1
210 FORMAT(3I10)
11 FORMAT(12F6.0)
DO 12 I.1PNDAT
00 13 J-1.12
K.(I—I)*12+J
13 2(K).Y(IpJ)*1.98*XMONS(J)
12 CONTINUE
WRITE(IOUT,402)
402 FORMAT(1H1p////pT25,* OUTPUT FROM DIF*//)
CALL IMSL SUBROTINE FTRDIF
45
50
55 ,
CALL FTRDIF(ID1PIO2.1PpISp1Z.Z.SHIFTAW 1 IER )
WRITE(IOUT.40)LN.SHIFT.IER
40 FORMAT(///pT20p*DIFFERENCED SERIES LENGTH .*,15/020.*SHIFT
.*pI5)
"PF10.2p/pT20p*ERROR NUMBER 1
AUTO AND PARTIAL AUTOCORRELATION PORTION
READ(IPT.10)KKpLpISW
WRITE(IOUTp401)
401 FORMAT(////pT25.*OUTPUT FROM AUT0*//)
CALL IMSL SUBROUTINE FTAUTO
Figure A-2. Listing of DIF-AUTO, SIMP and MAXL Programs and
Outputs.
13.0
188
60
65
70
75
CALL FTAUTOIZAW.KR,L,ISW,AMEAN,VAR,ACV,AC,PACV,WRAREA)
STD*SORTIVAR)
WRITE(TOUT0240) AMEAN,VAR,STD
**,F10.5,/,125,*VARIANCE **,F10.5,/,725,
240 PORMAT(///r125,*MEAN l*STAND. DEV **,110.5)
WRITE(IOUT,50)
50 FORMAT(///rT40,*AUTOCOPRELATION*)
WRITE(IOUT,260)AC
260 F0RMAT(/,20(1X.F5.3))
WRITE(IOUT,70)
70 F0RMAT(///0400*PARTIAL AUTOCORRELATION FUNCTION*)
WRITWOUT060)PACV
60 FORMATI/r20(1X,F5.3))
CALL SIMPIZ)
CALL MAXLIZ)
WRITEIIOUT,403)
403 FORMAT(///025,*DIFFERENCE0 SERIES *//)
41 FORMATI5X012(F8.4,2X))
STOP
END
Figure A-2. Listing of DIF-AUTO, SIMP and MAXL Programs, Continued
189
SUBROUTINE MAXI
/4 174
OPT.° TRACE
FTN 4.6+428
10/23/79
SUBROUT/NE MAXLIX/
1
PROGRAM MAXL CALL IMSL SUBROUTINE FTMAXL WHICH COMPUTES THE MAXIMUM
LIKELIHOOD ESTMATION OF ARIMA PARAMETERS
5
10
DEFINITION OF VARIABLES
15
-TIME SERIES DATA OF LENGTH INDU)
X
END -INPUT/OUTPUT VECTOR OF LENGTH 8
1-LENGTH OF SERIES X
2-NO. OF AR PARAMETERS IN MODEL
3-NO. OF MA PARAMETERS IN MODEL
4-NO. OF DIFFERENCING OPERATION
5-MAX. NO. OF ITERATIONS
6-NON-NEGATIVE CONVERGENCE PARAMETER
7.-NON-NEGATIVE IMPLIES 2S3 ABOVE ARE INPUTS
8-POSITIVE CONVERGENCE PARAMETER
ARPS0VECTOR OF LENGTH IND(2)+ IND(4) CONTAINING AR PARAMETERS
PMAS.VECTOR OF LENGTH IND(3) CONTAINING MA PARAMETERS
PMAC+OVERALL MOVING AVERAGE PARAMETER
NNV -OUTPUT ESTIMATE OF WHITE NOISE
GR-WORK AREA OF LENGTH 24(IN0(21+1N0(3)1
-WORK AREA
A
IER -ERROR PARAMETER
20C
25C
30C
35
10
40
11
12
45
1
FORMATI/1//,T25,40UTPUT FROM MAXL*//I
CALL IMSL SUBROUTINE FTMAXL
60
CALL FTMAXL(X.IND.ARPS , PMAS , PMAC , WNV.GR , AtI ER)
WRITECIOUT,6011N0(5)
FORMAT(///#120. 4 N0. OF ITERATIONS PERFORMED +0'0110)
J.IND(2)+IND(4)
IF(J.LE.0)GO TO 65
50C
55
DIMENSION X(192 ).IND(8),PMASI4I,GR(4) , AI5 0 0).ARPS( 4)
DATA IPT,IOUT/5,6/
READCIPT.10/(IND(I),I+1,81
FORMATIBI10/
IF(INDI7/.1.7.0)G0 10 12
IM1+IND(21
.
IM2+IND13/
IF(IND(2).GT.0 )READ(IPT.11)(ARPSIII1I+ 1 . 1 M 1 /
IFIINDI3).GT.OIREAD(IPT,11 1 (PMSSCI ), I+ 1, IM 21
FORMATI8F10.01
CONTINUE
12.IND(1)
WRITECIOUT,11
Figure A-2. Listing of DIF-AUTO, SIMP and MAXL Programs, Continued
13.03.1
190
74/74
SUBROUTINE MAXI
UPI.0
IKAlt
PRINT COMPUTED PARAMETERS.
60
65
70
75
DO 70 I.11,J
WRITE(IOUTIP801I,ARPS(1)
80 FORMAT(/(/#720,*P1-111$'12,*).*,F10.51
70 CONTINUE
65 IFIIND13/.1.E.0/G0 TO 90
JJ.IND(3)
DO 100 1.1tJJ
WRITEtIOUT,110)1,PMAS(I)
110 FORMAT(///fT20,*TNETA( 4 ,12,*) •*,F10.2)
100 CONTINUE
90 WRITE(IOUT,120)WNV
120 FORMAT(///0720,*WHITE NOISE VARIANCE .40E15.5)
WRITE(IOUT.130) PMAC
130 FORMAT(///,720,40VERAL1 MOVING AVERAGE PARAMETER •0 0 ,F15.5)
WRITE(IOUT,140)1ER
140 FORMAT(/020. 4 ERROR PARAMETER .4,15)
RETURN
END
Figure A-2. Listing of DIF-AUTO, SIMP and MAXL Programs, Continued
191
74 1 74
1
C
15
C
30
35
10/23/79 13.0
PROGRAM SIMP CALLS IMSL SUBROUTINE FISIMP WHICH ESTIMATES
TIME SERIES ARENA PARAMETERS.
10
25
FIN 4.6+428
SUBROUTINE SIMP(2)
5
20
OPT-0 TRACE
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
DEFINITION OF VARIABLES
Z
-TIME SERIES VECTOR OF LENGTH IP00(2)
1000-INPUT/OUTPUT VECTOR OF LENGTH 7
l(MODEL OPTION.NEGATIVE IMPLIES ELEMENTS3,4,5 OF IPDO ARE OUTP
ZERO IMPLIES ELEMTS 3E4 ARE INPUT AND ELEMENT 5 IS OUTPUT
POSITIVE IMPLIES ELEMENTS 3,4,5 OF IPDO ARE INPUT.
2:LENGTH OF SERIES
3:NO. OF AR PARAMETERS IN DIFFERENCED FORM OF MODEL
4 :NO. OF MA PARAMETERS IN MODEL
51NO. OF DIFFERENCING OPERATION TO OBTAIN STATIONARY OF THE SE
WORECASTING CONTROL PARAMETER; FORECAST UP TO IPD0(6) ARE CA
MUST BE POSTIIVE
7*IPD0(7) POSITIVE IMPLIES SIMULATE SERIES UD TO IPD0(6) STE
!SEED. INTERGER VALUE BETWEEN 1,2147483647 IF IPD0(7) IS POSITIVE
ALPHA-INPUT/OUTPUT VECTOR OF LENGTH 2
1:M1N SIGN. LEVEL OF MODEL
2:10011—ALPHA(2)) PERCENT IS PROBABILITY FOR FORECASTS
DARPS-VECTOR OF LENGTH IPD0(3)+IPD0(5) CONTAINING AR PARAMETERS OF
PMAS -VECTOR OF LENGTH IPD0(4) CONTAING ESTIMATES OF MA PARAMETERS
PMAC -ESTIMATE OF OVERALL MA PARAMETER
WNV -ESTIMATE OF WHITE NOISE
FCST .OUTPUT MATRIX OF DIMENSION 3XIPD0(6)
FCST(I,J) FOR LEAD TIMES J.102,. ..,1P00(6) CONTAINS WHEN
1.1:WEIGHTS FOR SHOCKS THAT GIVE FORECASTS ERROR
2: THE FORECASTS
3ICORRESPONDING DEVIATIONS FROM FORECASTS FOR 100(1—A
SIM*SIMLATED OUTPUT RESULTS WHEN IP00(7) IS POSITIVE
IS
-FIRST DIMENSION OF SIM AS IN CALLING PROGRAM
WK -WORKING AREA
IER -ERROR PARAMETER
DIMENSION 2(179) ALPHA(2),IPD0(7),DARPS(2),PMAS(2)
40DIMENSION FCST(3,10),SIM(10,2),WK(500)
DATA IPT,IOUT/5,61
,
READ CONTROL CARDS
45
10
20
50C
READ(IPT,10) (IPDO(I),Ialp7),ISEED
FORMAT(8110)
READ(IPT,20) (ALPHA(I),I21,2)
FORMAT(2F10.0)
READ TIME SERIFS DATA
L2. 1P 00(2)
CALL IMSL SUBROUTINF
55
CALL FTSIMP ( ZIPIP00,1SEED,ALPHA,DARPS,PMAS,PMAC,MNV,
1FCST,SIM,IS,WK,IER)
Figure A-2. Listing of DIF-AUTO, SIMP and MAXL Program, Continued
192
SUBROUTINE SIMP
74/74
OPT.0 TRACE
FTN 4.6+426
10/23/79 13.0
PRINT OUTPUT PARAMETERS
60
66
65
77
70
50
40
60
75
95
70
90
100
80
110
85
130
120
90
135
150
160
IF(IPDO(1).GT.0) GO 10 77
WRITE(IOUT,66) (IPD0(1),183,5)
FORMAT(///020," 4 OF AUTREG. PARAM. •
1 1 1/020," 1: OF M A
PAPAM. •
21/1," 1 OF DIFF. FOR STA •
M.IP00(3)+IPD0(5)
IF(M.LE.0) GO TO 60
DO 40 I.1,M
WRITE(IOUT,50) 1,0ARPS(I)
FORMAT(///,720,"AR(",13," )",2X,".",F10.5)
CONTINUE
IF(IPDO(4).1E.0) GO TO 90
12•IPD0(4)
DO 70 1.1,12
WRITE(IOUT,95) I,RMAS(I)
FORMAT(///,T20," M A (",13,2X,")
• ) ,F10.5)
CONTINUE
WRITE(IOUT,100) WNV
FORMAT(///,720,"WHITE NOISE VAR. • ",F10.5)
1F(IP00(6).1.E.0) GU TO 135
PCT•100.*(1-A1PNA(2))
WRITE(IOUT,110) PCT
FORMAT(///,T10,"STEPS AHEAD"p4WERR)JP WEIGHTS",4X,
PROB. DEVIATION")
1"FORECAST",3X,F5.2,"
12•IPD0(6)
DO 120 I.1101.2
WRITE( 1001,130) Ip(FCSTIJ,I),J.1,3)
FORMAT(T15,13,7X,F10.5,6X,F7.2,13X#F7.2)
CONTINUE
CONTINUE
WRITE(IOUT,160) IER
FORMAT(///,720,"ERPOR PARAMETER • ",I5)
RETURN
END
Figure A-2. Listing of DIF-AUTO, SIMP and MAXL Program, Continued
193
OUTPUT FROM DIF
DIFFERENCED
SERIES LENGTH m 192
SHIFT
ERROR NUMBER
.
•
-387.08
0
OUTPUT FROM AUTO
MEAN
-.05096
•
VARIANCE •
1.49063
STAND. DEV •
1.22092
AUTOCORRELATION
426
.264
.109
.068
.069
.004 -.066
.037
PARTIAL
426
.101 -.044
.017
.044 -.054 -.083
.124
.034 -.086 -.168 -.376 -.132 -.070 -.066
AUTOCORRELATION
.027 -.035 -.(
FUNCTION
.011 -.170 -.114 -.288
.186
.048 -.054
.115 -.097
OUTPUT FROM MAXI
NO. OF ITERATIONS PERFORMED •
PHI( 1).
10
.42648
WHITE NOISE VARIANCE •
1.21142
OVERALL MOVING AVERAGE PARAMETER •
-.02923
Figure A-2. Listing of DIF-AUTO, SIMP and MAXL Program, Continued
194
DIFFERENCED SERIES
-1.6746
. 1 .0981
1.1334
.7399
.4638
1.0993
.4950
-.9840
-.0703
1.2839
.5062
.8907
.40
..6816
1.9864
.0523
-.4776
.9114
.3723
.7300
.2024
.57
.-.6300
.2538
.3583
.9737
3.0554
-.1967
.3293
1.8755
-.3028
.6876
.3799
-1.8099
..-1.03
.-.4606
-2.3470
.-2.4426
-.7608
.1896
-2.7710
.5306
-1.5840
..•.1640
1.4642
.0371
.07
-.7286
1.5552
1.1226
2.1287
.5651
.1001
-.4749
-.0745
.3906
-.30
.7364
-.3506
1.1040
.....3628
.5274
1.4990
-.3170
.18
-.8064
-.1760
.0211
-.5362
.4538
-.3506
.3248
.9170
1.31
•.•.0350
-.1704
1.9063
1.4235
.8345
2.7485
1.9256
-.2878
.1669
..1.0759
-.71
-.8831
-2.6314
-1.3727
-.6192
.8646
.5058
-1.6969
.2532
-.1551
.6668
.4556
.10
-.9915
.2053
-.6737
.6962
.0213
-.97
.3114
-1.4963
.1448
.9191
-.3041
1.2189
-.0210
1.119430
.0440
. 1 .0481
-1.15
..4995
.6333
.-1.2074
.6254
.4395
.1195
-.3562
1.2951
1.2236
.8666
.1933
.6540
-.2931
.8986
.6578
-1.1096
-.9000
-1.3694
.4115
1.4"
1.1453
.8722
.6936
1.6182
1.2205
.1176
1.8122
1.3253
.....1220
.2610
.fl6182
-.9652
.-3.0316
-.3643
-.7774
-.6788
'1.0386
.0977
1.1;
-.0750
-1.0308
.1340
-.9470
-1.2492
-.0991
.1.2558
.8678
1.7275
Figure A-2. Listing of DIF-AUTO, SIMP and MAXL Program, Continued
APPENDIX B
CONVERSION FACTORS
195
196
Length
I meter-1.0936 yards
—3.2808 feet
—39.370 inches
1 foot-0.3048 meter
1 mile-1.6094 kilometers
—5280 feet
1 kilometer-0.62137 mile
Area
1 cm 2 -0.1550 in 2
1 in 2 -6.452 cm 2
1 m 2 -10.764 ft 2
I ft 2 -929.0 cm 2
1 acre-43,560 ft 2
—4047 m 2
1 hectare-10,000 m 2
—2.471 acres
1 mi 2-2.590 km 2
—640 acres
Volume
1 n-13 -1000 liters
—35.314 ft:
—264 gal (U.S.)
1 ft 3 -28.320 liters
—7.481 gal (U.S.)
1 gal-3.785 liters
1 acre foot-43,560 ft 3
—3.259 x i0 gal
- 1234 m 3
Discharge
1 ft 3 /min-0.472 liters/sec
1 acre foot/day-3.259 x 10 3 gal/day
1 ft 3 /sec-448.8 gal/min
—724 acre feet/year
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