# 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)Œ t (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. • • • • • 76 ✓ cs ai o i o o o o 0 In I I 1 o o 0 0000 I 0 0 0 N 0 ON I N N N . ... H N H U) -H 0 al 0 H N H Ç)o .7), ,r, 0 in 0 0 d CO dr 0 d' N m •1, s m Ln O ci en N 0 0 0 0 d' 0 Ln .7t, Ncn m LO .qn en r-- 0 0 0 0 0 0 O a) ci -H 4 H 0 0 0 0 7r, 0 0 0 0 0 0 0 0 CO 0 (U ' 0 0 dl' CO LI') H dr H CI N Ill N dl' N dl, N N H N N N N 1 i I I i • 4-) 0 O 0 U) 4-4 4-) O -H - ri5 O a) -P 4-4 4f •H O 4-' C..) En • u) CO H CO CO d' H N 01 0 H CO (U ' 0 W d' 0") N 0 N NW LflN dr in CO co H H H 1.11 1"-- C.) gl CO W a) • dr COo H • rQ O rd U -P U) a) N -H Ci •H rt:$ -P (1.) n-1 cn ...-- En — — — 4 — .— C/) CI) H CI) cr) Cf) CO 4:1 4 4 .-1 ni H ,--I 0 ...... o ,0 — 4 — 0 .q 1/4.o N s .:r N o •,:t, t.o 0 co - o H H o o co a) 4 a) 0 0 CR U) H H o H •Çr. CO0 CO 0 CO CO N N Cn H 0 Cl 11-1 If) W NW P 4 -) 4 4 Ln o o H - cf) 4 41 O 4-) O cU H ,-. c N N If)ci I I i I I 0 ta 0 U) 4J O ro (1) • 4-) .0 • ft -P • -P ts) -H -H CO 0 ct, CI) 4 -H O - H (I) 4 • H tr) •••••n E-1 0 • 4-) O r0 (ll 4 14 4J -H 0 .0 1-4 CO -i-JO W O )-I-1 o -x O 77 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). 0 H 78 0 N 0 N LO h . m H (-YI LO 0 H Ln cr *7t, . n0 0 7r nSi 0 . m 0 •V N Cocn in H . N CO WOOCoLOCoOLO .71. L9 Ls)W h LO Ln cf, LO H •V •1", Ln CoCO . . . N N in H N nSi 00 0 h CoLO h LO H Ln In . Coh LO '1 rl ct. .714 rn h h h CooD N Com 0 LO 0 CoH LO Ln Cr) H . 0 .:t, m N N .--I H •71, . 0 m . Coh N H CO NH h. cl, a) 1-1 m Co N •q, N CO m N •7t. C LO NH HO CO Cd LI 4 Cd di I-)1 .4 0000 0 LiD CO r21 n21 tri (1.) ›-. rd Z I'D H 0 In N •7t, OD 4 4 H U -.-1 P (:).4 rd F': z N Coco Co >i Cd CoCoH 0if)LO h N in 0 Coco N in . CS) Co ›.1 H M I'D r44 (T) 4-) ai (1) CO as di 2 0 4-) C.) 0 1 W 0 Z - 2 (1.) U (1) al 79 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 cN N o cs r-- N co LO tfl N cs N 0 N o N o 0 N N C,1 l0 ,--1 n.0 Ch n-I r.- N 111 n9 i.fl V) 01 01 CO d' 0 N CO kO COCO in CO CO k..0 LSD CO l0 Lo L.L) ,—, r-4 L.0 W CO , q, N CO s- Lo LO CO cs ro cr) Ln s co. Ln g) 0 N LD Lo do N cs) —I 0 ,—I .1. Ln r-- r.-- in Ln N g) Lo N o .1, O 4-) Cdd) O E-I o --i c4 o ci cd ..1, CO CO 00 in .çt, 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 o o o o 0 0 cr CV '1' •1 d, LO w o 01 ro W r-i CV rO s 0 cl, rO 0 •,:t, OD CV CO H Ln H Ln H m Ln H H H • H ro n..0 k.0 L.r) H H H H o O 0 o 0 l.0 o o co co o co h N . 03 CO , N .. CV lO H 0 0 0 0 0 0 0 0 CV 0 0 CV 0 0 00 . N 0 . Ul 41' (NH o o oo o cc co Ln o o 0 0 Ln HUl Ln CV • N CV 0 0 Ul 0 0 N CO 0 0 0 0 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 c„vacky 150 ••• •• •• •• C ••• •• •••Wre.:•••• •• ••• ••• 6. 4. I 140 130 120 110 0 200 400 600 800 Million Gallons 0 50 100 150 200 1 000 1200 250 300 Acres Figure 4.2. Kwanyaku Reservoir Characteristics. ▪ • 91 OLnr,100r1l0CDHCOhd'rn(ShOrnC7) N tfl k.0 LO rn rn rn dt, N crrnH d' d' dt, H Ln kg) d CO CO CO H k.0 N N 0 N •z1.1-nh-Ndr d,rnrnHIS) n.0NHHrnHN H UlinlDOMODhk.ONOOrnCrld'NhH LO CS) H h h h 0 h h LO LO m dr 0-n Ln H H 1/1COrnhCPHOrnHolL.0 LrlolLONk9HOhhCnCO H N HrnHMHN rn OrnNNNN nSDHOD m N H NHH 00S) ct. hOlflinhh nSDHdPHL11NCOdr OhhhhHONhHulrnh-Nrn0Orn 0INHO Lnd,NODNNN d' H d' CO C3 Lr) CO 0 d' dt. Cr) OD N W QD 0 k.ONhk.OHrnhh-NNNMOCACOMN rnHrnr\INhHNHHHO ns) m W H Lor1,71. oon->sinNrnoLno-) LnLner L.o coin H (:)-\ o mrnor-linscs") rnN moo rnN HHNN (:),-101NLn1"--Lnd'h-NC5-)Nh .14 nCNCO hhhdr, l-nOONdrOLO ro 0 I-- L.r) op 0 NHulrOH N CT) H n.o 7t, ro 0 coH 00HOONOOd.ONOH • hNCOkS) NLIINNNODd'rnrOHNdrNrnrn0 n0 HOMN nONNdt, t.OLOOLnhulNOCO N tD7r \C)cr NONCOHMG)(31M1-1 nIDCOdrMhk.0 OrnHOONHNuld'HO NNHHNHHNTP •vr H 00Wsr-iNsOoDcOm.10 LnO OrnomLoalsinsmoomrnNo LnNHHN ni CPNill hrnO)hCS)qDHC-OHrnNhtf) dr CO N kl) N 1.11 H d' d' CO CS) CO in CO O N H HHH HNrnd,u1VDh 0 hhhhhhhh n9 L11 CSOHNrld , nSDhhhhhhh CY)CnCT)CS)0")CACS)C5) HHHHHHHH ▪ ▪ ▪ 92 H CO • H •q' 0 U-) h H H O cr in co co kso co N m m co in N Lc) Lr-) H •qn O 0 r-- N (c) co oo Lc) r- co Lo m H kr)H N n.c) N • oom ns:)inN H H oo co n.c) o 0 04 7s( •ct, CO in N in H H 0-1 1:4 Lc) •tn in oW 7r, in N in r-- U) cs 0 ).c) H 0 OC) r n:) inr-i H H en H Nif) W W in HH H rflH LC) (r) if) CS) co CON NN ro.)N in Lc') r--W' VIL0001k..0 nD 0-1030-10DMOD H H H cr, co N 7t, H niO nsoin co coOi7) co co inH co N M 0 H N (5) M 0) CT) H H H H , 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 cc 0 cc'oD r rn 0 cc O W O 0 COH H o CO a) N H coN N H o co H in N CS) 0 N rn N LU co N cc ul W 0 H o o op Ln co oD N Nro Ln In os-) oD co H o rn LU N co o co cy 0 in co TI. cr •Lt cc N cc MI H N H intn •:t. m o h h H N o oLom h 0cc h d' 0 HNHH en o-1 0 0 CS) ccLUcoLU H LU 0 H W 0 W mLUCS) m co co v, r,-) •tn H H r-4 CON W '71' LU H h o co • t,h. cc inh h- co CS) C3 fr) z 1-D H . N . o co co 0 çf, 0 N co .7t, Ln o 00 H H N 0 H M CO LU M 0 0 CC) 00 CO CO 01 N N W MON H H N N H H N LU 00 0N H cc W N H cc N ccU) N H r co 7t, H H Ln oLnkso N 0 H cs0 H LU H H rn ul W N N r- r- N N I I I I I 0 ':1' Ln h h h h MM MCSIM H H H H H N N M • ▪ • • 95 NOOHNr--IH Ln NMH CnN o Q) o H N Oki) Ln 0 CO N Or--0 NONLON • NHH 00O3--1,-10(iC0 ‘zr LnNLn n9 co oNs ooN ornN H H ciNOCOHC071.71, Ci 0171, N LONN Ln o sLn sLnCio cs.1 œLl1H•qUIHNM0 •zzr ri co o o o •q. oNNscov, inCio co co o N LU N H N mo w o co LOHHCOOMHLON•q'00 HNHHNNN Ln s Ln H o HNH co o Nr-Lorco .t.sk.so Ci o HmLnsNLnLn N 0 Hm NCi m oH kso Lc) oo U1CON01010DLON01000U1 r-INHM‘l k9u1CONONOCONNci0 Ln co N Ci s tn o NN ok.so m CialLoLn CI^ 0 01 C N cs) 0 co 0 ooNcs w M NM in 01 o o OD N N •q'H 071.Nr'---0001.,:rCOMHO1C0 Nm tzt, oo Ln LnN COH71'NH N N NNLU CLU mH tzr HNM.1. Ln i in I O H Ln i nsor LUcc LU LnLU I o o Nd'0H•1"ill I I N LU I COCSI Ln i Ln I NMLU wNCO InLt1I.111f)LU alc 01 (51 01 HHHH H LU c H LU o H Lt11.11 0101 HH 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 -Q Q) N 00 MC-CO 01 CO CO OH Cd 1-) d'de drNMNOMH‘Vdr MONO0dr LU t.0 hhCOCS H GICS)Ndt , 000d4 hCOHCOh hLn Hdr HH o 00 00 H dr CL 0 d, LnNOLn OCS MHHCY)0)MlOdr CnNOCOO O LU Olhr-CS)N01HH hLO L.o o Ln 00N0k.0 0 rl 00 h (TI H wo rn 01 0 H dr N N 00 0 d' dr H H H H M N N H el H H mm H H d' o Pl LU M h h h LnO M h MO 0 Ln 00 LU Ln00 N LOMin nDl10 n.0 OLncnOr-OOLONCSH NNHONMLnhN end.C5)NdroOtnHHCO o co.q, mLs)LncoLnenLoNLnco o o ooLnInLn nSDNWOM Lo H N N N g:y N HulLOLC1N HNHOWONO)HOMMNN 0 04 LOul H H CO 01MOHLO U-1,--1M0')C-NOCOOLn 00 ,101--MOCSINd'N'.0 n91--00")HCOLnCSN 1,1HLU H•zV NMNHNHN O W COCOLOCOLOLOOODOOOLnd, Ln0 WQ)00000OHIn Nd'a)NLnkSDOdr H dr N HN H HHH m H d' dPCY)q)0H h0001inCOMOONOOLn0 LO ON d' L9 m N w O ON HrIHHMdr Ndr NO1 LO C1C\ld, NlONtn1/491.11LOd'rninHLOd. HHH d'a) 0 0 00 tr) 0 c0 0 w Mr-C7) ON • c0 N tr) CO QD oz) m rn N n.0 L0 0 CS) NO W dr hMOOM Cs) HolLnLOMWCOHNOCSn COCTL 0 d'N Mrnind'HhOCONNlOOOCOLn0 1f1HH olh o MLI)MCOhNHd'hlOOLOCO NMNHN 1.11NH NHMHNMHHNH C000h k.0 N H rn COMCOHCOdr MNd , M01--tn h rn H o .1., Lo r--- m Tr. m co dr NHd, NHHNH hMHHHHHHNHHH H W CO 0 0 01 H H W N CO CO 0 0 0 CO CO W MHWNd'enrdrOdrNd , H MHHHMHHNH H IC Ln Lc) Ln o-N COMLIIMCO HHH 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 0 o o OLn .7r o co HA en co o crn o r,-) co s co N .1, N co rn , ,H .cr (N 1.0 If) CO 0 0 o 0 H K:C -H E E rd rd E E E ro ro u) Z Q) a) a) a) U) u) Z u) Z co Z rd Z Lo E 0 5 0 'L.0 0 in ,--i r0 LO NQ)0 N 01 01 S-I H 10 H )-I '70 HI 75 I-1-1 a) r0 I a) 3 4--) Q) 0 ro O -H fa, -H o Lc) Lk 4-4 a) a) 3 a) cn a) I co T1 .7r a) a) 3-I Hi cr) a) - rd 14-1 (a u")k10 rd C) 3 O W-POW OWrd rd (CC) O W a)0 3-4 ta k, - a) El Z C4 ,--i ç4 1El 0 - ro lc al Cll >, I U) rd 0) >, I s rd rd C) ›, >, o c..) I a) I rd 0) >1 t s O --i rd W ›-1 i s 4-4 0 132 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 \ 14k 0 0.0 X 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. • ▪ 157 5 Q) Q)ni 3 O ai 0 -H 0 cii z Il >i .. . 5 +-I ni -H 0 > CI) • H a, a) 4-) 4-n a) 3 o Q)cf) U)a) >i CD VI (i-i 4-) I 0 Q)0 Q)5-41-1-1 o Ln H ni —1 ni G.4 0 0 04 ,-I ni 14 O rcl >1 ai Q) (N oo ni C.) Lo o 0 0 .0 .0 -I-I -H 3 3 O o nID r--) H co Ln N 00 o H cn X if) H •t. 0 0 P4 N Ti 0 0 0 -H ca ‹ RD 0 0 0 0 54 -H >i -H Cil O › P 0 zn w a) 3 ta o 1:4 c4 tZ 0 .-1 ni 3 4-1 -H -H -H O ra -H r P4 (1) Q., 5-4 -H 1 ›-• rz:5 W tv H ai Q)Q, U) Q) ni -s) O Iii cn ni C.) a) 0 OD N rd Q)m W W C.> -I--I -I-I Z W -H 01 -H -H X >--1 X Q)4-) a) -H -i-I U4..) -H -H ni W ni -P 0 4-.) En 0 › P P54W a) Ill W al g • ça E ::'i Q) Z -P (d In 3 >m W rd g ›, ni .Q OrO ni-si 3 -H 3 158 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 REFERENCES Abudu, A. 0. 1976. "Economic impact of the Volta River Project." Proceedings of the West Africa Conference, Tucson, Arizona, April. AESC (Architectural Engineering Services Corporation) Hydrology Division. 1978. Correspondence to author. Aluja, K. C. 1977. 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