Methodology for long-term water supply planning : Mexico City case
Item Type Dissertation-Reproduction (electronic); text
Authors Aguilar-Maldonado, Alexis
Publisher The University of Arizona.
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Link to Item http://hdl.handle.net/10150/191050 METHODOLOGY FOR LONG-TERM WATER SUPPLY
PLANNING: MEXICO CITY CASE
by
Alexis Aguilar-Maldonado
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF HYDROLOGY AND WATER RESOURCES
In Partial Fulfillment of the Requirements For the Degree of
DOCTOR OF PHILOSOPHY WITH A MAJOR IN WATER RESOURCES ADMINISTRATION
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 Alexis Aguilar-Maldonado entitled Methodology for Long-Term Water Supply
Planning: Mexico City Case be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy
As members of the Final Examination Committee, we certify that we have read this dissertation and agree that it may be presented for final defense.
Sh0/7 Date ,57/// 7 7 Date
Date
Date
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 reproduc- tion 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: Aleox(S (Nor---1o(dokiac60, To my wife, Dora,
I dedicate this work in deepest gratitude
for her continuing encouragement
that helped to make it a reality.
111 PREFACE
The material contained in this dissertation is a part of the report Master Plan for Mexico City Water Supply prepared by the author for the Comisi6n de Aguas del Valle de México under contract CAVM-76-181 between Ingenieria y Procesamiento Electronico, S.A. (IPESA), and the aforementioned commission.
The author wishes to thank the Consejo Nacional de Ciencia y
Tecnologia (CONACyT) for their financial assistance during academic year
1972-1973, and Ingenieria y Procesamiento ElectrOnico, S.A. (IPESA), for their financial support since he began his endeavors toward a doctoral degree.
To Dr. Daniel D. Evans, his dissertation director, Dr. Donald R.
Davis, and other committee members, the author is particularly indebted for stimulating his interests in the field of Water Resources
Administration.
Heartfelt gratitude is extended to the author's family and his wife's for their constant encouragement and support during his graduate work at The University of Arizona.
iv TABLE OF CONTENTS
Page
LIST OF TABLES vii
LIST OF ILLUSTRATIONS
ABSTRACT xiii
1. INTRODUCTION 1
1.1 Water Supply Problems of Mexico City 2 1.2 Development of Water Supply and Historical Background . 3 1.3 Objectives and Development Plan 7
2. LITERATURE REVIEW 8
3. PROPOSED METHODOLOGY 12
3.1 The Problem 12 3.2 The Methodology 15 3.3 Optimization Model I 24 3.4 Optimization Model II 29
4. DEVELOPMENT LEVELS IN THE CUTZAMALA RIVER BASIN 36
4.1 Objective 36 4.2 The Cutzamala River Basin 36 4.2.1 General Description 36 4.3 Development of the Cutzamala Basin for Water Supply . . 37 4.3.1 Hydrologic Analysis 37 4.3.2 Alternative Configurations of Development in the Cutzamala Basin 56 4.3.3 Cost Functions for Each Development Site and Aqueduct Reach 56 4.3.4 Development of Cutzamala Basin 67
5. LONG-TERM WATER SUPPLY PLANNING FOR MEXICO CITY METROPOLITAN AREA 86
5.1 General 86 5.2 Mexico City Sources of Water 89 5.2.1 The Cutzamala River Basin 89 5.2.2 The Tecolutla River Basin 93 vi TABLE OF CONTENTS--Continued
Page
5.2.3 The Amacuzac River Basin 101 5.2.4 The Oriental Groundwater Basin 112 5.3 Optimal Long-Term Water Supply Plan 112
6. CONCLUSIONS 128
APPENDIX A: SYNTHETIC GENERATION OF RUNOFF RECORDS IN UNGAGED STREAMS 131
LIST OF REFERENCES 136 LIST OF TABLES
Table Page
3.1 Tableau for Selecting the Most Recommendable Configuration for a Basin's Development Level 23
4.1 Characteristics of the Miguel Alema'n Hydroelectric System 39
4.2 Future Irrigation Water Demands in the Cutzamala River Basin 39
4.3 Main Characteristics of Existing Storage and Diversion Dams 41
4.4 Available Hydrologic Data 42
4.5 Results of the 18-Year (Monthly) Simulation Analysis for the System Tuxpan-Bosque-Colorines-Valle de Bravo- Villa Victoria 46
4.6 Results of the Simulation Analysis of the System Tuxpan- Bosque-Colorines-Valle de Bravo-Villa Victoria, Considering the Merging of Cutzamala's Water with Lerma's Water 48
4.7 Yields of the Sites of Development Considered in Each Configuration 64
4.8 Tabular Form of Presentation of Results of Optimization Model I for Each Configuration 72
4.9 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration I 74
4.10 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration II 76
4.11 Sites To Be Developed and the Amount of Water that Each Will Supply One for Several Levels of Development under Configuration III 78
vii viii
LIST OF TABLES--Continued
Table Page
4.12 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration IV 79
4.13 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration V 80
4.14 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration VI 82
4.15 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration VII 83
4.16 Comparison of Costs among Configurations for the Levels of Development 84
5.1 Characteristics of the Miguel AlemLi System 91
5.2 Estimated Budget for Cutzamala's First Stage 94
5.3 Composition of Estimated Budgets for Cutzamala's Three Stages 95
5.4 Sites of Development and Their Yields in Cutzamala Basin for Several Levels of Development 96
5.5 Main Characteristics of Cutzamala System 98
5.6 Characteristics of Necaxa Hydroelectric System 100
5.7 Estimated Budget for Tecolutla's First Stage 102
5.8 Composition of Estimated Budgets for Tecolutla's Two Stages 103
5.9 Development Sites and Their Yields in the Tecolutla Basin 104
5.10 Characteristics of the Tecolutla System 106
5.11 Estimated Budget for Amacuzac's First Stage 108 ix LIST OF TABLES--Continued
Table Page
5.12 Composition of Estimated Budgets for Amacuzac's Three Stages 109
5.13 Characteristics of the Amacuzac System 110
5.14 Estimated Budget for Oriental's Unique Stage 113
5.15 Characteristics of the Oriental System 114
5.16 Costs of the Basins' Stages To Be Used in Optimization Model II 118
5.17 Optimal Long-Term Water Supply Plan for an Electricity Price of 0.16 Pesos/KWH 119
5.18 Costs of the Basins' Stages To Be Used in Optimization Model II (Energy Price of $0.51/KWH) 122
5.19 Costs of the Basins' Stages To Be Used in Optimization Model II (Energy Price of $0.701KWH) 123
5.20 Optimal Long-Term Water Supply Plan for an Electricity Price of 0.51 Pesos/KWH 124
5.21 Optimal Long-Term Water Supply Plan for an Electricity Price of 0.70 Pesos/KWH 125
5.22 Comparison of Optimal Construction Sequences for Energy Prices of $0.16/KWH, $0.51/KWH, and $0.70/KWH 126 LIST OF ILLUSTRATIONS
Figure Page
1.1 Mexico City Metropolitan Area Population and Forecast 4
1.2 Mexico City Metropolitan Area Water Demand Forecast 5
3.1 Schematic Representation of the Planning Problem . . 13
3.2 Flow Chart for Long-Term Water Supply Planning . . 16
3.3 Cost Function for a Storage Dam 20
3.4 Conveyance Costs in a Given Development System Configuration 21
3.5 Construction Sequence of Basin's Stages 25
3.6 A Basin's Development Based in Three Sub-Basins . 26
3.7 Scheme of a Configuration for a Water Resources Development 30
3.8 Definition of T(q - q 2 ) 34
4.1 Geographical Location of Cutzamala Basin In pocket
4.2 The Cutzamala Basin In pocket
4.3 Scheme of the Miguel Alemaln. System 38
4.4 Scheme of the East Portion of the Cutzamala Basin 44
4.5 Purungueo I Dam: Function of Water Supply-Storage Capacity 49
4.6 Purungueo II Dam: Function of Water Supply- Storage Capacity 50
4.7 Tuzantla I Dam: Function of Water Supply-Storage Capacity 51 xi LIST OF ILLUSTRATIONS--Continued
Figure Page
4.8 Tuzantla III Dam: Function of Water Supply- Storage Capacity 52
4.9 Aguila II Dam: Function of Water Supply-Storage Capacity 53
4.10 Cerro Pelon Dam: Function of Water Supply- Storage Capacity 54
4.11 El Gallo Dam: Function of Water Supply-Storage Capacity 55
4.12 Scheme of Configuration I 57
4.13 Scheme of Configuration II 58
4.14 Scheme of Configuration III 59
4.15 Scheme of Configuration IV 60
4.16 Scheme of Configuration V 61
4.17 Scheme of Configuration VI 62
4.18 Scheme of Configuration VII 63
4.19 Tuzantla I Dam Cost Function 68
4.20 Aguila II Dam Cost Function 69
4.21 Aqueduct Tuzantla I-Aguila II Cost Function . • • 70
4.22 Aqueduct Purungueo I-Aguila II Cost Function . . 71
5.1 Cost Function of a Basin Development 88
5.2 Geographical Location of Studied Sources of Water In pocket
5.3 The Miguel Alemn System 90
5.4 Scheme of the Hydraulic System for the Development of Cutzamala Basin ...... 97
5.5 Scheme of Necaxa's Hydroelectric System 99
xii
LIST OF ILLUSTRATIONS--Continued
Figure Page
5.6 Scheme of the Hydraulic System for the Development of Tecolutla Basin 105
5.7 Scheme of the Hydraulic System for the Development of Amacuzac Basin 111
5.8 Scheme of the Hydraulic System for the Development of Oriental Basin 115
5.9 Water Demand Forecast for Mexico City Metropolitan Area 116
5.10 Optimal Long-Term Water Supply Plan (Electricity' Price of $0.16/KWH) 120 ABSTRACT
A complete methodology for long-term water supply planning is presented. Based upon the characteristics of the water resources development planning problem (nonlinearity of cost functions, and hydrologic variables), the author rejects the seeking of "optimal" solu- tions and supports the seeking of "good enough" solutions.
To answer the questions that are involved in long-term water supply planning, it is proposed to break down the problem into two simpler ones to be solved in a sequential fashion. Although mathemati- cal guarantee of optimality cannot be assured, the introduction of physical and engineering constraints greatly increases the confidence in the final results.
The proposed methodology allows deep analysis of the hydrologic aspects involved in water resources planning. The depth of hydrologic analysis is only restricted by available data and technology. In this respect, a method for synthetic generation of monthly runoff records in ungaged streams is proposed.
An application of the methodology to the development of a Mexico
City water supply plan is presented in full detail to appreciate its usefulness.
Mexico City population forecast for the year 2000 is 28 million 3 people. The estimated water demand in that year is 105 m /sec, more 3 than twice the present water supply of 50 m /sec. To satisfy this xiv demand, water has to be brought from four basins more than 150 km distant, and located at elevations more than 1,000 m below Mexico City's elevation (2,300 m above mean sea level). The water supply plan which resulted from this study indicates the most recommendable sequence for
the development of the four basins, and the amount of water to be obtained from each one. CHAPTER 1
INTRODUCTION
When planning long-term water supply for large urban areas, and after a forecast of demand has been obtained, consideration must be given to alternative sources of supply to meet the forecasted demand on
time at minimum cost. The study of supply requires a synthesis of hydrologic, technical, and economic factors. Nowadays, this type of study is usually conducted following these steps: first, the hydrolo- gist provides a detailed description of the space and time distribution of the available water resources in a river basin; second, the engineer determines, based upon his judgment, a project design to provide the demand of the last year of the planning horizon; and third, a schedule for the starting in operations of the different project components is proposed in order to follow as nearly as possible the demand forecast curve.
The preceding process might be valid when there is only one potential site to exploit within a basin; however, it becomes more and more inadequate as the number of potential sites increases because of the combinatory nature of the number of alternatives that can be formu- lated. What happens is that a very reduced number of alternatives is analyzed because of the computational effort needed for each one. Other
1 2 alternatives are rejected on the basis of subjective engineering judg- ment or are not analyzed at all.
The current decision process has stimulated the search and use of screening models for water resources planning, and the recent litera- ture contains a number of them, which will be discussed in Chapter 2.
Since the principal aim of this work is the proposition of a methodology for long-term water supply planning and to apply it to the Mexico City case, the characteristics of Mexico City's water supply problem, development of water supply facilities to date, and historical back- ground are presented first. The last section of this chapter contains the specific objectives anddevelopment plan of the dissertation.
1.1 Water Supply Problems of Mexico City
Mexico City, one of the world's largest cities, is located at an altitude of 2,300 meters above sea level in the Mexico Valley, and an important part of its water supply problems results from its location and also the enormous population growth rate.
By the year 1930, population of the Mexico City area was esti- mated at 1.6 million inhabitants. By 1940, its population had increased to 2.2 million people, and by 1950, it reached 3.6 million. During these two decades, the rate of population growth was 3.4%. In the decade 1950-1960, due to important industrial investments in the Mexico
Valley area, the rate of population growth increased to 4.9%. According to the last (1970) National Population Census, the population of the
Mexico City metropolitan area was 9.5 million, as the result of a rate of growth in the decade 1960-1970 of 4.9%. It has been estimated that, 3 in 1975, the estimated population of the area surpassed 12 million people.
The most accepted population forecast for the Mexico City metro- politan area gives 28 million people in the year 2000. Figure 1.1 shows the population growth from 1930 and the forecast to the year 2000. Even though a reduction in the population rate of growth is expected in the next 22 years, the order of magnitude of the water supply problems caused by the concentrated population is not importantly affected by the foreseeable reduction of the population growth rate.
In terms of water demand, the population growth means that, by the year 2000, it will be necessary to supply the city with 105 m3 /sec, 3 over twice the present water supply of 50 m /sec. The historical and forecasted water demand for the Mexico City area are shown in Figure 1.2
(Robledo-Cabello, 1976).
1.2 Development of Water Supply and Historical Background
Before 1950, the water supply to Mexico City was provided by an underlying aquifer, which, by 1950, was under intensive exploitation.
The subsoil consolidation and surface subsidence, due to the lowering of the water table, brought new and critical problems to the city; struc- tures were damaged and the sewage collection network was dislocated.
The downtown area, initially 3 meters above the lowest elevation of
Mexico Valley, subsided more than 5 meters and was put in a situation of continuous flooding risk. These problems led to the urgent necessity of building big hydraulic works to bring water from the nearby Lerma 4
,—i •—i a) 3-1 0 C313 orl rx. 5
3 Water Demand M /Sec
To Be Supplied By Remote Sources of Water
40 To Be Supplied By Near Sources of Water. 20
0
1930 190 1950 19 0 1 0 1980 1990 2000 2010 2020 2030
Figure 1.2 Mexico City Metropolitan Area Water Demand Forecast. 6
Valley aquifer in order to reduce the exploitation of the Mexico Valley aquifer.
In 1951, the federal government created the Comisi8n Hidrol8gica
de la Cuenca del Valle de México (CHCVM; Mexico Valley Hydrologic
Commission) to study Mexico City's water supply problem and to find a
solution. One of the major contributions of CHCVM was its realization
that there was not merely a Mexico City water supply problem, but a
Mexico City metropolitan area water supply problem which was much more
complex and difficult to solve. The commission also realized the
groundwater sources under exploitation could not meet the water demand
further than 1980, and that it was necessary to develop a long-term
water supply plan based upon water transfers from distant basins.
During the interval between 1951 and 1972, CHCVM studied several
alternative water transfer projects at a preliminary level. From its
studies, CHCVM concluded that there were four basins from which it may
be feasible to import water: the High Balsas River Basin, the Amacuzac
River Basin, the Oriental Groundwater Basin, and the Tecolutla River
Basin. The water transfer potentials were estimated to be 119, 19.5, 3 7, and 40 m /sec, respectively. However, a general development plan was
not recommended.
In 1972, CHCVM was discontinued and replaced by the Comision de
Aguas del Valle de México (CAVM; Mexico Valley Water Commission), which
continued the CHCVM studies. The new commission is taking those studies
to the feasibility and project construction levels. CAVM identified the
Cutzamala River Basin as a possible water transfer source, with an esti-
mated transfer potential of 60 to 70 m3 /sec. 7
1.3 Objectives and Development Plan
The present study has two main objectives. The first one is to provide a methodology to answer the questions that arise when planning long-term water supply for large urban areas based upon the development of nearby basins. These questions are: Which basins should be developed? How much should be transferred from each basin and how? and
Which construction sequence should be recommended? The second objective
is to apply the methodology to the long-term water supply of the Mexico
City metropolitan area.
The order of presentation is as follows. In Chapter 2, a selected literature review is presented. In Chapter 3, the proposed methodology for long-term water supply planning is presented in full detail. Chapters 4 and 5 contain the application of the methodology to the Mexico City case. In Chapter 4, detailed analyses are presented relative to the definition of feasible water transfers from the Cutzamala
River Basin and their costs; and in Chapter 5, the long-term water supply for the Mexico City metropolitan area is presented. Finally,
Chapter 6 is devoted to the presentation of conclusions. CHAPTER 2
LITERATURE REVIEW
Since a significant part of water resources development planning involves important decisions concerning the selection of configurations of hydraulic works and the scheduling of their construction, a number of researchers have studied the problem of arriving at those decisions in an optimal fashion. A selection of the most relevant works in recent years is presented in the following paragraphs.
Delucia and Rogers (1972) presented a linear programming model
(The North Atlantic Regional Supply Model) to select the minimum annual cost combination of water resources for meeting future water demands.
They assumed that the water-supply and water-demand activities in each basin are located in single points (nodes) in the model. The nodes are interconnected by the natural drainage network and interbasin transfers of water.
O'Neill (1972) used mixed-integer linear programming to select and schedule for construction the minimum cost configuration of water supply projects which will meet future water demands in the central area of southeast England. Demand centers, groundwater resources, reser- voirs, and diversions from streams are interconnected by the natural drainage or by pipelines.
8 9
O'Laoghaire and Himmelblau (1974) developed a methodology for the optimal expansion of a water resources system. The hydraulic system is studied through the Fulkerson out-of-kilter algorithm, and the scheduling is analyzed through a branch-and-bound algorithm. These two models are worked out in a heuristic fashion.
Moody (1976) developed a water resources planning model formu- lated as a mixed-integer linear program. In his work, Moody assumed:
1) estimates of optimum sizes of individual projects and their associ- ated yields and operating rules are given, and 2) project operating costs are linear functions.
Kindler (1975) used the out-of-kilter algorithm in a case study on the Vistula River to develop a model for water resources management.
Klemetson and Grenney (1975) developed a dynamic programming model, to be used as a management tool, for the sequential expansion of wastewater treatment plants at a minimum discounted future cost. Appli- cation to the Lower Jordan River region of Salt Lake and Davis counties in Utah was made using the available data.
Erlenkotter and Scherer (1975) considered the problem of scheduling investment in salinity control projects on the Colorado
River. As they stated, the major contribution of this work was to formulate and evaluate models for scheduling control projects. They used two different approaches, one using mixed-integer linear programming and the other using dynamic programming to minimize the present cost of salinity control.
Viessman et al. (1975) developed a model which joins simulation and optimization of a water resources system to select an optimal 10
arrangement of components for regional water resources development and
management. They used linear programming to maximize net annual bene-
fits subject to constraints imposed by the hydraulic system.
Bogardi, Duckstein, and Plate (1976) presented a method for
optimal sequencing and scheduling of a set of flood control projects
within a river basin. They considered the special case of "in parallel"
flood control reservoirs, located at the mouth of various sub-basins, to
protect downstream properties from floods. The core of the method
is a branch -and-bound algorithm. The assumptions involved are:
1) linear nature of operating and maintenance cost functions; 2) optimum
sizes of individual projects, their effects on flood reduction, and the
costs are given; and 3) additiveness of individual project effects of
the various flood control projects. In this work, two models were
developed to be worked out in a sequential, heuristic fashion: a
simplified hydrologic model and a branch-and-bound algorithm.
Brill, Velioglu, and Fuessle (1977) used linear programming in a
planning model to evaluate the major energy policy issues in large areas
for initial screening purposes. The model is designed to locate total
capacity to be installed instead of individual plants. The objective
function used was to minimize the sum of site-dependent costs of water
and the transportation costs of water, electricity, coal, and gas.
All the papers reviewed show emphasis on the mathematical formu-
lation of the programming models. The type of model ranges from single
linear programming or dynamic programming models to sequential heuristic ones, by using two optimization techniques. 11
The use of the models found in the recent literature reviewed has to be restricted to screening purposes and no executive decisions can be made on their basis because of the lack of adequate treatment of hydrologic aspects. The models which include a mathematical optimiza- tion of water resources allocation based upon runoff records are too rigid to be realistic because hydrologic analysis cannot be reduced to handling of equations. Also, cost functions of hydraulic works are not linear, as most models assume.
Though these models claim to arrive at optimal solutions for the problem of water resources development planning, the foregoing short- comings mean they arrive at optimal solutions only in the sense that they meet certain mathematical optimality requirements. CHAPTER 3
PROPOSED METHODOLOGY
3.1 The Problem
As stated in the introductory chapter, what is desired is a methodology that can be used to answer the questions that arise when planning long-term water supply for large urban areas based upon the development of nearby basins. Explicitly, these questions are:
1. Which basins should be developed?
2. How much should be transferred from each basin and how?
3. Which construction sequence is recommended?
To explain how these questions arise, let us consider a hypo- thetical city and four surrounding basins, as shown in Figure 3.1. Each of the four basins has a maximum yield, a distance and a pumping height for its water to reach the city, and can be developed to any magnitude up to its maximum yield.
Since the water demand for the last year of the planning horizon is assumed to be less than the total yield of the four basins, it is necessary to decide which basins to develop, how much water to take from each one, and their construction sequence. To make this decision, each basin has to be studied to define a function relating volumes of water to cost.
12 Figure 3.1 Schematic Representation of the Planning Problem.
Maximum Maximum Distance Pumping Yield to City Height Basin (in /sec) (km) (111)
1 15 300 250
2 25 200 650
3 18 300 325
4 10 150 500 13
Figure 3.1 Schematic Representation of the Planning Problem. 14
A given amount of water can normally be obtained from a basin in several alternative ways. These alternatives arise because one or both of the following occur and it is necessary to define which is the alter- native with the minimum cost:
1. There are several development sites in the basin, each one with
different yield-cost functions due to its location within the
basin.
2. There are several ways of interconnecting a given set of
development sites.
To meet the water demand to the planning horizon at a cost as low as possible, it is necessary to look for the most recommendable construction phasing. In this context, engineering design and construc- tion practices impose several constraints.
The problem cannot be handled by any single optimization model in which one inputs data and gets results because of the extreme diffi- culty of properly coding simple physical constraints, the nonlinear nature of the functions involved, and its multidimensional character- istics. Because of the foregoing, it is the author's opinion that, instead of seeking "optimal" solutions, efforts should be directed to looking for methodologies that render "good enough" results.
It is in this spirit that it is proposed to decompose the entire problem into two simpler problems to be treated in a sequential manner, i.e., instead of trying to answer questions 1, 2, and 3 in one step, it is proposed to answer first the question of how to develop each basin, and then to answer the remaining questions. The final solution obtained 15 through this procedure cannot be guaranteed to be an optimal one, but certainly it is close enough since the partition of the whole problem into two sequential ones allows the planner to introduce into each one many more physical characteristics of the actual, real-life problem and this is worth the loss of a mathematical guarantee of optimality.
The next section of this chapter contains a complete methodology for long-term water supply planning developed on the basis established above.
3.2 The Methodology
The flow chart shown in Figure 3.2 will be used in the exposi- tion of the methodology. Also, since some new expressions are used, the following definitions are given:
1. Development site is any physical location on a river where it is
feasible to divert water through a hydraulic work.
2. Configuration is any feasible way of interconnecting a set of
development sites in a basin.
3. Level of development is the amount of water diverted from a
development site, from a basin under a given configuration, or
from a set of basins.
If any long-term water supply planning is to be logical, it must be based upon a water demand forecast. This forecast must take into account the main factors that influence the amount of water used and consumed in the urban area under consideration. This amount will depend on its size, climate, level of industrial development, water
water saving technology, and the foreseeable evolution of these 16
FOPFfAT waTF 0 nrv , O
I_OFNTIFY ÇOURCF OF 1 3 ATFP
ESTIMATE ACTUAL AND FUTURE USES
ciTF
PERFORM DETAILED HYDROLOGIC STUDIES TO DEFINE YIELD AND SIZE OF 5 I wynPANI IF WORKS ESTIMATE COST FUNCTIONS RELATING 1 DEVELOPMENT LEVEL TO COST,
DEFINE ALTERNATIVE CONFIGURATIONS OF SYSTEM OF DEVELOPMENT. THE 7
Igz:::FOR EACH CONFIGURATION >"1,..•••••nn•nn•
ESTIMATE COST FUNCTION FOR EVERY I AOUEDUCT PORTION
DEFINE SEVERAL LEVELS OF ,pri- ) nrVFinp
w.... DEFINE SET OF MOST CONVENIENT DEVE- ...... 1 LOPMENT SITES AND THEIR YIELD. 10 SELECT THE MOST CONVENIENT CONFIGURATION 11 SELECT THE BASINS TO DEVELOPE AND 1 DEFINE CONSTRUCTION SEOUENCE. 12 Figure 3.2 Flow Chart for Long-Term Water Supply Planning. 17 factors to the planning horizon (Wollman and Bonen, 1971). Uncer- tainties associated with the determining factors of water use and con- sumption should be taken into account and several water demand forecasts should be produced, each one of them with a probability of occurrence attached to it. The next step is the identification of water sources. This involves a thorough search for both surface water and groundwater. The search should not be restricted to non-used water, but it should con- template, whenever feasible, the change from present water use to water supply for the urban area under consideration. Following the flow chart from box 2 through box 11, it can be noted that the objective is to obtain, for each of several levels of development in a basin, the most recommendable combination of develop- ment sites and conveyance systems. To accomplish this, the following steps are necessary: 1. Within each basin, a thorough search has to be carried out to determine the amount of water being used and consumed in the basin and a forecast of water use and consumption has to be made. If a change in water use patterns is feasible, it should be contemplated (for example, from hydroelectric generation to water supply) and its opportunity cost estimated. 2. An engineering search for new development sites is needed when the source under study is a surface water basin since water can be diverted at different altitudes as streams descend to the basin outlet. The technical feasibility of those sites must be checked on the basis of preliminary engineering studies. 18 3. For each identified development site, the following steps are necessary: a. Perform hydrologic studies to define the amount of water that can be diverted for water supply, taking into account that portion of the forecasted water demand in the basin that has to be supplied by the site under consideration. Because of water flow variability, storage might be required to store water from periods with high flows to those with low flows. The magnitude of this storage depends upon the relation of the mean annual volume demanded to the stream to its mean annual flow, the variability of river flow, and the degree of security desired in water supply. Water supply to urban areas is very restrictive in the sense that deficiencies are almost not allowed because of the magnitude of political and social pressures that develop when there is a shortage in water supply. When records of runoff are available, it is possible to perform simulation analysis with historical data and with synthetic information in order to obtain the storage requirements for several volumes of water supply under a given criterion to define the degree of certainty with which water will be supplied. This criterion is usually provided by the government agencies in charge of water supply systems. In the case of Mexico, the Secretaria de Agricultura y Recursos Hidrallicos (SARH; Agriculture and Water Resources Ministry) has established that a demand for water supply can 19 be imposed on a river if the results of simulation analysis over a period of 20 years with historical records meet the following specifications: Maximum annual deficit 10% Maximum deficit over the simulation period 3.5% Maximum number of years with deficit 3 The expected final results from the hydrologic study of each development site are the sizes of the hydraulic works needed to obtain different levels of development. b. Estimate the cost of getting each of the levels of develop- ment defined above. If the site under study requires a reservoir, Figure 3.3 shows the kind of results needed. 4. Once each development site has been studied, alternative con- figurations of the basin development system have to be proposed. Between any two of these configurations, the difference might be in the development sites considered and in the aqueduct routes. 5. For each proposed configuration, the following steps are necessary: a. Determine cost functions for water conveyance systems along the aqueduct routes of the configuration under study. These cost functions must include the aqueduct cost itself, the cost of pumping equipment when necessary, and maintenance and operation costs (see Figure 3.4). b. Propose a reasonable number of alternative levels of development in the basin covering the range of water avail- ability for the configuration under study. For example, if 20 WATER SUPPLY ( M3/sec) Figure 3.3 Cost Function for a Storage Dam. 21 LL UAL L LA_ LL City A ( D-® OS @) - 0 re/s e-0 m3is c)-0 m 3/s (Di - s Figure 3.4 Conveyance Costs in a Given Development System Configuration. 22 3 a configuration can render 60 m /sec, the analysis can be performed with the levels of development 0, 10, 20, 30, 40, 3 50, and 60 m /sec. c. For each level of development, apply an optimization model to choose the most convenient set of development sites and their sizes. 6. Once the most convenient set of development sites and their sizes has been determined for each level of basin development and for each configuration, the next step is to select the most recommendable configuration for each level of basin development. This is easily performed by analyzing a table like that shown in Table 3.1. In that table, the costs of obtaining several levels of development in the basin under consideration are given. For any one of the levels of development (rows of the table), the most recommendable configuration (columns of the table) is that with the lowest cost. Finally, to obtain the most convenient set of basins to develop, their level of development, and the construction sequence which is most recommendable, as indicated by box 12 of the flow chart (Figure 3.2), the following steps are necessary: 1. Thoroughly define the hydraulic works required for each level of development in the basins under consideration. Engineering design and construction practices are very important at this step to define construction and budget programs. 23 Table 3.1 Tableau for Selecting the Most Recommendable Configuration for a Basin's Development Level. Configuration Level of Basin Development I II III L A A A 1 1,I 1,II 1,III L A A A 2 2,1 2,11 2,111 L A A A 3 3,1 3,11 3,111 L A A A 4 4,1 4,II 4,111 L A A A 5 5,1 5,11 5,111 2. Define stages of construction in each basin. This is done by considering that the difference between two successive levels of development constitutes one stage. For example, if for one development L L and basin we have defined the levels of 1 , L2' 3' L it is possible to define level L as the first stage, the 4' 1 L and L (L - L ) as the second difference between levels 2 1 2 1 stage, the difference between levels L3 and L2 (L3 - L2 ) as the L4 and L third stage, and the difference between levels 3 - L ) as the fourth stage. The cost of each stage is (L4 3 obtained in a similar fashion from the costs of the levels of development. 3. Apply an optimization model to obtain the most convenient con- struction sequence of the stages of the basins under study to meet the forecasted water demand of the urban area. The optimi- zation criterion will be the minimum present cost. The results 24 of this last step might be a mixing along time of the individual basin stages as shown in Figure 3.5. The next two sections of this chapter contain the optimization models referred to in this section. 3.3 Optimization Model I Optimization Model I is designed to answer the question: Which is the most convenient way of obtaining a given level of development in a basin under a given configuration? To explain the model, let us consider the basin shown in Figure 3.6. There, a number of development sites have been located on the main tributaries of a river, and let us consider that it is desired to take water from each of them to a common point. Each of these sites can provide water up to a given maximum development level. Let us assume that, for each site, there are esti- mates of costs for several levels of development. These costs include catching, conveyance, pumping, and maintenance and operation costs. To define how much water it is most convenient to take from each site in order to obtain from the basin a given amount of water from zero to the total potential of the basin, the following model can be used. 3 Let Z be the minimum cost to provide W m /sec. Then, referring to Figure 3.6: Z(W) = Min {C(X1 ) + C(X2 ) + C(X3 )} [1] 25 Year Figure 3.5 Construction Sequence of Basin's Stages. 26 27 where X and X are the amount of 1 , X2' 3 water taken from sites 1, 2, and 3, respectively; and C(X1 ), C(X2 ), and C(X3 ) are the costs associated to take from each site the amounts of water X1 , X2 , and X3 . The variable X is restricted to take values on the set = {0 X X X and variables X and X are restricted to take 1' 11' 12' 13' 2 3 values on the sets 22 X23 ) and 23 31 32 33 =IO, X21' X22' = {0, X , X , X ), respectively. The Xji 's represent the level of development i on site J. X1 , X2 , and X3 are also subject to satisfying: X1 + X2 + X3 > W. This problem can be seen as a multistage decision problem where the stages are the sites to be developed, the decision variable is the amount of water to be provided at each stage, and the state variable is the amount of water that remains to be provided. By doing so, a func- 3 tion, F(S), can be defined as the minimum cost of providing S m /sec when it remains to decide about the level of development J sites. Also, the state transformation equation can be defined as: S- = S - X [2] J1 J J where S are the states at stages J and J-1, respectively; and X J' SJ-1 is the decision made on the level of development of site J (stage J). Equation [1] can be written as: F* (S=W) = Min {C(X ) + Min [C(X ) + C(X )11 3 3 1 2 [3] Or FI (S=W) = Min {C(X3 ) + F (S - X )1 [4] where 28 (S) = Min {C(X2 ) + Ft (S - X2)1 [5] with 0 < S and F! (S) = Min {C(X1) + F (S - X1)1 [6] with 0 and F* (S) = 0, for every S. 0 [7] Equations [4], [5], [6], and [7] are of a recursive nature and their use renders the desired solution. In a compact form, these equa- tions can be rewritten as: F* (S) = fC(X ) + F* (S - X )}, Min J- 1 for 0 < S < W [4] Fle) (S) = 0 , for every S [9] subject to: X in set2• +X +X > W [10] J' X1 2 3 — and J = 1, 2,3 [11] Equations [8] and [9] are simply the recursive equations of dynamic programming for an allocation process, and can be used for any number of sites and development levels in each one just by allowing 2 29 to have any number of elements, and J to vary from 1 to the desired number of sites. The recursive equations [8] and [9] are useful for the case depicted in Figure 3.7, where a decision in one development site does not affect the cost of a decision in another; but when the set of feasible sites is interconnected, as it is shown in Figure 3.7, where a very common situation has been depicted, it is necessary to introduce some changes in the form of handling costs because a decision made in one site affects the costs of conveying water from the point where aqueducts merge. To handle this case, the following is necessary: 1. Decompose C(X) into two components. One, Ci (XJ), will be associated to the decision of developing site J, and the other, C2 (XJ), will be associated to the amount of water that will flow ahead of site J after the decision in site J has been made. 2. Formulate the decision problem as follows: 1 (X) + C (W - S + X) + F* (S - X)} F* (S) = Min {C 2 J- 1 [12] F8 (S) = 0 [13] 3.4 Optimization Model II In order to obtain the most convenient construction sequence of the stages of the basins from which water will be transferred to an urban area to meet a water demand forecast, all the factors affecting the decision should be taken into account. Those factors are: the cost 30 Water Resources Development. Figure 3.7 Scheme of a Configuration for a 31 of each basin stage, its contribution to the satisfaction of demand, the shape of the demand curve, its slope along time, and the rate of dis- count to be used to compare alternative sequences. The preceding paragraph is significant because, usually, the decision on sequencing is made on the basis of the stages' unit cost, arranging them from that with the lowest cost to that with the largest. This criterion does not always lead to the best decision. As the number of basins and stages increases, the number of alternative sequences increases rapidly. For example, if there are five independent stages corresponding each one to one basin, the number of sequences is 120, but if there are 10 such stages, the number of alter- native sequences rises to 3,628,800. Thus, it is necessary to have an efficient tool to obtain the most convenient sequence. Such a tool is the dynamic programming model that follows (Butcher, Haimes, and Hall, 1969). Consider a function D = D(t) giving the water demand of an urban area as a function of time. Consider also that there are n independent basins, each of which can provide a supply capability Q. at a cost C i (i = 1,2,3, ..., n). If the n basin were developed, the water demand would be satisfied up to a time -1 t = D ( E Q.) . i=1 1 Since the n basins are independent, they can be developed in n! differ- ent sequences, and the problem is to find the most recommendable one. The figure of merit to find that sequence will be the present cost of 32 the alternative sequences. That sequence with the minimum present cost will be the most convenient. Let us define q as the supply capability of a sequence of con- struction. This sequence can have 1, 2, or more of the basins and, consequently, q can take values in the range: 0 < q < E Q. [14] n=1 and q can meet the water demand up to a time T(q) = D(q). Define also k. as the construction sequence of j basin developments, for k. k=1,2,3,...,nandf. 3 (q) as the minimum present cost of providing a supply capability q by a sequence of exactly j basin developments built in the sequence k.. A function relating q to the cost of developing a basin can be constructed as follows: gi (q) = 0 if q = 0 g 1 (q) = Ci if q < gi [15] gi (q) for i = 1,2,3, .. , n. With the foregoing definition in mind, consider now that any supply capability, q, is to be met by developing only one basin. Then: 1 f (q) = min {g(q)} [16] 1 33 for i = 1,2,3, ..., n; and k has only one element, k = {2. } , where 2, 1 1 is k 1 the stage for which f is 1 a minimum. Consider now that any supply capability is to be met by developing two basins. Then: r)-(t2) k 2 1 f (q) = min {g (q )(1 + + f (q - q )1 [17] 2 2 1 2 O q2 q t2 = T(q - q 2 ) for i = 1,2,3, ..., n not in 1(1 . In equation [17], r is the discount rate to obtain the present cost of the two developments, and q2 is the demand that has to be satisfied by the second one (see Figure 3.8). The set k2 now contains two elements k2 = {k1 , 2} , where 2, is the basin for which equation [17] is minimum. In general, if a supply capability is to be met by constructing m basins: -(tin) km-1 f m (q) = min {g i) (qm (1 + r) + f (q - qm)1 m m-1 [18] tm = T(q qm) where qm is the demand that has to be satisfied by the mth basin, and km contains in elements; k = {k and R., is the basin for which m l'»' 34 Figure 3.8 Definition of T(q - q2 ). 35 equation [18] is a minimum. In equation [18], only those i's not included in the set km are eligible. -1 Equation [18] is of a recursive nature and its use renders the optimal sequence of the n basins. When, for each basin, several stages have been defined, and they have to be built in a given sequence within each basin, the preceding model is still useful, but it has to be modified to accept one more restriction. This restriction is that the eligible i's have to be checked for location in the correct sequence within each basin. CHAPTER 4 DEVELOPMENT LEVELS IN THE CUTZAMALA RIVER BASIN 4.1 Objective The Cutzamala River Basin, one of the four remote sources of water for the Mexico City metropolitan area, is studied to define the most recommendable configuration of water supply developments to obtain different volumes of water. 4.2 The Cutzamala River Basin 4.2.1 General Description The Cutzamala River is one of the main tributaries of the Balsas River, one of the most important rivers in Mexico. Its basin is located between 18 ° 33 and 19 ° 50' north latitude, and between 99 ° 45' and 101 0 10' west longitude. The geographical location of the Balsas and Cutzamala rivers is shown in Figure 4.1 (in pocket). The Cutzamala Basin is shown in Figure 4.2 (in pocket). 2 The Cutzamala Basin has an area of 10,738 km . The mean annual precipitation in the basin is 1,049 mm, and the mean annual runoff 3 measured at the basin outlet gaging station is 3,307 million m . The most important streams in the basin are the rivers Tuxpan, Zitâcuaro, San José Malacatepec, Tilostoc, Temascaltepec, Tuzantla, and Purungueo. 36 37 At the present time, water resources developments in the basin are committed to hydroelectric generation through a system of storage and diversion dams, aqueducts, and hydroelectric plants. This system is named the Miguel Aleman System (MAS). A scheme of the MAS is shown in Figure 4.3 and its main characteristics are shown in Table 4.1. Agricultural developments in the basin are restricted to two areas, one located in the lowest part of the Tuxpan River Basin with 2,400 ha; and the other near the Cutzamala Basin outlet with 16,000 ha, which is named the Irrigation District of Ixtapilla. The Comision Federal de Electricidad (CFE; Federal Electricity Commission), the official agency that operates the MAS, has agreed to give up an important part of the water committed to hydroelectric 3 generation if it is granted an annual volume equivalent to 3 m /sec for peak energy generation. Also, the CFE has calculated the opportunity cost of the change in use of water. The CFE's estimate of this cost is 0.386 pesos per cubic meter. The Secretarla de Recursos HidrLlicos has already a project to increase the Irrigation District of Ixtapilla to 22,000 ha, and to open for irrigated agriculture 3,000 ha on the Temascaltepec River. So, the future water demands in the Cutzamala Basin are as shown in Table 4.2. 4.3 Development of the Cutzamala Basin for Water Supply 4.3.1 Hydrologic Analysis In order to develop the Cutzamala Basin for Mexico City water supply, it has been considered to use, on the one hand, the existing 38 39 Table 4.1 Characteristics of the Miguel Alema.n Hydroelectric System. Mean Annual Mean Annual Flow Power Generation Head 3 Plant (MW) (GWH) (in) (m /sec) Martinez de Meza 25 104.99 376.0 3.87 . . Agustin Milan 19 73.09 276.0 3.87 Durazno 16 89.77 105.5 10.82 Ixtapantongo 99 524.17 323.0 23.96 Sta. li.rbara 75 408.76 262.4 23.96 Tingambato 135 637.98 380.0 25.40 Infiernillo 1,003 3,315.00 92.0 444.00 La Villita 285 1,267.00 44.0 460.00 Table 4.2 Future Irrigation Water Demands in the Cutzamala River Basin. Irrigation District in /sec Tuxpan 0.73 Ixtapilla 7.07 Temascaltepec 1.45 Total Demand for Irrigation 9.25 40 facilities of the MAS and, on the other hand, to develop other important streams of the basin. ,After an exhaustive engineering search in the basin, several sites have been identified where it is feasible to build storage dams. These sites are the following: River Site Name Tilostoc Aguila II Temascaltepec Cerro Pelon Tuzantla Tuzantla I and Tuzantla II Purungueo Purungueo I and Purungueo II Tuxpan Tuxpan II In addition to these sites, and because of the important magni- tude of leakage from El Bosque dam, it has been considered to build a small storage to catch them. Figure 4.2 shows the development sites on the Cutzamala Basin, and Table 4.3 shows some characteristics of the existing dams. A hydrologic analysis was conducted to determine how much water can be transferred from each site to Mexico City. The first step of the analysis was the collection of all available information regarding precipitation, evaporation, and runoff in the basin. The available data are shown in Table 4.4. From a preliminary study of such data set, it was clear that, in terms of available hydrologic information, the basin could be divided into two areas: one in which enough information was available (18 years of monthly records), and another where almost no data were available, except for that of some precipitation gaging .1-or4nng in the area. In Figure 4.2, these two areas are shown. It is 41 Table 4.3 Main Characteristics of Existing Storage and Diversion Dams. S = storage dam; D = diversion dam. Mean Annual Storage Runoff Capacity 3 3 6 Dam Type Stream (m /sec) (m x 10 ) Villa Victoria S San José Malacatepec . 4.99 189 Valle de Bravo S Several streams 7.74 412 El Bosque S Zitacuaro 3.81 220 Tilostoc D San José Malacatepc 2.85 0.90 Ixtapan D Ixtapan 1.20 0.01 Tuxpan D Tuxpan 8.61 0.00 42 Table 4.4 Available Hydrologic Data. Available Length Hydrologic Data of Record Hydrometric Stations Villa Victoria Dam 1946-1965 Valle de Bravo Dam 1946-1965 El Bosque Dam 1947-1965 Tuxpan 1947-1965 Ixtapan del Oro 1948-1965 Cerro Pel8n 1950-1965 Las Jantas 1960-1965 Tiquicheo 1945-1965 El Gallo 1947-1965 Climatological Stations There are 36 climatological stations with available records of monthly precipitation for the period 1946-1968. Twelve stations out of the 36 also measure evaporation. 43 clear that the portion of the basin with hydrologic data is that under development by CFE, and that they have not taken data for the rest of the basin. The lack of runoff records in the western portion of the basin led to the necessity of generating synthetic records for those ungaged basins. To do this, the model presented in Appendix A was developed. Once a complete data set for the entire basin was available, the next step of the hydrologic analysis was to perform a simulation to define the water supply capability of the basins as follows: 1. The portion of the basin already developed by CFE was considered as a unit for water supply purposes (Figure 4.4). It was simulated as a system of reservoirs to supply water to meet demands for irrigation, electricity generation, and water supply to Mexico City. The latter demand was to be obtained from the simulation analysis, taking into account the conditions under which different mean annual water supplies were obtained. 2. The other developments in the basin were studied independently because the synthetic generation model for ungaged streams does not provide a guarantee of simultaneity of records of runoff with those of the gaged streams. For each of these develop- ments, the maximum amount of water to be transferred to Mexico City for each of several reservoir sizes was obtained. The individual water demands for irrigation were considered in every case. 44 E E c o ra m u -0 .0 Cl 0) ..., -0 C G) — u 0 ,..., cd s_ n 0- ,.,) • -, ..- 0 t... IX>1..L, c_ 45 The results of the simulation analysis for the portion of the basin already developed by CFE are shown in Table 4.5. The general operation rules under which the analysis was performed were the following: 1. To use first the water from Valle de Bravo dam in order to favor water transfers from El Bosque dam. 2. To transfer as much water as possible from El Bosque dam to reduce leakage. 3. To keep Tuxpan II reservoir as empty as possible during the rain season to improve the water catching and reduce overflows. 4. To complete the demand of Mexico City between Valle de Bravo and Villa Victoria dams. 5. To supply water to Mexico City considering a reduction of 10% of the mean annual demand during the rain season, and an increase of 10% of the mean annual demand during the dry season. This rule was obtained by observation of the records of water demand of the Departamento del Distrito Federal (DDF; Federal District Department), which operates the water supply system of Mexico City. From the results shown in Table 4.5, it was clear that a water 3 demand on the system greater than 23.5 m /sec (20.5 for water supply and 3.0 for hydroelectric generation) places the system far away from meeting the restrictions of the Ministry of Agriculture and Water Resources, which are the following: 46 N. 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Cd $-1 r•4 a) 0:1 1G) c0 r-I ,--... ..-. co 6n‘: 71 •...., /1 r-I •li.2 $4 a) ...." cd $4 4-I G) Q) 1-1 4-1 cd 0) .....• W 4-I cd 4-1 0 •r1 •r-I › 4 0. 4-1 I 4-4 "0 *T-1 c.) c.) 4 •1-1 4-I 0 ED CD 0 c.) 4 c0 •rl 4-1 4-1 •-i 0 0 0) 4-1 .1-1 '4-1 4-1 0 4- 1 4-1 -H 4F4 a) 0 en ,-1 - • U) 0 .61 4-1 44 .1-4 0 a) a) 3 Q4.) . 0 r4 ../ 4-1 •r4 W W 0 *-0 10 '4-1 ;-I 1:11 CO CGC) ›•1 (11 04 I-I $4 CO n 0 0 CO -?-1 4 4 °H 0 r-1 ••- 4-1 U3 r•4 Q.) t-1 14 4-) 4-1 r-1 I-1 4-1 4-1 14-1 r-1 a. c..) et a) 01 0 4 cd et (Q-i-4 4 .0 0 (Q Q) 4-1 Ca. al ,..0 o CG 4) 0 a) OC) 4-) .4-) 0 0 -0 0 d) 4-1 0 ›, c.) •ri 0 0 E 5 ,--i Cfl *--- rl 0 0 LI-I o o co ca cn cd 0 •,--1 cd 4-4 .1-4 a) 0 E t-1-1 4-1 0 0 ..1 E 0 N-I Q o "0 .--.. o o o (Q a) •-• 0 .—.. (Q4 4..) 0 ...I E E C.) 4-i 0 (Q4_-1 C) -,-i 0 $-4r4 4(Q 0 0 a) L4 -r-1 4-r (Q ca ca -0 cd r-I W c.)E al c.) a) 0 EU) a) t) a) -ri 3 0 C..) CO 4 •!--1 4 °H 4 4 .1-1 i-4 S-. ,.0r4 ,..o .6) o -r-i o -r-I --... LH m 8 9-4 E 4- X 4c" Eu-4 E 0 cd L-1 4.4 cd 4-1 re) Q) ea 0 a) 0 -r--I ett 6 0 a) 0 o a) o a) a) a) E A Z Z -0 Z Z z»-' Z -0 Z u Z 9-4i, Z 'V s•-•' 47 Maximum annual deficit 10% Maximum deficit in the simulation period 3.5% Maximum number of years with deficit 3 The preceding is true if we consider the Cutzamala development alone; however, the Cutzamala River will be only a part of the total water supply and, in particular, it will interconnect with the water 3 already coming from the Lerma aquifer from which a flow of 15 m /sec is being transferred to Mexico City. Considering both supplies simultane- ously and taking into account that the supply from the aquifer is secure, the results from the simulation are as shown in Table 4.6. In view of these results, it was considered safe to take 22 m 3 /sec as the mean annual supply to Mexico City from the portion of the Cutzamala Basin already developed by CFE. On the average, the 22 m 3 /sec will be supplied as follows: 4 m3 /sec from Villa Victoria dam 3 7 m /sec from Valle de Bravo dam 3 11 m /sec from the subsystem merging at Colonnes For the feasible developments in the basin located on the rivers Temascaltepec, Purungueo, Tuzantla, and Tilostoc, the simulation analysis performed with synthetic data in each development site rendered results that enabled the building of the graphs shown in Figures 4.5 through 4.11. In these graphs, the water supply extraction from the site is related to the storage capacity of the reservoir. The opera- tional restrictions under which these results were obtained were the same as before. 48 Table 4.6 Results of the Simulation Analysis of the System Tuxpan-Bosque-Colorines-Valle de Bravo-Villa Victoria, Considering the Merging of Cutzamala's Water with Lerma's Water. Average Deficiency in Maximum Annual the Period Deficiency Water Supply Demand Cutzamala Merged Cut zamala Merged 3 Alone with Lerma Alone with Lerma (m /sec) (% ) ( Z) (% ) (%) 23.0 0.311 0.184 5.13 2.93 23.5 0.601 0.338 10.32 5.96 24.0 1.120 0.615 15.39 8.98 24.5 2.060 1.139 20.36 11.99 25.0 3.100 1.725 22.84 13.58 25.5 4.300 2.395 24.50 14.70 26.0 5.510 3.098 26.09 15.79 26.5 6.700 3.807 27.63 16.87 27.0 7.870 4.500 29.10 17.90 49 Water Supply in M3 /Sec 10 0 Storage Capacity Million Cubic Meters. Figure 4.5 Purungueo I Dam: Function of Water Supply-Storage Capacity. 50 20 Water Supply in M3/Sc 15 10 I 500 1000 Storage Capacity Million Cubic Meters. Figure 4.6 Purungueo II Dam: Function of Water Supply-Storage Capacity. 51 t=:. = Li) 0 0) 5- (f) CI) 4-) n., 52 0 500 1000 Storage Capacity Million M 3 Figure 4.8 Tuzantla III Dam: Function of Water Supply-Storage Capacity. 53 500 Storage Capacity 1000 3 Million M Figure 4.9 Aguila II Dam: Function of Water Supply-Storage Capacity. 54 Stordge Capa ci ty 3 Figure 4.10 Cerro Felon Dam: Function of Water Supply-Storage Capacity. 55 500 Water Supply-Storage Capacity. Figure 4.11 El Gallo Dam: Function of 56 4.3.2 Alternative Configurations of Development in the Cut zamala Basin Once the water supply transfer potential of each development site in the basin was defined, they were integrated seven feasible con- figurations for the system of development. The difference between any two of these configurations lies either in the development sites in con- sideration or in the aqueduct routes, as can be appreciated in Figures 4.12 through 4.18. In Table 4.7, the sites of development of each configuration are presented, together with their maximum water transfer to Mexico City. 4.3.3 Cost Functions for Each Development Site and Aqueduct Reach As it was pointed out in the methodology chapter, it is neces- sary to develop cost functions in order to apply an optimization model most con- (Optimization Model I) to define, for each configuration, the several levels of venient set of development sites and their size for as development in the basin. These cost functions were obtained follows. a Cost of Dams. For each site, based upon topographic maps at and on scale of 1:50,000, the profile of the dam's mouth was obtained; of the side slopes of earth- the basis of geological surveys, the slopes volume for each dam was fill dams were defined. From this, the earth different sizes was calcu- estimated, and the cost of building them in of earth. lated by using a unit cost of 160.00 pesos per cubic meter Secretaria de Agricultura y This cost was obtained from records of the Recursos Hidraulicos (SARH). 57 C") 58 59 60 61 62 63 64 Table 4.7 Yields of the Sites of Development Considered in Each Configuration. -- In m3 /sec. Configuration Site of Development I II III IV V VI VII Villa Victoria 4 4 4 4 4 4 4 Valle de Bravo 7 7 7 7 7 7 7 Colonnes 11 11 11 11 11 11 11 Cerro Pelein - - 5 5 - 5 - Aguila II 12 12 - - 12 - 12 Tuzantla I - 8 - 8 - - 8 Tuzantla III 14 - 14 - - - - Purungueo I - 14 18 14 - - 14 Purungueo II 18 ------El Gallo - - - - 34 34 - Total Yield 66 56 59 49 68 61 56 65 Cost Estimation of Aqueduct Routes. To estimate the cost func- tions for aqueduct reaches, the first step was to draw on topographic maps at a scale of 1:50,000 the aqueduct routes, taking into account all the specifications that engineering practice recommends. After that, the profiles of the routes were obtained and the power needed at the pumping stations was calculated. Along the aqueducts, different types of hydraulic sections were considered; there are reaches of circular steel pipes, circular concrete pipes, channels, and tunnels. To estimate the cost of pumping stations, the following formula was derived from historical construction costs: 475 000 C = 85.85 QH [2,000 + ' H] 0.24 Q where C = cost of pumping stations, in pesos; H = hydraulic head, in 3 , meters; Q = rate of flow, in m /sec. To estimate the costs of steel and concrete pipes, their unit cost for all commercial sizes were obtained in the market. Since cost of pipes depends on the hydraulic head to be supported, along each aque- duct, the necessary calculations were made to estimate the hydraulic heads. Transitory overpressures were also estimated and it was consid- ered that pipes would take 20% of them. The estimates of channel conductions were obtained through a computer program by considering a set of feasible channel sections to be adapted to different topographic conditions. Unit costs were inputted to the cost items excavation and revestment. 66 The cost of tunnels was estimated through the following formula: C 0.7722 tu = 17,314.36 L D where C = total tu cost of the tunnel, in pesos; L = length of the tunnel, in meters; and D = diameter of the tunnel, in meters. To obtain the cost functions for each aqueduct, a computer pro- gram was developed to design the different components meeting all engi- neering practice restrictions, and to obtain the best overall design in terms of total cost. A range of rates of flow was covered to obtain the desired function relating rate of flow to cost. The annual operation costs of the system were calculated through an estimation of the annual consumption of energy at a unit cost of 0.16 pesos per KWH. The costs for pumping stations, pipes, tunnels, and operation were added to obtain the total aqueduct cost for each flow rate. To take into account the construction period in every hydraulic work, the following assumptions were made about the rates of expenditure: Percentage of Total Cost Number of To Be Spent Each Year Construction Hydraulic Work Years 1st 2nd 3rd 4th Dams 3 25 50 25 Pumping stations 2 50 50 Aqueducts 3 25 50 25 67 All the costs were set in pesos of the first construction year by using a discount rate of 15%. Figures 4.19 through 4.22 show some of the cost functions obtained for dams and aqueducts. It is important to point out that no definition was considered in the estimation of costs because what is required is an economic deci- sion analysis and not a financial one. 4.3.4 Development of Cutzamala Basin Once the cost functions are obtained, the next step is to apply Optimization Model I in order to obtain, for each configuration, the best combination of sites of development that meets a given demand. If no opportunity cost had been set on the use of water already committed to hydroelectric generation, the already developed cost func- tions would have been the only needed costs; but the CFE has considered that, for each cubic meter of water taken away from the MAS, a charge of 0.386 pesos should be paid. This cost has to be charged whenever a decision is made to transfer water from the sites that provide water to the MAS. In the following sections, the hydraulic works needed for each configuration are pointed out. Following the lines described in section 4.3.3, a cost function relating water rate of flow to cost was obtained for each hydraulic work. The use of Optimization Model I, described in section 3.3, rendered for each configuration the set of development sites and the amount of water to be taken from each site in order to get a given level of development from the basin at minimum cost. In Table 4.8, the tabular form in which the results of Optimization Model I 68 Cost Million Pesos Figure 4.19 Tuzantla I Dam Cost Function. 69 Cost Million Pesos 1100 1000 900 800 700 600 500 200 0 2 4 6 8 10 12 Figure 4.20 Aguila II Dam Cost Function. 7 0 71 Figure 4.22 Aqueduct Purungueo I-Aguila II Cost Function. 72 Table 4.8 Tabular Form of Presentation of Results of Optimization Model I for Each Configuration. Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration K. Basin's Level of Development L L L L Site of Development Ll 2 3 4 5 Site 1 Q11 Q12 Q13 Q14 Q15 Site 2 Q21 Q22 Q23 Q24 Q25 Site 3 431 Q32 Q33 Q34 Q35 Site 4 441 Q42 Q43 Q44 Q45 Site 5 Q51 Q52 Q53 Q54 455 Cost (million pesos) P1 P P P P 2 3 4 5 L.,: Amount of water provided by the basin (m3 /sec). Q. 4 : Amount of water provided by site i within the 1-1 basin's level development Li (m3 /sec). P.: Cost of developing the basin under configuration K at the level Lj-. 73 will be presented is shown. The columns of the table are the levels of development analyzed for the basin under a given configuration. The rows are the development sites constituting the configuration under study. The numbers on the table are the amount of water that each development site gives in order to obtain the desired level of develop- ment in the basin at minimum cost. Configuration I. For this configuration, the hydraulic works needed are: 1. Aqueduct Villa Victoria-Merging Point. 2. Aqueduct Valle de Bravo-Villa Victoria. 3. Aqueduct Colorines-Valle de Bravo. 4. Aqueduct Filtrations El Bosque-Channel Bosque to Colonnes. 5. Aqueduct Aguila II -Colonnes. 6. Aqueduct Tuzantla III-Aguila II. 7. Aqueduct Purungueo II-Tuzantla III. 8. Tuxpan II dam. 9. Aguila II dam. 10. Tuzantla III dam. 11. Purungueo II dam. Optimization Model I gave the results shown in Table 4.9. Configuration II. In this configuration, the hydraulic works are the same as for Configuration I, except for those corresponding to the development of the Tuzantla and Purungueo rivers: 1. Aqueduct Villa Victoria-Merging Point. 2. Aqueduct Valle de Bravo-Villa Victoria. 74 Table 4.9 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration I. Level of Development (m3 /sec) Site 22 30 40 50 60 Villa Victoria 4 4 4 4 4 Valle de Bravo 7 7 7 7 7 Colonnes 11 11 11 11 11 Aguila II 0 0 4 5 8 Tuzantla III 0 8 14 14 14 Purungueo II 0 0 0 9 16 Cost (million pesos) 5,263.7 8,182.3 11,585.5 14,994.2 18,436.6 75 3. Aqueduct Colorines-Valle de Bravo. 4. Aqueduct Filtrations El Bosque-Channel Bosque-Colorines. 5. Aqueduct Aguila II-Colonnes. 6. Aqueduct Tuzantla I-Aguila II. 7. Aqueduct Purungueo I-Tuzantla I. 8. Tuzantla I dam. 9. Purungueo I dam. 10. Aguila II dam. The results obtained from use of Optimization Model I are presented in Table 4.10. Configuration III. Under this configuration, the hydraulic works to be considered are: 1. Aqueduct Villa Victoria-Merging Point. 2. Aqueduct Valle de Bravo-Villa Victoria. 3. Aqueduct Merging Point I-Merging Point. 4. Aqueduct Cerro PelL-Merging Point I. 5. Aqueduct Filtrations El Bosque-Channel Bosque to Colonnes. 6. Aqueduct Colorines-Valle de Bravo. 7. Aqueduct Aguila II-Colonnes. 8. Aqueduct Tuzantla III-Aguila II. 9. Aqueduct Purungueo II-Tuzantla III. 10. Tuxpan II dam. 11. Aguila II dam. 12. Tuzantla III dam. 13. Purungueo II dam. 76 Table 4.10 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration II. Level of Development (m3 1 sec) Site 22 30 40 50 Villa Victoria 4 4 4 4 Valle de Bravo 7 7 7 7 Colonnes 11 11 11 11 Aguila II 0 8 6 9 Tuzantla I 0 0 5 6 Purungueo I 0 0 7 13 Cost (million pesos) 5,263.7 8,272.3 11,966.2 15,601.8 77 Optimization Model I using the corresponding cost functions gave the results shown in Table 4.11. Configuration IV. The hydraulic works under this configuration are the same as for Configuration III, except for those associated to the development of the Tuzantla and Purungueo rivers, which are the following: 1. Aqueduct Tuzantla I-Aguila II. 2. Aqueduct Purungueo II-Tuzantla I. 3. Tuzantla I dam. 4. Purungueo I dam. After feeding Optimization Model I with the corresponding cost func- tions, the results shown in Table 4.12 were obtained. Configuration V. For this configuration, the hydraulic works needed for the development of Villa Victoria, Valle de Bravo, Colonnes, and Aguila II are complemented with the following, which involve the development of the El Gallo site: 1. Aqueduct El Gallo-Aguila II. 2. El Gallo dam. Optimization Model I gave the results shown in Table 4.13. Configuration VI. Under this configuration, the hydraulic works which are necessary are the following: 1. Aqueduct Villa Victoria-Merging Point. 2. Aqueduct Valle de Bravo-Merging Point I. 3. Merging Point I-Villa Victoria. 78 Table 4.11 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration III. Level of Development (m3 /sec) Site 22 30 40 50 Villa Victoria 4 4 4 4 Valle de Bravo 7 7 7 7 Colo rifles 11 11 11 11 Cerro Pelon 0 4 4 4 Tuzantla III 0 4 14 14 Purungueo II 0 - 0 10 Cost (million pesos) 5,263.3 8,021.9 11,356.6 14,809.3 79 Table 4.12 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration IV. 3 Level of Development (m /sec) Site 22 30 40 Villa Victoria 4 4 4 Valle de Bravo 7 7 7 Colonnes 11 11 11 Cerro PelOn 0 4 4 Tuzantla I 0 4 5 Purungueo I 0 0 9 Cost (million pesos) 5,263.3 8,079.9 11,765.6 80 Table 4.13 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration V. Level of Development (m3 /sec) Site 22 30 40 50 60 Villa Victoria 4 4 4 4 4 Valle de Bravo 7 7 7 7 7 Colonnes 11 11 9 11 11 Aguila II 0 8 0 8 10 El Gallo 0 0 20 20 28 Cost (million pesos) 5,263.7 8,272.3 12,696.2 15,924.2 19,583.3 81 4. Aqueduct Colorines-Valle de Bravo. 5. Aqueduct Filtrations El Bosque-Channel El Bosque to Colonnes. 6. Aqueduct El Gallo-Colorines. 7. Tuxpan II dam. 8. El Gallo dam. The use of Optimization Model I rendered the results shown in Table 4.14. Configuration VII. This configuration contemplates an aqueduct route for the water coming from the Tuzantla and Purungueo rivers differ- ent to that used in the previous configurations. The relevant hydraulic works are the following: 1. Aqueduct Villa Victoria-Merging Point. 2. Aqueduct Valle de Bravo-Pumping Station 3. 3. Aqueduct Pumping Station 3-Valle de Bravo. 4. Aqueduct Colorines-Valle de Bravo. 5. Aqueduct Filtrations El Bosque-Channel Bosque-Colorines. 6. Aqueduct Tuzantla I-Pumping Station 3. 7. Aqueduct Purungueo I-Tuzantla I. 8. Tuxpan II dam. 9. Tuzantla I dam. 10. Purungueo I dam. The results obtained for this configuration are presented in Table 4.15. Comparison among the Analyzed Configurations for Each Basin Development Level. From the results of the application of Optimization Model I for each configuration, Table 4.16 was formed. In this table, 82 Table 4.14 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration VI. 3 Level of Development (m /sec) Site 22 30 40 50 60 Villa Victoria 4 4 4 4 4 Valle de Bravo 7 6 7 7 7 , Cerro Pelon 0 0 0 4 4 Colonnes 11 0 9 11 11 El Gallo 0 20 20 24 34 Cost (million pesos) 5,263.3 10,031.2 12,696.2 15,860.6 19,723.3 83 Table 4.15 Sites To Be Developed and the Amount of Water that Each One Will Supply for Several Levels of Development under Configuration VII. 3 Level of Development (m /sec) Site 30 40 50 Villa Victoria 4 4 4 Valle de Bravo 7 7 7 Colonnes 11 11 11 Aguila 8 0 10 Tuzantla I 0 6 5 Purungueo I 0 12 6 Cost (million pesos) 8,057.0 11,822.0 15,644.0 84 %.!) rr) CV CO CV CY1 in co CV Le) • cg'. H H H CC) ON l0 • cC Lf %.1j CA 0 LI") co con al %.0 Cr) Cr) ).0 O'N %.0 c4 tr) CV 0 Cf) CO Lñ CO 1-1 CV CO CV %.0 )1) 0 CV Cr) %.0 Ln oo H et r-I cf) u") (NI VO Cr) CNI Lf) %.0 VO 00 CO ON Cn H in4 ON st 111 . CO 1-4 C." o O o (NI 01 -4- If) ).0 85 the columns are the configurations under study in the basin and the rows are the different levels of development of the basin which were con- templated in the analysis. The numbers on the table are the minimum costs associated to a level of development of the basin under a given configuration, as obtained in the previous sections describing Configurations I-VII. The analysis of Table 4.16 leads to the following conclusions: 1. All the configurations render the same cost for the level of 3 development of 22 m /sec. 3 3 2. For the basin levels of development of 30 m /sec, 40 m /sec, and 3 50 m /sec, the least cost configuration is Configuration III. 3 3. For the level of development of 60 m /sec, the least cost con- figuration is Configuration I. CHAPTER 5 LONG-TERM WATER SUPPLY PLANNING FOR MEXICO CITY METROPOLITAN AREA 5.1 General As explained in Chapter 3, once there exist data for each of the basins that can be developed to supply water to an urban area, similar to that obtained for the Cutzamala River Basin, it is possible, through the use of Optimization Model II (described in section 3.4), to obtain the most convenient construction sequence of the water supply facilities to meet the expected water demand. In Chapter 4, interest was centered on the relative costs between alternative configurations within a basin and, consequently, costs common to all alternative configurations were not considered, i.e., the cost of conveying water beyond the Merging Point. In com- paring the development of alternative and complementary basins, it is necessary to consider all the costs because there are not, in general, common costs among them, and usually there exist large differences in cost items such as water treatment. Also, when comparing the development of different basins, it is most important to take into account the real-life construction programs of the developments, mainly because among basins there are usually large 86 87 differences in the problems arising from their construction. Those con- struction programs should be firmly based on engineering practice. From the information derived through the procedure developed in Chapter 4, graphs such as the one shown in Figure 5.1 can be drawn for each of the basins under consideration. If the assumption is made that the difference in cost between two levels of development is the cost of increasing the development of the basin by the amount given by the difference of the levels of development, then it is possible to define a set of stages for each basin, each one with its own cost. For each of those stages, a construction program can be formu- lated, and the construction, and operation and maintenance costs can be passed to the first year of construction of each stage by using a dis- count rate. All of the foregoing was performed on data for the four basins studied to supply water to the Mexico City metropolitan area, since all 1 of them have already been analyzed and there are available results of the type obtained in Chapter 4 for the Cutzamala River Basin. In the next section of this chapter, each of the basins under study will be briefly described, and the optimal water supply plan for the Mexico City metropolitan area is obtained. The term "optimal" is used here in the sense of most recommendable. 1. The Cutzamala River Basin and the Amacuzac River Basin were studied by the author. The others were studied by different teams. 88 O erl 4—) • r— V) r- 0 1-1 r— •f- CL) L.) L.) C0).) V) ...... r-1 4-) CO ...I r-4 = • M --) CL) L) I E a) 7:3 CV II- V) for ....1 0 s"... el rr C•1 or (1) = >.• > C) C:t 4-) 0 89 5.2 Mexico City Sources of Water The sources of water which have been studied to supply water to the metropolitan area of Mexico City are the following: 1. The Cutzamala River Basin. 2. The Tecolutla River Basin. 3. The Amacuzac River Basin. 4. The Oriental Groundwater Basin. Figure 5.2 (in pocket) shows the geographical location of the referred basins and schematically their hydraulic works. The following subsections contain a description of the develop- ment plans of each basin. 5.2.1 The Cutzamala River Basin The Cutzamala River tributary of the Balsas River is formed by the rivers San José Malacatepec, Ixtapan, Temascaltepec, Zitécuaro, Tuzantla, and Purungueo. Current and future uses of water in agricul- ture in the basin are small. The most important agricultural use in the basin is the Irrigation District of Ixtapilla with a future area of 22,000 ha. All irrigation water demands in the basin were considered as a compromise because of general national policy regarding agricultural development and social justice. The most important water user in the 'basin is the Federal Electricity Commission, which has installed an important hydroelectric system named the Miguel Alemén System (MAS). This system generates annually about 1,800 million kilowatt-hours (KWH). Figure 5.3 shows a scheme of this system, and Table 5.1 presents its main characteristics. 90 91 Table 5.1 Characteristics of the Miguel AlemL System. Mean Annual Mean Annual Flow Power Generation Head 3 Plant (MW) (GHW) (131) (m / sec) Martinez de Meza 25 104.98 376.0 3.87 - . Agustin Milian 19 73.09 276.0 3.87 Durazno 16 89.77 105.5 10.82 Ixtapantongo 99 524.17 328.0 23.96 Sta. B:irbara 75 408.76 262.4 23.96 Tingambato 135 637.98 380.0 25.40 Infiernillo 1,003 3,315.00 92.0 444.00 La Villita 285 1,267.00 44.0 460.00 92 Water transfer from this basin to Mexico City can raise up to 3 60 m /sec, as was shown in Chapter 4. The development of this basin was 3 divided into three stages yielding up to 40 m /sec because the water 3 demand for the last year of the planning horizon is about 125 m /sec and in the other basins it is possible to get water cheaper than that from the lower portion of the Cutzamala River Basin. 3 The first stage contemplates a transfer of 22 m /sec from the 3 upper portion of the basin. These 22 m /sec are obtained as follows: 4 m3 /sec from Villa Victoria dam with a dynamic hydraulic head of 198 m, 7 m3 /sec from Valle de Bravo dam with a dynamic hydraulic head of 3 1,016 m, and 11 m /sec from Colonnes dam with a hydraulic head of 1,187 m. The length of required aqueducts is 175.23 km. The diameter of the pipes is 2.5 m. A tunnel of 4.0 m in diameter and 14 km in length is needed to cross the Las Cruces ridge. The hydroelectric system Miguel Aleman will be partially affected as shown in Table 5.5 is (page 98). The investment to build the hydraulic works of this stage 7,428.48 million pesos. The second stage consists of developing the Temascaltepec Basin 3 3 /sec from and the Tuzantla Basin in order to bring 8 m /sec, taking 4 m each one. The dynamic hydraulic heads are 1,343.4 m and 2,576 m, respectively. To get this amount of water, it is necessary to build two storage dams and aqueducts with a length of 184 km. The investment needed for this stage is 7,327.67 million pesos. In the third stage, the Tuzantla River development is increased 3 of to yield an additional flow of 10 m /sec with a hydraulic head 2,576 m. The required investment is 4,285 million pesos. 93 Table 5.2 shows the budget for the first stage. Similar budgets were estimated for the second and third stages. Table 5.3 shows the composition of costs for the three stages. In Table 5.4, the sites of development and their yields are shown for several levels of development in the basin, and Figure 5.4 shows a scheme of hydraulic system. The most relevant characteristics of the Cutzamala system are presented in Table 5.5. 5.2.2 The Tecolutla River Basin The Tecolutla River discharges in the Gulf of Mexico and has as main tributaries the Necaxa, Laxaxalpan, Tehuantepec, and Apulco rivers. Nowadays, the rivers Necaxa and Laxaxalpan are committed to hydroelec- tric generation in the Necaxa System, whose annual electricity produc- tion is 900 million KWH. This system is also operated by the Federal Electricity Commission. Figure 5.5 and Table 5.6 show the main charac- teristics of this hydroelectric system. 3 The Tecolutla River Basin can provide a flow of 170 m /sec to Mexico City. It has been considered to transfer to Mexico City 40 m3 /sec in two stages (ATEC Consultores, 1977). 3 In the first stage, 16 m /sec will be taken from several streams 3 as follows: the Laxaxalpan will give 3.71 m /sec with a hydraulic head of 574.8 m, the Apulco River and some of its tributaries will give 3 4.75 m /sec with a dynamic hydraulic head of 1,314.4 m, and the Necaxa River will give 7.64 m3 /sec with a hydraulic head of 1,557.8 m. To get this, it is necessary to build several diversion dams, increase the storage capacity already available, and build an aqueduct of 289.0 km 94 Table 5.2 Estimated Budget for Cutzamala's First Stage. -- Q = 22 m3 /sec. Concept Thousand Pesos Dams, pumping stations, pipelines, and regulation tanks: Investment 3,483,391.60 Annual operation 424,458.90 Substations 127,413.97 Roads 211,545.30 Treatment plant: Investment 184,100.42 Annual operation 201,199.68 Transmission lines 243,525.00 Compensation CFE 278,400.00 Cost of electrical connection 724,869.00 Indemnifications 24,353.50 Tunnel at Atarasquillo 850,000.00 Subtotal investment 5,849,197.79 Studies, administration, social benefit works, unexpected costs (27% of investment) 1,579,283.46 Total investment 7,428,481.19 Total operation 904,058.58 95 Ln cd co 4.) CV CV CO 0 ret E-I 0 %.o cs4 0 0 1-1 ce) rir) 3-4 f`n r-1 •1-1 0 r•rr. r--1 A A r-1 1-1 -t4 co op CO cn 4-1 g O 4-) c0 o en 0.1 E 0 .6) 4..) en CO CO 1-1 en 00 0 0 a) 1:14 1-1 H Co cd CO cd 4-O C•J r•-• v--I 0 *1-1 cr) .1-J C.) 0 0 %.0 CO 0 CV CV •.0 0 10 C.) 0 r-1 0 0 4.4 C.) Co PO CO 4-4 0 0 CO 0 CO CT P:1 • 00 Tn co 1-1 0 • 00) r-1 r.110 1-1 4.1 C.) Z Co '.1-400 0 ‘.0 1/40 C.11 0 P • 0 C 14-4 p. 0 CV 0 (0E r--1 CO CV 0 0 A (-) r-1 1-1 0 co • r. 0 u) C.) fa, 0 E co 0 fl) CV 00 0 00) 1-1 44 01 -40 s-1 c.4 t-r) 96 Table 5.4 Sites of Development and Their Yields in Cutzamala Basin for Several Levels of Development. -- All figures are given in m3 /sec. Level of Development in the Basin Site 22 30 40 50 Villa Victoria 4 4 4 4 Valle de Bravo 7 7 7 7 Colonnes 11 11 11 11 ... Cerro Pelon - 4 4 4 Tuzantla - 4 14 14 Purungueo - - - 10 • 97 Tuxpan II 4"iTirat;ons . El Bosque 1 A Purungueo I? • Ce rro Pelt:in °Pumping Station A Projected Storage Dam .A Existing Storage and Divertion Dam. ..---m-Aqueduct . o•••• • ••••n, River. for the Development of Figure 5.4 Scheme of the Hydraulic System Cutzamala Basin. - •▪ 98 CNI -Zr %.0 1.0 • • • CO %.0 lif) r•-•1 cn r, N N • Lr Lr Lr Ln Ln 0 o N • • I", Is, CO 1.0 n50 Cs. r-I r-I Coco r-- L Lfl Ln r, co ch 0 .‘ n-1 (N1 Co ri %.0 CO CO Co Ln rs• r• 0 CO s.-." C,1 1/40 Ch <4 0 14-1 00 •0 0 0 C•n• Ln co 0 tn L %.C1 CI 0 In .1- N tfl CO N r, r, r, O crl In co co 0 • N N 4-7 4-I CD O E fa. a) rl 0 CO N 0 0 0 • rl "••••• N • CU Crl Q) s-1 a) 99 0::i L. \ . . > . \ ., .-- . ., ..., 100 Table 5.6 Characteristics of Necaxa Hydroelectric System. Mean Annual Mean Annual Flow Power Generation Plant (MW) (GHW) (m3 /sec) Necaxa 115.0 490.56 15.0 Tepeji 45.0 217.45 15.0 Patla 45.6 192.06 15.0 1 01 with a diameter of 2.6 m. The investment required for this stage reaches the figure of 7,864.27 million pesos. In the second stage, the development of the Tecolutla River is 3 3 increased to 24 m /sec. To do this, an additional flow of 2.0 m /sec is taken from the Apulco River and its tributaries with a dynamic hydraulic 3 head of 1,314.4 m, 3.33 m /sec are obtained increasing the transfer from 3 the Necaxa River, and finally 19.38 m /sec are obtained through the Coyutla dam and the diversion dam Laxaxalpan with a dynamic hydraulic head of 2,738 m. The additional length of aqueducts is 42.6 km. The investment required for this stage is 12,531.30 million pesos. The development of the Tecolutla River Basin for water supply will partially affect the Necaxa Hydroelectric System. Table 5.7 shows the budget for the first stage, and Table 5.8 shows the composition of costs for the two stages. In Table 5.9, the development sites and their yields are shown. Figure 5.6 shows a scheme of the system. The main characteristics of this system are presented in Table 5.10. 5.2.3 The Amacuzac River Basin The Amacuzac River is also a tributary of the Balsas River; its main sub-basins are the rivers Almoloya, Chontalcuatlân, and San 3 Jeronimo. It is possible to transfer to Mexico City a flow of 39 m /sec after the agricultural water demand in the basin reaches its maximum. Also, in this basin, the federal government imposed that no water is transferred if there are unsatisfied irrigation demands in the basin. 102 Table 5.7 Estimated Budget for Tecolutla's First Stage -- Q = 16 m3 /sec. Concept Thousand Pesos Dams, pumping stations, pipelines, and regulation tank: Investment 4,417,474.19 Annual operation 369,795.99 Substations 128,394.88 Roads 328,613.67 Treatment plant: Investment 134,728.03 Annual operation 192,937.25 Transmission lines 378,291.00 Compensation to CFE 126,112.00 Cost of electrical connection 753,542.12 Indemnifications 51,300.00 Subtotal investment 6,192,343.89 Studies, unexpected costs, administration, and social benefit works (27% of investment) 1,671,932.85 Total investment 7,864,276.74 Total operation 688,845.24 103 O 0 CO E-1 a, 1/40 -4' C1/41 104 Table 5.9 Development Sites and Their Yields in the Tecolutla Basin. -- All figures are given in m3 /sec. Level of Development of Tecolutla Site 16 40 Chignahuapan 1.95 1.95 Laxaxalpan 13.05 Coyutla 6.33 Necaxa 7.68 10.97 El Carmen 1.70 1.70 Xilita 0.69 La Gloria 0.50 Apulco I 2.61 2.93 Tecuantepec I 0.55 0.68 Tecuantepec IT 1.59 1.95 105 Laxaxalpan I To Mexico O Pumping Station Chigna apan &Projected Storage Dam 41. Existing Storage and Divertion Dam. Xi lita Figure 5.6 Scheme of the Hydraulic System for the Development of Tecolutla Basin. 106 • • CV CV 1-1 0 .0 .<4 N. 0% 00 r••• VD 00 7-1 7-1 0n1 00 r- 03 C'.1 oo 00 s..10 0 r-1 107 Three stages of development were defined by the writer [Ingenieria y Procesamiento ElectrOnico, S.A. (IPESA), 1977a]. The 3 first stage contemplates the transference of 13 m /sec from the upper 3 portion of the basin. This yield is formed as follows: 3.5 m /sec from 3 the Almoloya River with a hydraulic head of 1,076 m, 9.6 m /sec from the San Jerônimo and Chontalcuat1L rivers with a hydraulic head of 1,585 m. This development requires the construction of two storage dams of great size (more than 150 m high), an aqueduct of 147.4 km with a diameter of 2.9 meters, and a tunnel of 14 km and 3.1 meters in diameter. The required investments reach the figure of 10,876.31 million pesos. The second stage consists of the development of the lower por- tion of the Amacuzac Basin to provide an additional flow of 13 m3 /sec. To do this, a storage dam is needed and an aqueduct of 126 km has to be built. The hydraulic head in this stage is 1,800 m. The required investment reaches the figure of 6,120.95 million pesos. 3 In the third stage, an additional flow of 13 m /sec is obtained at the same site as that in the second stage. The additional investment is 4,808.75 million pesos. The development of this basin will affect the hydroelectric generation downstream on the Balsas River. Table 5.11 shows the budget for the first stage. Similar bud- gets were estimated for the other two stages. In Table 5.12, the compo- sition of budgets is presented for the three stages. In Table 5.13 and in Figure 5.7, the main characteristics of the development of this basin are presented. 108 Table 5.11 Estimated Budget for Amacuzac e s First Stage. -- Q = 13 m3 /sec. Concept Thousand Pesos Dams, pumping stations, pipelines: Investment 7,175,272.08 Annual operation 341,065.73 Substations 110,314.28 Roads 210,307.43 Treatment plant: Investment 107,949.79 Annual operation 117,976.18 Transmission lines 242,100.00 Compensation to CFE 71,895.17 Cost of electrical connection 647,428.16 Indemnifications 24,210.00 Regulation tank 46,440.00 Subtotal investment 8,564,023.00 Studies, unexpected costs, administration, and social benefit works (27% of investment) 2,312,286.21 Total investment 10,876,309.21 Total operation 530,937.08 109 .-1 Cu 0 1.0 0 VD OU) . •T-4 ,._ • 0 0 CA 4-1 $-1 CN1 t.r1 t-- 4O n.0 r•-• CV "0 ,--I ,—I 1--I <0 • r•-• C,1 (41 r o Cfn 1-1 CV 0 00 Cs4 en en en n-1 stl Cd r-I Cr1 • 110 O r-I r-1 N. ON ON • Ce1 r-I cs1 0 Lr1 - r-I r-i ce) ce) • r-1 L', co co o r-I I—I on on • r-I r-i 0 Ce) VO CO CV Cn1 VO O• ›-> 1--1 CV Ce1 1-4 4.1 $.4 ,•-n CO CO CO CO 0. • E O 0 CsO 01 in cq O CO co c•J n0 .4 0 4-1 O 0 1-1 n0 C.) gO ON cn r-- t', CO 0 cV Le-1 ON O, oo 01 01 r-- n ▪ .0 crs csi (NI 111 To Mexico City (so .0 To r \ Mexico City o n 41/ •• . \ % (A )0 6,\.1 ,o „ \ I./k t„, 0(9.,r\ Las Flores m -... t .m -.....4c, 0. El Sabino .o .e -s \ `co Jeriinimo \.... . '-. Chontalcuatlan'- '.,River Ri Storage Dam in Project. • Existing Dams , \. Amacuzac. C) 41 Figure 5.7 Scheme of the Hydraulic System for the Development of Amacuzac Basin. 112 5.2.4 The Oriental Groundwater Basin The groundwater basin of Oriental is located in the state of Puebla. Geohydrologic studies conducted by the Mexico Valley Water 3 Commission gave the figure of 17 m /sec as the safe yield of the aquifer. Because of the rapid increase of agricultural demand for water in the area, the Secretaria de Recursos HidrLlicos established a maxi- mum water transfer to Mexico City of 7 m3 /sec. Because of the small yield for water supply to Mexico City, only one construction stage has been considered (IPESA, 1977b). The development of the aquifer requires 95 wells and an aqueduct of 152 km with a diameter of 2.1 m. The hydraulic head to surpass the mountain ranges is 460.4 meters. The investment to build this system is 3,915.19 million pesos. Table 5.14 presents the budget. The most relevant characteristics of the Oriental system are shown in Table 5.15 and in Figure 5.8. 5.3 Optimal Long-Term Water Supply Plan The last step of the methodology for long-term water supply planning is to define the most convenient construction sequence of the various stages of each basin. This is accomplished through Optimization Model II (described in section 3.4). The necessary data are the demand forecast curve that has to be met, the interest rate of discount to be used to calculate the present cost of alternative sequences, and the cost of each basin stage. The demand forecast curve for Mexico City is shown in Figure 5.9, the interest rate of discount to be used is 14% which is the rate presently 113 Table 5.14 Estimated Budget for Oriental's Unique Stage. Concept Thousand Pesos Development of well fields: Investment 770,917.45 Annual operation 55,215.32 Pumping stations: Investment 157,471.02 Annual operation 173,819.29 Pipelines 932,081.20 Treatment plant: Investment 1,200.00 Annual operation 11,682.48 Regulation rank 25,000.00 Roads 373,464.90 Substations and cost of electrical connection 105,796.96 Transmission lines 429,920.00 Indemnifications 287,004.62 Subtotal investment 3,082,828.76 Studies, administration, unexpected costs, and social benefit works (27% of investment) 832,363.79 Total investment 3,915,192.53 114 Table 5.15 Characteristics of the Oriental System. Maximum Annual Level of Aqueducts Pumping Pumping Consumption Development Head Power of Energy Pipelines Channels 3 (m)(m /sec) (MW) (GWH) (km) (km) 7 594 36.23 264.49 229.62 0) •f-• (-) rzZ Ln 4-1 116 c) 117 used by Mexico's central planning agency, and the costs of the stages of each basin are those shown in Table 5.16. There are other data which depend on the special case under analysis, such as sequencing restrictions in the stages of each basin. This restriction arises because of engineering considerations. For the case of the Mexico City water supply plan, the stages of each of the four basins under consideration are restricted to be built as follows: 1. The first, second, and third stages of the Cutzamala Basin have to be built in exactly that sequence. 2. The first and second stages of the Tecolutla Basin have to be constructed in exactly that sequence. 3. The second and third stages of the Amacuzac Basin have to be constructed in exactly that sequence, but the first stage does not necessarily have to precede the second stage. 4. The single stage of the Oriental Basin does not have any restriction. The most recommendable sequence of basin stages obtained through Optimization Model II is shown in Table 5.17 and in Figure 5.10. The present cost associated to this optimal sequence is 8,294 million pesos. It can be observed in Table 5.16 that there is an important difference among the basin stages with respect to the importance in total cost of the operation cost. This is due to the difference in the reduction of electricity generation that the development of each basin produces, and in the energy consumption due to the difference in pumping height. 118 Table 5.16 Costs of the Basins' Stages To Be Used in Optimization Model II. -- In million pesos. Cost of Each Stage in Pesos of the First Construction Year of Yield Each Stage 3 Basin Stage (m /sec) Investment Operation Total Cutzamala 1st 22 3,814.3 1,998.7 5,813.0 2nd 8 4,365.1 1,334.0 5,699.1 3rd 10 2,663.4 2,044.5 4,687.9 Tecolutla 1st 16 3,949.7 1,658.7 5,608.4 2nd 24 6,333.8 3,286.3 9,620.1 Amacuzac 1st 13 6,173.4 1,493.0 7,666.4 2nd 13 3,433.6 4,401.4 7,835.0 3rd 13 2,748.4 4,835.0 7,583.4 Oriental 1st 7 2,546.5 168.4 2,714.9 119 Table 5.17 Optimal Long-Term Water Supply Plan for an Electricity Price of 0.16 Pesos/KWH. Accumulated Yield Order of Year of 3 Entrance Basin Stage Entrance (m /sec) 1st Oriental 1st 1981 7 2nd Cutzamala 1st 1985 29 3rd Tecolutla 1st 1995 45 4th Tecolutla 2nd 2000 69 5th Cutzamala 2nd 2008 77 6th Cutzamala 3rd 2011 87 7th Amacuzac 1st 2014 100 8th Amacuzac 2nd 2018 113 9th Amacuzac 3rd 2022 126 120 121 The cost of energy as stated by the Federal Electricity Commis- sion rates is 0.16 pesos per kilowatt-hour (KWH), and the cost of non- generated energy (opportunity cost) was estimated by CFE to be the same. However, it is common knowledge that electricity rates in Mexico are too low and that the CFE's financial situation is not good. So, the writer estimated the cost of hydroelectric generation and got the figure of 0.51 pesos per KWH. This figure was commented on with consultant engi- neers in the field of electricity generation and they considered that the estimate was good. Considering that CFE is a non-profit institution, that price for electricity would be right; but since CFE needs to increase its capital to face the increasing electricity investment to meet the demand for electricity, the writer considers that the price of electricity should be higher than 0.51 pesos per KWH and, just to have a figure, a cost of 0.7 pesos per KWH was proposed. Using these two figures (0.51 and 0.70 pesos per KWH), the operation costs were recalculated. Tables 5.18 and 5.19 show the total costs of each basin stage. The results of Optimization Model II with the costs associated to the two costs of energy are presented in Tables 5.20 and 5.21. Comparison of the results obtained with the three different prices of energy is provided by Table 5.22. It can be observed in Table 5.22 that, between optimal solutions for energy prices of 0.16 and 0.51 pesos per KWH, the difference is in the fifth basin stage entrance. There, Amacuzac's first stage replaces Cutzamala's second stage and moves Cutzamala's 2nd and 3rd stages to the 6th and 7th places. 122 Table 5.18 Cost of the Basins' Stages To Be Used in Optimization Model II (Energy Price of $0.51/KWH). -- In million pesos. Cost of Each Stage in Pesos of the First Construction Year of Each Yield Stage 3 Basin Stage (m /sec) Investment Operation Total Cutzamala 1st 22 3,814.3 4,980.0 8,974.3 2nd 8 4,365.1 3,232.4 7,597.5 3rd 10 2,663.4 5,055.9 7,719.3 Tecolutla 1st 16 3,949.7 3,946.0 7,895.7 2nd 24 6,333.8 8,026.4 14,360.2 Amacuzac 1st 13 6,173.4 3,699.4 9,872.8 2nd 13 3,433.6 7,221.9 10,655.5 3rd 13 2,748.4 7,930.7 10,679.1 Oriental 1st 7 2,546.5 453.6 3,000.1 123 Table 5.19 Costs of the Basin Stages To Be Used in Optimization Model II (Energy Price of $0.70/KWH). -- In million pesos. Cost of Each Stage in Pesos of the First Construction Year of Each Yield Stage Basin Stage (m3 /sec) Investment Operation Total Cutzamala 1st 22 3,814.3 6,671.1 10,485.4 2nd 8 4,365.1 4,339.3 8,704.4 3rd 10 2,663.4 6,822.3 9,485.7 Tecolutla 1st 16 3,949.7 5,238.3 9,188.0 2nd 24 6,333.8 10,753.5 17,087.3 Amacuzac 1st 13 6,173.4 4,953.2 11,126.6 2nd 13 3,433.6 8,832.2 12,265.8 3rd 13 2,748.4 9,697.9 12,446.4 Oriental 1st 7 2,546.5 622.6 3,169.1 124 Table 5.20 Optimal Long-Term Water Supply Plan for an Electricity Price of 0.51 Pesos/KWH. Accumulated Yield Order of Year of 3 Entrance Basin Stage Entrance (n /sec) 1st Oriental 1st 1981 7 2nd Cutzamala 1st 1985 29 3rd Tecolutla 1st 1995 45 4th Tecolutla 2nd 2000 69 5th Amacuzac 1st 2008 82 6th Cutzamala 2nd 2012 90 7th Cutzamala 3rd 2015 100 8th Amacuzac 2nd 2018 113 9th Amacuzac 3rd 2022 126 125 Table 5.21 Optimal Long-Term Water Supply Plan for an Electricity Price of 0.70 Pesos/KWH. Accumulated Order of Year of Yield 3 Entrance Basin Stage Entrance (m /sec) 1st Oriental 1st 1981 7 2nd Tecolutla 1st 1985 23 3rd Cutzamala 1st 1993 45 4th Tecolutla 2nd 2000 69 5th Amacuzac 1st 2008 82 6th Cutzamala 2nd 2012 90 7th Cutzamala 3rd 2015 100 8th Amacuzac 2nd 2018 113 9th Amacuzac 3rd 2022 126 126 Table 5.22 Comparison of Optimal Construction Sequences for Energy Prices of $0.16/KWH, $0.51/KWH, and $0.70/KWH. Energy Price Level Entrance $0.16/KWH $0.51/KWH $0.70/KWH Order Basin-Stage Basin-Stage Basin-Stage 1st Ori-lst Ori-lst Ori-lst 2nd Cut-lst Cut-lst Tec-lst 3rd Tec-lst Tec-lst Cut-lst 4th Tec-2nd Tec-2nd Tec-2nd 5th Cut-2nd Ama-lst Ama-lst 6th Cut-3rd Cut-2nd Cut-2nd 7th Ama-lst Cut-3rd Cut-3rd 8th Ama-2nd Ama-2nd Ama-2nd 9th Ama-3rd Ama-3rd Ama-3rd 127 Between the optimal solution for energy prices 0.16 and 0.70 pesos per KWH, the difference is that Tecolutla's first stage replaces Cutzamala's first stage in the 2nd position, and Amacuzac's first stage replaces Cutzamala's second stage in the 5th position, as in the case of an energy price of 0.51 pesos per KWH. However, the first basin stage to be constructed is consistently the Oriental single stage. CHAPTER 6 CONCLUSIONS In the preceding chapters, a methodology for long-term water supply planning and its application to the Mexico City case were pre- sented. The following conclusions can be drawn from this dissertation: 1. The proposed methodology encourages the study of hydrologic aspects of water resources development prior to any attempt of selecting configurations and scheduling the hydraulic works. The validity of any plan rests on the validity of water avail- ability analysis. 2. The proposed methodology encourages the analysis of the real- world costs of reservoirs, channels, pipelines, tunnels, and pumping stations through the use of available topographical maps and taking into account the engineering practice for the design of those hydraulic works. 3. The breakdown of the optimization problem, implicit in long- term water supply planning, into two simpler ones to be worked out in a sequential manner allows the analyst to introduce physical characteristics that would be difficult to do so in a single model. In addition to this, the amount of necessary simplifications diminishes. 128 129 4. The use of dynamic programming simplifies significantly the optimization models needed to solve the optimization problems. Dynamic programming allows a simple handling of nonlinear func- tions and of the restrictions concomitant with engineering practice. 5. Optimization Models I and II are very simple to implement with a digital computer. The data preparation phase is not time- consuming since data coding is simple. 6. The proposed methodology proved to be effective in the Mexico City case presented in this dissertation. 7. Although the amount of computational effort needed to apply the methodology is larger than the effort usually devoted to solve planning problems, the confidence in the quality of the plans obtained from its use more than justify the additional work. In the Mexico City case, the federal government, through the Comision de Aguas del Valle de Mexico (Mexico Valley Water Commission), has adopted the Mexico City long-term water supply plan resulting from this dissertation. 8. Once the calculation effort to apply the methodology has been made, a number of subproducts is left for subsequent applica- tion. Such is the case of computer programs for the overall design in an optimal fashion of aqueducts formed by reaches of steel pipe, concrete pipe, channels, tunnels, and pumping stations. 130 A word of caution if worthwhile. Planning has to be understood as a process where a great deal of feedback occurs as time elapses. "Good" plans formulated with today's information might not be good with tomorrow's. However, decisions must be made now with the information available. It is imperative to undertake periodic reviews of our original plans in the light of new information and to modify them if necessary. APPENDIX A SYNTHETIC GENERATION OF RUNOFF RECORDS IN UNGAGED STREAMS A.1 Introduction The west portion of the Cutzamala River Basin lacks runoff records for the rivers where storage dams can be built to divert water for Mexico City water supply. This lack of information leads to syn- thetically generating streamflow records on a monthly basis. The model that follows was developed to cope with the problem of synthetic generation of monthly runoff records for ungaged streams. A.2 The Model The annual volume of runoff in a stream, V, can be considered a non-autocorrelated variable. So, to generate synthetic records of annual runoff volume, the following model can be used: V. = E. [1] J NqhereV.istherllnO ff WhllnefOryearj,andE.is a stochastic vari- able with a certain probability distribution. To define the type of probability distribution and its parameters, attention should be directed to the available data in the basin where runoff records are required and in nearby gaged basins. 131 132 Usually, precipitation records are available and, by comparing the precipitation pattern of the ungaged basin with those of the gaged ones, it is possible to tell if the basins are meteorologically homo- geneous. Also, a survey and comparison of cover characteristics are needed. The type of probability distribution of the annual runoff in the ungaged basin can be assessed by analyzing the corresponding distribu- tions of the gaged streams, and taking into account the homogeneity analysis performed on precipitation and cover characteristics. To estimate the parameters of the type of probability distribu- tion chosen, the moments method may be used, but it remains to define the moments of the ungaged stream probability distribution. This can be done on the basis of available information for the gaged streams. Specifically, the first two moments can be estimated as a function of the basin's physical and meteorological characteristics: V = V(P, a, S, A, ...) = a (17 , a , S, A, . a-v where V = mean annual runoff; a- = standard deviation of annual runoff; P = mean annual precipitation; = standard deviation of annual precipitation; S = slope of the main stream; and A = area of the basin. 133 The actual form of equations [2] and [3] and the parameters that they involve are obtained through regression analysis by using the data pertaining to the gaged basins. As an example, the function - -a - Y V =PA So can be tried, where three parameters have to be esti- mated (a, f3, y), and at least four data points from gaged streams are necessary. With equations [2] and [3] to estimate the first two moments of the probability distribution of annual runoff, its parameters can be estimated and, through a Monte Carlo procedure, sequences of annual runoff can be generated. To distribute the annual runoff within the year, the average monthly distribution of runoff in the gaged streams can be used: V.. = V. M. Ji for i = 1,2, ..., 12 [4 ] whereVii isthevolumeofrunoffinmonthiofyearjandM.is the 1 average percentage of annual runoff that occurs in month i, calculated for the gaged streams. This procedure would produce similar hydrographs every year (they would be different only in scale). To avoid this deficiency, a stochastic variable, affecting the monthly distribution obtained from equation [4], can be considered. This stochastic variable is defined as the difference between the average percentage of total annual runoff for a given month and the actual percentage registered. This difference is to be expressed as percentage of annual runoff. Since, in most basins, the characteristics 134 of runoff change along the year, 12 stochastic variables are needed, one for each month. Again, a probability distribution can be fitted to each sample of the 12 stochastic variables. This can be done through the moments method by calculating the mean and standard deviation of the stochastic variable sample corresponding to each month. averiasynneticallygeneratedannualrunoff,v,the monthly distribution would be obtained as follows: V. = M.V. + m.V. = (M. + m.)V Ji 13 13 1 1 j [5] 12 E M. + m. = j for i = 1,2,3, ..., 12 i=1 whereVii istherunoffofmonthi,M.is the average percentage of annualrunoffthatoccursinmonthi,andm.is the stochastic deviation 1 from average runoff distribution for month i, expressed in percentage of annualrunoff.Thisvalue(m.)is obtained through a Monte Carlo method from the probability distribution fitted to the deviations from average for month i. A.3 Application The model described in section A.2 was applied to the west por- tion of the Cutzamala Basin. It was used to generate 50 years of monthly records of the ungaged streams at the sites where storage dams are feasible. Table A.1 shows the mean and standard deviation of annual runoff obtained. 135 CV CO n10 U") • • • (11 10 1.0 1.10 cn r-. ce) • cs% r- co cn %ID r-I .../* 01 01 CO Cc) C31 CO CN Cc) CV C*-1 Cc) Cc) • 0 0 0 0 0 Cr1 C+1 0 0 r-I 0 44 4r--1 r- v.) rn 11") 0.1 st ul 0 01 01 -4' CO r-I 1-1 r-f CV O o co co a) c..) r4 i-4 z o 4.) 4.4 to OD 4-) 0 0 0 0 cn CO CtS 0 0 0 N N 0 0 0 0 E-I E-I 0.n E-I LIST OF REFERENCES ATEC Consultores. 1977. Aprovechamiento del rio Tecolutla para el abastecimiento de agua potable a la Ciudad de México [Develop- ment of Tecolutla River for Mexico City water supply]. Prepared under contract for Comisi6n de Aguas del Valle de México, Mexico City. Bogardi, Janos F., Lucien Duckstein, and Erick F. Plate. 1976. 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