LIBRARY Michigan Sm , UM This is to certify that the thesis entitled Systems Analysis and Simulation of Upland Rice-Based Cropping Systems in the Philippines presented by Tirso B. Paris, Jr. has been accepted towards fulfillment of the requirements for Ph.D. dPgflwin Philosophy / Major professor ’(kzo Date January 3, 1979 0-7 639 OVERDUE FINES ARE 25¢ PER DAY PER ITEM Return to Book drop to remove this checkout from your record. SYSTEMS ANALYSIS AND SIMULATION OF UPLAND RICE-BASED CRDPPING SYSTEMS IN THE PHILIPPINES by Tirso B. Paris, Jr. A DISSERTATION Submitted to Michigan State University In partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1978 ABSTRACT .SYSTEMS ANALYSIS AND SIMULATION OF UPLAND RICE-BASED CROPPING SYSTEMS IN THE PHILIPPINES BY Tirso B. Paris, Jr. Current research in multiple cropping is done mostly through field experiments and socio-economic surveys. While these types of research are important, testing alternative cropping patterns for economic and biological stability is expensive and time-consuming. Hence, the possibility of simulating the effects of varying economic and environmental conditions on the performance of cropping systems was examined. This would enable testing of a large number of crop- ping patterns at various management levels and under varying economic and environmental conditions within a short period of time. A This study was conducted (1) to develop a systems model for simulating upland rice-based multiple cropping systems, and (2) to evaluate by means of the computer simulation model effects of environ- mental and economic influences and alternative cropping patterns on the performance of cropping systems. The computer simulation model, written in FORTRAN language, was designed for an upland area with data obtained mostly from the barrio Cale in Tanauan, Batangas, Philippines. Eight upland crops are included, namely, rice, corn, sorghum, mungbean, cowpea, peanut, soybean, and sweet potato.‘ The simulation model includes components for land allocation, rainfall generation, production, price generation, labor utilization, Tirso B. Paris, Jr.‘ and income accounting. Land allocation.is largely pre-determined with the user specifying the land area and planting dates of each crop in the pattern. Rainfall is generated weekly either synthe- tically using an incomplete gamma or lognormal distribution function or through the use of historical rainfall data. The production com- ponent estimates crop yield based on user-specified fertilizer, weed control, and insect control levels and drought stress during the various stages of crop growth. Yield is predicted using the reduction rates approach where potential yield is subjected to a series of re- duction factors for input levels and environmental conditions which are sub-optimal. The price generator, which determines the price of a crop at any given week of the year, employs price indices and ave- rage annual prices and can be used stochastically. The labor compo- nent accounts for the use of labor in the production process as well as determines labor hiring. Finally, the crop accounting component keeps track of all farm income and expenses. Several experiments were done with the computer simulation model primarily to show its usefulness, capabilities, and flexibility. These were of the following types: yield response to various levels of inptus, performance of specific cropping patterns with respect to variations in rainfall and prices; comparison of performance of crops between favorable and unfavorable conditions; comparison bet- ween intensive and non-intensive cropping patterns; and comparison of planting dates and yields using two strategies for choice of planting dates. The conduct of these experiments was facilitated by the availability of four different modes of running the model. f-u Tirso B. Paris, Jr. The model appears to be useful in evaluating the profitability of a cropping pattern and in determining the most profitable levels of inputs; for evaluating the stability of economic returns of a cropping pattern to rainfall and price variations;for determining the biological viability of a cropping pattern; and for determining' detailed labor utilization of a cropping pattern. With appropriate changes in the relevant parameters and structure, it can be adapted to other upland areas and other farm situations in the Philippines. The model developed thus far is still tentative in view of certain limitations in the model which are attributed to the lack of reliable data and some weaknesses in the model structure. Sugges- tions for overcoming the limitations are outlined. In view of the preliminary nature of the model, no definitive recommendations are suggested for Cale, Batangas. It is pointed out, however, that the various experiments have shown that rice in combination with legumes show considerable potential in the study area. ii To' Thelma and Ivan ACKNOWLEDGEMENTS I wish to express my profound gratitude to my major adviser, Dr. Robert D. Stevens, for his patience, encouragements, and guidance throughout the study, especially during the final critical stages. My profound gratitude also goes to Dr. warren H. Vincent for his guidance, critical comments, and very helpful suggestions. I also wish to thank the other members of my committee, namely, Dr. Thomas J. Manetsch and Dr. Lester V. Manderschied for their constructive criticism and helpful comments. I wish to acknowledge my indebtedness and gratitude to the following institutions for the financial support they have extended to during the various stages of the study: the Department of Agricultural Economics at Michigan State University for the graduate assistantship; the Philippine American Educational Found- ation and the Ford Foundation for the travel grants; the Inter- national Rice Research Institute for the financial support in the data collection and analysis; and the University of the Philippines at Los Bafios for the financial support it has extended me during the writing of the manuscript. Special thanks are due to some IRRI people, most especially to Dr. Edwin C. Price for his guidance, moral support, for his faith in me and his camaraderie; to Dr. Randolph Barker for his help during the initial stages of the study; to other senior staff iii iv members for their critical comments; to Mrs. Aida M. Papag and Mrs. Milagros L. Obusan for their assistance in the data processing; and to Mrs. Norma E. Dumalag for typing earlier drafts. I also wish to thank Miss Dorothy Yap for her excellent editing the first draft. Finally, I would like to thank my wife, Thelma, for her patience, understanding, and encouragements. TABLE OF CONTENTS INTRODUCTION 1.1 Background 1.2 Multiple Cropping in the Philippines 1.3 Multiple Cropping Research 1.4 Objectives of the Study 1.5 The Study Area 1.6 Plan of the Study METHODOLOGY OF SYSTEMS ANALYSIS AND SIMULATION IN AGRICULTURAL MANAGEMENT Introduction The Systems Concept System Identification Abstract Modeling Systems Simulation Advantages of Systems Analysis and Simulation Summary NNNNNNN O O NGUbWNH CONCEPTUAL MODEL OF A FAMILY FARM 3.1 Introduction 3.2 Gross Structure of a Farm System 3.3 A Modified Model for the Study 3.4 Summary LAND ALLOCATION COMPONENT 4 1 Introduction 4.2 Method of Land Allocation 4 3 Summary . RAINFALL GENERATOR 5.1 Introduction 5.2 Modeling Considerations} 5.2.1 Time interval of generated rainfall 5.2.2 Methods of rainfall generation 5.2.3 Historical data vs. synthetic rainfall generation \ONO‘#UJH ll 11 11 17 19 22 25 25 30 31 34 34 35 39 4O 4O 40 40 42 44 vi 5.3 Synthetic Rainfall Generation Methods 5.3.1 Tests of independence 5.3.2 Alternative probability distributions 4 Generating Variables of a Particular Distribution 5 Chi-square Tests 6 Options Using Historical Data 7 Validation of Rainfall Generating Component 8 Summary PRODUCTION COMPONENT Introduction Factors Affecting Yield Modeling Considerations Factors Considered Method of Simulating the Production Component Approaches to Yield Estimation Relation Between Rainfall and Yield Relationship Between Fertilizer Input and Yield Relationship Between Weeding Input and Yield 0 Relationship Between Insect and Disease Control and Yield 6.11 Computer Implementation of the Production Component 6.12 Validation of the Model 6.13 Summary O‘O‘O‘OO‘O‘O‘O‘O‘O‘ O O HOGNOUIL‘UNH PRICE GENERATOR 1 Introduction 2 Seasonal Price Indexes .3 Generating Prices 4 Summary LABOR UTILIZATION COMPONENTS 8.1 Introduction 8.2 The Labor Utilization Component Submodel 8.3 Sources of Data 8.4 Summary THE COMPUTER SIMULATION MODEL 9 1 Introduction 9 2 Structure of the Computer Model 9.3 Features and Options 9 4 Deck Set-up for Running the Model 9 5 Summary 102 104 104 107 107 108 111 115 116 116 116 119 124 126 126 126 131 136 141 CHAPTER vii , Page 10 EXPERIMENTATIONS, RESULTS, AND DISCUSSION 10.1 10.2 10.3 Introduction Results of Experiments 10.2.1 Yield response to nitrogen at zero, medium, and high levels of other inputs 10.2.2 Yield response to weeding labor at high vs. low fertilizer and insect control levels 3 Evaluation of specific cropping patterns . .4 Comparison of yield between favorable and unfavorable conditions 10.2.5 Comparison between intensive and non- intensive cropping patterns 10.2.6 Comparison of planting dates and yields using two strategies for choice of planting date Summary 11 SUMMARY, CONCLUSIONS, AND SUGGESTIONS FOR FURTHER 11.1 11.2 11.3 BIBLIOGRAPHY APPENDICES I. II. III. RESEARCH Summary Conclusions Suggestions for Further Research 11.3.1 Crop-Soil—Environment Relationships 11.3.2 Economic Relationships 11.3.3 Suggested Revisions in the Model Structure Time by Operation Matrices of Labor Utilization by Crops FORTRAN Source Program of the Computer Simulation Model Sample Outputs of the Computer Simulation Model 142 142 143 143 150 151 163 166 168 171 172 172 175 179 180 186 187 190 193 193 202 233 viii LIST OF TABLES TABLE 1.1 Types of cropping patterns in study area of 50 farmer- cooperators, Cale, Tanauan, Batangas, 1974-1975 5.1 Results of five tests of independence of weekly rainfall data, Ambulong, Tanauan, Batangas, 1949-1975 (devia- tion from.means) 5.2 Results of five tests of independence of weekly rainfall data, Ambulong, Tanauan, Batangas, 1949-1975 (devia- tion from medians) 5.3 Means and standard deviations of weekly rainfall data, Ambulong, Tanauan, Batangas, 1949-1975 5.4 Estimates of u and 0 parameters of a lognormal rainfall distribution by week, Ambulong rainfall, 1949-1975 5.5 Gamma and beta parameters of the incomplete gamma distribution fitted on weekly rainfall data, Ambulong, 1949-1975 5.6 Comparison of Chi-square statistics between incomplete gamma and lognormal distribution fitted on Ambulong rainfall data, 1949-1975 5.7 Annual totals and averages per week of 30 years of simulated rainfall based on gamma parameters Ambulong, Tanauan, Batangas rainfall data 5.8 Annual totals and averages per week of actual rainfall data, Ambulong, Tanauan, Batangas, 1949-1975 5.9 Comparison of weekly rainfall means and standard devia- tions, 30 years of simulated rainfall based on gamma parameters vs. actual data, Ambulong, Tanauan, Batangas 6.1 Regression equations for rice, Cale farmers, Tanauan, Batangas, 1973-1974 and 1974-1975 6.2 Regression equations for wet season and dry season corn, Cale farms, Tanauan, Batangas 1973-1974 and 1974-1975 Page 10 47 48 51 54 57 64 67 68 69 81 82 TABLE 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 6.11 6.12 7.1 7.2 8.1 8.2 9.1 9.2 ix b Yield reduction rates for different levels of moisture stress in drought weeks during the vegetative stage of various crops Yield reduction rates for different levels of moisture stress in drought weeks during the reproductive stage of various crops Yield reduction rates for different levels of moisture stress during the maturation stage of various crops Summary of regressions on yield vs. nitrogen input, Cale, Tanauan, Batangas, 1974 Yield reduction rates of different levels of fertilizer, various crops Yield reduction rates for different levels of weeding labor, various crops Most common pests and recommended chemical control, by crop Yield reduction rates for different levels of insect control, various crops Various crop data used in the Cropping systems simula- tion model Comparison between actual and simulated yields based on actual input levels and rainfall, 1973-1974 Base prices and monthly price indexes of various crops, Batangas, Philippines Annual rates of change in price and the form of trend lines by crop, Cale, Tanauan, Batangas, 1956-1975 Labor requirements by operation by crops, Cale, Tanauan, Batangas (in man-hours/hectare) Labor requirements for each week from planting week by crop Structure of labelled COMMON statements and the sub- routines using them Dates and corresponding week codes used in the simula- tion model 91 92 93 95 96 98 100 101 103 105 112 114 121 123 130 132 TABLE 9.3 9.4 9.5 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 10.10 10.11 10.12 10.13 Instructions for preparation of the option card Preparation of the policy card, Mode 1 Preparation of the planting date card Simulated yield response to fertilizer, zero weeding and insect control Simulated yield response to fertilizer, medium weeding and insect control Simulated yield response to fertilizer, high weeding and insect control levels Net returns of various crops to different levels of nitrogen fertilizer, medium level of other inputs Simulated yield response to weeding labor, low ferti- lizer and insect control levels Simulated yield response to weeding labor, high ferti- lizer and insect control levels Means and standard deviations of selected variables of the Rice - Mungbean cropping pattern with random rainfall and prices, medium level of inputs Means and standard deviations of selected variables of the Rice - Soybean cropping pattern with random rainfall and prices, medium level of inputs Means and standard deviations of selected variables of the Rice - Sweet Potato cropping pattern with random rainfall and prices, medium level of inputs Means and standard deviations of selected variables of the Rice - Peanut cropping pattern with random rainfall and prices, medium level of inputs Means and standard deviations of selected variables of the Rice - Corn - Corn cropping pattern with random rainfall and prices, medium level of inputs Comparison of net returns and labor utilization of selected cropping patterns due to joint rainfall and product price variability Comparison of simulated yield, favorable vs. unfavor- able condition Page 137 140 141a 145 146 147 149 152 153 156 157 158 159 160 162 164 TABLE 10.14 10.15 10.16 xi Comparison of economic performance by crop under favorable vs. unfavorable weather and input conditions (P/ha) Comparison between intensive and non-intensive cropping patterns at low and high input levels Comparison of planting dates and yields using two stra- tegies for choice of planting data, low input levels 165 167 169 FIGURE 2.1 2.2 2.3 2.4 2.5 3.1 3.2 6.1 9.1 10.1 10.2 xii LIST OF FIGURES Flow Diagram of the Systems Approach as a Problem Solving Methodology Flow Diagram of Feasibility Evaluation System Identification as Part of the Systems Approach Flow Diagram of Abstract Modeling Computer Simulation as an Iterative Problem Investigating Process Gross Structure of a Farm System Major Components and Interrelationships of the Simulation Model Flow Chart of the Production Component Flow Chart of the Main Program, Cropping Systems Simulation Model Simulated Yield Response of Upland Palay to Fertilizer, High vs. Low Weed and Insect Control Simulated Yield Response of Upland Palay to weeding Labor, High vs. Low Fertilizer and Insect Control 13 15 16 18 20 26 78 128 148 154 CHAPTER 1 INTRODUCTION 1.1 Background Multiple cropping is usually defined as the practice of growing two or more crops, either simultaneously or in sequence, on a given piece of land in one year. While it is an ancient technique, only recently has it gained emphasis and popularity in the Philippines and other underdeveloped countries. Prior to the 19603, the idea of multiple cropping had scarcely been mentioned in national develop- ment plans. With rapidly increasing population pressure in the face of limited land resources, however, the need to increase agricultural production other than by bringing new land into production has been recognized. While increased agricultural productivity as a develop- ment goal is primarily approached through the improvement of the technological and management package for farmers such as high yielding varieties, irrigation, fertilizer and other purchased inputs, and secondarily through the improvement of agricultural institutions supporting agriculture such as agrarian reform, credit, cooperatives, etc., multiple cropping is also recognized as an important means of increasing agricultural production. It is also cited as a means of increasing farm employment and supply of agricultural crops especially cash crops and vegetables. Agricultural research institutions have added to their list of priorities the study of multiple cropping practices, and the develop- ment of cropping systems that help improve resource utilization and farm incomes. For example, the Department of Agriculture of the 1 \ Philippines created a special program called Project ADAM (Agricultural Diversification and Markets), the main purpose of which is to identify potential areas for agricultural diversification. The Philippine Council of Agricultural and Resources Research has also listed multiple cropping as one of its priorities, and the two primary agricultural research institutions in the Philippines, the University of the Philippines at Los Bafios (UPLB), and the International Rice Research Institute (IRRI), have added the so-called "multiple cropping projects" to their basic research programs. The primary benefits from the practice of multiple cropping are as follows: it increases total production per unit of land; it improves land and labor utilization; it increases employment on the farm; it increases family income; and it provides more variety of food to the farm family and consumers. There are, however, some difficulties in the change from mono- culture to multiple cropping.1 First, it involves more expenditures to the farmer in terms of increased purchased and labor inputs. Although additional returns may be greater than additional costs, there are problems of obtaining the credit for increased expenditures. Secondly, the farmer may not possess the necessary technical knowledge to grow new crops, thus requiring some technical assistance from the public sector. Third, the farmer may not know what combina- tion of crops, sequences, and timings would give stable returns under 1For a comprehensive treatment of the policy issues in multiple cropping, see D. E. Dalrymple, Survey of Multiple Cropping_in Less Developed Nations, Foreign Economic Development Service, U. S. Department of Agriculture, Oct. 1971, pp. 101-105. .the climatic conditions of the area. Finally, the new crops grown by the farmer may not have a ready market and necessary infrastructure like irrigation facilities. If one of the objectives of the agricul- tural policy is to promote multiple cropping, then, some means of overcoming the difficulties have to be devised. 1.2 Multiple Cropping in the Philippines The extent to which multiple cropping is practiced in the Philippines is low compared to some other countries particularly Taiwan and Japan. On the national level, the multiple cropping index2 of the Philippines was 127 in 1938, 126 in 1948, and 136 in 1960.3 In contrast, the multiple cropping indexes for Taiwan are 134, 153 and 180 respectively for the same years. Multiple cropping patterns in the Philippines usually take the form of double cropping of rice and corn. Double cropping is possible only in areas where irrigation facilities are available. Multiple cropping is also practiced in upland areas in the form of inter- cropping and relay interplanting.4 In addition, vegetable crops with short maturity periods are grown in sequence mostly in the upland areas. However, multiple cropping indexes, vary from one region to another. In Central Luzon where irrigation facilities are available, farmers are able to plant about two crops of rice per year. In 2The index is derived by dividing total land area planted during the year by the amount of cultivated land physically available and in use (D. G. Dalrymple, op. cit., p. 6). ‘ 3C. M. Crisostomo, et.al., The New Rice Technology and Labor Absorption in Philippine Agriculture, Malayan EcOnomic Review, 16:2, 117-158 (1971). aRelay interplanting involves the sowing or planting of a second crop between the rows of the first crop before it is harvested. contrast, sugar producing provinces like Negros have multiple cropping indexes close to unity because sugar cane can be grown only once a year. On the whale, multiple cropping is still not a widespread practice in the Philippines, mostly for the reasons cited above. It will take considerable effort from the government to overcome the difficulties limiting multiple cropping in terms of research, extension and,the provisions of markets, infrastructure, and credit. 1.3 Multiple Crgpping Research Research institutions have only recently started to deal with multiple cropping research in a systematic fashion. At IRRI, Harwood laid down the research program of the multiple cropping project.5 The philosophy behind their research programs is the so-called cropping system approach.. The main objective is to integrate knowledge about farm resources (physical and socio-economic) and production technology through systems approach to find alternative cropping patterns which will result in improved farmer welfare. The resources which are recognized to have some effects on the cropping patterns are (1) natural resources - land, sunlight, and water, and (2) socio-economic resources - labor, credit, markets, and power source. The biological factors in cropping system design and production are varietal selection, weed control, insect manage- ment, disease control, tillage, soil facility, and interplant 5R. R. Harwood, "The concepts of multiple cropping: an intro- duction to the principles of cropping systems design," Training Lecture, IRRI, June 1973 (mimeo.).' relations. These factors are interrelated to one another. The IRRI approach is to study each of the factors as well as their inter- relationships. Most of the research at IRRI on multiple cropping is 'within the framework described above. The research at the University of the Philippines is more or ,1ess similar to that of IRRI. Both the IRRI and the UPLB research organizations are using the multi-disciplinary approach wherein the research staff is composed of agronomists, entomologists, weed specialists, and economists. Examples of specific research are (1) variety trials, (2) alternative cropping pattern trials, (3) intercropping and relay cropping experiments, (4) socio-economic studies of old and new cropping patterns, (5) effects of various management levels, (6) weed control, and (7) insect control, and others. Current research is being done mostly through field experiments and socio-economic surveys. While these types of research are important, the main limitation is that it takes years and years of continued testing and re-testing alternative cropping patterns before definitive conclusions can be reached regarding their economic and biological stability due to varying economic and weather conditions. In addition, the time-consuming experiments are expensive. Hence, if it is possible to simulate the effects of varying economic and environmental conditions on the performance of a cropping system and consequently on farmer welfare, then considerable time and financial resources can be saved. Many alternative crapping patterns can be tested at various management levels and varying economic and environmental conditions within a short period of time when simulation is aided by a digital computer. Another limitation of current research in multiple cropping is that very little economic analysis, if any, is done on the newly tested cropping patterns. With computer simulation, economic analysis can be facilitated. 1.4 Objectives of the Study There are two primary objectives of the study: (1) to develop a systems model for simulating upland rice-based multiple cropping systems, and (2) to evaluate by means of the computer simulation model the effects of environmental and economic influences on the economic performance of alternative cropping patterns. The first objective was accomplished by constructing a systems model of a typical upland farm, trimming it down to a manageable size, and expressing the various interrelationships in quantitative terms. The simulation model developed was initially designed to answer the following questions: What crop combinations are bio- logically feasible and economically profitable given the climatic and economic environment? What are the expected yields, net returns and labor requirements of the combination? What are the effects of various levels of management on the performance of alternative crop- ping systems? The second objective was achieved by using the crop, climatic, and economic data of a Philippine village, Barrio Cale, Tanauan, Batangas in the simulation model. The development of the simulation model was considered a major task in itself owing to the complexity of the farm system and the range of decisions which the farmer faces. Because of the complex nature of the system, it was necessary to focus only on important components and leave out numerous details simply to make the problem manageable. Thus, it should be recognized at the very outset that this study is a preliminary effort. It is hoped, however, that it will lay the foundations for more comprehensive models. 1.5 The Study Area Most of the data used in this study were obtained from agronomic experiments and economic surveys conducted in Barrio Cale in Tanauan, Batangas. The choice of the area of study was necessitated by the fact that Cale is an area which has been studied intensively by the Multiple Cropping Project of IRRI since 1973, and the studies are still going on at the time of this writing. Benchmark economic data were collected in 1973 and a daily record of all the farm and non-farm operations, input use, income and expenses were collected weekly from 1973 to date. In addition, agronomic experiments were conducted in Cale since 1973. Barrio Cale is in the northeastern part of Batangas province and is about forty kilometers southwest of Los Bafios, Laguna - the site of IRRI. The main crops of Cale are rice and corn, but it is considered a leading barrio in the production of vegetables. It is located seven kilometers northwest of the town proper. It has a population of 3,000 and 400 households, mostly farmers. It has a third class road mostly feeder roads covered with gravel and stones. Cale has no electricity and transportation is by jeepneys and by tricycles that ply from Tanauan town to the barrio. Water supply for the barrio comes mainly from artesian wells installed by the govern- ment, although some households dug their own wells.6 Farm sizes in Cale range from 0.09 hectare to 3.0 hectares with an average of 0.93 hectares. The majority of farmers own or rent several parcels of land located in different parts of the barrio. In general, farmers till one to six parcels of land with the majority of the farmers having three parcels which are generally within 12 minutes walking distance from the farmhouse. Most of the farmers have a trellis in addition to the open fields they are working. The average farmer is about 45 years old. The average educational attainment of the farmer and his wife is four years each. The size of households range from 2 to 12 with an average of 6.4 persons per family. Share tenants comprise the largest group in Cale (36 percent), followed by the part-owners (32 percent), and the full owners (20 percent), the rest being the share-lease tenants. 16E. V. Antonio and G. Banta, "Multiple Cropping in a Batangas barrio," ‘IRRI Saturday Seminar, June 29, 1974. Upland rice and corn are major crops grown in the area, with various vegetables being planted in smaller scale. The rice is broadcast in unpuddled soil in May-June and harvested in September- October while the corn is planted in October-November and harvested in January-February. Based on the sequence of planting of the major crops, 8 cropping patterns were found to exist in the area (Table 1.1). Fifty percent of the total study area is planted to rice followed by corn (green or dry grain) and others. Sugarcane growing is the next widely used pattern (13 percent). The average farm is growing nearly two crops per year. The barrio has a multiple cropping index of 181 making it one of the most intensive in the Philippines. 1.6 Plan of the Study This study.is_composed of 11 chapters; Chapter 1 deals with the introductory part of the study. Chapter 2 provides a brief expo- sition on the methodology of systems analysis and simulation. Chapter 3 is devoted to the development of a conceptual model of a family farm. In this chapter, the major components of a farming system are defined and the ones actually used in the study are identified. Chapters 4 to 8 are detailed discussion on specific components namely, land allocation component, rainfall generator, production component, price generator, and the labor component, respectively. Chapter 9 is a description of the features and options available on the computer simulation model. Chapter 10 discusses the various experiments done with the model and the results of experimentation. Finally, Chapter 11 presents the summary and conclusions of the study and some suggestions for further research. 10 Table 1.1. Types of cropping patterns in study area of 50 farmer cooperators, Cale, Tanauan, Batangas, 1974-75. Total area Percent of Pattern of study farms total gtudy under pattern area (hectares) ” Rice-corn and others 16 25 Rice-corn 16 25 Sugarcane 8 ‘ l3 Rice-garlic ‘ 6 10 Trellis 6 10 Vegetables-vegetables 5 ' 8 Rice-vegetablesb 3 5 Corn-corn and vegetables 3 4 Total ' 63 100 8Percent in sugarcane may be bigger for the entire barrio if the less intensive farms excluded from the study were included. bExcept garlic. Source: Antonio, E. V. and-Gt Banta, "Multiple Cropping in a Batangas barrio," IRRI Saturday Seminar, June 29, 1974. CHAPTER 2 METHODOLOGY OF SYSTEMS ANALYSIS AND SIMULATION IN AGRICULTURAL MANAGEMENT 2.1 Introduction This chapter deals with the conceptual and theoretical aspects of systems analysis and simulation. The general steps in undertaking such analysis are outlined and the methodology of systems analysis and simulation are described. Finally, the advantages and dis- advantages Of systems analysis are cited. 2.2 The Sygtems Concept The term "system" has been defined in various ways in the literature. Park and Manetsch1 define a system as a set of inter- connected elements organized toward a goal or a set of goals. Dent and Anderson2 state that a system implies a complex of factors that are interrelated; it implies interaction between these factors and it implies that a conceptual boundary may be erected around the complex as a limit to its organization autonomy. McMillan and Gonzales3 define a system as a set of objectives together with relationships between the Objectives and their interrelationships. There is not a complete agreement as to the definition of the term system. However, all definitionscontain the concept Of interaction. l . G. L. Park and T. J. Manetsch, Systems Analysis and Simulation with Applications to Econmmic and Social Systems, Preliminary ed., Part I and II, Michigan State U., January 1973. 2Dent, J. B. and J. R. Anderson, (eds), System Analysis in Agri- cultural_Menagement, Sydney: John Wiley & Sons, Australagia Pty.Ltd.,l971. 3C. McMillan and R. F. Gonzales, System Analysis: A Computer Approach to Decision Medals, R. D. Irwin, Homewood, 1965. __f " 11 12 Systems analysis can then best be defined as a method of analysis in which the interaction of the various components of a system are considered Of paramount importance. It implies that an isolated study of parts Of the system is not adequate to understand the complete system. The systems approach is thus a problem solving methodology which begins with a tentatively identified set of needs and has as a result, an Operating system for efficiently satisfying a perhaps redefined set of needs which are acceptable or "good" in the light Of tradeoffs among needs and resource limitations that are accepted as constraints in a given setting.4 Figure 2.1 shows the flow chart Of the systems approach. The major phases of the approach are (l) feasibility evaluation, (2) abstract modeling, (3) implementation design, (4) implementation, and (5) system Operation. It should be emphasized that in the systems approach each process phase is iterative. The outcome of each phase is to be tested for adequacy, completeness, and validity. If a process phase fails the test then it has to be repeated. Each process phase requires either positive or normative information or both. Positive information are those which do not have any reference to good or bad and right or wrong. Normative information are those which set value judgements as to whether an action or goal is good or bad. Feasibility evaluation has i§“iéé’gaai”£hé“generaiiafi'of“i;séi of feasible system alternatives capable of satisfying needs which have 4G.'L. Park and T. J. Manetsch, _p, cit. 13 Needs l Feasibility. r—— " . Evaluation ‘ I l l . * l A —-- - Abstract Modeling l i # v T Positive and l Implementation ; Normative -> |—- - -DI . H . Design Information | A l I , Y I l :- - - > Implementation fl:— I i r I, Y : . L-.. __ System ‘. Operation Figure 2.1. Flow Diagram of the Systems Approach as a Problem Solving Methodology 14 been identified and selected for satisfaction. A system alternative is a particular system, structural configuration, or management strategy devised as a means of satisfying existing needs. Figure 2.2 shows the flow diagram of feasibility evaluation phase. The major steps of the feasibility evaluation phase are (1) needs analysis, (2) system identification, (3) problem formulation, (4) system definition, (5) generation of system alternatives, (6) determination of physical, social and political realizability, and (7) determination of economic and financial feasibility. 2.3 Sy§tem Identification System identification forms a link between the statement Of needs and the specific statement of problems that must be solved in order to satisfy these needs. In this process, the proposed system is viewed as a "black box." In other words, every effort is exerted to determine the attributes that the system must possess if it is to satisfy the specified needs. More specifically, we seek information about system input variables, system output variables, and parameters which define aspects of system structure (Fig. 2.3). System input variables are 'Of two classes: (1) the exogenous or environmental input which refer to those which affect the system but are not, in turn, significantly influenced by it, for example, weather, and (2) the overt inputs referring to variables which are necessary for the system to carry out its intended functions. Overt inputs can either be controllable such as the amount of fertilizer applied to crops or non-controllable such as the amount of land area in the short run. 15 Primitive Need l Needs Analysis r— - - .I System H..____.. ; Identification l l + l r l |___. Problem .‘____. : Formulation I l i e e I Positive 1 Generation and L"— H of System ‘____a Normative Alternatives 5 Information I u I Determination of _._.. Physical, Social ‘____. and Political Realizability 1 a Determination of Economic and . I Financial Feasr- bility 4. F""""F“”‘""T*""’"" l 1 Set of viable alternatives Figure 2.2 Flow Diagram of Feasibility Evaluation 16 nomouee< esoumzm can we upon an cowumuwuwueoeH amummm m.N ounmwm 323:8 .38.... £55.... mouunomou .huwuwmsmo mo 30.: I zmsmwm HZMZMU<2o oaoeuaouucoocozv mundane teammate: mundane xwamwm whamzH ,cmuwmoa Amnocowoxov Amusanw Hmucoecouw>cm uuo>o mammaaonucoov HzmzzomH>zm ZHHmwm 17 System output variables can either take the form of outputs which are need fulfilling or undesired outputs which are unavoidable by-products. System design parameters are variables which serve to specify the structure of the system. Examples might include the physical location of the system, physical dimensions, and the number and types of components. The system identification concludes with the determination of performance criteria which can aid in the evaluation of the system alternatives. 2.4 Abstrgct‘Mpdeling Although some systems are more amenable to abstract modeling than others, it is safe to say that some form Of modeling or abstract representation can be useful in almost every situation. Figure 2.4 shows the flow diagram of abstract modeling. The main steps are (1) alternative selection, (2) modeling Of a particular alternative, (3) computer implementation, (4) validation, (5) sensitivity analysis, and (6) model application. The final outcome of abstract modeling is the specification Of good or best plans and policies. MOdels may be classified in two ways: (a) static or dynamic and (b) microscopic or macroscopic. While a static model provides information about model variables only at a single point in time a dynamic model is capable of generating time paths of model variables. Likewise, a microscopic model deals with individual units such as an individual farm.while a macroscopic model looks at aggregates Of units such as the whole agricultural sector. .18 ' Viable concepts . I Concept .‘L selection ' 4:; Mbdeling of "' " - 7' ~ ' Part icular -¢ concept ' . I Computer I--—-. . ‘: I Implementation Positive : and I :.; Normative+ v Informationl _ _. .y. Validation I¢ . . I __,~ Sensrt1v1ty I I Analysis I V _._. Medal H Application I“ I Specification of good or best plans and policies I— I I I 1 v L I I I I l I I I_ Figure 2.4 Flow Diagram of Abstract Modeling 19 2.5 Sygtems Simulation As stated earlier, a system.has important dynamic elements which make the state of the system time dependent. Moreover, the stage of the syStem is also influenced by uncontrollable elements which make it difficult to study and understand the system. However, with the use of simulation methods, considerable insight into both their operation and control can be achieved. Simulation may be defined as a step by step process of working out particular time paths of variables, starting from a given set of system inputs and specific values for model parameters. It also may be considered to embrace two distinct Operations: (1) develop- ment or synthesis that adequately represents the system under study, and (2) examination of the behavior of the model in relation to changes in its structure or in managerial policies. Basically, simulation includes four iterative steps: (1) problem definition, (2) mathematical modeling, (3) model refine- ment and testing, and (4) model application. As shown in Fig. 2.5 each step has to be repeated if more information is obtained either within the model or outside of the model. The main uses Of the simulation model are (l) to determine what policies are appropriate for good management, (2) to attempt to locate an improved basic organization, and (3) to determine points in the organization that are sensitive to managerial interference. Simulation can be done simply with paper and pen "seat of the pants" methods. However, this is limited by the amount of time - required to carry the calculation through hand methods. The advent 20 Problem Definition (through interaction between investigators and decision ‘— makers) V Mathematical Modeling and Simulation (including further interaction between -t investigators and decision makers) i Model Refinement and Testing (including further interaction between investigators.‘I-a~ and decision makers) I Model Application (including further interaction between investigators and .‘ decision makers) in solving problems I I r (Output 3 Figure 2.5 Computer Simulation as an Iterative Problem Investigating Process 21 of large scale electronic computers has made it possible to undertake simulation very rapidly thus saving time and money. Mureover, the computer provides for the possibility of increasing the number of alternative policies and programs that can be evaluated. It should be emphasized that the systems approach is not limited to any particular methodology in systems analysis. It is also not synonymous to simulation. But regardless Of the methodology involved, it is necessary for the analysis of a system to give attention to the interdependence of its components. Other techniques and methods of analysis are widely used in systems analysis. However, there are several characteristics of systems which make computer simulation a good and Often the best technique to use in systems analysis. In the first place, it may be impossible or extremely costly to Observe certain systems in the real world. The system may be so complex or so large in terms of the number Of variables, parameters, relationships and events to which the system is responsive to, that it becomes almost impossible to analyze it mathematically. It also contains relationships between the systemis entities and attributes which are not well behaved or mathematically tractable. Another reason for using simulation in systems analysis is that there may be insufficient numerical data available about a system to allow verification of a mathematical model and its solution, or such data may be extremely costly to obtain. Mbreover, many systems, particularly social systems, cannot be manipulated or experimented 22 with to determine the impact of changes in the system or its environment. In this case, simulation can serve as a systems laboratory. A further reason for using simulation is when a system contains random variables which are difficult or impossible to handle expedi- tiously with other types of mathematical models. Finally, real time for many systems may be either too slow or too fast to allow meaningful analysis of the system. Simulation can be used to expand or compress time to the analyst's specifications. The presence of any of the above characteristics Of a system can justify the use Of simulation as a method Of analysis. 2.6 Advantaggs Of§ystems Analysis and_§imulation There are many advantages to be gained from systems analysis: (1) it allows exploration of alternative solutions to problems for which an Optimum does not exist or cannot be found with optimizing methods; (2) a large number of heterogenous variables can be handled in a consistent manner; (3) the criteria of analysis as decision criteria can be broadened or increased in number; (4) the complex interrelationships between problem elements and the Objectives of numerous functional units may necessitate the use of Objective analysis of decision problems; and (5) it provides a method of reducing complex relationships to paper. There are also several advantages of simulation for system analysis. First, it is possible to handle multiple goals with ' simulation. Mathematical programming models usually imply Optimization 23 with respect to one variable. If more variables are involved, a great deal of ingenuity will be required to Obtain the appropriate relationships. Simulation has also the ability to handle sequential decisions within the planning period using different criteria. Decision rules within the model can depend on a number of variables, each of which may reflect different goals. Any type of function or relationship can be included in the simulation model. It does not require that relationships can be continuous or linear. A simulation model has also the ability to handle stochastic variables and action delays. Since there is no restriction to a formal algorithm in systems simulation the model can be as complex and as realistic as desired within the confines of available data and detailed structure Of the real system being modeled. No matter how complicated the finally constructed mathematical representation, it is possible, usually with the aid of a computer, to follow the detailed workings of the system and to trace the implications of input and decision changes on the output from the model. There are, however, some limitations of systems analysis and simulation. Park and Manetsch5 state that this problem solving methodology is not applicable when (l) the aims or goals of the system are not well-defined and recognizable if not quantifiable; (2) the decision-making process is not centralized; and (3) long-range planning is not possible. —— 5G. L. Park and T. J. Manetsch, 4E. cit. 24 2.7 Summagz This chapter discussed the conceptual as theoretical aspects of systems analysis and simulation. First, the system concept was clarified and the steps of the systems approach as a problem solving methodology were outlined. Some basic steps of the approach such as feasibility evaluation and abstract modeling were also elucidated. Finally, the use of computer simulation as a technique in systems analysis was discussed. Its advantages and disadvantages were also‘pointed out. CHAPTER 3 CONCEPTUAL MODEL OF A FAMILY FARM 3.1 Introduction This chapter presents the structural framework Of the simulation model. First, a comprehensive, idealized structure of a farm system is developed. The major components and their respective roles in the farm system are discussed. Second, a simpler version of the structural model for the purpose at hand is justified. This was done by eliminating components and variables which are not important for the purpose at hand, those for which data are not available or are too difficult to Obtain, and those components which are complicated and extremely difficult to develop conceptually and represent mathematically. 3.2 Gross Structure of a Farm Syspem Figure 3.1 shows a conceptualized structure of a farm system. The major components of the system are (1) production component, (2) land allocation component, (3) labor utilization component, (4) output disposal component, (5) storage and sales component, (6) investment funds allocation component, (7) cost and income accounting component, (8) product and input markets, (9) income allocation component, and (10) exogenous factors. Production component The production component determines the level of physical output of each crOp, given the level of inputs and the underlying _25 26 amummm ammm m «o ounuunuum mmouo H .H.m «usage A 3 azmzoazoo maeau=m zoeacoomaa ma , _ neosumo>ceuue azmzemm>ze 839.528 1 azuzomzou azuzommou I eoomueoz_ zoeeaooaaa mueae>eao< l/ H 88qu gmazoz J mowueanmnoo- woos seize 352; I J L IF m squamous emoeumsom- ezmzomzco .awl .a szmzomzco oaounH muonomnom House ozHHz=ooo< onaduHAHHS «ones A 0333 ammo Each @005 azmzoaaoo I uzeazeooo< emoo .D moamm _ HEEES He .17, mmonw 27 environment. Yield depends on a great number of factors including soil type, variety of crop, water availability, type and level of fertilizer, degree of insect and pest attack and control, environmental factors such as rainfall, wind, temperature, solar radiation, and so forth. For the purposes of yield prediction, the effect of each of the above factors must be accounted for. A difficulty that arises in modeling the production component is the fact that numerous factors are interrelated. For example, weed population may increase as more fertilizer is applied. Also, the yield of rice is more respOnsive to nitrogenous fertilizer when the degree of solar radiation is greater. Land allocation componeng The main purpose of the land allocation component is to determine how land is to be utilized during the entire year. The role of a land allocator in a farm simulation model depends on how the model is to be ultimately used. If it is to be used as a "laboratory" wherein alternative land allocation schemes are tested to determine their effects on the performance of the system, then a model of a land allocation sub-system is not necessary. It would suffice to predetermine the desired land utilization scheme at the start of each simulation run. On the other hand, if the model is to be applied in an Optimizing mode wherein land is to be allocated ’ in such a way as to maximize net returns, than a more sophisticated land allocator is desired. 28 Labor utilization comppnent The labor utilization component determine the periodic labor use on each crop, the total labor use of the farm, and the amount of outside labor hired by the farm. Family labor availability depends on family size and the age distribution of the children. Labor availability affects land.allocation which in turn affects labor utilization. Total labor utilization is dependent not only on labor requirements of each crop but also on the level of output. It is also affected by the degree of mechanization which is labor displacing. Labor is hired generally if family labor is less than labor require- ments but it is also affected by wage rates. Ougput digposal component The output disposal component apportions the physical output of each crop among the farmer, the landlord if the farmer is a tenant, and to the harvesters and threshers if they are paid in kind. Additionally, this component apportions the net share of the farmer to (1) home consumption, (2) marketable surplus, (3) losses, and (4) other uses. Storage and sales component The marketable surplus can either be stored for sale at a later date or can be sold immediately. The storage and sales component determines how much of the total amount in storage is to be sold at a given time period. This may depend on prevailing prices, cash»needs, and other factors. 29 Investment funds allocation component The investment funds allocation component determines how investment funds available to the farmer, either through credit or from surplus farm returns are allocated either to purchase current inputs, to hire labor, or to acquire fixed capital. This component also keeps track borrowing and loan repayment activities. Cost and income accountingpcomponent The cost and income accounting component keeps track of all farm income and expenses. It determines total production, value of production, cost of production, and net returns of each crop planted and for the whole farm. Product and input markets In the product and input markets, prices of each crop and costs of production inputs are determined. Prices and costs play important roles in determining the relative profitability of each crop. In this study, an effort was made to simulate the price movement of each crop. This was achieved by allowing price to vary both seasonally and randomly around its mean. Price could also be made to vary secularly by incorporating into the model trend lines of either linear or exponential farm. In this study, prices are exogenous to the farm. That is, a farm by itself cannot influence the movements of product and input prices. Income allocation component The function of the income allocation component is to allocate household disposable income to consumption (food and non-food) and to 30 savings. This component depends on a number Of factors which ' includes family size, age distribution of children, and cash needs for farm Operations. Exqggnous factors In this conceptual model of a family farm, the factors considered as exogenous are the crop environment and the product and input markets discussed above. In an upland setting, rainfall is considered to be the most important factor affecting crop yields. Since rainfall is the only source Of moisture for the plants, the simulation of rainfall is of prime importance. Other environmental influences such as solar radiation, temperature and relative humidity are also important and must be included if data are available. 3.3 A.Modified Model for the Study It is apparent from the above discussion and from Figure 3.1 that a farm system is indeed complex owing to the many components variables, and interrelationships involved. Not only are physical processes involved but also behavioral and decision processes. For the purposes of the study, it was therefore necessary to simplify the concept of a farming system in order to make the mathematical modeling and subsequent cOmputer implementation manageable. In the model developed below the major components that were included are:: land allocation component, a rainfall generator, pro- duction component, labor utilization component, price and cost 31 generator, and crap accounting component. Figure 3.2 shows the interrelationshipsof the above components.. The structure of each component, the variables included, the mathematical relationships, sources of data and the validation of each component are discussed in the next four chapters. In brief, the model as implemented in the computer works as follows: The policy variables are area, planting date, and current input levels (nitrogenous fertilizer), insect control, and weed control. The land allocation component determines the crops to be planted and their respective areas. The rainfall generator determines the rainfall pattern for the simulated year. Given the rainfall pattern, the areas, the planting dates and the current input levels, yield is determined in the production component. The labor component determines labor utilization of each crop and of the whole cropping system. It also determines the amount of labor hired on the basis of tptal labor requirements and available family labor. The price and cost generator determines the prices of each crop and the cost of inputs. All the above information are then passed on to the crop accounting component where the performance variables, namely yield of each crOp, gross returns, net returns, labor utilization and effective crop area, are computed. 3.4 Summagy In this chapter, the structural framework Of the simulation ‘mOdel was developed.' The major components of a comprehensive farm) system model are the production component, the land allocation mono mono o>wu00mmm nowumufiawua women 32 Homoeoo moo: Houunoo uoomom uowwawuuom .Hovoz nomumdnamm one no mawnmnowumaoquucH mom muconoeeOo memo: .~.n .mem muonuo ”w some; meow: mnunuom uoz .N - mflhfl 0 mmOH . a e o H ezmzomzcu eoeammzmo moaomwue> ozHez=oou< I mumoo monm IQImmmMHHOMHom memo museum 7 7 some» memos moowum , I azmzomzoo meo>om . ezmzomzoo onaauomm< aou< comm. ezwwmmuou .inmmm=H ', zomaoanoei .AJ Almuu< , nz noose noueavum JIIIIIIIIImImMIIII. no o o o wo>< unuuauam _ moamzoam me a .me mmozmuoxm a H as a 33 component, labor utilization component, output disposal component, storage and sales component, investment funds allocation component, cost and income accounting component, product and input markets, income allocation component, and exogenous factors. Each of these components and their interrelationships were discussed. Because of the complexity of the system, it was deemed necessary to adopt a simpler conceptual model of a farm to make the mathematical modeling and computer implementation manageable. Thus, for the purposes of the study, only the following components were included: land allocation component, rainfall generator, production component, labor utilization component, price and cost generator, and crop accounting component. 34 CHAPTER 4 LAND ALLOCATION COMPONENT 4.1 Introduction The purpose of the land allocation component in the simulation model is to determine how total land area is to be utilized during the crop year. Land utilization is concerned with the determination of the proportion of total available land brought to cultivation, the kind Of crops and area planted to each crop during the year, and the planting dates of each crop. The land allocation component can take many forms within a simulation model. It can be set as predetermined variables (area of each crop, planting dates, etc.) or it can be determined endoge- nously within the model. Dong Min Kimfs model1 handled the land allocation as a policy variable and the consequences of alternatives land allocation schemes were determined. This framework is compatible with one of the objectives of the study, which is, to determine the performance of alternative cropping schemes. If determined endo- genously, the range Of complexity varies from simple look-up functions to complex mathematical programming models. Prantilla,2 and Thodey I 1Dong Ming Kim, "Korean family farm simulation model," unpubl. paper, Michigan State University, 1975. 2E.B. Prantilla, Economic Optimization models of multiple cropping system: applied to the Philippines," Ph.D. thesis, Iowa State University, 1972 (unpublished). 35 and Sektheera3 both used linear programming models to find the optimum combination of crop that can maximize net return of farms. The problem.of land allocation is important in multiple cropping because the farmer must decide from among a number of choices as to what crops to plant at a particular time, their relative hectarage, and se- quencing. The decision usually takes into consideration a large number of factors including total land area, subsistence requirements, house- hold cash needs, weather and other environmental variables, labor avail- ability, prevailing crop prices, input prices, and many others. The final land allocation may depend on the particular decision criterion adopted. Some possible decision criteria are maximum net returns, mini- mum operating costs, minimum hired labor costs, and others. 4.2 Method of Land Allocation A fundamental question that was dealt with in the development of the model was whether land allocation can be achieved by optimization or simply by setting land allocation as a predetermined set of variables and observing the values of certain performance variables. It is obvious that the two divergent approaches imply a great difference in tasks, data requirements, and ease of computer implementation. An opti- mizing routine such as linear programming model of land allocation can be very complicated depending on the nature of constraints and objective function employed. On the other hand, pre-determining the land alloca- tion.simply entails specifying the land area of each crop and their respective planting dates. 3A. Thodey and R. Sektheera, "Optimal multiple cropping systems for the Chiang Mai Valley," Agricultural Economics Report No. 1, Faculty of Agriculture, Chiang Mai University, July 1974. 36 Notwithstanding the ease with which it can be done, a more basic question has to be consideredas to which methodology is appropriate for the problem at hand. The main objective of developing the simulation model, at least in this study, is to determine the cropping patterns which are appropriate for a particular locality or area. Appropriate- ness is not only concerned with the level of economic returns but also 'with economic, biological and environmental viability. A main concern in using linear programming is that, while it solves for the land allocation pattern that maximizes or minimizes a given objective function, it also determines the other unknowns of the system which the simulation model is designed to determine. Mbreover, in linear programming it is difficult to handle multiple decision criteria at a time. Another concern is that linear programming model assumes that the coefficients are fixed. Thus, yields, prices, costs, labor requirements, operating costs, etc., are held fixed in a particular run without regard for the fluctuations in rainfall pattern, prices, and other random variables. Finally, there is the problem of physically linking other components of the simulation model with the linear programming land allocator. Mathematical programming problems are usually solved nowadays, with software packages which are usually available in machine language. Although it is possible to write a separate linear programming routine in the same language as that of the simulation 37 model,4 the task is by no means easy; moreover it is also time consuming. To sum it up, there are several arguments against the use of a linear programming model as a land allocator for the purposes of the study: it competes with the simulation model in terms of the determina- tion of values of other unknowns in the system; it has very rigid assump- tions; and it involves difficulties in physically linking software linear programming packages with the simulation model. An alternative is the method of leaving out the land allocation component and viewing the rest Of.the system as a laboratory wherein experimentations on various land allocation schemes can be performed. This kind of experimentation tests the performance of alternative cropping patterns that is, a given set of crop combination, sequencing, Arelative achieved by first in putting alternative cropping patterns, making several iterations of each pattern and finally comparing the relative performance of each pattern. In this method the user simply specifies the kind of crops included in the pattern, their respective areas, and their planting dates. Total farm area is dictated by the user. It is apportioned among the crops included under the condition that total area planted does not exceed the farm area. Two plantings of a crop are allowed. For the present purposes, the crops are rice, corn, sorghum, mungbean, cowpea, peanut, soybean, and sweet potato. 4R. P. Strickland and J. D. Davis, "Interfacing the MPS/360 Linear Programming Routine with FORTRAN programs," U.S. Dept. of Agriculture, Econ. Res. Service, 1970. Also J. L. Kuester and J. H. Mize Optimization techniques with FORTRAN, McGraw-Hill Inc., 1973. 38 The method was preferred over other methods for the following reasons: 1. It is a very simple method. 2. It conforms with the experimental method of agronomists and thus, can supplement the results of actual experiments or predicts the outcome of a particular experiment. 3. Various levels of management input, different rainfall patterns and different market conditions are possible for a particular cropping pattern. 4. It is not restricted by a single performance criterion. The disadvantages are as follows: 1. Numerous computer runs have to be made in order to identify the cropping patterns suitable for a particular area. 2. There is a great number of possible crop combinations and an infinite number of possible land allocation schemes (in terms of proportion of total area planted to each crop) in a given combination. However, this is not considered to be a very serious limitation because the crop combinations or cropping patterns that are specified in this model are those which agronomists are interested in which is a limited number. Cropping patterns which are obviously inferior are no longer included. Although an optimizing method such as linear programming was not used in this study for reasons cited above, it can be of positive contribution to the simulation model. First, it helps reduce the number of possible crap combinations that are tested in the simulation 39 model by eliminating those combinations which are obviously inferior. Second, it helps in bounding the problem to manageable limit and in improving the logic of interrelationships between farm constraints and activities. 4.4 Summary In this chapter, alternative methods of land allocation were examined. Two methods of land allocation were examined in detail. The first simply presents the areas and planting dates of each crop. The other is an optimizing model which maximizes net returns subject to various constraints. The advantages, disadvantages and limitations of each method were discussed. In the model, the farmer method was used owing to its simplicity, flexibility and versatility. CHAPTER 5 RAINFALL GENERATOR 5.1 Introduction The purpose of the rainfall generator is to provide to the simulation model the rainfall pattern for the period covered in the simulation. Under upland conditions, rainfall is the only source of moisture for the crops. Indeed, as researchers have shown,1 rainfall is considered to be the most important factor affecting rice yields under upland conditions. In generating the rainfall pattern for the simulated period, there are two points that must be considered. They are (l) the time interval or the shortest unit of time for which rainfall is generated, and (2) the method of generating the rainfall pattern for the simula- tion model. 5.2 Medeling Considerapions 5.2.1 Time interval of generated rainfall In this study, rainfall is generated on a weekly basis. That is, the total rainfall for each of the 52 weeks of the year is generated and together they comprise the rainfall pattern for the simulated year. It was felt that weekly rainfall generation is a reasonable compromise between generating rainfall on a daily basis and generating rainfall on a monthly basis. 1S. Yoshida, "Factors that limit the growth and yield of upland rice in IRRI," :Major Researches in Upland Rice, Los Bafios, Phils., 1975, pp. 46-71. 40 41 There were several reasons why a weekly rainfall generation was preferred. First, weekly time increments are employed in the other components of the simulation model. Second, the time series data for most of the other variables in the model are available only on a weekly basis. Third, when historical data are to be used as the rainfall pattern for the simulated year, fewer are required in the model resulting in less programming difficulties. Although, daily rainfall generation is not incompatible with weekly time incrementation, it is more difficult to do so mainly because of the large degree of interdependence among daily rainfall observations and hence more modeling efforts required. 0n the other hand, the aggregation of daily rainfall observations into weekly totals removes to a large extent the interdependence among adjacent time observations.2 The queétion of independence among ‘weekly observations is examined below; Since the primary purpose of the rainfall generator is to determine the rainfall pattern of the simulated year for the purpose of predicting crop yields, a daily observation would have been ideal. This is because daily soil moisture levels are better predictors of yields than weekly observations.3 For instance, the weekly total may indicate a high level of rainfall, but if the rain fell only on 2See J. B. Philippa, "Statistical Methods in Systems Analysis," in Dent and Anderson (eds), _p, cit., pp. 34-52. 38cc J. C. Flinn, "The Simulation of Crop-Irrigation Systems," in Dent and Anderson (eds), _p§ cit. 42 one day while the rest of the week was dry, the effect on the crop would be quite different than if there was rainfall every day of the week adding up to the same total. On the other extreme, monthly rainfall totals are poor bases for predicting crop yields since the distribution of the rainfall within the month is ignored. With weekly data, some detail on distribution is still available. In terms of data handling and programming, however, monthly rainfall observations are easier to work with. They are also are more amenable to synthetic or probabilistic generation since they could easily pass tests of independence. 5.2.2 Methods of rainfall ggneration The method of generating rainfall depends on two main considera- tions: (1) correspondence with the real world situation, and (2) purpose for which the generated rainfall data is to be used. The first consideration is self-explanatory. The rainfall pattern that results from the generator must belong to the established patterns of a specific area. This implies that the statistical properties of a set of generated rainfall patterns must be close to the statistical characteristics of the historical data in that area. Since the rainfall generator can be used in several modes, each mode may call for a particular method of rainfall generation. One possible mode is to generate a rainfall pattern over a given period of time for a particular area to be used in a simulation run. Here, either a synthetic generator or the historical data of a randomly selected year can be used. Another mode is to verify the validity of 43 a cOmponent of the simulation model using the-data for a specific year. In this instance, the rainfall pattern to use must be the historical rainfall data for that particular year. Hence, a facility has to be provided such that the historical rainfall data for that particular year will be used automatically and not that of another. Another possible mode of using the rainfall generator is to use a pre-determined rainfall level for a particular simulation run. For example, a high, medium, or a low rainfall year may be desired for the particular run. Although this can also be achieved with rainfall probability distributions, it would be much easier to do so with historical data. Hence, a facility for achieving this is an added convenience. Because of the varying modes in which the rainfall generator may be used, five options were developed in this study: (1) to generate rainfall based on the parameters of a probability distribu- tion for each week synthesized from actual data, (2) to randomly select a year between 1949 and 1975 and to use the historical rainfall data of the Ambulong Weather Station for that year as the rainfall pattern for the simulation run, (3) to use the historical rainfall data of a pre-determined year, (4) to randomly select a high, medium, or low rainfall year on the basis of annual total rainfall and to use the historical data of the selected year in the simulation run, and (5) to use the average weekly rainfall of the Ambulong Weather Station from.l949 to 1975 as rainfall pattern for the simulation run. Note that there are two primary methods of rainfall generation 'namely (1) the use of probability density functions such as used in 44 the first option, and (2) the use of historical rainfall data such as used in the other four Options. 5.2.3 Historigal dapg vs. gynthetigraipfallpggperation Concerning the use of historical data as opposed to generated data in simulation models, J. B. Philippa states that: "The historical data represent nothing more than a sample from a much longer-term process than has been observed, and the result is that unnecessary restrictions are placed on the generality of findings based on the performance of the simulation model."4 Historical data have two important roles in model building. First, it serves as a basis for the generation of a series of observa- tions from a stochastic process. Second, it can be used as a device for testing the complete model against known historical information, and thus, assisting in the validation of the non-stochastic portions of the model. The basic objections to the use of historical data are: (1) it forces discreteness on the variable in that the sample will always be something less than a complete coverage of all possible values of the variables; and (2) even with fairly long series of historical data, a certain lack of smoothness will usually occur. The advantages of Synthetic rainfall generation are: (1) it provides additional benefits arising from a more complete understanding obtained of the way in which the process operates, (2) it enables less cumbersome computer programming, and (3) there are real economies fi— AJ. B. Phillips, pp, cit., p. 43. 45 obtained from using parameters of a process rather than a massive quantity of data as input. 5.3 Synthetic Rainfall Generation Methods One of the main methods of incorporating rainfall into the simulation model is by generating rainfall patterns through independent sampling from.some specified probability distribution function. This involves the estimation of the parameters of a particular probability density function for each week which are then used to generate the weekly rainfall. The generated rainfall is a random variable which belongs to the hypothesized distribution function. Three different distributions were tried on the historical weekly rainfall data taken from the Ambulong Weather Station over the period 1949-1976. The distributions are: (1) normal distribution, (2) log- normal distribution, and (3) the incomplete gamma distribution. In each of these distributions, the parameters were estimated and tests of correspondence or goodness of fit were conducted. As it will be seen below, the incomplete gamma distribution was finally adopted as the best distribution function which fits the actual rainfall data. 5.3.1 Tests of independence The use of the above-mentioned distribution functions in the generation of weekly rainfall assumes independence between successive values. Hence, the observed data for the variable to be synthesized ' must be examined for the existence of relationships between successive observations (i.e., autocorrelation). A number of tests are available' 46 for testing autocorrelation of time series data which includes both parametric and non-parametric tests. A computer program incorporating five separate tests for autocorrelation of weekly rainfall was developed in this study:5 (1) Anderson's circular autocorrelation coefficient, (2) Von-Neumann ratio, (3) Wald-Welfowitz test of randomness, (4) theory of runs, and (5) standard chi-square test for independence. The first two tests are parametric tests involving assumptions regarding the distribution of the parent population (usually normal). The last three tests are non-parametric requiring no assumption regarding the distribution of the parent population and thus, are much more general in their application. In doing the tests, the rainfall data were first transformed to remove seasonal patterns that exist in the series. The seasonal influences were removed by working with deviations from the mean for each time period (week). This involved the assumption that the seasonal pattern is adequately reflected in the average values of rainfall for each week. Since rainfall distribution is markedly skewed, however, the same tests were also done using the weekly median rainfall as a reflection of seasonal pattern. Tables 5.1 and 5.2 show the results of the tests based on deviations from the means and medians, respectively. It can be seen that in both cases, four out of the five tests indicate that the rainfall series is autocorrelated. Only the chi-square test supported 'the hypothesis of independence at 5 percent level. The result of the 5For a detailed discussion on the use of tests for serial correlation, see J. B. Phillips, loc. cit. 47 Table 5.1. Results of five tests independence of weekly rainfall data, Ambulong, Tanauan, Batangas, 1949-1975 (deviation from means). Testa Computed Expected Variance Significance Anderson's 0.165 -.00074 .00074 12 Von-Neumann 1.67 5.09 3.05 11 ' wald-Wblfowitz 682.90 -3.05 12377 1z Theory of runs 524.00 589.00 256.67 1% Chi-square 16.6311 n.s.b 8The null hypothesis is no autocorrelation among adjacent observations. bAt 5 percent level. 48 Table 5.2 Results of five tests of independence of weekly rainfall data, Ambulong, Tanauan, Batangas, 1949-1975 (deviation from'medians).’ Testa Computed Expected Variance Significance Anderson's 0.168 -0.00074 0.00074 . 12 Vbn-Neumann 1.66 5.34 3.21 12 Whld-Wolfowitz 1055.80 321.69 13688 11 Theory of runs 580.00 658.26 320.72 1% Chi-square 19.32 n,s.b aThe null hypothesis is no autocdrrelation among adjacent. observations. bAt 5 percent level. 49 tests have to be interpreted with caution, however, since a normal distribution has been assumed for the parent populations. Rainfall data in general, and Ambulong data in particular, are not distributed normally. Phillips6 state that if the time interval for which observations are to be genérated is weekly, it will be found that for such periods successive observations of rainfall can reasonably be assumed to be independent. Consequently, synthesis of the element can be undertaken by independent sampling. In this study, despite the fact that not all the tests indicated independence of weekly observations,7 it was assumed that weekly rainfall series are not autocorrelated. This is mainly because developing another rainfall generating model which accounts for autocorrelation is complex and time consuming. Moreover, the extra effort it takes to obtain a more accurate generated series may not be justifiable if it is only to be used together with data which are not themselves very accurate. In the final analysis, the acceptability of the rainfall generating model will be tested by the comparison of statistical characteristics of actual versus the generated data. 61bid., p. 39. 7A number of methods of varying complexity can be used in an effort to reproduce the desired relationships in the synthesized data. See for example M. M. Hufschimdt and M. B. Fiering, Simulation Techniques for Design of water Resource System, Harvard University Press, Cambridge, 1966 and A. Pattinson, S thesis of Rainfall Data, Civil Engineering Technique, Report 40, Stanford University, 1964. 50 5.3.2 Alternative probability distributions Normal distribution Fitting a normal distribution to a set of data is fairly straightforward. It simply involves finding the estimates of u and o from.the density function e-(x - 102/202 1 P - —— usabc) UV 211’ which by maximum likelihood method or method of moments are given by . fl = X = 2 xi and A Ski-502 02:32:- . n - 1 Table 5.3 shows the means and standard deviations of each week based on 27 years of rainfall data gathered from the Ambulong weather Station from 1949 to 1975. ngnormal distribution A variable X is lognormally distributed if Y = log X is normally distributed with mean u and variance 02. Thus X has a lognormal density if and only if it has the density induced by eY where Y is normal with parameters u and 02.8 That is, P (x) _ 1 exp -§%7—(log x - “)2 , x>0. 11,0 Xt/ Z'UO‘2 8J. Aitchison and J.A.C. Brown, The Lognormal Distribution with Special Reference to its Use in Economic, Cambridge University Press, 1957. 51 Table 5.3. Means and standard deviations of weekly rainfall data, Ambulong, Batangas, 1949-1975 (in inches) Week Mean Standard week Mean Standard Dev1ation Dev1ation 1 0.51 1.18 27 1.93 1.48 2 0.19 0.26 28 2.31 2.31 3 0.11 0.29 29 3.42 4.25. 4 0.13 0.20 30 2.27 2.15 5 0.12 0.24 31 2.56 2.11 6 0.07 0.11 32 3.15 2.43 7 0.11 0.28 33 2.63 2.15 8 0.13 0.25 34 1.84 1.67 9 0.20 0.31 35 2.60 2.38 10 0.22 0.43 36 3.37 4.58 11 0.21 0.46 37 1.61 0.87 12 0.13 0.33 38 2.42 1.74 13 0.11 0.32 39 1.55 1.37 14 0.07 0.17 40 2.36 2.21 15 0.27 0.51 41 2.43 ‘ 2.45 16 0.34 0.56 42 2.25 2.56 17 0.69 0.92 43 1.24 1.43 18 0.86 1.38 44 1.45 2.68 19 1.02 1.28 45 1.21 1.11 20 1.35 1.75 46 1.32 1.48 21 1.40 1.58 47 1.85 2.30 22 1.67 2.35 48 1.53 1.82 23 1.62 1.97 49 1.19 1.61 24 1.45 1.53 50 1.16 1.28 25 1.96 1.48 51 0.90 1.49 26 2.81 3.27 52 1.16 1.71 Source of basic data: Ambulong Weather Station, Tanauan, Batangas 52 The mean a and variance 82 of X are given by 2 a a eu +.5C and I 2 2114-02 02-1 2 2 B 8 e (e ) a a n where 2- nz - e0 1. Note that n is the coefficient of variation of the distribution. In estimating a and 82 , it is sufficient to estimate u and 02 which are then substituted to the above relationships. The maximum likelihood estimators m1 and s 2 of u and 02 are 1 given by _ 1 m1 - a 2 log xi and 2 s 1 2 81 n 2 (log xi ml) 3 n-l 2 n Y where 2 v - . O y n-l The estimator 312 is biased but consistent. If, however, 3 2 a v 2 1 y then m1 and 812 are minimum variance estimators and unbiased estimators of u and 02 , respectively. 53 With the method of moments, the estimators m and s 2 of U 2 2 and o2 are obtained by equating the first two sample moments w1 and w2 to the expressions given by substituting m2 and 522 for u and o2 in the equation - 2 x5 3 eJu + .SOj where Aj is the jth moment about the origin and j - l, 2. The jth sample moment about the origin is given by w. = l Xx.j . n 1 So w = exp (m + 1/2 s 2) 1 2 2 and w = exp (2m + 23 2) 2 2 2 Therefore, m2 = 2 log wl - 1/2 log w2 and 32 = log w2 - 2 log w1 . The estimates are both consistent. The two methods of estimation were tried with the Ambulong rainfall data. The maximum likelihood method gave better results with respect to the fit with actual data. Thus, in later comparisons with other distribution functions, only the maximum likelihood esti- mators were used. Table 5.4 shows the estimates of u and 0‘2 for each week. 54 Estimates of 11 and (3 parameters of a lognormal rainfall distribution by week, Ambulong, Batangas, 1949-75 Table 5.4. Ac AU. Week any Au. week 67342710151283034802384925 [46965456603456788468980731 I O O O O O O I. O O O O O O O O O O O O 00000000010000000100001011 32608111599854301713524563 4573697366361554231110327/4 O O I ......... O ..... O O 00000000000000004AW40000000 . _.. 78901234567890123456789012 222333333333344444444[44555 34096810884112098758290555 510080051671215202998097148 O O O O ..... O O O O 0 O O O O O 11211121111222111100010000 12345678901 11.— Ambulong Weather Station, Tanauan, Batangas Source of basic data: Week 67342710151283034802384925 46965456603456788468980731 O O I O O O O .0. O O O O O O O I I O O 00000000010000000100001011 32608111599854301713524563 45756973663615542311103274 O O O. ...... O O. O O. O O O O O O O O O 00000000000000000nw40000000 . _ ... 78901234567890123456789012 22233333333334444444444555 54 Table 5.4. Estimates of u and 0 parameters of a lognormal rainfall distribution by week, Ambulong, Batangas, 1949-75 AC Au. Week 12345678901 11 Ambule Weather Station, Tanauan, Batangas Source of basic data: 55 It must be noted that the lognormal density function is restricted to values of X > 0. Since rainfall data have a number of zero obser- vations, the value of 0.001 was substituted for each zero observation before logarithms were taken. Incomplete gamma distribution The gamma distribution has been found to give good fits to precipitation series and is the most frequently used distribution in fitting probability functions for rainfall data.9 The gamma distribution is defined by its frequency or probability density function, 1 xY-l e-x/B 8(X) =- elm) where B is a scale parameter, Y is a shape parameter, and P(y) is the ordinary gamma function of y. The method of moments of this density function give poor esti- mates of the parameters. Sufficient estimates are, however, avail- able and these are closely approximated by10 $=fi<1+m§> 9See for example G. L. Barger and H.C.S. Thom, "Evaluation of drought hazard," Agronomy Journal, 11:519-527; D.G. Friedman and B. E. James, "Estimation of rainfall probabilities," Univ. of Connecticut, Coll. of Agric. Bull. 332, 1957; and H. C. S. Thom, "A.note on the gamma distribution, " Monthly Weather Review, 86: 117-122, April 1958. 10See H. C. S. Thom, "Some methods of climatological analysis," Technical Note No. 81, World Meteorological Organization, 1966. 56 and where 2 ln x n A 8 1n i - Table 5.5 shows the estimates of B and y for each weed based on 27 years of weekly data in Ambulong, Tanauan, Batangas. 5.4 Generating Variables of a Particular Distribution There are two important methods for generating random variables, namely, the inverse transformation method and the rejection method.11 Inverse transformation method In the inverse transformation method, we seek to generate a series of random numbers (x1, x ,xn) which have the density 2,... function f(x). The procedure is as follows: a) Draw a series of random numbers (r1, r2,...,rn) which are uniformly distributed between zero and one. b) Determine the cumulative distribution function corresponding to f(x): F(x) - L: f(x)dx . c) Compute xi (i=l,2,...,n) as xi - F-1(ri) where F-1( ) is the inverse of the cumulative distribution function. _ llThissection draws heavily from G. Park and T. Manetsch, §1§tems Analysis and Simulation with Applications to Economic and Social Systems, Preliminary edition, Michigan State University, January 1973, Chapter 13. 57 Table 5.5 Gamma and beta parameters of the incomplete gamma distribution fitted on weekly rainfall data, Ambulong, 1949-1974. Week Gamma (y) Beta (6) Week Gamma (Y) Beta (8) 1 0.328 0.907 27 1.504 1.283 2 0.378 0.468 28 0.822 2.860 3 0.292 0.386 29 0.640 5.335 4 0.420 0.242 30 1.040 2.179 5 0.328 0.300 31 1.066 2.398 6 0.411 0.196 32 1.822 1.728 7 0.294 0.376 33 1.588 1.764 8 0.283 0.476 34 1.341 1.375 9 0.331 0.626 35 1.110 2.345 10 0.264 0.778 36 0.831 4.056 11 0.313 0.683 37 1.372 1.254 12 0.247 0.505 38 2.067 1.173 13 0.269 0.424 39 1.352 1.444 14 0.302 0.210 40 1.472 1.602 15 0.318 0.870 41 0.769 3.154 16 0.269 1.292 42 1.103 2.039 17 0.503 1.229 43 0.689 1.799 18 0.441 1.956 44 0.354 4.092 19 0.368 2.766 45 0.582 2.088 20 0.558 2.416 46 0.627 2.107 21 0.481 2.912 47 0.472 3.916 22 0.506 2.308 48 0.580 2.634 23 0.661 2.457 49 0.433 2.749 24 1.074 1.354 50 0.486 2.387 25 0.886 2.209 51 0.354 2.544 26 1.199 2.346 52 0.372 3.113 Source: Output of computer programs. 58 Rejection method This method can be used if the density function f(x) is finite and if x has a finite range: A §_x : B. ’The procedure for implementing this method is as follows: a) Normalize the range of the density function f by a scale factor c, such that cf(x)§l, where A§_x‘§_B. b) Define x as a linear function of the uniform (0,1) random number r, so that x = A + (B - A)r. Note that the range of x is (A,B) as required since x = A when r = 0 and x a B when r - 1. c) Generate pairs of (0,1) random numbers (rl,r2). d) Whenever a pair of random numbers that satisfies the relationship r2 5 cf{A + (B-A)}r1 then the pair is "accepted" and the random number x a A + (B-A)r1 has a density function of f(x). This method is particularly useful when it is difficult, or impossible, to obtain the inverse of the cumulative distribution function, F-l( ), required by the inverse transformation method. Generating normally distributed rainfall In order to generate random variables from a normal distribution, estimates of the mean ux and standard deviation Ox must be given. In practice, we usually generate random variables from the so-called standardized normal distribution (with ux-O and ox-l). Then by means of a simple transformation, we convert them to normal variables with the desired mean and standard deviation. Let y represent a standardized normal random.variable with zero mean and a standard deviation of one. 5.9 we then define the following transformation: x - Oxy +rux. The variable x is then a normally distributed random variable with meanux and standard deviation ox. The most efficient way to generate normal random variables is the inverse transformation method. Unfortunately, the inverse of the cumulative distribution function for the normal density function does not exist in a nice neat analytical form. It is therefore, necessary to approximate it. In this study, the practical approach was to use a subprogram to construct a piecewise linear approximation for the inverse cumu- lative distribution function. The method for computing normal random normal random variables with a specified mean and standard deviation by the above approach are as follows: 1. Generate a (0,1) uniformly distributed random number ri. 2. Compute a standardized normal variable Yi based on ri. 3. Compute a normal random variable with the desired mean, ux, and standard deviationox as Xi - oin + ux. Another approach to the generation of standardized normal distribution is by the use of the formula 1/2 Y - (-2 1n r cos ZITr2 1) where Y is now a random variable from the standardized normal distri- bution and ti, r2 are (0,1) uniformly distributed random.numbers. This approach is more convenient and has the advantage of being exact. However, it is much less efficient. 60 Generating gamma distributed rainfall. To generate rainfall which is distributed according to an incomplete gamma distribution, the weekly estimates of the gamma parameter G and of the beta parameter B are required. As indicated earlier, these are found by 1 _________ G - “ZZ- (l + 71 + 4A/3 ) Bai/G where Aslni-m_ n The general principle of the inverse transformation method is to find the value of x for a given random number uniformly distributed between zero and one. Since the inverse of the incomplete gamma distribution is difficult to obtain, the rainfall level Ri’ corres- ponding to a given probability level ri may be estimated as follows:12 ._ 2 _ x. x. x. x. r.F(G)e J x.=x.--l 1+-1—+—J—+ -4..— 1 J G G+1 0+2 °°° ij-l where j - i - 1, G is the gamma parameter, and xi is a preliminary estimate obtained by iteration. The initial estimate of xi begins at G-l; that is, xj - G-l. Iteration stops when x1.. and xj are approximately equal. Finally, the rainfall level is obtained by R. - x.- B i 1 12C.R. weaver and M; Miller, "Aprecipitation probability computer program," Research Circular 155, Ohio Agric. Res. and Dev. Center, wooster, Ohio, Nov. 1967. 61 where B is the beta or scale parameter. Normally, the above procedure requires only about 10 to 20 iterations. Generating_19gnprma11y distributed rainfall Generating lognormally distributed rainfall is more efficient than that of gamma distributed variables in terms of computer time. The procedure is as follows: 1. Provide estimates of the lognormal parameters p and o. of the following distribution: 1 e-(log x - U)/202 x/ 2H02 3(X) = By maximum likelihood estimation, A l H ' n X 108 xi and x2 ..1 2 o n 2 (log xi -u) . 2. Generate a random standardized normal deviate 21 (with mean 0 and standard deviation - l). 3. Generate Xi using the equation “1+ 8z Xi - eu i 5.5 Chi-Square Tests The computation of the parameters of both the incomplete gamma distribution and the lognormal distribution were done by means of a computer program. developed for this study. 62 In computing the parameters for a particular week, the estimation procedures as outlined earlier were used. In the case of the gamma function, the procedures are that of the modified method of moments, while for the lognormal function, the maximum.1ikelihood estimates were used. In order to test the goodness or fitness of a particular function to actual data, the latter were first tabulated according to classes based in magnitude of rainfall. A total of 20 classes were used in tabulating actual data, the class interval being one-half of an inch of rainfall. After obtaining the absolute frequency count for each class, the relative frequencies for the class were also computed. To compute the chi-square, the expected frequency for a given class was obtained by first finding the probability density of the mid-point of that class.and then multiplying it by the class interval to obtain an estimate of relative frequency of the class. Finally, the expected frequency was obtained by multiplying the relative frequency by the number of observations for that week, that is, 27 observations corresponding to the 27 years of available data. The chi-square statistics were computed according to the usual formula 2 _ (E--0)2 X E where E is the expected frequency and 0 is the observed frequency. 63 Results of thefgggdness of fit tests The choice as to which function to use depends on how well each one fits with the actual data. As in other goodness of fit tests the chi-square test was employed. Table 5.6 shows the comparison between the gamma distribution and the lognormal distribution in terms of the computed chi-square. The interpretation of the figures are as follows: if the computed chi-squares are greater than 34.80, 28.87, or 25.99, then the distribution generates figures which are significantly different from the actual data at one percent, five percent or ten percent significance 1 evel , respectively . Note that in the case of the incomplete gamma function, the computed chi-square values were consistently below the critical value at five percent level. There was no week in which the actual data was significantly different from those generated by the incomplete gamma function at five percent level. The results indicate that the incomplete gamma function is the more appropriate distribution function to use in generating simulated rainfall data for Cale, Batangas rather than the lognormal distribution. 5.6 Options‘Qsing‘Historig§1_Qg£§. As mentioned earlier, the rainfall generator component includes options using historical data. These options, though not intended to replace the rainfall generator using a distribution function, are able to provide alternative rainfall patterns for the simulated period. In addition, the added options provide facility in validating the other 6.4 Table 5.6 Comparison of chi-square statistics between incomplete gamma and lognormal distributions fitted on Ambulong rainfall data, 1949-75. week Gamma Lognormal week Gamma Lognormal l 15.71 12.98 27 26.31 35.83 2 13.48 10.48 28 24.69 25.82 3 10.39 57.23 29 22.41 33.61 4 10.00 40.64 30 25.57 21.28 5 9.58 61.36 31 25.36 27.23 6 8.13 77.71 33 25.82 23.59 7 10.29 52.93 33 25.82 23.59 8 11.40 28.55 34 26.28 22.28 9 13.99 12.08 35 25.41 41.53 10 13.52 17.58 36 23.57 15.31 11 14.02 30.65 37 26.36 40.45 12 10.95 59.55 38 26.05 13.39 13 10.45 63.25 39 26.43 17.49 14 6.69 132.73 40 26.03 36.03 15 15.30 16.49 41 24.34 28.15 16 15.92 10.26 42 25.72 44.94 17 20.58 8.16 43 24.01 17.43 18 20.80 30.21 44 20.74 40.60 19 20.36 9.27 45 23.02 18.90 20 22.91 30.76 46 23.55 17.35 21 22.12 18.60 47 22.11 39.85 22 22.49 21.21 48 23.22 13.98 23 23.96 25.88 49 21.38 19.61 24 26.03 24.03 50 21.94 18.47 25 25.26 45.57 51 19.94 22.69 26 25.34 35.09 52 20.66 38.12 Source: Output of computer programs. . i I- ll ‘ 65 components of the model and the pre—setting of the kind of rainfall pattern desired for a particular simulation run. (1) The first option using historical rainfall data is to randomly select a year from 1949 to 1975 and to use the rainfall data of the selected year as the rainfall pattern for the simulation run. This is achieved in the model by generating randomly a number between 0 and l and consequently multiplying the number by 27 which is the number of years for which data are available. The product is then used as an index for selecting the specific year in which year 1 corresponds to 1949 and year 27 corresponds to 1975. (2) The second option is to use the historical rainfall data of a specific year as the rainfall pattern for a simulation run. The desired year is simply specified and the program automatically feeds the rainfall data for that year for use in the simulation. (3) The third option using historical data is to randomly select a year of a given rainfall level based on annual total rainfall. Either a high, medium or low rainfall is specified and the program randomly selects from the array of years belonging to a particular level. High rainfall years are those years having total rainfall higher than 80.7 inches: medium rainfall years are those which have a total rainfall between 65.2 inches and 80.7 inches; and low rainfall years are those years having a total of less than 65.2 inches. The limitation of this option is that there is no g_priori reason to 'suppose that the rainfall pattern for a given period is dependent on total annual rainfall. Nevertheless, it allows for the use of this method of rainfall generation if desired. 66 (4) Finally, the fourth option using historical data is to use the mean weekly rainfall of the Ambulong Weather Station from 1949 to 1975 as rainfall pattern for the simulation run. The inclusion of this option is only for comparative purposes since no random elements are present in the means. It was specifically intended to show that average rainfall patterns can give different results from those individual year to year patterns. 5.7 Validation of theARainfall ngerating_Model The test of validity of a model can be done only by comparing the results of the model and with the actual data. In order to do this, some thirty years of weekly rainfall data was generated on a digital computer. The first comparison was annual totals and averages. Table 5.2 shows the annual totals and averages of the simulated rainfall data for the thirty years while Table 5.8 shows the annual totals and averages of the rainfall data from Ambulong Station, Tanauan, Batangas from 1949-1974. Note that the mean annual total for the actual data is 69.35 inches while that of the simulated data is 68.53 inches. In terms of the average rainfall per week, the simulated data gave 1.32 while the actual data gave 1.33 inches. The other test done was a comparison of the weekly averages and standard deviations. Table 5.9 shows the weekly means and standard deviations of the simulated and actual data. They are reasonably close, although the simulated data appear to be slightly drier 67 Table 5.7 Annual totals and average per week of 30 years of simulated rainfall based on gamma parameters computed from.Ambulong, Tanauan, Batangas (inches). Year Sum Average/week l 81.33 1.56 2 49.49 0.95 3 64.97 1.25 4 80.99 1.56 5 70.78 1.36 6 72.60 1.40 7 77.19 1.48 8 61.94 1.19 9 76.95 1.48 '10 51.28 0.99 11 66.69 1.28 12 69.89 1.34 13 81.74 1.57 14 60.03 1.15 15 65.14 1.25 16 84.11 1.62 17 85.01 1.63 18 76.42 1.47 19 51.30 0.99 20 46.41 0.89 21 51.11 0.98 22 65.86 1.27 23 70.59 1.36 24 91.77 1.76 25 73.61 1.42 26 71.59 1.38 27 55.38 1.07 28 59.35 1.14 29 82.07 1.58 30 60.29 1.16 Average 68.53 1.32 68 Table 5.8. Annual totals and averages per week of actual rainfall data, Ambulong, Tanauan, Batangas, 1949-1974 (inches). Year Annual total Average/week 1949 49.7 1.1 1950 67.3 1.3 1951 74.2 1.4 1952 84.3 1.6 1953 65.4 1.3 1954 54.1 1.0 1955 49.4 1.0 1956 80.4 1.5 1957 47.9 0.9 1958 53.0 1.0 1959 70.2 1.4 1960 89.8 1.7 1961 85.9 1.7 1962 96.2 1.9 1963 53.8 1.0 1964 66.8 1.3 1965 46.8 0.9 1966 81.7 1.6 .1967 76.6 1.5 1968 53.8 1.0 1969 49.7 1.0 1970 71.0 1.4 1971 88.2 1.7 1972 91.4 1.8 1973 67.6 1.3 1974 87.9 1.7 All 69.35 1.33 69 66“ |IIII““ . Q N . a; a: N: E. e HN.H 9H.H am.o cw.o mm w4.a om.a um.H mo.a nN me.H ca.c m~.o em.o Hm mm.a m<.H H~.H m~.H «N m~.H 9H.H Hm.c om.o on .H No.H hm.u wo.~ mu He.a mH.H nN.H hm.o as so . . 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A 3003 aaauu< vmumasafim Haauo< vmumasawm .Aaanoawv numsmumm .awauama .waoasna< .mumv Hanuuu .m> unaumamumm «Baum no woman Hammawmu vmuaaaawm mo munch on .maowumw>ou cumvsmum new names Hawmcwuu haxoua mo sonwumaaoo .pq.n wanna 70 especially during the first 20 weeks. For the ensuing weeks, the means and standard deviations for both the actual and simulated data differed only very slightly. 5.8 Summary This chapter discusses the purpose of the rainfall generator, the modeling considerations, and approaches to generating rainfall. The issue between the use of a synthetic generator and the use of historical data were also discussed. The testing of three different distribution functions and the eventual choice of the incomplete gamma distribution were also dealt with. Four other options using historical rainfall data were discussed. Finally, the validation of the rainfall generator was discussed. CHAPTER 6 PRODUCTION COMPONENT 6.1 Introduction The purpose of the production component is to determine the yield levels of the various crops given the environment under which they are grown, the management practices employed and the input levels. Perhaps, the production component is the most important component of the model as in other crop simulation models. It is also the most difficult to model quantitatively in view of complexity of the pro- duction process. There have been many attempts to predict yield though various types of quantitative models, but most of them are not adaptable for the purposes of the study because they are either too environment-specific or they include only a very limited number of factors affecting yield. An ideal yield prediction model is one which can predict yield to a reasonable degree under various environmental conditions (temporal or locational) given the levels of inputs and management practices. While this may be difficult or impossible to achieve, it is the ideal goal of model builders. 6.2 Factors Affecting:1ield Crop yield is the end result of the interaction of many bio- logical, physiological, and physical processes. The factors affecting these processes are numerous and it would be impossible, if not .71 72 impractical to include all of them in a yield prediction model. However, the more important factors affecting yield may usefully be classified as follows: A. Crop environment 1. Climate a. Rainfall b. Solar radiation c. Day-length d. Temperature e. Relative humidity 2. Soil a. Type b. Texture c. Topography d. Fertility 3. Others a. weed population b. Degree of insect and disease damage Crop characteristics 1. Yield potential and stability 2. Response to N, P, K 3. Seedling characteristics 4. Leaf characteristics 5. Growth duration 6. Plant height and culm characteristics 7.; Root system 73 8. Panicle and grain features 9. Tolerance to adverse environments 10. Other physiological characteristics C. Management practices 1. Land preparation 2. weeding 3. Fertilization 4. Pest and disease control 5. Irrigation It is clear from the above list that there is a multitude of factors affecting yield. Although the inclusion of the above factors in a yield prediction model would result in more realism and accuracy, the task would be too enormous and impractical for the purposes of the study. Hence, some guidelines and considerations were first defined. 6.3 Modeling considerations The kind of model to be developed must be tailored to the purpose at hand. If it is necessary to predict yields accurately, say to within one percent, then a very sophisticated model incorporating the detailed physiological processes down to the last stomate may have to be developed. However, if the degree of accuracy desired is modest, then a much simpler version of the model may suffice. The model developed in this study has been kept simple for expediency. Very little detailed physiological processes were taken into account in the model because of the lack of time and resources, 74 and expertise on the part of the author. Therefore, modeling was restricted mainly to the observed relationships between inputs and output.~ Moreover, only the more.important variables, that is, those variables which have the most impact on the yield of crops were included. Another consideration in deciding which factors to include in the model is the availability of data. Although the inclusion of a variable may aid in making a model more realistic, this may not be possible due to the unavailability of data on such variable. Thus, certain variables were ignored altogether if it was impossible to fill the data requirement. In summary, the main considerations in the choice of variables included in the model were: (1) the degree of importance of the variable in explaining yield, (2) the feasibility of including the variable into the model given the time, resources and capabilities of the model builder, (3) the level of realism required by the study, and (4) the availability of data. 6.4 Factors Considered Crop environment 0f the climatic variables, rainfall level and distribution were considered to be the most important variables. The subject of the study is an upland area which depends solely on rainfall for its moisture supply. Yoshida (1975) states that "...moisture stress is the primary limiting factor of growth and yield under upland 75 condition.1 Several authors have likewise made similar statements.2' Although solar radiation has been found to influence nitrogen response and yield,3 it was not accounted for in this study mainly because of lack of data on the crops considered in the study and specifically in the area being studied. If and when data for - relating solar radiation and yield are available, it should be included in the model, not only in relation to nitrogen response functions but also in relation to its role in water loss from the plant due to transpiration. , Temperature, relative humidity, and day length were not considered in the model because of their relatively negligible, and inconclusive quantitative effects on yield.4 Moreover, there is not yet enough data available on their effects on yield. Batangas soils are alfisols and the soil texture is clay loam” In the particular area of this study, it was assumed that the soil type is homogenous so that the innate fertility of the soil was not assumedto affect yield. Topography was also not regarded as an 1S. Yoshida, "Factors that limit the growth and yields of upland rice.". in IRRI, Major'Researchgs in Upland Rice, Los Bafios, Phils. 1975. pp. 46—71. 2See for example, Y. Murata, "Estimation and simulation of rice yield from climatic factors," AgriCultural Meteorology, 15:117-131. 1975. See also, S. K. De Datta and B. S. Vergara, Climate of upland rice regions in IRRI, Major Research in Upland Rigs, Los Bafios, Phils., 1975, 14-26. 3R. Barker and C. Montana, '"The effect of solar energy in rice yield response to nitrogen," (mimeo.) 1971. ..4A. K. Samsul Huda, et.al., "Contribution of climatic variables in predicting rice yield," ‘égricultural”Meteorology, 15:71-86, 1975. 76 important factor affecting yield. However, future refinements of the model may require the inclusion of these factors. Soil type affects mainly the moisture retention capabilities and innate fertility of the soil as they affect the base yields of crops. Thus, its inclusion as a factor in affecting yield is important in making the model more general in its application to other areas. Crop characteristics Crop characteristis could be summed up into one factor namely, variety. Varieties differ in their yield potential, drought resistance, maturity periods, and other physiological characteristics. In this study, however, no fine distinctions were made among different varieties of each crop. In the case of rice, only the figures for the local traditional variety (Dagge) which is planted by all Cale farmers were included. For corn, only the figures for the local variety (Tinumbaga or Cale orange flint) were included in the model. For the other crops, namely sorghum, mungbean, cowpea, peanut, soybean and sweet potato, the figures used were averages of several varieties. Manggementgpragtices From the farmer's point of view, the manipulation of yield consists of varying inputs such as labor, fertilizer, choice of variety, and levels of pest and disease control. Since it was not possible to allow for every combination of cultural practices, it was ’ assumed that farmers follow the recommended or customary land prepara- tion practices, seeding rates, timings of fertilizer and other labor 77 input. For example, it is assumed that fertilizer application is done during seeding and panicle initiation. The model does not allow for yield adjustments resulting from applying fertilizer at other times.‘ In summary, the major factors considered to be important in determining yield in this study are as follows: 1. Rainfall amount and distribution 2. Soil type and texture 3. Fertilizer level 4. Weed control 5. Insect and disease control level 6. Variety of crOp For present purposes, the above factors must be incorporated into the model as a minimum requirement. The choice of the above variables does not mean that data on them are immediately available. As a matter of fact, considerable problems were encountered in taking into account the effect of each factor on yield. Data availability and problems related to each factor will be discussed in detail later. 6.5 Method for Simulating the Production Component Figure 6.1 shows a causal flow diagram for simulating the produc- tion component. Among the factors considered to affect yield, only rainfall (level and distribution) is non-controllable from the point 'of view of the farmer.‘ The others, namely fertilizer input, weed control, pest and disease control, and variety of crops are controll- ablet- Thus, the former has to be provided exogenously or model 78 vamww .uomooaaoo cowuoaooum mnu mo guano 30am .H.o .mwm a ANH-HVAHH-HV sax» u » vamww Esawxmz moumm oowuusomm a mOH Henna wfiwvmmz WUHAom 4 nouwawuuum ZMMHHu>u=m ameos uHoo "some onmn mo mouoom .moowum>uomno ohm .mooHum>umvo omo .muomHonmuoo mo muouuo pudendum mum mononuoouon oH mounmmm any a .oumuoo: woo muoonloma :H HoomH pom moumuou: use sowouuHo mo mamuonHx oH uuNHkuuou mamamumoHHx n.¢H I and HV museum: you memo :H oHuHh “maoHHom mo onus pom: mums: mayo .uomonHamHm no: new xHaoumm on new: noowowumooo .Hm>mH unmouoa n no uamoHMHome a. chm.oV Acco.ov Acum.ov . No.0 mo>hom szooB on0 "pump onon no mouoom .oumuoun Hue muoonIoma QH nonoH poo moumuoo: woo mamumOHHx mH nouHHHuumw “mumuoon Hoe aouonHx ow vHon "mums pom: wows: unym .uomowmwome you mum mmeuuumm o: :uH3 mucowowwwooo .Ho>oH unmouoa m an oomonHomHm % Amo.mv aHmm.oV Aun.mmv ~m.o muou was Hmuumeauonxm “some owuuo mo oouzom mH ousumHoa HHom mHomHHm>o :Houuna xmua u on poonop mH Hum: usmoounm oh on mH cH m m H H o 0 HH ouauoa uaoam ooH ocH ooH ooH m a n N o o m :moasom ocH ooH ocH on oH m m N o o a genome coH coH ooH ooH cm a m N o o n «assoc ooH ooH ooH coH cm s m N o o m assumes: ooH cm o~ mH OH o m H o o a asamuom ooH ooH on ow oH o m H o o a anon ooH on cw mH OH H m H o o HH 66He .II ©II Ilw h mxmuw unwzouw mo uwnasz m N H o mxmos mo aouu m monaoz .Auououuo :Hv muons mooHum> no «mean mamas unmoouv uH amouum ousumHoa mo mHm>uH uuuummmwu now o>Humuowo> unu wcwuou mouse ooHuoovou vHon .m.o uHAmH 92 Table 6.4. Yield reduction rates for different levels of moisture stress in drought weeks during the reproductive stage of various crops (in percent). Number of __‘ Number of drought weeksa Crops weeks 0 l 2 3 4 Rice 2 O 3 7 20 100 Corn 3 O 3 7 20 100 Sorghum 3 O 3 7 20 100 Mungbean 3 0 ' 3 7 10 100 Cowpea 3 O 3 7 10 100 Peanut 3 O 3 7 10 100 Soybean 3 0 3 7 10 100 Sweet potato 2 O 3 7 10 100 aDrought week is defined as a week wherein available soil - moisture is less than .5 of an inch. Sources of basic data: Experimental and survey data (see text). 93 Table 6.5. Yield reduction rates for different levels of moisture stress in drought weeks during the maturation stage of various crops (in percent). Number of Number of drought weeksa Crop weeks 0 l 2 3 4 Rice 5 O 2 5 10 15 Corn 3 O 2 5 10 10 Sorghum. 3 0 2 5 10 10 Mungbean 3 O l 3 7 10 Cowpea 3 O l 3 7 10 Peanut 4 0 l 3 7 10 Soybean 4 O l 3 7 10 Sweet potato S 0 l 2 .4 8 aDrought week is defined as a week wherein available soil moisture is less than 0.5 inch. Source of basic data: Experimental and survey data (see text). 94 6.8 Relationship Begween Fertilizer Inpp£_Apd Yield Fertilizer input, especially nitrogenous fertilizer, is one of the most important management inputs. When rainfall is not limiting, studies have shown that nitrogen tends to be the major limiting factor that limit yields in upland areas.18 The main approach in obtaining the yield reduction rates for various levels of fertilizer was first to fit a yield response function to nitrogen of the form Y 8 a + bN + cN2 where Y is the yield, N is the level of nitrogen application, and a, b and c are constants. It was deemed appropriate to use experimental data since other factors are usually held fixed and usually at optimal levels. However, when no experimental data were available for other crops, survey data were used. Table 6.6 shows the yield response function to nitrogen for each crop. Based on these response functions, the reduction rates were computed and these are shown in Table 6.7. In the simulation program, the reduction rates were supplied as para- meters to the model. 6.9 RelationshippBetggen'Weeding Input And Yield The weeding operation can taken on many forms. It can be accomplished by hand, by animal drawn implements, or by the use of weedicides. Some operations such as plowing and harrowing can remove a major proportion of weeds while the soil is tilled. Hence, the term ‘ "weeding" must be clarified. Table 6.6. 95 Summary of regressions on yield vs. nitrogen input, Cale, Tanauan, Batangas, 1974. Coefficientsb 2 Crop a b c R Ricec 1498.16 24.82 .0417 0.54* Corn 548.09 21 25 -.0648 .68** Sorghum. 1187.96 24.34 .0638 .37** Mungbean 466.61 5.03 -.0728 .01118 Cowpead 466.61 5.03 -.0728 - Peanut 788.47 0.36 .0260 .19n8 Soybean 780.73 1.76 .0000 .58n8 Sweet potato 2980.20 93.13 -.4578 .21** * Significant at 5 percent level. ** Significant at 1 percent level. ns - not significant. aYield is expressed in kilogram.per hectare and fertilizer in kilogram of nitrogen per hectare. bThe regression equations are of the form. 2 YIELD 8 a + bN + cN where N is the nitrogen level. cBased on 1973-74 Cale weekly survey data. d The coefficients for mungbean were used for cowpea Source of basic data: Dennis Garrity's experimental data in Batangas, 1974, Multiple Cropping Project, IRRI. 96 Table 6.7. Yield reduction rates for different levels of fertilizer, various crops (in percent). Fertilizer input (kg. nitrogen/hectare) Crop . 0 20 40 60 x 80 100 \120 " 140 Rice 50 35 22 12 5 2 0 2 Corn 50 35 22 12 5 2 O 2 Sorghum. 50 35 22 12 5 O O 2 Mungbean 30 20 10 2 0 0 2 10 Cowpea 30 20 10 2 0 0 2 10 Peanut 40 30 20 10 5 0 0 0 Soybean 3O 20 10 2 0 0 2 10 Sweet potato 4o 30 20 10 5 0 0 o Source of data: Table 6.6. 97 In this study, the weeding operation is defined as that operation devoted solely to the elimination of weeds such as hand weeding or weeding which employs some hard tools. This implies that the labor used in land preparation operations such as plowing and harrowing as well as post-planting cultivation such as hilling-up and off-barring are not considered as weeding input. While these operations are also important forms of weed control, it was assumed in the model that their levels are equal among farmers, hence they do not affect yield. The model does not allow for yield changes resulting from different methods of land preparation and post—planting cultivation. The main approach in determining the reduction rates for weeding input was to estimate them from experiments using the same input levels and environment except weeding labor and from regression equations in which weeding labor has been included as an independent variable. Table 6.8 shows the reduction rates for different levels of weeding labor.. 6.10 Relationship Between'LQQEct And Disease Contrglpggzel And Yield Insect pests and diseases are other influences that may affect the yield of a crop. Therefore, its inclusion into the model can add to its realism and usefulness. There are, however, some problems that make it necessary to keep this aspect as simple as possible. First, there are a great number of insecticides in the market. Unlike fert— ilizers, which may be converted into a common unit such as kilograms nitrogen, insecticides are of extremely varied formulations and I chemical composition. The problem is to find a common denominator for 98 Table 6.8. Yield reduction rates for different levels of weeding labor, various crops (in percent). Weeding labor (man-hours/hectare) Crop O 20 40 ‘60 V 80 '7 lOO——- Rice 20 15 10 5 . 2 0 Corn 20 15 10 5 2 0 Sorghum. 20 15 10 5 2 O Mungb ean 20 15 10 5 2 O Cowpea 20 15 10 5 2 0 Peanut 20 15 10 5 2 0 Soybean 20 15 10 5 2 0 Sweet potato 30 20 15 10 5 0 Source of basic data: Experimental and survey data (see text). 99 various insecticides. One way of overcoming this problem is to express insecticide levels in monetary units. However, the limitation is that a peso of one chemical may not have the same effect on insect pest control as a peso of another chemical. Secondly, farmers typically apply insecticides only when insect damage is evident. There is also a great number of possible insects and diseases that may attack a crop. For the purpose of yield prediction, it would be ideal to predict first the degree of infesta- tion of each insect or disease as affected by external and internal influences. The farmers may then react to the predicted infestation with the necessary control measures. This entails a detailed plant- insect—environment modeling which in itself is a very complicated. matter. Because of the above problems, some simplifying assumptions had to be made in estimating the yield reduction rates for different levels of insect and pest control. It was assumed that only certain types of insect or disease attack a crop and only certain types of insecticide controls them. The types of pests selected were the most common pests attacking the crop. The insecticides used as basis for the reduction rates were the most effective insecticides controlling the pests. Table 6.9 shows the most common pests and the most effective insecticides used for each crop. Given the common pests and diseases and insecticides, the v reduction rates were based from-experiments, from observations and from qualitative opinions of agronomists and entomologists. There are shown in Table 6.10. It must be borne in mind that the reduction rates 100 Table 6.9. Most common pests and recommended chemical control wby crop. Crop Pest Chemical control Palay Rice borer, leafhopper Furadan, Basudin Corn Earworm, corn borer Furadan Azodrin Sorghum Earworm, borers Furadan, Azodrin Mungbean Cutworm, pod borer Furadan, Azodrin Cowpea Cutworm, pod borer Furadan, Azodrin Soybean Cutworm, pod borer Furadan, Azodrin Peanut Cutworm, pod borer Furadan, Azodrin Sweet potato Cutworm Furadan, Azodrin 101 -Table 6.10. -Yield reduction rates for different levels of insect control, various crops, in percent. Insect control level (in P/ha) Crop O 100 200 300 400 500 600 700 Rice 10 5 4 3 2 l O 0 Corn 15 7 6 5 4 3 2 O Sorghum. 15 5 4 3 2 l 0 0 Mungbean 20 8 6 5 4 3 2 l Cowpea 20 8 6 5 4 3 2 1 Peanut 20 8 6 5 4 3 2 l Soybean 20 8 6 5 4 3 2 1 Sweet potato 10 3 2 l O 0 0 0 102 are artificial and may be unrealistic owing to the strong simplifying assumptions. However, it was felt that the use of the reduction rates is an improvement over the alternative of ignoring the effect of insect control on yield completely. 6.11 Computer Implementatiop pf the Production Component In the computerized version of the production component, the potential yields of each crop as well as the reduction rates are provided exogenously to the model. Table 6.11 shows some of the crop data entered into the BLOCK DATA subprogram. The fertilizer levels, weeding labor levels, and the levels of pest and disease control for each crop planted are specified at the start of the simulation run. The rainfall pattern is determined within the model through the rainfall generator. Planting dates are specified before the simulation run but are subject to change depending on the generated rainfall pattern. The rule is that land preparation could not start unless a strong rain (at least 0.5 inch) has fallen and that planting could not be done unless there has been sufficient rainfall characteristics (number of drought weeks) are counted for each stage of crop growth throughout the growing season. Once these have been determined, the applicable reduction rates for each factor are determined by means of lackrup functions. Finally, the reduction rates and potential yield are fed into the yield formula. The computed yields of each crop are then passed to other sub-routines. 103 Table 6.11 Various crop data used in the cropping sytems simulation model. Cro Crop Number of Weeks in Stage Potential p Maturity Vege- Repro- Maturation Yield Periods tative ductive (ton/ha) (weeks) Rice 18 ll 2 5 4.0 Corn l3 7 3 3 4.0 Sorghum 15 9 3 3 4.5 Mungbean 11 5 3 3 1.5 Cowpea 12 5 3 3 2.0 Peanut 14 7 3 4 3.0 Soybean 13 5 3 5 2.5 S. Potato 18 ll 2 5 18.0 Source: IRRI, Multiple Cropping Project, Economics Section 104 6.12 Validation of the Model The purpose of validating a model is to compare the results of the model with the real world performance. If the simulation results are significantly different from actual figures then some adjustment should be done with the simulation model to make it more realistic and hence acceptable. The validation of the model was done mainly by plugging actual data on rainfall, fertilizer levels, weeding and pest control inputs and other data into the simulation model and comparing the simulated yield with actual yield. The final reduction rates used in the model already reflect the adjustments that have been made after several validation runs. Table 6.12 shows the comparison between simulation results and actual data. Although the results are different, the ) simulated results appear reasonable and therefore the production component was considered an adequate representation of the real-world production relationships. 6.13 Summagy This chapter discussed the production component of the simulation model with emphasis on the various factors affecting crop yield. Because of the complexity of the production processes, only key variables were included. The main considerations is the choice of variables included in the model were: (1) the degree of importance of the variable_in explaining yield,_(2) the feasibility of including the variable into the model gives the time, resources and capabilities of the model builder, (3) the level of realism.required in the study, and (4) the availability of data. On the basis of the above conside- 105 .Houoe ooHuonaHm unu ouoH moon> Hmouom onwono no vouHuuoou .mnoumHoa HHom Ho :osH m.c omen mmoH nuHs moo nH Home ano <0 .mosHu> Huuoa one onu mouse women .uo>numoo onus moumu wuHuomHe nonuo smoonuHnom H thooa oHuu onu sonm one some unu .onoo one ooHn nobo O0.0 OO.H Om me On no oooooe .O m~.H OO.H Om mm OH no enoanon OH.H Om.O OOH mHH Om no genome mm.H OO.H O me On no ooeaoo O0.0 um.O O No On an neonate: O~.~ On.~ OOH ONH On an anamnom OH.H HO.H O ON Om no _eeoO. HO.~ OO.H O OOH Hm ON ,ooHe OoooHoaHm Honooa Hoe\ev Hoe\OIsO Hoe\z.wxv noes . HoOHoO OHoHn oOHoHooooeH weneoo: noNHHHonoe neon: see no nonaez eoHe mono \moHOHIHNOH .nHo>oH oneeH one Hflwmfiwmu Hflfluom no fimmmn aux—”Owen vmumdflafim 9nd Hmauuw fimm3UM£ GOGMHQQEOU NH.© oHonn 106 rations, the major factors considered were rainfall level and distri— bution, soil type and texture, fertilizer level, weed conbrol, insect disease control level, and crop variety. Two approaches of yield estimation were contrasted: the regression approach and the reduction rates approach. It was concluded that the reduction rates approach was more appropriate for the study. The relationship between yield and rainfall, fertilizer, weed control, and insect and disease control were also discussed and the estimation of their corresponding yield reduction rates described. Finally, the computer implementation and the validation aspects of the production component were also described. CHAPTER 7 PRICE GENERATOR 7.1 Introduction The purpose of the price generator is to provide an appropriate price of each crop at any given week of the year. The basic assumption is that the production of an individual farm is such a small part of the total market that it cannot influence market prices. This assumption of a perfectly elastic supply is reasonable in the Cale environment since farm sizes are relatively small. Moreover, the main market in Tanauan is supplied by a large number of small farmers from several barriosa The implication of this assumptiOn is that Cale farmers are price takers; therefore, it is sufficient to deal only 'with the total market in the determination of prices at any given time. The prevailing prices at a particular time in Tanauan are also assumed to apply in Cale, the area of study. One approach to price determination would be the estimation of supply and demand functions of the market for each time period. This approach, however, was considered impractical for the purposes of the study. The dynamic nature of supply and demand functions necessarily makes the task very complicated requiring vast amounts of information. Hence, a relatively simple method of providing reasonable estimates of prices for each period was devised. The main approach in determining prices in this study was to use base prices and seasonal price indexes. The base price is the expected annual average price while the seasonal price indexes show the fluc- 107 108 tuations in price over the year. In this approach, it is the average price fluctuations in the past are assumed to persist to the present and future periods. 7.2 Seasonal Price Indexes The procedure is computing the seasonal price indexes used are well explained in many economics statistics textbooks.1 It is based on the premise that seasonal fluctuations can be measured from an original series (0) and separated from.trend (T), cyclical (C) and irregular (I) fluctuations. The seasonal component (8) is defined as the intra-year pattern of variation which is repeated constantly from year to year. The assumption adopted in this study that the seasonal, trend, cyclical, and irregular components are related in a multiplicative fashion. That is, O - T x S x C x I. The method of obtaining the seasonal indexes used is the ratio- to—moving average method. It is assumed that the seasonal variation (8) has a 12~month period and that the shape of the variation is the same each year. It is also assumed that the irregular variations (I) are independent for different periods (years). Briefly, the computa- tional process are as follows: 1See for example Taro Yamane, Statistics: An Introductogy, Analysis, Harper and Row: New York, 1964, Ch. 13. 109 The basic approach is estimating the price at any given week is to adjust the base price, which the expected annual average price, by the seasonal index applicable to that week. Since monthly price indexes are provided to the model, the price index during the given week was estimated by linear interpolation, assuming that the change in seasonal indexes from mouth to month is linear. In the model, this is achieved by means of a look up function (TABLI). As options, the prices can either be randomly or non-randomly generated. The normal distribution was assumed for random price determination. The mean is represented by the base prices (BP) multiplied by the estimated seasonal price index of the week. Standard deviation of prices for each month were computed from the series on irregular variations. These could be obtained from the outpmtof the Xrll variant of the Census Method II seasonal adjustment program. It was further assumed that the standard deviation of prices in a particular week is equal to the standard deviation of prices during the month the week falls on. The random component is obtained by generating a random number between 0 and 1. This is achieved by a built-in computer function in digital computers (RANF in CDC series and RANDU in IBM series). Then the normal standard deviate 2 corresponding to the random number is determined by'a function FNL. The estimated price is thus obtained by the following formula: P £81) xSI + 20’ 110 1. Compute a lZ-month moving average of the original series.2 This process smooths out the S x I from.the original series so the moving average is T x C. 2. Divide the original series by the 12~month moving average S x I. That is Original date . T x S x C x I Moving average T x S = S x I 3. Compute the monthly averages of the ratios-to-moving average (S x I) to remove the irregular fluctuations (I). The results are the seasonal indexes (S). Computing seasonal indexes on a desk calculator is a tedious and time consuming process. Fortunately, the procedures are easily programmed in a digital computer which allows the accurate computation of seasonal indexes for a large number of crops in a very short period of time. Moreover, some software packages have been developed recently to compute seasonal indexes and other time series analyses on prices. The particular software package used in this study is the X911 variant of the Census Method 11 seasonal adjustment program.3 Aside from.doing the three steps above, it does many other types of analyses. One of the useful features used in this study is the test for stable seasonality which is an F-statistics indicating whether it is reasonable to assume a regular seasonal pattern. fl 2The process-involves the following steps: (1) take the 12dmonth moving totals of the original series;- (2) divide by 12 to obtain the uncentered 12~month moving average; (3) "center" by taking the 2- month moving averages of the results of step 2. . 30.-S. Bureau of Census. The Xrll variant of the Census Method II Seasonal Adjusoment Program, Technical Paper No. 15 (1967 revision) U.S. Government Printing Office, Washington, D.C. 1967. 111 Source of data The primary source of data on crop prices was the Central Bank of the Philippines. Prices of various crops are available on a weekly basis from as early as 1948 to date for selected trading centers in the Philippines of which Tanauan, Batangas is one. For certain crops in which data were not available from the Central Bank, the prices were obtained from the Bureau of Agricultural Economics, the Bureau of Commerce, and other agencies. In cases where data were not available for the Tanauan market, price data for Manila markets were substituted. Finally, when no time series data were available for a crop (such as soybeans and sorghum), the seasonal price indexes of related crops were used as proxy. Table 7.1 shows the base prices and the monthly price indexes for each crop used in the study. 7.3 Generating Prices As stated earlier, the main function of the price generator is to provide the prevailing price of a crop in any given week. Thus, two items are specified in the sub-component: the week is question and the crop involved. The output of the sub-component is the price of the crop estimated to prevail at the particular week. In this study, the price of the crop is determined during the harvest week since no storage facilities are assumed. The week during which the scrop is harvested is determined in the model on the basis of the planting date and the number of weeks the crop matures. 112 .uoHuoom moHaoooom .uoononm wowooono oHoHuHsz .HmmH noonzom .usuonua on L OOH OOH OOH OOH OOH HOH OO OO OO OO HO OO OO.H ooeooe .O OO OO HOH OOH HOH OOH OOH HOH HOH OO OO HO OO.H . nooonom OOH OOH OOH OOH OO OO OO OO OO OOH OOH OOH O0.0 ononoe OOH OOH OOH OOH OO HO OO OO OO HO OOH OOH O0.0 ooeeoo OOH OOH OOH OOH OO HO OO OO OO HO OOH OOH O0.0 . nooomeez HOH OO OO , OO OO OOH HOH OOH OOH HO OOH OOH OH.H H anomnom HOH OO OO OO OO OOH HOH OOH OOH HO OOH OOH OH.H . onoO HOH OOH OOH OOH OOH OO HO HO OO OO OO HOH OO.H . ooHO O . 2 O O < H. O 2 HI 2 n H. HOH}: . IIIIIIII II IIIII III it. ooHnu _ . mono oxoooH oownm moon LL 4‘ .ooowooHHwnm .mowuouom .uaono mooHno> Ho monopuw ooHnu mHnuooa can mooHno doom w.H.~ oHnoH 113 where P is the estimated price during the given week, BP is the base price, SI is the seasonal index, 2 is the standard normal variable, and o is the standard deviation. Under the non-random option, the expected price is simply equated to the base price multiplied by the seasonal index. In the model, base prices are also allowed to vary as an option to allow for changes from year to year. If allowed to vary, two choices are available: linear or logarithmic trend. These two methods of price adjustments were supplied because it was found out that annual prices of crops included in the study showed either linear or exponential trends. Thus, associated to a crop is a code which either corresponds to a linear or exponential change. Linear adjustments in base prices are given by: BPt - BPo + rx where BPt - new based price at year t, BPo is the original base price, r is the average annual increase or decrease in price obtained by least-square regression methods, x is the number of years between year t and year 0. Exponential change is computed by: 81>t =- BPO (1 + r)x where BPt is the new base price at year t, 3P0 is the original base price, r is the average rate of change in price, and x is the number of years between year t and year 0. ~Table 7.2 shows the annual rates of change of prices for each crop and the corresponding shape of the trend line. The appropriate functional forms were determined by comparing the coefficients of 114 Table 7.2. Annual rates of change in price and the form of trend lines by crop, Cale, Tanauan, Batangas, 1956-1975. Rate of Shape of Crop, __f __7 chapgg‘ <___ trend line8 Rice 1.10 2 Corn 1.10 2 Sorghum. 1.10 2 Mungbean 1.11 2 Cowpea 1.11 2 Peanut 1.12 2 Soybean 1.06 2 Sweet potato 1.10 2 a1 - linear, 2 - exponential Source of basic data: Central Bank of the Philippines, Bureau of Agricultural Economics, Bureau of Commerce. 115 determination obtained by least-square regression method between linear and exponential trend lines. 7.4 Summary This chapter described the method of generating prices for use in the model. The main approach is to adjust the base price by means of seasonal indexes. Two options are available in the price determina- tion algorithm: random and non—random. Base prices are also allowed to vary either in a linear or in an exponential fashion. CHAPTER 8 LABOR UTILIZATION COMPONENT 8.1 Introduction The purpose of the labor component is to determine labor utilization by operation and time distribution of labor use of each planted crop. It also determines the total weekly labor use for the whole cropping pattern, compares it with weekly available family labor, and computes the»amount of labor hired each week. The labor component interacts primarily with the policy variables and the production component. The area planted determines the amount of labor required for land preparation, seeding, and other post- planting operations based on per-hectare labor requirements. The amount of fertilizer, weeding input, and insect and disease control applied to a crop also affect labor use. Finally, harvest and post- harvest labor are determined by the level of production. This implies that no labor is done when output is zero and that more labor is required with higher levels of output. 8.2 The Labor Utilization Cppponent Sub-Model As stated earlier, the labor component computes the following: (1) labor utilization by operation of each planted crop; (2) time distribution by week of total labor used of each crop; (3) total labor utilization by week of all crops; and (4) total labor hired by week. The computation of these items relies to a large extent on exogenous information which are provided as data to the model. These .116 117 include (1) labor requirements per hectare distributed by work and by operation for each crop,1 (2) harvest and post-harvest labor requirements per unit of output; (3) labor requirements per unit of fertilizer applied; and (4) family labor availability for each week of the year. Labor use by operation and labor use by time are determined through the use of the time by operation labor (TXOL) matrices (see Appendix I ). Before the totals by operations and by time are taken, however, the matrices are modified to allow for actual input usage and yield levels. Given fertilizer input, weeding labor input, and insect and disease control levels, labor use on fertilizing, weeding, and spraying are determined through fixed coefficients which are supplied as data.2 Harvest and post-harvest labor are determined through their respective labor requirement per unit of outputs which are also supplied as data. Harvesting is not usually accomplished in one week so total harvest labor must be allocated to each week of the harvest period. In this study, the harvest period was assumed to last for two weeks so that harvest labor was allocated into two equal parts in the TXOL matrix. Let lijt be an element of the time by operation labor (TXOL) matrix where 1 if the labor requirement for the jth operation (j-l, 1Twelve operations were distinguished in the model. The operaO tions are plowing, harrowing, other land preparation, furrowing, planting, off-barring, fertilizing, weeding, spraying, other care, harvesting, and post-harvest operations. 2In the case of weeding, however, the weeding labor input is simply carried to the relevant matrix element. 118 2,....,12), at time t (t-1, 2,....,24)3 of crop i (i-l, 2,....,8). Then, the labor use on operation j of crop i is given by 24 RLOPij ' i=1 lijt x A1 where A1.. is the area of crop i. Total labor use at time t of crop i is obtained by adding the labor requirements of each operation at time t. That is, The above calculations refer only to the relative timing of operations from the week of land preparation to the week of harvesting where t-5 is the planting period. The index t does not refer to any specific week of the year. To obtain a picture of the farm labor utilization for the whole year, the total labor use of crop i at time t or TLBit is assigned to the corresponding week n based on the" planting date specified.4 Let TLBYin - TLBit where TLBYin is the total labor use of crop i at week n, n-l, 2,..., 52. Then the total labor utilization of the farm during a given week is computed as the labor used by each crop during that week. That is, 3Since the planting operation is done at t-6, n is related to the planting date PD and t as follows: n - PD + t - 5. 4In simulation runs where planting date is allowed to vary according to the rainfall pattern, the specified planting may not be the actual planting date. 119 8 TLABn - §_l TLBYin where TLABn is the total labor utilization at week n. The amount of labor hired during each week was determined on the basis of total labor requirements and available family labor. Labor is hired if total labor requirements for a given week is greater than available family labor. There are some instances, however, wherein labor is hired even if the above condition is not met. This is so in the case of planting and harvesting, provided that the area planted is greater than three-tenths of a hectare and that total production is greater than 500 kilograms. This provision is in conformity with the observation that Batangas farmers usually hire labor for planting and harvesting, presumably so that the farmer can attend to supervisory activities. 8.3 SouréeS'of Data Available family labor Available family labor is based on the assumption that a farm family is composed of the farmer available for work full time, his wife available one-third manrequivalent and two children available one-half man-equivalent each or a total of 2.3 man-equivalents. It was assumed that on the average, a man-equivalent is available for work eight hours a day and six days a week. Therefore, the available family labor of 2.3 man-equivalents is about 110 man—hours per week.5 5Some downward adjustments may be necessary for certain weeks of the year such as those period when children are in school and during special events such as village feast and the Christmas season. 120 Labor requirements Table 8.1 shows the labor requirements by operation for each crop. These figures were obtained from the Cale weekly surveys and from economic data gathered from.agronomic experiments. The general pro- cedure was to add up the amount of time spent on each operation by each farm and the area of the farm. The average labor requirement for an operation is then obtained by dividing total time spent on each operation by the total area. There were several problems encountered in the process of tabula- tion. One was that in some farms, the data for an operation were either missing or no such operation was done. In this case, the procedure was simply to ignore those farms in which no data were available. Another problem was that for some crops, very few observa- tions were available because very few farmers planted those crops. Here, instead of using the Cale survey data, other sources were used. The.most important source of these was the economic data which were collected for agronomic experiments. In some cases, labor requirement from other similar crops (e.g. legumes) were used as substitute data as long as the same type of operation was concerned. Finally, there were some figures which did not seem reasonable, that is, either very large large or small were compared to the average. In this case, they were not included in the calculations. Labor use by time ,The time distribution of total labor utilization by crop and by operation were also tabulated. These data were the bases for the construction of the time by operation labor matrix which was mentioned .HH mom H m%o>nom thooz ono aonm ooumH=OHmo "monaom 121 O.HOO . O.OOO O.OOH O.OOO O.OOO O.OHH H.OOO H.OOH Hooon I O.OO O.OOH O.OO O.OOH O.OOH O.OH O.OO OeHHOOOHOeHOOooen O.OOH O.OOH O.OOH O.OOH O.OOO O.OOO O.OO O.OOH OeHoooenom O.HO I O.HO O.HO O.HO I I I oeoo eoOoO I I I I I O.OH I O.OH OeHHoneO O.OH O.HH O.OO O.OO O.OO H.OH O.OH O.OOH OnHOooz 0.00 O.HO 0.00 0.00 O.OH O.OO O.OO H.O OoHeHHHoeoe O.OO O.OO O.OO O.OO O.OO O.OO O.OH H.OO OeHneOOIOOO O.OO O.HO O.OO O.OO O.OO O.OO 0.00 O.OH OoHonHeHOeHOoOO O.OH O.OH O.OH O.OO O.OH O.OH H.OH O.OH OeHaonnne O.OH O.OH 0.0 O.OH O.O O.H O.HO 0.00 noHoonneone OeeH nonoO O.OO H.OO 0.0 O.OH O.OO O.OH O.OH H.HO OeHeonnom O.OO H.OO H.OO O.HO O.OO O.OO H.OO 0.00 OoHeoHe oumuom doom nooowm Immmwnom oommmu .wo:=.III :nou oon I. ooHumnono umoBm .Aonouoon\mnsonlooa GOV muwoouom .oozmoua .oHuu .moono an oowuonooo an muooaonHooon noooH .H.w oHAma 122 earlier. Table 8.2 shows the average labor requirements per hectare is in Cale, tabulated by week from.planting day of each crop. It should be noted that these figures are average figures. In simulation runs, the resulting labor utilization may be different depending on the level of inputs specified and the level of simulated physical output. Fortunately, Cale data are done on the daily basis so the construction of the labor by time matrix was relatively easy. It was noted, however, that farmers differ greatly in their timing of operations. Here, it was impractical to take average labor use by time period since it would result in figures which are inconsistent 'with total labor requirements. 7 The alternative was to take a sample 0f farmers (all farmers if number of observations was less than 15) and record the (1) frequency and (2) timing of each operation relative to planting date. From the sample data, the averages or model values of frequency and timing of operations were determined. A labor by time matrix was then constructed for each crop by distributing the labor requirements for an operation to each time an operation is performed. Some operations require more labor the first time it is done such as plowing and harrowing. On the other hand, some operations require less labor the first time it is done compared to the second or third time such as spraying. In these cases, labor requirement was distributed accordingly. In other cases, labor was simply divided equally among the number of times the operation.was done. 123 .HH moo H mhm>nsm thooz oHoo aonH ooumH30Hmo .GOMUQNHHHufl HOflQH OHQN OHOGOU GOSH“? wflfimmfiz Hoonoom .3003 wowuomHmo .useuoo Hoonzno Ho Ho>oH moHuHsmon men one ooHHHooom mHo>oH unooH one so wsHosoeoo noHHHo mus ooHumuHHHus noan on» .soHuoHoaHm can flH oQHUEHQW QQNGQUQQ HO GOfiuflNfiHflua HOQflH OMQHU>U USU UUOHHOH ”HAN“ USU Gfi awkflwwu ”SEQ OGOHUQNflHM03 HOQGH OHUN 090:0‘ mflflfifl> NaflmmMZG IIIIOOHOO O.OOO O.OOH O.OOO O.OOO O.OHH H.OOO H.OOH O.OH OH O.OOH O.OOH OH O.OOH O.OO O.OOH HO O.OOH 0.00 HO O.OOH 0.00 0.00 OO O.OOH O.OO O.HH O.OO OH O.HH O.OOH O.OOH O.OO OH O.HHH O.OOH O.OO O.OO HH O.OO 0.00 O.OOH H.OO OH O.OO O.OOH O.OO OH O.OOH 0.00 OH 0.0H O.O O.OH 0.0 0.0 H.OO OH O.OH O.O O.OO O.H 0.0 O.OH O.OO OH 0.00 O.O O.OO O.HH O.OH O.O 0.0 O.OO HH O.H 0.00 O.HH O.OH O.OH 0.0H OH O.H O.O O.OH O.OH O.OH O.OO I O.HO . O 0.00 I O.OO O.O O.HO O.HH O.OH H.O . O O.H 0.00H 0.00 O.HH O.OH O.HH I I . H O.OOH 0.00 O.HH O.HO O.HO O.HO 0.00 0.0H oO 0.0H O.HO H.O O.HH O.OO O.OH H.OH O.OO O 0.0H H.OO O.OH 0.00 O.OO 0.00 O.HH O.OO O O.OO 0.0H O.OO O.OO O.OO O.OH O.OH O.OO O O.OO I I I I I O.OO O.OO O 0.00 H oumuom coonwom uzooom somwnom mumsoo was: onoo oo«MI. 3003 uoosm A .onnmuoon\mnoonIumav mono no 3003 onuoOHo aonH 3003 soon now muuoaonHzoon noan .N.@ 0Hama 124 There were some crops for which no farm data were available as to timing of operations. The only recourse was to base the distribution of labor use on recommended cultural practices. For example, if the recommended practice is to apply fertilizer one-third at planting and two-thirds at 45 days after seeding, then one-third of the fertiliza- tion labor is allocated at planting and two-thirds is allocated at 45 days after seeding. Wage rates The assumed wage rate for hired labor was P6.00 per day or about 75 centavos an hour. It was noted that harvesting and threshing labor were usually paid in kind at an average rate of one-seventh of total production. That fact has been built-in into the simulation model to automatically compute for the harvest and threshing labor cost. There are several issues with respect to wage rate that remain unanswered. One is the;fact that wage rates for various type of operations have different wage rates. For example, plowing commands a higher wage rate than weeding. Another particularly important point which has as yet been ignored in the simulation model is the role of livestock (draft animals). A farmer's own draft animal is of course limited in capacity thus affecting the area that can hire men with animal power, a limit or the amount of operating capital restricts the.amount of hired animal power that can be hired. 8.4 Summary This chapter discussed the assumptions, the computational aspects and the sources of data of thelabor component. This component was designed to compute (l) labor utilization by operation of each planted 125 crop; (2) time distribution by week of total labor used of each crop; (3) total labor utilization by week of all crops; and (4) total labor hired by week. CHAPTER 9 THE COMPUTER SDMULATION MODEL 9.1 Introduction The purpose of this chapter is to provide a detailed description of the cropping systems simulation model. It describes the structure, the features, and the available options of the model. In addition, it describes the deck set-up required for running the model. It is felt that an understanding of how the model works is a prerequisite for the revision and the improvement of the model. Moreover, the potential user of the model will find the description of the various options and the program deck set-up in running a given job useful. 9.2 Structure of Computer Simulation Model The computer simulation model was written in FORTRAN computer language. The complete source listing of the program is found in Appendix II. The choice of FORTRAN as opposed to other languages1 was mainly influenced by the programming skills of the author. Although software packages were avilable for DYNAMO, GPSS, and GASP in the computer installation used, their use was not considered 1For a discussion of various computer languages suitable for simulation purposes, see Charlton, P.J., "Computer Languages for ' system simulation" in Dent & Anderson (edsx), System Analysis in .Agticultural Management, John Wiley and Sons, Australasia Pty. Ltd: Sydney, 1971, pp. 53-70. General purpose languages such as FORTRAN, ALGOL, AND PL/l) and special purpose languages such as CMPS, DYNAMO, GPSS, and SIMSCRIPT are described and compared. ,126 127 practical for the purpose at hand. It was felt that FORTRAN was adequate because of its universality in its usage and its flexibility in dealing with a number of discrete phenomena which are characteristic in this study. The computer model is composed of an executive routine (MAIN program) and eight major sub-programs. In addition, there are six minor sub-programs which are used by the major programs as needed. Figure 9.1 shows the flow chart of the main program. Note that it carries three functions, namely, job initialization,'run initialization, and simulation. Most of the job initialization is actually carried out is the compilation phase of the program.through the BLOCK DATA sub-program.which contains most of the exogenous data. However, when the subroutine CONTRL is called, it reads in the number of simulation runs desired, the title of the job, and other data which are not pos- sible to include in the BLOCK DATA. Before the first simulation run is executed, the job is first initialized through CONTRl which reads the mode and options desired in a particular run. CONTR2 initializes the policy variables, namely, area, planting date, fertilizer application level, weeding labor input. and input control expenditure level for each crop planted. These are either read from cards or set within the model depending on the mode of run. Given the values of the policy variables, and the options chosen, Simulation is carried out by calling the sub-programs RNGEN, PRODN, PRGEN, LABOR, CROPAC, and PRINT in sequence. These sub-programs correspond to the rainfall generator, production component, price 128 ‘ C snug TRUN- IRUN-I-l JOB INITIALIZATION CONTRl OPTION CHANGES RUN INITIALIZATION .1 Rainfall Generator Production Component Price > snmunou Generator ‘ Labor Component Accounting Printing Fig. 9.1. Flowchart of Main Program, Cropping Systems Simlation wdd. 129 generator, labor component, crop account component and the report generator, respectively. Recall that, as discussed in Chapter 4, land allocation is set by the user and is provided as an input to the prog- ram, hence no land allocator sub-program is called. The simulation phase is achieved simply by calling the above- mentioned sub-programs in sequence and not in an apparent interactive fashion. This is justified by.the fact that the model structure is such that the interrelationships among components are mostly "one-way". That is, if in the sequence subroutine A is called earlier than sub- routine B, then B depends on the values generated by A and not vice- versa. The operation and the resultant computed values of components called later depend on the values generated in the preceding sub-rou- tines called. Communication among subroutines and with the main program are achieved through labelled COMMON statements. Table 9.1 shows the structure of labelled COMMON statements in relation to the subroutines. The asterisks indicate that the subroutine uses some values of the variables which are included in the corresponding labelled COMMON variable. The values which are stored in the common memories are used by other subprograms and are eventually used by the printing subroutine or report generator (PRINT). Some of the values are passed on the next simulation run within the same job. 130 Table 9.1 Structure of labelled COMMON statements and the sub- routines using them. S U B R O U T I N E LABELLED cm 5 “O a a a 8 35’ H 5 o 8: g 8 8 g g E 5 g 0 Inc: o. 94 fl-I m ACC * * COND * a * * a k a ' * CONTR * a * * * * * * FCNVAL * * LAg * * * a * LABEL * a * * LEVELS * * PRDAT * * * * RNHIST * * * RNPAR * * * RRATES * * STAGE * s * s * smmr * * TMPDAT * * YIELD * a * 131 9,3 Features and Options , The next section discusses in detail the preparation of the input deck in accordance with the following features and options. Modes of Run. There are four modes of running the simulation program: Mode 1: Areas, planting dates, and input levels are specified by the user. The rainfall option is also set by the user. Mode 2: An input (fertilizer, weeding or insect control) chosen by the user is varied internally in the model with in- crements specified by the user. Other inputs are held fixed at levels (zero, low, medium, and high) desired by the user. The rainfall pattern can either be fixed or allowed to vary between runs. Mode 3: Planting dates are varied between runs while input . levels are held fixed. The different planting dates are set by the user and are provided to the model by means of input cards. As in Mbde 2, the rainfall pattern can either be fixed or allowed to vary between runs. Mode 4: Rainfall patterns are varied from.one simulation run- to another while input levels and planting dates are held fixed. The four modes of running the program.were designed to make the ,use of the simulation model.as flexible as possible. The different aspect of farm performance due to various influences such as input levels, rainfall pattern, and planting dates, could be studied sep- arately. 132 Rainfallygeneration options. There are five rainfall generation options available for use in the model. These options are designed I to give some flexibility on the kind of rainfall pattern that is desired for simulation. The options are as follows: 1. Generate rainfall based on the parameters of an incomplete gamma distribution for each week synthesized from actual data; 2. Randomly select a year between 1949 and 1975 and to use the historical rainfall data of the Ambulong weather Station for that year as the rainfall pattern for the simulation run; 3. Use the historical data of a pre—determined year; 4. Randomly select a high, medium, or low rainfall year on the basis of annual total rainfall and to use the historical data of the selected year in the simulation run. 5. Use the average weekly rainfall of the Ambulong Weather Station from 1949 to 1975 as rainfall pattern for the simulation run. The use of any option simply requires the specification of the option number. A seed for generation of a random number between 0 and 1 are required for option 1, 2, and 4 and must be provided by the user. In the case of option 3, the year desired is to be provided and in option 4, the level of rainfall year desired is also required. Price adjustment options- Prices are allowed to vary inter- seasonally through seasonal price indices which are provided in the model as data for each crop. However, base price could also be made to vary by trend if more than one run-is made and the additional runs are intended to be a simulation of succeeding years. If a trend ad- justment is allowed, the choices are exponential and linear adjustments. 133 The type of trend relationship which is appropriate for type of suitable for each crop'can be established. These are then provided to the model as data. Thus, it is possible for one crop to have a linear price trend adjustment while another crop has an exponential trend adjustment. 4 Another adjustment that can be made on prices is random or irre- gular variations. Here, the normal distribution is assumed. The base price multiplied by the seasonal price index appropriate for a given week is taken as the mean. Standard deviations or irregular price movements for each crop by month are also provided as data into the program. Through a routine which determines the normal deviate given a random number between 0 and l, the adjustment required for irregular or random price variations is also determined. Planting date options. The planting date of each crop is an input to the program, It is entered as a week number according to the code of weeks and corresponding dates as shown in Table 9.2. The default option in the model is for planting dates to be adjusted according to rainfall pattern. That is, if rainfall level is below a threshold level during the specified planting date, the latter is postponed by a week and the rainfall level during the new planting week is again re-tested if planting is possible. However, it may be desired that no adjustment in planting date is allowed, for example, . to determine the effect on yield of a crop if planted at a particular ~time of the year regardless of moisture conditions. Hence, an option of no change in planting date has also been provided. 134 Table 9.2 Dates and corresponding week codes used in the simulation model Date Week Date Week code code Jan 1-7 01 Jul 2-8 27 Jan 8-14 02 Jul 9-15 28 Jan 15-21 03 Jul 16-22 29 Jan 22-28 04 Jul 23-29 30 Jan 29-Feb 4 05 Jul 30-Aug 5 31 Feb 5-11 06 Aug 6-12 32 Feb 12-18 07 Aug 13-19 33 Feb 19-25 08 Aug 20—26 34 Feb 264Mar 4 09 Aug 27-Sep 2 35 Mar 5-11 10 Sep 3-9 36 Mar 12-18 11 Sep 10-16 37 ‘Mar 19-25 12 Sep 17-23 38 Mar 26-Apr 1 13 Sep 24-30 39 Apr 2-8 14 Oct 1-7 40 Apr 9-15 15 Oct 8-14 41 Apr 16-22 16 Oct 15-21 42 Apr 23-29 17 Oct 22-28 43 Apr 304May 6 18 Oct 29-Nov 4 44 May 7-13 19 Nov 5-11 45 May 14-20 20 Nov 12-18 46 May 21-27 21 Nov 19-25 47 May 28-June 3 22 . Nov 26-Dec 2 48 Jun 4 - 10 23 Dec 3-9 49 Jun 11-17 24 Dec 10-16 50 Jun 17-24 25 Dec 17-23 51 Jun 25-Jul l 26 Dec 24-31 - 52 135 Other options. Two other features which are useful to the user are options on the type of computer output and on statistical summary of results. The user can opt for a short print-out or a long print-out of the simulation output. The short print-out option yields (1) a rainfall generator output of the particular generation option in use; (2) a summary of planting dates, area, and input levels, number of dry weeks in each crop stage, and yield, harvest dates, and prices as determined by the simulation model; and (3) a summary of per- formance variables namely, yield, total production, gross returns, farm expenses, net returns and labor use. With the long print-out, in addition to the above computer outputs, the following are also printed: (1) available soil moisture by week, (2) labor utilization of cropping pattern by week showing available for family labor, required labor, and hired labor, (3) detailed cost and returns analysis for each crop planted, and (4) labor utilization by operation of each crop. Another option provides a statistical analysis of variables generated by several simulation runs of the same set of policy variables and cropping patterns. When this option is used, the means and standard deviations of yield, total production, prices, gross returns, farm expenses, net returns and labor utilization for each crop are computed and printed. Appendix 111 contains samples of types of output generated by the computer simulation model. 136 9.4 Deck Set-up for Running the Model The deck required for running the computer program.af the model is composed of 3 main parts: (1) the Job Control Language (JCL) cards, (2) the program.cards, and (3) the input cards. Job Control Langpage Cards- The job control cards required in any FORTRAN program.is dependent on the computer installation where the program.is run. In any case, they instruct the computer to do basically three things: (1) compilation, (2) linkage, and (3) execu- tion. The speed with which these functions are done depend on the computer. Source Pgogram. Normally, the source program deck can be run with the use of cards together with the input deck. However, the experience of the author is that it is very cumbersome and expensive since the length of the program.makes the deck very bulky and the comr pilation time very long, usually a minute and a half in IBM 370 Model 65. Considerable computer time could be saved by first compiling the program and saving the object deck on a magnetic tape or disk. On subsequent runs, only linkage and execution are the operations to be performed. Ipput Cards. The input cards instruct the program what job is to be performed. A job may consist of one or more simulation runs, but each job must utilize only one of the four modes of run discussed ' earlier. Basic to all jobs of any mode are the following three cards and the corresponding punching locations on a standard 80-column Hollerith card: ' 137 Table 9.3 Instructions for preparation of the option card. Columns g;:i::;;£me Format Explanation 1-9 IX. 19 Seed for random number generator ' (subroutine RANDU) 10 MODE Il Mode of simulation run 1 - Policy variables are set by the user 2 - A desired input is varied internally 3 - Planting dates are varied in each run 4 - Rainfall pattern is varied in each run 11 IROPT Il Rainfall generation option 1 - Gamma distribution 2 - Random year selection 3 - Specified year 4 - Predetermined rainfall level 5 - Average rainfall 12 LVR 11 Level of annual rainfall 1 - High 2 - Medium 3 - Low 13 INPUT I1 Input incremented while holding the rest fixed (Increments are specified by DELT) l - Fertilizer 2 - Weeding labor 3 - Insecticide 14 LVINP 11 Level of management inputs fixed by the user 1 - Zero 2 - Low 3 - Medium 4 - High 15 ' PSW 'Il - Planting date adjustment option 1 - No adjustment 2 - Adjust planting date according to rainfall situation Table 9.3 (continued) 138 Variable/ Columns Option Name Format Explanation 16 RSW 11 Price adjustment option 0 - None-random price adjustment 1 - Random price movements 17 LSW 11 Type of tenure of farm 0 - Owner operated l - Tenant operated 18 KPI 11 Print Option 0 - Short printout l - Long printout 19 KP2 11 Statistical summary option 0 - No statistical summary 1 - With statistical summary 20 IPOPT Il Trend Adjustment option for prices 0 - No trend adjustment 1 - With trend adjustment 21-24 IYR I4 Year specified if IROPT-3 Punched e.g. as "1971" 25-30 DL F5.2 The level of moisture or rainfall, in inches, below which drought occurs 31-35 DELT F5.2 Amount by which the variable input is incremented 139 Card 14:: Number of runs - Cols.'l-5 Card 2-: Title of job - Cols. l-8OI Card 3‘: Option card - See Table 9.3 The option card contains all the user-specified options which includes the mode of simulation run, rainfall generation option, planting date option, price adjustment options, printing option and threshold drought level. The other items in the option card are dependent on the mode of run and the other options. For example, if mode 2 is chosen, the input that is varied and the level of other fixed input must be specified. In addition, the level by which the input is varied per run must be specified in the option card Table 9.3 shows how the option card is prepared. The other input cards to be included depend on the mode of run desired of the simulation model. It will be recalled that with Mode l, the user specifies the policy variables, namely, area, planting date, input levels, and the rainfall generator option for each run. On the other hand, with the other modes, some of the variables are specified only for the first run and they either remain fixed in subsequent runs or are varied internally within the model. How these variables are varied also depend on the instructions given by the user as indicated in the option card. The remaining cards for each of the modes are as follows: . node 1. Under.mode 1, there are 16 policy cards that must be prepared for each run. Cards 4 through 11 are the policy cards for first croppingg of rice, corn, sorghum, mungbean, cowpea, peanut, soy- 140 bean, and sweet potato in that order. Cards 12 through 19 are the policy cards for second croppingg_of the same crops, respectively. Each additional run using mode 1 requires 16 additional policy cards. Each policy card is prepared by entering the area, planting date, and input levels of an individual crop included in the cropping pattern. Thus, if a crop is to be planted, Table 9.4 shows the respective columns and input format of each information. If a crop is not planted, its policy card is simply left blank. However, it has still be pro- vided. Table 9.4 Preparation of the Policy Card, Mode 1 Item Columns Format Area 1-5 F5.l Planting date 6-10 15 Fertilizer input (kg.N/ha) ll-15 F5.0 weeding labor (man-hours/ha) 16-20 F5.0 Insecticide (P/ha) 21-25 F5.0 .Mpdg_g, It will be recalled that under Mode 2, an input is varied internally while the other input are held fixed at levels specified by the user. The level of incrementation is equal to DELT .as indicated in the option card. The levels of other inputs are held fixed are determined by the option variable LVINP. When LVINP is equal to 1, it means that the input levels are to be specified by 141 the user. In this case, 16 policy cards have to be provided and are prepared the same way as indicated in Table 9.4. When LVINP has a value of either 2, 3, 4 or 5, the input levels are set withint the model corresponding to zero, low, medium or high, respectively. In this case, only a planting date card (card 4) has to be provided. The preparation of the planting date card is shown in Table 9.5. Mode 3. In mode 3, planting dates are varied in each run. Here, the additional cards to include are similar to those of mode 2 (l6 policy cards when LVINP equals 1 and a planting date card when LVINP is not equal to 1). With the exception that there will be as many sets of policy cards or planting date cards as there are runs. Mode 4. Under Mode 4, only the rainfall pattern is varied in between runs. The cropping pattern, input levels, and planting dates are fixed during the first run. Rainfall variation is achieved by .specifying rainfall optional, 2 and 4. The additional cards required are the same as in mode 2, that is, 16 policy cards if LVINP equals 1 or a planting date card if LVINP is not equal to l. 9.5 Summary The purpose of this chapter was to describe the structure of the simulation model; to describe its various features and options available; and toprovide instructions on how to prepare the program deck and run the model. This chapter would be particularly useful to those.who wish to run the model themselves. Table 9.5 Preparation of the planting date card Columns Crop 1-5 .First crop rice 6-10 First crop corn 11-15 First crop sorghum 16-20 First crop mungbean 21-25 ‘First crop cowpea 26-30 First crop peanut 31-35 First crop soybean 36-40 First crop sweet potato 41-45 Second crop rice 46-50 Second crop corn 51-55 Second crop sorghum 56-60 Second crop mungbean 61-65 Second crop cowpea 66-70 Second crop peanut 71-75 Second crop soybean 76-80 Second crop sweet potato 142 CHAPTER 10 EXPERIMENTATIONS, RESULTS, AND DISCUSSION 10.1 Introduction. In this chapter, the cropping systems simulation model as described in the preceding chapter is put to use. A number of experiments were performed and the results are discussed below. As stated earlier the model was developed primarily for evaluating cropping patterns and as an aid in the design and testing of cropping sytems. Thus a number of simulation runs concern the evaluation of cropping patterns which are of interest in the Philippines. However, the model was also used to simulate other experiments which are usually conducted in the field. specifically, the various experiments conducted are as follows: (1) yield response of various crops to different levels of nitrogen; (2) yield response of various crops to different levels of weeding labor; (3) evaluation of specific cropping patterns in terms of selected performance variables with respect to variations in rainfall and product prices; (4) comparison of economic performance of cropping patterns under favorable and unfavorable conditions; (5) comparison between intensive and non-intensive cropping patterns, and (6) com- parison of planting dates and yields using two strategies of choice of planting dates. V It Should be emphasized at the very outset that the results from these various experinmtations simply reflect the assumptions regarding 143 the model structure and the coefficients and parameters used. Whatever limitations there are of the model structure as well as of the estimates of‘the parameters are carried over in the results. It is recognized that a number of components need further refinements and many of the estimates of parameters and coefficients are still unsatis- factory. Hence, the results of the experiments conducted here should best be treated as illustrations of the usefulness and potentials of the simulation model. It is felt, however, that as long as the limitations are recognized, the present model could be of practical use not only to researchers in multiple cropping but also to farmers. 10.2 Results of Experiments 10.2.1 Yield response to nitrogen fertilizer at zero, medium, and .Ei§h levels of other inputs The purpose of this experiment was to test the simulation model for realism of estimated yield and income levels corresponding to various levels of fertilizer input. This was done using Mode 2 of the model where fertilizer is incremented in steps of 20 kilograms of nitrogen per hectare, holding the other inputs and the rainfall pattern constant. Weeding labor and insect control were held fixed at three levels: zero, medium, and high levels. The medium.level of other inputs consisted of 60 man-hours of weeding labor and P300 of insect control (insecticides) per hectare. The high level of other inputs consisted of lOO.man-hours of weeding labor and.P600 of insect control per hectare. Using the third option of the rainfall generator, 144 the rainfall pattern was held fixed using the 1973 historical rainfall data, a year which had a relatively good weather. Tables 10.1 to 10.3 show the simulated yield response of various crops to nitrogen fertilizer at zero, medium, and high levels of other inputs, respectively. Palay (rice) and Corn 1 are wet season crops with their planting dates set at week 18 (April 30 to May 6). The other crops are dry season crops with their planting dates set initially at week 38 (September 17-23). The actual planting dates will of course depend on soil moisture conditions and in the case of dry season crops, on whether the first crop has been harvested. As expected, higher levels of fertilizer resulted in higher yields for all crops although diminishing yields are apparent for very high levels of fertilizer application. The tables also show the fact» that some legumes such as mungbean, cowpea, and soybean are relatively un- responsive to high levels of nitrogen.- These observations of course reflect the base yields and the reduction rates which were used. It should be noted that yield levels of each crop increase as the level of weeding labor and insect control are increased. Yield levels are considerably higher in the case of high weeding and insect control levels than those at zero levels. As an illustration, figure 10.1 shows that the fertilizer response curve of upland palay is higher for high weeding and insect control levels than at zero levels. Table 10.4 shows the net returns of the various crops at different levels of fertilizer. These figures also reflect the prices 145 Table 10.1. Simulated yield response to fertilizer, zero weeding and insect control (tons/hectare).a Fertilizer level (kg N/ha) Crop 20 40 6O 80 100 120 140 Palay 2.1 2.5 2.8 3.0 3.1 3.2 3.1 Corn 1 2.2 2.6 3.0 3.2 3.3 3.4 3.3 Corn 2 1.6 1.9 2.1 2.3 2.4 2.4 2.4 Sorghum 0.9 1.1 1.2 1.3 1.4 1.4 1.4 Mungbean 0.6 0.7 0.8 0.8 0.8 0.8 0.8 Cowpea 0.9 1.0 1.1 1.1 1.1 1.1 1.1 Peanut 1.3 1.5 1.7 1.8 1.9 1.9 1.9 Soybean 1.1 1.2 1.3 1.4 1.4 1.4 1.4 Sweet potato 8.0 9.0 10.1 10.7 11.3 I 11.3 11.3 aMode-2, 1973 rainfall. Initial planting dates for palsy and corn 1 were set at week 18; the rest were set at week 38. 146 Table 10.2. Simulated yield response to fertilizer, medium weeding and insect control (tons per hectare).8 Fertilizer level (kg N/ha) Crop- 20 4O 60 80 100 120 140 Palay 2.4 2.8 3.2 3.5 3.6 3.6 3.5 Corn 1 2.3 2.7 3.1 3.3 3.4 3.5 3.4 Corn 2 2.3 2.7 3.1 3.4 3.5 3.5 3.4 Sorghum 2.4 2.9 3.3 3.5 3.6 3.7 3.6 Mungbean 1.1 1.2 1.3 1.4 1.4 1.3 1.2 Cowpea 1.4 1.6 1.8 1.8 1.8 1.8 1.6 Peanut 2.1 2.4 2.7 2.9 3.1 3.1 3.1 Soybean 1.8 2.0 2.2 2.2 2.2 2.2 2.0 Sweet potato 11.8 13.5 15.2 16.1 16.9 16.9 16.9 aMode-2, 1973 rainfall, weeding input - 60 man-hours/ha., insect control - P300/ha. Initial planting dates for palsy and corn 1 were set at week 18. All others were set at week 38. 147 Table 10.3. Simulated yield response to fertilizer, high weeding and insect control levels (tons/ha). Fertilizer level (ng/ha) Crop 20 40 60 80 100 120 140 Palay 2.8 3.3 3.8 4.1 4.2 4.3 ‘4.2 Corn 1 3.1 3.7 4.2 4.5 4.7 4.8 4.7 Corn 2 2.2 2.6 3.0 3.2 3.3 3.4 3.3 Sorghum 1.3 1.6 1.8 1.9 2.0 2.0 2.0 Mungbean 0.9 1.1 1.1 ‘1.2 1.2 1.2 1.2 Cowpea 1.3 1.5 1.6 1.6 1.7 1.6 1.5 Peanut 1.9 2.2 2.5 2.6 2.8 2.8 2.7 Soybean 1.7 1.9 2.0 2.1 2.1 2.0 1.9 Sweet potato 12.1 13.5 15.3 16.1 16.9 17.0 16.9 aMode - 2, 1973 rainfall, weeding input - 100 man-hours/ha., insect control - P600/ha. Initial planting dates for rice and corn 1 were set at week 18; the rest were set at week 38. 148 Honusou nooooH one one: so; .a> nuH: .noaHHHunom on comm osoHem no uncommon oHoH» sou-Hanan H.OH onsaHh 53:53:... 2.925. 0! ON. 00. on om 9 ON 0 . 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A significant point that should be noted is that as fertilizer level is increased net returns also increase but only up to a certain point. Further increases in fertilizer resulted in decreasing net returns. In the case of rice, for example, net returns increased as fertilizer level is increased from.zero to 80 kilograms of nitrogen. At higher levels, net returns started to decrease. Thus, this model is useful in determining the Optimal level of a particular input, given the level of other inputs. The results stated above, as mentioned earlier, simply reflect the assumptions that were incorporated in the production component and hence the outcome is not entirely unexpected. However, the value of such a feature in the model is that given the rainfall pattern and the level of other inputs, the yield of a crop can be predicted easily for a particular level of fertilizer application. To the extent that the reduction rates approach is valied, the joint effects of rainfall pattern, fertilizer, weed control, and insect control are all accounted for. 10.2.2 Yield response to weeding labor at high vs. low fertilizer and insect control levels This experiment was done to test the simulation model for realism of crop yield response to various levels of weeding labor at different levels of fertilizer and insect control inputs. The results of this experiment were also obtained using Mode 2 where weeding labor is incremented in steps of 20 man-hours per 151 hectare while holding fertilizer and insect control levels fixed. The rainfall pattern in 1973 was also used all throughout. The low levels of other inputs consisted of 20 kilograms of nitrogen fertilizer and P100 of insecticides while high levels of other inputs consisted of 100 kilograms of nitrogen fertilizer and P600 of insecticides. Tablele.5 and 10.6 show the simulated yield of various crops corresponding to different levels of weeding labor at low and high levels of other inputs, respectively. As expected, yield levels were higher at high fertilizer and insect control levels than at low levels for all crops. Moreover, yield increases as weeding labor is increased but only up to a certain point. Additional weeding labor has no effect on yield. Figure 10.2 shows the graphs of the simulated yield response of upland rice to weeding labor at low and high levels of other inputs. Note that the response curve at high levels of fertilizer and insect- icide is considerably higher than that of low levels of fertilizer and insecticide. As in the preceding experiment, the results in this experiment simply reflect the assumptions concerning the reduction rates, the base yields, and the yield equation. However, the prediction of yield is facilitated by the model. 10.2.3 Evaluation of specific cropping patterns Five specific rice-based cropping patterns were evaluated for biological and economic stability with respect to rainfall and price variability. The cropping patterns are: (l) rice-mungbean, (2) rice-- soybean, (3) rice-sweet potato, (4) rice-peanut, and (5) rice-corn-corn. 152 Table 10.5. Simulated yield response to weeding labor, law a fertilizer and insect control levels (tons/ha). Weedipg labor (manhours/ha), Crop 20 40 60 80 100 Palay 2.3 2.4 2.6 2.6 2.7 Corn 1 2.6 2.7 2.9 3.0 3.0 Corn 2 1.8 1.9 2.0 2.1 2.1 Sorghum 1.1 1.1 1.2 1.3 1.3 Mungbean 0.7 0.8 0.8 0.9 0.9 Cowpea 1.0 1.1 1.2 1.2 1.2 Peanut 1.6 1.7 1.8 1.8 1.8 Soybean 1.4 1.5 1.5 1.6 1.6 Sweet potato 9.9 10.3 10.9 11.5 11.5 aMode - 2, 1973 rainfall, fertilizer - 20 kg N/ha, insect control - PlOO/ha. Planting dates for palsy and corn 1 were set at week 18; the rest were set at week 38. 153 Table 10.6. Simulated yield response to weeding labor, higha fertilizer and insecttcontrol levels (tons/ha). weedingylabor (manhours/ha) Crop 20 40 6O 80 100 Palay 3.6 3.8 4.1 4.2 4.2 Corn 1 4.1 4.3 4.5 4.7 4.7 Corn 2 2.9 3.1 3.2 3.3 3.3 Sorghum 1.7 1.8 1.9 2.0 2.0 Mungbean 1.0 . 1.1 1.2 1.2 1.2 Cowpea 1.4 1.5 1.6 1.6 1.7 Peanut 2.4 2.5 2.7 2.8 2.8 Soybean 1.8 1.9 2.0 2.1 2.1 Sweet potato 14.6 15.2 16.0 17.0 17.0 aMode - 2, 1973 rainfall, fertilizer I 100 kg N/ha., insect control a P600/ha. Planting dates for rice and corn 1 were set at week 18, other crops at week 38. 154 Honuooo nooooH oso nouHHHunoh and .a> :uHm $2.3 9.33: 3 O.H-O Hos-H.HO «6 cocoa-3H 30H» Han-His... H.OH 83: 88. 06.30395. Santos Ow. oo. 8 8 0O. Ow o . O H H H H H o \ ON 83309.? IDIII I z 9.8 c1. I . 16» 8.98.8. 80¢ \ 0..» 29.09? 01 I .2} 155 The general procedure was to let the rainfall pattern and prices vary randomly over several runs and to compute the means and standard . deviations of selected performance variables. The means are to be interpreted as the expected values of the performance variables while the standard deviations are measures of the variability of the per— formance variables. The latter may give us an idea of the risk associated with the growing of a particular crOpping pattern. Ten runs of each pattern were done using Mode 4 of the model in which rainfall pattern was varied for each run while the input levels were held fixed at 100 kg of nitrogen fertilizer, 100 man-hours of weeding labor, and P300 worth of insect control (medium levels). The rainfall pattern was randomly generated using option 1 which makes use of the parameters of an incomplete gamma distribution. The prices were also allowed to vary randomly based on the base prices, seasonal indexes, and standard deviations assuming normal distribution. In each pattern, the area of farm was set at one hectare. The first crop was rice followed by another crop. The planting date of rice was initially set at week 18 while those of the other crops at week 38. In the case of the third crop corn, the planting date was set at week 50. Actual planting dates were, however, allowed to vary according to the rainfall pattern generated. Tables 10.7 to 10.11 present the means and standard deviations of yield per hectare, crop prices, gross returns, farm expenses, net ‘ returns, and labor utili-ation of each crop for the five cropping patterns. It was noted that the variations in yield over the ten simulation runs were very small for all patterns. 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N nuou H :uoo 00am N suou H :uoo ouwm 0Hnnwun> . coaumw>mv vumvnwum cum: .musmaw mo Ho>mH aawvma .mmuwum van Hammcwmu aoccwu nuwa :umuuam unannouo nuoolauOUIouwu onu mo mmanawuw> kuuuamm mo maowuaw>ov vamnamum can mamuz .HH.¢H.oHaaa, 161 explained by the fact that variations in yield were due solely to the variations in rainfall since input levels were held fixed during these runs. Yield varies from one run to another only in the event that the number of drought weeks in each stage of crop growth also varies. There were not enough variations, however, in the number of drought weeks resulting from the specified drought level (0.49 inch). Thus, the results reflect the rather crude and weak link between the rainfall variability and yield changes. This points to the need for a more refined production component which relates week to week variations in rainfall to changes in yield. The variations in gross returns are explained by the variations in yield and prices. The simulated prices appear to be reasonable. The variations in farm expenses are also explained by yield and price variations even if the input levels are held fixed since they both affect the cost of seeds, harvesting and threshing, and landlord's share. In this particular experiment, and in general using Mode 4 of the simulation model, variations in labor utilization are explained solely by variations in yield since input levels are held fixed. Labor utilization increases when yield increases since more harvest and post-harvest (threshing, husking, etc.) labor are required when total production is greater. Thus, the low standard deviations of labor utilization for almost all crops in the cropping patterns also ‘.-reflect the low variations in yield over the ten simulation runs. Table 10.12 summarizes the net returns and labor utilization of each of the five cropping patterns tested. In terms of net returns, 162 Table 10.12. Comparison of net returns and labor utilization of selected cropping patterns due to joint rainfall and product price variability. Net returns Labor use Cropping pattern (?/ha) (man-hours/ha) Rice-mungbean 3652.33 1376.1 Rice-soybean 4038.46 1238.7 Rice-Sweet potato 8115.85 1286.3 Rice-peanut 5210.93 1331.8 Rice-corn-corn 2230.90 1325.4 3Average of 10 runs, mode 4, rainfall option 2, random prices, fertilizer 8 60 kg N/ha., weeding labor - 60 man—hours/ha., insect control - P300/ha. 163 the rice-sweet potato cropping pattern showed the highest net returns per hectare of 18116,.followed by rice-peanut, rice-soybean, rice- mungbean, and rice-cornecorn in that order. In terms of labor utiliza- tion, the cropping pattern which was the most labor intensive was rice mungbean with 1376 manrhours per hectare followed by rice-corn- corn, rice-peanut, rice-sweet potato, and rice-soybean in that order. 10.2.4 Comparison of yields between favorable and unfavorable conditions The objective of this run was to determine the yield differences as well as differences in other performance variables when each crop is subjected to extremely unfavorable and extremely favorable growing conditions. Unfavorable conditions were simulated by using zero fertilizer, weed control, and insect control levels and low rainfall years. 'On the other hand, favorable conditions were simulated by high management levels along with high rainfall years. High and low rainfall years were randomly obtained using option 4 of the rainfall generator. Table 10.13 shows the means of five runs of the resulting yields of each crop under both conditions. It can be seen that the yield differences are considerable. Yield differences are particularly large for grains compared to legumes owing to the fact that in the model, the former are more fertilizer responsive than the latter. While the differences in yield could be attributed to the large gap ” in;mmnagement levels, the use of high rainfall versus low rainfall also contributed to the difference in yields since high rainfall years would show less drought weeks than low rainfall years. Table 10.14 164 Table 10.13. Comparison of simulated yield, favorable vs. - unfavorable conditions (tons/ha). Yield (t/ha) Crop UnfavorableU Favorableu 2 diff. Palay 1.53 4.23 176 Corn 1 1.61 4.56 183 Corn 2 1.56 4.71 202 Sorghum. 0.82 2.73 233 Mungbean 0.66 1.44 . 118 Cowpea. 0.88 1.92 118 Peanut 0.99 3.33 236 Soybean 1.07 2.42 126 Sweet potato 7.11 18.24 157 aMean of 5 runs; planting dates for palay and corn 1 were set at week 18 and the rest at week 38. bLow rainfall years, zero input of fertilizer, weeding labor, and insect control. cHigh rainfall years, fertilizer - 100 kg N/ha., weeding labor - 100 manehours/ha., insect control a r600/ha. 165 .on\aouunoo uoomnw mo 0003 can .uoan wowvoms mo muoonleoa_oca ..os\Hmuwkuuou mo 2 MM Goa use mama» Hanmcwmu em“: up woundsawm mums moowuwvooo manouo>mm .Houucou uuomsw coo mswvooz .uouwawuuom mo uoeew cums one whom» Hammewmu sod ha wouoaoawm mos maaouo>omn= .msdu m>wm mo amaze News euom «new «mam seems. Home combos human ceon emeN , «mad men name aNQm newsman mega sewn mama new moaoa «was saunas ones anon ones can comm inns amazon ocun e~s~ ooo~ one cows seam sausage: snag emu some men meam New aaemuom omen sens once man «man «mes N coco «Nun same mama mam some «sea A euoo anon same came com amen «was enema MQCHSUUH D h mu GOO H.— .m mGquUWH WORD uoz mono mmouu Aonxmv «.moowuwvaou some“ new Honuoos manouo>mmoo .m> manmuo>mm Hove: mono hp oosmahomume owaoeooo mo nomwuoeaoo .eH.OH canoe 166 further shows the considerable differences in gross and net returns of each crop subjected to extremes in management levels and rainfall conditions. 10.2.5 Comparison between intensive and non-intensive cropping patterns The objective of this run was to compare the gross returns, crop costs, net returns, and labor utilization between an intensive and a non-intensive cropping pattern. The non-intensive cropping pattern consisted of one hectare of palay in the wet season followed by one hectare of corn in the dry season. The intensive cropping pattern consisted of 0.6 hectare of palay and 0.4 hectare of corn in the wet season and 0.5, 0.3, 0.1 and 0.1 hectare of corn, sorghum, mungbean, and cowpea, respectively in the dry season. Both cropping patterns were subjected to both low and high management levels. Nine runs were done on each cropping pattern for both input levels. Rainfall was varied randomly using the first option of the rainfall generator. Table 10.15 shows the results of the simulation runs. It is apparent that in both cropping patterns, high management or input levels consistently resulted in higher gross returns, crop costs, net returns and labor utilization than low management levels. However, it is interesting to note that in the intensive cropping pattern with low input levels, the economic measures were higher than the non-intensive cropping pattern. Under high input levels, gross and net returns were higher with the nonrintensive cropping pattern. This can be attributed to the fact that the yield reduction rates for palay (rice) and corn in the model are such that they are more responsive 167 Table 10.15. Comparison between intensive and non-intensive cropping patterns at low and high input levels.a . . b . c Non-intensive Intensive Variable Low High Low High Cross returns 3710 8570 4819 8492, Crop costs 948 2667 1128 2760 Net returns 762 5903 3691 5735 Labor utilization (man-hours) 1160 1460 1254 1940 Effective crop area (hectares) 2.0 2.0 2.0 2.0 aMeans of nine runs, mode 4, rainfall option 1. Low inputi levels: fertilizer = 20 kg N/ha., weeding labor - 20 man-hours/ha., and insect control - PlOO/ha. High input levels: fertilizer - 100 kg N/ha., weeding labor - 100 man-hours/ha., and insect control - P600/ha. bl ha palay - 1 ha corn. cWet season: 0.6 ha palay, 0.4 ha corn. Dry season: 0.5 ha corn, 0.3 ha sorghum, 0.1 ha mungbean, and 0.1 ha cowpea. 168 to high input levels especially to fertilizer. As expected, the labor utilization levels are higher in the intensive cropping patterns at both levels of input. I ' 1 \ 10.2.6 Comparison of planting dates andgyields usin§_two strategies for choice of plantingfldate Two strategies for choosing planting dates were examined to determine their effect on the feasibility of a three-crop sequence, and the yields of the crops in the sequence. The simulated pattern was rice, followed by corn, followed by cowpea. One strategy was to prepare the land during the earliest week after March 1 or week 10 when 0.5 inch of rainfalls‘ and then to plant during the subsequent week when rainfall is 0.5 inch. The second strategy was similar, but with May 1 to 7 or week 18 selected as the earliest planting week. The rainfall option used was to randomly select an actual year of rainfall from 1949 to 1975 (option 2). No fertilizer, insecticide, or weeding labor applications were assumed. Nine runs were performed under each planting strategy, one rice crop was planted during the week March 5-11, all other planting dates were much later and closely comparable to the rice planting dates under the second strategy. Table 10.16 shows that an average diff- erence of 1.4 weeks or roughly ten days resulted from following the different strategies. The average planting date in the first strategy is 18.4 as compared to the intended planting date of week 10 or an average.delay of 8.4 weeks. This.can be attributed to the fact that .the rainfall pattern in Cale, Batangas is such that it is not feasible to plant any crop before week 17 (April 23-29). ,The average 169 Table 10.16. Comparison of planting dates and yields using two strategies for choice of planting date, low input levels.a Plant ASAP after March 1 Plant ASAP after May 1 Rainfall Palay Corn Rainfall Palay Corn years date date years date date 1965 21 40 1950 26 45 1960 20 39 1966 19 38 1958 22 41 1953 19 38 1956 20 39 1957 20 39 1955 21 40 1951 18 37 1971 17 36 1975 19 38 1974 18 37 1962 19 38 1952 10 30 1963 20 , 39 1973 17 36 1951 18 37 Av. date 18.4 37.6 Av. date 19.8 38.8 Av. yield, t/ha Av. yield 1.3 1.7 1.6 1.7 aMode 4, rainfall option 2, fertilizer = 20 kg N/ha., weeding labor a 20 manrhours/ha, insect control a P100/ha. 170 planting date in the second strategy is about week 19.8 as compared to the intended planting date of week 18. The average simulated yield of rice over the nine runs in the first strategy is 1.27 tons per hectare while that in the second strategy is 1.59 tons per hectare. The difference of about 0.3 ton is attributed to the more favorable rainfall distribution during the growing period of rice after week 18. The tendency of Cale farmers to plant at about the same time each year has been noted previously by researchers working in the area and this has been casually attributed to custom. However, it is apparent that the physical environment, combined with the motivation to plant early, almost fully explains the tendency. Corn yields were fairly uniform under both strategies, around 1.7 tons per hectare. This, and the fact that corn crops were usually planted in the earliest available week after rice harvest (i.e., no delays waiting for rain) indicate that soil moisture is usually ample during August. The yield reductions resulting from early planting would be more than offset in an average year by better cowpea yields. In 8 out of the 9 years when an early rice planting strategy was followed, a copwea crop was feasible and the average yield was 0.64 ton per hectare. In comparison, cowpea crop was possible in only 4 out of the 9 years when a late planting strategy was followed, with an average yield of 0.32 ton per hectare. .Although an average lO-day delay in planting the rice crop is small, it may nevertheless be critical to feasibility of planting a third crop towards the end of the wet season. 171 10.3 Summary In this chapter, several experiments were conducted to test the usefulness and potentials of the cropping systems simulation model developed. The experiments were (1) yield response of various crops to different levels of nitrogen; (2) yield response of various crops to different levels of weeding labor; (3) evaluation of specific cropping patterns in terms of selected performance variables with respect to variations in rainfall and product prices; (4) comparison of economic performance of cropping patterns under favorable and unfavorable conditions, and (5) comparison of planting dates and yields using two choiCes of planting dates. The yield response experiments simply showed that yield increases as the level of an input is increased, holding the other inputs fixed. Moreover, the yield response curve is higher, the greater the levels of the other inputs. Among the cropping patterns evaluated, rice- sweet potato and rice-peanut sequence seem to be promising in terms of level of net returns. As to be expected, crop yields were higher under favorable weather conditions and high input levels. Intensive cropping patterns result in higher labor utilization than non-inten- sive ones although the net returns depend on whether input levels, particularly nitrogen fertilizer, are kept high or low. Finally, it was found that the planting date for the first crop rice tended to be around week 18 or 19 no matter how early the intended planting date is set. Chapter 11 SUMMARY, CONCLUSIONS, AND SUGGESTIONS FOR FURTHER RESEARCH 11.1 Summary This study was conducted with the following objectives: (1) to develop a systems model for simulating upland rice-based multiple cropping systems, and (2) to evaluate by means of the computer simu- lation model the effects of environmental and economic influences, as well as alternative cropping patterns on the performance of the system. It was felt that a systems analysis and simulation approach of studying cropping systems was possible, useful and considered a worthwhile alternative to traditional methods of analysis such as linear programming. The simulation model developed in this study has been designed for an upland area. Eight upland crops were included, namely rice (palay) corn, sorghum, mungbean, cowpea, peanut, soybean and sweet potato. The data used were obtained mostly from the weekly economic surveys in Cale, Tanauan, Batangas from 1973 to 1975 conducted by the Multiple Cropping Project at the International Rice Research Institute in the Philippines. The major components of the simulation model are (1) land allo- cation component, (2) rainfall generator, (3) production component, (4) price generator, (5) labor utilization component, and (6)income component. The land allocation component has the function of allocating 172 1.73 limited land over time to various crop enterprises. The method for land allocation in this study was one wherein an experimenter allo— cates land by specifying a cropping pattern as well as the area and planting dates of each crop. The function of the rainfall generator is to provide to the model the rainfall pattern for the simulated year. There were five options developed in generating rainfall. The choice largely depends on the mode with which the simulation model is run. The generated rainfall data have some bearing on actual planting dates and on the yield of crops. The production component has the function of determining the yield of each crop based on (1) fertilizer level, (2) weed control level, (3) insect control level, and (4) number of drought stress weeks during the vegetative, reproductive and maturation stages of crop growth. The main approach used in the prediction of yield is the reduction rates approach. The approach suggests the use of potential yield as the initial point and then a series of reduction factors are applied to the potential yield to account for input levels and environmental influences which depart from optimal levels. The price generator estimates the price of a crop at any given week of the year. A relatively simple method was employed wherein the price at a given week is estimated by means of seasonal price ' indexes and base prices. 'The prices could be made to vary randomly '” under a normal distribution and also to change in trend as options. 174 The labor component merely accounts for the use of labor in the production process. For some farm operations labor requirements by time distribution were provided exogenously to the model. The labor requirements such as fertilization, weeding, harvesting and threshing were, however, determined endogenously depending on the level of the relevant input or the level of output. Thus, given the areas, input levels, and planting dates of each crop planted, the weekly labor utilization pattern is obtained for the entire simulated year. This component also determines the amount of labor hired by the farm. Finally, the crop accounting component has the function of keeping track of all farm income and expenses. It also determines most of the performance variables, namely, total production, value of production, cost of production, and net returns of each crop planted and for the whole cropping pattern. The simulation model could be run in four modes. In Mbde 1, areas, planting dates and input levels are specified by the user. The rain- fall option is also set by the user. In Mode 2, a chosen input is varied internally in the model with increments specified by the user. The other inputs are held fixed internally either at zero, low, medflmn or high levels. Alternatively, the user could opt for other levels of inputs desired. The rainfall pattern can either be fixed or allowed to vary between runs. Under Mode 3, planting dates are varied from one “.run to another while input levels are held fixed either at zero, low, medium, or high levels or some other desired levels. Again, the rain- fall pattern can either be held fixed or allowed to vary between runs. 175 Finally, under mode 4, the rainfall pattern is varied during each run while holding input levels and planting dates fixed. With these different modes of usage, various experiments are possible with the model. For example, Mode 2 may be used in yield response experiments while the evaluation of economic and biological stability of a cropping pattern with respect to rainfall variability can be done using mode 4. Several experiments were conducted using the computer simulation model primarily to show its various uses, capabilities, and flexibility. These were of the following types: (1) yield response to various levels of inputs, (2) performance of specific cropping patterns with respect to variations in rainfall and prices,(3) comparison of performance of crops between favorable and unfavorable conditions, (4) comparison between intensive and non-intensive cropping patterns, and (5) compa- 'rison of planting dates and yields using two strategies for choice of planting dates. The results of these experiments were discussed in Chapter 10. 11.2 Conclusions The cropping systems simulation model developed in this study can be a very useful tool in the design and testing of cropping systems. Its primary usefulness is in the evaluation of a particular ‘cropping pattern in terms of economic profitability, stability of"' economic returns, and.efficiency of labor utilization. As demonstrated in Chapter 10, the model can be used in several other ways such as 176 for the comparison of economic performance of a cropping pattern under unfavorable and favorable weather and price conditions; comparison between intensive and non-intensive cropping patterns; etc. Specifically, the uses and capabilities of the model are: (1) it can evaluate the profitability of a crOpping pattern and show the most profitable levels of inputs; (2) it can evaluate the stability of eco- nomic returns of a cropping pattern to rainfall variations; (3) it can be used to evaluate the economic stability of a cropping pattern to price fluctuations; (4) it can determine whether a particular cropping pattern is biologically viable on the basis of predicted yields; (5) it can determine the detailed labor utilization by operation for each crop and the labor utilization of the whole cropping pattern broken down by family labor and hired labor. While the present model is specifically applicable to upland areas in Batangas province, Philippines, it can be adapted to other upland areas with the appropriate modifications in the relevant parameters. Furthermore, it can easily be revised for application to lowland areas with irrigation as a controllable input. Despite its potential uses, the model developed thus far must be considered tentative in view of certain limitations which are due to lack of reliable data; to the lack of expertise on the part of the researcher on agronomic and biological aspects of cropping systems; and to the specific computer program developed for the model. In view of the preliminary nature of the model, no particular _ recommendations are suggested for Cale, Batangas. It may simply be noted that on the basis of the assumptions adopted in this study the 177 ’ experiments have shown that rice in combination with legumes show a lot of potential in Batangas. The model in this study was designed primarily to answer the questions of "what if" rather than to answer the question of "why". That is, it attempts to determine what will be the performance of a particular cropping pattern if it were subjected to certain levels of inputs and the normal variability of rainfall and crop prices in the study area. It does not attempt to answer why the farmer adopts a particular cropping pattern and how he determines the level of inputs he uses. A model which deals with the latter type of questions requires a much more elaborate model because it would have to include behavioral aspects of the farm and the household. These behavioral aspects are mostly concerned with decision making processes. A model which incorporatesbehavioral aspects with respect to land allocation, input use, output allocation, investment funds allocation, income allocation, etc. would be a powerful policy tool since more control or policy variables would be at the policy maker's disposal to affect the performance of the farm. Among them are crop prices, input prices, markets, extension, and credit. In building a more comprehensive model, the present model could serve as an integral component. Its role would be as a link between the behavioral aspects, that is, the decision criteria for the deter- mination'of cropping'pattern, input levels, land allocation and that of technical aspeets, namely, the determination of the farm performance given the cropping pattern, land allocation and input levels. 178 It is apparent that the principal bottleneck in the model build- ing process has been the lack of data. Indeed one contribution of the present research has been to identify data needs when a farming unit is viewed in a systems context. The rate at which the model can be improved depends on how fast the required data could be made available. This in turn depends on whether or not a concious effort is made to obtain the data. Data generation would be very slow indeed if we only hope passively that agronomists and economists would produce the necessary data in the course of pursuing their own research interests. It is therefore necessary to have a unified research program that would incorporate priority areas of study. Some suggestions for further research are discussed in the next and final section. It should be understood, however, that the suggestions for further research are not necessarily for the sake of model building. The out- come of the various research efforts would be interesting in themselves and would be useful for other purposes. Another point which needs underscoring is that a more realistic and useful model would result from a multidisciplinary effort where the expertise from various disciplines are pooled together in one research endeavor. Perhaps a major stumbling block that must be over— come towards this effort is to give crop simulation models more credié bility. It has been observed that the non-quantitatively inclined practictioners are skeptical about the value of simulating agricultural processes using the computer. It is therefore important to emphasize the fact that a model may not currently be as useful as desired prima- rily because the state of data availability has still a lot to be 179 desired. It is not implied that the model could never be made useful regardless of the amount of improvements done. Perhaps a significant by—product of the whole modeling exercise is that it attempted to bring together a host of known information about agronomic, biological and economic aspects of cropping systems. It also helped point out gaps in information and therefore helps iden- tify additional area‘for further research. Finally, it is concluded that the use of crop simulation models in the near future is not likely to be widespread. Although it has been shown to be a useful tool, considerable effort has still to be done in terms of improving the model structure; improving the estimates of parameters and coefficients; and generating the data needed for model specification and estimation of the parameters. 11.3 Suggestions for Further Research The model developed in this study was shown to have some potential as an aid in the design and testing of cropping systems which can help improve the economic returns of farmers from their small farms; give them a more stable farm income; and improve their family labor utiliza- tion. However, there are a number of characteristics of the model which presently limit its usefulness. Some of the limitations are concerned with the structure of the model itself which could be.improved by better model specification. The other limitations are concerned with the accuracy of the parameters used in the model. In either case, further research can be of great help towards the improvement of the model. 180 In this section some suggestions for improving the structure of the cropping systems simulation model and suggestions for further research needed for the generation of data for the model are discussed. These suggestions may be divided into the following categories: (1) those related to crop-soil-environment relationships; (2) those con- cerning economic relationships; and (3) those concerning the structure of the model itself. 11.3.1 Crop-Soil-Environment Relationships In crop simulation models the interrelationships between the crop and the various factors affecting its performance occupies a prominent role. It is therefore important that the model be able predict yield and other performance variables to a reasonable degree of accuracy given a specific set of soil and environmental influences which the crop is subjected to. The ability of a model to accurately predict depends to a large extent on how the model is specified and on the availability and reliability of the data used. In many cases, important components maybe omitted from the models primarily because it is not possible to estimate the required para- meters due to lack of reliable data. In this regard the crop scientists such.as the_agronomists, entomologists, plant physiologists and others would plAy a vital role not only in the modelling aspect but also in the generation of data needed for estimation of parameters and coeffi- cients of various_relationships. The crop-soil-environment interrelationships are embodied in the production component of this study. The purpose of the component is 181 to predict the yield of various crops depending on the particular set of factors affecting it. Thus the model must take into account not only the direct effects of the various factors affecting yield but also the interrelationships among factors. Some of the factors were identified in Chapter 6. These included: variety of the crop; soil type; fertilizer level; degree of land preparation; weed population and weed control; degree of insect and pest attack and the level of control; degree of post-planting cultivation; soil moisture level as affected by rainfall, irrigation, evapotranspiration, and water losses through seepage, runoff and direct evaporation; solar radiation; tempera- ture; and atmospheric humidity. As pointed out in Chapter 6, each.of the above factors may have direct and/or indirect effects on yield. Hence, it is important to know quantitatively not only the differential effects of each factor on yield but also the interrelationships among the factors. It is recognized that some scattered research has been done on the effects of certain factors on the yield of some crops by a number of research institutions in the Philippines and elsewhere. While these provide.us with valuable information, further studies are needed on the factors which have been left out and also on other crops. An ideal approach to achieve this is to undertake a unified research program whereby the effects of each relevant factor as well as of the inter- relationships among factors on the yield of various crops are systemr atically studied. This would of course entail large amounts of financial and human resources and would involve a considerable amount of time. ‘ 182 Specifically, the suggested priority areas for further research are as follows: 1. The effects of weedgpgpulation onpyield. Research on this aspect: should focus on three related studies. First, the effects of different densities and types of weeds on yield must be determined. Secondly, the quantitative effects of different soil types and levels of fertilizer, land preparation, post-planting cultivation, and soil moisture on the weed population needs to be investigated. Finally, the effects of various forms of weed control (manual, mechanical, and chemical) on weed population needs to be quantified. 2. The effects of various degrees of insect and pest attack on thegyield of various crops. Research on this area requires the deter- mination of the degree of insect and pest attack corresponding to the population and types of insects and pests attacking the crop. It is also essential to determine the population level and types of insects and pests attacking the crop which could be dependent on a number of factors including weed population, soil moisture, temperature, humidity and time of the year. Finally, the effects of various forms of insect and pest control on the population level, degree of damage, and hence yield must be investigated. Research on these related areas would improve the capability of the model is accounting for the effects of insect and pest control of crop yield. 3. The effects of fertilizer onpyield. Although this area has ' been reasonably well-investigated for most of the crops considered in this study, furtherresearch should be done on the.interrelationships' of fertilizer with other factors. One is the effect of solar radiation 183 on the yield response of crops to nitrogen fertilizer. Another is the interrelationship between soil moisture and fertilizer levels of crop yield, particularly the efficiency of fertilizer utilization under extremes of soil moisture conditions. Finally, more attention should be given on the effects of various levels of other elements particular- ly phosphorus and potassium on the yield of various crops. These studies will help greatly in improving the accuracy of the model para- meters pertaining to fertilizer application. 4. Effects of various moisture conditions on crop yield. The effects of various soil moisture conditions on yield has been relative- ly well studied for rice. Research efforts should now emphasize other crops. This research should enable the determination of the optimal moisture requirements of each crop for the entire growing period. More importantly, it should make possible the determination of the quantitative effects of too much or too little soil moisture on yield particularly since upland areas are affected by both extremes at diffe- rent times of the year. This would help identify the tolerance charac- teristics of crops for drought and excessive moisture as well as to quantify the differential effects of various degrees of drought stress and excessive moisture on yield. Further research on this area will make possible a more realistic accounting of the effects of various moisture regimes on yield instead of the simplistic assumption in this study of one drought stress level for all crops. .A related area which needs further study concerns the determina- . tion of-soil moisture level, given the soil type, topography, rainfall pattern, and the particular crop grown. Specifically, the study should 184 make possible the construction ofrealistic water-balance models for each soil type. Among the information that would be useful are: parameters on seepage, run-off, and water retention capacity character- istics of each soil type; parameters on direct evaporation of soil moisture; and evapotranspiration characteristics of various crops during different stages of crop growth. The results of this research would enable us to obtain more accurate measures of available soil moisture as it affects the growth and yield of a crop. It would also enable the introduction of irrigation water into the model as a policy variable in controlling soil moisture. 5. Specific crop combinations. There are also some possible interrelationships resulting from the sequential growing of crops as opposed to monoculture which should be investigated. For example, land preparation and weeding times may be reduced if one crop is immed— iately followed by another crop. Weed and insect populations may also be affected by specific sequences of crops. Another possibility is that fertilizer requirements of a crop may be reduced due to residual fertilizer from a previous crop. 6. Inter-cropping, Although inter-cropping was not formally included in this study, it is an important farming practice which warrants possible inclusion into the model. If included, however, a host of additional data would be necessary. Hence, more research effort must be devoted on intercropping. 7. Further work on the rainfall generator. In the rainfall gene- rator developed in this study the incomplete gamma distribution function was used. Although it generally fared better in goodness-of-fit 185 comparisons with the lognormal and normal distributions and also showed a close correspondence with the actual rainfall data in the area of study, further improvements are possible. The possibility of using one distribution function for certain weeks of the year and other distribution function for certain weeks of the year and other distribu- tion functions for other weeks may result in better rainfall simulation. This follows from the fact that the Chi-square tests have shown that for certain weeks of the year, the lognormal distribution fits the data better than the incomplete gamma distribution. Another area which needs further study is on the possibility of generating rainfall for periods longer than one week in view of the fact that the tests of independence showed that auto-correlation among weekly data exists. Another possibility is the generation of rainfall on a weekly basis but taking account for the fact that adjacent weekly observations may not be independent from one another. 8. The decision topplant behavior of farmers. In this model, the decision as to when to plant was assumed to depend on the weekly rainfall and on the condition that plowing and harrowing (land prepara- tion) have been used. The latter is also dependent on the rainfall during the week. While these observations are supported by facts other hypotheses could be forwarded concerning the decision to plant behavior of farmers. One is that farmers would plant depending on their expectations regarding rainfall based on past year's rainfall and the rainfall during the preceding weeks. 186 11.3.2 Economic Relationships In this study, economic relationships are involved only in the computation of costs and returns and the determination of labor utili- zation and hiring. The allocation of land to various crops and the level of input use are pre-determined and the model proceeds to compute various performance variables under varying rainfall and price condi- tions. On the basis of the means and variances of selected performance variables, a cropping pattern is judged to be superior to other patterns. It is felt that this procedure is very similar to research on cropping system design as they are actually practiced in experimental and field plots. In the present model, the components involving economic relation- ships are the price generator, the labor component, and the crop accounting component. Some directions for improving these components and further research are as follows: . 1. Price:generator. Although the use of seasonal price indexes is perhaps sufficient for the purposes of the study, alternative methods of price generation which give more emphasis on current trends rather than historical prices should be looked into. Since the.non-- deterministic generation of prices depend on measures of means and variances of prices, a study of price indexes would also be very useful. Another area which needs attention is on the price movements of .farm.inputs and wage rates.~ If a seasonal pattern can be discerned _ from past data then some form of seasonal indexes could be computed and incorporated into the price generator. This would lend it more ' 187 realism rather than the constant prices assumed for farm inputs and wages throughout the year in this study. 2. Labor component. The improvements that can be made on the labor component would mostly be in the form of better measures of labor requirements of various operations by crop. This could perhaps be achieved by more precise methods of observing actual labor use instead of estimates based on recall. Since the distribution of total labor requirements during the growing season by time is crucial in the decision to hire additional labor, more attention should be given along this aspect. Finally, there are operations which depend on the level of output (harvesting, threshing, husking, shelling) and on the level of inputs (spraying and fertilizing). Here, more accurate measures of labor requirement per unit of input.or output would be valuable. 11.3.3 Suggested Revisions in the Model Structure When the farm is looked at as a system where biological, technical, and economic interrelationships are well defined, then a systems model can provide us with the useful tool in the improvement of the farm as a business entity. Given a set of control variables and performance variables, the systems model maps out the effects of changes in control variables on the performance of the system. The set of control variables may be divided into two types: those controllable by the farmer and those controllable from the point of view-of policy makers. When the model is used at the farm level, the latter could be assumed as given. Conversely, from the policy point of view, the former is assumed as given or affected by the latter. 188 A suggested modification is therefore the inclusion of those components mentioned in Chapter 2 but were omitted. These are mostly those describing economic behavior of farmers, particularly decision making. This would then change the capabilities of the model from that of testing and design of cropping patterns to a complete analysis of the farm business. If it were possible to construct a model which incorporates decision making, what would be the value of such a model? The model would be very useful in finding ways to improve the farm. If we know the controllable factors or the policy variables then we can investigate how the alteration of these factors can influence the performance of the farm business. For example, if land allocation is controllable, then we can theoretically determine the optimal land allocation that will maximize net returns of the farm. Note that the way the problem is specified is similar to linear programming models. Another value of the model would be to help us understand why a farmer adopts one particular cropping pattern rather than another. We could trace this to several factors, perhpas relating to land allocation, labor availability, cash requirements, investment opportuni- ties, and exogenous factors such as markets, availability of farm in- puts, etc. A model which incorporates decision-making processes must as a minimum include a submodel for land allocation (how land is allocated among various crops at a given time); a sub-model for input use (how ,the levels of fertilizer, weeding, insect and pest control per unit of land area are decided upon); a sub-model for output disposal (how 189 total output is allocated among home consumption, sales and other uses); a sub-model for income allocation (how income is allocated among household expenditures, savings, and re-investment to the farm , business); a sub-model for investment (how available investment funds are allocated to various uses: acquisition of additional land, farm machinery, equipment, current inputs, etc.) There are additional decisions to be made aside from the above-mentioned ones. These include decisions as to when planting should start, alternative strategies when the first crap fails; and marketing decisions espe- cially if the product price periodically fluctuates. With the above components it would be possible to determine endogenously those variables which are predetermined in the current model, namely, land allocation, level of fertilization, weeding, and insect and disease control. If one were to build a satisfactory model incorporating the various components, it is obvious that considerable effort will be required. For each decision that has to be made there are a multitude of factors that have to be considered. How each fac- tor influences the decision; how much weight the factor carries; and how the form of the decision function is specified must be carefully investigated, tested and validated. B I B L I 0 G R A P H Y Aitchison, J. and J.A.C. Brown, The Lognormal Distribution with Special Reference to its Use in Economics, Cambridge, Univer- sity Press, 1957. Antonio, E. V. and G. Banta, "Multiple Cropping in a Batangas Barrio", IRRI Saturday Seminar paper, June 29, 1974.(mimeographed)o Barger, G.L. and H.C.S. Thom, "Evaluation of drought hazard", .Agronomy Journal, Vol. 11, pp. 519-527. Barker, R. and C. Montafio, "The effect of solar energy in rice yield response to nitrogen", (mimeographed), 1971. Charlton, P. J., "Computer languages for system simulation" in Dent and Anderson (eds. ), Systems Analysis in Agricultural Management, John Wiley and Sons, Australasia Pty. Ltd., Sydney, 1971, pp. 53-70. Crisostomo, C.M. et. al., "The New Rice Technology and Labor Absorption in Philippine Agriculture," Malayan Economic Review, Vol. XVI, No. 2, Oct. 1971, pp. 117-158. Dalrymple, D.E., Survey of Multiple Cropping in Less Developed Nations, Foreign Economic Development Service, U. S. Department of Agriculture, October 1971, pp. 101-105. De Datta, S.K., T. Chang and S. Yoshida, "Drought Tolerance in Upland Rice", in IRRI,‘Major Researches in Upland Rice, Los Bafios, Philippines, 1975, pp. l4-26. Denmead, O.T. and R. H. Shaw, "The Effects of Soil Moisture Stress at Different Stages of Growth on the Development and Yield of Corn", AgronomyJournal, Vol. 52, 1960, pp. 272-274. Dent, J.B. and J.R. Anderson, (eds.) Systems Analysis in Agricul- tural Manegement, Sydney: John Wiley and Sons, Australasia Pty. Ltd., 1971. Flinn, J.C., "The Simulation of Crop-Irrigation System" in Dent and Anderson (eds.), Systems Analysis in Agricultural Management, John Wiley_and Sons, Australasia Pty. Ltd., 1971. Friedman, D. G. and B. E. James, "Estimation of Rainfall Probabilities" University of Connecticut, Coll. of Agriculture Bulletin 332, 1957. 190 191 Gomez, A., "Optimizing Crop Production in Small Farms" (mimeo paper), paper presented in a seminar, IRRI, October 2, 1975. Harwood, R.R., "The Concepts of Multiple Cropping Systems Design", Training Lecture, IRRI, June 1973 (mimeographed). Huda, A.K.S., et. al., "Contribution of Climatic Variables in Predicting Rice Yield", Agricultural Meteorology, Vol. 15, 1975, pp. 71—86. Hufschmidt, M.M. and M.B. Fiering, Simulation Techniques for Design of water Resource System, Harvard University Press, Cambridge, 1966. Kim, Dong Min, "Korean Family Farm Simulation Model", unpublished paper, Michigan State University, 1975. Kuester, J.L. and J.H. Mize, Optimization Techniques with FORTRAN, McGraw Hill Inc., 1973. Llewellyn, R.W., "FORDYN - An Industrial Dynamics Simulator", Department of Industrial Engineering, North Carolina State University, Raleign, 1965. Longworth, J.W., "The Central Tablelands Farm.Management Game", Unpublished Ph.D. thesis, University of Sydney, 1969. McMillan, C. and R.F. Gonzales, Systems Analysis: A Computer Approach to Decision Models, Richard D. Irwin, Homewood, Ill., 1965. Murata, Y., "Estimation of simulation of rice yield from climatic factors", Agricultural Meteorology, Vol. 15, pp. 117-131, 1975. Park, G.L. and T.J. Manetsch, Systems Analysis and Simulation with Application to Economic and Social Systems, Preliminary edition, Parts I and II, Michigan State University, January 1973 O 0 Park, W.L. and J. L. Knetch, "Corn yields as influenced by nitrogen level and drought intensity", Agronomy Journal, Vol. 50, 1958, pp. 363-364. Pattinson, A. Synthesis of Rainfall Data, Civil Engineering Technique, Report 40, Stanford University, 1964. Phillips, J.B., "Statistical Methods in Systems Analysis" in Dent ' and Anderson (eds.), Systems Analysis in Agricultural‘Management, John Wiley and Sons, Australasia Pty. Ltd., Sydney, 1971. 192 Prantilla, E.B. "Economic Optimization.Models of Multiple Cropping Systems: Applied to the Philippines" Ph.D. Thesis, Iowa State University, 1972 (unpublished). Penman, H. P., "Natural evaporation from open water, bare soil, and grass", Proc. Royal Soc. Vol. 193A, 1948, pp. 120-145. Strickland, R. P. and D. J. Davis, "Interfacing the MPS/360 Linear Programming Routine with FORTRAN Programs", U. S. Department of Agriculture, Economic Research Service, 1970. Thodey, A. and R. Sektheera, "Optimal Multiple Cropping Systems for the Chung Mai Valley", Agricultural Economics Report No. 1, Faculty of Agriculture, Chung Mai University, July 1974. Thom, H.C.S., A note on the gamma distribution, Monthly Weather Review, Vol. 86, pp. 177-122, April 1958. Thom, H.C.S., "Some methods of climatological analysis", Technical Note No. 81, World Meteorological Organization, 1966. U.S. Bureau of Census, "The X-11 Variant of the Census Method II Seasonal Adjustment Program, Technical Paper No. 15, (1967 revision), U.S. Government Printing Office. weaver, C.R. and'M.‘Miller, "A Precipitation Probability Computer Program”, Research Circular 155, Ohio Agricultural Research and Development Center, Wboster, Ohio, November 1967. Wickham, T.H., "Predicting yield benefits in lowland rice through a water balance model", in IRRI, Water Management in Philips pine Irrigation Systems: Research and Operations, Los Bafios Philippines, 1973, pp. 155-181. Yamane, T., Statistics: An Introductory Analysis,.Harper and Row: New York, 1964. Yoshida, 8., "Factors that Limit the Growth and Yield of Upland Rice" in IRRI, Major Researches in Upland and Rice, Los Bafios, APPENDIX I TIME BY OPERATION MATRICES OF LABOR UTILIZATION BY CROPS APPENDIX I TIME BY OPERATION MATRICES OF LABOR UTILIZATION BY CROPS The following tables show the labor requirement of each crop by time and by operation. All planting operations are assigned to time period 6. The following are the codes used for each operation: Eggs Operation 1 Plowing 2 Harrowing 3 Other land preparation 4 . Furrowing 5 Seeding/planting 6 Fertilizing 7 Off-barring 8 Weeding 9 Spraying 10 Other care 11 Harvesting 12 Threshing/husking 1_93 194 .mhlcmaa one «summed .HH one H m>o>h=m >memz mamo Baum omumdsodmo .oowuoswdwuo Hosea oumu ouoooo newsman wowmmwzo “mouoom H.moe ~.a~ o.em~ o.eo ~.mmn e.n e.nm n.eo a.en m.nn a.em e.as sauce o.sa o.ss «a e.~sn e.so o.m~H «N o.m~H o.m~o «a an an ~.o~ ~.o~ as ~.e~ o.e ~.o~ we ~.c~ ~.o~ as ~.o~ N.o~ on. ~.s~ o.s N.o~ no a.m~ ~.o~ e.n «H ”.mm ~.o~ a.HH .mu m.o~ o.s m.HH e.s «a e.m~ N.HH a.oo as s.ea N.HH e.s on. m.e~ o.e e.HH m.HH a e.s e.s a a ~.as m.sH e.s s m.~n e.sn m.ao n ~.e~ m.eH n.s s c.n~ n.o a.ma m c.n~ m.» e.ma a c.~m c.~m H sauce NH on a m a e m s m N H sownmm d .oowumuwawuo wooed mo Nausea oowumuoeo he uses “mafia .H.H manna awoooem< 195 .mmlehma one «summed .HH one H ohe>une haxeoz eHeo scum oeueanoaeo “oonnom .nowueewawun wooed omen euonoo.eounmwu wnweewze h.oon I-l NInOuam aHsooz «Hue acne emumHaoHeo "cannon .nowueewawun wooed open euoneo newsman mnwmewZe o.ean o.se o.mmH o.wH o.No o.sm o.sm o.ms o.NN o.NH c.mH o.Hs Hanan «N NN. c.sm o.sm NN o.mNH c.sm . o.ea HN o.sa c.sa oN mH oH NH 9H o.aN nH «H o.a o.a NH o.AN o.aN NH o.NH o.NH HH. o.NH o.NH oH . o.aN o.aN a ;. o.m o.m a o.NH o.NH N o.Ha o.NH o.ms o.NN e c.HN o.NH c.a . m m.am o.a n.cn s n.om m.on N N H NH HH OH a a N e n s N N H lecHuoa HeuoH nowueueno mafia e.nowueewawun wooed mo Manuea nowueueno ho mews ”ennmuom .n.H «Home xHeaoss< .nNueNmH can sNINNNH .HH ecu H meo>u=m NHsomz «Hue acne eouaHauHao “saunas .nowuenwawun moped one» ouonoo «woman wnweewze 197 o.aan c.wcH o.emm m.oa N.mH N.mN m.mN N.m¢ ¢.¢a o.H o.oN o.Nn Heuoa. «N MN NN HN oN aH ma c.om c.0m . NH o.¢oa o.om o.mNH oH c.¢oH o.om o.mNH ma o.wNH c.mNH . «H o.o I ma ¢.m q.m NH o.a c.m . Ha o.mH e.m o.m ca m.mN m.mN a o.HH o.HH . m o.HH o.HH N o.Nn N.me ¢.ea . o o.nH o.H «.ma I n . «.mm «.ma c.oN e c.oN c.oN m . N . H H a N N e n a N N H eoHuoa Aesop NH NH 0 nowueuemo A saws e.nowueuwawun Hosea wo nausea nowueueno ho mafia "neon won: .¢.H eases uwonenn¢ 198 .mNueNmH was «NINNNH .HH was H mao>u=m aonm: «Hue acne wouaH=OHeo ”menace .noHueeHHHun HooeH ones euonoo eeuanu wnHeeHZF o.mmn c.NoH c.eoN o.HN o.nN o.eN o.cN c.¢m o.mH c.m c.Nm c.Nn Heuoa «N nN NN HN oN. o.unm theez oHeo noun oeueHnoHeo "sounom .noHueuHHHun HooeH ones euonoo mouanm wnHemH:e 199 oc.NNN co.ooH eo.oom o.NN o.om e.mN o.om o.on m.NH c.m s.o N.¢N Hanan «N «N NN oc.ooH o.ooH HN oo.onH c.omH oN cc.onH c.omH NH . mH NH oH nH «H NH o.m NH o.a O.HH HH o.me c.N H.os cH s.es s.eH s 0.0H O.HH a N.ms o.m s.cs N m.HN o.a o.om m.NH - . a N.N m N.s n o.aH N.s H.HH s s.oN s.cN m . N H H HH oH a m N e m s m N H eOHuoa Heuoa N A , nOHueueno . eaHH AL e.noHueeHHHun HooeH mo xHuuea noHueHono ho oaHH "unneem .o.H oHoeH NHonenno 200 .mNueNaH use «N-NNNH .HH can H uNu>N=m NHsomz «Hue acne emusHsoHoo “nuance .noHueeHHHun noneH open euonoo meuanm mnHemwze w.mm¢ N.mm o.moH m.NH N.No N.mn o.N¢ o.mH 0.0H N.Nm H.mm HeuoH «N MN NN HN oN o.NN o.NN mH o.HHH e.NN c.¢m mH o.¢w o.¢m NH oH mH «H mH NH o.m o.a HH oH m.m m.m m a ¢.NOH N.No N.mm . N 0.0e c.N< o.mH o N.NN o.OH N.NH m H.em c.o~ H.¢H o o.nN c.mN m N H Hence NH HH oH N N e m e N »N H eoHuae nOHuenemd eaHH .noHueuHHHun HooeH mo xHuuea nOHueueno No eaHH “neeohom .N.H eHoeH xHonenn< Q 201 .mNI«NmH one «NIMNmH .HH one H mhe>nnm NereS eHeo aouu oeueHnUHeo .noHueeHHHun noneH open muoneo mouanm wnHemHze "mounom o.Hom o.NOH o.NOH one. Infill-1H \ONVOOIHNONNOOC N€HHN <' OOOOOCOOMMOO I-I n.HN 0.0N m.«N 0.6m m.oH o.o« N.m o.o« m.om m.om m.oN n.0N w.OH c.Nn o.Nn Heuoa «N mN NN HN ON mH wH NH 0H nH «H NH NH HH OH HNMN‘TIHONQO‘ Hence HH OH H ooHuen maHN fl .noHueeHHHun noneH mo xHuuea nOHueueno NA eaHh "oueuom ueozm .e.H oHamN xHecmse< APPENDIX II FORTRAN SOURCE PROGRAM OF THE COMPUTER SIMULATION MODEL 202 FORTRAN SOURCE PROGRAM OF THE COMPUTER SIMULATIW MODEL I 0 0 n... 2 I 5 N I I R I III H I: 0.6 I 0 “IQ II I I I U 0 27. 0 I11 I I z 2‘ 00 II 5“. (II 5 (R 36 N A0 FR R TR N“ H E I UV I a... PD. .1 I0 I I 0 I I I, a 28 a. J z 5‘ 1*“ I (3 II I I 3 PR 022 N 6° 0‘ I I R IR P88 H II I In“ I ZIICZS I, 58.: IRON 58 ‘ I It!“ as“ U653vv 22 nool|lt UP? (I 594‘ III-IIINN F EC .c C0... (RF. IRRIQIQNHH IIINIIIII eel-Iozaa‘” COSHON/ STAGE/ HNRD.NNPPPHH YPE IN I ’ 0 z I. I: I I z Z I: U 5 I cl 2 III I I U N I I1... V II I a 26 E cl 2 I o N In I E 1‘ I c I, N I... 8|- 6 IN I- s F. 92 I Isl I A8 R I R I 5 HS J I II I X ,LD. Ll. 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