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EJI'¥.*: .‘LMI '* I‘M: A Ifi£~UI£3 1"” .‘I'frfll I. ‘ c: If. H M {1711'}... IL“ 'wfln “ I ‘ "$1“ . h.‘:.'« I; ‘4'? ‘31..” alu ; J" v 7'“?qu 1111' m} . 7.31%” ,. 37'? I tfih “(l-“#54“ WA: .12" 1J1 ‘ M“. , ,- \ . {I 5971;" "I, I ( lllllllllllllllMlllllllllllllllllll 311293 00086 1041 lIBRARY Michigan State University This is to certify that the dissertation entitled SIMULATION-MULTICRITERIA OPTIMIZATION TECHNIQUE AS A DECISION SUPPORT SYSTEM FOR RICE PRODUCTION presented by Evangelyn C. Alocilja has been accepted towards fulfillment of the requirements for Ph.D. degree in Electrical Engineering and Systems Science Major professor Date August 14, 1987 M5 U is an Affirmative Action/Equal Opportunity Institution 0-12771 MSU RETURNING MATERIALS: Place in book drop to LIBRARJES remove this checkout from your record. FINES will be charged if book is returned after the date stamped below. N U3 .a ~t ”I it SIMULATION-MULTICRITERIA OPTIMIZATION TECHNIQUE AS A DECISION SUPPORT SYSTEM FOR RICE PRODUCTION Evangelyn C. Alocilja A DISSERTATION Submitted to g, Michigan State University .. f in partial fulfillment of the requirements ‘ _ . for the degree of DOCTOR OF PHILOSOPHY ABSTRACT SIMULATION-MULTICRITERIA OPTIMIZATION TECHNIQUE AS A DECISION SUPPORT SYSTEM FOR RICE PRODUCTION :.53 By pl: Evangelyn C. Alocilja low-yielding rice-growing countries can benefit from the agrotechnologies developed and made available through experimental stations and from high-yielding countries. However, the conventional method of agrotechnology transfer may be costly and time-consuming, ' and the farmers’ perception of risk within the context of the economic l 2” environment in which they function is sometimes a major barrier to ;§%“;@dapting high-yielding agrotechnologies. :5nt;~ ‘-;\‘§' The rice simulation model reported here is a computer software ' Rage designed to aid in the initial selection of new varieties and -;enent practices in various soil types and climatic environments Dedicated to ”I. EVIL-NJ J u , my husband and best friend, Rex, diatom-1' A ‘ and my mother. Rosario. "I‘DR‘ C-i :' ' of ' .o . - as . .— .. A‘ . ;.«‘- an"; (Cl? Ch. 5 if an“ id; ““ ‘ q‘ L ‘ ~ 1‘ . x ’9 ;-'t‘ 9%?é a . ”5 3‘. $2M ’EWléIl‘xg fil}pp.}ff Wei the 2;? Bible ‘ g , v~.'i°£’.’ euthana, Rex” :51;:‘~“"” ACKNOWLEDGMENTS For the success of this dissertation research, I acknowledge: With gratitude the guidance of the Lord Almighty, through Jesus Christ, my Source of wisdom and strength. Dr. Herman E. Koenig for directing my research. His enthusiasm for my work challenged me to aim for relevance and excellence. Dr. Joe T. Ritchie for the financial, moral, and spiritual support. His direct involvement with my research provided a boost in the formulation of the simulation model and insight in the development of the multicriteria optimization procedure. Dr. Thomas J. Manetsch for his guidance in my academic program which provided a good base for my research undertaking. His spiritual support was a motivation. Dr. Robert O. Barr and Dr. R. Lal Tummala for their invaluable encouragement during the conduct of the research and their enthusiastic endorsement of the results. The International Benchmark Sites Network for Agrotechnology Transfer (IBSNAT) for the financial support through Dr. Joe T. Ritchie. My officemates, especially Dale Magnusson, Brian Baer, and Sharlene Rhines for providing support to my office needs. The prayer support of the 2:7 Bible study group and friends. The love and prayers of my husband, Rex. CHAPTER I CHAPTER II CHAPTER III CHAPTER IV TABLE OF CONTENTS INTRODUCTION AND NEEDS ANALYSIS OBJECTIVES AND SCOPE OF RESEARCH 2. 2. 1. 2. Objectives Scope SYSTEM IDENTIFICATION 3. 3. 1. 2. The Exogenous Input Variables The Controllable Input Variables The Output Variables The System Parameters Performance Criteria The Multicriteria Optimization .1. Pareto Optimization .2. Min-max Optimization AGRONOMY 0F UPLAND RICE PRODUCTION The Effect of Temperature on Rice Growth Rice Phenology .1. Germination .2. Seedling Emergence .3. Juvenile Stage .4. Panicle Initiation .5. Heading .6. Grain Filling iv 11 ll 12 12 l3 l4 l6 l7 19 20 21 22 23 24 25 26 26 V 4.3. The Influence of Solar Radiation on Plant Growth 27 4.4. Photosynthesis 28 4.5. Carbohydrate Partitioning 29 4.6. Grain Yield 30 4.7. Soil-Water Condition and Water Losses 31 4.8. The Importance of Nitrogen Fertilization 35 CHAPTER V THE ANALYTICAL STRUCTURE OF THE RICE SIMULATION MODEL 38 5.1. Sowing Stage (ISTAGE 7) 43 5.2. Germination Stage (ISTAGE 8) 44 5.3. Emergence Stage (ISTAGE 9) 45 5.4. Juvenile Stage (ISTAGE 1) 48 5.5. Panicle Initiation (ISTAGE 2) 53 5.6. Heading Stage (ISTAGE 3) 55 5.7. Beginning of Grain Filling (ISTAGE 4) 57 5.8. End of Grain Filling (ISTAGE 5) 60 5.9. Physiological Maturity (ISTAGE 6) 62 CHAPTER VI THE ANALYTICAL STRUCTURE OF THE MULTICRITERIA OPTIMIZATION PROCEDURE 64 6.1. The Monte Carlo Search Method 66 6.2. Pareto Optimization 66 6.3. Min-max Optimization 68 6.4. Function Minimization 70 6.5. The Analytical Representation of the Objective Functions 71 6.6. The Economic Scenario of the Rice Farm 73 7"" l l 'I , “ ‘ ’ “ri'? f' _, 115v“ . " . Ill vi !r\_ , ififliPTER VII THE ALGORITHM OF THE SIMULATION-MULTIGRITERIA . .2} ,U 1.}; OPTIMIZATION TECHNIQUE CHAPTER VIII DISCUSSION OF RESULTS 8.1. The Rice Growth Simulation Model 'J' 8.2. The Simulation-Multicriteria Optimization ' Technique (snor) CHAPTER IX CONCLUSION APPENDIX A GOODNESS-OF-FIT TEST TO DETERMINE THE PROBABILITY DISTRIBUTION OF GRAIN YIELD APPENDIX B FORTRAN PROGRAM OF THE SIMULATION- MULTICRITERIA OPTIMIZATION TECHNIQUE APPENDIX C USER DOCUMENTATION OF THE RICE SIMULATION MODEL APPENDIX D SAMPLE OUTPUT OF THE SIMULATION- MUETICRITERIA OPTIMIZATION TECHNIQUE 75 80 80 99 123 127 134 211 228 235 .10 .11 LIST OF TABLES COMPARISON BETWEEN PREDICTED AND OBSERVED PHENOLOGICAL OCCURRENCE OF 3 RICE VARIETIES, DAYS AFTER SOWING (DAS) COMPARISON BETWEEN PREDICTED AND OBSERVED PHENOLOGICAL OCCURRENCE OF IR36 VARIETY (Sowing Date: January 9, 1980) PREDICTED AND OBSERVED BIOMASS OF IR36 VARIETY AT 4 TREATMENTS OF NITROGEN FERTILIZER ON 4 SAMPLING INTERVALS. 795 mm WATER APPLIED. PREDICTED AND OBSERVED STRAW WEIGHT AT HARVEST OF IR36 VARIETY AT 2 IRRIGATION LEVELS AND 4 NITROGEN TREATMENTS PREDICTED AND OBSERVED STRAW WEIGHT AT HARVEST OF IR36 VARIETY AT 4 NITROGEN TREATMENTS AND 2 IRRIGATION LEVELS GRAIN YIELD OF IR36 VARIETY AT 2 IRRIGATION LEVELS AND 4 NITROGEN TREATMENTS GRAIN YIELD OF IR36 VARIETY AT 4 NITROGEN TREATMENTS AND 2 IRRIGATION LEVELS PREDICTED LAI or IR36 VARIETY ON 7 SAMPLING INTERVALS, DAYS AFTER SOWING (DAS) ROOT WEIGHT, LEAF WEIGHT, STEM WEIGHT, PANICLE WEIGHT, AND LAI OF IR36 VARIETY ON 9 SAMPLING INTERVALS, DAYS AFTER SOWING (Sown on Nov. 6, 1984, with 100 Kg N/Ha in flooded condition, IRRI, Philippines) PREDICTED ROOT WEIGHT, LEAF WEIGHT, STEM WEIGHT, AND PANICLE WEIGHT OF IR36 VARIETY ON 7 SAMPLING INTERVALS, DAYS AFTER SOWING (DAS), WITH 0 N PREDICTED ROOT WEIGHT, LEAF WEIGHT, STEM WEIGHT, AND PANICLE WEIGHT OF IR36 VARIETY ON 7 SAMPLING INTERVALS, DAYS AFTER SOWING (DAS), WITH 30 Kg N/Ha 82 84 85 88 89 90 91 92 93 95 95 .12 .13 viii PREDICTED ROOT WEIGHT, LEAF WEIGHT, STEM WEIGHT, AND PANICLE WEIGHT OF IR36 VARIETY ON 7 SAMPLING INTERVALS, DAYS AFTER SOWING (DAS), WITH 60 Kg N/Ha PREDICTED ROOT WEIGHT, LEAF WEIGHT, STEM WEIGHT, AND PANICLE WEIGHT OF IR36 VARIETY ON 7 SAMPLING INTERVALS, DAYS AFTER SOWING (DAS), WITH 120 Kg N/Ha IDEAL VECTOR OF OBJECTIVE FUNCTIONS, PARETO OPTIMAL SOLUTIONS, AND MIN-MAX OPTIMUM SOLUTION FOR ul-June 20, ug and u3 VARYING IDEAL VECTOR OF OBJECTIVE FUNCTIONS, PARETO OPTIMAL SOLUTIONS, AND MIN-MAX OPTIMUM SOLUTION FOR ul-June 20, u2 VARYING, u3-400 plants/m IDEAL VECTOR OF OBJECTIVE FUNCTIONS, PARETO OPTIMAL SOLUTIONS, AND MIN-MAX OPTIMUM SOLUTION FOR ul-Sept. 1, u2 and u3 VARYING GRAIN YIELD, PROBABILITY DENSITY, AND PROFIT WITHIN i 1 STANDARD DEVIATION FOR LOW-RISK, MIN-MAX, AND HIGH-RISK STRATEGIES YEARLY COMPARISON BETWEEN LOW-RISK AND MIN-MAX STRATEGIES YEARLY COMPARISON BETWEEN HIGH-RISK AND MIN-MAX STRATEGIES PREDICTED GRAIN YIELD (MT/Ha) OF IR36 VARIETY OVER 25 SIMULATION RUNS WITH ACTUAL WEATHER DATA GROUPING OF GRAIN YIELD DATA INTO k CLASSES OBSERVED AND EXPECTED FREQUENCIES OF GRAIN YIELD 96 96 101 105 107 113 117 119 120 129 131 132 LIST OF FIGURES Flowchart of the simulation-multicriteria optimization technique (SMOT) Comparison between predicted and observed biomass of IR36 variety with 0 N Comparison between predicted and observed biomass of IR36 variety with 30 Kg N/Ha Comparison between predicted and observed biomass of IR36 variety with 60 Kg N/Ha Comparison between predicted and observed biomass of IR36 variety with 120 Kg N/Ha Leaf area index (LAI) of IR36 variety with 0 N, 30, 60, and 120 Kg N/Ha Observed LAI of IR36 variety sown on Nov. 6, 1984 in flooded condition with 100 Kg N/Ha Predicted root weight, leaf weight, stem weight, and panicle weight of IR36 variety with 0 N Predicted root weight, leaf weight, stem weight, and panicle weight of IR36 variety with 120 Kg N/Ha Observed plant parts of IR36 variety sown on Nov. 6, 1984 in flooded condition with 100 Kg N/Ha Pareto optimal curve and min-max optimum point for ul-June 20, u2 and u3 varying Pareto optimal curve and min-max optimum point for ul-June 20, u2 varying, u3-400 plants/m Pareto optimal curve and min-max optimum point for u1-Sept. l, u2 and u3 varying Pareto optimal curves and min-max optimum points for ul-June 20 (curve 1) and ul-Sept. 1 (curve 2) Normal curves of low-risk, min-max, and high-risk strategies 79 86 86 87 87 92 94 97 97 98 103 109 109 111 115 8.2.7 8.2.8 Profitlines of low—risk, min-max, and high-risk strategies Yearly comparison between low-risk and min-max strategies Yearly comparison between min-max and high-risk strategies Histogram of grain yield data Normal distribution function superimposed on histogram of grain yield data 116 121 121 130 130 CHAPTER I INTRODUCTION AND NEEDS ANALYSIS While there is food surplus in some regions of the world, serious food deficiency, leading to malnutrition and starvation, is a grim reality in many others. Unfortunately, these food-deficient regions are not economically able to gain access to the food surplus. To eliminate the destructive effect of food deficiency, the concerned countries must find ways and means to increase food production in pace with population growth. Food supply is a direct function of weather and soil environments, market system, government policies and programs, agrotechnology, and the producer's objective of profit and income stability. Plants provide as much as 95 percent of the world's food supply (MSU Agricultural Experiment Station, 1981). To more than a third of the world's population, predominantly iJI Asia, rice is a primary staple in the diet and the center of existence (Barker et a1., 1985). This makes rice the most important food crop in the world today. De Datta (1981) reported that in 1976—1978, rice was harvested from about 143.5 million hectares from Asia (accounting for 90 percent of the total), Africa, South and Central America, Australia, and part of the United States. Rice, grown as flooded wetland or dryland crop, has 2 received considerable research, political and economic attention from all over the world. But in many of the Asian, African, and Latin American rice-growing countries today, production is not enough to meet the food needs of their population, making the daily food supply unreliable and driving the cost of subsistence proportionately high relative to income. Particularly for upland rice agriculture, the regional average grain yield is very low: from 0.5 to 1.5 MT/Ha in Asia, about 0.5 MT/Ha in Africa, and 1 to 4 MT/Ha in Latin America (De Datta, 1975). However, under ideal conditions in experiment stations, yields are reported to be between 5.4 to 7.2 MT/Ha. In order to increase rice production, the low-yielding countries will have to do one or a combination of two things: increase the area devoted to production and/or increase the frequency and intensity of cultivation. At the present rate of population growth, agricultural land is continuously reduced in favor of urbanization, so increasing production by increasing land area is at best only a partial and short-term solution. Hence, rice productivity must come from increases in output per unit area, per unit input, per unit time through high-yielding, science-based technologies tailored to the unique combination of soil, climatic, biological, economic, and cultural conditions of the local area (Wortman and Cummings, 1978; Swaminathan, 1975; Ruttan, 1982) . However , the generation of technology is a complex process . Plant agriculture is a complex system . It is characterized by unique properties and non-linear functions (Baker and Curry, 1976). It is a system which requires natural resources as part of the inputs, imposing their stochastic behavior in the transformation process from input to output (Amir et ll; .JIEEEEH 3 al., 1978). The development of science-based technologies is evolutionary in. nature and requires a long-term investment (Sahal, 1980). Agricultural research techniques are costly, time-consuming, site-specific and, by its own nature, a trial-and-error undertaking. In many of the food~deficient countries, there is an increasing uncertainty as to whether the current agricultural research methods are adequate to meet the food requirements of the growing population and provide for the management skills required to keep food production going. Thus, the complex circumstances surrounding the rice production system, particularly' in narrowing the yield gap of upland rice agriculture, requires the development of a nwthodology that will hasten the evaluation of appropriate transferable agrotechnologies, in the fornl of varieties and field management practices, from high- yielding rice-growing countries to the low-yielding countries, or from its site of origin to another location, at lower cost, minimum failure, and shortest waiting time. Such a nwthodology can be embodied in a computer software that can simulate a rice production system for any chosen variety and management practices considering the stochastic factors of the production environment. But increased yield per hectare is not in itself a sufficient goal. Agricultural production is increasingly dependent on the degree to which cost-effective technology is employed (Avery, 1985), and to which the farmer's vulnerability to the uncertainties of the environmental factors are reduced, rather than simply striving for maximum yield. The level and stability of income to the farmer govern the intensity of rice production. What is needed is a procedure for 4 'RVKBuviromental conditions. This need translates into an analytical, I imnlticriteria, resource-allocation optimization procedure through .Ihieh the tradeoffs can be evaluated between two conflicting .objectives: maximum profit and minimum risk. To the author's Enowledge, this is the first time that. multicriteria optimization technique of the type presented here has been applied to agriculture ' production in general and to upland rice production in particular. CHAPTER II OBJECTIVES AND SCOPE OF RESEARCH 2.1. Objectives The general objective of this dissertation research is to develop an interactive computer software on rice simulation and multicriteria- resource-allocation optimization technique (to be referred to as SMOT) as a decision support system for use by farmers, agricultural extension workers, researchers, and government policy-makers in the design and management of the rice production system. 'IT.‘ . The specific objective of the dissertation research is to develop a practical and flexible computer software for simulating an upland rice production system for use as a tool in the effective transfer of ‘ Sipagrotechnologies among and within countries in the tropics and fpsubtropics from its site of origin to new locations and, based on this \ .- :_ sfi‘fififiiflzation software as an analytical tool in evaluating profit and ”a! “if: maturation risk, subject to constraints in resources, environment and T"""____—_——_—7i 2.2. Scope The rice simulation software is developed for upland condition in the tropical and sub-tropical environments. The software is designed primarily to predict: l. the phenological development or duration of growth stages as influenced by plant genetics, weather, and environmental factors, 2. biomass production and partitioning, and 3. the effect of soil water deficit and nitrogen deficiency on the photosynthesis and photosynthate partitioning in the plant system. The simulation software provides the foundation for the simulation-multicriteria optimization technique (SMOT). SMOT is designed as a decision support system for upland rice production where profit and production risk are quantitatively evaluated subject to the simultaneous constraints on resources, environment, and. production policies. Through the use of SMOT, alternative production strategies can be identified based on the level of profit and risk as well as the capability of the producer to finance the operation. As with all software packages, SMOT has its limitations. Diseases and insect pests, for example, which are highly variable with respect to location, are important considerations in rice production. Conceptually, the rice simulation model has been bifurcated into (1) a plant system without the destructive effect of pest, and (2) one with the influence of pest. The first system, devoid of the effect of pests, is considered here. Incorporation of pest models remains as a l future activity. In the work reported here, it is assumed that pests 7 are controlled to the extent that they have no economic effect and that the cost of this control can be represented as a fixed cost in the optimization technique. As structured, the simulation software assumes that: 1. The production field is not bunded, i.e., runoff is allowed to occur. 2. Method of planting is by direct-seeding. 3. Fertilizer application is basal, i.e., fertilizer is to be applied once at the beginning of the planting season. 4. Except for nitrogen, all nutrients required for plant growth are non-limiting, that is, sufficient to support a normal growth. 5. There are no highly problematic soil conditions such as high salinity and acidity, heavy compaction, or deficiencies in trace elements. 6. The effects of typhoons are negligible. As structured, SMOT assumes further that the market situation, including the price of grain and input costs, are constant over the period of the optimization. The optimization procedure, however, can be repeated as often as desired for alternative prices and costs. For the present application, capital is assumed a constraint factor while labor is in abundant supply. This asSumption is based on the fact that majority of rice production is an activity among highly populated, low-income developing countries. Consequently, harvesting is assumed to be done manually and cost of harvest is on per weight basis. Harvesting mechanization, however, can be implemented by SMOT. The ‘present applications of SMOT also assumes that the and pesticide pollution have negligible impact on the 4 @mvironment. However, where necessary, these by-products can be i I J ‘ganalytically incorporated as constraints on the inputs to the 1‘" Motion and/or optimization processes of SMOT. FM.” CHAPTER III SYSTEM IDENTIFICATION The rice production system is governed by the input-process- output relationship, as a function of time, t. The vector of inputs fall into two classes: (1) the exogenous input variables which are uncontrollable and may be stochastic in nature, and (2) the controllable input variables which are deterministic in nature. The vector of exogenous input variables is represented analytically as 3(t) and the vector of controllable input variables as 5(t). The vector of state variables is denoted by §(t). The vector §(t) describes the internal as well as the external behavior of the plant system. The system parameters are the coefficients in the analytical equations which define the analytical structure describing the system. The vector of outputs also fall into two classes: (1) the desired output variables, represented. as y(t), and (2) the undesired, unavoidable by-products which are generated when the system produces the desired outputs. The performance criteria are defined in order to evaluate whether the desired outputs are acceptable. The rate of change of the state variables at time t (:(t)), as well as the output variables at time t (y(t)), depend upon the inputs 3(t) and 3(t), the state of the system, §(t), and time, t. This relationship is expressed by the functions g and h in a state-space .0 IILI 10 representation as follows: in) - mm. Gm. at). t) Wt) - F(§(t). Rt). €(t). t) The rice production system forms a class of system characterized technically as stochastic, continuous-time, with memory, non-linear, time-varying, and dynamic. The system is stochastic because the weather variables can only be described probabilistically, that is, they can not be described exactly for all time. It is also continuous-time because the environmental-biological interactions in the plant system occur continuously during the growth process. The system has memory because the output of the system at a given time t1 depends not only on the input applied at t1 but also on the input applied before t1 (Swisher, 1976). The non-linearity of the system is due to the fact that the relaxed system, or zero initial condition of the system, can only be described. sufficiently’ with non-linear relationships as mentioned in Chapter I. In this case, the principle of superposition (Swisher, 1976) will not hold true, that is, L {a1u1(t) + 32u2(t)} !‘ a1L(u1(t)) + a2L{u2(t)} for any two inputs u1(t) and u2(t) as functions of time t, and any constant scalars a1 and a2. The state of the plant system during its growth vary with time, hence the system is time-varying. The rice production system is also a dynamic system because the two conditions describing a dynamic system are properties of the rice production system. The two conditions are (Swisher, 1976): (1) A real output y(t) exists for all t > to given a real input 3(t) for all t, where to is initial time. ll (2) Outputs do not depend on inputs 3(1) for r > t. Because of the second condition, rice production systent is also considered as causal, that is, the output of the system at time t does not depend on the input at times after time t. 3.1. The Exogenous Input Variables The major contribution of the exogenous input variables make rice production seasonal, geographically dispersed, and uncertain. These exogenous variables are grouped into two categories, namely: physical and socio-economic. The physical exogenous input variables are solar radiation, daylength variations, air temperature, and rainfall. The socio-economic exogenous input variables are product prices, input costs, and marketing costs. 3.2. The Controllable Input Variables The controllable input variables in the rice production system are classified into the following: manpower (such as the farmers and hired workers); budget allocation; material flow inputs (such as seeds, fertilizers, water, pesticides), capital facilities (such as irrigation system, storage or barns, farm animals, tractors, threshers, and land); and cultural management practices (such as sowing or planting date, plant density, sowing depth, amount and frequency of fertilizer application, amount of irrigation, and type of pest control). 12 3.3. The Output Variables Rice production involves the transformation of inputs into desirable outputs such as grain yield and straw. However, there are unavoidable, undesirable by-products in the process such as pesticide pollution, nitrate leaching, runoff, and sometimes, the build-up of insect populations. These by-products degrade the environment and, while there is no apparent cost to the rice producer at the moment, the future generation will pay for the damage if not dealt with now. 3.4. The System Parameters The system parameters determine the functional relationship in the input-process-output and define the structure of the system. They are classified into two categories, namely: (1) the system design parameters, which are manageable, and (2) the natural system parameters which are unmanageable. The system design parameters depend upon the technologies used and how these technologies are organized into a production system. The design parameters for rice production are grouped into (a) genetic-dependent, and (b) labor- or mechanization-dependent. The genetic-dependent parameters, which describe the variety, are: (l) the time required for the plant to develop from seedling stage to floral initiation; (2) the rate of photo-induction; (3) optimum photoperiod; (4) the time required to complete grain filling; (5) the plant's conversion efficiency from sunlight to carbohydrates; and, (6) tillering characteristic. The labor- or mechanization-dependent variables are: (1) method l3 , of land preparation; (2) method of fertilizer application; (3) method of pesticide control; (4) irrigation method; and, (5) method of harvesting. The natural system parameters are: (l) the latitude of the production area; and, (2) the properties and initial conditions of the soil profile such as soil nutrition and toxicities, water saturation ‘ properties, landscape hydrology, textural profile of the soil, and the topographic position of the field. The system parameters are affected directly or indirectly by socio-economic and institutional factors such as availability of farm inputs. access to credit and markets, inflation and interest rates, local and international market situation, consumers' demands, consumers' nutritional requirements, customs reflecting preference for certain varieties by consumers and farm practice by farmers, production policies by the government (price support, production input I subsidies, government-supported storage facilities, etc.), form of government or political system (socialism, capitalism, communism, etc.), the needs of the rice industry, and the availability of agrotechnologies from research institutions. The exogenous input variables, the system parameters and the socio-economic and institutional factors determine the type of agriculture in any particular environment. 3.5. Performance Criteria The criteria upon which the performance of the rice production system are evaluated, are: (1) farmer's profit; and, (2) production 14 risk. These two criteria are conflicting in the sense that production strategies that generate higher profit are usually very risky operations. Thus, the evaluation procedure will exercise tradeoffs to identify simultaneously the best acceptable values of the two objective functions. The process is called simulation-multicriteria optimization technique. 3.6. The Multicriteria Optimization Optimization is an analytical procedure or a mathematical programming technique used to find the optimum solution that would maximize or minimize an objective function subject to some defined equality or inequality constraints. The optimization techniques were developed in response to such questions as "Are we making the most effective use of our scarce resources?" or "Are we taking risks within acceptable limits?" (Bazaraa and Shetty, 1979). The simultaneous growth of fast computing facilities had facilitated the use of these techniques. Problem optimization can either be linear or non-linear programming. Within the class of non-linear programming is another classification according to the number of objective functions: the single criterion and the multicriteria or vector optimization problem. The class of problem to be dealt with here is nonlinear, multicriteria optimization problem due to the nonlinearity of the system, the nonlinearity of some of the constraint functions, and the nonlinearity of the objective functions. In a multicriteria optimization problem, the objective functions form a vector of cI‘iteria (Osyczka, 1984). The formulation requires a definition of 15 the objectives to be maximized or minimized, the decision variables that must be optimized, and the constraint functions surrounding the problem. Multicriteria optimization has had its applications in engineering fields. It is an analytical procedure of finding the "optimum" solution which would give acceptable values or tradeoffs for all the objective functions to be considered simultaneously. The goal of the multicriteria optimization is to help decision-makers make the right decision in conflicting situations (Osyczka, 1984). Recently, multiple criteria or multi-objective decision-making has gained popularity and applications in management science due to the realization that a decision has more than one dimension which affects successive actions or decisions. For example, Shapiro (1984) argued that the assumption that a firm is interested only in profit is an , oversimplification. He presented research results indicating that management decides upon allocation of scarce resources with reference to several, sometimes conflicting, goals such as profit, market share, balanced business portfolio, long-range growth rate, and risk, in the strategic (long-term) sense, as well as employment level, management- labor relations, and product quality, in the tactical (short-term) sense. There are also nonfinancial demands that need to be addressed t to, including such issues as equal employment opportunities, pollution ‘ control, product safety, and work safety. The nonlinear multicriteria optimization will use the Pareto Optimization and min-max optimization techniques. The Monte Carlo Search method, which assigns random numbers to generate new and random Points, will be employed to search the space of feasible solution. l6 3 . 6 . l . Pareto Optimization The concept of Pareto optimization originated in 1896 from a man named Vilfredo Pareto who began a study of efficient solution theory as applied to welfare economics (French et al., 1983). French et a1. indicated that Pareto’s study provided the earliest recognition of the difficulty of reducing decision problems to forms involving a single objective. However, its application to engineering and management science did not gain momentum until in the early 1970's, and the idea of multi-objective or multicriteria decision-making became formalized. The original version of Pareto optimality theory was quoted by Cirillo (1979) as follows: ”There are, as we have noted, two problems to be resolved in obtaining the maximum well-being for a collectivity. Given certain rules of distribution, we can investigate what positions, following these rules, will give the greatest well-being to the members of the collectivity. Let us consider any particular position and let us suppose that a very small move is made compatible with the relations involved. If in doing so the well-being of all the individuals is increased, it is evident that the new position is more advantageous for each one of them, vice-verse, it is less so if the well-being of all the individuals is diminished. The well-being of some may remain the same without these conclusions being affected. But, if on the other hand, this small move increases the well-being of certain individuals and diminishes that of others, it can no longer be said that it is advantageous to the community as a whole to make such a I I b ‘ 17 move. We are, hence, led to define a position of maximum ophelimity as one where it is impossible to make a small change of any sort such that the ophelimities of all individuals with the exception of those that remain constant, are either all increased or all diminished." In short, Pareto optimality states that an optimum position is reached when it is not possible to increase the utility of some consumers without diminishing that of others (Cirillo, 1979). Mathematically, Osyczka (1984) defined Pareto optimization as follows: A point 5* E U is Pareto optimal if for every 5 e U either, (131(5) - m?» or, there is at least one i e I such that rid) > 1515*) Intuitively, Pareto optimization is that point 3* where no criterion can be improved without worsening at least one other criterion. Pareto optimum usually gives a set of rmn-inferior solutions. This set is denoted as Up. Fp denotes the map of Up in the space of objective functions. 3.6.2. Min-max Optimization Min-max optimization procedure was developed by Osyczka (1984). It uses the information of the separately attainable minima of the objective functions. These minima can be obtained by solving the optimization problems for each criterion separately. Then the values Of the objective functions are compared to these minima through their 2Telative deviations. The min-max optimum is that point 3* which gives i4yr 18 the smallest values of the relative increments of all the objective functions. The detailed analytical presentations of both the Pareto and min- max optimization procedures are presented in Chapter VI. CHAPTER IV THE AGRONOMY 0F UPLAND RICE PRODUCTION Upland rice agriculture is the method of rice production on unbunded flat and slopping fields with land preparation and seeding under dry conditions, and that depend mostly on rainfall for moisture (De Datta, 1975). Primarily a tropical or subtropical crop, rice (Oryza sativa L.) is grown from 53 degrees north to 35 degrees south latitude, and from sea- or below sea-level to elevations of about 2,000 meters (Yoshida, 1981). The growth cycle of a rice plant takes about 3-6 months depending on the climatic condition of the production area and the genetic characteristics of the variety with regards to photosensitivity and thermosensitivity (Tanaka et al., 1966; Yoshida, 1981). Because of the weather factors, especially temperature and daylength, and genetic interactions in the plant system, the growth duration is highly location and season specific. During the growth cycle, the plant completes several stages, generally classified as the vegetative, reproductive, and ripening stages. The vegetative stage can. be further' sub-divided into germination, emergence, juvenile, and floral or panicle initiation, While the reproductive and ripening stages can be sub-divided into heading, grain filling, and physiological maturity. The duration of 19 20 the vegetative stage varies among varieties and largely determines the growth duratiorl of the plant (IRRI, 1964; Yoshida, 1981). The duration of the vegetative stage is said to have a minimum and maximum limit (IRRI, 1964). The minimum limit which is relatively constant for a 'variety, is known. as the basic vegetative phase, and the duration between the minimum and maximum limits is known as the photoperiod sensitive phase. The duration of the phOUnmriod sensitive phase varies with the daylength or photoperiod, which is the interval between sunrise and sunset (unit: hours). Photoperiod is a function of the latitude of the production area. The vegetative stage is characterized by’ active tillering, increase in plant height, leaf emergence, and increase in the leaf area (Yoshida, 1981). The reproductive and ripening stages are characterized by panicle and grain growth. 4.1. The Effect of Temperature on Rice Growth An optimum temperature for different physiological processes has been observed (Yoshida, 1981). This optimum temperature varies with variety. The optimal temperature appears to shift from high to low as growth advances from the vegetative to the reproductive and ripening stages (IRRI, 1972; Yoshida, 1981). Within the critical high and low temperatures, high temperatures are required for active growth at early stages while low temperatures favor spikelet production during the reproductive stage, confirming the observation that the length of ripening is inversely correlated with daily mean temperature (Yoshida, 1981). However, extremely high or low temperatures are not favorable .1“ l I 21 to plant growth. Yoshida (1981) reported that high percentage of spikelet sterility occurred when temperatures exceeded 35°C at anthesis and lasted for more than 1 hour. Injury to rice occurred when the daily mean temperature dropped below 20°C. Low temperatures, such as 12°C, induced 100 percent sterility when they lasted for 6 days. Other injuries due to cold temperatures were failure to germinate, delayed seedling emergence, stunting, leaf discoloration, panicle tip degeneration, incomplete panicle exsertion, delayed flowering, and irregular maturity. Crop duration is directly related to temperature and modelled as thermal time or degree-days (Yoshida, 1981). It is calculated as follows: Degree-days - 2 (daily mean temperature - threshold temperature) Rice has been observed to have a threshold temperature of 8°C. Yoshida (1981) indicates that the concept of thermal time or degree- days assumes that the growth or development of a plant is linearly related to temperature or the total amount of heat to which it is exposed. However, he cautions that this concept should be handled carefully because there are some physiological and biochemical processes in the plant which are not linearly dependent on temperature. He demonstrated the presence’of the "idling effect" of high temperatures, suggesting that a "ceiling temperature" existed. 4.2. Rice Phenology Phenology is concerned with the duration of the growth stages of ‘tiwe plant. As mentioned in the earlier section, the growth stages are f——————_———i '[ 1: 22 germination, emergence, juvenile, panicle initiation, heading, grain filling, and physiological maturity. 4.2.1. Germination The concept of thermal time was applied to the germination study by Livingston and Haasis (1933) in order to determine the thermal time requirement for complete germination in rice seeds. The result showed that it took about 45 degree-days to germinate healthy rice seeds within the temperature range of 15° to 37°C. At the incubation temperature of 42°C, only about 8 percent germinated in 10 days and no germination was observed in a period of 6 days at 45°C. At germination, the coleoptile emerges and the first leaf follows (Yoshida, 1981). A study by Yoshida (1973) indicates that temperature affects the rate of leaf emergence. At 22°C one leaf emerged every 5.4 days while a leaf emerged every 3.5 days at 31°C. The concept of thermal time was applied on the above study. The temperature ranges were converted to degree-days using a threshold temperature of 8°C. Plotting the degree-days against the number of leaves per culm or stem showed that the relationship was linear and that the slope, number of leaves per degree-day, was 0.012. The inverse of the slope is 83.3 degree days/leaf. The 83.3 is also known as the phyklocron interval. However, phytotron studies to determine the phyllocron interval for some rice varieties conducted at the Duke University during the period 1983-84 (unpublished results) showed an average value of 90 degree- days/leaf. Most varieties develop 10-22 leaves on the main culm (Yoshida, 1973, 1981). _r,__________i 23 Roots develop immediately after germination. Root growth is observed to be regulated by both varietal characteristics and root environment. A study on rice growth under controlled environment by Yoshida (1973) showed that at the very early stage of plant growth, root to shoot ratio was about 0.21, decreasing exponentially as the plant weight increased, and stabilizing at about 0.10 as the plant weighed 1 gram or more. Root weight was not markedly affected by temperature, at least within the range of 22° to 31°C. HOWever, water stress was found to increase root growth relative to shoot growth (IRRI, 1974). 4.2.2. Seedling emergence Seedling emergence is the time when the tip of a seedling emerges from the soil surface, and so start the growth process in the field (Yoshida, 1981). Thus, the time required for emergence is a function of the sowing depth. Until this point, plant growth is supported by the nutrients in the endosperm, often known as the seed reserve (Yoshida, 1973; IRRI, 1973). The concept of thermal time was applied on the seedling growth experiment by Yoshida (1973) in order to evaluate growth rate. The result showed that growth was linearly related to thermal time up to 120 degree-days, with a slope of 0.00008265 grams dry weight/plant/degree-day. 24 4.2.3. Juvenile Stage Juvenile stage is characterized by root growth, leaf emergence, leaf growth, and tillering. During the initial stages of seedling growth (first and second week after sowing), growth of the coleoptile and subsequent leaves is largely dependent on the seed reserve (Yoshida, 1973 and 1981). Photosynthesis takes over carbohydrate production after the second week of growth. ‘Yoshida (1973, 1981) reported that within the temperature range of 22°C to 31°C, photosynthesis was responsible for about 30 percent of growth during the first week, 84 percent during the second week, and 100 percent thereafter. Yoshida also indicated that during the first week after sowing and until the middle growth stages, growth rate increased almost linearly' with increasing temperatures. Studies (IRRI, 1968) have shown that tillering is initiated when the total nitrogen uptake becomes greater than 10 mg/plant or the dry weight is greater than 300 mg/plant, demonstrating that tillering initiation depends on the size of the main tiller. The tiller number was observed to increase when the nitrogen content of the leaf blade was higher than 2 percent, but tillering stopped when nitrogen content dropped below 2 percent. Tillering ability is known to be a varietal character, that is, high-tillering varieties tiller more actively than low-tillering ones. Tillering increase by a plant population follows a curvilinear shape, increasing monotonically until the maximum tiller number stage. Tiller number decreases after the heading stage. High temperatures encourage tillering (IRRI, 1972). “v.1", 'fl'!""" 1“; “t i 25 Leaf area development of a rice variety is highly related to its tillering capacity at conventional plant spacing (Yoshida and Parao, ‘ 1972). A high-tillering variety tends to have a vigorous vegetative growth. 4.2.4. Panicle Initiation Since rice is a short-day crop, rice initiates panicle primordia in response to short photoperiods (Yoshida, 1981). The duration of this stage varies with the degree of photosensitivity of the variety. f Depending on the daylength condition. of the production area, the duration could be at its shortest or longest. The daylength at which the duration from sowing to flowering is a lninimum is called the optimum photoperiod (Yoshida, 1981; IRRI, 1966). The optimwn photoperiod of most varieties is observed to be 9-10 hours (Yoshida, 1981; IRRI, 1969). The critical photoperiod is the longest photoperiod at which the plant will flower; flowering will not occur beyond the critical photoperiod (Yoshida, 1981; IRRI, 1966). The critical photoperiod of most varieties ranges from 12 to 14 hours (Yoshida, 1981; IRRI, 1969). Short photoperiods decrease the growth period of the plants. Photosensitivity is a varietal character, that is, the critical and optimum photoperiod differ among varieties. The , growth of a variety that is less sensitive to photoperiod does not fluctuate as much as a highly sensitive variety under various , daylength conditions (Tanaka et al., 1966). , It is usually during the panicle initiation stage that the plant reaches the maximum tiller number (Yoshida, 1981). There is a period A .jal'. V 'Snu. 26 before the maximum tiller stage when the tiller number becomes numerically equal to the panicle number at maturity. 4.2.5. Heading Yoshida (1981) defines heading as the time when 50 percent of the panicles have exserted. From his experience, complete heading in the field takes about 10-14 days. As the rice plant grows, the leaf area index (LAI) increases. LAI is the sum of the leaf area of all the leaves divided by the ground area where the leaves have been collected. Studies by Yoshida (1981) show that LAI increases curvilinearly with time and reaches a maximum at around heading. After heading, LAI decreases as the lower leaves senesce. The same studies demonstrate that a rice crop can attain maximum LAI values of 10 or more at heading time, with a LAI value of 5-6 at maximum crop photosynthesis. Tiller number also starts to decrease during the heading stage. The non-bearing tillers and. weak-bearing tillers are killed as a result of shading and senescence (IRRI, 1964). The number of tillers and the number of panicles become equal at harvest. 4.2.6. Crain Filling Grain filling is characterized by increase in grain size and weight, resulting in the increase in panicle weight. It is also characterized by changes in grain color and senescence of leaves (Yoshida, 1981). The process of grain growth is quantified by the 27 increase in dry weight and the decrease in water content. Yoshida observed that the rate of grain growth was faster and the grain filling period was shorter at higher temperatures. Grain growth was initially slow, then entered a linear phase where the growth rate was fast, and then slowed down toward maturity. During the grain filling period, some of the assimilates from the other plant organs are translocated to the grains. Studies have shown that about 5 percent of the assimilates absorbed by the plant during the panicle development, and 30-50 percent of the assimilates absorbed after flowering, are translocated to the grains (IRRI, 1964). The duration of grain filling, that is, the time required to reach maximum weight, varies with the variety. 4.3. The Influence of Solar Radiation on Plant Growth Aside from temperature, solar radiation influences rice yield by directly affecting the physiological processes involved in grain production. Photosynthesis in green leaves uses solar energy in wavelengths from 0.4 to 0.7 pm, often referred to as the photosynthetically active radiation (PAR) (Yoshida, 1981). The ratio of PAR to total solar radiation is close to 0.50 in both the tropics and the temperate regions. This ratio represents a weighted. mean between the fractions for direct radiation and diffuse sky radiation. The solar radiation requirements of a rice crop differs from one growth stage to another with the greatest effect on grain yield during the reproductive and ripening stages (Yoshida, 1981). ....e h. 28 4 . 4. Photosynthesis Photosynthesis is a process by which solar energy is captured and converted into chemical energy and stored in the form of carbohydrates (Yoshida, 1981). It supplies organic substances which are used as building blocks in the process of plant growth and as energy sources for respiration (IRRI, 1965). About 80-90 percent of the dry matter of green plants is derived from photosynthesis; the rest (minerals) come from the soil (Yoshida, 1981). The photosynthetic activity occurs in the leaves which intercept the incident solar radiation. Thus, a rice plant with more surface leaf area is likely to intercept more solar energy than a rice plant with less surface leaf area. Yoshida (1981) outlined the factors that determine crop photosynthesis in the field. These factors were: incident solar radiation, photosynthetic rate per unit leaf area, leaf area index (LAI), and leaf orientation. The photosynthetic rate per unit leaf area is controlled by varietal characters and nitrogen nutrition at a given stage (IRRI, 1968). The leaf area index (LAI) is estimated from one surface of the leaf blade. It is a function of (a) tiller number per unit field area; (b) leaf number per tiller; and (c) average leaf size (IRRI, 1964). An active tillering variety tends to have a large LAI. Environmental and genetic factors influence leaf size. Studies have shown that LAI increases with increase in the dry weight of the leaves (IRRI, 1964). But, while photosynthesis increases with increase in LAI, the photosynthetic activity by one plant is not linearly proportional to the total photosynthetic activity of a plant community i If 7“] 1]"? I“ , 0 29 due to the effect of mutual shading. The fully exposed leaves receive more light than they are able to utilize while the leaves further down receive less sunlight than they need (IRRI, 1964). The degree of mutual shading is expressed by' the light transmission ratio (LTR) (IRRI,1964). LTR is the light intensity at the ground level of the plant population (I) divided by the light intensity at the top of the population (10). This ratio is expressed as the negative exponential function of the product between LAI and the extinction coefficient K. The result of the relationship is written as follows: LTR _ I _ e-(K - LAI) K measures leaf orientation. The optimum K value increases with the decrease in LAI (Tanaka et al., 1966). Studies indicate that the LAI values necessary to intercept 95 percent of the incident light in rice canopies range from 4 to 8. A large LAI and K values imply long, wide leaves while short leaves have smaller LAI and K values (Tanaka et al., 1966). In many studies, the I concept of mutual shading explain why tiller number, plant weight, ' LAI, and grain yield decrease when the surrounding plants increase in . leafiness (IRRI, 1964). 4.5. Carbohydrate Partitioning The distribution of assimilates or carbohydrates into the different plant organs varies with the growth stages and environmental conditions (Suzuki, 1983). Generally, the organs actively developing at the time of growth get a large proportion of the carbohydrates such 30 as sugars and starch (IRRI, 1964). Suzuki (1983) indicated that the ratio of distribution to roots and blades was high in the early growth stages, then a higher distribution to the stem and leaf sheath was evident during the middle growth stages, and finally after heading, the distribution to the panicle was predominant. A research study (IRRI, 1964) showed that during the early growth stage and until panicle development, about 50 percent of the carbohydrates assimilated became part of the cell walls and was not translocated, however, only 10,percent was retained after flowering. Yoshida (1981) reported that carbohydrates began to accumulate sharply about 2 weeks before heading and reached a maximum concentration in the plant's vegetative parts, mainly in the leaf sheath and culm, at heading. The concentration began to decrease as ripening proceeded and rose slightly again near maturity. Another study (IRRI, 1970) on the distribution of carbohydrates revealed that, 10 days before flowering, about 18 percent went to the leaf, 22 percent to the sheath and stem, 55 percent to the panicle, and about 5 percent was lost by respiration and senescence. Carbohydrates lost from the vegetative parts during grain filling and not used for respiration, are translocated to the grains (IRRI, 1964). 4.6. Grain Yield Rice yield is generally reported as rough rice at 14 percent moisture content (IRRI, 1964; Yoshida, 1981). Grain yield is a function of panicle number per square meter, spikelet or grain number per panicle, percent filled spikelets, and grain weight. The product r l‘: I < 31 of panicle number/m2 and number of spikelets or grains/panicle is the number' of spikelets or grains/m2. The relationship is written as follows (Yoshida, 1981): Grain yield (MT/Ha) - Panicle No./m2 - Spikelet No./Pan. - 2 filled Spikelets - 1,000-grain weight (g) - 10'5 - Spikelet No./m2 - 2 filled Spikelets 1,000-grain weight (g) - 10'5 The equation above shows that grain yield is directly related to spikelet or grain number. In most conditions, the 1,000-grain weight of rice is relatively constant and a very stable varietal character (IRRI, 1967; Murayama, 1979; Yoshida, 1981). The constant 1,000-grain weight of a given variety does not mean however, that individual grains have the same weight per grain. The percent filled-spikelet is also observed to be about 85 percent over a wide range of grain number (IRRI, 1971, 1972), although it has been observed to decrease to 60 percent when grain number is very large. At the wider spacing, grain yield is directly related to the panicle number, that is, the larger the panicle number, the larger is grain yield (Yoshida and Parao, 1972). 4.7. Soil-Water Condition and Water Losses The soil conditions of upland rice are diverse. De Datta and Feuer (1975) reported that soil texture varied from sand to clay; pH, from 3 to 10; organic matter content, from 1 to 50 percent; salt content, from almost 0 to 1 percent; nutrient availability, from acute deficiency to over supply. 32 Soil texture affects particularly the moisture status of upland rice soils. A clayey textural profile with a medium texture on the surface horizon. is suggested to be the most favorable for rice cultivation (De Datta and Feuer, 1975). Yoshida (1975) indicates that the soil texture determines the capillary ascent of water in soils. Water moves upward at a slow rate but for a longer distance in a fine soil compared to a rapid capillary action for a short distance in a coarse soil. For an illustration, he reported Kramer's work in 1969 which showed that with a water table 60 cm deep, water moved upward at 5 mm/day in a coarse-textured soil but only at 2 mm/day in a fine- textured soil. Different soils vary in their water storage capacitites. Yoshida (1975) defined. the water storage capacity as the water readily available to plants (in the range between the field capacity and permanent wilting point), measured in millimeters of water per unit depth of soil. He demonstrated that the storage capacity ranged from 4.3 to 8.6 mm/30 cm in fine sand to 77.0 mm/30 cm in a clay. As a result, plants growing in soils that had low storage capacities exhausted the readily available water and suffered from drought much sooner than plants growing in soils with high storage capacities. Yoshida further indicated that the extent to which ground water could supply the needed moisture to the root zones was primarily determined by the depth of the water table and the soil texture. A higher water table would supply more moisture to the root zones than a lower water table. A major difference between upland rice soils and lowland rice soils is the soil water regime. Unlike lowland rice soils, 33 Ponnamperuma (1975) explains that upland rice soils are not submerged or saturated with water for a long period of time during the growing season. However, he indicates that the rice plant is physiologically, morphologically, and anatomically adapted to submerged, anaerobic soils. So, under upland conditions, the rice plant has to adjust to a dry, aerobic soil condition. Ponnamperuma (1975) further illustrates that nutrients are delivered by mass flow and diffusion, the delivery rate decreasing with moisture content. So, the low soil moisture content in upland soils reduces the potential supply of nutrients to the roots. Thus, moisture stress is a primary limiting factor on the growth and yield of upland rice (Ponnamperuma, 1975; IRRI, 1974). This observation was supported by Chang and Vergara (1975) who reported that, under severe water stress, rice yield was poor despite heavy fertilization and effective weed control. Ponnamperuma adds that unlike submerged soils, upland soils are not able to adjust their pH levels to the favorable range of 6.5 to 7.0, a condition which could result to manganese and aluminum toxicities in strongly acid soils, and iron deficiency in alkaline soils. Finally, Ponnamperuma suggests that upland rice does best on the lower members of the toposequence of slightly acid soils, discouraging the use of sodic, calcareous, and saline soils, acid sulfate soils, and soils low in organic matter. Consistent with Ponnamperuma's findings, Yoshida (1975) observed that nitrogen became the major limiting factor for yield if adequate water was provided either through rainfall or irrigation. Water stress is brought about through many processes. One is by transpiration. Transpiration is the amount (grams) of water lost from 34 plant surfaces per gram of dry matter or carbohydrate produced. It is needed for plant growth. Yoshida (1975) reported that the transpiration ratio was generally around 250 to 350 g/g, implying that dry matter production was proportional to the amount of water transpired by the plant. Aside from transpiration, water is lost through evaporation, surface run-off, percolation, and seepage. Evaporation is the loss of water from free water surfaces (Yoshida, 1981). The combined water losses due to evaporation and transpiration are called evapotranspiration. The potential evapotranspiration, which is the amount of water lost through transpiration by a vegetation that completely covers a ground that is never water deficient, represents the maximum possible evaporative loss from a vegetative~covered surface. Yoshida presented several methods of calculating the potential evapotranspiration. These methods are the Penman equation, the Thornwaite method, and the van Bavel method. The procedure proposed by Priestley and Taylor (1972) is the method used in the CERES crop models. Yoshida (1981) further defines percolation, seepage, and run-off. Percolation, which occurs in a vertical direction, is largely affected by the topography, soil characteristics, and depth of the water table. Seepage is the water lost through the horizontal movement of water in a levee as determined by the slope and roughness of the soil surface in upland fields. Generally, percolation and. seepage are taken as a measure of the water-retaining capacity of the field. Surface run-off or overland flow occurs when rainfall intensity exceeds the surface storage capacity and the percolation-plus-seepage 35 rate or infiltration rate. Water stress severely affects shoot growth more than root growth, while tillering is least affected (IRRI, 1974). The analytical relationship of the soil-water balance and the water losses by evapotranspiration, surface run-off, percolation, and seepage are presented and discussed by Ritchie (1985) . 4.8. The Importance of Nitrogen Fertilization As plants grow, they absorb nitrogen from the soil to support photosynthesis. Studies have shown that photosynthesis and respiration, and correspondingly grain yield, increase with increasing levels of nitrogen, especially in fields short of the element (IRRI, 1964). This absorption will deplete the amount of nitrogen in the soil (IRRI, 1963). In order to maintain a high leaf photosynthetic activity for assimilating a large amount of carbohydrates and to supply more nitrogenous compounds to grains during the ripening stage, Murayama (1979) indicated that additional nitrogen must be supplied from the soil to the plant. He reported that high-yielding rice plants had high nitrogen concentration throughout its growth cycle. The straw of ordinary varieties contained 0.5-0.6 percent nitrogen at maturity while the high-yielding varieties contained 0.7-1.0 percent. For a high yielding plant, he reported that the optimum nitrogen concentration in the leaf blade was 2.3-4.0 percent at the early panicle formation stage and 2.2-3.3 percent at the heading stage. He further added that about 50-60 percent of total plant nitrogen in high-yielding plants with high nitrogen concentration had been 36 absorbed by the early panicle formation, and about 70-80 percent by heading and finally about 20-30 percent of nitrogen was absorbed during the ripening stage. Nitrogen compounds are mobile in the plant. They are constantly translocated from old organs to new ones (IRRI, 1963). During the ripening stage, about 70 percent of the nitrogen absorbed by the straw are translocated to the grain (Yoshida, 1981). Nitrogen content of the grain does not fluctuate. Patnaik and Rao (1979) outlined the many sources of nitrogen that could be applied to regulate nitrogen nutrition in the soil. Soil organic matter is one good source and the process of supplying nitrogen from this source to the plant is through mineralization by biochemical or microbial means. Another source of nitrogen is organic and green manures. Organic and green manures are crop residues such as straw or well-rotted compost incorporated into the soil. Chemical fertilizers, such as urea, ammonium sulfate, and ammonium phosphate to name a few, have been identified as the major sources of nitrogen. Choice of the form depends upon the availability and condition of the soil. The incorporation of fertilizer nitrogen into the reduced subsurface layer during land preparation is one method of application. This method has been observed to minimize losses resulting from runoff, volatilization, leaching, and denitrification. The amount of application is recommended to be between 40-50 Kg N/Ha with a maximum of 60 Kg N/Ha during the wet season, and 80-100 Kg N/Ha with a maximum of 120 Kg N/Ha during the dry season. Without nitrogen fertilization in soils not able to meet the nitrogen requirements of the plant, the plant suffers a rfitrogen 37 deficiency. Nitrogen deficiency eventually results in low yield. However, higher nitrogen application does not always bring about higher yields. Many studies have shown that when plants grow taller and actively tiller, the field become crowded with leaves, especially at high nitrogen levels, resulting in serious mutual shading, and sometimes lodging. This event could cause an imbalance between photosynthesis and respiration in the later stages of the growth and reduce the effectiveness of the nitrogen applied (IRRI, 1963). Thus, the nitrogen effect tends to decrease with increase in growth duration (Tanaka et al., 1966). The nitrogen transformation processes under upland condition, such as nitrogen mineralization, denitrification, and nitrate leaching follow that outlined for the CERES-Wheat model by Godwin and Vlek (1985). CHAPTER V THE ANALYTICAL STRUCTURE OF THE RICE SIMULATION MODEL In adapting the system to a digital computer, the state-space description has to be transformed into a discrete-time system so that the problem can be solved recursively by using difference equations. In discrete-time system representation, the rice production system is described in the following state-space equation: SE(1 TBASE; TEMPMX(k) < 33°C Otherwise, DTT(k) is estimated by dividing a 24-hour day into eight 3- hourly sections, calculate a temperature correction factor for each section (TMFAC), interpolate the air temperature for that section (TTMP), and then calculate the appropriate thermal time at time k. That is, TMFAC(k)i - 0.931 + 0.1141 - 0.070312 + 0.005313, 1 = 1, ..., 8 TTMP(k)i - TEMPMN(k) + TMFAC(k)i - (TEMPMX(k) - TEMPMN(k)) i-l, ..., 8 42 r 8 _£_ 2 (TTMP(k)i - TBASE) , TBASE s TTMP(k)i s 33°C 8 1-1 (33 - TBASE) 8 DTT(k) — < z [1 - ammoi - 33)/9], 8 1-1 33°C < TTMP(k)i < 42°C O , otherwise. L The production and distribution of carbohydrates are affected at each phenological stage by temperature, water, and nitrogen stresses. So these stress factors have to be estimated quantitatively. A temperature-related stress factor at time k (PRFT(k)), taking on real values in the closed interval 0-1, affects carbohydrate production. PRFT(k) is calculated from TEMPMN(k) and TEMPMX(k) weighted accordingly, with optimum at 26°C mean temperature. PRFT(k) - 1 - 0.0025 . [{0.25~TEMPMN(k)+O.75-TEMPMX(k)}-26]2 PRFT(k) 6 [0,1] Another temperature-related stress factor at time k is SLFT(k). SLFT(k) takes on real values in the closed interval 0-1 and affects leaf senescence due to temperatures below 6°C. 1, TEMPM(k) > 6°C and TEMPMN(k) > 0°C SLFT(k) - < 1 - ° ’ TEMPM(k) , 0° 5 TEMPM(k) s 6°C 6 1 o, TEMPM(k) < 0°C or TEMPMN(k) < 0°C 43 The water—related stress factors at time k are SWDF1(k) and SWDF2(k), while the nitrogen-related stress factors at time k are NDEFl(k) and NDEF2(k). These factors take on real values in the closed interval 0-1. SWDFl(k) and NDEF1(k) are the water stress and nitrogen. stress factors, respectively, affecting LLAO, where SW(k)A0 is the soil water content of the seed layer A0 at time k and LLAO is the lower limit of plant extractable soil water of that layer. Otherwise the extractable soil water at the sowing depth at time k (SWSD(k)), calculated proportionately between SW(k)Ao and LLAO and the soil water content and lower limit of plant extractable soil water of the next layer, SW(k),\0+1 and LLA0+1 respectively, has a value of 0.02 or greater. That is, SWSD(k) - (SW(k)Ao - LLAo)-0.65 + (SW(k)A0+1 - LLA0+1)~0.35 2) The mean air temperature at time k is between 15° and 42°C, that is, 15°C 5 TEMPM(k) s 42°C , 3) the accumulated degree-days from sowing time (k7) until time k is 45 or more, that is, 45 k 2 DTT(k) 2 45 , k7 4) the duration of the seeds in the ground is s 40 days If germination does not occur 40 days after sowing, crop failure is assumed. If germination occurs, the initial rooting depth (RTDEP(k), cm) is equivalent to the sowing depth (SDEPTH), that is, RTDEP(k) - SDEPTH 5.3. Emergence Stage (ISTAGE 9) Emergence stage covers the period from germination to emergence of the seedling from the soil surface. The duration, in degree-days, required from germination to emergence is P9. P9 is a linear function of the sowing depth (SDEPTH) with a slope of 7 degree-days/cm depth. P9 - 7 . SDEPTH During the emergence stage, the seedling gets its food supply from the seed reserve. The potential carbohydrate production at time k (PCARB(k)) under optimum water, nitrogen, and temperature conditions is a linear function of the thermal time at time k (DTT(k)). That is, within the optimal high and low temperature range, growth is faster at higher temperatures than at lower temperatures. From Chapter IV, the slope of potential dry matter or carbohydrate production is given as 0.00008265 g carbohydrate/plent/degree-day. At this stage, seedling growth is not affected by plant competition, so the total potential carbohydrate production is the product of a single plant’s production and the plant population per square meter (PLANTS). 46 PCARB(k) - 0.00008265 - PLANTS - DTT(k) However, the actual carbohydrate production at time k (CARBO(k)) is not always equal to the potential production due to environmental constraints. The actual carbohydrate produced can be less than the potential due to reduction by the most limiting of either the temperature stress (PRFT(k)) or soil water deficit (SWDFl(k)). CARBO(k) - PCARB(k) - min(PRFT(k), SWDFl(k)) The carbohydrates produced during this stage are distributed between the leaves and roots in proportional fractions. The fraction going to the roots at time k (PFR(k)) is represented as the negative exponential function of the seedling weight at time k-l (PLTWT(k- 1)/PLANTS), where PL'I'WT(k-l) is the total plant weight per square meter area at time k-l. PFR(k) _ 0.21 . e-(PLTWT(k-l)/PLANTS) The fraction of carbohydrates going to the leaves at time k PFL(k)) is 1 less PFR(k). PFL(k) - l - PFR(k) Root growth (GRORT(k)) and leaf growth at time k (GROLF(k)) are rtional to the amount of carbohydrates allocated to these parts a k. That is, )RT(k) - CARBO(k) - PFR(k) .F(k) - CARBO(k) - PFL(k) might of the roots (RTWT(k)) and the leaves (LFWTUO) at the sum of their respective weights at time k-l and growth that is , ' RTWT(k-l) + GRORT(k) 47 LFWT(k) - LFWT(k-l) + GROLF(k) During this stage, the increase in the rooting depth at time k is a linear function of the thermal time (DTT(k)) at time k with a slope of 0.15 cm/degree-day. So the rooting depth at time k (RTDEP(k)) is the sum of the rooting depth at time k-l and the increase in the rooting depth at time k, that is, RTDEP(k) - RTDEP(k-l) + 0.15 - DTT(k) The nitrogen content of the roots at time k (ROOTN(k)) is determined from the actual nitrogen concentration of the roots (RANC(k-l)), in g N/g root, and total root weight (RTWT(k—l)) at time k-l. ROOTN(k) - RANC(k-l) - RTWT(k-l) The nitrogen content of the stover at time k (STOVN(k)) is calculated from the total stover weight (STOVWT(k-l)) and the actual nitrogen concentration of the tops (TANC(k-l)), in g N/g top weight, at time k-l. STOVN(k) - STOVWT(k-l) - TANC(k-l) The leaves will start to grow during this stage. Leaf emergence per plant at time k (TI(k)) is a linear function of the thermal time at time k (DTT(k)) with a slope equivalent to the phyllocron interval. The phyllocron interval used in the simulation model is 83 degree- days/leaf. DTT(k) 83 TI(k) = The total number of fully expanded leaves from k=0 to time k (CUMPH(k)) is the sum of the daily leaf emergence (TI(k)). 48 k CUMPH(k) - z TI(k) k-O 5.4. Juvenile Stage (ISTAGE 1) Juvenile stage covers the period from emergence to the end of the basic vegetative phase. The duration in degree-days is the genetic coefficient P1. The root length density for the soil layers at time k (RLV(k)A), in cm root/cm3 soil, is first estimated at this stage. RLV(k),\ is initialized as a function of the plant population (PLANTS) and the thickness of the soil layer (DLAYRA). A is the soil layer index going from 1 through the total number of soil layers (NLAYR), A0 being the index for the seed layer. For each soil layer above the seed layer, RLV(k) is proportional to the plant population by a factor of 0.2 cm root/cm2 soil/plant, that is, Rmac)A - 0'2 ' PLANTS , A - 1, ..., 10-1 DLAYRA However, RLV(k) in the seed layer is reduced by a unitless fraction proportional to the difference between the cumulative depth of the seed layer (CUMDEP) and the rooting depth of the plants at time k (RTDEP(k)). That is, RLV(k)10' 0.2 - PLANTS . (1 _ CUMDEP - RTDEP(k) DLAYRA0 DLAYRA0 RLV(k) is zero after the seed layer, that is, ) RLV(k)A - 0 , A - A0+l, ..., NLAYR 49 When the seed reserve is still available for the plant to use, the potential carbohydrate production at time k (PCARB(k)) for each seedling is a logarithmic function of the thermal time at time k (DTT(k)) by :1 factor of 0.001 g carbohydrate/plant/degree-day. The total potential production is multiplied by the plant population/m2 (PLANTS). That is, PCARB(k) - 0.001 - PLANTS - log(DTT(k)) Then CARBO(k), PFR(k), PFL(k), ROOTN(k), and STOVN(k) are calculated as in ISTAGE 9. When the seed reserve is gone, growth is supported by photosynthesis. Photosynthesis is the process where the plant converts the intercepted light or solar radiation at time k (SOLRAD(k)) into carbohydrates. The plant utilizes the photosynthetically active radiation (PAR(k)) which is 50 percent of solar radiation (SOLRAD(k)). Thus, PAR(k) - 0.50 - SOLRAD(k) where PAR(k) has the unit MJ/m2. In Chapter IV, the Light Transmission Ratio (LTR) was given as the negative exponential function of the product of the leaf area index (LAI(k)) and the extinction coefficient K. That is, e-(K - LAI(k)) This means that the interception can be written as 1 _ e-(K - LAI(k)) The intercepted light, in the form of PAR(k), is then converted into carbohydrates as inluenced by the plant's genetic or varietal character for conversion efficiency, Cl. Intuitively, Gl defines the 50 erectness or droopiness of the leaves. When used in this equation, Cl has the unit g carbohydrate/MI of intercepted PAR(k). Thus the equation is stated as follows: -(K ° LAI(k-l)) PCARB(k) - 01 . PAR(k) . [1 - e ] where LAI(k-l) is the leaf area index at time k-l. K varies with LAI (k-l) , thus , r e-(LAI(k-l)) LAI(k—l) s 0.6 K - 1 0.58 - 0.04 - LAI(k-1) , 0.6 < LAI(k-l) s 5.0 , 0.36 LAI(k-l) > 5.0 The actual carbohydrates produced at time k (CARBO(k)) can be less than the potential production due to shading (POPFAC), temperature stress (PRFT(k)), and the most limiting effect due to water (SWDFl(k)) and nitrogen (NDEFl(k)) stresses at time k. That is, CARBO(k) - PCARB(k) - POPFAC - PRFT(k) - min(SWDF1(k), NDEF1(k)) When photosynthesis takes over carbohydrate production completely, a very slow growth in the stem occurs. The distribution of carbohydrate to the plant parts then changes. The fraction going to the leaves at time k (PFL(k)) is now a linear function of thermal time at time k with a slope of 0.001/degree-day. PFL(k) - PFL(k-l) + 0.001 - DTT(k) , PFL(k) s 0.84 PFL(k), however, is bounded on the right by 0.84. This condition ensures that a fraction of carbohydrates going to the leaves is at most 0.84, and allows for positive fractions going to the stem and roots, under a favorable growing day. The fraction going to the stem at time k (PFC(k)) is also a function of thermal time with a slope of 51 0.00002/degree-day, that is, PFC(k) - PFC(k-l) + 0.00002 - DTT(k) and the fraction that goes to the roots (PFR(k)) is 1 less PFL(K) and PFC(k). PFR(k) - l - PFL(k) - PFC(k) However, during the presence of a water deficit (SWDF2(k)) or nitrogen deficiency (NDEF1(k)) at time k, the plants redistribute their carbohydrates or assimilates in favor of the roots, reducing PFL(k) by the most limiting factor of the two stresses. This redistribution is active until just before the beginning of grain filling. Daily root growth (GRORT(k)) and leaf growth (GROLF(k)) are calculated, while root weight (RTWT(k)) and leaf weight (LFWT(k)) at time k are updated, as in ISTAGE 1. That is, GRORT(k) - CARBO(k) - PFR(k) GROLF(k) - CARBO(k) - PFL(k) RTWT(k) - RTWT(k-l) + GRORT(k) LFWT(k) - LFWT(k-l) + GROLF(k) Daily stem growth (GROSTM(k)) at time k is proportional to the amount of carbohydrates distributed to the stem. GROSTM(k) - CARBO - PFC(k) The stem weight at time k (STMWT(k)) is the sum of the weight at time k-l and the growth at time k. STMWT(k) - STMWT(k-l) + GROSTM(k) The total stover weight (STOVWT(k)) is the sum of LFWT(k) and STMWT(k), that is, STOVWT(k) - LFWT(k) + STMWT(k) The juvenile stage is characterized by leaf expansion. When the 52 seed reserve is used up, leaf area expansion at time k (PLAG(k)) is calculated. PLAG(k) is a function of leaf growth at time k (CARBO(k)-PFL(k)) and the number of leaves/plant emerging at time k (TI(k)). Leaf expansion is also a function of the plant's genetic characteristic for tillering (TR-Cl), which is a varietal character to form tillers or new plants thus, is given the unit: number of plants. As indicated in Chapter IV, a high value of (TR-Cl) indicates that the plant has a high capacity for tillering (or forming new plants) and therefore bigger capacity for leaf expansion. The conversion factor is 0.037 m2 leaf area expansion/leaf/g of leaf growth. Leaf expansion is however reduced by the most limiting of the three stress factors at time k: soil water deficit (SWDF2(k)), nitrogen stress (NDEF2(k)), and low temperature (SLFT(k)). That is, PLAG(k) - 0.037 - TR - Gl - TI(k) - CARBO(k) - PFL(k) min[SWDF2(k), NDEF2(k), SLFT(k)] Total leaf area at time k (PLA(k)) is the sum of the leaf area at time k-l and the expansion at time k, that is, PLA(k) - PLA(k-l) + PLAG(k) In this situation, PLA(k) is numerically equal to the leaf area index at time k (LAI(k)). Thus, LAI(k) - PLA(k) Tillering is also a characteristic of the juvenile stage. The tiller number per square meter at any time k (TILNO(k)) is the sum of the tiller number at time k-l and the tillering growth at time k. The tillering growth at time k is a function of the number of leaves/plant emerging at time k (TI(k)), the fraction of carbohydrates going to the leaves at time k (PFL(k), unitless), the plant's genetic 53 characteristic for tillering (TR-Cl, number of plants), and a population factor (lOO/PLANTS, per square meter). The conversion factor is 32 tillers/leaf. Thus, TILNO(k) - TILNO(k-l) + 32 ° TI(k) - PFL(k) - TR-Gl - (lOO/PLANTS) 5.5. Panicle Initiation (ISTAGE 2) Panicle initiation stage covers the period from end of juvenile stage to panicle initiation. The photoperiod or daylength in hours at time k (HRLT(k)) is determined from the daylength variation at time k (DLV(k)), which is a function of the solar declination, in radians, at time k (DEC(k)), the sine and cosine of the latitude of the production area (LAT), and the angle of the sun at civil twilight (in radians). The solar declination at time k (DEC(k)) is a sine function of the day of the year (JDATE), that is, (l) DEC(k) - 0.4093 - sin(0.0172 - (JDATE-82.2)) The daylength variation (DLV(k)) is calculated from the sine and cosine of both the latitude of the area (LAT) and the solar declination. DLV(k) is adjusted by the angle of the sun at civil twilight (0.1047). Thus, - sin(LAT) . sin(DEC(k)) - 0.1047 cos(LAT) - cos(DEC(k)) (2) DLV(k) - However, DLV(k) is bounded on the left by -0.87. Finally, the photoperiod is an arccosine function of the daylength variation, that is, 54 (3) HRLT(k) - 7.639 - arccos(DLV(k)) The rate of floral induction per degree-day at time k (RATEIN(k)) is a constant 1/136 if the photoperiod is less than or equal to the optimum photoperiod (P20). However, if the photoperiod at time k (HRLT(k)) is greater than P20, RATEIN(k) is slowed down and becomes a function of the photoperiod HRLT(k), the optimum photoperiod (P20), and the rate of photo-induction (P2R). l 136 + P2R - (HRLT(k) - P20)) RATEIN(k) - Panicle initiation stage is completed when the sum of the product of RATEIN(k) and DTT(k) from the beginning of this stage (k2) until time k is 1.0. That is, k E RATEIN(k) - DTT(k) - 1.0 k-k2 Panicle initiation stage is characterized by root growth, leaf emergence and leaf growth, stem growth, and tillering. The fraction going to the roots is set to 0.15. The fraction going to the leaves is decreasing, with a negative slope of 0.001/degree~day, in favor of the stem. That is, PFR(k) - 0.15 PFL(k) - PFL(k-l) - 0.001 - DTT(k) PFC(k) - l - PFR(k) - PFL(k) As in ISTAGE l, PFL(k) is adjusted in favor of PFR(k) whenever there is a water deficit or nitrogen deficiency. Daily root growth (GRORT(k)), leaf growth (GROLF(k)), stem growth (GROSTM(k)), root weight (RTWT(k)), leaf weight (LFWT(k)), stem weight (STMWT(k)), and stover weight (STOVWT(k)) at time k are updated, as in 55 ISTAGE 1. That is, GRORT(k) - CARBO(k) ~ PFR(k) GROLF(k) - CARBO(k) - PFL(k) GROSTM(k) - CARBO - PFC(k) RTWT(k) - RTWT(k-l) + GRORT(k) LFWT(k) - LFWT(k-l) + GROLF(k) STMWT(k) - STMWT(k-l) + GROSTM(k) STOVWT(k) - LFWT(k) + STMWT(k) 5.6. Heading Stage (ISTAGE 3) Heading stage covers the period from the enul of panicle initiation to heading where 50 percent of the panicles have exserted. The duration of this stage is P3. It is equivalent to 450 degree-days plus 15 percent of the accumulated degree-days from the beginning of the juvenile stage (k1) until just before heading stage (k3), that is, k3 P3 - 450 + 0.15 - 2 DTT(k) k=k1 The heading stage is characterized by root growth, leaf growth, emergence of last leaf, stem elongation, increase ix1 plant height, panicle growth, and decline in tiller formation. I PFR(k) is set to 0.10 during this stage. PFL(k) is reduced linearly with thermal time by a slope of 0.0014/degree-day, but bounded on the left by 0, while PFC(k) is increasing monotonically as a linear function of thermal time with a slope of 0.00072/degree-day. That is, 56 PFR(k) - 0.10 PFL(k) - PFL(k-l) - 0.0014 - DTT(k) PFC(k) - PFC(k-l) + 0.00072 - DTT(k) Since panicle growth is also a characteristic of this stage, the fraction going to the panicles at time k (PFP(k)) is positive. The positive fraction is guaranteed because the rate of decrease from PFL(k) is greater than the rate of increase for PFC(k). PFP(k) - l - PFR(k) - PFL(k) - PFC(k) The panicle growth at time k (PAWT(k)) is proportional to the amount of carbohydrates allocated to it, that is, PAWT(k) - CARBO(k) - PFP(k) The panicle weight at time k (PPAWT(k)) is the sum of the weight at time k-l and growth at time k. PPAWT(k) - PPAWT(kol) + PAWT(k) One panicle is allowed to grow as a linear function of thermal time with a slope of 0.00095 g/degree-day. This single panicle will be used to estimate the total number of panicles during harvest. Thus, the single panicle growth at time k (PNWT(k)) and the single panicle weight at time k (PERPAWT(k)) are estimated and updated as follows: PNWT(k) - 0.00095 - DTT(k) PERPAWT(k) - PERPAWT(k-1) + PNWT(k) As in ISTAGE l, PFL(k) is adjusted in favor of PFR(k) whenever there is a water deficit or nitrogen deficiency. Daily root growth (GRORT(k)), leaf growth (GROLF(k)), stem growth (GROSTM(k), root weight (RTWT(k)), leaf weight (LFWT(k)), stem weight (STMWT(k)), and stover weight (STOVWT(k)) at time k are updated, as in 57 ISTAGE 2. That is, GRORT(k) - CARBO(k) - PFR(k) GROLF(k) - CARBO(k) - PFL(k) GROSTM(k) - CARBO - PFC(k) RTWT(k) - RTWT(k-l) + GRORT(k) LFWT(k) - LFWT(k-l) + GROLF(k) STMWT(k) - STMWT(k-l) + GROSTM(k) STOVWT(k) - LFWT(k) + STMWT(k) The biomass at time k (BIOMAS(k)) is the sum of LFWT(k), STMWT(k), and PPAWT(k), while the total plant weight at time k (PLTWT(k)) is the sum of BIOMAS(k) and RTWT(k), that is, BIOMAS(k) - LFWT(k) + STMWT(k) + PPAWT(k) PLTWT(k) - BIOMAS(k) + RTWT(k) At the end of heading stage, the leaves stop to grow. 5.7. Beginning of Grain Filling (ISTAGE 4) Beginning of grain filling stage covers the period from the time when 50 percent of the panicles have exserted to beginning of grain filling. The duration is 170 degree-days. A temperature-related stress factor is modelled to affect the percentage of grain filling (FERTILE). When the mean temperature at time k (TEMPM(k)) is between 17°C and 35°C, FERTILE is a constant 85.3 percent, however this percentage is reduced by shading effects due to plant population (PLANTS). That is, FERTILE - 0.853 - 0.00028 ~ PLANTS Otherwise, at extremely high or low temperatures, the percentage of 58 grain filling is estimated as follows: FERTILE - 0.75-0.1 - (mum-35) , TEMPM > 35°C - 0.75-0.1 . (l7-TEMPM) , TEMPM < 17°C PFR(k) is set to a fixed fraction of 0.10 during this stage. PFL(k) continues to decrease linearly with thermal time by a slope of 0.0006/degree-day. PFL(k) - PFL(k-l) - 0.0006 - DTT(k) During this growth stage, there is a possibility of assimilate translocation from the leaves to the panicle. This event occurs when the value of PFL(k) becomes negative. The absolute value is added to the fraction allocated to the panicle. The negative value of PFL(k) causes a negative value of leaf growth and leaf expansion. This negative growth and negative leaf expansion represents leaf senescence. Although leaf senescence has occurred slightly during the previous growth stages as part of a natural process, it is during this stage that leaf senescence is clearly demonstrated since leaves have stopped to grow. Leaf senescence at time k (PLAG(k)), in m2 leaf area senescence/m2 of land area, is estimated to be influenced by the weight of leaf senescence at time k (CARBO(k)-PFL(k)) in proportion to the varietal characteristic for tillering (TR-G1). Leaf senescence is hastened in the presence of water, nitrogen, and temperature stresses. The conversion factor is 0.004 m2 leaf area senescence/gram-weight of leaf senescence/plant. Thus, leaf senescence is modelled as follows: PLAG(k) - 0.004 - CARBO(k) - PFL(k) - TR - Gl - {2 - min[SWDF2(k), NDEF2(k), SLFT(k)]} Since PLAG(k) is negative, leaf area (PLA(k)) and leaf area index (LAI(k)) at time k are correspondingly reduced. 59 PLA(k) - PLA(k-l) + PLAG(k) LAI(k) - PLA(k) PFC(k) is also starting to decline linearly with thermal time by a slope of 0.00215/degree-day but bounded on the left by 0. PFP(k) is increasing monotonically. That is, PFC(k) - PFC(k-l) - 0.00215 - DTT(k) PFP(k) - 1 - PFR(k) - PFL(k) - PFC(k) As in ISTAGE 1, PFL(k) is adjusted in favor of PFR(k) whenever there is a water deficit or nitrogen deficiency. Daily root growth (GRORT(k)), leaf growth (GROLF(k)), stem growth (GROSTM(k)), panicle growth (PAWT(k)), single panicle growth (PNWT(k)), root weight (RTWT(k)), leaf weight (LFWT(k)), stem weight (STMWT(k)), panicle weight (PPAWT(k)), single panicle weight (PERPAWT(k)), stover weight (STOVWT(k)), biomass (BIOMAS(k)), total plant weight (PLTWT(k)) at time k are updated, as in ISTAGE 3. That is, GRORT(k) - CARBO(k) - PFR(k) GROLF(k) - CARBO(k) - PFL(k) GROSTM(k) - CARBO(k) - PFC(k) PAWT(k) - CARBO(k) - PFP(k) PNWT(k) - 0.00095 - DTT(k) RTWT(k) - RTWT(k-l) + GRORT(k) LFWT(k) - LFWT(k-l) + GROLF(k) STMWT(k) - STMWT(k-l) + GROSTM(k) PPAWT(k) - PPAWT(k-l) + PAWT(k) PERPAWT(k) - PERPAWT(k-l) + PNWT(k) STOVWT(k) - LFWT(k) + STMWT(k) 60 BIOMAS(k) - LFWT(k) + STMWT(k) + PPAWT(k) PLTWT(k) - BIOMAS(k) + RTWT(k) Beginning this stage until maturity, the leaves stop to grow, that is, TI(k) - 0. 5.8. End of Grain Filling (ISTAGE 5) End of grain filling stage covers the period of grain filling. The duration, in degree-days, is 95 percent of the genetic coefficient PS. This stage is characterized by grain growth, leaf senescence, and the rate of root growth being equal to the rate of root senescence. The latter event is represented as PFR(k)-0. During this stage, there is a translocation of assimilates from both the leaves and the stem to the panicles where the grains are growing. PFL(k) and PFC(k) continue to decrease as a function of thermal time while PFP(k) continues to increase. The translocation from both the leaves and the stem trigger an equivalent amount of senescence in those organs as will be demonstrated by the reduction of their respective weights. PFL(k) - PFL(k-l) - 0.7 - 0.0009 - DTT(k) PFC(k) - PFC(k-l) - 0.3 - 0.0009 - DTT(k) PFP(k) - PFP(k-l) + 0.0009 - DTT(k) Daily root growth (GRORT(k)), leaf growth (GROLF(k)), stem growth (GROSTM(k)), panicle growth (PAWT(k)), single panicle growth (PNWT(k)), root weight (RTWT(k)), leaf weight (LFWT(k)), stem weight 61 (STMWT(k)), panicle weight (PPAWT(k)), single panicle weight (PERPAWT(k)), stover weight (STOVWT(k)), biomass (BIOMAS(k)), total plant weight (PLTWT(k)) at time k are updated, as in ISTAGE 4. That is, GRORT(k) - CARBO(k) - PFR(k) GROLF(k) - CARBO(k) - PFL(k) GROSTM(k) - CARBO(k) - PFC(k) PAWT(k) - CARBO(k) - PFP(k) PNWT(k) - 0.00095 - DTT(k) RTWT(k) - RTWT(k-l) + GRORT(k) LFWT(k) - LFWT(k-l) + GROLF(k) STMWT(k) - STMWT(k-l) + GROSTM(k) PPAWT(k) - PPAWT(k-l) + PAWT(k) PERPAWT(k) - PERPAWT(k-l) + PNWT(k) STOVWT(k) - LFWT(k) + STMWT(k) BIOMAS(k) - LFWT(k) + STMWT(k) + PPAWT(k) PLTWT(k) - BIOMAS(k) + RTWT(k) A single grain-growth concept is introduced during this stage. The rate of grain growth is a linear function of thermal time with a slope of 0.000083/degree-day. This single grain size will be used to estimate the number of grains per square meter during harvest. Grain growth at time k (GROCRN(k)) and grain weight at time k (GRNWT(k)) are calculated as follows: GROGRN(k) - 0.000083 - DTT(k) GRNWT(k) - GRNWT(k-l) + GROGRN(k) During this growth stage, the nitrogen concentration in the panicle and grain are estimated. The estimation process is part of 62 the nitrogen transformation and uptake which are outlined by Jones et a1. (1986). 5.9. Physiological Maturity (ISTAGE 6) The duration of the physiological maturity is the time required to complete P5 or when DTT(k) is less than or equal to 0. The latter condition allows for maturity even with insufficient degree-days accumulation due to low temperatures. When the time is completed, the grains are harvested. At harvest time, k=h. Panicle number per square meter at harvest (PNO(h)) is calculated from the total plant panicle weight (PPAWT(h)) divided by the weight of 1 panicle (PERPAWT(h)). PPAWT(h) PERPAWT(h) PNO(h) - Grain number per square meter at harvest (GRAIN(h)) is calculated from 90 percent of PPAWT(h), divided by a single grain weight in grams per grain (GRNWT(h)), and multiplied by the percentage of grain filling (FERTILE). PPAWT(h) - 0.9 GRNWT(h) GRAIN(h) = FERTILE The total weight of straw at harvest (PSTRAW(h)) is the sum of the total stover weight (STOVWT(h)) and 10 percent of the panicle weight (PPAWT(h)). PSTRAW(h) - STOVWT(h) + (PPAWT(h) - 0.1) Plant-straw ratio at harvest (PSRATIO(h)) is the ratio of the total panicle weight to the total straw. 63 PPAWT(h) PSTRAW(h) PSRATIO(h) - Dry grain yield (DYIELD(h)) is calculated as a product of the grain number (GRAIN(h)) and single grain weight (GRNWT(h)), adjusted to MT/Ha by multiplying with 0.01. DYIELD(h) - GRAIN(h) - GRNWT(h) - 0.01 Commercial grain (YIELD(h)) is dry grain yield adjusted to 14 percent moisture. DYIELD(h) 0.86 YIELD(h) - CHAPTER VI THE ANALYTICAL STRUCTURE OF THE MULTICRITERIA OPTIMIZATION PROCEDURE The multicriteria optimization procedure is a two-objective function resource allocation technique. It uses the Monte Carlo search method to explore the space of decision variables, 3(k), for feasibility. While the Pareto optimization procedure is conducted to identify a set of optimal, non-inferior solutions, the ideal vector of objective functions is also generated. From the set of Pareto optimal solutions, the min-max optimization procedure is used to identify the best compromise solution considering all the criteria simultaneously and on equal terms of importance. The general analytical structures of the algorithms of the Monte Carlo seardh method, the generation of the ideal vector, the Pareto optimization, and the min-max optimization used here were developed by Dr. Andrezj Osyczka (1984). The analytical structures were modified, when rmmessary, to incorporate the simulation model and to fit the peculiar structure of the problem. Hence, the definitions and the basic structure of the equations were taken from Osyczka's publication. The multicriteria optimization problem is formulated as follows: find a vector of input decision variables, u(k), which satisfies constraints and optimizes a vector of objective functions, f(fi). That 64 65 is, Find 3* such that R?) - opt Edi) (6.1) subject to: gmG) 20 m-l,2, M (6.2) where 3(k) - [u1(k),...,un(k)]T is a vector of decision variables defined in n-dimensional Euclidean space of variables E“, where n=3. The 3 decision variables are: u1(k) - day of the year for planting; u2(k) - amount of nitrogen fertilizer, in Kg N/Ha; and, u3(k) - plant population, in plants/m2. All 3 decision variables are input signals of the Kronecker delta sequence at k-0. Hence, 3(k) is 3(0) at k=0. The vector 5(0) will be hereinafter represented as a, u1(k) will be written as ul, u2(k) as u2, and u3(k) as u3. The variable k will be redefined as will be seen next. f(u) - [f1(§),...,fk(l—l)]T is a vector function defined in k-dimensional Euclidean space of objectives Ek, where k-2, and which are non-linear functions of the variables ul, u2, and u3. This vector function represents the criteria that will be considered in the optimization. The two criteria or objective functions are to maximize profit (151(3)) and to minimize production risk (£2(E)) as a function of E. The inequality constraints gm(u) given by (6.2) define the feasible region U and represent the restriction imposed on the decision variables, :1. gm(fi) are linear and non-linear functions of the variables ul, u2, and u3. Any point {I e U defines a feasible solution and the vector function f(§) maps the set U in the set F, which represents all possible values of the objective functions. The optimal solution (or set of optimal solutions) is denoted by 66 5*. I-[1,2] is used to denote the set of indices for the two objective functions; i will be used as a generic index for any variable. 6.1. The Monte Carlo Search Method The Monte Carlo seardh method is an exploratory method used to randomly generate new values of the vector 3 by using the formula (Osyczka, 1981, pp.70-7l): u. - u? + a.(u° - u?) for i - 1,2,3 (6.3) 1 1. 1. l 1 where uia is the given lower limit for ui, uib is the given upper limit for ui, and “i is a random number between 0 and 1. 'If A8 points of decision variables are desired to be evaluated, then the optimization procedure will generate Aa random numbers, one random number for each point. Equation (6.3) is used to obtain a new value of the decision variable ui. Each generated point will be tested for constraint violation and discarded if it is not a feasible solution. If the point is in the feasible region, the simulation and optimization will proceed. The random number generator is taken from the weather generator component of the CERES crop models. 6.2. Pareto Optimization As Osyczka (1984) presented it, Pareto optimization is based on the contact theorem which says that given a negative cone in Ek which 67 is the set C— - (f e Ek | f s 0} a vector f is a Pareto optimal solution for the multicriteria optimization problem if and only if (c‘ + f*) n F - (?*). Then he defines a Pareto optimum as follows: a point 3* e U is Pareto optimum if for every 3 e U either, A (£15) - fi<fi*>) (6.4) 161 or, there is at least one i e I such that f1(°) > fi(fi*) (6 5) To demonstrate the Pareto optimization concept, Osyczka's illustration is presented (1984, pp.66). Consider two solutions 3(1) and 5(2) for which there may be two specific cases (1) (c‘ + f(fi(1))) c (c‘ + ?(E(2))) (6.6) (2) (0" + E(E(1))) 5 (0‘ + f(fi(2))) (6.7) The following are defined: 30>- (1) (A) umfl' [u1 , u2 ,..., n - any given point in U, --(1) _ - is discarded. If none of the solutions from the set of Pareto optimal solutions satisfies either (6.6) or (6.7), then {10) becomes a new Pareto optimal solution. This intuitively means that the point 3* is chosen as the optimum if no criterion can be improved without worsening at least one other criterion. A set of these optimal, non-inferior solutions is generated to form a Pareto optimal curve. 6.3. Min-max optimization Min-max optimization uses the information of the optimum values of each objective function when solved separately. These values form the ideal vector of objective functions. The vector of objective functions for each point in the Pareto optimal curve is compared with the ideal vector. Relative deviations are calculated and the best solution is the one whose objective functions are as close as possible to their separately attainable minima. 69 Following Osyczka's outline (1984, pp.32-33), the nun-max optimization concept is presented as follows: Consider the ith objective function for which the relative deviation can be calculated from , _ l £1(E) - £2 I zi(u) - (6 3) l .9 1 , _ l f1(°) - £2 I zi(u) - 7 (6.9) I £15) I For (6.8) and (6.9) to be valid we have to assume that for every i e I and for every u e U, fio # 0 and fi(C) e 0. Let 2(3) - [21(3), 22(3)]T be a vector of relative increments which are defined in E2. The components of the vector E(E) will be evaluated from the formula .A (21(3) - max{z;(fi), 22(3)) (6.10) 161 Then the min—max optimum is defined as follows: A point 5* e U is min-max optimal, if for every 5 E U the following recurrence formula (6.11) is satisfied: Step 1 v1(E*) - min max{z.(E)} uEU 161 and then 11={i1}, where i1 is the index for which the value of 21(3) is maximal. TIIlr.——_ r! 70 If there is a set of solutions U1 6 U which satisfies Step 1, then Step 2 u2(5*) - min max{z.(u)} ueU iel l 1611 and then 12-{il,i2), where i2 is the index for which the value of 21(3) in this step is maximal. (6.11) Intuitively, this optimum means that knowing the extremes of the objective functions which can be obtained by solving the optimization problems for each criterion separately, the desirable solution is the one which gives the smallest values of the relative increments of all the objective functions. 6.4. Function Minimization For the sake of convenience, all the objective functions will be minimized, so the first objective function, to maximize profit, will be converted into a form which will allow for its minimization. This is done by employing the identity max £1(E) - m1n(-f1(fi)) (6.12) Now, the first objective function is to minimize the negative function of profit. In the same way, the inequality constraints of the form gm(3) s 0 m - 1,2,...,M can be multiplied with -l to convert them to the form -gm(fi) 2 0 m = 1,2,...,M 71 if necessary. 6.5. The Analytical Representation of the Objective Functions The purpose of the simulation-multicriteria optimization technique (SMOT) is to be able to predict grain yield, and correspondingly estimate profit and production risk, under a highly stochastic agricultural environment. Profit will be calculated from the expected value of grain yield, which is its mean. Production risk will be quantitatively expressed through a measure of the dispersion or variability from the mean, known as the standard deviation. The probability that a grain yield of one cropping season is within i 1 standard deviation is 0.682. To illustrate the concept, an example is presented. Suppose a certain production strategy is expected to yield 5 MT/Ha of grain with a standard deviation of i 0.5 MT/Ha. The probability that the actual yield will be in the range 4.5-5.5 MT/Ha (i 1 standard deviation) is 0.682. That is, for every 100 trials, 68 of those trials will yield between 4.5-5.5 MT/Ha. Compare this data with a second production strategy which is expected to yield 6 MT/Ha with a standard deviation of :I: 1.0 MT/Ha, and which is more costly. The probability of the actual yield being within the i 1 standard deviation is still 0.682. However, the actual yield could be in the range 5-7 MT/Ha. The first production strategy has a smaller dispersion or variability (:1: 0.5 MT/Ha) compared to the second production strategy which has a wider dispersion or variability (i 1.0 MT/Ha). Thus, a larger value of the standard deviation corresponds to a more risky operation. 72 The probability distribution of the occurrence of grain yield must be known in order to find the maximum likelihood estimators of its mean and standard deviation. A goodness-of-fit test with two parameters (mean and variance) unknown, as outlined by Larsen and Marx (1981), was used to test the hypothesis (Ho) that rice grain yield can be described by a normal probability distribution with mean, p, and variance, 02. Since there was no available actual yield data for a period long enough to be useful in the goodness-of-fit test, the simulation model was run for 25 years using actual weather conditions. The simulated grain yield data were used in the goodness-of—fit test. The underlying theorems and detailed calculations are in Appendix A. The hypothesis testing showed that grain yield (y) is normally distributed, that is, y1' y2' "" yNCYCLE has N(p, 02) distribution, where NCYCLE is the sample size. This probability distribution is described as follows: 1 e-wnw-M/alz JR: 0 pY (y) - , 0 < y < a (6.13) The maximum likelihood estimators for the mean, p, and variance, 02 9 are 8 and 82, respectively (Larsen and Marx, 1981, p.269-271): 1 NCYCLE fi - 2 yi (6.14) NCYCLE i=1 NCYCLE .2 1 . 2 0 ' ______ E (y. - p) (6.15) NCYCLE i=1 73 Larsen and Marx indicated that ii, the maximum likelihood estimator for p, is unbiased, efficient, and consistent. If 02 is known, 11 is sufficient. However, while 82, the maximum likelihood estimator for 02, is consistent, and sufficient if p is known, the estimator is biased; specifically, it tends to underestimate 02. In practice, 02 is estimated by the sample variance, 52, which can be expressed as follows: NCYCLE NCYCLE 2 NCYCLE - 2 y - ( z y.) 2 1-1 1 i-l 1 s _ (6.16) NCYCLE (NCYCLE - 1) Therefore, profit (f1(E)) and risk (232(5)) is mathematically represented as follows: f1(U) - PRICE - fi - TOTAL COST (6.17) f2(u) - s (6.18) where PRICE - market price of grain (S/MT), TOTAL COST - total cost of production per hectare (S/Ha) s - standard deviation, which is the square root of $2 (MT/Ha) 6.6. The Economic Scenario of the Rice Farm For an application of SMOT, the economic scenario is patterned after a rice farm in Laguna, Philippines, except that the dollar ($) sign is used in the monetary value instead of the Philippine peso sign. The farm could be briefly outlined as follows (Capule and Herdt, 1983): 74 the farmer is renting the land at $ 699/Ha land preparation, $ ZOO/Ha cost of seeds, $ 80.00/Ha hired labor for land preparation and weed control, $ 606.00/Ha complete pest (except weeds) control, $ 133/Ha weed control, $ 385/Ha cost of maintenance, 3 156.00/Ha opportunity cost of owned capital, 3 215.00/Ha imputed value of family labor, $221.00/Ha cost of nitrogen fertilizer, $ 70 per 50 Kg bag no irrigation (water from rain) hired labor for harvesting, $ l48/MT the farmer has at most $ l400/Ha to spend for fertilizer effective farm price of grain, $ 1020/MT the allowable limit of fertilizer is 900 Kg nitrogen as urea in one hectare of land area CHAPTER VII THE ALGORITHM OF THE SIMULATION-MULTICRITERIA OPTIMIZATION TECHNIQUE The algorithm of the simulation-multicriteria optimization technique (SMOT), will be discussed by module. One module can be made up of one or more subroutines. There are 10 modules, namely: the initialization module, the Monte Carlo search module, the random number generator module, the constraint function module, the simulation module, the objective function module, the ideal vector module, the Pareto optimization module, the min-max optimization module, and the Print module. The general algorithm of SMOT is outlined as follows: A. Initialization Module (1) Set IPAR - l, IWRITE - l (2) Read n, Aa, IPARCRV, NCYCLE, ula, 01b, uga, 02b, 1138, u3b from subroutine LIMITS (3) Set k - 2, ja - 1, fio - m and filp - m for i-l,2 (4) Set A - l (5) If IWRITE - 1, read the initial values of the decision variables 3(A), and other input data needed to run the rice simulation model. 75 76 Do steps 6 through 15 for A - l,2,...,Aa B. Simulation Module (6) Run the rice simulation model NCYCLE times to generate the mean grain yield, 0. C. Objective Function Module (7) Calculate fi(5(*)) for i - 1,2 (8) Print A, E<*>, a, fi(fi(*>) for i-1,2 (9) Set IWRITE - 0 D. Ideal Vector Module (10) Replace £10 by £i(fi(*)) for every i for which fi(fi(*>) < fio. E. Pareto Optimization Module (11) Call subroutine PARETO to check if the point E(*) is Pareto optimum. (12) If A < Aa then A - A + l and go to 13, otherwise go to 16. F. Monte Carlo Search Module (13) Call subroutine RANDOM to generate new values for u2(x) and u3(A). G. Constraint Function Module (14) Check constraint functions for feasibility. (15) If the point E<*) is in the feasible region go to 6, otherwise go to 12. 77 Do step 16 for j - 1,2,...,ja H. Min-max Optimization Module (16) Call subroutine MINMAX to check if the point Ejp is the min-max optimum. I. Print Module (17) Print “(33-P and 'ij for j - l,2,...,ja and If", 11*, at?) EEG"). Do steps 18,19 if IPARCRV > 1. (18) If IPAR < IPARCRV then IPAR-IPAR+1 and go to 19, otherwise end. (19) Call subroutine RANDOM to generate a new value for ul(A). Go to 3. The algorithm of subroutine PARETO is as follows: (1) Read k, n, ja, 3(A), f(E(A)), and fi (2) Set j - 1 (3) If for every i E I we have fi(u(A)) < fijp then substitute EjP - 3(A), fjp - ?(E(*)), and fijp - fi, and go to 7, otherwise go to 4. (4) If for every i e I we have £i(3(*>) > fijp then go to 8, otherwise go to 5. (5) Set j — j + 1 (6) If j > ja then ja - ja + 1 and EjaP - EU), PjaP = RUM), and fijp - fl, and go to 8, otherwise go to 3. 78 (7) If j < ja then j - j + l, and go to 3. (8) Return The algorithm of subroutine MINMAX is outlined as follows: (1) Read k, n, j, ja, i0, EjP, 'f'J-P, and fijP forj - l,2,...,ja (2) Evaluate the vector §(fijp) using formula (6.10) (subroutine MAX) (3) If 5(519) - 0, then retain this solution as the optimum since there is no better solution, and go to 5, otherwise go to 4. (4) Find the maximal values of all the steps of formula (6.11) for the point GjP. (5) Return The algorithm of subroutine RANDOM is as follows: b b (1) Read ula, ulb, uza, u2 , uga, u3 (2) Generate random number a1 (subroutine RANDN) (3) Generate the point 5(A) following formula (6.3) (4) Return A flowchart of the SMOT algorithm is presented in Figure 7.1. The Fortran program of SMOT is in Appendix B. [ IPAR-l. INTI-1 I I. [lead n. x‘, imam. acme. u 2 . u: for 1-1.2.3 k-Z. 1‘-1. ‘1'” 221-- for 1-1.2 I A I l. WRITE-l Y Reed initial values of 1.1“) and other input data to m the I am: < m In the emotion nodel was I Calculate ! (u( )) {or 1-1. 2 I I Print \. «IL; Him) to: 1-1.2I E -(X) Replace f1 by ! 1(u(k) for every I. to: which I (u 0 )‘ft J. [Cell eubroutine 9mm I . Cell eubroutine RANDOM for “EU . ugu I Check constraints I Print 5" . ?° for 3-1.2,...,3 , u', 1', ?(6'). 3(5') .1 3 mm . IPARCRV a Figure 7.1. Flowchart of the simulation-multicriteria optimization technique (SMOT) IPAR- IPAR+1 Call subroutine RANDOM for “IMIL CHAPTER VIII DISCUSSION OF RESULTS Two computer software packages have been developed as output of this dissertation research. These are the rice crop growth simulation model and the multicriteria optimization procedure. These two software packages comprise the simulation-multicriteria optimization technique (SMOT) as a decision support system to evaluate profit and production risk for use by agricultural research scientists, extension workers, farmers, and policy-makers involved in rice production under upland condition. 8.1. The Rice Growth Simulation Model The rice simulation model is a growth simulation model for upland condition. It is designed to predict the growth components and yield of different rice varieties under the tropical and sub-tropical agroclimatic environments. The simulation model is programmmed in Fortran 77 and set-up to run interactively in any IBM—compatible microcomputer with at least 256 K bytes of random access memory (RAM). In a Compaq microcomputer with 640 K bytes RAM, simulation time of one cropping season takes about 25 to 40 seconds. In the Hewlett Packard (HP) 9000 minicomputer system, the user time is between 9.3 to 9.9 80 81 seconds. For instructions on how to run the simulation model, a user documentation has been developed (Appendix C). Model validation is based on observed, field-measured data, whenever available, and intuitive knowledge of experts, whenever data is lacking. The validation covers the phenology, growth and partitioning, leaf area index, and grain yield under water and nitrogen constraints. Table 8.1.1 presents a comparison between the predicted (P, model) and the observed (0, field-measured) phenological occurrence, days after sowing (DAS), of 3 upland rice varieties, namely: IR43, UPLRIS, and UPLRI7. The data were the result of a series of experiments for drought tolerance conducted at the upland experimental farm of the International Rice Research Institute (IRRI), Los Banos, Philippines during the period 1983-1984. Actual weather data, collected from the site, were used in the simulation. Due to lack of information, some of the soil parameters were estimated based on expert opinion. The sowing dates were based on actual information. For each simulation, plant population was 400 plants/m2 and was applied with 60 Kg N/Ha of fertilizer a day before sowing time. The three phenological events being compared are the time of emergence, heading, and physiological maturity. The comparison showed that from an average of six experiments, the predicted time of emergence was one day less than the observed for the three varieties. However, the predicted time of heading was one day earlier for IR43, two days later for UPLRIS', -and four days earlier for UPLRI7, compared with the observed data“ The predicted occurrence for physiological maturity was very good: on the average of six experiments, only a day earlier 82 TABLE 8.1.1. COMPARISON BETWEEN PREDICTED AND OBSERVED PHENOLOGICAL OCCURRENCE OF 3 RICE VARIETIES, DAYS AFTER SOWING (DAS) Variety Sowing Date Emergence Heading Maturity Name (1983) P O P O P O IR43 May 26 4 8 99 97 128 125 Jun 30 4 6 96 99 127 134 Jul 8 4 4 97 99 128 127 Aug 4 4 4 95 100 127 123 Aug 28 4 4 94 100 127 127 Nov 10 4 6 98 93 129 134 (Average) 4 5 97 98 127 128 UPLRIS Jun 20 4 4 98 95 121 119 Jun 30 4 6 98 92 120 116 Jul 8 4 4 97 95 120 120 Aug 4 4 4 94 100 118 123 Aug 28 4 4 93 93 117 116 Nov 10 4 6 96 91 119 125 (Average) 4 5 96 94 119 120 UPLRI7 May 26 4 8 92 91 119 116 Jun 20 4 4 89 88 117 112 Jun 30 4 6 88 91 116 116 Jul 8 4 4 88 89 117 119 Aug 4 4 4 86 99 115 123 Aug 28 4 4 84 93 115 116 (Average) 4 5 88 92 117 117 83 than the observed for IR43 and UPLRIS while about the the same for UPLRI7. A rice simulation model that is able to predict the phenological occurrence of the crop will provide good opportunities for a rice farmer to plan out and optimize the farm operations. Some farmers may want to apply fertilizer and/or irrigation just before heading. A good prediction on the physiological maturity will also allow the farmer to plan for harvesting and marketing. In the Philippines and other Asian countries where harvesting and marketing are mostly done manually with the help of hired labor, an advanced planning will ensure early contracts for hired labor and hence, harvest operation and marketing transportation may be done on schedule. Other farmers may want to plant cash crops following rice to make use of the residual fertilizer and soil moisture. An evaluation of the maturity duration of the different varieties within the climatic area will give the farmer insight as to the kind of rice variety appropriate for the season in order to maximize the cropping pattern. The next set of comparison between predicted and observed is on IR36 variety. The data were from a Ph.D. dissertation by A. Chinchest (1981) on the effects of water regimes and amount of nitrogen on the growth of some selected rice varieties. The experiment was replicated four times and conducted at the upland farm of IRRI during the 1980 dry season. Actual weather data for the duration of the experiment, collected from the site, were used in the simulation run. Some of the soil parameters needed in the model were estimated. The simulation inputs include sowing date, plant population, fertilizer application, and irrigation levels, according to actual information. 84 Table 8.1.2 presents the result of the phenological comparison. Model predictions regarding the time of occurrence for floral initiation and heading were a day earlier while the occcurrence for maturity was two days earlier compared to the observed time of occurrence. TABLE 8.1.2. COMPARISON BETWEEN PREDICTED AND OBSERVED PHENOLOGICAL OCCURRENCE OF IR36 VARIETY (Sowing Date: January 9,1980) Phenologicel stage Predicted Date Observed Date Floral Initiation Febuary 27, 1980 Febuery 28, 1980 Reading or Flowering March 29, 1980 March 30, 1980 Maturity April 26, 1980 April 28, 1980 Using Chinchest's observed data, more comparisons between the predicted output of the simulation model and the observed data were done on the growth components of IR36 with 4 nitrogen treatments (0, 30, 60, and 120 Kg N/Ha) and 2 irrigation levels (about 810 and 795 mm of water). A biomass comparison, from 4 sampling dates on the 4 nitrogen treatments and irrigation of about 795 mm water, was conducted. The predicted and observed values are presented in Table 8.1.3. From an average of 4 sampling intervals, the comparison showed 12.6 percent, 18.1 percent, 21.2 percent, and 21.0 percent difference in biomass between the predicted and observed for 0, 30, 60, and 120 Kg N/Ha, respectively. The simulation model tends to underpredict biomass at all sampling intervals as demonstrated graphically in Figures 8 1.1 (0 N), 8 1.2 (30 Kg N/Ha), 8.1.3 (60 Kg N/Ha), and 8.1.4 (120 Kg N/Ha). 85 TABLE 8.1.3. PREDICTED AND OBSERVED BIOMASS OF IR36 VARIETY AT 4 TREATMENTS OF NITROGEN FERTILIZER ON 4 SAMPLING INTERVALS. 795 mm WATER APPLIED. Nitrogen Sampling Predicted Observed Percent Treatment Interval Difference (x; N/He) (DAS) (s/mz) (s/mz) O 57 202. 228. 11.4 69 343. 349. 1.7 89 604. 829. 27.1 106 850. 946. 10.1 (Average) 12.6 30 57 268. 318. 15.7 69 427. 501. 14.8 89 722. 983. 26.6 106 1009. 1192. 15.3 (Average) 18.1 60 57 319. 366. 12.8 69 496. 548. 9.5 89 821. 1233. 33.4 106 1145. 1614. 29.1 (Average) 21.2 120 57 381. 390. 2.3 69 589. 793. 25.7 89 963. 1302. 26.0 106 1342. 1920. 30.1 (Average) 21.0 1000' SOOJ 600‘ Biomass, 2 g/m 400- Figure 8.1.1. 1400 1 T 1200 ~ 1000 .. 800 Biomass, 2 600 S/m 400 200 O'J 0 Figure 8.1.2. 86 Legend: e—e Observed w—u Predicted r “r ‘fi 80 100 r— T fir ‘1 I I 40 60 Days After Sowing r 20 Comparison between predicted and observed biomass of IR36 variety with O N. Legend: 0.0 Observed ._‘ Predicted U r I l’ I ]— ! I r [ fi 20 4O 6O 80 100 Days After Sowing Comparison between predicted and observed biomass of IR36 variety with 30 Kg N/Ha. 87 Biomass, 1000‘ g/m2 800- Legend: 0-0 Observed 01 ‘-* Predicted ' r I 1 ' I f I _' l r 0 20 40 60 80 100 Days After Sowing Figure 8.1.3. Comparison between predicted and observed biomass of IR36 variety with 60 Kg N/Ha. 20001 1 18001 1600. 1400— 12001 . Biomass, 1000‘ q g/m2 800- d 600- q 4001 0 r7 I . . 1 0 20 40 60 Days After Sowing Legend: 0-0 Observed fi-fi Predicted ' I I 80 100 I r 1 Figure 8.1.4. Comparison between predicted and observed biomass oi IR36 variety with 120 Kg N/Ha. 88 Table 8.1.4 shows a comparison on the straw weight at harvest on the 4 fertilizer treatments and 2 irrigation levels, 810 mm (W1) and 795 mm (W2) water applied. From an average of‘4 nitrogen treatments, the difference in straw weight between predicted and observed is 3.1 percent for W1 and 4.7 percent for W2. TABLE 8.1.4. PREDICTED AND OBSERVED STRAW WEIGHT AT HARVEST OF IR36 VARIETY AT 2 IRRIGATION LEVELS AND 4 NITROGEN TREATMENTS. Irrigation Nitrogen Predicted Observed Percent Level Treatment Difference (mm) (x; N/Ba) (almz) (almz) 810 mm (W1) 0 419. 405. 3.4 30 512. 523. 2.1 60 589. 564. 4.4 120 700. 683. 2.5 (Average) 3.1 795 mm (W2) 0 416. 420. .0 30 506. 490. 3.3 60 581. 600. .2 120 683. 613. 11.4 (Average) 4.7 Table 8.1.5 is a rearrangement of the entries in Table 8.1.4 in order to demonstrate the effect of nitrogen treatments on the prediction of straw. It shows that the simulation model is able to predict consistently better at fertilizer treatments 0, 30, and 60 Kg N/Ha (2.2, 2.7, and 3.8 percent difference, respectively) than at the 120 Kg N/Ha treatment (7.0 percent difference). 89 TABLE 8.1.5. PREDICTED AND OBSERVED STRAW WEIGHT AT HARVEST OF IR36 - VARIETY AT 4 NITROGEN TREATMENTS AND 2 IRRIGATION LEVELS. Nitrogen Irrigation Predicted Observed Percent Treatment Level Difference (Kg N/Ba) (mm) (g/mz) (g/mz) 0 810 419. 405. 3.4 795 416. 420. 1.0 (Average) 2.2 30 810 512. 523. 2.1 795 506. 490. 3.3 (Average) 2.7 60 810 589. 564. 4.4 795 581. 600. 3.2 (Average) 3.8 120 810 700. 683. 2.5 795 683. 613. 11.4 (Average) 7.0 90 Grain yield comparison between predicted and observed, at 14 percent moisture content, on the 4 nitrogen treatments (0, 30, 60, and 120 Kg N/Ha), and 2 irrigation levels (810 and 795 mm, W1 and W2 respectively), is shown in Table 8.1.6. From an average of 4 nitrogen treatments, the difference in yield is 8.8 percent for W1 and 8.6 percent for W2. TABLE 8.1.6. GRAIN YIELD OF IR36 VARIETY AT 2 IRRIGATION LEVELS AND 4 NITROGEN TREATMENTS. Irrigation Nitrogen Predicted Observed Percent Level Treatment Difference (mm) (x; N/fla) (s/mz) (s/mz) 810 mm (H1) 0 4.3 4.6 6.5 30 5.0 5.6 10.7 60 5.6 6.7 16.4 120 6.6 6.7 1.5 (Average) 8.8 795 mm 0 4.3 4.6 6.5 30 4.9 5.3 7.5 60 5.5 6.9 20.3 120 6.5 6.5 0.0 (Average) 8.6 The entries of Table 8.1.6 were rearranged and presented in Table 8.1.7 in order to show the effect of nitrogen treatments on the prediction of yield. Table 8.1.7 shows that grain yield prediction is best at 120 Kg N/Ha treatment (0.8 percent difference); prediction is poorest at 60 Kg N/Ha treatment (18.4 percent difference). 91 TABLE 8.1.7. GRAIN YIELD OF IR36 VARIETY AT 4 NITROGEN TREATMENTS AND 2 IRRIGATION LEVELS. Nitrogen Irrigation Predicted Observed Percent Treatment Level Difference (x; N/Ha) (mm) (slmz) (slmz) 0 810 4.3 4.6 6.5 795 4.3 4.6 (Average) 6.5 30 810 5.0 5.6 10.7 795 4.9 5.3 7.5 (AVOIOBO) 9.1 60 810 5.6 6.7 16.4 795 5.5 6.9 20.3 (Average) 18.4 120 810 6.6 6.7 1.5 795 6.5 6.5 0.0 (Average) 0.8 92 The predicted leaf area index (LAI) on the 4 fertilizer treatments and 795 mm water irrigation for 7 sampling dates is shown in Table 8.1.8. The graphical illustration of the LAI curve is shown in Figure 8.1.5. TABLE 8.1.8. PREDICTED LAI OF IR36 VARIETY ON 7 SAMPLING INTERVALS, DAYS AFTER SOWING (DAS). 045 0 u 30 x; N/Ha 60 x; N/Na 120 Kg N/a. 4 0. o. 0. 0. 35 0.9 1.6 2.0 2.2 49 2.1 3.0 3.7 4.4 00 2.9 4.0 4.9 5.9 09 2.7 3.0 4.7 5.7 107 1.9 2.0 3.5 4.4 108 1.9 2.0 3.5 4.4 8.0. Legend: a—e 0 N H 60 Kg N/Ha H 120 Kg N/Ha 6.0‘ LAI 4 0- 2.0. OeOJ ‘ I T l f I v ‘1 1 fl 0 20 40 E) 80 100 120 Days After Sowing Figure 8.1.5. Leaf area index (LAI) of IR36 variety with 0 N, 30, 60, and 120 Kg N/Ha. 93 For lack of observed (field-measured) data on LAI of this experiment, the observed LAI values of IR36 sown on November 6, 1984 with 100 Kg N/Ha in flooded condition at the IRRI experimental farm, is presented in column 6 of Table 8.1.9. The corresponding LAI curve is presented in Figure 8.1.6. The purpose of presenting this observed data is to provide aproximate comparison with the predicted results in Table 8.1.8 and Figure 8.1.5. The shape of the predicted LAI curve (Figure 8.1.5) approximates that of the observed LAI (Figure 8.1.6). The maximum LAI of the predicted at 60 Kg N/Ha is 4.9 while the maximum LAI of the observed is 4.6. Both maxima occurred 80 days after sowing. TABLE 8.1.9. ROOT WEIGHT, LEAF WEIGHT, STEM WEIGHT, PANICLE WEIGHT, AND LAI OF IR36 VARIETY ON 9 SAMPLING INTERVALS, DAYS AFTER SOWING (Sown on Nov. 6, 1984, with 100 Kg N/Ha in flooded condition, IRRI, Philippines). DAS Root Leaf Stem Panicle LAI Weight Height Height Weight (g/mz) (g/mz) <3/m21 (g/mz) 30 4.0 4.8 3.6 0. 0.1 40 9.8 11.4 9.4 0. 0.3 50 19.8 44.2 34.3 9.8 1.2 60 53.5 107.6 94.7 25.5 2.9 70 82.0 173.3 214.3 46.9 4.3 80 73.0 195.7 341.0 60.9 4.6 90 93.1 193.4 537.9 82.4 4.6 100 99.7 178.5 302.9 591.4 3.7 110 105.3 162.3 242.0 652.6 3.4 94 OeO ' '— r 1 U I V I r U V j 0 20 40 60 80 100 120 Days After Sowing Figure 8.1.6. Observed LAI of IR36 variety sown on Nov. 6, 1984 in flooded condition with 100 Kg N/Ha. To evaluate growth and partitioning, the predicted results of root weight, leaf weight, stem weight, and panicle weight of 7 sampling dates on the 4 nitrogen treatments are presented in Table 8.1.10 (0 N), Table 8.1.11 (30 Kg N/Ha), Table 8.1.12 (60 Kg N/Ha), and Table 8.1.13 (120 Kg N/Ha). For graphical illustration, the plant parts with O N and 120 Kg N/Ha are shown in Figures 8.1.7 and 8.1.8, respectively. For an approximate comparison, the root weight, leaf weight, stem weight, and panicle weight of IR36 sown on November 6, 1984 in flooded condition are presented in Table 8.1.9 and Figure 8.1.9. 95 TABLE 8.1.10. PREDICTED ROOT WEIGHT, LEAF WEIGHT, STEM WEIGHT, AND PANICLE WEIGHT OF IR36 VARIETY ON 7 SAMPLING INTERVALS, DAYS AFTER SOWING (DAS), WITH 0 N. DAS Phenological Root Leaf Stem Panicle Stage Height 'Weight Height Weight (s/mz) (g/mz) (g/mz) (g/mz) EHERGENCE 0.0 0.1 0.0 0.0 35 END JUVENILE 32.6 49.7 0.4 0.0 STAGE 49 FLORAL 103.4 110.3 24.0 0.0 INITIATION 80 READING 180.8 150.3 220.0 92.5 89 START GRAIN 187.6 144.3 291.7 168.4 FILL 107 END GRAIN FILL 171.4 92.7 274.2 491.0 108 PHYSIOLOGICAL 171.4 92.7 274.2 491.0 HATURITY TABLE 8.1.11. PREDICTED ROOT WEIGHT, LEAF WEIGHT, STEM WEIGHT, AND PANICLE WEIGHT OF IR36 VARIETY ON 7 SAMPLING INTERVALS, DAYS AFTER SOWING (DAS), WITH 30 Kg N/Ha. DAS Phenological Root Leaf Stem Panicle Stage Weight Height Height Weight (g/mz) (a/mz) (a/mz) (g/mz) 4 EMERGENCE 0.0 0.1 35 END JUVENILE 45.8 82.8 STAGE 49 FLORAL 135.4 159.4 30.4 0.0 INITIATION 80 READING 222.6 205.0 252.5 104.7 89 START GRAIN 229.9 197.9 333.3 190.4 FILL 107 END GRAIN PILL 210.1 136.7 312.8 568.2 108 PHYSIOLOGICAL 210.1 136.7 312.8 568.2 HATURITY 96 TABLE 8.1.12. PREDICTED ROOT WEIGHT, LEAF WEIGHT, STEM WEIGHT, AND PANICLE WEIGHT OF IR36 VARIETY ON 7 SAMPLING INTERVALS, DAYS AFTER SOWING (DAS), WITH 60 Kg N/Ha. DAS Phenological Root Leaf Stem Panicle Stage Weight Weight Weight Weight (almz) (s/mz) (s/mz) (s/mz) EMERGENCE 0.0 0.1 0.0 0.0 35 END JUVENILE 49.8 103.5 0.8 0.0 STAGE 49 FLORAL 148.6 195.1 34.9 0.0 INITIATION 80 HEADING 242.6 248.4 281.0 116.0 89 START GRAIN 251.1 240.1 370.1 210.6 PILL 107 END GRAIN PILL 229.5 170.0 346.9 638.9 108 PHYSIOLOGICAL 229.5 170.0 346.9 638.9 MATURITY TABLE 8.1.13. PREDICTED ROOT WEIGHT, LEAF WEIGHT, STEM WEIGHT, AND PANICLE WEIGHT OF IR36 VARIETY ON 7 SAMPLING INTERVALS, DAYS AFTER SOWING (DAS), WITH 120 Kg N/Ha. DAS Phenological Root Leaf Stem Panicle Stage Weight Weight Weight Weight (G/mz) (s/mz) <5/m21 (s/mz) 4 EHERGENCE 0.0 0.1 0.0 0.0 35 END JUVENILE 48.5 114.3 0.9 0.0 STAGE 49 FLORAL 153.3 231.9 41.0 0.0 INITIATION 80 HEADING 254.8 302.1 325.9 134.3 89 START GRAIN 266.2 291.5 428.7 243.2 PILL 107 END GRAIN PILL 243.2 207.7 400.9 746.8 108 PHYSIOLOGICAL 243.2 207.7 400.9 746.8 MATURITY 97 800 1 Legend: W Root weight . H Leaf weight H Stem weight 600- H Panicle weight « 1- / / Weight, 400‘ / 2 ’/ g/m ‘ , 200‘ 01 - — r I -. . . . . . I I 0 20 40 60 80 100 120 Days After Sowing Figure 8.1.7. Predicted root weight, leaf weight, stem weight, and panicle weight of IR36 variety with 0 N. 800 Legend: ‘1 0-0 Root weight H Leaf weight . H Stem weight H Panicle weight 600 " Weight, . 2 g/m 400‘ 200~ 0“ r g I ' I 'l I w I I l ' l 0 20 40 60 80 100 120 Days After Sowing Figure 8.1.8. Predicted root weight, leaf weight, stem weight, and panicle weight of IR36 variety with 120 Kg N/Ha. 98 800- Legend: H Root weight J 0-0 Leaf weight H Stem weight 600.. H Panicle weight Weight, ‘ 2 8411 400‘ 200‘ 0 y T f I T I t 1 0 20 40 60 80 100 120 Days After Sowing Figure 8.1.9. Observed plant parts of IR36 variety sown on Nov. 6, 1984 in flooded condition with 100 Kg N/Ha. A simulation model that is able to predict the yield of rice will be useful to farmers and agricultural extension workers in evaluating the economic farm plans. A more extensive discussion on the economics of rice production will be covered in the next section. The rice simulation model will also provide insight to rice physiologists and agronomists as to the rice plant's mechanism to respond to various climatic environments. 99 8.2. The Simulation-Multicriteria Optimization Technique (SMOT) To demonstrate the capability of SMOT, it was implemented three times in a farm environment representative of the Philippines. SMOT, however, can be reparameterized to fit the different agricultural environments in the tropics and subtropics. The first implementation had the following conditions: u1-l7l (June 20), u2 and u3 varying randomly; the second implementation had u1-171 (June 20), u2 varying randomly, and u3-400 plants/m2; and, the third implementation had u1-244 (September 1), u2 and u3 varying randomly. For each u1, SMOT is run 200 times to generate 200 new points of u2 and u3. Every feasible combination of ul, uz, and u3 represents a point B e U. Thus, a maximum of 200 6 points are generated. Let every point 3 e U be called a production strategy. Each point B e U goes through 25 simulations of the rice model (with actual weather data collected from Los Bafios, Philippines), and comprises one SMOT run. Hence, the maximum total number of iterations for each implementation is 5000 (200 x 25). For every 25 simulations, that is, one SMOT run, the user time in the HP 9000 minicomputer system is about 165 seconds, thus, the total user time for the 200 runs is estimated to be 33,000 seconds or 9 hours and 12 minutes. For each SMOT run, the mean yield (fi), profit (f1), and sample standard deviation (f2) are calculated. As indicated earlier, the sample standard deviation is used as a measure of risk: a low value of the standard deviation means a lower risk relative to a high value which means a higher risk. During the 200 SMOT runs, the set of Pareto optimal solutions is 100 generated and the ideal solutions are identified. From the set of Pareto optimal solutions, the min-max optimum solution is determined. The min-max optimum solution is the solution where profit and risk are considered simultaneously and of equal importance. A sample of SMOT output is shown in Appendix D. SMOT output for the first implementation is presented in Table 8.2.1 and Figure 8.2.1. Table 8.2.1 presents the ideal vector of objective functions, the set of Pareto optimal solutions, and the min- max optimum solution. Figure 8.2.1 shows the corresponding Pareto optimal curve and the min-max optimum point. In Figure 8.2.1, the vertical axis is profit ($/Ha) and the horizontal axis is the sample standard deviation (MT/Ha) as a measure of risk. Each point in the Pareto optimal curve represents a set of production strategy including the sowing date (ul), nitrogen fertilizer treatment (u2) and plant population (u3). The Pareto optimal curve shows that profit increases with risk. The curve then provides a range of feasible strategies, depending on the choice of profit and risk level. In this case, for example, the SMOT user who is risk-averse would probably choose a lower value of the sample standard deviation, with corresponding lower profit. The min-max optimum point represents the "best compromise" production strategy where both profit and risk are equally weighted. In this particular example, 3* (the min-max optimum solution) has the components: u1*-June 20, u2*-100 Kg N/Ha; u3*-761 plants/m2. The corresponding grain yield is 4.94 MT/Ha, with a profit of $ 1473.72/Ha and a standard deviation of i 0.708. The ideal vector of objective functions provides an estimate as to the maximum profit (£10) if risk is not a factor to consider, and 101 TABLE 8.2.1. IDEAL VECTOR OF OBJECTIVE FUNCTIONS, PARETO OPTIMAL SOLUTIONS, AND MIN-MAX OPTIMUM SOLUTION FOR ul-June 20, u2 AND u3 VARYING A. The ideal vector of objective functions are: £10 - S 3494.49/Ha £2° - 0.302 MT/Ha B. The set of Pareto optimal solutions are: 31-2 9—3 Y——1 ° 1 d £1 £2 0. 400. 3.16 61.42 .302 498. 792. 7.33 2996.08 1.021 526. 611. 7.63 3191.91 1.060 463. 541. 7.69 3313.66 1.091 195. 574. 6.46 2662.32 .966 544. 333. 7.64 3367.96 1.096 153. 460. 5.96 2225.57 .862 399. 434. 7.74 3494.49 1.134 490. 394. 7.64 3439.37 1.109 111. 530. 5.24 1666.77 .749 100. 761. 4.94 1473.72 .706 120. 256. 5.36 1767.71 .781 621. 647. 7.29 2751.00 .996 62. 436. 4.37 971.67 .574 631. 411. 7.92 3304.15 1.089 137. 508. 5.69 2058.25 .834 136. 744. 5.54 1926.66 .824 62. 561. 4.71 1269.66 .645 613. 499. 7.65 3241.00 1.077 150. 563. 5.86 2201.54 .669 102. 639. 5.04 1467.94 .717 23. 164. 3.49 282.49 .407 594. 652. 7.60 3090.10 1.042 12. 770. 3.25 66.09 .356 179. 666. 6.01 2266.04 .905 104. 311. 5.12 1563.26 .729 172. 665. 6.11 2352.64 .910 123. 344. 5.46 1858.63 .794 203. 500. 6.62 2726.58 .991 59. 705. 4.22 645.24 .558 539. 795. 7.35 2942.21 1.013 571. 595. 7.66 3163.56 1.058 203. 443. 6.66 2763.21 .997 490. 394. 7.64 3439.37 1.109 563. 629. 7.30 2632.90 1.003 415. 607. 7.53 3243.11 1.087 441. 761. 7.33 3066.60 1.040 491. 759. 7.36. 3023.54 1.026 93. 173. 4.67 1406.66 .694 550. 779. 7.36 2966.53 1.016 TABLE 8.2.1 (cont'd.) £2 13 529. 610. 30. 266. 516. 660. 13. 726. 523. 435. 29. 736. 442. 713. 472. 736. 45. 217. 527. 402. 467. 751. 464. 463. 107. 266. 174. 313. 465. 672. 75. 407. 166. 461. 221. 655. 49. 517. 67. 256. 192. 506. 125. 297. 17. 566. 574. 617. C. * “1 - 171 “2 . 10°. .32 .66 .55 .26 .69 .60 .41 .40 .96 .67 .39 .64 .16 .23 .19 .62 .44 .67 .06 .43 .46 .46 .39 .65 NUHOODGQONOUVNNUVNUVUNUN yield. - 4.94 102 The min-max optimum solution is: £1 2917. 442. 3119. 92. 3416. 370. 3132. 3056. 703. 3399. 3046. 3437. 1597. 2460. 2676. 1169. 2640. 2766. 793. 1025. 2676. 1674. 167. 3133. t 21 . * £2 ' 11 14 64 30 33 97 36 69 75 64 25 63 54 17 69 65 77 19 04 06 35 90 69 53 S 1473.72/Ha 0.706 MT/Ha £2 .012 .442 .049 .360 .102 .434 1.052 .039 .510 1.100 ..e .033 1.106 .736 .936 .005 .622 .960 .000 .520 .596 .967 .799 .379 .052 103 3500* 3000- 2500‘ 2000‘ Profit, 1 S/Ha 1500‘ min-max optimum point 10005 5004 fl r 7'1 c> r I T 0 0.2 0.4 0.6 0.6 1.2 Standard Deviation, HT/Ha Figure 8.2.1. Pareto optimal curve and min-max optimum point for ul-June 20, u2 and u3 varying. the minimum risk (£20) if profit is not an issue. Their corresponding production strategies can be generated from the SMOT output. For example, Table 8.2.1 shows that the maximum possible profit (£10) is $ 3494.49. But this profit level has the largest standard deviation (i 1.134), equivalent to the highest point in the Pareto optimal curve of Figure 8.2.1. In the same manner, Table 8.2.1 also shows that the minimum possible risk (£20) is i 0.302, which has the lowest profit (3 61.42), and equivalent to the lowest point in the Pareto optimal curve of Figure 8.2.1. In most rice production, the conventional plant population is 400 plants/m2. SMOT was, therefore. run with a fixed plant population (u3) of 400 plants/m2 with the same planting date (ul). The objective 104 is to see how changes in nitrogen treatments with fixed plant population affect the shape of the Pareto optimal curve and the values of the min-max optimum solution. The ideal vector of objective functions, the set of Pareto optimal solutions, and the min-max optimum solution are presented in Table 8.2.2. The corresponding Pareto optimal curve and min-max optimum point are shown in Figure 8.2.2. The shape of the Pareto optimal curve in Figure 8.2.2 is smoother, although the slope is about the same, compared to that of Figure 8.2.1. This result is expected because u2 is the only component of E e U that varied randomly in the second implementation. The min-max optimum solution, 3*, has the components: u1*-June 20, u2*-93 Kg N/Ha, and u3*-4OO plants/m2, with a mean yield of 4.95 MT/Ha, profit of $ 1481.9l/Ha, and sample standard deviation of i 0.689. This optimum solution shows a higher profit and lower standard deviation compared to the first implementation implying that the min- max strategy of the second implementation is better than the min-max strategy of the first implementation. The maximum profit (£10) and the minimum risk (£20), however, are about the same as the first implementation. The SMOT results of the third implementation are presented in Table 8.2.3 and Figure 8.2.3. The ideal vector of objective functions, the set of Pareto optimal solutions, and the min-max optimum solution are presented in Table 8.2.3 while the corresponding Pareto optimal curve and the min-max optimum point are illustrated in Figure 8.2.3. The Pareto optimal curve in Figure 8.2.3 is more ”wigly" compared to the Pareto optimal curve in Figure 8.2.1. The min-max optimum solution has the components: u1*-September 1, u2*-100 105 TABLE 8.2.2. IDEAL VECTOR OF OBJECTIVE FUNCTIONS, PARETO OPTIMAL SOLUTIONS, AND MIN-MAX OPTIMUM SOLUTION FOR ul-June 20, u2 VARYING, u3-4OO plants/m2 A. The ideal vector of objective functions are: £10 - 6 3474.44/Ha 22° - 0.302 MT/Ha B. The set of Pareto optimal solutions are: $2 IiOld £1 £2 0. 3.16 61.42 .302 232 6.95 3011.63 1.056 697 7.93 3236.97 1.066 790 7.94 3105.74 1.064 735 7.93 3172.52 1.065 647 7.92 3301.45 1.066 646 7.94 3037.29 1.084 498 7.65 3449.06 1.107 157 6.03 2264.67 .696 211 6.73 2624.97 1.016 399 7.72 3474.44 1.134 195 6.55 2734.62 .983 550 7.69 3411.44 1.097 111 5.27 1693.36 .755 100 5.06 1593.36 .717 120 5.43 1631.05 .765 150. 5.92 2260.32 .678 62. 4.36 966.22 .575 137 5.72 2060.42 .640 136. 5.70 2066.19 .637 62. 4.75 1304.92 .646 23 3.54 322.74 .407 226. 6.69 2962.65 1.046 12. 3.33 135.00 .355 215. 6.78 2662.63 1.026 594. 7.91 3356.43 1.092 179. 6.34 2556.99 .949 108. 5.22 1647.29 .745 161. 6.37 2561.14 .955 123. 5.46 1875.97 .795 200. 6.61 2765.95 .993 59. 4.30 913.66 .564 213. 6.75 2844.60 1.022 442. 7.79 3465.62 1.122 162. 6.11 2350.64 .911 93. 4.95 1461.91 1.097 30. 3.69 456.70 .437 13. 3.34 150.54 .360 29. 3.67 437.34 .433 165. 6.15 2387.97 .918 TABLE 8.2.2 C. 45. 209. 107. 174. 172. 75. 166. 227. 221. 231. 222. 10. 49. 67. 192. 125. 17. (cont'd.) yield £1 4.01 735. 6.71 2605. 3.20 1631. 6.26 2496. 6.25 2473 4.61 1168. 6.44 2636. 6.90 2971. 6.84 2916. 6.94 3004 6.85 2927 3.29 103. 4.10 607 4.46 1053 6.51 2702. 5.52 1906 3.42 214 106 The min-max optimum solution is: e u1 u2 t e u3 171 93. 400. yield. - 4.95 57 33 93 11 .63 65 92 29 30 .23 .71 74 .57 .06 20 .26 .69 H H H H f1 ‘2 .507 .013 .742 .939 .934 .622 .966 .046 .036 .054 .040 .346 .523 .595 .977 .601 .376 i S 1461.91/Ha 0.669 MT/Ha 107 TABLE 8.2.3. IDEAL VECTOR OF OBJECTIVE FUNCTIONS, PARETO OPTIMAL SOLUTIONS, AND MIN-MAX OPTIMUM SOLUTION FOR ul-Sept. 1, u2 AND U3 VARYING A. The ideal vector of objective functions are: £10 - S 3126.53/Ha 22° - 0.246 MT/Ha B. The set of Pareto optimal solutions are: £2 £3 L—i ° 1 9 £1 £2 0. 400. 3.07 -15.61 .246 316. 513. 7.06 2970.00 1.114 313. 454. 7.12 3025.76 1.124 150. 563. 5.69 2055.24 .759 195. 574. 6.24 2467.26 .669 399. 434. 7.32 3126.53 1.169 261. 393. 6.66 2671.07 1.056 329. 576. 7.01 2927.71 1.106 111. 530. 5.12 1561.51 .643 100. 761. 4.63 1374.12 .582 136. 744. 5.39 1794.16 .702 153. 460. 5.79 2076.26 .784 62. 436. 4.27 667.41 .480 137. 506. 5.54 1929.93 .736 62. 561. 4.61 1167.92 .532 319. 496. 7.09 2997.05 1.121 155. 722. 5.67 1966.50 .757 102. 639. 4.92 1366.01 .599 29. 738. 3.51 292.40 .355 203. 500. 6.39 2524.22 .906 12. 770. 3.16 '6.35 .284 215. 365. 6.50 2621.61 .958 179. 666. 5.61 2069.00 .600 106. 777. 4.94 1406.35 .611 172. 665. 5.92 2164.92 .605 232. 462. 6.66 2778.49 .977 59. 705. 4.13 765.68 .450 203. 443. 6.43 2562.01 .914 266. 649. 6.79 2603.41 1.051 273. 512. 6.69 2692.13 1.057 30. 266. 3.56 354.92 .364 13. 726. 3.19 16.64 .269 29. 736. 3.51 292.40 .355 49. 517. 3.99 711.70 .436 75. 407. 4.51 1100.66 .525 355. 413. 7.23 3045.74 1.163 227. 436. 6.65 2753.33 .971 319. 560. 7.01 2924.41 1.105 341. 593. 7.02 2934.69 1.113 315. 432. 7.13 3035.39 1.131 108 TABLE 8.2.3 (cont'd.) £2 23 yield 67. 256. 4.32 192. 508. 6.26 104. 311. 5.00 17. 566. 3.30 C. The min-max optimum solution is: t t “1 - 2“ YiCId . ‘.83 t \12 - 100. £1 £2 930.99 .522 2466.76 .876 1457.61 .640 111.72 .311 4 r1 - s 1374.12/Ha 22' - 0.562 MT/Ha 109 3500- 3000* 2500‘ Profit, 2000 SIHa ‘ 1500- min-max Optimum point 1000- 500- V I T’ r' I . I ' I O 0.2 0.4 0.6 0.8 1.0 1.2 Standard Deviation, MT/Ha Figure 8.2.2. Pareto optimal curve and min-max optimum point for ul-June 20, 62 varying, 63-400 plantSImZ 32504 2750« 2250* 1750‘ Profit, . $/Ha 12509 min-max optimum point 750' 2504 -250~ . , . . . . . O 0.2 014 6.6 018 110 *1 Standard Deviation, MT/Ha .2 Figure 8.2.3. Pareto optimal curve and min-max optimum point for u u2 and u3 varying. l-Sept. 1, 110 Kg N/I-Ia, and u3*-761 plants/m2, with a mean yield of 4.83 MT/Ha, profit of $ 1374.12, and a standard deviation of i 0.582. Except for a difference in the value of u1*, the min-max optimum u2* and u3* for the first and third implementations have the same values. waever, the mean yield, and correspondingly profit, of the first implementation is higher than that of the third implementation. Their standard deviations are inversely related to profit. To provide more comparison between the Pareto optimal curves of the first and third implementations, Figure 8.2.1 and Figure 8.2.3 were drawn on the same x,y axes, and illustrated in Figure 8.2.4. It is demonstrated that the Pareto optimal curve of the first implementation (curve 1) is always to the right of the Pareto optimal curve of the third implementation (curve 2) until about the point (l.000,2750). The position of curves 1 and 2 relative to each other shifted after this point, that is, curve 1 is now to the left of curve 2. This graph demonstrates that as long as the farmer chooses a point of risk less than i 1.0 standard deviation, a production strategy along curve 2 is always as or more profitable than a production strategy along curve 1. However, for a risk level higher than i 1.0 standard deviation, a production strategy along curve 1 will give more profit than those along curve 2. There is another way of looking at the graph in Figure 8.2.4. Note that, except for a difference in the sowing date (ul), all other treatments corresponding to the min-max points of both curves 1 and 2 are the same. But the min-max point in curve 1 gives a higher profit ($ 1473.72) than the min-max point in curve 2 ($ 1374.12), although the standard deviation in curve 1 is higher (i 0.708) than in curve 2 (i 0.582). Tables 8.2.1 and 8.2.3 111 show that for the same treatments including fertilizer and plant population, rice sown on June 20 (curve 1) gives a higher profit than rice sown (”1 September 1. (curve 2). Their corresponding standard deviation, however, are inversely related. Tables 8.2.1 and 8.2.3 also reveal that the Pareto optimal curve is highly influenced by the amount of nitrogen fertilizer applied. The fertilizer level of the production strategies along the lower portion of the two curves (between i 0.2-0.4 standard deviation) range between 0-30 Kg N/Ha while the fertilizer level around the top portion of the curves (above i 1.0 standard deviation) range between 260-630 Kg N/Ha. Thus, if fertilizer is not a constraint and the risk level is above 1.0, sowing on June 20 is a better strategy over sowing on September 1. Legend: 3250.1 5...; Curve 1 ‘ H Curve 2 ‘ V Min-max optimum point 2750‘ 2250- 1750- Profit, 4 $/Ha 1250- 4 750— 250‘ -250 . . , , T. I 1 0 0.2 6.4 0'.6 6.8 1.0 1.2 Standard Deviation, MT/Ha Figure 8.2.4. Pareto optimal curves and min-max optimum points for ul-June 20 (curve 1) and ul-Sept. 1 (curve 2). 112 To illustrate the concept of utilizing the standard deviation of a mean as a measure of risk, 3 representative points (lowest, highest, and min-max) from the Pareto optimal curve in Figure 8.2.1 were chosen for variability analysis. The mean (0) and standard deviation (s) of each of the 3 points were fitted in a normal probability distribution function (N(fi,sz)). Column 3 of Table 8.2.4 gives the calculated probability density values. The 3 normal curves are shown in Figure 8.2.5. In this graph, the horizontal axis represents the mean grain yield, while the vertical axis represents the probability density. The normal curve to the left has a mean yield of 3.16 (profit of $ 61.42) and a sample standard deviation of i 0.302. The components of E are: ul-June 20; u2-0 Kg N/Ha; u3-400 plants/m2, equivalent to the strategy with the lowest risk. The normal curve to the right has a mean yield of 7.74 (profit of $ 3494.49) and a sample standard deviation of i 1.134. The components of G are: ul-June 20; u2-399 Kg N/Ha; u3-434 plants/m2, equivalent to the strategy with the highest risk. The normal curve at the middle has a mean yield of 4.94 (profit of $ 1473.72) and a sample standard deviation of :t 0.708. The components of E are: ul-June 20; u2-100 Kg N/Ha; u3-761 plants/m2, equivalent to the min-max optimum strategy. It is demonstrated that associated with a larger mean yield is a wider dispersion or variability, or for this application, greater risk. It should be noted that the right tail of the low-risk normal curve ceases to have a positive probability density at the grain yield interval (4.2-4.4 MT/Ha) where the left tail of the high-risk normal curve starts to have a positive probability density. This interval is the "convergence interval" between the low-risk and high-risk strategies. TABLE 8.2.4. 113 GRAIN YIELD, PROBABILITY DENSITY, AND PROFIT Description Yield Probability Profit (MT/Ha) Density (S/Ha) fl - 3.16, s - t 0.302 2.00 0.00 -951.00 (0 N, 400 plants/m2) 2.20 0.01 -776.60 2.40 0.06 -602.20 2.60 0.24 —427.60 2.60 0.65 -253.40 3.00 1.15 -79.00 3.20 1.31 95.40 3.40 0.96 269.60 3.60 0.46 444.20 3.80 0.14 616.60 4.00 0.03 793.00 4.20 0.00 967.40 8 - 4.94. s - 1 0.706 2.60 0.00 -567.60 (100 x; N/Ha, 2.60 0.01 -393.40 761 plants/m2) 3.00 0.01 -219 00 3.20 0.03 -44.60 3.40 0.05 129.60 3.60 0.09 304.20 3.80 0.15 476.60 4.00 0.23 653.00 4.20 0.33 627.40 4.40 0.42 1001.60 4.60 0.50 1176.20 4.60 0.55 1350.60 5.00 0.56 1525.00 5.20 0.53 1699.40 5.40 0.46 1673.60 5.60 0.36 2046.20 5.60 0.27 2222.60 6.00 0.16 2397.00 6.20 0.12 2571.40 6.40 0.07 2745.60 6.60 0.04 2920.20 6.60 0.02 3094.60 7.00 0.01 3269.00 7.20 0.00 3443.40 TABLE 8.2.4. (cont'd.) 114 Description Yield Probability Profit (MT/6a) Density (S/fla) fl - 7.74, s - t 1.134 4.40 0.00 511.60 (399 r; N/Ea, 4.60 0.01 666.20 434 plants/m2) 4.80 0.01 660.60 5.00 0.02 1035.00 5.20 0.03 1209.40 5.40 0.04 1363.60 5.60 0.06 1556.20 5.60 0.06 1732.60 6.00 0.11 1907.00 6.20 0.14 2061.40 6.40 0.16 2255.60 6.60 0.21 2430.20 6.60 0.25 2604.60 7.00 0.26 2779.00 7.20 0.31 2953.40 7.40 0.34 3127.60 7.60 0.35 3302.20 7.60 0.35 3476.60 6.00 0.34 3651.00 6.20 0.32 3625.40 6.40 0.30 3999.60 6.60 0.26 4174.20 6.60 0.23 4346.60 9.00 0.19 4523.00 9.20 0.15 4697.40 9.40 0.12 4671.60 9.60 0.09 5046.20 9.60 0.07 5220.60 10.00 0.05 5395.00 115 Legend: 1 “j H Low-risk strategy ’ o—o Min-max strategy 13~-EI High-risk strategy le2-1 1.0‘ 0.8—I Probability . DQQSity 0 6.- 1 0.4- A. I 2.0 4.0 6.0 Grain Yield, MT/Ha Y' I 6.0 10.0 12.0 Figure 8.2.5. Normal curves of low-risk, min-max, and high-risk strategies. Extending the analysis to profit, each point on the normal curve corresponding to grain yield with positive probability density (Figure 8.2.5) was converted into profit (column 4 of Table 8.2.4). The 3 normal curves in Figure 8.2.5 are now represented by 3 profitlines in Figure 8.2.6, where the horizontal axis is grain yield and the vertical axis is profit. The low-risk strategy has the leftmost profitline and consistently to the left, while the high-risk strategy has the rightmost profitline and consistently to the right. The profitline of the min-max strategy is consistently at the middle. The 3 profitlines do not cross each other. The low-risk profitline has its maximum at the point where the high-risk profitline has its minimum. The yield interval between the two profit points is the convergence interval. Figure 8.2.6 shows that if the yield is between 116 3.4-4.0 MT/Ha, the low-risk strategy is more profitable than the min- max strategy. However, the low-risk strategy has only a maximum profit of $ 793/Ha and can loss as much as $ 776.60 (as indicated by a negative profit), whereas the min-max strategy can have a maximum profit of $ 3269/Ha (maximum yield of 7.0 MT/Ha) with a possible loss of as much as $ 393.40. If the yield is between 4.6-7.0 MT/Ha, the min-max strategy is more profitable than the high-risk strategy. However, the min-max strategy can only yield at most 7.0 MT/Ha while the high-risk strategy can yield at most 10 MT/Ha or a profit of as much as $ 5395. If the yield is within the convergence interval, the min-max strategy provides for an alternative between the low-risk strategy and the high-risk strategy. 6000 '7 x I 50005 / 40001 t 6...... 3°°°J // $/Ha * // 2000‘ 1000- x' ' ,6? Legend: fl/ 0‘ m! 9—9 High-risk strategy ‘ (x’fit 0—0 Min-max strategy -1000 . I r I, . r 4f 9:4 Low-risk sirategy 0 2 0 4.0 6.0 6.0 10.0 12.0 Grain Yield, MT/Ha Figure 8.2.6. Profitlines of low-risk, min—max, and high-risk strategies. 117 To give a more concrete handle on the use of standard deviation as a measure of risk, Table 8.2.5 presents i 1 standard deviation within the mean of the low-risk, high-risk, and min-max strategies so far discussed. The low-risk strategy is expected to yield 3.16 MT/Ha with a standard deviation of i 0.302 MT/Ha. The probability of the actual yield being between 2.86—3.46 MT/Ha is 0.682. However, the profit range is between $ -201.08 - 322.12. Thus, the low-risk strategy has 0.682 probability of lossing as much as $ 201.08 or gaining up to $ 322.12. The min-max strategy is expected to yield 4.94 MT/Ha with a standard deviation of i 0.708 MT/Ha. It has 0.682 probability that the actual yield will be between 4.23-5.65 MT/Ha, with profit between $ 853.56 - 2091.80. In the same manner, the high- risk strategy is expected to yield 7.74 MT/Ha with a standard deviation of i 1.134 MT/Ha. It has 0.682 probability that the actual yield will be between 6.61-8.87 MT/Ha, with profit between S 2508 92- 4479 . 64 . TABLE 8.2.5. WITHIN i 1 STANDARD DEVIATION FOR LOW-RISK, MIN-MAX, AND HIGH-RISK STRATEGIES Strategy Yield Range Profit Range (HT/Ha) (S/Ha) Low-risk (fi-3.16, s-t 0.302) 2.66-3.46 -201.08 - 322.12 Min-max A (“-4.94, s-t 0.706) 4.23-5.65 853.56 ' 2091.80 High A (fl-7.74. S-t 1.134) 6.61-6.67 2506.92 - 4479.64 118 Each point in the Pareto optimal curve and the min-max optimum solution represents an average condition over the 25 simulations. For example, in Table 8.2.1 and Figure 8.2.1, the min-max strategy is more profitable than the low-risk strategy "on the average." But is the min-max solution My; more profitable than the low-risk strategy over the 25 simulation runs? In the same way, is the min-max solution always less profitable than the high-risk strategy ? Tb answer this question, a yearly comparison was done in such a way that the only difference were the specification of the production strategy, 3. Since SMOT is using actual weather data and field-measured soil data, these conditions provide for a "common scenario" in the yearly comparison. This yearly comparisons are presented in Tables 8.2.6 and 8.2.7; the graphical illustrations are shown in Figures 8.2.7 and 8.2.8. The vertical axis in Figure 8.2.7 is profit for the low-risk strategy while the horizontal axis is the profit for the min-max strategy. The vertical axis in Figure 8.2.8 is profit for the high-risk strategy while the horizontal axis is the profit for the min-max strategy. The 45° line in Figures 8.2.7 and 8.2.8 is a path along which there is no difference in performance between the two strategies (Manetsch, 1986). Figure 8.2.7 shows that the yearly profit of the min-max strategy are consistently greater than the low-risk strategy, while Figure 8.2.8 illustrates that the yearly profit of the high-risk strategy is consistently greater than the min-max strategy. These results, however, do not provide for an outright conclusion in favor of high profit due to the high-risk strategy because of cost functions, model limitations, and greater variability. The high-risk strategy involves high inputs and, consequently, high cost. Capital and input 119 TABLE 8.2.6. YEARLY COMPARISON BETWEEN LOW-RISK AND MIN-MAX STRATEGIES Simulation Profit for Low-Risk Profit for Min-max Run 86. (8) (S) 1 -105.16 1211.08 2 -61.56 1661.96 3 200.04 2161.56 4 200.04 1533.72 5 -9.24 1296.28 6 -113.66 993.08 7 479.08 2632.44 8 69.24 1647.08 9 363.16 2196.44 10 278.52 1906.68 11 173.68 1060.26 12 313.40 1795.32 13 -715.56 173.40 14 -163.64 435.00 15 -70.26 1141.32 16 139.00 2013.32 17 173.68 1516.26 18 452.92 2623.72 19 304.68 1926.12 20 162.60 1716.64 21 ‘216.52 1219.80 22 -67.72 1333.16 23 ~201.08 914.60 24 104.12 616.68 25 ~157.46 662.28 120 TABLE 8.2.7. YEARLY COMPARISON BETWEEN HIGH-RISK AND MIN-MAX STRATEGIES Simulation Profit for Min-Max Profit for High-Risk Run No. (8) (S) 1 1211.08 3267.56 2 1681.96 3677.40 3 2161.56 5656.64 4 1533.72 4061.06 5 1296.28 3666.68 6 993.06 2805.40 7 2632.44 5116.20 6 1647.06 3703.56 9 2196.44 4470.92 10 1908.66 3721.00 11 1060.28 2979.80 12 1795.32 3433.24 13 173.40 1671.60 14 435.00 2430.44 15 1141.32 2474.04 16 2013.32 4235.48 17 1516.26 2968.52 18 2623.72 4793.56 19 1926.12 4436.04 20 1716.84 3572.76 21 1219.60 2726.92 22 1333.16 4148.26 23 914.60 3093.16 24 816.66 2055.48 25 662.28 2168.64 Profit (low-risk strategy), $/Ha Figure 8.2.7. Profit (high-risk strategy), $/Ha Figure 8.2.8. -1000 I 121 -500 q rvuvIrTrIrI'I'I -500 0 500 1000 1500 2000 2500 3000 Profit (min-max strategy), $/Ha -1000 Yearly comparison between low-risk and min-max strategies. I I 1 f l’ r I V 0 1000 2000 vrri 4000 Profit (min-max strategy), $/Ha r ' I 3000 r I r U 5000 r'I 6000 Yearly comparison between min-max and high-risk strategies. 122 availability are major constraints in developing countries. The possibilities of typhoons, pest infestation, and other natural catastrophies, which are assumed to have no destructive effect on the simulation, are major contributors to the risk factor for the producer. These risks are in addition to an already existing variability of i 1.134 MT/Ha due to the stochastic weather conditions. The market system, which has been assumed constant in the model, introduces additional uncertainty with which the rice producer will have to reckon. Thus, the high-risk strategy is good only if the producer has (1) access to capital and inputs, and (2) courage to "play the high-risk game.” To ”play well" the user of SMOT must incorporate information derived from this tool with information on the market situation, forecasts on pest infestation and occurrence of typhoon, government policies, and other factors to arrive at a final production strategy. CHAPTER IX CONCLUSION The needs analysis indicates that rice deficiency in many countries is due largely to low yields and that the technology exists for increasing yields commensurate with population growth in the near future. The primary barrier to implementation of high-yielding agrotechnologies is the economic environment of the farmer and his/her perceptions of profit and risk in this environment. Under present economic conditions, the farmer cannot, and does not, strive for maximum yields or maximum profit alone because the perceived risks are too high and the cost of inputs may be beyond reach. Both issues, profit and risk, must be dealt with simultaneously at policy levels as well as the farm level to overcome the low-yield syndrome. The rice simulation model and the simulation-multicriteria optimization technique presented here are developed as computer software tools in support of analysis and strategic planning at both the policy and farm levels of organization. The rice simulation model is a first approximation to a practical and flexible computer software for simulating upland rice production. The simulation software is intended to be used as a tool in assessing the yield potential of alternative agrotechnologies from high-yielding countries to low—yielding countries, or from its site of origin to new 123 124 locations within the tropical and subtropical regions of the world. The conventional research/demonstration method of transferring new rice varieties and management practices from one soil type and climatic environment to another requires time, money, and careful field evaluation. In using the simulation model, the initial trial- and-error experimentation in selecting new varieties and management practices under a specific soil type and climatic environment can, to a degree, he done in the computer. Those varieties and management practices that look promising are the principal technologies to be tried in the field. This procedure is expected to reduce dramatically the cost, time, and risks involved in agrotechnology transfer. The simulation-multicriteria optimization technique (SMOT), using the rice simulation model, is an initial attempt to develop a software package that quantifies the trade-offs between profit and risk of alternative rice technologies under farm conditions. SMOT is presented as a first generation decision support system for use by extension workers, researchers, and policy-makers in the economic analysis of rice farms. Alternative production strategies can be tested through SMOT to help identify problems and issues before they actually occur in the field. As with all computer software packages, a note of caution is in order when using SMOT. SMOT will not, and is not, intended to eliminate all the uncertainties in decision-making. It will help to illuminate some of its dimensions. The value of SMOT in the decision- making process depends upon the user's understanding of its strength and limitations as well as his/her attitude toward profit and risk. Attitude is conditioned by the user's expectations of the performance 125 of SMOT, the amount of information available at the time the choice of production strategy is made, and the user's access to the controllable inputs. SMOT is not intended to replace the vital role of the farmer or farm advisor or the policy-maker in the decision-making process. SMOT is not a decision-making instrument. It should be viewed as a tool to increase the farm advisor's or policy-maker's understanding of the system performance, help quantify preferences, and improve overall decision-making ability. As an initial work, SMOT can provide a base for further research activities in order to improve its capability and usefulness. The rice simulation software has been structured in a modular form so that a pest module or other "plant stress" modules hopefully can be added as a logical and useful extension with minimum effort. An upcoming addition is the nitrogen transformations under lowland, flooded condition. Consequently, the method of planting will include transplanting of seedlings from seedbeds. This particular addition will expand the utility of SMOT to paddy rice production. Another area of planned expansion is in the timing of fertilizer application, i.e., fertilizers to be applied at different times during the growing season. Phosphorus, potassium, and zinc are nutrients which are important in rice production. These nutrients can be modelled and incorporated in the simulation software. SMOT is set up in such a way that any of the CERES crop simulation models can be incorporated in place of the rice simulation model. Hence, SMOT as a decision support system can be expanded to include the evaluation of profit and production risk involving other crops. 126 To the extent that the price of grain, input costs, marketing costs, and interest rates can be characterized by stochastic parameters, these parameters can be included as non-deterministic factors in SMOT. Incorporation of these factors will increase the usefulness of SMOT among the market-oriented rice producers. In many Asian countries, the occurrence of typhoon during the monsoon season is practically a yearly event which can completely destroy production areas. To the extent that these events can be characterized stochastically, they can also be incorporated into SMOT with a concomitant increase in its utility. One procedure for including environmental issues such as nitrate leaching and runoff in SMOT is to include them as constraint functions. Any production strategy violating these constraints will be discarded from the set of Pareto optimal solutions. An alternate procedure is to redefine the objective functions in SMOT so that it can be used to evaluate profit versus nitrate leaching in the soil, or profit versus run-off. APPENDICES APPENDIX A GOODNESS-OF-FIT TEST TO DETERMINE THE PROBABILITY DISTRIBUTION OF GRAIN YIELD In the analytical evaluation of the two objective functions, to maximize profit and to minimize production risk, information of the mean and standard deviation of grain yield is necessary. The probability distribution of grain yield, that is, its probability density function, must be known in order to find the best (maximum likelihood) estimators for its mean and standard deviation. This information can be generated by applying the goodness-of-fit test. The hypothesis that the probability distribution of grain yield is normal was evaluated. That is, 1 e-(‘fiHY-M/alz J27”: H = PY (y) - 90(7) - o ,0 x2 . — l-a,k-l ." 1-1 np. 1.0 Theorem 9.3 states that: "Suppose p1(0),p2(6),..., emu! pk(0) are continuously differentiable functions for 0 in some interval I, satisfying the following conditions for each 0 E I: k (a) 2 pi(0) - 1. 1-1 (b) pi(0) > e > 0, 1 s 1 s k (c) p;(0) s o, 1 s 1 s k. Then for each n there is a maximum-likelihood estimator, 9n, such that 9n converges to 9. Furthermore, the cdf of k [X - up (a )12 i i n Cl - 2 1-1 npi(8n) 129 converges to the cdf of a x2 distribution with k-2 degrees of freedom." Larsen and Marx made a comment that "in the more general case, where the pi’s are functions of r unknown parameters, the analogous Cl is asymptotically chi square with k-l-r degrees of freedom." In these theorems, n represents the total number of observations, k represents the grouping or class of the n observations, 1 is used to index the p's, and cdf means cumulative distribution function. Table A.l presents the predicted grain yield of the 25 simulation runs . TABLE A.1. PREDICTED GRAIN YIELD (MT/Ha) 0F IR36 VARIETY OVER 25 SIMULATION RUNS WITH ACTUAL WEATHER DATA 5.12 5.74 6.25 5.45 5.30 4.83 6.64 5.67 6.42 6.05 4.66 5.79 3.61 4.10 5.00 6.22 5.46 6.63 6.03 5.71 5.11 5.26 4.60 4.54 4.56 A histogram of these data is shown in Figure A.1. The A distribution looks normal (N(fi,52)) with p - 5.43 MT/Ha and 52 =- (0.76)2. Figure A.2 shows the N[5.43,(O.78)2] density superimposed over the histrogram of Figure A.1. Following Theorems 9.2 and 9.3, the data from Table A.1 was grouped into a set of nonoverlapping intervals and the probability associated with each one was determined from Ho. Table A.2 presents the grouping into k-4 classes. 130 61 5. Frequency 3. . 2‘ .____1. 14 0 r, e I- . see . - - T4, 47 3.60-4.09 4.60-5.09 5.60-6.09 6.60-7.09 Grain Yield, MT/Ha V’fi Figure A.1. Histogram of grain yield data. 0.607 0.50‘ ~ \ 0.404 7’ ‘ Probability , \ Density I . \ 0.30. \ 0.204 0.10. 0.004-‘6' - - . - - - - - - - 3.60-4.09 4.60-5.09 5.60—6.09 6.60-7.09 Grain Yield, MT/Ha Figure A.2. Normal distribution function superimposed on histogram of grain yield data. 131 TABLE A.2. GROUPING 0F GRAIN YIELD DATA INTO k CLASSES 1 Grain Yield Observed frequency, Vi 1 S 4.60 5 2 4.61-5.30 7 3 5.31-5.60 6 4 Z 5.61 7 k-‘ 25 Using the continuity correction together with the usual 2 transformation, and given 1'} - 5.43 and s - 0.78, the expected frequency is calculated as follows: For class 1: P( Y < 4.80) P(-m < Y < 4.80) P( _m < Z < 4.805-5.43 ) 0.78 P(-0 < Z < -0.80) 0.2119 - 0 (from Table A.l of Larsen and Marx, 1981) 0.2119 - P10 The expected frequency is 5.2975: “Pic - 25(0.2119) - 5.2975 For class 2: 4.805-5.43 < Z < 5.305-5.43 0.78 0.78 P(4.8l < Y < 5.30) - P( ) P(-0.80 < Z < -0.l6) 0.4364 - 0.2119 (from Table A.l) 0.2245 - 02° 132 And the expected frequency is 25(0.2245) - 5.6125. For class 3: 5.305-5.43 < Z < 5.805-5.43 0.78 0.78 P(5.31 < Y < 5.80) - P( ) P(-0.16 < Z < 0.48) 0.6844 - 0.4364 (from Table A.1) 0.2480 - 630 And the expected frequency is 25(0.2480) - 6.2000. For class 4: P(Y > 5.81) - P(5.8l < Y < o) _ P( 5.805-S.43 < 2 < m ) 0.78 - 1.0 - 0.6844 (from Table A.1) - 0.3156 - 54° The expected frequency is 25(0.3156) - 7.890. Table A.3 lists the 610's and the expected frequencies (npio's) for the 4 classes in Table A.2. Table A.3 also shows that the calculated value of C1 is 0.4666. TABLE A.3. OBSERVED AND EXPECTED FREQUENCIES OF GRAIN YIELD 1 Grain Yield yi 61° npio cl-(yi-25610)2/n610 l S 4.60 5 0 2119 5.2975 0.0167 2 1-5.30 7 0 2245 5.6125 0 3430 3 31-5.60 6 0.2460 6.2000 0 0065 4 Z .61 7 0 3156 7.6900 0 1004 k-4 25 1.0000 25.0000 0.4666 - C1 133 Since there were r-2 parameters estimated and k-4 classes, the number of degrees of freedom associated with C1 is 4‘1-2, or 1. At the a - 0.05 and a - 0.10 levels of significance, the corresponding critical values are 3.841 (x20_95’1) and 2.706 (x20.90'1), respectively. Based on theorems 9.2 and 9.3, the conclusion is to accept the normality assumption of grain yield. APPENDIX B FORTRAN PROGRAM OF THE SIMULATION -MULTICRITERIA OPTIMIZATION TECHNIQUE 134 Jun 30 14:40 1967 optim1.f Page 1 000 0000000000000000000000 000000 000 C C C PROGRAM SMOT THIS Is THE SIMULATION-MULTICRITERIA OPTIMIZATION TECHNIQUE, VERSION 1.0 49* DEVELOPED AND PROGRAMMED BY E. c. ALOCILJA 4444......4.4.44444444444 444 wITfi FINANCIAL suppopr FROM IBSNAT fittitttiittittttttfiititfittiittiti 44* MICHIGAN STATE UNIVERSITY, EAST LANSING, MI 48624 4.444.444.4444.... DIMENSION XO(2,10),FO(2),X(10),F(2),XOP(10),FOP(2),XSTAR(10), + FSTAR(2),G(20),XP(10,500),FP(2,500),XA(10),XB(10),YMEANP(SOO) THE OPTIMIZATION MODEL IS SET-UP FOR THE FOLLOWING: MAX. NO. OF OBJECTIVE FUNCTIONS, K I 2, 1.9. F(1),F(2) MAX. NO. OF DECISION VARIABLES, N I 10, 1.3. X(l),X(2),...,X(N) MAX. NO. OF CONSTRAINT FUNCTIONS, G i 20, 1.0. G(1),G(2),...,G(20) MAX. NO. OF SEARCH RUNS, LA 3 500 THE FOLLOWING VARIABLES ARE DEFINED: . L ' COUNTER FOR NO. OF RUNS, 1.3. L-1,2,...,LA J - COUNTER FOR NO. OF PARETO OPTIMAL SOLUTIONS JA I MAX. NO. OF PARETO OPTIMAL SOLUTIONS, 1.0. J31,2,...,JA NCYCLE - MAXIMUM NO. OF SIMULATION RUNS FOR EVERY SET OF DECISION VARIA M 3 MAXIMUM NO. OF CONSTRAINTS THE USER-SUPPLIED SUBROUTINES ARE: CONST, FUNC, LIMITS SUBROUTINE CONST MUST BE CALLED FIRST BEFORE ANY SIMULATION RUN TO CHECK IF THE INPUTS (DECISION VARIABLES, X) ARE WITHIN THE LIMITS OF THE CONSTRAINT FUNCTIONS. IN THIS CASE, INPUT FILES MUST BE READ FIRST BEFORE CALLING SUBROUTINE CONST. 4444444 ops“ STATEMENTS 444444444446eeseeeeeeeeeeeeseeeeeesees4444444444444 OPEN (100,FILE='OUTOPT',ACCESSt'SEQUENTIAL',STATUs-'OLD') ***** INITIALIZATION FOR NUMBER OF PARETO CURVES TO BE GENERATED '********* IWRITE=1 IPAR=1 CALL LIMITS (IPARCRV,LA,N,NCYCLE,XA,XB) assess INITIALIZATION of VARIABLES eeeeeeeeeeeeeeeeeeeeteeeeeeseeeseeeeset4 1 DO 5 JL-l,20 G(JL)=O.+1.E-10 5 CONTINUE K32 JASl FO(1)81000000000. FO(2)-1000000000. FP(1.1)=1000000000. FP(2,1)'1000000000. L=l '****'***** SUBROUTINE RANDOM WILL GENERATE RANDOM POINTS OF X'S *********** IF (IPAR.GT.l.AND.IPAR.LE.IPARCRV) CALL RANDOM (1,1,XA,XB,X) 10 IF (L.GT.1) CALL RANDOM (2,N,XA,XB,X) 135 Jun 30 14:40 1987 optim1.f Page 2 C C 4*9444444494 sUEROUTINE CONST WILL CHECK FOR FEASIBLE POINTS 4444444444~444 C IF (NCYCLE.GT.1.AND.IWRITE.NE.1) THEN CALL CONST (G,M,X) Do 20 JL-1.H IF (G(JL).LT.0.) THEN LIL+1 IF (L.LE.LA) GO TO 10 L'L-l GO TO 50 END IF 20 CONTINUE END IF C C **"* SUBROUTINE RICE IS THE CERES-RICE MODEL WHICH WILL ESTIMATE YIELD **** c 4464. GIVEN FEASIBLE INPUT VARIABLES eseeeeeeeeeeeeeeeeeeseeseeeescassette4e C NSIM-O YSUM-O. YSQRSUM-O. DO 25 I-1,NCYCLE YIELD-0. NSIM-NSIM+1 CALL RICE (IPAR,IWRITE,NCYCLE,NSIM,X,YIELD) YSUM-YSUM+YIELD YSQRSUM-YSQRSUM+(YIELD**2) IF (LA.EQ.1.AND.NCYCLE.GT.1) WRITE (100,200) I,YIELD 200 FORMAT (5X,'I - ',IS,5X,'YIELD - ',F6.2) 25 CONTINUE YSUMSQR-YSUM'*2 YMEAN‘YSUM/NCYCLE C C 9'999999999 SUBROUTINE FUNC CONTAINS THE OBJECTIVE FUNCTIONS ***'****'****' C '********" THIS SECTION WILL GENERATE THE IDEAL VECTOR F0 ***'************ C IF (NCYCLE.EQ.1) GO TO 999 C CALL FUNC (F,YMEAN,YSQRSUM,YSUMSQR,NCYCLE,X) C CALL OUTP (F,IPAR,IPARCRV,IWRITE,L,LA,NCYCLE,X,YMEAN) C DO 30 I81,K IF (F(I).LT.FO(I)) THEN FO(I)=F(I) DO 40 I1=1,N X0(I.Il)=X(Il) 40 CONTINUE END IF 30 CONTINUE C C '*'**‘ SUBROUTINE PARETO WILL CREATE A SET OF PARETO OPTIMAL SOLUTIONS *'**~ C CALL PARETO (K,N,X,F,JA,XP,FP,YMEAN,YMEANP) IF (L.LT.LA) THEN L=L+1 136 Jun 30 14:40 1987 optim1.f Page 3 GO TO 10 END IF 50 DO 60 J=I,JA DO 70 Jl'l,N X(Jl)-XP(J1,J) 7O CONTINUE DO 60 J2'1,K F(JZ)IFP(JZ,J) 80 CONTINUE CALL MINMAX (K,N,J,JA,FO,X,F,XOP,FOP,YMEANP,YSTAR,ZMIN) 60 CONTINUE ZSTAR-ZMIN CALL OUTPT (FO,XO,FP,XP,FOP,XOP,JA,K,L,N,YMEANP,YSTAR,ZSTAR) C **** END OF EACH PARETO OPTIMAL CURVE AND MIN-MAX OPTIMUM EVALUATION *** C IF (IPAR.LT.IPARCRV) THEN IPAR-IPAR+1 GO TO 1 END IF C ***THE ABOVE SECTION DETERMINES THE NUMBER OF PARETO OPTIMAL CURVES TO C BE GENERATED AS AFFECTED BY THE SOWING OR PLANTING DATE '********* C 999 END SUBROUTINE MINMAX (K,N,J,JA,FO,X,F,XOP,FOP,YMEANP,YSTAR,ZMIN) DIMENSION XO(1),FO(2),X(10),F(2),XOP(10),FOP(2),ZI(2),ZMAX(500), + ZI2(SOO),XTEMP(10),FTEMP(2),YMEANP(500) C CALL MAX (K,ZI,F,FO) IF (ZI(1) .EQ. 0 .AND. ZI(2) .EQ. 0) THEN ZMIN-O. DO 5 JJ-1,N XOP(JJ)-X(JJ) S CONTINUE DO 7 II-1,K FOP(II)-F(II) 7 CONTINUE J=JA YSTARfiYMEANP(J) GO TO 66 END IF ZMAX(J)'AMAX1(ZI(1),ZI(2)) DO 10 I‘1,K IF (ZI(I) .NE. ZMAX(J)) ZIZ(J)=ZI(I) 10 CONTINUE IF (J .EQ. 1) THEN ZMIN=2MAX(J) DO 20 Jl=1,N XOP(J1)'X(Jl) 20 CONTINUE D0 30 J2=l,K FOP(J2)=F(JZ) 137 Jun 30 14:40 1987 optim1.f Page 4 30 CONTINUE YSTAR-YMEANP(J) GO TO 66 END IF IF (ZMAX(J) .LE. ZMIN) THEN IF (ZMAX(J) .EQ. ZMIN) THEN DO 40 J3-1,N XTEMP(J3)-XOP(JJ) 4O CONTINUE DO 50 J4-1,K FTEMP(J4)-FOP(J4) 50 CONTINUE 2I2MIN‘AMIN1(ZI2(J),ZIZ(J-l)) IF (ZIZMIN .EQ. ZI2(J)) THEN 2MIN-2MAX(J) DO 60 J5-1,N XOP(JS)-X(JS) 60 CONTINUE DO 70 J6-1,X FOP(JG)-F(J6) 7O CONTINUE YSTAR-YMEANP(J) ELSE DO 60 J7-1,N XOP(J7)-XTEMP(J7) 80 CONTINUE DO 90 36-1,K FOP(J6)-FTEMP(JB) 9O CONTINUE YSTAR-YMEANP(J) END IF ELSE ZMIN-ZMAX(J) DO 100 J9-1,N XOP(J9)-X(J9) lOO CONTINUE DO 110 J10-1,K FOP(JlO)-F(J10) 110 CONTINUE YSTAR-YMEANP(J) END IF END IF 66 RETURN END "**** SUBROUTINE MAX CALCULATES THE FUNCTION RELATIVE INCREMENTS AND CHOOSES THE MAXIMUM INCREMENT **"*"*'***'**‘***"*** 0000 SUBROUTINE MAX(K,ZI,F,FO) DIMENSION ZI(2),F(2),FO(2) DO 10 1.1,K FO(I)-FO(I)+1.0E-10 F(I)'F(I)+l.0E-10 ZI(I)-ABS(F(I)-FO(I))/ABS(FO(I)) Z=ABS(F(I)-FO(I))/ABS(F(I)) IF (2 .GT. 2I(I)) ZI(I)'Z 138 Jun 30 14:40 1987 optim1.f Page 5 10 CONTINUE RETURN END 9". PARETO SUBROUTINE SELECTS THE SET OF PARETO OPTIMAL SOLUTIONS **** 000 SUBROUTINE PARETO (K,N,X,F,JA,XP,FP,YMEAN,YMEANP) DIMENSION X(10),F(2),XP(10,500),FP(2,500),YMEANP(500) J-l 25 KA-O DO 20 I-1,K IF (P(I) .LE. EP(I,J)) KA-KA+1 20 CONTINUE IF (KA .EQ. K) GO TO 30 IF (KA .EQ. 0) GO TO 40 J-J+1 I? (3 .GT. JA) THEN JA-JA+1 DO 55 JJ-1,N XP(JJ,JA)-X(JJ) 55 CONTINUE DO 65 II-1,K FP(II,JA)-F(II) 65 CONTINUE YNEANP(JA)-YNEAN GO TO 40 ELSE GO TO 25 END IE 30 DO 50 Jl-l,N XP(J1,J)-X(Jl) 50 CONTINUE DO 60 I-1,K FP(I,J)-F(I) 60 CONTINUE YNEANP(J)-YHEAN IF (J.LT.JA) THEN J-J+1 GO TO 25 END IE 40 RETURN END C C fitntittfittat SUBROUTIflE To GENERATE RANDOM POINTS tttnttttttitttettt C SUBROUTINE RANDOM (N1,N,XA,XB,X) DIMENSION XA(10),XB(10),X(10) DO 10 I-N1.N CALL RANDN(RAN) X(I)-XA(I)+INT(RAN*(X8(I)-XA(I))) 10 CONTINUE RETURN END C C***‘*THE FOLLOWING SUBROUTINE GENERATES A UNIFORM RANDOM NUMBER ON 139 Jun 30 14:40 1987 optim1.f Page 6 C*****THE INTERVAL 0 - 1 SUBROUTINE RANDN(YFL) DIMENSION K(4) DATA K/2510,7692.2456,3765/ xI4) - 34x(4)+x(2) K(3) - 34x(3)+x(1) x121-3-x(2) K(1) - 3*K(1) I-K(1)/1000 K(1)-K(1)-I*1000 x(2)-x(2) + I I - K(2)/100 K(2)-K(2)-100*I K(3) - K(3)+I I - K(3)/1000 K(3)-K(3)-I*1000 K(4)-K(4)+I I - K(4)/100 K(4)-K(4)-100*1 VEL-(((ELOAT(M(1))4.001+ELOAT(K(2)))~.OI+ELOAT(H(3)))4.001+ELOAT *(K(4)))t.01 RETURN END 140 May 26 14:53 1987 optim2.f Page 1 SOPTION TRACE OFF 0000000000000000000000000000 0000000000 ..ififi. ONECTIVE FUNCTION SUBROUTINE itiiiififiiiiiifiifififiitiiiififiiifitiiii. 494994 THE OBJECTIVE FUNCTIONS ARE DEFINED As FOLLOWS: F(1) - -(MAXIMIZE PROFIT (REVENUE-COST)) F(2) - MINIMIzE THE YIELD STANDARD DEVIATION 94494. THE FOLLONINC DECISION VARIABLES HAVE BEEN DEFINED: X(1) - DATE OF sowINc x(2) . xc. N/HA. OF FERTILIZER (THE RICE MODEL Is SET FOR BASAL APPLICATION) X(3) - PLANT POPULATION, HILLS/SO.M. (TRANSPLANTED) PLANTS/SO.M. (DIRECT-SEEDED) *****VARIABLE 6 FIXED COST PER HA. INCLUDES THE FOLLOWING : IRRIGATION : IF IIRR ' 1 - (NO IRRIGATION APPLIED) NO COST 2 - (IRRIGATION APPLIED USING FIELD SCHEDULE) CORRESPONDING COST 3 - (AUTOMATIC IRRIGATION AT THRESHOLD SOIL WATER) FIXED COST LAND PREPARATION PEST CONTROL : WEEDING, INSECT AND DISEASE CONTROL FERTILIZER APPLICATION SEEDS HARVESTING INTEREST OF LOANS OPPORTUNITY COSTS IMPUTED COSTS ********* OTHER DEFINITIONS: PRICE-price of grain/ton SUBROUTINE FUNC (F,YMEAN,YSQRSUM,YSUMSQR,NCYCLE,X) DIMENSION F(2),X(10) PRICE'1020.00 FIXCOST-2695.00 TRCOST-O. IRCOSTtO. FERBAG-X(2)/SO HARCOST-YMEAN‘74.*2. IF ((FERBAG-AINT(FERBAG)).GT.0) FERBAG-AINT(FERBAG)+1 F(1)'-(YMEAN‘PRICE-TRCOST-IRCOST-FERBAG'70.-HARCOST-FIXCOST) F(2)‘SQRT((NCYCLE'YSQRSUM-YSUMSQR)/(NCYCLE*(NCYCLE-1))) RETURN END eeeeeeee CONSTRAINTS SUBROUTINE seeseseeseeeeeeeeeeeeseeeeeeeseee ***'*“* CONSTRAINTS ARE LIMITS IMPOSED ON THE DECISION VARIABLES USUALLY BY THE ENVIRONMENT SUCH AS FARMER'S FINANCIAL CAPACITY, INPUT COSTS, MARKETING COST, AVAILABILITY OF INPUT PRODUCTS, ACCESS TO LENDING INSTITUTIONS, PRODUCTION PRACTICES, CONSUMER PREFERENCE, GOVERNMENT PRODUCTION POLICIES, AVAILABLE TECHNOLOGY, AVAILABILITY OF LABOR. ETC. M 3 TOTAL NO. OF CONSTRAINT VARIABLES (MAXIMUM IS 20) SUBROUTINE CONST (G,M,X) DIMENSION X(10),G(20) FERBAGIX(2)/50 IF ((FERBAG-AINT(FERBAG)).GT.0) FERBAG-AINT(FERBAG)+1 141 May 26 14:53 1987 optim2.f Page 2 G(l)I14OO.OO-70.00*FERBAG MIl RETURN END C C *********** SUBROUTINE LIMITS DEFINE UPPER AND LOWER LIMITS OF X'S **** C ***'***'*** THE FOLLOWING VARIABLES HAVE BEEN DEFINED: C XA(1) I LOWER LIMIT OF SOWING DATE: XB(l) I UPPER LIMIT OF SOWING DATE C XA(2) I LOWER LIMIT OF N FERTILIZER: XB(2) I UPPER LIMIT OF N FERTILIZER C XA(3) I LOWER LIMIT OF PLANT POPULATION: XB(3) I UPPER LIMIT OF PLANT POPULAT C N I NO. OF DECISION VARIABLES DEFINED C LA I MAXIMUM NO. OF RUNS TO SEARCH FOR X(2)-X(3) POINTS (MAXIMUM IS 500) C NCYCLE I MAXIMUM NO. OF SIMULATION RUNS FOR EVERY SET OF C DECISION VARIABLES C IPARCRV I MAXIMUM NO. DEFINED TO SEARCH FOR X(1)-POINT, WHERE X(l)IISOW C SUBROUTINE LIMITS (IPARCRV,LA,N,NCYCLE,XA,XB) DIMENSION XA(10),XB(10) C OPEN (30,FILEI'LIMITS',ACCESSI'SEQUENTIAL',STATUSI'OLD') REWIND 30 READ (30,200) IPARCRV,LA,N,NCYCLE READ (30,210) XA(1),XB(1) II2 10 READ (30,220) XA(I),XB(I) IF (XA(I).GE.0) THEN III+1 GO TO 10 END IF RETURN C 200 FORMAT (I6,1X,I6,2(1X,I2)) 210 FORMAT (IG,1X,IG) 220 FORMAT (F6.2,1X,F6.2) END 142 5 May 29 11:47 1987 Optim3.t Page 1 c ........ NRITEs OUTPUT OF THE OPTIMIZATION PROCEDURE ............ c SUBROUTINE OUT? (F,IPAR,IPARCRV,IWRITE,L,LA,NCYCLE,X,YMEAN) DIMENSION F(10),X(10) Isow-X(1) IE (IwRITE.E0.1) UNITE (100,500) IPARCRV,LA,NCYCLE IF (L.E0.1) WRITE (100,510) IPAR,Isow F1--F(1) WRITE (100,520) L,X(2),X(3),YMEAN, F1,F(2) INRITE-o RETURN 500 FORMAT (15X,'FARM PRODUCTION MULTICRITERIA OPTIMIZATION',/, 15x, 'ififiittittitittititittttiitiiiiiiiiiittttii"///' 5X,'OBJECTIVE FUNCTIONS:',/, 8X,'1) HAXIHIZE PROFIT, P(l) ($/Ha)',/, 8X,'2) NINIMIZE FARM PRODUCTION RISK, P(Z) (std. deviation', ' from the ',/,15X,'mean yield)',//, 5X,'DECISION VARIABLES:',/, ax,'1) SOWING DATE, 0(1), (Julian day)',/, ax.'2) AMOUNT OF N FERTILIZER APPLIED, 0(2), (Kg N/Ra)',/, 0x,'3) PLANT POPULATION, U(3), (hills/sq.netcr - transplanted)’, /,35X,'(p1ants/sq.meter - direct-seeded)',//, 5X,'NO. OF U(1)-POINT SEARCH : ',IJ,/, 5X,'NO. OF U(2),U(3)-POINT SEARCH :',IS,/, 5X,'NO. OF SIMULATION CYCLES To GET AVE.YIELD (NT/Ha):',IS) 510 FORMAT (//,SX,'SET NO. ',13,/,5x,'-=-----',/, +++++++++++++ 5X,'THE SET OF FEASIBLE SOLUTIONS ARE :'/, 5x0 .------- .......................... ' 0//I 5X,'U(1) : 'oI3o/p 5X,'(SOHING DATE)',//, 5X,'RUN NO.',5X,'U(2)',9X,'U(3)',22X,'F(1)',6X,'F(2)',/, 14X,'(N FERT.)',2X,'(POPULATION)',2X,'AVE. YIELD', 5X,'(PROFIT)',3X,'(RISK)') 520 FORMAT (6X,IS,5X,F6.0,SX,F7.0,3X,F8.2,6X,F10.2,4X,F5.3) END +++++++ 143 May 29 11:50 1987 optim4.f Page 1 C SUBROUTINE OUTPT (FO,XO,FP,XP,FOP,XOP,JA,K,L,N,YMEANP,YSTAR,ZSTAR) DIMENSION FO(2),XO(2,10),FP(2,500),XP(10,500),FOP(2),XOP(10), + YMEANP(500) WRITE (100,220) FOlI-FO(1) FO2IFO(2) WRITE (100,230) F01,F02 WRITE (100,240) 00 41 JZI1,JA FPlI-FP(1,J2) WRITE (100,250) J2,INT(XP(1,J2)),XP(2,J2),XP(3,J2),YMEANP(J2), + FP1,FP(2,J2) 41 CONTINUE WRITE (100,270) WRITE (100,300) L,ZSTAR WRITE (100,280) WRITE (100,310) INT(XOP(1)),XOP(2),XOP(3),YSTAR WRITE (100,290) FOPlI-FOP(1) WRITE (100,320) FOP1,FOP(2) RETURN 220 WFORMAT (//,5X, 'TME IDEAL VECTOR OF OEJECTIVE FUNCTIONS ARE: '/, 5X, """" '/) 230+ FORMAT (5X, 'FO(1)I ',F10.2,5X,'FO(2)I ',F6.3) 240 FORMAT (//,5X,'THE SET OF PARETO OPTIMAL SOLUTIONS ARE: '/, + 5x0. — ——— _ '0/0 + 7X,'POINT NO.',5X,'U(1)',5X,'U(2)',5X,'U(3)',5X,'YIELD', * 5X,'F(1)',SX,'F(2)',/) 250 FORMAT (11X,I5,4X,I5,3X,F6.0,3X,F6.0,5X,F5.2,1X,F8.2,1X,F8.3) 270 FORMAT (//,5X,'THE SET OF OPTIMAL SOLUTION IN THE MINIMAX SENSE:'/, + 5x,'— ') ' 280 FORMAT (/.5X,'A) OPTIMAL VALUES OF DECISION VARIABLES:'/) 290 FORMAT (/,5X,'3) OPTIMAL VALUES OF OBJECTIVE FUNCTIONS:'/) 300 FORMAT (5X,'L‘ I ',I3,2X,'z* I ',F10.2) 310 FORMAT (5X,'U*(1)I ',I3,5X,'U'(2)I ',F5.O,8X,'U*(3)I ',F5.0,5X, + 'YIELD‘ I ,F5.2) 320 FORMAT (5X, 'F'(1)I ,F10.2,8X, 'F'(2)I ,F6. 3,//, + 5X, '*3###'#QQ##‘;3#”##iflft##3fi#33”;#0‘330#3‘###3#3‘##£##$333') END 144 May 28 13:24 1987 cerice1.f Page 1 SOPTION TRACE OFF c it. C C C C C SUBROUTINE RICE CERES-RICE GROWTH AND DEVELOPMENT MODEL Version 1.10 - (IPAR,IWRITE,NCYCLE,NSIM,X,YIELD) fitttiiiiiifiitittttitiitt tor Upland Condition DEVELOPED BY E.C. ALOCIIJA, J.T. RITCHIE, AND U. SINGH NITROGEN ROUTINES DEVELOPED BY GODWIN, JONES, ET AL IBSNAT STANDARDIZED I/O STRUCTURES iiifiififlfiiittfififiiifiitittfitiifittittitittiiittitiiiiiitfiiiflfiiiiitfiiitflitt CHARACTER '12 FILE1,FILE2,FILE3,FILE4,FILE5,FILE6,FILE7,FILE8, FILE9,FILEA, FILEB CHARACTER *7 OUT1,0UT2,0UT3,0UT4 CHARACTER PEDON'12,TAXONI60,VARTY*16 CHARACTER ANS'l,INSTS'Z,SITES'Z,YR'2,EXPTNO*2,TITLER*20 CHARACTER INSTE‘Z,SITEE‘Z,TITLEE*40,TITLET*40 CHARACTER INSTW*2,SITEW*2,TITLEW*40,BDATE‘B,EDATE*8,DWFILE*12 CHARACTER *1 IECHC,IEHVC,IFIN CHARACTER FTYPE'40 INTEGER TRTNO,YEAR REAL IFOM,IFON, LAT,LAI,LL,LFWT,NDEM,NFAC,NDEF1,NDEF2,NDEF3, NH4,NO3,NNOM,NHUM,INSOIL,NOUT,NUP,MF COMMON/OBDATA/ XYIELD,XGRNWT,XPNO,XPPAWT,XLAI,XBIOMAS, XSTRAW,XPSRAT,JDHEAD,JDMAT,XAPTNUP,XATANC COMMON/SOILI/ IDUMSL,PEDON,TAXON- COMMON/TITLEI/ COMMON/TITLEZ/ COMMON/TITLEJ/ COMMON/TITLE4/ COMMON/TITLES/ COMMON/TITLEG/ COMMON/TITLE7/ INSTE.SITEE TITLEE,TITLET INSTS,SITES YR,EXPTNO INSTW,SITEW TITLEW,TITLER BDATE,EDATE,DWFILE COMMON/NWRIT/ ATLCH,ATMIN,ATNOX,ATANC,ANFAC COMMON/WRITl/ AES,AEP,AET,AEO COMMON/WRITZ/ ASOLR,ATEMX,ATEMN,ARUNOF,ADRAIN,APRECP COMMON/WRIT3/ ASWDF1,ASWDF2 COMMON/WRIT4/ IOUTGR,IOUTWA,JHEAD,KHEAD COHMON/IPEXPI/ COMMON/IPEXPZ/ COMMON/IPEXPJ/ COMMON/IPEXP4/ COMMON/IPEXPS/ COMMON/IPEXP6/ COMMON/IPTRTI/ COMMON/IPTRT2/ COMMON/IPTRTJ/ COMMON/IPTRT4/ COMMON/IPTRTS/ COMMON/IPTRTG/ COMMON/IPTRT7/ COMMON/IPWTHI/ COMMON/PROGRI/ COMMON/PROGRZ/ COMMON/OPSEAl/ COMMON/IPFREI/ NFEXP.NWFILE.NSFILE FILE1,FILE2,FILE4,FILES,FILE6,FILE7,FILE8,FILE9 FILEA.FILEB OUT1,0UT2,0UT3,0UT4 EFFIRR DSOIL,THETAC PHFAC3 P1,P2R,P5,PZO Gl,TR STRAW,SDEP,SCN,ROOT NFERT,JFDAY,AFERT,DFERT,IFTYPE SWCON1,SWCON2,SWCON3 NIRR,JDAY,AIRR Sl,C1 NDEF1,NDEF2 SWDF1,SWDF2,SWDF3 AMTMIN KOUTGR,KOUTNU,KOUTWA 145 May 28 13:24 1987 cerice1.f Page 2 COMMON/SOILRI/ COMMON/SOILRZ/ COMMON/SOILR3/ COMMON/SOILNl/ COMMON/SOILNZ/ COMMON/SOILN3/ COMMON/SOILNl/ COMMON/SOILNS/ COMMON/SOILNG/ COMMON/CALDAI/ COMMON/MINIMl/ CEP,CES,CET NH4,N03 SUME51,SUME52 FOM,FON IFOM.IFON RDCARB,RDCELL,RDLIGN SNH4,SNO3 TEMPMN,TEMPMX TIFOM,TIFON MO,ND,IYR,JDATE,JDATEX TIMOB,TMINF,TMINH,TNNOM COMMON/WATBAI/ COMMON/PHENOZ/ COMMON/PHENO3/ COMMON/PHENOd/ EO,EP,ES,ET CSD1,CSD2 RNO3U,RNH4U CNSDI,CNSD2 DIMENSION ESW(10),RLV(10),PNUP(10), NNOM(10),DTNOX(10),CNI(10),WFY(10),TFY(10),RNTRF(10), FOM(10),FON(10),IFOM(10),IFON(10),NHUM(10),HUM(10),FLUX(10), FLOW(10),SWX(10),NOUT(10),NUP(10),DECR(10),CNR(10),SCNR(10), RNFAC(10),RNLOSS(10),TMFAC(8),LOC(4),WRN(10),RNO3U(10), RNH4U(10),RLDF(10),JFDAY(10),AFERT(10),DFERT(10),IFTYPE(10), OC(10),SNH4(10),SNO3(10),NH4(10),N03(10), FAC(10),BD(10),PH(10),ST(10),T0(5),JDAY(26),AIRR(26), JCNT(12),DLAYR(10),DUL(10),LL(10),SW(10),SAT(10),WF(10), WR(10),RWU(10),FOCNR(10),SWINIT(10),X(3) ++++++++§ LOGICAL IECHON,IHVON ... THE SAVE COMMAND (COMMENTED SECTION BELOW) WILL HAVE TO BE ACTIVATED WHEN RUNNING THIS MODEL IN THE HP SYSTEM ~-*a*** i...QOQ...iiflfiflfiflfi..fitiititifiitfiititflIfifiififlfifii...itflfiififlfififlfltiifiiitfitfi SAVE DLAYR,LL,DUL,SAT,SWINIT,WR,BD,OC,SW,PH,NSENS,NREP, NTRT,TRTNO,ISOILT,KVARTY,ISIM,SDEPTH,IIRR,ISWNIT,ISWSWB, CUMDEP,NLAYR,DEPMAX,SALB,U,SWCON,CN2,TAV,AMP,DMOD,RWUMX, IVAR,IVARTY,LAT,IPY,INITDA,DSFIL£,YEAR 0000 0 + + + C iififiiiifliiflfiiitfiiiiiifiiitfiiittitOititt...flifii.iififiififiifitifitflfiiifiififitifi C C .... SECTION ADDED WHEN RUN WITH OPTIMIZATION ........................ C ISOW=X(1) AFERT(1)=X(2) PLANTS=X(3)-0.2s~0.90 JFDAY(1)IISOW-1 IF (NSIM.EQ.1.AND.IWRITE.EQ.1) THEN C ..iififlfififlfifififlflfl.fitfifififlfifififiiiiitiifififlifititfifi...fiiifiiifiifiiifififififitfifififiitfi NREP-o K0UTCR-7 HOUTNUav HOUTWA-7 C OPEN (40,FIL£='SIM.DIR‘,STATUS='OLD') C C WRITE (*,101) C101 FORMAT (//,5x,' C E R E s R I C E M O D E L ',/ 146 May 28 13:24 1987 cericel.£ Page 3 iii 0.. 000 000000 10 C 120 105 I D 0 It D D 000 00 00 0 130 + 5X.’ Version 1.10 - Upland Condition ') PAUSE Version 1.10 is for upland rice incorporating a standardized I/O with variables passed as argument List *****fi********** END IF END OF IF-THEN BLOCK pop (NSIM.EQ.1) tttittfititfittittitiititiitfit ...... BEGINNING OP SIMULATION LOOP OF ONE TREATMENT ................... NREPINREP+1 NSENSIO ICOUNTI1 IQUITIO IF (NSIM.EQ.1.AND.IWRITE.EQ.1) THEN CALL IPEXP (NSENS,NREP,NTRT,TRTNO,ISOILT,KVARTY,ISIM,ISOW, PLANTS,SDEPTH,IIRR,ISWNIT,ISWSWB,YEAR,IPLANT,JTRANSP) WRITE (*,105) FORMAT (30(/).2X,'RUN-TIME OPTIONS? ', //2x,°0) RUN SIMULATION ', //2x,'1) SELECT SIMULATION OUTPUT FREQUENCY ', //2x,'2) MODIFY SELECTED MODEL VARIABLES INTERACTIVELY ', //2x,'<----- CHOICE ? ( DEFAULT - 0 1') READ (5,110) NSENS FORMAT (12) IF (NSENS.LT. 0 .OR. NSENS.GT. 2) THEN GO TO 120 ELsE IF (NSENS.EO.1) THEN CALL IPFREQ (KOUTGR,KOUTNU,KOUTWA) Go TO 120 ELSE IF (NSENS.E0.2) THEN CALL IPEXP (NSENS,NREP,NTRT,TRTNO,ISOILT,KVARTY,ISIM,ISOW, PLANTS,SDEPTH,IIRR,ISWNIT,ISWSWB,YEAR,IPLANT,JTRANSP) END IF CALL IPTRT (IIRR,NTRT,NSENS,CUMDEP,NLAYR,ISOILT,DEPMAX,SALB,U, SWCON,CN2,TAV,AMP,DMOD,RWUMX,DLAYR,LL,DUL,SAT,SWINIT,WR,BD, OC,KVARTY,IVAR,VARTY) END IF END OF IF-THEN BLOCK FOR (NSIM.EQ.1) ........................ IF (NSIM.EQ.1) CALL IPWTH (FILE1,LAT,IPY,INITDA,ISOW,ISIM) CALL IPSWIN (FILES,DSFILE,DLAYR,SW,PH,SWINIT,NTRT) THE IF-THEN CONDITION BELOW IS ADDED WHEN RUN WITH OPTIMIZATION ** IF (NCYCLE.EQ.1) THEN WRITE (',130) FORMAT (T21,' FOR NONE.') READ (5,140) TITLER FORMAT (A20) ‘1 ,1 {.91- 147 May 28 13:24 1987 cericel.t Page 4 150 160 170 180 000 WRITE (8,150) FORMAT (' Do you want input data echoed to screen (Y/N)?') READ (5,160) IECMC FORMAT (A1) IF (IECHC.EQ.'Y'.OR.IECHC.EQ.'y') IECHON-.TRUE. WRITE (*,170) FORMAT (' Do you want post harvest comparison with observed', 4. ‘ data ',/,' displayed on the screen (Y/N) ?') READ (5,180) IEHVC FORMAT (A1) IF (IEMVC.EQ.'Y'.OR.IEHVC.EQ.'y') IHVONI.TRUE. END IF a... END or CONDITION it.tititfltitfitttttflittiitiitiOtiitttittttititttfit 30 CALL PROGRI (APTNUP,CRAIN,CUMDTT,CUMPH,DTT,GNP,GRAINN,GPP, #+++ + 4. IF IF GRN,GRNWT,ISTAGE,ICSDUR,INSOIL,ITRANS,IOUTNU,JDATEX,LAI,LFWT, NFAC,NHDUP,PA,PAN,PLA,PDL,PDLWT,PERPAWT,PLANTS,PLTWT, PPAWT,PRECIP,RANC,RNFAC,ROOTN,RTWT,SEEDRV,STMWT,STOVN,STOVWT, SUMDTT,TANC,TBASE,TILNO,TMNC,TMFAC,TNUP,TRWU,XSTAGE,WTLF) (NCYCLE.EQ.1) CALL OPSEAS (NREP,NTRT,VARTY,IIRR,IECHON,YEAR) (ISWSWB.NE.0) CALL SOILRI (AIRR,CN2,CRAIN,CUMDEP,DEPMAX, DLAYR,DUL,ESW,FLOW,FLUX,IDRSW,IIRR,INSOIL,JDAY,LL,NLAYR, RTDEP,RWU,RWUMX,SALB,SAT,SMX,SW,SWEF,SWCON,T,TLL,U,WF,WR) 40 READ (11,70,ENDI50) IYR,JDATE,SOLRAD,TEMPMX,TEMPMN,RAIN SOLRADISOLRAD'23.87 ++++ + + + + +++++ IF IF IF IF IF IF (ISWNIT.NE.0.AND.ICOUNT.EO.1) CALL SOILNI (AED.ALx,AMP,ANG, BD,CNI,CTNUP,CUMDEP,DD,DEPMAX,DLAYR,DMINR,DMOD,DT,DTNOX, DUL,HUM,JDATE,LL,NHUM,NLAYR,NNOM,NOUT,NUP,OC,PESW,PH,PNUP, RCN,RNLOSS,SALB,SAT,SOLRAD,ST,STO,SW,T0,TA,TAV,TFY. TMN,TPESW,HFY,WRN,Z) (NCYCLE.EQ.1.AND.ICOUNT.EQ.1) CALL ECHO (IECHON,ISWNIT, YEAR,NTRT,VARTY,LAT,SDEPTH,IIRR,SALB,U,SWCON,CN2,NLAYR,DUL, DLAYR,LL,SW,SAT,ESW,WR,DEPMAX,TLL,PLANTS,IPLANT,JTRANSP) (JDATEX.EQ.367) CALL CALDAT (IYR,JDATE,JDATEX,MO,ND) (ISWNIT.NE.0) CALL MINIMO (ABD,ALX,AMP,ANG,BD,CNI, CNR,CUMDEP,DD,DECR,DLAYR,DMINR,DT,DUL,FAC,FOCNR,HUM, IFOM,JDATE,LL,NHUM,NLAYR,NNOM,PESW,POMR,PONR,RNTRF, SALB,SAT,SCNR,ST,5T0,SOLRAD,SW,TA,TAV,TMN,T0,TFY,WFY,Z) (ISWSWE.NE.0) CALL WATEAL (BD,CUMDEP,DEPMAX,DLAYR,DRAIN, DTNOX,DTT,DUL,ESW,FAC,FLOW,FLUX,GRORT,HUM,ICSDUR,IDRSW, IIRR,ISTAGE,ISWNIT,JDATE,LAI,LL,MU,NLAYR,NO3,NOUT,NUP,PESH, PRECIP,RAIN,RNFAC,RNLOSS,RLDF,RLV,RTDEP,RUNOFF,RWU,RWUMX, SALE,SAT,SMx,SOLRAD,ST,SW,SWCON,swx,SWEP,T,TLL,TSW,TRWU,U, WF,WR) (JDATE.EQ.ISOW.OR.ISTAGE.NE.7) CALL PHENOL (ISWNIT,ISWSWB, IQUIT,JTRANSP,NCYCLE,PLANTS,SDEPTH,YIELD,SOLRAD,TMFAC,TEMPM, “Ft—“m = “firm—— 148 May 28 13:24 1987 cerice1.f Page 5 0 00000 190 200 210 50 70 60 220 99 +++++++ + IVARTY,VARTY,CUMDTT,SUMDTT,DTT,ISTAGE,TBASE,CUMPH,SWSD, PLTWT,PPAWT,PERPAWT,PDLWT,WTLF,GRNWT,PLA,LAI,PDL,SEEDRV,GRN, PA,PAN,TILNO,GPP,GRORT,LFWT,RTWT,STMWT,CUMDEP,ESW,ICSDUR,RLV, CRAIN,RTDEP,TANC,TCNP,RCNP,RANC,TMNC,VANC,VMNC,XSTAGE,GNP, NFAC,DSTOVN,ROOTN,STOVN,PDWI,STOVWT,PGRORT,NDEM,PANN,RNFAC, RNLOSS,TNUP,KOUTGR,FAC,PNUP,DLAYR,LL,SW,NLAYR,RWU,IHVON, BIOMAS) IF (ISWNIT.NE.0.AND.NCYCLE.EQ.1) CALL NWRITE (APTNUP,STOVN, PLANTS,NOUT,TMINF,TMINH,DTNOX,KOUTNU,ISTAGE,IOUTNU, + TANC,NDEF2,NHDUP,APANN,PANN,NO3,NH4,JDATE,NLAYR) IF (NCYCLE.EQ.1) CALL WRITE (CRAIN,PRECIP,KOUTGR,KOUTWA,ISTAGE, + SOLRAD,RUNOFF,DRAIN,JTRANSP,JDATE,SW,PESW,CUMDTT,CUMPH,LAI, + BIOMAS,RTWT,STMWT,LFWT,PPAWT,TILNO,RTDEP,RLV,ITRANS) ICOUNTIO IF (IQUIT.NE.1) GO TO 40 titittit. sup 0? DAILY SIMULATION LOOP itifittttittitiiifiafittttt **“‘ THIS SECTION ADDED WHEN RUN WITH OPTIMIZATION *‘***'***'** X(1)IISOW X(2)IAFERT(1) X(3)IPLANTS/(0.25*0.90) IF (NSIM.EQ.NCYCLE) CLOSE (11) IF (NCYCLE.NE.1) GO TO 99 WRITE (*,190) FORMAT (//,' Simulation complete for this treatment',/, ' Do you want to simulate another treatment (Y/N) ?') READ (5,200) IFIN FORMAT (A1) IF (IFIN.EQ.'Y'.OR.IFIN.EQ.'y') THEN CLOSE (11) GO TO 10 ELSE WRITE (*,210) FORMAT (‘ END OF SIMULATION RUN.') END IF GO TO 99 WRITE (41,220) WRITE (*,220) CLOSE(11) FORMAT (5X,IZ,1X,I3,1X,F5.2,3(1X,F5.1)) FORMAT (5X,F6.2) FORMAT (15X,' END OF WEATHER DATA. ') RETURN END 149 May 20 15:10 1987 cerice2.t Page 1 c ithiiiti..fififiitfiitiitiiiiitfitfitifit.iIiit.tfittfitititCtttttittttttitttt c OOOOOOOOCOOOO PROGRAM INITIALIZATION iittttiitfiitittfifittititttt.tfiitt c fit.fit...itittitfiitiiififiittttit...*fiiiitittifitttfifitititiitttifititttttt SUBROUTINE PROGRI (APTNUP,CRAIN,CUMDTT,CUMPH,DTT,GNP,GRAINN,GPP, + GRN,GRNWT,ISTAGE,ICSDUR,INSOIL,ITRANS,IOUTNU,JDATEX,LAI,LFWT, + NFAC,NHDUP,PA,PAN,PLA,PDL,PDLWT,PERPAWT,PLANTS,PLTWT,PPAWT, + PRECIP,RANC,RNFAC,ROOTN,RTWT,SEEDRV,STMWT,STOVN,STOVWT,SUMDTT, + TANC,TBASE,TILNO,TMNC,TMFAC,TNUP,TRWU,XSTAGE,WTLF) REAL INSOIL,LAI,LFWT,NDEF1,NDEF2,NFAC COMMON/PROGRI/ NDEF1,NDEF2 COMMON/PROGRZ/ SWDF1,SWDF2,SWDF3 COMMON/WRIT4/ IOUTGR,IOUTWA,JHEAD,KHEAD DIMENSION RNFAC(10),TMFAC(8) DO 20 LI1,10 RNFAC(L)I1.0 20 CONTINUE IOUTGRIO IOUTWAIO IOUTNUIO ITRANSIO JHEADIO KHEADIO NHDUPIO PLTWTI0.0044 STMWTIO. PPAWTIO. PDLWTIO. TILNOIO. PLAIO. LAIIO. PAIO. PERPAWTIO. GRNWTIO. PDLIO. LFWTI0.0035 RTWTI0.0009 STOVWTI0.0035 WTLFI0.4 CUMPHI0.8 SEEDRVI0.024*PLANTS PANI0.00095 GRNI0.000083 GPPIO. ISTAGE-7 TBASEIB. JDATEXI367 CUMDTTIO. SUMDTTIO. OUTDTTIO. DTTIO. GRAINNI1.0 APTNUPI0.0 TMNCI0.004S XSTAGE=0.1 150 May 20 15:10 1987 cerice2.t Page 2 DO 30 II1,8 TMFAC(I)I0.931+0.114*I-0.0703*I**2+0.0053*I**3 30 CONTINUE SWDF1I1.0 SWDF2I1.0 SWDF3I1.0 INSOILI1.1 TRWUI0.0 NFACI1.O ICSDURIO NDEF1I1.0 NDEF2I1.0 TANCI0.0 RANCI0.0 STOVNI0.0 ROOTNI0.0 GNP-1.0 TNUPI0.0 CRAINIO. PRECIPIO. RETURN END c Oii.t....fiiifififlfifiififififiitfitfittfiifififiitifitflfifii...tfififififififitfiiitfi...iitfittt C lfiiitfl. OUTPUT FREQUENCY SELECTION fittititttfiiiififiifiittttfiititiititttt C tiii.iflfifittttififiitiiitifiifittiiitfltfiitttfifiltiiitifiititittit...tittiiiti SUBROUTINE IPFREQ (KOUTGR,KOUTNU,KOUTWA) WRITE (*,100) 100 FORMAT(30(/)) 200 WRITE (*,300) KOUTWA 300 FORMAT(1X,I2,' Days ',' TO CONTINUE LISTING' WRITE (t,' ,a, ' READ (5,'(Al)')ANS WRITE (*.'(7(/))') NVARS - 1 WRITE (*,100) END IF 205 READ (19,300,END I 505) IVAR,VARTY,P1,P2R,P5,P20,Gl,TR WRITE (*,400) IVAR,VARTY 400 FORMAT(25X,I4,3X.A16) GO TO 205 505 REWIND 19 800 WRITE (*, 900) KVARTY 900 FORMAT(/1X,I4,']',1X.' to continue. Screen prompts, options, and screen inputs The first prompt is for user to press the key to continue. At this stage, press the key. The second prompt is a list of experiments to be simulated. The screen display will vary depending on the list of experiments defined in RIEXP.DIR file. For this entry, the screen would display the following experiments: 215 INST. SITE EXPT. LIST OF EXPERIMENTS TO BE SIMULATED ID ID NO YEAR IRRI, LDS BANDS, PHENDLDGY STUDY, 1983 IR PI 01 1983 IRRI, LDS BANDS, IRRIG. & N STUDY, 1980 IR PI 01 1980 <-- CURRENT EXPERIMENT SELECTION. <--- NEW SELECTION? 3. Press the number corresponding to the experiment selection. A. The third prompt is a list of treatments under the experiment chosen in step 3. The screen display will depend upon the treatments of the experiment defined in FILE8. For experiment no. 2 of step 2, the following list of treatments would be displayed on the screen: INST. SITE EXPT. IRRI, LDS BANDS, IRRIG. & N STUDY, 1980 ID ID NO YEAR IR36, 120 Kg N/Ha, Wl irrig. level IR PI 01 1980 IR36, 0 Kg N/Ha, W2 irrig. level IR PI 01 1980 IR36, 30 Kg N/Ha, W2 irrig. level IR PI 01 1980 IR36, 60 Kg N/Ha, W2 irrig. level IR PI 01 1980 IR36, 120 Kg N/Ha, W2 irrig. level IR PI 01 1980 <-—- CURRENT TREATMENT SELECTION <--- NEW SELECTION? 5. Press the number corresponding to the treatment selection. 45. The fourth prompt is the run-time options. The user could proceed to run the simulation (0), select the simulation output frequency (1), or modify selected inputs interactively (2). The screen should display the following: RUN-TIME OPTIONS? 0) RUN SIMULATION 1) SELECT SIMULATION OUTPUT FREQUENCY 216 2) MODIFY SELECTED MODEL INPUTS INTERACTIVELY < CHOICE 7 [ DEFAULT - o ] 7. Press the number corresponding to the run-time option. 8. If Choice is 0, proceed to step 11. 9. If Choice is 1, the user has the option to change the frequency of writing the simulation output to the output files. These are the choices on the screen: " 7 Days <--OUTPUT FREQUENCY FOR WATER BALANCE COMPONENTS. <--- NEW VALUE? " Press the frequency of output according to Choice. " 7 Days <--OUTPUT FREQUENCY FDR GROWTH COMPONENTS. <--- NEW VALUE? " Press the frequency of output according to choice. " 7 Days <--OUTPUT FREQUENCY FOR NITROGEN COMPONENTS. <--- NEW'VALUE? " Press the frequency of output according to choice. 10. If Choice is 2, the user has the option to Change selected inputs interactively from the screen. 11. The next prompt is for the user to enter a run identifier to label the simulation run. A character string of at most 20 is acceptable as input. This is optional. n < ENTER RUN IDENTIFIER, HIT FDR NONE. " Enter run identifier and/or press the key to continue. 12. The next prompt is a querry if the user is interested to 217 write on the screen selected inputs and summary outputs. "Do you want input data echoed to screen (Y/N)?" Press ”Y" for "yes" or "N" for "no". 13. The next prompt is a querry if the user is interested to display on the screen post harvest comparison with field—measured data. "Do you want post harvest comparison with observed data displayed on the screen (Y/N) ?" Press "Y" for ”yes" or "N" for "no". 14. If the choice for steps 12 or 13 is "Y" , some information will be displayed on the screen during the simulation. 15. When the simulation is done, a querry if the user is interested to simulate another treatment is displayed on the screen. "Simulation complete for this treatment. Do you want to simulate another treatment (Y/N) ?" Press ”Y" for "yes" or ”N” for "no". 16. A choice of "Y" will re-initialize the simulation. In this case, go back to step 2. 17. A Choice of ”N" will end the simulation. "END OF SIMULATION RUN." 8.7. Output Files There are four output files. The filenames are user-supplied with at most 7 character strings defined in RIEXP.DIR file. For this demonstration, the output files are OUT80.1, OUT80.2, OUT80.3, and OUT80.4. ‘ ‘ ‘1'“- 218 OUTPUT FILE NO. 1 - contains some selected inputs and the summary output. The following codes are part of output no. 1: RUN IDENTIFIER - identifies the simulation run for the user; any character string of 20 or less is valid. RUN NO. - A counter on the number of simulation runs INST_ID - Institute identification code SITE_ID — Site or Location identification code EXPT_NO - Experiment number YEAR - Calendar year of the experiment TRT_NO - Treatment number EXP. - Title of experiment TRT. - Title of treatment WEATHER - Title of weather file used in the simulation SOIL - Soil type where experiment was conducted VARIETY - Name of the rice variety used in the simulation LATITUDE OF EXPT. SITE - Latitude of the experimental site PLANT POPULATION - Number of plants/m2 SOWING DEPTH - Depth of sowing, in cm Pl - Degree-days required from emergence to end of juvenile stage P2R - Rate of photo-induction, degree-days/hr P5 - Degree-days required for grain filling P20 - Optimum photoperiod, in hr 61 - Conversion efficiency from intercepted PAR (photoynthetically active radiation) to dry matter production, s/MJ PAR TR - Tillering factor, unitless JUL DAY - Day of the year 219 IRRIGATION (MM) - Amount of irrigation, in mm PEDON - SCS pedon number SOIL ALBEDO - Bare soil albedo, unitless UPPER LIMIT OF SOIL EVAPORATION - Upper limit of stage 1 soil evaporation, in mm SOIL WATER DRAINAGE CONSTANT - Soil water drainage constant, fraction drained/day SCS RUNOFF CURVE NO. - SCS curve number used to calculate daily runoff DEPTH OF LAYER-cm - Thickness of the soil layers, in cm LOWER LIMIT - Lower limit of plant-extractable soil water of the soil layer, cm3/cm3 UPPER LIMIT - Drained upper limit soil water content of the soil layer, cm3/cm3 SAT. CONTENT - Saturated water content of the soil layer, cm3/Cm3 EXTR. WATER - Extractable soil water content of the soil layer, the difference between UPPER LIMIT and LOWER LIMIT WATER CONTENT - Soil water content of the soil layer, cm3/cm3 ROOT FACTOR - Weighting factor of the soil layer to determine new root growth distribution, unitless SOIL N03 - Initial soil nitrate in the soil layer, mg elemental N/Kg soil SOIL NH4 - Initial soil ammonium in the soil layer, mg elemental N/Kg soil KG/HA - Amount of nitrogen fertilizer applied, in Kg N/Ha DEPTH - Depth of application, in cm SOURCE - Type of fertilizer 220 DATE - Date of the event according to the calendar year PHENOLOGICAL STAGE - Phenological stages of the rice crop TILLER NO. - Number of tillers/m2 BIOMASS - Biomass of the crop, in g/m2 ROOT WT. - Weight of roots, in g/m2 LEAF WT. - Weight of leaves, in g/m2 STEM WT. - Weight of stem, in g/m2 PANICLE WT. - Weight of the panicles, in g/m2 LAI - Leaf are index PREDICTED - Output of the simulation W OBSERVED - Field-measured data OUTPUT FILE NO. 2 - contains the simulation outputs on the growth components, output frequency varying with user option. The following codes are part of output no. 2: RUN - Run number and run identifier, as defined in output no. 1 INST_ID, SITE_ID, EXPT_NO, ‘YEARW TRT_NO, EXP., 'TRT., WEATHER, SOIL, VARIETY - as defined in output no. 1 IRRIG. - Type of irrigation strategy JUL DAY - Day of the year CUM. DTT - Cumulative thermal time, in degree-days LEAF NO. - Number of leaf tips that have emerged LAI, BIOMASS, ROOT WT., LEAF WT., STEM WT., PANICLE WT., TILLER NO. - as defined in output no. 1 ROOT DEPTH - Depth of rooting, in cm ROOT LENGTH DENSITY, L1, L3, L5 - Root length density of the soil layers 1, 3, and 5, in cm root/cm3 soil 221 OUTPUT FILE NO. 3 - contains the simulation output on the water balance components, frequency of output varying with user option. The following codes are in output no. 3: RUN - Run number and run identifier, as defined in output no. 1 INST_ID, SITE_ID, EXPT_NO, YEAR, TRT_NO, EXP., TRT., WEATHER, SOIL, VARIETY - as defined in output no. 1 IRRIG., JUL DAY - as defined in output no. 2 AVERAGE EP - Average plant evaporation, in mm/day AVERAGE ET - Average plant transpiration, in mm/day AVERAGE EO - Average potential evapotranspiration, in mm/day AVERAGE SR - Average solar radiation, MJ/day AVERAGE MAX - Average maximum temperature, in °C AVERAGE MIN - Average minimum temperature, in °C PERIOD PREC - Total precipitation for the period, in mm SW CONTENT W/ DEPTH, SW1, SW2, SW3, SW4, SW5 - Soil water content of the soil layers 1, 2, 3, 4, and 5 TOTAL PESW - Total plant extractable soil water in the profile, in cm OUTPUT FILE NO. 4 - contains the simulation output on the nitrogen components, frequency of output varying with user option. The following codes are part of output no. 4: RUN - Run number and run identifier, as defined in output no. 1 INST_ID, SITE_ID, EXPT_NO, 'YEAR" TRT_NO, EXP., 'TRT., ‘WEATHER, SOIL, VARIETY - as defined in output no. 1 IRRIG., JUL DAY - as defined in output no. 2 222 TOPS N1 - Actual nitrogen concentration in plant tops, percent NFAC - Average nitrogen stress factor affecting leaf area expansion, O-l unitless TOP N UPTK - Total nitrogen in the stover, in g/m2 PAN N UPTK - Total nitrogen in the panicle, in g/m2 LEACH - Total amount of nitrogen leached from all soil layers, in Kg N/Ha MINLN - Total amount of nitrogen released by mineralization, in Kg N/Ha DENTT - Tbtal amount of nitrogen lost from all soil layers by denitrification, in Kg N/Ha N03 1, 2, 3 - Amount of soil nitrate in layers 1, 2 and 3, in Kg N/Ha NH4 1, 2 - Amount of soil ammonium in layers 1 and 2, in Kg N/Ha A sample of each output files follows. The output filenames are OUT80.1, OUT80.2, OUT80.3, and OUT80.4. 223 Jun 30 14:51 1987 OUT80.1 Page 1 RUN IDENTIFIER : vangie RUN NO. 1 INPUT AND OUTPUT SUMMARY INST_ID :IR SITE ID: PI EXPT NO: 01 YEAR : 1980 TRT_NO: 1 EXP. :IRRI, Lo§ aauos. IRRIG. & N STUDY, 1980 TRT. :IRJG, 120 kg N/ha, w1 irrig. level WEATHER :IRRI 1980 UPLAND DATA SOIL :Typic Eutrandept VARIETY :IR 36 LATITUDE OP EXPT. SITE I 15.0 degrees PLANT POPULATION I 368.00 plants per sq. meter 1 SOWING DEPTH I 2.5 cm. GENETIC SPECIFIC CONSTANTS Pl I 550.00 92R I 149.00 P5- 550.00 P20 I 11.7 GI I 4.000 TR I .730 IRRIGATION SCHEDULE JUL DAY IRRIGATION (mm.) 35 150. 59 165. 68 45. 78 55. 98 245. 115 115. 116 35. SOIL PROFILE DATA [ PEDON: IRRI PEDON ] SOIL ALBEDO I .14 UPPER LIMIT OF SOIL EVAPORATION I 5.0 SOIL HATER DRAINAGE CONSTANT I .60 SCS RUNOFF CURVE NO.I 60.0 DEPTH OP LOWER UPPER SAT. EXTR. WATER ROOT SOIL SOIL LAYER-cm LIMIT LIMIT CONTENT WATER CONTENT FACTOR N03* N34. O.- 15. .120 .260 .430 .140 .260 1.000 4.7 2.0 15.- 30. .220 .350 .400 .130 .350 .900 3.1 2.0 30.- 45. .210 .330 .390 .120 .330 .500 3.8 2.0 45.- 60. .210 .330 .390 .120 .330 .100 3.5 2.0 60.- 75. .210 .330 .390 .120 .330 .050 3.5 2.0 TOTAL 0.- 75. 14.5 24.0 30.0 9.5 24.0 30. 16. * NOTE: Units are in kg N / ha. FERTILIZER INPUTS JUL DAY KG/HA DEPTH SOURCE 8 123.00 10.00 UREA 224 Jun 30 14:51 1987 OUT80.1 Page 2 OUTPUT SUMMARY DATE JUL PHENOLOGICAL TILLER BIOMASS ROOT LEAP DAY STAGE NO. . WT. (- - - grams per sq. 1/ 9/80 9 SOWING 0. 1/12/80 12 GERMINATION 0. 1/13/80 13 ENERGENCE 0. .1 .0 .1 2/13/80 44 END JUVENILE STAGE 555. 117.8 48.1 116.9 2/27/80 58 FLORAL INITIATION 726. 282.0 153.7 239.9 3/29/80 89 READING 830. 781.4 256.2 312.5 4/ 7/80 98 START GRAIN PILL 822. 985.7 267.9 301.7 4/25/80 116 END GRAIN PILL 722. 1385.0 244.8 216.1 4/26/80 117 PHYSIOLOGICAL 722. 1385.0 244.8 216.1 HATURITY COMPARISON BETWEEN PREDICTED AND FIELD-MEASURED DATA PREDICTED OBSERVED READING DATE (DAY OF YEAR) 89 90 NATURITY DATE (DAY OF YEAR) 117 118 GRAIN YIELD (NT/HA) 6.6 6.7 1,000 GRAIN WEIGHT (G) 29.65 23.00 NO. PANICLES PER SQ. METER 722. 522. PANICLE WEIGHT (KG/NA) 7607. 0. PANICLE-STRAW RATIO 1.09 .00 LAI AT HEADING 6.12 .00 BIOMASS (KG/HA) 13850.1 .0 STRAW (KG/HA) 7003.5 6830.0 STEM PANICLE WT. WT. meter - - - -) .0 .0 .9 .0 42.1 .0 332.2 136.7 436.6 247.4 408.2 760.7 408.2 760.7 LAI Jun 30 14:20 1987 OUT80.2 Page 1 RUN INST_ID :IR SITE ID: PI 1 vanqie EXPT NO: 225 01 YEAR : PAN. NT. ' ) .00 .00 .00 .00 .00 4.11 24.03 59.39 110.88 136.72 213.32 465.98 exp. :IRRI, LOS nanos, IRRIG. & N STUDY. 1980 TRT. :IR36, 120 kg N/ha, W1 irrig. level WEATHER :IRRI 1980 UPLAND DATA SOIL :Typic Eutrandept VARIETY : IR 36 IRRIG. :ACCORDING TO THE FIELD SCHEDULE. JUL CUM. LEAP LAI 810- ROOT LEAP STEM DAY DTT NO. MASS WT. WT. WT. (- - - grams per sq. meter - 26 296. 4. .10 5. 1.39 5.27 .01 33 423. 5. .58 29. 12.50 29.09 .13 40 546. 7. 1.66 87. 32.80 86.00 .57 47 666. 8. 2.67 145. 61.68 142.17 2.86 54 794. 10. 4.08 239. 117.88 215.20 23.33 61 924. 11. 4.93 318. 170.87 256.42 57.79 68 1053. 13. 5.61 423. 205.71 290.89 108.53 75 1187. 14. 6.04 548. 230.87 310.88 177.55 82 1318. 16. 6.12 693. 247.83 313.83 267.80 89 1443. 18. 6.12 781. 256.22 312.51 332.17 96 1578. 18. 5.99 940. 265.97 305.56 420.86 103 1716. 18. 5.56 1171. 261.28 274.61 430.48 110 1853. 18. 5.08 1298. 252.27 244.31 419.52 634.28 1980 TRT_NO: 1 TILLER ROOT NO. DEPTH (CE-) 244. 55. 378. 75. 493. 75. 599. 75. 689. 75. 747. 75. 794. 75. 823. 75. 830. 75. 830. 75. 826. 75. 806. 75. 769. 75. ROOT LENGTH DENSITY L1 L3 L5 .4 .0 .O .6 .1 .0 1.0 .3 .0 1.5 .5 .O 2.3 1.2 .1 2.6 2.0 .2 3.0 2.5 .3 3.2 2.8 .3 3.3 3.0 .3 3.4 3.1 .4 3.5 3.1 .4 3.6 3.1 .4 3.6 3.1 .4 226 Jun 30 14:20 1987 OUT80.3 Page 1 RUN 1 vanqie INST_ID :IR SITE ID: PI EXPT N0: 01 YEAR : 1980 TRT_NO: 1 EXP. mun. IDS mos, IRRIG. & N STUDY, 1980 TRT. :IR36, 120 kg N/ha, W1 irrig. level WEATHER :IRRI 1930 UPLAND DATA SOIL :Typic Eutrandept VARIETY : IR 36 IRRIG. :ACCORDING TO THE FIELD SCHEDULE. JUL ---------- AVERAGE --------- PERIOD SW CONTENT W/DEPTH TOTAL DAY EP ET EO SR MAX MIN PREC SW1 SW2 SW3 SW4 SW5 PESW 14 .0 .7 4.2 390. 29.7 20.9 .00 .19 .32 .32 .33 .33 7.9 21 .1 1.2 3.7 337. 29.5 21.7 1.60 .21 .33 .32 .32 .32 8.1 28 .2 .9 2.7 254. 28.7 21.9 .24 .20 .32 .32 .32 .32 7.6 35 1.3 2.2 4.6 425. 31.4 21.7 21.57 .30 .37 .36 .35 .35 11.4 42 1.9 3.5 3.5 347. 29.6 20.6 .39 .18 .32 .32 .33 .33 7.7 49 2.2 3.3 3.3 330. 29.4 21.3 1.96 .17 .30 .31 .32 .32 6.7 56 4.2 5.2 5.5 539. 32.4 20.5 .00 .11 .24 .24 .28 .30 3.0 63 3.9 4.5 4.9 480. 33.3 19.9 23.57 .22 .32 .32 .33 .33 8.4 70 4.4 4.9 4.9 479. 33.5 20.2 7.09 .26 .34 .34 .34 .34 9.6 77 4.6 5.0 5.0 489. 32.7 21.5 .00 .17 .27 .29 .31 .32 6.0 84 3.7 4.1 4.1 402. 31.2 21.1 23.14 .33 .37 .36 .35 .35 11.8 91 3.5 3.8 3.8 377. 30.3 22.6 1.53 .22 .32 .31 .33 .33 8.1 98 4.8 5.3 5.3 511. 32.8 22.3 35.30 .32 .35 .35 .35 .35 11.3 105 5.2 5.8 5.8 510. 33.0 22.5 1.77 .24 .30 .30 .32 .32 7.6 112 4.3 4.8 4.8 421. 32.2 23.8 12.13 .20 .30 .30 .32 .33 7.3 227 Jun 30 14:20 1987 OUT80.4 Page 1 RUN 1 vangie INST_ID :IR SITE_ID: PI EXPT_NO: 01 YEAR : 1980 TRT_NO: 1 EXP. :IRRI. LOS BANOS, IRRIG. & N STUDY, 1980 TRT. :IR36, 120 kg N/ha, WI irrig. level WEATHER :IRRI 1980 UPLAND DATA SOIL :Typic Eutrandept VARIETY : IR 36 IRRIG. :ACCORDING TO TEE FIELD SCHEDULE. JUL TOPS NPAC TOP N PAN N LEACH MINLN DENIT N03 N03 N03 DAY N 3 UPTK UPTX 1 2 3 26 3.72 .84 156. 0. 10.6 4.6 16.2 68.2 4.9 4.7 33 3.44 .75 893. 0. 10.6 4.6 16.2 64.2 4.9 4.8 40 3.10 .72 2082. 0. 270.8 5.1 12.4 13.5 16.0 12.9 47 2.80 .62 3227. 0. .6 4.2 12.9 11.0 15.0 12.6 54 2.45 .55 4507. 0. .6 4.1 12.9 9.4 12.0 10.1 61 2.14 .47 5427. 0. 104.2 4.0 9.7 2.0 5.6 7.4 68 1.98 .50 6277. 0. 5.0 4.9 6.6 1.1 4.1 6.6 75 1.80 .52 6932. 0. 4.8 5.4 5.0 1.0 2.9 5.1 82 1.63 .54 7483. 0. 7.1 4.9 4.1 1.0 1.6 3.9 89 1.51 .58 7801. 0. 28.7 4.6 1.6 1.0 1.0 1.3 96 1.38 .56 8108. 0. .8 4.6 1.6 1.0 1.1 1.4 103 1.19 .78 5628. 33. 13.3 5.1 .4 1.0 1.1 1.0 110 .83 .58 4063. 55. 2.4 5.1 .1 1.0 1.0 1.0 -' up"... 5 GGOOGGOQQOOONH. Z 3: h ...u . ' I. 41.5 ‘ HHHHHHHHHHHNN . C O O O O D I O O I I mmto HHHHHHPHHHUUU APPENDIX D SAMPLE OUTPUT OF THE SIMULATION-MULTICRITERIA OPTIMIZATION TECHNIQUE FARM PRODUCTION MULTICRITERIA OPTIMIZATION ****************************************** OBJECTIVE FUNCTIONS: 1) MAXIMIZE PROFIT, F(l) ($/Ha) 2) MINIMIZE FARM PRODUCTION RISK, F(2) (std. deviation from the mean yield) DECISION VARIABLES: 1) SOWING DATE, U(l), (Julian day) 2) AMOUNT OF N FERTILIZER APPLIED, U(2), (Kg N/Ha) 3) PLANT POPULATION, U(3), (plants/sq.meter) NO. OF U(1)—POINT SEARCH : 1 NO. OF U(2),U(3)-POINT SEARCH : 200 NO. OF SIMULATION CYCLES TO GET AVE.YIELD (MT/Ha): 25 SET NO. 1 THE SET OF FEASIBLE SOLUTIONS ARE : U(l) : 171 (SOWING DATE) RUN NO. U(2) U(3) F(1) F(2) (N FERT.) (POPULATION) AVE. YIELD (PROFIT) (RISK) 1 0. 400. 3.16 61.42 .302 2 873. 698. 7.55 2628.23 1.025 3 676. 717. 7.51 2872.54 1.023 4 783. 316. 7.88 3055.13 1.085 5 711. 344. 7.89 3137.58 1.085 6 647. 549. 7.78 3177.19 1.063 7 805. 352. 7.91 3008.46 1.084 8 751. 236. 7.81 2997.68 1.087 9 463. 541. 7.69 3313.68 1.091 10 604. 152. 7.69 3104.52 1.106 11 316. 513. 7.41 3280.54 1.105 12 841. 868. 7.27 2456.04 .987 228 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 313. 469. 157. 769. 211. 872. 399. 458. 195. 544. 269. 329. 261. 523. 802. 868. 111. 100. 860. 120. 876. 643. 852. 153. 283. 768. 759. 62. 806. 424. 845. 611. 137. 625. 136. 420. 82. 697. 508. 335. 866. 155. 102. 23. 226. 395. 498. 378. 621. 348. 12. 816. 215. 752. 229 454. 216. 690. 490. 110. 655. 434. 340. 574. 333. 242. 578. 393. 249. 632. 740. 530. 761. 331. 256. 164. 550. 593. 480. 591. 569. 722. 436. 571. 524. 784. 402. 508. 553. 744. 539. 579. 305. 160. 541. 745. 722. 639. 164. 726. 567. 154. 829. 847. 832. 770. 820. 365. 124. \JO‘NWVVNVNO‘U’U‘IUVNNN4-‘\JU'|\JU'|\J\J\I\I9N\INU'INNVU'INbUNNVVNVVQVVN¢VUNN .48 .67 .89 .89 .47 .62 .74 .77 .46 .84 .11 .38 .17 .75 .66 .48 .24 .94 .89 .38 .74 .78 .72 .96 .16 .76 .51 .37 .76 .67 .41 .91 .69 .77 .54 .64 .70 .86 .65 .45 .47 .84 .04 .49 .64 .56 .63 .14 .29 .08 .25 .35 .76 .69 3334. 3294. 2162. .91 2593. 2689. 3494. 3377. 2662. 3367. 3084. 3250. 3138. 3296. 2791. 2568. 1666. 1473. 2926. .71 2798. 3175. 2778. 2225. 3132. .49 .46 971. 2878. 3363. 2575. .32 2058. 3167. 1928. 3338. 1266. 3181. 3203. 3312. 2561. 2118. 1487. .49 2743. 3336. 3259. 2970. 2751. 2986. 68. 2523. 2848. 2889. 3063 1787 2950 2731 3294 282 01 24 90 60 77 49 00 32 96 62 21 44 16 42 26 77 72 60 36 04 35 57 74 67 96 72 32 25 26 86 71 92 17 96 00 12 56 94 41 98 98 46 00 74 09 65 23 12 H HHHHH H HHHr—‘r—‘t—‘H r-‘H HHH HHr—IH Hr—‘r—‘H HHt—‘H .114 .123 .884 .074 .031 .035 .134 .118 .966 .098 .106 .095 .095 .105 .041 .016 .749 .708 .084 .781 .093 .063 .049 .882 .071 .056 .020 .574 .055 .106 .006 .090 .834 .063 .824 .103 .645 .086 .121 .106 .015 .878 .717 .407 .004 .102 .124 .040 .996 .044 .356 .998 .026 .102 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 594. 179. 108. 897. 181. 780. 232. 354. 123. 536. 564. 883. 790. 267. 203. 869. 59. 849. 553. 522. 539. 735. 103. 822. 82. 571. 604. 613. 772. 203. 483. 288. 213. 293. 563. 758. 438. 490. 273. 319. 697. 162. 415. 592. 441. 491. 93. 550. 529. 30. 866. 526. 518. 230 652. 888. 777. 390. 857. 642. 462. 323. 344. 765. 316. 461. 260. 887. 500. 334. 705. 781. 115. 342. 795. 162. 893. 542. 561. 595. 462. 863. 499. 627. 443. 387. 649. 295. 708. 829. 775. 357. 394. 512. 496. 254. 378. 607. 288. 761. 769. 173. 779. 810. 268. 799. 611. 660. \JVVWVV#NVVVO‘VNV\JNVNMO‘VNO‘NNVUNpNJ-‘NNNNNb‘dO‘O‘NflNNU‘INO‘NO‘NU‘O‘V .60 .01 .07 .93 .06 .64 .95 .56 .46 .39 .83 .94 .84 .71 .62 .89 .22 .41 .61 .83 .35 .74 .92 .81 .71 .68 .20 .26 .85 .66 .66 .83 .12 .69 .07 .30 .42 .75 .84 .20 .45 .82 .10 .53 .82 .33 .36 .87 .38 .32 .68 .38 .63 .55 3090. 2266. 1515. .41 2309. .43 3018. 3334. 1858. 2982. 3296. 2968. 3017. 2738. 2726. 2928. 845. 2579. .38 3361. 2942. 3000. .04 2920. .66 3163. .41 .41 3241. 2867. .21 .27 3090. 2962 2846 3104 1385 1269 22 2725 2763 3429 2792 3047 3066 1408 2917 10 04 21 18 30 40 83 71 04 39 21 57 58 63 24 63 00 21 98 96 56 00 58 62 .81 .88 2832. 2656. 3435. 3439. 3166. 3310. 3145. 2340. 3243. 3287. .80 3023. .66 2968. 90 01 03 37 13 57 56. 84 11 54 54 53 .11 442. 2484. 3191. 3119. 14 15 91 84 H HHHHH t-‘r-‘H P'P‘P‘F‘h‘ H r-‘r-‘t-‘Hr-‘t-‘O-‘l—‘l-‘t-‘H HHHH r-‘r-‘H r-‘H .042 .905 .734 .083 .911 .039 .048 .140 .794 .021 .096 .080 .086 .006 .991 .084 .558 .007 .121 .101 .013 .096 .710 .062 .645 .058 .317 .993 .077 .042 .997 .111 .060 .026 .058 .003 .009 .124 .109 .084 .109 .088 .911 .087 .093 .040 .028 .694 .016 .012 .442 .003 .060 .049 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 13. 523. 256. 29. 442. 165. 459. 297. 558. 337. 472. 45. 383. 527. 891. 325. 209. 821. 517. 404. 463. 764. 484. 788. 107. 174. 764. 485. 843. 172. 464. 657. 350. 732. 75. 498. 186. 759. 355. 714. 227. 221. 852. 101. 263. 101. 319. 231. 753. 222. 589. 672. 341. 255. 231 728. 435. 846. 738. 713. 254. 356. 179. 760. 753. 736. 217. 290. 402. 537. 298. 234. 871. 716. 708. 298. 791. 463. 233. 268. 313. 657. 872. 850. 665. 682. 762. 809. 821. 407. 792. 461. 898. 413. 286. 436. 655. 451. 674. 332. 149. 560. 386. 737. 351. 185. 514. 593. 221. \JVNVO‘VO‘NpNMNmO‘VNVO‘V#NNNNO‘NN\IO‘U‘NNNNNVVO‘NNNNUNVVNNO‘VU’O‘VU .28 .89 .71 .60 .41 .08 .78 .19 .41 .17 .40 .98 .60 .87 .81 .43 .60 .27 .46 .36 .74 .39 .84 .81 .16 .23 .61 .19 .30 .11 .48 .43 .12 .34 .62 .33 .44 .22 .62 .85 .92 .67 .96 .00 .14 .99 .37 .93 .48 .82 .73 .84 .40 .00 92. 3416. 2732. 370. 3132. 2325. 3388. 3154. .00 3063. 3056. 703. 3374. 3399. 2859. 3297. 2714. 2451. 3041. 3096. 3353. 2633. 3437. 2997. 1597. 2460. 2824. 2878. 2481. 2352. 3123. .52 3019. 2659. 1189. 2996. 2640. 2481. 3393. 3100. 2989. 2768. 2982. 1454. 3114. 1442. 3239. 2993. 2709. 2904. 2928 2806 3203 2986 30 33 27 97 38 14 51 18 90 69 75 19 84 10 34 27 49 77 31 23 30 63 15 54 17 36 69 53 64 75 85 20 65 08 77 80 90 53 20 19 29 58 73 O6 02 83 76 22 .04 3161. 3268. .03 15 19 p—u—u—u—u—u—J r-‘I-‘r-‘l-‘H HHD—‘D—‘H t-‘f-‘l-‘r-‘H HHH H H HHHD—‘HHHH .360 .102 .004 .434 .052 .912 .118 .128 .019 .062 .039 .510 .143 .100 .062 .133 .016 .987 .035 .063 .120 .005 .106 .087 .736 .938 .035 .005 .991 .910 .054 .013 .049 .998 .622 .021 .960 .981 .135 .086 .041 .000 .083 .711 .096 .723 .097 .054 .017 .040 .102 .070 .097 .097 ' ’ 7' 52‘ 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 THE IDEAL VECTOR 0F OBJECTIVE FUNCTIONS ARE: F0(1)- 318. 308. 487. 10. 315. 310. 765. 348. 49. 575. 67. 463. 192. 125. 200. 609. 150. 104. 486. 262. 417. 631. 17. 425. 848. 574. 3494.49 232 703. 316. 751. 694. 432. 360. 239. 705. 517. 211. 258. 346. 508. 297. 190. 135. 583. 311. 787. 112. 617. 411. 586. 393. 383. 617. FO(2)- wuuuwumummuo‘mo‘ubwkwuuuwwuu .302 .17 .38 .39 .23 .49 .42 .82 .26 .08 .75 .43 .78 .48 .48 .47 .67 .86 .12 .33 .89 .52 .92 .39 .76 .93 .65 THE SET OF PARETO OPTIMAL SOLUTIONS ARE: POINT NO. \OCDVO‘U‘bU-DNH U(l) 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 U(3) 400. 792. 611. 611. 541. 574. 333. 480. 434. 394. 574. 333. 530. 761. 256. 611. \lU‘pU'IVO‘VNUIVO‘VNVNw YIELD .16 .33 .63 .63 .69 .46 .84 .96 .74 .84 .46 .84 .24 .94 .38 .63 3070. 3248. 3046. 54. 3347 3284. 3000. 3148. 793 3221. 1025 3386 2676. 1874. 2662. 3085. 2201. 1563. 2995. 2893. 3232. 3304. 187. 3439. 3027. 3133. 71 25 25 83 .07 88 73 31 .04 30 .08 .06 35 90 70 92 54 28 81 44 40 15 69 28 56 53 P(l) 61.42 2996.08 3191.91 3191.91 3313.68 2662.32 3367.96 2225.57 3494.49 3439.37 2662.32 3367.96 1666.77 1473.72 1787.71 3191.91 F‘P‘P‘ h‘k‘h‘h‘ P‘P‘F‘P‘ P‘P‘ P‘F‘P‘h‘ H .068 .124 .033 .347 .119 .121 .087 .075 .520 .100 .598 .117 .967 .799 .998 .108 .869 .729 .024 .117 .084 .089 .379 .128 .084 .052 F(2) .302 .021 .060 .060 .091 .966 .098 .882 .134 .109 .966 .098 .749 .708 .781 .060 17 18 19 20 21 22— 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 171 233 153. 498. 621. 62. 498. 631. 137. 136. 82. 613. 150. 102. 23. 621. 498. 621. 594. 12. 594. 179. 104. 172. 123. 498. 203. 59. 539. 82. 571. 613. 203. 490. 563. 490. 172. 415. 441. 491. 93. 550. 529. 30. 526. 518. 13. 523. 29. 442. 472. 45. 527. .487. 484. 107. 480. 792. 847. 436. 792. 411. 508. 744. 561. 499. 583. 639. 164. 847. 792. 847. 652. 770. 652. 888. 311. 665. 344. 792. 500. 705. 795. 561. 595. 499. 443. 394. 829. 394. 665. 607. 761. 769. 173. 779. 810. 268. 611. 660. 728. 435. 738. 713. 736. 217. 402. 751. 463. 268. U'IVVNUJVNUNLJVNUVNbNNNO‘NNNGNNpNPO‘VU‘O‘UO‘NWNNNVU’U‘LflVkU‘U‘INVJ-‘NVU'I .96 .33 .29 .37 .33 .92 .69 .54 .71 .85 .86 .04 .49 .29 .33 .29 .60 .25 .60 .01 .12 .11 .46 .33 .62 .22 .35 .71 .68 .85 .66 .84 .30 .84 .11 .53 .33 .36 .87 .38 .32 .68 .63 .55 .28 .89 .60 .41 .40 .98 .87 .39 .84 .16 2225 2996 2996 2058 1487 282 2751. .08 2996 2751. 3090. .09 3090. .04 .28 .64 .83 2996. .58 845. .21 1269. 3163. .00 .21 3439. .90 3439. 68 2266 1563 2352 1858 2726 2942 3241 2763 2832 2352 3066 3119 92. 3416. 370. 3132. 3056. 703. 3399. .25 3437. 1597. 3046 .57 .08 2751. 971. .08 3304. .25 1928. 1269. 3241. 2201. .94 .49 00 67 15 86 66 00 S4 00 00 10 10 08 24 66 56 37 37 .64 3243. 11 .80 3023. 1408. 2968. 2917. 442. 3191. .84 54 66 53 11 14 91 30 33 97 38 69 75 84 63 54 P‘H‘ F‘F‘ P‘F‘P‘ P‘h‘h‘ H P‘h‘ .882 .021 .996 .574 .021 .089 .834 .824 .645 .077 .869 .717 .407 .996 .021 .996 .042 .356 .042 .905 .729 .910 .794 .021 .991 .558 .013 .645 .058 .077 .997 .109 .003 .109 .910 .087 .040 .028 .694 .016 .012 .442 .060 .049 .360 .102 .434 .052 .039 .510 .100 .033 .106 .736 234 71 171 174. 313. 6.23 2460.17 .938 72 171 485. 872. 7.19 2878.69 1.005 73 171 172. 665. 6.11 2352.64 .910 74 171 75. 407. 4.62 1189.65 .622 75 171 498. 792. 7.33 2996.08 1.021 76 171 186. 461. 6.44 2640.77 .960 77 171 221. 655. 6.67 2768.19 1.000 78 171 487. 751. 7.39 3046.25 1.033 79 171 , 49. 517. 4.08 793.04 .520 80 171 67. 258. 4.43 1025.08 .598 81 171 192. 508. 6.48 2676.35 .967 82 171 125. 297. 5.48 1874.90 .799 83 171 150. 583. 5.86 2201.54 .869 84 171 104. 311. 5.12 1563.28 .729 85 171' 631. 411. 7.92 3304.15 1.089 86 171 17. 586. 3.39 187.69 .379 87 171 574. 617. 7.65 3133.53 1.052 THE SET OF OPTIMAL SOLUTION IN THE MIN-MAX SENSE: {313663.11 """" i3} """""""""""" A) OPTIMAL VALUES OF DECISION VARIABLES: U*(1)- 171 U*(2)- 100. 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