MODULE-1 WATER RESOURCES SYSTEMS 1.1 CONCEPT OF A SYSTEM: A large number of definitions of the term system are available. A system may be defined as a set of objects which interact in a regular, interdependent manner. Sinha (1991) defined a system as a collection of objects arranged in an ordered form, which is, in some sense, purpose or goal directed. According to Mays and Tung (1992), a system is characterised by: the system boundary which is a rule that determines whether an element is to be considered as part of the system or of the environment, 2) statement of input and output interactions with the environment, and 3) statements of interrelationships between the system elements, inputs and outputs, called feedback. In the context of water resources, Dooge (1973) defined a system "as any structure, device, scheme, or procedure, real or abstract, that inter-relates in a given time reference, an input, cause or stimulus, of matter, energy, or information, and an output, effect, or response, of information, energy or matter". Systems analysis, as applied to water resources, is a rational approach for arriving at the management decisions for a particular system, based on the systematic and efficient organisation and analysis of relevant information. The use of systems techniques requires digital computers and therefore, applications of systems analysis to water resources problems started only with the computer age in early 1960s. Votruba et al. (1988) defined systems approach as a comprehensive method of investigation of phenomena and processes, including their internal and external relationships. When scarce resources must be used effectively, systems analysis techniques stand particularly promising. There are many ways to classify systems. A physical system is the one that exists in the real world. A sequential system is a physical system which consists of input, output and some working medium (matter, energy, or information) known as throughput passing through the system. Sinha (1991) classified systems as: a) static and dynamic systems, b) linear and nonlinear systems, c) time-varying and time-invariant systems, d) deterministic and stochastic systems, e) continuous-time and discrete-time systems, and f) lumped parameter and distributed parameter systems. The output of a static system depends only on the current inputs while output of a dynamic system depends on the current and previous inputs. As explained by Mays (1997), the kernel of a time-invariant system does not change with time whereas it changes with time in a time-variant system. The kernel and inputs of a deterministic system are known exactly while these for a stochastic system are not known exactly. For a stochastic system, either the parameters in the kernel or the inputs are not known exactly and are described by statistical concepts. In a continuous time, system, the time varies continuously while the inputs, outputs, and parameter values in the kernel are known at discrete time only. Water resources systems are generally distributed with respect to time and space. For the purpose of solution, these systems may be divided into sub-systems and each sub- system may be treated as lumped. The hydrologic system is, therefore, a physical, sequential, dynamic system. For a catchment system, the input consists of water and energy in various forms. The input-output relationship of the system may be represented mathematically (Singh, 1988) by: y(t) = ϕ[x(t)] (1.1) where x(t) and y(t) are, respectively, time functions of input and output, and ϕ  is the transfer function which represents the operation performed by the system on the input to transform it
into an output. The well-known unit hydrograph is an example of a transfer function of the catchment system. The concept of state is basic to the systems theory. The state represents the conditions of the system or is an indicator of the activity in the system at a given time. In water resources systems, the state typically may be the volume of water in the reservoir, the depth of flow of the river, or the head of ground water at a location. If the behaviour of the system can be altered by modification of the working of the system, the steps taken are known as exerting control. The control applied to hydrologic systems may be either natural or artificial. For example, in a catchment system, the climatic trend and cycles are the nature-applied controls that may alter the characteristics of the catchment. The manmade dams and reservoirs on river basins represent artificial controls. Systems engineering is concerned with making decisions with respect to those aspects of a system on which some control can be applied. Water resources systems engineering can make most significant contribution to the process of decision making. Systems engineering was defined by Hall and Dracup (1970) as "the art and science of selecting from a large number of feasible alternatives, involving substantial engineering content, that particular set of actions which will accomplish the overall objectives of the decision makers, within the constraint of law, morality, economic resources, political and social pressures and laws governing the physical life and other natural sciences." Thus systems engineering is useful in making selections from a large number of alternatives by way of elimination. The necessity for elimination may be readily noted by a very simple example. Suppose there are twenty farming areas and water is to be allocated to each of them. Let there be 100 alternative ways one could allocate water to any one area, each being different (say, in terms of quantity) and theoretically requiring an "evaluation" to see which might be the "best". For twenty areas, there would be (100) 20 different combinations. Suppose neither judgment nor systems analysis is used to f'md the "best" of these different combinations of allocations to the twenty areas. Let a high speed computer is employed and is capable of completely evaluating one alternative in 0.001 seconds, compare the "worth" of that alternative to any other and keep the best of the two. After one "earth age" (estimated by geologists as 3 x 109 years) it would be able to check out 9.45 x 1019 of the possibilities, which is only an infinitesimal fraction of 10020. Obviously, even simple problems involving just a few different values of the decisions cannot possibly be evaluated directly. In the problem cited, one could have used a bit of logic based on the knowledge of the twenty farming areas and the effects of different levels of water supply and picked a pretty good solution on the basis of judgement alone. However, even for simple problems, after applying judgment, there may still be a lot more potentially valuable alternatives that cannot be evaluated directly with the available time and money. It is for these situations that the science of systems engineering is best suited. The theories and methods used in systems engineering are termed as systems analysis. Applied systems analysis is a general term including fields like operations research, decision-theory, benefit-cost analysis, planning and scheduling, design, theory of information, application of artificial intelligence in management, and decision-making. As noted by Votruba et al. (1988), in view of the importance of systems analysis, a famous institute, namely IIASA (International Institute for Applied Systems Analysis, Laxenburg, Austria, website: www.iiasa.ac.at), has been specifically set up for this purpose. The range of the fields and problems contained in applied systems analysis is apparent from the research program of this institute, which includes: • Resources and environment: ecological problems, problems of water resources research, problems of food and agriculture, etc.
• • • Human settlement and services: problems of population, health, education, communication, etc. Management and technology: man-made artifacts, institutes, economic systems, technologies, etc. Systems and decision sciences: mathematical and computational problems in the analysis of large systems, etc. 1.2 SYSTEMS ANALYSIS TECHNIQUES: The systems techniques can be grouped under four major categories as follows: • • • • Analytical optimization models and techniques: This group includes optimization methods - they may be based on classical calculus and Lagrangian multipliers or mathematical programming and control theory. These modelling techniques are descriptive, i.e., they usua1ly incorporate quantitative relationships between variables of the system. These are also prescriptive in the sense that the algorithm provides the optimal solution. The mathematical programming techniques include linear, non-linear, and dynamic programming, goal programming, and multi-objective optimization. Probabilistic Models and Techniques: This group of techniques includes the techniques for analyzing stochastic system elements with appropriate statistical parameters. It encompasses all the descriptive techniques of stochastic processes to study the behaviour of some aspects of the system. The important techniques in this group are the queuing and inventory theory which are concerned with the study of queues or waiting times and inventory stocks. Such studies are associated with decisions regarding service and storage capacities. Often queuing models are combined with other optimization methods and utilize either analytical techniques or simulation and search approaches. Many reservoir problems are some type of inventory problems and have been solved using approaches that combine various techniques. Statistical Techniques: This class of techniques includes multivariate analysis and statistical inference. The techniques of multivariate analysis, including regression and correlation, factor analysis, principal component analysis, and discriminant analysis, have numerous applications in the water resources area. Simulation and Search techniques: Simulation is a descriptive technique. A simulation model incorporates the quantifiable relationships among variables and describes the outcome of operating a system under a given set of inputs and operating conditions. Most simulation models do not contain algorithms for seeking optimal solutions. However, such models usually permit far less drastic simplification and approximation than is required when using an analytic optimization model. Often a simulation model is run many times with various input and parameter data. The output of these runs describes the response of the systems to variations in inputs and parameters. If the simulation model includes an objective function, the values of the objective for several runs generate a response surface. The model then can be combined with sampling or search techniques that explore the response surface and seek near-optimal solutions. Systems analysis techniques do not merely deal with the engineering aspects of water resources development but also cover a multi-disciplinary approach encompassing physical, social, economic, political, biological, and other characteristics of specific problems and situations. This powerful technique enables the planners, designers and water managers to evaluate alternative development scenarios and to place before the decision makers, the effects and advantages of various alternative feasible options. Mathematical analysis of water resources problems using systems approach is one of the most important developments in the water sector.
1.3 ISSUES IN SYSTEMS APPROACH: Despite significant theoretical developments and availability of infrastructure facilities, the systems techniques are not routinely applied to planning and design of water resources projects. Rogers and Fiering (1986) carried out an extensive study in which they examined more than 2500 research papers of selected reputed journals dealing with water resources. It was reported that only 38 of 723 systems oriented paper dealt with identifiable water resources projects, only three of the 38 projects studied were built and only one of these was designed according to the optimization model presented in the paper. Although considerable time has elapsed since this study, the situation may be only marginally different now. This analysis also points towards a wide gap between theory and practice in planning and design. The situation in respect of applications for management is somewhat better. Then there are differences between developed and developing countries -- there is a resistance to the use of systems analysis by many government agencies in developing countries. The resistance is not always based on blind prejudices, it may be based on some genuine and reasonable doubts. According to Rogers (1980), the following five questions need to be satisfactorily answered to convince those who are opposed to systems analysis. Appropriateness: Most of the applications of systems techniques have been made in developed countries. Decision-makers in developing countries are quite rightly suspicious of the direct transference of such methods into situations in which the distribution of resources, structure of society, and the governing institutions are so different. This question is best answered by successful case studies of developing country applications. Reliability of database: In most developing countries, the data on economic, social and natural resources are usually very poor in the conventional sense of time series, spatial coverage and accuracy. Most systems analysis applications are very data intensive and very sensitive to the quality of data. In such situations, responsible administrators have every reason to be suspicious of the use of systems analysis. This question is best answered by showing how systems analysis can improve decision making even using the shakiest data and how it can also be used to evaluate the existing data and structure additional data acquisition. It can be argued that with a less reliable database the benefits from using systems analysis will be much greater than conventional analysis. Model credibility: Obviously if no models have been attempted, how can one assess their credibility. Again, the answer is to rely upon case studies of other applications which are deemed credible by their sponsors. Note that there are many levels of application and many different user groups for systems analysis models. Some may find them credible while others may or may not. Manpower and equipment requirements: In most developing countries, there is a shortage of skilled manpower and this is an important hindrance to the use of systems analysis in these countries. A long-term solution is to develop indigenous expertise by introducing relevant courses in academic institutions or through foreign gaining. The analysis could be tailored to the available resources and reliable personnel hired whenever the need arises. Time and money aspects: The systems analysis studies cost more than the conventional techniques and require more time. But it should be borne in mind that the magnitude of benefits from water resources projects is very large. An improvement by a few percentages will translate into big amounts in real terms and costs will be much smaller than the benefits accruing due to improved planning and management.