The second half of the twentieth century can clearly be identified as an epoch having a strong, lasting imprint on our paradigms and methods of resource use and management. Ideas, compassions, and concepts which dominate our thinking and debates have emerged and evolved during the last four or five decennia. Nothing manifests this better than the so-called Brundtland Report (WCED, 1987). Ever since its publication, the term and concept of sustainable development cannot be missed in any declaration or framework issued or developed in seeking better conditions for humans and the environment alike. The recent millennium was a welcome opportunity to summarize this process and endorse principles and set new objectives. As far as the ethical, political, and practical aspects of water resources management are concerned, the large intergovernmental environmental conferences like the United Nations Conference on Environment and Development (UN, 1992) and the World Summit on Sustainable Development (WSSD, 2002) can be mentioned along with the formulation of UN Millennium Development Goals (MDGs, 2000) and the Millennium Ecosystem Assessment (2005). Beyond these general conferences and assessments, where water took a substantial part of the agenda, the world water fora (Marrakech, 1997; The Hague, 2000; Kyoto, 2003; Mexico City, 2006) and the Bonn Conference on Freshwater 2001 provided the broadest platforms for stakeholder dialogue involving ministerial, NGO, scientific, professional, and other interest groups, and indigenous people participation. The impacts of these conferences were analyzed by, among others, Bogardi and Szöllösi-Nagy (2004).

Reservoir systems are operated in somewhat uncertain environments. The uncertainty is mainly due to forecasting of expected rainfall caused by events such as typhoons and resulting river inflows. The problem of optimizing real-time short-time on-line operation of complex reservoir systems under uncertainty is very difficult particularly during extreme events like floods or droughts. Practically no general solution is available for this type of problem. Thus, it is important to fully appreciate the problem of real-time reservoir operation under uncertainty before expedient methods for its solution can be developed. This section describes how far DP based operation can be used in the phase of short-term “emergency” operation or how far this type of short-term operation can be embedded in DP or SDP based rules.

Several operational modes can be employed for a water resources system. For example, in real-time on-line operation of a multipurpose reservoir, the importance of a purpose or particular demand may vary either periodically with the annual cycle or randomly due to the occurrence of floods. Real-time on-line operation may be defined as an interaction between the operator and the system while the operation is being executed, and the response time is critical within a definite time step. Consequently, real-time on-line operation may imply operational mode changes to respond to this critical situation. One of the most challenging decisions inherent in the operation of a reservoir is to decide when to change release policy and allocate storage space, for example for the purpose of flood control instead of for conservation storage, and vice versa.

When a flowing river is dammed and becomes an impoundment, two major changes occur. First, creating an impoundment greatly increases the time required for water to travel the distance from the headwaters to the discharge at the dam. Second, thermal or density and therefore chemical stratification may take place. Both have a marked effect on water quality. Both the increased detention time and thermal stratification in an impoundment change the characteristics of the water discharged at a given geographical location from what they were when the stream was free flowing. Some effects of impoundments improve water quality; others deteriorate it. This also implies the possibility of using the reservoirs for control of the quality of water besides merely satisfying the quantity requirement.

The increased emphasis on water quality accents the need for formulation of methodologies for operating reservoirs for control of water quality. Considering reservoir dynamics while applying optimization techniques for operational decisions enables policies for a reservoir accounting for the quality of water supplied besides satisfying quantity requirements. The assumption of complete instantaneous mixing of water in a reservoir throughout its entire volume is an over-simplification compared to the real behavior of reservoirs that undergo mixing and stratification cycles. This chapter presents models that assume complete mixing in reservoirs while deriving optimum operation policies when quality aspects are of interest.

There have been relatively few studies of optimum reservoir operation in which water quality has been considered.

GENERAL

The water resource has a major influence on human activities. It is a major input in almost all sectors of human endeavor. Water serves essential biological functions and no human can survive in its complete absence. Water's contributions to human welfare include its role as a basic element of social and economic infrastructure. Also important are water's natural attributes that contribute to human aesthetic enjoyment and general psychological welfare. But water also has negative impacts on human well-being. Floods, inundations, and water-borne diseases are also associated with water.

Water has played a major role in socio-economic development due to the magnitude and widespread occurrence of its positive and negative impacts. The quality of human life is directly dependent on how well these resources are managed. Water management activities are intended to enhance the positive contributions of water or control its negative impacts.

Ancient civilizations grew up in the river valleys of the Tigris and Euphrates, Nile, Indus, Yellow River, etc., where there was plenty of water. Water management activities, particularly irrigation, played a central role in the development of these civilizations. In those days the planning and management of the water resources were primarily for single uses. The continuing growth of the human population, especially since the nineteenth century, together with rapid industrial development and rising expectations of a better life necessitated more complex and consistent water resources management. These competing demands and uncontrolled use, along with the pollution of water, have made it a scarce resource.

Very often reservoirs are built and operated to satisfy water quantity requirements such as irrigation or drinking water consumption, hydropower production, etc. Operation of these reservoirs is vital to maximize benefits and DP in various forms can be applied for this purpose. This chapter illustrates the applicability of several different forms of incremental dynamic programming (IDP) in the derivation of optimal operation patterns for different reservoir systems.

IDP IN OPTIMAL RESERVOIR OPERATION: SINGLE RESERVOIR

Dynamic programming can be applied to derive optimal operation policies for a single reservoir. Use of conventional DP in this task is one possibility. This section shows the application of IDP for two reservoir systems: (a) the Kariba Reservoir in Zambia and Zimbabwe, and (b) the Ubol Ratana Reservoir in Thailand, based on the analysis of Budhakooncharoen (1986, 1990). The IDP technique, which considers only a limited state space at a time, has lower computer storage requirements.

Application of IDP to the Kariba Reservoir

The Kariba Reservoir is a single-unit water resource system that utilizes the water resource of the Zambezi River to produce hydroelectric energy. The Zambezi River rises in northern Zambia. After flowing through Angola, it forms the boundary between Zambia and Zimbabwe. Finally, it passes through Mozambique to discharge into the Indian Ocean north of Beira. Figure 2.1 shows the Zambezi River basin. The catchment area of the basin up to the Kariba Dam is about 665 600 km2. The Kariba Reservoir is shared and operated by CAPCO (Central African Power Corporation).

USE OF DYNAMIC PROGRAMMING IN MULTIPLE-RESERVOIR OPERATION

In general, straightforward optimization of multiple-reservoir system operation with DP and SDP does not achieve the accuracy level relevant for real-world applications. The analysis of multiple-reservoir system operation imposes significant dimensionality problems due to the inevitable introduction of three inherent computational difficulties:

1. (a) Increase in dimensionality of the problem is reflected in the number of state and decision variables necessary to describe a multiple-reservoir system and its operation.

2. (b) Operation of complex reservoir systems involves multiple, and often noncommensurate objectives. Often these cannot be approximated by a single, clearly defined surrogate objective or criterion.

3. (c) Additional difficulties arise when it is necessary to consider stochasticity, which is an inherent feature in the operation of reservoir systems. Although it is common to reduce this aspect to river flow uncertainty only, the problem does not seem to be significantly alleviated because multiple reservoirs imply consideration of multiple, independent or cross-correlated, stochastic inflow processes.

Although regarded as a very promising stochastic optimization technique, SDP is still hampered by well-known dimensionality restrictions and the resulting huge computational requirements imposed when applied to multiple-state–multiple-decision problems. In general, and this was also reported by Yeh (1985), systems analysts have opted for one of the following three remedies, or combinations thereof, to overcome these difficulties:

1. (a) Decomposition of the system into smaller and simpler subsystems thus reducing the complex problem to a set of tractable tasks (e.g., decomposition based on physical or functional structure of the system, multilevel hierarchical decomposition, etc.) (Bogardi and Milutin, 1995; Bogardi et al., 1995; Ampitiya et al., 1996).

2. […]

The principles of air–water mass transfer are often difficult to apply in field measurements and thus also in field predictions. The reasons are that the environment is generally large, and the boundary conditions are not well established. In addition, field measurements cannot be controlled as well as laboratory measurements, are much more expensive, and often are not repeatable.

Table 9.1 lists some of the theoretical relationships from Chapter 8, for example, and the difficulties in applying these relationships to field situations. Eventually, application to the field comes down to a creative use of laboratory and field measurements, with a good understanding of the results that theory has given us and to make sure that we do not violate some of the basic principles of the theoretical relationships.

The value of β has not been attempted in the field to date. So, how do we determine KL for field applications? The determination of dynamic roughness, z0, has also been difficult for water surfaces. The primary method to measure KL and KG is to disturb the equilibrium of a chemical and measure the concentration as it returns toward either equilibrium or a steady state. Variations on this theme will be the topic of this chapter.

Gas Transfer in Rivers

Measurement of Gas Transfer Coefficient

Rivers are generally considered as a plug flow reactor with dispersion. Determination of the dispersion coefficient for rivers was covered in Chapter 6, and determination of the gas transfer coefficient is a slight addition to that process.