DYNAMIC PROGRAMMING FOR OPTIMAL CAPACITY EXPANSION OF WASTEWATER TREATMENT PLANTS1

ABSTRACT: A dynamic programming procedure for the planning and operation of a wastewater treatment plant over a long period of time is presented. In order to meet increased demands for wastewater treatment in the future, the expansion of existing plants must be considered. Dynamic programming is employed to determine the optimal schedule of expansion at each plant, simultaneously determining an optimal operating policy (treatment level). The optimal schedule of expansion at each plant depends on the following: (1) the shape of the projected wastewater demand function; (2) the interest rate used; (3) the locations and capacities of the facilities available; and (4) the rates of increase of the costs of construction, labor, chemicals, and electric power. An example illustrating the use of the procedure is presented.     

RISK OF EXTREME EVENTS IN A MULTIOBJECTIVE FRAMEWORK1

ABSTRACT: This paper summarizes advances made in risk-based decisionmaking in water resources through use of the partitioned multiobjective risk method (PMRM). (Risk is a measure of the probability and severity of adverse effects.) In the PMRM, the risk of extreme events is differentiated from risk involving less extreme damage severity and is evaluated within a multiobjective framework. Study of the extreme-event risk function f₄(*) has addressed the following issues: methods for calculating f₄(*); the sensitivity of f₄(*) to various parameters, particularly to the partitioning point of the extreme-event range and the selection of probability density functions; insight provided by the statistics of extremes; and the impact of f₄(*) on risk management, for example, in the application of the PMRM to water resources problems. In particular, this paper shares with the reader recent research results on the PMRM, the relationship between the statistics of extremes and the conditional expected value, derived formulas for f₄(*), distribution-free estimates of f₄(*), documented case studies in dam safety, and future research directions.     

Announcing climate policy: Can a green paradox arise without scarcity?

Unintended consequences of a pre-announced climate policy are studied within a framework that allows for competition between polluting and clean energy sources. We show that early announcement of a carbon tax gives rise to a “green-paradox,” in that it increases emissions in the interim period (between announcement and actual implementation), irrespective of the scarcity of fossil fuels. The paradoxical outcome is driven by consumption-saving tradeoffs facing households who seek to smooth consumption over time and holds both when the announced implementation date is taken as a credible threat and when households are skeptical about the (political) will or capability of the government to implement the policy as announced.     

Scarcity, growth and R&D

The limits to economic growth due to resource scarcity can be alleviated only by the development of backstop substitutes. This paper combines resource-based economic growth with R&D to reduce the cost of backstop technologies. Characterizing the entire dynamics of optimal growth and R&D processes, we find that an economy's growth prospects depend on its type, as determined by its production technology and learning ability, and by its knowledge–capital endowment. A wide variety of growth patterns emerges, ranging from cases in which an economy that without R&D eventually stagnates (converges to a steady state) is diverted by R&D onto a path of sustained growth, to cases in which R&D is not warranted. Resource scarcity is shown to encourage R&D due to the increased reliance on the backstop technology.     

Cost-sharing approach for air quality control implementation A case study

The objective of the study was to investigate and develop new alternative approaches to effectively meeting the federal SOx and particulate ambient air quality standards at cost savings. Since air pollution control costs would very likely be passed along to the consumer, it is in the best interests of the consumer and industry to find the least-cost alternative policies. Cost-sharing possesses advantages not shared by other control schemes, such as emissions taxes, auctioning of “pollution certificates,” or other methods. The results of this paper indicate that the cost-sharing approach is useful for particulates control in order to minimize the burden of plants already performing substantial control who may require significant added capital investment beyond their initial amount. For SO_ξ emissions control the cost-sharing analysis calculations show significant savings in nearly all situations, whether or not stack gas treatment methods were assumed available. Furthermore, the cost-sharing approach may allow further savings when the particular cost requirements of an individual firm differ substantially from the average engineering cost estimates. A cost-sharing option should thus be included in implementation plans as an option to be used by industries at their own initiative. The spatial characteristics of emissions resulting from a particular application of the cost-sharing approach are considered. A spatial airshed emissions allocation model is discussed as a useful method of evaluating cost sharing.     

Time perspective and climate change policy

The tendency to foreshorten time units as we peer further into the future provides an explanation for hyperbolic discounting at an inter-generational time scale. We study implications of hyperbolic discounting for climate change policy, when the probability of a climate-induced catastrophe depends on the stock of greenhouse gasses. We characterize the set of Markov perfect equilibria (MPE) of the inter-generational game amongst a succession of policymakers. Each policymaker reflects her generation's preferences, including its hyperbolic discounting. For a binary action game, we compare the MPE set to a “restricted commitment” benchmark. We compare the associated “constant-equivalent discount rates” and the willingness to pay to control climate change with assumptions and recommendations in the Stern Review on Climate Change.“…My picture of the world is drawn in perspective…. I apply my perspective not merely to space but also to time”—Ramsey.     

MODELING AND CONTROL OF THE POLLUTION OF WATER RESOURCES SYSTEMS VIA MULTILEVEL APPROACH1

ABSTRACT. The problem of modeling and control of water pollution is considered. A general mathematical model, where the pollution effluent is discharged directly into the river, into the lake, or into a bypass pipe leading to an advanced Waste Water Treatment (AWT) plant, is developed. The Water Resource System (WRS) under consideration is decomposed into N subsystems. The pollution effluent input vector to each subsystem includes the water quantity and different water characteristics such as BOD, DO, pH, conductivity, temperature, algae, phosphates, nitrates, etc. Treatment cost functions and quality transition functions as well as system model constraints are introduced, where all functions can be nonlinear. A system Lagrangian is formed to incorporate the system constraints and coupling. The Lagrangian is decomposed into N independent subsystems, and a two level optimization methodology is introduced. Each subsystem is independently and separately minimized at the first level assuming known Lagrange multipliers. At the second level, the total Lagrangian is maximized with respect to the Lagrange multipliers using optimal values for effluent inputs from all subsystems obtained from the first level. Economic interpretation on the Lagrange multipliers reveals that they are merely prices imposed by the central authority (second level) for the pollution caused by the subsystems. Advantages of the multilevel approach are discussed.     

The buffer value of groundwater with stochastic surface water supplies

When utilized with a stochastic source of surface water for irrigation, groundwater may serve to mitigate fluctuations in the supply of water. The benefit corresponding to this service is the buffer value of groundwater. We show that the buffer value is positive. Numerical studies reveal that its magnitude can be significant. The paper also offers a characterization of groundwater extraction in such a setting.     

Pathological alterations typical of human Tay-Sachs disease, in the retina of a deep-sea fish

 Micrographs of retinas from the deep-sea fish Cataetyx laticeps revealed visual cells containing membranous whorls in the ellipsoids of the inner segments resulting from stretching and modifications of the mitochondria membranes and their cristae. These pathological structures seem to be homologous to the whorls observed in retinas of human carriers of Tay-Sachs disease. This disease, a genetic disorder, is found in humans and some mammals. Our findings in fish suggest that the gene responsible can be found throughout the vertebrate evolutionary tree, possibly dormant in most taxa. Received: 20 April 2000 / Accepted in revised form: 16 June 2000