Assessing marginal water values in multipurpose multireservoir systems via stochastic programming

The International Conference on Water and the Environment held in Dublin in 1992 emphasized the need to consider water as an economic good. Since water markets are usually absent or ineffective, the value of water cannot be directly derived from market activities but must rather be assessed through shadow prices. Economists have developed various valuation techniques to determine the economic value of water, especially to handle allocation issues involving environmental water uses. Most of the nonmarket valuation studies reported in the literature focus on long-run policy problems, such as permanent (re) allocations of water, and assume that the water availability is given. When dealing with short-run allocation problems, water managers are facing complex spatial and temporal trade-offs and must therefore be able to track site and time changes in water values across different hydrologic conditions, especially in arid and semiarid areas where the availability of water is a limiting and stochastic factor. This paper presents a stochastic programming approach for assessing the statistical distribution of marginal water values in multipurpose multireservoir systems where hydropower generation and irrigation crop production are the main economic activities depending on water. In the absence of a water market, the Lagrange multipliers correspond to shadow prices, and the marginal water values are the Lagrange multipliers associated with the mass balance equations of the reservoirs. The methodology is illustrated with a cascade of hydroelectric-irrigation reservoirs in the Euphrates river basin in Turkey and Syria.