Conjunctive multibasin management: An optimal control approach

Abstract

The economic effects of conjunctive management of ground and surface water supplies for irrigation are formulated as an optimal control model. An empirical hydroeconomic model is estimated for the Yolo County district in California. Two alternative solution methodologies (analytic Riccatti and mathematical programing) are applied and compared. Results show the economic potential for interbasin transfers and the impact of increased electricity prices on optimal groundwater management.The conjunctive use of groundwater and surface water is being strongly advocated in the western states due to increasing water demands by agricultural, urban, and industrial users. Given the public nature of groundwater supplies, empirical decision rules for regional managers of interdependent basins are a necessary prerequisite to conjunctive use. Empirical analysis of optimal conjunctive management has been performed using a dynamic programing approach by' Burns [ 1963], Butt [ 1974], Cummings and Winkleman [ 1970], and Biere and Lee [972]. Unfortunately, use of dynamic programing restricts the specification of the ground and surface water systems to low-dimension representations of the system. Invariably this aggregation is unsatisfactory for multibasin regional analyses. In addition to overcoming the dimensionality problem inherent in dynamic programing [Murray and Yakowitz, 1979], the optimal control apprceach presented in this paper yields additional insights on economic management by using the resulting optimal user costs of groundwater stocks.The approach demonstrated in this article combines the linearized output of hydrologic and economic models in a discrete time, linear, quadratic control problem. Given/this approximate specification, analytical solutions are available for the resulting control problem. The analytical control solutions are compared with numerical solutions which allow a less restrictive model specification. The advantages and disadvantages of these alternative approaches are compared. The methodological problem is motivated by an empirical analysis of a Northern California region comprised of six hydrologic subbasins, two reservoirs, and a river system.In the first section the theoretical basis for optimal water allocation is derived using an optimal control approach, and economic interpretations are derived from the resulting necessary conditions. In the following section the empirical regional multibasin model is described, and the hydrologic and economic submodels that generate the control model parameters are briefly reviewed. The empirical results address a number of policy questions: What is the value of Copyright 1982 by the American Geophysical Union. Paper number 2W0830. 0043-1397/82/002 W-083055.00 groundwater stocks, and how would this stimulate interbasin transfer? How would ground and surface water be optimally allocated over a 30-year horizon, and what is the impact of increased energy costs on the optimal allocation? A THEORETICAL BASIS FOR MULTIBASIN ALLOCATION Water allocation can be consi...

Groundwater use under incomplete information

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“…For example, for preferences that are characterized by constant relative risk aversion (CRRA), i.e., (19) may hold with either sign and so f may be either convex or concave. 10 In the CRRA case, absolute risk aversion is decreasing and convex in wealth,…”

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Integrative assessment of hydrological, ecological, and economic systems for water resources management at river basin scale

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