Optimal Regional Conjunctive Water Management

Abstract

An optimal control model is used to determine the socially optimal spatial and temporal allocation of groundwater and surface water among agricultural and urban uses. The control model is described briefly and its advantages over other dynamic models are enumerated. Optimal rates of groundwater pumpage over the planning horizon were highly sensitive to increasing energy costs. Groundwater basins are shown to react differently to alternative economic and hydrological parameters. In a dynamic setting, a policy of pump taxes was shown empirically to be superior to pro-rata quotas and uncontrolled pumpage.Key words: control model, groundwater, energy cost, pro-rata allocation, Pigovian taxation.The severe drought in the western United States in 1976-78 brought the problems of allocating extremely limited water resources to the attention of agriculturalists and urbanites alike. Greatly reduced surface water supplies exacerbated the already critical pressure on remaining groundwater stocks in the same areas.The chronic overdraft of many western states groundwater basins can be attributed directly to their common pool nature. The lack of explicit property rights to groundwater stocks results in individual users of the resource evaluating only their own private pumping costs in their decision framework and implicitly assigning a zero opportunity cost to the stock portion of the resource. Thus, the private decision does not take into account any user cost and results in a divergence in the private and the social optimal rate of pumping. 1 The objective of this paper is to describe briefly an optimal control model which can be used to determine the socially optimal spatial and temporal allocation of groundwater and surface water among agricultural and urban uses. The control model is then applied to a representative region of California under several sets of energy costs. Two policies, prorata allocation and taxation, are evaluated empirically as alternatives for accounting for externalities due to the common pool problem. The Conceptual FrameworkSeveral authors have investigated the conjunctive use of groundwater and surface water using various techniques. Buras developed a dynamic programming algorithm to solve the problem of conjunctive use of reservoirs and aquifers. His operating policy, however, considered the physical system as a single unit and thus ignored differences in hydrology that occur in a complex groundwater system. Burt (1964, 1966, 1967a, b) utilized a mathematical programming approach to develop a demand function for irrigation water used in a dynamic programming formulation of the aquifer management problem. Bredehoeft and Young used a simulation model to estimate the solution of problems involving the development of a stream-aquifer system in an economic model of irrigation. Bear and Levin studied optimal utilization of an aquifer as one element of a Jay E. Noel is a resource economist with Auslam and Associates,

Pareto‐Improving Water Management over Space and Time: The Honolulu Case

“…3). This falls between the low estimates obtained in several studies (e.g., 0.01% in Gisser and Sanchez 1980;Gisser 1983;Allen and Gisser 1984;0.28% in Nieswiadomy 1985;0.3% in Dixon, 1989; 2.6% in Knapp and Olson 1995; 2.2% in Burness and Brill 2001;and 4% in Provencher and Burt 1994), and high estimates in others (e.g., 10% in Noel, Gardner, Moore 1980;14% in Feinerman and Knapp 1983;17% in Brill and Burness 1994). While a detailed analysis of the reasons for the size of the gains is beyond the scope of this article, it is worth noting that the recharge to storativity ratio and the demand slope to storativity ratio in Honolulu are small compared with those in Gisser and Sanchez (1980).…”

“…There are other excellent models in the literature with spatial and temporal components (e.g., Provencher 1993;Provencher and Burt 1994;Zeitouni and Dinar 1997;Reinelt 2005;Taghavi, Howitt, and Marino 1994;Dinar and Xepapadeas 1998;Noel, Gardner, and Moore 1980;Noel and Howitt 1982). However, they usually either add transport costs in the numerical simulations, after the analytical model has already been articulated, or their optimization objectives are different from ours, e.g., some minimize cost rather than maximize welfare; some use an exogenous water price; and some do not attempt to provide analytical results such as our equation (10).…”

Current Issues in the Economics of Groundwater Resource Management

“…Noel et al (1980) found that control increases the value of groundwater in the Yolo basin in California by 10%. Lee et al (1981) found that control raised the net benefit of groundwater in the Ogallala basin by only 0.3%.…”

The Tradeoffs between Market Returns from Agricultural Crops and Non-Market Ecosystem Service Benefits on an Irrigated Agricultural Landscape in the Presence of Groundwater Overdraft

“…This dual use of groundwater and surface water is known as conjunctive water management. Both the economic and institutional aspects of conjunctive water management are well studied [1][2][3], but the influence of irrigation management on the non-market benefits of multiple ecosystem services (in particular, groundwater supply, surface water purification, and greenhouse gas (GHG) reduction) has received less attention. The choice to use conjunctive water management changes the aquifer volume, which in turn affects the crops grown, and the crop production decisions influence nutrient and sediment runoff and GHG emissions.…”