Groundwater management under quadratic criterion functions

Temporal allocation of groundwater is analyzed for quadratic measures of economic net output from a basin. The two variables of the net output function are rate of use and quantity of stocks. It is shown that an optimal policy for groundwater utilization over time is dependent upon the mean recharge rate but not on higher moments of its probability distribution for the case of quadratic criterion functions, provided that inequality constraints on rate of use are unnecessary. The optimal policy is derived, and some analysis of the probability distribution of groundwater stocks is made. Some consideration is given to approximately optimal policies for the situation arising when inequality constraints on rate of use are binding.