Aquifer Depletion in the face of Climate Change and Technical Progress.

A dynamic optimization framework is applied to the problem where groundwater stock and the state of technology and the climate are the state variables and groundwater pumping is the control variable and the objective is to maximize the net present value of the stream of rents from irrigation over the life of the aquifer. Dynamical systems govern the evolution of the aquifer, the climate, and the rate of technical progress. These dynamical systems may be dependent upon periodic groundwater allocations, as in the case of the aquifer, or independent of the periodic allocations as in the case of climate and technical change. Alternative plans are considered where the planner ignores one or more of the state variables when prescribing an extraction path. The ``information effect'' in these plans is assessed by comparing extraction, depletion, and rents from irrigation paths. A well accepted formulation of hydrologic dynamics for the aquifer is employed and simple dynamic trends for climate and technology are developed. A simplified example of the model incorporating only deterministic aquifer and technical change dynamics is presented as a linear-quadratic optimal control problem. Numerical results from Sheridan County, KS, suggest that prescribing a pumping schedule ignoring the dynamics of climate change is most costly. Furthermore, once on the optimal path, relatively large savings in groundwater may be achieved with relatively small portions of profits foregone