Inter-temporal and spatial choice between ground and surface water in municipalities with land subsidence
Hultberg, Sylvestre Gaudin
Doctor of Philosophy
The impact of land subsidence on optimal inter-temporal use of groundwater is analyzed for a growing city where surface water is a feasible alternative and the goal is to maximize net social benefits. The problem is dynamic, since pumping and subsidence externalities increase costs in all future periods when groundwater is mined. It is also spatial because surface water costs increase with distance. The distance to which surface water is delivered is shown to depend on population densities, city size, and the proportion of surface water to groundwater use. The model is solved using dynamic programming and numerical techniques. Parameter values are chosen to simulate the case of Houston. The demand side is specified using consumer surplus from a Stone-Geary demand function, estimated with panel data. The simulation results confirm the analytical predictions that at first only groundwater is used and as demand grows, water levels go down and subsidence occurs. When the social marginal cost of groundwater reaches the marginal cost of surface water, it becomes optimal to use surface water. Because of increasing returns to scale in water treatment, surface water is used in large quantities right away. A period follows during which water levels increase and subsidence stops. Water levels start decreasing again when decreasing returns to dispersion dominate. Unless a water treatment plant is built in a different location, the use of groundwater keeps increasing and subsidence eventually resumes. The simulations indicate that if surface and groundwater have been used optimally in Houston, the discount rate must be low or subsidence costs are assumed very high. The recent reversal in water level declines is explained by increasing returns in treatment but because of increasing dispersion water levels should be allowed to drop again, as long as new treatment plants are built in different locations before subsidence resumes.