Long-term management and discounting of groundwater resources with a case study of Kukio̕ Hawaii̕

Abstract

Long-term management strategies for groundwater resources are examined with theoretical examples and with a case study of Kuki'o, Hawai'i. In Part I a groundwater mining and a dryland salinization optimal management problem are solved analytically, and used to examine the implications of how one values the future through discounting. Exponential and hyperbolic discounting functions are tested with the full range of discount rates and time-scales for the hydrologic system. While the optimal management strategies change depending on the form of the discounting function, they are relatively insensitive to the discount rate itself. For all solutions an initial Dirac delta of pumping brings the system from initial conditions to the optimal trajectory. Following this initial spike of pumping, the exponential pumping solutions are constant over all time. The hyperbolic pumping solutions are more complex, time-dependent functions and they asymptotically approach the no-discounting solution at late times. In Part II a hydrologic-economic model is constructed for a dual coastal and high-level aquifer system at Kuki'o, Hawai'i. The high-level aquifer is modeled as a leaky bucket, while the coastal aquifer is modeled using a sharp-interface formulation of the basal lens. Salinization of pumping wells due to saltwater upconing is superimposed upon the sharp-interface model using an empirical equation based on data from the area.

(cont.) Energy costs, coastal and high-level capital costs, and various forms of the demand curve are incorporated. It is found that it is always optimal to first use the coastal aquifer then turn to the high-level aquifer when the coastal wells become too saline. The optimal trajectories are most sensitive to the form of the demand curve and to leakage from the high-level to coastal aquifer. It is determined that the long-term sustainable yield of the region is roughly 12x103 m3/yr, which is 3 times what the near-future demand is anticipated to be. However, this economically optimal strategy completely mines the high-level aquifer, salinizes the coastal aquifer to 1/3 of seawater and lowers groundwater flux to the ocean by 75%.