Analytical versus numerical estimates of water-level declines caused by pumping, and a case study of the Iao Aquifer, Maui, Hawaii

Comparisons were made between model-calculated water levels from a one-dimensional analytical model referred to as RAM (Robust Analytical Model) and those from numerical ground-water flow models using a sharp-interface model code. RAM incorporates the horizontal-flow assumption and the Ghyben-Herzberg relation to represent flow in a one-dimensional unconfined aquifer that contains a body of freshwater floating on denser saltwater. RAM does not account for the presence of a low-permeability coastal confining unit (caprock), which impedes the discharge of fresh ground water from the aquifer to the ocean, nor for the spatial distribution of ground-water withdrawals from wells, which is significant because water-level declines are greatest in the vicinity of withdrawal wells. Numerical ground-water flow models can readily account for discharge through a coastal confining unit and for the spatial distribution of ground-water withdrawals from wells.

For a given aquifer hydraulic-conductivity value, recharge rate, and withdrawal rate, model-calculated steady-state water-level declines from RAM can be significantly less than those from numerical ground-water flow models. The differences between model-calculated water-level declines from RAM and those from numerical models are partly dependent on the hydraulic properties of the aquifer system and the spatial distribution of ground-water withdrawals from wells. RAM invariably predicts the greatest water-level declines at the inland extent of the aquifer where the freshwater body is thickest and the potential for saltwater intrusion is lowest. For cases in which a low-permeability confining unit overlies the aquifer near the coast, however, water-level declines calculated from numerical models may exceed those from RAM even at the inland extent of the aquifer.

Since 1990, RAM has been used by the State of Hawaii Commission on Water Resource Management for establishing sustainable-yield values for the State?s aquifers. Data from the Iao aquifer, which lies on the northeastern flank of the West Maui Volcano and which is confined near the coast by caprock, are now available to evaluate the predictive capability of RAM for this system. In 1995 and 1996, withdrawal from the Iao aquifer reached the 20 million gallon per day sustainable-yield value derived using RAM. However, even before 1996, water levels in the aquifer had declined significantly below those predicted by RAM, and continued to decline in 1997. To halt the decline of water levels and to preclude the intrusion of salt-water into the four major well fields in the aquifer, it was necessary to reduce withdrawal from the aquifer system below the sustainable-yield value derived using RAM.

In the Iao aquifer, the decline of measured water levels below those predicted by RAM is consistent with the results of the numerical model analysis. Relative to model-calculated water-level declines from numerical ground-water flow models, (1) RAM underestimates water-level declines in areas where a low-permeability confining unit exists, and (2) RAM underestimates water-level declines in the vicinity of withdrawal wells.