Estimation of the Thickness of a Freshwater Lens Using an Exact Random Field Generator

An exact random field generator, which exploits the efficiency and speed of the fast Fourier transform, is illustrated using a case study. It can cope with n >= 50,000 grid points in many cases, even on a relatively modest computer. The random field generator is used to produce spatial realizations of the permeability of a Pacific atoll island. These realizations are used in a sharp interface model to estimate the thickness of a freshwater lens. Several sets of realizations are used in Monte Carlo simulation to determine prediction limits for the thickness of the lens for a given freshwater extraction rate. Prediction limits for a model response can be used to assess the risks associated with various management strategies.