Zhao, Z.; Zhao, J.; Xin, P.; Jin, G.; Hua, G., and Li, L., 2016. A hybrid sampling method for the fuzzy stochastic uncertainty analysis of seawater intrusion simulations.

The traditional fuzzy stochastic hybrid method requires hundreds or even thousands of simulations to obtain a statistically stable result, which is a significant challenge for some nonlinear problems, such as simulating seawater intrusion. A hybrid sampling (HS) method was developed based on the Monte Carlo (MC) uncertainty analysis whose input parameters are characterized by both stochastic variables and fuzzy numbers. The HS method is a restricted sampling method that fully captures statistical information on the stochastic variables and the fuzzy memberships provided by fuzzy numbers. In HS, samples of stochastic variables and fuzzy numbers are generated using Latin hypercube sampling and restricted stratified sampling, respectively. After they have been generated, samples of different variables are paired to form inputs in a restricted manner for the simulations. This ensures that the samples are distributed across each variable's range of uncertainty. The correlations between different variables are also controlled during the restricted sampling process. The simulations of seawater intrusions show that the means and variances of the samples generated using the HS method converge more quickly compared with those generated using a random sampling method. The number of MC simulations required was significantly reduced by using the HS method, which improves the effectiveness of predicting seawater intrusion for the management of coastal aquifers.