First‐order reliability approach to stochastic analysis of subsurface flow and contaminant transport

The first‐order reliability method is an attractive approach to stochastic analysis of subsurface flow and contaminant transport. The method can be used with either analytical or numerical solutions, allowing a uniform but flexible approach to solving a variety of problems, and it can fully utilize any level of probabilistic information from the minimum knowledge of second moments to complete knowledge of the full joint distribution. Therefore the first‐order reliability method is particularly useful when statistical information is incomplete, as is common for problems in the subsurface environment. Additionally, correlation and nonnormal marginal distributions may be incorporated into the solution. Results from a first‐order reliability analysis include an estimate of the probability of exceeding a specified performance criteria and measures of sensitivity of the stochastic solution to changes in random variables and their statistical moments. Three subsurface flow and contaminant transport example problems are used to illustrate the capabilities of the method; results from these examples compare well with previously published Monte Carlo simulation results.