Analysis of accuracy of approximate, simultaneous, nonlinear confidence intervals on hydraulic heads in analytical and numerical test cases

Inaccuracies in parameter values, parameterization, stresses, and boundary conditions of analytical solutions and numerical models of groundwater flow produce errors in simulated hydraulic heads. These errors can be quantified in terms of approximate, simultaneous, nonlinear confidence intervals presented in the literature. Approximate confidence intervals can be applied in both error and sensitivity analysis and can be used prior to calibration or when calibration was accomplished by trial and error. In this paper, the method is expanded for use in numerical problems, and the accuracy of the approximate intervals is evaluated using Monte Carlo runs. Four test cases are used to compare results. In two numerical test cases, the approximate, simultaneous confidence intervals are generally accurate and are calculated efficiently enough to indicate that the method is useful for real-world problems. In one of the two analytical test cases considered, the approximate intervals are too wide to be of practical interest. Improving the method used to approximate the uncertainty of the model inputs could make the confidence intervals useful in more problems.