Non-Linear Uncertainty Analysis

In contrast to linear uncertainty analysis, non-linear methods do not suffer from the limitation of assuming a linear relationship between model predictions and model parameters. Given that such relationships are rarely linear, this is an important consideration. Nevertheless, non-linear methods are not free of assumptions, can sometimes incur a higher implementation cost than linear methods, and do not facilitate the calculation of value-added quantities such as data-worth.

This tutorial demonstrates workflows for non-linear uncertainty analysis using the PEST++IES iterative ensemble smoother. PEST++IES samples the posterior parameter probability distribution. It commences by using a suite of random parameter fields sampled from the prior parameter probability distribution. Using an iterative procedure, IES adjusts the parameters of each realisation in order to reduce the misfit between simulated and measured observation values. The outcome of multi-realisation parameter adjustment process is an ensemble of parameter fields, all of which allow the model to adequately replicate observed system behaviour. These parameter fields can be considered samples of the posterior parameter probability distribution. By making a prediction using all members of this ensemble, the posterior probability distribution of that prediction is sampled.

This tutorial is part of a series of tutorials which demonstrate workflows for parameter estimation and uncertainty analysis with the PEST/PEST++ suites. These are not the only (or necessarily the best) workflows; their purpose is to take the reader through the fundamentals of how to accomplish common tasks whilst also providing insights in how to apply the outcomes.