A Highly Efficient Method for Calibration-Constrained Model Predictive Uncertainty Analysis

A method is presented for undertaking numerically efficient uncertainty analysis in conjunction with the use of complex environmental models that require many parameters. The method allows generation of random parameter fields that all respect constraints imposed by the need to respect historical observations of system state. That is, the method allows generation of many different (geo)hydraulically reasonable parameter fields, all of which calibrate a model.

In recognition that the “cost of uniqueness” in achieving a calibrated model is a parameter field that is, of necessity, a simplified form of reality (or, in mathematical terms, a projection of reality onto a low-dimensional “solution space” of the inverse problem of model calibration), the methodology starts by defining both this space, and its orthogonal compliment (the “calibration null space”) on the basis of the calibrated parameter field. The latter space embodies components of parameterisation detail that cannot be captured by the calibration process, but which may nevertheless be salient to predictions made by the model. Different parameter realisations are then generated, based on a suitable statistical descriptor selected on the basis of expert judgement. Differences between these fields and the calibrated parameter field are then projected onto the calibration null space; the projected difference is then re-added to the calibration field. Discrepancies between model outputs and historical field measurements are then corrected through adjusting calibration solution space components in a highly-efficient re-calibration step.

The methodology has been successfully applied in both groundwater and surface water modelling contexts. Examples are presented from both of these fields.