Outcomes of Numerical Groundwater Model Simplification and Calibration

Author: Ty Watson

Watson, Ty, 2017 Outcomes of Numerical Groundwater Model Simplification and Calibration, Flinders University, School of the Environment

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Calibration of numerical models as a precursor to predictive uncertainty analysis is now regarded as standard practice in groundwater modelling for management and decision support. Despite computational advances facilitating increasingly complex and realistic model-based representations of natural systems, model simplifications/imperfections relative to the incomprehensible detail of reality is unavoidable.

Calibration of a simplified/imperfect model may lead to additional error in model predictions that is undetectable through standard uncertainty analysis approaches. This calibration-induced “bias” increases the risk of underestimation of potential predictive error, which defines ultimate failure of a modelling process. Assurance against modelling failure thus requires that calibration-induced predictive bias is forestalled or quantified. This thesis makes several key contributions to the knowledge base pertaining to calibration-induced predictive bias identification, and exposition of its origins, towards providing best-practice guidance for repressing its occurrence.

The first component of work is a proof of concept for the “paired model analysis” (PMA) methodology for bias identification and reduction presented by Doherty and Christensen (2011). PMA has not previously been tested for empirical consistency with theoretical expectation. PMA is applied to a highly studied synthetic example, demonstrating good agreement between PMA-quantified uncertainty with the results of established methods. The reliability of PMA in identifying calibration-induced predictive bias is systematically demonstrated, together with its capacity to reduce the consequential inflation in potential predictive error.

The second component of work builds upon the mathematical exposition of model simplification outcomes developed by Doherty and Christensen (2011). In particular it is extended to express “null-space entrainment”; a concomitant outcome of the parameter surrogacy that may occur during calibration and which is the fundamental cause of calibration-induced predictive bias. The developed linear concepts are employed in conjunction with PMA to examine the outcomes of two simplifications of a one-dimensional Richards equation-based vadose zone model. Substantial parameter surrogacy and consequential null-space entrainment is demonstrated to occur for both comparatively modest simplification (i.e., assumption of vertical homogeneity), and more drastic simplification (i.e., replacement with a lumped parameter “bucket” model). Nonetheless, both simplified models are shown to make largely unbiased predictions of future recharge. This demonstrates that, for predictions that are similar in nature to the available calibration dataset, a model’s physical basis becomes less important to its predictive performance than attainment of a “good fit”.

The final component of work explores the outcomes of employing the increasingly popular pilot-point-based regularized inversion approach for calibration in a categorically heterogeneous environment. PMA is used to thoroughly examine model performance in making multiple predictions subject to several regularization weighting strategies. For some predictions, ignoring the existence of preferential flow features does not compromise the ability of the calibration and uncertainty analysis processes to substantially reduce and quantify potential predictive error. Simultaneously, calibration unavoidably inflates the potential error in other predictions beyond prior uncertainty. The results emphasize the need for prediction-specific tuning of the modelling process, to the extent that the most pragmatic approach for some predictions may be to forego calibration entirely and quantify uncertainty based on geologically realistic expressions of “expert knowledge” alone.

Keywords: Groundwater modelling, calibration, parameter estimation, prediction, uncertainty, linear uncertainty analysis, nonlinear uncertainty analysis, model simplification, model complexity, predictive bias, paired model analysis, null-space entrainment

Subject: Environmental Science thesis

Thesis type: Doctor of Philosophy
Completed: 2017
School: School of the Environment
Supervisor: Adrian Werner