Efficient Calibration and Uncertainty Analysis Using Surrogate Models Conjunctively with a Complex Groundwater Model.

Author: Wesley Burrows

Burrows, Wesley, 2016 Efficient Calibration and Uncertainty Analysis Using Surrogate Models Conjunctively with a Complex Groundwater Model., Flinders University, School of the Environment

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This PhD research addresses some of the impediments to calibration and uncertainty analysis of complex groundwater models, whose long runtimes and sometimes questionable numerical stability often renders those analyses intractable. Research documented herein explores the use of surrogate and proxy models in overcoming these impediments. More specifically this research focuses on the application of surrogate and/or proxy models conjunctively with an original complex model, in facilitating and expediting gradient-based calibration and uncertainty analysis.

Gradient methods have the advantage over so-called global methods in that they are generally much faster and can readily be adapted to include formal mathematical regularisation which can accommodate large numbers of adjustable parameters. This supports calibration and uncertainty analysis for a broad range of physically-based, distributed models wherein complex environmental processes are simulated within heterogeneous media. Gradient methods are, however, highly dependent on the so-called Jacobian matrix which is comprised of derivatives of all model generated equivalents to calibration dataset observations with respect to all adjustable parameters. These derivatives are usually calculated from model outputs using finite-differencing methods. When parameters are many and model runtimes are long, population of the Jacobian matrix can be extremely computationally demanding. Also, the integrity of finite-difference derived derivatives can be severely degraded by numerical inconsistencies that often attend complex model outputs. Research documented herein demonstrates the novel use of a faster running and more numerically stable surrogate model for population of the Jacobian matrix that can overcome these difficulties, therefore promulgating calibration and uncertainty assessment of problematic complex models when it was otherwise not possible.

This study exemplifies a number of differing simplification strategies that can be implemented in this novel approach including: (1) use of a single model based on a coarser grid; (2) use of multiple surrogate models based on parameter-specific grid coarsening; (3) use of a model that employs an alternative simulation algorithm and; (4) use of a large suite of observation-specific analytical proxies.

Results from these demonstrations give great cause for optimism that the surrogate- enabled gradient methods have a bright future in modern groundwater modelling. As models become more complex, and as decision makers and stakeholders increasingly demand that predictions of future environmental outcomes made by models are accompanied by estimates of the uncertainties associated with those predictions, the need for parameterisation complexity will grow. So too will be the requirement that calibration and uncertainty analysis be based on gradient methods. It is anticipated that in the next generation of modelling in support of the decision-making process, the role of surrogate and proxy models in that process will expand.

Keywords: Model Calibration, Uncertainty Analysis, Surrogate models, Conjunctive model usage

Subject: Environmental Science thesis, Water Management thesis, Environmental management thesis

Thesis type: Doctor of Philosophy
Completed: 2016
School: School of the Environment
Supervisor: Craig Simmons