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Model Variable Augmentation (MVA) for Diagnostic Assessment of Sensitivity Analysis Results
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Model Variable Augmentation (MVA) for Diagnostic Assessment of Sensitivity Analysis Results

by Juliane Mai and Bryan A Tolson (University of Waterloo, Canada)


The method of Model Variable Augmentation (MVA) was introduced to assess the quality of SA results without performing any additional model runs or requiring bootstrapping. MVA is proven to perform well when only a small number of model runs was used to obtain the sensitivity indexes. MVA augments the original model input variables with additional variables of known properties. The sensitivities of the augmented model variables are used to draw conclusions on the reliability of the other "original" model parameters' sensitivities. The MVA method is already successfully tested with two global SA methods: the variance-based Sobol' method and the moment-independent PAWN method. The full paper can be found here.

Step-by-Step Tutorial

The step-by-step tutorial describes all the steps to estimate sensitivity indexes for (original) model variables and the augmented parameters. It also explains how to analyse these results and how to draw conclusions on the reliablility of the sensitivity indexes of the original model variables. Details can be found here.


We provide some case studies to show how MVA can help:

  • to check the implementation of the sensitivity analysis method (see here)
  • to obtain a robust ranking of the model variables (see here)
  • to estimate the uncertainty of the sensitivity indexes without the necessity of bootstrapping (see here)


J Mai & BA Tolson (2019).
Model Variable Augmentation (MVA) for diagnostic assessment of sensitivity analysis results.
Water Resources Research, 55, 2631– 2651.

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