Multi-model Analysis for Groundwater Models: A Useful Tool for Uncertainty Analysis
The following is the abstract of a presentation given by Judith Schenk, Ph.D., (retired) Senior Project Manager at Lytle Water Solutions (LWS), during the 17th Biennial Symposium on Managed Aquifer Recharge, hosted by the Arizona Hydrological Society and the Groundwater Resources Association of California.
Multi-model analysis (MMA) considers multiple model interpretations of a natural system. Limited data used to create groundwater models can result in different groundwater models that may reproduce the same groundwater system response and match the observation data equally well. Considering multiple models using MMA for groundwater models can aid in evaluating different model structures, and provides decision makers with critical information regarding uncertainty of model predictions.
Multi-model analysis is designed to find the balance between model fit and model complexity. MMA provides a joint probability of within-model uncertainty of model parameters and between-model uncertainty of model structure. Information Criteria (IC) equations are used to evaluate the strength of evidence that a model represents the true but unknown system. All IC equations include a goodness-of-fit term, but have different added penalty terms for model complexity. An IC score is calculated for each model. An increase in the penalty for model complexity must be met with a decrease in the model error, so that lower IC scores indicate a higher probability that the model represents the true, but unknown system.
Click HERE to see the video presentation, on the LWS YouTube channel.
Predictions produced by each model are model-averaged based on each model’s probability in a set of models. An example problem of a synthetic model using the Kashyap information criteria (KIC) illustrates the process of performing MMA. For that example, the simplest model and the most complex models in the model set had the highest model probabilities. The probability density function of the model-averaged prediction is based on the weighted average of all the models in the set. The two models with the highest probability however, have the greatest influence on the model-average prediction.
Anna Elgqvist, EI anna@lytlewater.com
Bruce Lytle, P.E. bruce@lytlewater.com
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