Document Type



DOI 10.1111/gwat.12470

Publication Date



Area Metric, validation, multi-model, groundwater, epistemic, aleatory, uncertainty


We demonstrate the application of the Area Metric developed by Ferson et al. (2008) for multi-model validity assessment. The Area Metric quantified the degree of models’ replicative validity: the degree of agreement between the observed data and the corresponding simulated outputs represented as their empirical cumulative distribution functions (ECDFs). This approach was used to rank multiple representations of a case study groundwater flow model of a landfill by their Area Metric scores. A multi-model approach allows for the accounting for uncertainties that may either be epistemic (from lack of knowledge), or aleatory (from variability inherent in the system). The Area Metric approach enabled explicit incorporation of model uncertainties, epistemic as well as aleatory, into validation assessment. The proposed approach informs understanding of the collected data and that of the model domain. It avoids model overfitting to a particular system state, and in fact is a blind assessment of the models’ validity: models are not adjusted, or updated, to improve their fit. This approach assesses the degree of models’ validity, in place of the typical binary model validation/invalidation process. Collectively, this increases confidence in the model’s representativeness that in turn, reduces risks to model users.


Published as:

Aphale, O., and DJ Tonjes. 2017. Multi-model validation assessment of groundwater flow simulation models using area metric approach. Groundwater 55(2):219-226.DOI 10.1111/gwat.12470



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.