Information-theoretic summary statistics for diagnostic calibration of the groundwater models using approximate Bayesian computation

This paper presents a novel approach to analyzing uncertainty in complex groundwater models based on the approximate Bayesian computation (ABC) framework and information-theoretic summary statistics. Two summary statistics using the concepts of mutual information and variation of information are formulated as distance function measures of the ABC. These signatures are utilized within an ABC rejection (ABC-REJ) algorithm to measure the similarity and dissimilarity of the generated samples to the true posterior distribution of the groundwater model parameters. This method was applied to groundwater model calibration and uncertainty analysis in an arid region of Oman with a complex hydrogeological setting and a hardrock-alluvial aquifer system. MODFLOW unstructured-grid was used for modelling groundwater dynamics. A three-dimensional stratigraphic model was developed based on borehole data, and five-layer grid cells were defined according to the material and elevations of the stratigraphic model. Results show that the model reproduces the observed data behaviour very well, including peaks and abrupt declines in the head, as well as the trend of fluctuations in the observation wells. A notable match between the observed and simulated heads indicates the accuracy of the ABC-REJ algorithm based on summary statistics for calibrating and analyzing groundwater models.