A flexible Integrated Bayesian Multi-model Uncertainty Estimation Framework (IBMUEF) is presented to simultaneously quantify conceptual model structure, input and parameter uncertainty of a groundwater flow model. In this fully Bayesian framework, the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm with a novel likelihood function is combined with Bayesian Model Averaging (BMA). Four alternative conceptual models, representing different geological representations of an overexploited aquifer, have been developed. The uncertainty of the input of the model is represented by multipliers. A novel likelihood function based on a new heteroscedastic error model is included to extend the applicability of the framework. The results of the study confirm that neglecting conceptual model structure uncertainty results in unreliable prediction. Consideration of both model structure and input uncertainty are important to obtain confident parameter sets and better model predictions. This study shows that the IBMUEF provides more reliable model predictions and accurate uncertainty bounds.
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