Predictive uncertainty analysis for a highly parameterized karst aquifer using null-space Monte Carlo

Inverse problems in hydrogeology pose a great challenge for modelers as they are ill-posed, resulting in a non-unique solution. High computational resources are needed for the calibration process, especially in the case of highly parameterized aquifers like karst limestone, characterized by significant heterogeneity. The null-space Monte Carlo (NSMC) is a parameter-constrained Monte Carlo approach that can be used to quantify uncertainty, as it produces a set of solutions that calibrate the model. This method is used to assess uncertainty in the calibration of a karst aquifer in Qatar, which has high heterogeneity. Pilot points were used to reflect the geostatistics of the calibrated field, and the calibration results at these points were interpolated over the aquifer area using kriging. The NSMC was then used to produce 200 realizations of the null-space parameter field using the constrained random variable of hydraulic conductivity. The null-space realizations were then incorporated into the parameter space derived from the calibrated model. Statistical analysis of the calibrated hydraulic conductivity revealed a variation ranging from 0.1 to 350 m/d, indicating a considerable variability in the aquifer’s hydraulic parameters. The areas with high hydraulic conductivity were concentrated in the central and eastern parts of the aquifer, and these same areas exhibited a high standard deviation. Based on the findings of this study, while the NSMC method is effective for uncertainty analysis in solving inverse problems, it is important to note that a considerable number of runs are necessary to reach the threshold of calibration error. This is because of the significant non-linearity inherent in the karst aquifer.