AbstractsMathematics

Hydraulic head data is frequently used for the calibration of groundwater flow models, usually with the main objective to improve the model performance. The hydraulic parameters in a groundwater flow model depend on the underlying geometry of the subsurface and the permeability of the soil. In the current calibration routines, the geometry is considered known, such that all uncertainties of the hydraulic parameters are ascribed to the permeabilities. After calibration these permeabilities may have physically unreasonable values, indicating that the estimate of the geometry is likely to be wrong. In this thesis the roles are reversed. A calibration procedure that focuses on the uncertainty of the geometry is performed. This shift introduces a dependency between the hydraulic parameters that is not considered in the current calibration method. An EnKF and EnKF-GMM are applied to a synthetic test case where only the geometry of one aquitard is considered uncertain. The filters are performed with the objectives to 1) localise the extent of the aquitard, and 2) find a probability distribution function for the thickness of the aquitard. In a series of experiments it is shown that the EnKF is only suitable in situations where the exact extent of the aquitard is known. In other cases, the probability distribution function of the thickness is bimodal, resulting in an EnKF that performs poorly and produces physically unrealistic outputs. As a solution, the EnKF-GMM is proposed. This extension of the regular EnKF can be used in more general scenarios as it allows a multimodal distribution as posterior distribution. Roughly speaking, the EnKF-GMM is an application of two EnKFs simultaneously. For two separate populations (modes) an EnKF is performed, and after each iteration the inhabitants of the population have the possibility to cross over to the other population. The cross-over probabilities are based on the likelihood of each population. The results of the experiments show that the EnKF-GMM is able to define probabilities on the extent of the aquitard. However, it fails to find a proper probability distribution function of the thickness. Filter divergence occurs as a result of the insufficient amount of information that hydraulic head data contains.