[1] This study reports on two strategies for accelerating posterior inference of a highly parameterized and CPU-demanding groundwater flow model. Our method builds on previous stochastic collocation approaches, e.g., Marzouk and Xiu (2009) and Marzouk and Najm (2009), and uses generalized polynomial chaos (gPC) theory and dimensionality reduction to emulate the output of a large-scale groundwater flow model. The resulting surrogate model is CPU efficient and serves to explore the posterior distribution at a much lower computational cost using two-stage MCMC simulation. The case study reported in this paper demonstrates a two to five times speed-up in sampling efficiency.

The Boom Clay has been investigated for more than 30 years as a candidate host formation for the disposal of high-level and long-lived radioactive waste in Belgium. The very low hydraulic conductivity (on the order of 10 -12 m/s) in combination with limited hydraulic gradients over the host formation (0.02 ~ 0.04) results in water flow in the Boom Formation being negligible and diffusion the dominant transport mechanism. The assessment of the long-term barrier function of the host clay formation in the framework of radioactive waste disposal requires rigorous quantitative characterization of key formation properties such as the hydraulic conductivity (K). Hydraulic conductivities of Boom Clay measured through various testing techniques in the laboratory, i.e. tracer percolation experiments, constant head permeameter experiments and isostatic experiments, exhibit similar K values in the order of 10 -12 m/s. Based on a largeset of test samples, the impact of sample scale, hydraulic gradient range adopted in the tests, stress controlled methods and pre-existing fissures in the sample on the K value is shown to be quite limited. In situ measurements obtained from both several-centimetre long piezometer filters and percolation into a 7-metre long gallery and 21-meter long shaft at the HADES underground research facility yield K values that are very similar to values measured in the laboratory on samples of a few centimetres. This indicates that the K measurements for the Boom Clay obtained through various techniques are very consistent. K values measured on a centimetre-scale are also representative at the metre-scale, which is often the size of grid cells used in numerical simulations for long-term safety assessments. Spatial analysis of K values across the Boom Clay at the Mol site reveals a typical profile with a very homogenous 61-m thick central part, i.e. the so-called Putte and Terhagen Members, which is also the least permeable part of the Boom Clay. The geometric mean of the vertical (K v ) and horizontal (K h ) hydraulic conductivities for the Putte and Terhagen Members at the Mol site are 1.7×10 -12 and 4.4×10 -12 m/s, respectively, with a vertical anisotropy K h /K v of about 2.5. Higher K values, but still low (10 -12 to 10 -10 m/s), are observed in the more silty zones above and below the Putte and Terhagen Members, i.e. the Belsele-Waas Member and the Boeretang Member, as well as in the double band of the lower Putte Member.A regional analysis of vertical K variability of the Boom Clay in the northeast of Belgium based on test results from five boreholes shows an increase in hydraulic conductivity from the east towards the west. Statistical analyses indicate that the effect of the samples" stratigraphic position on hydraulic conductivity is strongly related to different grain-size characteristics. However, a general Kgrain-size model does not explain the geographical differences in K values satisfactorily. Geographical differences can be best explained by different Kgrain-size relationships at the diffe...

Abstract. The rate at which low-lying sandy areas in temperate regions, such as the Campine Plateau (NE Belgium), have been eroding during the Quaternary is a matter of debate. Current knowledge on the average pace of landscape evolution in the Campine area is largely based on geological inferences and modern analogies. We performed a Bayesian inversion of an in situ-produced 10Be concentration depth profile to infer the average long-term erosion rate together with two other parameters: the surface exposure age and the inherited 10Be concentration. Compared to the latest advances in probabilistic inversion of cosmogenic radionuclide (CRN) data, our approach has the following two innovative components: it (1) uses Markov chain Monte Carlo (MCMC) sampling and (2) accounts (under certain assumptions) for the contribution of model errors to posterior uncertainty. To investigate to what extent our approach differs from the state of the art in practice, a comparison against the Bayesian inversion method implemented in the CRONUScalc program is made. Both approaches identify similar maximum a posteriori (MAP) parameter values, but posterior parameter and predictive uncertainty derived using the method taken in CRONUScalc is moderately underestimated. A simple way for producing more consistent uncertainty estimates with the CRONUScalc-like method in the presence of model errors is therefore suggested. Our inferred erosion rate of 39 ± 8. 9 mm kyr−1 (1σ) is relatively large in comparison with landforms that erode under comparable (paleo-)climates elsewhere in the world. We evaluate this value in the light of the erodibility of the substrate and sudden base level lowering during the Middle Pleistocene. A denser sampling scheme of a two-nuclide concentration depth profile would allow for better inferred erosion rate resolution, and including more uncertain parameters in the MCMC inversion.

Saturated hydraulic conductivity (K) is one of the most important parameters determining groundwater flow and contaminant transport in both unsaturated and saturated porous media. Although several well‐established laboratory methods exist for determining K, in situ measurements of this parameter remain very complex and scale dependent. Often, the limited accessibility of subsurface sediments for sampling means an additional impediment to our ability to quantify subsurface K heterogeneity. One potential solution is the use of outcrops as analogues for subsurface sediments. This paper investigates the use of air permeameter measurements on outcrops of unconsolidated sediments to quantify K and its spatial heterogeneity on a broad range of sediment types. The Neogene aquifer in northern Belgium is used as a case study for this purpose. To characterize the variability in K, 511 small‐scale air permeability measurements were performed on outcrop sediments representative over five of the aquifer's lithostratigraphic units. From these measurements, outcrop‐scale equivalent K tensors were calculated using numerical upscaling techniques. Validation of the air permeameter‐based K values by comparison with laboratory constant head K measurements reveals a correlation of 0.93. Overall, the results indicate that hand‐held air permeameters are very efficient and accurate tools to characterize saturated K, as well as its small‐scale variability and anisotropy on a broad range of unconsolidated sediments. The studied outcrops further provided a qualitative understanding of aquifer hydrostratigraphy and quantitative estimates about K variability at the centimetre‐scale to metre‐scale. Copyright © 2013 John Wiley & Sons, Ltd.

Various approaches exist to relate saturated hydraulic conductivity (K s ) to grain-size data. Most methods use a single grain-size parameter and hence omit the information encompassed by the entire grain-size distribution. This study compares two data-driven modelling methods-multiple linear regression and artificial neural networks-that use the entire grain-size distribution data as input for K s prediction. Besides the predictive capacity of the methods, the uncertainty associated with the model predictions is also evaluated, since such information is important for stochastic groundwater flow and contaminant transport modelling.Artificial neural networks (ANNs) are combined with a generalised likelihood uncertainty estimation (GLUE) approach to predict K s from grain-size data. The resulting GLUE-ANN hydraulic conductivity predictions and associated uncertainty estimates are compared with those obtained from the multiple linear regression models by a leave-one-out cross-validation. The GLUE-ANN ensemble prediction proved to be slightly better than multiple linear regression. The prediction uncertainty, however, was reduced by half an order of magnitude on average, and decreased at most by an order of magnitude. This demonstrates that the proposed method outperforms classical data-driven modelling techniques. Moreover, a comparison with methods from the literature demonstrates the importance of site-specific calibration. The data set used for this purpose originates mainly from unconsolidated sandy sediments of the Neogene aquifer, northern Belgium. The proposed predictive models are developed for 173 grain-size K s -pairs. Finally, an application with the optimised models is presented for a borehole lacking K s data.

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