Functional error modeling for uncertainty quantification in hydrogeology

Approximate models (proxies) can be employed to reduce the computational costs of estimating uncertainty. The price to pay is that the approximations introduced by the proxy model can lead to a biased estimation. To avoid this problem and ensure a reliable uncertainty quantification, we propose to combine functional data analysis and machine learning to build error models that allow us to obtain an accurate prediction of the exact response without solving the exact model for all realizations. We build the relationship between proxy and exact model on a learning set of geostatistical realizations for which both exact and approximate solvers are run. Functional principal components analysis (FPCA) is used to investigate the variability in the two sets of curves and reduce the dimensionality of the problem while maximizing the retained information. Once obtained, the error model can be used to predict the exact response of any realization on the basis of the sole proxy response. This methodology is purpose-oriented as the error model is constructed directly for the quantity of interest, rather than for the state of the system. Also, the dimensionality reduction performed by FPCA allows a diagnostic of the quality of the error model to assess the informativeness of the learning set and the fidelity of the proxy to the exact model. The possibility of obtaining a prediction of the exact response for any newly generated realization suggests that the methodology can be effectively used beyond the context of uncertainty quantification, in particular for Bayesian inference and optimization.

Natural Tracers in recent groundwaters from different Alpine aquifers

Groundwater with underground residence times between days and a few years have been investigated over more than 20 years from 487 remote sites located in different aquifer types in the Alpine belt. Analysis of the data reveals that groundwaters evolved in crystalline, evaporite, carbonate, molasse, and flysch aquifers can be clearly distinguished based on their major and trace element composition and degree of mineralisation. A further subdivision can be made even within one aquifer type based on the trace element compositions, which are characteristic for the lithologic environment. Major and trace element concentrations can be quantitatively described by interaction of the groundwater with the aquifer- specific mineralogy along the flow path. Because all investigated sites show minimal anthropogenic influences, the observed concentration ranges represent the natural background concentrations and can thus serve as a “geo-reference” for recent groundwaters from these five aquifer types. This “geo-reference” is particularly useful for the identification of groundwater contamination. It further shows that drinking water standards can be grossly exceeded for critical elements by purely natural processes

Recharge Areas and Geochemical Evolution of Groundwater in an Alluvial Aquifer System in the Sultanate of Oman

A regional hydrogeochemical model was developed to evaluate the geochemical evolution of different groundwaters in an alluvial aquifer system in the Interior of Oman. In combination with environmental isotopes the model is able to extract qualitative and quantitative information about recharge, groundwater flow paths and hydraulic connections between different aquifers. The main source of water to the alluvial aquifer along the flow paths ofWadi Abyadh andWadi M’uaydin in the piedmont is groundwater from the high-altitude areas of the Jabal Akhdar and local infiltration along the wadi channels. In contrast, the piedmont alluvial aquifer alongWadi Halfayn is primarily replenished by lateral recharge from the ophiolite foothills to the east besides smaller contributions from the Jabal Akhdar and local infiltration. Further down gradient in the Southern Alluvial Plain aquifer a significant source of recharge is direct infiltration of rain and surface runoff, originating from a moisture source that approaches Oman from the south. The model shows that the main geochemical evolution of the alluvial groundwaters occurs along the flow path from the piedmont to the Southern Alluvial Plain, where dedolomitization is responsible for the observed changes in the chemical and carbon isotope composition in these waters.