Multi-fidelity approach to Bayesian parameter estimation in subsurface heat and fluid transport models

The increased use of the urban subsurface for competing purposes, such as anthropogenic infrastructures and geothermal energy applications, leads to an urgent need for large-scale sophisticated modelling approaches for coupled mass and heat transfer. However, such models are subject to large uncertainties in model parameters, the physical model itself and in available measured data, which is often rare. Thus, the robustness and reliability of the computer model and its outcomes largely depend on successful parameter estimation and model calibration, which are hampered by the computational burden of large-scale coupled models. To tackle this problem, we develop a novel Bayesian approach for parameter estimation, which allows us to account for different sources of uncertainty, is capable of dealing with sparse field data and makes optimal use of the output data from expensive numerical model runs. This is achieved by combining output data from different models that represent the same physical problem, but at different levels of fidelity, e.g. reflected by different spatial resolution. By applying this new approach to a 1D analytical heat transfer model and a large-scale semi-3D numerical model while using synthetic data, we show that the accuracy and precision of parameter estimation by this multi-fidelity framework by far exceeds the standard single-fidelity results. The consideration of different error terms in the Bayesian framework also allows assessment of the model bias and the discrepancy between the different fidelity levels. These are emulated by Gaussian Process models, which facilitate re-iteration of the parameter estimation without additional model runs.