Uncertainty quantification of groundwater flow impacts on borehole heat exchanger field performance using polynomial chaos-Kriging surrogates

• Polynomial chaos-Kriging surrogates efficiently quantify hydrogeological uncertainty. • Balanced thermal loads reduce performance uncertainty by more than 50%. • Darcy flux parameters explain approximately 90% of the output variability. • Unbalanced operation yields a failure probability of about 17% at the study site. Shallow geothermal systems, particularly large borehole heat exchanger fields, are increasingly deployed to support the decarbonization of urban heating. Their long-term performance, however, can be highly sensitive to hydrogeological conditions that are often poorly characterized during the design phase. This study presents a polynomial chaos-Kriging surrogate modeling framework to quantify how hydrogeological uncertainties influence the performance and reliability of a planned large-scale borehole heat exchanger field in Hannover, Germany. Surrogate models trained on high-accuracy thermo-hydraulic simulations enable efficient Monte Carlo analyses of uncertainty propagation, reliability, and global sensitivity. The results show that balanced thermal loads, supported by photovoltaic-thermal collectors for subsurface regeneration, reduce performance uncertainty by more than 50% compared with unbalanced operation. Global sensitivity analysis reveals that Darcy flux parameters dominate the variance of the seasonal coefficient of performance, explaining approximately 90% of total output variability. Groundwater flow magnitude governs the transition from conduction- to advection-dominated heat transfer, while flow direction primarily controls temperature changes at property boundaries through advective heat transport. Seasonal groundwater-level uncertainty is negligible due to the small ratio of groundwater level to borehole heat exchanger length (∼0.1). Reliability analysis under unbalanced thermal loads yields a failure probability of ∼17%, highlighting the risk of long-term temperature degradation. Additional scenario analyses show that a deeper groundwater table can significantly influence uncertainty quantification results, whereas the thermal conductivity of the underlying claystone has a limited impact. Overall, the proposed framework is computationally efficient and physically interpretable, enabling site-specific optimization of shallow geothermal systems and supporting the robust decarbonization of the urban heating sector.