Geothermal simulations are widely used in both scientific and applied industrial contexts. Typically, the temperature state is evaluated on the basis of the heat equation, with suitable parameterizations of the model domain and defined boundary conditions, which are calibrated to obtain a minimal misfit between measured and simulated temperature values. We demonstrate the essential need for global sensitivity studies for robust geothermal model calibrations since local studies overestimate the influence of the parameters. We ensure the feasibility of the study by using a physics-based machine learning approach, that reduces the computation time by several orders of magnitude.

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<p>In Geosciences, we face the challenge of characterizing uncertainties to provide reliable predictions of the earth surface to allow, for instance, a sustainable and renewable energy management. In order, to address the uncertainties we need a good understanding of our geological models and their associated subsurface processes.</p><p>Therefore, the essential pre-step for uncertainty analyses are sensitivity studies. Sensitivity studies aim at determining the most influencing model parameters. Hence, we require them to significantly reduce the parameter space to avoid unfeasibly large compute times.</p><p>We distinguish two types of sensitivity analyses: local and global studies. In contrast, to the local sensitivity study, the global one accounts for parameter correlations. That is the reason, why we employ in this work a global sensitivity study. Unfortunately, global sensitivity studies have the disadvantage that they are computationally extremely demanding. Hence, they are prohibitive even for state-of-the-art finite element simulations.</p><p>For this reason, we construct a surrogate model by employing the reduced basis method. The reduced basis method is a model order reduction technique that aims at significantly reducing the spatial and temporal degrees of freedom of, for instance, finite element solves. In contrast to other surrogate models, we obtain a surrogate model that preserves the physics and is not restricted to the observation space. As we will show, the reduced basis method leads to a speed-up of five to six orders of magnitude with respect to our original problem while retaining an accuracy higher than the measurement accuracy.</p><p>In this work, we elaborate on the advantages of global sensitivity studies in comparison to local ones. We use several case studies, from large-scale European sedimentary basins to demonstrate how the global sensitivity studies are used to learn about the influence of transient, such as paleoclimate effects, and stationary effects. We also demonstrate how the results can be used in further analyses, such as deterministic and stochastic model calibrations. Furthermore, we show how we can use the analyses to learn about the subsurface processes and to identify model short comes.</p>

The societal importance of geothermal energy is significantly increasing because of its low carbon-dioxide footprint. However, geothermal exploration is also subject to high risks. For a better assessment of these risks, extensive parameter studies are required that improve the understanding of the subsurface. This yields computationally demanding analyses. Often, this is compensated by constructing models with a small vertical extent. This paper demonstrates that this leads to entirely boundary-dominated and hence uninformative models. It demonstrates the indispensable requirement to construct models with a large vertical extent to obtain informative models with respect to the model parameters. For this quantitative investigation, global sensitivity studies are essential since they also consider parameter correlations. To compensate for the computationally demanding nature of the analyses, a physics-based machine learning approach is employed, namely the reduced basis method, instead of reducing the physical dimensionality of the model. The reduced basis method yields a significant cost reduction while preserving the physics and a high accuracy, thus providing a more efficient alternative to considering, for instance, a small vertical extent. The reduction of the mathematical instead of physical space leads to less restrictive models and, hence, maintains the model prediction capabilities. The combination of methods is used for a detailed investigation of the influence of model boundary settings in typical regional-scale geothermal simulations and highlights potential problems.

Abstract. Transient processes play a major role in geophysical applications. In this paper, we quantify the significant influence arising from transient processes for conductive heat transfer problems for sedimentary basin systems. We demonstrate how the thermal properties are affected when changing the system from a stationary to a non-stationary (transient) state and what impact time-dependent boundary conditions (as derived from paleoclimate information) have on the system's overall response. Furthermore, we emphasize the importance of the time-stepping approach adopted to numerically solve for the transient case and the overall simulation duration since both factors exert a direct influence on the sensitivities of the thermal properties. We employ global sensitivity analyses to quantify not only the impact arising from the thermal properties but also their parameter correlations. Furthermore, we showcase how the results of such sensitivity analysis can be used to gain further insights into the complex Central European Basin System in central and northern Europe. This computationally very demanding workflow becomes feasible through the construction of high-precision surrogate models based on the reduced basis (RB) method.