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

Menberg, Kathrin; Bidarmaghz, Asal; Gregory, Alastair; Choudhary, Ruchi; Girolami, Mark

doi:10.1016/j.scitotenv.2020.140846

Cited by 11 publications

(9 citation statements)

References 62 publications

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“…The discrepancies between the modelled and measured temperatures are a consequence of the compounding of uncertainties in the model. Menberg et al [23] identified a number of critical parameters to which the semi-3D modelling approach has proven to be sensitive. Amongst these are the initial ground temperature; the hydraulic and thermal properties of the geological materials; surface cover types; and density of basements.…”

Section: Discussionmentioning

confidence: 99%

Effect of anthropogenic heat sources in the shallow subsurface at city-scale

et al. 2020

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Rapid rates of urbanisation are placing growing demands on cities for accommodation and transportation, with increasing numbers of basements and tunnel networks being built to meet these rising demands. Such subsurface structures constitute continuous heat sources and sinks, particularly if maintained at comfortable temperatures. At the city-scale, there is limited understanding of the effect of heat exchange of underground infrastructures with their environments, in part due to limited availability of long-term underground temperature data. The effects of underground temperature changes due anthropogenic heat fluxes can be significant, impacting ventilation and cooling costs of underground spaces, efficiency of geo-energy systems, quality and quantity of groundwater flow, and the health and maintenance of underground structures. In this paper we explore the impact of anthropogenic subsurface structures on the thermal climate of the shallow subsurface by developing a heat transfer model of the city of Cardiff, UK, utilising a recently developed semi-3D modelling approach.

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Section: Discussionmentioning

confidence: 99%

Effect of anthropogenic heat sources in the shallow subsurface at city-scale

et al. 2020

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“…We employ a multi-fidelity approach developed by Menberg et al (2020), which extends the Kennedy and O’Hagen “single-fidelity” Bayesian framework (Kennedy and O’Hagan, 2001) (hereafter KOH) by including outputs from numerical models at both high and low levels of fidelity for the calibration. The advantage of this method is that the low-fidelity model may be run at a lower computational cost than the high-fidelity one, albeit with lower accuracy, and thereby more frequently, providing a greater number of numerical data points for calibration.…”

Section: Methodsmentioning

confidence: 99%

“…The correlation hyper-parameters are an indication for the smoothness of the covariance functions. The priors for the hyper-parameters are given in Table 4, is chosen in accordance with work done in previous studies (Menberg et al, 2020; Chong and Menberg, 2018; Guillas et al, 2009).…”

Section: Tablementioning

confidence: 99%

“…A possible issue with such an approach, however, is that it often requires a large number of forward runs of the original model which can be computationally expensive. An alternative methodology is proposed by Menberg et al (2020), based on the work by Kennedy and O’Hagan (2001) and Goh et al (2013). It employs models of two different levels of fidelity (i.e., mesh resolutions) to generate a large set of numerical data to train Gaussian Processes (GP) emulators for use in the calibration.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian parameter inference for shallow subsurface modeling using field data and impacts on geothermal planning

Kreitmair

Makasis²,

Menberg³

et al. 2022

DCE

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Understanding the subsurface is crucial in building a sustainable future, particularly for urban centers. Importantly, the thermal effects that anthropogenic infrastructure, such as buildings, tunnels, and ground heat exchangers, can have on this shared resource need to be well understood to avoid issues, such as overheating the ground, and to identify opportunities, such as extracting and utilizing excess heat. However, obtaining data for the subsurface can be costly, typically requiring the drilling of boreholes. Bayesian statistical methodologies can be used towards overcoming this, by inferring information about the ground by combining field data and numerical modeling, while quantifying associated uncertainties. This work utilizes data obtained in the city of Cardiff, UK, to evaluate the applicability of a Bayesian calibration (using GP surrogates) approach to measured data and associated challenges (previously not tested) and to obtain insights on the subsurface of the area. The importance of the data set size is analyzed, showing that more data are required in realistic (field data), compared to controlled conditions (numerically-generated data), highlighting the importance of identifying data points that contain the most information. Heterogeneity of the ground (i.e., input parameters), which can be particularly prominent in large-scale subsurface domains, is also investigated, showing that the calibration methodology can still yield reasonably accurate results under heterogeneous conditions. Finally, the impact of considering uncertainty in subsurface properties is demonstrated in an existing shallow geothermal system in the area, showing a higher than utilized ground capacity, and the potential for a larger scale system given sufficient demand.

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“…One reason might be that multifidelity approaches often require bespoke handling for combining data of various fidelities in contrast to single fidelity approaches where robust techniques and software are readily available for use independently of the physical system under study. However, multifidelity methods have recently gained more attention in water resources modeling for computationally expensive problems of parameter estimation and uncertainty quantification (e.g., Mahmoodian et al, 2018;Moreno-Rodenas et al, 2018;Zhang et al, 2018;Zheng et al, 2019;Man et al, 2020;Menberg et al, 2020;Wu et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Multifidelity Surrogate Models for Efficient Uncertainty Propagation Analysis in Salars Systems

Christelis

Hughes

2022

Front. Water

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Salars are complex hydrogeological systems where the high-density contrasts require advanced numerical models to simulate groundwater flow and brine transport. Applying those models over large spatial and temporal scales is important to understand the various subsurface processes in salars, but the associated computational cost hinders an analysis based on repetitive numerical simulations. Single fidelity surrogate modeling is a common approach to alleviate computational burden with computationally expensive physics-based models of high-fidelity. However, due to the complexity in salars modeling it might not be affordable to run high-fidelity simulations many times until we build a surrogate model of acceptable accuracy. Here, we investigate if multifidelity surrogate methods, that exploit information from inexpensive lower fidelity models, can show promise for computationally demanding tasks for salars systems. Additive, multiplicative and co-Kriging multifidelity surrogates are developed based on the combination of training data from low fidelity sharp interface models and a higher fidelity variable-density flow and solute transport model. Their performance is compared against a single fidelity Kriging surrogate model, and they are all employed to conduct a Monte-Carlo-based uncertainty propagation analysis where recharge, hydraulic conductivity and density differences between freshwater and brine are considered uncertain model inputs. Results showed that multifidelity methods are a promising alternative for time-intensive numerical models of salars under limited high-fidelity samples. In addition, sharp interface models, despite commonly used in coastal aquifer problems, can also be applied in salars modeling as cheap lower fidelity models for interface calculations via a multifidelity framework. The Monte-Carlo outputs based on the surrogate models, resulted in estimated probability density functions characterized by long tails, thus, highlighting the need to reduce parametric uncertainty in real world models of salars.

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

Cited by 11 publications

References 62 publications

Effect of anthropogenic heat sources in the shallow subsurface at city-scale

Effect of anthropogenic heat sources in the shallow subsurface at city-scale

Bayesian parameter inference for shallow subsurface modeling using field data and impacts on geothermal planning

Multifidelity Surrogate Models for Efficient Uncertainty Propagation Analysis in Salars Systems

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