Quantifying model structural error: Efficient <scp>B</scp>ayesian calibration of a regional groundwater flow model using surrogates and a data‐driven error model

Xu, Tianfang; Valocchi, Albert J.; Ye, Ming; Liang, Feng

doi:10.1002/2016wr019831

Cited by 66 publications

(64 citation statements)

References 69 publications

(145 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, an LSM may be overfitted by parameter optimization if the model structural errors caused from simplified or even incorrect conceptualization of the real land system are not sufficiently considered (Kennedy & O'Hagan, ). Recently, by assuming the prior distributions of structural errors, parametric uncertainty in a groundwater flow model (Xu et al, ; Xu & Valocchi, ) and a climate model (McNeall et al, ; Williamson et al, ) were investigated, but Brynjarsdóttir and O'Hagan () demonstrated that only with realistic priors on the model structural errors could they uncover the true parameter values. Therefore, acceptable prior distributions of model structure errors are necessary to reasonably calibrate the parameters.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Land Surface Subprocesses and Their Impacts on Model Performance With Global Flux Data

Guo

Chen

et al. 2019

J Adv Model Earth Syst

View full text Add to dashboard Cite

Study on the uncertainties in land surface models (LSMs) helps us understand the differences and errors in climate models. Meanwhile, uncertainty in model structure, derived from the many possible parameterization schemes for the same physical subprocess, is a primary source of land model uncertainties. To attribute structural errors and model parameterization scheme uncertainties, it is critical to identify the key subprocesses involved and investigate the interactions of these subprocesses on LSM behavior, which will ultimately help us identify the “optimal” parameterization schemes for various plant functional types, soil types, and different locations. Here, we conduct physical ensemble simulations for multiple sites from FLUXNET and then apply a variance‐based sensitivity analysis method to quantitatively assess the impacts of uncertainties in the parameterization schemes of subprocesses in the Noah with multiparameterization (Noah‐MP) LSM on model performance. The results show that three subprocesses—surface exchange coefficient, runoff and groundwater, and surface resistance to evaporation—have the most significant impacts on the performance of the simulated sensible heat flux, latent heat flux, and net absorbed radiation in the Noah‐MP LSM. The interaction between two subprocesses could contribute up to 50% of the variation in model performance for some sites, which highlights the need for taking into consideration the interactions of subprocesses to improve LSMs. Finally, a statistical optimal combination of the parameterization schemes is recommended for global land modeling, although it is noticed that the optimal schemes vary with regions and can be different even for neighboring sites.

show abstract

Section: Introductionmentioning

confidence: 99%

Evaluation of Land Surface Subprocesses and Their Impacts on Model Performance With Global Flux Data

Guo

Chen

et al. 2019

J Adv Model Earth Syst

View full text Add to dashboard Cite

show abstract

“…Using multiple summary metrics that measure relevant parts of system behavior, we can gain information about how and where the model may be improved (Sadegh et al, 2015;Vrugt & Sadegh, 2013). In future works, we can simultaneously consider the surrogate and the model structural errors by combining the approach proposed in this work with methods that address model structural inadequacy (e.g., Duan et al, 2007;Madadgar & Moradkhani, 2014;Xu et al, 2017;Xu & Valocchi, 2015;Ye et al, 2010;Zeng et al, 2016;Zeng et al, 2018;Zhang et al, 2019).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Surrogate‐Based Bayesian Inverse Modeling of the Hydrological System: An Adaptive Approach Considering Surrogate Approximation Error

Zhang

Zheng

Chen

et al. 2020

Water Resources Research

View full text Add to dashboard Cite

Bayesian inverse modeling is important for a better understanding of hydrological processes.However, this approach can be computationally demanding, as it usually requires a large number of model evaluations. To address this issue, one can take advantage of surrogate modeling techniques. Nevertheless, when approximation error of the surrogate model is neglected, the inversion result will be biased. In this paper, we develop a surrogate-based Bayesian inversion framework that explicitly quantifies and gradually reduces the approximation error of the surrogate. Specifically, two strategies are proposed to quantify the surrogate error. The first strategy works by quantifying the surrogate prediction uncertainty with a Bayesian method, while the second strategy uses another surrogate to simulate and correct the approximation error of the primary surrogate. By adaptively refining the surrogate over the posterior distribution, we can gradually reduce the surrogate approximation error to a small level. Demonstrated with three case studies involving high dimensionality, multimodality, and a real-world application, it is found that both strategies can reduce the bias introduced by surrogate approximation error, while the second strategy that integrates two methods (i.e., polynomial chaos expansion and Gaussian process in this work) that complement each other shows the best performance.

show abstract

“…While it is possible in principle to further modify the MCMC scheme used to incorporate such constraints, our approach offers a simple and direct way of controlling the number of fine model runs used. Xu et al (2017), Zhang et al (2018), and Lødøen and Tjelmeland (2010) apply the KOH method to account for the approximation errors, and these are incorporated into an adaptive multifidelity MCMC sampler (see, e.g., Peherstorfer et al, 2018), the differential evolution adaptive metropolis (Vrugt et al, 2009;Laloy & Vrugt, 2012) sampler, and the Metropolis-Hastings algorithm (see, e.g., Chib & Greenberg, 1995), respectively. Again, these require more sophisticated understanding and control of the MCMC scheme used and 10.1029/2018WR024240 involve infinte-dimensional stochastic processes following the approach of KOH.…”

Section: Premarginalizationmentioning

confidence: 99%

Incorporating Posterior‐Informed Approximation Errors Into a Hierarchical Framework to Facilitate Out‐of‐the‐Box MCMC Sampling for Geothermal Inverse Problems and Uncertainty Quantification

Maclaren

Nicholson

Bjarkason

et al. 2020

Water Resources Research

View full text Add to dashboard Cite

We consider geothermal inverse problems and uncertainty quantification from a Bayesian perspective. Our main goal is to make standard, "out-of-the-box" Markov chain Monte Carlo (MCMC) sampling more feasible for complex simulation models by using suitable approximations. To do this, we first show how to pose both the inverse and prediction problems in a hierarchical Bayesian framework. We then show how to incorporate so-called posterior-informed model approximation error into this hierarchical framework, using a modified form of the Bayesian approximation error approach. This enables the use of a "coarse," approximate model in place of a finer, more expensive model, while accounting for the additional uncertainty and potential bias that this can introduce. Our method requires only simple probability modeling, a relatively small number of fine model simulations and only modifies the target posterior-any standard MCMC sampling algorithm can be used to sample the new posterior. These corrections can also be used in methods that are not based on MCMC sampling. We show that our approach can achieve significant computational speedups on two geothermal test problems. We also demonstrate the dangers of naively using coarse, approximate models in place of finer models, without accounting for the induced approximation errors. The naive approach tends to give overly confident and biased posteriors while incorporating Bayesian approximation error into our hierarchical framework corrects for this while maintaining computational efficiency and ease of use. Key Points: • We consider geothermal inverse problems and uncertainty quantification from a Bayesian perspective • We present a simple method for incorporating posterior-informed approximation errors into a hierarchical Bayesian framework • Our method makes standard out-of-the-box MCMC sampling feasible for more complex models while correcting for bias and overconfidence Supporting Information: • Supporting Information S1 , M. J. (2020). Incorporating posterior-informed approximation errors into a hierarchical framework to facilitate out-of-the-box MCMC sampling for geothermal inverse problems and uncertainty quantification. Water Resources Research, 56, e2018WR024240. https://

show abstract

Quantifying model structural error: Efficient Bayesian calibration of a regional groundwater flow model using surrogates and a data‐driven error model

Cited by 66 publications

References 69 publications

Evaluation of Land Surface Subprocesses and Their Impacts on Model Performance With Global Flux Data

Evaluation of Land Surface Subprocesses and Their Impacts on Model Performance With Global Flux Data

Surrogate‐Based Bayesian Inverse Modeling of the Hydrological System: An Adaptive Approach Considering Surrogate Approximation Error

Incorporating Posterior‐Informed Approximation Errors Into a Hierarchical Framework to Facilitate Out‐of‐the‐Box MCMC Sampling for Geothermal Inverse Problems and Uncertainty Quantification

Contact Info

Product

Resources

About