A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow

Yustres, Ángel; Asensio, Laura; Alonso, J.; Navarro, Vicente

doi:10.1007/s10596-011-9249-z

Cited by 32 publications

(16 citation statements)

References 134 publications

(178 reference statements)

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“…Furthermore, Refs. [24,68,69], etc. also have studied conceptual model uncertainty based on IC-BMA method.…”

Section: Uncertainty Analysis Of Groundwater Conceptual Modelmentioning

confidence: 99%

Review of the uncertainty analysis of groundwater numerical simulation

Zeng

2013

Chin. Sci. Bull.

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Groundwater system is a complex and open system, which is affected by natural conditions and human activities. Natural hydrological processes is conceptualized through relatively simple flow governing equations in groundwater models. Moreover, observation data is always limited in field hydrogeological conditions. Therefore, the predictive results of groundwater simulation often deviate from true values, which is attribute to the uncertainty of groundwater numerical simulation. According to the process of system simulation, the uncertainty sources of groundwater numerical simulation can be divided into model parameters, conceptual model and observation data uncertainties. In addition, the uncertainty stemmed from boundary conditions is sometimes refered as scenario uncertainty. In this paper, the origination and category of groundwater modeling uncertainty are analyzed. The recent progresses on the methods of groundwater modeling uncertainty analysis are reivewed. Furthermore, the researches on the comprehensive analysis of uncertainty sources, and the predictive uncertainty of model outputs are discussed. Finally, several prospects on the deveolpment of groundwater modeling uncetainty analysis are proposed.groundwater modeling, uncertainty analysis, model parameter, conceptual model, observation data Citation:

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“…Furthermore, Refs. [24,68,69], etc. also have studied conceptual model uncertainty based on IC-BMA method.…”

Section: Uncertainty Analysis Of Groundwater Conceptual Modelmentioning

confidence: 99%

Review of the uncertainty analysis of groundwater numerical simulation

Zeng

2013

Chin. Sci. Bull.

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“…As alternative approaches, the Bayesian inverse methods, e.g., Markov Chain Monte Carlo (MCMC) [ Haario et al ., ], are able to directly incorporate system nonlinearity and different sources of uncertainties. Thus, they are becoming increasingly popular in characterizing uncertainties in hydrologic models [ Laloy et al ., ; Liu et al ., ; Shi et al ., ; Smith and Marshall , ; Vrugt et al ., ; Wang and Jin , ; Wang and Zabaras , ; Yustres et al ., ; Zeng et al ., ]. In the Bayesian approach, all the quantities are modeled as random variables with certain probability distributions.…”

Section: Introductionmentioning

confidence: 99%

“…In many existing studies of Bayesian methods in geophysical inverse problems [ Liu et al ., ; Yustres et al ., ], sampling locations were assumed to be already given before parameter estimation. However, if there is little relevant information provided by measurement data, it is understandable that the knowledge of parameters will be hardly improved, no matter what estimation method is used.…”

Section: Introductionmentioning

confidence: 99%

Efficient Bayesian experimental design for contaminant source identification

et al. 2015

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In this study, an efficient full Bayesian approach is developed for the optimal sampling well location design and source parameters identification of groundwater contaminants. An information measure, i.e., the relative entropy, is employed to quantify the information gain from concentration measurements in identifying unknown parameters. In this approach, the sampling locations that give the maximum expected relative entropy are selected as the optimal design. After the sampling locations are determined, a Bayesian approach based on Markov Chain Monte Carlo (MCMC) is used to estimate unknown parameters. In both the design and estimation, the contaminant transport equation is required to be solved many times to evaluate the likelihood. To reduce the computational burden, an interpolation method based on the adaptive sparse grid is utilized to construct a surrogate for the contaminant transport equation. The approximated likelihood can be evaluated directly from the surrogate, which greatly accelerates the design and estimation process. The accuracy and efficiency of our approach are demonstrated through numerical case studies. It is shown that the methods can be used to assist in both single sampling location and monitoring network design for contaminant source identifications in groundwater.

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“…However, it is difficult to obtain the analytical solution and compute the numerical solution in Equation 14because of the unknown formulation of hydrologic models and too many model parameters [28]. The Markov Chain Monte Carlo (MCMC) scheme provides a simple and effective way around the computational efforts for estimation of the posterior distribution in Equation 14.…”

Section: Model Calibrationmentioning

confidence: 99%

The Use of River Flow Discharge and Sediment Load for Multi-Objective Calibration of SWAT Based on the Bayesian Inference

Cheng

Chen

Wang³

et al. 2018

Water

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The soil and water assessment tool (SWAT) is widely used to quantify the spatial and temporal patterns of sediment loads for watershed-scale management of sediment and nonpoint-source pollutants. However few studies considered the trade-off between flow and sediment objectives during model calibration processes. This study proposes a new multi-objective calibration method that incorporates both flow and sediment observed information into a likelihood function based on the Bayesian inference. For comparison, two likelihood functions, i.e., the Nash–Sutcliffe efficiency coefficient (NSE) approach that assumes model residuals follow the Gaussian distribution, and the BC-GED approach that assumes model residuals after Box–Cox transformation (BC) follow the generalized error distribution (GED), are applied for calibrating the flow and sediment parameters of SWAT with the water balance model and the variable source area concept (SWAT-WB-VSA) in the Baocun watershed, Eastern China. Compared with the single-objective method, the multi-objective approach improves the performance of sediment simulations without significantly impairing the performance of flow simulations, and reduces the uncertainty of flow parameters, especially flow concentration parameters. With the NSE approach, SWAT-WB-VSA captures extreme flood events well, but fails to mimic low values of river discharge and sediment load, possibly because the NSE approach is an informal likelihood function, and puts greater emphasis on high values. By contrast, the BC-GED approach approximates a formal likelihood function, and balances consideration of the high- and low- values. As a result, inferred results of the BC-GED method are more reasonable and consistent with the field survey results and previous related-studies. This method even discriminates the nonerodible characteristic of main channels.

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A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow

Cited by 32 publications

References 134 publications

Review of the uncertainty analysis of groundwater numerical simulation

Review of the uncertainty analysis of groundwater numerical simulation

Efficient Bayesian experimental design for contaminant source identification

The Use of River Flow Discharge and Sediment Load for Multi-Objective Calibration of SWAT Based on the Bayesian Inference

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