Although uncertainty about structures of environmental models (conceptual uncertainty) is often acknowledged to be the main source of uncertainty in model predictions, it is rarely considered in environmental modelling. Rather, formal uncertainty analyses have traditionally focused on model parameters and input data as the principal source of uncertainty in model predictions. The traditional approach to model uncertainty analysis, which considers only a single conceptual model, may fail to adequately sample the relevant space of plausible conceptual models. As such, it is prone to modelling bias and underestimation of predictive uncertainty. In this paper we review a range of strategies for assessing structural uncertainties in models. The existing strategies fall into two categories depending on whether field data are available for the predicted variable of interest. To date, most research has focussed on situations where inferences on the accuracy of a model structure can be made directly on the basis of field data. This corresponds to a situation of ‘interpolation’. However, in many cases environmental models are used for ‘extrapolation’; that is, beyond the situation and the field data available for calibration. In the present paper, a framework is presented for assessing the predictive uncertainties of environmental models used for extrapolation. It involves the use of multiple conceptual models, assessment of their pedigree and reflection on the extent to which the sampled models adequately represent the space of plausible models. � 2005 Elsevier Ltd. All rights reserved.

A Framework for Dealing With Uncertainty due to Model Structure Error

SnowModel is a spatially distributed snow-evolution modeling system designed for application in landscapes, climates, and conditions where snow occurs. It is an aggregation of four submodels: MicroMet defines meteorological forcing conditions, EnBal calculates surface energy exchanges, SnowPack simulates snow depth and water-equivalent evolution, and SnowTran-3D accounts for snow redistribution by wind. Since each of these submodels was originally developed and tested for nonforested conditions, details describing modifications made to the submodels for forested areas are provided. SnowModel was created to run on grid increments of 1 to 200 m and temporal increments of 10 min to 1 day. It can also be applied using much larger grid increments, if the inherent loss in high-resolution (subgrid) information is acceptable. Simulated processes include snow accumulation; blowing-snow redistribution and sublimation; forest canopy interception, unloading, and sublimation; snow-density evolution; and snowp...

A Distributed Snow Evolution Modeling System (SnowModel)

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2018WR024592

Predicting CO 2 Plume Migration in Heterogeneous Formations Using Conditional Deep Convolutional Generative Adversarial Network

Hydrogeological conceptual model building and testing: A review

Surrogate models are commonly used in Bayesian approaches such as Markov Chain Monte Carlo (MCMC) to avoid repetitive CPU-demanding model evaluations. However, the approximation error of a surrogate may lead to biased estimation of the posterior distribution. This bias can be corrected by constructing a very accurate surrogate or implementing MCMC in a two-stage manner. Since the two-stage MCMC requires extra original model evaluations after surrogate evaluations, the computational cost is still high. If the information of measurement is incorporated, a locally accurate surrogate can be adaptively constructed with low computational cost. Based on this idea, we integrate Gaussian process (GP) and MCMC to adaptively construct locally accurate surrogates for Bayesian experimental design in groundwater contaminant source identification problems. Moreover, the uncertainty estimate of GP approximation error is incorporated in the Bayesian formula to avoid over-confident estimation of the posterior distribution. The proposed approach is tested with a numerical case study. Without sacrificing the estimation accuracy, the new approach achieves about 200 times of speed-up compared to our previous work which implemented MCMC in a two-stage manner.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2016WR018598

An adaptive Gaussian process-based method for efficient Bayesian experimental design in groundwater contaminant source identification problems

Assessing the pollution risk of a groundwater source field at western Laizhou Bay under seawater intrusion

Estimating marginal likelihood is of central importance to Bayesian model selection and/or model averaging. The nested sampling method has been recently used together with the MetropolisHasting (M-H) sampling algorithm for estimating marginal likelihood. This study develops a new implementation of nested sampling by using the DiffeRential Evolution Adaptive Metropolis (DREAMzs) sampling algorithm. The two implementations of nested sampling are evaluated for four models of a synthetic groundwater flow modeling. The DREAMzs-based nested sampling outperforms the M-H-based nested sampling in terms of their accuracy, convergence, efficiency, and stability, which is attributed to the fact that DREAMzs is more robust than M-H for parameter sampling. The nested sampling method is also compared with four other methods (arithmetic mean, harmonic mean, stabilized harmonic mean, and thermodynamic integration) commonly used for estimating marginal likelihood and posterior probability of the four groundwater models. The comparative study requires hundreds of millions of model executions, which would not be possible without using surrogate models to replace the original models. Using the arithmetic mean estimator as the reference, the comparison reveals that thermodynamic integration outperforms nested sampling in terms of accuracy and stability, whereas nested sampling is more computationally efficient to reach to convergence. The harmonic mean and stabilized harmonic mean methods give the worst marginal likelihood estimation. Accurate marginal likelihood estimation is important for accurate estimation of posterior model probability and better predictive performance of Bayesian model averaging.

https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1002/2017WR020782

Xiaobin Zhu

Papers

Assessing the pollution risk of a groundwater source field at western Laizhou Bay under seawater intrusion

Improved Nested Sampling and Surrogate-Enabled Comparison With Other Marginal Likelihood Estimators

Evaluating two sparse grid surrogates and two adaptation criteria for groundwater Bayesian uncertainty quantification

Assessing Bayesian model averaging uncertainty of groundwater modeling based on information entropy method

Identifying key factors of the seawater intrusion model of Dagu river basin, Jiaozhou Bay