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Model Uncertainty in Water Science: Conceptualization, Assessment and Communication
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Model Uncertainty in Water Science: Conceptualization, Assessment and Communication

A special issue of Water (ISSN 2073-4441). This special issue belongs to the section "Hydrology".

Deadline for manuscript submissions: closed (31 December 2019) | Viewed by 31696

Special Issue Editors

Dr. Rodrigo Rojas

E-Mail Website
Guest Editor
CSIRO Land and Water, EcoSciences Precinct, Brisbane, QLD, Australia
Interests: uncertainty quantification; multi-model techniques; Bayesian model averaging; socio-hydrology; climate change impacts on hydrological cycle
Dr. Anneli Guthke

E-Mail Website
Guest Editor
Department of Stochastic Simulation and Safety Research (LS³), University of Stuttgart, Germany
Interests: model error and uncertainty; model selection and combination; stochastic hydro(geo)logical modelling; risk assessment
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Substantial research has been devoted to uncertainty quantification in water sciences in the last few decades. More recently, an actively-investigated aspect is the uncertainty arising from the definition of alternative model conceptualizations describing complex hydro(geo)logical systems. Such systems are, more often than not, conceptualized on the basis of limited, or even biased, data and knowledge, therefore accepting multiple interpretations. This ‘conceptualization problem’ will have substantial impacts on uncertainty quantification and ultimately on risk assessment and water management. This line of research has opened multiple questions from ways to properly define alternative conceptualizations, the value of data/information/knowledge to reduce model uncertainty, model structure diagnostics, frameworks to efficiently combine (or select from) multiple conceptualizations/working hypotheses, to the link with robust risk assessment frameworks. This Special Issue aims to collate contributions addressing the conceptualization, assessment and communication of model uncertainty in water sciences and how these aspects interlink with other domains such as information theory, risk assessment, safety research, water management and decision making. We welcome a broad spectrum of contributions in the form of state-of-the-art reviews, case studies and methodological papers on topics ranging from (but not limited to) frequentist and Bayesian approaches, multi-model techniques, value of data to reduce uncertainties, to applied aspects covering water management, decision making and risk management under model uncertainty.

Dr. Rodrigo Rojas
Dr. Anneli Guthke
Guest Editors

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • conceptual model uncertainty
  • model structural adequacy
  • predictive uncertainty
  • perceptual model development
  • model structure diagnostics
  • multi-model approaches
  • data-worth analysis
  • decision making under model uncertainty
  • risk assessment under model uncertainty
  • communication of model uncertainty

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Published Papers (7 papers)

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Research

23 pages, 3193 KiB  
Communication
Being Bayesian: Discussions from the Perspectives of Stakeholders and Hydrologists
by Ty P.A. Ferre
Water 2020, 12(2), 461; https://doi.org/10.3390/w12020461 - 9 Feb 2020
Cited by 3 | Viewed by 3019
Abstract
Bayes’ Theorem is gaining acceptance in hydrology, but it is still far from standard practice to cast hydrologic analyses in a Bayesian context—especially in the realm of hydrologic practice. Three short discussions are presented to encourage more complete adoption of a Bayesian approach. [...] Read more.
Bayes’ Theorem is gaining acceptance in hydrology, but it is still far from standard practice to cast hydrologic analyses in a Bayesian context—especially in the realm of hydrologic practice. Three short discussions are presented to encourage more complete adoption of a Bayesian approach. The first, aimed at a stakeholder audience, seeks to explain that an informal Bayesian analysis is the default approach that we all take to any decision made under uncertainty. The second, aimed at a general hydrologist audience, seeks to establish multi-model approaches as the natural choice for Bayesian hydrologic analysis. The goal of this discussion is to provide a bridge from the stakeholder’s natural approach to a more formal, quantitative Bayesian analysis. The third discussion is targeted to a more advanced hydrologist audience, suggesting that some elements of hydrologic practice do not yet reflect a Bayesian philosophy. In particular, an example is given that puts Bayes Theory to work to identify optimal observation sets before data are collected. Full article
(This article belongs to the Special Issue Model Uncertainty in Water Science: Conceptualization, Assessment and Communication)
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16 pages, 1144 KiB  
Article
Bayesian Model Weighting: The Many Faces of Model Averaging
by Marvin Höge, Anneli Guthke and Wolfgang Nowak
Water 2020, 12(2), 309; https://doi.org/10.3390/w12020309 - 21 Jan 2020
Cited by 10 | Viewed by 5276
Abstract
Model averaging makes it possible to use multiple models for one modelling task, like predicting a certain quantity of interest. Several Bayesian approaches exist that all yield a weighted average of predictive distributions. However, often, they are not properly applied which can lead [...] Read more.
Model averaging makes it possible to use multiple models for one modelling task, like predicting a certain quantity of interest. Several Bayesian approaches exist that all yield a weighted average of predictive distributions. However, often, they are not properly applied which can lead to false conclusions. In this study, we focus on Bayesian Model Selection (BMS) and Averaging (BMA), Pseudo-BMS/BMA and Bayesian Stacking. We want to foster their proper use by, first, clarifying their theoretical background and, second, contrasting their behaviours in an applied groundwater modelling task. We show that only Bayesian Stacking has the goal of model averaging for improved predictions by model combination. The other approaches pursue the quest of finding a single best model as the ultimate goal, and use model averaging only as a preliminary stage to prevent rash model choice. Improved predictions are thereby not guaranteed. In accordance with so-called M -settings that clarify the alleged relations between models and truth, we elicit which method is most promising. Full article
(This article belongs to the Special Issue Model Uncertainty in Water Science: Conceptualization, Assessment and Communication)
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15 pages, 2241 KiB  
Article
Application of the Iterative Ensemble Smoother Method and Cloud Computing: A Groundwater Modeling Case Study
by Kevin Hayley, Alexis Valenza, Emma White, Bruce Hutchison and Jens Schumacher
Water 2019, 11(8), 1649; https://doi.org/10.3390/w11081649 - 9 Aug 2019
Cited by 7 | Viewed by 4127
Abstract
Numerical groundwater modelling to support mining decisions is often challenging and time consuming. Simulation of open pit mining for model calibration or prediction requires models that include unsaturated flow, large magnitude hydraulic gradients and often require transient simulations with time varying material properties [...] Read more.
Numerical groundwater modelling to support mining decisions is often challenging and time consuming. Simulation of open pit mining for model calibration or prediction requires models that include unsaturated flow, large magnitude hydraulic gradients and often require transient simulations with time varying material properties and boundary conditions. This combination of factors typically results in models with long simulation times and/or some level of numerical instability. In modelling practice, long run times and instability can result in reduced effort for predictive uncertainty analysis, and ultimately decrease the value of the decision-support modelling. This study presents an early application of the Iterative Ensemble Smoother (IES) method of calibration-constrained uncertainty analysis to a mining groundwater flow model. The challenges of mining models and uncertainty quantification were addressed using the IES method and facilitated by highly parallelized cloud computing. The project was an open pit mine in South Australia that required predictions of pit water levels and inflow rates to guide the design of a proposed pumped hydro energy storage system. The IES calibration successfully produced 150 model parameter realizations that acceptably reproduced groundwater observations. The flexibility of the IES method allowed for the inclusion of 1493 adjustable parameters and geostatistical realizations of hydraulic conductivity fields to be included in the analysis. Through the geostatistical realizations and IES analysis, alternative conceptual models of fractured rock aquifer orientation and connections could be conditioned to observation data and used for predictive uncertainty analysis. Importantly, the IES method out-performed finite difference methods when model simulations contained small magnitude numerical instabilities. Full article
(This article belongs to the Special Issue Model Uncertainty in Water Science: Conceptualization, Assessment and Communication)
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25 pages, 1298 KiB  
Article
Making Steppingstones out of Stumbling Blocks: A Bayesian Model Evidence Estimator with Application to Groundwater Transport Model Selection
by Ahmed S. Elshall and Ming Ye
Water 2019, 11(8), 1579; https://doi.org/10.3390/w11081579 - 30 Jul 2019
Cited by 6 | Viewed by 4025
Abstract
Bayesian model evidence (BME) is a measure of the average fit of a model to observation data given all the parameter values that the model can assume. By accounting for the trade-off between goodness-of-fit and model complexity, BME is used for model selection [...] Read more.
Bayesian model evidence (BME) is a measure of the average fit of a model to observation data given all the parameter values that the model can assume. By accounting for the trade-off between goodness-of-fit and model complexity, BME is used for model selection and model averaging purposes. For strict Bayesian computation, the theoretically unbiased Monte Carlo based numerical estimators are preferred over semi-analytical solutions. This study examines five BME numerical estimators and asks how accurate estimation of the BME is important for penalizing model complexity. The limiting cases for numerical BME estimators are the prior sampling arithmetic mean estimator (AM) and the posterior sampling harmonic mean (HM) estimator, which are straightforward to implement, yet they result in underestimation and overestimation, respectively. We also consider the path sampling methods of thermodynamic integration (TI) and steppingstone sampling (SS) that sample multiple intermediate distributions that link the prior and the posterior. Although TI and SS are theoretically unbiased estimators, they could have a bias in practice arising from numerical implementation. For example, sampling errors of some intermediate distributions can introduce bias. We propose a variant of SS, namely the multiple one-steppingstone sampling (MOSS) that is less sensitive to sampling errors. We evaluate these five estimators using a groundwater transport model selection problem. SS and MOSS give the least biased BME estimation at an efficient computational cost. If the estimated BME has a bias that covariates with the true BME, this would not be a problem because we are interested in BME ratios and not their absolute values. On the contrary, the results show that BME estimation bias can be a function of model complexity. Thus, biased BME estimation results in inaccurate penalization of more complex models, which changes the model ranking. This was less observed with SS and MOSS as with the three other methods. Full article
(This article belongs to the Special Issue Model Uncertainty in Water Science: Conceptualization, Assessment and Communication)
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24 pages, 4506 KiB  
Article
Hydrogeological Bayesian Hypothesis Testing through Trans-Dimensional Sampling of a Stochastic Water Balance Model
by Trine Enemark, Luk JM Peeters, Dirk Mallants, Okke Batelaan, Andrew P. Valentine and Malcolm Sambridge
Water 2019, 11(7), 1463; https://doi.org/10.3390/w11071463 - 15 Jul 2019
Cited by 10 | Viewed by 4903
Abstract
Conceptual uncertainty is considered one of the major sources of uncertainty in groundwater flow modelling. In this regard, hypothesis testing is essential to increase system understanding by refuting alternative conceptual models. Often a stepwise approach, with respect to complexity, is promoted but hypothesis [...] Read more.
Conceptual uncertainty is considered one of the major sources of uncertainty in groundwater flow modelling. In this regard, hypothesis testing is essential to increase system understanding by refuting alternative conceptual models. Often a stepwise approach, with respect to complexity, is promoted but hypothesis testing of simple groundwater models is rarely applied. We present an approach to model-based Bayesian hypothesis testing in a simple groundwater balance model, which involves optimization of a model in function of both parameter values and conceptual model through trans-dimensional sampling. We apply the methodology to the Wildman River area, Northern Territory, Australia, where we set up 32 different conceptual models. A factorial approach to conceptual model development allows for direct attribution of differences in performance to individual uncertain components of the conceptual model. The method provides a screening tool for prioritizing research efforts while also giving more confidence to the predicted water balance compared to a deterministic water balance solution. We show that the testing of alternative conceptual models can be done efficiently with a simple additive and linear groundwater balance model and is best done relatively early in the groundwater modelling workflow. Full article
(This article belongs to the Special Issue Model Uncertainty in Water Science: Conceptualization, Assessment and Communication)
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24 pages, 4679 KiB  
Article
Analysis of the Effect of Uncertainty in Rainfall-Runoff Models on Simulation Results Using a Simple Uncertainty-Screening Method
by Mun-Ju Shin and Chung-Soo Kim
Water 2019, 11(7), 1361; https://doi.org/10.3390/w11071361 - 30 Jun 2019
Cited by 4 | Viewed by 3046
Abstract
Various uncertainty analysis methods have been used in various studies to analyze the uncertainty of rainfall-runoff models; however, these methods are difficult to apply immediately as they require a long learning time. In this study, we propose a simple uncertainty-screening method that allows [...] Read more.
Various uncertainty analysis methods have been used in various studies to analyze the uncertainty of rainfall-runoff models; however, these methods are difficult to apply immediately as they require a long learning time. In this study, we propose a simple uncertainty-screening method that allows modelers to investigate relatively easily the uncertainty of rainfall-runoff models. The 100 best parameter values of three rainfall-runoff models were extracted using the efficient sampler DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm, and the distribution of the parameter values was investigated. Additionally, the ranges of the values of a model performance evaluation statistic and indicators of hydrologic alteration corresponding to the 100 parameter values for the calibration and validation periods was analyzed. The results showed that the Sacramento model, which has the largest number of parameters, had uncertainties in parameters, and the uncertainty of one parameter influenced all other parameters. Furthermore, the uncertainty in the prediction results of the Sacramento model was larger than those of other models. The IHACRES model had uncertainty in one parameter related to the slow flow simulation. On the other hand, the GR4J model had the lowest uncertainty compared to the other two models. The uncertainty-screening method presented in this study can be easily used when the modelers select rainfall-runoff models with lower uncertainty. Full article
(This article belongs to the Special Issue Model Uncertainty in Water Science: Conceptualization, Assessment and Communication)
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24 pages, 1571 KiB  
Article
Evaluation of Four GLUE Likelihood Measures and Behavior of Large Parameter Samples in ISPSO-GLUE for TOPMODEL
by Huidae Cho, Jeongha Park and Dongkyun Kim
Water 2019, 11(3), 447; https://doi.org/10.3390/w11030447 - 3 Mar 2019
Cited by 8 | Viewed by 4319
Abstract
We tested four likelihood measures including two limits of acceptability and two absolute model residual methods within the generalized likelihood uncertainty estimation (GLUE) framework using the topography model (TOPMODEL). All these methods take the worst performance of all time steps as the likelihood [...] Read more.
We tested four likelihood measures including two limits of acceptability and two absolute model residual methods within the generalized likelihood uncertainty estimation (GLUE) framework using the topography model (TOPMODEL). All these methods take the worst performance of all time steps as the likelihood of a model and none of these methods were successful in finding any behavioral models. We believe that reporting this failure is important because it shifted our attention from which likelihood measure to choose to why these four methods failed and how to improve these methods. We also observed how large parameter samples impact the performance of a hybrid uncertainty estimation method, isolated-speciation-based particle swarm optimization (ISPSO)-GLUE using the Nash–Sutcliffe (NS) coefficient. Unlike GLUE with random sampling, ISPSO-GLUE provides traditional calibrated parameters as well as uncertainty analysis, so over-conditioning the model parameters on the calibration data can affect its uncertainty analysis results. ISPSO-GLUE showed similar performance to GLUE with a lot less model runs, but its uncertainty bounds enclosed less observed flows. However, both methods failed in validation. These findings suggest that ISPSO-GLUE can be affected by over-calibration after a long evolution of samples and imply that there is a need for a likelihood measure that can better explain uncertainties from different sources without making statistical assumptions. Full article
(This article belongs to the Special Issue Model Uncertainty in Water Science: Conceptualization, Assessment and Communication)
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