Epistemic uncertainties and natural hazard risk assessment ­ Part 1: A review of the issues

Abstract. Uncertainties in natural hazard risk assessment are generally dominated by the sources arising from lack of knowledge or understanding of the processes involved. There is a lack of knowledge about frequencies, process representations, parameters, present and future boundary conditions, consequences and impacts, and the meaning of observations in evaluating simulation models. These are the epistemic uncertainties that can be difficult to constrain, especially in terms of event or scenario probabilities, even as elicited probabilities rationalized on the basis of expert judgements. This paper reviews the issues raised by trying to quantify the effects of epistemic uncertainties. Such scientific uncertainties might have significant influence on decisions that are made for risk management, so it is important to communicate the meaning of an uncertainty estimate and to provide an audit trail of the assumptions on which it is based. Some suggestions for good practice in doing so are made.

[1]  Cosma Rohilla Shalizi,et al.  Philosophy and the practice of Bayesian statistics. , 2010, The British journal of mathematical and statistical psychology.

[2]  Robert McCaffrey,et al.  Global frequency of magnitude 9 earthquakes , 2008 .

[3]  Stefano Tarantola,et al.  A General Probabilistic Framework for uncertainty and global sensitivity analysis of deterministic models: A hydrological case study , 2014, Environ. Model. Softw..

[4]  D. Spiegelhalter,et al.  Twenty tips for interpreting scientific claims , 2013 .

[5]  Keith Beven,et al.  Fuzzy set approach to calibrating distributed flood inundation models using remote sensing observations , 2006 .

[6]  Richard Robertson,et al.  The Eruption of Soufriere Hills Volcano, Montserrat from 2000 to 2010 , 2015 .

[7]  Antonella Peresan,et al.  Recent Achievements of the Neo‐Deterministic Seismic Hazard Assessment in the CEI Region , 2008 .

[8]  Chris R. Johnson,et al.  A Next Step: Visualizing Errors and Uncertainty , 2003, IEEE Computer Graphics and Applications.

[9]  J.R.A. Giles,et al.  Introduction to integrated environmental modelling to solve real world problems: methods, vision and challenges , 2016, Special Publications.

[10]  Christopher G Newhall,et al.  Constructing event trees for volcanic crises , 2002 .

[11]  Andrea Saltelli,et al.  Sensitivity Analysis for Importance Assessment , 2002, Risk analysis : an official publication of the Society for Risk Analysis.

[12]  R. M. Cooke,et al.  Evaluation of a Performance-Based Expert Elicitation: WHO Global Attribution of Foodborne Diseases , 2016, PloS one.

[13]  Luc Anselin,et al.  Visualizing Seismic Risk and Uncertainty , 2008, Annals of the New York Academy of Sciences.

[14]  N. Addor,et al.  Bias correction for hydrological impact studies – beyond the daily perspective , 2014 .

[15]  Robert L. Wilby,et al.  Major droughts in England and Wales, 1800–2006 , 2007 .

[16]  F. Brissette,et al.  Finding appropriate bias correction methods in downscaling precipitation for hydrologic impact studies over North America , 2013 .

[17]  Francesco Serinaldi,et al.  Dismissing return periods! , 2015, Stochastic Environmental Research and Risk Assessment.

[18]  Jeroen P. van der Sluijs,et al.  A framework for dealing with uncertainty due to model structure error , 2004 .

[19]  R. T. Cox Probability, frequency and reasonable expectation , 1990 .

[20]  Keith Beven,et al.  Informal likelihood measures in model assessment: Theoretic development and investigation , 2008 .

[21]  Keith Beven,et al.  A framework for uncertainty analysis , 2014 .

[22]  Alex Pang,et al.  Visualizing Uncertainty in Natural Hazards , 2008 .

[23]  Keith Beven,et al.  Concepts of Information Content and Likelihood in Parameter Calibration for Hydrological Simulation Models , 2014 .

[24]  Keith Beven,et al.  Climate change and fluvial flood risk in the UK: more of the same? , 2008 .

[25]  Jim W. Hall,et al.  Flood Risk Management: Decision Making Under Uncertainty , 2014 .

[26]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[27]  Y. Ben-Haim Info-Gap Decision Theory: Decisions Under Severe Uncertainty , 2006 .

[28]  George B. Arhonditsis,et al.  Bayesian calibration of mathematical models: Optimization of model structure and examination of the role of process error covariance , 2013, Ecol. Informatics.

[29]  Robin K. S. Hankin,et al.  Bayesian calibration of a flood inundation model using spatial data , 2011 .

[30]  R. Cooke Experts in Uncertainty: Opinion and Subjective Probability in Science , 1991 .

[31]  Jim W. Hall,et al.  Towards risk-based flood hazard management in the UK , 2002 .

[32]  Prospect Theory by Peter P. Wakker , 2010 .

[33]  Adrienne Grêt-Regamey,et al.  Visualization of uncertainty in natural hazards assessments using an interactive cartographic information system , 2011 .

[34]  Robert M. Hirsch,et al.  Flood trends: Not higher but more often , 2015 .

[35]  Gary J. Hunter,et al.  Responding to the consequences of uncertainty in geographical data , 2002, Int. J. Geogr. Inf. Sci..

[36]  Jerome L. Stein,et al.  Shallow Versus Deep Uncertainties in Natural Hazard Assessments , 2013 .

[37]  David R. Easterling,et al.  Probable maximum precipitation and climate change , 2013 .

[38]  Keith Beven,et al.  Stage‐discharge uncertainty derived with a non‐stationary rating curve in the Choluteca River, Honduras , 2011 .

[39]  P. Diggle,et al.  Monte Carlo Methods of Inference for Implicit Statistical Models , 1984 .

[40]  Richard G. Jones,et al.  Comparison of the use of alternative UKCP09 products for modelling the impacts of climate change on flood frequency , 2012, Climatic Change.

[41]  Keith Beven,et al.  I believe in climate change but how precautionary do we need to be in planning for the future? , 2011 .

[42]  Paul D. Bates,et al.  Improving River Flood Extent Delineation From Synthetic Aperture Radar Using Airborne Laser Altimetry , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[43]  Deborah G. Mayo,et al.  Error and the Growth of Experimental Knowledge , 1996 .

[44]  Jeremy E. Oakley,et al.  Probability is perfect, but we can't elicit it perfectly , 2004, Reliab. Eng. Syst. Saf..

[45]  V. Kreinovich,et al.  Experimental uncertainty estimation and statistics for data having interval uncertainty. , 2007 .

[46]  B. M. Hill,et al.  Theory of Probability , 1990 .

[47]  K. Beven,et al.  A limits of acceptability approach to model evaluation and uncertainty estimation in flood frequency estimation by continuous simulation: Skalka catchment, Czech Republic , 2009 .

[48]  Julian J. Bommer,et al.  The Use and Misuse of Logic Trees in Probabilistic Seismic Hazard Analysis , 2008 .

[49]  Eva Rubio,et al.  Random sets of probability measures in slope hydrology and stability analysis , 2004 .

[50]  David Wooff,et al.  Bayes Linear Statistics , 2007 .

[51]  Warner Marzocchi,et al.  Testing for ontological errors in probabilistic forecasting models of natural systems , 2014, Proceedings of the National Academy of Sciences.

[52]  Yakov Ben-Haim,et al.  Chapter 2 – Uncertainty , 2006 .

[53]  S. Dessai,et al.  Is Weather Event Attribution Necessary for Adaptation Funding? , 2011, Science.

[54]  Keith Beven,et al.  Flood frequency estimation by continuous simulation under climate change (with uncertainty) , 2000 .

[55]  Jim W Hall,et al.  Uncertainty analysis in a slope hydrology and stability model using probabilistic and imprecise information , 2004 .

[56]  Keith Beven,et al.  Modelling extreme rainfalls using a modified random pulse Bartlett–Lewis stochastic rainfall model (with uncertainty) , 2000 .

[57]  Jim W. Hall,et al.  Sensitivity analysis of environmental models: A systematic review with practical workflow , 2014, Environ. Model. Softw..

[58]  Jim W. Hall,et al.  A framework for uncertainty analysis in flood risk management decisions , 2008 .

[59]  Jim Freer,et al.  Towards a limits of acceptability approach to the calibration of hydrological models : Extending observation error , 2009 .

[60]  Demetris Koutsoyiannis,et al.  Statistical analysis of hydroclimatic time series: Uncertainty and insights , 2007 .

[61]  J. Vrugt,et al.  Toward diagnostic model calibration and evaluation: Approximate Bayesian computation , 2013 .

[62]  Keith Beven,et al.  Causal models as multiple working hypotheses about environmental processes , 2012 .

[63]  Julian J. Bommer,et al.  DETERMINISTIC VS. PROBABILISTIC SEISMIC HAZARD ASSESSMENT: AN EXAGGERATED AND OBSTRUCTIVE DICHOTOMY , 2002 .

[64]  D. G. Rees,et al.  Foundations of Statistics , 1989 .

[65]  Donald W. Newton,et al.  Realistic Assessment of Maximum Flood Potentials , 1983 .

[66]  Keith Beven,et al.  On the colour and spin of epistemic error (and what we might do about it) , 2011 .

[67]  Keith Beven,et al.  Towards the use of catchment geomorphology in flood frequency predictions , 1987 .

[68]  Yan Y. Kagan,et al.  Tohoku earthquake: a surprise? , 2011, 1112.5217.

[69]  J. C. Refsgaard,et al.  The role of uncertainty in climate change adaptation strategies—A Danish water management example , 2013, Mitigation and Adaptation Strategies for Global Change.

[70]  David J Spiegelhalter,et al.  Don't know, can't know: embracing deeper uncertainties when analysing risks , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[71]  Mark A Burgman,et al.  Policy: Twenty tips for interpreting scientific claims , 2013, Nature.

[72]  E.Marshall Hansen,et al.  Probable maximum precipitation for design floods in the United States , 1987 .

[73]  D. J. Nott,et al.  Approximate Bayesian Computation and Bayes’ Linear Analysis: Toward High-Dimensional ABC , 2011, 1112.4755.

[74]  Peter Walley,et al.  Towards a unified theory of imprecise probability , 2000, Int. J. Approx. Reason..

[75]  Natalia I. Deligne,et al.  Recurrence rates of large explosive volcanic eruptions , 2010 .

[76]  David B. Stephenson,et al.  Calibration Strategies: A Source of Additional Uncertainty in Climate Change Projections , 2012 .

[77]  J. Freer,et al.  Benchmarking observational uncertainties for hydrology: rainfall, river discharge and water quality , 2012 .

[78]  Keith Beven,et al.  Framework for assessing uncertainty in fluvial flood risk mapping , 2014 .

[79]  Robert S. Anderson,et al.  Risk and Uncertainty Assessment for Natural Hazards , 2014 .

[80]  Luis A. Dalguer,et al.  Earthquake supercycle in subduction zones controlled by the width of the seismogenic zone , 2015 .

[81]  Peter J. Baxter,et al.  Chapter 22 Evaluating the respiratory health risks of volcanic ash at the eruption of the Soufrière Hills Volcano, Montserrat, 1995 to 2010 , 2014 .

[82]  Maarten S. Krol,et al.  Identification and classification of uncertainties in the application of environmental models , 2010, Environ. Model. Softw..

[83]  Keith Beven,et al.  Towards a coherent philosophy for environmental modelling. , 2002 .

[84]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[85]  Michael Goldstein,et al.  Reified Bayesian modelling and inference for physical systems , 2009 .

[86]  P. Walley Statistical Reasoning with Imprecise Probabilities , 1990 .

[87]  A. Barros,et al.  Probable Maximum Precipitation Estimation Using Multifractals: Application in the Eastern United States , 2003 .

[88]  T. Wigley,et al.  Global temperature variations between 1861 and 1984 , 1986, Nature.

[89]  Peter A. Vanrolleghem,et al.  Uncertainty in the environmental modelling process - A framework and guidance , 2007, Environ. Model. Softw..

[90]  B. D. Finetti La prévision : ses lois logiques, ses sources subjectives , 1937 .

[91]  Caio A. S. Coelho,et al.  On the visualization, verification and recalibration of ternary probabilistic forecasts , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[92]  Louis Anthony Cox,et al.  Confronting Deep Uncertainties in Risk Analysis , 2012, Risk analysis : an official publication of the Society for Risk Analysis.

[93]  Leonard A. Smith,et al.  An Evaluation of Decadal Probability Forecasts from State-of-the-Art Climate Models* , 2013 .

[94]  Thorsten Wagener,et al.  A vulnerability driven approach to identify adverse climate and land use change combinations for critical hydrologic indicator thresholds: Application to a watershed in Pennsylvania, USA , 2014 .

[95]  R. Wilby,et al.  Scenario-neutral approach to climate change impact studies: Application to flood risk , 2010 .

[96]  Keith Beven,et al.  The uncertainty cascade in model fusion , 2014 .

[97]  Peter C. Young,et al.  Visualization approaches for communicating real‐time flood forecasting level and inundation information , 2010 .

[98]  W. Marzocchi,et al.  BET_VH: a probabilistic tool for long-term volcanic hazard assessment , 2010 .

[99]  Helen Couclelis,et al.  The Certainty of Uncertainty: GIS and the Limits of Geographic Knowledge , 2003, Trans. GIS.

[100]  G. Di Baldassarre,et al.  Towards understanding the dynamic behaviour of floodplains as human-water systems , 2013 .

[101]  Wisdom M. Dlamini,et al.  A Bayesian belief network analysis of factors influencing wildfire occurrence in Swaziland , 2010, Environ. Model. Softw..

[102]  J. Douglas,et al.  Toward a ground-motion logic tree for probabilistic seismic hazard assessment in Europe , 2012, Journal of Seismology.

[103]  Demetris Koutsoyiannis,et al.  A probabilistic view of hershfield's method for estimating probable maximum precipitation , 1999 .

[104]  Ulrich Raape,et al.  Explicit Modeling and Visualization of Imperfect Information in the Context of Decision Support for Tsunami Early Warning in Indonesia , 2011, HCI.

[105]  Mark Gahegan,et al.  Visualizing Geospatial Information Uncertainty: What We Know and What We Need to Know , 2005 .

[106]  Y. Ogata,et al.  Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogues , 1993 .

[107]  Keith Beven,et al.  Probabilistic flood risk mapping including spatial dependence , 2013 .

[108]  F. Dottori,et al.  Detailed data is welcome, but with a pinch of salt: Accuracy, precision, and uncertainty in flood inundation modeling , 2013 .

[109]  Robin K. McGuire,et al.  Deterministic vs. probabilistic earthquake hazards and risks , 2001 .

[110]  S. Funtowicz,et al.  Combining Quantitative and Qualitative Measures of Uncertainty in Model‐Based Environmental Assessment: The NUSAP System , 2005, Risk analysis : an official publication of the Society for Risk Analysis.

[111]  Benjamin P. Bryant,et al.  Thinking Inside the Box , 2010 .

[112]  David B. Stephenson,et al.  Serial Clustering of Extratropical Cyclones , 2006 .

[113]  Keith Beven,et al.  Facets of uncertainty: epistemic uncertainty, non-stationarity, likelihood, hypothesis testing, and communication , 2016 .

[114]  D. Berry,et al.  Statistics: Theory and Methods , 1990 .

[115]  Demetris Koutsoyiannis,et al.  Climate change, the Hurst phenomenon, and hydrological statistics , 2003 .

[116]  Joseph Y. Halpern Reasoning about uncertainty , 2003 .

[117]  Jim W. Hall,et al.  Handling uncertainty in the hydroinformatic process , 2003 .

[118]  Keith Beven,et al.  Developing a Translational Discourse to Communicate Uncertainty in Flood Risk between Science and the Practitioner , 2007, Ambio.

[119]  P. Wakker Prospect Theory: Frontmatter , 2010 .

[120]  Julien Ruffault,et al.  Projecting future drought in Mediterranean forests: bias correction of climate models matters! , 2014, Theoretical and Applied Climatology.

[121]  Jim W. Hall,et al.  Information gap analysis of flood model uncertainties and regional frequency analysis , 2010 .

[122]  Keith Beven,et al.  So how much of your error is epistemic? Lessons from Japan and Italy , 2013 .

[123]  Jim W. Hall,et al.  Probabilistic climate scenarios may misrepresent uncertainty and lead to bad adaptation decisions , 2007 .

[124]  Praveen Kumar,et al.  Typology of hydrologic predictability , 2011 .

[125]  Yan Y. Kagan,et al.  Accuracy of modern global earthquake catalogs , 2003 .

[126]  Servando De la Cruz-Reyna,et al.  A statistical method linking geological and historical eruption time series for volcanic hazard estimations: Applications to active polygenetic volcanoes , 2008 .

[127]  Willy P Aspinall,et al.  An expert judgement assessment of future sea level rise from the ice sheets , 2013 .

[128]  G. Holland,et al.  A Weibull Approach for Improving Climate Model Projections of Tropical Cyclone Wind-Speed Distributions , 2014 .

[129]  Wayne J. Graham Should dams be modified for the probable maximum flood , 2000 .

[130]  David B. Stephenson,et al.  Serial clustering of intense European storms , 2009 .

[131]  Keith Beven,et al.  A guide to good practice in modeling semantics for authors and referees , 2013 .

[132]  Keith Beven,et al.  Modelling everything everywhere: a new approach to decision-making for water management under uncertainty , 2012 .

[133]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[134]  Gottfried Grünthal,et al.  A Statistical Method for Estimating Catalog Completeness Applicable to Long-Term Nonstationary Seismicity Data , 2012 .

[135]  P. Reed,et al.  Hydrology and Earth System Sciences Discussions Comparing Sensitivity Analysis Methods to Advance Lumped Watershed Model Identification and Evaluation , 2022 .

[136]  Jeremy E. Oakley,et al.  Uncertain Judgements: Eliciting Experts' Probabilities , 2006 .

[137]  Demetris Koutsoyiannis,et al.  A blueprint for process‐based modeling of uncertain hydrological systems , 2012 .

[138]  Alberto Montanari,et al.  What do we mean by ‘uncertainty’? The need for a consistent wording about uncertainty assessment in hydrology , 2007 .

[139]  Peter J Mumby,et al.  Temporal clustering of tropical cyclones and its ecosystem impacts , 2011, Proceedings of the National Academy of Sciences.

[140]  F. Vaccari,et al.  Neo-Deterministic and Probabilistic Seismic Hazard Assessments: a Comparison over the Italian Territory , 2011 .

[141]  D. Leedal,et al.  Translating Uncertainty in Flood Risk Science , 2014 .

[142]  T. Utsu,et al.  43 - Statistical Features of Seismicity , 2002 .

[143]  P. Wakker Prospect Theory: For Risk and Ambiguity , 2010 .

[144]  Izuru Takewaki,et al.  Info-gap robust design with load and model uncertainties , 2005 .

[145]  Florian Pappenberger,et al.  Visualizing probabilistic flood forecast information: expert preferences and perceptions of best practice in uncertainty communication , 2011 .

[146]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[147]  K. Beven Towards a coherent philosophy for modelling the environment , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[148]  Mike Pearson,et al.  Visualizing Uncertainty About the Future , 2022 .

[149]  Hiroo Kanamori,et al.  Seismicity and the subduction process , 1980 .

[150]  A. Scolobig,et al.  Insights from socio-hydrology modelling on dealing with flood risk - Roles of collective memory, risk-taking attitude and trust , 2013 .

[151]  David M. Hershfield,et al.  Estimating the Probable Maximum Precipitation , 1961 .

[152]  F. O. Hoffman,et al.  Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. , 1994, Risk analysis : an official publication of the Society for Risk Analysis.

[153]  Dorota Kurowicka,et al.  Eliciting conditional and unconditional rank correlations from conditional probabilities , 2008, Reliab. Eng. Syst. Saf..

[154]  F. Pappenberger,et al.  Ignorance is bliss: Or seven reasons not to use uncertainty analysis , 2006 .

[155]  Thorsten Wagener,et al.  Probabilistic Projections of Climate Change for the Mid-Atlantic Region of the United States: Validation of Precipitation Downscaling during the Historical Era* , 2012 .

[156]  M. V. Asselt,et al.  The future shocks: On discontinuity and scenario development , 2005 .

[157]  Hilary McMillan,et al.  Rating curve estimation under epistemic uncertainty , 2015 .

[158]  Jim W. Hall,et al.  Imprecise probabilities of climate change: aggregation of fuzzy scenarios and model uncertainties , 2007 .

[159]  Durga Rao Karanki,et al.  Uncertainty Analysis Based on Probability Bounds (P‐Box) Approach in Probabilistic Safety Assessment , 2009, Risk analysis : an official publication of the Society for Risk Analysis.

[160]  Jonathan Rougier,et al.  Probabilistic Inference for Future Climate Using an Ensemble of Climate Model Evaluations , 2007 .

[161]  Keith Beven,et al.  Smiling in the rain: Seven reasons to be positive about uncertainty in hydrological modelling , 2013 .

[162]  Willy P Aspinall,et al.  Volcanic Risk Management , 2015 .

[163]  D. Abbs,et al.  A numerical modeling study to investigate the assumptions used in the calculation of probable maximum precipitation , 1999 .

[164]  Roger M. Cooke,et al.  Messaging climate change uncertainty , 2015 .

[165]  S. Wiemer,et al.  Assessing the Quality of Earthquake Catalogues: Estimating the Magnitude of Completeness and Its Uncertainty , 2005 .

[166]  Jonathan A. Tawn,et al.  Statistical models for overdispersion in the frequency of peaks over threshold data for a flow series , 2010 .

[167]  Roger M. Cooke,et al.  Expert Elicitation and Judgement , 2013 .

[168]  Gordon Woo,et al.  Thirty-Year Bayesian Updating of PSHA for Hinkley Point NPP , 2015 .

[169]  Serena H. Chen,et al.  Good practice in Bayesian network modelling , 2012, Environ. Model. Softw..

[170]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[171]  Stanley G. Benjamin,et al.  Global Ensemble Predictions of 2009’s Tropical Cyclones Initialized with an Ensemble Kalman Filter , 2011 .

[172]  Demetris Koutsoyiannis,et al.  HESS Opinions "A random walk on water" , 2009 .

[173]  Suraje Dessai,et al.  Robust adaptation to climate change , 2010 .

[174]  W. Walker,et al.  Defining Uncertainty: A Conceptual Basis for Uncertainty Management in Model-Based Decision Support , 2003 .

[175]  Jim W. Hall,et al.  Sensitivity analysis of environmental models: A systematic review with practical workflow , 2014, Environ. Model. Softw..

[176]  W. Aspinall A route to more tractable expert advice , 2010, Nature.

[177]  Isaac Levi,et al.  Imprecise and Indeterminate Probabilities , 2000, ISIPTA.

[178]  N. Abrahamson,et al.  On the Use of Logic Trees for Ground-Motion Prediction Equations in Seismic-Hazard Analysis , 2005 .

[179]  Jim W Hall,et al.  Imprecise probability assessment of tipping points in the climate system , 2009, Proceedings of the National Academy of Sciences.

[180]  Marco Marani,et al.  Long‐term oscillations in rainfall extremes in a 268 year daily time series , 2015 .

[181]  Demetris Koutsoyiannis,et al.  Hydrology and change , 2013 .

[182]  Paul Rosen,et al.  From Quantification to Visualization: A Taxonomy of Uncertainty Visualization Approaches , 2011, WoCoUQ.

[183]  Jon C. Helton,et al.  Guest editorial: treatment of aleatory and epistemic uncertainty in performance assessments for complex systems , 1996 .

[184]  W. P. Aspinall Scientific uncertainties: A perspective from probabilistic seismic hazard assessments for low-seismicity areas , 2011 .

[185]  Robert J. Stern,et al.  SUBDUCTION ZONES , 2002 .