Using Dempster-Shafer theory to model uncertainty in climate change and environmental impact assessments

We present a methodology based on Dempster-Shafer theory to represent, combine and propagate statistical and epistemic uncertainties. This approach is first applied to estimate, via a semi-empirical model, the future sea level rise induced by global warming at the end of the century. Projections are affected by statistical uncertainties originating from model parameter estimation and epistemic uncertainties due to lack of knowledge of model inputs. We then study the overtopping response of a typical defense structure due to (1) uncertain elevation of the mean water level and (2) uncertain level of storm surges and waves. Statistical evidence is described by likelihood-based belief functions while imprecise evidence is modeled by subjective possibility distributions. Uncertain inputs are propagated by Monte Carlo simulation and interval analysis and the output belief function can be summarized by upper and lower cumulative distribution functions.

[1]  B. Merz,et al.  Flood risk assessment and associated uncertainty , 2003 .

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

[3]  Rory A. Fisher,et al.  Statistical methods and scientific inference. , 1957 .

[4]  M. Sklar.  Fonctions de repartition a n dimensions et leurs marges , 1959 .

[5]  A. Dempster.  Upper and Lower Probabilities Generated by a Random Closed Interval , 1968 .

[6]  M. S. Bartlett,et al.  Statistical methods and scientific inference. , 1957 .

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

[8]  Paul D. Bates,et al.  Quantified Analysis of the Probability of Flooding in the Thames Estuary under Imaginable Worst-case Sea Level Rise Scenarios , 2005 .

[9]  Scott Ferson,et al.  Constructing Probability Boxes and Dempster-Shafer Structures , 2003 .

[10]  B. Merz,et al.  Flood risk curves and uncertainty bounds , 2009 .

[11]  Anny Cazenave,et al.  Comparing climate projections to observations up to 2011 , 2012 .

[12]  N. White,et al.  A 20th century acceleration in global sea‐level rise , 2006 .

[13]  Yu Guo,et al.  Variable Fuzzy Sets and its Application in Comprehensive Risk Evaluation for Flood-control Engineering System , 2006, Fuzzy Optim. Decis. Mak..

[14]  Daisuke Mizuno,et al.  A Semi-Empirical Approach to Projecting Future Sea-Level Rise , 2007 .

[15]  Geoffrey Gregory,et al.  Foundations of Statistical Inference , 1973 .

[16]  Glenn Shafer,et al.  Belief Functions and Parametric Models , 1982, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[17]  Anthony C. Davison,et al.  Statistics of Extremes , 2015, International Encyclopedia of Statistical Science.

[18]  Martijn J. Booij,et al.  Uncertainty analysis in statistical modeling of extreme hydrological events , 2010 .

[19]  Didier Dubois,et al.  Possibility theory and statistical reasoning , 2006, Comput. Stat. Data Anal..

[20]  Arthur P. Dempster,et al.  The Dempster-Shafer calculus for statisticians , 2008, Int. J. Approx. Reason..

[21]  John D. Kalbfleisch,et al.  Examples of Likelihoods and Comparison with Point Estimates and Large Sample Approximations , 1969 .

[22]  Guo Yu,et al.  Variable Fuzzy Sets and its Application in Comprehensive Risk Evaluation for Flood-control Engineering System , 2006 .

[23]  Anna M. Bonner,et al.  Acknowledgments , 2019, The Neurodiagnostic journal.

[24]  S. Rahmstorf,et al.  Global sea level linked to global temperature , 2009, Proceedings of the National Academy of Sciences.

[25]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[26]  Y. Goda.  Irregular Wave Deformation in the Surf Zone , 1975 .

[27]  Thierry Denoeux,et al.  Combining statistical and expert evidence using belief functions: Application to centennial sea level estimation taking into account climate change , 2014, Int. J. Approx. Reason..

[28]  Ben Gouldby,et al.  The joint probability of waves and water levels in coastal engineering design , 2002 .

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

[30]  Elmar Kriegler,et al.  Utilizing belief functions for the estimation of future climate change , 2005, Int. J. Approx. Reason..

[31]  Die Küste,et al.  Die Küste, 73 EurOtop (2007), 1-178 , 2008 .

[32]  L. Wasserman.  Belief functions and statistical inference , 1990 .

[33]  H. Joe,et al.  The Estimation Method of Inference Functions for Margins for Multivariate Models , 1996 .

[34]  T. Severini.  Likelihood Methods in Statistics , 2001 .

[35]  Thierry Denux,et al.  Likelihood-based belief function: Justification and some extensions to low-quality data , 2014, Int. J. Approx. Reason..

[36]  Gunky Kim,et al.  Comparison of semiparametric and parametric methods for estimating copulas , 2007, Comput. Stat. Data Anal..

[37]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[38]  G. Barnard,et al.  Likelihood Inference and Time Series , 1962 .

[39]  P. Bates,et al.  A probabilistic methodology to estimate future coastal flood risk due to sea level rise , 2008 .

[40]  W. T. Pfeffer,et al.  Kinematic Constraints on Glacier Contributions to 21st-Century Sea-Level Rise , 2008, Science.

[41]  B. Dawson,et al.  INTERGOVERNMENTAL PANEL ON CLIMATE CHANGE (IPCC) , 2008 .

[42]  Mikel Aickin,et al.  Connecting Dempster–Shafer Belief Functions with Likelihood-based Inference , 2000, Synthese.

[43]  A. Edwards.  Likelihood (Expanded Edition) , 1972 .