Hydrologic drought prediction under climate change: Uncertainty modeling with Dempster–Shafer and Bayesian approaches

Representation and quantification of uncertainty in climate change impact studies are a difficult task. Several sources of uncertainty arise in studies of hydrologic impacts of climate change, such as those due to choice of general circulation models (GCMs), scenarios and downscaling methods. Recently, much work has focused on uncertainty quantification and modeling in regional climate change impacts. In this paper, an uncertainty modeling framework is evaluated, which uses a generalized uncertainty measure to combine GCM, scenario and downscaling uncertainties. The Dempster-Shafer (D-S) evidence theory is used for representing and combining uncertainty from various sources. A significant advantage of the D-S framework over the traditional probabilistic approach is that it allows for the allocation of a probability mass to sets or intervals, and can hence handle both aleatory or stochastic uncertainty, and epistemic or subjective uncertainty. This paper shows how the D-S theory can be used to represent beliefs in some hypotheses such as hydrologic drought or wet conditions, describe uncertainty and ignorance in the system, and give a quantitative measurement of belief and plausibility in results. The D-S approach has been used in this work for information synthesis using various evidence combination rules having different conflict modeling approaches. A case study is presented for hydrologic drought prediction using downscaled streamflow in the Mahanadi River at Hirakud in Orissa, India. Projections of n most likely monsoon streamflow sequences are obtained from a conditional random field (CRF) downscaling model, using an ensemble of three GCMs for three scenarios, which are converted to monsoon standardized streamflow index (SSFI-4) series. This range is used to specify the basic probability assignment (bpa) for a Dempster-Shafer structure, which represents uncertainty associated with each of the SSFI-4 classifications. These uncertainties are then combined across GCMs and scenarios using various evidence combination rules given by the D-S theory. A Bayesian approach is also presented for this case study, which models the uncertainty in projected frequencies of SSFI-4 classifications by deriving a posterior distribution for the frequency of each classification, using an ensemble of GCMs and scenarios. Results from the D-S and Bayesian approaches are compared, and relative merits of each approach are discussed. Both approaches show an increasing probability of extreme, severe and moderate droughts and decreasing probability of normal and wet conditions in Orissa as a result of climate change. (C) 2010 Elsevier Ltd. All rights reserved.

[1]  Lian-zeng Zhang,et al.  Representation, independence, and combination of evidence in the Dempster-Shafer theory , 1994 .

[2]  R. Reynolds,et al.  The NCEP/NCAR 40-Year Reanalysis Project , 1996, Renewable Energy.

[3]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[4]  P. P. Mujumdar,et al.  Climate change impact assessment: Uncertainty modeling with imprecise probability , 2009 .

[5]  Didier Dubois,et al.  Possibility theory , 2018, Scholarpedia.

[6]  Robert L. Wilby,et al.  Uncertainty in water resource model parameters used for climate change impact assessment , 2005 .

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

[8]  Subimal Ghosh,et al.  Modeling GCM and scenario uncertainty using a possibilistic approach: Application to the Mahanadi River, India , 2008 .

[9]  Richard L. Smith,et al.  Regional probabilities of precipitation change: A Bayesian analysis of multimodel simulations , 2004 .

[10]  D. Dubois,et al.  On the Combination of Evidence in Various Mathematical Frameworks , 1992 .

[11]  R. Yager.  On the dempster-shafer framework and new combination rules , 1987, Inf. Sci..

[12]  Murray C. Peel,et al.  Global streamflows - Part 1: Characteristics of annual streamflows , 2007 .

[13]  Philippe Smets,et al.  The Normative Representation of Quantified Beliefs by Belief Functions , 1997, Artif. Intell..

[14]  A. Munot,et al.  All-India monthly and seasonal rainfall series: 1871–1993 , 1994 .

[15]  A. Hoekstra,et al.  Uncertainty in climate change impacts on low flows. , 2006 .

[16]  M. G. Morgan,et al.  Subjective judgments by climate experts. , 1995 .

[17]  Mike Hulme,et al.  Representing uncertainty in climate change scenarios: a Monte-Carlo approach , 2000 .

[18]  Upmanu Lall,et al.  Probabilistic multimodel regional temperature change projections , 2006 .

[19]  R. Wilby,et al.  A framework for assessing uncertainties in climate change impacts: Low‐flow scenarios for the River Thames, UK , 2006 .

[20]  R. Prinn,et al.  Uncertainty and Climate Change Assessments , 2001, Science.

[21]  Wuben Ben Luo,et al.  Using Dempster–Shafer Theory to Represent Climate Change Uncertainties , 1997 .

[22]  Andrew McCallum,et al.  An Introduction to Conditional Random Fields for Relational Learning , 2007 .

[23]  Christel Prudhomme,et al.  Uncertainty and climate change impact on the flood regime of small UK catchments , 2003 .

[24]  Richard M. Vogel,et al.  PROBABILITY DISTRIBUTION OF ANNUAL MAXIMUM, MEAN, AND MINIMUM STREAMFLOWS IN THE UNITED STATES , 1996 .

[25]  T. McKee,et al.  THE RELATIONSHIP OF DROUGHT FREQUENCY AND DURATION TO TIME SCALES , 1993 .

[26]  J. C. Helton,et al.  Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty , 1997 .

[27]  Kari Sentz,et al.  Combination of Evidence in Dempster-Shafer Theory , 2002 .

[28]  R. Célleri,et al.  Predicting climate change impacts on water resources in the tropical Andes: Effects of GCM uncertainty , 2009 .

[29]  J. Kacprzyk,et al.  Advances in the Dempster-Shafer theory of evidence , 1994 .

[30]  M. Collins,et al.  Projections of future climate change , 2002 .

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

[32]  R. Leconte,et al.  Uncertainty of the impact of climate change on the hydrology of a nordic watershed , 2008 .

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

[34]  Kay,et al.  Comparison of uncertainty sources for climate change impacts : flood frequency in England , 2009 .

[35]  Subimal Ghosh,et al.  Nonparametric methods for modeling GCM and scenario uncertainty in drought assessment , 2007 .

[36]  Andrei P. Sokolov,et al.  Quantifying Uncertainties in Climate System Properties with the Use of Recent Climate Observations , 2002, Science.

[37]  P. Mujumdar,et al.  Constraining uncertainty in regional hydrologic impacts of climate change: Nonstationarity in downscaling , 2010 .

[38]  C. Prudhomme,et al.  Assessing uncertainties in climate change impact analyses on the river flow regimes in the UK. Part 1: baseline climate , 2009 .

[39]  J. Houghton,et al.  Climate change 2001 : the scientific basis , 2001 .

[40]  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.

[41]  R. Katz.  Techniques for estimating uncertainty in climate change scenarios and impact studies , 2002 .

[42]  Andrew McCallum,et al.  Introduction to Statistical Relational Learning , 2007 .

[43]  William F. Caselton,et al.  Decision making with imprecise probabilities: Dempster‐Shafer Theory and application , 1992 .

[44]  Belur V. Dasarathy,et al.  Sensor Fusion: Architectures, Algorithms, and Applications , 1998 .

[45]  Mort Webster,et al.  Communicating Climate Change Uncertainty to Policy-Makers and the Public , 2003 .

[46]  Richard L. Smith,et al.  Quantifying Uncertainty in Projections of Regional Climate Change: A Bayesian Approach to the Analysis of Multimodel Ensembles , 2005 .

[47]  David P. Rowell,et al.  A Demonstration of the Uncertainty in Projections of UK Climate Change Resulting from Regional Model Formulation , 2006 .