International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Addressing uncertainty in ensemble sea-level rise predictions Thomas, Matthew A.; Lin, Ting Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Addressing Uncertainty In Ensemble Sea-Level Rise PredictionsMatthew A. ThomasGraduate Student, Dept. of Civil, Construction and Environmental Engineering,Marquette University, Milwaukee, USATing LinAssistant Professor, Dept. of Civil, Construction and Environmental Engineering,Marquette University, Milwaukee, USAABSTRACT: Sea-level rise represents a looming hazard to coastal communities which remains diffi-cult to quantify. Ensemble climate change predictions incorporate epistemic uncertainty in the climatemodeling process and climate forcing scenarios help portray a range of radiative forcing changes. Thisstudy proposes a method for incorporating both model and scenario uncertainty in ensemble projectionsof thermosteric sea-level rise. A Markov Chain Monte Carlo algorithm is utilized to weigh the contribu-tions of eight process-based climate models as well as the four Representative Concentration Pathwaysbased on convergence criteria and observational data. Hazard analysis and deaggregation combine thesecontributions over a range of sea-level rise thresholds and quantify the relative contributions of each path-way and prediction model. The hazard maps generated suggest improved accuracy in modeling regionaltrends over typical ensembles. Deaggregations effectively represent model and scenario differences andthe impacts of the methods used.1. INTRODUCTIONSea-level rise (SLR) is an ongoing hazard, threaten-ing coastal communities around the world. Semi-empirical SLR models (Vermeer and Rahmstorf,2009; Grinsted et al., 2010; Kemp et al., 2011;Jevrejeva et al., 2012) and physics-based climatemodels (Taylor et al., 2012; IPCC, 2013) provide ameans of estimating future sea-levels. Quantifyingthe uncertainty inherent in these SLR predictionswill help decision makers understand and accountfor this hazard.Uncertainty in SLR estimates is linked to naturalclimate variability, an incomplete knowledge of theclimate system (Paté-Cornell, 1996), and anthro-pogenic factors (IPCC, 2014) such as populationgrowth, economic growth, policy decisions (Naki-cenovic et al., 2000; Webster et al., 2003), and thedevelopment of new technologies. A comprehen-sive analysis of SLR hazard incorporates all sourcesof uncertainty.Multimodel ensembles allow researchers to ad-dress epistemic uncertainty in climate model pre-dictions, although ensemble results are often dif-ficult to interpret and may ignore extreme behav-ior (Knutti et al., 2010). Models may be assignedweights to reflect characteristics of the ensembleusing criteria such as expert assessments (Hortonet al., 2014) or probabilistic methods (Tebaldi andSans, 2009; Smith et al., 2009). Although power-ful, the results of the latter reflect the underlying as-sumptions of the method used (Lopez et al., 2006).Working Group I of the Fifth Assessment Reportof the Intergovernmental Panel on Climate Changeutilized equal-weight ensembles for the Represen-tative Concentration Pathways (RCPs) of process-based climate models to project SLR (IPCC, 2013).The RCPs include four forcing scenarios, RCP2.6, RCP 4.5, RCP 6.0, and RCP 8.5, numbered byan associated radiative forcing by 2100 in W/m2(IPCC, 2013). These scenarios range from very lowto very high emission pathways but avoid makingexplicit assumptions about anthropogenic activity.Running climate model simulations along the RCPsis informative but tells us little about the likelihood112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Figure 1: Process for generating hazard maps and deaggregation plotsof observing rates of SLR.In earthquake engineering, probabilistic seismichazard analysis (Cornell, 1968) combines the con-tributions of many sources and models to quantifythe total seismic hazard at a specific site. Lin (2012)suggested a framework for applying this concept toSLR in which the contributions of forcing factorsand SLR prediction models are combined to deter-mine total hazard. Hazard may be deaggregatedto determine the contributions of individual sourcesand models.This study combines a modified version of theunivariate Bayesian method for quantifying uncer-tainty in ensembles of climate models developedby Smith et al. (2009) with Lin (2012)’s proposedframework to determine the total uncertainty inthermosteric SLR predictions, considering the con-tributions of process-based climate models and cli-mate forcing scenarios. Model ensembles for eachRCP scenario and RCP ensembles for each climatemodel are evaluated using data available from theFifth Phase of the Coupled Model IntercomparisonProject (CMIP5) (Taylor et al., 2012). Hazard mapsare developed to represent the likelihood of expe-riencing SLR above a certain threshold and theseresults are deaggregated to reveal the relative con-tributions of different models and scenarios.2. METHODSModel and RCP scenarios are evaluated using aMarkov Chain Monte Carlo (MCMC) algorithmto calculate posterior distributions and weights foreach ensemble. The MCMC results are combinedas in Lin (2012)’s framework to generate SLR ex-ceedence maps and deaggregated to calculate thecontributions of each model and RCP. Figure 1 de-tails this process.2.1. Data Selection and InterpolationThis study utilizes a combination of global meanthermosteric SLR and dynamic sea-surface heightprojections collected by CMIP5. These data setswere combined to create sea-level prediction mapsfor each model and scenario combination. SLR val-ues are evaluated relative to January 2006, the be-ginning of the RCP scenarios.For the purposes of this study only climate mod-els with high-resolution ocean components simu-lated for each RCP were considered. To minimizecorrelation between prediction models, only thenewest model from each institute was utilized. Anexception was made for the MIROC5 and MIROC-ESM-CHEM models which produced significantlydifferent SLR predictions. Table 1 characterizes theclimate models meeting these restrictions.The MCMC algorithm updates ensemble distri-butions using observational data. In recent years,satellite altimetry has provided an accurate meansof measuring regional sea-levels across the globe(Shepherd et al., 2012). This study utilizes a satel-lite altimetry data set developed by CSIRO combin-ing data collected by the TOPEX/Poseidon, Jason-1 and Jason-2/OSTM satellites. The altimeter datacovers sea-levels between 65◦ latitude north andsouth of the equator resolved over a 1◦ by 1◦ grid.This covers the majority of developed coastlinesand is consistent with the resolution and precisionof CMIP5 SLR predictions.To facilitate calculations, the sea-level predictionmaps were linearly interpolated to match the al-212th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Model Name Institute ID Vintage Grid Resolution Layers‡CSIRO-Mk3-6-0 CSIRO-QCCCE 2009 0.9◦ x 1.875◦ 31GISS-E2R NASA GISS 2011 1◦ x 1.25◦ 32IPSL-CM5A-LR IPSL 2010 2◦ x 2-0.5◦† 31MIROC-ESM-CHEM MIROC 2010 1.4◦ x 1.4-0.5◦† 44MIROC5 MIROC 2010 1.4◦ x 1.4-0.5◦† 50MRI-CGCM3 MRI 2011 1◦ x 0.5◦ 51NorESM1-ME NCC 2012 1.125◦ x 1.125◦ 53bcc-csm1-1 BCC 2011 1◦ x 1◦ 40Table 1: Process-based General Circulation Models of recent vintage incorporating high-resolution oceancomponents available from CMIP5† For models with variable grids, resolution is higher near the equator.‡ The number of vertical ocean layers incorporated in the model.timeter grid. Due to modeling assumptions, thelocations of null values representing land are notequivalent for each simulation. Prediction modelsnot providing data at a grid point have a weight ofzero.Many studies such as Smith et al. (2009) accountfor natural climate variability through the use ofdecadal or multidecadal averages. This study uti-lizes eight year SLR means, limited by the differ-ence between recent altimeter data and the begin-ning of the RCP scenarios. While not ideal, thelimited average is sufficient for this study.2.2. Bayesian Modeling of Uncertainty in Cli-mate EnsemblesThe MCMC algorithm from Smith et al. (2009) isadapted to create posterior probability distributionsand weights for sea-level rise prediction modeland RCP ensembles. The algorithm incorporatesBayesian updating to produce posterior probabilitydistributions for ensembles of climate models, as-signing weights based on convergence criteria andeach model’s ability to reproduce sea-level obser-vations.Smith et al. (2009) propose univariate and mul-tivariate versions of the MCMC algorithm which,respectively, represent regional climate predictionswith a single random variable and incorporate termsfor regional and model deviations from the globalmean. The univariate assumptions prove to be moreappropriate for this study as the multivariate as-sumptions do not scale well from the 22 regionsused in Smith et al. (2009) to the thousands of gridpoints used here.Equations (1) through (3) define algorithmic as-sumptions that climate data takes normal distribu-tions with the following means and variancesX0i = N(µ0i,λ0i) (1)Xi j = N(µi,λi j) (2)Yi j = N(νi,λi j) (3)where X0i is the observed sea-level and Xi j andYi j represent present and future simulation data forgrid point i and model j. µi and νi represent presentand future true global sea-level while λi j and λ0irepresent inter model variability and natural vari-ability as estimated from the eight years of altime-ter data respectively. The relative weights of indi-vidual models, P(Si j), in an ensemble are inverselyrelated to the uncertainty for a given model and re-gion. This method for model ensembles is extendedto RCP ensembles.P(Si j) =λi j∑ j λi j(4)The MCMC algorithm updates the hyperparam-eter values until they reach stable probability dis-tributions. In this study, Gibbs sampling is used tocollect 1,000 samples of each posterior distribution,drawing ensemble νi values every 100 iterations. A312th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015(a) (b)Figure 2: Posterior distributions of multimodel ensembles generated using the MCMC algorithm for 2093 to 2100for (a) RCP 4.5 (predictions by individual models are marked for reference) and (b) each RCP scenarioP(Hi > yi) =∑j∑kP(Hi > yi|Si j,Rik)P(Si j)P(Rik) (5)P(Si j|Hi > yi) =1P(Hi > yi)∑kP(Hi > yi|Si j,Rik)P(Si j)P(Rik) (6)P(Rik|Hi > yi) =1P(Hi > yi)∑jP(Hi > yi|Si j,Rik)P(Si j)P(Rik) (7)Metropolis-Hastings updating step is used to iterateaλ and bλ , hyperparameters which constrain λi j. Aburn-in period of 250,000 iterations ensured sam-pling from stable distributions.Figure 2 depicts the posterior distributions gen-erated by the prediction model ensembles for eachRCP scenario. Ensemble distributions tend to berelatively narrow due to the differential weighingof the MCMC algorithm.2.3. Probabilistic Sea-Level Rise Hazard AnalysisProbabilistic hazard analysis combines the contri-butions of the eight CMIP5 models and four RCPscenarios. Hazard rate is determined using the totalprobability theorem described in Equation 5, whereHi represents SLR at grid point i, yi a given SLRthreshold, Si j an SLR prediction model j, and Rikan RCP scenario k. The summation along j or kis carried out through the generation of posteriordistributions by the MCMC algorithm. These con-ditional distributions are then summed using themodel or RCP weights as determined using the con-ditional probabilities calculated by Equation 4. Ex-ceedance rates are deaggregated to quantify the rel-ative contributions of each SLR prediction modeland RCP scenario using an application of Bayes’Rule as illustrated in Equations 6 and 7. For thepurposes of this study, global mean contributionsare considered in lieu of creating contribution mapsor focusing on specific grid points.3. RESULTSFigure 3 represents these probability of exceedingvarious thermosteric SLR thresholds as calculated412th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015(a) (b)(c) (d)Figure 3: Probabilities of exceeding a global mean of (a) 0.08 m, (b) 0.16 m, (c) 0.24 m, and (d) 0.32 m ofthermosteric sea-level rise between 2006 to 2013 and 2093 to 2100 weighing prediction models and RCPscenarios with the MCMC algorithm and using Equation 5(a) (b)(c) (d)Figure 4: Probabilities of exceeding a global mean of (a) 0.08 m, (b) 0.16 m, (c) 0.24 m, and (d) 0.32 m ofthermosteric sea-level rise between 2006 to 2013 and 2093 to 2100 with all prediction models and RCP scenariosweighed equally512th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015(a) (b)Figure 5: Deaggregated contributions of (a) CMIP5 prediction models and (b) RCP scenarios to global meansea-level rise thresholds as calculated using Equations 6 and 7using the methods described here. These maps de-pict SLR hazard on a regional basis, quantifyinguncertainty at every grid point. Figure 4 depicts asimilar hazard map for the same thermosteric sea-level rise thresholds as predicted by an ensemble inwhich all models and RCPs are weighed equally.3.1. Hazard AnalysisThreshold exceedance rates tend to be significantlyhigher or lower for the maps generated using prob-abilistic hazard analysis. This results from the char-acteristics of the MCMC algorithm which producesrelatively narrow probability distributions due tothe differential weighing of models and scenar-ios, favoring prediction models and RCP scenarioswhich are near the ensemble consensus and effec-tively recreate altimeter measurements.Regional deviations in hazard rate are relativelylarge for the maps generated using probabilisticmethods. Effectively, a subset of predictions, con-sidered accurate by the weighing criteria, deter-mines hazard at every grid point. This allows mod-els to contribute to regions for which they are accu-rate while minimizing influence on others for whichthey are not. Additionally, the Bayesian methodsused allow models or scenarios diverging from theensemble consensus to dominate SLR hazard ina region where they best reproduce observationaldata. An equal-weight ensemble cannot make suchdistinctions.3.2. DeaggregationFigure 5 depicts the deaggregation of individ-ual prediction model and RCP contributions toglobal mean thermosteric sea-level rise. Visual-izing these contributions demonstrates their util-ity as well as the impact of the modeling assump-tions. The contribution of MIROC-ESM-CHEM,for instance, increases with SLR threshold as it pre-dicts higher SLR than other models for most gridpoints. For similar reasons, the relative contributionof MIROC5 peaks toward the middle of the thresh-old range and the contribution of MRI-CGCM3 de-creases with threshold.Unsurprisingly, the contribution of RCP 8.5 alsoincreases with SLR threshold. The contributionsof RCP 4.5 and RCP 6.0 peak near the center ofthe threshold range as expected, but are also con-sistently higher than RCP 2.6 even for lower SLRthresholds. This likely results from the convergencecriteria utilized in the MCMC algorithm, as moder-ate prediction scenarios will be favored over moreextreme scenarios.612th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20154. CONCLUSIONSIn this study, an MCMC algorithm for creatingposterior distributions of a multimodel ensembleusing model weighing criteria is combined witha probabilistic hazard analysis framework to cre-ate hazard maps incorporating the projections offour RCPs and eight climate models with high-resolution ocean components. These results differsignificantly from ensembles weighing each RCPand model equally, allowing hazard in particularregions to be controlled by an appropriate subsetof models. Additionally, the relative contributionsof each model and RCP were deaggregated, depict-ing how contributions change along a range of sea-level rise thresholds and the impact of the algorith-mic assumptions. This represents a novel step to-ward fully quantifying the uncertainty in sea-levelrise predictions.The accuracy and precision of the results in thisstudy depend on the assumptions made in the prob-abilistic model and the data used. A greater numberof prediction models and forcing scenarios wouldhelp better account for the full range of climate un-certainty. Effectively introducing spatial and tem-poral dependence into the probabilistic assumptionsmay lead to improved predictions. Finally, incor-porating mass-balance and other SLR contributionsinto the methods described may provide a morecomprehensive assessment of SLR hazard, allow-ing decision makers a greater means of exploringstrategies for adapting to and mitigating changes insea-level.5. ACKNOWLEDGMENTSWe acknowledge the World Climate Research Pro-gramme’s Working Group on Coupled Modelling,which is responsible for CMIP, and we thank theclimate modeling groups (listed in Table 1 of thispaper) for producing and making available theirmodel output. For CMIP the U.S. Department ofEnergy’s Program for Climate Model Diagnosisand Intercomparison provides coordinating supportand led development of software infrastructure inpartnership with the Global Organization for EarthSystem Science Portals.We also acknowledge the Commonwealth Sci-entific and Industrial Research Organization formaking the combined TOPEX/Poseidon, Jason-1and Jason-2/OSTM sea level fields data set avail-able at http://www.cmar.csiro.au/sealevel/sl_data_cmar.html.This work was supported in part by the Com-mittee on Research at Marquette University, un-der the Regular Research Grant and the SummerFaculty Fellowship awarded to the corresponding(second) author. The Regular Research Grant pro-vided research assistantship support for the present-ing (first) author. Any opinions, findings, conclu-sions, or recommendations presented in this mate-rial are those of the authors, and do not necessarilyreflect those of the funding source.6. REFERENCESCornell, C. A. 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