Analyzing Investments For Managing Lake Erie LevelsUnder .
WATER RESOURCES RESEARCH, VOL. 35, NO. 5, PAGES 1671-1683, MAY 1999Analyzinginvestmentsfor managingLake Erie levelsunderclimate change uncertaintyBoddu N. VenkateshICF ResourcesIncorporated,Fairfax,VirginiaBenjaminF. HobbsDepartmentof nsUniversity,Baltimore,MarylandAbstract. Analysesof investmentsthat are the optionof delayinga decision.For instance,the benefitsof manywaterresourceprojectscouldchangeif globalwarmingoccurs.The magnitudeof thatwarmingis uncertain,anddelayingprojectsuntil moreinformationis availablemightbe optimal.We examine whether this is true for construction of an outflow control structure for LakeErie. UsingBayesianMonte Carlo(BMC)-baseddecisionanalysis,we findthatconsideringclimateuncertaintydoesmakea difference.Climatechangebeliefs,in theformof naffectthe optimalstrategy:in oreattractive.The optionvalueof deferringthe decisionto buildis ashighas 20million.Ignoringthe possibilityofclimatewarmingcaninflictan expectedpenaltyaslargeas20%of thecostof thecontrolstructure.We alsocompareclimaterisksto uncertaintiesin stage-damagecurvesandfindthat they are approximatelyof equalimportance.in hydropowerlosses[InternationalJoint Commission(IJC),1993a].Becausethe commitmentof capitalfor sucha structureTraditionaleconomicanalysesof water resourcesprojects is irreversibleand postponeable,and its future benefitsarecalculate the net benefits of construction now versus not maksubjectto climatechangeandotheruncertainties,it is suitableingtheinvestmentat all.However,accordingto thenewtheory for an optionsanalysis.The possibilityof delayuntil we getof investment[DixitandPindyck,1994],evaluationsof invest- further informationregardingclimatechangeis a real optionmentscharacterizedby irreversibility,uncertaintyin futurere- whosevalue shouldbe consideredin project evaluation.wards,and flexibilityin timingneedro explicitlyconsidertheOption valueshave previouslybeen calculatedfor otherfull costof exercisingthe option of makingthe investment, cludwhichincludesthe foregonebenefitof delayinga commitment. ing shoreprotection[Chao and Hobbs, 1997] and tmentflexibility restoration[Bloczynskiet al., 1999].However,thoseanalysescan be viewedas "real" optionswhich,like financialoptions, useda simplefirst-orderMarkov processto characterizeuninvolvediscretionarydecisionswith no obligationsto acquire certaintiesin Lake Erie levelsand consideredonly one climateor exchangean assetfor a specifiedalternativeprice.The real warmingscenario.The presentstudymore realisticallycharoptionsincludedeferral, expansion,contraction,abandon- acterizesclimate and lake level uncertaintiesby applyingament,andotheralterationsof capitalinvestment.Suchoptionsmore sophisticatedlake levels model for the entire Great1.Introductionhave a definitevalue that shouldbe consideredwhen apprais-Lakes and includingseveralalternativewarming scenarios.ingprojectsunderuncertainty.For example,an optimaldeci- The alsionconcerninga projectmay often be to wait until new in- cost functions; here a detailed simulation model calculatesformation is obtained or better economicconditionsoccur;butsevencategoriesof economicbenefitsand environmentalimthis benefit of delayingconstructionnow is ignoredin mostpacts.projectanalyses[U.S. WaterResourcesCouncil(USWRC),Recently,the InternationalJoint Commission(IJC) con1983].The value of the optionof waiting(or "quasi-optionducteda multiyear,multimilliondollar studyto analyzethevalue"[CogginsandRamezani,1998])shouldbe addedto theLake Erie controlproposal[IJC, 1993a].The analysisassumednet benefitsof the "donothing"alternative[BrealeyandMyers,that pastnet basinsupplies(NBS) to the lakeswill repeatin1992]and can often changethe decision.the future. Uncertaintiesin climate, other possibleNBS sceThis paper presentsan applicationof the new theoryofnarios,andflexibilityin timingwerenot considered.Thispaperinvestmentto a proposalto constructa controlstructureat theattemptstoincludetheseissuesintheevaluationso that weoutlet of Lake Erie, one of the LaurentJanGreat Lakes ruction.North America.The purposeof sucha structurewouldbe tolessenfluctuationsin lake levels;highlevelscauseerosionand We also calculatethe expectedvalue of includingclimateflooding,whilelow levelsimposecostson shippingandresult changeuncertainty(EVIU) andthe expectedvalueof perfectclimatechangeinformation(EVPI). This enablesusto answerCopyright1999by the AmericanGeophysicalUnion.the followingquestion:Are climatechangeuncertaintiesrelePaper vant to decisions about the Lake Erie control structure? Al-thoughtherearemanystudiesof thewaterresourceimpactsof1671
ng,few studieshave carefullyaddressedwhether suchimpactsshouldaffect today'swater investmentdecisions[Chao and Hobbs, 1997;Hobbset al., 1997;Rogers,1997].A BayesianMonte Carlo (BMC)-based frameworkis usedto addresstheseissues.To our knowledgethis is the first timethat the BMC techniquehas been combinedwith sequentialdecisiontree analysisfor obtainingoptimalmanagementstrategies.Like formationon userbeliefs(codedas subjectiveprobabilities),uservalues(here,weightson variousobjectives),andevidence(possiblefuture NBSs) to define optimal decisionstrategies[Morganet al., 1990].At eachfuture decisionstage,beliefs concerningthe likelihood of various climate changescenariosare updatedbasedon the observ.ed NBS. The CaseWestern Reserve University Great Lakes Hydraulic, SocioEconomic and Environmental Impact Simulation Model(CWRU ImpactModel) is usedto quantifythe benefits[Chaoand Wood,1998;Venkatesh,1996].To assessthe importanceofclimate changecomparedto other uncertainties,we comparethe EVPI and EVIU for climatechangewith valuesassociatedwith uncertaintyin shoreline(flooding and erosion) stagedamagecurves.We concludethat under our assumptions,climate changeand shorelinedamageuncertaintiesare of comparableimportancein termsof the expectedpenaltysufferedifthey are disregarded.It is possible,however,that other uncertainties that we have not examined,especiallypolitical andeconomicones,might be more important.Thispaperis organizedasfollows.Firstwe discussthe GreatLakeslevelsmanagementproblem(section2). Then in section3 we summarizethe BMC-basedapproachusedin section4 toanalyzethe proposedLake Erie controlstructure.Conclusionsabout the robustnessof the analysisand the usefulnessof themethodologyfor other water investmentproblemsconcludethe paper (section5).INVESTMENTSOptionsfor decreasingthe impactof ctivestructuresand mandatory setbacks)and dischargecontrolstructures.The latter arethe subjectof this paper. Lake Superior'soutflow into LakeHuron is presentlygovernedby control structuresin the St.Mary's River. Lake Ontario's outflow to the St. LawrenceRiver is alsoregulated[InternationalSt. LawrenceRiverBoardof Control(ISLRBC), 1963].In the courseof the IJC PhaseIIstudy,both three-lakeplans(includinga newcontrolstructureto regulateLake Erie) andfive-lakeplans(two newstructures,one for Erie and the other for Lakes Huron and Michigan)were formulated[IJC, 1993b].The three-lakeplansturnedoutto be moreviablethan the five-lakeoptionsand are the subjectof thispaper.The variousthree-lakeplansdifferedin termsoftheir capacityto alter the naturaloutflowof Lake Erie. Thefocus of the IJC study, and therefore this paper, is upon astructurethatcouldalterflowsby 50,000feet3/s(1400m3/s).On the basisof interviewswith U.S. Army Corpsof Engineerspersonnel,we assumethe followingoperatingrule: The naturaloutflowis loweredby 50,000feet3/sif LakeErie'slevelfallsbelow173.95m, while an equalamountis addedto the naturalreleaseif the levelrisesabove174.05m. The goalis to dampenyear-to-yearvariationsin Lake Erie levels.By decreasingthe likelihoodof highlake levels,floodinganderosiondamagesare anticipatedto diminish.Simultaneously,increasing lake levels during droughts will increase hydropowerproductionon the Niagara River and decreasenavigationcostsby allowingshipsto carrymore cargo.Also, weproject that the probabilityof anoxiaoccurringin the LakeErie centralbasinwill fall, basedupon a model of El Shaawari[1984]. On the other hand, decreasedlake fluctuationswillharm shorewetlandsbecausehigh levelsare neededto keepwoody terrestrial plants from invading,while low levels arerequiredfor germinationof emergentwetland vegetation.These benefitsand costs of a LakeEriecontrolstructurewould be affectedby climatechange.Global warmingwouldincreaseevapotranspirationand possiblyprecipitation,likely2. Lake Erie Levels Management and Climateleadingto decreasedNBSs and lake levels.Net basinsupplytoChangea lake is definedasP - E R, whereP is precipitationonThe Great Lakescontainroughly20% of the world'ssupply the lake surface,E is evaporationfrom the lake surface,andRof fresh surfacewater. Their drainage basin includeshighly is runoff from the basin. In calculatingNBS for a lake, theindustrializedstatesand provincesin the United States and lake'sdischargeaswell as inflowsfrom upstreamGreat LakesCanada.This basin'spopulationrelieson the lakesfor drinking are excluded, since lake outflows are decision variables andwater,transportationof goods,wastedisposal,electricity,food, NBS is uncontrolledand climatedependent.Our Great Lakesand recreation. Becauseof their large size and low outflows model(baseduponthat of Croley[1990])maintainsmassbal(lessthan 1% of their volumeper year),the lakesare sensitive ancesfor eachlake, accountingfor inflowsfrom upper lakes,to the effectsof pollution.The largesizeof watershedresults NBS, changesin storage,and outflows.Croley[1990] andHartmann [1990]usedrunoff models,opin spatialvariation in physicalcharacteristicssuchas climate,soils,and topography.Lake Superioris the largestlake, while erational regulationplans, and hydraulicrouting models ofLake Erie is the smallestby volume amongthe Great Lakes. outlet and connectingchannel flows to estimate NBSs andThe upper lakes (Superior,Michigan,and Huron) ultimately water levelsin Great Lakes under alternativesteadystate clidrain into Lake Erie through St. Clair River, Lake St. Clair, mate scenarios. Such scenarios assume a constant concentraand Detroit River. Lake Erie dischargesinto Lake Ontario tion of greenhousegassesover time. They also assumedthatthoroughthe Niagara River, while Lake Ontario flowsthrough the last30 years(1951-1980)of rainfallandtemperaturewerethe St. Lawrence River into the Atlantic Ocean.representativeof 1 x CO2 conditions(i.e., preindustrialgreenIn the mid 1980s,after nearlytwo decadesof aboveaverage housegasconditions).To obtaina 2 x CO2 precipitationandprecipitation, the Great Lakes (excludingLake Ontario) temperaturescenario(whichis anticipatedto occurby someachievedtheir highestlevelsof this century.This causedmil- time in the nextcentury),theyadjustedupwardsor downwardslions of dollars of flooding and erosion damagesalong the the historical daily temperaturesand precipitation at eachlakes'shorelines[Grima, 1993;IJC, 1993a].In responseto this point within the watershedby the annual averagedifferenceconcern the governmentsof Canada and the United States betweengeneralcirculationmodel (GCM) 1 x CO2 and 2 xasked the IJC to study methods of alleviatingthe adverse CO2 resultsfor the nearestGCM grid cell centroid.The steadyconsequencesof fluctuatinglake levels.state GCM climatescenariosthey consideredincludedthose
VENKATESHAND HOBBS: ANALYZINGINVESTMENTS1673Expected Benefits(M 1yr)ClimateChangeNBSUncertaintyUncertaintyP(BOC) 0. . 884.50 P(MPI) 0.167 876.76846.86P(GFDL) 0.1673Lake 879.90/'""P(UKMO) 0.167 879.24P(iIBOC,g) 1/17 P(MPIIg) 3Lake 880.202 Lake902.12P(BOClg) 0.25880.200.38851.32FDLIg) 0.14P(UKMOIg) 0.22899.11891.95906.29P(BOClg) 0.25831.61 p(G ' Lig) 0.14-- 906.83P(UKMOIg) 0.22P( g Low NBS) 0.34T Yearsof Low901.84NBS891894.64P(BOCIg) 0.54 1873.74890.22879.9089P(UKMOIg) 0.16P(g MediumNBS) 0.34 892.38897.72P(BOCIg) 0.54 TYearsofMediumNBS2Lake",,, 6 ,.,,.,,. P(MP g) 0.11860.68896.99P(UKMOIg) 0.16P(g High NBS) 0.32902.18T Years of High NBS863.98 864.36P(BOCIg) 0.723Lake FDLIg)--0.17P(UKMOIg) 0.11862.97 P(MPIIg)808.42 0.01855.31870.24863.632Lake 864.36P(MP g) 0.01Unce ainNBS,Years1-20 P(GFDLIg) 0'17 804.09859.38878.93ClimateUnce aintiesNBSTime 0Time 20 yearsUncertaintiesTime 80 yearsFigure 1. BayesianMonte Carlosimulation-basedtwo-stagedecisiontree.from the OregonStateUniversity,GoddardInstituteof Space fewer flood and erosion control benefits under climate tudies,and General Fluid DynamicsLaboratory(GFDL) ing;however,GCMs.After inputtingthe historicalandmodified(2 x CO2) andwater qualitybenefitsmightincrease.Below,we analyzethe possibilityof thesechangescouldaftemperaturesand precipitationin their runoff and routing whetherconsideringmodels,they estimatedthat meanlake levelscouldfall be- fect the decision to build such a structure.tween 0.4 and 2.5 m, dependingon the lake and the otherprojectionsof hydrologicimpactsin the omicand environmentalimpacts.Someof them lineinundationanderosioncosts,water qualitydeterioration,and fisherychanges[SmithandTirpak,1990].As a result,a controlstructuremightprovide3.3.1.Modeling ProceduresSummary of Decision FrameworkWe posethe investmentproblemwith the optionof delayasa two-stagedecisionprocess,with 20 yearsbetweenthe decisionstages(Figure1). Venkatesh[1996]alsoconsideredtreeswith additionaldecisionstagesalongwith treeswith lessthan
1674VENKATESHAND HOBBS: ANALYZINGINVESTMENTSTable 1. PercentageChangein NBS for the Great LakesThe Bayesianmodelof Bloczynskiet al. [1999],for example,and Three GCMs After 70 Yearsincludes both NBS and the results of international studies ofANBS ,%Lake jMPIGFDLUKMOSuperiorMichigan-Huron-39.6-38.47.1- 12.616.38-28.1St. 55.5-3.52climatechangein the updatingprocess.Each of the transientGCM outputsconsistof a set of differencesbetweenmonthlyaverages(overa 10-yearperiod)ofprecipitationand temperaturefor the eighthdecadeof simu-lationandthe startingdecade.Usingthe IPCC (1994)procedure and methodsdescribed'in section3.3, we downscaledtheprecipitationand temperaturechangesand estimatedNBSvaluesfor eachof thefivelakes'basins.The resultingimpactofeachof the climatescenariosuponNBS after70yearsisshownin Table 1. We will assumethat in interveningyearsthat theexpectedNBS for eachlake changeslinearlyfrom year 0 to20 yearsbetweendecisionpoints.The generalconclusionscon- year 70 under those scenarios.At the endof eachbranchof a decisiontreeisthepayoffforcerningthe relevanceof climate uncertaintiesand the value ofdelayinga decisionare unchangedby thoseassumptions.In stage1 (year 0) of Figure 1, there are two choices:builda controlstructureon Lake Erie ("3 Lake"),whichwouldbeimplementedbyyear10,or uperior("2 Lake").Thisdecisionmaya particularcombinationof a decisionand NBS sequence.Here, payoffis annualizednet benefit(dollarsper year),defined as a weightedsum of economicand environmentalob-jectives.The tree in Figure1 showsthe averagevalueacrossNBS realizationsfor a particulardecisionandclimatescenario.depend on degree of belief in variousclimate scenarios,asreflectedin prior probabilities.Consistentwith the Bayesian 3.2. BayesianMonte Carlo Analysisphilosophy,thesepriorsrepresenta particularuser'sdegreeofThe heartof Bayesiananalysisis the useof observationsorbeliefin the scenarios,whichmaybe basedon )#toreviseapriormodelingresults,or justguesswork;the tree thencalculatestheP( 0) of a "stateof nature"0 (modelparameterorimplicationsof thosebeliefsfor the optimal strategy.The distributionsomeotheruncertainquantity),yieldinga posteriordistribumodelcanbe easilyrerunfor alternativeassumptions.A rangetion P(O/#) [Clemen,1996].Bayes'law is usedto make thatof possibleNBS time seriesare consideredby the model calculation:throughthe planninghorizonof 80 years.We fter that time.P(O/g) P(g/O)P(O)/P(g)(1)If the decisionat time zero is to do nothing,thenthe deciwheresionis revisitedafter20 years,whichis stage2 of the process.P(g) is the unconditionalprobabilityof observingg,During the interveningperiod, NBSs can be observedandinferencesdrawnasto whetherthe regionalclimateis changP(g) oP(g/O)P(O)(2)ing. The inferenceprocessconsistsof applyingBayes'law tothe prior probabilities,yieldingposteriorprobabilitiesof the andP( g/0 ) istheconditionalprobabilityof observingg, givenclimatescenarios.Upon the basisof thoseprobabilities,either stateof nature0. If 0 is a continuousquantity thenan integraltwo-lakeregulationis continuedor a three-lakeplanis imple- is substitutedfor the summationin (2). In our case,g consistsmented.The evaluationat that time is basedon the expected of an observationoverthe first 20 yearsof whetherthe NBSsbenefitsundera rangeof possibleNBSsovertheremaining60 havebeenlow,medium,or high,while 0 are alternativeclimateyears.scenarios(nochange(BOC), GFDL, MPI, or UKMO). BayesWe considerfourclimatescenariosin thistree,consistingof ian analysishaspreviouslybeenwidelyusedto estimatewaterone 1 x CO2scenario(no climatechange,whichthe IJC called systemparameters.By embeddingBayesiananalysiswithinthe "basisof comparison,"or BOC) and threetransientsce- decisiontreessuchasFigure1,it canbeusedto optimizewaternarios. The latter scenarios are obtained from the Max Plancksystemcontrolanddesign[e.g.,Daviset al., 1979;KrzysztofowInstitute(MPI), GFDL, andUnitedKingdomMeteorological icz, 1983].Bayesiananalysishasbeen recommendedas a suitOffice(UKMO) GCMs (IntergovernmentalPanelon Climate ableapproachfor , Climate changescenarios:Projectionsfor evaluatingwater resourcedevelopmentstrategiesunder cliIPCC WorkingGroupII assessment,editedby S. Grecoet al., mate uncertainty[Krzystofowicz,1994;Hobbs, 1997;Hobbsetworkingdocument,Washington,D.C., 1994)(hereinafterre- al., 1997;M.B. Fieringand P. Rogers,Climatechangeandferredto asIPCC, 1994).We assumethattheusercanquantify waterresourcesplanningunderuncertainty,draft report,Intheir prior (year 0) degreeof belief in eachscenarioby a stitutefor Water Resources,U.S. Army Corpsof Engineers,subjectiveprobability.We alsoassumethatit is appropriateto Fort Belvoir,Virginia, 1991],and analyzingclimatechangeupdate these probabilitiesby Bayes'law, and that the best preventionstrategies[e.g.,Arrowetal., 1996].However,a pracsource of information are the observedNBSs themselves, ticaldifficultyin applyingBayesiananalysishasbeenthe needrather than other climate variables. This is because the imfor tractablemethodsto calculateP(g/O) andP(O/g). Often,menseuncertaintiesinvolvedin downscalingGCM scenarios simplificationsaremade.For instance,ChaoandHobbs[1997]to 94; andBloczynskiet al. [1999]assumethatLakeErie levels(oneRogers,1994]meanthat evenif globalclimatewarmingwas of their sourcesof informationg) followa first-orderMarkovconcludedto be definitelyunderway,the implicationsfor Lake process,giventhe climatescenario0. This permittedthemtoErie wouldstillbe highlyuncertain.However,moregeneral usestochasticdynamicprogramming(SDP) to determinetheformulationsare possiblein which severalvariablescan be optimaltiming for shoreprotectioninvestmentsand wetlandmonitoredsimultaneously,if their correlationsare considered. rehabilitation,given uncertaintiesin lake levels and climate
yand Mathier [1994]havefound thatmore complexmodels better representNBSs for the GreatLakes. For instance,Rassamet al. [1992] model annual NBSfor each of the five Great Lakes by a shifting-meansprocessthat accountsfor both persistenceover time and correlationsamongthe lakes.A multivariateannual-monthlymodelis usedto disaggregateannualvaluesfor eachlake into monthlyvalues.Analyticalexpressionsfor P( #/0 ) are not possiblein thatcase,andthe statespacebecomestoo largefor a SDP (asstatevariableswould be requiredfor eachlake, alongwith an additional set of statevariablesspecifyingthe probabilityof eachpossiblemeanin the shiftingmeanmodel).BayesianMonte Carlo (BMC) analysis,first introducedbyHornbergerand Spear[1980] and Spearand Hornberger[1980]and further developedby Dilks et al. [1992], offers a practicalalternativewhen complexstochasticprocessmodelsunderliethe P(#/0). The approachis asfollows.Simulationis usedtoquantifyP(#/0) by assuminga value of 0 and then makingrandom drawsof the other variablesand noting the resultingdistributionof #. This is repeatedfor all valuesor a sampleof0. The outcomesof the simulationscanbe useddirectlyas thedistributionP(#/0) underthe assumptionthat eachoutcomeis equiprobable,as we do below; or an analyticalform ofP(#/0) can be fit to the results.Then, givenactualobservations of #, the prior P(0) can be updated numericallybyBayes'law.Dilks et al. [1992] apply the BMC techniqueto a model ofriver dissolvedoxygento determineposteriordistributionsfornine uncertain parameters, such as reaeration rate. Patwardhanand Small [1992] use BMC analysisto evaluateuncertaintiesassociatedwith the predictionsof sealevel rise andthe role that observeddata and researchplaysin reducingthisuncertainty.Brandand Small [1995]presentBMC methodsforupdatinguncertaintyin the predictionsof an integratedenvironmentalhealth risk assessmentmodel.Dakins et al. [1996]employBMC analysisto computehow much a samplingprogramwouldreduceuncertaintiesin PCB concentrations.Patwardhanand Small [1992] and Dilks et al. [1992] stressthat the basicchallengeis the developmentof a likelihoodfunctionfor the observedmodel outputs.They also state thatthe technique'sweaknessis its computationalrequirements.Our casestudyreinforcesthesepoints.We useBMC analysisto computethe posteriorprobabilityof climatechangeby developinga likelihoodfunctionfor theNBSsfor years1-20 basedon Monte Carlo samplingusingthemodelof Rassamet al. [1992].Then usingthe prior distributionINVESTMENTS1675Step 1. Generate synthetic Basis-ofComparison NBS (without climate change)I Step2.IntroduceClimateChange]trend into synthetic NBS tracesStep 3. Use each NBS trace to drive Hydraulic, Economic, &Environmentalmodelsto obtain net benefitsof each alternativeI Step4.ClassifyNBStracesasLow,MediumorHigh,Iand calculate prior and posterior probabilitiesI StepS'InsertbenefitsintøtwøIobtain optimal decision strategy and its expected worthStep 6. ComputeEVPI, EVIU,and option value of waiting[ Step7.RepeatStepsS,6foratwostagedecision]problem under shoreline damage uncertaintyFigure 2. Flow chart of the analysis.values.Step 6 usesthe tree to computeEVPI, EVIU, and theoptionvalueof waiting(sections4.2-4.4). Finally,in step7, asimilar analysisis undertakenfor shorelinedamageuncertainties, permitting an assessmentof the importanceof climateuncertaintycomparedto anotherplanninguncertainty(section4.5).3.3.Net Basin Supply Scenario Generation (Steps 1 and 2)In the first two stepswe generatea sampleof monthlyNBSfor each lake for 90 yearsunder each climate scenario0. LetNBS0h {NBSohjt;j Superior,Michigan-Huron,St.Claire, Erie, Ontario;t 1, 2, ., 1080} be the h th (h 1, 2, ., No) sampletime seriesof monthlyNBS (in cubicmeters) under climate scenario0 (0 BOC, MPI, GFDL,UKMO). In step1 the "noclimatechange"NBSs(NBSBoc )are generatedusingthe methodof Rassamet al. [1992].In thatmodel random annual NBSs are generatedfor each lake, accountingfor autocorrelationsand between-lakecorrelations;then the annual NBSs are disaggregatedto monthlyvalues.The randomnessin NBS stemsfrom naturalvariabilityin rainof the climate scenariosand this likelihood function, we com- fall and evapotranspiration.A varietyof distributionsare usedpute the posteriorprobabilityof eachscenario.Having devel- for each lake and time period, includingnormal, lognormal,oped the posteriordistribution,we can fold backthe decision and gamma.The model includesa Markov shifting-meanreptree (Figure 1) to computethe Bayesoptimaldecision.Figure resentationto accountfor persistencein the historicalrecord.2 summarizesthe stepsto be undertakenin this analysis;in the In our analysis,NBoc 100 samplesof NBS were drawn forremainder of this section, and in section 4, we describe the that scenario.In the BMC method, each of the samplesismethodsused in each step and their results.Steps 1 and 2 assumedto be equiprobable;that is, P(z NBSBoc /0 (section3.3) generatesyntheticNBS seriesassumingno cli- BOC) 0.01.An exampleof a Lake Erie BOC NBS trace ismate changeand then introduceclimatewarming into these shownas the upper line in Figure 3.The creation of hydrologicalscenariosunder changedclitraces.Step3 (section3.4) usesthe NBS tracesgeneratedinsteps1 and 2 to obtainnet benefitsfor eachalternativeusing mate conditions(step2) is controversialandrightfullyso.Ourthe CWRU Impact Model. Step 4 (section3.5) classifiesthe procedureis an attemptto be transparent,uncomplicated,andof the procedureNBS tracesgeneratedin step 3 as low, medium, or high, the to yield plausibleNBSs. Some assumptionscategoriesused to calculateposteriorprobabilitiesof the cli- are as follows:1. The downscalingprocedurefor mean temperatureandmate scenarios.In step5 (section4.1) the probabilitiesandnetbenefitsdevelopedin steps3 and4 are pluggedinto a decision precipitationchangesusedby Croley[1990] is appropriate.2. The responseof expectedannualNBS to the transienttree, yieldingan optimal strategy,giventhe user'sbeliefsand
800NBSarea400mm overlake-400ii!,,-800YearErie NBS IxCO2--'Erie NBS MPI.Erie NBS 2xCO2Figure 3. Exampleof NBS tracegeneratedfor Lake Erie under 1 x GO2 conditionsandthe corresponding2 x CO2 and transienttraces(MPI downscalingresults).scenarios'changesin mean precipitationand temperatureinyear 70 are similar in nature to the responsesCroley[1990]calculatedfor three steadystateGCM 2 x CO2 scenarios.Thisassumptionmay exaggeratethe impactsof climate warminguponNBS, sincegroundwaterand soilmoisturestoragemeansthat there are lagsin the hydrologicsystem'sresponseto climate shifts.That would imply that transientresponsesare lessthan the steadystateresponsesCroley[1990] calculated.3. The mean annual NBS in each year changeslinearlybetweenthe year 0 meanand the estimatedyear 70 mean.Thisassumptionis adoptedfor simplicityandbecauseno particularnonlinearassumptionis more plausible.The resultingmethod for obtaining NBS0h for 0 MPI,GFDL, UKMO can be briefly summarizedas follows.First,GCM precipitationand temperaturescenariosare downscaledto eachlake. Second,statisticalrelationshipsbasedon work byCroley[1990] are usedto infer the impactof downscaled2 xCO2 S. Third, 2 x CO2 NBS traces correspondingto eachthe end pointsof Figure l's tree. Theseare the annualizednetbenefitsB(NBSoh, dk) for each NBS sample and decisionsequence.B(NBSoh, d :) is computedusingthe CWRU ImpactModel.We assumethat we are already10 yearsinto globalwarmingatthe time of the study.Thus the first 10 yearsof simulatedNBSare disregarded.Sincethere are 400 samplesand three decisionsequences,the impactmodelwasrun 1200timesfor years11-90. The costconsideredis the expenseof implementingthethree-lakeplan; the benefitsare expressedby sevensocialandenvironmentalindices. These include value of hydropowerfrom Great LakesandSt. Lawrencefacilities(dollarsperyear),erosionand inundationdamagesestimatedfrom stage-damagecurves(dollarsper year), avoidedshoreprotectioncosts(dollarsper year), navigationcostsbasedon the effectof levelsonloadabilityof ships(dollarsper year; basedon the model ofKeith .[1989]),wetlands(by lake) (meters of vertical extentbetweenlandwardupper edgeand lakewardlower edges[IJC,1993c]),and expectedoxygenatedhypolimnionin the LakeNBSBo½&(e.g.,the dottedline in Figure3) are generated Erie shipsbetweenCroley's[1991]1 x CO2To compute annualizedvalues, presentworths were firstand 2 x CO2 NBS scenarios.Finally, eachtransientscenario'sobtainedbasedon an interestrate of 5% and then multipliedNBS in eachmonth over the time horizon(the middleline inby the Figure3) is obtainedasa convexcombinationof the generated1 x CO2 and 2 x CO2 NBS scenarios,with the weightgivento and operation and maintenancecostsare then subtractedtothe 2 x CO2 scenarioincreasinglinearly over time. These yield net annualizedbenefits.The assumed5% real rate iscloseto the 8 5/8% nominalrate usedfor waterplanningby thecalculationsare explainedfurther in the appendix.federal governmentat the time of analysis,givenan inflation3.4.Net Benefit Calculationfor Each NBS Realizationandrate of 3%. The effectsof alternativerates(2% and10%) wereDecision (Step 3)examinedby Venkatesh[1996];the lower rate had the predictThe next stepis to calculatehowwell eachpossibledecision able effect of increasingthe maximuminvestmentthat couldperformsfor each NBS sampleNBS0h. Let dk designateone be justified,and the higherrate had the reverseeffect.Trigeorparticular decisionsequence.Thus, in the decisiontree of g/s[1996]notesthat traditionaldecisiontree analysessimilartoFigure 1, there are three possiblesequences:d {two-lake the onewe
study, both three-lake plans (including a new control structure to regulate Lake Erie) and five-lake plans (two new structures, one for Erie and the other for Lakes Huron and Michigan) were formulated [IJC, 1993b]. The three-lake plans turned ou
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Jack Carr Bonar Lake . Troy Turley Center Lake . John Bender Diamond Lake . Sandra Buhrt Elizabeth Lake . Chuck Brinkman Irish Lake . Jeff & Pam Thornburgh James, Oswego, & Tippecanoe Lake . Debra Hutnick Palestine Lake . Sandra Buhrt Rachel Lake . Toney Owsley Ridinger Lake .
Lake Michigan Lake Geneva OkaucheeLake Lake Mendota Big Green Lake Chain of Lakes Long Lake (Chippewa Co.) Long Lake (Washburn Co.) Lake Owen Turtle ‐Flambeau Flowage Lake Tomahawk Trout Lake Lake Superior Found in 175 Lakes
Great Central L Phillips Arm Powell Lake Mahood L Canim L Carpenter Lake Lillooet Lake Harrison Lake Stave Lake Alouette L Pitt Lake Ross Lake . Fish and Wildlife Regional Office (604) 586-4400 200-10428 153 St . ALOUETTE LAKE No vessels in swimming areas, as buoyed and signed; speed restriction (8 km/h) at south end of lake, south of a .
