Climate change, cyanobacteria blooms and ecological status of lakes: A Bayesian network approach

(1)

ContentslistsavailableatScienceDirect

Ecological Modelling

jo u r n al ho m e p ag e :w w w . e l s e v i e r . c o m / l o c a t e / e c o l m o d e l

Climate change, cyanobacteria blooms and ecological status of lakes:

A Bayesian network approach

S. Jannicke Moe

^a,∗

, Sigrid Haande

^a

, Raoul-Marie Couture

^a,b

aNorwegianInstituteforWaterResearch(NIVA),Gaustadalléen21,0349Oslo,Norway

bUniversityofWaterloo,200UniversityAveW,Waterloo,Ontario,N2L3G1,Canada

a r t i c l e i n f o

Articlehistory:

Received10July2015

Receivedinrevisedform21April2016 Accepted7July2016

Availableonline1August2016

Keywords:

Phytoplankton Biologicalindicators Eutrophication Probabilisticmodel Uncertainty

Waterframeworkdirective

a b s t r a c t

Eutrophicationoflakesandtheriskofharmfulcyanobacterialbloomsdueisamajorchallengeforman- agementofaquaticecosystems,andclimatechangeisexpectedtoreinforcetheseproblems.Modellingof aquaticecosystemshasbeenwidelyusedtopredicteffectsofalteredlanduseandclimatechangeonwater quality,assessedbychemistryandphytoplanktonbiomass.However,theEuropeanWaterFramework Directiverequiresmoreadvancedbiologicalindicatorsfortheassessmentofecologicalstatusofwater bodies,suchastheamountofcyanobacteria.WeappliedaBayesiannetwork(BN)modellingapproach tolinkfuturescenariosofclimatechangeandland-usemanagementtoecologicalstatus,incorporating cyanobacteriabiomassasoneoftheindicators.ThecasestudyisLakeVansjøinNorway,whichhasa historyofeutrophicationandcyanobacterialblooms.Theobjectivewas(i)toassessthecombinedeffect ofchangesinlanduseandclimateontheecologicalstatusofalakeand(ii)toassessthesuitabilityofthe BNmodellingapproachforthispurpose.TheBNwasabletomodeleffectsofclimatechangeandman- agementonecologicalstatusofalake,bycombiningscenarios,process-basedmodeloutput,monitoring dataandthenationallakeassessmentsystem.Theresultsshowedthatthebeneﬁtsofbetterland-use managementwerepartlycounteractedbyfuturewarmingunderthesescenarios.Mostimportantly,the BNdemonstratedtheimportanceofincludingmorebiologicalindicatorsinthemodellingoflakestatus:

namely,thatinclusionofcyanobacteriabiomasscanlowertheecologicalstatuscomparedtoassessment byphytoplanktonbiomassalone.Thus,theBNapproachcanbeausefulsupplementtoprocess-based modelsforwaterresourcemanagement.¹

1. Introduction

Eutrophication of lakes due to nutrient run-off from the catchmentsisamajorchallengeforenvironmentalmanagement world-wide (Schindler, 2012). Theconsequences of eutrophica- tionforaquaticecosystemincludeharmfulcyanobacterialblooms (reviewedby Merel et al., 2013)and altered ﬁsh communities (Jeppesen et al.,2010).Climatechangeis expectedtoreinforce theproblems witheutrophicationdue toi.a.higher watertem- peratureandincreasednutrientrun-off(Jeppesenetal.,2009).In particular,alteredconditionsinlakesduetoclimatechangecan favourcyanobacteriaoverotherphytoplanktonspecies(Paerland Huisman, 2008).Therefore, climatechange maycounteract the

∗Correspondingauthor.

E-mailaddress:[email protected](S.J.Moe).

1 Abbreviations: BN=Bayesian network; Chl-a=chlorophyll a; WFD=Water FrameworkDirective.

effectsofmitigationmeasuresfornutrientenrichment,andmake itmoredifﬁculttoobtainmanagementtargetsforlakes.

Modellingofaquaticecosystemshasbeenusedwidelytosup- portwatermanagement,andtopredicteffectsofalteredlanduse and/orclimate(Galetal.,2014;Mooijetal.,2010;Recknageletal., 2014;Trolle etal.,2012).Process-basedmodelsfor catchments and lakes typically aim at predicting changes in water chem- istry(e.g.phosphorus,nitrogenandoxygen)orphysicalconditions (e.g.transparency,thermalstratiﬁcation)(e.g.,Jackson-Blakeetal., 2015).Manylakemodelsalsopredictchlorophylla(chl-a),which isaproxyofphytoplanktonbiomass(e.g.SalorantaandAndersen, 2007),andatraditionalindicatorofwaterquality.However,the Europeanlegislationforwatermanagement(theWaterFramework Directive–WFDEC,2000)requiresuseofmoreadvancedbiological indicatorsfor theassessment ofecologicalstatus ofwaterbod- ies.Thekeyindicatorsoflakeeutrophicationshouldrepresentnot onlyphytoplanktonbiomass,butalsootheraspectsoftheplank- toncommunity.ManyEuropeancountrieshavethereforeincluded intensityofcyanobacterialbloomsasanindicatorintheirassess- mentsystems(Poikaneetal.,2015).

http://dx.doi.org/10.1016/j.ecolmodel.2016.07.004

0/).

(2)

The relationships between climatic variables, nutrients and cyanobacteriahavebeenthoroughlystudiedbyexperiments(e.g.

Davisetal.,2009),long-termmonitoring(e.g.Nõgesetal.,2010) andanalysisoftimeseries(e.g.Huberetal.,2012;Wagnerand Adrian,2009)andofmulti-lakedatasets(Carvalhoetal.,2013;

Rigosietal.,2015).However,onlyafewprocess-basedlakemod- elshavesofarincorporatedsuchknowledge,accordingtoarecent review(Elliott, 2012).ThesemodelsarePROTECH(Elliott,2010;

Elliott and May, 2008), PCLake (Mooij et al., 2007), DYRESM- CAEDYM(Trolleetal.,2011),CLAMM(HowardandEasthope,2002), PROBE&BIOLA(Arheimeretal.,2005)andPROTBAS(Markensten and Pierson,2007).For example,an applicationof PROTECHto EsthwaiteWater(arelativelyshallowEnglishlake),predictedthat under scenarios of increasedwater temperature and decreased ﬂushing rate, cyanobacteria abundance increased, comprised a higherproportionofthephytoplanktonandhadalongerduration (Elliott,2010).However,lakemodelsthatcomprisecyanobacteria havenotyetbeenusedineffortstoassessecologicalstatus(sensu WFD),toourknowledge.

In this study, we apply a Bayesiannetwork (BN) modelling approach to link future scenarios of climate changeand land- usemanagementtoecologicalstatus,incorporatingcyanobacteria biomassaswellasotherindicators.ABNprovidesaframework forsummarisinglargeamountsofinformation(e.g.,fromprocess- basedmodels)andforintegratingdifferenttypesofinformation.

Italsoprovidesa toolfor displayingeffects ofdifferentscenar- ios,wherethechangeineachcomponentcanbeeasilyvisualised.

Theprobabilisticoutputcanreadilybeinterpretedastheriskof failingacertainmanagementtargetandsupportdecisionmaking.

For thesereasons,BNshavebeen increasinglyusedin environ- mentalmodelling(reviewedbyAguileraetal.,2011),andapplied inthecontextofe.g.riskassessment(Lecklinetal.,2011;Moe, 2010),resourcemanagement(Bartonetal.,2012)andecosystem services(Landuytetal.,2013).TherearemanyexamplesofBNmod- elsaddressingwaterresourcemanagement (Bartonetal.,2005;

Borsuketal.,2004;CastellettiandSoncini-Sessa,2007;Keshtkar etal.,2013;MartíndeSantaOlallaetal.,2007;Molinaetal.,2010;

Ticehurstetal.,2007;VarisandKuikka,1999).Here,wefocusonthe assessmentofecologicalstatusclassesofwaterbodiessensuWFD (High,Good,Moderate,PoorandBad).TheBNmethodologytypi- callypredictstheprobabilityofdifferentstates,andcantherefore beparticularlysuitableforthispurpose(Lehikoinenetal.,2014).

AsacasestudyforthisBNmodelwehaveselectedLakeVansjø in South-EastNorway. Thislake hasa history ofhigh levelsof phosphorusandphytoplanktonbiomass,andhasexperiencedsev- eral cyanobacterialblooms (Haande et al., 2011). The lake has beenmonitoredsince 1980,andhasbeen subjecttomodelling by process-based models (Couture et al., 2014; Saloranta and Andersen,2007)aswellasBayesiannetworks(Bartonetal.,2014 (basinVanemfjorden); Barton etal., 2008(basin Storefjorden)).

However,thisistheﬁrstefforttoincorporatecyanobacteriaina modelforLakeVansjø,andtolinkthemodeltoclimatechange scenarios.Theobjectiveofthestudyis(i)toassessthecombined effectofchangesinlanduseandclimateontheecologicalstatus ofalake,consideringbothphysico-chemicalindicatorsandphy- toplankton,includingcyanobacterialblooms,and(ii)toassessthe suitabilityoftheBNmodellingapproachforthispurpose.

2. Materialandmethods

2.1. Studysite

TheVansjø-Hobølcatchment(area690km²), alsoreferredto astheMorsacatchment,islocatedinsouth-easternNorway.The HobølRiverdrainsasub-catchmentofca.440km²intoLakeVansjø,

which is the catchment’s mainlake. LakeVansjø hasa surface areaof36km²andconsistsofseveralsub-basins,thetwolargest beingthedeeper,siliceousbasinStorefjorden(easternbasin)and theshallower,calcareousbasinVanemfjorden(westernbasin).In addition,therearesixsmallersub-basinswhichtogetherrepresent lessthan15%ofthelakesurfacearea.TheStorefjordenbasinwater ﬂowsintotheVanemfjordenbasinthroughashallowchannel.In thisstudywehaveuseddatafromthemostimpactedbasin,Vanem- fjorden(nationalwaterbodycode003-291-L,59.443^◦N,10.755^◦E).

Thisbasinisshallow(meandepthis3.8mandmaximumdepth is19.0m)andthewatercolumndoesnotstratifystably.Thesur- faceareais12km²,theresidencetimeis0.21yearandthewater bodyishumic.Thephytoplanktongrowthinthissystemisproba- blylimitedbylight,becauseofthehighhumiccontentinthelake andhencelowtransparencyinthewatercolumn(Skarbøviketal., 2014).

Thecurrentphysico-chemicalandecologicalstatusofVanem- fjordenaremoderate(Haandeetal.,2011),henceitfailstheWFD’s requirementof good ecologicalstatus (EC, 2000).However, the WFDalsorequiresthatthecurrentstatusofawaterbodyshould notbeworsened.Wearethereforealsointerestedintheriskof deteriorationfrommoderatetopoorstatusofVanemfjorden.

2.2. Dataandotherinformation 2.2.1. Scenarios

Thefuturescenariosapplyfortheperiod2030–2052(i.e.,40 years after thereference period 1990–2012) and are described in detail by Couture et al. (2014). In this study we have used the outcome of a climate scenario, “Had”: The global climate modelHADCM3combinedwiththeregionalclimatemodel(RCM) HADRM3.Thisscenariopredictschangesinbothyearlymeanair temperature(+1.6^◦C)andyearlyprecipitation(+78.8mm).Daily resolution scenario data for surface air temperature and precipitation werederived froma sub-set of theRCMsimulations andimplementedbyscalingtheobservedweather(1990–2012).

Theobservedtemperatureswerechangedtoreﬂecttheincrease in both median and variance predictedby theclimate models.

Precipitationwasscaledusingaratioof changeapproach, mul- tiplying observationbytheratio ofobserved (1990–2012)over predicted (2030–2052) precipitation.Climate conditions during thereferenceperiodarereferred toasclimate“Ref”.Theman- agementscenariosarereferredtoas“Ref”=reference(historical data), “Best”=bestcase (water-quality focus), “Worst”=“worst case”(economicfocus).The“Best”scenarioisdefinedbyfourcri- teria:(1)a10%reductioninagriculturalland,whichisconverted toforest,(2)a25%decreaseinvegetableproduction,whichiscon- vertedtograssproduction,(3)a25%decreaseinP-basedfertilizer application,and(4)a90%improvementintheP-removingperfor- manceofWWTPs.Conversely,the“Worst”scenarioisdefinedby (1)a10%reductionofforestcover,whichisconvertedtoagricul- turallands,(2)ashiftof25%ofthegrassproductiontovegetable production,(3)anincreaseofP-basedfertilizerapplicationby25%, and(4) a25%increase inthePloadof effluentsfromscattered dwellingsandWWTPsthroughoutthecatchment.Moredetailson theapplicationoftheseandotherscenariostothecatchmentand lakeprocess-basedmodelsaregivenbyCoutureetal.(2014).

2.2.2. Process-basedmodeloutput

Allaspectsofcatchmentandlakeprocess-basedmodellingare described by Couture et al. (2014). In brief, the effects of the climateand management scenarios onthe riverhydrology and chemistryweremodelledbythecatchmentmodelsPERSiST(Futter etal.,2013)andINCA-P(Wadeetal.,2002),respectively.PERSiST simulateddailyrunoffintheriversystemusinginputsofcatch- mentcharacteristicsanddailytemperatureandprecipitationtime

(3)

Table1

OverviewofnodesintheBayesiannetworkmodel.ModulesaredeﬁnedinFig.2.

Module Nodename Unit No.ofvalues Nodestates

1 2 3 4 5 6

1 Management Ref Worst Best

1 Climate Ref Had

1 Year 1990–1995 1996–2001 2002–2007 2008–2012

1 Month May Jun Jul Aug Sep Oct

1 Season May–Jun Jul–Aug Sep–Oct

2 Irradiance ␮mol/m²s 251,280^a 0–100 100–150 150–200 200–300

2 Secchi(pred.) m 251,280 0–2 2–2.6 2.6–5

2 TotalP(pred.) ␮g/L 251,280 0–20 20–25 25–30 30–39 39–50 50–80

2 Chl-a(pred.) ␮g/L 251,280 0–5 5–10.5 10.5–15 15–20 20–25 25–60

2 Temp.(pred.) ^◦C 251,280 0–10 10–15 15–19 19–30

3 Secchi(obs.) m 191 0–2 2–2.6 2.6–5

3 TotalP(obs.) ␮g/L 250 0–20 20–39 39–80

3 Chl-a(obs.) ␮g/L 250 0–10.5 10.5–20 20–60

3 Temp.(obs.) ^◦C 195 0–19 19–30

3 Cyano ␮g/L 103 0–1000 1000–2000 2000–6000

3 CyanoMax ␮g/L 103^b 0–1000 1000–2000 2000–6000

4 StatusSecchi HG M PB

4 StatusTotalP HG M PB

4 StatusChl-a HG M PB

4 StatusCyano HG M PB

4 StatusPhys-chem. HG M PB

4 StatusPhytoplankton HG M PB

4 Statusoflake HG M PB

aThenumberofvaluesinModule2isgeneratedbysimulationofweeklyvaluesduringMay-Octfor23yearswith60differentparametersetsfor6scenarios.

b CyanoMaxhasonly9uniquevalues(oneforeachyearofobservation).

series.INCA-Pproduceddailypredictionsofdischargeandmaterial transportintheriver(concentrationofsuspendedsolids,soluble reactivePandtotalP(TP)),whichwerethenpassedtothelake model.Thesuccessiveeffectsofthescenariosonthephysicalcon- ditionsandtheconcentrationofdifferentPfractionsinthelake weremodelledbytheprocess-basedmodelMyLake(Salorantaand Andersen,2007).InMyLake,phytoplanktonhasaconstantC:Pratio of106:1 andanorganic-P:Chl-a ratioof 1:1,suchthatparticu- lateorganicPisaproxyforChl-a(SalorantaandAndersen,2007).

TheMyLakemodelwasautomaticallycalibratedagainstmonitor- ingdatafromtheyears2005–2012,usingaprobabilisticBayesian inferencecalibrationscheme.Inthisschemeeachparameterwas givenapriorandaposteriordistribution,withintheframework ofaself-adaptivedifferentialevolutionlearningscheme(DREAM), implementedinMatlab(StarrfeltandKaste,2014).TheMCMCalgo- rithmwasrun alongeight chainsuntilconvergence,monitored visually,wasobtained.Fourhundred iterationsweresavedand usedtodetermineposteriorparameterdistribution.Anenvelope of60parametersetsofequallikelihood wassampledtogener- atea setof 60 model realisations withdaily resolution for 23 years(1990–2012).Thevariabilityamongthesesets(medianand interquartilespace)wasdiscussedby Coutureetal.(2014).For theBNmodel,all60realisationsoftheprocess-basedmodelsare usedasinputandconsideredasourceofuncertainty.Speciﬁcally, thefollowingoutcome ofthelakemodelwasusedasnodes in theBNmodel(see Table1):surfacewatertemperature(hence- forthreferredtoas“temperature”),Secchidepth,totalP(TP)and Chl-a. Secchi depth(SD)was calculated using thelight extinc- tion coefﬁcient (␩) calculated by MyLake and the relationship

␩=1.7/SD(Frenchetal.,1982).Temperatureandconcentrations wereaveragedfordepths0–4m(tomatchthemonitoringdata).In additionweincludedsurfaceirradianceatnoon(aninputvariable forMyLake),torepresentseasonalchangeinadditiontotempera- ture.Foreachvariable,valuesforonedayperweekwereselected (tomatchthesamplingfrequencyofthemonitoringdata).

2.2.3. Lakemonitoringdata

Themaindatasourceforthisstudywasthedataseriesfrom LakeVansjø,thebasinVanemfjorden(seeTable1andFig.1).All

dataweredownloadedfromNIVA’smonitoringdatabase(http://

www.aquamonitor.no).Thefollowingdatawereincludedinthis study: water temperature (years 1993–1996, 2005–2012), Sec- chi depth (2000–2001, 2005–2012), total P (1990–2012), Chl-a (1990–2012) and biomass of cyanobacteria (2004–2012). Inte- gratedwatersamplesfrom0to4mwerecollectedforthechemical and biological analyses. Only data fromthe months of Mayto Octoberwereincluded(followingthenationalclassiﬁcationsys- tem;section2.2.4).From2005allvariablesweremeasuredweekly, exceptforcyanobacteria,whichweremeasuredbi-weekly.

Inaddition,thelargerdatasetEUREGIwasusedforevaluation ofthemodel(asdescribedinsection3.3).TheEUREGIlakedataset resultsfromtheregionaleutrophicationsurveyinNorwayin1988 (Oredalen andFaafeng,2002).Thedatasetincludesquantitative analysesfrommorethan400lakes,sampledminimum4times.

Thelocationsareselectedinordertocoverthebroadestpossible gradientofhumaninﬂuence.Parametersthattypicallyrepresent eutrophication(TPandChl-a)rangeovertwoordersofmagnitude inthisdataset.Eutrophiclakesareoverrepresentedregardingthe proportionofareacoveredbytheselakes;nevertheless,thedataset containsmoreoligotrophicthaneutrophiclakes.Almost75%ofthe lakesareclear-waterlakes,ofwhichthemajorityiscalcium-poor lakes.Theremaining25%arehumiclakes;this grouphasequal proportionsofcalcium-poorandcalcium-richlakes.Intotal599 samplesfromEUREGIwereusedinthisstudy;samplesthatcom- prisedvaluesforwatertemperature,Chl-aandcyanobacteria.

2.2.4. Nationalclassiﬁcationsystemforlakes

The status assessment in this study is based on the main eutrophication indicators and their combination rules in the Norwegianlakeclassificationsystem,² withstatus classbound- aries defined for the lake type L-N8 (lowland, large, shallow, siliceous/moderatealkalinity,humic).Threeoftheindicators in the classification system were obtained from MyLake model predictions, and included in this study: seasonal averages of

2http://www.vannportalen.no/Revidertklassiﬁseringsveileder140123VZIS-.

pdf.ﬁle.

(4)

Fig.1. Observed(openblackcircles)andpredicted(redcurves)valuesof(a)temperature,(b)Secchidepth,(c)totalP,(d)chl-aand(e)cyanobacteria.Predictedvalues aremedianvalues(with25and75percentiles)of60runsoftheprocessmodel MyLakewithdifferentparametercombinations(seesection2.1.1).(Predictedvalues forcyanobacteriaarenotavailablefromthismodel).Bluetrianglesrepresentsea- sonalmeanvaluesforSecchidepth,totalPandchl-a,andseasonalmaximumvalue forcyanobacteria(correspondingtothenodeCyanoMax).Horizontallinesindicate theboundariesbetweenecologicalstatusclasses:High-Good(H-G),Moderate(M) andPoor-Bad(P-B).

Secchidepth,TPandChl-a.Accordingtotheclassiﬁcationsystem, physico-chemicalindicators(here:Secchidepthand TP)should becombinedbyaveraging.Phytoplanktonstatusshouldinprin- ciple beassessedby fourindicators: Chl-a, totalphytoplankton biomass,PTI(ameasureofsensitivevs.toleranttaxa;(Ptacniketal., 2009))andtheyearlymaximumofcyanobacterialbiomass.Allfour indicescanbecalculatedfromthemonitoringdata,buttheyareall correlated,andonlyonecanbepredictedbyMyLake(Chl-a).We

thereforechosetoincludeonlyoneadditionalphytoplanktonindex intheBN,namelytheyearlymaximumofcyanobacteria(termed

“CyanoMax”).Combinedphytoplanktonstatusshouldbeobtained asfollows:ifCyanoMaxhaveworsestatusthanchl-a,thenthetwo indicatorsshouldbeaveraged;ifCyanoMaxhasequalorbettersta- tusthanchl-a,thenCyanoMaxshouldbeignored.Thus,including cyanobacteriacanonlyresultinworseorequalstatusofphyto- planktoncomparedtothestatusdeterminedbychl-aalone.Finally, whiletheoverallecologicalstatusofthelakeisdeterminedpri- marilybybiology(here:phytoplankton),itcanbecompromised byphysico-chemicalelements.

IfthestatussetbybiologyisHighorGood,andthephysico- chemicalstatusisworsethanthebiologicalstatus,thentheoverall ecologicalstatusshouldbereducedbyoneclass(i.e.,fromHigh toGoodor fromGoodtoModerate).(Moredetailsare givenin AppendixA).Thefullclassiﬁcationsystemcomprisesseveralmore indicatorsincludingbothphysico-chemicalqualityelements(e.g.

TotalN)andbiologicalqualityelements(BQEs;macrophytes,ben- thicinvertebratesandﬁsh).Inthisstudy,however,weincluded only the indicators that couldbe predicted by MyLakeor that couldbelinkedtoMyLakepredictionswithhighconﬁdence(i.e., cyanobacteria).

2.3. Bayesiannetworkmodelling

ForconstructingtheBNmodel,wefollowedrecentguidelines foruseofBNinecologicalmodelling(Marcotetal.,2006;Pollino andHenderson,2010):(1)Deﬁningtheobjectiveofthemodeland itsﬁnalnode(here:ecologicalstatusofthelake);(2)generating aconceptualmodel(nodesandarrows)basedonknowledgefrom theliteratureandonexpertknowledge;(3)establishingthemodel statesandquantifyingtherelationships.TheBNmodelwasdevel- opedandruninthesoftwareHuginExpert,version8(http://www.

hugin.com).

2.3.1. Modelstructure

Ina BNmodel,eachnode(variable)istypicallydeﬁnedbya discrete probability distribution acrossa number of alternative states(i.e.,intervalsorcategories).Thisstructureenablesdiffer- enttypesofinformationtobelinkedbyconditionalprobability tables(CPT)(see Table2and section3.1).Althoughcontinuous variablesmayalsobeincludedinaBNwithcertainrestrictions, thistypeofnodesarenotconsideredhere.Allnodeswithoutgoing arrowsaretermed“parentnodes”,whileallnodeswithincoming arrowsaretermed“childnodes”.InaCPT,theprobabilisticdepen- denciesbetweenachildnodeanditsparentsaredeﬁned.Whenthe modelisrun,probabilitydistributionofthechildnodeisupdated accordingly, giventhestates oftheparentnodes,following the Bayes’theoremforconditionalprobabilitycalculation(Koskiand Noble,2009).TheprobabilitydistributionsintheCPTscanrepre- sentthenaturalvariabilityinthesystemaswellasanyothertype ofuncertaintyconcerningtherelationshipbetweenthevariables.

Inourmodelthemainsourcesofvariabilityare(1)thetempo- ralvariationinthepredictedandobservedtimeseries(withinthe speciﬁedtimeintervals)and(2)uncertaintyinthepredictionsof theprocess-basedmodelsthatareincludedintheBN.Thecom- plexityofaBNgrowsexponentiallywiththenumberofnodesand arrows;thereforeitisoftendesirabletolimitthenumberofnodes (VarisandKuikka, 1999).Thecomputingcapacity ofcomputers haveincreasedtotheextentthatevenrelativelycomplexandbig networkscanbebuiltandrun(Lehikoinenetal.,2013),butmore complexBNsneverthelessrequiremoredataorotherinformation thansimplerones.Inthisstudy,weaimedatincludingonlythe nodesthatwerenecessaryto(i)runthemodelaccordingtoselected scenarios,(ii)representparticularprocessesthatwereimportant

(5)

Table2

Examplesofconditionalprobabilitytables(CPT)foreachmoduleoftheBNmodel.Eachcolumncontainstheprobabilitydistributionofachildnodeforagivencombination ofstatesoftheparentnodes.Thebottomrow(“Experience”)containsthetotalcountofobservationsforeachcombinationofparentnodes.

(a)CPT(theﬁrst8columns)forChl-a(predicted)conditionalonmanagement,years,irradianceandwatertemperature.Thefulltablecontains3(managementscenarios) x4(yearintervals)x4(irradianceintervals)x4(temperatureintervals)=192columns.

Management Reference

Years 1990–1995

Irradiance 0–100 100–150

Temp.(pred.) 0–10 10–15 15–19 19–25 0–10 10–15 15–19 19–25

Chl-a(pred.)

0–5 0.013 0.012 0 0 0.124 0.067 0.004 0

5–10.5 0.104 0.106 0.117 0.117 0.588 0.180 0.065 0.092

10.5–15 0.066 0.020 0.017 0.017 0.148 0.223 0.082 0.042

15–20 0.297 0.085 0.000 0.000 0.036 0.026 0.033 0.000

20–25 0.313 0.264 0.104 0.104 0.050 0.168 0.018 0.000

25–60 0.206 0.512 0.763 0.763 0.055 0.337 0.798 0.867

Experience 3015 2445 540 0^a 420 1200 1980 480

(b)CPTforCyanobacteriaconditionalonChl-a(observed)andwatertemperature(observed).

Chl-a(obs.) 0–10.5 10.5–20 20–60

Temp.(obs) 0–19 19–25 0–19 19–25 0–19 19–25

Cyano

0–1000 1 1 1 0.923 0.333 0.323

1000–2000 0 0 0 0.077 0.333 0.290

2000–6000 0 0 0 0 0.333 0.387

Experience 20 1 22 13 3 31

(c)CPTforCyanoMaxconditionalonCyanobacteriaandSeason.

Cyano 0–1000 1000–2000 2000–6000

Season May–Jun Jul–Aug Sep–Oct May–Jun Jul–Aug Sep–Oct May–Jun Jul–Aug Sep–Oct

CyanoMax

0–1000 0.618 0.724 0.667 0 0 0 0 0 0

1000–2000 0.088 0.138 0.111 0.167 0.167 0 0 0 0

2000–6000 0.294 0.138 0.222 0.833 0.833 1 1 1 1

Experience 34 29 27 6 6 2 1 12 2

(d)CPTforStatusoflakeconditionalonstatusofphytoplankton(PP)andstatusofphysico-chemical(PC)variables.HG=High-Good,M=Moderate,PB=Poor-Bad.

StatusPP HG M PB

StatusPC HG M PB HG M PB HG M PB

StatusLake

HG 1 0 0 0 0 0 0 0 0

M 0 1 1 1 1 0 0 0 0

PB 0 0 0 0 0 1 1 1 1

aAssumedprobabilitydistributionsinsertedwherenoobservationswereavailable.

forthecyanobacteriaandotherphytoplanktonand(iii)assessthe effectsofthescenariosonthestatusindicators.

ABN is usuallynot a dynamic model, meaning thatit does nothaveatimedimension.Instead,thepredictionsofa BNcan representtheprobabilityofrealisingdifferentoutcomesduringa speciﬁedperiod.TheBNinourstudyrepresentsthewholeperiod forwhichtheMyLakemodelwasrun(1990–2012).However,there hasbeensubstantialchangesintheconcentrationsofTPandchl-a duringthisperiod(Fig.1candd),whichcouldbeusefultoaccount forintheBN.Wethereforeincludedanode“Year”thatdividedthe 23-yeartimespaninto4periodsof5–6years;thiswaytheeffects ofthedifferentscenariosonwaterquality(i.e.,theCPTs)couldbe estimatedseparatelyfortheseperiods,andtheBNcouldberunfor selectedperiods.(ThedefaultsettingoftheYearnodewasauni- formprobabilitydistribution,correspondingtorunningtheBNfor thewhole23-yearperiod).Moreover,anode“Month”wasincluded toaccountforseasonalchangesinthewaterquality.

The BN model developed in this study (Fig. 2) comprises fourmodules,correspondingtothefoursourcesofinformation describedabove.

Module1containsalltheparentnodes,representingthecli- mateandmanagementscenarios,aswellasthenodesrepresenting speciﬁcperiods(yearsandmonth).

Module2linksthesescenariostotheoutputfromtheprocess- basedmodels,i.e.thepredictedeffectsonphysico-chemistryinthe lake.

Module3links thesemodelpredictionstotheobservedtime seriesforasetofphysical,chemicalandbiologicalvariables,and furthermoreprovidesalinkfromtwoofthesevariables(chl-aand water temperature)to theobserved cyanobacterialbiomass. In addition,theyearlymaximumofcyanobacteria(“CyanoMax”)is setequaltothehighestobservedcyanobacteriabiomassacrossall samplesinagivenyear.Thus,eachobservationofCyanoisasso- ciatedwithaCyanoMaxfromthesameyear,butpossiblyfroma differentmonth.

Module4linkseachofthephysico-chemicalandbiologicalindi- catorstothelakeclassiﬁcationsystem.Thisenablespredictionof theprobabilityofdifferentstatusclassesforeachindicatoraswell asfortheoverallecologicalstatusofthelake.

(6)

Fig.2.StructureoftheBayesianNetwork(BN)modelforecologicalstatusofLakeVansjø,basinVanemfjorden.Themodelconsistsoffourmodules:(1)Climateand managementscenarios(2),outputfromtheprocess-basedlakemodelMyLake;(3)monitoringdatafromLakeVansjø(1990–2012);(4)thenationalclassiﬁcationsystemfor ecologicalstatusoflakes.Thepriorprobabilitydistributionforeachnodeisdisplayedbothashorizontalbarsandbypercentages(theﬁrstcolumnineachnode),acrossthe states(thesecondcolumn).Thesetofarrowspointingtoonenoderepresentstheconditionalprobabilitytableforthisnode.Statusclasses:HG=High-Good(requiredbythe WFD),M=moderate,PB=Poor-Bad.

Thecausallinksbetweenthenodes(i.e.,thearrowsandtheir directions)canbedeterminedindifferentways.Fornodesthatare basedondata,itispossibletoletthesoftwareestimatesuggesta setofarrowsandtheirdirectionsgivenspeciﬁccriteria.Neverthe- less,wechosetodevelopthestructurebasedonknowledgeand theoryaboutcausalrelationshipsamongthenodes.Forthenodes inModule2,regressiontreeanalyseswereperformedtoexplore whichparentnodeshadsigniﬁcanteffectonthechildnodes.The analyseswereperformedwiththepackagesrpart(Therneauetal., 2015)andparty(Hothornetal.,2006)inthesoftwareR(RCore

Team,2015).Allindicatornodesvariedwithyearandwithmonth.

ThenodeManagementhadsigniﬁcanteffectsonallindicatornodes predictedbyMyLake(Secchi,TPandChl-a).Watertemperature affectedChl-a,butnotTotalP.ThenodeIrradiancewasincluded as a parent for Chl-a, becauseof the particularimportance for phytoplanktongrowth.Thepurposewastodistinguishbetween effectsofIrradianceandTemperature;bothvariablesvarieddur- ingtheyear,butonlyTemperaturewasaffectedbyClimate.TPand Chl-awerestronglycorrelated,asiscommonlyobservedinlakes (Phillipsetal.,2008),andthereforebothvariablescouldhavebeena

Fig.3. RegressiontreeforeffectsoftemperatureonthevariableCyanoMax(seasonalmaximumofcyanobacteriabiomass).Thenumbersonthebranches(18.85and20.2) showthesigniﬁcantbreakpointsalongtemperaturegradient.ThebarplotsineachresultingnodeshowtheprobabilitydistributionofCyanoMaxacrossthethreestatus classes:1:High-Good(<10.5␮g/L),2:Moderate(10.5–20␮g/L),Poor-Bad(≥20␮g/L).n=numberofobservationsineachnode.

(7)

suitableparentnodeforCyanobacteria.WechoseChl-aasthepar- entnode,becausethisvariablehaslatelybeenreportedtobea betterpredictorofcyanobacteriabiomassthanthemorecommonly usedTP(Ptacniketal.,2008).

2.3.2. Nodestatesandpriorprobabilitydistributions

Continuousvariablesmustbediscretisedintointervals(states) foruseindiscretenodesinaBN.Thenumberofstatesforeachnode istypicallykeptlow, becausethemodel complexityalsogrows quicklywiththenumberofstates.Inthisstudy,therefore,wetried tominimisethenumberofstates,whilestillobtainingamodelwith sufﬁcientsensitivitytorespondtothescenarios.Anoverviewofthe statesofallnodesisgiveninTable1.

Forallstatusnodes(Module4),theﬁveecologicalstatusclasses werelumpedintothree states(High-Good,Moderateand Poor- Bad).ThecorrespondingindicatornodesinModule3(Monitoring data:Secchi,TotalP,Chl-aandCyanoMax)werediscretisedinto threeintervals,withbordersdeterminedbytheclassboundariesof thenationalclassiﬁcationsystem(seeTableA1a–d).Observedtem- peraturewasdividedintotwointervals,determinedbyaregression treeanalysis(Fig.3):Abreakpointintheeffectoftemperatureon cyanobacteriawasestimatedat19^◦C (abovewhich therewasa higherprobabilityofhighcyanobacteriaconcentrations).Forthe correspondingvariablespredictedbyMyLake(Module2),thelarge amountofsimulateddataalloweddiscretisationwithhigherres- olution:predictedTotalP,Chl-aandTemperatureweregiven6,6, and4statesrespectively.Thestatesfromthecorrespondingvari- ablesinModule3wereusedasastartingpoint;thenthestate(s) withthehighestproportionoftheobservationsweresplitintotwo ormoreintervalstoobtainamoreevenprobabilitydistribution.

Forexample, theTPstate30–39␮g/L wassplitinto3 intervals (20–25,25–30and30–39)whilethestate39–80␮g/Lwassplit intotwointervals(39–50and50–80).Theyears(Module1)were groupedintofour5-or6-yearperiods(1990–1995,1996–2001, 2002–2007and2008–2012).Themonthsweregroupedintothree 2-monthsperiodsin a separatenode“Season” (May-June,July- AugustandSeptember-October);thepurposetoobtainaparent nodeforCyanoMaxwithfewerstatesthantheMonthnode.

AllpriorprobabilitydistributionsaredisplayedinFig.2(and inSupplementarydata).Thepriorprobabilitydistributionswere deﬁnedasfollows.For parentnodesrepresentingscenarios and timeintervals(Module1),equalprobabilitywasassumedforeach state.Thiswassimplyastartingpointforrunningthemodel,and isnotmeanttorepresentourbeliefsorknowledge.Foreachsubse- quentchildnode,thepriorprobabilitydistributionwasdetermined bytheirCPTincombinationwiththepriorprobabilitydistributions oftheirparentnodes.Hence,thepriorprobabilitydistributionsof allchildnodesthroughouttheBNrepresentallthedifferentsce- nariocombinationswithequalprobability.

3. Calculation

3.1. Constructionofconditionalprobabilitytables

The discrete probability distributions in the CPTs are also obtainedby different approaches in the different BN modules.

Table2containsexamplesofCPTsforeachmodule,whileallCPTs areincludedinSupplementarydata.

In Module 2 (Process-based model output), the conditional probabilitydistributionofeach childnodewasthereforecalcu- latedasthefrequencydistributionofthisvariableacrosseachof itsparentnodesin thereferencescenariofor both climateand management,for all60realisations ofMyLakepooledtogether.

For example, for predictedchl-a, the probability of the lowest chl-ainterval (0–5␮g/L)undera givencombinationofstates of

theparentnodes(e.g.Management=Reference,Year=1990-1995, Irradiance=0-100andTemperature=0-10)wasdeterminedbythe countofpredictedchl-avaluesobtainedinthisintervalforthispar- ticularcombinationofstatesoftheparentsnodes(40)dividedby thetotalnumberofobservationsforthiscombination(3015).I.e., theprobabilityis40/3015=0.013(theupperleftcellinTable2a).

Thus,theprobabilitydistributioninthis columnarisesfromthe variabilitybetweenthe60MyLakemodelrealisationsaswellas from thetemporal variability during theperiod 1990–1995. In caseswhereagivencombinationofparents’statesintherefer- encescenariodidnotoccurinthecountdata(Experience=0in theCPT),valuesbasedonexpertjudgementwereinsertedtoallow themodeltorun.Forexample,forTotalP(obs.),thecountwas zerofor thelowestinterval ofTotalP (pred.)(TableB1a);here anassumedprobabilitydistributionbasedontheneighbourcol- umnwasinserted.For thenodes in module2,where theCPTs hadahighnumberofcolumns,columnswithExperience=0were populatedwithprobabilitydistributionsfromtheneighbourcol- umn(seeexampleinTable2a).(Testingshowedthattheassumed probabilitydistributionsinsuchcaseshadnegligibleeffectsonthe posteriorprobabilitydistributionsofthechildnodes).

InModule3(Monitoringdata),likewise,thelinksfromthepre- dictedMyLake outcome totheobserved monitoring datawere basedonthejointfrequencydistributions ofthetwo variables.

Theobserveddatawerepairedwiththecorrespondingpredicted dataforthesameweek,andtheconcentrationintervalswerecom- pared(TableB1).TheCPTfortheCyanonodewascalculatedfrom theobservationsofTemperature,Chl-aandCyanobacteriafromthe samedate.

TheCPTforCyanoMax(themaximumofCyanoforeachyear) wasobtainedbycountingthenumberofobservedCyanoineach concentrationintervaland eachseason,andcalculating thefre- quencydistributionacrossthecorrespondingCyanoMaxintervals foralloftheseobservations.Forexample,outofthe34observations ofCyanoconcentrationbelow1000␮g/LintheMay-Juneseason, 10 observations(probability0.29) camefrom ayear wherethe CyanoMaxinthesameyearexceeded2000␮g/L.Thetotalnumber ofcyanobacteriasamples(90)wasrelativelylowforcalculatingthe 9frequencydistributionsintheCPTofCyano(andofCyanoMax;

Table2candd).Wethereforecomplementedthetemporaldata forthetargetlakewiththelargerspatialdatasetfromtheregional datasetEUREGI(describedinsection2.2.3).

InModule4(Ecologicalstatus),eachofthefourindicators(Sec- chi,TP,Chl-aandCyano)hasastatusnodewherethethreestates (High-Good,ModerateorPoor-Bad)correspondtothethreeinter- valsoftheparentnode.Forthesenodes,theCPTissetto1foreach cellwithmatchingstatesand0forallothercells(TableA1a–d).For thesubsequentnodes(Physico-chemicalstatus,Phytoplanktonsta- tusandLakestatus),theimplementationofthecombinationrules intotheCPTsisdescribedinAppendixA.

3.2. RunningtheBNmodel

ABNmodelcanberunbyalteringtheprobabilitydistribution ofoneormorenodes(e.g.,selectingonemanagementscenario) andtherebyupdatingtheprobabilitydistributioninallthenodes thatarelinkedbyCPTsthroughoutthenetwork(e.g.,thestatus ofthelake).Acommonwaytorunthemodelisto“setevidence”

foroneormoreoftheparentnodes,i.e.toselectoneofthestates (assign100%probabilityforthisstate)(Fig.4).Inthisstudy,the mainmodelruns(the6scenarios)wereperformedbysettingevi- denceforeachcombinationofthemanagementandclimatenode states,andrecordingtheposteriorprobabilitiesinthechildnodes.

Inaddition,forthepurposeofmodelevaluation,alternativemodel

(8)

Fig.4.ExamplesofBNmodelpredictions(posteriorprobabilitydistributions)fortwoscenarios.(a)Scenariowithcurrentclimate(Ref)andreferencemanagement(Ref).(b) Scenariowithfutureclimate(Had)and“bestcase”management.NotetheshifttohigherprobabilityofHGstatusformostofthenodesunderthelatterscenario.Formore details,seeFig.2.

runswereperformedbysettingevidenceforotherselectednodes inthenetwork(seenextsection).

3.3. Modelevaluation

Modelevaluationisanimportantstepingoodmodellingprac- tice,butevaluationofBayesiannetworkmodelsisoftenneglected (Aguileraetal.,2011).Ideally,onepartofadatasetshouldbeused for“training”(modelcalibration)whileanotherpartisreserved forevaluationbycomparisonwithmodelpredictions(Chenand

Pollino,2012).However,thedataonthemostcrucialcomponent ofthismodel–Cyanobacteria–couldnotbedividedwithoutcom- promising the calibration (constructionof CPTs; see Table2b).

Moreover, predictions based on future scenarios could not be comparedtorealdata.Other,morequalitativeformsofmodeleval- uationhavebeensuggested(ChenandPollino,2012;Marcot,2012), suchasapplyingdifferentcombinationsofinputsandexamining theresultingprobabilitiesthroughoutthenetwork,totestwhether thebehaviourofthemodelisconsistentwithcurrentunderstand- ingaboutthesystem.Here,weidentiﬁedthreecriticalpartsofthe

(9)

modelandinspectedthesensitivityofthemodeltoalterationsof theseparts.

(1)Thelinkfromprocess-basedmodelpredictionstoobserveddata.

Thecorrespondencebetweenpredictedandobservedvaluesis capturedintheCPTsforthemonitoringdata(TableB1).Asa roughevaluationbasedontheproportionsofmatchingstates intheseCPTs,thegoodness-of-ﬁtoftheMyLakemodelpredic- tionscanbecharacterisedasgood(temperature),intermediate (chl-a)andlessgood(TP),respectively.Adetailedassessment oftheMyLakemodelpredictionsandexplanationsforthedevi- ationsaregivenbyCoutureetal.(2014).Toassesstheinﬂuence ofthepredictionvs.observationuncertaintyonthemodelper- formance,werantwoversionsofthemodel:oneversionthat wasbased ontheprocess-based model predictionswithout accountingforthemismatchwithobservations(version1)and anotherthatincorporatedthisuncertaintyintheCPTs(version 2).

(2)The CPT for cyanobacteria. Due to the limited number of cyanobacteriaobservations(Table2b),toreserveasubsetof thecyanobacteriadataforevaluationpurposeswouldnotbe meaningful.Instead,weusedtheindependentEUREGIdataset (seesection2.2.3)toconstructanalternativeCPTforcyanobac- teria(modelversion3,basedonversion1)andcomparedthe outcomeofthisversionwiththatofversion1.

(3)Effectsofwatertemperature.AcriticalcomponentofthisBNis theeffectofwatertemperatureoncyanobacteria.Moreover, sincetheconditionalprobabilitiesusedforcalculatingposterior probabilitiesforcyanobacteriaarebasedonveryfewobser- vationsforsomeoftheparentstatecombinations(Table2b), itisimportanttocheckthattheseCPTsdonotprovidespuri- ousresults.Wethereforeinspectedmorecloselyrelationship betweentemperature,Chl-aandcyanobacteriabysettingevi- dence(ﬁxatingprobabilities)forthenodesTemperatureand Chl-a.Inaddition,theeffectofSeasonwaschecked.

4. Resultanddiscussion

4.1. Effectsofmanagementandclimatescenariosonlakestatus Theresultsreportedinthissectionarebasedonversion1ofthe BN(deﬁnedinsection3.3;thechoiceoftheversionisexplained insection4.2).Themodeloutcomeofthisversionisequaltothe outcomeoftheMyLakemodel(TPandChl-a)asreportedbyCouture etal.(2014).TheBNmodelhasachievednewresultsinthreemain ways:(1) includingtheCyanobacteriacomponentinthemodel, aswellasSecchidepth,(2)assessingtheprobabilitydistribution ofstatusclassesforthefourindicatorvariables,and(3)usingthe combinationrulesofthenationalclassiﬁcationsystemtoassessthe overalllakestatus.Inthisstudywefocusmoreontheresulting statusclasses(High-Good,Moderate andPoor-Bad)than onthe exactvaluesoftheindicators.

Theclimatescenariohada limitedeffectoftheTemperature node(seeFig.4):theprobabilityof“awarmyear”(>19^◦Cwater temperatureduringMay-October)increasedfrom17%to27%.All subsequentclimatechange effects in theBN arebased on this increase.

Secchidepthvalues, both observed and predicted(MyLake), wereinthePoor-Badstatusduringthewholetimeseries(Fig.1a).

Accordingly,thisindicatorhada100%probabilityofPoor-Badsta- tus,forthereferencesscenarioaswellasforallotherscenarios (Fig.5a). Hence,theeffects ofthedifferentscenarios onSecchi deptharenotgivenmoreattentionhere.Nevertheless,theSec- chidepthstatusaffectedthePhysico-chemicalstatus(Fig.5c)and thereby potentially the overall lake status (Fig. 5g). Therefore,

inclusionoftheSecchidepthnodeisimportantforobtainingamore correctoverallstatusassessment.

ForTP,thebest-casemanagementincreasedtheprobabilityof obtainingabetterstatus(Fig.5bandd).Theprobabilityofgoodor highstatuswas<0.1%forallscenarios.Theprobabilityofmoderate status,however,increasedfrom61%underreferencemanagement to84% withthe best-casemanagement, and decreased toonly 1.5%withtheworst-casemanagement.Inthecombinedphysico- chemicalstatusassessment(Fig.5c),whichincludedbothSecchi depthandTP,theprobabilityofmoderatestatuswashalvedcom- paredtotheassessmentforTPalone.Thisresultreﬂectsthefact thattheCPT forthephysico-chemicalstatus node(AppendixA) weightedthecontributionsfromTPandSecchiequally.

ThestatusindicatedbyChl-awasbetterthanthestatusofTP, with30%probabilityofgood(orhigh)statusunderthereference scenario.Thiscanbeexplainedbythepoorlightconditionsinthe lake:aSecchidepthof1–1.5mandnostablestratiﬁcationisproba- blycausingthephytoplanktontobecontinuouslymixedtodepths beyondthephoticzone.Hence,thephytoplanktonislight-limited, and notableto utilizetheavailableP foroptimalgrowth.Chl- astatuswasaffectedbytheclimatescenariosaswellasbythe managementscenarios(Fig.5d).Undercurrentclimateconditions, best-casemanagementincreasedtheprobabilityofobtaininggood orhighstatusto35%withthebest-casemanagement,whileworst- case management decreased it to 18%. Climate change slightly reducedtheprobabilityofgoodorhighstatusineachcase.

ThestatusprobabilitydistributionofCyanoMax(Fig.5e)dif- feredfromthedistributionofChl-a:CyanoMaxhadhighprobability of both thebest and theworst status but a low probability of the intermediate status. This strongly bimodal distribution of CyanoMaxreﬂectsthetendencyofcyanobacteriatooccurineither veryloworveryhighabundance(blooms)(Fig.1e).Nevertheless, thestatusofCyanobacteriarespondedtothemanagementandcli- matescenariosinasimilarwaytoChl-a.Inotherwords,reducing nutrientconcentrationscounteractedtheincreasedcyanobacterial riskassociatedwithhighertemperatures,inagreementwiththe conclusionofRigosietal.(2015).

Thestatus distributionofthecombinedPhytoplankton node (Fig.5f)wasmoreaffectedbytheChl-anodethanbytheCyanobac- terianode,ascouldbeexpectedfromthecombinationrule(section 2.2.4).Notably,thePhytoplanktonnodehadgenerallyworsesta- tusthaneitherofitstwoparentnodes.Theprobabilitiesofgood orhighstatus were22%, 25% and13% (forReference, Best and Worstmanagementrespectively)undercurrentclimate,and18%, 21%and10%underclimatechange.Thisresultisconsistentwith thecombinationruleforphytoplankton:includingCyanobacteria intheassessmentcanonlyworsen (ornotaffect)thecombined Phytoplanktonstatus.

Intheoveralllakestatusassessment(Fig.5g),thebestpossible statuswasModerate,duetotheinﬂuenceofthephysico-chemical node.Ingeneral,theprobabilityofmoderate(orbetter)status(e.g., 32%intheReferencescenario)wasclosertothephysico-chemical node(31%)thantothephytoplanktonnode(51%);i.e.thelakesta- tuswasworsethanindicatedbyphytoplanktonalone.Thisresult reﬂectsthewhole-lakecombinationrule,whichselectedtheworse status (ora compromise)whenever the status of thetwo par- entnodesdiffer.Nevertheless,thewhole-lakestatusalsoshowed negativeimpactofclimatechange,whichwasinheritedfromthe Phytoplankton node(sinceclimatechangeimpacts onphysico- chemistrywerenotincorporatedinthisBN).Hence,allofthefour indicatornodes(Secchidepth,TP,chl-aandcyanobacteria)played importantrolesintheoverallassessmentoflakestatusunderthe managementanddifferentscenarios.

TheecologicalstatusofVanemfjordenassessedbytheBN(35%

probabilityofModerateand65%probabilityofPoor-Badforthe referencescenario;Fig.5g)wassomewhatworsethanthemost

(10)

0 20 40 60 80 100

Ref Had Ref Had Ref Had

Climate scenario

Worst Ref Best

Management scenario Secchi depth

Probability (%)

(a)

0 20 40 60 80 100

Climate scenario

Worst Ref Best

Management scenario Total P

(b)

0 20 40 60 80 100

Climate scenario

Worst Ref Best

Management scenario Phys.-chem.

(c)

0 20 40 60 80 100

Climate scenario

Worst Ref Best

Management scenario Chla

Probability (%)

(d)

0 20 40 60 80 100

Climate scenario

Worst Ref Best

Management scenario Cyanobacteria

(e)

0 20 40 60 80 100

Climate scenario

Worst Ref Best

Management scenario Phytoplankton

(f)

Poor-Bad Moderate High-Good

0 20 40 60 80 100

Climate scenario

Worst Ref Best

Management scenario Lake

Probability (%)

(g)

Fig.5.Effectsofclimateandmanagementscenariosontheprobabilitydistributionofstatusclassesforallnodesinthemodule“Lakeclassiﬁcationsystem”(Fig.2).The climatescenariosarereference(“Ref”)andHadRM3(“Had);themanagementscenariosareeconomyfocus(“Worst”),reference(“Ref”)andwater-qualityfocus(“Best”).The distributionofstatusclasses(High-Good,ModerateandPoor-Bad)forSecchidepth(a)andtotalP(b)arecombinedintheplot“Physico-chemical”(c),whiletheresultsfor Chl-a(b)andCyanobacteria(e)arecombinedintheplot“Phytoplankton”(f).Finally,theresultsforPhysico-chemicalandPhytoplanktonarecombinedintheplot“Lake”(g).

recentofﬁcialecologicalstatusassessment,whichisinthemiddle oftheModerateclass(Haandeetal.,2011).Thiscanbeexplained bydifferencesintheselectionofdatafortheassessment(where thedataselectedfortheBNwereconstrainedbythelinktothe MyLakeoutput).Firstly,theofﬁcialstatusisbasedondatafrom 2004and2010only,whiletheBNalsoincludesdatafromyears prior to2004,duringwhich conditions wereworse(Fig.1c–d).

Secondly,thepreviouslypublishedassessmentdidnotconsider Secchidepth,whichimposedPoor-Badstatus,butinsteadincluded TotalN,whichwasassociatedwithModeratestatus.Thirdly,itdid notincludecyanobacteria(whichcouldhavereducedthephyto- planktonstatus),butinsteadincludedmacrophytes(whichwere associatedwithModeratestatus).

Theeffectsofclimatechangeconsideredinthisstudywerelim- itedtowatertemperatureandeffects onphytoplankton.Higher water temperatureis likely toaffect otherbiological groups as well,especially fish(Hering etal., 2013;Jeppesen et al.,2012), whichhavesofarnotbeenmonitoredinVanemfjorden.Theclimate changescenarioalsocomprisedincreasedprecipitation,whichwas includedintheprocess-basedmodelsforthecatchmentandlake (Coutureetal.,2014),butprecipitationhasnotyetbeenincorpo- ratedexplicitlyasanodeintheBN.Increasedprecipitationhas thepotentialtoinfluenceecological statusin severalways. For example,increasedrun-offofnutrientsfromagricultureislikelyto givehigherTPconcentrations(Jeppesenetal.,2009).Ontheother hand,increasedflushingofthelakemayreducetheconcentration ofphytoplanktonandinparticularofcyanobacteria,whichtendto haveslowergrowthratethanotherphytoplankton(Carvalhoetal.,

2011;Elliott,2012).Suchcontrastingeffectsofalteredprecipita- tionpatternscouldbeconsideredinamoreadvancedversionof thisBN.

4.2. Modelevaluation

4.2.1. Thelinkfromprocess-basedmodelpredictionstoobserved values

Theaccuracyof theMyLakemodel predictionsvariedhighly amongthedifferentindicatorvariables.Themodelperformance isdiscussedindetailbyCoutureetal.(2014);hereweonlycon- sidertheaccuracyatthelevelofnodestates(intervals)andfocus ontheimplicationsfortheBNmodel.ForSecchidepth,thematch betweenpredictionand observationwas100%,becauseallpre- dictionsandobservationswereinthesameinterval(0–2m).For water temperature the match was generally good (Table B1c), althoughthehighestobservedtemperatures(19–25^◦C)werefre- quentlyunderestimatedby MyLake(as15–19^◦C). Thisnegative bias in theprediction of temperaturemay have contributed to themismatchbetweenpredictedandobservedChl-a(TableB1b).

AlthoughtheprecisionofpredictedChl-awasratherlow(43%of theobservedvaluespredictedtothecorrectinterval),theaccuracy wasgoodintermsofthebalancebetweenunderestimations(28%) andoverestimations(29%).TPwaslesswellpredicted:althoughthe precision(66%)washigherthanforchl-a,theaccuracywaslower:

10%underestimationsvs.23%overestimations.Theunderestima- tionsaremostlyfromtheperiod1990to1999(Fig.1c),i.e.before thecalibrationperiodofMyLake(2005–2012).Abettermatchcould

(11)

havebeenobtainedbyusingonlydatafromthecalibrationperiod, buttherangeofpredictedvaluesinthisperiodwasnarrowcom- paredtothewholetimeseries(e.g.,predictedTotalPwasonlyin moderatestatus).Moreover,ourintentionwastomakeuseofas muchdataaspossibleforﬁllingintheCPTs.

Accountingforthemismatchbetweenpredictedandobserved valuesintheCPTs(TableB1)hadclearconsequencesfortheBN modelpredictions(BNversion2,Fig.B1).ForTP(Fig.B1b),theBN nolongerpredictedapositiveeffectofbettermanagementonthe probabilityofmoderatestatus,butinsteadaweakincreaseinthe probabilityofpoor-badstatus.Forthecombinedphysical-chemical indicator(Fig.B1c)therewasnoobviousresponsetothemanage- mentscenarios.TheChl-avariable(Fig.B1d)andthusthecombined phytoplanktonindicator(Fig.B1f)displayedsimilarresponsesto themanagement scenariosasinthedefaultBNversion(Fig.5d andf),buttheeffectsofthescenariosweremuchweaker.Thisis consistentwiththehighaccuracyandlowprecisionofpredicted Chl-afromtheprocess-basedmodel.Thetotallakeassessmentwas mostdominatedby thephytoplanktonnode(asdeterminedby theclassiﬁcationrules),butthephysical-chemicalindicatorcon- tributedwithadditionaluncertainty.IntheBNversion2,theoverall lakeassessmentforthereferencescenario(Fig.B1g)wascloseto thedefaultversion(Fig.5g),buttherewasalmostnoeffectofthe managementorclimatescenarios.Thisisacommonproblemfor BNmodelsthatincorporateseveralsourcesofuncertainty:nodes furtherdownthecausalchainhavegreaterpredictiveuncertainty (Borsuketal.,2004;Marcotetal.,2006).

Our decision not toinclude the mismatch betweenMyLake predictionsandobservationsinthedefaultBNversioncanbejus- tiﬁedbythefactthatthisuncertaintyshouldalreadyhavebeen accountedforinthecalibrationofMyLake.Theresulting60param- etersetswereinsteadincludedasasourceofuncertaintyintheBN.

Incorporatingtheprediction−observationmismatchasanaddi- tionalsourceofuncertaintywouldnotonlymaketheBNmodel non-responsivetothescenarios,butalsointroduceasystematic errorforTP.

4.2.2. TheCPTforcyanobacteria

AminorityoftheEUREGIobservationswerefromlakeswith highdegreeofeutrophication;only45outof559observationswere inthehighestChl-ainterval(vs.34outof90observationsfromLake Vansjø).Likewise,thenumberofcyanobacteriaobservationsinthe highestintervalwasrelativelylow:22outof559(vs.13outof90 fromLakeVansjø).Nevertheless,theEUREGIdatasetgavesimilar probabilitydistributionsintheCPTforcyanobacteria(TableB2)to thosefromLakeVansjø(Table2b-c).Consequently,modelversion 3withCPTfromtheEUREGIdatasetpredictedeffectsofclimate and management scenarios on ecologicalstatus of cyanobacteria(Fig.B2e)thatwereverysimilartothedefaultmodelversion (Fig.5e). Thefactthat anindependent,large-scaledatasetgave similarCPTsandconsequentlyverysimilarmodelpredictionsas theoriginaldatafromLakeVansjøstrengthenedourconﬁdencein thecyanobacteriacomponentofthemodel.

4.2.3. Effectsofwatertemperature

Sincethefuture climatescenariohad a limitedeffect ofthe Temperaturenode(probabilityof“awarmyear”increasedfrom 34%to44%),weinvestigatedmorecloselyhowthephytoplankton nodesrespondedtochangesinwatertemperatureinthemodel.

OnewaytoinspectthetemperatureeffectsintheBNwastoselect thewarmestmonths,July-August(“summer”).Thefullmodelis basedonalldatafromMaytoOctober,becausethisisacriterion inthenationalassessmentsystemforecologicalstatus.However, sincethere islargeseasonalvariationin manyof thevariables, selectingonlysummermonthswouldreducethetemporalvari- ation,andmightthereforeimprovetheprecisionofthemodel(i.e.,

resultinnarrowerprobabilitydistributionsoftheindicators).We thereforecomparedthedefaultmodeloutcome(Fig.5)withthe correspondingresultsfromsummermonths(Fig.B3).(Tosimplify thecomparisonwehavedisplayedtheresultinterms ofstatus classes,althoughitisnotstrictlycorrecttobasethestatusassess- mentofsummervaluesonly).LowerprobabilityofModerateor betterstatuscanbeseenforallindicators,exceptcyanobacteria;

thisislikelybecauseCyanobacteriastatusisbasedontheseasonal maximum,whichislesssensitivetotheselectionofmonths.This resultshowsthatthemodelbehavesasexpectedregardingsea- sonalvariationintemperatureandinindicatorvariables.

Furtherinspectionofthewatertemperatureeffects wasper- formedbysettingevidencefor“awarmyear”(100%probabilityof temperature≥19^◦C)vs.“acoldyear”(<19^◦C)(Fig.B4).Thetem- peratureeffectwasstrongerforChl-athanforcyanobacteria:from acoldtoawarmyear,theprobabilityofmoderateorbetterChl- astatusdroppedfrom58%to24%(worstmanagement)andfrom 70%to48%(bestmanagement).Thecorrespondingprobabilities forcyanobacteriawereadropfrom64%to47%(worstmanagement)andfrom71%to60%(bestmanagement),butthisresponse includedboththedirecteffectofthetemperaturenodeandthe indirecttemperatureeffectthroughtheChl-anode.Furthermore, weﬁxedtheChl-anodeatPB,MorHGstatusundercoldandwarm year,respectively(Fig.B5a).Theadditionaltemperatureeffecton cyanobacteriawasmostevidentwhenChl-awasinmoderatesta- tus(Fig.B5b).ThisresultisinlinewiththeconclusionbyRigosietal.

(2015),thatthecyanobacteriaconcentrationsofmesotrophiclakes wereparticularlysensitivetowarming.Thistemperatureeffecton cyanobacteriahadasmall,butnoticeableeffectonthetotalphyto- planktonstatus(Fig.B5c).Althoughthiseffectwassmall,itshows thattheBNgeneratedreasonableresults.

4.3. AssessmentoftheBNapproachformodellingofecological status

Overall,theBNmodelsatisﬁedourobjective:tointegrateinfor- mationfromscenarios,process-basedmodels,monitoringdata– especiallycyanobacteria,and thelakeclassiﬁcation system.The BNapproachgivesapossibilitytoaccountformismatchbetween process-modelpredictionsandobservationsforcertainvariables, byincorporatingthisuncertaintyintheirCPTs(cf.TableB1)and evaluatingitsconsequences.Sincetheselectedmodel(version1) doesnotaccountfor themismatchbetweenMyLakeprediction andobservations,theresultspredictedbytheBNshouldnotbe interpretedintermsofabsoluteprobabilityvalues.Nevertheless, thequalitativeeffectsofthescenariosonthedifferentindicators predictedbytheBNshouldbevalid.

The components involving cyanobacteria gave reasonable results,andhadimportancetotheoverallassessment.Our con- ﬁdenceinthesecomponentswasstrengthenedbythecomparison withanindependentdataset(Fig.B2);atthecoarsescaleoftheeco- logicalstatus(ratherthanexactconcentrations),theresultswere verysimilar.Thisimpliesthatourapproachcanbeusedforother lakesthat areatrisk ofalgal blooms.Forlakes withmorelim- iteddataoncyanobacteriathanLakeVansjø,weshowthatﬁlling thedatagapsusingcyanobacteriaobservationsfromotherlakes incombinationwithexpertknowledgeonlaketype,localcondi- tionsetc.isaviableoption.Rigosietal.(2015)demonstratedthis possibility:usingphysicochemical,biological,andmeteorological observationscollatedfrom20lakeslocatedatdifferentlatitudes andcharacterizedbyarangeofsizesandtrophicstates,theycon- structedaBNtoanalysethesensitivityofcyanobacterialbloom developmenttodifferentenvironmentalfactorsandtodetermine theprobabilitythatcyanobacterialbloomswouldoccur.Theabil- itytoutilizeotheravailabledatasetsforansweringmanagement