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EnvironmentalModelling&Software55(2014)250e265
ContentslistsavailableatScienceDirect
Environmental Modelling & Software
journal homepage: www.elsevier.com/locate/envsoft
Flood inference simulation using surrogate modelling for the Yellow
River multiple reservoir system
M.E. Castro-Gamaa, I. Popescua,*, S. Lia, A. Mynetta, A. van Damb
aUNESCO-IHE,InstituteforWaterEducation,P.O.Box3015,2601DADelft,TheNetherlands
bDeltares,Roterdamseweg185,2629HD,TheNetherlands
a r t i c l e i n f o a b s t r a c t
Articlehistory: TheYellowRiver,inChina,isoneofthelargesthydrosystemsintheworld.Floodingisamajorproblem
Received15February2013 fortheriver,andthereforeoverthelast50yearsalargenumberofinterventionshavebeenmadeinits
Receivedinrevisedform reachesandtributaries,inordertocontrolthefloodingeventsinthelowlandarea,downstreamofthe
24January2014
Huayuankou hydrological station. The development of new technologies and approaches to decision
Accepted1February2014
supporthasraisedpossibilitiesforcreatingnewwaysofmanagingtheriverandreducinglossoflife,in
Availableonline28February2014
thecaseofflooding,forthepeoplelivingwithintheembankmentareaoftheriver.Giventheimportance
of the river for the development of economic activity in China, it is essential to increase the under-
Keywords:
standingofthegeneralfloodingprocessestriggeredbyseveralreservoiroperationscenarios,andthen,
Reservoiroperation
YellowRiver afterapplying them to a flooding model of a specific area,totest the findings. The main goal of the
Floodmodeling researchpresentedhereistoinvestigateanddevelopthestatisticalinferencebetweentheoperationof
Surrogatemodeling reservoirsontheYellowRiverandasetofvariablesrelatedtothedownstreamflooding,suchasthetotal
flooding volumeandthepeakdischarge.Theresearchshowsthatitispossibletousesuchinference
modelsasdecisionsupporttools,byreducingthenumberofexplanatoryvariablestobeincludedinthe
simulationscarriedouttodeterminetheappropriatereservoiroperation.
(cid:1)2014ElsevierLtd.Allrightsreserved.
1. Introduction maximumortheminimumofanobjectivefunction.Thetechniques
used during an optimization of reservoir operations range from
Therearemanymodelsthatserveastoolsfordecision-making deterministic,stochastic,andsimulationtoheuristicapproaches.A
in river management institutions around the world. When man- number of years ago Yeh (1985) studied most of the operation
aging and operating single- or multi- purpose reservoirs, it is researchtechniquesusedforthedevelopmentofreservoiropera-
necessarytolookatrelevantmeasuredvariablessuchasreservoir tion for simplified schemes and found that these models were
storage,releaseddischarge,reservoirwaterlevels,waterqualityor difficulttoadapttorealoperationalapplications,whenmodifica-
total sediment in order to assess the objective of a reservoir tions were required to respond to changes on a daily basis. Rani
(Hassaballahetal.,2012;LoucksandvanBeek,2005;WMO,2008). et al. (2010) compiled an extensive overview of the simulation
Theobjectivesshouldbeanalyzedduringdifferenttimescales:for and optimization techniques used for reservoir operation under
peakorlowmagnitudeextremeevents,seasonalapproaches(e.g. climate change conditions, in view of the continuous need for
winter, summer, for crops), annual approaches, or even, in some adaptation strategies for flood management. Main conclusion is
cases,fortheprojectlifespan.Theobjectivesforreservoiropera- thatnowadaysoptimizationmethodsrequireextensiveamountof
tion can be broad and include hydropower generation, flood data and information of the systems modeled (Celeste and Billib,
management,irrigation,recreationandwatersupply. 2009) and long running times to achieve calibration (Dittmann
The evaluation of reservoir management strategies implies a et al., 2009), therefore models can not be easily updated to be
search for an optimization problem, while trying to achieve the usedindailyreservoiroperations.
While implementing and developing any of the above ap-
proaches, one issue is mentioned every time; the “curse of
* Correspondingauthor.Tel.:þ31152151895;fax:þ31153122921. dimensionality”.Whendealingwithmodelingfloodingeventsthe
E-mailaddresses:[email protected](M.E.Castro-Gama),i.popescu@ complexity of the task is determined by the identification of the
unesco-ihe.org (I. Popescu), [email protected] (S. Li), [email protected]
propervariablesandconstraintsthatdrivetheoptimaloperation,
(A.Mynett),[email protected](A.vanDam).
http://dx.doi.org/10.1016/j.envsoft.2014.02.002
1364-8152/(cid:1)2014ElsevierLtd.Allrightsreserved.
Author's personal copy
M.E.Castro-Gamaetal./EnvironmentalModelling&Software55(2014)250e265 251
Acronyms(alphabeticalorder) INI% InitialWaterLevelinareservoiras%fromtotal
reservoirwaterdepth
ALL Thesetofexplanatoryvariablesusedintheregression L LuhunReservoir
model MAX% MaximumWaterLevelinareservoiras%fromtotal
DoF DegreesofFreedom reservoirwaterdepth
FMA Maximumfloodedarea(fromHuayuankoutoGaocun MR MultivariateRegression
hydrologicalstations) Qb BasedischargeofaGammaorTriangularinflow
FMV Maximumfloodedvolume(fromHuayuankouand hydrographinareservoir
Gaocunhydrologicalstations) Qp PeakDischargeofaGammaorTriangularinflow
FTA Timetoreachmaximumfloodedarea hydrographinareservoir
FTV Timetoreachthemaximumfloodingvolume r correlationoftraining
t
G Guxianreservoir r correlationofvalidation
v
GAM Asetof1000GammaFunctionhydrographs S SanmenxiaReservoir
G10 Asetof10,000GammaFunctionshydrographs SK SkewnessoftheinflowGammatypeofhydrographs
HQa AverageDischargeatHuayuankouhydrologicalstation SSE SquareSummoftheEstimatedResiduals
HQp PeakdischargeatHuayuankouhydrologicalstation SSR SquareSummofResiduals
HTa Averagetimeofhydrograph(centroid)atHuayuankou STO SummofTotalerrors
hydrologicalstation TRI Thesetof1000Triangularhydrographs
HTp TimetopeakdischargeatHuayuankouhydrological Tp TimetopeakoftheGammaorTriangularinflow
station hydrograph
HVL TotalhydrographvolumeatHuayuankouhydrological UNI thesetof1000Uniform(constant)hydrographs
station X XiaolangdiReservoir
X Thesetofselectedexplanatoryvariables
SEL
andanyreductionofthenumberofvariablesisimportantforthe regarding the strategies to reduce the number of explanatory
modelersintheirtimelyresponsetodecisionmakers.Inorderto variablesincaseofcomplexdesignproblemscanbefoundinShan
addresstheissueofcomputationaltime,oneoftheapproachesto andWang(2010a,2010b);Rattoetal.(2007);andYoungandRatto
solvereservoiroperationissurrogatemodeling,inwhichamodelis (2009). All presented strategies are mostly based on sensitivity
buildtorepresentthefunctionalityofthereservoirsystembyusing analysis. Hejazi and Cai (2009) developed a heuristic approach
asetofexplanatoryvariablesforthereservoiroperationinorderto called “modified minimum redundancy maximum relevance”
estimate the flooding in the downstream of the reservoir. The (mMRMR), and coupled it with a generalized regression neural
extentoffloodingdownstreamofthereservoirsystemisdescribed network model (GRNN) as defined by Specht (1991). The meta-
by a set of dependent variables. Castelleti et al. (2012) classified modelobtainedwasused to solve the case ofdaybydayrelease
surrogatemodelsintwocategories;responsesurfacemodeling,in forecastfor22reservoirsinCalifornia,USA.
whichthesetofdependentvariablesarerepresentedasaresulting Theapproachproposedhereinisasimulation-basedone,which
surfaceandlowerfidelitymodeling,inwhichalesscomplexmodel aims at supporting decision-making during a flood event. The
(with less explanatory variables) is run in order to reduce the methodofferstheadvantagethatmodelerscanlearnthebehavior
computationaleffortandstillmaintaintheaccuracyoftheresults. ofthesystembytestingtheeffectofdifferentinflowhydrographs
Themainapplicationsofsurrogatemodelingaremainlytobefound on the operation strategies for the reservoir in order to avoid
instatisticsandcomputerscience.(Hussainetal.,2002;Ganoetal., floodingdownstream.Thesurrogatemodelcanoffersupporttothe
2006;RattoandPagano,2010).Castelletietal.(2012)alsopoints operatorsbyallowingthem,incaseofextremefloodingevents,to
out that just recently surrogate modeling emerged in environ- comparetheincomingobservedhydrographwithaknown,already
mentalrelatedfields.Inagro-ecosystemsplanning,Pineros-Garcet testedincoming hydrograph intothe reservoirs. Research tries to
etal.(2006)usedmetamodelingfornitrateleachingandAudsley addresstwomainissues:willtheoperatorbeabletoanticipatethe
et al. (2008) used a surrogate for estimating the socioeconomic behaviorofthesystem,byusingtheknowledgedevelopedbythe
impactofclimatechangeonagricultureintheUK.Forwaterdis- surrogate model?; and based on the predicted behavior of the
tributionsystemoptimizationBroadetal.(2005)usedmetamod- systemcanmodelersgiveadvicetothedecisionmakerssothatthe
eling for a design problem. Recently, Castelleti et al. (2010) used operationstrategyisadaptedaccordingtothenewconditions.
linearization of multiobjective surface responses for water re- The approach aims to provide a surrogate model that reduces
sourcesemulation.Castellettietal.(2007)usedaneuro-dynamic theday-to-daymodelingcomputationaleffortofreservoiropera-
programming approach for designing optimal reservoir network tionsforfloodmanagement,bybuildingapredefinedmodelthat
management policies. Ravazi et al. (2012), presents a review of could be updated with new explanatory variables. This would
differentsurrogatemodelingapproachesspecificallyforwaterre- eliminate modelers’ guesswork of the process and reduce the
sources.However,casesonreservoiroperationforpredictingflood numberofexplanatoryvariablesforthestateofthehydro-system.
variableswerenotreportedbythereview. In its current state the research is exploratory and it is not
The main challenge in using surrogate modeling is the deter- intendedtobeusedattheYRCC.However,theimplicationofthe
minationof thepropersetofexplanatoryvariablestobeusedas results suggests that it could be implemented for flood manage-
input for a model as shown by Bowden et al. (2005). The same mentforrealdatahydrographsandthatmoreresearchshouldbe
authors classify the procedure for selecting the explanatory vari- performed on flooding patterns, extending the research to
ables in three categories;knowledgebased,mainlyperformed as computationalintelligencetechniques.
aninitialfilterofdatainanearlymodelingstage;statisticalcross- The paperisstructuredinfiveparts.Section One isthe intro-
correlationandheuristicinformationbasedselection.Adiscussion duction.SectionTwocontainsadescriptionofthecharacteristicsof
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252 M.E.Castro-Gamaetal./EnvironmentalModelling&Software55(2014)250e265
theYellowRiver,alongwiththefeaturesthatmakeitspecialfroma is1.6*109t.Amongthe13largeriversoftheworldwhoseannual
hydraulicandmanagerialperspective.InSectionThreetheconcept sedimenttransportexceeds100*106t,theYellowRivershowsthe
andthemethodologyappliedtosimulatethefloodingeventsare largestamountofsedimenttransportandaveragecontent.
detailed.Theproposedstatisticalinferencemodelfortheflooding Another special aspect of the Yellow River is the so-called
ofthesystemisalsointroduced.SectionFourpresentstheobtained “hanging river”, as its most downstream part is usually called.
resultsandadiscussion.Finally,theconclusionsandanalysisshow Thisisduetothefactthattheriverbedis,onaverage,higherthan
howaninferencemodel,suchastheonepresentedhere,couldbe the land surface by 4e6 m. The lowland area is protected from
usefulfordecisionmakingduringfloodingeventsandfortheun- floodingbyhighembankmentsthatdelimittheriverbanks.Around
derstandingofthecause-effectbehaviorofreservoir-drivenrivers. thecityofKaifengthedifferencebetweentheYellowRiverbedand
thelandisapproximately13m.The highestdifferential between
2. Casestudy:theYellowRiversystem theriverbedandthelandoccursatXinxiangcity,whichisaround
20 m. This aspect is an important element to be analyzed in any
The study presented here looked at the middle section of the floodingstudyoftheareaandhasnoparallelintheworld.
Huang He River, most commonly known as the Yellow River, in Flooding on the Yellow River has been an important issue
China.Theriverbasincoversavastareacomposedofthreemain throughouthistory.Recordsdatingfromthepre-QinDynastyshow
regions(Fig.1): thattheriverhadoverflowed1590timesandchangedcourse26
times in the previous 2542 years which means that on average
1) theupperriversection,withthelargestproportionofthebasin, thereisafloodingeventtwiceineverythreeyearsandonecourse
isknownforitscomplexitywithregardtowaterandsediment change everycentury (Guoying, 2010). The flooding events occur
volumes.ItislocatedbetweentheSanmenxiaReservoirandthe mainly in the areas from Tianjin city (between Hekou and the
spring of the river in a mountainous region in the Qinghai SanmenxiaReservoir)andJianghuai.
province.Mostofthetotalsedimentvolumeoftheriver(90%), Afloodingeventalongtherivercanvaryintimeduration,and
andmorethanhalfofthetotalflow(56%ofthewatervolume) given the catchment characteristics, it is known that flooding
originatesinthisarea. eventscandeveloprangingfromaweektomorethanonemonth.
2) the midYellowRiver, whichis characterized bythe systemof Adaptationstrategiesandreductionoffloodriskhavealwaysbeen
reservoirsdevelopedforthemanagementoftheriverincaseof very important, and therefore the overall water resources man-
extreme flooding events and used for irrigation, water supply agementandtheoperationofitsstructureshavebeenentrustedto
andhydropowergenerationinnormalhydrologicalconditions. YRCC(Guoying,2010).
Theriverismainlyconveyedinsidedykes.
3) the most downstream area of the river, as from Dongpinghu 2.1. TheYellowRiverstructures
stationtowheretheriverwatersaredischargedintotheBohai
sea. In the middle reach of the Yellow River, there is a system of
reservoirsthatiscombinedwithaseriesofdykestructuresasthe
TheYellowRiverhasseveralspecialaspectsthatmakeitunique main elements for flood protection. The reservoir system is
intheworld.Themainaspectisthehighratioofsedimenttowater composedoffourreservoirs(Fig.1);twooftheminparallel(Guxian
volume.Thereisasmallamountofannualnormalnaturalrunoffof andLuhun)alongtheYiheandYilohuetributaries;andtwoofthem
thebasin,ofabout58*109m3,whiletheannualsedimenttransport inseries(SanmenxiaandXiaolangdi)locatedonthemainreachof
Fig.1. TheYellowRiverlocationandthestudyarea:theMiddleYellowRiverreach.
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M.E.Castro-Gamaetal./EnvironmentalModelling&Software55(2014)250e265 253
theYellowRiver.Thepointatwhichthewaterfromthefourres- andcurrentlyresearchisbeingconductedtofinalizeanintegrated
ervoirscomestogetherisimmediatelybeforeHuayuankou,wherea toolforthemanagementofthecomplexexistingreservoirsystem
hydrologicalstationofvitalimportancefortherivermanagement (Li,2013).
exists.Accordingtothisconfigurationthesystemcanbedefinedas This research relates to the above aim and deals with the re-
complex(LundandGuzman,1999).Thelargestreservoirintermsof lationsbetweentheoperationofreservoirsandfloodingevents.
storagecapacityisXiaolangdi(101.20*109m3)whilethesmallestis TheYellowRiverusesanumericalmodel,alsoknownas“digital
Guxian (11.09*109 m3). The combined resulting capacity of YellowRiver”,forday-to-daymodelingoftheflowprocessesandit
179*109m3andthemaximumsimultaneousrelease(discharge)of constitutes as the main decision support tool for decision and
50,156 m3/s are amongst the largest hydro-systems in the world managementofthereservoirsystem.Themainoutcomeofsucha
(Table1).Themainreachoftheriverdownstreamofthereservoirs’ model is a single flooding responsewith each run. This response
region is composed of a main channel and lateral embankments canbeusedtoforecasttheamountoffloodedareain thedown-
thatareenclosedbetweenthedykes.Themainchannelisnotable stream river valley, or the length of time for maximum flooding
to convey a hydrograph with a peak higher than 4,000 m3/s, extent,butbecauseoftheextensivetimerequiredforthesimula-
withoutinducingafloodeventinthelaterallowlandareas. tion process to be performed, this cannot be done in a multi-
In order toreduce the risk offlooding byminimization of the scenarioapproach.Inthisregarditshouldbestatedthatduringa
flooding peak discharge, and in order to reduce the evacuation flooding event operational meetings are performed almost every
tasksinthelowlandareainsidethedykes,thefourreservoirson 4e8h(dependingonthecase)anddecisionsaremadeeachtime
the Yellow River were designed as the primary solution at the onhow tooperatethereservoirs basedonreal-time forecasts. In
beginning of the 20th century. In chronological order the first order to operate the reservoirs properly in the case of extreme
reservoirs built are the ones along the Yihe reaches, Luhun and events, it is necessary to have the largest amount of information
Guxian,andthenthelargesttworeservoirs,SanmenxiaandXiao- possibleatalltimes,aboutthepossibleriverbehavior.Ifthecurrent
langdi. The last reservoir built was Xiaolangdi, which entered in existingmodelisoperatedduringemergencyfloodingevents,then
operationduring2001.Morereservoirsareplannedtobebuiltin themodelresponseswillbegatheredtoolate,andtheanswersthey
the future, but as of now this will take more than 10 years to provide after the decision has been made will be useless (inde-
become a reality, and thereforetheyare nottaken into consider- pendentofthemodelaccuracy).
ationinthisstudy. At YRCC, decision makers may not wait for the digital model
Downstream of the reservoirs, after the confluence of the resultswhiletakingdecisionsbecausethecostwillbelossoflife.
branches of the river, at Zhengzhou city, lateral dyke structures Moreover, in addition to the computation requirements, several
werebuiltintheriverforfloodprotection.Thislargedykestructure otherexplanatoryvariablesneedtobeconsideredbeforerunning
(1,371kmlong)allowsthedevelopmentoftheeconomyoutsideof themodel,suchastheoperationofthereservoirs,theobjectivesof
themainreachoftheriver,butitisalmostimpossibleforChinese eachstakeholderatthetable,andthenumberofpossiblescenarios
people living inside the dyke area (1.97 million inhabitants) to for response provided by the digital model. Such a huge task is
evacuateandtoavoidlargefloodingeventswithoutincurringloss difficulttoaddressinanemergencysituation.
of life (Guoying, 2010). In order to increase confidence during Toeasethisworkitiscommonthatpreparationforsuchevents
extreme events and to cope with discharges for flooding events is done well in advance bysimulating different possible flooding
withareturnperiodof1/100years(16,000m3/s)atHuayuankou eventsandtheestimatedresultsaretakenintoaccount.
station,bothdykeshavebeenraisedduringthelastfourdecades. Inthispapertheproposedsurrogatemodelhelpsthedecision
Downstreamintherivertherearetwostorageareas,Beijingdiand makersinaddressingthisissue.Moreoverbyusingsuchmodelsthe
Dongpinghu,whicharepartofthesystemaswell,thelatterorig- memoryandexperienceofpasteventsiskeptwiththemodelitself,
inallybeinganaturallake.TheYRCCusesthesestorageareasonlyif with its database of results, and it is not lost whenever a new
the input hydrograph at Huayuankou is over the established modelertakesoverthetaskofrunningthemodel.Assuchdecision
thresholdof16,000m3/s.Thesestorageareasarelocatedoutsideof makersdonotneedtodependonasmallgroupofpeoplewhohave
thestudyareaandthereforearenotpartofthemodelingprocess. expertise because of using the model, but they can rely on the
modelitself.
2.2. Managingfloodingevents
2.3. ManagingoftheYellowRiversediments
Whendealingwithfloodingevents,rivermanagementauthor-
ities from the YRCC have to address the questions of when to One of the main features of the Yellow river is the sediment
evacuate, which areas are more susceptible to flooding and how volumeanditstransport.ThewatervolumeconveyedbytheYel-
longitwouldtakeforafloodingeventtoberoutedoutofabasin.In lowRiverissmallifcomparedwiththeothermainriverinChina,
China, effort is constantly being made for the improvement and i.e. Yangtze. Yellow River carries on average only 1/17 of the
developmentofsoftwaretoolsforfloodmanagement(Balicaetal., Yangtze’sRiverwatervolume,howevertheannualsedimentload
2013;Gichamoetal.,2012;Popescuetal.,2010;Vanetal.,2012) ofYellowRiveris3timeshigherthantheoneoftheYangtzeRiver
Table1
MaincharacteristicsoftheYellowRiverreservoirs.
Variable UNIT Xiaolangdi Sanmenxia Luhun Guxian All
Latitude DEGN 34(cid:2)55’23.5800 34(cid:2)49’42.9900 34(cid:2)12’1.1300 34(cid:2)14’22.3900
Longitude DEGE 112(cid:2)21’51.1300 111(cid:2)20’43.7400 112(cid:2)10’57.2500 111(cid:2)16’41.9300
MinimumLevel masl 200 290 290 478
MaximumLevel masl 275 335 333 551
MinimumStorage 109m3 0.2 0.0 0.3 0.1
MaximumStorage 109m3 101.2 54.6 12.5 11.1 179.3
MinimumRelease m3/s 2,830.8 0.0 112.0 150.0
MaximumRelease m3/s 16,030.1 15,060.0 5638.6 13,427.0 50,155.7
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254 M.E.Castro-Gamaetal./EnvironmentalModelling&Software55(2014)250e265
(Guoying,2010).TheheavysedimentloadofYellowRiverimposes objectiveintheoperationofaparticularreservoirsystem(suchas
theneedtobeproperlymanagedbyYRCC.AsasolutiontheSan- the one analyzed here) is flood management (Guoying, 2010;
menxiadamwasbuilt,onthemainbranchofYellowRiverandput Popescu et al., 2012; Jonoski and Popescu, 2011), obtaining the
onoperationon1960ThepresenceofSanmenxiareservoirchanged optimaldownstreamscenarioofthereservoiroperationmakesit
themorphologicalequilibriumofYellowRiver(Wangetal.,2005). difficultfordecisionmakerstoperformananalysisofthemagni-
Historically,ithasbeenrecordedthattheriverbedcanbescoured tudeandoutcomeofanextremefloodingevent.
10min24h(WanandWang,1994),howeverwiththeoperationof ThemethodologypresentedhereisdemonstratedontheYellow
Sanmenxiareservoirabalanceofsedimentismaintainedbyusing River.Withtheinsightsgivenbythepolynomialregressionmodel,
the transport capacity of the river itself to flush and carry the itwaspossibletoforecastthebehavioroftheriverinthecaseof
sedimentduringnonfloodingseason(Wangetal.,2005). extreme flooding events at the Yellow River Huayuankou hydro-
The existing digital Yellow River model helped understanding logicalstation.
betterthatthoughthemorphologicalstabilityofthelowerYellow Thestudycarriedoutanalysisintwosteps:
Riverreachisnotachievable,thesedimentloadsaremanageable
due to the existing regulation policies (Li, 2013; Liu, 2012). The (cid:3) ananalysisandselectionofexplanatoryvariablesofthereser-
managementofthesedimentsisprimarilydoneduringthesum- voirsandincominghydrographswhichinfluencethepatternof
merandoutsideofthefloodingseason(Wu,1992;Li,2013). thehydrographsatHuayuankouhydrologicalstation;and
Duringfloodingevents YRCC manages just thewater volumes (cid:3) an analysis of the flooding pattern (e.g. area, volume) by
thatarereleasedthroughreservoiroperation,inordertominimize modelingthefloodswithanintegrated1D-2Dunstructuredgrid
damagesinthedownstreamareas. modeluptothemostdownstreamobservationstationlocated
The model developed for the present research aims at atGaocun.
addressingtheoperationofreservoirsincaseofextremeflooding
events. Sediment modeling was not included in the proposed Forthesecondsubjectofanalysis,anewmultivariateregression
methodology model is valid under current morphological condi- was performed between the explanatory variables of the first
tions to inform daily operation under flooding emergency. After approachandtheresultsoffloodingeventsduetothe1D-2Dmodel
eachfloodingeventtheinsitusituationneedstobeanalyzedandif between Huayuankou and Gaocun. In similar reviewed studies
morphological conditions have changed significantly, then model (SchmitzandCullman,2008;Saavedraetal.,2010),theuseoflarge
needstobere-calibrated. hydrological databases was used in combination with computa-
tionalintelligencemethods,butduetothelackofthisdatabaseora
3. Thesurrogatemodel hydrologicalinputinthecurrentresearch,theoperationofreser-
voirsisexplicitlydrivenbytheincominghydrographs.Itisimpor-
3.1. Modeldescription tant to mention that, ensemble forecasting for online reservoir
operationswasnotusedintheresearchpresentedhere,becausethe
Presentresearchproposesasurrogatemodelthatusesapoly- hydrologicalinputisnotdifferenttotheincominghydrographs.In
nomialmultivariateregressionmeta-modelinordertoaddressthe general,thesecondanalysisshowedthatthisisanongoingfieldof
reservoir operation of the Yellow River. The selection of input study because low correlations were obtained between the
explanatoryvariablesfortheregressionmodelisdonebasedonthe explanatoryvariablesofthereservoirsandthefloodingvariables.
decision makers knowledge of the system. Li (2013) presents in Fig.2presentstheschematizationofthesimulationmodeland
detailhowdecisionmakersmeetingsaretakingplaceatYRCCand itscomponentsalongwiththesurrogatemodel.Asetofexplana-
what are the most important variables to consider when dealing toryvariablesisgeneratedfortheoperationofthereservoirsystem
withfloods.Theinitialselectionofexplanatoryvariablesis20.In using Monte Carlo simulation. Inputs to the reservoir system are
ordertoreducefurtherthecomputationaltimeofthemodel,cor- floodhydrographsthatareroutedbythereservoirsthroughoper-
relation analysis is used for the selected number of explanatory ationrules.ReleasesfromthereservoirsareroutedtoHuayuankou
variables. Stepwise (backwards or forward) approach can also be hydrologicalstation.Theroutinggeneratesasetofoutputhydro-
usedtoreducethenumberofvariableshoweverwhenusedinthis graph variables. The obtained hydrographs are used as upstream
research it did not show significant reduction of the number of boundaryconditionfora2DfloodmodelbetweenHuayuankouand
explanatoryvariables(CastroGamaetal.,2013). Gaocunhydrologicalstations.Thisgeneratesasecondsetofoutput
Itisnowknownthatclimaticvariabilityisapartofthemodeling variablesrelatedtoflooding.
process (Millyet al., 2002; Stocker and Raible, 2005) and during A multivariate regression model is built between the set of
simulationoffloodingeventsthetypicalapproachesforsettingup explanatory variables and the sets of output variables related to
modelsbasedondesignflowsseemtolacksignificancewhenthese hydrographsatHuayuankouandthefloodingvariables.Theinput
arecreatedbasedonlyonhistoricalrecords(Merwadeetal.,2008; variableselectionforthemultivariateregressionisperformedus-
JungandMerwade,2012).YellowRiverhistoricalrecordsshowthat ingcorrelationanalysis.Thebestfittedmodelsareselectedbased
theshapeofthehydrographsatHuayuankouhydrologicalstation on analysis of variance of the regressions and model training
changedintimefromtallandthintolowandwidefrom1962to correlation.
2003(Heetal.,2008).Inordertocomplywiththisbehaviorcurrent
researchusessynthetichydrographs,ofdiverseshapes,tosimulate
extreme flood events entering the Yellow river reservoir system. 3.2. Mathematicalformulation
Thesetofvariableswhichdefinethehydrographshapehasbeen
Givenariversystemofreservoirs, Xallisavectorofnexplan-
createdusingaMonteCarloanalysis.
atory variables that are the input for the operation of a reservoir
Moreover, in the case of wide large rivers, such as the Yellow
systemandforafloodroutingsimulationmodel:
River(Fig.1)ortheYangtzeRiver,inChina,andthoseinColorado
(Gilmore,1999)orTennessee,inUSA,determiningarepresentative Xall ¼ fX ;X ;X ;:::;Xng (1)
number of explanatory variables for each reservoir becomes 1 2 3
extremelyuseful.Withtheimplementationofsoftwaremodeling Let Y be the set of m variables as a total set of the variables
toolsforreservoirmanagement(Li,2013),andgiventhatthemain describing the reservoir output hydrographs (YH) and the set of
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M.E.Castro-Gamaetal./EnvironmentalModelling&Software55(2014)250e265 255
Fig.2. Thesurrogatemodel.
variables describing the flooding (YF), as they are obtained by increase of the dimensionality the computational effort becomes
runningasimulationmodelwithXallasinputparameters: higher.
Thesecondlimitationoftheproposedsurrogateisthatthebest
Y ¼ fYHUYFg ¼ fY1;Y2;Y3;:::;Ymg (2) fitted multivariate regression model of the surface response of Y
canonlybeusedinsidetherangeofvariabilityoftheXsel.However,
Corresponding to Xall there is a selected set of explanatory
variables Xsel, for which a maximum correlation (r) with each Yj as presented in the discussion section, a comparison with more
sophisticated tools provided similar results, while this approach
canbeobtained:
hastheadvantageofareducedcomplexityoftheobtainedmodel.
(cid:1) (cid:3) (cid:4) (cid:5) (cid:6)
X ¼ X˛X (cid:3)r X ;Y ¼ MAX with j ¼ 1;.;m (3)
sel i all sel j
4. ApplicationofthesurrogatemodeltoYellowRiver
With each set of selected explanatory variables Xsel, a multi-
b
variateregressionmodeliscreatedforeachYjandaforecastY is
j Theapplicationof thesurrogatemodelforthe YellowRiver is
determined:
detailedbelow.Thestepsfollowedintheapplicationofthemodel
b arehighlightedinFig.2.
Y ¼ fðX Þ (4)
j sel
Several multivariate regression models are created with the 4.1. Explanatoryvariables
samesetofexplanatoryvariablesXsel,andtheselectedbestfitted
modelistheonethatprovidesthelowestsquaresumofresiduals. Asubsetofexplanatoryvariables,relatedtotwomaininputsfor
X (cid:7) (cid:8) themodels,isused;thetypeofhydrographsandtheoperationof
SSR ¼ nS¼s1 Ybj(cid:4)Yj 2S with S ¼ 1;.;ns (5) tchuessiroensesrwvoitirhs.spTehceiailnisptustfrvoamriathbeleYsRuCbCse(tLiw,2a0s13se).lected after dis-
wherenSisthenumberofsamplesconsidered.
4.1.1. Incominghydrographs
Climaticvariabilityisoneofthefactorsexploredfortheselec-
3.3. Limitationsofthesurrogatemodel tionofhydrographsasinputforthereservoirsystem.Thisisdone
fortwomainreasons;oneistotrytoaddressthecurseofdimen-
Thereareseverallimitationswhenusingasurrogatemodelas sionality (Labadie, 2004; Yeh, 1985; Wurbs, 1993) for reservoir
theonepresentedabove.Thefirstlimitationisgivenbytheinput operations by incorporating simple variables in the subsequent
variableselectionthatwillbeaddressedbyusingonlycorrelation regressionmodel,andthesecondispartlyduetoapossiblelackof
analysis.Themajordisadvantageofthistechniqueisthatisableto data in the regression model based on historical records, and
detectonlylineardependencebetweenvariables,denyingtheex- becauseasubsetofexplanatoryvariablescaneffectivelyreducethe
istenceofnon-linearrelationships.Howeverothertechniquessuch requirementswithoutreducingtheaccuracyofthefloodforecast.
as heuristic input selection have the disadvantage that with the Presentstudydidnotuserainfall-runoffmodeling,Threekindsof
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256 M.E.Castro-Gamaetal./EnvironmentalModelling&Software55(2014)250e265
upstreamhydrographsweredefined:a)Gammafunctions(NERC, variables.ThisvariableisusuallydescribedinliteratureastheFlood
1975;Todini,2007),b)triangularfunctions;andc)uniformvalues. Limited Water Level (FLWL) (Li X.et al., 2010; Li S., 2008). Both
InthecaseofGammafunctions,fourexplanatoryvariablesare variablesweretakenaspercentages.Therangeofinitialreservoir
requiredinordertorepresentthebaseflow(Qb),peakflow(Qp), wasselectedtobelargerthan50%andlessthan99%,totakeinto
timetopeakflow(Tp)andskewnessofthehydrograph(SK),fora account reservoir operations that are related to an almost full
total of 12 explanatory variables, because Sanmenxia and Xiao- reservoir.Giventhisrestriction,themaximumcapacityoftheres-
langdiarelocatedinseries,soonlythreehydrographsarerequired ervoirs (MAX%) was restricted to the range of 75%e100%. The
ineachsimulation. rangesofvaluesusedforINI%andMAX%arepresentedinFig.3.A
Inthecaseoftriangularhydrographs,only9explanatoryvari- set of 1000 pairs of initial and maximum levels was randomly
ablesareusedbecausetheskewnesscoefficientbecomesirrelevant. generated.
Inthecaseofuniformtypeofhydrographs,only3explanatory
variablesareuseful.Acomparisonwithsteadyflowcouldbemade 4.2. Operationofreservoirs
tomeasuretherelevanceofthepeakdischargeandthetimetothe
peakdischargeintheanalysissectionofthisstudy. ThespecialistsattheYRCCsuggestedthatthereservoirsystem
Therangesforthebasedischargesandpeakdischargesofthe isoperatedbasedonanexplicitreservoirlevelpoolmethod(Chow
correspondingbasinsarebasedonhydrologicalvaluesprovidedby etal.,1988).Therearethreebasicoperationrules,whichareper-
the YRCC, andarepresented as box-plots in Fig. 3. The following formedbasedontheexistingreservoirvolumeatthemomentthat
variablesarerepresented;Qb:Baseflowoftheinputhydrograph; an event occurs. Firstly, if the reservoir is full then the input is
Qp:Peakdischargeoftheinputhydrograph;Tp:Timetothepeakof released, and secondly, if the level given by the balance is lower
inputhydrograph;Sk:Skewness,shapeofhydrograph;G:Guxian than the minimum, the release is restricted to a minimum
Reservoir; L: Luhun Reservoir; S: Sanmenxia Reservoir; and X: ecologicalflow.Thisensuresaminimumflowinthesummerperiod
XiaolangdiReservoir. and/or ecological flow (Dong, 2007). Thirdly, between the
A total of 1000 combinations of input hydrographs were syn- maximumandtheminimumwaterlevelsinthereservoir,thegoal
theticallygeneratedbyrandomgenerationintherangesspecified. istostoreasmuchwateraspossible.Thepresentmodelisdevel-
The same explanatory variables were used for each type of opedinaccordancewiththeserules.
incominghydrograph(Gamma,triangular,anduniform).Thevar-
iableselectedfortheuniformvaluewasthepeakdischarge. 4.3. Floodroutingbetweenbranches(1D)
Thetotaltime,ofeachgeneratedhydrograph,is60days,with
valuesdefinedatintervalsof2h.Afterthe60days,thebaseflow Toconnectthedischargesbetweenreleasesofthereservoirs,a
wastakenasauniformvalueuntilreaching100days,foreachof MuskingumeCunge model was applied (Cunge, 1969; Todini,
theconsideredhydrographs. 2007). The data used for this model are based on data surveys
performed every year on the river by the YRCC. The time dis-
4.1.2. Reservoirvariables cretizationusedfortheroutingschemeis2h,foratotalsimulation
Two explanatory variables were defined for each of the four periodof100days.Theresultoftheconnectionofallbranchesand
existingreservoiroperations,theinitialreservoirlevel(INI%),and reservoirsisahydrographatHuayuankou.
themaximumreservoirlevels(MAX%).Theybothincorporatethe After obtaining the hydrograph, variables such as the peak
flood management, and it results in a total of 8 explanatory dischargeofthehydrograph(HQp),thetimetopeakdischargeof
Fig.3. Explanatoryvariables.
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M.E.Castro-Gamaetal./EnvironmentalModelling&Software55(2014)250e265 257
the hydrograph (HTp), the average discharge of the hydrograph 4.4.2. Calibrationoffloodingevents
(HQa), the average time of the hydrograph (HTa) and the total Severalstudiesonfloodshavefocusedoncalibrationofknown
volumeofwaterroutedatHuayuankou(HVL)wereestimated.This extremeeventswithdifferent approaches,byvaryingthesetsof
setofvariablesiscalledhydrographvariables. information and sources of data from the topographic, hydraulic
Theresultsineachcasevary,dependingonthetypeofincoming and hydrological pointof view,while at the same time trying to
hydrographsintothereservoirs. reduce the sources of uncertainty (Dinh et al., 2012; Gichamo
et al., 2012; Hunter et al., 2005; Merwade et al., 2008; Moya
4.4. Floodmodelingmethodology Quiroga et al., 2013; Schumann et al., 2009). Design hydro-
graphsorrecordeddatawereusedtokeeptheuncertaintyofthe
TheresultinghydrographsatHuayuankouprovidetheinputfor input out of the scope, and the calibration was performed for
afloodingmodelthatcoversthedownstreampartoftheriver,until roughnesscoefficients inthe main channel andlowlandareas of
theGaocunstation. the river. The results obtained from these studies are often pre-
Thetotalnumberoffloodingmodelsusedwas339.Themodels sented as a flood map. In general, two mutually exclusive ap-
wererun fora total combined runtime ofapproximately2000 h, proaches were taken to classify the results into deterministic or
split into several computers of different configurations and pro- probabilistic maps. Acritical discussion of these approaches was
cessing capacities. The results were stored in separated netCDF reviewed(Schumannetal.,2009),butthereisnocasestudywith
files.Finally,thefloodingvariableswerecalculated.Thenewvari- a reservoir-driven system calibrated for spatial flooding under
ablescomprise:1)themaximumfloodedarea(FMA),2),thetime different operation scenarios. This particular omission is of
required for this maximum area to be flooded (FTA), 3) the extreme importance for the YRCC authorities. If a calibrated hy-
maximum flooding volume (FMV) and 4) the time required for draulic model is already available to decision makers, then
maximumfloodingvolumetooccur(FTV). knowing which explanatory variables of the reservoir are more
relevanttoavoidfloodinginlowlandareasismoreusefulrather
4.4.1. Floodingmodel(2D) thanjustknowingtheprobabilityoffloodinginaparticularcellof
AcoarserectangulargridmodelhasbeendevelopedatYRCCfor themodel.
flooding simulations, however the flooding extent were not well
representedbythemodel(Guoying,2010).Inthepresentresearch 4.4.3. Correlationanalysis
the alternative was to change the basic network and reduce the Havingthesetofexplanatoryvariables(Xall),reservoiroutput
number of cells without loss of accuracy. In order to do this an hydrographandfloodingvariables,thesimulationsetwassplitin
unstructuredgridapproachwasselected.Theadvantageintheuse two sets: 800 value sets for training of the model; and 200 for
ofunstructuredgridsisthatitallowsanincreaseintherefinement validationoftheresults.
for narrow areas, while using coarse refinement in areas where Withthetraininggroupofsimulations,ananalysisofcorrelation
solutions are not fundamentally required (Hartanto et al., 2011; was performed between explanatory variables and the resulting
Kernkamp et al., 2011). The modeling tool used was D-FLOW hydrographvariables.
FMbeta,1whichhasaFiniteVolumeMethodsolutionsolverofthe The hypothesis of no correlation against the alternative that
vertically integrated 1D2D shallow water equations (Kramer and there is a non-zero correlation was used. The significance of the
Stelling,2008;Kernkampetal.,2011). correlationwasbasedonp-valuesbiggerthan0.05,thatcreatesa
The flooding model represents the flooding between selectionofrelevantexplanatoryvariablesforeachhydrographand
Huayuankou and Gaocun and inside the dykes, for a total river floodingvariable.Thenewsubsetofexplanatoryvariablesiscalled
lengthof240km.Nostorageareasarelocatedinsidethemodeled Xsel(selected).Thesetvariesdependingonthe hydrographvari-
area. able,thefloodingvariableandthetypeofhydrograph.
Thedataforthecreationofnetworkarebasedonfreelyavailable
ShuttleRadarTopographyMissiondataofthearea(CIAT,2004)and 4.5. Multivariateregression
transformedintoaprojectedsystemofcoordinates,UTM50.The
useofthisinformationforlongwiderivershasbeentestedbefore Amultivariatelinearregressionmodelwasdevelopedbetween
fortheAmazonRiver(LeFavourandAlsdorf,2005)andMississippi thesetofselectedexplanatoryvariables(Xsel)aspredictors,andthe
(Quinnetal.,2010;Musteetal.,2010). hydrograph(YH)andfloodingvariables(YF)asdependentvariables
A3mwaterlevelintheriverwasprovidedastheinitialcon- (Y).Thedatawaspartitionedusingacross-validationtypesplitting
dition of the model. The calibration of this model was based on withhold-out,asdetailedbyBennettetal.(2013),intoatraining
knowledgeofthesolutionofafloodingeventof3400m3/s,where setof800samplesandavalidationsetof200samples.
nofloodingoccurredoutsideofthemainchanneloftheriver.The Inordertoobtainthecorrelationcoefficientsbb,theleastsquares
obtained water levels are the initial condition for each flood estimationwasused:
simulation. (cid:7) (cid:8)
TheManningroughnessofthesystemwassetto0.025tomatch bb ¼ ZT $Z $ZT $U (6)
sel sel sel
datafromapreexistingmodeloftheriver.Nodistinctionwasmade
between the main channel and embankments. Coincidently this Basedoneq.(6),fourkindsofregressionmodelsweredefined
value is also suggested for the Amazon (LeFavour and Alsdorf,
2005). 1) Linear:U¼Y,andZsel¼Xsel;
The upstream boundarycondition is set tobe the hydrograph 2) LogX:U¼Y,andZsel¼log(Xsel);
obtainedatHuayuankouduetoroutingofthehydrographsthatare 3) LogY:U¼log(Y),andZsel¼Xsel;
obtainedduetoreservoiroperation.Forthedownstreamboundary 4) LogeLog:U¼log(Y),andZsel¼log(Xsel).
condition,aratingcurveatGaocunhasbeendevelopedbytheYRCC
basedonseveralsurveys. An analysis of variance was made for every regression model
whichincludedthedegreesoffreedom(k¼numberofpredictor
variables XSELorXALL),sumofsquaresofregression (SSR), sumof
1 DevelopedbyDeltaresSoftwareCentre. squaresoferrors(SSE),totalsumofsquares(SSTO),meansquareof
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258 M.E.Castro-Gamaetal./EnvironmentalModelling&Software55(2014)250e265
regression(MSR),varianceofmodel/meansquareerror(MSE),test variables. However such relations maygreatly overlook the exis-
statistic for ANOVA (Fratio) and f(0.05,k,n(cid:4)k(cid:4)1), the coefficient of tenceofnon-linearrelationships(PovedaandMesa,1997;Wood,
determination R2, the adjusted coefficient of determination Ra2dj, 1997;Harnoldetal.,2001).
andthecorrelationr.Thesinglebesttypeofregressionmodelwas Asaconsequenceoftheassumptionsanduncertaintiesoneof
selected for each type of incoming hydrograph and for each themainlimitationofthereservoirmodelisrelatedtotheuseof
dependenthydrographandfloodingvariable,basedonMSEandr. triangularandGammahydrographs,whicharehavingonesingular
Theseregressionmodelswerechosenasthebestmodelforeach peakalongthewholesimulationdomain.Ifadoublepeakhydro-
variable.Atotalof5bestmodelswerefoundforeachdependent graph is used as an input for each reservoir, a different filling
variable based on each type of hydrograph. The correlation (r) patternwouldoccur.Thefillingofthereservoirwithafirstpeakof
showsalinearrelationshipbetweenoriginalandmodeledregres- the hydrograph would limit the amount of available volume to
siondata,whiletheMSEallowsfortakingintoaccountthebiasin capture the second peak and consequently the release routed at
theregressionmodel(Bennettetal.,2013). Huayuankouwouldbehigherthanforthecaseofthesinglepeak
An additional set of 10,000 simulations based on Gamma hydrographs.Thiswillhaveaneffectintheflooding,becausethe
hydrographs (G10) was developed to test the regression models main channel downstream of Huayuankou will not be able to
whilechangingthetotalnumberofsimulationsorsamplepoints. conveythesameamountofwater,spreadingmuchfasterthewater
Thefinalselectionofregressionmodelsforeachvariablewasbased inthelowlandarea.Thislimitationcanbeovercomebysimulating
onthevalidationresultsandFstatisticsobtained. the system with hydrographs from historical records, which are
Subsequentlythesebestmodelsweretestedwiththevalidation withdifferentnumberofpeaks.
setstochecktheirperformanceandcapabilities. The influence of the initial conditionin the main reach of the
The process was repeated also taking into account all the Yellow river is also a limitation of the physically based model
explanatory variables, to test the significance of the increase in becauseitinfluencestheamountofwaterthatisfloodingthebanks
fitnessoftheregressionmodels. inside the river dykes. The analysis can be extended to take into
considerationvariableinitialriverwaterlevels,whichneedstobe
4.6. Assumptions,uncertaintiesandlimitationsofthesimulation usedasanadditionalexplanatoryvariable.
model
5. Resultsanddiscussion
Theresearchpresentedhereinproposesamethodthatentailed
several assumptions. These assumptions, along with the un- The resultshavebeen split intotwocategories because of the
certaintiesrelatedtothemodelinputs,structureandobservations differencesfoundduringthemodelingresults.Thefirstcategoryis
may lead to limitations in the application of the proposed the suggested model between the reservoir system and the
methodology. resultinghydrographsatHuayuankou,andthesecondcategoryis
Themainassumptionsofthemethodologyare:theinitialsetof themodelbetweenthereservoirsystemandthefloodingvariables
explanatoryvariablesmustnotbecorrelated,inordertoguarantee uptoGaocun.
thatthesurrogateMRisnotbuiltwithcross-correlatedvariables;
thesurrogatehasonaveragezeroresiduals,toguaranteethatthe 5.1. Reservoirexplanatoryvariablesandhydrographsat
model errors are random; sediment is not important in case of Huayuankou
extreme flooding events; roughness is the same in the main
channelandthefloodplain;andtheinitialconditionintheriveris TherangesofthevariablesofthehydrographsatHuayuankou
assumedtobethesameineverysimulationcorresponding,i.e.a arepresentedinFig.4,AeE.Followingtheproposedmodel,ahy-
flowof3,400m3/s. pothesisonthecorrelationofexplanatoryvariablesthataremore
A correlation analysis of the explanatory variables show that relevant for each hydrograph variable is obtained. This result is
thereisamoderatecorrelationbetweentheinitialandmaximum presented in Table 2 in columns 1 to 7. Each row represents the
volumeofareservoir,howeverthisisacorrelationimposedbythe correlation of explanatory variables with respect to the hydro-
constraintthatcomesfromthephysicaldefinitionofareservoir,i.e. graph’svariablesatHuayuankou(rP-H).Theboldvaluesrepresent
the minimum volume of a reservoir cannot be larger than its significantp-valuesforeachhydrographvariable.
maximumvolume. For the peak discharge at Huayuankou (HQp), a total of 6
The simple routing of the flow, using the MuskingumeCunge explanatory variables showed p-value significance. The peak
method, between the toe of the reservoirs and the Huayuankou discharge entering Sanmenxia shows the highest correlation
station,insteadofusingafullydynamicnumericalsolutionofthe (0.834). For HQp the time to the peak discharge at Sanmenxia
SaintVenantequations,isanassumptionthatwasusedbecauseof (0.160), the maximum storage at Sanmenxia (0.079) and Luhun
the mild slope of the reaches and taking into consideration the ((cid:4)0.098)reservoirsandthepeakdischarge(0.116)andskewnessof
constant YRCC effort to keep up to date the MuskingumeCunge hydrograph (0.091) entering Guxian (0.018) have a significant
parameters. correlationaswell.
All assumptions along with the model structure lead to un- ThetimetopeakdischargeatHuayuankou(HTp)showsasig-
certainties.Inthemodelstructureoneofthemainsourcesofun- nificantcorrelationwith7explanatoryvariables;thehighestcor-
certaintylieswiththefloodmodel(2D),whichwasnotcalibrated relation is with the time to peak of the hydrograph entering
using an extreme flood event, however this was not possible Sanmenxia(0.901)andthemaximuminversecorrelationistothe
because no comparable records exist for the simulated events. A peak discharge at the same reservoir ((cid:4)0.234). In addition, this
secondsource ofuncertaintyinthephysically based flood model variable shows another interesting inverse correlation with the
structureisthelackofknowledgeofthevariabilityofthemainriver initialstoragecapacityatXiaolangdiReservoir.
reach. This could change the developmentof patterns of inunda- ThepeakdischargeandtimetopeakdischargeatHuayuankou
tion,duetoerosionandaccretionofthebanks. havesimultaneouscorrelationwiththepeakdischargeandtimeto
Fromtheperspectiveofthesurrogatemodelthemainsourceof peak discharge entering Sanmenxia. Theyalso sharea significant
uncertaintyistheneedtofixapredefinedmodelstructure(Specht, correlationwiththetimetopeakofthedischargeatGuxianandthe
1991),i.e.thelinearrelationbetweenexplanatoryanddependant maximum storage capacity at Sanmenxia. So the main driver of