ECOLab_ShortScientific

MIKEBYDHI2008ECOLABShortScientificDescription23PleaseNoteCopyrightThisdocumentreferstoproprietarycomputersoftwarewhichisprotectedbycopyright.Allrightsarereserved.CopyingorotherreproductionofthismanualortherelatedprogramsisprohibitedwithoutpriorwrittenconsentofDHI.Fordetailspleaserefertoyour'DHISoftwareLicenceAgreement'.LimitedLiabilityTheliabilityofDHIislimitedasspecifiedinSectionIIIofyour'DHISoftwareLicenceAgreement':'INNOEVENTSHALLDHIORITSREPRESENTATIVES(AGENTSANDSUPPLIERS)BELIABLEFORANYDAMAGESWHATSO-EVERINCLUDING,WITHOUTLIMITATION,SPECIAL,INDIRECT,INCIDENTALORCONSEQUENTIALDAMAGESORDAMAGESFORLOSSOFBUSINESSPROFITSORSAVINGS,BUSINESSINTERRUPTION,LOSSOFBUSINESSINFORMATIONOROTHERPECUNIARYLOSSARISINGOUTOFTHEUSEOFORTHEINA-BILITYTOUSETHISDHISOFTWAREPRODUCT,EVENIFDHIHASBEENADVISEDOFTHEPOSSIBILITYOFSUCHDAMAGES.THISLIMITATIONSHALLAPPLYTOCLAIMSOFPERSONALINJURYTOTHEEXTENTPERMITTEDBYLAW.SOMECOUN-TRIESORSTATESDONOTALLOWTHEEXCLUSIONORLIMITA-TIONOFLIABILITYFORCONSEQUENTIAL,SPECIAL,INDIRECT,INCIDENTALDAMAGESAND,ACCORDINGLY,SOMEPORTIONSOFTHESELIMITATIONSMAYNOTAPPLYTOYOU.BYYOUROPENINGOFTHISSEALEDPACKAGEORINSTALLINGORUSINGTHESOFTWARE,YOUHAVEACCEPTEDTHATTHEABOVELIMITATIONSORTHEMAXIMUMLEGALLYAPPLICA-BLESUBSETOFTHESELIMITATIONSAPPLYTOYOURPUR-CHASEOFTHISSOFTWARE.'PrintingHistoryNovember2003June2004April2006October20074MIKEZero5CONTENTS6MIKEZero1INTRODUCTION.....................................72WHATISBEHINDECOLAB?.............................93ECOLABSETOFORDINARYDIFFERENTIALEQUATIONS.........113.1Specialhandlingofsettlingprocess.....................123.2SpecialhandlingoflightpenetrationinECOLab..............133.3Handlingofbuiltinconstantsandforcings..................143.4Handlingofsitespecificprocesses......................143.5ExampleofordinaryECOLabdifferentialequation:............144INTEGRATIONWITHADENGINES.........................175INTEGRATIONMETHODS..............................195.1Eulerintegrationmethod............................195.2RungeKutta4thorder.............................195.3RungeKutta5thorderwithqualitycheck..................2071INTRODUCTIONECOLabisapieceofnumericalsimulationsoftwareforEcologicalMod-ellingdevelopedbyDHI.Itisanopenandgenerictoolforcustomisingaquaticecosystemmodelstosimulateforinstancewaterquality,eutrophi-cation,heavymetalsandecology.ECOLabfunctionsasamoduleintheMIKEsimulationsoftware.Themoduleisdevelopedtodescribeprocessesandinteractionsbetweenchemicalandecosystemstatevariables.Alsothephysicalprocessofsedi-mentationofstatevariablescanbedescribed(movesthestatevariablephysicallydownthewatercolumn).ThemoduleiscoupledtotheAdvection-DispersionModulesoftheDHIhydrodynamicflowmodels,sothattransportmechanismsbasedonadvec-tion-dispersioncanbeintegratedintheECOLabsimulation.ThedescriptionoftheecosystemstatevariablesinECOLabisformulatedasasetofordinarycoupleddifferentialequationsdescribingtherateofchangeforeachstatevariablebasedonprocessestakingplaceintheeco-system.AllinformationaboutECOLabstatevariables,processesandtheirinteractionarestoredinaso-calledgenericECOLabtemplate.INTRODUCTION8MIKEZero92WHATISBEHINDECOLAB?ECOLabusesaso-calledECOLabCOM(1)objecttoperformtheECOLabcalculations.TheECOLabobjectisgenericandsharedwithanumberofdifferentDHIflowmodelsystems.ItconsistsofaninterpreterthatfirsttranslatestheequationexpressionsintheECOLabtemplate(2)tolistsofinstructionsthatenablestheobjecttoevaluatealltheexpressionsinthetemplate.Duringsimulationthemodelsystemintegratesonetimestepbysimulatingthetransportofadvectivestatevariablesbasedonhydrodynamics.InitialconcentrationsorupdatedADconcentrations,coefficients/constantsandupdatedforcingfunctionsareloadedintotheECOLabobjectandthentheECOLabobjectevaluatesalltheexpres-sions,integratesonetimestep,andreturnsupdatedconcentrationvaluestothegeneralflowmodelsystemthatadvancesonetimestep.Anillustra-tionofthedataflowisshowninFigure2.1.Figure2.1Figure1:Dataflowbetweenthehydrodynamicflowmodel,inthiscaseMIKE3,andECOLab.1MicrosoftCOMstandard2AnECOLabtemplatecontainsthemathematicaldefinitionofanECOLabmodel.Itcontainsinformationabouttheincludedstatevariables,constants,forcings,processesandthestatevariables'rate-of-changedifferentialequations.WhatIsBehindECOLab?10MIKEZero113ECOLABSETOFORDINARYDIFFERENTIALEQUATIONSIngeneralanordinarydifferentialequationisspecifiedforeachstatevari-able.Theordinarydifferentialequationsummariestheprocessesinvolvedforthespecificstatevariable.Ifaprocessaffectmorethanonestatevariable,orthestatevariablesaffecteachother,thedifferentialequationsaresaidtobecoupledwitheachother.Theprocessescontainmathematicalexpressionsusingargumentssuchasnumbers,constants,forcingsandstatevariables.Processesalwaysdescribetherateatwhichsomethingchanges.Inthiscontextconstantsarevaluesalwaysconstantintime,andforcingsarevaluesthatcanbevaryingintime.(3.1)TheUnitfor‘Rateofchange’ofPccanbespecifiedas3types:zg/m2/dzmg/l/dzUndefinedIngeneralthepartoftheunitthatrelatestotimeshallalwaysbespecifiedas‘perday’inthetemplate.InECOLabtherearetwokindsofprocesses:transformationandsettlingprocesse