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TheSearchforCatchment-ScalePhysics:SpatialScaling&SimilaritywithHydrologicalHeterogeneity
RossWoodsUniversityofBristol
SymposiuminHonorofEricWood:ObservationsandModelingacrossScales,
June2-3,2016,Princeton,USA
TheChallenges
1. “…onecouldattempttofindsimpleequilibriumlawsatthemacroscaleinmuchthesamewayasinthestatisticalmechanicsapproach”
2. “Unfortunately,inhydrologywehavenotestablishedanyprincipleofsimilarityforcatchmentbehavior…
andthusareinthesituationthatpertainedinhydraulics100yearsagobeforetheintroductionoftheReynoldsnumberandtheFroudenumber.”
Definitions(Blöschl &Sivapalan,HP1995)
• Scale - characteristiclength(ortime)ofprocess,observation,model• Scaling - transferofinformationacrossscales
• Similarityispresentwhen…• characteristicsofonesystemcanberelated tothecorrespondingcharacteristicsofanothersystembyasimpleconversionfactor,calledthescalefactor• Examples:
• ratioofcatchmentareasforrelatingflowsoftwocatchments• ln(a/tanb)forrelatingdepthstowatertableoflocations
• NBonlyexactunderverystrongassumptions!
ResponsestotheseChallenges
1. REA(RepresentativeElementaryArea)proposedasthefundamentalscaleforcatchmentmodelling
2. HydrologicSimilarity explicitlyincludesrunoffgenerationprocesses(“whattoroute”iswhatmatters!)
Woodetal1990,ReviewsofGeophysics
1.SamplingRunoffoverScales
EffectsOfSpatialVariabilityandScaleWithImplicationsToHydrologicModelingWoodetal,1988,J.Hydrol,Eric’smosthighlycited1st authorpaper
TOPMODELrunoff
Manydifferentcatchmentsizes
1km2
StableVariable
REA– Debate• REAsuggests:it’soktousesimplermodelsatscales>~1km2
• But,but,but…
• Natureismorecomplicatedthanthis(Woodsetal,1995,Seyfried andWilcox,1995)
• REAiscase-specific(Blöschl etal1995)
• Many,many,questions(Fan&Bras,1995)
• LuiswillsaymoreaboutREAimplications
REW– RepresentativeElementaryWatershed• FormulateREW-scaledynamics(Reggiani etal,AWR,1998)
• NeedclosureequationsforfluxesatREW-scale(Beven,HP2006)• “HolyGrail”,experimentaldataarecrucial– progresssofar?
WhatElseCanWeTry?
• Catchmentresponse=“integration”overadistributionofparameters• Howdoessimplecatchment-scaleresponseemergefromheterogeneity?• A1.Catchmentsdointegrateinspaceandtime• A2.Emergentprocesses• A3.Perhapsalsobecauseparametershavethesamedistributionindifferentcatchments?
Allcatchmentshaveeffectivelythesametopographicindexdistribution(Woods&Sivapalan,WRR1997)Doesthisworkforotherparametersandtheircross-correlations?
CurrentApproachesUpscaled PointEquations
• Assumptionthat“point”scaleequationscan“work”atscalesoftensandhundredsofmetres• Challengetofindtheeffectiveparametervalues,giventheconstraintsofcomputingresources
“Macroscale”Equations• Varietyof(conceptual)modelstructuresascompetinghypotheses• Acceptstructuresthatareconsistentwithobservations• Challenges:obtainrelevantobservations;weaktheoreticalbasisforsubsurfacesub-models
Argumentscanbemadeforeitherapproach.Shouldwedoboth?Why?How?
2.Similarity– Wood,Hebson,Sivapalan,Beven• Seriesof3WRRpapers(1986,1987,1990)• PriorsimilarityanalysesforfloodresponsebyHenderson&Wooding,Eagleson,Rodriguez-Iturbe,…,• Verysimplerunoffgeneration,focusontheroutingprocesses
• “Inthissequenceofpapersouraimistoprovideagreaterunderstanding oftheinterrelationshipsthatunderliethestormresponseofcatchmentsofdifferentscalesandphysicalcharacteristicsbyfocusingonconceptsofsimilarity”(Sivapalan etal,WRR1987)• Floodfrequency,stormresponse• Identifiedandlinkedtogetherkeycontrollingvariablessuchas
• dimensionlesssoil-topographicindex(saturationexcess)• ratioofrainfalltosaturatedsoilhydraulicconductivity(infiltrationexcess)• spatialCVofcatchmentrain(ratioofstormareatocatchmentarea)• ratioofstormdurationtotraveltime(routing)
Similarity- Implications• Potentiallyapowerfulapproachtomakingmeaningfulapproximatestatementsabouthydrologicalfunctioning
• Thinkintermsofrelativeamounts(fluxes,stores)forallhydrologicalprocesscomponents• Apotentialbasisforcatchmentclassification• Testable methodtotransferestablishedknowledge• Acrossspacetoungaugedcatchments• Acrosstimescalesinacatchment(e.g.climate→floodfrequency)• Acrossspacescales(e.g.spatialdownscaling)
• Wehavebeenbetteratdevelopingideasthantestingthem• Sowe’remissingtheopportunitytohaveideasfail,andlearnsomethingnew!
Similarity– ExamplesatOtherTimeScalesRecession:Lyon&Troch2007WRR
Season:Laio etal2001,AWR
Averagerunoff:Milly,1994WRR
Hereare3independent,relevantindices
Usecombinationsofthe3todefineclasses
(Berghuijs etalWRR2014)
Application
Catchmentsinthesameclasshavesimilarhydrologicalsignaturesso:1.Itmakessensetoanalyseclassmembersasagroup2.Theseindicesare(uncalibrated,apriori) broad-scalepredictorsofhydrological similarity
Seasonality
FDC
Floodfreq
Thislooksgoodbutitisonlyafirststep• Atheory-ledempiricalassociationbetweenclimateandhydrology• Separatesnatureintogroups,butdoesn’tpredicteachgroup’sresponse• Whatextrainformationdoweneedforthis?
Similarity– FailureCanBeGood!• Similaritypredictsthatcatchmentresponseswillberelatedbyspecificscalingfactors• Deviationsfromthescalingareasignofincompleteknowledge• Consistentdeviationscanbeinformative!
Snow-dominatedcatchmentsproducemorerunoff(NB:thispictureismerelysuggestive)Berghuijs etal(2014NatureClimateChange)
Similarity– FurtherProgress• Stillamajorgapbetweentheevent/recession/within-seasontimescaleandtheannual/longerscales,withnotableexceptions:• Laio etal(2002,JGR)• Sivapalan etal(2005WRR)• Iacobellis/Manfreda/Fiorentino
• Thisgapmanifestsas• Limitedtheoreticalconnectionacrosstimescales• Noconsistencyintreatmentofspatialheterogeneitywithscale• Limitedtreatmentoftransportprocessesacrossscales(thoughthatischanging)• Lackofpracticalutilityforsimilarityindicesattimescaleslessthanannual
• Alsogapsforconnectivity;groundwater-dominatedsystems• WearestillwaitingfortheGUTH- GrandUnifiedTheoryofHydrology
Summary• REA:proposedasfundamentalscaleforcatchmentmodelling• TheREAinspiredthesearchforasoundlinkagebetweenpoint-scaleandcatchmentscalerepresentationsofhydrology• Stilllookingforsoundly-basedcatchment-scalephysics
• Hydrologicsimilaritygivesussimplewaystounderstandhydrology• Thereareopportunitiestolinkacrosstimescalesandspacescales• Thereareopportunitiestolearnthroughreal-worldtesting,especiallyonlarge,challenging,diversedatasets• Similarityisextremelyvaluableforgeneratingbetterwaystoclassify