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!

Definitions(Blöschl &Sivapalan,HP1995)• Heterogeneity (orvariability)– atmultiplescales

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!

TheoreticalPromiseofProcessRepresentation

Wageneretal2007GeographyCompass

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