Table Of ContentHydrol.EarthSyst.Sci.,21,2817–2841,2017
https://doi.org/10.5194/hess-21-2817-2017
©Author(s)2017.Thisworkisdistributedunder
theCreativeCommonsAttribution3.0License.
Unravelling abiotic and biotic controls on the seasonal water
balance using data-driven dimensionless diagnostics
SimonPaulSeibert1,ConradJackisch1,UweEhret1,LaurentPfister2,andErwinZehe1
1KarlsruheInstituteofTechnology(KIT),InstituteforWaterandRiverBasinManagement,ChairofHydrology,
Kaiserstrasse12,76131Karlsruhe,Germany
2LuxembourgInstituteofScienceandTechnology,DepartmentEnvironmentalResearchandInnovation,
CatchmentandEco-hydrologyresearchgroup,5avenuedesHauts-Fourneaux,4362Esch/Alzette,Luxembourg
Correspondenceto:SimonPaulSeibert([email protected])
Received:4March2016–Revised:9March2016–Accepted:3April2017–Published:9June2017
Abstract. The baffling diversity of runoff generation pro- nosticsareusedtocomparethesitesandtorevealthedomi-
cesses, alongside our sketchy understanding of how phys- nantcontrolsonrunoffformation.
iographic characteristics control fundamental hydrological ThekeyfindingsarethatdDMCaremeaningfulsignatures
functions of water collection, storage, and release, continue forcatchmentrunoffformationattheseasonaltoannualscale
to pose major research challenges in catchment hydrology. andthatthetypeofscalingstronglyinfluencesthediagnos-
Here, we propose innovative data-driven diagnostic signa- tic potential of the dDMC. Adding discrimination between
tures for overcoming the prevailing status quo in catchment growing season and winter period was of fundamental im-
inter-comparison. More specifically, we present dimension- portanceandeasytoimplementbymeansofatemperature-
less double mass curves (dDMC) which allow inference of index model. More specifically, temperature aggregates ex-
informationonrunoffgenerationandthewaterbalanceatthe plain over 70% of the variability of the seasonal summer
seasonalandannualtimescales.Byseparatingthevegetation runoff coefficients. The results also show that the soil topo-
andwinterperiods,dDMCfurthermoreprovideinformation graphic index, i.e. the product of topographic gradient and
on the role of biotic and abiotic controls in seasonal runoff saturated hydraulic conductivity, is significantly correlated
formation. withwinterrunoffcoefficients,whereasthetopographicgra-
Akeyaspectweaddressinthispaperisthederivationof dient and the hydraulic conductivity alone are not. We con-
dimensionlessexpressionsoffluxeswhichensurethecompa- cludethatproxiesforgradientsandresistancesshouldbein-
rabilityofthesignaturesinspaceandtime.Weachievethis terpretedasapair.Lastly,thedDMCconceptrevealsmem-
by using the limiting factors of a hydrological process as a ory effects between summer and winter runoff regimes that
scalingreference.Weshowthatdifferentreferencesresultin arenotrelevantinspringbetweenthetransitionfromwinter
differentdiagnostics.AssuchwedefinetwokindsofdDMC tosummer.
which allow us to derive seasonal runoff coefficients and to
characterize dimensionless streamflow release as a function
of the potential renewal rate of the soil storage. We expect
these signatures for storage controlled seasonal runoff for- 1 Introduction
mation to remain invariant, as long as the ratios of release
over supply and supply over storage capacity develop simi- Understandingcatchment-scalerunoffformationandtheun-
larlyindifferentcatchments. derlyingcontrolsisthekeyforbuildinghydrologicalmodels,
Wetesttheproposedmethodsbyapplyingthemtoanop- whichworkfortherightreasons(Kirchner,2006),aswellas
erational data set comprising 22 catchments (12–166km2) for hydrological similarity assessment (Larsen et al., 1994;
from different environments in southern Germany and hy- BartholdandWoods,2015)ingeneral.
drometeorologicaldatafrom4hydrologicalyears.Thediag- The latter includes what we call “forward” and “back-
ward”classificationapproaches:forwardinthesenseofpos-
PublishedbyCopernicusPublicationsonbehalfoftheEuropeanGeosciencesUnion.
2818 S.P.Seibertetal.:Unravellingabioticandbioticcontrolsontheseasonalwaterbalance
tulating similarity of runoff generation based on similar- manycatchmentinter-comparisonstudies(Merzetal.,2006;
ity of catchment structural attributes; backward as a search Oudinetal.,2008;Sawiczetal.,2011;WangandWu,2013;
for data-driven measures to detect similarity in hydrolog- Viglioneetal.,2013).Inmodelevaluation,thesignatureval-
ical response variables based either on suitable diagnos- uesobtainedfromtheobservationarecomparedtothesigna-
tic fingerprints or dimensionless similarity indicators (Siva- turevaluesobtainedfromthesimulation(VrugtandSadegh,
palan et al., 1987; Wood et al., 1990). Prominent forward 2013).
approachesincludeforinstancehydrologicalresponseunits Ideally, we expect that similarity of data-driven diagnos-
(HRUs)(Leavesley,1973),theconceptofhydrologyofsoil tics can be explained by similarity in the architecture of
types(HOST)(Boormanetal.,1995),orthetopographicin- the catchment and hence that forward and backward ap-
dex(Kirby,1975)whichdescribessimilarityofpointswithin proaches will yield consistent results. However, such com-
a catchment with respect to event-scale runoff formation parisons often fail to be conclusive. One possible explana-
(BevenandKirkby,1979).Thecommongroundofforward tion is that similarity in hydrograph-based signatures may
approaches is that they are often used in connection with indeed be caused by several reasons. For instance, charac-
hydrologicalmodelstosubdividethecatchmentorhillslope teristics of the flow duration curve such as low slope val-
into control volumes of similar runoff generation, which is ues of the 33rd and 66th streamflow percentiles, implying
represented by similar parameter sets or closure relations. dampedrunoffresponse,canarisefrompersistentyear-round
Uptonow,alargesetofHRUtypesandseparationmethods rainfallregimesorfromthedominanceofgroundwatercon-
hasbeensuggested(Woodetal.,1990;Peschkeetal.,1999; tribution to streamflow. In consequence groupings of catch-
ScherrerandNaef,2003;Schmocker-Fackeletal.,2007;Pel- ments based on either signatures or physiographic proper-
letier and Rasmussen, 2009; Santhi et al., 2008). Also, the ties can be rather inconsistent, as highlighted in the catch-
representativeelementarywatersheds(REW)concept(Reg- mentinter-comparisonstudyofAlietal.(2012)where“[...]
giani et al., 1998, 2000; Varado et al., 2006; Zhang et al., catchmentgroupingsobtainedusingphysicalpropertiesonly
2006)canbeseenasamathematicallyrigorousandthermo- didnotmatchthoseobtainedusingflowindices,meantran-
dynamicallyconsistentinterpretationoftheHRUidea.More sittimesorstorageestimates”.Similarfindingsarereported
recently a hierarchy of more specific functional units, de- by Oudin et al. (2010) and Ley et al. (2011). Although the
finedonthebasisofsimilarityofterrestrialandatmospheric potential of signatures for similarity assessment and diag-
controlsondrivinggradientsandresistanceterms,waspro- nosingfunctionalsimilarityisbeyondquestion,theexisting
posed by Zehe et al. (2014) as a refinement of the HRU approaches to define and to detect similarity differ consid-
idea.Theforwardclassificationschemesarestronglymodel- erablywithrespecttotheunderlyingassumptions,methods,
dependent,whichleavesuswithquestionsaboutconclusive- andproposedmeasures.Asacommonlyagreeduponunder-
nessandtransferabilitytootherlandscapesandhowtodefine standingof“signatures”and“hydrological,functionalorbe-
similarityincatchmentresponsebehaviourindependentlyof havioural similarity” is still missing, we can not yet distil a
models. convergenceofapproaches.
Thesequestionsarethescopeofthebackwardapproaches, In the present study we add bits and pieces to this puz-
which aim at detecting similarity in hydrological response zlebyproposingandtestingdata-drivendimensionlessback-
variablesbasedonsuitablediagnosticfingerprintsinadata- wardsignaturestodiagnoseandcharacterizeseasonalrunoff
driven way. The use of backward approaches has also been formation. As depicted in Fig. 1, these signatures shall un-
promoted by the Prediction in Ungauged Basins (PUB) ini- ravel the influences (i) of the hydrometeorological forcing,
tiative (Sivapalan, 2003; Hrachowitz et al., 2013), which i.e. radiation and precipitation, (ii) of key catchment struc-
suggested diagnosing catchment functioning through runoff tural attributes, specifically of biotic (functional vegetation)
“signatures”.Theunderlyingassumptionisthat“[...]runoff and abiotic controls (e.g. topographic gradient, subsurface
variabilitycanbebrokenupintoseveralcomponents,eachof hydraulic conductivity), and (iii) of the state of the catch-
themamanifestationofcatchmentfunctioning,albeitatdif- ment.Therelativeimportanceoftheseconcurringinfluences
ferent time scales, [...]” (Blöschl et al., 2013, p. 7). Today, on runoff generation depends on the scale. Intuitively one
runoffsignaturesarecommonlyacceptedandusuallydefined mightexpectthewetnessstateofthecatchmenttobeofthe
asspecificcharacteristicsofthehydrographsuchasautocor- highestimportanceforrunoffgenerationduringevents,while
relation,slopeoforbiasintheflowdurationcurveordiffer- vegetationsurelyhasthestrongestimpactonseasonalrunoff
ent segments thereof, rising limb density, peak distribution, production.
and/or as flow statistics such as mean, variance, skewness, So what could suitable data-driven diagnostic signatures
or the coefficient of variation (Pokhrel and Yilmaz, 2012; looklike?Inspiredbythediagnosticapproachtomodeleval-
Casper et al., 2012; Pfannerstill et al., 2014; Euser et al., uation(Guptaetal.,2008),McMillanetal.(2011)proposed
2013,2015).Runoffsignaturesarewidelyusedforsimilarity combining recession analysis, soil moisture dynamic analy-
assessmentbutalsoformodelevaluation.Intheformer,sim- ses,andevent-scalewaterbalanceinvestigationstoobtainin-
ilarity in the signature values is interpreted as hydrological sightsintodifferentrunoffresponsetimescalesandtoassess
similarityamongcatchments,whichisalsothefoundationof the impact of pre-storm wetness conditions on catchment
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S.P.Seibertetal.:Unravellingabioticandbioticcontrolsontheseasonalwaterbalance 2819
Storage Precipitation In this study we propose and test dimensionless diagnos-
ticsignaturestocharacterizeseasonalrunoffformationbased
State Forcing
on rainfall–runoff data, which shall ultimately separate the
Binding Baseflow
Radiation terrestrial controls on runoff formation from the meteoro-
forces nal es Runoff serE logical forcing. The proposed concept relates to the idea of
om pv
Seasregi behaviour seno tne Wageneretal.(2007)thatcatchmentshavethreemainfunc-
Long-term tions, i.e. to partition, store, and release water. In line with
memory
Black(1997)wetreatcatchmentsaslumpedterrestrialfilters
Architecture/ andfollowingKirchner(2009)weassumethatannualrunoff
structure formationisessentiallyamonotonouslyincreasingfunction
Topography Subsurface ofwaterstorageinthecatchment.Accordingly,accumulated
Vegetation runoffisexpectedtobelimitedbyaccumulatedwatersupply
(rainfallminusevaporation).Waterstorageiscontrolledand
Figure1.Conceptualsketchofthemajortemporalscalesofrunoff
limitedbywatersupplyduetorainfall,theavailablesubsur-
formation,i.e.long-termbehaviour,seasonalregimes,generationof
facestoragevolume,aswellasbyitsrechargeanddrainage
baseflowandeventrunoffproduction,andcorrespondingfirst-order
controls. properties.Consequently,weevaluatewhetheradiagramthat
plotsaccumulatedwaterreleasescaledwithtotalannualsup-
plyagainstaccumulatedwatersupplyscaledbytheavailable
runoff dynamics. Hrachowitz et al. (2011) suggested com- storage capacity provides the means to detect similarity in
biningeventrunoffcoefficientsanddifferenttracerstoinfer catchment seasonal runoff formation. Such a signature for
knowledge of hydrological processes in small catchments. storagecontrolledseasonalrunoffformationisdeemedtore-
Tracerdataarealsowidelyusedtoestimatetransittimechar- main invariant during simple scaling operations, as further
acteristicswhichareconsideredausefulsimilarityindexfor explainedbelow.
process-basedcatchmentclassification(Soulsbyetal.,2010; In line with these thoughts we hypothesize that dimen-
Capell et al., 2012). Therefore, breakthrough or flushing of sionless and season-specific double mass curves (dDMC),
either contaminants (Gassmann et al., 2013), artificial trac- which relate dimensionless accumulated runoff to dimen-
ers (Wienhöfer et al., 2009), sediments (Martínez-Carreras sionless accumulated precipitation, are suitable for discrim-
et al., 2010), or even diatoms as smart tracers (Martínez- inating differences in how a catchment releases water as
Carreras et al., 2015; Klaus et al., 2015) are used. More re- a function of the accumulated water supply. We test this
cently, McMillan et al. (2014) proposed a “targeted analy- hypothesis by addressing the following research questions
sesofcatchmentresponsedata”andcombinedhydrograph- withinacatchmentinter-comparison.
based signatures with signatures that evaluate characteris-
tics of the water balance, recession analysis, and hydrolog- Q1: Howcanweobtainproperdimensionlessdoublemass
ical thresholds to examine the extent to which hydrological curvesusingsite-specificcharacteristicstoensurecom-
behaviour varies within a 50km2 catchment. The common parabilityamongcatchmentsbasedonoperationaldata
ground of the mentioned approaches is that they combine sets?
multiple sources of information from rather different obser-
vations. Q2: Aretemperatureindicesfromvegetationecologysupe-
This is however only possible in well-instrumented re- riorcomparedtocalendaricaldefinitionsforseparating
search catchments. As our focus is on providing diagnos- summerandwinterregimes?
tic fingerprints for comparative hydrology (Sivapalan et al.,
2003), we constrain our work to operational hydrometeoro-
Q3: Can we identify physiographic and ecological proper-
logical data sets. These commonly consist of meteorologi-
ties which explain differences in seasonal runoff be-
cal variables like precipitation, air temperature, and humid-
haviourrevealedbydifferencesinthedDMC?
ity,anddischargedata.Informationonthecatchment“state”
intermsofgroundwaterlevelorsoilmoisturedataismoni- Additionally we evaluate whether flow duration curves
tored only occasionally and often at a coarse spatial resolu- (FDC), which are widely used as diagnostic signatures (Ye
tion.Theadvantageofoperationaldatasetsisthattheyallow etal.,2012;Euseretal.,2013;Viglioneetal.,2013),might
ustoincludesufficientcatchmentswithratherdifferentphys- provide similar insights into seasonal runoff behaviour to
iographicandclimatecharacteristics(end-members)forour dDMC. The paper is structured as follows: in the method
analysis.Adrawbackofsuchdatasetsisthattheymostlyex- section in chap. 2 we introduce the data set, the concept of
istonlyforscalesof50km2 andlargerandthatspecificdata dDMC,theseparationofseasons,andtheunderlyingstatis-
suchastracers,piezometricheads,orsoilhydraulicproper- tical methods we apply to address Q3. After presenting the
tiesareusuallynotavailable. resultsinSect.3weclosewithadiscussionandconclusions
inSect.4.
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2820 S.P.Seibertetal.:Unravellingabioticandbioticcontrolsontheseasonalwaterbalance
2 Concept,methods,andstudyarea
2.1 Studyarea
We propose and explore the potential of signatures to char-
acterize seasonal runoff generation based on an operational
data set of sub-basins from the Danube in Bavaria. In this
chapter we introduce the data set and detail the differences
in the climate and physiographic setting of our test catch-
ments.Beforethat,wewillbrieflydiscussthequalityofthe
database,whichinfactwasinmostcatchmentssopoorthat
themajorityofthesiteshadtobeexcludedfromtheanalysis.
2.1.1 Dataqualityandselectionofheadwater
catchments
In our analysis we focus on lower mesoscale headwater
catchments (<200km2) as routing effects are still small
(Robinsonetal.,1995)andbecausethegeologicalandpedo-
logicalset-upisoftenstillfairlyhomogeneousatthisscale.
Figure2.UpperDanubecatchmentinsouthernGermanywithse-
In addition, non-convective storms often cover the majority lectedheadwaterbasins(bluepolygons),correspondinggauges(red
of the catchment area and we may hence assume that the triangles), and major river networks (blue lines). The site identi-
hydrometeorological forcing is well observed by the given fiers(IDs)refertothecorresponding(hydro)geologicalunit(colour
station and that it is fairly uniform within the entire head- codedmapinthebackground,adaptedfromBGRandSGD,2015)
water. We hence select all gauged headwaters of this size and a single Arabic numeral. Moving from the north-west to the
withintheBavarianpartoftheDanubebasin.Forthis,hourly south,wedifferentiateTriassic(TRI),Jurassic(JUR),BavarianFor-
est (BFO), Faulted Molasse (MOL), Alpine Foreland (AFO), and
hydrometeorological time series from the period 1 Novem-
Alpine (ALP) locations. Table C1 provides links between the site
ber 1999 until 31 October 2004 are available. The database
IDs and the real gauge names. The inset in the upper left corner
of130potentialreferencecatchmentsisanalysedaccording
showsGermany’sfederalstateboundaries,theindividualheadwa-
toasetofqualitycriteria:weonlyincludecatchmentswhere
teroutlets,andthebasinoftheDanube(greyarea).Thegridcoor-
(i)atleastonemeteorologicalstationwascloserthan20km
dinatesrefertotheGauss–Krügerzone4projection(CRSidentifier
(which is less than in the Mopex data set, Schaake et al., EPSG:31468).
2000; Duan et al., 2006), (ii) the total accumulated water
balance error of the entire period of 4 hydrological years,
considering simulated evaporation, was smaller than 5% of
TRI1(Fig.3,topleft)receivesafairlyconstantinputinpre-
totalprecipitation,(iii)theamountofmissingand/orimplau-
cipitation(P)throughouttheyear,butreleasesdischarge(Q)
siblemeteorologicaldatawas<5%,and(iv)thestreamsare
with a strong seasonality and pronounced minimum during
notsubjecttoanysevereregulation.Thisscreeningresulted
summer. Compared to the other sites the inter-annual varia-
in 22 catchments being classified as suitable for the analy-
tioninevapotranspiration(E)isratherlarge.Thecatchment
sis. The sites represent very different hydrological regions
AFO4 (Fig. 3, top right) in contrast shows seasonality in P
(Fig.2)andwereroughlyclassifiedbasedupongeology,cli-
butafairlyconstantoutputinQ.ALP4(Fig.3,bottomleft)
mate,andelevation.Movingfromthenorth-westtothesouth
andALP2(Fig.3,bottomright),whicharebothAlpinesites,
wedifferentiateTriassic(TRI),Jurassic(JUR),BavarianFor-
show a pronounced minimum in Q during February due to
est(BFO),FaultedMolasse(MOL),AlpineForeland(AFO),
snow storage. ALP2 however shows a very large range in
andAlpine(ALP)landscapes.Thecatchmentidentifiersre-
both P and Q during summer, which suggests little buffer-
flecttheseunitsandincludeanindexofthesamplesize,e.g.
ing and a high reactivity. In contrast, ALP4 has a much
MOL1, ..., MOL7. Catchment locations, real gauges, and
moredampedresponsetoP duringsummerandamorepro-
correspondingstreamnamesareprovidedinTableC1inthe
nouncedseasonalityinE.
Appendix.
Tocharacterizethestructuralset-upofthedifferentcatch-
2.1.2 Dataandphysiographicsiteproperties ments, we employ various landscape analysis techniques.
Using these methods we derive nearly 30 different physio-
TheBavarianpartoftheDanubebasinexhibitsconsiderable graphiccharacteristicsforeachofthecatchments.Theyare
differencesinthehydrometeorologicalregimes.Toillustrate summarized in Tables A1 and A2 in Appendix A. Topo-
them we plot regime curves for four different catchments graphic information was extracted from a digital elevation
in different environmental settings in Fig. 3. The catchment model with a resolution of 25m. We use it to calculate the
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S.P.Seibertetal.:Unravellingabioticandbioticcontrolsontheseasonalwaterbalance 2821
calibratedandinoperationaluseattheBavarianfloodfore-
casting agency, was made available by the LfU. To obtain
arealestimatesweforcedthemodelusingobservedhydrom-
eteorological station data like temperature (T), wind speed,
humidity,radiation(R),andP,amongothers.LARSIMsim-
ulates E using the Penman–Monteith equation. Interpola-
tion is done using the grid point method (NOAA, 1972). It
is important to note that we use LARSIM exclusively as a
uniform interpolation tool for P and E and that we do not
use any other model output. Note that Table A1 also pro-
vides hydrometeorological catchment characteristics like 4-
yearmeanannualprecipitation(P),discharge(Q),runoffco-
efficient(CR),andstreamflowcoefficientofvariation(ν ).
Q
These quantities are all calculated based upon the available
observables, except for E. Additional information on the
BavarianpartoftheDanubebasin,thehydrometeorological
data, and the LARSIM model can be obtained from Seibert
etal.(2014).
2.2 Dimensionlessdoublemasscurvestocharacterize
runoffformationandthewaterbalance
Figure3.Regimecurvesofobservedarealprecipitation(P)(grey),
discharge(Q)(blue),andcalculatedarealmeanevapotranspiration
Essentially, we suggest that dDMC, describing dimension-
(E, Penman–Monteith) (green) of four selected headwater catch-
lessaccumulatedreleaseasafunctionofdimensionlessaccu-
ments.Thewidthoftheindividualbandsillustratestheinter-annual
mulated rainfall supply, are feasible for characterizing stor-
variation during the 4-year long period. The curves are based on
kerneldensityestimatesusingidenticalkernelsandbandwidthsfor age controlled runoff formation in a scale-invariant way.
variablesofthesametype.P,Q,andE providethe4-yearmean In this chapter we provide the corresponding principles
annualaverageofthedifferentvariables,respectively. (Sect.2.2.1)andintroducetwodifferentapproachestoderive
dDMC(Sect.2.2.2)whichallowustoaddressQ1.Toaddress
research questions Q2 and Q3 we employ a temperature-
median topographic gradient (φ) (–) of each catchment ac-
index method to obtain season-specific dDMC and relate
cordingtoMcGuireetal.(2005)astheflowpathlengthfrom
their properties to the available catchment descriptors. The
eachpixeltothestreamdividedbythecorrespondingdiffer-
corresponding methods are described in chaps. 2.3 and 2.4,
enceinheightusingtheWhiteboxgeographicanalysistool-
respectively.
box (Lindsay, 2014). Areal shares of various surface cover
and soil properties like average sand, silt, or skeleton con-
2.2.1 Theory
tents, root-zone effective field (eFC) (mm), and air capaci-
ties (AC) (mm) among others were derived from CORINE
Pfister et al. (2002) introduced double mass curves as a
landusedataasof2006andthedigitalsoilmapofGermany
straightforwardwayofcomparingseasonalrunoffformation
(scale:1:1000000)(Hartwichetal.,1995).Theaveragesat-
andrunoffcoefficientsamongcatchmentssituatedindiffer-
urated hydraulic conductivity (Ks) (ms−1) is estimated for
ent geologies in the Alzette basin. The double mass curve
each catchment based on available grain size distributions
quantifies cumulated runoff as a function of cumulated pre-
usingRosetta’spedo-transferfunctions(Schaapetal.,2001).
cipitation within the hydrological year. These diagrams are
Due to Darcy’s law we also included a soil topographic in-
also helpful for learning about the inter-annual variability
dex(τ)(ms−1),i.e.theproductofthetopographicgradient
of the interplay of streamflow release and rainfall supply
and saturated hydraulic conductivity, in the analysis, as we
(Jackisch,2015)andasadiagnosticsignaturetoimprovethe
expectthemtoactinagroup:
development of perceptual models (Wrede et al., 2015). A
τ =φ·Ks. (1) straightforwardmeansofensuringthecomparabilityofdou-
ble mass curves within the same clean geological and cli-
Lastbutnotleast,weemployedtheconceptualhydrolog- matesettingistorelatefluxesinsteadoftheflows.Thisim-
icalLargeAreaRunoffSimulationModel(LARSIM)(Lud- pliesindependenceofasimplescalingoftherespectiveflows
wig and Bremicker, 2006) to simulate E and snow water withcatchmentarea.Jackisch(2015)andPfisteretal.(2002)
equivalent (W) and to obtain areal estimates of E, P, and showedthattheinter-annualvariationofdoublemasscurves
W foreachcatchment.Forthispurposeagriddedversionof and their shape is rather invariant within a given geological
LARSIM(spatialresolution:1km2;timestep:1h),whichis setting but reveals distinct differences among different ge-
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2822 S.P.Seibertetal.:Unravellingabioticandbioticcontrolsontheseasonalwaterbalance
ologies.Thekeyquestionis,however,whetherthesediffer- unit area. The latter is often used as a “diagnostic” variable
encesindeedreflectnon-trivialdifferencesinterrestrialcon- to detect scale-invariant differences in generation of runoff
trolsofrunoffformationorwhethertheseare(partly)caused volume(Merzetal.,2006;Graeffetal.,2012).
byvolumetric“scaleeffects”,i.e.differencesinstoragevol- As the double mass curve will relate the accumulated di-
ume,whicharisefromdifferentverticalextentsandnotfrom mensionlesswaterreleasetothedimensionlessaccumulated
differencesinspecificsoilandbedrockporosity. water supply of the catchment, the dependent and indepen-
A nice example that underlines that a dimensionless for- dent variables need to be scaled properly. We define the di-
mulation removes such simple scale effects is the dimen- mensionlessaccumulatedwaterrelease(Q∗)(–)ofthecatch-
sionless breakthrough curve (BTC). BTCs are used in soil ment based on the ratio of accumulated specific discharge
P
physicstoreveal(dis)similaritiesintransportandadsorption (cum.Q) (mm) and annual totals of P ( P ) (mm) of the
yr
propertiesofasoil“filter”independentlyofthespatialextent correspondinghydrologicalyear:
oftheprobe(Hillel,2004).Conceptually,BTCsareplotsof
cum.Q
scaled cumulated solute outflow against cumulated infiltra- Q∗= . (2)
P
tion scaled by the pore volume of the sample. The BTC is Pyr
henceinvariantforagivensoluteaslongastheratioofaccu-
Weareawarethatthisdefinitionis,whilebeingclosetothe
mulatedwatersupplyandstoragecapacityremainsthesame.
definition of a runoff coefficient, not exactly the desired ra-
Thekeytoscaleindependenceistousetheratioofcumulated
tioofaccumulatedreleasetototalannualsupply.Thelatter,
irrigationandstoragevolumesinsteadofusingthecumulated
i.e. infiltration, needs to be determined based on the differ-
irrigationalone.
enceofaccumulatedP andaccumulatedE.Asevaporation
The essential difference between a breakthrough experi-
ishowevernoteasytoobserve,Eq.(2)mightstillbeasuit-
ment and the catchment water balance is, however, that the
abledata-drivenestimate.
catchment releases water vapour to the atmosphere and liq-
Removing the dimension of the abscissa of the double
uid water to the stream at two different interfaces and that
masscurve,i.e.cum.P (mm),islesstrivial.Aneasywayis
thesubsurfaceextentofthestoragevolumeandtheflowpath
P
touse P (mm)againtoscaleaccumulatedrainfallsupply
lengthtotheriparianzonearelargelyunknown.Withinour yr
(Eq. 3). This nicely scales both axes to the range of [0...1]
analogy,weregardliquidwaterreleaseastheanaloguetoso-
andallowsustocomparemultiplesitesandyears.
lutebreakthrough,becausebothprocessesarecontrolledby
gravity-driven water fluxes through the subsurface. In con-
cum.P
trast,E feedsmostlyfromsoilwaterwhichisstoredagainst P∗= (3)
P
P
gravity. This part of soil water is largely immobile similar yr
to adsorbed solutes (Zehe and Jackisch, 2016). The second An advantage of plotting Q∗ against P∗ is that it yields
difference is that the underlying controls on Q and particu-
curvesthatarefairlyintuitivetointerpret,asthisscalingpre-
laronE donotonlydependonpropertiesofthesoilbutare
servestheshapeoftheoriginaldoublemasscurve.
also a function of time-dependent system states and bound-
aryconditionslikethemeteorologicalforcingorthepressure – In snow-free periods with negligible E catchment “fil-
difference between the groundwater system and the stream. ter” properties naturally are expected to cause dDMC
WhereasthedrivingforceonQ,i.e.gravity,isconstant,the with overall slopes smaller than unity. Step changes
radiative forcing and the impact of vegetation on E follow anddeviationsfromtheoverallpatterntowardssmaller
apronouncedseasonalcycle–atleastintemperateenviron- slopessuggesteitheractivationofadditionalstorageor
ments. that water leaves the catchment in the form of evapo-
ration, or both. Differentiation among these options is
2.2.2 Derivationofdimensionlessdoublemasscurves unfortunately not straightforward. A possible remedy
is to focus onsummer and winter periods individually,
Thekeytoobtainingscale-invariantdimensionlessquantities because snow is not relevant during summer and be-
istodivideastatevariableofinterest–forinstanceaforce, cause E is deemed to be small during winter (see also
velocity, or length, by a characteristic quantity of the sys- chap. 2.3). To indicate the activation of storage in the
tem(BlöschlandSivapalan,1995).Apopularexampleisthe snowpack, we highlight dDMC periods with tempera-
Reynolds number in fluid mechanics, which relates inertial tures<0◦C.
forcestoviscousforces.Itisdefinedasflowvelocitytimesa
characteristiclengthdividedbythedynamicviscosityofthe – Segments with slopes of 1 indicate that release equals
fluid,whichissuitedtocomparingturbulenceinopenchan- supplyandthatwaterisneitherstoredinthesystemnor
nel flow independent of the channel width. The best known that significant amounts of water leave the catchment
example of a dimensionless response measure in hydrology in the vapour phase. Segments with a slope of one or
istherunoffcoefficient(CR)(–)definedasspecificdischarge close to it are expected to occur during intensity con-
overspecificrainfall,bothwithunitsofvolumepertimeper trolled runoff formation, i.e. Hortonian overland flow
Hydrol.EarthSyst.Sci.,21,2817–2841,2017 www.hydrol-earth-syst-sci.net/21/2817/2017/
S.P.Seibertetal.:Unravellingabioticandbioticcontrolsontheseasonalwaterbalance 2823
(Horton, 1933) or preferential flow (Beven and Ger- In accordance with Eq. (5) we define the type II dDMC as
mann, 2013). These mechanisms are not controlled by accumulatedstreamflowreleasescaledbytheannualprecip-
storagecapacitybutbyinfiltrabilityandconductivityof itationamount,plottedagainstcum.P(t)scaledbyS .We
max
thesubsurface(StruthersandSivapalan,2007).dDMC expectthiscurvetobesensitivetodifferencesamongcatch-
segments with slopes close to one may however also mentswithrespecttotheratioofrainfallsupplyandstorage
indicate fast responding catchments e.g. due to domi- volume as well as to differences that arise from the second
nance of poorly developed shallow soils, impermeable factor.Differencesinthelattermightarisefromdifferences
substratumorstrongtopographicgradients. inhowcontributingareasgrowwithrelativesaturationofthe
soilstorage.Weexpectthelattertobeidentifiableduringthe
– SegmentsofthedDMCthatexposeslopeshigherthan1
wet period. When increasing β to values larger than 1, the
indicatethatreleaseislargerthansupply.Providedthat
second factor becomes non-linear, which yields an increas-
routingeffectandrunoffconcentrationtimesarenegli-
ingly convex function, which implies increasingly smaller
gible, these phenomena should be restricted to periods
winterslopesinthetypeIIdDMC.Whendecreasingβtoval-
ofsignificantsnowmelt.Theyshouldhenceonlyocca-
uessmallerthanunity,thesecondfactorbecomesnon-linear
sionally occur in the winter and coincide with periods
andincreasinglyconcave,whichimpliesincreasinglylarger
ofsnowaccumulationthatarefollowedbywarmingpe-
typeIIdDMCwinterslopes.Differencesinthechangeinwa-
riods.
terstoragedS/dtduetodifferencesinE (compareEq.B6)
A considerable disadvantage of scaling the abscissa using are expected to reflect the inter-annual variations at a given
P
Pyr (mm),namedtypeIdDMChereafter,ishoweverthat site (warm and cold summer) or climate differences among
the same ordinate values in different hydrological years do different sites. Those differences should be identifiable dur-
not correspond to the same mass input. A comparison of ingthesummerperiod.
typeIdDMCamongdifferentsitesandyearsmightthussug- Deriving type II dDMC requires however an estimate of
gestgreatersimilaritythanthereactuallyis. S , i.e. information about the characteristic vertical ex-
max
Motivated by the dimensionless breakthrough curve, we tent of the storage volume, which is largely not observable.
proposeanalternativeapproachtoscaletheaccumulatedwa- StandarddataforsoilstoragethatareavailableinGermany
tersupply,namedtypeIIdDMChereafter.Itcanbederived (Hartwichetal.,1995)includeestimatesofspecificeffective
from the widely used HBV beta store (Bergstroem, 1976). fieldcapacity(eFC)andaircapacity(AC)(bothinmm/dm)
Thelatterconceptualizesstoragecontrolledformationofdi- whichwemultipliedbyrootzonedepthtoobtainasuitable
rect runoff (Qd) as a function of the relative saturation of unit (mm). Though these data are uncertain, particularly at
thesoilstorage(Sm(t)),actualprecipitationP(t),andaform thecatchmentscale,weusethemtoscalecumP.
parameter(β)(Eq.4).
cum.P
Q (t)=P(cid:18)Sm(t)(cid:19)β (4) P∗= eFC+AC (6)
d
S
max 2.3 Season-specificevaluationofthedoublemasscurve
Considering the mass balance and Q as a surrogate for
d
rainfall-driven streamflow generation, it can be shown from During the growing period evapotranspiration often makes
Eq. (4) that accumulated Q within the interval t and t up the largest portion of the water balance. A possible way
d 0 e
scales with the ratio of accumulated precipitation amount to isolate abiotic controls on runoff formation from the im-
(cum. P) (t ) and total storage (S ) as one key factor as pactofthevegetationistofocusondatafromfrost-freeperi-
e max
showninEq.(5).Thesecondfactorthatimpactstheintegral odsofthe“dormant”fallandwinterseason.Accordinglywe
of Q is the integral of the relative storage change scaled deriveseason-specificdoublemasscurves.Thishoweverre-
d
withtherelativesaturationofthesoilstoragepowerofβ−1. quiresameaningfulseparationofthedormant,i.e.the“win-
Whereasbothfactorsarestronglydependentontheunknown ter period” and the vegetation dominated “summer period”.
formparameterβ,thesecondfactorimplicitlyalsodepends Such a separation of seasons is not straightforward – par-
on E. In Appendix B we derive Eq. (5) from the beta store ticularforinter-comparisonstudies.Conventionaldefinitions
concept,Eq.(4),andillustratetheroleofthedifferentterms likehydrologicalyearsortheastronomicalequinoxes(vary-
usingthecaseβ=1(compareEq.B7). ing between 19 and 21 March and 22 and 24 September in
central Europe) are easy to implement and thus frequently
Zte Q dt = cum.P(te)(cid:18) Sm(te)β (cid:19) used.However,theyoftenintroduceuncertaintyastheyfail
d S (S )β−1 inpredictingtheonsetofvegetationandthustheendofthe
max max
t0 dormantperiod.Furthermore,theperiodofactivevegetation
Zte (cid:18)cum.P(t) (cid:18)S (t)(cid:19)β−1dS(cid:19) does not only depend on the location of a catchment with
− β m dt (5) respecttolatitudebutalsowithrespecttoaltitude.
S S dt
max max Asanalternativewetesttemperatureaggregateswhichare
t0
used as predictors of bulk ecological activity in plant phys-
www.hydrol-earth-syst-sci.net/21/2817/2017/ Hydrol.EarthSyst.Sci.,21,2817–2841,2017
2824 S.P.Seibertetal.:Unravellingabioticandbioticcontrolsontheseasonalwaterbalance
iology (Mäkelä et al., 2004). Specifically we use a temper- erageflowvariability.SpecificallywecompareCR (–)and
S
ature index model (Menzel et al., 2003) to define the onset CR (–)againstsFDCbetweenthe33rdand66thpercentiles
W
andthedurationoftheperiodofvegetation.Inthisapproach withinalinearregressionanalysis.Sinceexceedanceproba-
thegrowingseasonisdefinedastheperiodbetweenthelast bilitiesarenotsensitivetoseasonality,wealsoderiveseason-
springfrostandthefirstfallfrostinwhichtheaveragedaily specificFDCbasedonthetemperature-indexedderivedsea-
temperature constantly equals or exceeds 5◦C. We evaluate sons. Using the seasonal FDC we calculate inter-percentile
this method visually by plotting the results into the double slopesofthedormantperiod(sFDC (–))andthatofthepe-
W
mass curves and by comparing them to the Gregorian defi- riodofvegetation(sFDC (–))andincludethemintheanal-
S
nition of the beginning of spring which is 20 March in our ysis.
climate. This way we address the second research question
(Q2).
3 Results
Theseparationofseasonsallowsustoderiveaveragesum-
merandwinterrunoffcoefficients,CR (–)andCR (–),re-
S W 3.1 Dimensionlessdoublemasscurves
spectively,forthetypeIdDMC,bycalculatingtheslopeof
linearregressionlineswhichwefittothesummerandwin-
3.1.1 TypeIdDMCandtemperature-index-based
tersegmentsofthetypeIdDMC.ForthetypeIIdDMCwe
seasonseparation
evaluate only the winter regimes, as we expect them to be
primarily sensitive to the shape parameter β, and not to E, Theseason-specificevaluationofthetypeIdDMCrevealed
as suggested by the proof in Appendix B. Analogously to asurprisinglyconsistentpatternwithsimilarmasscurvesin
thetypeIdDMC,wefitlinearregressiontothewinterseg- allcatchmentsintermsofafairlysteepincreaseduringwin-
mentsofthetypeIIdDMC.Here,theregressionslope(mW) terandaclearregimeshifttowardsmuchflatter,partlyzero
(–)characterizeshowfastrelativereleaseincreaseswiththe regressionslopesinthevegetationperiod.Infacttheslopes
potentialrenewalrateofthesoilstock. of the dDMC for different years of a catchment are almost
constant,justshiftedinparallel,duringtheperiodofvegeta-
2.4 Catchmentinter-comparisonandstatistical tion at many sites and for many years as depicted in Fig. 4.
evaluationofthedoublemasscurves As indicated by Table 1 the seasonal winter runoff coeffi-
cients(CR =0.67)exceedtheaveragesummerrunoffco-
W
To explain differences in seasonal runoff formation and efficients (CR =0.32) by a factor of 2 on average which
S
hence to address Q3 we compare dDMC properties of the is in line with the findings of (Hellebrand et al., 2008) –
22catchmentbasedontheiraveragemW (–),CRS (–),CRW withexceptionofthetwoAlpinesitesALP2andALP3.The
(–)andCRYR(–)valuesandcorrespondinginter-annualvari- inter-annual variation of the seasonal runoff coefficients are
ations.Specificallywecomparethespatialpatternsofthedif- twiceaslargeduringwinter(σ =0.1)asduringsummer
CRW
ferentquantitiesandtestiftheycoincidewiththegroupings (σ =0.06),indicatingaratherstronghomogeneityduring
CRS
ofourcatchmentswhichisbasedonhydrologicalregionsas summer.
outlinedinchap.2.1.2.Inastatisticalevaluationweattribute AsdepictedinFig.4thetemperature-basedestimatesfor
differencesinmW(–),CRS(–)andCRW(–)tothestructural thebeginningandendofwinterandsummerperiod(Menzel
andclimaticpropertiesofthecatchmentslistedinTablesA1 etal.,2003)nicelycoincidewiththepointswheretheslope
and A2 to identify the underlying controls but also to eval- of the dDMC changes (in terms of cum.P/PP). This ap-
uatethedifferentscalingschemesofthedependentvariable pliesfordifferentyearsandtheentirerangeofphysiographic
against the dimensionless formulation of accumulated sup- conditions of our catchments, except for the Alpine region
ply. For this we use simple and multiple linear regression which is shown in the bottom left panel of Fig. 4. In the
analyses and corresponding tests of significance which are Alpine settings the accumulation and melting of snow has
implementedinthestatisticalcomputingplatformR(RCore astrongerimpactontheseasonalwaterbalancethanthepe-
Team,2015).Inthemultipleregressionanalysiswekeptall riod of vegetation. The spring and fall equinoxes (drawn as
variablesthatincreasedther2 byatleast5%andwhichhad hatchedareasinFig.4)andthetemperature-basedestimates
p-values≤0.05. Assuming that linear relationships would ofthetippingpointsdeviateby−38±17and−26±15days,
suffice to identify important explanatory variables, we did respectively.Thisconfirmsthattheuseofconventionaldefi-
not test non-linear relationships as clear hypotheses on the nitionsfortheonsetandendoftheperiodofvegetationmay
kindoftheserelationshipsweremissing. yieldsignificantlydifferentresultscomparedtotemperature-
Last but not least we compare what we learn from the based estimates. We conclude that temperature aggregates
dDMCagainstwhatistobelearnedfromthewell-knownand can be included easily in hydrological analyses and suggest
widely used FDC. FDC describe the distribution of stream- that they may have a higher explanatory power than static
flowmagnitudeswithrespecttoexceedanceprobability.Ac- conventionaldefinitionsforthebeginningandendofthepe-
cording to Sawicz et al. (2011) the slope of the flow dura- riodofvegetationsuchastheequinoxes.
tion curve (sFDC (–)) can be considered as a proxy for av-
Hydrol.EarthSyst.Sci.,21,2817–2841,2017 www.hydrol-earth-syst-sci.net/21/2817/2017/
S.P.Seibertetal.:Unravellingabioticandbioticcontrolsontheseasonalwaterbalance 2825
0 0
1. Reg. winter MOL2 TRI3 1.
Reg. period of vegetation
8 Onset period of vegetation 8
) 0. End period of vegetation 0.
−
P (6 Temperature < 0 6
0. 0.
(cid:229)Q / 4 4
um. C0.00.20. Mar 20 Sep 22 Mar 20 Sep 22 0.00.20.
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
0 0
1. BFO1 AFO2 1.
8 8
) 0. 0.
−
(
P 6 6
0. 0.
(cid:229)um. Q / C0.00.20.4 Mar 20 Sep 22 Mar 20 Sep 22 0.00.20.4
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
0 0
1. ALP3 JUR1 1.
P (−) 60.8 60.8
0. 0.
(cid:229)um. Q / C0.00.20.4 Mar 20 Sep 22 Mar 20 Sep 22 0.00.20.4
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
(cid:229) (cid:229)
Cum. P / P (−) Cum. P / P (−)
Figure4.TypeIdimensionlessdoublemasscurvesforcatchmentsofdifferentgeologicalunitsforthehydrologicalyears1999–2003.Onset
and end of the period of vegetation are determined using a temperature-index model. Regression lines are fitted to both periods (dotted
lines in red/green); their slopes are interpreted as seasonal runoff coefficients. Periods with temperatures<0◦C are highlighted in blue.
P
Gregoriandefinitionsforthefirststartofspring(20March)andthelaststartofautumn(22September)areaddedtothecum.P/ P plane
ashatchedrectangles(toimprovereadability)tohighlighttheirdifferencestotemperature-basedestimatesattheonsetandendoftheperiod
ofvegetation.StatisticalpropertiesofthedDMCaresummarizedinTable1.
3.1.2 Season-specificevaluationoftypeIIdoublemass ear progression. More importantly, these curves reveal dif-
curves ferencesamongthedifferenthydrologicalyears.Dryandwet
yearsarenicelyseparated,asindicatedbytheendpointsof
theindividualcurves.ThetypeIIdDMCisalsomuchmore
The type II dDMC, which scale accumulated supply by the suited to revealing differences among catchments, in terms
specific storage volume of the soil in Fig. 5 reveal a sim- ofhow“fast”thecatchmentsreleaseafractionofrainfallin-
ilar shape as the type I dDMC in Fig. 4. They exhibit an put in terms of how often the annual rainfall supply could
obvious regime shift between steep winter and flat summer potentially renew the soil water stock. This is particularly
regression slopes but expose a larger spread and a less lin-
www.hydrol-earth-syst-sci.net/21/2817/2017/ Hydrol.EarthSyst.Sci.,21,2817–2841,2017
2826 S.P.Seibertetal.:Unravellingabioticandbioticcontrolsontheseasonalwaterbalance
0 0
1. Reg. winter MOL2 TRI3 1.
Reg. period of vegetation
8 Onset period of vegetation 8
) 0. End period of vegetation 0.
−
P (6 Temperature < 0 6
0. 0.
(cid:229)Q / 4 4
um. C0.00.20. Mar 20 Sep 22 Mar 20 Sep 22 0.00.20.
0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7
0 0
1. BFO1 AFO2 1.
8 8
) 0. 0.
−
(
P 6 6
0. 0.
(cid:229)um. Q / C0.00.20.4 Mar 20 Sep 22 Mar 20 Sep 22 0.00.20.4
0 2 4 6 8 0 2 4 6 8
0 0
1. ALP3 JUR1 1.
P (−) 60.8 60.8
0. 0.
(cid:229)um. Q / C0.00.20.4 Mar 20 Sep 22 Mar 20 Sep 22 0.00.20.4
0 10 20 30 40 50 0 5 10 15
Cum. P / (eFC+AC) (−) Cum. P / (eFC+AC) (−)
Figure5.TypeIIdimensionlessdoublemasscurvesforsixcatchmentsofdifferentgeologicalunits.ThedDMCdepictedherearethesame
asthosedepictedinFig.4butwiththedifferencethattheabscissaisscaledusingthesumofaverageeffectivefieldcapacity(eFC)andair
capacity(AC).AllotherpropertiesareanalogoustoFig.4.
visible when comparing the ALP3 catchment in the lower located in the Faulted Molasse, Triassic, and pre-Alpine re-
left panel of Fig. 5, with a potential renewal rate of 30 to gions (MOL2, TRI3, and AFO2) (Fig. 5, red lines). Step
40 times the soil pore volume, against the catchments from changes towards dDMC segments with smaller slopes indi-
theothersettingswithpotentialrenewalratesalmost1order cateactivationofadditionalstorageandthusaslowergrowth
of magnitude lower. Another advantage is the visibility of ofcontributingareaswithcatchmentrelativestorage.Relat-
differences in winter slopes, which are more uniform in the ing to the beta store concept, this corresponds to a larger β
non-AlpinecatchmentscomparedtotypeIdDMC.Average parameter. This is particularly visible in the winter periods
m valuesandcorrespondinginter-annualvariations(σ ) of the Alpine catchments (ALP3), but also in the Bavarian
W mW
areprovidedinTable1. Forest (BFO1) due to storage in the snowpack. This is also
With respect to the shape of the winter segment of the suggested by temperature data as these segments coincide
typeIIdDMC,wefindthatitisfairlylinearforcatchments with frost periods and are followed by segments of warm-
Hydrol.EarthSyst.Sci.,21,2817–2841,2017 www.hydrol-earth-syst-sci.net/21/2817/2017/
Description:on the role of biotic and abiotic controls in seasonal runoff formation. main invariant during simple scaling operations, as further explained below.
