Laboratoire de Biogâ¢ochimie Isotopique, Universit⢠Pierre et Marie Curie, Paris, France. Abstract. Hydrograph deconvolution using geochemical tracers is ...
WATER RESOURCES RESEARCH, VOL. 32, NO. 4, PAGES 1051-1059, APRIL 1996
Comparison of hydrograph deconvolutionsusing residual alkalinity, chloride, and oxygen 18 as hydrochemical tracers O. Ribolzi
and V. Vall•s
Unit• de Sciencedu Sol,InstitutNationalde la RechercheAgronomique, Avignon,France T. Bariac Laboratoirede Biog•ochimieIsotopique,Universit• Pierre et Marie Curie, Paris,France
Abstract. Hydrographdeconvolution usinggeochemical tracersis currentlywidelyused for determiningthe hydrologicmechanisms occurringin watersheds.However,few chemicalparameterscanbe usedas tracersbecausetheir involvementin biogeochemical processes preventsthem from behavingin a conservative way. The aim of this studywasto combineseveralgeochemically controlledparametersinto a singletracer.Residual alkalinityis a combinationof severalcontrolledparametersand is conservative in a wide rangeof natural environments. It wasusedin this studyfor quantifyingthe contributions of surfacerunoffand of groundwaterflow duringa flood in a Mediterraneanwatershed underlainby sedimentary rock.A preliminarygeochemical studyrevealedthat interactions with calcite,dolomite,and the clay-humuscomplexcontrolledcalciumand magnesium concentrations aswell as carbonatealkalinity(Alkc), whichpreventedusingthem as tracers.Nevertheless, althoughresidualalkalinity(mlkresidual) is a combinationof these
threeparameters (mlkresidual = Alkc - 2[Ca2+]r- 2[Mg2+]r),it provided results that werehighlycomparable to thoseobtained usingchloride and8•80.Contrary to themost casesin the literature,the contributionof directrunoffwasdominant(about80% at peak discharge). Accuracyestimates, whichtook into accountanalyticalerrors,temporal variationsin the isotopicsignatureof rainfall, and the spatialvariabilityof chemical elements,supportedthisresultand confirmedthat residualalkalinityis a usefulconceptin hydrology. 1.
Introduction
Tracers have many environmentalapplications.They are often used for analyzingwater and solutetransfersin mono-
temperature,etc.) [Nakamura,1971;Pilgrimet al., 1979;Shanley and Peters,1988;Matsubayashi et al., 1993] or chemical characteristics[e.g.,Pinderand Jones,1969;Robsonand Neal,
1990;Eshlemanet al., 1993,1995].Chemicaltracersare being
liths [e.g.,Juryet al., 1982;Whiteet al., 1986;l/allks,1987; usedincreasingly, thanksto the EMMA approach(end mem-
Hornberger et at., 1991].They alsohelp predictchangesaffect- ber mixinganalysis)[Christophersen et al., 1990;Hooperet al., ing the chemicalcompositionof natural solutions[At-Droubi, 1990;Ogunkoyaand Jenkins,1993;Bazemoreet al., 1994]. 1976; Gac, 1977; Dosso, 1980; Vailkset at., 1989, Ribohi et at., Irrespectiveof which kind of tracer is used, there is a con1993;Barbi•ro, 1-994]. strainingrequirementin quantitativestudiesthat the tracer's Tracersare usedin hydrologyfor identifyingand occasion- behaviorshouldbe entirely predictable.Most of the many ally quantifyingprocesses that are often quite complex.For elementsthat existare involvedin complexgeochemical, physinstance,the deconvolutionof flood hydrographsusinggeo- icochemical,or biologicalinteractions.Nevertheless,many chemicaltracershas challengedor refined some of the com- tracersare neededfor cross-checking resultsand quantifying monly establishedideas on how dischargeis generated.The the contributionof the varioushydrologicalprocessesthat main resultswere obtainedby usingisotopictracersof water, occur during floods. bothnaturalandstable(•80 or2H)[e.g.,Skiash andFarvotden, The aim of thisstudywasto combineseveralgeochemically 1979;Hooper armShoemaker, 1986;Pearce etal.,1986,Hubert, controlledparametersinto a singletracer that can be usedfor 1989],andanthropogenic andradiogenic (3H) [e.g.,Matosze- deconvolutingflood hydrographs.Residual alkalinity [Van wskiet at., 1983]. They showedin particularthat pre-event Beekand Van Breemen,1973],whichis derivedfrom the residwater in the soil or the groundwatercontributedlargely to ual carbonateconcept[Eaton,1950],is calculatedby subtractflood discharge[e.g.,Crouzetet al., 1970;Btavoux,1978;SMash and Farvotden,1979;M•rot et at., 1981;Bottomryet at., 1984; Hooper and Shoemaker,1986; Pearceet at., 1986; Maute and Stein,1990;McDonnellet at., 1990; Travi et at., 1994].Water can alsobe tracedby usingits physical(electricconductivity,
ing the total concentrationof divalent cationsin the soil water
from the carbonatealkalinity(Alkc) (mlkresidual = Alkc -
2[Ca2+]r- 2[Mg2+]r). It is expressed as equivalents per liter. Residualalkalinitywasfirstappliedto qualitativepredictions of how the chemicalfaciesof solutionschangeduring evaporation [Van Beek and Van Breemen, 1973; Al-Droubi,
Copyright1996 by the American GeophysicalUnion.
1976;Vall•s,1987].Thisconcepthassincebeengeneralizedto
Paper number 95WR02967.
successiveprecipitation of several minerals, such as calcite followedby gypsum[e.g.,Al-Droubi, 1976; Vall•s et al., 1989,
0043-1397/96/95 WR-02967 $05.00
1051
1052
RIBOLZI
ET AL.: COMPARISON
OF HYDROGRAPH
1991]or calcitefollowedby fluorite [Barbi•ro,1994].Although residualalkalinityis a combinationof severalparameterscontrolled by dissolutionor precipitationof mineralssuchas calcite or dolomite,it shouldbe fairly conservative[Vallbset al., 1991]overa widerangeof highlydiverseenvironments [Ribolzi et al., 1993]. In this study,residualalkalinitywas usedfor a quantitative purpose.A flood hydrographwas deconvolutedinto two components:surfacerunoffand groundwaterdischarge.The study
DECONVOLUTIONS
tweenthe clay-humuscomplexand the soilsolutionmay,under certain circumstances, significantlyaffectcalciumand magnesium concentrations.
2.3.
Residual Alkalinity
Residual alkalinity is generallyused for understandingthe changesaffectingthe chemicalfaciesof natural solutionsundergoingevaporation[Al-Droubi,1976].This quantityisjust as conservative duringconcentration[Vallbset al., 1991;Ribolziet areawasa 0.91-km 2 cultivatedcatchment underlainby sedial., 1993] as during dilution.Assumingthat calciteand dolomentarydepositssubjectto a Mediterraneanclimate.Results mite are the only mineralswith rather high solubility,which were testedby successively deconvolutingthe hydrographuscan dissolvein this catchment,then the calcite plus dolomite ing chlorideconcentrations, 8•80 and residualalkalinityas residualalkalinity(mlkresidual), expressedas equivalents/liter) tracers. Numerical solutions obtained with each of these meth(eq/L), may be definedas odswere analyzedin the light of error estimatesthat took into accountboth the analyticalerror and the variability of the mlkresidual =mlk c- 2[Ca2+]- 2[Mg2+] (2) geochemicalsignaturesof the end members. If, for instance,rainwater(subscriptin the followingequations) comesinto contactwith a soil containingcalciteand dolomite,both mineralswill dissolveaslong asthermodynamic 2. Definitions and Theoretical Properties equilibrium (subscripte) is not reached.The dissolutionof 2.1. Tracers these mineralsincreasescarbonatealkalinity and calciumand Generallyspeaking,a traceris a conservative quantitythat is magnesiumconcentrationsaccordingto stronglyrelatedto the water itselfbut doesnot interactwith its (3) Alkc,e = Alkc,, + e environment.Natural water isotopesare intrinsicmarkersof water moleculesand henceprovide ideal tracersfor discrimi[Ca2+]e= [Ca2+]t+ . (4) nating between"new" water and "old" water. The chemical tracercontentof water canonlychangethroughprocesses such [Mg2+]e= [Mg2+],+ /3 (s) asconcentrationor dilution,proportionatelyto changesaffecting the volumeof water. In either case,tracingis onlyfeasible where e, ,, and/3 are the changesin concentration.Substitutif the isotopicor chemicalsignaturesof the end-membersdif- ing (3)-(5) into (2), we obtain fer.
2.2.
Alkresidual, e: Alkc,c- 2[Ca2+],-2[Mg2+]iq-8- .Carbonate, Calcium, and Magnesium Alkalinities
calciteCaCO3(s)+ 2H+ Ca2++ CO2(a) + H20 (7) dolomiteCaMg(CO3)2(s) Ca2++ Mg2++ 2CO•(8) indicates
that
partof alkalinity thatcanbe attributed to HCO•- andCOWanions.TheseanionsmayformionpairswithNa+, K+, Ca2+ andMg2+ cations. Carbonate alkalinitymaythusbewrittenas Alkc= [HCOj] + [NaHCO3 ø]+ [KHCO3 ø]+ [MgHCO•]
e -- "calcite q- 2. dolomite
(9)
"= "calcite q- "dolomite
(10)
/• '-- "dolomite
( ] ])
Therefore
+ 2[CO3 2-] + 2[NaCO•-]
+ 2[KCOj] + 2[MgCO•]+ 2[CaCO(•] + ...
(6)
However, the stoichiometryof equilibria,
Alkalinity can be defined as the capacityof a solutionto neutraliseacids[Stummand Morgan,1981].In other words,it is the sum of the productsof the alkalinecompoundconcentrationsby the number of protonseach compoundcan neutralise, minus the proton concentration[Bourri•, 1976, 1978; Bourd• and Lelong,1990]. Carbonatealkalinity(Alkc) is the
+ [CaliCOS] + "'
/•
(1)
8 -- . -- /• -- "calcite q- 2"dolomite -- "calcite -- "dolomite
-- "dolomite = 0 where values between square bracketsare molalities. Total alkalinity(Alk) is equivalentto Alkc, providedthat the proton and hydroxideion concentrations and noncarbonate alkalinity are negligible[Vorob?evaand Zamana, 1984; Keller et al., 1987].Alkalinity is conservative inasmuchas it is affectedneither by addition or loss of CO2 nor by the dissolutionor precipitationof a salt of a strongacid or base[Bourd•, 1976; Stummand Morgan,1981].Alkalinity is alsoconservative with respectto hydrologicalmixingof waters,as long as precipitation or dissolution of salts of weak acids or bases doesn't occur.
However, in natural solutions,interactionswith minerals, es-
peciallywith calcite,are the main factorscontrollingAlk and calcium activity. Some carbonateor silicate minerals play a major role in controllingmagnesium.Cation exchangebe-
(12)
where "calciteand d,1omite are the changesin concentration due to the precipitationof calciteand dolomite,respectively. Equation (6) thussimplifiesto
Alk ....dual, e = Alkresidual, t
(•3)
Equation(13) indicatesthat residualalkalinityremainsconstantirrespectiveof the dissolutionof calciteand dolomite.As soon as the soil solutionis saturatedwith respectto calcite, calcite precipitationremovesidentical amountsof carbonate alkalinityand calcium.Dolomite precipitationis rare in soils. Nevertheless,the magnesiumcontentof the solutionis often controlledby cationicexchangebetweenclaysand the solution [e.g.,Vall•s, 1987].As a result,when the solutionconcentrates
I•IBOLZI ET AL.: COMPARISONOF HYDROGRAPHDECONVOLUTIONS 9
Equations(13) and (17) indicatethat residualalkalinitybehavesas a tracer whateverthe saturationstatewith respectto calcite.In short,residualalkalinityremainsconstantirrespective of calciteprecipitationand/or dissolution,dolomite dissolution, and cationicexchangeof calciumand magnesiumwith the clay-humuscomplex. Under other circumstances the solutionmay become saturated with respect to other minerals containing calcium or carbonate.For instance,if gypsumprecipitatesafter calcite, one would use the calciteplus dolomiteplus gypsumresidual alkalinity(Figure 1) definedas
meq/I
I
>
Chloride
Sulphate
Alkalinity
Nitrate
ANIONS ,
Maghesium Calcium
Potassium
Sodium
CATIONS ,
1053
,
Alkresidual ß
Calcite
Calcite+dolomite Calcite+dolomite+gypsum
mlkresidua] = mlkc- 2Ira 2+] - 2[Mg2+]+ 2[SO4 2-]
Figure 1. Stablerdiagramof initial concentrations in stream. Shownare examplesof generalizedresidualalkalinity accord- 3. ing to solidphaseinteractions.
Materials
3.1.
(18)
and Methods
Site Description
The studyarea is a catchmentlocatedin the French Medi-
(subscript f), magnesiumentersthe soil'sexchangecapacity, terranean area, in the H6rault watershed, some 10 km from therebydisplacingcalciumwhichprecipitatesas calcite.These P6zenas(Lambert zone III coordinates:679-680, 132-133) two processes can be describedwith the followingthree equa- (Figure 2). Most of the catchmentarea is used as vineyards tions: (81% of the usableagriculturalarea) [Andrieuxet al., 1993]. The climate is of the subhumidMediterranean type with a Alkc,f= CF- (Alkc,e - /•) (14) prolongeddry season.Mean annual rainfall recorded by the
[Ca2+]f= CF- [Ca2+]e [mg2+]f= CF' ([mg2+]e - /•)
(15)
nearest station is 650 mm, with maxima in October and Feb-
(16)
mary. Mean annual temperature is 15øC.Dry northerly winds are the most frequent and the strongest.Mean annual potential evapotranspiration,calculatedaccordingto the Penman
where /x is the change in magnesiumconcentrationand in alkalinity,and CF is the concentrationfactor. For calciumthe precipitationof one equivalentof calciteis compensatedfor by the desorptionof one equivalent from the cation exchange complex.Substituting (14), (15), and (16) into the definitionof residualalkalinity,yieldsthe followingequation:
Alkresidual ,f = CF' mlkresidual 'e
(17)
method, is about 1094 mm. The elevation
of the watershed
varies between
Watershed boundary Montpellier
Altitude, in meters
Drainage network /
•
Mediterranean sea
Studysite
Out let
1328 ''•'• Rain recorder
Waterlevelrecorder
Runoff samples Geomorphological units: :.
NORTH '::"• • •" '":: .... 1320-200m
..... :
•.
. ..
I Plateau I Terraced slopes • • FaR l-----1 Depression
(LAMBERT III system) I
6792
6796
75 and 125 m
abovesea level. The site coversfour geomorphologicentities: a plateauandits edges,steep(10 to 20%) terracedslopes,a fan with a gentle (2 to 7%) slope,and a central depressionwhose downstreampart is almost flat (Figure 2). Lower Miocene depositshave been identifiedup to an elevationof 90 m. The
6800
Figure 2. Geographicallocationof the studyarea (redrawnfromAndrieuxet aL [1993]).
1054
RIBOLZI
ET AL.: COMPARISON
OF HYDROGRAPH
DECONVOLUTIONS
Table 1. IsotopicSignatureof the Outlet Before the Flood and Signatureof Rainfall as a Function
of Time
Corresponding PrecipitationDepth,
Time 18.83 19.03 19.17 19.30 12.67
Rain, 8•80, %o* -6.91 -5.71 -5.60 -5.29
_+ 0.1 _ 0.1 _+ 0.1 _+ 0.1
mm
Rain, 8•80 %0?
12.50 1.00 0.75 1.00
-6.9 -6.8 -6.8 -6.7 ....
_+ 0.1 _+ 0.2 + 0.3 _+ 0.5
Groundwater, 8•80, %05 ... ""' ". 5.4 _+ 0.1
*Concentrationplus or minusanalyticalerror. ?Incrementalmean plus or minuscumulativeerror. $Initial stream'sconcentrationplus or minusanalyticalerror.
top of this seriesendswith massivedolomiticlimestones.The plateauis coveredwith continentalformations(Villafranchian andPliocene).Theseformationsare stonyand silicatematerial is dominant.The fan containsmostlymaterialfrom the plateau and reworkedmaterial from the bluff. The central depression is filled with typicallyfine-grainedmaterial and containsthin layersof sandor gravel. Runoff is collectedby a network of ditchesconnectedto a main channel.The fan and depressionareas have an unique permanentwatertabledraweddownby the networkof ditches. On the plateaua perchedwater table appearstemporarily.Its leachingmakesspringsand seepage,which refill the groundwater of the fan-depressionsystem. 3.2.
Sampling and Analysis
Sampleswere taken on April 14, 1993, duringa springtime flood resultingfrom a 15.5mm hailstorm(Figure 3). Prestorm dischargein the brookwas 18 L/s. The bulk of the showerled to a responsewhosepeak dischargewas101.5L/s after a lag of 30 min (from the center of massof the showerto peak discharge).Rainfall lastedabout 65 min but 80% of the precipitation occurredduring the first 15 min. Stream dischargereverted back to its initial value 47 min after the peak value had
dium hydroxide[Vorob•yeva and Zamana, 1984;Keller,1987]. Finally,the oxygen18 concentrationwere determinedby mass spectrometry after equilibrium with carbon dioxide was reached[Epsteinand Mayeda,1953]. 3.3.
Concentration Diagrams
Concentrationdiagramsprovide a first approachto identifyingtracers.Their shapesdiffer accordingto whichelementis involved[e.g.,Al-Droubi, 1976; Gac, 1980;Fritz, 1981; Vallks, 1987;Ribolziet al., 1993].The concentrationdiagramof solute
X is a graphof log ([X]f) as a functionof log (CF). If the soluteis tracerT, in whichcase[T]i = CF. [T]f, thevariationswithin the diagramare representedby a straightline with a slopeof 1, whoseequationis
log([ T]•) = log (CF) + log([ T],)
(19)
In evaporationpan experiments[e.g.,Al-Droubi, 1976;Gac, 1980; [/allks, 1987; Barbi•ro, 1994] the concentrationfactor (CF) is obtaineddirectlyby weighing.Its valueundernatural conditionscan be estimated by using a reference tracer R whosepropertieshavebeencheckedin the contextof the study [e.g., Gac, 1980; Gonzalez-Barrios, 1992;Ribolzi et al., 1993; Barbi•ro,1994].The valuefor CF is then estimatedasthe ratio occurred. betweenthe tracercontentin the sample(subscript s) and the The brook was sampled33 times during the flood, which tracercontentof the mostdilutedsolutioninvolved(subscript lasted about 1.5 hours. The chemicalsignatureof the surface d). runoff was determinedfrom a total of 10 samplescollected from the four geomorphologic entities(Figure 2). Changesin CF = [R ],/[R ]d (20) the isotopicsignatureof the rain were evaluatedby sampling the storm duringfour samplingintervals(Table 1). Groundwater sampleswere previouslycollectedduringa studyon the geochemicalcontrolof water by calcite[Ribolziet al., 1993]. 11o Dischargeat the outlet of the catchmentwasrecordedwith 1 lOOa pressurewater level recorderlocatedin a Venturi-typeflow 90Rain channel.Precipitationwasmeasuredusinga seriesof four rain 80gaugeswith a time step of 5 min. Temperatureandp H were measuredin the field. After microfiltrationat 0.45/am, samples were storedin polyethyleneflasksfor lessthan 24 hoursat 4øC 5• 60' in the dark. In the laboratory,sodium,nitrate, and chlorideion 6t = 50concentrations were measured with specific electrodes 407' 0 (ORION, 84-11,94-17B,and93-07)in the presenceof an ionic -8 30' strengthadjusterand an interferencesuppressor solution.Total magnesium,potassium,and calcium concentrationswere 20measured by atomic absorption spectrometry (PERKIN1c 18.25 18'.75 19'.25 19'.75 20:25 20'.75 21.25 ELMER, 2100) whereassulphateion concentrations were anTime (Decimalhours) alyzedby capillaryelectrophoresis (WATERS, CapillaryIon Analyzer). Carbonate alkalinity was determined using the Figure 3. Hydrographand hyetographof the April 14, 1993, method of Gran [1952], togetherwith back titration with so- flood.
RIBOLZI
ET AL.: COMPARISON
OF HYDROGRAPH
The diagramspresentedin the Figure 4 have been built accordingto this method. 3.4.
Table
2.
DECONVOLUTIONS
Mean
Concentrations
and Calcite Plus
Dolomite ResidualAlkalinity (Alkresidual) in the Stream DischargeBefore the Flood
Saturation Diagrams
Surface Runoff,*
Saturationdiagramsconfirm and completeour understandSolute ing of what regulatessomeof the variouselements.The diaChloride grams used in this study were calculatedfrom equilibrium Sulphate constantsat 298øK[Helgeson,1969;Helgesonet al., 1971]: Alkalinity (1)
CaSO4'2H20(s) Ca2++ 8042-(a) + 2H20 logK=-4,
85
(21)
(log K = 9.76 and -16.1, respectively, for equilibria(7) and (8)).
law.
Hydrograph Deconvolution
Deconvolutinga hydrographfrom tracer data is equivalent to solvingfor eachoutlet samplingtime (superscriptt) a system of n mixing equationswith n unknownvariables(the variouscontributions to the flood).Let usassumethat twoflow systems contributeto outletdischarge: groundwaterflow (subscript#) andsurfacerunoff(subscript r). Assumingthat there
Groundwater,?
meq/L
meq/L
0.4 _+ 0.3
2.57 _+ 0.05
0.3 _+0.2 1.07 _+0.68
3.45 + 0.04 5.11 + 0.05
Nitrate
0.14 _+ 0.08
0.05 _+ 0.01
Calcium (2)
1.33 + 0.35
8.6 _+0.1
0.154 _+0.033
2.20 _+0.03
Magnesium(3) Sodium Potassium
Alk .... dual, equal to (1)
The activities of ions in solution, which are enclosed in
parentheses in the figures,were calculatedfrom the total concentrationsby usingthe ionic association model of the AQUA softwarepackage[Vallbsand Cockborne,1992] derived from the GYPSOL model [Vallbs,1987]. This model is based on Scatchard's[1936] extensionof the Debyeand Hiickel [1923]
3.5.
Chemical
1055
0.2 ___0.1 0.11 + 0.08
1.38 _+ 0.03 0.014 _+ 0.004
--0.4 +--0.2
--5.7 --+0.4
- (2) - (3)
*Mean concentrationplus or minus standarddeviation. ?Initial concentrationin streamplus or minus analyticalerrors.
time-pointmeasurementandits standarddeviationasthe measurementaccuracy.The latter takesinto accountthe accuracy of the headmeasurement (H) by the pressuresensor(H _+1 cm) and the error due to the conversionof head to discharge
(10%whenQte < 22 L/s,5% when22 < Qte < 59 L/s and1% when59 L/s < Qte).
One hundred random valueswere drawn from a lognormal distributionfor each parameter and each sample,usingthe appropriate expectation and standard deviation estimates. Both flow componentswere calculatedfor each draw, using is a tracerwhoseconcentrations (Ca andCr) aresignificantly mixingequations(22) and (23). The 100 pairs of flow values different from each other and remain constant within each flow were then used for calculatingthe mean and standarddeviasystem,then solvingthe systemof equationsyieldsthe contrition of thesecomponents. bution of each term:
Qta Cto- Cr
4.
Q•= Ca- C,. Qtr
(22) 4.1.
C
Qto outlet dischargeat time t;
Q[ groundwater flowat timet;
3.6.
Choosing a Chemical Reference Tracer
(23) reference tracer. Chloride is often used as an experimental
where
outlet
and Discussion
As mentionedabove,the concentrationdiagramsrequired a
Q•=1 a
Qtr surfacerunoff at time t; C'o tracer concentration at the
Results
at time t.
Estimated Accuracy of Model Results
The accuracyof the hydrographdeconvolutionwas estimated by Monte Carlo analysis[Bazemoreet al., 1994]. An expectationand standard deviation value were assignedto eachinput parameterof the mixingequations.Irrespectiveof the tracerused,the expectation of Ctowasassumed to correspondto the value measuredat time t, and its standarddeviation was that of the analyticalerror.
Residualalkalinityand chloridesignatures (Ca and C•) were assumedto remain constantover time accordingto measurementscarriedduringother events.C• wascalculatedasthe mean of valuesmeasuredin surfacerunoff samplesand the
tracer both in monoliths[e.g., Whiteet al., 1986] and in limestonewatersheds[e.g., Webband Sasowsky, 1994].Within the rangeof concentrations studied(ionic strength-
