Transient features of the erosion of shales in the Mackenzie basin (Canada), evidences from boron...

tters 245 (2006) 174–189www.elsevier.com/locate/epsl

Earth and Planetary Science Le

Transient features of the erosion of shales in the Mackenzie basin(Canada), evidences from boron isotopes

D. Lemarchand ⁎, J. Gaillardet

Laboratoire de Géochimie-Cosmochimie, Institut de Physique du Globe de Paris, CNRS UMR 7579, Université Paris 7, 4 Place Jussieu,75252 Paris Cedex 05, France

Received 10 September 2005; received in revised form 17 January 2006; accepted 27 January 2006Available online 17 April 2006

Editor: V. Courtillot

Abstract

In order to refine our knowledge of the mechanisms that drive the weathering reactions and the rate at which elements areexported out of a shale basin, we have analyzed the boron concentrations and isotopic compositions of 24 rivers contributing to theMackenzie basin (Canada). Boron has been chosen to conduct this study because of the relatively high sensitivity of its isotopicsystem to water/rock interactions. After examination of the chemical composition of the Mackenzie River samples, boron appearsto be regulated, in the largest part, by reactions involving silicate rocks. The other contributions of rainwaters and the dissolution ofcarbonate and evaporite rocks can locally control the B budget but they remain of second importance at the regional to continentalscales. It also appears that dissolved B in rivers is regulated by input of groundwaters.

The comparison between the isotopic composition of the B being exported by rivers (soluble and particulates) and of its bulksource indicates that it is behaving out of steady state in most of the Mackenzie tributaries and particularly in rivers draining theplain. A model of transport/reaction is proposed in this study, which demonstrates that B is controlled by rapid ion exchanges at themineral/water interface and by long-term dissolution of shales. The responses of the model to tested conditions reveal that the Bisotopic ratio of river waters is highly sensitive to hydrological conditions and to changes of the weathering rate of shales, of itspartition coefficient with adsorbing surface, and of the water velocity.

The departure of the B geochemical cycle from a steady state is interpreted as the record of changes in the weathering regime inthe Mackenzie basin. The temporal evolution of the B cycle modeled here implies an increase of the weathering rate of shales in theMackenzie basin and/or an increase of the partition coefficient between soluble B and adsorbing surfaces. It also appears that thesechanges are consistent with timescales of the recent deglaciation of the basin. This study demonstrates that the present B fluxes areactually responding to past changes of the water/rock interactions and that the weathering history is a key parameter to interpret themodern geochemical fluxes. This conclusion is valid for any other element that has similar chemical properties with solid surfaces.© 2006 Elsevier B.V. All rights reserved.

Keywords: boron isotopes; weathering; shales; model; ion exchange; Mackenzie

⁎ Corresponding author. Present address: Centre de Géochimie de laSurface, CNRS UMR 7517, Université Louis Pasteur, EOST, 1 rueBlessig, 67084 Strasbourg Cedex, France.

E-mail address: [email protected] (D. Lemarchand).

0012-821X/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.epsl.2006.01.056

1. Introduction

The weathering of continental rocks regulates thequality of river waters, the development of soils and actson the global seawater composition as well as on the

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175D. Lemarchand, J. Gaillardet / Earth and Planetary Science Letters 245 (2006) 174–189

climate at geological timescales. In this scheme, thereactions of silicate weathering represent a vast domainof particular interest because they involved numerousminerals, a large range of reaction intensity and wea-thering products. So far, the weathering rate of plutonicand volcanic rocks and the transport of associated mate-rials have been the most often investigated. In return, theweathering of sedimentary silicates (namely clays) hasbeen relatively neglected because they are usuallyconsidered as minor phases in terms of alterability andpotential sources of dissolved cations to rivers. Howev-er, they are among the most adsorbing surfaces that havethe potential to regulate, at a large scale, the rate atwhich dissolved compounds are released and exported.

To investigate in more detail the mechanisms thatcontrol the transport of elements in a sedimentarybasin, we have focused on the behavior of boron in theMackenzie River tributaries (Canada). Boron is amobile element that is partitioned during chemicalweathering into soluble and solid phases. Both Bcontent and its two stable isotopes (10B and 11B) showa wide range of variability in the Earth's material: over4 orders of magnitude in concentration and rangingfrom −30‰ up to +60‰ in isotopes [1,2] (variationsare expressed as the permil deviation from standard andnoted δ11B). Most of the reactions that induce Bisotopic fractionations involve water, making boron aparticularly suited element for studying water–rockinteractions. To date, precise analyses of dissolved δ11Bin rivers or soil solutions ([B] in the range of μmol/L)are still delicate and the behavior of B duringcontinental rocks erosion remains a field of investiga-tion poorly explored [3,4]. In a systematic analysis oflarge rivers [5,6] it has been shown that most of thecontinental waters have a boron isotopic compositionenriched in 11B by about +10–20‰ compared to themean continental crust. The reason of this difference isnot well understood so far. In one hand, analyses of Bisotopes in a soil profile of the upper Orinoco Basin(Venezuela) show that B is partially removed with aslight shift of its isotopic value, from 1.6‰ for theunweathered zone to −1.0‰ for the weathered zone[3]. This result suggests that the silicate weatheringprocesses, responsible for the mobilization of B, maynot induce an important fractionation of its isotopes. Inthe other hand, the isotopic compositions of dissolvedB in Himalayan rivers are proposed to result fromisotopic fractionation induced by reactions in soils [4].From our present knowledge, it is still unclear what thebehavior of boron during the global water cycle is andthe principal mechanisms that regulate the B signatureof rivers still need to be established.

The Mackenzie drainage basin has been chosenbecause the weakness of the atmospheric inputs tosurface waters [7,8] and the dominant presence ofcarbonaceous shales as well as the quite pristine con-ditions of the Mackenzie River basin are particularconditions that facilitate investigations on the behaviorof boron isotopes during chemical weathering. It is thena unique opportunity to test at a large scale the impact ofshales on both the geochemical cycle of B and on theelemental fluxes controlled by the weathering ofsilicates in sedimentary basin.

2. The geological settings and geochemical fluxes ofthe Mackenzie basin

The Mackenzie River drains about 1.78 ·106km2 inNorthern Canada with a mean annual discharge of308km3/yr (the 15th largest river on Earth). TheMackenzie basin can be divided into three main geo-logical units: the Canadian Shield, the Interior Platformand the Cordillera corresponding to the units 1, 2 and 3on Fig. 1, respectively. The Canadian Shield is mainlycomposed of Precambrian age crystalline rocks(N2.5Ga) like granite, gneiss, schists, and greenstonebelts with scattered metamorphosed sedimentary rocks.The Interior Platform runs northwestward between theCanadian Shield and Mackenzie mountains. Most of theplain is composed of tectonically undeformed Cambrianto Cretaceous and tertiary shales, and sandstones. Lime-stones and evaporites are also present. Paleozoic andMesozoic stratigraphic units host about 33% and 84% ofshales, respectively [9], where illite is the dominantmineral [10]. Interior plains are covered by quaternarytills hosting drift aquifers. The Cordillera mountainsresult from a tectonically continental margin still activeand consist in two main belts: the Rocky mountainsproper on the east are mostly composed of metamorphicand igneous rocks (sub-unit 3a on Fig. 1) and the coastmountains on the west composed of volcanic rocks (sub-unit 3c on Fig. 1). Interior consists in a basin composedof Proterozoic to Devonian carbonate and dolomiticlimestones now elevated and greatly indented by rivervalleys (sub-unit 3b on Fig. 1). For the wholeMackenzie basin, the proportions of rock types exposedto the water drainage are 68% of sedimentary rocks(clastics and carbonates), 29.2% of non-sedimentaryrocks (igneous and metamorphic, where about 75% ofthem are from the Canadian Shield) and 2.5% ofevaporites (halite and gypsium) [11].

The compositions in major ions of the river watersamples are presented in a couple of previous papers[8,12] in which Sr isotopes are also used to trace the

Fig. 1. Map of the sampling locations in the Mackenzie drainage basin. Sample numbers correspond to those reported in Table 1. Geological units arealso reported: 1. Canadian Shield; 2. Interior Platform; 3. Cordillera subdivided in three units: 3a. Rocky mountains proper; 3b. Cordillera interior; 3c.coast mountains.

176 D. Lemarchand, J. Gaillardet / Earth and Planetary Science Letters 245 (2006) 174–189


source of major solutes and calculate the chemicaldenudation rates. On the same samples, U-series havebeen analyzed to deduce the timescales of erosion in theMackenzie basin [13]. Short-lived nuclides from the Useries permitted to calculate typical timescales oferosion from 9 to 28kyr and proposed that chemicalerosion rates may have changed recently in response tothe last deglaciation. The dominant feature that emergesfrom previous works is that the Mackenzie River basinis dominated by the weathering of carbonates andshales. Silicate weathering rates are extremely low, inagreement with the low temperature and precipitationrates. However, a fourfold increase of silicate weather-ing rates is observed in the vast lowland regioncompared to the eastern part of the basin dominatedby the Rocky and Mackenzie mountains. Based on thetrend observed between the silicate weathering rate andthe concentration of dissolved organic carbon, this shiftwas attributed to the catalytic action of the organicmatter [8].

3. Sample collection

Samples analyzed here have been selected from thelist of samples published by Millot et al. [8]. TheMackenzie basin was extensively sampled with about110 sampling stations corresponding to the maintributaries of the Mackenzie River and head waters. 24of these samples were chosen for the determination of theboron isotopic composition in the dissolved load (seesampling locations on Fig. 1). Among them, 4 rivers arenot connected to the Mackenzie River, they are theFraser, the Skeena, the Stikine and the Nass rivers. Theserivers flow over igneous and Precambrian metamorphicrocks and have been included to this study to test theinfluence of various natures of silicates on the riverinedissolved δ11B. Water samples were collected duringhigh water stages (August 1996 and June 1999). Sampleswere filtered on site through 0.2μm acetate cellulosefilters with a pressurized Sartorius® Teflon filtration unitandwere stored in acid washed polypropylene containersto prevent contamination. Water temperature and pHwere measured on site. Alkalinity was immediatelydetermined by acid titration and Gran plot method.

4. Analytical methods

4.1. Concentrations

Concentrations of major elements (Na, K, Mg, Ca,Cl, NO3 and SO4) have been determined by ionchromatography (Dionnex 4000I). Separate analyses

of samples and standard solutions show a reproducibil-ity better than 5% (±2σ) for most of the elements. Bconcentrations have been determined by isotopicdilution using the 10B enriched standard solutionNIST SRM 952. Precision is in the order of 1% or better.

4.2. Boron isotopic determination

About 250ng of B are separated from the watersamples by ion chromatography using the B specificresin Amberlite IRA 743. Boron isotopic compositionswere measured by Positive Thermal Ionization MassSpectrometry (PTIMS) performed on a Thomson CSFTHN 206 type mass spectrometer (30cm radius and 60°sector). The procedure for isotopic analysis followsthe Cs2BO2

+ method using graphite and mannitol as firstproposed by Leeman et al. [14] with slight modifi-cations. Details on the B chemical purification andthe isotopic analysis techniques can be found inLemarchand et al. [15]. Repeated analyses of the NBSSRM 951 standard and river waters lead to externalreproducibility is 0.35‰ (±2σ). Boron isotopic compo-sitions are expressed as the deviation (in permil unit)from the standard NIST SRM 951 (certified 11B / 10Bvalue=4.04362):

d11B ðxÞ ¼ ðRsample=Rstandard−1Þ � 103

where Rsample is the 11B / 10B ratio of the sample;Rstandard is the 11B/ 10B ratio of the standard solutionNIST SRM 951 processed through the full chemicalprocedure (4.0547±0.0003, n=14).

5. Results

Major elements (Na, K, Mg, Ca, Cl, NO3, SO4), pH,alkalinity and both B concentrations and B isotopiccompositions were determined in the dissolved load of24 river samples from the Mackenzie basin (Fig. 1,Table 1). Although the Fraser, Skeena, Nass and StikineRivers are not really tributaries of the Mackenzie River,they have been added to this study for comparisonbecause of their high runoff and because three out ofthem flow over volcanic bedrocks.

5.1. Major elements

The concentrations of major elements and DOC inthe samples of Mackenzie tributaries analyzed in thisstudy are presented and discussed in detail inMillot et al.[8]. Briefly, concentrations in major elements are greatlyvariable (especially Na and K) and span over about one

Table 1Dissolved concentrations of dissolved load and B isotopes systematics in rivers

River (number) pH TSS § TDS§ Na K Mg Ca Cl NO3 SO4 Alk. B δ11B

Mackenzie basin riversMackenzie at Tsiigehtchic (96-6) 8.06 296/230 223 282 21 418 919 163 4 452 1949 12.0 15.0Mackenzie (96-25) 8.12 11 179 354 25 276 710 220 2 254 1674 15.2 16.7Peel at Fort McPherson (96-5) 8.1 100/ 286 167 13 673 1142 37 6 761 2381 10.1 14.1Red Arctic at Tsiigehtchic (96-7) 7.82 267/1100 337 134 18 845 1418 13 7 1334 2085 11.6 15.5Athabasca (96-13) 8.2 16 193 133 12 374 813 22 n.d. 285 1964 6.6 7.5Athabasca (96-42) 8.2 52 192 324 34 322 734 34 n.d. 209 2046 20.3 20.3Lesser slave (96-40) 7.79 10 162 323 57 239 596 27 2 73 1886 20.1 29.1Little Smocky (96-14) 7.7 291 135 243 29 186 550 21 n.d. 61 1561 11.2 13.7Peace (96-37) 7.98 102/470 187 168 20 302 806 33 n.d. 203 1998 11.7 14.9Slave (96-38) 7.96 102 167 227 24 265 694 66 n.d. 160 1786 15.0 17.5Salt River (96-36) 8.19 8 869 115,391 73 2466 13,770 110,709 n.d. 14,295 2087 367 12.0Toad (99-60) 7.99 365 210 42 10 467 915 7 n.d. 647 1620 3.1 6.8Racing (99-64) 7.56 576 191 22 12 493 775 9 n.d. 408 1770 5.9 3.8Racing (96-19) 7.82 69 221 30 14 589 842 10 10 477 2047 7.7 3.6Fort Nelson (96-23) 7.95 n.d. 263 141 17 507 1146 11 4 602 2334 14.2 12.6Liard (96-26) 8.05 163/490 245 106 16 483 1062 16 3 503 2273 9.4 12.1Wecho (99-84) 6.71 n.d. 11 75 24 61 101 44 n.d. 13 n.d. 4.4 24.3Wopmay (99-86) 6.84 n.d. 31 35 17 69 121 14 n.d. 21 330 3.5 20.5Yellowknife (99-90) 6.8 n.d. 31 74 23 67 104 47 n.d. 25 310 4.3 20.3Yellowknife (96-31) 7.08 n.d. 29 62 21 64 99 35 2 25 280 4.2 21.0

Western Canadian cordillera riversFraser (99-21) 7.54 756 96 24 7 124 442 5 n.d. 50 1080 1.0 11.8Skeena (99-28) 7.53 53 55 57 6 63 227 4 n.d. 51 550 4.2 4.95Nass (99-30) 7.6 294 58 43 6 80 230 4 n.d. 70 550 2.4 −1.8Stikine (99-39) 8.04 451 69 57 9 113 249 3 n.d. 92 610 5.5 2.6§ TDS and TSS are given in mg/L. Concentration of major elements are given in μmol/L and B in μg/L.


order of magnitude (from 22 to 354μmol/L and from 6to 73μmol/L, respectively). The concentrations of theseelements systematically increase from Rocky Mountainsto Low lands. Ca and Mg are much more homogeneousand the range of concentrations mostly reflects theweathering of carbonate terrains. After the total alka-linity, sulfate ions are the dominant anions and, to theopposite of Na and K, higher concentrations are obser-ved in the mountainous areas. Mackenzie Tributaries arecharacterized by very low Cl concentrations, which donot correlate with Na. After Millot et al. [8], dissolutionof carbonates and gypsum controls about 95% of theTDS in the Rocky and Mackenzie Mountains and about80% of the TDS in the Interior Platform. The weatheringrate of silicate is therefore very low but keeps an intri-guing feature as it is enhanced by a factor of 3 to 4 in theInterior Platform compared to the Rocky Mountains thatis contrary to what is observed in other large river basins.

5.2. B concentrations

Concentrations of dissolved boron range from1μgB/L for the Fraser Rivers to 20.3μgB/L for theAthabasca River. The Salt River, flowing over evapor-

ites, shows a very high B concentration (367μgB/L).This high concentration is explained by the predomi-nance of halite in the drained terrain and will beconsidered in the following as the evaporitic end-member. Rivers flowing over the Canadian Shield aswell as rivers flowing over volcanic bedrocks in theRocky Mountains are characterized by low B concen-trations covering a narrow range of values (3.5–4.4 and2.4–5.5μgB/L, respectively). Samples collected in theInterior Platform show a systematical increase indissolved B with typical concentrations of 12–20μgB/L. Concentrations of dissolved B correlate withconcentrations of dissolved Na, K, Si and the part ofthe TDS derived from the weathering of silicate rocks(TDSsil.) as estimated by Millot et al. [8] (see Fig. 2). Incontrast, no relationship appears between [B] and Ca,Mg, TDS, pH or any anion (Cl−, NO3

− and SO42−).

5.3. B isotopic compositions

The isotopic compositions of dissolved B range from−1.8‰ in theNass River up to 29.1‰ in the Lesser SlaveRiver. Rivers flowing over volcanic bedrocks as well asrivers draining the Rocky Mountains are characterized

Fig. 3. Relationship between B isotopic composition in riverinedissolved phase and the concentration of the total dissolved solutes(mg/L).

Fig. 2. Relationships between concentrations in the riverine dissolvedphase of B (μg/L) and those of Na, K, Si (μmol/L) and of the totaldissolved solutes (mg/L) derived from the weathering of silicate rocks(see Millot et al. [8] for the details of the calculation). Circles, trianglesand crosses correspond to rivers draining the RockyMountains and theInterior Platform, rivers draining volcanic terrains on the west coast ofthe cordillera and the Canadian Shield, respectively.


by lower isotopic compositions (from 3.6‰ to 12.1‰)compared to those draining the Interior Platform (from13.7‰ to 29.1‰). It then appears that, like concentra-tions, the isotopic composition of dissolved B evolvesalong the course of the rivers, from lower values inmountains to higher values in plains. Rivers drainingvolcanic bedrocks show relatively light isotopic compo-sition (from −1.8‰ to 4.95‰). Rivers flowing over theCanadian Shield show much heavier B isotopic compo-sitions (from 20.3‰ to 24.3‰) than other rivers ingeneral and rivers flowing over volcanic bedrocks inparticular.

Along the course of the rivers, from mountains toplains, we observe that both [B] and δ11B increase inthe dissolved phase. An intriguing correlation betweenB isotopes and the dissolved salts resulting from theweathering of silicates (noted TDSsil.) is illustrated inFig. 3. TDSsil. values were calculated by Lemarchandet al. [6], by subtracting the contributions of atmos-

pheric deposits and the dissolution of carbonates andevaporates from the total concentration of salts (TDS).It appears that the highest fluxes of cations derivedfrom the chemical weathering of silicates rocks areassociated with the heaviest δ11B values (up to+29.1‰). This feature appears contradictory to ourpresent knowledge of the B isotopic distribution onsurface continental reservoirs. First, silicate rocks havenegative isotopic compositions (typically from −10‰to 0‰) lower than any other source of B and no orslight isotopic fractionation is expected by dissolutionof these rocks [3]. Then, an increase of the silicateweathering rate should be followed be a decrease of theB isotopic signature of the fluids. A second intriguingfeature is that a clear relationship exists between theisotopic ratio of dissolved B and the runoff (Fig. 4)where the lowest δ11B values are associated withhighest runoff. This second observation needs also tobe explained because rivers under high runoff condi-tions have a B isotopic signature tending to light valuesin contradiction to common moderate to heavyrainwater values (e.g. Chetelat et al. [16]).

5.4. Temporal variations of dissolved B

In order to evaluate the variability of the B signaturein rivers, the Racing (# 96-19, 99-64) and the Yellow-knife Rivers (# 96-31, 99-90) have been sampled atdifferent stages of the water cycle, both in Aug. 1996 andJune 1999. Analyses of B concentrations and isotopesshow no significant variation and suggest that both [B]

Fig. 4. Relationship between B isotopic composition in riverinedissolved phase and runoff (mm/yr). Circles, triangles and crossescorrespond to rivers draining the Rocky Mountains and the InteriorPlatform, rivers draining volcanic terrains on the west coast of thecordillera and the Canadian Shield, respectively.


and δ11B values are rather constant or vary only slightlyat a given location.

5.5. Boron in river particulates

Boron in river particulates is either bounded to thesilicate lattice or adsorbed on the mineral surfaces. The Bisotopic composition of the lattice bounded B has beenanalyzed by Chetelat [17] and shows a narrow range ofnegative values compared to that of the river waters. Theδ11B values are around −7‰, consistent with valuesmeasured in samples from the Mississippi River [3] andwith the range of typical isotopic values for silicaterocks (see Palmer and Swihart [2] for review).

In order to assess the influence of the B adsorptiononto suspended particulates in rivers on the totaldischarge of dissolved B, we have conducted water-leaching experiments of the suspended load carried outby the Mackenzie River (sample # 96-6). The calculatedpartition coefficient (Kd) between adsorbed B recoveredby water leaching and dissolved [B] in the MackenzieRiver is 21. Given the concentration of suspended par-ticulates (in the order of 100mg/L), it comes that about0.2% of the total dissolved B in the Mackenzie River isadsorbed on solid phases. As a result, no significantmobilization of B is expected during its transport inrivers. This conclusion is consistent with previous workconducted on Himalayan rivers [4].

6. Sources of dissolved B to rivers

6.1. Atmospheric inputs

The contribution of the atmospheric B inputs to theriver waters needs assessment because of its potentialhigh impact on rivers characterized by the lowest Bconcentration. Studies focusing on B content inrainwaters are sparse and no data are available on theB concentration in rainwaters falling on the Mackenziebasin. Though no consensus has been reached, the laststudies tend to indicate that atmospheric B is mostlyderived from an oceanic component and therefore doesnot result from continental contribution [18–23]. Thecontribution of continental aerosols to the atmosphericdeposits is estimated to be less than 0.2% of the totalamount of atmospheric B [22].

B concentrations in rainwaters are highly variable,especially for coastal rain events, ranging from 3 to30μgB/L [16,21,24]. A global decrease of B concentra-tion in rainwaters with increasing distance from coast isobserved [23,24]. B concentrations in continental rainsrange from 0.2 to 2μgB/L with a mean concentration of0.5μgB/L in the north east of Washington DC (USA)[22] and from 0.3 to 8μgB/L with a mean concentra-tion of 0.9μgB/L in Central Nepal [23]. Examination ofrainwaters chemistry provided in literature indicatesthat the Cl /B ratio is rather constant with a mean valueof about 200±100. In order to estimate the maximumcontribution of atmospheric deposits to dissolved B, weconsider that all the dissolved Cl in rivers originatesfrom rainfalls. We then calculate that the correspondingconcentration of B that should have an atmosphericorigin does not exceed 15% of the total dissolved B inthe Mackenzie tributaries. Calculations for eachsampled rivers are illustrated in Fig. 5. A few rivers(such as # 96-25) deviate from this estimation becauseof a significant contribution of the dissolution of haliteto dissolved chlorine as revealed by the waterchemistry. This observation is consistent with aprevious study concluding that the impact of marineatmospheric deposits on the Mackenzie basin is almostnegligible because of the presence of the mountainousbarrier along the Pacific coast, which keeps the InteriorPlatform free from marine aerosols [11].

6.2. Dissolution of carbonates

The dissolution of carbonate rocks controls about90% of the TDS in the Mackenzie basin [8]. The Bconcentrations in continental carbonate rocks aretypically in the order of 1ppm, and never exceed

Fig. 5. Estimation of the relative contributions of the various B sourcesto dissolved B discharged by rivers. The relative proportions of eachsource are assessed from the chemical composition of the river sampleand that of the expected sources of B. Contributions other than silicatesrocks are maximum because they are calculated from extremehypotheses. The contribution of the silicate rocks is calculated as theremainder after correction of the contributions of rainwaters, carbonateand evaporite dissolution.


5ppm [25,26]. This gives a minimum Ca /B molar ratioin carbonates exposed to weathering of 20,000. Giventhat, for the Mackenzie basin, all the dissolved Ca inrivers originates from the dissolution of carbonates, wecalculate that their maximum contribution to totaldissolved B is 15%. Nevertheless, small rivers out-flowing from small drainage basins, such as the ToadRiver, show a carbonate contribution to dissolved B upto 30%. This indicates that the flux of dissolved B inrivers is not controlled by the dissolution of carbonates(see Fig. 5). A similar conclusion has been reached afterexamination of the Himalayan rivers chemistry [4].

6.3. Dissolution of evaporites and intrusion of relics ofdeep marine waters

Although evaporites (essentially halite and gypsum)do not represent an important proportion of the rocksexposed to chemical weathering, their rapid dissolutionrate together with very high B concentrations maypotentially impact the riverine dissolved B [27,28]. Anestimation of the maximum contribution of the disso-lution of halite to dissolved B in rivers can be calculatedconsidering that all dissolved Cl originates from halitedissolution. Rivers in which TDS is exclusively con-trolled by the dissolution of halite are characterized byCl /B ratios ranging from 1000 to 3000 (Salt River inthis study, [29]). Taking the lower Cl /B ratio as an upperlimit, we calculate that the contribution of the halitedissolution never exceeds 15% of the total dissolved Bin the Mackenzie tributaries analyzed in this study and iscommonly lower than 5%.

The relative contribution of the dissolution of gypsum isestimated from SO4 concentrations in rivers and usingSO4/B ≈8000 (after Vengosh et al. [30]). This assumesthat all sulfate concentrations are derived from gypsumdissolution. Again, this assumption gives a maximumcontribution because of the possible source of sulfateresulting from the oxidative weathering of sulfide. Thecalculated contributions of gypsum dissolution are typical-ly less than 10%, but can locally increase up to 30% for theToad River (see Fig. 5). With respect to the B geochemicalcycle, this latter river appears to be very peculiar comparedto other rivers sampled in this study because of the massivedissolution of carbonates and gypsum.

At the scale of the Mackenzie basin, it then appearsthat the cumulated contributions of the dissolution ofevaporites have only a limited impact on the flux of Bexported by rivers out of the Mackenzie basin. However,it is observed that the B fluxes out of small watershedscan be locally controlled by dissolution of evaporites(either halite or gypsum).

Finally, several studies have focused on the originsand ages of waters in the glacial till deposits in theMackenzie basin and Saskatchewan [31–34]. It isdemonstrated that the first 20m in depth hold modernfresh waters and that fossil glacial meltwaters (25–30kyr in age) are still present between the 20 and 60mdepth. These works also indicate that the vertical tran-sport of Cl is dominated by diffusion and that theCretaceous clay stratigraphic layer is not a source ofelements for the till waters. Because Cl behaves as aconservative element it is a good indicator of the originof elements when waters merge, we therefore concludethat B in the shallow groundwaters (down to 60m) is notsignificantly impacted by contribution from the Creta-ceous clay layer. In the following, the behavior ofdissolved B (supply and removal) will then beinterpreted as the result of interactions between ground-waters and hosting rocks.

6.4. Silicate weathering and the B budget in theMackenzie basin

The contribution of the weathering of silicate rocks tothe riverine dissolved B is more difficult to characterizebecause of the heterogeneous compositions of theminerals involved. We then consider that the contribu-tion of the silicate weathering to dissolved B is theremainder after correction of the contribution of other


sources (atmosphere, evaporites and carbonates). Itcomes that, for most of the rivers, the fraction of riverinedissolved B related to weathering of silicate rocksrepresents about 60% to 90% of the total dissolved B(Fig. 5). This indicates that, even in a drainage basindominated by carbonate rocks such as the MackenzieRiver basin, fluxes of dissolved B are still controlled byreactions involving silicates, here clay minerals such asillite (see Section 3 for details on the geological settingsand mineralogy). This conclusion is consistent with thecorrelation observed in this study between concentra-tions of B and Na, K, Si and total dissolved solutesoriginating from silicate weathering (TDSsil). Here, It isimportant to emphasize that these estimations are coarseand are affected by large uncertainties mostly subduedby our limited knowledge on the sources of dissolved Bin rivers but they demonstrate however that the releaseof B to river waters must, for the major part, becontrolled by the weathering of silicate rocks in theMackenzie basin.

Analyses of river waters running on various silicaterocks, namely shales in the Interior Platform andvolcanic rocks in small catchments on the WesternCordillera (Skeena, Nass and Stikine rivers), giveevidence that the nature of the weathered silicatesinfluences the isotopic signature of dissolved B.Volcanic terrains systematically lead to light δ11Bvalues (from −1.8‰ to 5‰) and low B concentrations(from 1 to 5.5ppb) compared to rivers draining shales(from 4‰ up to +29‰ and from 11 to 20ppb,respectively).

Because the Mackenzie basin is mainly composed ofshales (sedimentary rocks that are not expected toundergo further intense weathering reactions) andbecause the cold and relatively dry climatic conditionsof North Western Canada are not favorable to intenseweathering processes, we will assume that the particu-lates carried out by the Mackenzie tributaries arerepresentative of the silicate part of the source rocksexposed to weathering (i.e. they have not lost a signi-ficant amount of lattice-bounded B during weatheringreactions and they are not themselves the products ofthe weathering of silicate source rocks). We thereforeconclude that the mean δ11B value of the shales formingthe sedimentary platform has, on average, a B isotopiccomposition close to that of the particulates in rivers(about −7‰). Assuming this value as representative ofthe mean B isotopic composition of the suspendedsediments carried out by the Mackenzie tributaries, it ispossible to calculate the mean isotopic composition ofthe total B being exported by both the particulate andthe soluble phases in river waters. A relatively large

range of values is calculated: from −6‰ for riversdraining the mountainous areas and those dischargingthe largest concentrations of suspended sediments(N500mg/L) to +20–27‰ for basins draining theinterior platform.

It comes therefore that the isotopic composition oftotal B exported by rivers does not match that of its bulksource, which is estimated between −7‰ and +0‰depending on the relative contributions of the non-silicate sources of B. This indicates that almost all theMackenzie tributaries are currently preferentiallyexporting 11B. This feature appears particularly evidentfor rivers draining the Interior Platform. The firstconclusion at the scale of the Mackenzie basin is thatthe B cycle is not at a steady state and this raises thequestion of the cause(s) of the perturbation and of itstemporal evolution.

7. Model of the B geochemical cycle in sedimentarybasin

7.1. Control of boron by ion exchange reactions insaturated zones

After examination of δ11B plotted as a function ofCl /B molar values (Fig. 6), it appears that mixturesbetween bulk silicates, rainwaters, carbonates andevaporites, whose chemical and isotopic signatures arediscussed above, cannot explain the full range of Bisotopic data, in particular the samples that arecharacterized by low Cl /B and heavy δ11B values.Additional data on B in porewater samples from aquifersand aquitards in Saskatchewan [34] and the Liard basin[31] have chemical and isotopic characteristics moreconsistent with data of the present study. The porewatersamples were collected from selected wells and piezo-meters at depth between 1 and 80m. Concentrations ofB in these porewaters are in the order of 500–1000ppb.Their B isotopic compositions range between +3 and+40‰ that span over the values measured in rivers. Thismeans that a contribution as small as 1–5% ofgroundwaters to the rivers in terms of water masses isenough to fully explain the concentrations of dissolvedB measured in rivers (5–20ppbB).

Here, we examine the hypothesis that heavydissolved δ11B values reflect isotopic exchanges of Bat the water/clay minerals interface in saturated zones.This hypothesis is based on the partitioning of Bisotopes between solution and adsorbing surfaces (clayminerals, oxides and organic matter). The affinity ofboron for surfaces is a major characteristic of the borongeochemical cycle. Adsorption of B onto solid surfaces

Fig. 6. Diagram showing the mixing of expected sources of B. Cl /B isreported as a molar ratio. Gray areas represent endmembers as they aredefined by previous published works (see text for details). Circles,triangles and crosses represent data from this study. They correspondto rivers draining the Rocky Mountains and the Interior Platform,rivers draining volcanic terrains on the west coast of the cordillera andthe Canadian Shield, respectively. Open symbols correspond to watersamples collected in selected wells and piezometers from the Liardbasin and the Saskatchewan province. Open triangles are from Lemay[31] and open circles are from Vengosh and Hendry [34].


preferentially removes 10B with an 11B/ 10B shift of−25‰ (clays) to −40‰ (oxides) at pH 8 depending onthe type of surface (e.g. [35,36]) that leads, by isotopicbalance, to the relative enrichment of 11B in solutions.This hypothesis is supported by the high affinity of B forillite surface and by the relatively elevated pH value ofsolutions (around pH 8), buffered by the largedissolution of carbonates thus promoting the adsorptionof B on solids (see Goldberg [37] for review). It is alsosupported by the modeling of the reactive transport of Bin soils [38] and by the very large release of B during theweathering of illites and shales compared to otherpotential source rocks [39].

Given that the water / rock ratio in saturated zone is inthe order of 0.1mL/g (i.e. about 20–30% of totalporosity), that about 30% all the sedimentary rock iscomposed of illite (showing the most efficient Badsorbing surface amongst clay minerals) and that a Bpartition coefficient (Kd) of about 20 occurs (see Section5.5 above) in groundwater/soil system, it comes that98.5% of total B is adsorbed onto illite surfaces. Thislarge removal of B onto adsorbing surface then leaves afractionated pool of dissolved B with is enriched in 11Bby about +25‰ compared to the bulk B. Moreover,

under the above conditions, it comes that a concentra-tion of 500ppb B in solution, as commonly observed innatural groundwaters, corresponds to a concentration of10ppm of adsorbed B after equilibration with solidsurfaces. This value appears reasonable by comparisonwith the 15ppm B of desorbable B on silicate sedimentsin contact with seawater [36]. This mass budget calcu-lation also explains that such a large B reservoir canmaintain the B signature in rivers nearly constant at theyearly timescale.

The immediate conclusion is that a huge pool ofexchangeable B exists in groundwaters, which is largerby about 2 orders of magnitude than the complementaryamount of B remaining in solution. This gives evidencethat the flux of soluble B leaving the groundwater/rocksystem is fully controlled by ion exchange reactions andis hence affected by any departure from equilibrium ofthe exchangeable pool.

7.2. Factors controlling the B fluxes

In a homogeneous system where the B fluxes areregulated by water/rock interactions, the key parametersare the release rate of B by weathering of the hostingrock and its subsequent partition between solution andsolid surfaces. Then, any change in the ambientconditions affecting these parameters has the potentialto substantially modify the flux and the isotopicsignature of B leaving the system. In particular, changesin temperature and pH of porewaters modify thepartition coefficient as well as changes in the hydrologyof the saturated zone affect the ratio between the wateradvection and the weathering rate. A model ofadvection/diffusion/reaction can evaluate in what extentthe geochemical cycle of B in the Mackenzie basincould be actually affected by modifications of theambient conditions. Several models already existcoupling hydrological and geochemical approaches. Inthat field, Johnson and DePaolo [40,41] have developeda mathematical approach that builds the framework ofthe isotopic evolution in water/rock systems governedby rapid ion exchanges and long term dissolution/precipitation reactions. However, this mathematicalapproach can predict the evolution of an isotopic ratiothrough space and time provided that the hydrologicalsettings of the basin are known in detail. In theMackenzie basin, no data are available to successfullyapply this type of numerical approach. We have thensimplified this approach by developing a discretizedmodel in order to catch a first order estimation of thetemporal evolution of the B budget in the Mackenziebasin.


The scheme of the behavior of B in groundwater/rocksystem proposed for the Mackenzie basin is that the bulkB input splits by ion exchange between porewaters andsolid surfaces. We have then considered the transportand reaction of B through connected elementaryvolumes representative of the groundwater/rock system.In each of these volumes, B is supplied by incomingwater and by weathering of the hosting rocks. Then, Bequilibrates according to the prevalent conditions beforebeing exported to the next connected volume (Fig. 7).To make this approach as close as possible to theconditions of the Mackenzie basin, the followingassumptions are made

– The groundwater/rock system is homogeneous at thescale of the Mackenzie tributary basins;

– Transport of B only occurs by advection in a 1Dgroundwater/rock system (i.e. the diffusion of B isnegligible);

– The evaluated period of time is short enough toconsider that the chemical and physical properties ofthe hosting rocks are constant;

– B in porewaters is at equilibrium with adsorbedboron, which is validated by the rapid rate of Bexchange compared to the water advection;

– The pH of water is constant in space and time and isclose to that of rivers. This is a reasonable hypothesishere because groundwaters are buffered by dissolu-tion of carbonaceous shales;

– Relative variations of the B isotopic abundances aresmall enough to assume that the amount of 10B isproportional to total B;

Fig. 7. Scheme of the discretized 1D model developed in this study toestimate the temporal evolution of the B isotopes in the Mackenziebasin. The groundwater/rock system is modeled by 50 connectedvolumes through which water flows. Boron is supplied by incomingwaters and by the weathering of the hosting rocks (here mostly fromshales). It then splits between porewaters and adsorbing clay surfaceswhere it is controlled by its partition coefficient and its isotopicfractionation factor. Because the kinetic of the B adsorption is expectedto be rapid compared to the water advection, the partition of B isassumed at equilibrium in each of the volumes.

– A partition coefficient of B (Kd ≈20) and anisotopic fractionation (α ≈0.975) occur betweensolids and solutions at pH 8 [3,36], which lead tothe following mass balance equations solved for[B]sol. and Rsol.:

½B�sol: ¼½B�iads

Kd þ xrð1Þ

Rsol ¼1þ xr

Kd

� �dRT

aþ xrKd

ð2Þ

where [B]sol. and [B]adsi are the concentration of B in

solution and initially adsorbed, respectively, beforeincoming water equilibrates in the volume; ωr is thewater / rock ratio; Rsol and RT are the B isotopic ratioof the solution and bulk B in the volume,respectively;

– Only reactions of dissolution are taken into accountbecause of the cold climatic conditions and thepresence of shale does not favor intense precipitationof secondary minerals;

– A release rate (J) of B by weathering of the hostingrock is assigned to each volume of the model. Thisrate is directly related to the nature of the hostingrock, the ambient conditions (temperature, pH,…)and the water velocity that govern the time of water/rock contact. In fact, the ratio of the reaction flux tothe advection rate is described by the Damköhlernumber (e.g. see Johnson and DePaolo [40]).Because no estimation of this parameter is availablefor the groundwater/rock systems in the Mackenziebasin, we have arbitrary taken 50 connected volumesalong the x-axis and then adjusted the weathering rateper volume to reach a steady state of 500ppbB inporewaters in order to best compare with commonmeasured B concentrations in groundwaters. Aminimum of 50 connected volumes is required inour model to avoid numerical artifacts and tocorrectly represent the system as a continuousmedia (Fig. 8a).

The responses of the B isotopic ratio to changes inthe weathering rate, in the partition coefficient and in thebulk source of B, are illustrated in Fig. 8. Here, the unityused for the x-axis is the residence time of water in thesystem of interest. This substitution has the advantage toclearly illustrate that the exchange reactions retard theevolution of the B isotopic ratio compared to the wateradvection. Increasing the weathering rate leads to a

Fig. 8. Modeled responses of the B isotopic ratio of groundwaters to changes in the hydrological and geochemical settings of the groundwater/rocksystem. The characteristic time corresponds to the residence time of water in the system. a) Tests validating the discretized approach developed in thisstudy. The curves simulate the B isotopic response to a doubled weathering rate applied at t=0. Numbers correspond to the number of connectedvolumes used for the simulations. It is shown that models of more than 50 connected volumes give similar characteristic time and shape of thesolutions. b) B isotopic evolution in response to modifications of the weathering rate. The numbers give the factor by which the weathering rate hasbeen changed. c) B isotopic responses to modifications in the partition coefficient between soluble and exchangeable B. d) Responses tomodifications by +10‰ of the bulk B source. The two curves are calculated for different water / rock ratios reported on the graph.


larger supply of soluble B, this immediately causes theexcess of B to be massively adsorbed onto surfaces (10Bpreferentially). The B isotopic ratio in solution thenevolves towards heavy values and the groundwater/rocksystem is exporting fractionated B isotopes for a periodof time. Then, the system slowly evolves back to asteady state that only depends on the isotopic ratio of thebulk B input. Any decrease in the weathering rate willhave the exact reverse effect leading to the partialdesorption of the exchangeable pool enriched in 10B(Fig. 8b). From these sensitivity tests, it comes that theonly change in the weathering rate, all parameters beingconstant, can temporarily modify the isotopic signatureof the groundwaters. In the exact same manner, changesin the partition coefficient of B can change its isotopiccomposition in solution (Fig. 8c). To the opposite,change in the bulk source of B defines a new isotopic

steady state towards which the groundwaters convergewith time. Finally, a modification of the water / rock ratioalone does not affect the isotopic composition ofdissolved B but this parameter has a direct andproportional influence on the time of establishment ofthe new steady state (Fig. 8d).

The B isotopic responses predicted here are consis-tent with the mathematical model developed by Johnsonand DePaolo [40,41], who have demonstrated that anisotopic ratio evolves after being disturbed followingtwo steps. The first step is controlled by ion exchangereactions during which the evolution at the boundary ofthe system of the isotopic ratio of an exchangeableelement is retarded compared to water advection by afactor equal to 1+Kd /ωr (Fig. 8a). Reduced affinity ofthe element for the adsorbing surface (lower Kd) orhigher water / rock ratio will decrease the time taken by

Fig. 9. Scenario of the temporal evolution of the B isotopic ratio inwaters of the Mackenzie basin in response to changes in theweathering conditions caused by the past glacial events. An isotopiccomposition of −7‰ is assumed for the silicate source of B. However,the other sources of B (rain, carbonates and evaporates) should slightlyincrease this value up to 0‰, depending on their relative contributions(see Section 6 for details). In that case, the modeled curve must betranslated toward higher values.


the exchange front to reach the boundary of the system.After the perturbation front has passed through thesystem, a new steady state has been established wherethe isotopic ratio of porewaters is no longer controlledby exchange reactions but is only regulated bydissolution/precipitation reactions.

7.3. Model of the ephemeral signature of the dissolvedB isotopes in response to changes in the weatheringconditions

The results of the model developed above shows that,within a homogeneous rock unit, it is possible tosimulate considerable variations in the δ11B values ofcontinental waters during a limited period of time. Theduration of the perturbation is then proportional to theratio Kd /ωr, which characterizes both the chemicalproperties of the element of interest and the hosting rocktogether with the hydrological settings of the basin. Therelatively heavy values of δ11B measured in the plainswould then reflect a transient perturbation of theweathering regime whereas steady state conditions arealready achieved in the Rocky and Mackenzie Moun-tains. It means that the flux of B derived from theweathering of silicate minerals cannot instantaneouslyadjust to climatic changes. Since most of the InteriorPlatform is covered by about 100m of glacial,glaciofluvial and lacustrine deposits, it is expected thatthese sediments have been in contact with a largeamount of water and then that a very small fraction of Bwas adsorbed at the time of their deposit (the presentconcentration of exchangeable B on riverine particulatesis about 0.3ppm). A scenario of the evolution of the Bisotopic signature of groundwaters in the Mackenziebasin after the deposition of glacial tills is presented inFig. 9. The initial conditions are: [B]ads.=0.3ppm,Kd=20, ωr =0.3. The rock /water ratio in sedimentsincreases as well as their time of contact as soon as theburial of sediment starts. As a result, the reaction rateincreases compared to advection resulting in a net fluxof B onto adsorbing surfaces and in a consecutiveincrease of the δ11B value in porewaters. Following thenumerical approach developed here, it comes that Bisotopes are controlled by ion exchanges only during atemporary period. By addition of freshwaters, theexchange front propagates through the system with aretardation factor of 1+Kd /ωr (here about 70) comparedto the residence time of water in the system. The mostshifted isotopic ratios consistent with the observedvalues are modeled in the interval of 20–50 times theresidence time of water (Fig. 9). For a groundwater/rocksystem where the residence time of water is 500yr, the B

isotopic signature of groundwaters will be dominated byion exchange over 10–25kyrs after the system wasdisturbed. To the opposite, for a system with muchshorter water residence time (10yr), the system willreach the new steady state by 0.2–0.5kyr.

Then, the full range of B isotopic data in theMackenzie tributaries can be interpreted by recentchanges in the weathering conditions consistent withthe timescale of the last glacial periods. Assuming thatthe sediments composing the Mackenzie basin arehomogenous, variations of B isotopes from one basin tothe other should then be related to the residence time ofgroundwaters. In the mountainous drainage basins, therunoff is much higher and the residence time of water isshorter than it is in plain that makes those mountainousbasins to be controlled by exchange reactions during aproportionally shorter period of time. The capacity ofhigh runoff to more rapidly establish steady conditionscan then explained the global trend observed betweenrunoff and B isotopic ratio (Fig. 4). It is important tonote moreover that in the Mountains, the hosting rockshave undergone a significant diagenesis and lowmetamorphism that reduces the water / adsorbing surfaceratio, which also contributes to speed up the propagationof the exchange front. In addition, glacial deposits arelimited to valleys and then less abundant than in theplains. We therefore conclude that the mountainousrivers are now tightly controlled by the dissolutionreactions. To the opposite, the larger groundwatersystems in the Interior Platform have a longer residence


time and their heavy isotopic ratios indicate that they arestill dominated by exchange reactions. However, somelight values (+2‰ or +5‰) are found in some locationsin plains [31], which should reflect groundwatersystems that are limited in size and/or hosting rocksshowing less adsorbing surface. Additionally, themodern melting of the permafrost should also play animportant role by re-activating flow paths and changingthe conditions of the water/rocks interactions and,hence, maintaining changing boundary conditions.

These interpretations of the boron isotopic variationshave several important implications.

– Boron in rivers is mainly derived from groundwatershaving interacted with mineral surfaces for longtimeperiods.

– The present pattern of B geochemistry does notreflect modern climatic conditions, but is ratherinherited from the changes induced by the last glacialevents. This conclusion remains valid for elementsbeing controlled, at least in part, by ion exchanges onmineral surface. Arsenic may be one of thoseelements because it is associated with shales and isinvolved in surface complexation reactions [42] likeboron, and more generally trace elements forminganions in aqueous solutions (Mo, Cr, Se, V) [43].This also can modify during a more or less longperiod of time the ratio of major elements that mayhave important implications in calculating therelative weathering rates of source rocks (e.g. Grasbyet al. [44]).

– The boron isotopic composition of rivers in theMackenzie River is highly sensitive to hydrologicalconditions (type of aquifers), and ultimately togeology (type of rocks, presence of surface deposits).The presence of permeable and clay-rich driftaquifers in the Mackenzie basin is probably ofmajor importance for the acquisition of the boronisotopic composition of waters. This questions thegenerality of the interpretations found here.

Finally, if the non-steady state of boron isotopesreported in the Mackenzie River basin is actually due toion exchange reactions as we suggest here, it is importantto keep in mind that the adsorption curves of boron ontosurfaces that have been experimentally established so farshow a maximum of adsorption at pH close to 9, and astrong decrease towards lower pH values [37]. Whateverthe type of surface, high pH values are therefore anecessary condition for boron sorption, which, in nature,will be achieved by carbonate dissolution. Carbonatedissolution and the exchange reactions that fractionate

boron isotopes may therefore be coupled and the highboron isotopic composition found in the plains isindirectly due to carbonate dissolution.

8. Conclusions

Boron isotopes in the rivers of the Mackenzie Basinboth reflect the sources of boron and water/rockinteractions in groundwater systems. The major featureis that the B geochemical cycle in the Mackenzie basinis not at a steady state because rivers are exportingfractionated 11B compared to its bulk source. It is shownhere that most of the dissolved boron is derived from theweathering of silicates. The large discrepancy betweenthe boron isotopic composition of waters and that of thecontinental rocks can be explained by a transport/reaction model of B considering rapid exchangereactions and long-term dissolution of the shalesoccurring in saturated zones. The model proposed herepredicts that the B flux has been disturbed by changes inthe weathering regime consistent with the timescale ofthe recent glacial events. The new steady state definedby the modern conditions is established at various ratesdepending on a large part of the residence time ofgroundwaters in the basins.

The results and conclusions presented in this studyhighlight the potential of B isotopes to be used as atracer of the water/rock interactions, and in particular inweathering reactions involving silicates. Boron isotopesdo appear as good tracers of silicate weatheringreactions. Because of the great reactivity of boron forsolid surfaces, and the huge isotopic isotopic affectassociated to Boron sorption, we show here that boron isan excellent tracer for coupling geochemical andhydrological processes. These features also make B agood indicator of recent changes in the weatheringconditions (including hydrological and climatic fluctua-tions). Here boron isotopes shows that chemicalweathering in the Mackenzie basin is not operating atsteady state, implying that the weathering history is akey parameter to understand the modern state. Finally,boron isotope data in the rivers of the Mackenzie Riversemphasize the importance of chemical interactions ingroundwaters, where, despite low temperature, longresidence times facilitate chemical reactions. Theimportance of groundwaters to the chemical featuresof large rivers has probably been neglected.

Acknowledgments

Authors want to thank C.J. Allègre for helpfuldiscussion as well as B. Dupré, B. Bourdon, R. millot


and C. Gariepi for their help in sampling river waters.This manuscript largely benefits from constructivecomments from Y. Godderis and an anonymousreviewer and discussions with J. Gibson, S. Brantley,J. Schott, F. Chabaux A. Clément and E. Lajeunesse.This work was supported by the INSU-CNRS programPNSE. This is IPGP contribution no. 2126.

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