Barium stable isotopes as a fingerprint of biological cycling in the Amazon River Basin

Biological cycles of rock-derived nutrients on the continents is a major component of element cycles the Earth’s surface, but its magnitude still remains elusive to this day. The use of the stable isotope composition of rock-derived nutrients, which can be fractionated during biological uptake, provides a promising path forward in quantifying biological cycling and its overall contribution to global element cycling. In this paper, we rely on the nutrient-like behaviour of the trace element barium (Ba) and use its elemental and stable isotopic compositions in dissolved and sediment load river samples to investigate 5 biological cycling in the Amazon Basin. From these measurements, we show that dissolved Ba derives mainly from silicate rocks while a correlation between dissolved Ba and K abundances suggests a role of biological cycling on the Ba river budget. Further, the isotope composition of Ba (δBa) in the dissolved load was found to be significantly different from that of the parent silicate rocks implying that dissolved Ba isotopic signatures are affected by i) precipitation of soil-forming secondary phases and ii) biological uptake and release from dead organic matter. 10 Results from an isotope mass balance applied to the river dissolved load data indicate that after its release to solution by rock weathering, Ba is partitioned between the river dissolved load, secondary weathering products such as those found in soils and river sediments, and the biota. In most sub-catchments of the Amazon, river Ba abundances and isotope compositions are significantly affected by biological cycling. Relationships between estimates of Ba cycled through biota and independent metrics of ecosystem dynamics (such as Gross Primary Production and Terrestrial Ecosystem Respiration) allow us to discuss 15 the role of environmental parameters such as climate or erosion rates on the biological cycling of Ba, and by extension of major rock-derived nutrients. In addition, catchment-scale mass and isotope budgets of Ba show that the measured riverine export of Ba is lower than the estimated delivery of Ba to the Earth surface through rock alteration. This indicates the existence of a missing Ba component, that we attribute to the formation of Ba-bearing particulate organics, possibly accumulating as soil organic matter or currently 20 growing biomass within the catchments; and to organic-bound Ba exported as "unsampled" river particulate organic matter. Given our findings on the trace element Ba, we explore whether the river fluxes of most major rock-derived nutrients (K, Mg, Ca) might also be significantly affected by biological uptake or release. A first-order correction of river-derived silicate weathering fluxes from biological cycling shows that, at the Amazon at mouth, the CO2 consumption by silicate weathering could be several times higher than the yet-reported value of 13×10 mol of CO2/yr (Gaillardet et al., 1997). 25

As a consequence, biological cycling acts as a "traffic officer" for elements and their isotopes through the critical zone, directing their circulation across the Earth surface (e.g. Chaudhuri et al., 2007;Cenki-Tok et al., 2009;Schmitt et al., 2012; 60 Baronas et al., 2018). For simplicity, it has been commonly assumed that from the geochemical point of view element cycling by the biota is at "equilibrium" at the river scale (e.g. Viers et al., 2014) or, in other words that the flux of nutrient uptake is compensated for by an equivalent flux of release from the biota (e.g. Gaillardet et al., 1999a). However, more and more studies are now showing that higher plants are a significant reservoir of major rock-derived nutrients such as Ca, Mg, K or Si at the ecosystem scale (Burghelea et al., 2018) and that nutrient cycling is a key critical zone mechanism for understanding the 65 partitioning of elements at the Earth surface (e.g. Uhlig et al., 2017).
The abundance and isotope signature of elements involved into biological cycling can be used to appraise nutrient uptake and the subsequent fluxes of elements passing through the critical zone. Barium (Ba), an alkali earth element, that has seven stable isotopes ( 130 Ba 132 Ba, 134 Ba, 135 Ba, 136 Ba, 137 Ba, 138 Ba; although unstable, 130 Ba is considered to be stable given its half-life of 10 21 yrs). Besides the formation of secondary phases such as clays or oxides  and adsorption (Gou et al.,70 2019) that are considered to be major fractionation processes for a variety of weathering stable isotope tracers, previous studies indicate that Ba is sensitive to uptake by plants and bacteria (Bullen and Chadwick, 2016;Cam et al., 2016;Blondeau et al., 2018). Despite the lack of any known benefit of Ba for plants (Marschner, 2011) and the fact that accumulation of Ba in plants is toxic (Lamb et al., 2013;Myrvang et al., 2016, and reference therein), Ba shares similar chemical properties (ionic radius, charge) with major important rock-derived nutrients such as Mg, Ca, and K (Bullen and Bailey, 2005;Kabata-Pendias and 75 Mukherjee, 2007), leading to significant uptake of Ba in plants and to a "nutrient-like behaviour". In addition to the sizeable amount of Ba usually found in plants, the isotopic composition of Ba has been found to faithfully trace nutrient cycling, to an even better extent than Sr or Ca stable isotopes (Bullen and Chadwick, 2016). This, together with its lack of sensitivity to redox conditions (unlike some of the transition metals or major constituents of the biosphere such as C, N, or S), makes Ba stable isotopes a potentially powerful tool to quantify biological cycling within the critical zone, and leads us to consider in this work 80 that at first order Ba can be used as a proxy for the cycling of major rock-derived nutrients.
The study of Ba stable isotope fractionation at the Earth surface has started only recently (Von Allmen et al., 2010) and most contributions have hitherto focused principally on seawater (Horner et al., 2015;Cao et al., 2016;Hsieh and Henderson, 2017;Bates et al., 2017;Charbonnier et al., 2018), marine sediments (Bridgestock et al., 2018) and sedimentary barite (Crockford et al., 2019). In addition, the isotope composition of Ba dissolved in continental waters has been reported only for a few rivers, 85 such that constraints are still lacking on the global dissolved Ba riverine flux to the ocean as well as on its isotope composition (Cao et al., 2016;Hsieh and Henderson, 2017;Gou et al., 2019).
In this study, we aim to provide estimates of rock-derived nutrient cycling, to reveal its controlling parameters, and to discuss the potential implications thereof through the use of the abundance and isotope signature of Ba in the Amazon, the world largest river basin. We rely on the abundance and isotopic composition of river dissolved and sediment Ba for a series of 90 sub-catchments in the Amazon Basin spanning a variety of different parent rock lithologies, reliefs, climates, and vegetation types. We test different hypotheses to identify the principal drivers of the dissolved Ba isotopic composition of these rivers and demonstrate the significant role of biological cycling on the river Ba isotope signature. Using a set of river-scale elemental and isotopic mass budgets for Ba in the Amazon River, we further show that biological cycling has a significant impact on the routing of Ba between the different compartments of the critical zone. We examine how this routing is dependent on the 95 environmental conditions and in particular how it shifts between the mountainous regions of the Andes and the flatter, more expansive areas of the Amazon Basin. Finally, we explore how the export fluxes of major dissolved species from the Amazon Basin might be impacted by biological cycling and how this might bias estimates of chemical weathering rates based on river chemistry. Altogether, our study opens up new perspectives for the use of Ba isotope in sedimentary archives to trace past changes in ecosystem dynamics, provides further constraints on the isotope composition of Ba delivered globally to the oceans, 100 emphasizes the role of biological cycling on the routing of elements at the Earth surface, and highlights the role played by life on riverine export.

Geographical and geological setting
The Amazon Basin, the world largest river basin with a drainage area of 5,500,000 km 2 and a discharge of 6,300 km 3 /yr 105 (Milliman and Farnsworth, 2013), can be divided into three regions ( Fig. 1): • The Andean belt results from the subduction of the Nazca plate below the South American plate. The Northern part of the Amazon Andes is composed of a mixture of igneous rocks such as andesites and sedimentary rocks (e.g. shales and carbonates) of Paleozoic, Tertiary and Quaternary ages (Stallard and Edmond, 1983;Putzer, 1984;Moquet et al., 2011) and is drained by the Solimões tributaries, such as the Marañon, Ucayali, Huallaga, Morona, Tigre, or Pastaza. The

110
Southern part of the Amazon Andes is composed almost exclusively of sedimentary rocks deposited during the same geological periods as in the Northern part, and drained by the Madeira tributaries, such as the Beni, Alto Beni, Chepete, Quiquibey, Madre de Dios, Mamoré or Orthon rivers. Most Andean rivers are characterized by high erosion rates (higher than 500 t/km 2 /yr; Wittmann et al., 2011) due to steep slopes, making the Andes the quasi-sole source of sediment to the Amazon mainstream (Gibbs, 1972;Allègre et al., 1996). These sediment-laden rivers, called "white waters" (Gibbs,   phytoplanktonic photosynthetic activity. There, precipitation rate is higher (around 2,300 mm/yr) and the temperature warmer (26°C) than in the Andes.
• The Amazon Plain where all tributaries of the Solimões and the Madeira join, and underlain by sediments derived from the Andean belt and the Shields. Rivers draining only the Amazon Plain, such as the upper Negro River, are dilute, sedimentpoor, and typically of the "black water"-type, i.e. characterized by a high dissolved organic carbon concentration. In the 130 Amazon Plain, Andean-fed rivers carrying sediments (around 200 t/km 2 /yr; Wittmann et al., 2011) have developed floodplains which store river sediments over periods of time up to several 10 6 yrs (Wittmann et al., 2011), before their release to the Amazon hydrographic system. Precipitation (2,130 mm/yr) and temperature (25°C) are relatively similar to those encountered in the Shield basins.
Throughout the remainder of the text, we will distinguish our set of sampling sites ( Fig. 1) as (1) Northern Andean rivers 135 (Solimões sub-basin); (2) Southern Andean rivers (Madeira sub-basin); (3) "dilute" rivers, lumping together rivers draining the Shields and the Amazon Plain only; (4) the "main tributaries", with sampling sites in the plain, but resulting from the mixing of waters derived from several regions (Andes, Shields, Plain).
River waters were collected in acid-washed polypropylene containers and were filtered on site using Teflon filtration units (0.2-µm porosity). Water samples were acidified at pH ≈ 2 with ultra pure HNO 3 and stored in a cold room at 4 • C after collection. Major anion and cation concentrations were measured using ion chromatography, dissolved silica concentration by 145 UV-VIS spectrophotometry and trace elements by quadrupole ICP-MS.
Sampling procedures for river sediments are reported in Dosseto et al. (2006) and Bouchez et al. (2011). Briefly, at several locations, river sediments were sampled at different depths in the river channel and at the river bottom, in order to access the whole range of river sediment grain size. Major and trace element concentrations were measured by ICP-AES and ICP-MS, respectively, at the SARM (Service d'Analyse des Roches et des Minéraux, INSU facility, Vandoeuvre-les-Nancy, France; 150 analytical details available at http://helium.crpg.cnrs-nancy.fr/SARM). In order to characterize the chemical and isotope composition of typical Andean bedrock, outcropping rocks were collected in 2001 and 2005. These rocks were crushed to obtain homogeneous powders, digested using a mix of HNO 3 /HF and repeatedly taken up in HCl 6 N until full dissolution. Concentrations of major and trace elements in rocks were measured using quadrupole ICP-MS at IPGP.
In order to investigate the relative solubility of Ba (i.e. compared to soluble alkali and alkali-earth elements), we produced 155 a compilation of existing data on the chemical composition of the dissolved load of rivers draining single rock types that are significantly present in the Amazon Basin (andesites, shales, plutonic igneous rocks such as granites, and carbonates), as well as a data compilation for the composition of the rock types themselves. The river data compilation is made of a combination of literature data (Edmond et al., 1995;Louvat and Allègre, 1997;Louvat et al., 2008) and our own new data, while rock data are derived from the GEOROC database (http://georoc.mpch-mainz.gwdg.de/georoc/; see Fig. S1 and data Tables in repository   160 doi:10.5281/zenodo.4050339).

Barium chemical separation and isotope measurements
For each river water sample, a volume of 5 to 15 mL of water was evaporated at 100 • C in a Teflon beaker, and the residue was taken up in 0.5 mL HCl 2.5 N. For each solid sample (river sediment or rock), aliquots of homogeneous powders (around 50 mg of crushed powders allowing not only for Ba isotope measurements but also other analyses) were digested using a mix of 165 HNO 3 /HF, evaporated to dryness, and repeatedly taken up in HCl 6 N until full dissolution of the residue. A sample aliquot containing at minimum 250 ng of Ba was evaporated, and the residue was taken up in 0.5 mL HCl 2.5 N.
The chemical separation of Ba was carried out by ion chromatography using the ion-exchange AG50W-X8 resin where the matrix elements such as Na, K, Ca, Mg, Fe, and Al were eluted in a volume of 13 mL of HCl 2.5 N, and Ba was eluted in a volume of 15 mL of HCl 6 N (Van Zuilen et al., 2016b). To ensure a proper purification of Ba from the matrix, the separation 170 procedure was carried out twice in a row. Ba purification from river waters and sediments does not require the use of carbonate co-precipitation, a method usually performed for Ba purification in sea water, and which can entail a loss of Ba (e.g. Horner et al., 2015). Therefore the double-spike method (e.g. Van Zuilen et al., 2016b) was not used here, and we rather corrected the mass instrumental fractionation using the sample-standard-bracketing method (see below). However, to ensure correct and accurate Ba isotope measurements, yield and eluate purity were checked for all samples by quadrupole ICP-MS (Table S.1).

175
The total procedural blank was checked for each separation session, with a maximum of 0.2 ng of Ba, negligible compared to the typical amount of Ba present in samples.
The isotope ratios of Ba were measured using MC-ICP-MS (Thermo Fisher Neptune) using a SIS spray chamber. The Faraday cups were placed to collect masses 129 (L4), 130 (L3), 131 (L2), 132 (L3), 134 (C), 135 (H1), 136 (H2), 137 (H3) and 138 (H4). The concentration of samples and standards were adjusted to 100 µg/L. Over a session, the reproducibility 180 of the isotope measurement of a pure Ba solution was checked to be in the same range as the values reported by Nan et al. (2015). The isobaric interference by Xe on mass 134 was corrected by on-peak zeroes. Although the presence of residual Ce and La in the eluate can in principle lead to interferences on 138 Ba, the very low concentration of these two elements in the river water samples did not significantly impact our measurement, as mass-dependent fractionation was shown for all dissolved load samples by plotting 137 Ba/ 134 Ba vs. 138 Ba/ 134 Ba (Fig. S2). For solid samples, the presence of residual yet measurable 185 amounts of Ce and La in the eluate were shown to affect the 138 Ba signal to some extent. Therefore for the whole sample set, mass-dependent fractionation was rather checked using the 137 Ba/ 135 Ba and 137 Ba/ 134 Ba ratios (Fig. S2). For the sake of consistency, all data were measured as δ 137 Ba and are reported here as δ 138 Ba, using the mass-dependent relation δ 138 Ba ≈ 1.33 × δ 137 Ba, with the δ 13x Ba defined as: 190 with x = 7 or 8, the subscript smp indicating the sample isotope ratio, and the subscript std indicating the reference isotope ratio (NIST SRM 3104a).

Results
The concentration and isotope composition of dissolved and particulate Ba in the Amazon river system are available at doi: 10.5281/zenodo.4050339.

Ba abundance 205
The concentration of river dissolved Ba in the Amazon Basin ranges from 0.049 µmol/L to 0.490 µmol/L with an average of 0.202 µmol/L. As water flow can exert a strong control on elemental concentrations through dilution, normalization to a conservative element such as Na helps comparing dissolved Ba abundances between different water samples. The most Ba-enriched river (highest Ba/Na ratio) is the Negro river. Andean tributaries from the Solimões and Madeira basins show homogeneous Ba/Na ratios, despite the fact that they drain different rock types. The main tributaries of the Amazon (Solimões 210 and Madeira) show significant Ba enrichment with respect to their Andean tributaries.
Our compilation of Ba abundance (expressed as Ba/X ratios) for rocks and rivers draining single rock types ( Fig. S1) highlights that Ba is depleted with respect to other alkali (Li, Na) and alkali Earth (Mg, Ca, Sr) elements during chemical weathering and thus that Ba is affected by processes in the critical zone after its release from rocks at least to a larger extent than these elements are.

215
The concentration of Ba in the suspended sediments of the Amazon River Basin is heterogeneous (from 222 mg/kg to 836 mg/kg). This is likely due to the variable quartz abundance throughout the water column and a subsequent dilution effect (Bouchez et al., 2011). Once normalized to thorium (Th) concentration (Th being an insoluble element with a magmatic compatibility similar to that of Ba), Ba abundance is even more variable, with Ba/Th ratios ranging from 13 to 125. Within this range, some Ba/Th values differ significantly from the reported ratio for the Upper Continental Crust (UCC) (Ba/Th ≈ 50;

220
Taylor and McLennan, 1995;Rudnick and Gao, 2003), suggesting that processes can enrich or deplete Ba in river sediment compared to source rocks and/or that Amazon river sediment Ba is at least partially sourced from other rock types.
The fraction of river-borne Ba exported by Amazon rivers as dissolved species is calculated as:   Nan et al., 2018) reported in the literature is also shown.

Ba isotope composition
The isotopic composition of river dissolved Ba shows a wide range of δ 138 Ba diss values from 0.29‰ to -0.10‰ without any clear difference between the various types of rivers. We acknowledge that, at this stage, we lack time series of δ 138 Ba diss values. This could be problematic as it has been shown, for example, that δ 138 Ba diss displays temporal variations in the monsoonal Yellow River Basin . However, this variability was attributed to variable degrees of Ba sorption 235 onto particles, enabled by the very high concentration of suspended particulate matter in the Yellow River (several g/L; Gou et al., 2019). As the rivers of the Amazon Basin display much lower sediment concentration than that of the Yellow River (on the order of 100 mg/L for the largest tributaries; Bouchez et al., 2011), we contend that temporal variability in δ 138 Ba diss is much less significant.
The Ba isotope composition of river sediments, δ 138 Ba sed ranges from 0.06‰ to -0.25‰, with no significant difference between river suspended and bed sediments. The reported average values for plutonic rocks and andesites are 0.00±0.17‰ (S.D.) and 0.07±0.02‰ (S.D.), respectively (Charbonnier et al., 2018;Nan et al., 2018). Our own measurements of shale rocks collected in the Andes yield an average value for δ 138 Ba rock of -0.02±0.04‰ (S.D.) (Fig. 2). Ba in secondary weathering products is thus depleted in the "heavy" Ba isotopes with respect to i.e. the parent bedrocks that have lower isotope ratios, whereas Ba in the dissolved load is enriched in the "heavy" Ba isotopes (i.e. have higher isotope ratios). This observation is 245 consistent with the premise that the dissolved and suspended loads are complementary phases formed during the partitioning of Ba isotopes by chemical weathering (Fig. 2; Gong et al., 2019).
The Ba isotope composition of river sediments does not show any systematic variation with respect to the Al/Si ratio (a tracer for sediment grain size), with Al-rich samples (typically suspended matter sampled near the river channel surface) enriched in fine clays and Si-rich samples (typically bedload samples) enriched in coarse quartz (Bouchez et al., 2011, Fig. S3). This

250
observation contrasts with what has been previously reported for other isotope systems such as 87 Sr/ 86 Sr or 7 Li/ 6 Li (Bouchez et al., 2011;Dellinger et al., 2014) and highlights that Ba isotopes in solid phase weathering products are poorly sensitive to grain size, as shown previously for Ge isotopes (Baronas et al., 2018).

Discussion
Significant Ba isotope fractionation is observed in the Amazon Basin between the dissolved and particulate loads of rivers ( Fig.   255 2). In the following sections, we discuss the potential causes for this observation and show the influence of biological cycling on Ba isotope signatures.

Influence of critical zone processes on dissolved Ba
Variations in the dissolved Ba abundance and associated isotope composition could be controlled by variations in the sources of Ba and/or of critical zone processes affecting Ba after its release from rocks.

260
Although there are several possible sources of solutes contributing to the overall river chemistry, we show in Appendix A that silicate rocks are the main source of dissolved Ba to the river dissolved load in the Amazon Basin, consistent with previous observations from other river systems . This suggests that processes in the critical zone act to shift the abundance of river dissolved Ba between different basins. The fact that dissolved Ba is depleted with respect to elements classically considered as soluble (such as Na, Ca, or Mg) compared to rocks further lends support to this inference (Fig. S1).

265
Although still largely unconstrained, it is suspected that Ba incorporation into secondary weathering products (clays or oxi-hydroxides) occurs in the critical zone . River dissolved Li abundance and isotope composition can serve as a proxy for the contributions of secondary weathering products to the overall dissolved solute flux (von Strandmann et al., 2012;Dellinger et al., 2015b). When dissolved Ba is compared against dissolved Li, no correlation emerges between Ba*/Na* and Li*/Na* ("*" referring to the dissolved element concentration corrected from non-silicate inputs; see Appendix A 270 for details) nor between Li*/Na* and δ 138 Ba diss (Fig. 3a,b) even when these elemental ratios are corrected for the source rock   Figure 3. Scatter plots of Ba*/Na* and δ 138 Ba diss vs. Li*/Na* and K*/Na* for the dissolved load of the Amazon rivers ( "*" refers to dissolved element concentration corrected from non-silicate inputs; see Appendix A for details).
composition (these "corrected ratios" actually correspond to the so-called f Ba diss and f Li diss parameters; see below and Fig. S4). This lack of correlation implies that at least one other critical zone process (that is, in addition to the formation of secondary weathering products) scavenges dissolved Ba after its release from rocks. This inference is also supported by the absence of any significant differences in the Ba isotope compositions between shales (which are clay-and oxide-rich sedimentary rocks), unweathered igneous rocks, and river sediments (Fig. 2), which is in contrast to what is observed for Li (Dellinger et al., 2014).
It has been suggested that the isotope composition of Ba in soils is mainly driven by biological uptake and release (Bullen and Chadwick, 2016). This can be tested using the K abundance, which is known to be strongly impacted by biological activity at the Earth Surface (Chaudhuri et al., 2007;Tripler et al., 2006;Uhlig et al., 2017;Uhlig and von Blanckenburg, 2019) -in addition to having a magmatic compatibility (Hofmann, 1988) and a high abundance in shales (Taylor and McLennan, 1995; 280 Rudnick and Gao, 2003) similar to those of Ba, altogether suggesting a similar behaviour of Ba and K at the Earth Surface regarding "inorganic" processes (Kabata-Pendias and Mukherjee, 2007). The significant positive relationship between river dissolved Ba*/Na* and K*/Na* (Fig. 3c) suggests that the common behaviour between Ba and K extends to the biological realm. However, no correlation is observed between δ 138 Ba diss and K*/Na* (Fig. 3d).
Overall, the lack of correlation between δ 138 Ba diss and a range of elemental ratios indicates that a combination of several 285 processes is required to explain the Ba isotope signatures throughout the Amazon. In order to quantify the relative role of each of these processes on the river dissolved Ba budget, we first need to calculate the fraction of weathering-derived Ba that remains in solution after Ba uptake by different processes. This can be done using Na as a reference element, i.e. under the assumption that dissolved Na is released to rivers only by weathering and is not significantly re-incorporated in solid secondary weathering products during their formation, nor taken up as a nutrient by the biota (Gislason et al., 1996;Georg et al., 2007;290 Millot et al., 2010;Dellinger et al., 2015b): with Ba * /N a * the dissolved Ba/Na ratio corrected from non-silicate inputs, and (Ba/N a) 0 the bedrock ratio (details about calculation are given in Appendix B). Assuming that Ba and Na are not fractionated with respect to one another during their release from rocks, f Ba diss is then a proxy for the re-incorporation of Ba into secondary weathering solids (clays, oxides) or into 295 organic matter.
The calculated fraction of initially dissolved Ba left in the dissolved load of rivers, f Ba diss , ranges from 0.04 in rivers draining only the Andean belt, to 1.63 for the Negro River. This latter value for a parameter which in principle should be lower than < 1, is somewhat surprising, and will be discussed later (section 4.5).
f Ba diss does not show any correlation with dissolved δ 138 Ba diss (not shown), supporting the idea that several compartments 300 incorporate Ba in the critical zone following its release from rocks, and that the various processes responsible for this incorporation are characterized by different isotopic fractionation factors. In the following, in order to quantitatively tease these effects apart, we use a mass balance approach that accounts for the two processes likely to fractionate Ba in the critical zone: secondary phase formation and biological uptake. 4.2 Assessing the relative role of biological uptake on the Ba cycle in the Amazon Basin 305 Element fluxes and isotope composition can be used in tandem to estimate the role of various processes on elemental budgets (e.g. Bouchez et al., 2013;Baronas et al., 2018). To this aim, we consider the behavior of Ba in the critical zone at the catchment scale under a scenario in which dissolved Ba, originally derived from the partial dissolution of rocks, is partitioned into different net uptake and dissolved export fluxes following the framework developed by Bouchez et al. (2013). The partitioning of Ba after its release from rock minerals can be written as follows: with F Ba 0 the dissolution flux of Ba from rocks; F Ba diss the flux of river dissolved Ba exported from the system; F Ba bio the net Ba uptake by the biota ("net" meaning Ba uptake minus Ba release during organic matter remineralization); F Ba sec the Ba flux associated with the net formation (i.e. precipitation minus re-dissolution) associated to Ba-bearing secondary weathering products such as clays or oxides.

315
Then dividing both sides of the eq. (5) by F Ba 0 , we obtain the relative proportion of all fluxes with respect to the dissolution flux: where the terms f Ba i reflect the relative role of each process on Ba fluxes within the critical zone, with respect to the "initial" release flux of Ba from rocks F Ba 0 , and where f Ba diss represents in particular the "residual" dissolved Ba flux after each process, 320 i.e. is equivalent to that in eq. (4). In other words, these terms represent the net formation fluxes of different critical zone compartments: f Ba bio is the net uptake of Ba by the biosphere and f Ba sec is the net flux of precipitation of Ba-bearing secondary phases of weathering. It should be emphasized that while these terms reflect the net formation of these pools, in reality the dynamics of these compartments result from the competition between their formation and their destruction. For example, clays formed deep within weathering profiles that are generally in equilibrium with solute-rich waters, can be destabilized 325 when exposed to more dilute waters (Dellinger et al., 2015b); and organic matter can be remineralized in reservoirs with long residence times such as soils or floodplains (Bouchez et al., 2014b). A negative net formation (f Ba i < 0) thus indicates that the pool i releases more Ba to the dissolved compartment in the critical zone than it incorporates Ba from this dissolved compartment, at least on the time scale over which f Ba i is estimated.
Following Bouchez et al. (2013), we can introduce the corresponding isotope mass balance, which importantly is valid only 330 at steady state: with δ Ba diss the Ba isotope composition of the river, δ Ba rock the composition of the dissolved load after rock dissolution (assuming congruent dissolution, this parameter equals the isotopic composition of the average bedrock); ∆ Ba bio−diss the Ba isotope fractionation factor during biological uptake; and ∆ Ba sec−diss the Ba isotope fractionation factor associated with the formation 335 of secondary weathering products.
In order to quantify the role of nutrient cycling in the biogeochemical dynamics of Ba at the catchment scale, eq. (7) can be solved for the term f Ba bio . Replacing f Ba sec by (1 -f Ba bio -f Ba diss ) eq. (6) in eq. (7) and re-arranging leads to: can be estimated. We also acknowledge that eq. (8) relies on a steady-state assumption, which is also discussed in Appendix B.
Using these constraints, the calculated f Ba bio values over the Amazon Basin range from -0.39 +0.25 −0.30 to 0.57 +0.35 −0.17 , and f Ba bio of the Amazon at mouth is 0.28 +0.25 −0.12 (Table S.2). Only a few rivers show a f Ba bio close to 0, which challenges the following common assumption that biological cycling operates at steady-state from the point of view of the river dissolved load (i.e. that nutrient 345 uptake equals nutrient release) at the catchment scale. Some of the rivers such as the Mamoré show a net release from the biosphere (f Ba bio < 0), emphasizing that, locally in time and space, the biota can also act as a source of rock-derived nutrients to the river dissolved load.
The most significant findings of this analysis are the net uptake of Ba (f Ba bio > 0) by the biota across many regions of the Amazon Basin and the fact that the extent of this net biological uptake (the exact value of f Ba bio ) displays significant spatial 350 variation. Therefore, in the following section we explore the geomorphological, climatic, and ecological controls on the extent of Ba biological uptake.

Controls on Ba elemental and isotope partitioning by the weathering regime
The first hypothesis we set out to test regarding the spatial variation in Ba partitioning amongst critical zone compartments (f Ba i ) across the Amazon Basin is the role of the Earth surface denudation, which varies significantly between the mountainous 355 Andes and the flatter Amazon lowlands. Denudation rates exert a strong control on the so-called "weathering regime", which in turn influences the behavior of elements and of their isotopes in the critical zone (Bouchez et al., 2013;Dellinger et al., 2015b;Frings et al., 2016). The catchment-scale denudation rate D is the sum of the chemical weathering W and physical erosion E rates measured from river material, typically using estimates of weathering-derived solute fluxes (e.g. Gaillardet et al., 1999b) for weathering and sediment gauging for erosion. Alternatively, denudation rates can also be estimated using cosmogenic 360 nuclides such as 10 Be in sediments (e.g. Wittmann et al., 2011). The three rates D, E, and W are typically expressed in units of t/km 2 /yr (or in mm/yr using a rock-density based conversion). At one end of the spectrum of D, the "kinetically limited" weathering regime is characterized by high values of D and short particle residence time in the critical zone (West et al., 2005).
Under these conditions, the extent of chemical reactions is limited by the kinetics (or how fast the reaction can proceed), leading to a low share of solute export (W for weathering) to total export rates (low values of the W/D ratios, used as an index for weathering intensity; Bouchez et al., 2014a). On the other end of the spectrum, the "supply-limited" regime, in which D values are low and particles reside for a long time within the weathering reactor, allows for more intense weathering and is characterized by higher W/D ratios (Riebe et al., 2004). To summarize the relation between these different metrics, low W/D ratios of mountainous regions are typically associated with both high W and D fluxes, and high W/D ratios characteristic of flatter areas are typically associated with both low W and D fluxes.

370
Weathering intensity, bounded by these "kinetically-limited" and "supply-limited" weathering regime endmembers, also translates into isotope signatures: for example, denudation exerts a strong control on the behavior of Li stable isotopes within the critical zone by modulating the extent of secondary mineral formation (Dellinger et al., 2015b;Frings et al., 2016). Unlike for Li isotopes, there is no direct relationship between δ 138 Ba diss and D or W/D in our dataset (Fig. S5). This is because several critical zone processes act in conjunction to set the river dissolved Ba isotope signature in the Amazon Basin, as 375 explained in section 4.1, while only the formation of secondary products drives dissolved Li isotopes (Lemarchand et al., 2010). However, the individual role of each critical zone process can be evaluated through the examination of the relationships between f Ba i (eqs. (4) and (8)) fractions estimated above using our mass balance approach, and W/D as markers of the weathering regime.  The relative role of the dissolved export to the total Ba input into the critical zone (f Ba diss ) displays a positive relation with 380 W/D (Fig. 4a). This observation is in contrast to what has been reported for Li, which shows a lesser extent of Li scavenging from the solution (higher f Li diss ) when W/D is high or low, resulting in a so-called "boomerang" relationship (Dellinger et al., 2015b). For Ba, it is thus likely that even if, as for Li, Ba scavenging during formation of secondary weathering products is hampered at low W/D because of a kinetic limitation, another process scavenging dissolved Ba is being enhanced at low W/D, the nature of which is discussed below. f Ba bio does not show any trend with W/D (Fig. 4b), whereas f Ba sec shows a negative 385 relation with W/D (Fig. 4c).
As for each river the sum of the three f Ba i values is equal to 1 by construction, some of the observed co-variation between f Ba i is spurious, as this closure constraint induces a negative covariance between the different f -terms. In order to independently examine the role of each process, we translate these Ba fractions (equivalent to non-dimensional Ba fluxes) into area-specific, dimensional fluxes F Ba i (express as a kg of Ba per year per km 2 ) using the fact that by definition from eq. (6): with i = bio, sec, or diss. In eq. (10) we can calculate F Ba diss using Q the river discharge (in m 3 /yr), [Ba] * the concentration of silicate-derived river dissolved Ba (µg/L), and S (in km 2 ) the drainage area of the catchment (yielding a flux in mg/km 2 /yr; The area-specific flux of dissolved Ba remains constant across the range of denudation rates (Fig. 5a) or weathering regime indexed as the W/D ratio (Fig. 5b). Barium fluxes associated with both biological uptake and the formation of secondary weathering products is high where denudation is high. The flux of Ba associated to secondary phase formation is positively related to the denudation rate and, hence, to the flux of Ba linked to biological uptake. In settings with the highest denudation rates, the formation of secondary weathering products is thought to become kinetically limited (Bouchez et al., 2013;Pogge von 400 Strandmann and Henderson, 2015; Dellinger et al., 2015b). However, such limitation is not apparent for the corresponding Ba flux. This indicates again that the relevant processes for scavenging dissolved elements in the critical zone are distinct between Ba and Li.
The absolute flux of dissolved export Ba (F Ba diss ) being relatively constant across the Amazon Basin, combined with the fact that the fluxes of Ba associated to biological uptake and secondary phase formation are the highest where D is high, explains 405 why f Ba diss (the relative dissolved Ba flux) increases with W/D (Fig. 4a). Regardless of the explanation for this relatively invariant F Ba diss , it is critical to note that such a behaviour, observed here for Ba across the whole Amazon Basin, is in stark contrast with what has been reported for Li in the Andean part of the Amazon Basin (Dellinger et al., 2015b). In addition, it should be emphasized that the relationships shown in Figs. 4 and 5 include pure Andean rivers (e.g. Alto Beni), pure "dilute" rivers (e.g. Tapajós), and mixed rivers with active floodplains (e.g. Amazon at Óbidos). Dellinger et al. (2015b) have shown a 410 specific behaviour of Li isotopes in floodplains, expressed as a strong enrichment of heavy Li isotopes in rivers featuring active floodplains, and a loss of dissolved Li between the upstream reaches and the downstream reaches of these rivers. Although we cannot fully exclude a role of processes specific to floodplains on the Ba cycle and isotope fractionation in the Amazon Basin, we note that no such loss of dissolved Ba is observed across the few floodplain reaches where such a calculation can be made (See Supporting text for details and Table S.3 for data; Bouchez et al., 2012;Dellinger et al., 2015b). In most floodplain 415 reaches the river dissolved Ba flux actually increases downstream, which can be explained by the relative enrichment of Ba of pure "dilute" tributaries (as shown by their relatively high dissolved Ba/Na ratios; section 4.1) that also contribute water to large rivers featuring active floodplains.
The most interesting and novel observation of Fig. 5 remains the increase of the Ba biological uptake flux with denudation rates. Although this finding relies on isotope mass balance equations that inherently bear some uncertainties -in particular 420 related to the steady state assumption itself, or to parameter estimates (Appendix B), such result is consistent with what has been observed at the much smaller soil scale reporting that biological cycling can be influenced by rock supply rate or age (e.g. Vitousek et al., 2003;Porder et al., 2007). In the following section, we explore potential reasons why such a relationship might exist at the scale of large catchments in the Amazon Basin, in particular using independent estimates of parameters relevant to ecosystem dynamics.

Relationships between biological uptake, weathering regime, and ecosystem dynamics
In the previous section, variations in catchment-scale Ba biological uptake fluxes across the Amazon Basin were examined as a function of D and W/D as metrics of the weathering regime. This analysis shows in particular how the partitioning of the nutrient-like element Ba in the critical zone differs from that of the non-nutrient Li. The prominent role of ecosystem dynamics (especially in terms of ecosystem nutrition) in setting Ba partitioning in the critical zone is thus further explored in the present 430 section.
The fluxes of Ba associated to biological uptake are here compared to: (1) two catchment-scale carbon fluxes, that we believe capture the first-order mass balance dynamics of ecosystems: the Gross Primary Production (GPP; in t/km 2 /yr) and the Terrestrial Ecosystem Respiration (TER; in t/km 2 /yr), both retrieved from remote sensing data (Table S. to the release of nutrients to the ecosystem, such that catchment-scale TER can be rather used as a proxy for the recycling of rock-derived nutrients (and of elements characterized by a nutrient-like behavior such as Ba) through litter remineralization.

440
Such constraints (GPP, TER, MAP, MAT) do not rely on any geochemical tool, and thus offer a fully independent piece of information on biological activity across the Amazon Basin compared to the Ba isotope approach used in this study until now.
Ecosystem dynamics, in particular as probed by GPP, are also related to rock-derived nutrient cycling as calculated for Ba isotopes (Fig. 6a,b) has shown by the broad difference between Andean and Plain tributaries, lending further confidence to the validity of our determination of F Ba i . In addition, F Ba bio is broadly negatively related to both MAP and MAT ( Fig. 6c and Fig.   445 6d), suggesting a role of climatic factors on Ba biological cycling.
The relationships of Fig. 6 indicate that in the poorly-erosive, tectonically-quiescent, warm and humid areas of the Amazon Basin such as the Shields and Amazon Plain, the elevated GPP (Fig. 6a) suggests that the size of the biota is large (as in particular allowed by high MAP and MAT), while the high TER (Fig. 6b) is indicative of efficient recycling of rock-derived nutrients from litter, resulting on average in smaller net fluxes associated to Ba biological uptake (F Ba bio ). On the contrary, in 450 the highly-erosive, colder and drier areas of the Andes, the relatively low GPP (Fig. 6a) suggests a smaller size of the biota reservoir. TER is also relatively low there (Fig. 6b), indicating a lower efficiency in nutrient recycling of rock-derived from litter, thereby leading to a higher net flux of Ba biological uptake by the biosphere. This comparison between independent sets of constraints further strengthens our inference that some catchment-scale relationship exists between weathering regime, climate, and nutrient cycling across the Amazon basin.
To summarize, biological uptake as indexed by F Ba bio is higher in the Andes than in the lowland regions of the Amazon Basin. Based on existing knowledge on ecosystem nutrition, a set of mechanistic interpretations can be proposed to explain this finding. First, enhanced nutrient supply to ecosystem through rejuvenation of the Earth surface by denudation and subsequent weathering (high W and D in the Andes) might simply allow for more vigorous uptake of rock-derived nutrients (e.g Vitousek et al., 2003;Porder et al., 2007;Hahm et al., 2014;Uhlig and von Blanckenburg, 2019), although we note that no relation 460 exists between W and F Ba bio in our dataset (not shown). Second, in mountainous regions lower temperature and precipitation combined with the short residence time of solid in the critical zone might lead to inefficient release of nutrients from litter (Trumbore et al., 1996). In the plains, higher temperature and precipitation increase the energy available for efficient nutrient recycling, with slow denudation and subsequent longer residence time of solid material allowing for a nearly-closed "recycling loop". Other factors influencing biological uptake and litter remineralization that might differ between the Amazon plains and 465 the Andes include the role of soil humidity (Grubb, 1971) and the residence time of water in the subsurface (Torres et al.,

2015).
Altogether, a change in nutrient recycling efficiency is a likely explanation for the shift in rock-derived nutrient uptake fluxes between the Andes and the plain, as suggested by Ba isotopes. As a matter of fact, in most ecosystems the major nutrition acquisition pathway relies on the rapid recycling of litter (e.g. Cleveland et al., 2013;Wilcke et al., 2017;Uhlig 470 and von Blanckenburg, 2019). Nonetheless, recycling is never complete as a small fraction of litter is exported from soils by erosion before remineralization (Selva et al., 2007;Scalley et al., 2012), as shown by the presence of particulate organic carbon of biogenic origin in river material (Selva et al., 2007;Bouchez et al., 2014b). Therefore, a slow but sustained supply from rock dissolution is needed to balance the loss from un-recycled nutrients by litter erosion, defined as the "geogenic" pathway (Uhlig and von Blanckenburg, 2019). Our results on the Amazon Basin suggest that a shift occurs in the relative role of these 475 two pathways for acquisition of rock derived-nutrients, from the predominance of the organic pathway in the hot and humid environment of the plains, to an increased importance of the geogenic pathway in the colder, drier, and more erosive Andes (Fig. 6).
The above interpretation can further be tested using a so-called "river-scale mass budget", which allows for probing the form under which rock-derived nutrients are exported. Such a test is performed for Ba in the next section. River-scale mass budgets, based on a hypothesized chemical complementarity between the weathered (chemical export) and eroded (physical export) material exported by rivers, have been used to test whether the chemical composition of the material exported by rivers can be explained by the composition of the rock undergoing erosion and weathering at the scale of large 485 catchments (Stallard, 1995;Gaillardet et al., 1995Gaillardet et al., , 1999a. A failure in such test can be indicative of issues in estimating the composition of the source rock (Gaillardet et al., 1999a) or in the determination of the composition of the riverine export (Bouchez et al., 2011), of timescale issues related to the typical integration time of the values used for the parameters of the river mass budget (Stallard, 1995;Lemarchand and Gaillardet, 2006), or any combination thereof.
In the scope of the present study on Ba isotopes, such river mass budget can be used to test whether all Ba released from 490 rock dissolution is found in the total (that is, dissolved plus particulate) riverine export, in which case the mass budget can be considered to be "equilibrated". A lack of Ba in the riverine export would then mean that Ba is either currently accumulating in the catchment, and/or that the adopted sampling techniques do not capture the entirety of the riverine Ba export, or at least does not integrate the full river Ba export over the time scale that is relevant to establish the Ba river mass budget. As shown below, the form under which Ba is accumulated in, or exported from the catchment, can also be discussed based on the results 495 of such a river-scale mass budget.
In addition, it is important to note that whereas strong uncertainties affect the different parameters used to compute f Ba bio above (in particular on the isotope fractionation factors ∆ Ba sec−diss and ∆ Ba bio−diss ), river-scale mass budgets as performed in the following are based only on the relative partitioning of Ba and its isotopes between the dissolved and solid phases of rivers (Bouchez et al., 2013).

Testing the equilibrium of the Ba river mass budget in the Amazon Basin
To assess whether the Ba river budget is "at equilibrium" in the Amazon, we can compare the fraction of Ba transported as a dissolved species (w Ba ; eq. (3)) against the relative loss of Ba in river sediments compared to the source rocks. To quantify this loss, we normalise the Ba/Th ratio of river sediments to the Ba/Th ratio of the source rocks (the full derivation of the following equation is presented in Appendix C).

505
(Ba/T h) n + w Ba f luxes = 1 (11) The two parameters (Ba/T h) n and w Ba f luxes (as determined from eq. (3)) represent the fraction of dissolved and solid Ba transported in rivers relative to the denudation fluxes, respectively. Eq. (11) means that when the Ba river mass budget is at equilibrium, the sum of (Ba/T h) n and w Ba f luxes is equal to 1; in other words data points should lie on the down-sloping diagonal in a w Ba f luxes vs. (Ba/T h) n diagram ( Fig. S6 and 7a). Rivers plotting below this line are characterized by an export 510 of Ba lower than that expected from the basin-scale denudation rate and the Ba concentration in the source rock.
Such a test for an equilibrated river mass budget can also be performed using isotope ratios (Bouchez et al., 2013;Uhlig et al., 2017): In a w Ba iso vs. w Ba f luxes diagram, if the river mass budget is at equilibrium the data points should lie along the 1:1 line, while in 515 a w Ba iso vs. (Ba/T h) n diagram, they should lie along the down-sloping diagonal. Note that the w Ba iso vs. (Ba/T h) n evaluation, unlike the w Ba f luxes -(Ba/T h) n comparison explained above, does not depend on fluxes. In order to provide an example of an equilibrated river mass budget, in Fig. S6 we re-visit the data provided by Dellinger et al. (2015a), who showed that in the Amazon the sum of the solid and dissolved Li fluxes exported by rivers, as well as their combined isotope composition, can be accounted for by independent estimate of flux and isotope composition of Li eroded and weathered from rocks. The 520 river mass budget of Li shows that at the scale of the Amazon Basin, time scale issues stemming from the comparison of various parameters integrating Earth surface processes over different timescales (e.g. dissolved fluxes or particulate fluxes) are negligible, at least regarding the "inorganic" part of element cycles in the critical zone. This observation, combined with the fact that estimates of Ba abundance and isotope composition of source rocks can be considered as fairly reliable (Appendix B), suggests that any disequilibrium that might arise in the Ba river mass budget should find its origin in the nutrient-like behaviour 525 of Ba.
The comparison between w Ba f luxes and (Ba/T h) n (eq. (C5); Fig. 7a) shows that in most of the Amazon rivers, there is less Ba exported by rivers than expected from denudation rates. Notable exceptions are the "dilute" tributaries (Rio Negro, Trombetas and Tapajós). It is possible that in such rivers, the export of Th as a dissolved species induced by organic colloids compromises the use of the river mass budget (in particular eqs. (C2) and (C3); Appendix C). We also note that in these lowland areas, the 530 input from dust (Abouchami et al., 2013;Moran-Zuloaga et al., 2018) can be significant which could bias river-scale mass budgets. In the following, we focus our interpretations on the other river systems, which all display a negative offset from the equilibrium line in Fig. 7a. For these rivers, we note that if a dust component was included in the left-hand sides of (C1) or (C2), the observed disequilibrium would go in the same direction and would even be larger, thus leaving this inference unchanged.
The observed disequilibrium in the Ba river mass budget also remains when comparing w Ba iso (eq. (12)) to (Ba/T h) n (eq. 535 (C5), Fig. 7b) or w Ba f luxes to w Ba iso (Fig. 7c), despite significant uncertainty on the values of w Ba iso due to both analytical uncertainties and error propagation (for example when δ Ba diss and δ Ba sed are close; see eq. (12) and discussion in Bouchez et al., 2013).
From here, in order to identify the potential causes for the lack of equilibrium in the river-scale mass budgets observed for most tributaries of the Amazon Basin, we can test the different scenarios that could reconcile the isotopic and elemental exports 540 of Ba by Amazon rivers with denudation rates. As there is less Ba exported by rivers than expected from denudation (Fig. 7a), these different scenarios will all consider that to reconcile the two measures, the addition of a "missing Ba component", associated with a specific isotopic signature called hereafter δ Ba miss , is needed. To illustrate these scenarios, arrows in the panels of Fig. 7 indicate in which directions the values on the three diagram axes will change upon addition of the missing Ba component: 545 1) the missing Ba is under a dissolved form and its isotopic signature (δ Ba miss ) is lower than δ Ba diss 2) the missing Ba is under a dissolved form and δ Ba miss is higher than δ Ba diss 3) the missing Ba is under a particulate form and δ Ba miss is lower than δ Ba sed 4) the missing Ba is under a particulate form and δ Ba miss is higher than δ Ba sed For scenarios 1 and 2, adding the missing (dissolved) Ba would increase w Ba f luxes (eq. (3)) but leave (Ba/T h) n unchanged.

550
Scenarios 3 and 4 would result in a decrease of w Ba f luxes , while the shift they would induce on (Ba/T h) n would depend on the Ba/Th ratio of the missing Ba component. We contend that this ratio is relatively high, as we expect -as discussed below in section 4.5.2 -that this missing Ba solid component would be of biological nature, and as Th is not a nutrient. In this case, scenarios 3 and 4 would result in the addition of Ba-rich material to the river solid load, and thus to an increase in (Ba/T h) n , leading to non-vertical vectors in Fig. 7b and Fig. 7c. Finally, following eq. (12), w Ba iso would increase if δ Ba miss is higher than 555 δ Ba diss (scenario 1) or than δ Ba sed (scenario 3); and decrease if δ Ba miss is lower (scenarios 2 and 4). While by construction all these scenarios bring the data points closer to the equilibrium line in Fig. 7a, it appears that scenario 2 can be immediately excluded because adding dissolved Ba with a high δ Ba miss would shift the river mass budget toward stronger disequilibrium (Fig. 7b and c). In addition, the direction given by the vector of scenario 4 is also unlikely to reconcile w Ba iso and (Ba/T h) n for any river in Fig. 7b and w Ba iso and w Ba f luxes for most rivers in Fig. 7c. Indeed, some rivers (Beni 560 at Riberalta and Rurrenabaque, Ucayali, and Madeira) are above the equilibrium line in Fig. 7c, and their Ba river mass budget could be reconciled if the vector 1 had a sub-horizontal direction, which could be the case if the difference between δ Ba diss and δ Ba miss was small. However, we first note that for these rivers the uncertainty on w Ba iso is large. Second, the most important finding   Figure 7. Test for the equilibrium of the river mass budget of Ba in the Amazon Basin using elemental (eqs. (3) and (C4)) and isotopic (eq. (12)) ratios. Uncertainties on w Ba f luxes and (Ba/T h)n have been calculated through gaussian error propagation. Values of w Ba f luxes have been calculated following two ways (using river gauging: circles and cosmogenic nuclides: diamonds; for a given river both estimates are linked by a stippled line) allowing us to partially account for potential timescale issues in the estimation of sediment export (see Appendix C). Uncertainties on w Ba iso have been evaluated using Monte Carlo error propagation based on the uncertainties on individual parameters in eq. (12), and are shown here as 68%CI. In panel c, "B@Rur", "B@Rib", "Mam", "U", "M", "A" and "S" reflect the sampling sites: Beni at Rurrenabaque, Beni at Riberalta, Mamoré, Ucayali, Madeira, Amazon, and Solimões, respectively. regarding this comparison between w Ba iso and w Ba f luxes in Fig. 7c is still that the observed disequilibrium cannot be explained by scenario 2 and is unlikely to be explained by scenario 4.

565
To summarize, ruling out scenarios 2 and 4 allows us to infer that the isotopic composition of the missing Ba (δ Ba miss ) is lower than that of Ba exported by rivers. Therefore, the remaining valid scenarios are 1 (the missing Ba is dissolved) and 3 (the missing Ba is solid). However, the nature of (and the uncertainties encountered in) the analysis performed above prevents a full assessment of the exact nature of this missing Ba (dissolved or solid), and of its isotopic composition. Nevertheless, the difference between the Li (Fig. S6) and Ba (Fig. 7) river mass budgets, and the fact that the Ba isotopic composition of the missing reservoir is low (hence consistent with the Ba isotope composition of a biological component; Bullen and Chadwick, 2016, and Fig. 2) are strong arguments towards a role of biological cycling in forming this Ba component missing from the river-scale mass budget. In the following, we further explore this hypothesis by comparing estimates of the amount of missing Ba to other independent estimates of Ba fluxes across the Amazon Basin.

4.5.2
What is the nature of the "missing Ba" component in the Amazon riverine export?

575
Given the role of biological uptake on Ba abundance and isotope ratio in the rivers of the Amazon Basin, here we test for the influence of biological uptake on the "missing Ba" inferred from the river mass budget above.
First, we quantify the missing Ba as a relative flux (f Ba miss ) as the difference between the Ba flux actually exported by rivers and the Ba export that should result from denudation and the concentration of Ba in rocks. This actually corresponds to the graphical offset (vertical or horizontal) between (Ba/T h) n (or equivalently w Ba f luxes ) and the down-sloping diagonal line in 580 Fig. 7: It is important to note that f Ba miss can be interpreted either as an actual relative flux of Ba exported from the catchment but missed by our sampling scheme; or as a relative rate of Ba build-up into a reservoir within the catchment; or a combination thereof. We return to this distinction later when discussing the interpretation of f Ba miss , but name this metric a relative "flux" for 585 the moment, for the sake of simplicity. To compare the flux of missing Ba (f Ba miss ) with the amount of Ba cycled by the biota in the Amazon (f Ba bio ), we first convert f Ba miss into a dimensional flux: with F Ba miss the area-specific flux of missing Ba in rivers, expressed in e.g. kg/km 2 /yr. We note that the denudation rates derived from the sum of sediment gauging (E integrating over decades) and silicate weathering flux (W ) vs. cosmogenic 590 nuclides which already represents the total denudation flux (D integrating over thousands of years; Wittmann et al., 2011;Dellinger et al., 2015a) can differ (especially in the Beni River system). Therefore, for rivers where both constraints are available, we calculate two values of F Ba miss : one based on D calculated as E from sediment gauging, plus the silicate weathering flux; and the other based on D determined from cosmogenic nuclides. Despite significant uncertainty, it is clear that the missing flux F Ba miss (eq. (14)) is of the same order of magnitude as F Ba bio 595 (Table S.6; Fig. 8) across the Amazon Basin. This observation further supports that biological uptake is a viable explanation for the disequilibrium in the river mass budget of the Amazon Basin. Interestingly, the relationship between F Ba miss and F Ba bio is stronger when F Ba miss is calculated using cosmogenic isotopes in eq. (14) (Table S.6; Fig. 8). The cosmogenic-derived denudation rates integrate over longer timescales compared to that of sediment gauging (von Blanckenburg, 2005), suggesting that the link between Ba biological uptake and the Ba river mass budget is a long-term feature of the Ba cycle in the Amazon Basin.

600
Altogether, these observations further support that the existence of the missing Ba flux in the Amazon Basin, inferred from the river-scale mass budget performed in section 4.5.1, is indeed linked to biological cycling.  Figure 8. Flux of Ba biological uptake (F Ba bio ; eq. (9)) vs. the missing Ba flux as quantified from the river-scale mass budget (F Ba miss ; eq. (14) ) in the Amazon Basin. Uncertainties have been propagated using a combination of Monte Carlo simulation and gaussian error propagation.
A first possibility to account for such a missing Ba flux could derive from groundwater contributions that can export a significant amount of dissolved Ba. Thus, sampling schemes focusing only on river export might miss this potentially large dissolved Ba flux coming from the groundwater. However, with the magnitude of the river Ba dissolved flux and that of F Ba miss 605 in the Amazon Basin being similar (Tables S.2 and S.6) coupled with observed Ba concentration in groundwater being similar to those measured in the rivers, this explanation would require that the groundwater discharge of the Amazon River is similar to that of the river discharge. Although seasonal groundwater storage in the Amazon Basin appears to be a significant component of the regional hydrological budget, especially in the central part of the Amazon Basin (Frappart et al., 2019), such a high contribution of groundwater to the overall water export of the whole Amazon basin seems unlikely. In addition, we do not see 610 any particular reason why such a groundwater export would affect Ba and not Li ( Fig. 7 and Fig. S6). It also appears unlikely that F Ba miss could be interpreted as a dissolved pool of Ba accumulating in the catchments given the typical residence times of groundwater even in large catchments and the fact that the observed disequilibrium in the Ba river mass budget seems to hold over long time scales (see above). Therefore, the most likely interpretation for the existence of a significant missing Ba is the export (if interpreted as an actual 615 flux) or accumulation (if interpreted as a pool building up) of Ba-bearing solids. Given the relationship observed between F Ba bio and F Ba miss (Fig. 8), it is plausible that these particulates are of organic nature, i.e. living beings, or dead organic matter (litter and/or river particulate organic carbon). In support of this interpretation, we note that there exists a relationship between TER, MAP, and MAT vs. F Ba miss (Fig. 9a,b,c), showing a more pronounced Ba missing flux, in basins for which precipitation, temperatures and the efficiency of the remineralization are lower and, thus, where the formation (and possibly export) of litter 620 and dead particulate organic matter is stronger (Section 4.4).   Accumulation of organic-bound Ba within catchments could explain the existence of the missing Ba. For example, a pool of solid, organic-bound Ba could be forming through accumulation of litter in soils, or through increase in the biomass -this can be the case in areas where forests grow again after deforestation in the Amazon Basin. Although this hypothesis needs to be tested further, current growth of biomass in some regions of the Andes would support this scenario (e.g. Feeley and Silman, Alternatively, the missing Ba could also reflect the existence of a particulate, organic debris flux. Uhlig et al. (2017) have suggested that the export of Mg and other rock-derived nutrients as particulate organic matter in mountain belts could represent a crucial missing riverine elemental flux, but is traditionally challenging to sample, notably because this export is mostly episodic, and, thus, difficult to constrain resulting in a typical timescale issue in the river mass budget, where the sampling 630 frequency of river material does not allow to capture the entirety of the long-term riverine export. In large river systems such as the Amazon, the effect of episodic export on the total organic matter flux is likely to be smeared out, as suggested by the relative regularity of particulate organic carbon fluxes throughout the hydrological cycle (Bouchez et al., 2014b). However, large woody debris (e.g. trunks) or river macrophytes could in principle represent a significant fraction of the particulate export of large rivers and be essentially unaccounted for due to limited amount of water that can be withdrawn with the sampling 635 scheme commonly used (only a few liters with river point samplers) (Bouchez et al., 2011).
To test for the validity of this scenario, we can predict the flux of particulate organic carbon that would be needed to account for the computed F Ba miss : with F C miss the missing flux of organic carbon and (Ba/C) org the Ba/C ratio of the organic matter exported by rivers. F C miss 640 can then be compared with E C org , the flux of particulate organic carbon exported by the river: with POC representing the relative content of particulate organic carbon in the river sediments (Bouchez et al., 2014b), and E the erosion rate (from sediment gauging) (Table S.6).
Two estimates can be proposed for the value of (Ba/C) org to calculate F C miss (eq. (15)). In the first estimate, we take the 645 average concentration of Ba in organic matter of 15 mg/kg based on our own compilation (Li, 2000;Chiarenzelli et al., 2001;Bullen and Bailey, 2005;Vaganov et al., 2013, Table S.7), and a concentration of C in organic matter around 50%. In the second estimate, we use the ratio between the fluxes of Ba and C escaping litter decay, quantified as: where NPP is the Net Primary Productivity calculated as GPP-TER, and corresponding to the net accumulation of carbon by 650 the ecosystem. The values of (Ba/C) org calculated this way differ significantly between the Andes and the plains. In the Andes, the Ba abundance in organic matter estimated using eq. (17) is much lower than that derived from our compilation (around 0.60 mg/kg; Table S.6). In the plains, the calculated Ba concentration in organic matter is even lower (around 0.01 mg/kg; Table. S.6). At face value, the difference between the values obtained for the Andes and the plain from eq. (17) suggests that the more efficient nutrient recycling is, the more weakly Ba is retained in the organic material exported by the river.

655
However, and regardless of the value used for (Ba/C) org , the comparison between E C org (eq. (16)) and F C miss (eq. (15)) suggests that more than 99% of the particulate organic carbon would be missed when estimating the POC flux through a "classical" sampling scheme. We believe that it is unlikely that such a high proportion of the POC flux can be unaccounted for.
It remains thus challenging to identify the exact form of the missing Ba (i.e. flux vs. pool, or a combination thereof) inferred from the river-scale mass budget. However, the most likely interpretation for the existence of this missing component is the 660 partitioning of Ba into biological material after uptake. As a consequence, our analysis emphasizes the role of biological cycling on the routing and transport of rock-derived nutrients at the large catchment scale.
To summarize the above discussion, this examination of the Ba elemental and isotope budgets for a range of different river catchments throughout the Amazon Basin shows how stable isotope signatures can be used to explore nutrient cycling in the critical zone and, further, opens the possibility for an application to other isotope systems and other locations. Additionally, 665 applying this approach to Ba provides novel information on the dynamics of the rock-derived nutrients, and possible of organic matter, at the scale of large catchments.
4.6 A conceptual model for the influence of biological cycling and weathering regime on the fate of Ba as a nutrient-like element in the Amazon Basin.
To summarize our analysis, we propose the following interpretation for the behavior of Ba as a nutrient-like, broadly reflecting 670 the behaviour of major rock-derived nutrients in the Amazon Basin: -Except for some rivers draining the lowlands (see below), in the plain regions litter remineralization outpaces litter erosion, allowing the biosphere to efficiently recycle Ba -and thus possibly rock-derived nutrients -from the litter, and thus does not require a significant uptake of "new" Ba deriving from rock dissolution (Cleveland et al., 2013). In such conditions, primary production is strong, as promoted by high MAP and MAT, and soil stability allowed by low erosion 675 rates leads to a weak export of particulate organic carbon from the catchment.
-In mountains regions of the Amazon, nutrient recycling by vegetation from litter is slower than litter erosion. As a consequence, the biota continuously extracts Ba and possibly major rock-derived nutrients from the surrounding rocks, which compensates for the loss of litter by erosion. Primary production is lower because the growth of biota is limited by the low MAP and MAT, strong denudation rates and short residence times of material, whereas export of rock-derived nutrients by particulate organic matter from the catchment (or accumulation within the catchment) is high.
-Some "dilute" rivers draining the lowlands are enriched in Ba with respect to the source rocks, which implies a net export of dissolved Ba from the biomass / organic matter component of the critical zone and thus suggests that these pools are currently not at steady state. 4.7 Using Ba stable isotopes to refine the river mass budget of major elements 685 The above analysis shows that the cycling of Ba (and those of other rock-derived nutrients) by land biota is a significant component of terrestrial biogeochemical cycles. As a consequence, biological cycling within a catchment and the routing, or exchange, of rock-derived elements amongst the different compartments of the critical zone could bear consequence on the dissolved riverine export of major nutrients (Ca, Mg, K) that are traditionally used to estimate alkalinity fluxes and CO 2 consumption by chemical weathering at the catchment scale. In other words, nutrients that are taken up by the biota to a 690 significant extent simply "go missing" in the river dissolved export fluxes. In the following, we add to existing inventories of river-borne cations concentrations deriving strictly from silicate weathering a component taken up by the biota, in order to update estimates of CO 2 consumption fluxes by silicate weathering reaction at the basin scale in the light of our findings (see Appendix D for details).
First noting that the biological uptake flux of any nutrient X is: with [X] bio the concentration of a major soluble element X (Ca, K or Mg, [N a] bio being negligible as Na is not a nutrient) retained by the biosphere, and (X/Ba) bio the X/Ba ratio of the organic component. The (X/Ba) bio ratio is obtained from our own compilation of the chemical composition of the vegetation (Li, 2000;Chiarenzelli et al., 2001;Bullen and Bailey, 2005;Vaganov et al., 2013, ;Table S.7).
[X] bio can then be added to the silicate-derived dissolved river concentration of X 700 in the calculation of "corrected" silicate weathering fluxes (R (sil+bio)/sil ). To that aim, we express the impact of biological cycling on silicate weathering fluxes as the ratio between cation deriving from silicate weathering added from that deriving from biological cycling (W silcorr ) and uncorrected cation (W sil ): W sil is calculated using the sum of the concentration of each X element from silicate weathering and is expressed in meq/L, Dellinger et al. (2015b)). As our primary interest is to quantify the effect of biological cycling on CO 2 consumption, we do not consider the SiO 2 component of the weathering flux in our analysis. R (sil+bio)/sil values range from 1.1 +1.7 −0.1 (Huallaga River) to 4.8 +3.0 −1.6 (Trombetas River; Table S.8), while the value for the Amazon at mouth is 2.1 +1.1 −0.5 . These numbers show that the CO 2 consumption by silicate weathering, once corrected for 710 biological uptake, could be higher by a factor of around two across the Amazon Basin compared to previous estimates. Despite significant uncertainties, this analysis shows that river-derived weathering fluxes warrant re-evaluation regarding the potential role played by the biota as a storage of rock-derived nutrients.

Conclusions
In the Amazon, the abundance and isotope composition of Ba -which we show to be sourced mainly from silicate rocks -is controlled by a combination of the formation of secondary weathering products and biological uptake, with a stronger isotope effect of the latter. This "nutrient-like behavior" enables the use of Ba as a surrogate for major rock-derived nutrients, and allows us to examine the relationships between rock-derived nutrient cycling, weathering, and ecosystem dynamics.
Using isotope mass balance and estimates of isotope fractionation factors, we are able to propose a quantitative pattern for the partitioning of Ba liberated in the critical zone through rock weathering amongst secondary phases of weathering, the The proportion of Ba remaining in solution compared to that "initially" released by mineral dissolution is negatively correlated to denudation rates and positively correlated to weathering intensity, reflecting the combined effects of scavenging by secondary mineral precipitation and biological uptake. Biological uptake of Ba is found to be stronger in the Andes, possibly reflecting the need for the biota to compensate for the loss of organic components lost by erosion. In the plains, where de-730 nudation rate is low and energy available for litter remineralization is high, organic-bound Ba can be released from litter such that additional biological uptake from rock weathering is not required to replace the loss or nutrients bound to solid organic material by the ecosystem.
Finally, using the estimated uptake of Ba by the biosphere, we re-assess silicate weathering fluxes calculated from the cation loads of rivers with the effect of biological uptake now corrected for. We show that the cation dissolved load at the mouth of the 735 Amazon is significantly underestimated, shifting best estimates of CO 2 consumption deduced from the cation dissolved load.
This observation should be confirmed by using other rock-derived nutrients to reduce the uncertainties. Further, we believe that the method developed in this study to account for contributions from biological cycling should be extended to other large rivers in order to re-assess the CO 2 consumption at a global scale.
To conclude, our work shows that barium and its isotopes can be used to track biological cycling of rock-derived nutrients in 740 large river basins and reveal its impact on the routing of nutrients throughout the critical zone. Such an informative approach warrants extension to other settings and other isotope systems in order to further reveal the role played by Life on chemical weathering process.

Appendices
Appendix A: Identification of dissolved Ba sources in the Amazon Basin rivers 745 Spatial variation in dissolved Ba abundance and isotope composition throughout the Amazon Basin could be due to source effects. For this reason, it is necessary to assess the relative contribution of atmospheric deposition and of release from different rock sources to the Ba river dissolved load .
Rain water is most likely not a significant source of Ba given the low concentration of dissolved Ba in surface seawater (a common source of solutes to rainwater) compared to that of dissolved Ba in rivers (Gaillardet et al., 2003). It is possible to 750 further quantify the contribution of rain-derived Ba following: where [Ba] * riv is the dissolved concentration of dissolved Ba in the river corrected from rain inputs, [Ba] riv the measured concentration of Ba of the river, [Cl] atm the concentration of dissolved Cl derived from the atmosphere following Gaillardet et al. (1997), and (Ba/Cl) atm the seawater Ba/Cl ratio ≈ 2x10 −7 assuming that sea salts are the sole Ba contributor to rain.

755
Following this calculation, Ba derived from rain inputs is less than 1% of the total dissolved Ba for all rivers analyzed here.
Carbonate rocks formed in ancient marine environments are one of the most important sources of dissolved alkali-earth elements to rivers. However, the abundance of Ba in modern oceans is controlled by barite formation, rather than by carbonate precipitation (Dehairs et al., 1980). None of the Ca*/Na* vs. Ba*/Na* and δ 138 Ba vs. Ca*/Na* plots (Fig. S7a,b) show a correlation that could indicate mixing between a silicate and a carbonate weathering end member as a control on dissolved 760 Ba abundance. We can assess the proportion of river dissolved Ba derived from carbonate weathering using the α carbonate Ca (proportion of riverine dissolved Ca derived from carbonate weathering) from Dellinger et al. (2015b) using: where [Ba] * * riv is the dissolved concentration of Ba corrected from both rain and carbonate inputs; [Ca] riv is the measured concentration of dissolved Ca in the river; and (Ba/Ca) carb the Ba*/Ca* ratio of rivers draining only carbonate rocks (see 765   Table S.2), corrected from rain inputs, equal to 5x10 −5 (median of n = 12 measurements; Fig. S1). The highest proportion of dissolved Ba derived from carbonate rocks was found for the Madre de Dios river (about 10%), whereas carbonate weathering inputs to the Ba dissolved load for other tributaries do not exceed 5%.
In aqueous solutions, Ba shows a high affinity for sulfate ions, which leads to the formation of barite (BaSO 4 ) in oceans and marine sediments. In particular, pre-concentration of Ba and SO 4 induced by organic matter decay in micro-environments 770 leads to the precipitation of BaSO 4 (Griffith and Paytan, 2012). It has been also shown that the weathering of organic-rich sedimentary rocks such as black shales can be an important input of dissolved Ba to rivers (Dalai et al., 2002) which could be due to presence of barite in these rocks (Arndt et al., 2009). In addition, as an alkali-earth element, Ba could be contained in trace but significant amounts in gypsum, which could also contribute to the river dissolved Ba budget. To test for both the influence of gypsum and barite dissolution, SO 4 */Na* vs. Ba*/Na* and δ 138 Ba vs. SO 4 */Na* are plotted in Fig. S7c ,d. No 775 correlation can be observed between these parameters, implying that neither gypsum nor barite represent significant sources of river dissolved Ba in the Amazon Basin. To conclude, dissolved Ba in the Amazon Basin is almost exclusively derived from silicate rocks, and in our analysis we use our estimates of [Ba] * of eq. (A1) as reflecting silicate-derived inputs.

Appendix B: Parameters and assumptions of the Ba isotope mass balance
The estimation of f Ba bio from eq. (8) requires the estimation of several parameters, which we review hereafter.

780
Source rock Ba abundance ((Ba/N a) 0 ) In order to compute the values of f Ba diss , the source ratio (Ba/N a) 0 first needs to be constrained. In the case of lithologically mixed basins, it can be calculated as:  Fig. S1).

790
The value of δ Ba rock to be used in eq. (8) depends on the relative contribution of each source rock type to the Ba dissolved flux. Three main silicate rocks have to be considered as potential sources of Ba for the Amazon basin: shales, andesites and plutonic rocks. First, using the relative contribution of Na (α N a i ) calculated by Dellinger et al. (2015b), we can estimate the relative Ba contribution from each rock following: Then, the average δ Ba rock value can then be calculated as: with δ Ba rock the Ba isotope composition of each source rock i. We use our own measurements for shales (δ Ba rockshales = -0.02±0.04‰; n = 4) and data from literature (Van Zuilen et al., 2016b;Nan et al., 2018) for andesites (δ Ba rockandesite = 0.07±0.02‰; n = 7) and plutonic rocks (δ Ba rockplutonic = 0.00±0.04‰; n = 71).

800
Ba isotope fractionation factor associated to the formation of secondary weathering products (∆ Ba sec−diss ) As discussed above in section 4.1, secondary phases, e.g. clays or oxy-hydroxides, can at least partially drive the isotope composition of dissolved Ba in rivers . No experimental study on Ba isotope fractionation during precipitation of secondary weathering phases has been carried out to date, except for sorption on silica hydrogel which did not result in a strong Ba isotope fractionation (Van Zuilen et al., 2016a). Nevertheless, we can try to assess a Ba isotope fractionation factor 805 during formation of clays and oxides using our own measurements and previously published data. Marine clays do not show large variations in δ 138 Ba, with an isotope composition slightly depleted (by ∼ -0.05 ‰) in heavy isotopes with respect to igneous and sedimentary rocks (Bridgestock et al., 2018). Barium isotope fractionation during formation of secondary weathering products can also be estimated from data on soils. The difference between soil water and bulk solid soil Ba isotope composition over a latosol profile in China ranges from -0.01‰ to -0.18‰ (average value of -0.09‰), likely induced by the difference in 810 mineralogical composition, and by the varying respective role of sorption and precipitation over the profile .
The large river approach undertaken here likely mitigates such effects of mineralogical heterogeneity, allowing for considering one "lumped" isotope fractionation factor (Bouchez et al., 2013). Our own measurement of Ba isotopes in sediments from the Amazon rivers show the same slight depletion in heavy isotopes compared to shales from the Amazon Basin (this study), or to published data on andesites (Van Zuilen et al., 2016b), with δ 138 Ba values ranging from -0.05 to -0.10 ‰, consistent with the 815 estimates reached above. Therefore, taking into account the above constraints and the associated uncertainty, we estimate that ∆ Ba sec−diss = -0.09±0.05‰. Ba isotope fractionation factor associated to biological uptake (∆ Ba bio−diss ) Bullen and Chadwick (2016) showed that the isotopic composition of dissolved Ba in the critical zone is strongly impacted by biological processes. However, no proper estimate of the Ba isotope fractionation factor associated to biological uptake is 820 available yet. In order to represent the poor constraints on this parameter we consider ∆ Ba bio−diss = -0.25 to -0.75 using three δ 138 Ba values reported by Bullen and Chadwick (2016) for vegetation samples, and propagated uncertainty on this parameter in the following calculations assuming a uniform distribution between these values.

Discussing the steady-state assumption
Eq. (7) assumes that the Ba-bearing materials exported by rivers (excluding primary minerals, i.e. dissolved Ba, organics, 825 and secondary weathering phases) correspond to all Ba derived from rock dissolution, thereby achieving Ba steady-state for all critical zone compartments. In such case, the net formation of each secondary phase can be envisaged to be compensated for by an erosion flux, as proposed in Bouchez et al. (2013).
In first "non-steady state scenario", the organic reservoir (biota + soil solid organics) grows simply because litter fall and erosion of organic matter are outpaced by biological uptake. In such a scenario, the isotopic composition of the dissolved Ba 830 exported by rivers would not change. Therefore, in this case, the strict steady-state assumption can be relaxed for the organic (biota plus soil organic matter) reservoir without undermining the validity of the steady state isotope mass balance of eq. (7).
Another possibility for non-steady state dynamics is the scenario where litter remineralization releases Ba to waters faster than Ba is taken up by vegetation (implying that the organic reservoir decreases in size), in which case the steady state assumption of the dissolved Ba reservoir is not met, compromising the use of eq. (7) above which derives from a steady-state 835 framework (Bouchez et al., 2013). We first note that negative f Ba bio values, which should result from such cases where reminer-alization is outpaced by uptake, are only observed for three rivers from our dataset. Second, if f Ba bio < 0, over sufficiently short time scales the isotope composition of dissolved Ba can then rather be interpreted as a mixture between i) a "rock-derived" end-member, possibly affected by the formation of secondary phases of weathering and ii) an organic-derived end-member.
Appendix C: River mass budget assumption and derivation 840 Here we present in detail the different assumption and derivation requiered to performed river mass budget in section 4.5.
Quantitatively speaking, for an "equilibrated" mass budget, the amount of Ba delivered to the Earth surface by rock uplift and conversion into critical zone material, should be equal to the sum of Ba dissolved (F Ba diss ) and solid (F Ba sed ) exports by rivers: Using term D × [Ba] rock (with [Ba] rock the abundance of Ba in the source rock) in eq. C1 is equivalent to assuming that 845 the denudation rate D is a proxy for the supply of rock material to the Earth surface. We acknowledge that D can be seen as an imperfect proxy for the supply of rock material to the Earth surface because its validity requires that the export of material by the river is equal to the supply of rock at depth, hence that some form of steady state exists for the regolith covering the Earth surface. However, we take the fact that in the Amazon the Li river mass budget (using eq. (C1)) is at equilibrium (Dellinger et al., 2015a) as a good indicator that this approach is reliable. We also note that this estimate of Ba supply to the Earth surface 850 neglects inputs from rock-derived nutrients from global dust (Abouchami et al., 2013;Moran-Zuloaga et al., 2018), which can be important in the Amazon lowlands (see discussion in section 4.5).
The same equation can be written for Th, which is an insoluble element with a magmatic compatibility close to that of Ba (Gaillardet et al., 1999a), thus minimizing the influence of the crustal composition when using rock Ba/Th ratios (see below): The term (Ba/T h) n in eq. (C4) correspond to the inverse of the α-depletion factor of soluble elements in river sediments, introduced by Gaillardet et al. (1999a); and is conceptually equivalent to 1 + τ Ba,T h where τ Ba,T h is the mass transfer coefficient developed for quantify the depletion in soluble elements in soils (Brimhall and Dietrich, 1987). Finally, given the definition of w Ba (eq. (3), called hereafter "w Ba f luxes " (for better distinction with "w Ba iso " calculated below), an equilibrated river 865 mass budget should thus result in: Both parameters should in principle take values between 0 and 1, and we note that in our dataset, as Ba is always depleted over Th in the measured river sediment material compared to rocks, (Ba/T h) n is between 0 and 1. Regarding w Ba f luxes , it is important to note that eq. (3) can be used based on river sediment gauging (yielding the averaged [spm]) as in eq. (3), or 870 through: Using eq. (3), w Ba f luxes is by construction between 0 and 1, whereas if eq. (C6) is used, it is possible that w Ba f luxes takes values higher than 1 because the numerator and the denominator of the right-hand side of eq. C6 are evaluated in independent ways, and using metrics reflecting different time scales of critical zone dynamics. However, in our dataset, regardless of the way 875 w Ba f luxes is calculated all values calculated for w Ba f luxes in the Amazon Basin are between 0 and 1. (Ba/T h) rock in (Ba/T h) n is estimated for each river using the rock contributions given by Dellinger et al. (2017), and the Ba/Th ratios of individual rock types (equal to 48 for igneous plutonic and shale rocks -which have a similar Ba/Th ratio -and of 140 for andesites; Table S.6).
The isotope mass balance model presented in section 4.3 allows to estimate f Ba bio , which is a relative, hence non-dimensional flux of Ba biological uptake, with respect to the flux of Ba release from rock partial dissolution. In section 4.7, our analysis  Dellinger, M., Gaillardet, J., Bouchez, J., Calmels, D., Louvat, P., Dosseto, A., Gorge, C., Alanoca, L.,