Philippe Négrel
email: p.negrel@brgm.fr

Romain Millot

Lithium isotopic fingerprints of sources and processes in surface waters of the Ebro River Basin (Spain)

Keywords: Ebro River, Li isotopes, dissolved load, evaporite, carbonate

The Ebro River in north-eastern Spain is among the largest contributors of freshwater to the Mediterranean Sea and ends in the Ebro delta, one of the major wetlands in Europe. The bedrock of the Ebro River basin mainly consists of carbonate rocks and evaporites of Paleozoic and Mesozoic age, and the river flows through several large cities, and agricultural and industrial areas. The Ebro River outlet at Amposta was sampled once a month for a year (2006), and a field campaign in April of the same year sampled the Ebro along its main course as well as its principal tributaries. In the present study, the behaviour of Li and its isotopes was investigated at basin scale, with the objective of elucidating the processes controlling the isotope signatures of a large river draining mostly sedimentary bedrock. δ 7 Li values ranged from +17.1‰ to +18.3‰ along the Ebro main stream, and between +16.3 and +18.9‰ at the outlet. In the major tributaries, the δ 7 Li values ranged from +12.9‰ to +20.9‰, with bedrock values ranging from +0.5 to +29.3‰. Comparing Li concentrations with Cl and SO4 ones, it appears that evaporite weathering plays an important role in controlling Li, but no anthropogenic agricultural or industrial influence on Li concentrations was detected. The Na/Li, Cl/Li and SO4/Li ratios clearly reflect the role of halite dissolution for some tributaries (Gallego, Ega and Aragon), gypsum dominating others (Guadalope, Matarrana, Huerva and Segre), and little influence of carbonate in all tributaries, the Ebro itself being a mixture of all tributaries. We tentatively applied the simple Rayleigh fractionation model, but most δ 7 Li values of the Ebro water samples plotted away from the fractionation line, reinforcing the major role of mixing processes in the Ebro basin, rather than fractionation processes during water/rock interactions. A comparison of δ 7 Li values and 87 Sr/ 86 Sr ratios further demonstrates the role of gypsum/anhydrite and limestone in the Ebro and its tributaries.

Sr-isotopes show a non-negligible role of carbonate dissolution, generally considered to be weak in the control of the lithium cycle in catchments.

-Introduction

Lithium is one of the modern tools for studying water-rock interaction processes. This is done by coupling geochemical processes during such processes, with the capability of lithium to go into the fluid phase with significant mass-dependent fractionation between the two stable isotopes 6 Li (natural abundance 7.5%) and 7 Li (natural abundance 92.5%) [START_REF] Huh | Lithium and its isotopes in major world rivers: implications for weathering and the oceanic budget[END_REF][START_REF] Huh | Lithium isotopes as a probe of weathering processes: Orinoco River[END_REF][START_REF] Pistiner | Lithium-isotope fractionation during continental weathering processes[END_REF][START_REF] Rudnick | Extreme lithium isotopic fractionation during continental weathering revealed in saprolites from South Carolina[END_REF]Kisakürek et al., 2004;[START_REF] Pogge Von Strandmann | Riverine behaviour of uranium and lithium isotopes in an actively glaciated basaltic terrain[END_REF], 2014, 2021;[START_REF] Millot | Multi-isotopic (Li, B, Sr, Nd) approach for geothermal reservoir characterization in the Limagne Basin (Massif Central, France)[END_REF]Millot et al., , 2010a, b;, b;[START_REF] Négrel | Heterogeneities and interconnections in groundwaters: Coupled B, Li and stable-isotope variations in a large aquifer system (Eocene Sand aquifer, Southwestern France)[END_REF][START_REF] Dellinger | Lithium isotopes in large rivers reveal the cannibalistic nature of modern continental weathering and erosion[END_REF]2015;[START_REF] Henchiri | Riverine dissolved lithium isotopic signatures in low-relief central Africa and their link to weathering regimes[END_REF]Négrel and Millot, 2019;[START_REF] Qi | Lithium and its isotopes as tracers of groundwater salinization: a study in the southern coastal plain of Laizhou Bay, China[END_REF][START_REF] Martin | Lithium and strontium isotope dynamics in a carbonate island aquifer, Rottnest Island, Western Australia[END_REF][START_REF] Steinhoefel | Lithium isotopic fractionation during weathering and erosion of shale[END_REF][START_REF] Millot | Lithium isotopes in the Loire River Basin (France): hydrogeochemical characterizations at two complementary scales[END_REF]. Recently, the variation in δ 7 Li values of water was used for distinguishing between natural and anthropogenic inputs because lithium isotopes have been shown to be a probe for tracing anthropogenic activity [START_REF] Choi | The impact of anthropogenic inputs on lithium content in river and tap water[END_REF][START_REF] Négrel | Lithium isotopes as tracers of groundwater circulation in a peat land[END_REF]Négrel et al., , 2019;;[START_REF] Millot | Lithium isotopes in the Loire River Basin (France): hydrogeochemical characterizations at two complementary scales[END_REF].

Lithium and its isotopes are of increasing interest in weathering studies through rivers dissolved and suspended loads and groundwaters because Li is solubilized from minerals and rocks during water-rock interactions (e.g. a mobile element) and not constrained by biological processes. Such chemical weathering induces isotopic fractionation resulting in an enrichment of the heavy isotope (7Li) in solution, the light isotope (6Li) being preferentially retained in secondary weathering mineral phases (see Négrel and Millot (2019) and references therein).

In systems where few secondary phases are formed, lithium can evolve in terms of a tool tracing the mixtures between waters (see [START_REF] Négrel | Lithium isotopes as tracers of groundwater circulation in a peat land[END_REF] and references therein).

The weathering of silicate rocks is a major process at the earth's surface and to better understand this process, many studies have deployed the use lithium isotopes(e.g., [START_REF] Burton | Lithium isotopes as tracers in marine and terrestrial environments[END_REF]Steinhoefel et al., 2021 and references therein). However, carbonate and evaporite weathering processes have hardly been studied through Li-isotope variations [START_REF] Gou | Li isotopes in the middle Yellow River: Seasonal variability, sources and fractionation[END_REF][START_REF] Martin | Lithium and strontium isotope dynamics in a carbonate island aquifer, Rottnest Island, Western Australia[END_REF]. This can be explained by two features: i) Li contents in evaporite and carbonate are low (<12 µg g -1 ) compared to silicate rocks (20-40 µg g -1 in granite and around 60 µg g -1 in shales); and ii) the most common rock types in Europe are 39% plutonic and metamorphic rocks, 37% shales, 14% carbonate rocks, 9.5% sandsandstones, and volcanic rocks and evaporites playing a subordinate role [START_REF] Caritat | Comparing results from two continental geochemical surveys to world soil composition and deriving Predicted Empirical Global Soil (PEGS2) reference values[END_REF].

Here, we focus on Li-isotope data from the dissolved load of 25 river-water samples collected in the Ebro Basin and of 2 groundwater samples. Among the rivers providing freshwater in the Mediteranean Sea, the 2017 Mediterranean Quality Status Report (downloaded at https://www.medqsr.org/fr/node/230 on February 2023, 14th) classified the rivers having their outlet in the Mediterranean through their annual climatological discharge of freshwater in cubic metres per second. The Rhone and Po rivers have the highest discharge (1500-1800m 3 /s), then the Nile (1000-1500m 3 /s) followed by the Ebro and the Drin with 500-1000m 3 /s, reflecting the importance of the Ebro in the hydrologic cycle of the Mediterranean Sea. The last rivers supplying the Mediterranean are the Ceyhan, the Evros and the Tiber (150-500m 3 /s) and the Moulouya and Shellif (10-150m 3 /s). We measured lithium and its isotope values in all reservoirs, in parts of the basin affected by salinization and secondary processes (precipitation, re-dissolution, mixing of water and anthropization), as well as in the main bedrocks. Studies on river drainage basin having evaporite-type bedrocks are scarce and in these cases, the evaporitic deposits are often located in headwaters and are not very important in terms of surface area compared to the general geology (mainly silicate rocks) and to the size of these of large river basins. The δ 7 Li values generally observed in rivers draining evaporites are either around +20 ‰ [START_REF] Huh | Lithium and its isotopes in major world rivers: implications for weathering and the oceanic budget[END_REF][START_REF] Huh | Lithium isotopes as a probe of weathering processes: Orinoco River[END_REF][START_REF] Gou | Li isotopes in the middle Yellow River: Seasonal variability, sources and fractionation[END_REF]Yoon, 2010) but other rivers also influenced by evaporite dissolution have low δ 7 Li values, around +8‰ (Chen et al., 2002; Chetelat et al., 2008, 2009; Wang et al., 2015; Ma et al., 2020), whereas carbonate-dominated rivers are characterized by high δ 7 Li values (> +20‰). The objectives of our study were to constrain the Li cycling in a major river basin underlain by sedimentary rock and affected by climatic impact (drought and water deficit), and to examine Li in the rock-soil cycle through weathering processes and water use (agriculture, water reservoirs and industry), again within a climate-change context.

-Characteristics of the Ebro Basin

The Ebro River basin (Fig. 1) lies in north-eastern Spain, starting near the Atlantic coast in the Cantabrian Mountains and flowing to the western Mediterranean Sea. Over its 85,530 km² drainage basin and along its 928-km course, the Ebro River flows through several large cities (Lleida, Logroño, Vitoria, Zaragoza, Huesca and Barcelona), and through agricultural, mining and industrial areas. It is the largest Spanish river system and one of the largest contributors of freshwater to the Mediterranean Sea (CHE, http://www.chebro.es/).

The geology of the Ebro Basin consists of (Guillén and Palanques, 1992;[START_REF] Luzón | Sedimentary record of Pleistocene paleodoline evolution in the Ebro basin (NE Spain)[END_REF][START_REF] Mochales | Magnetic prospection as an efficient tool for doline detection: a case study in the central Ebro Basin (northern Spain)[END_REF] Mediterranean Sea (lower part of the Ebro River). The occurrence of evaporite deposits in the Ebro River basin has been documented in detail [START_REF] Castillo Herrador | Le Trias évaporitique des bassins de la Vallée de l'Ebre et de Cuenca[END_REF]Birnbaum, 1976;[START_REF] Ortì | Introducción a las evaporitas de la Cuenca Terciaria del Ebro[END_REF][START_REF] Utrilla | Oxygen and sulfur isotope compositions as indicators of the origin of Mesozoic and Cenozoic evaporites from Spain[END_REF][START_REF] Elorza | Geomorphology of the Tertiary gypsum formations in the Ebro Depression (Spain)[END_REF].

The main tributaries of the Ebro are the Aragon, Gallego, Cinca and Segre rivers (northern part of the basin, Fig. 1) flowing through silicate rocks of the Pyrenees Mountains in their upper part, and through sedimentary rocks downstream. In the southern part of the basin, the main tributaries are the Huerva, Guadalope and Matarrana (Fig. 1), flowing over sedimentary rocks. The catchment of the Ega River, a tributary in the upper part of the basin, consists of sedimentary and metamorphic Palaeozoic and Mesozoic rocks of the Iberian Chain. The four described climatic areas in the Ebro Basin [START_REF] Batalla | Reservoir-induced hydrological changes in the Ebro River Basin, NE Spain[END_REF] are the Atlantic headwaters (annual average precipitation about 900 mm and contribution to runoff 23%), the west-central Pyrenees (950 mm, 31%), the eastern Pyrenees (800 mm, 41%) and the southern Mediterranean zone (500 mm, 5%), with a mean annual runoff of approximately 6837.10 6 m 3 . Basin. The main river was sampled upstream and downstream from the confluences of the main tributaries, numbers 1 to 5 (number 5 being Tortosa); the tributaries were sampled at numbers 7 to 14. The Ebro outlet at Amposta (number 6; [START_REF] Cruzado | Nutrient fluxes from the Ebro River and subsequent across-shelf dispersion[END_REF] [START_REF] Négrel | Long-term fluxes of dissolved and suspended matter in the Ebro River Basin (Spain)[END_REF]. b-Geological sketch map of ythe Ebor Basin, modified from [START_REF] Luzón | Sedimentary record of Pleistocene paleodoline evolution in the Ebro basin (NE Spain)[END_REF][START_REF] Mochales | Magnetic prospection as an efficient tool for doline detection: a case study in the central Ebro Basin (northern Spain)[END_REF].

Pyrenees C a t a l a n C h a i n

The discharge of the Ebro River decreased from around 590 m 3 s -1 in the "natural" period 1914-1935, by 28% to 430 m 3 s -1 in the period 1960-1990 because of increased water use for irrigation, reservoir storage and electricity production, and domestic consumption [START_REF] Che | Plan Hidrológico de la cuenca del Ebro[END_REF][START_REF] Ibáñez | Changes in the hydrology and sediment transport produced by large dams on the lower Ebro River and its estuary[END_REF]. The main water use is for irrigation with almost 700,000 irrigated hectares (total water demand of 6310 Hm 3 y -1 , [START_REF] Che | Plan Hidrológico de la cuenca del Ebro[END_REF]INE, 2003), causing a huge hydraulic deficit. Nearly 60% of the surface area of the Ebro River Basin is covered by agricultural land, and around 50% of Spain's electricity is provided by hydroelectric power plants along the Ebro system, causing another deficit. Around 14% of land use concerns urban areas and industry, mainly located in the valleys.

More information on dissolved and suspended matter fluxes and weathering processes can be found in the different investigations we have conducted in the Ebro River catchment several, studying fluxes of [START_REF] Négrel | Long-term fluxes of dissolved and suspended matter in the Ebro River Basin (Spain)[END_REF][START_REF] Négrel | Tracing water cycle in regulated basin using stable δ 18 O-δ 2 H isotopes: The Ebro river basin (Spain)[END_REF][START_REF] Négrel | Ca and Sr isotope constraints on chemical weathering processes: A view through the Ebro river basin, Spain[END_REF][START_REF] Petelet-Giraud | Dissolved fluxes of the Ebro River Basin (Spain): Impact of main lithologies and role of tributaries[END_REF].

-Material and methods

Water and rock sampling

The Ebro River and its main tributaries were sampled in the centre of each river channel from bridges (April 2006, Fig. 1). The main channel (samples 1 to 5, Fig. 1) was sampled upstream and downstream from the confluences of the main tributaries (7 to 14, Fig. 1). In order to monitor compositional variations over time in the river flow, the Ebro outlet at Amposta (6, Fig. 1; [START_REF] Cruzado | Nutrient fluxes from the Ebro River and subsequent across-shelf dispersion[END_REF]

Methods

After collection, the water samples were filtered through pre-cleaned 0.45 μm acetate filters;

100 mL was acidified with double-distilled nitric acid to pH around 2 and stored in precleaned polyethylene bottles for major-cation analyses, and a further 100 mL was stored unacidified in polyethylene bottles for anion analysis. The water samples were analysed by ion chromatography for major ions, and by ICP-AES for Ca, Na, K, Mg and ICP-MS for trace elements (accuracy 5-10%) using protocols under accreditation. External and in-house standards as well as reference materials was used to calibrate and validate the values.

Alkalinity was determined by the Gran titration method. We used HCl acid to titrate beyond the equivalence point. The quantity of acid added to the pH around 3 is used to determine this equivalence point with a mathematical method Lithium-isotopic compositions [START_REF] Millot | Accurate and high precision measurement of lithium isotopes in two reference materials by MC-ICP-MS[END_REF] were measured with a Neptune

Multi-Collector ICP-MS (Thermo Fisher Scientific). Chemical separation of lithium from the matrix before mass analysis used cationic resin (BioRad AG® 50 W-X12, 200-400 mesh)

and HCl acid (0.2 N) for 30 ng of lithium. Blanks for total chemical extraction were less than 20-30 pg Li, which is negligible as it represents a 10 -3 blank/sample ratio. The 7 Li/ 6 Li ratios were normalized to a δ 7 Li determination of about 0.1-0.2‰ (2σm). Accuracy and reproducibility of the total method (purification procedure + mass analysis) were tested by repeated measurement of a seawater sample (IRMM BCR-403) after separation of lithium from the matrix, for which we obtained a mean value of δ 7 Li=+30.8‰ ± 0.4 (2σ, n=15) over the duration of the analyses. This mean value agrees with our long-term measurements (δ 7 Li=+31.0‰ ± 0.5, 2σ, n=30).

-Results

Table 1 contains all analytical results for the different bedrocks and Table 2 contains data for the river water and groundwater.

Bedrock

The highest lithium content is observed in Trias-Keuper D anhydrite with a maximum around 11.3 µg g -1 , whereas the Oligocene B gypsum and Oligocene H carbonate have low lithium contents (about 1.4 to 1.7 µg g -1 ). The δ 7 Li ranges from +0.5 to +0.9‰ for the lowest values, observed in Miocene A continental gypsum (Li content about 8.8 µg g -1 ) and in Paleocene G continental carbonate (Li content about 3.7 µg g -1 ), up to +29.5‰ in Trias-Keuper D anhydrite and a highest Li content of around 11.3 µg g -1 .

Tributaries, Ebro main channel, and outlet survey 193

The eight sampled tributaries of the Ebro River (Fig. 1) show a minimum Li content of around 194 12 µg l -1 in the Rio Aragon and a maximum value of 66.9 µg l -1 in the Rio Guadalope. The 195 δ 7 Li value ranges from +12.9‰ in Rio Matarrana to +20.9‰ in the Rio Cinca. 196 Similar to other studies of downstream and/or seasonal changes of lithium isotope 204 ratios in river systems [START_REF] Farber | The origin and mechanisms of salinization of the Lower Jordan River[END_REF][START_REF] Manaka | Downstream and seasonal changes of lithium isotope ratios in the Ganges-Brahmaputra river system[END_REF]Pogge von Strandmann et al., 205 2017), we present their variation along the Ebro. Samples were collected from 100 km 206 downstream of the river source to nearly the outlet, 450 km downstream.. The Li contents in 207 tributaries, the main channel and the sampling-location distance from the source are plotted 208 on Figure 2a, and the δ 7 Li values on Figure 2b. 209 ) and (b) δ 7 Li (‰) values with distance from the source (0 km) to the outlet (500 km) for the Ebro main channel and tributaries. The variations at the outlet (Amposta, number 6 in Fig. 1a) are plotted with their sampling month; the red circle marks the Amposta sampling at the same time as the Ebro main-stream sampling.

The Li content in samples collected along the Ebro increases from 5 µg L -1 farthest upstream, to 23 µg L -1 350 km downstream, and then decreases to 15 µg L -1 just before Amposta. During the survey in Amposta, Li contents varied between 12 µg L -1 in May and 36 µg L -1 in November. The δ 7 Li values along the main channel increased slightly from +17.1‰ in Miranda de Ebro up to +18.3‰ in Lodosa and then, until Tortosa, remained invariant around +16.5‰ (Fig. 2b). At Amposta, the δ 7 Li value ranged between +16.3 and +18.9‰. Please note the difference between the δ 7 Li values in Amposta and Tortosa (a few km upstream), whereas Li contents remained similar. This agrees with the discrepancies noted for the δ 44 CaSW and Ca contents in the same sample set [START_REF] Négrel | Ca and Sr isotope constraints on chemical weathering processes: A view through the Ebro river basin, Spain[END_REF]. This difference may be related to the fact that these isotopic systems are sensitive to fractionation processes [START_REF] Dellinger | Riverine Li isotope fractionation in the Amazon River basin controlled by the weathering regimes[END_REF][START_REF] Négrel | Li and δ 7 Li as proxies for weathering and anthropogenic activities: application to the Dommel River (Meuse basin)[END_REF]2021), and to the presence of dams between Tortosa and Amposta increasing fractionation [START_REF] Gou | Li isotopes in the middle Yellow River: Seasonal variability, sources and fractionation[END_REF]

-Discussion

Relative contribution to the dissolved Li load

It is generally agreed that dissolved Li in most of the world's major rivers comes from silicate weathering, and that the fraction derived from carbonate rocks or evaporite is negligible (e.g., Kisakűrek et al., 2005;[START_REF] Gou | Li isotopes in the middle Yellow River: Seasonal variability, sources and fractionation[END_REF][START_REF] Murphy | Tracing silicate weathering processes in the permafrost-dominated Lena River watershed using lithium isotopes[END_REF][START_REF] Martin | Lithium and strontium isotope dynamics in a carbonate island aquifer, Rottnest Island, Western Australia[END_REF]. In addition, atmospheric deposition from cyclic salts plays a very minor role in the dissolved Li budget [START_REF] Dellinger | Riverine Li isotope fractionation in the Amazon River basin controlled by the weathering regimes[END_REF][START_REF] Song | Deciphering the signatures of weathering and erosion processes and the effects of river management on Li isotopes in the subtropical Pearl River basin[END_REF]. To overcome this input on the Ebro Basin, we corrected only for marine aerosols using the characteristics of modern seawater

The Li concentration from atmospheric input is given by multiplying the Cl concentration from rainwater by the Li/Cl ratio in seawater [START_REF] Négrel | Erosion sources determined from inversion of major, trace element values and strontium isotopic values in riverwater: the Congo Basin case[END_REF][START_REF] Dellinger | Riverine Li isotope fractionation in the Amazon River basin controlled by the weathering regimes[END_REF]. With a maximum estimated chlorine concentration of 85 µmol L -1 deriving from marine input [START_REF] Avilla | Relationship between precipitation chemistry and meteorological situations at a rural site in NE Spain[END_REF], and a seawater Li/Cl ratio of 5x10 -5 (Millot et al., 2010a), the calculated Li input from rain is low, with a maximum estimated contribution of rainwater-derived Li in the Ebro Basin of 0.04-0.20% for the main tributaries, 0.10-0.40% for the Ebro, and 0.09-0.20% for the outlet. In the Ebro Basin, due to its geological framework, the contribution of carbonate and evaporite dissolution to the dissolved load should be the major input, while the one from silicate can be ignored [START_REF] Négrel | Long-term fluxes of dissolved and suspended matter in the Ebro River Basin (Spain)[END_REF]2021;[START_REF] Petelet-Giraud | Dissolved fluxes of the Ebro River Basin (Spain): Impact of main lithologies and role of tributaries[END_REF].

Figure 3 shows the binary plots between chemical elements in Ebro water, Li is compared to Cl (Fig. 3a) and SO4 (Fig. 3b). The dissolved load of the Ebro basin (tributaries, main channel, outlet and groundwater) is clearly controlled by gypsum/anhydrite and halite dissolution; few or none of the samples are close to the seawater dilution line regardless of the concentrations (Ega and GA2 groundwater (16, Fig. 1). As can be seen in Figures 3, two main evolution trends explaining most of the Ebro Basin samples, namely the halite-dissolution and gypsum/anhydrite -evolution lines, respectively constrained by variations in Cl and in SO4 concentration.

In the Cl vs. Li plot (Fig. 3a), the gypsum/anhydrite -evolution line explains the sample values in the Matarrana, Segre and Guadalope tributaries. The halite-dissolution line explains the Aragon, Ega and Gallego tributaries, as well as the samples from the Ebro at 103 km and 241 km from the river source, several outlet results, and groundwater GA15. The rest of the samples plot between these two trends. In the SO4 vs. Li plot (Fig. 3b), the gypsum/anhydrite -evolution line explains the Gallego, Huerva, Segre and Guadalope tributaries, the Ebro sample at 103 km and 241 km from the river source, and groundwater GA15. The halite-dissolution line explains the Matarrana, Ega, Aragon and Cinca tributaries,

the Ebro samples at 281 km, 336 km and 543 km from the source, and all samples from the outlet surveys. The distribution along the two main evolution lines confirms that evaporite weathering plays an important role in controlling Li concentrations, as shown for Cl-SO4 [START_REF] Négrel | Long-term fluxes of dissolved and suspended matter in the Ebro River Basin (Spain)[END_REF][START_REF] Petelet-Giraud | Dissolved fluxes of the Ebro River Basin (Spain): Impact of main lithologies and role of tributaries[END_REF]. This is in agreement with [START_REF] Isidoro | River water quality and irrigated agriculture in the Ebro basin: An overview[END_REF] who argue that the salinity of water in the Ebro basin originates from three major sources, associated with three minerals, namely gypsum/anhydrite, halite and calcite.

Regarding a possible anthropogenic control on Li concentrations, in addition to bedrock sources of dissolved chloride-sulphate, the streams in the Ebro Basin are likely to integrate input from farming and industrial activities. Pollutant investigations have revealed high concentrations near industrial sites for persistent organic pollutants and heavy metal [START_REF] Bovolo | Climate change, water resources and pollution in the Ebro Basin: Towards an integrated approach[END_REF]. Among framing impacts, the main pressure on water quality in the Ebro basin is from irrigated areas through the irrigation return flow. The different components of the irrigation return flow are bypass waters, tail-waters and subsurface drainage waters that may be enriched in phosphorous, pesticides, salts and agrochemicals [START_REF] Aragües | Water quality of irrigation return flows[END_REF] and constitute generally the primary source of pollution. Heavy metal, pesticide and nutrient pollution are widespread in relation to farming activities (pesticides and fertilizers uses).Nitrates fluctuate little, between 4 mg L -1 (Gallego) and 19 mg L -1 (Huerva) for the maximum range observed in tributaries. Regarding the Ebro itself, the highest NO3 value (16 mg L -1 ) is observed at 281 km from the river source, decreasing to 9 mg L -1 at 543 km from the source. All outlet survey samples agree with this range of values (6 to 14 mg L -1 ).

No relation is observed between NO3 and Li concentrations and NO3 and Cl concentrations, except that the highest NO3 values correspond to the lowest Li ones. This shows the unrelated behaviour of these elements and the fact that no anthropogenic agricultural or industrial influence on Li can be detected in the Ebro Basin. Even in the two groundwater samples, the high NO3 concentrations (GA2 = 56 mg L -1 , GA15 = 88 mg L -1 ) are not mirrored by high Li contents, confirming the different origins of Li and NO3, with a major lithological control for Li.

Constraints added by Li isotopes: lithological control and fractionation processes

It is now well agreed that δ 7 Li values in river waters are higher than in the parent rocks, due to the strong fractionation between the 7 Li and 6 Li isotopes during weathering (e.g., [START_REF] Huh | Lithium and its isotopes in major world rivers: implications for weathering and the oceanic budget[END_REF][START_REF] Huh | Lithium isotopes as a probe of weathering processes: Orinoco River[END_REF][START_REF] Pistiner | Lithium-isotope fractionation during continental weathering processes[END_REF][START_REF] Kisakurek | Li and δ 7 Li in Himalayan rivers: proxies for silicate weathering? Earth Planet[END_REF][START_REF] Vigier | Quantifying Li isotope fractionation during smectite formation and implications for the Li cycle[END_REF]Millot et al., 2010a;[START_REF] Verney-Carron | Experimental determination of the role of diffusion on Li isotope fractionation during basaltic glass weathering[END_REF][START_REF] Dellinger | Riverine Li isotope fractionation in the Amazon River basin controlled by the weathering regimes[END_REF][START_REF] Wang | Behavior of lithium isotopes in the Changjiang River system: sources effects and response to weathering and erosion[END_REF][START_REF] Bagard | Lithium isotope fractionation in the Ganges-Brahmaputra floodplain and implications for groundwater impact on seawater isotopic composition[END_REF]Négrel and Millot, 2019;[START_REF] Gou | Li isotopes in the middle Yellow River: Seasonal variability, sources and fractionation[END_REF][START_REF] Steinhoefel | Lithium isotopic fractionation during weathering and erosion of shale[END_REF]. While the 6 Li isotope is preferentially retained and incorporated into secondary weathering products such as clays and oxides, the 7 Li isotope is enriched in the dissolved load, leading to relatively high δ 7 Li values in rivers.

The δ 7 Li values are commonly correlated with the Na/Li ratio (Millot et al., 2010;[START_REF] Dellinger | Riverine Li isotope fractionation in the Amazon River basin controlled by the weathering regimes[END_REF][START_REF] Wang | Behavior of lithium isotopes in the Changjiang River system: sources effects and response to weathering and erosion[END_REF][START_REF] Négrel | Li and δ 7 Li as proxies for weathering and anthropogenic activities: application to the Dommel River (Meuse basin)[END_REF] and less with the Cl/Li and SO4/Li ratios [START_REF] Liu | Isotope compositions of dissolved lithium in the rivers Jinshajiang, Lancangjiang, and Nujiang: Implications for weathering in Qinghai-Tibet Plateau[END_REF]. Figure 4 plots Na/Li ratios versus Cl/Li (4a) and SO4/ Li (4b) ones and, in addition to the halite and gypsum/anhydrite dissolution end-member, we consider here [START_REF] Parker | Composition of the Earth's crust[END_REF] carbonate dissolution end-member. Na/Li vs. SO4/Li ratios (in mol/mol). Na/Li versus Cl/Li ratios (Fig. 4a) show the role of halite and gypsum/anhydrite psum dissolution, but less that of carbonate. All samples plot along a linear trend with increasing Na/Li and Cl/Li ratios. More precisely than the relationships shown on Figure 3, because concentration effects are reduced when using element ratios, it appears that the Guadalope, Matarrana, Huerva and Segre tributary samples agree with gypsum/anhydrite dissolution, whereas the Gallego, Ega and Aragon ones and GA2 (groundwater) reflect the dissolution of halites. The Ebro samples at 103.5 km from the source appear shifted to the right due to carbonate dissolution, but some samples from the outlet surveys (August to November) are more influenced by halite dissolution when compared to the rest of the survey. The Na/Li versus SO4/Li ratios (Fig. 4b) reflect a more complex behaviour. Guadalope, Matarrana, Huerva and Segre still agree with gypsum/anhydrite dissolution, but Aragon and Cinca for the tributaries, and samples from the Ebro and the outlet show a lowering of SO4/Li ratios through carbonate dissolution. Gallego and Ega tributary samples and the August to November ones for the outlet are also affected by halite dissolution. Na and Li thus seem to be good indicators of rock-weathering processes in the Ebro Basin, combined as either Na/Li or Li/Na ratios.

It is generally accepted that a positive relationship between the Na/Li molar ratio and the δ 7 Li value relates to silicate weathering (Millot et al., 2010;[START_REF] Liu | Isotope compositions of dissolved lithium in the rivers Jinshajiang, Lancangjiang, and Nujiang: Implications for weathering in Qinghai-Tibet Plateau[END_REF][START_REF] Dellinger | Riverine Li isotope fractionation in the Amazon River basin controlled by the weathering regimes[END_REF][START_REF] Wang | Behavior of lithium isotopes in the Changjiang River system: sources effects and response to weathering and erosion[END_REF][START_REF] Négrel | Li and δ 7 Li as proxies for weathering and anthropogenic activities: application to the Dommel River (Meuse basin)[END_REF][START_REF] Steinhoefel | Lithium isotopic fractionation during weathering and erosion of shale[END_REF], whereas no relationship exists when water is strongly affected by evaporite dissolution [START_REF] Liu | Isotope compositions of dissolved lithium in the rivers Jinshajiang, Lancangjiang, and Nujiang: Implications for weathering in Qinghai-Tibet Plateau[END_REF][START_REF] Wang | Behavior of lithium isotopes in the Changjiang River system: sources effects and response to weathering and erosion[END_REF]. In the case of water-evaporite interaction, the Na/Li molar ratio can fluctuate strongly (200 to 550 on the Qinghai-Tibet Plateau; [START_REF] Liu | Isotope compositions of dissolved lithium in the rivers Jinshajiang, Lancangjiang, and Nujiang: Implications for weathering in Qinghai-Tibet Plateau[END_REF], but less than the variation observed in the Ebro Basin (400 to 3800; Fig. 5a). Referring to Figure 5, the Segre, Huerva, Matarrana and Guadalope samples are influenced by gypsum/anhydrite dissolution, whereas the Aragon, Gallego and Ega ones show halite-dissolution influence. Thus (Fig. 5a), as these two groups of rivers constitute the extremes of the Na/Li molar-ratio values, the main influence on this ratio is that of the nature of the weathered rocks rather than a fractionation effect (see below). The main feature of Figure 5a is the evidence of two end-members in the tributaries, one marked by gypsum/anhydrite dissolution with low Na/Li molar ratios and the other one marked by halite dissolution with a higher Na/Li molar ratio. Both end-members help explaining the variations observed in the Ebro itself and at the outlet, even if the variations are more marked for the Na/Li molar ratios rather than on the δ 7 Li values (Fig. 2a). This scheme reflects a mixing for Li and its isotopes in water being mainly affected by evaporite dissolution, even if the role of carbonate dissolution (less marked in Na concentrations) and a possible influence of Li-isotope fractionation cannot be precluded. The samples collected along the Ebro itself evolve along this mixing scheme. The most upstream value corresponds to an end-member characterized by halite dissolution, and farther downstream the samples are increasingly marked by a component defined by gypsum/anhydrite dissolution. Most of the samples collected at the Ebro outlet can be explained by a component characterized by gypsum/anhydrite dissolution, except for the samples from August to December, with a higher influence of the end-member defined by halite dissolution. Using O and H isotopes, [START_REF] Négrel | Tracing water cycle in regulated basin using stable δ 18 O-δ 2 H isotopes: The Ebro river basin (Spain)[END_REF] showed that from September to November, the Ebro at the outlet is mostly supplied by groundwater and some water retained by dams, as the main river discharge is low. This causes a data shift towards the halite-dissolution end-member, which is well reflected in the groundwater sample that exceeds the Na/Li molar ratio in the Gallego and Cinca waters, reflecting a large influence of evaporite dissolution. This can be due to a double influence of mainly halite dissolution and, secondarily, gypsum/anhydrite dissolution (Figs 2a

and 2b) for the E16 groundwater sample from a 7-m-deep irrigation well in Lleida (16, Fig. 1).

In order to complete this interpretation, we tentatively applied the simple Rayleigh fractionation model (Fig. 5b) that can describe Li removal from water to secondary phases, using the Li/Na molar ratio and the δ 7 Li values [START_REF] Bagard | Lithium isotope fractionation in the Ganges-Brahmaputra floodplain and implications for groundwater impact on seawater isotopic composition[END_REF][START_REF] Manaka | Downstream and seasonal changes of lithium isotope ratios in the Ganges-Brahmaputra river system[END_REF].

This model is described by the general equations:

δ 7 Liw=δ 7 Lii+1000(α-1) ln(f Li w)
(Eq. 1)

f Li w=Li/Naw/Li/Nai (Eq. 2)
where δ 7 Liw and δ 7 Lii are the Li isotope composition of the dissolved phase w and its initial value in the rocks i, α is the fractionation factor, and f Li w is the Li fraction remaining in the dissolved phase.

However, such a model requires an initial value for calculating the fractionation effect on the Li isotopes. Due to the congruent dissolution of evaporite deposits, we applied Eq. 1 on two initial values representative of the extreme rock end-members, and then examined the Rayleigh fractionation curves obtained by applying Eqs. 1 and 2. These end-members are the two gypsum samples, one from Miocene continental deposits (A in Table 12) with a δ 7 Lii of 0.49 and Li/Nai of 0.29, and the other from Oligocene continental deposits (B in Table 1) with a δ 7 Lii of 4.11 and Li/Nai of 0.0091. Values generally used for the fractionation factor α range from 0.996 to 0.993 [START_REF] Bagard | Lithium isotope fractionation in the Ganges-Brahmaputra floodplain and implications for groundwater impact on seawater isotopic composition[END_REF][START_REF] Manaka | Downstream and seasonal changes of lithium isotope ratios in the Ganges-Brahmaputra river system[END_REF]-the latter being accepted for the Ganges, and down to 0.991 for the Amazon River [START_REF] Dellinger | Riverine Li isotope fractionation in the Amazon River basin controlled by the weathering regimes[END_REF]. This range of the fractionation factor α is generally used for silicate weathering studies [START_REF] Golla | The evolution of lithium isotope signatures in fluids draining actively weathering hillslopes[END_REF], or for large watersheds of varied geology, such as the Ganges or Amazon Basins [START_REF] Dellinger | Riverine Li isotope fractionation in the Amazon River basin controlled by the weathering regimes[END_REF][START_REF] Pogge Von Strandmann | The lithium isotope response to the variable weathering of soils in Iceland[END_REF][START_REF] Yoshimura | The influence of weathering, water sources, and hydrological cycles on lithium isotopic compositions in river water and groundwater of the Ganges-Brahmaputra-Meghna river system in Bangladesh[END_REF]. by [START_REF] Day | Lithium isotopes and partition coefficients in inorganic carbonates: Proxy calibration for weathering reconstruction[END_REF]. It therefore seems confirmed that the Rayleigh fractionation model, as described in Equation 1 and shown on Figure 5b, is not valid in the case of the Ebro. This may be explained by three points. The first concerns the non-removal of Li from water to secondary phases caused by the presence of many dams on the river and its tributaries that trap the suspended load, which is reduced to a few mg/L at Amposta [START_REF] Négrel | Long-term fluxes of dissolved and suspended matter in the Ebro River Basin (Spain)[END_REF] precluding this process. The second explanation concerns the impossibility of applying a fractionation model in this particular case, which may be due to the fact that i) the model was generally applied in rivers draining silicates [START_REF] Kisakurek | Li and δ 7 Li in Himalayan rivers: proxies for silicate weathering? Earth Planet[END_REF]Millot et al., 2010a;[START_REF] Dellinger | Lithium isotopes in large rivers reveal the cannibalistic nature of modern continental weathering and erosion[END_REF]2015), and that ii) the derived α values were defined under specific weathering conditions or in laboratory experiments, but not under evaporite and carbonate weathering [START_REF] Song | Deciphering the signatures of weathering and erosion processes and the effects of river management on Li isotopes in the subtropical Pearl River basin[END_REF], 2021). The third explanation concerns another process that can control Li at the Ebro Basin scale: in the limestone-evaporite dominated rivers from the Ebro Basin, we have modelled the Sr isotopes as a mixture between carbonate and evaporite endmembers that cover the variability of all samples from the Ebro Basin [START_REF] Négrel | Ca and Sr isotope constraints on chemical weathering processes: A view through the Ebro river basin, Spain[END_REF]. This reinforces the major role of mixing processes in the Ebro Basin rather than fractionation processes, previously reported and discussed for silicate rocks.

Coupling Li and Sr isotopes: lithological control and mixing processes

Several studies [START_REF] Phan | Factors controlling Li concentration and isotopic composition in formation waters and host rocks of Marcellus Shale, Appalachian Basin[END_REF][START_REF] Manaka | Downstream and seasonal changes of lithium isotope ratios in the Ganges-Brahmaputra river system[END_REF] have shown that δ 7 Li combined with 87 Sr/ 86 Sr isotopes has the potential of distinguishing between the different rock types subject to weathering, or of explaining mixing processes (Henrichi et al., 2016;[START_REF] Li | Lithium isotope behavior in Hawaiian regoliths: Soilatmosphere-biosphere exchanges[END_REF]. Sr isotopes are a robust tracer of mixing because these isotopes do not fractionate [START_REF] Millot | Chemical, multi-isotopic (Li-B-Sr-U-H-O) and thermal characterization of Triassic formation waters from the Paris Basin[END_REF] and combine with Li when the effects of weathering (and/or mixing) supplant those of the fractionation between water and secondary phases [START_REF] Schmitt | Processes controlling the stable isotope compositions of Li, B, Mg and Ca in plants, soils and waters: A review[END_REF]. Figure 6a illustrates the relationship between δ 7 Li values and 87 Sr/ 86 Sr ratios in the dissolved load from the Ebro Basin and the various carbonate and evaporite bedrocks. We first note that the Li and Sr isotopes are scattered in the different bedrocks, whose three apexes are the carbonates G (continental Paleocene) and H (Oligocene carbonate), and the evaporite D (Trias anhydrite).

Furthermore, all water samples collected in the Ebro Basin lie within the area defined by the bedrocks and define a positive trend (grey arrow on Fig. 6a). (tributaries, mainstream, outlet, groundwater) and bedrock (A to H, Table 1). b -Extended view of the relationship between the δ 7 Li values and 87 Sr/ 86 Sr ratios in the Ebro basin samples. The carbonate end-member is from Négrel et al., 2021 and this study). Solid lines show theoretical mixtures between the different end-members.

The relationships between several end-members in Figure 6a are represented by hyperbolae [START_REF] Langmuir | A general mixing equation with application to Icelandic basalts[END_REF][START_REF] Négrel | Lithium isotopes as tracers of groundwater circulation in a peat land[END_REF] and can be expressed as by equation 3, Figure 6b shows the relationships between the δ 7 Li values and the 87 Sr/ 86 Sr ratios, and the mixtures between different end-members are represented by curves according to Eq. 3.

Considering only mixing processes, all samples are explained by mixing lines with different end-members, here represented by the Matarrana and Guadalope samples for the gypsum/anhydrite dissolution end-member, and by the Cinca and Gallego ones for the halite dissolution end-member (Figs. 4 and5). [START_REF] Négrel | Ca and Sr isotope constraints on chemical weathering processes: A view through the Ebro river basin, Spain[END_REF] found that the Segre water is strongly influenced by carbonate dissolution, and was therefore selected to represent this endmember. Mixtures between Matarrana-plus-Segre and Guadalope-plus-Cinca (and a mixture between Matarrana and Cinca) explain all Li-Sr relationships in the Ebro Basin samples. This mixing scheme again illustrates the major role of evaporite dissolution on Li isotopes, with a non-negligible role of carbonate dissolution, generally considered to be weak in controlling the lithium cycle in watersheds [START_REF] Kisakurek | Li and δ 7 Li in Himalayan rivers: proxies for silicate weathering? Earth Planet[END_REF][START_REF] Wang | Behavior of lithium isotopes in the Changjiang River system: sources effects and response to weathering and erosion[END_REF].

-Conclusions

The Ebro River Basin is the largest catchment of the Iberian Peninsula and one of the largest in the Mediterranean region. Investigations of surface waters and groundwaters defined a detailed behaviour of Li isotopes in the weathering environment at catchment scale. In the rivers dominated by limestone-evaporite bedrock, the waters are isotopically in accordance with the bedrock for their δ 7 Li signatures.

Li, Cl and SO4 concentrations show that they are controlled by evaporite weathering, and that a possible anthropogenic agricultural or industrial influence on Li concentrations can be discarded. The Na/Li, δ 7 Li, Cl/Li and SO4/Li ratios reflect the role of halite dissolution for some tributaries, gypsum/anhydrite dissolution dominates others, but the role of carbonate weathering is minor. Samples from the Ebro main channel and from the outlet logically showed a mix of waters.

Application of the Rayleigh fractionation model cannot explain the observed data. This fact reinforces the major role of mixing processes in the Ebro Basin as fractionation cannot explain the mineral concentrations in most samples. The mixing model is further confirmed by comparison of δ 7 Li values and 87 Sr/ 86 Sr ratios.

Compared with results from other large basins, such as the Amazon, Congo and Ganges-Brahmaputra ones, as well as with data from much smaller catchments and even soil profiles, our study confirms that lithium isotopes are a powerful tool for tracing basin evolution, through different weathering regimes, relief and climate conditions observed in various bedrock-types catchments, including carbonate-evaporite-dominated catchments.

  sedimentary and metamorphic Palaeozoic rocks (Iberian and Pyrenees mountains, Priorat Massif); Jurassic and Cretaceous carbonate rocks in the Iberian Chain forming the southern margin of the Ebro Basin; sedimentary Tertiary rocks of the Pyrenees foothills and the Ebro Valley; and Neogene and Recent delta-plain deposits near the

Figure 1

 1 Figure 1. a-General location of the Ebro basin in Spain, location of sampling points in the Ebro

  Figure 2a, b. (a) downstream variation of the Li concentrations (µg L -1 ) and (b) δ 7 Li (‰)

  , both factors influencing the isotopic values. Concerning the dams, their physical role is the retention and release of water stocks. Depending on the periods of filling and emptying, the water stocks have different ages as shown by Négrel et al., (2016) using H-O isotopes of the water molecule. These fillingemptying processes must affect the isotopic values of chemical elements like calcium and lithium which are subject to fractionation processes.The PHREEQ-C code[START_REF] Parkhurst | User's guide to PHREEQC (Version 2): A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF] allows to calculate the distribution of aqueous species in water samples and the saturation index for minerals based on the water data (e.g. the temperature, pH, redox and the concentrations of chemical elements) and using the database of the thermodynamic parameters of the minerals (e.g. the most recent Lawrence Livermore National Laboratory LLNL database). None of the water samples in the Ebro Basin were undersaturated with respect to gypsum and anhydrite when calculated with PHREEQ-C."Additionally, water samples of the tributaries and the Ebro were systematically supersaturated for calcite, aragonite and dolomite. Samples from Amposta showed various saturation degrees. Between December and May, the water samples were undersaturated for calcite and dolomite (October to May for aragonite) and supersaturated between June and November (or September for aragonite).

Figure 3 .

 3 Figure3. Data from the Ebro Basin regarding tributaries, main channel, outlet and groundwater for concentrations of (a) Cl vs.Li, and (b) SO4 vs. Li (all values in µg L -1 ).

Figure 4 .

 4 Figure 4. Data from the Ebro Basin concerning tributaries, main channel, outlet and groundwater for concentrations of: (a) Na/Li vs. Cl/Li ratios (in mol/mol), (b)Na/Li vs. SO4/Li ratios (in mol/mol). Na/Li versus Cl/Li ratios (Fig.4a) show the role of halite and gypsum/anhydrite psum

Figure 5 .

 5 Figure 5. (a) Relationship between dissolved δ 7 Li values and molar Na/Li ratios in samples from the Ebro Basin (tributaries, mainstream, outlet, groundwater) and from bedrock. (b) Relationship between dissolved δ 7 Li values and molar Li/Na ratios with the simple Rayleigh fractionation model (dotted lines).

Figure

  Figure 5b illustrates the relationship between dissolved δ 7 Li values and molar Li/Na

  below, Imix being the isotope composition of the mixed solution:Imix = {([ ]a x Ia x m)/( [ ]mix)} + {( [ ]b x Ib x (1-m))/ [ ]mix} (Eq. 3)where [ ]a, [ ]b and [ ]mix are the Li or Sr concentrations for the solution mix from two endmembers a and b, Ia, Ib and Imix are the Li or Sr isotope compositions or value for the solution mix from two end-members a and b, and m is the mixing proportion.

Table 2 :

 2 Sample ID, distance to Ebro source, river discharge ([CHE]), δ 7Li and Li content 197 for surface water (Ebro survey at the Amposta station, Ebro main channel, tributaries, Fig.1)198and groundwater (Fig.1) in the Ebro River Basin. Na and Sr contents, and 87 Sr/ 86 Sr ratios 199 are fromNégrel et al., 2021. 200

		Samples	Station	Sampling date	Distance to the source	Discharge	δ	7 Li	Li	87 Sr/	86 Sr	Sr	Na
					km	m 3 s -1	‰	µg L -1			µg L -1	µg L -1
		Ebro survey Amposta Station
		jun.	E6	6/15/2005	552	150.7	17.4	13.3	0.70847		65
		jul.	E6	7/15/2005	552	141.6	17.3	15.4	0.70848		77
		Aug.	E6	8/11/2005	552	119.0	17.7	16	0.70854		141
		Sep.	E6	9/20/2005	552	124.5	17.7	23.3	0.70859		171
		Oct.	E6	10/10/2005	552	118.3	18.9	28.3	0.70854		239
		Nov.	E6	11/14/2005	552	120.8	18.3	35.8	0.70857		245
		Dec.	E6	12/21/2005	552	300.0	17.6	32.8	0.70844		142
		Jan.	E6	1/17/2006	552	402.3	17.5	23.2	0.70841		97
		Feb.	E6	2/15/2006	552	173.0	17.6	17.9	0.70850		84
		Mar.	E6	3/14/2006	552	452.0	16.3	13.6	0.70842		65
		Apr.	E6	4/19/2006	552	202.1	17.9	15.2	0.70849		69
		May	E6	5/22/2006	552	225.3	17.3	12.5	0.70858		55
		Ebro main stream
		Miranda	E1	04/18-20-2006	104	-	17.1	5.3	0.70864	704	48
		Lodosa	E2	04/18-20-2006	241	68.2	18.3	6.9	0.70856	855	42
		Gallur	E3	04/18-20-2006	281	97.1	16.7	16.6	0.70837		96
		Presa de Pina	E4	04/18-20-2006	336	105.9	16.2	23.5	0.70842		138
		Tortosa	E5	04/18-20-2006	543	138.0	16.5	14.7	0.70849		70
		Tributaries
		Ega	E7	04/18-20-2006	216	7.8	15.4	16.3	0.70807		128
		Aragon	E8	04/18-20-2006	233	9.4	13.9	12	0.70814	973	88
		Galliego	E9	04/18-20-2006	328	2.6	19.0	20.7	0.70861		223
		Huerva	E10	04/18-20-2006	324	-	20.2	40.9	0.70862		101
		Guadalope	E11	04/18-20-2006	397	80.9	17.1	66.9	0.70786		68
		Matarrana	E12	04/18-20-2006	457	3.8	12.9	14.8	0.70796		21
		Cinca	E13	04/18-20-2006	422	0.2	20.9	20.7	0.70877		118
		Segre	E14	04/18-20-2006	422	3.0	18.9	16.2	0.70897		53
		Groundwater
		G15	E15	04/18-20-2006	200	-	17.4	126	0.70840		732
	201 202	GA-2	E16	04/18-20-2006	370	-	18.1	21.1	0.70847		262
	203

  Relationship between dissolved δ 7 Li values and 87 Sr/ 86 Sr ratios in the samples from the Ebro Basin

										Ebro_Amposta
		0.7094	a							Ebro_mainstream Tributaries	0.709	b								Segre
										Groundwater						carbonate dissolution
		0.7092				H				evaporate bedrock carbonate bedrock	0.7088				end-member					Cinca
		0.709																	Gallego
							Segre
		0.7088			E		Gallego		Cinca			0.7086										Huerva
	87 Sr/ 86 Sr	0.7084 0.7086						Huerva		Sr 87 Sr/ 86	0.7084									halide dissolution end-member
		0.7082	B		Aragon		F				0.7082				Aragon
		0.708	A		Matarrana		Ega						Matarrana			Ega
			G				Guadalope				0.708
		0.7078
							C			D								Guadalope
		0.7076										0.7078	gypsum-anhydrite dissolution end-member
		-4	0	4	8	12	16	20	24	28	32		12	13	14	15	16	17	18	19	20	21	22
						δ7Li (‰)											δ7Li (‰)
	Figure 6. a -

Negrel et al. (2021)

found that the Sr-isotope levels in the Aragon, Ega, Matarrana and Guadalope samples are explained by a mixing scheme that is mainly influenced by evaporite weathering (gypsum/anhydrite and halite), whereas the Huerva, Gallego, Cinca and Segre samples show a shared role of evaporite (halites) and carbonate weathering.

Acknowledgement

This work was funded by the BRGM Research Division and by the European Union (integrated project AquaTerra, Project GOCE 505428) under the thematic priority "Sustainable Development, Global Change and Ecosystems (FP6) Water Cycle and Soil Related Aspects". The views expressed are purely those of the writers and may not under any circumstances be regarded as stating an official position of the European Commission. We thank M. Brach for collecting the samples along the Ebro basin and D. Barcelo's team (CSIC Barcelona, Spain) for assisting in sample collection. We are grateful to Dr. Laura Rosell, Dr. Federico Orti and Dr. Lluis Cabrera for providing the bedrock samples. The authors acknowledge the support on the information received from the Agencia Catalana de l'Aigua and the Confederación Hidrográfica del Ebro (CHE). We are grateful to Dr. H.M. Kluijver for proofreading and editing the English text.


Giuseppe Habib
email: habib@mm.bme.hu

Francesco Romeo
email: francesco.romeo@uniroma1.it

Comparative Analysis of NES and TMD Performance via High-Dimensional Invariant Manifolds

Keywords: Nonlinear energy sink, Tuned mass damper, Multi-modal vibration absorber, Impulsive energy dissipation 13.1 Introduction

A comparative study between a tuned mass damper (TMD) and a nonlinear energy sink (NES), attached to a linear two-degree-of-freedom (DoF) mechanical system under impulsive excitation, is performed. The analysis involves different scenarios; namely, we consider the cases in which only one or both modes of the primary system are initially excited. First, exploiting a harmonic balance approach, the invariant manifolds describing the slow dynamics of the system are identified. Then, introducing the so-called relative dissipation power, the performance of the two absorbers is carefully compared, based on analytical computations. Results illustrate that the two absorbers have similar performance, albeit resorting to different mechanical properties: the NES achieve a broad frequency band of operation exploiting nonlinearity, while the TMD by increasing damping. An interesting feature, highlighted by the invariant manifold, is that the NES is generally unable to resonate with more than one mode of the primary system at the same time, rather, it experiences a sort of modal cascade.

in the literature; a common classification distinguishes between active, semi-active, passive and hybrid techniques which, in turn, can rely on devices characterized by linear and nonlinear behaviours. Among the passive linear vibration absorbers, tuned mass dampers (TMDs) are undoubtedly an established benchmark for mitigation of resonances [START_REF] Frahm | Device for damping vibrations of bodies[END_REF][START_REF] Hartog | Mechanical Vibrations[END_REF]. As known, their effectiveness lies in the tuning of their own natural frequency with that of the resonance to be mitigated, which implies that a single TMD can be used to optimally damp only one resonance of the host structure. Such intrinsic limitation of TMDs has prompted the engineering challenge of expanding the absorbers bandwidth of operation, giving the start to an extensive and multifaceted research activity. Among the proposed passive linear strategies, multiple tuned mass dampers (MTMDs) and spatially distributed MTMDs have been considered in literature, as reported in the recent review article [START_REF] Elias | Research developments in vibration control of structures using passive tuned mass dampers[END_REF]. Alternatively, willing to keep a single device in the control system, nonlinear absorbers designed to resonate for broad frequency band have been recently proposed. This brought the development of the nonlinear energy sink (NES), consisting of a small mass connected to the primary system by an essential nonlinear spring [START_REF] Gendelman | Energy pumping in nonlinear mechanical oscillators: part i-dynamics of the underlying Hamiltonian systems[END_REF][START_REF] Kerschen | Irreversible passive energy transfer in coupled oscillators with essential nonlinearity[END_REF]. Given the inherent different dynamic regimes involved in the passive linear and nonlinear absorbers during the vibration mitigation processes, a comparison between the performance of the two families of devices is not straightforward. Moreover, the variety of excitations, host structure typology, design constraints and objectives have so far lead to partial and incomplete performance comparisons between the two families of devices. In [START_REF] Gendelman | Quasiperiodic energy pumping in coupled oscillators under periodic forcing[END_REF] it is illustrated that, in some specific conditions, the NES can outperform the TMD for resonance mitigation of a single-degree-of-freedom (DoF) linear primary system, exploiting quasiperiodic motions. In [START_REF] Starosvetsky | Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: optimization of a nonlinear vibration absorber[END_REF], a comparative analysis about the relevance of damping for NES and TMD revealed that, for low damping of the absorber, the NES can be more effective than the TMD also in narrow-band energy dissipation; increasing damping, the TMD behaves better than the NES. A comparison between NES and TMD performance in a periodically excited linear beam is performed in [START_REF] Parseh | Performance comparison of nonlinear energy sink and linear tuned mass damper in steady-state dynamics of a linear beam[END_REF].

In this work, an attempt is made to qualitatively and quantitatively compare the TMD and the NES capabilities for the mitigation of broadband impulsive energy, considering various engineering scenarios. By exploiting the high-dimensional invariant manifold of a two-DoF host system, an effective performance measure is introduced, the so-called relative dissipation power.

Mathematical Model and Invariant Manifold Derivation

We consider the simple model shown in Fig. 13.1. The dynamics of this system is governed by the equations

M x 1 + kx 1 + k (x 1 -x 2 ) + k nl (x 1 -x a ) 3 + c a x 1 -x a = 0 M x 2 + kx 2 + k (x 2 -x 1 ) = 0 mx a + k nl (x a -x 1 ) 3 + c a x a -x 1 = 0 (13.1)
where x 1 and x 2 refer to the displacements of the primary 2 DoF system, while x a refers to the displacement of the absorber; m is assumed much smaller than M and the prime denote differentiation with respect to time t. The choice of considering an undamped hosting structure reflects results obtained in previous works [START_REF] Romeo | Dynamics of a linear oscillator coupled to a bistable light attachment: numerical study[END_REF], where it is illustrated that small damping in the primary system does not affect the overall qualitative dynamics. We divide the system of Eqs. (13.1) by M, introduce the dimensionless time T = ω n t and dimensionless variables

y 1 = √ λ 3 (x 1 + x 2 ) /2, y 2 = √ λ 3 (x 1 -x 2 ) /2 and y 3 = √ λ 3 (x 1 -x a )
, where ω n = √ k/M and λ 3 = k nl / mω 2 n , obtaining the governing equations in primary system dimensionless modal coordinates, i.e.

ÿ1 + y 1 = ε - y 3 3 2 -μ a ẏ3 ÿ2 + 3y 2 = ε - y 3 3 2 -μ a ẏ3 ÿ3 + y 1 + 3y 2 + (1 + ε) y 3 3 + 2μ a ẏ3 = 0 (13.2)
where ε = m/M, μ a = c a / (2mω n ) and the overdots denote differentiation with respect to T . Starting from Eqs. (13.2), by considering ε 1 as a perturbation parameter, an analytical framework enabling to design the NES and to optimize its performance is derived.

In order to study the slow dynamics of the system, we collect terms of order ε 0 , reducing the system to ÿ1 + y 1 = 0 (13.3) ÿ2 + 3y 2 = 0 (13.4) ÿ3 + 2μ a ẏ3 + y 3 3 = -y 1 -3y 2 .

(13.5)

We define an approximate solution by adopting the harmonic balance method [START_REF] Luongo | Dynamic analysis of externally excited nes-controlled systems via a mixed multiple scale/harmonic balance algorithm[END_REF][START_REF] Luongo | Aeroelastic instability analysis of NES-controlled systems via a mixed multiple scale/harmonic balance method[END_REF], assuming 1:1 resonance between the primary system and the absorber. The solutions of Eqs. (13.3) and (13.4) are y 1 = A 1 e i T + c.c. and y 2 = A 2 e √ 3i T + c.c., where A 1 and A 2 are complex and c.c. stands for complex conjugate. The approximate solution of Eq. (13.5) is expressed by y 3 = B 1 (t 1 ) e i T + B 2 (t 1 ) e √ 3i T + c.c. We substitute the approximate solutions of y 1 , y 2 and y 3 into Eq. (13.5) and collect harmonics of e i T and e √ 3i T , obtaining

e i T : -B 1 + A 1 + 3B 2 1 B1 + 6B 1 B 2 B2 + 2μ a i B 1 = 0 e √ 3i T : -3B 2 + 3A 2 + 3B 2 2 B2 + 6B 1 B1 B 2 + 2 √ 3μ a i B 2 = 0. (13.6) By defining B 1 = 1/2b 1 e iβ 1 , B 2 = 1/2b 2 e iβ 2 , A 1 = 1/2a 1 e iα 1 and A 2 = 1/2a 2 e iα 2 ,
and separating real and imaginary parts of the first equation of (13.6), we have

1 2 a 1 cos α 1 = 1 2 b 1 1 - 3 4 b 2 1 - 3 2 b 2 2 cos β 1 + μ a b 1 sin β 1 1 2 a 1 sin α 1 = 1 2 b 1 1 - 3 4 b 2 1 - 3 2 b 2 2 sin β 1 -μ a b 1 cos β 1 .
(13.7)

We calculate the squares of the two equations of (13.7) and we sum them up attaining

a 2 1 = b 2 1 1 - 3 4 b 2 1 - 3 2 b 2 2 2 + 4μ 2 a b 2 1 . (13.8)
Repeating the same operation with the second equation of (13.6) we obtain

a 2 2 = b 2 2 1 - 1 4 b 2 2 - 1 2 b 2 1 2 + 4 3 μ 2 a b 2 2 .
(13.9)

Equations (13.8) and (13.9) describe the invariant manifold that relates the slow dynamics of y 3 with respect to y 1 and y 2 . A detailed analysis of the obtained manifold is performed in the following sections by considering separately the cases in which the excitation involves either a single or both modes.

We notice that, although the absorber is characterized by the three parameters ε, μ a and λ 3 , thanks to the performed non-dimensionalization the only parameter left in the manifold equation is μ a . λ 3 simply scales the amplitude of the variables, while ε is proportional to the energy dissipation rate, but, if it is kept small, it has no qualitative effect on the slow dynamics of the system, which can be captured by the adopted approach.

Single Mode Dynamics

We consider at first the case when only the first mode of the primary system is initially excited. In this case, y 2 is assumed of order ε, therefore the invariant manifold is defined only by Eq. (13.8), with b 2 = 0, i.e.

a 2 1 = b 2 1 1 - 3 4 b 2 1 2 + 4μ 2 a b 2 1 . (13.10)
The relative manifold is illustrated in Fig. 13.2a for μ a = 0.1. The black line in the figure is the result of a numerical simulation, which qualitatively confirms analytical results. Modal amplitudes were obtained through a wavelet transformation of the system time series. Although stability of the manifold was not studied, it can be guessed that, if for a single a 1 value there are three different b 1 values, the middle one is unstable.

The invariant manifold enables one to predict the amplitude of oscillation of y 3 depending on the oscillation amplitude y 1 . Large values of y 3 (i.e. b 1 ) correspond to high dissipation power. Adopting the hypothesis of single harmonic response, dissipation power in one period is given by εμ a b 2 1 . However, from an engineering point of view, it is more significant to indicate the energy dissipated in one period with respect to the energy present in the primary system, that is (if only the first mode is activated) P r = εμ a b 2 1 /a 2 1 . This curve is illustrated in Fig. 13.2b for μ a = 0.1 and ε = 0.01.

The shape of the P r function gives important information about the performance of the NES. For very high values of a 1 , P r is very low (P r tends to zeros for a 1 → ∞); however, at large amplitudes additional harmonics, overlooked by the adopted analytical approach, might become more relevant. Reducing a 1 , P r increases until it reaches a high peak (called P in the figure), whose exact position can be calculated and it is P = 4μ a / √ 3, ε/(4μ a ) . For a 1 < 4μ a / √ 3, P r has a sudden decrease and it reaches an almost constant plateau until a 1 = 0 (for a 1 → 0, P d = εμ a /(1 + 4μ 2 a )). This lower limit corresponds to the minimum energy threshold below which the NES is not activated, a feature which has been extensively studied [START_REF] Kerschen | Irreversible passive energy transfer in coupled oscillators with essential nonlinearity[END_REF]. Numerical results, represented by black dots in the figure, agree very well with the analytical prediction. The main difference consists in the slightly mismatching position of the peak.

During the design of an NES, the position of point P is clearly a key parameter for defining the performance of the device and the range of operation. Since the amplitude was normalized with respect to √ λ 3 , this parameter can be tuned to adjust the energy level of optimal operation. Furthermore, the a 1 -coordinate of point P grows linearly with μ a . Increases of μ a also enlarge the peak and lower P, reducing the maximal dissipation power, but widening the amplitude range of operation.

The same procedure performed for the NES, can be analogously computed for the TMD, in order to compare the two absorbers. The analysis leads to the invariant manifold described by the equation

a 2 1 = b 2 1 1 -γ 2 2 + 4μ 2 a b 2 1 or a 1 = b 1 1 -γ 2 2 + 4μ 2 a , (13.11)
where γ is the ratio between the natural frequency of the TMD and of the primary system. Orange lines in Fig. 13.2a and b illustrate the manifold and the relative dissipation power for the TMD, which can be directly compared with the NES. It is particularly interesting that, if γ = 1, the relative dissipation power of the TMD is always equal to the maximum P r of the NES. This clearly highlights the superiority of the TMD over the NES when it is properly tuned and only one mode is involved. Also in this case, numerical results qualitatively confirm analytical predictions.

Two Modes Dynamics

In the hypothesis that both modes of the primary system are activated, Eqs. (13.8) and (13.9) form a unique system of equations. This defines the invariant manifold, that is a 2-dimensional surface in the 4-dimensional space (a 1 , a 2 , b 1 , b 2 ). Figure 13.3 illustrates the manifold exploiting two projections: x-and y-axes mark the modal amplitude in the primary system of the first (a 1 ) and second (a 2 ) mode, respectively; z-axis indicates the modal amplitude related to the first (b 1 , Fig. We notice the interesting feature that, for given a 1 and a 2 values, either b 1 is large and b 2 is small, or the opposite is verified. An ideal line, splitting in two the a 1 , a 2 space, divides the two regions where either b 1 or b 2 is larger. This consideration has important practical consequences, indeed it means that the NES, although is able to interact with modes at different frequencies, it works well with only one at a time.

A numerical validation of this phenomenon is illustrated in Fig. 13.4. Figure 13.4a shows time series for the three system coordinates, while Fig. 13.4b depicts the instantaneous frequency of the NES motion (y 3 ), obtained through a wavelet transformation. For T < 1500, Fig. 13.4b clearly illustrates that the NES has a strong coupling with the second mode (at 1.732 rad/s), while it does not interact with the first one. This is consistent with the manifold in Fig. 13.3; in fact, for the adopted initial conditions (y 1 (0) = 6 and y 2 (0) = 4), b 1 is relatively small, while b 2 is much larger. This causes a relatively rapid dissipation of energy on the second mode of the primary system, while the first one is almost unaffected by the absorber, as it can be verified from the time series in Fig. 13.4a. At T ≈ 1500, the NES abruptly disengages from the second mode and it couples with the first one, forming a sort of modal cascade. In terms of invariant manifold, this coincides to reach the boundary dividing the regions where either b 1 or b 2 is large. The correspondence between analytical and numerical results is given by the black dots in Fig. 13.3a and b: although the black dots, indicating the modal amplitude in the NES b 1 and b 2 , do not exactly lie on the manifold, the transition between second and first modes is well predicted in terms of modal amplitudes a 1 and a 2 . For 1500 < T < 8000 the energy decreases on both modes; however, the dissipation rate for the second mode is significantly diminished, in virtue of the discussed modal transition. At T ≈ 8000 the NES disengages also from the first mode, causing a sudden drop of its oscillation amplitude and of the energy dissipation on the first mode. Considering that at this point most of the energy was only on the first mode, this phenomenon practically coincides with the drop illustrated in Fig. 13.2 for the case of single mode dynamics. Superand sub-harmonic resonances, visible in Fig. 13.4b, are overlooked by the analytical framework adopted.

We notice that, if the system is initially in the region where the first mode is prevalent but there is some energy also on the second mode, the NES will have a stronger coupling with the first mode, but it will still dissipate some energy on the second mode. This cancels the modal cascade, which seems to occurs only from higher modes to lower ones. We also remark that the ideal line dividing the two regions of modal coupling follows a somehow different trend for low amplitude. The minimum energy threshold of each mode and the S shape observed in Fig. 13.2a is dominant over the interaction between the two modes, causing a drop of modal amplitude for the first mode at a 1 = 0.23 and for the second mode at a 2 = 0.23. Indeed, the best dissipation performance are obtained for a 1 and a 2 only slightly larger than these limits.

NES-TMD Comparison

In the following, we compare the NES and TMD performance while operating on the primary system with both modes activated. We consider the initial conditions y 1 (0) = y 2 (0) = 0, ẏ1 (0) = ẏ2 (0) = v 0 and identify parameters providing the minimum dissipation time, given ε = 0.01. For the NES, the only parameter to be optimized is μ a as a function of the initial velocity v 0 ; we remind that the amplitude is scaled with √ λ 3 , therefore, in principle, the system can be set to any energy level. For the TMD, optimization is performed tuning μ a and γ ; because of the linearity of the system, dynamics is invariant with respect to v 0 .

As optimal conditions, we obtain for the NES that 70% of the initial energy is dissipated in 147 time units for μ a = 0.1248, if v 0 = 0.504. Regarding the TMD, In these conditions the NES outperform the TMD by 17% in terms of dissipation time.

Extensive numerical simulations show that, for optimal parameter values, the NES has a strong interaction with the first mode, keeping, at the same time, a weak interaction with the second one, therefore the modal cascade shown in Fig. 13.4 is no longer present. This can be clearly seen from the wavelet transformation of y 3 in Fig. 13.5c, which refers to the optimal NES. Figure 13.5a and b depict the energy decrement on the first and on the second mode of the primary system, respectively. It can be noted that energy decreases on both modes at a similar rate, until T ≈ 150, when the NES disengages from both of them almost simultaneously.

Referring to an optimal TMD, because the value of γ is only slightly larger than 1, y 1 oscillation amplitude undergoes a much rapid decrement than y 2 ; this was verified through direct numerical simulations, not shown here for the sake of brevity. Nevertheless, energy of the second mode is still dissipated thanks to the quite large damping (μ a = 0.204).

A comparison of the energy decrement obtained by the NES and by the TMD is illustrated in Fig. 13.5d, which shows that the NES only slightly outperforms the TMD. However, after dissipating 70% of the energy, it becomes almost ineffective, while the TMD works also for small amplitude. Figure 13.5e and f, depict the energy decrement adopting the same absorbers, but changing initial conditions. For ẏ1 (0) = 1 and ẏ2 (0) = 0.5 (more energy on the first mode, Fig. 13.5e) the NES has a significant deterioration of its performance, while the TMD an improvement. Conversely, increasing the initial energy on the second mode ( ẏ1 (0) = 0.5 and ẏ2 (0) = 1, This behavior can be better understood by plotting the relative dissipation power P r as a function of a 1 and a 2 . This is defined by the equation P r = εμ a b 2 1 + 3b 2 2 / a 2 1 + 3a 2 2 and it is illustrated in Fig. 13.6 (colored surface) for ε = 0.01 and μ a = 0.1248. In the figure, we notice that there are two peaks; the smaller is related to the first mode and the higher one to the second mode. These correspond to the points with maximum dissipation power (their height is ε/(4μ a ) and 3ε/(4μ a ), respectively, as it can be computed by the hypothesis of single mode dynamics). For the initial conditions ẏ1 (0) = ẏ2 (0) = 0.504 the NES fully exploits the smaller peak, obtaining a good energy dissipation for the first mode. Increasing the initial energy on the first mode ( ẏ1 (0) = 1), the peak of the second mode is still not exploited, while some additional time is required before reaching the peak of the first mode. This results in a deterioration of the performance. On the contrary, increasing the energy on the second mode ( ẏ2 (0) = 1), the NES first exploits the peak relative to the second mode and then the one relative to the first one. This can be recognized observing that the energy decrement approximately consists of three linear segments. These correspond to dissipation of the energy on the second mode, then on the first mode and finally slowly dissipated residual energy.

Overlapping the relative dissipation power surface of the TMD (orange surface in Fig. 13.6) over the one of the NES, we can directly estimate the relative performance of the two absorbers. In general, for the same a 1 , a 2 values, the surface with the higher P r value is the one providing better performance.

Conclusions

The dynamics of an NES attached to a two-DoF linear oscillator was investigated, evaluating the performance of the absorber against impulsive excitations. Invariant manifolds, describing the slow dynamics of the system, proved to be an effective tool to predict quite accurately the behavior and the performance of the absorber. In particular, they allowed us to explain how the NES couples with the primary system when more than one mode is activated. If the energy content on both modes is sufficient, the NES first dissipates energy on the higher mode and then, once a threshold is reached, it couples with the lower one abruptly decoupling from the higher one. A direct comparison between the NES and the TMD illustrated which conditions are required for the NES to outperform the TMD. Prediction of the comparative behavior based on the invariant manifold was confirmed by direct numerical simulations.

The verification of the existence of the described modal cascade for primary systems with large number of DoF will be the subject of a future study.

Fig. 13. 1

 1 Fig. 13.1 A three-DoF system consisting of two coupled symmetric linear oscillators and an NES connected to one of them

Fig. 13. 2 a

 2 Fig. 13.2 a Invariant manifold for the first mode (μ a = 0.1, γ = 1 for TMD); b Estimated relative dissipation power based on the invariant manifold (μ a = 0.1, ε = 0.01, γ = 1 for TMD). Blue and orange lines refer to analytical results of NES and TMD, respectively, black lines refer to numerical results

  13.3a) and to the second mode (b 2 , Fig.13.3b) in the NES.

Fig. 13. 3 Fig. 13. 4 a

 34 Fig. 13.3 Invariant manifold projected on the (a 1 , a 2 , b 1 ) (a) and on the (a 1 , a 2 , b 2 ) (b) spaces for μ a = 0.1. The black dots mark the instantaneous modal amplitude of the time series in Fig. 13.4 calculated through a wavelet transformation. Subplots c and d offer top views of subplots a and b, respectively

  Fig. 13.5 a, b Energy decrement on the first and on the second mode for system (13.2) with μ a = 0.1248, ε = 0.01, ẏ1 (0) = ẏ2 (0) = 0.504 and y 1 (0) = y 2 (0) = 0; c wavelet transformation of y 3 ; d, e, f energy decrement comparison with TMD (μ a = 0.204, γ = 1.04) for the initial conditions y 1 (0) = y 2 (0) = 0 and ẏ1 (0) = ẏ2 (0) = 0.504 (d), ẏ1 (0) = 1 and ẏ2 (0) = 0.5 (e), ẏ1 (0) = 0.5 and ẏ2 (0) = 1 (f)

Fig. 13. 6

 6 Fig. 13.6 Relative dissipation power for the NES (colored surface) and the TMD (orange surface) with ε = 0.01 and μ a = 0.12 (NES) or γ = 1.04 and μ a = 0.204 (TMD)

Acknowledgements GH acknowledges the financial support of the European Union, H2020 Marie Skłodowska-Curie Individual Fellowship, Grant Agreement 704133. FR acknowledges the financial support of PRIN 2015 N. 2015TTJN95.