Virgyl Camberlein

Nour Nicolas Kraupner

Bou Karroum

Emmanuelle Lipka

Rebecca Deprez-Poulain

Benoit Deprez

Damien Bosc

Azide-Alkyne Cycloaddition

Virgyl Camberlein

Nour Bou Karroum

Multi-Component Reaction for the Preparation of 1,5-Disubstituted 1,2,3-Triazoles by In-Situ Generation of Azides and Nickel-Catalyzed Azide-Alkyne Cycloaddition

Keywords: click chemistry, molecular diversity, multicomponent reactions, regioselectivity, synthetic methods

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Introduction

Spearhead of the heterocycles generated by click chemistry, 1,2,3-triazoles are broadly found in several domains such as materials science, [1] organometallic science [2] but also chemical biology [3] and medicinal chemistry [4] . This considerable importance is due to the favorable properties linked to this heteroaromatic ring but also thanks to the easiness of access of the 1,4-disubstituted 1,2,3-triazoles by copper-catalyzed azide-alkyne cycloaddition (CuAAC). [5] This methodology is indeed powerful with excellent regioselectivity, high yield and is easy to implement. Noteworthy, the 1,5-disubstituted 1,2,3triazoles are less represented. As there is a high interest for 1,5-disubstituted regioisomers in drug discovery as disulfide bond surrogate [6] or cis-peptide bond mimetic [7] or enzyme modulator [8] , it is valuable to facilitate the access of this scaffold. Several teams have worked on this purpose and to date there are few methods to synthesize 1,5-disubstituted 1,2,3-triazoles, which are for most of them with very limited scope. The main methodologies use azide-alkyne cycloadditions either mediated by metal acetylide or metal catalysts. [9] The alkynes can also be replaced by nitroolefins with the use of metallic additives to afford 1,5-disubstituted 1,2,3-triazoles substituted by aryl groups. [10] Moreover, in a lesser extent, other functional moieties have also been used for playing the role of dipolarophile in 1,5disubstituted 1,2,3-triazole synthesis. [11] An alternative method based on a cascade Michael addition was also described for the construction of 1,5-disubstituted 1,2,3-triazoles. [12] Regrettably, most of these methodologies have scope constraints. Besides, most of them require the handling of isolated organic azides, which are not often commercially available and are known to be unstable, especially those of low molecular weight. [13] In order to bypass these drawbacks, only few methods, most of them being multicomponent, have been developed. [14] These methodologies have the advantage to be safer by preventing the manipulation of organic azides. However, they suffer from a very limited substrate scope, often requesting high temperatures, strict inert atmosphere conditions or an inconvenient sequential pattern, all of which have confined their use. In order to provide an extensive procedure that circumvent all these drawbacks and that afford functionalized 1,5-disubsituted 1,2,3-triazoles suitable for diverse applications, we investigated the feasibility to implement an efficient and safe one-pot, two-step method. This procedure would allow the in situ bromides conversion by nucleophilic substitution with sodium azide into azides, which react consecutively with alkynes by NiAAC (Scheme 1). Scheme 1. Strategies for the synthesis of 1,5-disubstituted 1,2,3-triazoles.

Results and discussion

First we performed the screening of different reaction conditions on the model substrates 4-tertbutylbenzyl bromide 1a and phenylacetylene 2A (Table 1). Reaction conditions close to the recently published NiAAC ones [9g] were applied with the combination of bromide 1a (1.0 equiv), sodium azide (1.0 equiv), alkyne 2A (1.2 equiv) in presence of nickelocene (Cp2Ni) precatalyst (20 mol%), bidentate Xantphos ligand (20 mol%) and Cs2CO3 (1.0 equiv) at room temperature for 2 h in water. Under these conditions, the bromide 1a was converted into azide but the cycloaddition was not observed (entry 1).

To facilitate the triazole formation, several conditions were screened. First, dimethylformamide, often used as a solvent for azide formation from bromide and shown to be efficient for the NiAAC, was evaluated (entry 2). Pleasantly, this solvent allowed the triazole formation with good yield (71 %) contrary to other solvents such as dichloromethane, ethanol and tetrahydrofuran (entries 2-5). In order to improve the reaction conversion into triazole, the reaction vessel was slightly heated at 50°C under microwave irradiation for 1 h (entry 6). This heating condition was beneficial for the regioselectivity (from 88:12 to 93:7) without compromising the yield (entries 2 vs 6). Higher temperature (80 °C or 100 °C) resulted to a lower yield and a poorer regioselectivity (entries 7 and 8), probably due to the catalyst degradation. Increasing reaction time to 4 h improved yield (86 %, entry 9) but slightly decreased the regioselectivity (from 93:7 to 92:8). In the attempt to improve the yield of the 1,5disubsituted 1,2,3-triazole 3aA, the bromide 1a and the sodium azide were defined as excess reagents (1.2 equiv and 1.5 equiv respectively) (entries 10). Appealingly, after 4 h under microwave irradiation at 50°C, the calculated yield fo triazole 3aA was excellent (89 %) with no secondary products and Metal azide alkyne cycloaddition [9d-g] × ×

This work: one-pot NiAAC Sequential one-pot RuAAC [14f] Azide-free one-pot cycloaddition using tosyl hydrazine [14c] [Ru], [Sm], [Ni] NaN 3 1.

2.

NaN 3 × Narrow scope excellent regioselectivity (92:8). To investigate the mechanism of this multicomponent method, 4-tertbutylbenzyl bromide 1a was submitted to sodium azide at room temperature for 2 h in DMF with or without the Cp2Ni/Xantphos catalytic system. For both conditions, 4-tert-butylbenzyl azide was formed in quantitative yield. Thus, the nickelocene precatalyst in association with its Xantphos ligand has no influence on the SN2 event and only has positive effect for the azide-alkyne cycloaddition and its regioisomerism. a Reaction conditions: Run on a 0.5 mmol scale of alkyne 2A (1.2 equiv), bromide 1a (1.0 equiv), NaN3

(1.0 equiv), solvent (2 mL), Cp2Ni (20 mol%), Xantphos (20 mol%), Cs2CO3 (1.0 equiv). b Run on a 0.5 mmol scale of alkyne 2A (1.0 equiv), bromide 1a (1.2 equiv), NaN3 (1.5 equiv), solvent (2 mL), Cp2Ni

(20 mol%), Xantphos (20 mol%), Cs2CO3 (1.0 equiv). After determining the optimized conditions for this one-pot procedure, we explored the scope with various alkynes and bromides. The integrity of the 1,5-disubstituted 1,2,3-triazole template was validated by NMR NOESY and HSQC experiments to corroborate the distinctive 13 C chemical shift of the triazole CH at ∼133 ppm. [14] The evaluation of substrate scope with various aromatic (2A-2E) and aliphatic alkynes (2F-2H) in reaction with bromide 1a is summarized in Table 2. Except for alkynes 2D and 2E, the attempts to separate and isolate the two regioisomers 3 and 4 were not fruitful either by classical flash column chromatography, or by C-18 reversed-phase flash column chromatography with the use of classical or pentafluorophenyl columns. However, because of the high regioselectivity rates associated with this methodology (from 66:34 to >99:1), flash chromatography was still performed to afford 3 in mixture with 4 in order to evaluate the efficiency of this one-pot multicomponent procedure. Modest to excellent calculated yields ranging from 27% to 84% were obtained. Besides, in order to isolate and characterize properly the 1,5-regioisomers 3, the reaction crude mixtures were also purified by semi-preparative supercritical fluid chromatography (SFC) and comparable isolated yields (24% to 72%) were obtained.

The regioselectivity of the reactions was determined by supercritical fluid chromatography (SFC)

analysis of the crude reaction mixtures obtained after the work-up of the reactions carried out with alkynes 2A-2E and 2H, or according to the 1 H-NMR spectra for reactions carried out with alkynes 2F

and 2G, whose separation of the two regioisomers by SFC was not optimal. Modest to excellent regioselectivities were obtained. Considering the regioselectivity obtained with the pnitrophenylacetylene 2B (ratio 66:34) compared to the phenylacetylene 2A (ratio 89:11) and then the pfluorophenylacetylene 2C (ratio 91:9) and the p-methoxyphenylacetylene 2D (ratio >99:1), a positive mesomeric effect on the phenyl ring seems to induce a positive contribution to the regioselectivity without having an effect on the yield. Noteworthy, heteroaryl and alkyl chains are accepted for this procedure (2E-2H). Interestingly, the scope was widened by hydroxyl and carbamate moieties, which were compatible with this process. a Reaction conditions: Run on a 0.3-0.6 mmol scale of alkyne 2 with 1a (1.2 equiv), NaN3 (1.5 equiv), Cp2Ni (20 mol%), Xantphos (20 mol%), Cs2CO3 (1.0 equiv), DMF (2.0 mL), 50 °C (MW), 4 h. Isolated yields of 3 obtained after SFC purification; 3/4 ratio determined from the crude product by SFC analysis unless noted otherwise; in brackets: calculated yields of 3 obtained after flash column chromatography purification (in mixture with 4); b Isolated yield of 3 obtained after flash column chromatography purification; c Determined by 1 H-NMR. Boc, tert-butoxycarbonyl; Cp, cyclopentadienyl; t-Bu, tert-butyl.

The substrate scope was also examined with various bromides (Table 3). Aromatic benzyl bromide possessing either electron-donating (1a and 1b) or electron-withdrawing (1c-1g) groups are tolerated and afforded the 1,5-regioisomers (3aA-3gA) with modest to high yields both after flash chromatography purification (calculated yield: 64% -79%) and after semi-preparative SFC purification (isolated yield: 31% -84%). The ortho isomer 3gA was obtained with the lowest yield in the series, probably due to steric effect. Besides, regioisomerism of the phenyl substitution (1e-1g) has only minor impact on the yield and does not influence the regioselectivity. Strikingly, high to excellent regioselectivities from 85:15 to 97:3 ratios were also obtained. Interestingly, the scope of this one-pot procedure could be efficiently enlarged with non-saturated bromide (1i-1l). Noteworthy, functional groups such as carbamate-protected amine and ester are well tolerated with these reaction conditions (1k-1l) providing the related 1,5-disubstituted 1,2,3-triazoles with high to excellent yields and regioselectivities. Briefly, we succeeded in providing a procedure to efficiently access diverse 1,5-disubstitued 1,2,3-triazoles in a fast and simple manner. Remarkably, one of the advantages of this one-pot reaction is the in situ generation of azides from bromides, which are commercially available with a large diversity. Thus, this one-pot method prevents the sequential and time-consuming synthesis and isolation of azides, which could be unstable and are rarely commercially available. It makes this procedure very convenient, especially when sensitive low-molecular weight azides are required. A diverse range of functional moieties including N-protected amines, hydroxyls and esters are tolerated by these reaction conditions. This method will enable the synthesis of libraries of functionalizable 1,5regioisomers especially useful for drug discovery and chemical biology purposes.

Table 1 .

 1 Condition screening a .

			NaN 3
			Cp 2 Ni, Xantphos
			Cs 2 CO 3			1,4-regioisomer
			solvent, temp., t
	1a	2A		3aA		4aA
	Entry Solvent	Temp (°C)	Time	cYield	Ratio
				(h)	(%) c	3aA/4aA d
	1	H2O	rt	2	-e	-e
	2	DMF	rt	2	71	88:12
	3	EtOH	rt	2	-e	-e
	4	DCM	rt	2	-e	-e
	5	THF	rt	2	-e	-e
	6	DMF	50 °C (MW)	1	73	93:7
	7	DMF	80 °C (MW)	1	49	64:36
	8	DMF	100 °C (MW) 1	-e	-e
	9	DMF	50 °C (MW)	4	86	92:8
	10 b	DMF	50 °C (MW)	4	89	92:8

Table 2 .

 2 Substrate scope with various alkynes a .

		NaN 3
		Cp 2 Ni (20 mol%)
		Xantphos (20 mol%)
		Cs 2 CO 3 (1.0 equiv)		1,4-regioisomer
		DMF, 50 °C (MW), 4 h
	1a	2A-2H	3aA-3aH	4aA-4aH
	3aA	3aB	3aC	3aD
	72 (64)	24 (37)	34 (84)	76 b
	89:11	66:34	91:9	>99:1
	3aE	3aF	3aG	3aH
	73 b	36 (27)	56 (70)	34 (34)
	92:8	86:14 c	89:11 c	67:33

Table 3 .

 3 Substrate scope with various alkynes a .

		NaN 3
		Cp 2 Ni (20 mol%)
		Xantphos (20 mol%)
	R-Br	Cs 2 CO 3 (1.0 equiv)	1,4-regioisomer
		DMF, 50 °C (MW), 4 h
	1a-1l	2A	3aA-3lA	4aA-4lA
	3aA	3bA	3cA		3dA
	72 (64)	67 (69)	68 (64)	68 b
	89:11	85:15	85:15	97:3
	3eA	3fA	3gA		3hA
	84 (73)	73 (79)	31 (64)	89 (25)
	93:7	95:5	94:6		93:7
	3iA	3jA	3kA		3lA
	46 (65)	45 (67)	64 (90)	34 (34)
	91:9	94:6	96:4		81:19
	a Reaction conditions: Run on a 0.49 mmol scale of alkyne 2A with 1 (1.2 equiv), NaN3 (1.5 equiv),
	Cp2Ni (20 mol%), Xantphos (20 mol%), Cs2CO3 (1.0 equiv), DMF (2.0 mL), 50 °C (MW), 4 h.
	Isolated yields of 3 obtained after SFC purification; 3/4 ratio determined from the crude product by
	SFC analysis unless noted otherwise; in brackets: calculated yields of 3 obtained after flash column
	chromatography purification (in mixture with 4);

b

Isolated yield of 3 obtained after flash column chromatography.

Boc, tert-butoxycarbonyl; Cp, cyclopentadienyl; Me, methyl; Ph, phenyl; t-Bu, tert- butyl.

Acknowledgements

We are grateful to the institutions that support our laboratory: Université de Lille, Institut Pasteur de Lille, INSERM. The authors thank Nicolas Lefebvre for technical assistance. The authors thank the members of the Laboratoire d'Application de Résonance Magnétique Nucléaire (LARMN), Lille, France for NMR acquisitions and for their technical assistance. The postdoctoral fellowship of N.B.K. is funded by I-SITE-ULNE (contract CSB0120_ I-SITE Molecular Design For Health). V.C. is a recipient of a doctoral fellowship from Université de Lille and Universität des Saarlandes. N.K. is a recipient of a doctoral fellowship from Université de Lille.


Alexandre Leblanc
email: ale.leblanc@gmail.com

Ros Kiri Ing

Antoine Lavie

AW aveSuperposition Method Based on Monopole Sources with Unique Solution forAll Wave Numbers

Keywords: no, 43, 20, Rz, 43, 40, Rj

Asimple solution for the uniqueness problem of the wave superposition method is proposed in this paper.Many authors have pointed out the discrete set of wavenumbers for which the solution of the underlying integral equations is not unique. So far, the usual solutions are theoretically sophisticated and/or numerically disadvantageous. Here, by adding some sources interior to the virtual surface defined by the wave superposition method, the uniqueness problem can be easily removedwith lowcomputational effort. Furthermore, dealing with simple monopoles, this method is well-suited for practical applications.

Introduction

The boundary integral equations have been thoroughly studied since the 1960s for analyzing acoustic radiation and scattering from anya rbitrary vibrating body.A pplied in an infinite domain, Boundary Element Methods (BEMs)a re recognized to be more efficient than Finite Element Methods (FEMs), especially through the reduction of the computational dimension of the problem by one. Furthermore, the Sommerfeld condition is automatically satisfied so that the external domain doesn'tn eed to be bounded. The twom ajor drawbacks of the BEMs lie on numerical computation of the Helmholtz integral equation: the treatment of singular integrals and the nonuniqueness solutions at the eigenfrequencies of the corresponding Dirichlet interior problem. The latter problem is of primary influence on BEM results as fictitious eigenvalues density raises quickly with the frequency. Several approachs have been proposed in order to eliminate the non-uniqueness problem. Three typical ones are the CHIEF method presented by Shenck [START_REF] Schenck | Improvedintegral formulation for acoustic radiation problems[END_REF], the Burton-Miller method [START_REF] Burton | The application of integral equation methods to the numerical solution of some exterior boundary-value problems[END_REF] and the Null-field method [START_REF] Jones | Integral equations for the exterior acoustic problem[END_REF]. The CHIEF method is based on the Helmholtz integral equation on the surface of the radiating body combined with Helmholtz equation for some interior points. The resulting overdetermined set of equations is usually solved by the least-square approach. The Burton-Miller approach, inspired by Panich formulation [START_REF] Panich | On the question of solvability of the exterior boundary value problems for the wave equation and Maxwell'se quations[END_REF], forms alinear combination of the Helmholtz boundary integral equation and its normal derivative,p roviding also av alid solution at any frequencyb ut leading to hyper-singular integrals which can be handle following Guiggani algorithm [START_REF] Guiggiani | Ag eneral algorithm for the numerical solution of hypersingular boundary integral equations[END_REF][START_REF] Silva | Anumerical imof ahypersingular boundary element method applied to 3D time-harmonic acoustic radiation problems[END_REF]. The Null-field method, which is combined with the Helmholtz integral surface equation [START_REF] Stupfel | Combined integral equation and null-field method for the exterior acoustic problem[END_REF], uses the known bilinear expansion for the simple wave source to express the integral relation in aset of equations leading to aunique solution.

Another BEM related approach is the Wave Superposition Method (WSM): as imple numerical technique for free-field radiation and scattering problems, originally formalized by Koopmann [START_REF] Koopmann | Am ethod for computing acoustic fields based on the principle of wave superposition[END_REF]. The principle of the WSM can be found in the literature under various denominations as the Method of Fundamental Solutions [START_REF] Kondapalli | Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions[END_REF] (MFS), the sources simulation method [START_REF] Kress | On the simulation source technique for exterior problems in acoustics[END_REF], the auxiliary [START_REF] Ya Ng | Ab oundary integral equation method using auxiliary interior surface approach for acoustic radiation and scattering in twodimensions[END_REF] or equivalent [START_REF] Johnson | An equivalent source technique for calculating the sound field inside an enclosure containing scattering objects[END_REF] sources method. The main aspects of the most usual methods dealing with sound source reconstruction can be found in ar ecent review [START_REF] Magalhaes | Sound sources reconstruction techniques: ar eviewo ft heir evolution and newtrends[END_REF]. While different in theoretical aspects, all theses formulations are based on the idea that the real body is substituted by as et of elementary sources located in its interior,s ot he global acoustic field of interest can be approximated by the sum of the fields due to each sources. Being astraightforward direct method, the WSM offers several advantages. First, computational cost is lower than BEM or FEM. Second, the WSM constitutes an efficient and economical simulation technique for practical applications. As as etback to the simplicity of this principle, the determination of the source strengths leads to numerical and analytical difficulties, extensively discussed overt he past twod ecades. Following the first WSM stability analysis [START_REF] Song | Numerical errors associated with the method of superposition for computing acoustic fields[END_REF], numerous alternativesh avee merged to overcome one of the major drawbacks of the method: the non-uniqueness of solutions at fictitious resonant frequencies [START_REF] Wilton | Aclarification of nonexistence problems with the superposition method[END_REF]. To solvethis issue, one elegant solution is to use ahybrid combination of single and double layer potentials [START_REF] Jeans | The wave superposition method as arobust technique for computing acoustic fields[END_REF] as the Burton-Miller formulation. This method still one of the most reliable [START_REF] Marburg | Cat'se ye radiation with boundary elements: comparative study on treatment of irregular frequencies[END_REF] even for high frequencies, butt he use of such an analytical sophistication may compromise practical applications. Aside the optimal sources placements studies [START_REF] Wang | Ar etracted boundary integral equation for exterior acoustic problem with unique solution for all wave numbers[END_REF][START_REF] Song | Numerical errors associated with the method of superposition for computing acoustic fields[END_REF], numerical schemes as Tikhonovr egulation or Singular Va lues Decomposition (SVD)were also successfully applied [START_REF] Sarkissian | Method of superposition applied to patch near-field acoustic holography[END_REF][START_REF] Fahnline | Anumerical solution for the general radiation problem based on the combined methods of superposition and singular-value decomposition[END_REF] to improve WSM results, butalso somewhat overlooked as as olution for the non-uniqueness problem. Indeed, only asevere regulation or high SVD truncation allows to smoothen enough the resonant responses. Thus, and as ac ounterpart of this significant change in sources to field positions dependencies, the WSM error rises to an unacceptable level. Another attempt wastoadd an appropriate damping to the virtual source system by the mean of acomplexradius vector [START_REF] Yu | Wave superposition method based on virtual source boundary with complexradius vector for solving acoustic radiation problems[END_REF]. Though this technique can insure the unique solutions for all wave numbers if enough damping is introduced, choosing the complexradius vector is adifficult task, as too much damping will deteriorate the method accuracy.

The aim of this paper is to present am erged formulation of the twoconceptions behind the superposition methods. The first is the discretization of the interior form of Helmholtz integral equation and the second is the search of fundamental solutions for randomly placed sources. The performance of the proposed method at critical wave numbers and its application in accurate free-field radiation prediction are then evaluated through numerical experiments.

General theory

p (r) + k 2 p (r) = 0 r ∈ Σ, (1)
where p is the pressure at point r in the surrounded fluid Σ (assuming an implicit e -jωt dependence). This equation is associated with Neumann boundary condition on the surface Γ,

∂p (r) ∂n = jωρv n (r) r ∈ Γ, (2)
in which ∂n denotes normal differentiation at the point r in the direction from the interior region Ω toward Γ, v n (r) is the normal component of the velocity at point r and ρ is the fluid density modulus. The pressure must also satisfy the radiation condition lim

R→∞ S R ∂p (r) ∂r 0 -jkp (r) 2 r=R dS = 0, (3)
where r 0 is the radial distance from the origin of coordinates and S R is asphere of radius R centered at the origin and surrounding r and Γ. The single-layer potential seeks to represent p as

p (r) = Γ σ (r s ) G (r, r s ) dΓ r s r ∈ Σ, ( 4
)
where G is the free-space Green'sfunction and σ is adensity function on Γ.A pplying the boundary condition of a givennormal pressure on Γ,leads to the boundary integral equation

- 1 2 σ (r) + Γ σ (r s ) ∂G (r, r s ) ∂n dΓ r s = ∂p (r) ∂n r ∈ Γ. (5)

The Wave Superposition Method

The simple idea behind this method is that the acoustic field of ac omplexr adiator (cf. Figure 1) can be reconstructed as as uperposition of individual simple sources.

The equivalencyo ft he WSM to the Helmholtz integral formulation has been shown by Koopman [START_REF] Koopmann | Am ethod for computing acoustic fields based on the principle of wave superposition[END_REF], thus validating the superposition integral:

p (r) = jωρ Ω q (r s ) G (r, r s ) dΩ (r s ) r ∈ Γ ∪ Σ, (6)
ρ is the density of the medium, ω is the angular frequency of the harmonic vibration of the surface Γ defining the interior region Ω.T he source strength is denoted by q (r s ), evaluated at r s inside Ω.

To reduce equation ( 6) to anumerical form, it'sconvenient to assume the sources distributed on Γ inside Ω.I f this surface is divided into N sufficiently small elements, we can approximate the normal velocity on the surface of the radiator,

u n (r) ≈ N i=1 Q i ∂G (r, r s ) ∂n r r ∈ Γ r s ∈ Γ , ( 7
)
where Q i is the volume velocity of the simple source. Since u n (r) is known, Q i is giveninmatrix form by

Q = [D] -1 u n . ( 8
)
After finding the source strength vector Q,t he pressure field is calculated from

p (r) = jωρ N i=1 G (r, r s ) Q i r ∈ Γ ∪ Σ r s ∈ Γ , (9)
thanks to the linearized Euler equation

jωρu n (r) = ∂p(r) ∂n r . ( 10
)
While there is much scope for discussion on the number and location of the interior sources for optimum accuracy, the method is claimed to be superior to the usual boundary integral formulation of the exterior acoustic problem since the source and collocation points neverc oincide, there are no problems associated with singularity.H owever,the superposition integral exhibits non-uniqueness at critical wave numbers, revealed by the layer potential formulations of the WSM principle.

The Method of Fundamental Solutions

Forthis method, equation ( 6) is still satisfied, because the sources can be placed anywhere inside the radiator.S o, on numerical aspect, the MFS is an another version of the WSM as the source intensities satisfy the same equation [START_REF] Fairweather | The method of fundamental solutions for scattering and radiation problems[END_REF],

u n (r) = M i=1 A i ∂G (r, r s ) ∂n r r ∈ Γ r s ∈ Ω, (11)
Here, aleast-square functional of this equation can be minimized [START_REF] Kondapalli | Analysis of acoustic scattering in fluids and solids by the method of fundamental solutions[END_REF], to obtain the best positions for the fictitious sources providing the optimal solutions. Another optimal MFS positioning has been recently proposed using the image method [START_REF] Chen | Equivalence between Trefftz method and method of fundamental solution for the annular Green'sfunction using the addition theorem and image concept[END_REF].

The difference between these the WSM and the MFS approaches is that the randomly distributed sources lead to higher condition number,u nsuitable for effective numerical calculation, butt he MFS does not exhibit critical wave numbers, except for some special sources positioning [START_REF] Chen | Using the method of fundamental solutions in conjunction with the degenerate kernel in cylindrical acoustic problems[END_REF]. Thus, and apart from these particular cases, this method cannot be written in terms of alayer potential because these sources do not respect the Helmholtz integral positioning requirements. However, the MFS allows the system of equation to be overdetermined by ag reater number of collocation points.

Non-uniqueness

Considering the vibration cavity of the Figure 1, the three main types of the WSM established on av irtual surface Γ placed in Ω (with interior region Ω and exterior region Σ ), are as follows:

(1) Single-layer potential integral (2) Double-layer potential integral

p (r) = Γ σ (r s ) G (r, r s ) dΓ r s , r ∈ Γ ∪ Σ. (12)
Γ µ (r s ) ∂G (r, r s ) ∂n r s dΓ r s = p (r) , if r ∈ Σ p (r) + µ(r) 2 , if r ∈ Γ (13)
(3) Hybrid combination

Γ γ (r s ) G (r, r s ) + α ∂G (r, r s ) ∂n r s dΓ r s (14) = p (r) , if r ∈ Σ p (r) + γ(r) 2 , if r ∈ Γ
in which G (r, r s ) is the free-space Green'sfunction evaluated between the observation point and the source, located respectively at r and r s .Onthe virtual surface Γ ,Green's theorem leads to the Helmholtz boundary integral equation for interior region and its differentiated form.

Considering the case of the Single Layer Potential formulation (WSM-SLP), Jeans [START_REF] Jeans | The wave superposition method as arobust technique for computing acoustic fields[END_REF] shows that if the excited wave number k equals or is close to an interior Dirichlet eigenvalue, equation ( 12) has anon-unique solution. Fort he Double Layer Potential formulation (WSM-DLP), non-uniqueness for equation ( 13) occurs at interior Neumann eigenvalues. The Hybrid combination (WSM-H, equation 14)e nsures aunique solution with an imaginary α because ar eal coefficient define an interior Robin eigenproblem.

Figure 2s hows the Mean Squared Error (MSE)o btained with the previous formulations and for an infinite cylinder (radius R). This estimator is defined as

MSE = N i=1 |P2 i -P1 i | 2 N i=1 |P1 i | 2 , ( 15
)
where P 2isthe reconstructed pressure and P 1its known values. The velocity distribution on the surface is generated by ap oint source located at 1.1a of the center (a = 0.1R). This figure highlights the fictitious frequencies arising from the classic WSMs, and the solution obtained by the WSM-H and with the MFS where the sources (N = M = 100)a re located randomly on the inscribed circle (radius a). These eigenfrequencies for single-layer potential formulation are such that

J n (ka) = 0,n = 0 , 1 , 2 ,... ( 16
)
and for double-layer-potential

J n (ka) = 0,n = 0 , 1 , 2 ,... ( 17
)
where J is the Bessel function and J its derivative.W ith the WSM approach, adirect determination of the sources strength is made, it thus differs from the minimization process usually employed in fundamental solutions determination.

Combined Wave Superposition Method

To achieve uniqueness, we propose to merge the rigorous formalism underlying the WSM with the ease of choice for MFS sources locations. From the numerical formulation of WSM and MFS, we can write

[D WSM ][ D MFS→WSM ] [D WSM→MFS ][ D MFS ] {Q} {A} = {u n } WSM {u n } MFS , ( 18
)
where

[D WSM ]i st he classic WSM dipole, [D MFS ]t he MFS coefficient matrix, [D MFS→WSM ]t he coefficient matrix between MFS sources and WSM collocation points and [D WSM→MFS ]t he coefficient matrix between WSM sources and the MFS collocation points.

The basic idea here is to keep asufficient butsmall MFS terms number because those sources (refereed for the rest of the paper as the complementary sources)a re incorporated in WSM formulation only for achieving uniqueness at critical wave numbers and not for improving the global accuracy. The resulting formulation of equation ( 18) is named the Combined WSM (CWSM)asitcombines MFS sources with the WSM formulation. The main difficulty with this method is, as for CHIEF,t he selection of interior points away from the internal standing wavesn odes of the corresponding Dirichlet problem. The step-by-step method proposed by Petrov [START_REF] Petrov | An adaptation of auxiliarysources method for stationary acoustic problems[END_REF] for the source coordinates calculation could be an efficient algorithm to solvet his particular problem.

Numerical investigations

Ill-conditionning and regularization

Basic rank-revealing decompositions showt he rankdeficient nature of numerical problems defined by superposition methods. Fort he previous defined problem, the Figure 3shows that only the first singular values (zone I) of the influence matrix ([D]inequation 8) are clearly relevant while additional values improvedslightly the results (zone II)and others add numerical noise (zone III). Thus, one common wayt oi mprove sources methods is to perform aT runcated SVD [START_REF] Hansen | The truncated SVD as amethod for regularization[END_REF]. Applied to the formulations previously presented, results of Figure 4, with af actor of 10 4 between the max and min singular values taken into account, exhibit areal improvement for the MFS butc an be of consequence for the WSM results, without improving the solutions at eigenfrequencies. It must be remembered here that these critical wave numbers have nothing to do with ill-conditioning buta re due to the nature of WSM method. Nevertheless, the number of singular value to takei nto account is not at rivial task, as optimal WSM solutions (Figure 2) are recoveri nt his case with only twomore singular values.

Other direct regularization methods likeT ikhonovregularization have also been tested on superposition formulations, producing comparable or higher errors [START_REF] Sarkissian | Method of superposition applied to patch near-field acoustic holography[END_REF].

Fictitious eigenfrequencies

In order to demonstrate the accuracyo ft he proposed method (equation 18), the cylinder of the section 1.3 is reused, with 20 sources subtracted from the primary WSM sources network (N = 80)and disposed on an inner circle of radius b = 0.95a = 0.095R to form the complementary sources network (M = 20). Simple SVD inversion scheme is used to solvee quation [START_REF] Wang | Ar etracted boundary integral equation for exterior acoustic problem with unique solution for all wave numbers[END_REF].F igure 5s hows the improvement brought by the CWSM (applied to the SLP form)a tt he critical wave numbers. However, with this configuration, the improvement is not optimal.

One efficient solution is to dispatch the complementary sources randomly,a sa ny basic MFS do. Figure 6h ighlights the benefits of this configuration for aw ider band of frequencies. Here, the CWSM matches the hybrid formulation accuracy, while saving athird of the computation time [START_REF] Benthien | Nonexistence and nonuniqueness problems associated with integral equation methods in acoustics[END_REF].

Theoretically,i ti ss u ffi cient to have ac omplementary source on an on-zero nodal line to overcome the uniqueness problem. But usually,this task is non-trivial because of non-regular geometry or while computing at high frequencies. As aconsequence, the randomization of complementary sources appears to be good compromise between the computational cost of CWSM and its accuracy. Following the usual rule of discretization of four subdivisions per wavelength [START_REF] Benthien | Nonexistence and nonuniqueness problems associated with integral equation methods in acoustics[END_REF], experiments have shown satisfying results for an umber of complementary sources approximately equal to atenth of the WSM sources.

Alast 2D application is performed on an infinite cylinder of rectangular section (cf. Figure 7a)toinvestigate the reliability of the CWSM at high frequencies.

Figure 7b shows the results for ka from 22 to 23.5, the CWSM performed as well as the previous cases. Thus, its accuracydepends solely of the classic frequencycriterion, setting the maximum recommended distance between two WSM sources.

3D Application

The method is nowa pplied to as phere of radius R.S uperposition surface is set on ai nterior centered sphere of radius a = 0.1R.Figure 8shows the MSE for the surface pressure reconstruction with classic WSM and with the CWSM, for av elocity distribution generated by as ingle point source at 1.1a of the center.Asfor the planar examples, uniqueness of solutions is achievedwith M ≈ N/10 internal sources at random position (N = 2450).

More sophisticated geometries and surface velocity distributions can be carried out using this approach. Nevertheless, as the classical WSM, the accuracyofthe CWSM can be altered for geometries with corners (difficulties to takeinto account the discontinuity at tangent n).

Conclusion

The proposed combination of the wave superposition method and some internal sources provides au nique solution at anyfrequencywith simple radiating monopoles. The computational cost for this Combined Wave Superposition Method is almost equivalent to the single layer potential formulation of the WSM. The positions of the superposition sources remain subject to the usual rules of thumb and the added source are preferentially placed at random positions. This distribution is the easiest way to avoid source placements at nodal lines, and to achieve uniqueness solutions for lowtomid frequencies. As aconsequence, if these nodal lines are known, the number of complementary sources can be optimized.

Figure

  Figure 1shows the geometry of the radiation problem. the well-known Helmholtz differential equation governs the propagation in finite fluid domain Σ,

Figure 1 .

 1 Figure 1. Vibrating body and the virtual sources.

Figure 2 .

 2 Figure 2. Critical wave numbers for three WSM formulations and the MFS.

Figure 3 .

 3 Figure 3. Singular Va lue Decomposition of influence matrix.

Figure 4 .

 4 Figure 4. Truncated SVD influence on precision.

Figure 5 .

 5 Figure 5. Complementary CWSM sources uniformly disposed.

Figure 6 .

 6 Figure 6. Random disposition of the complementary sources.

Figure 7 .Figure 8 .

 78 Figure 7. Reliability of the CWSM at high frequencies.

©S.Hirzel Verlag • EAA

Vol. 96 (2010)


Huy Duc

Zhirou Dang

Wei Zhang

Benjamin Wang

Farid Oursel

Cecile Juillot

Hugues Dupouy

Stéphane Lemonnier

Mounier

Tropical mangrove forests as a source of dissolved rare earth elements and yttrium to the ocean

Keywords: Rare earth elements, yttrium, water stable isotopes, mangrove, estuary

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Over the past decade, rare earth elements (REEs or the lanthanide series), Y and REE isotopes have received significant attention in geochemistry as tracers of the geological history of the continental crust and provenance study [START_REF] Bayon | Rare earth elements and neodymium isotopes in world river sediments revisited[END_REF]. In paleoenvironmental studies, REEs are also commonly used as proxies to reconstruct water chemistry and oxygen saturation as per the distinct behaviour of Ce during redox transitions (Auer et al., 2017;Wallace et al., 2017). The fractionation between the light REEs (LREEs), heavy REEs (HREEs) and the non-lanthanide Y can also highlight the mechanisms of particle transport, sediment deposition and even geological features (e.g., iron formation) over the Earth's history [START_REF] Bayon | Rare earth elements and neodymium isotopes in world river sediments revisited[END_REF]Planavsky et al., 2010). More recently, because of the implication of REEs in novel technologies, REE anomalies (increased in concentrations of a specific REE relative to its neighbouring REEs) could also be used as a proxy for emission sources (Dang and Zhang, 2021;Ma et al., 2019;Tepe et al., 2014).

However, the environmental chemistry of REEs remains fragmented, mostly regarding their anomalous behaviour across the river-estuarine-coastal water mixing zone where the fractionation between LREEs and HREEs is often associated with the redistribution of REEs among the dissolved and particulate fractions and the formation of stable dissolved complexes (Nozaki et al., 2000;Sholkovitz and Szymczak, 2000;Sholkovitz, 1995). As a consequence, the ocean mass budget of REEs remains unbalanced with missing fluxes at the global scale (Arsouze et al., 2009;Garcia-Solsona and Jeandel, 2020;Pourret and Tuduri, 2017;Tachikawa et al., 2003).

The interpretation of estuarine REE behaviour is fundamental to highlight their geochemistry at the continent-ocean interface. One conventional feature derived from decades of investigation on REEs' estuarine geochemistry is that large-scale removal of dissolved REEs (especially LREEs) occurs in the estuarine mixing zone (Elderfield and Greaves, 1982;Lawrence and Kamber, 2006;Nozaki et al., 2000;Pourret and Tuduri, 2017;Sholkovitz, 1995). This phenomenon minimizes the effective continental flux of REEs to the ocean and subsequently affects the marine budget calculations of REEs (Nozaki et al., 2000). Various factors would lead to such extensive removal of REEs. These include planktonic uptake, coprecipitation with ferromanganese oxyhydroxides and salt-induced coagulation of colloids (Hoyle et al., 1983;Nozaki et al., 2000;Sholkovitz and Szymczak, 2000). However, a limited number of publications pointed out a supply of dissolved REEs in the mid-estuary zones (Lawrence and Kamber, 2006;Nozaki et al., 2000). This REE release could be associated with desorption from terrigenous suspended particles or remineralization in the estuarine system. Moreover, most of the estuarine systems investigated so far for REEs geochemistry were major well-oxygenated riverine systems. However, it has been demonstrated that REEs cycling in marine waters can be impacted by redox variations (Bau et al., 1997). This process is particularly important as it can increase the effective continental REE flux to the oceans through enhanced supply to the water column upon dissolution of REEs-bearing oxyhydroxide phases. Therefore, further insights on REE behaviour across the redox-sensitive estuarine mixing zone are needed to strengthen our understanding of the REE geochemistry at the continent-ocean interface.

Tropical mangrove forests are of great interest to investigate these environmental conditions. First, they cover a large surface area (150,000 km 2 ) where complex hydrological processes balance abundant precipitation, surface runoff, and evaporation (Spalding, 2010). Moreover, the combination of elevated and annually constant temperature patterns with high bioavailability of natural organic matter boosts bacterial respiration, promoting hypoxia (Dubuc et al., 2019). To date, very limited studies on REEs focused on this critical ecosystem as it is generally assumed that the mangrove systems act as a buffer zone retaining trace elements and thus contribute a minor input for REEs to the oceans (Marchand et al., 2012).

Here, we investigated REE internal cycling within two estuarine mangrove systems in the subtropical region of New Caledonia. We meticulously measured dissolved REEs and Y over a 24-hour cycle in mangrove stations during a dry season and the spatial variations across the estuary in a rain season. To track whether additional water masses alter the mixing between the fresh and seawater endmembers, we also measured stable water isotopes (δ 18 O and δD) to assess the hydrologic regime. We compared the stable water isotopes in these mangrove systems with other river waters collected in southeastern New Caledonia to verify the signature of the freshwater endmembers. Altogether, the data highlights REE behaviour during the estuarine mixing and document the mangrove forest's role on REE cycling at the continent-ocean interface. This dataset will help answer whether the REE continental flux from the tropical mangrovedominated estuaries should be included in the REE marine budget.

Materials and Methods

Study site description

In the Southwest Pacific Ocean, New Caledonia is surrounded by the Coral Sea (Figure 1A,B).

The main island "Grande Terre" is 400 km long and 64 km wide with a semi-arid tropical climate along the west coast. The whole island is also bordered by a coral reef enclosing a lagoon of over 20,000 km 2 . The rich reef diversity and associated ecosystems were inscribed as a UNESCO World Heritage Site in 2008. On the other hand, most of the island is mountainous with vast ultramafic masses, schists and outcrops of basalt (Lillie and Brothers, 1970). Weathering of the ultramafic rocks' surface led to the formation of thick lateritic regoliths (tens of meters) hosting deposits of transition metallic elements of prime economic importance (Dublet et al., 2014;Noël et al., 2014). Between the lucrative mineral-rich land and the sea of tremendous ecological importance, the mangrove system acts as a buffer zone to filter heavy metals from reaching the reef (Marchand et al., 2012).

The hydrological behaviour of the Grande Terre is clearly distinct between the southwestern and northeastern coasts because of the 'rain-shadow' effect across the central massif divide [START_REF] Terry | Rain-shadow hydrology: Influences on river flows and flood magnitudes across the central massif divide of La Grande Terre Island, New Caledonia[END_REF] (Figure 1B). Accordingly, the southwestern coast (leeward) tends to be drier than the windward northeastern coast. Overall, the hydrologic regime is characterized by high annual variability of rainfall amount and extreme events. Moreover, high and steep watersheds are associated with flash floods and thus rapid water transfer to the lagoons [START_REF] Desclaux | Suitability of a lumped rainfall-runoff model for flashy tropical watersheds in New Caledonia[END_REF].

The Voh-Kone region (Northwest of the Grande Terre, Figure 1B) is an area of great economic and ecological interest. The Koniambo Massif hosts a large mine (Koniambo mine, Figure 1C), one of the largest nickel reserves in New Caledonia. The ore is conveyed to a coastal smelting site (Koniambo Nickel SAS, Figure 1C). Besides, the hydrologic system mainly comprises of two major rivers (Temala and Voh) discharging into the mangroves, then the bays of Chasseloup and Vavouto, respectively. Moreover, the hydrologic system comprises also of relatively smaller streams, such as the Coco River. These small tributaries have their flows significantly reduced during the dry season.

This study focused on the Temala and Coco Rivers (Figure 1C) in the Voh region. The Temala River originates from outside of the Koniambo Massif and discharges into Chasseloup Bay. It is, therefore, considered not impacted by mining activities. On the other hand, the Coco River's sources are in the Koniambo Massif hosting the Koniambo Mine. Along its course toward Vavouto Bay, the Coco River meanders parallelly to the ore conveyor. The Koniambo Nickel SAS smelting site is indeed only ca. 1.2 km away from the stream (Figure 1 C). Therefore, it is highly probable that this river is subject to anthropogenic impacts. Besides this contrasted exposition to anthropogenic sources, the natural geological settings of both rivers also differ. The Temala River catchement is made of soils developed on volcano-sedimentary rocks (cherts, basalts), whereas the Coco River catchment is composed of Ni-laterites developed on ultramafic rocks (peridotites) [START_REF] Merrot | Nickel and iron partitioning between clay minerals, Fe-oxides and Fe-sulfides in lagoon sediments from New Caledonia[END_REF].

We also investigated river waters (Dumbea, Coulee, Tontouta, Pirogue, Table 1) around Noumea in the Grande Terre's Southeast (Figure 1B) as a reference site for hydrological assessment using salinity and water isotope mixing.

Water sampling

We organized multiple sampling trips to investigate the hydrologic regime and REE cycling. The During a dry season (June 2019), the first campaign aimed for a high-temporal resolution sampling in the mangrove forests (sites C2 and T6, hereafter referred to as "mangrove stations", Figure 1C). For that purpose, two automatic samplers (ISCO) were deployed during high tide . The samplers were programmed to collect water samples one hour after installation to ensure the resettlement of resuspended sediments during deployment. The first water samples were collected at 9h AM at C2, and 10h AM at T6. Following samples were collected every hour.

At the end of the 24-hour automatic sampling cycle, all samples were filtered (0.22 µm, cellulose acetate, Sartorius) directly on site. The filtered waters for stable water isotopes were filled to the top to avoid water-air exchange, while samples for elemental analysis were acidified to pH<2 with ultra-trace HNO3 (Merck). The samples were then immediately shipped by air to Trent University for analysis.

In 2020, during the rain season, a series of samples were collected across the salinity gradient along the Temala (T1-T8) and Coco (C1-C5) rivers (hereafter referred to as the "estuarine stations", Figure 1C). An additional sample was collected in the lagoon to serve as a marine endmember (M, Figure 1C). The samples were treated with the same protocol as in 2019 before being shipped to Trent University.

All the filters, sampling and storing bottles were previously rinsed with 10% HCl and milli-Q water (18 MΩ cm) in the laboratory and with river or lagoon water in the field.

Water stable isotopes

Water stable isotopes (δ 18 O and δD, deuterium) were measured using a Liquid Water Isotope Analyzer (LWIA-24d, Los Gatos Research) at the Water Quality Center (Trent University, Ontario, Canada). The delta notation was calculated relative to the V-SMOW (Vienna-Standard Mean Ocean Water) standard. Analytical recovery was assessed using two isotopic natural water reference materials (CRMs, Elemental Microanalysis, UK), covering the range of δ values found in natural waters (Table S1). Averages and standard deviations of each measurement (standards and samples) were calculated based on eight injections (i.e., n = 8, 750 nL each). We also used ultra-high purity water (18.2 MΩ cm) as an in-house standard to bracket every two samples to monitor analytical drift and eliminate any memory effects. However, no correction was necessary. Analytical recovery of stable water isotopes is reported in Table S1.

Elemental analysis

To accurately determine the concentrations of REEs and Y at the ng/L levels in complex environmental matrices (seawater), we have performed a preconcentration step using column chromatography before analysis by Inductively Coupled Plasma Mass Spectrometry (ICP-MS). A full description of the REE column chromatography and ICP-MS analysis were reported elsewhere (Dang and Zhang, 2021;Ma et al., 2019). Briefly, REEs and Y in the filtered water samples were preconcentrated using 0.2 mL Nobias Chelate-PA1 resin (Hitachi High-Technologies). An aliquot of 50 mL of samples buffered at pH 6 was loaded on previously washed and conditioned resin. The seawater matrix was then washed off with 40 mL 0.05 M acetate buffer solution (pH = 6). REEs and Y were collected by eluting 20 mL of a 1 M HNO3 solution through the column. This aliquot was collected into a 30 mL PTFE vessel and completely evaporated on a hotplate at 100 o C. A final 2 mL of 0.5 M HNO3 was added to retake the REEs and Y.

All acids used to clean and wash the resins were double-distilled trace metal grade. The acetate buffer was also passed through the Nobias column for purification. We also meticulously checked procedural blanks and column recovery in every batch of 10 samples. Procedural blanks were between 0.1 to 29 pg of REEs and Y and significantly less than their mass in natural samples. Several aliquots (50 mL) of certified reference seawater CASS-6 (National Research Council of Canada, NRCC) were also repeated to test column recovery (Ma et al., 2019). European interlaboratory calibration (Yeghicheyan et al., 2019). Excellent recovery was observed; the detailed data are reported in Table S2.

Normalization of REE patterns and calculations of anomalies

A common practice in the scientific community to eliminate the Oddo-Harkins effect and compare samples is to normalize the measured REE concentrations to geological materials (e.g., upper continental crust, shales, chondrite) or offshore seawater (Piper and Bau, 2013). Here, we normalized the measured concentrations of dissolved REEs to Post-Archean Australian Shale (PAAS (McLennan, 2001)) (Goldstein and Jacobsen, 1988;Ma et al., 2019;Piper and Bau, 2013). The shale-normalized concentrations are hereafter referred to as REEPAAS.

In the current literature, excess or depletion of an REE relative to its neighbouring REEs are referred to as positive or negative anomaly of this element (REE/REE*). Accordingly, the REE anomalies could be determined by several approaches (e.g., arithmetic mean, geometric extrapolations, modelling the shape of PAAS-normalized patterns, third-order polynomial fit).

Using all these approaches, Hatje et al. have demonstrated minor variability in the final results (Hatje et al., 2016). Therefore, we calculated Ce, Eu, and Gd anomalies using the following equations (arithmetic mean).

𝐶𝑒 𝐶𝑒 ⁄ = 2 × 𝐶𝑒 𝑃𝐴𝐴𝑆 𝐿𝑎 𝑃𝐴𝐴𝑆 + 𝑃𝑟 𝑃𝐴𝐴𝑆 (𝐸𝑞. 3) 𝐸𝑢 𝐸𝑢 ⁄ = 2 × 𝐸𝑢 𝑃𝐴𝐴𝑆 𝑁𝑑 𝑃𝐴𝐴𝑆 + 𝑆𝑚 𝑃𝐴𝐴𝑆 (𝐸𝑞. 4)
𝐶𝑒 𝐶𝑒 ⁄ = 𝐺𝑑 𝑃𝐴𝐴𝑆 0.33 × 𝑆𝑚 𝑃𝐴𝐴𝑆 + 0.67 × 𝑇𝑏 𝑃𝐴𝐴𝑆 (𝐸𝑞. 5)

Results and Discussions

Physical-chemical properties

At both mangrove stations (C2 and T6, Figure 1B), pH values varied within a narrow range (7.8 ± 0.1, n = 48, Table 1 andFigure S1B). Besides, the daily variations in salinity followed a sinusoidal curve, typical of estuarine systems (Figure 2A). This variation pattern is more noticeable at Temala with low tide (S = 26) recorded at 4h and 16h, and high tide (S = 33) at 22h.

However, the salinity pattern at Coco is significantly distinct, with two events marked by steep drops at 13h, 19h and a third gradual decrease from midnight until 7h AM (1 st , 2 nd , 3 rd as marked in Figure 2A). The variation range of salinity in Coco is also narrower (29.6 to 34.2) than in Temala (26.0 to 33.0) (Table 1). 1) with temperature drops at 11h and 21h (Figure S1A). Minimums in water temperatures at Coco are lagged by two hours relative to the salinity minimums (13h and 19h, Figure 2A).

Across the entire estuaries (estuarine stations), salinities ranged from 0 to 34.9 for the river water and marine endmembers, respectively (Figure 2B). On the other hand, all the river samples collected from the Southeast of New Caledonia are freshwater with a salinity of zero (Figure 2C).

Stable water isotopes and the hydrologic regime

The δD and δ 18 O pairing. As the mangrove stations have narrow daily salinity variations (Table 1), so too is the range of stable water isotope compositions relative to the whole estuaries (Figure To explain the difference in the intercepts (higher values in the dry season than the rain season), we calculated the deuterium excess (d-excess) using the conventional approach: d-excess = δD -8×δ 18 O. This variable is valuable as it quantifies the deviation of a given dataset from the Global Meteoric Water Line (GMWL) by differential kinetic fractionation effects between D and 18 O.

Such effects are related to humidity, moisture recycling and post-deposition process (Dansgaard, 1964). Low d-excess tends to reflect slow evaporation due to high humidity, while high d-excess values indicate fast evaporation due to low humidity (Lee et al., 2003). This interpretation is coherent with our observations as high d-excess values (15.8±1.3‰ and 15.9±2.9‰ at Coco and Temala, respectively) were observed at the mangrove stations in dry season while low d-excess values were typical of rain season and across the estuaries (0.4±5.8 ‰) (Table 2).

Pairing δD and δ 18 O with salinity. The linear relationships between δ 18 O, δD and salinity have been used to estimate the stable water isotope composition of a freshwater endmember, defined as the δ 18 O and δD values when salinity equals zero. This extrapolation should be interpreted with careful consideration of the contributions of regional precipitation, river water and runoff.

However, it has been demonstrated that the extrapolated δ 18 O and δD of freshwater endmembers in the Great Barrier Reef (NE Australia) reflected the isotope composition of local river water with relatively insignificant contributions of regional precipitation and runoff (Munksgaard et al., 2012).

Accordingly, δ 18 O and δD values in the samples collected in the mangroves of Coco and Temala varied linearly with salinity (Figure 3 and Table 2). In addition, all linear relationships converged to a common signature of the marine endmember (blue diamond in Figure 3). We extrapolated these linear relationships toward salinity of zero to determine the isotope composition of each river water endmember (Table 2). It is important to note that the interpretation of such relationships often requires a spatial and temporal assessment of the two systems (Conroy et al., 2017). As the samples were collected simultaneously in the dry season, the difference in water isotope composition between the freshwater endmembers at Coco and Temala can thus be only attributed to distinct water sources in each river system.

In the mangrove stations, the two linear regression lines are significantly distinct between Coco and Temala, except for a few stations at Temala that fall on the regression line of Coco (encircled data, Figure 3B). These data represent the last samples collected during the high tide over the 24hour series (3 rd discharge event of the Coco River, Figure 2A). All physical-chemical properties and stable water isotopes of the two rivers overlap during this period (grey zone in Figure 2 A,D,G). This probably reflects a common blackish water mass formed during the high tide.

Therefore, we excluded these data from Temala's δD-salinity regression because of the lack of more robust proxies to confirm this phenomenon and assuming that it may be minor. The exclusion of these three data did not affect the fact that the water isotope composition is significantly more depleted in the Coco River than Temala during the dry season. This depletion is more noticeable for δD (-72.9±8.9‰ vs. -36.0±2.8‰, respectively) than δ 18 O (-9.9±1.7‰ vs. -8.4±1.2‰, respectively) (Table 2).

However, across the estuaries and during the rain season, the δD-S and δ 18 O-S relationships for both river systems are significantly similar (p<0.05) and align along with consistent equations (δD=1.0×S-33.7 and δ 18 O =0.2×S-5.2, Table 2 and Figure 3A). Both the slopes and intercepts are close to the Temala mangrove during the dry season (δD=1.0×S-36.0 and δ 18 O =0.2×S-8.4, Table 2). This observation suggests that the hydrologic regime in the Temala River differs only slightly within seasons with relatively constant water isotope compositions of the river endmember (𝛿𝐷 𝑅𝑖𝑣𝑒𝑟 𝑇𝑒𝑚𝑎𝑙𝑎 ~ -34 to -36‰ and 𝛿 18 𝑂 𝑅𝑖𝑣𝑒𝑟 𝑇𝑒𝑚𝑎𝑙𝑎 ~ -5.2 to -8.4‰). These values are close to the four southeastern rivers over an annual cycle (Figure 3A) (𝛿𝐷 𝑅𝑖𝑣𝑒𝑟 𝑆𝐸 = -31 ± 6‰ and 𝛿 18 𝑂 𝑅𝑖𝑣𝑒𝑟 𝑆𝐸 = -5.8 ± 1.0‰, Table 2), confirming reasonably consistent δD-S and δ 18 O-S relationships and hydrologic regimes of major river systems along the western coast of New Caledonia.

It is important to note that the Coco River is a small tributary with a relatively dry riverbed with significantly decreased flow during the dry season. Consequently, the Coco River's isotopic compositions differ substantially during the dry and rain seasons (Table 2) due to less precipitation and enhanced evapotranspiration during the dry season.

In summary, the difference in stable water isotope composition between the Coco and Temala rivers is related to the natural effects of a depleted hydrologic reservoir with enhanced evaporation. This effect is naturally more noticeable in small reservoirs during the dry season, such as the Coco River than the major streams (Temala and the four southeastern rivers). Overall, we observed a relatively conservative hydrologic system with the mixing of only two water masses: the river freshwater and the marine endmembers. Water isotopic data allow excluding the contribution of a third water mass (e.g., groundwater discharge) in these mangrove-dominated estuarine systems.

Rare earth element cycling in the mangrove system.

The PAAS-normalized REE patterns are typical of coastal seawater with a gradual enrichment of heavy REEs relative to light REEs (Hoyle et al., 1983;Nozaki et al., 2000;Piper and Bau, 2013) (Figure 4). Moreover, we observed a depletion of Ce but an enrichment of Eu and Gd relative to their neighbouring REEs that are commonly referred to as anomalies. The anomalies of Ce and Eu were already extensively discussed in the literature. The negative Ce anomaly was shown to develop progressively with increasing salinity as dissolved Ce(III) undergoes continued oxidation to insoluble Ce(IV) across the estuarine zone (Nozaki et al., 2000). The positive Eu anomaly was also reported in the dissolved fractions of various major rivers (Amazon, St Lawrence, Piper and Bau, ( 2013)) and the clay fractions of river sediments worldwide [START_REF] Bayon | Rare earth elements and neodymium isotopes in world river sediments revisited[END_REF]. Several previous studies have recorded positive Eu anomaly in continental materials (e.g., suspended load, atmospheric aerosol and dust, Censi et al., 2004;Goldstein and Jacobsen, 1988). Therefore, the positive Eu anomaly observed in the dissolved loads was interpreted as the result of dissolution from suspended particles and formation of stable dissolved complexes during transport (Nozaki et al., 2000).

On the other hand, the Gd anomaly is commonly associated with anthropogenic emissions, such as medical sources (medical resonance imagery) or wastewater (Hatje et al., 2016;Tepe et al., 2014). We observed Gd anomaly (Gd/Gd* up to 3.5) only during the dry season in the Coco river, in the first and second freshwater discharge events (Figure S3 and Figure 2A). We have previously suggested that the 3 rd event may be associated with a common brackish water at both

Coco and Temala rivers formed during the high tide from 4h to 9h AM (Figure 2A), which is Gd-anomaly-free (Figure S3D). No Gd anomaly (Gd/Gd* = 1) was indeed observed in the marine endmember (blue diamonds, Figure 4 C,D). Given the absence of major medical facilities and considering the low population along the Coco river, a possible medical or wastewater origin for this Gd anomaly can be ruled out. However, the Coco River is associated with the nickel mined lateritic Koniambo regolith where a 13km long ore conveyor was built parallel to the river and the Koniambo Nickel SAS smelting plant is adjacent to the Coco mangrove (Figure 1C).

While there is no precedent study reporting Gd anomaly associated with lateritic ores extraction and processing, the Gd anomaly observed in the Coco river might be associated with those activities.

Estuarine mixing behaviors of REEs and Y.

The REE concentrations in the marine endmembers are typically low; the sum of all REE concentrations (ΣREEs) approximates 6 ng/L. However, there was a significant difference in REE total concentrations between the two river endmembers, with Temala containing more REEs than Coco (ΣREEs of 24 and 2.6 ng/L, respectively). This trend was also observed at the mangrove stations (Figure S3A). The higher REE concentrations measured in the Temala River waters compared to the Coco River are directly associated with the geology of their watersheds. The Temala watershed is indeed made of soils developed on volcano-sedimentary rocks, whereas the Coco river meanders on lateritic soils developed on ultramafic rocks (Figure 1C) [START_REF] Merrot | Nickel and iron partitioning between clay minerals, Fe-oxides and Fe-sulfides in lagoon sediments from New Caledonia[END_REF]. As volcaniclastic bedrock tend to contain higher REE and Y concentrations than the granitic regolith (Chapela [START_REF] Lara | The effects of lithology on trace element and REE behavior during tropical weathering[END_REF], the difference in the watershed's geology could be directly associated with higher REE concentrations in Temala river waters than Coco.

Moreover, we did not observe any REEs and Y removal during estuarine mixing between the rivers and the marine endmember, as commonly assumed for REE estuarine geochemistry (see section 1). In fact, we measured very high REE concentrations in the mangrove forest (salinity range of 25-33, see La concentrations in Figure 5A). The high REE (La) concentrations in the mangrove area seem to be conservatively mixed with the freshwater mass (y=0.6x+3.5, r 2 = 0.97) and the marine endmember (y=-5.2x+183, r 2 = 0.84). This situation was not reported previously.

It is commonly assumed that approximately 60-90% of REEs are removed from the low salinity region of an estuary by flocculation/coagulation of dissolved organic-bound Fe and colloidal materials depleting REEs from the dissolved pool (Lawrence and Kamber, 2006;Pourret and Tuduri, 2017;Sholkovitz and Szymczak, 2000;Sholkovitz, 1995). Minor releases of REEs during an estuary mixing were only reported in the turbid-clear water transition zone (S=12-15)

in the Chao Phraya estuary (Thailand) (Nozaki et al., 2000) and the mid-salinity zone of the Elimbah Creek (Australia) (Lawrence and Kamber, 2006). Such REE release was attributed to several mechanisms, including desorption from suspended particles, coastal erosion, and mineralization during early diagenesis. In addition, the reductive dissolution of ferromanganese oxides has been shown to significantly release REEs into the porewater, although LREEs tend to sorb back onto the newly formed ferromanganese oxides at the sediment-water interface (Och et al., 2014).

Although the La-salinity biplots (Figure 5A) could be interpreted as mixing of three water masses (river, mangrove forest, and marine), stable water isotopes (Figure 3) allow to rule out the possibility of a third water mass in the estuaries of Coco and Temala. Thus, the high La concentrations in the mangrove are instead explained by specific biogeochemical processes leading to the substantial release of dissolved REEs. Given the subtropical weather condition and the high availability of fresh organic matter in the mangrove forest (Noël et al., 2014), it is highly probable that bacterial activity contributes to this REEs solubilization in the sediments porewater (Och et al., 2014). In the mangrove system, the tidal conditions with water pushing up through the porous sediment (seawater circulation cell, Figure 6A) would then favour REE remobilization to the water column. A previous study has demonstrated significant fluxes of REEs from such a seawater circulation through diagenesis-active sediments (i.e., organic matter degradation and reductive dissolution of ferromanganese oxides (Paffrath et al., 2020), Figure 6).

Other processes such as passive diffusion fluxes or sediment resuspension events induced by waves and tides (Dang et al., 2020) or bioturbation could also contribute to the REE release towards the water column (Figure 6 C). At a larger scale of the Northwestern Mediterranean Sea, upward diffusion of REEs (Nd) from sediment porewater counts for 30% of the Nd marine budget (Garcia-Solsona and Jeandel, 2020). Moreover, given the organic mater-rich surface waters in the mangrove system and the high affinity between REEs and dissolved organic carbon (Davranche et al., 2004;Marsac et al., 2010;Pourret and Davranche, 2013), it is also highly possible that the formation of stable organic complexes could contribute to maintaining REEs in solution in this mid-salinity region [START_REF] Mclennan | Relationships between the Trace Element Composition of Sedimentary Rocks and Upper Continental Crust[END_REF][START_REF] Goldstein | Rare Earth Elements in River Waters[END_REF][START_REF] Hatje | Increases in Anthropogenic Gadolinium Anomalies and Rare Earth Element Concentrations in San Francisco Bay over a 20 Year Record[END_REF][START_REF] Conroy | Constraints on the Salinity-Oxygen Isotope Relationship in the Central Tropical Pacific Ocean[END_REF][START_REF] Rohling | Progress in Paleosalinity: Overview and Presentation of a New Approach[END_REF][START_REF] Wolfe | Classification of Hydrological Regimes of Northern Floodplain Basins (Peace-Athabasca Delta, Canada) from Analysis of Stable Isotopes (D18O, D2H) and Water Chemistry[END_REF][START_REF] Dansgaard | Stable Isotopes in Precipitation[END_REF][START_REF] Lee | Climatic Controls on the Stable Isotopic Composition of Precipitation in Northeast Asia[END_REF][START_REF] Munksgaard | First Continuous Shipboard δ 18O and ΔD Measurements in Sea Water by Diffusion Sampling-Cavity Ring-down Spectrometry[END_REF].

Fractionation of HREEs/LREEs and elemental ratios. All the water samples collected showed a progressive enrichment of HREEs relative to the PAAS shale (Figure 4). This is consistent with the conventional REE behaviours in the aquatic environment where the fractionation between the dissolved and particulate loads of HREEs and LREEs leads to this characteristic REE curve (Piper and Bau, 2013). Therefore, elemental ratios between representative HREEs and LREEs (e.g., Er/Nd (Nozaki et al., 2000), Nd/Lu (Sholkovitz, 1995), Ho/Er (Lawrence and Kamber, 2006)) could help determine whether this fractionation occurs in the freshwater endmember or the estuary. As the interpretations using different ratios are very similar, we choose to discuss only the Er/Nd (weight ratios).

The Er/Nd ratios in both UCC (Rudnick and Gao, 2003) and PAAS (McLennan, 2001) approximate 0.08, while those in the river endmembers are significantly above this value (0.2 and 0.3 at Temala and Coco, respectively, Figure 5B). This indicates that the fractionation between HREEs and LREEs occurred in the freshwater system. It is important to note that such fractionation is pH-dependent. At the pH range observed in Temala and Coco rivers (7.7-7.9, Table 1), REE adsorption on particles is enhanced, leading to significant fractionations by preferential LREE removal (Sholkovitz, 1995). Furthermore, the measured Er/Nd in the estuarine samples varied with salinity along the conservative mixing line of Temala (Figure 5B), suggesting no further fractionation (Lawrence and Kamber, 2006). This is consistent with the occurrence of dissolved organic-REE complexes in the mangrove waters, as previously suggested. Previous studies have demonstrated that the presence of dissolved organic matter significantly reduced REE sorption on ferromanganese oxides and the subsequent fractionation between LREEs and HREEs (Davranche et al., 2005(Davranche et al., , 2004)).

On the other hand, a negative departure from the conservative mixing line (i.e., Er/Nd ratios decreased) was noticed at the mangrove stations (black arrow in Figure 5B). This indicates a preferential release of LREEs (Nd) relative to the HREEs (Er). This observation is in agreement with the hypothesis that LREEs previously bound to the solid fraction are released toward solution when the oxide phases undergo reductive dissolution (Bau et al., 1997). High REEs concentrations in porewater promote upward diffusion from the sediments by the seawater circulation cell or diffusive flux (Figure 6).

Furthermore, variations in the Y/Ho ratios are also of great interest. Although these two elements have similar ionic radii, their electronic configurations differ. Yttrium has no f-electron while Ho has 10 electrons filling up the f orbitals (Lawrence and Kamber, 2006). Therefore, the ability to form strong surface and solution complexes using the f orbitals (Byrne and Lee, 1993) drives the fractionation of this pair during weathering, riverine transport or in the marine environment (Lawrence and Kamber, 2006;Nozaki et al., 2000). As a result, Ho tends to form more stable surface complexes than Y (Bau et al., 1997;Byrne and Lee, 1993;Lawrence and Kamber, 2006).

Therefore, two conditions could lead to Y/Ho fractionation during estuarine mixing. First, coagulation, flocculation and sedimentation of Ho-bearing colloidal particles preferentially remove Ho from solution. Second, as Y tends to form weaker surface complexes than Ho, this fractionation is enhanced by the salt effect (competition for surface sorption sites), which favors Y release from colloidal particles toward solution. Both processes were well documented in the literature to support the increase in the Y/Ho ratio during the estuarine mixing (Figure 6B) (Lawrence and Kamber, 2006).

The Y/Ho ratio in the Temala river endmember (28.4) approximates UCC and PAAS (25.3 (Rudnick and Gao, 2003) and 27.2 (McLennan, 2001), respectively), indicating that there was no significant fractionation between Y and the REEs in the Temala river (Figure 5C) (Lawrence and Kamber, 2006). However, in the Coco river endmember, the Y/Ho ratio is significantly lower (18.6). A situation where Y-Ho fractionation leads to lower Y/Ho ratios relative to the UCC is scarcely reported in the literature. While considered a minor process in natural water systems, it was previously reported by Bau et al. in the slightly acidic solutions of low complex-forming capacity of a stream from an abandoned mine (Bau et al., 1995). Interestingly, the Coco River, where this phenomenon is suspected to occur, is connected to the Koniambo mine.

In the estuary, we also observed the conventional Y/Ho fractionation (Figure 6B) as the Y/Ho ratios were beyond the conservative mixing lines (Figure 5C). However, the positive departure is even more noticeable in the mangrove forest, with Y/Ho reaching up to 80 (black arrow in

Figure 5C

). This suggests that additional processes took place in the mangrove forest area, further fractionating this pair. A previous study has suggested that the fractionation between Y and Ho could be redox driven (Bau et al., 1997). Accordingly, a redox change is expected to occur at the sediment-water interface (Figure 6C) where the upward diffusive flux from mangrove sediments confronts the freshly formed ferromanganese oxyhydroxides. As discussed previously, these reactive surfaces tend to further remove Ho relative to Y. Such preferential removal of Ho increases the Y/Ho ratios as observed in Figure 5C.

Calculations of REE flux from the mangrove systems

Fluvial fluxes of dissolved constituents in the oceans are essential to balance their marine budget.

The current ocean box models for REEs consider major inputs as river-borne dissolved and particulate load, atmospheric dust, groundwater discharge, porewater diffusion and dissolution of reworked sediments (Arsouze et al., 2009;Garcia-Solsona and Jeandel, 2020;Tachikawa et al., 2003).

Goldstein and Jacobsen have suggested a simple empirical approach to calculate the dissolved REEs flux (𝑅 𝑖 𝑒𝑓𝑓. ) from the continent (Goldstein and Jacobsen, 1988) as detailed in the following equation.

𝑅 𝑖 𝑒𝑓𝑓. = 𝐶 𝑖 𝑅 × 𝐹 𝑅 × 𝜙 𝑖 × 𝐶𝐹 (𝐸𝑞. 6)
where 𝐶 𝑖 𝑅 is the dissolved concentration of an element in the continental endmember (ng/L), FR is the annual river discharge, Φi is the effective factor, and CF is a correction factor to convert the final units into kg/year.

Here, we applied this calculation to our preliminary dataset to determine whether the fluxes of REEs and Y from the tropical mangrove system could be of interest in the global oceanic budget.

Therefore, it is important to note a few assumptions in this simple calculation. First, because of the conservative mixing of REEs and Y between the mangrove system and the seawater (Figure 5A), we can assume a full effective factor (i.e., absence of estuarine removal or Φi =1). Second, the local Water Agency (DAVAR, Service de l'eau) monitored the hydrologic regime of the local river systems. According to the most recent report, the monthly discharges of the rivers in the leeward side (southwestern, e.g., Boghen, Poya, Pouembout-Boutana Rivers) of Grand Terre in 2019 and 2020 average 18.6 m 3 /s in February and 0.6 m 3 /s in May (the month preceding the two sampling campaigns) (DAVAR Service de l'eau, 2020). The variability of the river discharge that could differ Coco and Temala, although not individually determined, could be consisted within the variability of major river systems of the leeward sides. Third, the concentrations of REEs and Y of the mangrove endmember (𝐶 𝑖 𝑅 ) are those of the samples with salinity in the range of [START_REF] Mclennan | Relationships between the Trace Element Composition of Sedimentary Rocks and Upper Continental Crust[END_REF][START_REF] Goldstein | Rare Earth Elements in River Waters[END_REF][START_REF] Hatje | Increases in Anthropogenic Gadolinium Anomalies and Rare Earth Element Concentrations in San Francisco Bay over a 20 Year Record[END_REF][START_REF] Conroy | Constraints on the Salinity-Oxygen Isotope Relationship in the Central Tropical Pacific Ocean[END_REF][START_REF] Rohling | Progress in Paleosalinity: Overview and Presentation of a New Approach[END_REF][START_REF] Wolfe | Classification of Hydrological Regimes of Northern Floodplain Basins (Peace-Athabasca Delta, Canada) from Analysis of Stable Isotopes (D18O, D2H) and Water Chemistry[END_REF][START_REF] Dansgaard | Stable Isotopes in Precipitation[END_REF][START_REF] Lee | Climatic Controls on the Stable Isotopic Composition of Precipitation in Northeast Asia[END_REF][START_REF] Munksgaard | First Continuous Shipboard δ 18O and ΔD Measurements in Sea Water by Diffusion Sampling-Cavity Ring-down Spectrometry[END_REF][START_REF] Conroy | Spatiotemporal Variability in the Δ18O-Salinity Relationship of Seawater across the Tropical Pacific Ocean[END_REF] (the mangrove forest, Figure 5A). Finally, the calculated fluxes (𝑅 𝑖 𝑒𝑓𝑓. ) of dissolved REEs and Y from the mangrove system are reported with standard deviations reflecting the errors propagating through the calculations and variability of all variables.

S3 while the annual average fluxes are showed in Table 3. The fluxes of REEs and Y are significantly higher in the rain season and dry season (Table S3), as reported in other major estuarine systems (Pourret and Tuduri, 2017). Overall, the annual averages of REE and Y fluxes from the Coco and Temala range from 0.05 (Lu) to 16.1 (Y) kg per year (Table 3).

To extrapolate our data toward a general perspective of the global mangrove system, we first normalized the calculated fluxes to mangrove watershed surface areas (SW, km 2 ) and the fraction of vegetation coverage (fV). Equation 7allows the calculation of area-normalized fluxes of REEs and Y from the two mangrove forests (𝑅 𝑖 𝑆-𝑀𝐹 , kg/yr/km 2 ).

𝑅 𝑖 𝑆-𝑀𝐹 = 𝑅 𝑖 𝑒𝑓𝑓.

𝑆 𝑊 × 𝑓 𝑉 (𝐸𝑞. 7)

The watershed of the Voh region has a vegetation coverage of approximately 43±16% (Taureau et al., 2019), thus fV =0. From the 𝑅 𝑖 𝑆-𝑀𝐹 values, we attempted an extrapolation to the global surface of mangroves (150,000 km 2 ) (Spalding, 2010) and thus calculated the global fluxes of dissolved REEs and Y from this unique ecosystem (Table 3). These global fluxes calculated for the mangrove systems could then be compared to the published global river-borne dissolved Nd loads (Arsouze et al., 2009;Garcia-Solsona and Jeandel, 2020;Tachikawa et al., 2003). Currently, the Nd oceanic budget is the most comprehensive as extensive studies reported both Nd concentrations and isotope composition to calibrate its ocean box models. In these models, the river inputs of dissolved Nd range from 260 to 500 tons per year (or Mg per year) (Rousseau et al., 2015;Tachikawa et al., 2003). Relative to these values, we estimate that the mangrove systems supply 13.3±5.6 tons per year of dissolved Nd, representing 2.6-5 % of the total river input of dissolved Nd. Compared to other sources (e.g., dust dissolution of 400 tons of Nd per year, Nd release from suspended particles of 5,700±2,600 ton per year) (Arsouze et al., 2009;Rousseau et al., 2015;Tachikawa et al., 2003), the mangrove systems appear to be a minor source. However, it is important to note that even though this study documents a significant release of REEs and Y within the mangrove system for the first time, we assess only two small mangrove systems representing <1% of the global mangrove surface. Further studies are therefore required to better characterize the contribution of the mangrove system to the global marine budget.

4.

Implications for the role of mangrove on REE cyling and oceanic budgets.

The conventional estuarine REE behaviour often implies a sharp removal of REEs when a riverine water mass enters an estuary. However, our data revealed a significantly release of dissolved REEs and Y (7.3 times for Y, 6.4 times for La and 3.3 times for Lu) in the mangrove system. Although other water masses could supply REEs to the water column (e.g., groundwater discharge (Kim and Kim, 2011)), our stable water isotopes data confirm a sole binary mixing between the fresh and seawater endmembers in the mangrove estuaries of New Caledonia. This release of REEs and Y has thus to be associated only with internal recycling or biogeochemical processes within the mangrove forests. This dataset thus strengthens the hypothesis that tropical mangroves act as a source of dissolved REEs and Y to the marine system.

This finding first redefines the role of tropical mangroves in the cycling of trace elements at the continent-ocean interface. While mangrove forests are often referred to as a buffer zone to filter trace metals from reaching the open sea (Marchand et al., 2012), this assumption might be valid only for the particulate loading. This specific ecosystem produces large amounts of organic matter that is bioavailable for bacterial degradation (Marchand et al., 2012) and thus boosts early diagenesis. These biogeochemical processes lead to the complex recycling of REE-bearing phases. The reductive dissolution of ferromanganese oxides occurs within the subsurface layers of the sediments and is thus responsible for releasing trace elements (Dang et al., 2015(Dang et al., , 2014)).

However, the redox boundary at the seawater-sediment interface leads to forming a thin layer of newly formed Fe-and Mn-oxyhydroxides with large reactive surface areas that efficiently sorb trace elements and thus minimize their upward diffusive flux (Dang et al., 2015;Rigaud et al., 2013). Although we could not evaluate the relative amounts of REEs being diffused upward from the sediment porewaters relative to REEs retained at the interface, the diel variation in oxygen concentrations associated with hypoxia events in the mangrove (Dubuc et al., 2019) strongly suggests that the fraction of REEs being retained would be minor regarding the low stability of Fe-and Mn-oxyhydroxides in such redox-dynamic conditions (Bau et al., 1995).

Over the past 30 years, several works aimed to understand and revisit REE behaviour during estuarine mixing and accumulation in sediments [START_REF] Bayon | Rare earth elements and neodymium isotopes in world river sediments revisited[END_REF]Lawrence and Kamber, 2006;Sholkovitz and Szymczak, 2000;Sholkovitz, 1995). This first dataset reporting REEs release in a tropical mangrove may provide an important insight into the contribution of mangrove forests to the oceanic budgets and mass balance of REEs and Y. However, these box models remain unbalanced with a significant missing flux (e.g., 800 Mg per year) (Tachikawa et al., 2003). Pourret and Tuduri (2017) recently suggested the continental shelves as a potential resource of REEs to be included in the oceanic mass balance of REEs. Moreover, mangrove is growing in 123 tropical and subtropical countries and covers a total surface of 150,000 km 2 (Spalding, 2010). Our simple flux calculation suggests that this atypical system supplies a significant proportion of REEs toward the oceans (2.6-5% of the global dissolved loading). ''DYNAMINE''). We also wish to thank Florence Royer (Ifremer) and Etienne Lopez (Ifremer)

for their technical assistance during freshwater sampling in the south, as well as the technical (LAMA, US IMAGO) and administrative staff at IRD Noumea for their help and support relative to field campaigns.

  two first sampling campaigns were organized in June 2019 (dry season) and March 2020 (rain season) to collect samples in the Voh-Kone region (Temala and Coco Rivers). We also collected samples in four southeastern rivers (Dumbea, Coulee, Tontouta, Pirogue) in January, March, October and November of 2018. The March samples were collected during and after the Hola tropical cyclone while other samples are collected during the dry season.

  REEs and Y were determined using a triple quadrupole ICP-MS (8800 Agilent Technologies) at the Trent Water Quality Center. All REEs and Y were analyzed in MS/MS mode with O2 as the reaction cell gas. Detection limits were in the range of 0.1-0.4 ng/L. Although there were no certified reference materials for REEs, we compared the REEs and Y concentrations measured in an NRCC natural water certified reference material (SLRS-6) to the values reported in a

  At the mangrove stations, the δD-δ 18 O relationship has the equation of δD = 4.3 × δ 18 O + 5.5 (n=40, Figure S2). The slope of 4.3 ± 0.6 is typically lower than other tropical Pacific regions (5.1 to 6.5, Conroy et al. (2014)), and the global seawater average of 7.4 (Rohling, 2007). This indicates a strong influence of the evaporation process in the mangrove during the dry season. Across the estuaries, the δD-δ 18 O relationship of Coco and Temala waters aligns with southeastern rivers with the equation of δD = 4.8 × δ 18 O -4.6 (n=29, r 2 =0.9, Figure S2). The slope (4.8 ± 0.3) is very similar to the mangrove stations (4.3 ± 0.6), only the intercepts differ (-5.3 across the estuary and +5.5 in the mangrove during the dry season). According to the interpretation of the local evaporation line, as described by Wolfe et al. (2007), local surface waters often plot in linear clusters to the right of the Meteoric Water Line along a slope in the range 4 to 6. Our observations of consistent slopes (4.3 ± 0.6 and 4.8 ± 0.3) fall into this conventional interpretation (Figure S2) considering the Local Meteoric Water Line (LMWL) of δD = 7.1 × δ 18 O + 12.6 (retrieved from the online isotopes in precipitation calculator, www.waterisotopes.org).

43 .

 43 The surfaces of the Temala and Coco watersheds (SW) approximates 163 km 2 and 42 km 2 , respectively (FalconBridge NC, 2001). The calculated area-normalized fluxes of REEs and Y range from 1.6×10 -3 (Lu) to 0.4 (Y) kg/yr/km 2 .

  However, it remains uncertain about the representativity of the Coco and Temala systems of the global mangroves. Therefore, further research on the REE cycling within mangrove systems is needed to determine whether the mangrove estuaries should be considered a significant input in ocean mass budget to balance the global REE distribution. Aknowledgements: The authors thank the Trent University's Internal Operating Grant (#26090) for financial support to D.D.H. Besides, C.D., F.J., H.L., S.M. and B.O. also acknowledge funding from CRESICA (grant CDEI 2017-2021 -VI-3), CDEI 2017-2021 -VI-3 (grant EC2CO-Bioeffect/Ecodyn/Dril/MicrobiEn ''TREMOR'') and CNRT (grant CSF 9PS2013

Figure 1 :

 1 Figure 1: Map of New Caledonia (A), the two regions under investigation: Voh-Kone region (red circle) and four rivers in the Southeast of Grande Terre (red star), around Noumea (B), and a zoom into the Voh-Kone region with sampling locations (C). The position of the CMD (Central Massive Divide) in B is approximative. The southwestern basins of the CMD are considered leeward while the northeastern are windward. See text for more details on the study sites.

  Figures and TablesClick here to access/download;Figure;Dang et al. Figures and Tables.docx

Figure 2 :

 2 Figure 2: Variations in salinity, δD and δ 18 O in waters collected from the Temala (red symbols) and Coco (green symbols) Rivers of the Voh-Kone regions and four rivers of the Southeast (yellow boxes). Left panels (A, D, G) show the daily variations recorded within 24 hours in the mangrove forest (stations T6 and C2). The arabic numbers (1 st , 2 nd , 3 rd ) indicates the three events where freshwaters were discharged from the Coco river toward the lagoon. The greyed zone shows the last samples collected of the 24-hour series during high tide where all physicalchemical properties and stable water isotopes of the two rivers overlaps. Those data are excluded from the δD-salinity regresssion of Temala River as justified in text. Middle box plots (B, E, H) summarize the spatial variations of Temala and Coco estuaries. The right box plots (C, F, I) show the annual variations of the four rivers in the Southeast of New Caledonia. For all box plots, the horinzonal lines in boxes show median values while box boundaries indicate the 25 th and 75 th percentiles. The whiskers demark the 10 th and 90 th percentiles and scatters are values of the 5 th and 95 th percentile range.

Figure 3 :

 3 Figure 3: (A) δD-Salinity biplots of all waters collected from the Coco (green symbols), Temala (red symbols) and the box plot of four rivers in the Southeast (yellow, salinity = 0, see legend of

Figure 2

 2 Figure 2 for more details). Samples collected in the mangrove forests (full red and green symbols), across the estuaries (open red and green symbols) and the marine endmember (blue diamond) are also shown. A zoom in the Coco and Temala system during dry season is provided in panel (B). Their respective regression lines are shown in red (Temala) and green (green) while the black regression line represents all samples from Temala and Coco estuaries. The regression for Temala River excludes the data (encircled in B) that are observed on the Coco River regression lines. See text for justification.

Figure 4 :

 4 Figure 4: Rare earth element patterns in the waters of the mangrove stations (T6 and C2) at Temala (A) and Coco (B), and across the estuarine mixing of Temala (C) and Coco (D). The blue diamonds show the REE patterns in the marine endmember. The gray intensity of the symbols in panels A and B is associated with the 24-h time-series (black symbols corresponding to the first sampling). The symbol size in panels C and D reflect the salinity (small symbols reflecting freshwater). The green rectangle in B demarks Gd anomalies observed in Coco River water.

Figure 5 :

 5 Figure 5: Variations of La concentrations (A), Er/Nd (B) and Y/Ho (C) ratios as the function of salinity at Temala (red symbols) and Coco (green symbols). Samples in the mangrove forests are shown by full symbols while estuarine samples are presented as open symbols. The blue diamond symbols represent the marine endmember. The horizontal dotted lines show the values in the Upper Continental Crust (UCC) and PAAS shale. The dotted green and red lines are conservative mixing line for Coco and Temala estuaries, respectively.

Figure 6 :

 6 Figure 6: Schematic represention of the REE cycle in tropical mangrove-dominated estuaries (A). Panels (B) and (C) provide a zoom into the mechanisms occuring across the estuarine mixing and within the mangrove forest, respectively. In (B), the flocculation of either dissolved organic Fe III complexes (Fe III -DOM) or colloidal particles is presented.

  Temperature variations also help distinguish the two systems. Water temperatures increased from 16.8 o C at 11h and held constant at ca. 17.5 o C at Temala (FigureS1A, average of 17.3 ± 0.2 o C, n = 24, Table1). However, the temperature pattern at Coco showed broader variations(15.5 o C to 16.5 o C, average of 16.1 ± 0.3 o C, n = 24, Table

Table 1 :

 1 Variations in the physical-chemical properties of water collected over a 24-hour cycle in the dry season in the Temala (T6) and Coco (C2) mangrove forest.

	Parameters	Temala (n=24) Range Average SD Range Average SD Coco (n=24)
	Temperature 16.8-17.7	17.3	0.2 15.5-16.6	16.1	0.3
	pH	7.7-7.9	7.8	0.1 7.6-8.0	7.7	0.1
	Salinity	26.0-33.0	29.5	2.1 29.6-34.2	32.3	1.2

Table 2 :

 2 Summary of the δD-S and δ18 O-S relationships in the Coco and Temala rivers during rain and dry seasons. Values in brackets show the r 2 values. The stable water isotope compositions of the Coco and Temala endmembers (δDi and δ 18 Oi) were calculated by the extension of the δD-S and δ 18 O-S relationships. For the Southeastern rivers and the marine endmembers, the δDi and δ18 Oi values were calculated as the average of all river samples with salinity = 0 and the values recorded at station M, respectively. For the See text for more details.

		Endmembers	δD-S relationship	δ 18 O-S relationship	δDi (‰)	δ 18 Oi (‰)	d-excess (‰)
	Mangrove stations -Dry	Coco (n=17)	y=2.1x-72.9 (0.8)	y=0.2x-9.9 (0.6)	-72.9±8.9 -9.9±1.7 15.8±1.3
	season	Temala (n=19)	y=1.0x-36.0 (0.9)	y=0.2x-8.4 (0.6)	-36.0±2.8 -8.4±1.2 15.9±2.9
	Estuarine stations -Rain	Temala and Coco (n=15)	y=1.0x-34.6 (0.9)	y =0.2x-5.0 (0.9)	-34.6±1.9 -5.0±0.4 0.4±5.8
	season
		Marine (n=1)			-1.6±0.2	-2.1±0.2
	Freshwater stations	Southeastern rivers (n=14)			-31.2±6.2 -5.8±1.0

Table 3 :

 3 The fluxes (𝑅 𝑖 𝑒𝑓𝑓. , kg/yr) of REEs and Y from the two mangrove systems in New Caledonia (NC) and the extrapolation toward the global flux (ton, or Mg per year).

		Annual fluxes from
		mangroves in NC Global flux
		Temala	Coco
	Y 16.1±4.6 6.1±1.3	42.1±21.2
	La 6.2±1.2	2±0.6	14.8±7.6
	Ce 6.4±1.7	3.9±1.3	22.8±14
	Pr 1.1±0.3	0.4±0.1	3.0±1.5
	Nd 5.5±1.1	1.8±0.4	13.3±5.6
	Sm 1.2±0.2	0.4±0.1	2.9±1.4
	Eu 0.3±0.1	0.1±0	0.8±0.7
	Gd 1.6±0.4	0.6±0.3	4.2±3.3
	Tb	0.3±0	0.1±0.03	0.6±0.3
	Dy 1.8±0.4	0.6±0.2	4.5±2.7
	Ho 0.4±0.1	0.1±0	1.0±0.6
	Er 1.1±0.3	0.5±0.2	3.1±1.8
	Tm 0.1±0.03 0.1±0.02	0.4±0.3
	Yb 0.8±0.3	0.4±0.2	2.4±2.5
	Lu 0.1±0.03 0.05±0.01	0.3±0.2