Intermediate water ﬂows in the South West Paciﬁc from OUTPACE and THOT Argo ﬂoats

o E-150 o W, around 19 o S) are described. In the Coral sea, we highlight minima in dissolved oxygen of 140 µ mol.kg − 1 that are associated with the signature of a southward transport of waters between two zonal jets: from the North Vanuatu Jet to the North Caledonia Jet. This transport 5 takes place in the core of a cyclonic eddy or via the path between a cyclonic eddy and an anticyclonic one, highlighting the importance of mesoscale dynamics in upper thermocline and surface layers. Further east, we observe a strong meridional velocity shear with long-term ﬂoat trajectories going either eastward or westward in the lower thermocline. More interestingly, these trajectories also exhibit some oscillatory features. Those trajectories can be explained by a single Rossby wave of 160 days period and 855 km wavelength. Considering the thermohaline context, we conﬁrm the meridional shear of zonal velocity and 10 highlight a permanent density front that corresponds to the interface between Antarctic Intermediate Waters and North Paciﬁc Deep Waters. Hence both circulation and thermohaline contexts are highly favorable to instabilities and wave propagation. Our study complete these observations of the surface circulation both in space, by focusing on intermediate levels, and in time, by using the time series (more than two years) of the autonomous Argo ﬂoats deployed during the cruise. Abstract. Thanks to the autonomous Argo ﬂoats of the OUTPACE cruise and of the THOT project, some features of intermediate ﬂow dynamics, around 1000 m depth, within the Southwest and Central Paciﬁc Ocean (156

. Once again, we also replace the float trajectories in their thermohaline and circulation context. In order to explain their displacement at mid-depths we choose a wave approach and compare our results, taking into account Doppler shift, to different cases of Rossby, Kelvin and Kelvin-Helmholtz instability waves. Then, we discuss the proposed hypothesis for the two areas and what they imply for the OUTPACE observations. Finally, we conclude and propose some method improvements.
2 Data sets and methodology 5

Autonomous floats
In the present study we benefit from the deployment during the 2015 spring of several Argo floats under the auspices of the OUTPACE cruise  and of the THOT project (Martinez et al., 2015). We analyze the two first years of data.
All OUTPACE and THOT floats are related to the Argo international program and have the same type of sampling cycle. For memory, it begins with the descent of the float to a depth around 1000 m, called the parking depth where the floats drift for a 10 programmed time. This time can be remotely modified in the last generation of floats, like those used in this study. Here we use the measurements made while the floats rise to the surface. At the surface, these data are transmitted via satellite. Even if this cycle is the same for all floats, the time spent at the parking depth (in our cases, 5 or 10 days), and hence the corresponding sampling frequency (∆t), are not the same for all of them. Two types of float are available: ARVOR (Argo-Core) floats and PROVBIO floats (Bio-Argo). Because they were all immersed during the same months, they all have a close WMO code : 15 #6901XXX. Hereafter, to ease the writing of the float number, we only use the three last digits to point to them, i.e. float 656 refers to #6901656. Details and data are accessible via the CORIOLIS operational center (www.coriolis.eu.org). In order to get the average velocity of the floats during their cycles, we follow the method of Ollitrault and Rannou (2013) taking different time slots over the float cycle in order to calculate, for the n th cycle, the surface velocity V n (0) and the velocity at 1000 m where L first and L last are the first and the last transmitted location in the same cycle (PROVBIO floats transmit only two locations per cycle using Iridium whereas ARVOR floats transmit seven locations per cycle using ARGOS) and t is the corresponding time. After some verifications we have concluded that, even if the mean surface velocity is ten times greater than the mean deep velocity, each float stays such a short time at the surface that its displacement there can be neglected compared to the deep 25 displacement. Hence we can consider that the trajectory dynamics are mainly due to deep circulation processes. The discussion of such consideration is thoroughly made by Ollitrault and Rannou (2013).
In the case of the 656 float, we also consider the dissolved oxygen concentration (DOXY) measurements. These data were calibrated (A. Fumenia, personal communication) based on the CTD profiles made just before the float was immersed during the OUTPACE cruise. The calibration for the 656 float is: where DOXY raw is the dissolved oxygen concentration data from the float and DOXY clb is the calibrated dissolved oxygen concentration data, both expressed in µmol.kg −1 .

Trajectory description for the a wave approach
Here the objective is to explain the float trajectories influenced by waves. Thus, we describe the float trajectories as Lagrangian description of waves, using the period T and the wavelength λ as well as the frequency ω (ω = 2π/T ) and the wavenumber k The wavenumber is defined as: where k v is the vertical wavenumber, k H the horizontal one, k lon the longitudinal one and k lat the latitudinal one. In our case, the dynamics of the floats do not allow us to raise information concerning the vertical component because data on float locations are only measured at the surface. The displacements of the floats are mostly directed by the currents, and only secondarily by 10 waves. Since the prevailing currents are mainly zonal, we consider hereafter, to simplify, that the wavenumbers derived from the observations correspond to the longitudinal component (k = k lon ). To clarify the methodology, we choose to name "float wave" the measured wavy trajectory of a float and "theoretical wave" the process that could lead to such trajectory.
We tried to describe the float waves with a Fourier transform or a wavelet analysis on the float time series, but the description of the different frequencies contained in them was incomplete. This is due to the shortness of the time series (2 years) with 15 regard to the sampling period. If the floats are still functional in a few years, these methods should be reconsidered.
So instead, we developed the method presented here, with Lagrangian and Eulerian wave descriptions and the estimations of wavenumbers. In order to maximize the information derived from the portions of the trajectories where the floats oscillate, we choose to determine half float wave characteristics rather than full float wave ones, for each float studied (floats 660, 671, 679 and 687, Fig.2). Hence, we obtain a double number of more precise measurements of λ/2 from the position maps, and of 20 T /2 from the float time series of latitude.
Because the floats are, by definition, Lagrangian devices, we need to be careful before comparing the float waves to the classical Eulerian oceanic waves. We first use a simple case to get a basic relation between Eulerian wave parameters and Lagrangian ones. Because of the zonal tendency of the studied float trajectories (Fig. 2), we express a simple case of the current perturbations due to a plane wave propagation with the following system of equations : where u 0 and v 0 are zonal and meridional velocities considered as constants, ω Te is the frequency, k Te is the wavenumber and ϕ Te is the phase shift term of the Eulerian theoretical wave. Note that v 0 is the amplitude A Te of the Eulerian theoretical wave.
By convention, the subscript 'T' is used for theoretical, 'M' for measured, 'e' for the Eulerian description of the wave and ' ' for the Lagrangian one (Tab. 1). After performing some tests (Appendix A), we choose to set the zonal velocity of the floats as  In such a configuration, the Lagrangian observation of the float can be represented by a Doppler effect on the perception of 5 the theorical wave. So we can express the Lagrangian properties of the theoretical wave (ω T , k T and A T ) as a function of ω Te , k Te , A Te and u 0 : But these equations derive from one common expression, hence this system cannot be solved like a 3 equations -3 unknowns one. Solving 6 is then not trivial without setting either ω Te or k Te . So we need another method to find the Eulerian properties of 10 the theoretical wave that better fits the float trajectories. Hereafter, we use those equations in order to build an index I for the  differences between the Lagrangian properties of the float waves (ω M and k M ) and the Lagrangian properties of the potential theoretical waves (ω T and k T ). I is defined by the following expression: where a is the float considered.
We made the calculations for a range of Eulerian frequencies and wavenumbers (ω Te and k Te ), thanks to Equations 6, in This method could be used with several other floats and be expressed by the following formulation: where N is the total number of floats considered, in our study N = 2. Using this numerical approch, we can find all the couples (ω T e , k T e ) that minimize I, and hence that could fit the float trajectories.
In order to compare the couples that minimize I and find the one that better fits the 660 and 687 float trajectories, we make a simulation of the idealized trajectory for each couple. The simulations use Equations 4, integrating them to express the longitude x(t) and the latitude y(t) of Lagrangian particles as a function of time: where x 0 and y 0 define the initial position of the float. The simulations run with a time step of 1 day for 642 days ( t end − t 1 660 = t end − t 58 687 = 642 days in Equations 5). In order to compare the simulations to the float trajectories, we interpolate the latitudes of the float, y int , at the longitudes of the corresponding simulations. Then we calculate the sum of the differences of 5 latitude using an index J, defined as: where a is the considered float, y simu are the latitudes of the simulation and m is the total number of days, here m = 642.
Because the value of ϕ Te can influence the value of J, we made several simulations for each couple (ω Te , k Te ) varying ϕ Te from −π to π with a step of 1 10 π. As for index I, we can sum J 660 and J 687 to get the couple that minimizes the trajectory 10 differences of both floats 660 and 687. This method could also be used with several other floats and be expressed by the following equation: These two steps give us the couple (ω T M e , k T M e ) of the theoretical wave that better fits the trajectories of floats 660 and 687. This couple can now be compared to classical Eulerian oceanic waves such as Kelvin, Rossby and Kelvin-Helmoholtz 15 instability waves.

Ancillary data
In order to evaluate the possible link between oxygen anomalies and surface currents in the Coral Sea, we use the AVISO altimetry products (www.aviso.altimetry.fr). We select ocean-level elevation anomaly products, reworked from all satellites, to obtain geostrophic velocity anomaly fields (u g and v g ) with a 1/4 degree resolution. From those data we calculate the 20 geostrophic velocity amplitude. We also use HYCOM (HYbrid Coordinate Ocean Model) re-analysis GLBu0.08 of the experience 91.1 from March 2015 to March 2016 (www.hycom.org). This system is a hybrid isopycnal-sigma-pressure (generalized) coordinate ocean model with 1/12 degree horizontal resolution and 40 vertical levels, assimilating in situ data.
In order to replace our analyses within the global thermohaline context, we used the ISAS13 atlas (In Situ Analysis System, Gaillard, 2012) that provides a climatology of thermohaline properties. This atlas collects and processes all the profiles provided 25 by the Argo floats from 2004 to 2012 in order to calculate a monthly global climatology over the entire depth of the oceans.
More details are provided by Gaillard et al. (2016). We apply the same methods to calculate the density as those used for HYCOM re-analysis. In the following, whatever is the source for the temperature and salinity fields, the density of the water masses is computed with the Matlab toolbox Gibbs-Seawater based on the TEOS-10 convention (www.teos-10.org/software.htm).

Coral sea
The trajectory of float 656 can be clearly associated with the flow along the New Caledonian coasts at the entrance of the Coral  and D2 do not correspond to the classical characteristics of the NCJ (Gasparin et al., 2011), whereas the float is exactly on its pathway. We therefore seek to know its origin. Based on the work of Gasparin et al. (2014) and Rousselet et al. (2016), we hypothesize that this signature originates from the NVJ waters whose theoretical and observed pathway is located 4 o further 25 north. The figure of Appendix B shows the depth variability of the DOXY minimum of each profile during D2 and helps to understand the link between the deoxygenation events and the properties of NVJ waters.

Thermohaline and circulation context
We focus on D2 that is longer and stronger than D1. The geostrophic velocity fields from AVISO ( Fig. 5a) allow us to visualize the position of the float during D2 in relation to the surface circulation. We notice that, during the whole duration of D2, the   float is located on the Queensland plateau where we can note that the deepest measurements are shallower than the parking depth (also visible in Figures 4a,b,c). This leads to short displacements over the whole event, making the interpretation of the results easier. We can identify a very large cyclonic structure to the east of the plateau centered at 156 o E, that we name C1, and a much weaker cyclonic structure, C2, located to the north-west of the plateau. Between them, we observe an anticyclonic Using the HYCOM re-analysis, we can compare the AVISO observations to the modeled velocity field at different depths.
At 300 m, the depth of the DOXY minimum, we can clearly identify structures C2 and A but C1 is harder to locate (Fig.5b).
C1 may be located 1 o farther south. A is much more circular in the HYCOM re-analysis than in the AVISO surface data. These data also allow us to consider the densities of these water masses and thus enable us to track the potential NVJ waters down to 10 the NCJ pathway. Figure 5b clearly shows that the NVJ waters can be associated with C2 for instance.
Otherwise, studying the AVISO product and HYCOM re-analysis for D1, we do not identify an eddy structure or a circulation shape that could explain that DOXY anomaly. Nevertheless, due to the large scale features of water masses and the low values of DOXY, observed in Figure 4c, we could hypothesized that such deoxygenation events are related either to the intrusion of waters transported by mesoscale eddies or by NVJ meanders. Because we can observe such circulations with AVISO products, they definitely affect the surface layers and then impact the studied diazotrophic zones of the OUTPACE cruise. In the section 4.1, we will further discuss such aspects.
It should be noticed that it still remains difficult to interpret observations of different nature, i.e. from an Eulerian versus Lagrangian point of view, and that further work is required to replace the float observations in their complete dynamical context. following the method described in section 2.2, we first estimate the Eulerian characteristics of the theorical waves (ω Te ,k Te and ultimately ω TMe ,k TMe ) that better fit the floats.

15
To simplify the presentation, we only use the 660 and 687 float waves properties. We choose these two floats because they are the ones with the most regular trajectories (neither going northward like float 679 or southward like float 671). As explained in section 2.2, since the two regions of minima cross, the two observed float waves can be the signature of a single theoretical wave. Considering this hypothesis, we find that this wave is defined in the ranges from 0 to 0.075 rad.day −1 for the frequency and from -0.04 to 0.02 rad.km −1 for the wavenumber (Fig. 6a). In order to get a better resolution and minimize the calculation 20 time, we make a zoom on those ranges of frequencies and wavenumbers before doing the minimum calculation. We set a resolution of 5 · 10 −5 rad.day −1 and 5 · 10 −5 rad.km −1 and find 8083 minima, mostly in the westward region (Fig. 6b).
In order to compare the couples (ω T e , k T e ) to classical oceanic waves, we calculate the dispersion equation of Kelvin and Rossby in a vertical baroctropic case, Kelvin-Helmholtz instability wave in a two layers case and Rossby waves in several baroclinic cases (the different cases are explained in Appendix C). We observe that the characteristics of the Kelvin and Kelvin-

25
Helmholtz instability waves are not in the same ranges as the ones of the couples we want to identify. Rossby waves (R) are the ones that better fit them. The barotropic case R b is out of range but most solutions are located around the curves of the baroclinic cases with a thermocline at 35 m (R 35 ) and 200 m (R 200 ).
Using the J index, we are able to select the couple that better fits both the 660 and the 687 float trajectories. The results give us a wave of 160 days period and 855 km westward wavelength. Figure 7 illustrates the agreement between the observed and 30 the reconstructed trajectories obtained from it. Obviously, some other processes with small-scale signatures also influence the observed float trajectories. Nevertheless, a single wave, added to the float respective zonal background currents, can mainly  explain the two float trajectories that would otherwise be classified, at first sight, as behaving differently. Such observations of a potential plane wave have been rarely highlighted so far, and even less at such depth.

Thermohaline and circulation context
Using HYCOM re-analyses, we are able to replace the trajectory of the floats into the circulation at 1000 m depth. Figures 8 a   and b highlight the current striations as mentioned in the introduction. We observe that the modeled striations have, on average, widths of 1 o to 1.5 o of latitude, which are smaller than those observed by Ollitrault and Colin de Verdière (2014) (Fig. 1c). The mean shear of zonal velocity observed by the floats 660 and 687 is equal to 4.2 cm.s −1 (zonal velocities used in the Appendix

5
A for case b). We note a difference between the Eulerian modeled zonal velocities and the Lagrangian zonal velocities of the floats, which is not surprising taking into account the Eulerian versus Lagrangian description.
We also use the HYCOM re-analysis fields of temperature and salinity in order to calculate the density context of the studied area (Fig. 8c).

Coral Sea
Analyzing the DOXY measurements of float 656, we were able to describe two distinct events with well marked oxygen minima (D1 and D2, Fig. 4) between 150 m and 400 m depth, i.e. near the upper part of the main thermocline. Inspired by the previous study of Rousselet et al. (2016), we associate these oxygen minima to the NVJ waters, much more deoxygenated than 5 those of the NCJ. We propose that the NVJ waters were indeed transported by mesoscale eddies. To support this hypothesis, we compare the geostrophic currents at the surface with AVISO data and also use the HYCOM reanalyses at 300 m. Even if the comparison was not clear enough for D1 to be fully conclusive, in the case of D2 we have been able to identify a cyclonic structure (C2, Fig. 5) and an anticyclonic structure (A1) in the two sets of data. These vortex structures are involved in the transport of NVJ waters southward to the NCJ pathway. Maps of density resulting from the HYCOM re-analysis inform us clear difference forms a density gradient of 0.6 kg.m −3 over 3 o of longitude approximately. From this, we can hypothesize that the signature of the oxygen minimum is due to C2 carrying NVJ waters in its core. Otherwise, the common branch of C2 and A forms a local southward current exactly toward the position of the float 656. Hence, we can also make a second hypothesis that the NVJ waters could be carried by the northern branch of A and then be transported southward thanks to the current located between A to the east and C2 to the west. The first hypothesis fits the results of (Rousselet et al., 2016), with the difference that 5 the structure transporting NVJ waters is cyclonic and not anticyclonic. Hence the two possibilities that we propose widen the comprehension of the connection processes between the NVJ and the NCJ and claim for the explicit consideration of mesoscale eddies variability in future modeling approach.
Thanks to the analysis of the OUTPACE observations, Fumenia et al. (2018) hypothesize that the location of nitrogen sources and sinks could be decoupled. Thus, the authors propose that the transport of rich nitrogen thermocline waters from N 2 fixation 10 could join the subtropical gyre through the EAC (Fig. 1a). Bouruet-Aubertot et al. (2018) also observe a westward increase of turbulences during OUTPACE. This leads to a strong turbulent regime in the Melanesian Archipelago, located at the entrance of the Coral Sea, highly visible in nitrogen measurements during the long term stations. Extending these conclusions to the Coral Sea set a favorable context to the exchanges between NVJ and NCJ. Specific exchanges from NVJ to NCJ could, then, strengthen the recirculation in the subtropical gyre of rich nitrogen waters. Thus understanding their dynamics could help us to 15 better understand their impact on the propagation of biogeochemical components.

Central Pacific Ocean
The trajectories of OUTPACE and THOT Argo floats give us two groups of float waves with different characteristics. Whereas the long-term mean displacement of the floats could be explained by the presence of alternating striations as deduced from the displacement of the Argo floats at their parking depth, we focused on their quite-surprising oscillation characteristics. In this 20 study, we show that their oscillating trajectories can be caused by a single theoretical wave of 160 days period and 855 km wavelength superimposed to the zonal background current. Focusing on Figure 7, the fit over the trajectory of float 687 is very convincing. It is less so for float 660. We can explain this by recalling that the beginning of the 660 trajectory is, partially or entirely, influenced by an eddy passing through (Fig. 8a,b). Another explanation could be that, in Eq. 4 and 5, we consider the zonal velocity u 0 as constant during the entire simulations. But a variable zonal velocity is likely to strongly impact the float 25 trajectory. We detail this point with two examples that can be observed on the 660 and 687 trajectories, respectively. The first one takes place on the 660 trajectory between 159 o W and 158 o W (Fig. 7). It happens when the zonal velocity decreases while keeping the same direction eastward (Fig. 10a). This leads to a smaller local wavelength. The second one takes place on the 687 trajectory around 158 o W. It happens when the zonal velocity changes direction, from westward to eastward (Fig. 10b).
This leads to a loop in the Lagrangian trajectory. The impact of a variable zonal velocity does not refute our hypothesis of a Based on the HYCOM re-analysis, we confirm that both the 660 and the 687 floats move in shear environments. This shear context is supported by a density front which is permanent all year round. This front could be associated with the base of the northern edge of the Antarctic Intermediate Waters that reach this latitude near our study zone (Bostock et al., 2013). The 5 best fitting wave that we found is close to a Rossby wave in a baroclinic ocean case with a thermocline at 200 m. This case is close to the real context of the studied zone where the upper thermocline waters are located around 200 m (GLODAPv2 database, Fumenia et al., 2018). Moreover, this zone is precisely located where Rossby waves are frequently found and their signatures can be observed through sea level anomalies (Maharaj et al., 2007). Those arguments strengthen the hypothesis of a Rossby wave close to 160 days period and 855 km wavelength. These observations lead to a large discussion of the possible

Conclusions & Perspectives
In this study, we have been able to highlight different pattern of the intermediate flows in the South Tropical Pacific Ocean through the description of the characteristic trajectories of some autonomous floats of the international Argo project deployed 20 during the OUTPACE cruise  and by the THOT project (Martinez et al., 2015). Relying on the measurements of dissolved oxygen concentration (DOXY) onboard a PROVBIO float, we have found a meridional southward transport of NVJ waters by mesoscale eddies causing oxygen minima intrusions in the NCJ pathway around 300 m depth. Our results widen those of Rousselet et al. (2016), since we show that the transport can occur inside the core of a cyclonic eddy or between a couple of anticyclonic and cyclonic structures. Moreover, the hypothesis that the waters can be transported on the edge of several eddies is a new proposed pathway, as far as we know. To ensure the mechanisms 5 of this meridional transport, the fronts between the described cyclonic and anticyclonic eddies could be studied using Finite Size Lyapunov Exponents calculations. These calculations could be applied to both AVISO and HYCOM data to provide information at different depths. Another solution is to replace the Lagrangian observations in their finer circulation context; a study based on dynamic attractors (Mendoza and Mancho, 2010) could be useful to test our assumptions. Otherwise, since DOXY is the parameter that can differentiate NVJ from NCJ, recourse to biogeochemical models could help visualizing and 10 studying the connection between the NVJ and the NCJ. Finally, how these differences in the partition between the jets influence the other biogeochemical parameters and the phytoplankton biology remain to be specifically investigated.
In addition to the description of water masses properties, we observe dynamical features such as wavy float trajectories in the central part of the Pacific Ocean corresponding to a circulation mechanism occurring near 1000 m depth (parking depth). The shear of zonal velocity (∆u = 4.2 cm.s −1 for the floats) associated with a permanent density front (∆ρ = 0.15 15 kg.m −3 ) form a favorable context for the development of instabilities. Correcting the impact of the Lagrangian observation in a simplified case, we concentrated on two floats, heading in opposite zonal directions. We found that their behaviors, apparently opposite, could be described with a single wave of 160 days period and 855 km wavelength heading westward. This couple of parameters can be identified as a Rossby wave in a baroclinic context for a two layers ocean with a thermocline at 200 m. To get a better float wave description, using Fourier transformation or a wavelet analysis, would require to wait until the 20 time series are longer. In addition, to refine the method and results, we suggest to improve the Lagrangian simulation, that we used to fit the trajectories, by taking into account the temporal variations of zonal velocity for each float. Whereas, to improve the comparison to classical waves, the dispersion equation of a Rossby wave could be calculated in the 3D context of the interface between Antarctic Intermediate Waters and the North Pacific Deep Waters. The baroclinic instability of the density front is an alternative hypothesis that could also be considered in order to explain the float trajectories. Because the front is 25 permanent, other immersions of floats at different latitudes on two meridians enclosing the study zone would also consolidate the observations of this process. Nevertheless, all these perspectives are beyond the scope of this paper and will be considered in future works.
Thanks to this study, we underline the importance of eddies as well as waves in the mesoscale dynamics of intermediate flows.
We stress the importance of taking into account individual float measurements and trajectories in further studies in order to better understand water mass transport, mixing processes and their potential impacts on biogeochemical cycles.
Second, we take a baroclinic ocean with two layers separated by the thermocline. Still considering k H = k, the dispersion 10 equation is: with c the phase speed, f 0 the Coriolis parameter at 19 o S equal to −4.7 · 10 −5 s −1 . In this case the phase speed of the wave is expressed by the following equation: with ρ 1 and ρ 2 respectively the densities of the upper and lower ocean layer, ∆ρ = ρ 2 − ρ 1 and h 1 and h 2 the corresponding height of the layers. Using the climatology of ISAS13 atlas and HYCOM re-analysis we make the calculations for four different cases (Tab. C1).