The model used in this study is based on the Nucleus for European Model.ing of the Ocean (NEMO, code version 4.0.6, ), which solves the three-dimensional primitive equations on a staggered Arakawa-C-type grid. The model grid consists of a host grid (TROPICO12) at 1/12∘ horizontal resolution that spans the Pacific Ocean basin from 142–290∘ E and 24∘ N–46∘ S (Fig. a). The ridge features 125 vertical levels with 0.5 m thickness at the surface increasing toward 150 m in the deep ocean with 75 vertical levels in the upper 1000 m (Fig. b). In the vertical, the model uses a partial-step z coordinate with a nonlinear free surface.

Further, the model setup features a horizontal grid refinement (nesting), named CALEDO60, at 1/60∘ horizontal resolution (∼1.7 km grid box spacing). In this particular region, it is expected to allow the model to be submesoscale-permitting. The nesting grid is located in the southwestern tropical Pacific from 159.2–172.4∘ E and 15.7–28.8∘ S and encompasses New Caledonia (see Fig. a). The nesting was set up using an Adaptive Grid Refinement In Fortran (AGRIF, ), a tool explicitly designed for NEMO to set up regional simulations embedded in a pre-defined configuration. AGRIF enables the two-way lateral boundary coupling between the host and the nesting grid to be integrated sequentially during the whole length of the simulation.

Laplacian isopycnal diffusion coefficients for tracers were chosen to be mesh-size-dependent such that the tracer diffusion is scaled down from the host grid of 93 m2 s-1 to the nesting grid of 4 m2 s-1. Vertical eddy diffusivity is estimated by a turbulent kinetic energy (TKE) closure scheme . It is based on a prognostic equation for turbulent kinetic energy and a closure assumption for turbulent length scales depending on vertical shear, stratification, vertical diffusion, and dissipation. The advection of momentum is parameterized by means of a third-order scheme based on upstream-biased parabolic interpolation (UBS).

Initial conditions for temperature and salinity for TROPICO12 and CALEDO60 are prescribed by the GLORYS2V4 oceanic reanalysis (10.48670/moi-00023). Atmospheric forcing is taken from ERA5 produced by the European Centre for Medium-Range Weather Forecasts (ECMWF, ) provided at hourly temporal resolution and a spatial resolution of 1/4∘ to compute surface fluxes using bulk formulae and the prognostic sea surface temperature from the model. Wind stress is computed following the methodology from , i.e., wind speed minus surface currents.

Both domains are forced by the tidal potential of the five major tidal constituents (M2, S2, N2, K1, O1). TROPICO12 is forced at its open lateral boundaries with daily currents, temperature, and salinity, likewise using GLORYS2V4. In addition, TROPICO12 is forced at the open lateral boundaries by SSH and barotropic currents of the same five tidal constituents taken from the global tide atlas FES2014 (Finite Element Solution 2014, ). We made this limited choice to allow the separation of these constituents at monthly timescales.

Recent studies have highlighted the importance of taking into account remote forcing of high-frequency oceanic variability for regional simulations, as it may represent a non-negligible source of energy . Further, it was suggested that tidal accuracy and predictability increase when implementing a two-way nesting framework between the high-resolution regional domain and the lower-resolution host grid . The authors show that mass and energy are conserved with no evident discontinuities along the nesting boundaries.

Apart from increasing predictability through higher horizontal resolution of the nesting grid, it is argued that a realistic bathymetry product is also essential. For the CALEDO60 domain, we used a specific bathymetric product based on the GEBCO_2019 grid and a compilation of multibeam echosounder data acquired over the years in the New Caledonia economic zone . The latter product, initially at 200 m resolution, only covers the area 155∘ E–175.1∘ N, 14.1–26.6∘ S. It has been combined with the GEBCO_2019 bathymetry product to cover the full domain.

Internal tides represent a large source of diapycnal mixing in the open ocean. The associated parameterization scheme developed by is usually used in NEMO simulations. Here, it has been turned off because our simulation has a resolution large enough to resolve the internal wave dynamics. In fact, it has been recently suggested that turning off background components of the vertical mixing scheme improves the modeled kinetic energy levels .

The bottom friction is parameterized using a logarithmic boundary layer with a drag coefficient of 3×10-3 (maximum value of 0.1), a roughness of 2.5×10-3 m, and a background kinetic energy of 1×10-2 m2 s-2. These values yielded the best visual agreement with respect to the mean regional circulation, i.e., the location and magnitude of zonal jets.

The model has been spun up for 2 years (model years 2012–2013) before being run for a total of 5 years (model years 2014–2018). Here, if not noted otherwise, we only focus on 2014 (neutral El Niño–Southern Oscillation conditions) with instantaneous fields saved hourly for the three-dimensional temperature, salinity, velocity, and surface fields (including SSH) for CALEDO60. For TROPICO12, the instantaneous three-dimensional variables are given at daily resolution, whereas the surface fields are saved at hourly resolution. A twin experiment with identical forcing and parameterization has been initialized, but without barotropic tide forcing. Being subject to a future study, here, it is only used to compare the energy spectrum with the tidal simulation.

The modelization of the regional circulation in the Coral Sea represents a challenge due to the numerous islands that serve as obstacles, forming boundary currents and westward jets as well as recirculation and eastward countercurrents . The main feature is a westward inflow from the South Pacific subtropical gyre, which splits into strong zonal jets, western boundary currents, and eastward countercurrents when encountering bathymetric features . The 2014–2018 mean near-surface (20–100 m) simulated velocity field (Fig. a) is compared to the Argo–CARS merged velocity (see Sect.  for a description, Fig. b). The model 5-year mean shows good agreement with the observed regional circulation. The westward zonal jets are well represented with the South Equatorial Current (SEC) being split into the North Vanuatu Jet (NVJ) and the North Caledonian Jet (NCJ) north of New Caledonia and the South Caledonian Jet (SCJ) south of New Caledonia. West of the main islands (New Caledonia, Vanuatu, Fiji), the observed surface eastward countercurrents are also well simulated . The circulation south of New Caledonia seems more variable, with less clearly defined mean currents in both products. There is evidence of the presence of the surface-intensified eastward Subtropical Countercurrent (STCC) that emerges from the East Australian Current (EAC) recirculation . It is clearly intensified in the model, but the Argo merged product south of New Caledonia should be taken with caution since limited observations do not average out the signatures of ubiquitous mesoscale eddies. Overall, the mean circulation is well simulated, which is essential for the proper description of eddy–internal-tide interactions that are the subject of Part 2 of this study.

The large-scale circulation around New Caledonia is subject to barotropic and baroclinic instability of horizontally and vertically sheared currents giving rise to mesoscale eddy variability. Here, the spatial pattern of the surface model mesoscale EKE (Fig. a) is compared to the mesoscale EKE as observed by satellite altimetry (Fig. b). We computed the modeled EKE as closely as possible to the altimetric EKE. To do so, we computed the 5 d mean of the model SSH to eliminate high-frequency variability such as tidal and inertial motions before horizontally binning the data onto the grid of present-day altimetry (1/4∘). For proper comparison between model and altimeter observations, we also computed the 5 d average for altimetric SSH before the derivation of mesoscale EKE. Mesoscale EKE is maximum south of New Caledonia where mesoscale activity is expected to be generated through baroclinic instabilities of the vertically sheared SEC and SCJ–STCC . Elevated levels of EKE are also found along the eastern boundary current system between New Caledonia and Vanuatu as well as in the northwest of the domain through horizontal shear between the westward NCJ and the eastward Coral Sea Countercurrent (Figs. , a). The spatial pattern of simulated EKE is in good agreement with satellite altimetry (Fig. b). Maximum levels of EKE in the southern domain where mesoscale activity is high are essentially lower than in the model (>250 cm2 s-2 compared to >400 cm2 s-2). We argue that this can be attributed to the present-day two-dimensional gridded satellite altimetry products. They are derived by gridding and optimal interpolation of available along-track SSH data, projected onto a 1/4∘ horizontal grid, and do not resolve wavelengths smaller than 150–200 km in our study region . The model, even though gridded to 1/4∘ resolution, might contain dynamics that are associated with smaller scales.

In situ observations are also used to validate energy levels from seasonal down to tidal frequencies obtained from a full-year in situ current meter mooring (see Sect. , Fig. ). Model energy levels are very close to observations from seasonal to inertial timescales (180 d to 36 h), i.e., for mesoscale and submesoscale processes. Inertial and tidal energy peaks are also in good agreement. For higher frequencies, the simulation with tidal forcing (red line) introduces a major improvement to the simulation without tidal forcing (blue line). This is especially true for the internal wave continuum raising the energy levels closer to the observations for frequencies >f. This validation, even if only performed at one location, gives us confidence in the ability of the numerical simulation to correctly represent the tides and their interaction with mesoscale processes.

The barotropic tide in both the host grid (TROPICO12) and the nesting grid (CALEDO60) is compared with the empirical estimates from the barotropic tide model FES2014 (see Sect. ) by applying a harmonic analysis to the full-model hourly SSH. Note that the daily output of the three-dimensional variables from TROPICO12 does not allow for a decomposition between the barotropic and baroclinic tide through the projection onto vertical modes. Therefore, we treat the full-model SSH as a proxy for the barotropic tide. For the sake of consistency, we treat CALEDO60 similarly. The M2 tides of TROPICO12 (Fig. a) and CALEDO60 (Fig. c) are in overall accordance with FES2014 (Fig. c and Fig. d, respectively). The amphidromic points are well located and amplitudes of SSH are of the same order of magnitude. Note that the modulations at shorter wavelengths in Fig. c and d are attributed to the baroclinic SSH signatures, which are presented at a later stage in Sect. .

Finally, in order to study internal-tide dynamics, a correct representation of the ocean's stratification is essential. Internal tides are expressed inter alia in the vertical displacement of isopycnal surfaces , which can be decomposed by a sum of discrete baroclinic modes that only depend on buoyancy frequency and water depth (see Sect. ). We compare the vertical hydrographic structure of CALEDO60 with a hydrographic climatology (CARS2009, see Sect. ). The model mean density was horizontally binned to the climatological grid (1/2∘), whereas the climatological density was vertically interpolated onto the model grid. The water masses (not shown) and buoyancy frequency profiles correspond well to each other. An example of such a comparison is illustrated by looking at a stratification profile south of New Caledonia (166∘ E, 26∘ S, Fig. a). The maximum stratification around 100 m depth is slightly reduced in the model compared to climatology. This is attributed to a reduced salinity maximum in the thermocline in the model (not shown). The normalized modal structures for the four lowest modes and for both the displacement and vertical velocity (Fig. b) agree well with climatology. In particular, the depths of the zero crossings correspond well to each other.

Overall, we conclude that our model simulation is capable of realistically simulating both background ocean dynamics and internal tides. This encourages us to study the internal-tide field around New Caledonia in detail including its tidal energy budget, its vertical structure, and finally its SSH signature.

Tidal energy conversion from the barotropic to baroclinic tide is closely linked to the bathymetry that is shortly presented in the following for the regional model domain (Fig. a). It is characterized by a complex northwest–southeast-extending ridge system, deep-reaching trenches, small-scale basins, seamounts, and shallow lagoons. The ridge system is composed of two major ridges, Norfolk Ridge and Loyalty Ridge. Norfolk Ridge extends from north of the Grand Passage all the way to the northern tip of New Zealand. The main New Caledonia island (Grande Terre) is located on the northern segment of Norfolk Ridge, also referred to as the New Caledonia Ridge. Loyalty Ridge stretches parallel to Norfolk Ridge, giving rise to the Loyalty Islands . Seamounts are ubiquitous around New Caledonia and most prominent south of Grande Terre .

As the M2 barotropic tidal energy flux curves southwestward around New Caledonia, the region is subject to barotropic-to-baroclinic energy conversion (Fig. a). Positive conversions represent energy transfer from the barotropic to the baroclinic tide; negative conversions are argued to be a measure of the energy transfer from the baroclinic tide to the barotropic tide due to pressure work . However, they may also reflect limitations in the baroclinic–barotropic decomposition . Thus, they remain difficult to explain physically and will not be further discussed here.

In the full-model domain, a total 21.16 GW of barotropic tidal energy is lost, 72 % (15.27 GW) of which is transferred to baroclinic tidal energy, whereas 28 % (5.89 GW) is dissipated due to bottom friction. This is a significant loss of barotropic tidal energy. For comparison, barotropic tidal energy loss has been estimated at 18.35 and 2.73 GW, 94 % and 84 % of which are converted to baroclinic tidal energy for the Luzon Strait and the Hawaiian Ridge , respectively.

In the whole domain (not shown), conversion is observed at all depths up to 4000 m and over a broad range of slopes. However, tidal conversion peaks in shallow waters with overall 25 % of the area-integrated energy that is associated with the upper 500 m. Moreover, two-thirds of the tidal conversion occurs on critical and supercritical slopes. Mode 1 clearly dominates, explaining almost 70 % of the total tidal energy conversion. Higher modes play only a minor role (15 % for mode 2 and 7 % for mode 3). For the whole domain, 93 % of this generated baroclinic energy is finally dissipated inside the domain, while little energy (1.06 GW) leaves the domain (Fig. a). Note that this quantity is representative of the net baroclinic flux of inward and outward energy propagation.

Here, we identify four regions of internal-tide generation which together represent roughly 60 % of the full-domain area-integrated M2 barotropic-to-baroclinic conversion. These hot spots are illustrated by the black boxes in Fig. a–b and Fig. a and defined as North (1), South (2), Norfolk Ridge (3), and Loyalty Ridge (4). The conversion and energy budget are discussed for each area in light of its topographic characteristics (Fig. ). The energy budget and the part dissipated locally are also provided for each subregion to better infer where the dissipation occurs and where tidal mixing is expected (Fig. , see also Table ).

The North (1) domain is characterized by a very steep (with critical and supercritical slopes) shelf break at the eastern flank of the New Caledonia Ridge and a 500 m deep, 50 km wide passage (Grand Passage) that is located between the d'Entrecasteaux Reef and the main island reef (Fig. a–b). Two-thirds of the tidal energy conversion occurs at depths shallower than 500 m (Fig. b), predominantly on critical and supercritical slopes (Fig. b–c). The region features the highest dissipation rate of barotropic energy compared to the other three regions. Of the 3.83 GW that is lost by the barotropic tide, 1.66 GW (43 %) is directly lost through bottom friction (Fig. a). Of the 2.17 GW that is converted to baroclinic energy, 32 % (0.70 GW) dissipates locally, while the remaining 68 % (1.47 GW) radiates away.

The South (2) domain has similar bathymetric characteristics in terms of depth and slopes. It represents the southward extension of the New Caledonia Ridge, just south of the New Caledonian lagoon. The most prominent bathymetric feature is Pines Ridge: it is a very steep (critical and supercritical slopes) and narrow ridge (a few tens of kilometers wide) of 100 km length that may be as shallow as 500 m (Fig. a–b). This region will be analyzed in more detail in Sect.  since it is subject to the most intense energy conversion with a total of 3.92 GW (Fig. b), primarily in depths shallower than 500 m (Fig. c). Further, local dissipation is essentially higher than in the North (1) domain.

Norfolk Ridge (3) exhibits different bathymetric characteristics. It is defined as the >100 km wide north–south-stretching ridge between 24.5 and 28.5∘ S. It is dominated by subcritical slopes at depths >1000 m (Fig. c) and also features steep (critical) slopes at mid-depths (400–700 m) which are mostly associated with seamounts. It is mainly characterized by energy conversion at subcritical slopes peaking at depths in the range 1000–2000 m with the 50th percentile at around 1500 m and the 90th percentile below 2000 m (Fig. d). Similarly to South (2), approximately half (53 %) of the converted baroclinic energy (2.04 GW) is dissipated locally (1.07 GW), while the other half (47 %) is radiated away (0.96 GW, Fig. c).

Loyalty Ridge (4) is a deep and narrow ridge composed of seamounts and guyots . These seamounts and guyots are located between 1000 and 2000 m depth, but deeper ones are also found between 2500 and 3000 m. They are characterized by supercritical and critical slopes, respectively (Fig. b–c). It features the most efficient energy conversion from the barotropic to baroclinic tide. Of the 1.28 GW that is lost by the barotropic tide, only 0.31 GW (24 %) is directly lost through bottom friction (Fig. d). The area-integrated baroclinic energy accounts for 0.97 GW, 45 % of which dissipates within the region (0.44 GW) and 55 % leaves the domain (0.53 GW).

Most of the tidal energy conversion discussed above is dominated by mode 1, explaining 75 %, 84 %, and 76 % for North (1), South (2), and Norfolk Ridge (3), respectively (Fig. a–c). In these, regions, mode 2 (7 %–12 %) and mode 3 (4 %–6 %) contribute little to the total baroclinic energy conversion. Loyalty Ridge (4) represents an exception with notable contributions of higher vertical modes: 43 %, 31 %, 11 %, and 6 % associated with mode 1 through mode 4, respectively (Fig. d).

These findings are partly consistent with the literature. In shallow depth ranges, the tidal energy conversion is expected to be largest for mode 1 . Also, we expect mode 1 to be dominant for steep, tall, narrow structures such as in the North (1) and South (2) domains, similarly found for the Hawaiian Ridge . In the case of a deeper ocean bottom with small-scale bathymetric structures, such as Loyalty Ridge (4), higher modes are expected to become more important. The general presence of critical and subcritical slopes suggests a superposition of numerous vertical modes forming beams . Nevertheless, we did not find any clear relationship between the bathymetric slope and excitement of vertical modes. The high dissipation rates in South (2) and Norfolk Ridge (3) could be explained by the successive bathymetric obstacles encountered by the internal-tide beams emanating from the generation spots with low modes scattered to higher modes before being dissipated locally . Surprisingly, the fraction of energy dissipation around Loyalty Ridge (4) is slightly reduced even though higher vertical modes are generated, which should imply more local dissipation.

Briefly summarized, the bulk of energy conversion from the barotropic to the baroclinic tide is confined to four hot spot regions in shallow waters (500 m), closely linked to the complex bathymetry (i.e., shelf breaks, ridges, and seamounts), and dominated by mode 1. Approximately half of the locally generated energy dissipates in the near field, whereas the other half propagates outside the hot spot regions. This suggests a quick attenuation of baroclinic energy. Our model results show that the fraction of coherent internal tides that loses energy locally (q=Dbc/C) is elevated in our study region compared to 36 % and 20 % for the Luzon Strait and the Hawaiian Ridge , respectively. Potential factors that may contribute to this loss of energy will be discussed later in Sect. . Particularly, we will point out that the high dissipation rates observed in our analysis may not be solely associated with actual energy dissipation, but also with a loss of tidal coherence. This will be explored in more detail in Part 2 of this study.

In the following, we compare our M2 modal conversion for the four subregions with the semi-analytical model estimates from (Falahat14) and (Vic19) in Fig. . Recall that both products represent the energy conversion in depths >700 m and on subcritical slopes only (see Sect. ). The model conversion is given for the full model (considering the full water column and subcritical, critical, and supercritical slopes), the full model but only considering depths >700 m, and the full model but only considering both depths >700 m and subcritical slopes. The latter ensures the best comparison between the semi-analytical and numerical model estimates.

Overall, there is good agreement between our full-model estimates and those from semi-analytical theory concerning the conversion's modal content, with mode 1 being clearly dominant. Higher modes appear to only increase in relative importance for Loyalty Ridge (4) (Fig. d). The full-model energy conversion tends to be excessive in the South (2) domain (Fig. b). When correcting the full model for conversion in the upper 700 m in addition to conversion on critical and supercritical slopes, our model conversion compares better with the semi-analytical estimates. Even though corrected for the upper 700 m, there is no good comparison with Vic19 in the North (1) domain (Fig. a). This could be related to violation of linear theory that leads to unrealistic conversion rates larger than the energy lost by the barotropic tide. Remaining discrepancies among the products may be attributed to the associated bathymetry products that differ in both horizontal resolution and the correct representation of those bathymetric structures that are key for internal-tide generation.

While semi-analytical theory has proven very valuable in providing a first-order estimation of internal-tide generation on global scales, it reaches its limits in regions with shallow and complex bathymetry with critical to supercritical slopes. In fact, we find for the subregions around New Caledonia that roughly 50 %–90 % of the energy conversion may be missed locally when not allowing for conversion in the upper 700 m and on critical to supercritical slopes. This highlights the need for realistic, high-resolution numerical simulations to more faithfully represent the local internal-tide generation and dynamics.

The propagation of baroclinic tidal energy is expressed mainly by two predominant tidal beams that emerge from the North (1) and South (2) domains (Fig. a). They are 100–200 km in width and feature magnitudes well above 20 kW m-1 (locally up to 30 kW m-1) near the respective generation sites but propagate not more than 800 km toward the open ocean. In contrast to the southern tidal beam that propagates from its generation site at Pines Ridge southwestward and northeastward (though the northeastward beam is more limited), the northern tidal beam mainly propagates northeastward. This is attributed to the energy conversion that is confined to the shelf break east of the Grand Passage, whereas the Grand Passage itself is subject to only minor energy conversion (not shown). Tidal beams also emerge from Norfolk Ridge (3) and Loyalty Ridge (4). However, they are overall less pronounced and smaller in magnitude (5 kW m-1).

The rather quick attenuation of the tidal beams may be associated with the high dissipation rates, which are in large part constrained to the hot spot regions (Fig. b). This is reflected in the regional energy budgets and sheds light on the high fraction (∼50 %) between local energy dissipation and generation (see Sect. ). Dissipation also occurs away from the hot spot regions, but to a lower degree.

The South (2) domain deserves special attention for two reasons: first, it represents a study area of the SWOT–AdAC program accompanied by an extensive field campaign. This will be further addressed in Sect. . Second, it represents the predominant hot spot of internal-tide generation contributing more than 40 % and 25 % to the area-integrated barotropic-to-baroclinic energy conversion associated with the four subregions and full regional domain, respectively.

In total, 6.16 GW is lost by the barotropic tide, 64 % (3.92 GW) of which is converted to internal tides (Fig. a). The bulk of energy is generated when the incoming barotropic tidal flow encounters Pines Ridge, featuring conversion rates well above 1 W m-2 on both its western and eastern flanks. Further internal-tide generation is localized downstream along a secondary ridge parallel to Pines Ridge and across the western shelf break. Locally, positive conversion is also evident around seamounts that are present in the area, namely, Munida, Antigonia, Jumeaux Est, and Stylaster.

In contrast to the conversion map which shows isolated spots, baroclinic energy dissipation is observed throughout the domain, accounting for a total of 2.09 GW (Fig. b). In other words, well above 50 % of the locally generated energy dissipates within the South (2) domain. Dissipation maxima are located near the generation sites such as Pines Ridge and around the seamounts with dissipation rates >0.5 W m-2, i.e., around Munida, Brachiopode, Jumeaux Ouest, and Stylaster. Increased levels of dissipation are also found along the barrier reef that encloses the southern Caledonian lagoon. Further energy dissipation occurs uniformly westward and eastward of Pines Ridge across the shelf break with constant dissipation rates >0.1 W m-2.

The non-dissipated energy propagates away from the main generation site within well-confined tidal beams in southwestern and northeastern directions characterized by energy fluxes >20 kW m-1 which attenuate gradually to roughly 10 kW m-1 within 100 km distance of the generation site in the annual mean. A net energy flux of 1.83 GW leaves the South (2) domain, accounting for 47 % of the locally generated baroclinic tidal energy.

We present the spatial maps of mode 1 and mode 2 of the M2 SSH amplitude in Fig. a and b in comparison with the satellite-altimetry-derived empirical estimates from the HRET model (see Sect. ) in Fig. c and d for mode 1 and mode 2, respectively. Dominated by mode 1, the spatial distribution of SSH reveals multiple interference patterns with M2 tidal waves emanating from multiple generation sites and summing constructively and destructively as they propagate (Fig. a). Amplitudes may reach more than 6 cm in the internal-tide hot spot regions. Following a similar pattern but strongly reduced in amplitude, mode 2 features significant amplitudes of up to 2 cm at some locations. Overall, the M2 SSH signature resembles the energy flux in Fig. a with the predominant tidal beams to the north and south of New Caledonia. There is good agreement with the HRET model concerning the spatial representation of the M2 SSH for both mode 1 (Fig. c) and mode 2 (Fig. d). Overall, mode 1 seems to be enhanced in our model, whereas mode 2 is underestimated in some regions. Note that the given differences may be associated with the different time periods the datasets are referenced to as well as the length of the time series for the model (1 year) and altimetry (25 years).

Wavenumber SSH spectra are commonly used to investigate dynamical regimes at work and to explore the relative importance of balanced and unbalanced motions which may feature similar wavelengths: the wavenumber slopes and relative levels of variance both provide information on these issues e.g.,and many more.

Here the objective is to describe for two given transects in the tidal beam direction (red lines in Fig. a) the SSH signature with regard to the different dynamics that are separated in terms of frequency bands: subinertial frequencies (ω<f, SSHsubinertial) for mesoscale and submesoscale dynamics, as well as superinertial frequencies (ω>f, SSHsuperinertial) for internal gravity waves while distinguishing between the coherent internal-tide (SSHcoh) and supertidal frequencies (ω>1/10 h, SSHsupertidal).

Further, we will examine how SWOT observability may be limited in a region with strong internal tides. SWOT observability of mesoscale and submesoscale dynamics (balanced motion in this case) is ultimately governed by the transition scale Lt that separates balanced from unbalanced motion. The transition scale is a quantitative measure to estimate above which scales in spectral space the geostrophic balance is valid to derive balanced motion. Here, we define it as the intersection of subinertial and superinertial spectra. In other words, the transition scale is set to wavelengths where subinertial variance equals superinertial variance.

For both regions, subinertial processes explain almost all of the SSH variance for scales larger than 200 km (Fig. e, f). For scales smaller than 200 km, SSH variance is governed by superinertial processes, which are largely dominated by the coherent internal tide clearly expressed in spectral space with mode 1 and mode 2 around 160 and 80 km wavelength. In the annual mean, Lt is set to (i) 204 km and (ii) 163 km, meaning that the observability of balanced motion is largely limited below these scales as unbalanced motion dominates the SSH variance.

The correction of the total SSH for the coherent internal tide may be a promising attempt to assess balanced SSH dynamics. Doing so, Lt is reduced (i) from 204 km to 92 km and (ii) from 163 to 83 km. The right sub-panels of Fig. e and Fig. f show the monthly evolution of Lt and the corrected transition scale Ltcorr over 1 model year. Temporal variations of the transition scale may be the result of the relative importance of subinertial motion, which undergoes seasonal variability . This was explicitly shown for New Caledonia by , who attributed the increasing importance of mixed layer instabilities and frontogenesis to more available potential energy in the Southern Hemisphere winter months.

Other temporal variations of the transition scale may be related to temporal variability of the internal tide. The coherent internal tide is by definition constant, but the incoherent internal tide (not shown here) depends on the seasonally varying stratification and/or the interaction with the background currents (see Sect.  for references). Moreover, the incoherent signal remains in the corrected SSH signal. Therefore, the extent to which we can increase observability of mesoscale and submesoscale dynamics in areas with internal-tide activity depends on the amplitude of the incoherent internal tide. Understanding the temporal variations of the transition scale, its link to the incoherent internal tide, and its implication for SWOT SSH measurements is beyond this scope of this paper's objective, but it will be specifically addressed in Part 2.

Briefly, the dominance of unbalanced motion in the mesoscale to submesoscale band strongly restricts SSH observability of geostrophic dynamics to large eddy scales in our study regions. However, a correction for the coherent internal tide may improve the observability to well below 100 km.

The barotropic and baroclinic energy budget of the dominant M2 tide shows that in the regional model domain surrounding New Caledonia, 21.16 GW of the barotropic tidal energy is lost, 72 % (15.27 GW) of which is converted into baroclinic tidal energy. The main conversion zones are associated with the most prominent bathymetric structures such as the Grand Passage (2.17 GW) and Pines Ridge (3.92 GW) north and south of New Caledonia, respectively. This confirms that New Caledonia is a hot spot of internal-tide generation. The amount of energy converted is comparable to what has been estimated in the Luzon Strait and the Hawaiian Ridge , taking into account that the exact numbers depend on the size of the domain. The area-integrated M2 conversion is estimated as 15.27 GW around New Caledonia, 16.97 GW in the Luzon Strait, and 2.34 GW along the Hawaiian Ridge. Conversion integrated in the smaller subregions North (1) and South (2) are similar to the Hawaiian Ridge (2.17 and 3.92 GW, respectively). Local conversion rates are of the same order of magnitude (well above 1 W m-2) among all regions. Further, all regions feature similar energy propagating away from the formation site within well-defined tidal beams. Maximum M2 baroclinic energy fluxes vary from 10 kW m-1 at the Hawaiian Ridge up to 30 kW m-1 around New Caledonia and 40 kW m-1 at the Luzon Strait.

Interestingly, the New Caledonia region stands out compared to other previously studied regions in terms of modal content. Our modeling results suggest that barotropic tidal energy is converted, overwhelmingly, into baroclinic mode 1 (75 % of the full-domain energy conversion and up 85 % in the South (2) domain). Modes 2–4 represent a comparable amount of energy only at Loyalty Ridge (4) characterized by deep topography. For comparison, this mode-1 conversion percentage was estimated to be around 30 % at global scale, 35 % for the Pacific basin , 30 %–60 % around Hawaii , and about 9 % over the northern Atlantic Ridge . The reasons behind this strongly dominant mode 1 are not completely understood. A dominance of mode 1 in the western Pacific has been previously suggested with semi-analytical models , but not to that extent. Mode 1 has been suggested to be dominantly generated in shallow depths . Apart from topographic characteristics such as height, width, and depth , the modal content is argued to be primarily governed by roughness and, thus, by the topography's spectral shape . On the other hand, it has been observed and argued by many that critical and supercritical slopes are conducive to beam-like patterns, requiring the presence of higher vertical modes . Fully understanding the strong dominance of mode 1 in our region characterized by the presence of steep, tall, and shallow ridges with critical and supercritical slopes, as well as 25 % of the conversion taking place above 500 m, would require further analyses.

An important lesson learned is that New Caledonia represents a complex area for linear semi-analytical models that break down for critical and supercritical slopes and shallow bathymetry, which in turn are key for internal-tide generation at our study site. Such semi-analytical models, although very useful and widely used to estimate tidal energy conversion, its modal distribution, and tidal mixing e.g.,, miss a significant part of the conversion (50 %–90 %) in our area, pointing out the limitation of these approaches in such complex areas. This issue was also presented in . However, it was only addressed on global scales, highlighting the relevance of realistic numerical simulations on regional scales.

Our model results suggest elevated ratios (q) between local tidal energy dissipation and generation of ∼50 % compared to other internal-tide generation hot spots in the Luzon Strait (36 %, ) and the Hawaiian Ridge (20 %, ). This is surprising considering the clear dominance of mode 1 in most parts of our nesting model domain where mode 1 dominates the baroclinic tidal energy propagation. Nonetheless, the elevated levels of local energy dissipation provide an explanation for the relatively small propagation distance of the tidal beams (e.g., around 800 km for the tidal beam emanating from South (2)), essentially smaller compared to the tidal beams emanating from the Luzon Strait and the Hawaiian Ridge that may propagate several thousand kilometers toward the open ocean. Several processes of tidal energy dissipation have been discussed in the literature that are well summarized in : nonlinear wave–wave interactions, wave breaking through shoaling, dissipation on critical slopes, and scattering by abyssal hills. The interaction with the topography may explain the largest fraction of energy dissipation . This especially concerns the scattering and energy transfer of the low-mode internal tide to higher modes leading to increasing dissipation. Nonlinear wave–wave interactions were shown to facilitate the energy transfer of low-mode internal tides to both superharmonic and subharmonic frequencies . Particularly the latter, which is associated with parametric subharmonic instability, can be an important energy sink for low-mode internal tides near the critical latitude band (around 29∘ N/S for the semi-diurnal tide) south of New Caledonia. The mechanisms of tidal energy dissipation and their relative contributions in our study area remain an open question. This is beyond the scope of this study and requires further investigation.

Recall that here the tidal energy dissipation (residual between energy flux divergence and conversion) corresponds to a coherent tidal analysis. Due to the length of the harmonically analyzed time series (full-model calendar year), it must be assumed that a non-negligible fraction of the coherent dissipation is not associated with true dissipation but with a loss of coherence or scattering of energy to the incoherent tide, i.e., with increasing distance from the internal-tide generation site . The actual fraction of true energy dissipation will be addressed in more detail in Part 2 of this study involving the full semi-diurnal signal and tidal incoherence. A potentially important contribution to elevated dissipation rates could also be linked to the chosen bottom friction and drag parameterization (see Sect. ). The tidal dissipation’s sensitivity to the given parameterization, however, was not addressed and would require a dedicated analysis.

The SWOT mission is dedicated to documenting two-dimensional fine-scale features down to 15 km wavelength that include both subinertial (mesoscale to submesoscale dynamics) and superinertial (such as internal tides) frequencies. Disentangling these different dynamics in terms of SSH is of interest for SWOT observability. Here, we have investigated the transition scale that separates the larger scale dominated by balanced geostrophic motion from the smaller scale dominated by unbalanced wave motions in the two main pathways of the internal-tide energy flux. Further, we analyzed what impact the correction for the coherent tide in the SSH signal has on the transition scale.

Wavenumber spectra of SSH reveal the dominance of unbalanced, rapidly changing motion, largely governed by the internal tide, in the mesoscale band at spectral wavelengths below 200 km. The separation length scale between balanced and unbalanced motion is in good agreement with estimates deduced from along-track satellite altimetry in see their Fig. 6. Our findings also align with the global model analysis from , where the SSH-derived transition scale is estimated to be slightly below 200 and 160 km north and south of New Caledonia, respectively.

Correcting our model for the coherent internal tide, we are able to improve the observability of mesoscale and submesoscale SSH around New Caledonia to well below 100 km in the annual mean. The limited observability even after the correction of the coherent internal tide is potentially linked to the temporally varying tide. The study region may be subject to strong interactions between internal tides and mesoscale eddies, giving rise to tidal incoherence. This is especially true south of the New Caledonia that is characterized by elevated levels of EKE (see Fig. ).

This work is the first modeling approach to characterize the internal-tide dynamics around New Caledonia. Part 1 focuses on the coherent part of the main M2 component. Giving first insight into internal-tide generation, propagation, and dissipation as well as SSH observability, this study is meant to serve as a basis for future studies such as eddy–internal-tide interactions and their expression in SSH. Internal tides may be strongly sensitive to the background currents both at the generation sites and along propagation, with implications for tidal energy conversion from the barotropic to baroclinic tide and tidal energy dissipation. This will be the subject of Part 2 of this study. Further, a twin simulation experiment, with the same forcing and parameterizations but without tidal forcing, has been performed. Comparing the two simulations will help us understand how tides impact the mesoscale and submesoscale fields, as well as the forward and inverse energy cascades among spatial scales (work in progress).

The results obtained will play an important role when confronted with in situ observations. The dedicated SWOTALIS in situ experiment was carried out in March–May 2023 during the SWOT fast sampling phase (related to SWOT–AdAC) beneath the SWOT swaths and nadir track. Observational platforms such as moorings, repeated hydrographic sections, and long fixed stations spanning several semi-diurnal tidal cycles with microstructure measurements in the hot spots of internal-tide generation and dissipation as well as in the propagation direction will provide further insight into the internal-tide life cycle south of New Caledonia, in combination with the SWOT data. Our simulations will help link the full water column dynamics and the SSH measurements.

Finally, this study provided first hints on internal-tide dissipation spatial variability. Yet, the impact of tidally driven mixing on temperature, other tracer fields, and biological variables in this area of high biodiversity remains to be quantified. It is expected that strong vertical velocities along bathymetric slopes, reefs, and seamounts may influence nutrient inputs into the euphotic layer and primary production, potentially up to high trophic levels and marine fauna . Such effort has been recently initialized in the framework of the ScInObs (Science, Innovation and Observatories of seamounts) project led by the French Research Institute for Exploitation of the Sea (IFREMER) and in collaboration with the Japan Agency for Marine–Earth Science and Technology (JAMSTEC) south of New Caledonia at the Stylaster seamount (Fig. ). Overall, observing and understanding the local impact of internal tides on the ecosystem are of large socioeconomic interest for the island's conservation management. We hope that our results will pave the way to a better understanding of the processes and ultimately help marine conservation.