| 04 Feb 2026
Internal tides off the Amazon shelf – Part 2: temperature variability at tidal frequencies
Abstract. The northern Brazilian region constitutes one of the most energetic tidal environments of the tropical Atlantic, where distinct mixing regimes coexist over short spatial scales. While barotropic tidal motions exert a dominant control on turbulent mixing across the shallow continental shelf, energy dissipation associated with internal tides (ITs) governs the intensity and distribution of mixing at the shelf-break and in offshore waters. As demonstrated in the Part 1 companion study (Assene et al., 2024), these contrasting processes strongly influence upper-ocean thermal structure. Yet, the expression of tidal forcing in temperature variability at tidal timescales—particularly at semidiurnal (principal solar: M2 and principal lunar: S2) and fortnightly (lunisolar synodic: MSf) frequencies—remains poorly documented in this region. In this study, we investigate the role of tides, with a focus on ITs, in shaping temperature variability throughout the NBR by combining long-term satellite sea surface temperature (SST) records with high-resolution three-dimensional numerical simulations operated with and without tidal forcing.
The main findings are as follows:
- At semidiurnal frequencies, temperature variability at the sea surface is very weak offshore and remains modest over the continental shelf, consistent with the prevalence of barotropic mixing that acts largely as a depth-integrated process in shallow waters. In contrast, pronounced temperature variability emerges at thermocline depths, with mean amplitudes reaching approximately 0.6 °C for S2 and exceeding 2 °C for M2. The spatial structure of these subsurface signals aligns closely with simulated mode-1 and mode-2 IT wavelengths, propagation pathways, and dissipation hot-spots, underscoring the central role of ITs in driving semidiurnal thermal variability below the surface mixed layer;
- Fortnightly (MSf) variability contrasts sharply with the semidiurnal response. Both satellite observations (MUR, TMI) and tidal simulations reveal low amplitudes on the order of 0.15 °C, with maximums confined to the northwestern shelf where Spring–Neap modulation of barotropic tidal currents is the dominant tidal process. Composite analyzes contrasting Spring versus Neap conditions further suggest that this MSf variability manifests primarily as a net cooling with the same amplitude. At the surface, neither model nor satellite observations exhibit a significant SST expression at MSf frequency along internal tide propagation pathways. This may reflect a rapid atmospheric heat flux adjustment that counteracts internal tide–induced cooling and/or the inherently incoherent nature of internal tide dynamics that disperses energy across frequencies, preventing harmonic methods from capturing a clear MSf signature. At subsurface depths (~120 m), MSf temperature variability becomes more pronounced along IT pathways, particularly near the shelf break and downstream of generation sites where dissipation is strongest.
- The vertical penetration depth of tidally driven temperature variability decreases systematically with increasing tidal period, from penetration depths approaching 2500 m for M2, to 800–1000 m for S2 and 600–800 m for MSf. These contrasts indicate that the capacity of tidal motions to influence the water column depends strongly on the available energy at each frequency and points to a frequency-dependent control of deep-ocean mixing and heat redistribution.
Together, these findings provide the first regional quantification of temperature variability at tidal frequencies in the northern Brazilian region and demonstrate that internal tides constitute a major driver of subsurface thermal structure across this dynamically energetic margin. This improved characterization is essential for understanding heat redistribution, interpreting coastal and open-ocean temperature variability, and ultimately constraining the representation of tidal processes in ocean and climate models.
Review of ‘Internal tides off the Amazon shelf – Part 2: temperature variability at tidal frequencies’ by Fernand Assene et al., submitted for publication in Ocean Science (egusphere-2026-557).
I find this paper not suitable for publication in Ocean Science, because it lacks fundamental knowledge on barotropic and baroclinic tides, both in shallow seas and oceans, and because it is based on limited sea-surface temperature observations, instead of observations in the oceans’ interior, and numerical modelling that barely resolves internal tidal length scales.
Detailed comments.
Abstract: Is too long and not a single paragraph.
l.33: (and further on): the naming of tides is reversed; the S (in S2) stands for sun, the M in M2 for moon.
l.35: Abbreviations like NBR should be spelled out on first use.
l.36: SST data instead of elevation data have very limited view on internal waves.
l.41: I have no idea what is meant by ‘consistent with barotropic mixing...depth-integrated process in shallow waters’. Barotropic tidal mixing is mainly frictional, both at the bottom and, hampered, across internal stratified layers (e.g. Maas and van Haren, JMR1987).
l.43: Confusing: subsurface signals are not obtained from SST data, so I assume they are from modelling efforts. This should be made clear upfront.
l.44: What is meant by ‘pathways’ and ‘hot-spots’? Please define.
l.47: Here and elsewhere, abbreviations like MUR and TMI should be spelled out on first use (in the abstract and in the main text).
l.49: I would not name (spring-neap) ‘modulation’ as a (dominant no less) tidal ‘process’.
l.51-52: Please explain how MSf frequency can exist ‘along internal tide propagation pathways’. As M2 and S2 are different frequencies, their propagation directions are divergent (for given stratification and source). Besides, internal tides are highly intermittent, and do not generally yield MSf modulation.
l.74-75:Internal waves can provide temperature variations are tidal frequencies, but turbulent mixing due to breaking internal waves less likely so.
l.79: What is meant by ‘assessment’?
l.86: Yes, precisely, this causes internal wave intermittency.
l.91:Please define/quantify ‘high-frequency’.
l.94-95:References are made to limited (east-Asian) waters; I think such MSf temperature variability has been observed in other ocean areas as well, no?
l.109-110:Quite some work in barotropic tidal motions in stratified waters has been done in other areas, e.g. the NorthWest European shelf seas (Prandle, GAFD1982; Maas and van Haren, JMR1987)
l.116-117; Internal wave mixing is indeed primary cause of exchange in tidally dominated shelf seas (van Haren et al. GRL1999).
l.131:Daily data do not resolve semidiurnal motions.
l.134:Where were non-tidal simulations described, perhaps I missed something?
l.143:25 km scales do not resolve internal tides, which have typical excursion length scales of 1 km.
l.161: Can you indicate which purpose?
l.164: Does an ocean circulation model resolve internal tides?
l.179: Why daily data to extract fortnightly variations, you can use hourly data as well for that purpose.
Table 1 is out of place, as it refers to Fig. 6. If it is kept it should be placed closer to Fig. 6.
l.214-216: Unclear what is done in the spectral analysis. If you compare it with results from harmonic analysis I would expect band-pass filtering, which is not mentioned.
l.226-227:This is not surprising at all (see remark above on internal wave intermittency).
l.228-232: I do not understand. Harmonic analysis provides amplitude and phase at a predescribed frequency for a time series of a particular quantity. It does not provide cross-correlation results like time/phase lags.
l.296-297: I do not see evidence for this conclusion.
l.331-332: IT surface elevation? Internal waves in general provide very little variations in sealevel height.
l.389: I would remove ‘first’, because it has little meaning.
l.440: How comparable is the Irish Sea with the North Brazilian shelf, in terms of depth and tidal flows?
l.447: The quoted work by van Haren et al. (2016) is from around 1700 m depth, not 120 m.
l.453: Arbitrary depth penetration values. Internal waves can penetrate to greater depths.