*4.3. Global Scale*

A global perspective on SST tidal fluctuations (Figure 5) is obtained by combining the map of maximum SST gradients (Figure 2) and maps of tidal current amplitudes (Figure 1) as described in Section 3. In this case, since the maximum SST spatial gradient climatology has coarser spatial resolution, it was remapped to onto the grid of the tidal current amplitudes using a bilinear interpolation. Over Northwest Australia and South Madagascar, climatological values of maximum gradients are about 0.3 ◦C/km and 0.4 ◦C/km respectively, which is between 2 and 6 times more than maximum SST gradients in the two scenes selected (Figures 3 and 4). The same ratio directly reflects into expected tidal SST fluctuation amplitudes.

Baroclinic tidal currents cause largest SST fluctuations around western boundary currents main flow paths, except in the case of the Gulf Stream where the baroclinic tidal current is weak or non-existent (see Figure 1), and nearby upwelling areas. The signal is in general weaker for latitudes within ±15◦ equatorial areas. When barotropic currents are large, they induce largest SST signals, i.e., in coastal areas, and with a geographical distributions that thus significantly differs from that associated to baroclinic currents. The amplitude of barotropic tidal SST fluctuations is about three times larger than the one induced by baroclinic currents.

**Figure 4.** (**a**) SST captured by METOP on the 5 June 2014. (**b**) Sobel gradient of SST. (**c**) **M2 barotropic FES** amplitude current. Gray contour correspond to the bathymetry. (**d**) Estimation of the amplitude of M2 barotropic signature on SST. (**e**) **M2 baroclinic HRET** amplitude current for areas with a bathymetry deeper than 1000m. Gray contour lines correspond to the bathymetry. (**f**) Estimation of the amplitude of M2 IW signature on SST.

**Figure 5.** (**a**) Estimation of the amplitude of M2 IW signature on SST. (**b**) Estimation of the amplitude of M2 barotropic signature on SST.

#### **5. Discussion and Conclusions**

Baroclinic tidal currents derived from the HRET database correspond to the stationary part of the internal tide signal, i.e., fluctuations that keep a fixed phase relationship with astronomical forcings. These currents represent a fraction of actual baroclinic tidal currents [7]. Therefore, present estimates of baroclinic tidal SST fluctuations may underestimate true fluctuations. This is in particular true over western boundary currents paths (see SST fluctuations minima on Figure 5), where the baroclinic tides are non-stationary to a large extent.

For the sake of brevity, this study has focused on one tidal constituent (M2). Constructive interference with other constituents may therefore modulate present estimates of SST tidal fluctuations. The present analysis may be adapted in order to quantify the amplitude of these modulations. It may also be adapted in order to estimate SST fluctuations by other types of fast oceanic motions such as near-inertial waves [33]. Near-inertial currents are for example at least as energetic as baroclinic tidal ones.

Can we hope to capture SST tidal fluctuations in satellite observations? Consecutive observations of SST may allow the identification of propagating SST fluctuations. This identification may be conditioned by the relative importance of SST tidal fluctuations compared to that induced by other geophysical processes (diurnal cycle, mesoscale, submesoscale motions) and noise. SST tidal fluctuations inherits their spatial structures from frontal features, i.e., of the order of kilometers, which is marginally larger than satellite resolutions. These small scale fluctuations will occur coherently over tidal currents spatial scales (Figure 1) nonetheless, and this may be leveraged in order to identify SST tidal fluctuations. The diurnal cycle of SST is expected to have large spatial scales and thus be clearly distinguishable from SST fluctuations induced by tides [34]. Mesoscale and submesoscale fluctuations

have comparable spatial structures on the other hand, but are slower and non-propagating which may be leveraged in order to distinguish their contributions to SST fluctuations. The small scale structure of tidal SST fluctuations indicates that pixel noise is the source of noise that may limit the observation of these fluctuations.

We have estimated the noise present in the granules used, assuming it is Gaussian [35]. Given this assumption, the standard deviation of the noise *σ* can be estimated using the *K-clipping method* [36]. This method exploits the dominance of noise at short wavelengths and can be explained as follows. A first guess of *σ* is obtained as the standard deviation of a high-pass frequency version of the initial field. Then those values with amplitude higher than *K* times *σ* are rejected, and a new estimation of *σ* is obtained from the standard deviation of the remaining values. This is performed iteratively until *σ* is obtained, then. In practice three iterations (*K* = 3) are enough [36]. The estimated noise standard deviation of the granules considered in the case studies presented in this work is shown in Table 3. It is in general comparable with or smaller than expected SST tidal fluctuations.

Despite the signature of IW on SST exhibit fine-scale spatial structures and thus IR SST observations are more suitable to quantify tidal fluctuation in SST, we explored whether microwave SST observations could be used to extract low-mode stationary internal tides. Figure A2 shows an example of microwave SST captured by AMSR2 for the same case study shown in Section 4.2. Only stronger gradients of SST are captured and its amplitude is halved compared to the IR SST field shown in Figure 4. Similar results have been already reported by [37] in other regions such as the Gulf Stream or California. Despite these weaker values, the larger amount of available microwave data may be beneficial for the extraction of temporally coherent tidal signals and this should be subject for future work.

The following steps are therefore to search for consecutive snapshots of SST in areas of interest. Infrared geostationary satellites may be useful for this purpose (Himawari, SEVIRI). The global maps in the present paper highlights several regions (on top of the two selected here) where tidal variability is important and cloud density is favorable: Patagonian shelf, west Florida shelf, Moroccan shelf, Persian Gulf, East Indian shelf, Strait of Gibraltar.


**Table 3.** Noise standard deviation of the SST images considered.

**Author Contributions:** The idea of this study was initially designed by Aurélien Ponte. C.G.-H. did most of the work during her PostDoctoral contract at IFREMER. E.A. developed the software to select L2 SST granules from the entired data catalog. All the authors contributed to formal analysis. The paper was written by C.G.-H. and A.P. E.A. contributed to the writing-review and editing of the paper.

**Funding:** Aurélien Ponte benefited from funding via the ANR project EQUINOx (ANR-17-CE01-0006-01) and CNES TOSCA project "New dynamical tools for submesoscale characterization in SWOT data". Cristina González-Haro benefited from funding by CNES.

**Acknowledgments:** The authors would like to acknowledge Peter Cornillon (University of Rhode Island) and Stéphane Saux Picart (Météo-France) for providing the atlas of maximum gradient of SST, as well as Ed Zaron for providing the HRET internal tide database. The data from the EUMETSAT Satellite Application Facility on Ocean & Sea Ice used in this study are accessible through the SAF's homepage http://www.osi-saf.org. The MODIS L2P sea surface temperature data are sponsored by NASA. The data from the Naval Oceanographic Office are made available under Multi-sensor Improved Sea Surface Temperature (MISST) project sponsorship by the Office of Naval Research (ONR). The authors want to acknowledge the anonymous reviewers for their valuable and helpful comments.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
