**1. Introduction**

Internal waves (IW) have recently been shown to significantly contribute to sea level variability at scales smaller than about 100 km [1–3]. The contamination of IW at theses scales limits our ability to infer ocean currents from altimetric data because IW currents are not related to sea level via geostrophy unlike slower/mesoscale balanced structures [4]. Some IW are of tidal origin and stationary with respect to astronomical forcings, such that the signatures of these waves on altimetric data can be predicted harmonically and eventually removed [5]. Unfortunately most IW are either


In both cases, we have no means today to predict these waves.

A direction of research that has been poorly explored yet deals with the signature of IW on satellite data of non-altimetric nature (e.g., sea surface temperature, color) and potential synergies in order to disentangle IW and balanced signatures in altimetric data. We recently proposed in an idealized context a tentative method in order to carry such synergies [8]. While it is premature to apply this method with real data, it may be time to start collecting remote sensing data that: (1) will allow us to verify critical assumptions for such methods (e.g., smallness of IW signature on SST image) and (2) will ultimately be suitable in order to test such methods. The present work is relevant to the former task. We more precisely focus on the quantification of SST fluctuations induced by stationary baroclinic tides because atlases of their distributions are now available [9]. We will also quantify SST fluctuations induced by barotropic tides because the same methodology may be employed for that purpose.

Sea Surface Temperature (SST) is a challenging parameter to define precisely as the upper ocean (within the first 10 m) has complicated vertical variability that is linked to ocean turbulence and air-sea heat fluxes [10]. Methods for determining SST from satellite remote sensing include thermal infrared (IR) and passive microwave radiometry. Both methods have strengths and weaknesses. Thermal IR SST measurements are derived from radiometric observations at wavelengths of ∼3.7 μm and/or near 10 μm. They provide high spatial resolution SST observations (∼1 to 10 km) and good accuracy (0.1–0.8 K) [11,12], however they are affected by cloud coverage and provide observations only for cloud-free pixels. On the contrary, microwave observations (4–10 GHz) provide a better spatial coverage since they are not affected by cloud coverage but their spatial resolution (∼25 to 50 km) is coarser than IR observations ([13] and references therein). In addition, SST measured from space are representative of a depth that is related to the frequency of the satellite instrument. For example, IR instruments measure a depth of about 20 μm, while microwave radiometers measure a depth of a few millimeters [14].

Internal wave modulations of SST from IR aerial observations have been reported at kilometric scales in low-wind conditions [15–19]. Two mechanisms have been considered in order to explain these modulations: fluctuations of the cool-skin temperature (The ocean surface is generally 0.1–0.6 ◦C cooler than the temperature just below the surface. And this "skin", or ultra-thin region, is less than a 1mm thick. For further details see http://ghrsst-pp.metoffice.com/pages/documents/DocumentFiles/ GDS-v1.0-rev1.5.pdf [last access 8 August 2019]) induced by the internal wave straining field and modulations of the upper diurnal surface layer by vertical displacements of the seasonal thermocline. Internal waves imprint their spatial structure on SST in the aforementioned papers. The present work focuses instead on quantifying of Eulerian, i.e., fixed point, modulations of a pre-existing SST distribution induced by tidal currents and the spatial structure of these modulations is thus not expected to reflect the structure of tidal motions.

This study is based on SST satellite observations, tidal current atlases and an atlas of SST gradients which are described in Section 2. The method to quantify internal wave signature on IR SST observations is explained in Section 3 and results are shown in Section 4. Finally, Section 5 discusses to which extent we may capture SST fluctuations of tidal origin in satellite observations and the main limitations for observing these fluctuations (i.e., pixel noise). All the acronyms used in the manuscript are detailed in the Abbreviation table at the end of the manuscript.

#### **2. Data**

#### *2.1. Tidal Current Atlases*

Barotropic tidal currents are extracted from FES2014 which is the current version of the FES (Finite Element Solution) tidal database [20]. Tidal solutions are obtained from an assimilation of tide gauges and altimetric data and delivered on a 1/16◦ grid. Tidal currents for the M2 constituents are typically of the order to 2–3 cm/s in the open ocean and exhibit a spatial structure characterized by large spatial scales modulated by topography (Figure 1b).

Baroclinic tidal currents are derived from the High Resolution Empirical Tide (HRET) Models [http://web.cecs.pdx.edu/ zaron/pub/HRET.html]. This database has been created to provide baroclinic tide corrections for sea level measurements collected by the upcoming SWOT mission [21]. It was created from an harmonic analysis of sea level anomalies collected by exact repeat altimetric missions (1992–2015). Maps of tidal sea level are provided on a 0.05-degree near-global grid for the 6

most important constituents (M2, S2, K1, O1, N2, and P1 tides). Tidal currents are derived from sea level maps assuming the following momentum equations [9]:

$$-i\omega u - fv = -g\partial\_x \eta - u/\tau,\tag{1}$$

$$-i\omega v + fu = -g\partial\_y \eta - v/\tau,\tag{2}$$

where *u*, *v* are zonal and meridional currents, *η* represents sea level, *g* is gravity, *τ* = 20 days is damping time scale, and *ω* is the tidal frequency. Solutions to (1)–(2) are given by:

$$
\mu = \frac{-i\omega\_{\pi}g\partial\_{\pi}\eta + fg\partial\_{\eta}\eta}{\omega\_{\pi}^2 - f^2},
\tag{3}
$$

$$v = \frac{-f\mathcal{g}\partial\_{\mathcal{X}}\eta - i\omega\_{\mathbb{T}}\mathcal{g}\partial\_{\mathcal{Y}}\eta}{\omega\_{\mathbb{T}}^2 - f^2},\tag{4}$$

where *ωτ* = *ω* + *i*/*τ*. M2 baroclinic currents exhibit a spatial structure characterized by interfering beams originating from well-defined generation spots (e.g., islands archipelagos, sills) and typical amplitudes around 10 cm/s in the open-ocean (Figure 1a)

**Figure 1.** (**a**) HRET M2 baroclinic current amplitude for regions with bathymetry(h) deeper than 1000 m (**b**) FES2014 M2 barotropic current amplitude. The colormap is saturated at 10 cm/s on both figures. Two black boxes delimit the regions of the case study presented in Sections 4.1 and 4.2, respectively.

#### *2.2. Atlas of SST Gradients*

The climatology of the maximum SST gradient magnitude is courtesy of Peter Cornillon, Graduate School of Oceanography, University of Rhode Island (URI). This climatology is obtained from the entire (1985–1996) Pathfinder 9 km resolution SST dataset and is based on the automated procedure by [22] and [23–25] and developed by [26–28]. Further technical details may be found in this report from the Danish Meteorological Institute (DMI) [29]. The distribution of maximum SST gradient indicates SST spatial gradients exceeding 0.5 ◦C near western boundary currents, upwelling areas, the antarctic circumpolar current (Figure 2). The coarser resolution of the SST used for this climatology compared to the SST observations described in Section 2.3 may impact the expected amplitudes of tidally induced SST fluctuations using the climatology. The later may be underestimated compare to what would be estimated with higher resolution SST data to an extent that is difficult to anticipate.

**Figure 2.** Maximum of the annual climatology of the maximum spatial gradient of SST from University of Rhode Island (URI) Pathfinder 9 km frontal database.
