**3. Method**

In order to estimate SST fluctuations associated with tidal currents, we assume that tidal motions follow a dynamics that is linear about other motions and adiabatic. Among both assumptions, that of linearity may be occasionally broken for short solitary-type internal waves of tidal origins but is expected valid for open-ocean low-mode internal tides and barotropic tides. Under the aforementioned assumptions, tidal currents transport SST gradients according to:

$$
\partial\_t T\_w = -\mu\_w \partial\_x T\_s - \upsilon\_w \partial\_y T\_{s\prime} \tag{5}
$$

where *Tw* is the variation of SST due to tidal currents (*w* stands for wave), *uw* and *vw* are the zonal and meridional components of tidal currents, respectively, and *Ts* stands for the SST. Assuming that:

$$T\_w = \Re(T\_\varepsilon e^{-i\omega t}), \ u\_w = \Re(u\_\varepsilon e^{-i\omega t}), \ v\_w = \Re(v\_\varepsilon e^{-i\omega t}),\tag{6}$$

where *Tc* = *Tr* + *iTi*, similarly for *uc* and *vc*, and *ω* is the tidal frequency (for M2 constituent *ω* = 1.405 × <sup>10</sup>−<sup>4</sup> rad/s), the amplitude of tidal fluctuations of SST can be estimated as:

$$|T\_{\mathfrak{c}}| = \left| \frac{u\_{\mathfrak{c}} \partial\_{\mathfrak{x}} T\_{\mathfrak{s}} + v\_{\mathfrak{c}} \partial\_{\mathfrak{y}} T\_{\mathfrak{s}}}{i\omega} \right| \tag{7}$$

The quantification of the SST tidal fluctuations is splitted in three steps:

