From the gridded climatology, we build the distribution at each latitude of the three main characteristics of the gridded UOP – intensity, depth and thickness. This captures the main meridional variations of the UOP characteristics, which are shown for the winter and summer seasons in Figure 4 . Winter and summer maps are also shown in Figure 5 to display the spatial variations of the three UOP characteristics.

As seen earlier the UOP thickness has limited seasonal and spatial variability. We thus focus here on describing into more detail the seasonal cycle of the UOP intensity and depth. Based on the monthly maps of the UOP climatology, we found monthly maximum and minimum values for the UOP intensity and depth to evaluate the amplitude of the UOP seasonal cycle, shown in Figure 6 . Along with the amplitude, we also show the corresponding seasons when the UOP characteristics are minimum and maximum in Figure 7 .

At midlatitudes, some oceanic regions have a seasonal ratio between the maximum and minimum stratifications larger than 10 ( Figure 6A ): the Kuroshio Extension, the Bering Sea, the Sea of Japan, the North Atlantic basin north of 30°N, the Mediterranean Sea, and some sections of the ACC. While seasonality is important over the full width of the North Atlantic basin, most of the seasonality is concentrated on the western side of the North Pacific basin. The seasonal ratio of the UOP intensity is larger than 50 in the Labrador sea and in the Nordic seas. These regions have thus the strongest seasonality in the global ocean. Within the subtropical gyres, the amplitude of the UOP depth exceeds 100 m. It becomes greater than 200 m in some regions of the ACC and around the North Atlantic Current ( Figure 6B ). The largest depth amplitude occurs in the region of the Irminger Sea and around the Rockall plateau. Outside the intertropical band, the minimum UOP stratification occurs in winter, except in the northern and eastern part of the North Pacific, and in some places of the ACC, where it occurs later in spring ( Figure 7A ). In this part of the global ocean, the winter season also corresponds to the maximum depth of the UOP ( Figure 7D ). The maximum UOP stratification occurs generally in summer outside the intertropical band with a few exceptions in the Atlantic part of the ACC ( Figure 7B ). The summer season also corresponds to the shallowest UOPs, with a few regions where it occurs earlier in spring (i.e., Agulhas leakage, East Australian Current region, the Indian midlatitudes, and the North Pacific Subtropical Countercurrent region).

At midlatitudes of the northern hemisphere, the timing of the UOP intensity is consistent with the minimum and the maximum of sea surface temperature and the stratification index used by Somavilla et al. (2017), that occurs respectively at the end of winter and at the end of summer. The timing of the maximum MLD estimated by Somavilla et al. (2017) and by Johnson and Lyman (2022) also agrees with the maximum UOP depth occurring at the end of winter. However, while the minimum of the MLD estimate used by Somavilla et al. (2017) also occurs at the end of winter, we find that the minimum UOP depth occurs in summer, consistently with Johnson and Lyman (2022) who found a similar timing for the minimum of their MLD estimate. This difference with Somavilla et al. (2017) is possibly due to their method used for estimating the MLD (González-Pola et al., 2007).

In the intertropical band (20°S– 20°N), the seasonality is different from the other latitudes. The seasonal ratio of the maximum and the minimum UOP stratification is small, with most of the regions having a ratio smaller than 2 ( Figure 6A ). The seasonal amplitude of the UOP depth is also limited and less than 100 m, with most of the regions having a seasonal amplitude less than 50 m ( Figure 6B ). The smallest amplitude is found close the western boundaries of the Pacific and Atlantic equatorial ocean, with values less than 20 m. The seasons of the maximum and minimum UOP characteristics is more complex in the equatorial region, though some patterns seems to emerge ( Figure 7 ). A minimum stratification may be noticed close to the equator in summer and in autumn, particularly in the Pacific ocean, while it mostly occurs in spring closer to the tropics ( Figure 7A ). The reverse behavior is similar for the maximum intensity, occurring in winter and spring close to the equator, and in autumn closer to the tropics ( Figure 7B ). Between 0° and 5°N the minimum UOP depth tends to occur in winter and spring in the Pacific and Atlantic basins ( Figure 7C ). Between the equator and the tropics, the minimum depth rather occurs in autumn and sometimes in summer. As for the UOP intensity, the seasonality is reversed for the maximum UOP depth, occurring mainly in autumn and summer between 0° and 5°N and in spring in the rest of the 10°S–10°N band. Note that the tropical Indian ocean is apart and has an even more complex UOP timing than the other basins, linked to the specific regime of the reversing monsoon in this area (Schott et al., 2009) and to the seasonality of the Great Whirl (Beal and Donohue, 2013). Thus, the complex UOP seasonality in the intertropical band is to be investigated in the future, but should be partly explained by precipitation regimes occurring in this region.

We now focus on intermediate seasons using the upper ocean stratification index UOSI, which corresponds to the stratification index SI(z) of equation 3 estimated at the UOP lower limit ( h U O P − ). As shown in section 2, the variations of this quantity may be linked to the intensity of buoyancy forcing (e.g., Herrmann et al., 2008). Thus, the stratification index UOSI may be useful to capture restratification periods due to the ease of adverse surface buoyancy fluxes or to the relative importance of lateral fluxes, including those associated with submesoscale motions (e.g. Johnson et al., 2016; du Plessis et al., 2017).

The largest UOSI occurs around the equator, between 10°S and 10°N, where the UOP is the most difficult to erode due to large stratification values ( Figure 8A ). In these low-latitude regions, the UOSI seasonality is very limited and values are larger than 1 m ².s ^–2 on the meridional distribution ( Figure 8A ). These large UOSI values concern most areas near the equator as shown by autumn and spring maps ( Figures 8C, D ), and suggest that exchanges between the upper ocean and the interior ocean are very limited all time of the year in these regions.

The UOSI decreases with latitude, with a larger drop in spring between 10° and 20° ( Figure 8A ). The minimum in UOSI occurs in spring at latitudes higher than 15–20°, consistent with a newly stratified layer forming near the ocean surface during this season, that can be easily eroded by external buoyancy loss ( Figure 8B ). Latitudes higher than 40° in the Southern Ocean and in the North Pacific tend to have the smallest UOSI in spring, with values smaller than 0.1 m ².s ^–2 ( Figure 8D ). In spring, the eastern and northern sides of the North Pacific remains with UOSI values comparable to those in autumn, while the rest of the basin has reduced values ( Figures 8C, D ). This corresponds to a bump at 50°N on the meridional distribution ( Figure 8A ) and is linked to a minimum UOSI reached latter in summer in these regions ( Figure 8B ).

Since the UOSI integrates information on the depth, intensity and thickness of the UOP, we focus on the variation of this former quantity. The variability described here includes both sub-monthly and interannual variability as well as spatial variability with scales smaller than the bin size (i.e., 2°). We evaluate the relative variability of UOP characteristics for each month and each spatial bin using the coefficient of variation CV, that is simply the ratio of the standard deviation and the mean. Results for the maximum CV and the corresponding season are shown in Figure 9 . The variability characterised here includes both sub-monthly variability and interannual variability. Coefficient of variations are also given for the UOP characteristics –intensity, depth, and thickness – in Supplementary Materials , to complement the UOSI coefficient of variation.

Regions of large relative variability for the UOSI are similar to region with large UOP seasonal amplitude ( Figure 6A ), with the largest variability occurring north of 40°N in the North Atlantic basin and along the Indian and Pacific part of the ACC ( Figure 9 ). Large variability is also noticed to a lesser extent in the Kuroshio Extension, in the regions of the Pacific subtropical mode waters offshore of California and offshore of Chile, in the Agulhas leakage region, and in the Coral Sea. In all these regions, the coefficient of variation CV exceeds 150%. The maximum relative variability is generally reached in spring for latitudes higher than 10–15°, with a few regions having the maximum occurring in winter ( Figure 9B ). In the intertropical band, between 15°S and 15°N, the coefficient of variation is weaker especially in the eastern side of the basins with values smaller than 50% ( Figure 9A ). This minimum in variability generally occurs in autumn and summer ( Figure 9B ). Note that the regions with large CV in UOSI as described above tend to correspond with spring MLD distributions being skewed towards deeper values and having stronger tails than a normal distribution (see Figures 8, 9 in Johnson and Lyman, 2022).

The climatological map of the permanent ocean pycnocline (POP) is shown in Figure 10 , along with the location of the aforementioned regions of study and the corresponding stratification profiles N ²(z) in February and in August. Consistent with results from the previous section, the median N ² profiles confirm that the upper ocean stratification varies seasonally outside the tropics with substantial variations associated with the UOP (blue and orange plain lines in stratification panels of Figure 10 ). The summer stratification peak associated with the UOP is large and sharp, while the winter stratification peak is much less marked on average. The upper ocean stratification is also much less variable near the equator, as is the UOP (e.g., PWP profiles). In the PWP region, a first stratification variation occurs at around 50 m, between the surface and the UOP, and is probably linked to salinity barrier layers (e.g., Lukas and Lindstrom, 1991; Vialard and Delecluse, 1998). This density variation is related to a subsurface halocline that is distinct and shallower than the thermocline. While this layer imprints on certain MLD variables (de Boyer Montégut et al., 2007; Mignot et al., 2007), it is not captured by our UOP method, either because of the absence of a clear stratification peak or because its amplitude is much weaker than the stratification peak associated with the permanent pycnocline.

In most of the regions plotted, the median winter UOP is located where the winter and summer stratification profiles start to differ (KE, NPESTMW, GS, RP, SPESTMW, AL). In the two Pacific regions where subtropical mode waters are formed (i.e., NPESTMW and SPESTMW), the mode water signatures are clear with a local minimum in stratification located between the summer UOP and POP. In winter, this minimum disappears suggesting that the mode water layer may be influenced by air-sea exchanges.

The POP values taken from the climatology of Feucher et al. (2019), shown with black dotted lines in Figure 10 , seem consistent with our dataset since the POP is located on a local maximum of the median stratification profile (i.e., KE, NPESTMW, GS, RP, SPESTMW). In these regions, the winter UOP is always shallower than the POP, suggesting that the UOP does not always merge with the POP in winter. In all the regions of study, the UOP is located below the MLD (blue and orange dash lines), except in winter in the Labrador Sea (LS). The depth separating the MLD and the UOP is usually small in summer, but it may slightly increase in winter (e.g., KE, NPESTMW, AL). In the Labrador Sea, the median winter MLD (∼250 m) is found to be much deeper than the median winter UOP depth (∼150 m). This inverse behavior could be due to a sensitivity of our method to very small stratification peaks in a region with very small stratification values over the 0–2000 m depth range. We will discuss later the relative position of the MLD and the upper limit of the UOP, along with the validity of our peak detection method.

To complement the analysis made with the stratification profiles that showed only two months of the year of the median UOP depth, we show the full monthly seasonal cycle of the median UOP in the intensity-depth space, plotted on a log-log scale for the different regions of study ( Figure 11 ). In some regions, the seasonal cycle in the intensity-depth space looks regular and describes an ellipsoid trajectory ( Figures 11A, C, D, I ). In other regions, depth changes during restratification times in spring occurs more abruptly than stratification changes, yielding instead a D-shape ( Figures 11B, E, F, H ). The seasonal cycle is even more distorted around the Rockall plateau (RP) where the UOP deepening also occurs more abruptly than destratification during late autumn and early winter ( Figure 11B ). As shown earlier for the global climatology, the seasonal cycle in the Pacific Warm Pool (PWP) is very limited ( Figure 11F ).

These results suggest that the seasonal evolution of the UOP does not occur at the same pace everywhere in the global ocean. This is consistent with the variety of MLD seasonal cycles showed by Johnson and Lyman (2022), with sometimes abrupt or more gradual rise of the MLD (see their Figure 2 ). Note that the monthly median UOPs are generally concentrated in distinct areas of the intensity-depth space for winter and summer, while months of intermediate seasons connect these summer and winter areas.

The regional and temporal variability of February and August UOPs are analyzed with intensity-depth paired distribution shown in Figure 11 . In general, the amplitude ratio (i.e., the maximum over the minimum) of the UOP variability is larger in winter than in summer. The winter UOP has only moderate variability in the Pacific mode water regions (NPESTMW, SPESTMW, Figures 11B, H ), of the same order as in summer, and less than in the other regions in winter at mid and high latitudes (e.g., KE, GS, LS, RP, IACC, AL). In the two major western boundary currents of the northern hemisphere, the depth variations are important in winter with the UOP depth being as shallow as 20 m and possibly reaching 700 m and 1000 m in the Kuroshio Extension (KE) and in the Gulf Stream (GS), respectively ( Figure 11A, C ). The stratification however remains weak to moderate in winter (10^–5 s ^–2 to 3.10^–4 s ^–2). A similar picture is found in the regions of the Indian ACC (IACC) and of the Agulhas Leakage (AL) for the winter month ( Figure 11F, I ). Around the Rockall plateau the winter UOP intensity is concentrated around weak values of stratification without much variability O(10^–5 s ^–2) ( Figure 11E ). However, the depth variability is much more pronounced in winter spanning a range from 40 m to 2000 m. In winter, the Labrador Sea (LS) has the widest distribution both in stratification and depth, as well as the deepest and least stratified UOPs ( Figure 11D ). The distribution spans a range of 20 m to 2000 m in depth and a range of 5.10⁻⁶ s ⁻² to 5.10⁻⁴ s ⁻² in intensity, consistent with deep MLDs observed in this region (e.g. Johnson and Lyman, 2022).

Interestingly, it is possible to find moderately deep UOPs in summer at mid and high latitudes that may reach 80 m to 100 m depth (e.g., NPESTMW, RP, SPESTMW, AL), and even more in the Indian ACC ( Figure 11F ). This result is consistent with a recent statistical monthly climatology of the global ocean surface mixed layer (Johnson and Lyman, 2022), that shows distribution tails of the MLD reaching up to 100 m in late summer. The UOP stratification generally remains larger than 10^–4 s ^–2 in summer, except in regions involving the ACC (IACC and AL). This is consistent with the summer climatology of UOP intensity ( Figure 5B ), showing moderately stratified values Ο(10^–5 s ^–2) along the ACC. Finally, the variability is similar between August and February in the Pacific Warm Pool (PWP), of the same order as summer variability in the other regions, and consistent with a weak seasonal cycle of the median in this region. Note that both winter and summer UOP distributions may partially overlap in certain regions (NPESTMW, GS, LS, IACC, AL). The depth variations of the UOP described here agree with the statistical monthly climatology of the MLD produced by Johnson and Lyman (2022), who showed much wider MLD distributions in winter than in summer (see their Figure 5 in particular).

The location of the POP and its thickness are represented in the intensity-depth space in Figure 10 . In all the regions studied where the POP is available, the winter UOP paired distribution overlaps with the POP ( Figures 11A–C, E, G, H ). This gives confidence in the consistency between our method, that finds the UOP (corresponding sometimes to the POP during winter months), and the method developed by Feucher et al. (2019), that finds the POP. In some regions (i.e., GS, SPESTMW, AL), the POP is located on the distribution tail, which may suggest that the UOP does not reach the POP on average but merging between the UOP and the POP could rather happen intermittently (in space and time). In the other regions, and especially around the Rockall Plateau, the POP is closer to the center of the UOP distribution, suggesting that the UOP is more likely to merge with the POP.

The seasonal cycle of upper ocean stratification statistics is investigated in each region using the monthly distributions of the UOSI, illustrated with boxplots in Figure 12 . Similar seasonal cycles for the UOP depth and intensity are also given in Supplementary Materials . The eddy active regions studied at midlatitudes (i.e., KE, GS, IACC, AL) see their median UOSI gradually decreasing throughout autumn and winter to reach a minimum in April in the northern hemisphere regions ( Figures 12A, C ) and in October/November in the southern hemisphere regions ( Figures 12F, I ). Note that this gradual decrease is halted in the Agulhas Leakage (AL) region between September and October with a notable drop in UOSI. According to equation 4, a negative variation in UOSI in winter means that the upper ocean layer experiences adverse buoyancy fluxes during this season, i.e. large winds and cooling. The Labrador Sea (LS) shows a similar seasonal pattern ( Figure 12D ), with the specificity of having amongst the smallest values of UOSI in winter. This small UOSI means that the upper ocean stratification may be easily eroded during this time of the year in this region. The gradual decrease in UOSI is consistent with the ellipsoid trajectory of the seasonal cycle in the intensity-depth space for the regions KE, GS, LS and AL ( Figures 11A, C, D, I ).

In the region of the Pacific mode waters (NPESTMW, SPESTMW) and around the Rockall plateau (RP), the upper ocean layer gains buoyancy (i.e., positive fluxes) throughout winter with an increase of the UOSI after a first decrease in autumn. In this case, the UOSI increases because the effect of the deepening of the UOP during wintertime counteracts the effect of the weakening in UOP stratification (see the depth and intensity boxplots in Supplementary Materials ). A substantial jump in UOSI occurs in these regions in early spring, depicting the rapid formation of a weakly stratified layer near the surface, with the possibility of burying a fossil layer just below. This is associated with a jump to shallower UOP depths during this same month and the D-shape trajectory of the seasonal cycle in the intensity-depth space ( Figures 11B, E, H , see also the UOP depth boxplots in Supplementary Materials ).

All the regions show a gradual increase in UOSI throughout spring and summer after the minimum value has been reached in spring, meaning that the rise and the intensification of the UOP occur smoothly after restratification has taken place. The timing of the minimum UOSI is also consistent with the maps shown in Figure 8D and with the stratification index of Somavilla et al. (2017) studied in a few midlatitude regions.

The UOSI variability generally intensifies throughout winter and reaches its maximum in early spring ( Figure 12 ), consistently with the map of the timing of maximum relative variability ( Figure 8D ). In some regions the UOSI variability during spring restratification is much larger than the variability levels noticed for the rest of the year (SPESTM, NPESTMW, AL). The upper ocean restratification is generally followed by a reduction in UOSI variability as the newly formed layer near the surface stabilizes in time and space. In the Pacific Warm Pool (PWP), the seasonality of the median UOSI is small but the variability levels remain substantial all year long, with amplitude ratio comprised between those noticed for summer and those noticed for winter at higher latitudes. In this region, no restratification phase may be noticed as the UOSI remains large.

Overall, this regional study shows that the seasonal cycle of the UOP in the intensity-depth space and the process of restratification are not homogeneous over the global ocean with different behavior. In particular, restratification occurs when a minimum in UOSI is reached, generally associated with a large variability whose amplitude depends on the region. Restratification may sometimes occurs gradually or more abruptly depending on the region as shown by the shape of the seasonal cycle in the intensity-depth space ( Figure 11 ) and by the seasonal distribution of the UOSI ( Figure 8 ).

In order to evaluate the capacity of our UOP definition to be consistent with the position of the mixed layer, we compared the location of the UOP upper boundary h U O P + relative to the minimum of classical MLD estimates h M L D M I N , as defined in section 2.

On the zonal distribution, h U O P + and h M L D M I N are very close outside the intertropical band (15°S–15°N), with very little spread on the distribution for the summer season. Near the equator, the difference is however significant with the full distribution showing that h U O P + is deeper than h M L D M I N (around 30 m deeper for the median). The largest differences noticed near the equator on the meridional distribution may reach 90 m and are explained by large differences in the Pacific Warm Pool region seen both on summer and winter climatological maps ( Figures 13B, C ). As already discussed in section 5, this is explained by the salinity barrier layers having an imprint on the stratification that is too small to be captured by our UOP method.

In winter, the high latitudes have larger differences between h U O P + and h M L D M I N with a large dispersion at around 55–60°N. This is mainly due to the UOP upper boundary being shallower than the minimum of the MLD estimates in the Labrador Sea and in the Nordic Seas (<25 m). Although the absolute difference is substantial in these regions, the relative difference represents less than 20% (see Supplementary Materials ) so that one may suggest that the correspondence between the UOP and the minimum of the MLD estimates is actually acceptable. Much deeper UOPs than MLD estimates (>50 m) occur around the Rockall Plateau and along the ACC south of Tasmania and New Zealand. This is due to the presence of vertically compensated layers in these regions (de Boyer Montégut et al., 2004): the temperature threshold MLD estimate h M L D Δ Θ captures a shallower mixed layer as the first thermocline is compensated by salinity effects and does not imprint on the density profile. The resulting pycnocline is indeed deeper than the thermocline is these regions. A few regions of the subtropics, including the Eastern Pacific mode water regions also show an UOP upper limit deeper than 25 m compared to the minimum of the MLD estimates. In these regions, the presence of salinity barrier layers not captured by the UOP method is also possible (e.g., de Boyer Montégut et al., 2007).

We remind here that the peak detection threshold is based on the vertical standard deviation of the stratification profile. Thus, the detection of peaks close to the surface may fail when its change in density is much smaller relative to the change in density of the main pycnocline. Missing such a peak may happen in the Pacific Warm Pool when the change in density due to the salinity barrier layer is much smaller than the main equatorial pycnocline, as illustrated by the stratification profile in the PWP region of Figure 10 .

On the opposite, the detection of very small stratification peaks may happen due to the same definition of the peak threshold: when the profile is very weakly stratified over the whole 0–2000 m depth range, the stratification variance is small and leads to the detection of weak stratification peaks. In such cases, the UOP upper boundary may be located above the MLD estimates as it happens on average in the Labrador sea and in the Nordic seas in winter ( Figure 13B , see also the stratification profile in the region LS of Figure 10 ). This method drawback could be overcome by trying to impose a lower limit to the threshold when the stratification variance is small, but it remains to be tested in the future.

One motivation for this study was the way upper ocean stratification trends have been evaluated in climate studies (e.g., Yamaguchi and Suga, 2019; Sallée et al., 2021). Here, we aim to investigate the capacity of two quantities that have been used to capture the relevant upper ocean stratification peak, : 1) the averaged stratification in a 15 m layer below the MLD, 2) the density difference between 0 and 200 m. Using our UOP climatology, we evaluated first the percentage of profiles that corresponds to a UOP peak located in the 15-m layer thickness below a MLD defined with a density threshold of 0.03 kg.m ^–3 ( h M L D Δ σ ) . Thus, the method that consists in taking the buoyancy frequency averaged in a 15 m layer below the MLD (e.g. Sallée et al., 2021) only captured the UOP peak at best 57.4% of the profiles in June and at worst 44.9% of the profiles in September ( Table 1 ). Secondly, we evaluated the number of profiles for which the UOP depth is shallower than 200 m, so that the UOP is included in the density difference between 0 and 200 m. We found that this density difference included more regularly the UOP peak for at best 99% of the profiles in May and at worst 91.9% of the profiles in September ( Table 1 ). The density difference method generally fails to capture the UOP peak in winter along the ACC and at high latitudes of the North Atlantic basin ( Figure 5C ).

Although the density difference between 0 and 200 m succeeds in capturing the density jump associated with the UOP in most of the oceanic regions, Somavilla et al. (2017) argued that it does not provide any information about the tendency of the water column to be mixed, linked to the shape of the upper ocean density profile. On its side, the upper ocean stratification index (UOSI) is able to capture the characteristics of the density profiles as it integrates density variations down to the UOP bottom. The UOSI is, however, interpreted as the amount of buoyancy needed to destratify the upper ocean rather than the tendency of the water column to be mixed.

Our current UOP climatology does not make any distinction with the permanent ocean pycnocline (POP) so that we are not able to quantify accurately the occurrences when the UOP merges with the POP. However, we compared the POP climatology with the UOP distribution in some regions of the global ocean and we found a clear overlap in winter between the UOP depth and the POP location. To go a bit further, we computed the percentage of winter profiles in each bins when the UOP depth falls into the POP layer as estimated by Feucher et al. (2019). Results are shown in Figure 14 . In the northern hemisphere, merging between the UOP and the POP might happen in the Kuroshio Extension, in the NPESTMW region, and around the Rockall Plateau. The NPESTMW region has the highest percentage of profiles meeting the POP layer. In the southern hemisphere, the SPESTMW region, the Agulhas Leakage and the region offshore of Brazil fed by the south equatorial current show large percentage of profiles with the UOP likely to merge with the POP layer.

This comparison complements the stratification configurations illustrated in section 3 from the gridded T/S climatology. It also provides additional insights about the relative positions of the upper and the permanent pycnoclines and how deep the ocean surface may communicate with the ocean interior. However, the exact distance between the UOP and the POP remains to be quantified for each profile. Finding the POP could be done based on its smaller variability over time and space and on signatures complementary to the stratification peaks, such as the temperature or the salinity at the bottom of the peak that would reflect the interior ocean. This work is left for the future.

While the full dynamics of the OSBL is complex and involve several oceanic processes (e.g., Ferrari and Boccaletti, 2004; Johnston and Rudnick, 2009), one result of our study is that the UOP thickness is relatively constant over the global ocean. Is there a general physical process that might set this thickness? The existing literature suggests that two main regimes may drive vertical mixing and entrainment in forced stratified shear flow (Caulfield, 2021; Smith et al., 2021), such as those occurring at the base of the mixed layer. A weak stratification may favor a shear-driven overturning regime involving Kelvin-Helmholtz-like instabilities that broadens the stratification interface, while a strong stratification may favor a scouring regime of Holmboe-like instabilities that sharpens the stratification interface. While a laboratory experiment showed that the transition between Kelvin-Helmholtz and Holmboe instabilities existed in the physical world (Hogg and Ivey, 2003), recent direct numerical simulations explored the transition between these two kinds of instabilities and highlighted an hybrid regime mixing, characteristics of both instabilities (Smith et al., 2021).

Dohan and Davis (2011) noticed two different behaviors of the OSBL following two consecutive storms. The first storm was associated with a deepening of the MLD and a sharpening in the UOP thickness (from 35 m to 25 m), with the stratification effects being more important than the shear effects (i.e., a gradient Richardson number larger than unity). The second storm was associated with little change in the MLD but a broadening of the UOP (from 25 m to 45 m) with a dominance of shear effects over stratification (i.e., a gradient Richardson number larger than 0.6). The OSBL turbulence regime during the first storm seems dominated by external mixing with potentially scouring effects at the interface, while the turbulence regime during the second storms seems to be internally driven by shear instabilities. Using a Lagrangian float to study instabilities in the region, Kaminski et al. (2021) showed that intermittent Kelvin-Helmholtz instabilities indeed drives intermittent vertical mixing with substantial effects of both stratification and shear leading to a UOP thickness of 10-20 m.

The change in UOP thickness due to different turbulent regimes is potentially small compared to typical vertical scales due to other phenomena occurring in the ocean (e.g., internal waves, submesoscale features). This hampers to draw any conclusions on the dynamical regimes from the unique knowledge of the UOP thickness. Using additional measurements of shear and turbulent dissipation would be a solution, but they are only available in a few spots of the global ocean and a global coverage of these quantities seems out of reach. Some regions where the UOP thickness departs significantly from the global UOP thickness, such as areas around the Rockall Plateau, would however benefit to have these additional measurements. In this region, we found that the stratification was weak in winter (O(10^–5 s ^–2), Figure 11E ) and that the UOP thickness was larger than average (∼50 m, Figure 5E ). Thus, it would plausible that an overturning regime would be favored due to a small stratification rather than a scouring regime, which would be consistent with a broadening of the stratification peak.