Similarities and Contrasts in Stationary Striations of Surface Tracers in Pacific Eastern Boundary Upwelling Systems

Eastern boundary upwelling systems feature strong zonal gradients of physical and biological ocean properties between cool, productive coastal oceans and warm, oligotrophic subtropical gyres. Zonal currents and jets (striations) are therefore likely to contribute to the transport of water properties between coastal and open oceanic regions. Multi-sensor satellite data are used to characterize the signatures of striations in sea surface temperature (SST), salinity (SSS), and chlorophyll-a (Chl-a) in subtropical eastern North/South Pacific (ENP/ESP) upwelling systems. In the ENP, tracers exhibit striated patterns extending up to ~2500 km offshore. Striations in SST and SSS are highly correlated with quasi-zonal jets, suggesting that these jets contribute to SST/SSS mesoscale patterns via zonal advection. Chl-a striations are collocated with sea surface height (SSH) bands, a possible result of mesoscale eddy trains trapping nutrients and forming striated signals. In the ESP, striations are only found in SST and coincide with SSH bands, consistently with quasi-zonal jets located outside major zonal tracer gradients. An interplay between large-scale SST/SSS advection by the quasi-zonal jets, mesoscale SST/SSS advection by the large-scale meridional flow and eddy advection may explain the persistent ENP hydrographic striations. These results underline the importance of quasi-zonal jets for surface tracer structuring at the mesoscale.


Introduction
Eastern boundary upwelling systems (EBUS) such as those found along the California and Chile coasts facing the eastern North and South Pacific subtropical gyres (Figure 1a) are unique regions known for their cool surface waters, extreme biological productivity and key influence on climate [1,2]. In sharp contrast, regions located further offshore are warmer and comparatively deprived from marine life. Oceanographic processes that exchange water between EBUS and neighboring oceanic regions are of particular interest because they may drive strong spatio-temporal variations in marine ecosystems and climate. Among such processes, mesoscale eddies are known to actively participate to cross-shelf transport of ocean properties [3,4].
In the Pacific subtropical EBUS, striations extend from the coast off California in the eastern North Pacific (ENP) but emerge farther offshore off Chile in the eastern South Pacific (ESP) (Figure 1b, see also Figures 2g, 3g), reflecting different generation mechanisms. California Current meanders anchored by coastline geometry provide vorticity sources, which generate Rossby waves/mesoscale eddies that propagate westward [16,24]. Similar processes are invoked in the ESP, except for vorticity sources driven by topographic steering of gyre flow over deep-ocean escarpments rather than by eastern boundary current instabilities [17].
Despite their weak amplitude (~1 cm/s), striations may advect the background temperature field [25], contribute to tracer mixing [23,26], ventilate oxygen minimum zones [27,28], transport floating debris [29], and modify surface winds [30], affecting marine ecosystems and climate. In particular, [26] showed from idealized modelling that striations may contribute much more to zonal mixing than eddies do when the background large-scale flow is predominantly zonal. The Lagrangian modelling study of [29] suggested the existence of an outflow from the ESP subtropical gyre dominated by striations, with its transport balancing 13-35% of convergence into the gyre. And [30]'s high-resolution coupled model study reported striated SST anomalies of ±0.05-0.1°C off Peru in the tropical ESP as well as their impacts on the wind stress curl pattern. Considered together, these studies suggest that striations have a significant impact on water mass balances. Such effects may be further amplified in regions with strong along-striation (primarily zonal) physical and biogeochemical tracer gradients such as the cool, highly productive subtropical EBUS.
A complete understanding of the physical processes leading to the impact of striations on water masses is however missing. Zonal advection of background sea surface temperature (SST) in regions of well-defined zonal gradients like the tropical central/eastern South Pacific has been invoked in [30]'s modelling study. Conversely, [5] reported subsurface temperature anomalies in phase with the sea surface height (SSH) signature of striations in the ENP and ESP EBUS from in situ and model data. This implies that the striated mesoscale temperature field is in phase quadrature with the geostrophic current, which discards advection as the primary driver. [25] found that zonally-elongated satellite SST fronts were frequently associated with time-mean and transient striations. However, they focused on transient fronts within background meridional gradients and did not detail the relationship between time-mean fronts and striations. [23] found staircase-like meridional profiles in tropical Pacific subsurface salinity and oxygen cruise data, with fronts/homogeneous regions inside eastward/westward jets, respectively. Such structure was hypothesized by [25] in the presence of meridional large-scale gradients, which characterize subsurface tropical Pacific salinity and oxygen [23], and anticipated from the theories of [22] and [31]. Whether these findings are relevant to the extra-tropics and different background properties (e.g. zonal gradients) remains unclear.
Multi-year satellite records are now available not only for such variables as SST or ocean color as a proxy for surface chlorophyll-a (Chl-a), but recently also for the less studied sea surface salinity (SSS), allowing to grasp a broader picture of striation impacts on surface water masses. Here, we present observational evidence from multisensor data of striation effects on the aforementioned surface tracers in the North and South Pacific subtropical EBUS. In addition to SST and for the first time, SSS and Chl-a reveal contrasted footprints of striations in these climatically and biologically important regions. The differences found among the patterns in different variables and regions are attributed to the differences among large-scale tracer distributions and the embedded striations. Detailed analysis of advection terms from surface tracer equations is used to assess the dynamics responsible for the existence and persistence of striated SST and SSS signals in the ENP.

Satellite Data
Whenever possible and unless stated otherwise, the data are considered over a common period from July 2 nd 2012 to December 31 st 2018 for the ENP (defined as 111.5°W-151.5°W, 22°N-47°N) and ESP (70°W-110°W, 25°S-50°S). The time span of the shorter SSS dataset is specified in Section 2.1.3.

SSH and Currents
Altimetry data are used to characterize striations in SSH and geostrophic currents (e.g. Figure 1b). We used the daily gridded (0.25°) SSALTO/DUACS DT2018 delayedtime level-4 merged two-satellite product distributed by the Copernicus Climate Change Service. Absolute dynamic topography (i.e. SSH) and zonal geostrophic velocity (U g ), available from 1993 onwards, were extracted for the study period.
Total surface currents including the Ekman flow are however required for the estimation of surface tracer advection (see Section 2.2). In particular, Ekman currents are expected to contribute significantly to large-scale surface flow and associated advection.
We used the daily gridded 0.25° GlobCurrent MULTIOBS_GLO_PHY_REP_015_004 level-4 product available from January 1 st 1993 to May 31 st 2020 and distributed by the Copernicus Marine Service [32]. It combines SSALTO/DUACS DT2018 altimetric geostrophic current and modeled Ekman surface current using wind stress from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis [33].
Because the GlobCurrent and SSALTO/DUACS data are fully consistent in terms of the geostrophic currents that should dominate mesoscale velocities, another product is needed to test the sensitivity of striation properties to the choice of dataset (see Section 2.2). For this purpose, near-surface currents derived from altimeter SSH and scatterometer surface winds and consistent with Lagrangian drifter trajectories were obtained from the Surface CUrrents from Diagnostic model (SCUD) data available from APDRC/IPRC [34]. Daily gridded (0.25°) zonal (U) and meridional (V) velocities are publicly available from February 14 th 2012 to December 31 st 2018.

SST
Following [25], remotely-sensed microwave data are used to extract the striated patterns in SST. We use 3-day average gridded (0.25°) Advanced Microwave Scanning Radiometer 2 (AMSR-2) [35] version 8 available from July 2 nd 2012 onwards. The UK Met Office Group for High Resolution Sea Surface Temperature (GHRSST) Operational Sea surface Temperature and sea Ice Analysis (OSTIA) 0.05° infrared data [36] exhibited mesoscale structures almost identical to AMSR-2 except in the coastal region (not shown), and were therefore discarded in subsequent analyses.

SSS
The SSS signature of striations is extracted from the NASA Soil Moisture Active Passive (SMAP) observatory [37], available from April 4 th 2015 onwards. We used the JPL SMAP level-3 CAP standard mapped image 8-day running mean V4.3 validated 0.25° daily data from April 4 th 2015 to December 31 st 2018 [38]. Soil Moisture Ocean Salinity (SMOS) data [39] have also been analyzed, but they were found much noisier in terms of mesoscale structures (not shown) and were not further considered in this study.

Chl-a
Striations in surface Chl-a are evaluated using satellite ocean color data. We use a merged product of the MODIS-AQUA and VIIRS datasets provided by the GlobColour project from July 2012 to December 2018. Monthly level-3 binned images (~25 km resolution) include all level-2 products accumulated over one-month periods and merged using a bio-optical model-based procedure validated at the global scale [40].

Data Processing and Analysis
SSH and U g daily maps are time-averaged over the study period and spatially high-pass filtered with a 4° half-width 2-D Hanning window to extract stationary striations in dynamical fields ( [17], and references therein). As shown by [17] and others, stationary striations are stable over time, and our results show little sensitivity to the exact averaging period. The same procedure is applied to daily U, SST, SSS, and monthly Chl-a. In the latter case, logarithmic transformation is applied beforehand to reduce the strong gradient between the oligotrophic open ocean and the productive EBUS (see Appendix A). Such transformation is commonly used for the analysis of Chl-a data (e.g. [41], their Appendix A and references therein). Note that although permutating log-transformation and 2-D filtering does not theoretically lead to identical results, they are similar despite somewhat noisier signals than the ones presented in Section 3. In such case, the computed large-scale component of Chl-a (which is removed to extract the mesoscale component, as for other variables [17]) is influenced by the strong near-zonal gradient, leading to possibly less accurate extraction of other large-scale features and therefore aliasing the extracted striations. Applying log-transformation first also allows assessing the impact of striations relative to background Chl-a (Appendix A). All the variables were filtered twice to remove any residual large-scale signal, which was significant for SSH and tracers after the first filter application (not shown).
Following [17], 2-D Fast Fourier Transform (FFT) is applied to the previously obtained mesoscale mean fields in order to compare the spatial scales of any striated patterns in the tracers and dynamical fields. For each variable and subdomain, FFT is computed in the area where tracer and dynamical striations are most evident from visual inspection (black dashed boxes on Figures 2 and 3). Such method was however unsuccessful for ENP Chl-a because of the very strong near-meridional, alongshore signal associated with exceptional coastal productivity that prevented the extraction of the weaker near-zonal signals in the coastal transition zone (Figures 2e,f). Approximate spatial scales for the striated signal in Chl-a are then estimated from FFT applied to a region that excludes the coastal band while capturing part of the striated pattern (orange dashed box on Figures 2e,f).
Besides zonal and meridional wavelengths, the average tilt of striations from the zonal direction is derived from the energy spectra. The angle of the dominant wave vector connecting the symmetric most energetic peaks is used for such purpose (white dashed lines on Figures 4,5). In a few specific cases in the ESP (U g averaged over the shorter SSS record, and SSH for both time spans, Figures 5e,g,h,i), secondary maxima with meridional wavelengths consistent with that found for the single peak in U g (averaged over the SST record, Figure 5d) were used instead. The angle obtained from the U g spectrum is used to average mesoscale fields in the along-striation direction (solid boxes on Figures 2 and 3), allowing to compare cross-striation profiles. For each tracer, cross-correlation with SSH and U g profiles is used to assess the possible role of zonal advection in striated pattern formation. Interpolating profiles at a 0.01°r esolution allows the computation of accurate lags. For each variable pair, the statistical significance at the 5% level of the correlation coefficient is computed using a  170  171  172  173  174  175  176  177  178  179  180  181  182  183  184  185  186  187  188  189  190  191  192  193  194  195  196  197  198  199  200  201  202  203  204  205  206  207  208  209  210  211  212  213  214  215  216  217  218  219  220  221  222  223  224 Monte Carlo technique with 1000 iterations, where the first profile is correlated with a synthetic profile obtained from Fourier analysis of the second profile and a random phase [42]. spatially high-pass filtered SSALTO/DUACS U g (cm s -1 ) and (right) GlobCurrent full surface current velocity (shading, cm s -1 ) and vectors. Chl-a units are mg m -3 for (f) the full field and % of the latter for (e) the high-pass filtered field (Appendix A). The black dashed boxes are where 2-D FFT is applied to the tracer fields and U g , except for (third row) Chl-a, for which the orange dashed box is used. The solid boxes are tilted with the striation angle in SSALTO/DUACS U g determined from 2-D FFT. The associated tilted red and blue dashed lines on all the panels indicate the approximate locations of eastward and westward jets, respectively, as inferred from (g) SSALTO/DUACS U g . The 07/02/12-12/31/18 averaging period is considered throughout, except (second row) where the 04/04/15-12/31/18 period is used due to shorter SSS record, resulting in slightly larger striation tilt (9.7° vs. 8.8°, see Table 1).  spatially high-pass filtered SSALTO/DUACS U g (cm s -1 ) and (right) GlobCurrent full surface current velocity (shading, cm s -1 ) and vectors. Chl-a units are mg m -3 for (f) the full field and % of the latter for (e) the high-pass filtered field (Appendix A). The black dashed boxes are where 2-D FFT is applied to the tracer fields and U g . The solid boxes are tilted with the striation angle in SSALTO/DUACS U g determined from 2-D FFT. The associated tilted red and blue dashed lines on all the panels indicate the approximate locations of eastward and westward jets, respectively, as inferred from (g) SSALTO/DUACS U g . The 07/02/12-12/31/18 averaging period is considered throughout, except (second row) where the 04/04/15-12/31/18 period is used due to shorter SSS record, resulting in larger striation tilt (12.7° vs. 5.8°, see Table 2).
Finally, a decomposition of SST and SSS advection terms is computed in the ENP, where advection is found to play a dominant role (Section 3). However, striations being associated with eddy trains in subtropical gyres [25,43] and particularly the ESP [17], both advection by the mean jets and nonlinear advection by individual eddies are candidate mechanisms. Moreover, additional processes should balance such advection in order to explain the persistence of hydrographic striations in multi-year averages (Section 3). The decomposition allows addressing these questions by separating nearzonal, along-striation advection from near-meridional, cross-striation advection; timemean fields from anomalies relative to the mean (Reynolds decomposition); and largescale components from mesoscale components for currents and hydrographical data.  The general equation of a surface hydrographical tracer F (either SST or SSS) is: where t represents time, V is the surface velocity vector, and K is for diffusivity. The term on the left hand side represents local (Eulerian) time derivative of F (or tendency). It is driven by the three terms on the right hand side: from left to right, advection by ocean currents (both horizontal and vertical), turbulent mixing (horizontal and In this study, we focus on stationary striated patterns at the ocean surface, where horizontal advection is expected to dominate. In a near-Cartesian orthogonal frame slightly rotated counterclockwise and aligned with mean striation axis, horizontal advection of F may be written as: (2) where u a and v c are the along-striation and cross-striation components of V, and x a and y c are along-striation and cross-striation coordinates, respectively. The terms on the right hand side of (2) represent along-striation and cross-striation advection of F.
A Reynolds decomposition is then applied to the surface currents and tracer: where overbars are for time-averaging over the available record and prime marks are for anomalies relative to the time-averaged fields.
Averaging (2) over time yields: The terms on the right hand side of (6) represent the long-term averages of nonlinear (or eddy) along-striation advection, mean along-striation advection, nonlinear crossstriation advection, and mean cross-striation advection, respectively.
Finally, spatial scale separation is applied to the anomalous and mean surface currents and tracer: u a '+ u a =u aL '+u aH '+ u aL +u aH (7) v c '+ v c =v cL '+v cH '+ v cL + v cH (8) F'+ F =F L '+F H '+ F L + F H , (9) where H and L subscripts refer to mesoscale and large-scale components obtained from spatial high-pass filtering with a 4° half-width 2-D Hanning window.
Incorporating (7), (8), and (9) into (6) gives: The sixteen terms on the right hand side of (10) are the considered SST/SSS advection terms. After 2-D mapping, cross-striation profiles are computed and key terms are cross-correlated as described above. Figure 2 shows the time-averaged, spatially filtered and full (raw, unfiltered) satellite surface tracer and current observations in the ENP. Striated signals in SST and SSS are visible over a large region extending between the California coast and ~145°W (Figures 2a,c). Despite the weak signals, with values of ~0.05°C and 0.05 PSU, striations stand out slightly above noise level (~0.04°C and 0.03 PSU, see Appendix B), are zonally coherent, and appear connected to stronger signals closer to the coast, suggesting they are likely real features. Similar meridionally-alternating bands are found in Chl-a data with magnitudes reaching ~10% of full Chl-a but they do not extend beyond ~500 km offshore (Figure 2e). Meridional wavelengths L y inferred from spectral analysis (Figure 4) range from 3.0° to 3.7° for different tracers, and striation axes are tilted counterclockwise from the zonal orientation by an angle α varying from 9.2° to 14.4° (28.9° for Chl-a, Table 1). These figures agree well with the dynamical fields (U, U g , SSH) having L y range from 2.8° to 3.9° and α from 8.8° to 11.3° (17.6°, 17.6°, and 27.3° for U, U g , and SSH in the region with striated Chl-a signals). Remarkably, warm and salty (cool and fresh) anomalies are aligned with eastward (westward) jets (Figures 2a,c,g), suggesting they may result from advection by the striated currents. Indeed, the region through which the jets extend southwestward has strong background along-striation gradients of SST and SSS (Figures 2b,d) between the California EBUS and the subtropical gyre (Figure 2h). In contrast, the striated geostrophic velocities tend to coincide with zero-crossings of Chl-a anomalies, i.e. bands of locally more (less) productive waters are collocated with negative (positive) meridional shear of near-zonal jets, that is, along striation troughs (crests) (Figures  2e,g). Interestingly, the offshore extent of Chl-a striations corresponds to that of the background Chl-a gradient between coastal and open-ocean waters (Figure 2f).  The same analysis yields strikingly different results for the ESP. While multiple near-zonal SST bands of amplitude ~0.1°C (again slightly above standard error 0.07°C, Appendix B) are evident in a region far offshore central Chile (Figure 3a), SSS and Chl-a patterns are noisier (Figures 3c,e). Spectral analysis confirms that the mesoscale properties of the SSS and Chl-a fields are inconsistent with those of the dynamical fields ( Figure 5). L y are larger in the former (5.6-8.5° vs. 2.6-3.7°) and α are smaller (-3.8-2.5° vs. 3.7-13.2°) ( Table 2). Let us however note that similarly to the ENP, some kind of banded structure is detected for mesoscale Chl-a in the coastal transition region, although with reduced zonal extent and away from the most obvious quasizonal jets located farther offshore along the subtropical gyre poleward edge ( Figures  3e,g,h). On the other hand, the values found for SST are within the range of those extracted from dynamical fields (Table 2). Besides, striations in SST tend to be in phase quadrature rather than in phase with those in U g (Figures 3a,g). Part of the differences from the ENP may reside in different jet locations relative to large-scale tracer fields. As subtropical EBUS, both systems exhibit similar gradients of SST, SSS, and Chl-a (Figures 2b,d,f and 3b,d,f). However, unlike the ENP (Figure 2g), ESP striations are observed farther offshore and do not extend eastward to the coast (Figure 3g), consistently with distinct formation processes [16,17]. As a result, ESP striations are found within weak zonal gradients of SST, SSS, and Chl-a (Figures 3b,d,f,g). On the other hand, this region features a strong meridional SST gradient between the subtropical gyre and higher latitudes. Phase quadrature between striations in SST and U g then implies that eastward (westward) jets correspond to mesoscale meridional SST gradients that sharpen (flatten) the large-scale gradient, in qualitative agreement with [23]. Mesoscale gradients are however too weak (<10 -3 °C km -1 , ~1/10 of the large-scale gradient) to generate any significant staircase profile in raw SST.

Striated Surface Tracers
To further support our findings and more objectively assess the relationship between surface tracers and either U g or SSH, variables are averaged in the alongstriation direction and in the area where striations are most evident (solid boxes on Figures 2 and 3), before cross-striation profiles are computed ( Figure 6). Lagcorrelation analysis confirms that near-periodic ENP SST and SSS are both highly (~0.8) and significantly correlated with U g , with a small lag of about 0.1-0.2° (Figures  6a,b). Correlations are also high (~0.9) and statistically significant with SSH but with larger lag (~0.6-0.7° latitude) in the opposite direction, consistently with nearquadrature and dominant periodicity L y~3°. Conversely, Chl-a and SSH (U g ) exhibit high, statistically significant negative correlation ~0.7-0.8 with meridional lag ~-0.25°(~+ 0.5°) (Figure 6c). In addition, correlation at zero lag is significant with SSH only and higher (-0.64) compared to U g (-0.40). This confirms that zonal advection is not the dominant driver for striations in Chl-a, unlike physical tracers.
In the ESP, SST and SSH are approximately in phase, particularly between 37°S and 41°S (Figure 6d) with high (~0.8), statistically significant correlation. Quadrature with U g , particularly evident also from 37°S to 41°S, is confirmed with maximum correlation ~0.7 at lag -0.8°. On the other hand, SSS and Chl-a appear poorly correlated with SSH and U g (Figures 6e,f). In fact, SSS and Chl-a profiles do not exhibit clear periodicity, unlike SST and dynamical fields. Note that these results did not change much when the striation angle from SSH instead of U g was used to compute alongstriation averages (not shown), consistently with the generally similar α values (Tables  1, 2).   24   25   368  369  370  371  372  373  374  375  376  377  378  379  380  381  382  383  384  385  386  387  388  389  390  391  392  393  394  395  396 397 398

ENP Tracer Advection
In this section, we focus on striation patterns in SST and SSS in the ENP that are consistent with the advection of large-scale water masses by the near-zonal jets, and perform a decomposition of the associated advection terms (Section 2.2). For both tracers and as expected, tilted near-periodic zonally-elongated bands are found in the advection of the large-scale mean tracers by the mesoscale time-mean along-striation (Figures 7a,c). SST advection is stronger near the eastern boundary (Figure 7a), consistently with both swifter mesoscale zonal currents ( Figure  2g) and stronger background near-zonal SST gradients associated with coastal upwelling (Figure 2b). SSS advection is highest much further offshore, betweeñ 140°W and ~130°W and weaker closer to the coast (Figure 7c). This is likely the result of the structure of the background SSS gradient oriented mostly in the alongshore direction, which coincides with the cross-striation axis (Figure 2d  Similar bands are also found in the advection of mesoscale mean tracers by the large-scale mean cross-striation flow −V cL ∂ F H /∂ y c , except they are located near the continental boundary for both SST and SSS, and weaken sharply west of 130°W, though retaining their banded structure through 135-140°W (Figures 7b,d). This term is banded because its mesoscale structure is defined by the cross-striation tracer gradients (Figures 2a,c). The large-scale surface flow is typical of subtropical gyres with equatorward (i.e. cross-striation) currents in the eastern branch and weaker velocities west of ~130°W (Figures 1a,2h), thus modulating the intensity of −V cL ∂ F H /∂ y c . Unlike the previous term, it appears to be in phase quadrature with the striated mesoscale SST/SSS (white contours on Figures 7b,d).
In an attempt to synthesize the information obtained from the sixteen SST and SSS advection terms displayed on Equation (10), Figures 8 and 9 present the corresponding cross-striation profiles, as well as those of mesoscale SST and SSS. The profiles were derived after averaging in the along-striation direction as described earlier, except for the tilted box for SST advection, which was shifted by three degrees eastward to better grasp the −V cL ∂ F H /∂ y c term (Figure 7b). Figures 8 and 9 confirm that the aforementioned two terms are the dominant advection terms. In addition, the eddy terms (advection of mesoscale tracer anomalies by the mesoscale anomalous alongstriation and cross-striation currents −U aH ' ∂ F H ' /∂ x a and −V cH ' ∂ F H ' / ∂ y c ) also present mesoscale variations along the cross-striation axis, although with no obvious periodicity (Figures 8d, 9d). Importantly, these four mesoscale advection terms are not negligible compared to large-scale advection, especially for SSS (Figures 8a, 9a). Noteworthy, these terms are similar in magnitude for SST, while −U aH ∂ SSS L /∂ x a is 2-3 times higher than other SSS advection terms. Such a result should however be interpreted with caution as it is likely sensitive to the location of the box used to compute cross-striation profiles, due to spatial variations in the intensity of different advection terms (Figure 7).  (Figures 8b and 9b).

Discussion
The mesoscale SST and SSS budgets depicted above are not closed. Other terms in the tracer balance (Equation (1)) that were not included in this study, such as horizontal/vertical mixing and vertical advection may be important. Future modelling studies at eddy-resolving resolution (typically 0.1° and higher) and the analysis of extensive in situ data records from e.g. Argo profiling floats [7,45] may help to address this limitation.
In the light of our results, the processes responsible for the generation and persistence of striations in SST and SSS may be conceptualized as follows. Mean quasizonal jets in the ENP advect the large-scale tracer gradients extending between the coast and the subtropical gyre, leading to tracer field deformation (e.g. [23], their Figure 13a). The resulting wavy pattern in the initially near-meridional (i.e. cross-jet) tracer isolines generates near-zonal frontal anomalies that appear as striations in the time-mean mesoscale field. These features are however partly embedded in large-scale equatorward flow typical of subtropical gyres and EBUS. Such current then advects warm/salty anomalies from the north into the tracer front that separates them from a band of cooler/fresher waters to the south, and cool/fresh anomalies into the front delineating a band of warmer/saltier waters. Cross-striation advection does not explain the banded tracer pattern by itself given its shorter near-zonal extent and the phase lag with the tracer field. Other processes such as mixing, vertical advection and horizontal eddy advection likely contribute to the mesoscale SST/SSS patterns as well, allowing to reach equilibrium and maintain striations in SST and SSS.
Unlike striations in SST and SSS, striations in Chl-a appear π out of phase with the striated SSH signal in the ENP. Cyclonic mesoscale eddies are thought to contribute to the offshore nutrient and plankton export in EBUS by trapping coastal water during their formation, unlike anticyclonic eddies generated beyond the upwelling front in more oligotrophic environments [46,47]. The observed relationship between the bands in Chl-a and SSH is then consistent with such hypothesis, given that time-mean striations manifest themselves in snapshots as eddy trains [17,25,43]. However, upwelled trapped water is also cooler compared to background open-ocean conditions, which should lead to in-phase SST-SSH relation rather than the phase quadrature evidenced here. Such discrepancy may result from the different locations for the studied physical and biological tracers in the offshore and coastal transition regions, respectively, where different dynamics may be involved.
To verify this hypothesis, cross-striation profiles of SST and SSS are computed in the same region as Chl-a (tilted box on Figure 2e) and shown on Figure 10. SST is highly (~0.8) and significantly correlated with both SSH and U g , with phase lags ~-0.5°a nd ~+0.25° latitude, respectively. The smaller lag with U g suggests that eddy trapping may not be the dominant driver for striations in SST in this region. Indeed, correlation at zero lag is significant with U g only and higher (0.69) compared to SSH (0.38). Nevertheless, the examination of Figure 10a reveals that SST is more aligned with U g north of ~37°N and with SSH to the south. These results thus suggest that both eddy trapping and advection probably contribute to the striated tracer patterns in the coastal transition region. Note that SSS is poorly correlated with both SSH and U g , and its periodicity is not as marked as for other variables (Figure 10b), which may have to do with the mostly alongshore background SSS gradient (Figure 2d). In contrast, striations in the ESP are only evident in the SST field. Phase quadrature between the latter and geostrophic velocity in a region of marked meridional SST gradient suggests a potential role of inhomogeneous isopycnal mixing [22,23].
Except for Chl-a in the ENP, the striated tracer signals reported here are relatively weak (yet significant). Nevertheless, the associated mesoscale meridional SST (SSS) gradients are typically ±10-20% (±20-50%) of the large-scale gradient and locally over ±30% (near ±100%) (Figure 11), implying significant modulation of zonal tracer fronts by striated currents. Besides, instantaneous tracer anomalies associated with eddy trains are likely much stronger than time-mean signals as one might expect from the SST/SSS signatures of mesoscale eddies [25,48]. A composite analysis of those eddies organized in striations may be necessary to extract these transient signals and their contribution to SST/SSS variability in EBUS. Despite their similarities, the California and Chile EBUS feature striated patterns of surface tracers with quite distinct characteristics. This is attributed mostly to the location of quasi-zonal jets, either within the large-scale near-zonal tracer gradients and meridional flow (ENP) or much farther west (ESP). These variations among regions and tracers make it difficult to generalize our results to other EBUS regions such as the Benguela and Canary current systems in the Atlantic. Diverse theories for the existence of striated currents [12][13][14][15][16][17][18][19][20][21][22][23] suggest the possibility of different generation mechanisms in different regions. Combined with the variety of water masses in the global ocean and their spatial properties, particularly the strength and direction of background tracer gradients, such diversity suggests large regional variations in the existence and characteristics of striated tracer fields. Our findings advocate for further research to understand the complex influences of different striations on ocean properties and their variations between different regions.

Conclusions
Multi-year satellite records from various sensors were used to characterize the effects of striations on SST, SSS, and Chl-a in the subtropical ENP and ESP EBUS. The results vary significantly among the two regions and three surface tracers. In the ENP, while striations in SST and SSS coincide with those in zonal current, suggesting a dominant role of advection, striations in Chl-a are collocated with those in SSH, possibly involving water mass trapping by mesoscale eddy trains. In the ESP, striations were found in SST but neither in SSS nor in Chl-a, except for some meridionallyalternating Chl-a anomalies in the coastal transition zone without clear connections with quasi-zonal jets. Besides, striations in SST are highly correlated with SSH rather than with zonal currents. Unlike the ENP, ESP striations are located far offshore, outside the area of strong background zonal gradients of ocean properties, which explains the weak effects of zonal advection. Therefore, striations probably contribute to coastal/open-ocean exchanges in the ENP, but likely not in the ESP. The decomposition of SST and SSS advection in the ENP into along/cross-striation, mean/eddy, and mesoscale/large-scale parts identifies a dominant contribution from the advection of large-scale mean tracers by the mean quasi-zonal jets, and secondary contributions from the advection of mesoscale mean tracers by the large-scale mean meridional flow and from eddy advection, although mixing and vertical advection likely contribute as well. The persistence of hydrographic striations is thus suggested to result from an interaction between mesoscale (quasi-zonal jets, fronts, and eddies) and large-scale features (tracer gradients and meridional flow). The processes leading to the alignment of the SSH signature of striations with Chl-a in the ENP and SST in the ESP are not confirmed and require future investigation.

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.

Appendix A
A logarithmic transformation is applied to time-averages of monthly Chl-a data as stated in Section 2.2. Let A = log(Chl-a). A is high-pass filtered as described in Section 2.2. By construction, mesoscale A is then the difference between A and large-scale A, which may be viewed as an anomaly relative to the large-scale component: where H and L subscripts refer to mesoscale and large-scale components, respectively. For 2-D visualization purposes, it is useful to represent Chl-a expressed in mg m -3 with a logarithmic color scale (Figures 2f, 3f). This is done by plotting A with a linear color scale, and indicating the associated Chl-a values. For consistency, it is desirable to represent A H in such a way that it may be compared quantitatively with full (unfiltered) Chl-a. Raising 10 to the power of Equation (A1) after moving A L to the left hand side yields:

Chla=γ 10
where γ= 10 A H . Permutating low-pass filtering and logarithmic transformation does not make much difference on large-scale Chl-a outside a narrow coastal band in both the ENP and ESP (not shown). Therefore: Using scale separation as in (A1) but applied in the original Chl-a space, it can be shown that: The ratio between mesoscale and full Chl-a may thus be approximated with the nondimensional coefficient (γ−1)/ γ , which can be readily derived from A H . A linear color scale is then used for A H , which we made vary from -0.05 to 0.05 in units of the logarithmic space. The associated (γ−1)/ γ values then range approximately from -0.11 to 0.12 (Figures 2e, 3e).
On the other hand, cross-striation profiles of mesoscale log(Chl-a) do not require such inverse transformation because of the normalization by their standard deviation (Figures 6c,f). The latter may be expressed either in units of the logarithmic space (i.e. of A H ) or as a ratio between mesoscale and full Chl-a (i.e. (γ−1)/ γ ) according to the aforementioned derivation.

Appendix B
Assuming that nominal errors of satellite sensors are normally distributed, standard error of the mesoscale time-mean SST/SSS fields may be estimated as: where F is SST or SSS, subscript H refers to the mesoscale component, σ F H is the standard deviation of mesoscale F time series, n is the number of independent observations of mesoscale F, x and y are zonal and meridional coordinates, respectively.
In the regions where hydrographic striations are observed (tilted boxes on Figures   2a,c and 3a), σ SST H is of order 0.25°C and 0.35°C in the ENP and ESP, respectively, whereas σ SSS H is of order 0.15 PSU in the ENP ( Figure B1). Note that no striated SSS signals were found in the ESP (see Section 3).
On the other hand, striations are associated with the time-averaged signature of westward mesoscale eddy propagation [16,17]. A typical time scale T separating two consecutive independent observations may thus be defined as the time spent by an individual eddy passing through a fixed location. Under the Gaussian eddy approximation, such time corresponds to eddy diameter D divided by eddy zonal translation velocity c, which may be estimated from [44] (their Figures 12 and 22). According to their results, c is typically 2 cm s -1 in the 30-45°S latitude band (ESP) and 2.5 cm s -1 in the 25-40°N band (ENP), while D is roughly equal to 150 km in both regions. T=D/c is then ~70 days and ~90 days in the ENP and ESP, respectively. Finally, n is obtained by dividing the period of record (2374 days and 1368 days for SST and SSS, respectively) by T and retaining the integer part of the result. This yields 33 and 26 independent SST observations in the ENP and ESP, respectively, and 19 independent SSS observations in the ENP. The application of Equation (B1) to the aforementioned estimates of σ SST H , σ SSS H , and n then yields standard errors of SE SST H~0 .04°C and 0.07°C in the ENP and ESP, respectively, and SE SSS H~0 .03 PSU in the ENP.