W9.1) just like it did during this event. This study attempts to understand the mechanism of the vertical displacement of the forearc during gigantic earthquake cycles via numerical modeling. The results suggest that the interseismic subsidence rate in the forearc increases with the duration of the locking of the asperity of the gigantic earthquake over several hundred years, due to the increasing slip deficit rate on the deeper parts of the plate interface. The increasing slip deficit rate is caused by both the decreasing the shear stress in the shear zone owing to the continuous locking of the asperity and the increasing the mobility of the continental lithosphere owing to the viscoelastic relaxation in the mantle wedge. The deep slip deficit rate extending to ~100 km depth of the plate interface is necessary to explain the observed interseismic forearc subsidence rate. The results also suggest hundreds of years of continuous locking of the asperities of a gigantic earthquake in the western Kuril subduction zone, where fast forearc subsidence has been observed as well.The forearc in Northeast Japan subsided (3–4 mm/year) in the interseismic ~100 years before the 2011 Tohoku earthquake (M This subduction zone recently experienced a gigantic earthquake, called the 2011 Tohoku earthquake (Mw9.1), in which a very large fault slip (50–65 m) occurred on the shallow plate interface near the trench . Similar past events with recurrence interval of ~600 years were identified based on the tsunami deposits4.The Northeast Japan (NEJP) arc is an island arc located around the subduction zone where the old Pacific plate subducts from the Japan Trench at a rate of 8.3–8.4 cm/year5  above the deeper extended portion of the large coseismic slip area of the 2011 Tohoku earthquake is characterized by fast subsidence (3–4 mm/year) in the forearc and uplift in the backarc during the interseismic period10. The coupling ratio is defined as vpl and v indicate the long-term plate convergence rate and interseismic fault slip rate, respectively. The models assuming a layered elastic and viscoelastic structure suggest that only shallow (<40 km depth8 or <25 km depth9) interplate coupling can produce the observed interseismic subsidence rate9. Therefore, different assumptions of the rheological structure yield substantially different results for the deep interplate coupling to explain the observed forearc subsidence rate. Therefore, using realistic rheological structures for modeling is needed to reveal the mechanism of the interseismic forearc subsidence.Several studies have attempted to explain the observed interseismic subsidence rate in the forearc region via kinematic modeling of the crustal deformation caused by interplate coupling and earthquake cycles. The models assuming an elastic half-space suggest that very deep interplate coupling, which is 50–30% of the coupling ratios at 50–100 km depth, is necessary to produce the observed interseismic subsidence rate in the forearc11). Therefore, the estimated partial coupling ratio on a deeper part of the plate interface in previous studies10 suggests slip deficit caused by locking of the asperities at the shallower parts. Deeper in the plate interface, the behavior shifts from frictional slip on the fault plane to volumetric and ductile deformation in shear zones, with increasing temperature at the plate interface. This is based on the geological evidences of the fossil shear zone12. The ductile deformation rate in the shear zone may also contribute to the interseismic deformation of the NEJP forearc above the deep part (50–100 km depth) of the plate interface. Therefore, considering the segmentation of asperities, frictionally stable parts (fault creep parts), and ductile shear zones is important to understand the mechanism of the vertical displacement in the forearc during gigantic earthquake cycles.Locking of asperities on the plate interface causes a slip deficit rate 10 and the last gigantic earthquake occurred in the 17th century13.This study aims to analyze the physical mechanisms beyond the vertical displacement in the NEJP forearc during gigantic earthquake cycles. Clarifying it will deepen understanding of the deep interplate coupling and afterslip mechanisms in gigantic earthquake cycles. Furthermore, it is important to understand these phenomena for estimating the potential of future gigantic earthquakes in the western Kuril subduction zone, where fast interseismic forearc subsidence has been observed as wellFor this purpose, we built a model of the crustal deformation due to interplate coupling and earthquake slip during earthquake cycles using the finite-element method. The model considers a realistic heterogeneous rheological structure, the frictionally stable part (fault creep part) at the plate interface via a thin low-viscosity layer, and a deep viscoelastic shear zone Fig. .Figure 2W9.1), we define the range of leveling data used in this study by two lines that are parallel to the arc-perpendicular direction at the center of the range so that the range corresponds to the surface projection of the large coseismic slip area (>30 m) of the 2011 Tohoku earthquake2  was caused by coal mining5.We used the leveling data analyzed by Kunimi W7.3)16 (postseismic only), the 1964 Niigata earthquake (MW7.6)17, and the 1983 Japan Sea earthquake (MW7.85)18. We calculated the vertical displacement due to co- and post-seismic deformation of these earthquakes in accordance with Thatcher et al.16 and subtracted it from the leveling data . Our model considers only the main asperity of the 2011 Tohoku earthquake located within 75 km of the trench, and the other part of the plate interface mechanically creeps during the interseismic period represented by a thin low-viscous layer21  in the model based on the backslip model. The modeled slip deficit rate on the fault creep part and across the shear zone is measured as the modeled relative motion across the thin viscoelastic layer and the shear zone, respectively. Soon after the locking of the asperity is initiated (t = 10 year), the slip deficit rate on the fault creep part exhibits a similar slip deficit rate on an infinite crack in the elastic space due to the locking of a circular asperity; the slip deficit rate decreases with the distance from the asperity by a square-root form11. However, the slip deficit rate on the fault creep part increases and deviates from the square-root form with time. In addition, the slip deficit extends to the shear zone with time. Generally, the slip deficit in the deep plate interface causes the surface above to subside . Namely, the increase in the modeled subsidence rate in the forearc with time is caused by the increasing slip deficit rate in the deep plate interface with time.Figure To examine the causes of increase in slip deficit rate with time, we model several special cases. The first case is for all model elements to be elastic except for the thin viscoelastic layer in the fault creep part and the shear zone Fig. . The sliTherefore, the increase in slip deficit rate with time is mainly caused by (1) decreasing viscoelastic shear deformation rate in the shear zone owing to the shear stress decrement caused by the locking of the asperity and (2) increasing the mobility of the continental lithosphere with progressing viscoelastic relaxation in the mantle wedge. Therefore, the model results indicate that the observed interseismic subsidence in the forearc region was caused by the continuous locking of the shallow asperities located in the large slip area of the 2011 Tohoku earthquake for several hundreds of years with the viscoelastic response in the mantle wedge and shear zone.vsd/vpl values of at least 0.35–0.1 for 70–100 km depth) is necessary to explain the observed forearc subsidence rate. Changing the shape of the shear zone does not considerably affect the results  from geodetic observations24.The rate of the afterslip exhibits a long decay constant and is controlled by the viscoelastic relaxation rate in the shear zone. Figure t′ = 600 year, where t′ is the time from the fifth earthquake, are 0.5, 0.4, and 0.2 at 45 km, 70 km, and 100 km depths, respectively  afterslip, which releases the cumulated deep slip deficit, occurs after the 2011 Tohoku earthquake25.The afterslip with a long decay constant diminishes, and instead, the slip deficit owing to the locking of the asperity gradually extends to deeper parts ~200 years after the earthquake Fig. . The subely Fig. . These at′ = 600 year (3.0–3.7 cm/year) is roughly consistent with the observed interseismic horizontal displacement rate in the forearc region (38–39°N) by the GNSS during 1997–2000 (~3–4 cm/year)5. We also made a rough comparison between the modeled vertical displacement rates and the observed ones by the GNSS observations during 1997–2005 in Supplementary Information, and these are roughly consistent with each other , which did not rupture during 1996–2011, for the middle to deeper part of the plate interface (see Methods section and Supplementary Information).The cross-sectional images of the modeled velocity vectors in the continental crust and mantle for 100, 250, and 600 years after the earthquake are shown in Supplementary Fig. her Fig. . Howeverw7.5 Miyagi-oki earthquake, our results cannot strictly be compared with short-term geodetic observations whose observation period is shorter than the recurrence interval of the ~Mw7.5 Miyagi-oki earthquake. Because the model approximately represents the frictionally stable portion via a thin viscous layer, the results cannot explain early periods of afterslip. In addition, we assume a Newtonian viscoelasticity, whereas the actual mineral flow law has power-law stress dependency26 especially for the earlier postseismic period . Therefore, our results underestimate the deformation rate in the early postseismic period and cannot be compared with the observed postseismic deformation for several tens of years after the 2011 Tohoku earthquake. Future numerical modeling that considers fault friction law including the asperities of the ~Mw7.5 Miyagi-oki earthquake and power-law rheology with modeling absolute stress will resolve this problem. The postseismic transient viscosity recovers to a steady state viscosity within a maximum of 50 years from the occurrence of a large earthquake27, i.e., the deformation rate with a Newtonian rheology and that with a power-law rheology become almost identical. Therefore, our model is effective unless we focus on the deformation whose time scales are greater than 50–100 years and that except for the earlier postseismic period. Thus, our model is effective to derive the conclusions and suggestions written in this manuscript and is useless to predict the crustal deformation decades after the 2011 Tohoku earthquake. Because a two-dimensional problem is assumed in this study, our model cannot explain the along-arc variation of the observed vertical displacement rate that decreases with the distance from the range used in this study , where the accumulated slip deficit may have been released by the afterslip following the 2011 Tohoku earthquake.The model results reveal that a slip deficit at greater depths corresponding to ely Fig. , is neceely Fig.  is simil5. Therefore, the postseismic uplift of 2.5–3.5 m due to the afterslip of 20–24 m is required to balance the sum of interseismic and coseismic subsidence. However, the observed postseismic uplift in the forearc region rapidly decays5; therefore, the postseismic uplift of 2.5–3.5 m due to the afterslip of 20–24 m is unlikely5. Therefore, Nishimura5 hypothesized that the observed interseismic fast subsidence rate in the forearc region and the large slip deficit rate in the deeper parts are limited in the later stages of the gigantic earthquake cycle. Our modeling results support this hypothesis and elucidate the physical mechanism.The model result suggests that the observed fast subsidence of the forearc (3–4 mm/year) occurs only in the later stages of the gigantic earthquake cycle. If the observed forearc subsidence rate had continued through the gigantic earthquake cycle (~600 years), the cumulative interseismic subsidence on the forearc would exceed 2 m. The corresponding cumulative slip deficit in the deeper parts of the plate interface is 24–20 m for 50–70 km depth. In addition, coseismic subsidence of 0.4–1.2 m occurred in the forearc region28. Therefore, a similar large uplift with a long duration will occur after the 2011 Tohoku earthquake (MW9.1). Our results suggest that the long-duration postseismic uplift is caused by the long-duration afterslip controlled by the viscoelastic relaxation rate in the shear zone. The long-duration afterslip  balances the large slip deficit in the deeper plate interface that accumulates late in the gigantic earthquake cycle  and the cumulative postseismic uplift around the coastal line in the forearc region is ~0 m, ~0.5 m, and ~0.75 m at 40 years, 100 years, and 200 years from the 2011 Tohoku earthquake, respectively Fig. . Becausecle Fig. , and thecle Fig. . This isW7.5 Miyagi-oki earthquake at 30–50 km depth of the plate interface repeatedly ruptured29: 1897 M7.430, 1936 MW7.519, and 1978 MW7.519  on the asperities of the ~MW7.5 Miyagi-oki earthquake including its afterslip during 1900–2000 is lower than the half of the plate convergence rate. This is consistent with our result that the modeled slip deficit rate (vsd = vpl − v for 500–600 years after the gigantic earthquake in this region (30–50 km depth) is 4–5 cm/year . Therefore, we suggest that the large lack of the slip rate on the asperities of the ~MW7.5 Miyagi-oki earthquake was caused by the long-term locking of the shallow asperities of the 2011 Tohoku earthquake for several hundred years and was probably compensated by the coseismic slip of the 2011 Tohoku earthquake on the asperities of the ~MW7.5 Miyagi-oki earthquake (~8–15 m of the coseismic slip3).There is another evidence for the large slip deficit rate in the deeper plate interface in this region in the later stages of the gigantic earthquake cycle. The asperities of the ~M519 Fig. . Yamanakear Fig. , which iW7.5 Miyagi-oki earthquake is shorter early in the gigantic earthquake cycle and increases with time because of decreasing loading rate of the asperities of the ~MW7.5 Miyagi-oki earthquake with decreasing background slip rate on the deeper plate interface. This will be compared with the recurrence intervals of future Miyagi-oki earthquake. In addition, the predicted large afterslip in this study (up to 9–10 m) will partly be included as the slip rate excess due to the shorter interval of the Miyagi-oki earthquake and its afterslip for the next 50–100 years.The results of this study suggest that the recurrence interval of the ~M31. This helps to understand the rheological properties and behavior of the shear zone in the subduction zones.The results suggest that the shear zone is critical to the slip deficit rate and afterslip in the deeper parts of the plate interface during a gigantic earthquake cycle. The modeled vertical displacement rate in the forearc region is very sensitive to the viscosity and width of the shear zone, which control the deformation rate in the shear zone. The results suggest that the absolute deformation rate in the shear zone decreases by few tens percent of the plate convergence rate in the later interseismic period and is much faster than the plate convergence rate in the postseismic period Fig. . The vis10, where the gigantic earthquake occurred in the 17th century13. We suggest that the fast subsidence at the east coast of Hokkaido is caused by the long-term locking of the asperities of the gigantic earthquake in the 17th century for ~400 years. Therefore, slip deficit of at least 30 m may have accumulated on the asperities of the 17th century event at present.The range of the observed fast subsidence in the forearc region coincides with the extent of the dip of the large slip area of the 2011 Tohoku earthquake Fig. . This co7. Ikeda7 proposed that the interseismic fast subsidence in a forearc region and the large slip deficit and afterslip in the deep plate interface are limited to old subduction zones and correlate with the temperature condition of the deep plate interface. We suggest that the temperature conditions of the deep plate interface control the depth location, rheological properties, and development of the shear zone in subduction zones, and therefore, are responsible for the variations in the behavior of the deep plate interface in the subduction zones of various ages.The interseismic fast subsidence in a forearc region is limited to observations for the NEJP and the western Kuril subduction zones, both of which are subduction zones of an old oceanic lithosphere32, and Shibazaki et al.33 modification for viscoelasticity. The model treated the arc-perpendicular two-dimensional deformation assuming a plane strain condition. The model region was 1600 km in arc-perpendicular horizontal length, 800 km in vertical length, and 10 km in arc-parallel length , the actual slip rate, and the long-term steady-state plate convergence rate at the plate interface, respectively. ξ indicates the spatial coordinate value along the plate interface and t indicates the time. Because the cumulative long-term vertical displacement rate on the NEJP forearc is 0.1–0.2 mm/year and that around the volcanic front is up to 0.6 mm/year36, which are one order of magnitude smaller than those in the interseismic period  in the surrounding frictionally stable part of the plate interface11. The model approximately represents the fault creep on the frictionally stable part (fault creep part) by introducing a thin viscoelastic layer with very low viscosity along the plate interface following Hu et al.21 , 1936 (MW 7.519), and 1978 (MW7.519)   Fig. . Therefo19) Fig. . Therefoth) Fig. .38 , we used D9040, which is a deep cutoff depth above which 90% of the crustal earthquakes are located. We used the results of the seismic wave velocity observations and experiments on xenoliths under lower crust conditions in the NEJP41 to constrain the temperature in the lower crust under the island arc. We assumed local high temperature column with 10 km width under the volcanic front and considering effect of partial melting on viscosity based on several previous studies42. For the thermal structure of the oceanic lithosphere, we used the thermal structure model by McKenzie et al.43. The thermal structure below the oceanic lithosphere was assumed to be a mantle adiabatic thermal gradient. We assumed the mantle potential temperature to be 1315 °C43 for both the continental and oceanic mantles. We assumed that the continental crust is saturated in water. Water content in the oceanic asthenosphere and background water content in the continental mantle were assumed to be 810 H/Si ppm44. Water content in the oceanic lithosphere was assumed to be zero (dry)44. If the water content exceeded the saturated solubility of water in olivine45, we assumed that the water content in olivine is equivalent to the saturated solubility. The thermal structure, water content, and lithological units to construct the rheological structure of our model are shown in Fig. For the thermal structure, water content, and serpentinization in the continental mantle, we used the results of numerical simulations of the mantle corner flow considering dehydration, water transport, and serpentinization by Horiuchi & Iwamori51 for each layer in the model are listed in Supplementary Table 52 following Shibazaki et al.53. We assumed that the strain rate is 10−7/year based on the typical interseismic strain rate in the NEJP region54 and constant in time and uniform in space. Assuming the constant strain rate in time means assuming a Newtonian rheology. This assumption overestimates the viscosity early in the postseismic deformation, where the strain rate is much faster, i.e., the deviatoric stress is much larger, than that in the interseismic period. However, we focus on the crustal deformation during the earthquake cycle for long time scales, e.g., a hundred years. Therefore, this assumption does not matter much.We obtained the viscosity distribution by substituting the thermal structure, water content or water fugacity, pressure, and strain rate to the flow law of minerals. The flow-law parameters of the minerals obtained from rock experiments12). We assumed that the transition depth from the brittle regime  to the ductile regime (volumetric ductile deformation in the shear zone) is 70 km (Fig. 34. However, the viscosity, width, and shape of the shear zone are not well understood. Therefore, we tested different scenarios for the shear zone and selected the optimal one that best explained the observed vertical crustal deformation. The width increased from ~3 km to ~10 km and the viscosity linearly increased from 2 × 1017 Pa∙s to 2 × 1019 Pa∙s toward the deeper parts (Fig. 12.Deeper in the plate interface, the behavior shifts from frictional slip on the fault plane to volumetric and ductile deformation in shear zones (e.g., ref. km Fig.  based onrts Fig.  to repreSupplementary Information


From microbes to large predators, there is increasing evidence that marine life is shaped by short-lived submesoscales currents that are difficult to observe, model, and explain theoretically. Whether and how these intense three-dimensional currents structure the productivity and diversity of marine ecosystems is a subject of active debate. Our synthesis of observations and models suggests that the shallow penetration of submesoscale vertical currents might limit their impact on productivity, though ecological interactions at the submesoscale may be important in structuring oceanic biodiversity. Short-lived three-dimensional submesoscale currents, responsible for swirling ocean color chlorophyll filaments, have long been thought to affect productivity. Current research suggests they may not be effective in enhancing phytoplankton growth, but may have important contributions to biodiversity. BDisentangling whether submesoscale phytoplankton patches are generated by stirring of existing biological gradients, or are an active response to submesoscale physics, is therefore key to quantifying their global impact on marine ecosystems: are they nothing more than astonishing rearrangements, or do they reflect a complex response of the ecosystem to forcings that are difficult to observe, model and quantify? Submesoscale currents are continuously forming, moving, and dissipating over time scales ranging from days to weeks, making them particularly difficult to sample and model. Because biological response time scales are long enough to allow displacement of the biological response from the proximate physical forcing, submesocale forcings are even more difficult to relate to ecosystem dynamics. Satellite altimeters, used to provide global maps of upper-ocean currents, do not presently resolve velocity features smaller than about 100 km, and so entirely miss submesoscale currents. Numerical models require extremely fine grid resolution to explicitly resolve these dynamics, which is computationally challenging. And the logistical issues of sampling and modeling short time-scale, small spatial-scale dynamics are compounded by a lack of tools to quantify biological properties—particularly rates, such as growth and grazing—in a fast-moving frame of reference.Submesoscale phytoplankton features form through an assortment of often-concurrent, highly interconnected mechanisms that drive planktonic ecosystem reactions, affecting diversity, competition, and marine food-web structure. We propose here a conceptual framework to sort the mechanisms responsible for the formation of submesoscale patchiness, guide our synthesis of observations and high-resolution models, and focus our discussion of their biogeochemical and ecological implications. We begin by analyzing the ways in which submesoscale dynamics drive active responses in phytoplankton growth rates—the central topic of this review. For example, strong submesoscale vertical velocities may bring limiting nutrients into the euphotic zone, causing a rapid, local increase in phytoplankton growth rates Fig. . We then129, and from time series of moored current arrays in the early 1960s130. These indicated the presence of time-variable currents with amplitudes relatively large compared to their mean values. It took another decade for a shadow of the spatial structure of these disturbances to be revealed by the USSR POLYGON experiment and the US Mid-Ocean Dynamics Experiment MODE131. Both of these used tightly coordinated campaigns of ship-based observations and current-meter arrays to piece together a picture of “mesoscale” dynamics; both programs focused on relatively small regions in the North Atlantic. They revealed elliptical eddies with lateral scales of about 100–200 km and time scales of months.A discussion of submesoscale dynamics requires some historical and conceptual understanding of the mesoscales. Up through the 1950s, basic theory considered the ocean to be characterized by gyre-scale currents and meters-scale turbulence, with little in between. Oceanic “eddies” were first inferred from the erratic patterns of John Swallow’s trackable floats132, the spatial and temporal scales of mesoscale eddies are consistent with baroclinic instability  which converts the massive potential energy stored in the ocean’s sloping density surfaces—an energy source 1000 times as large as the kinetic energy of oceanic currents—into turbulent eddies. The dominant lateral scale of baroclinic instability is near the Rossby deformation scale, LD = NH/f, where N is the buoyancy frequency, f is the Coriolis frequency (which vanishes at the equator and is maximum at the poles), and H is roughly the depth of the thermocline. This is the scale at which rotational and buoyancy effects play equally important roles in the dynamics. Typical values of LD range from tens of kilometers in the polar oceans to hundreds of kilometers in the tropics.As first explained by Gill et al.133. Altimetric measurements show the spatial patterns of sea-surface height, from which currents can be estimated via geostrophic balance: on a rotating planet horizontal pressure gradients are approximately balanced by the Coriolis force, causing currents to flow around elevated regions . As technology improved, a global synoptic view of the mesoscale ocean at last emerged with the TOPEX/Poseidon program in the 1990s134. Observations from this satellite revealed eddies nearly everywhere , with scales of order 100 km, decreasing with increasing latitude, roughly proportional to but larger than the latitudinal scaling of LD. However, ocean variability on smaller scales is difficult to infer from current satellite-based altimetric instruments, which have an effective resolution near the deformation scale—about 100 km. Features seen in satellite altimetry are intrinsically dynamic, thus the absence of such global measurements at smaller scales is a severe limitation on our ability to separate dynamic from kinematic effects in submesoscale structures.Satellite altimetry, beginning with the short-lived SEASAT program in 1978, revolutionized oceanography, enabling synoptic views of entire ocean basins11: unlike mesoscale dynamics, submesoscale dynamics are not well-approximated by geostrophic balance, and so all the terms in the equations of motion are potentially important. Submesoscale dynamics are often closely linked with fronts. The purpose of this box is to give a brief overview of the physical forcings that lead to fronts and submesoscales, and the phenomenology of the flows themselves.Submesoscale motions, with lateral scales a decade or so below the mesoscale, are best defined in terms of dynamical balances135. All such submesoscale motions derive their energy from lateral density gradients in the surface ocean (see schematic). These density gradients are driven by atmospheric forcing: heat and fresh-water exchanges, and winds, which inhomogeneously mix the upper ocean. Horizontal straining by mesoscale eddies (red arrows) can squeeze these density contrasts into nearly vertical planes (gray surfaces), intensifying their geostrophic along-front, sheared currents (green arrows)—this is an example of frontogenesis. Fluid instabilities feed off these localized sources of potential and kinetic energy, generating submesoscale vortices and filaments that carry of some of this energy away. A sufficiently strong front will generate a cross-frontal ageostrophic secondary circulation—an overturning circulation directed in the sense of trying to flatten the density surfaces in the front (yellow arrows). Next we describe persistent fronts, submesoscale fronts, and a more complicated scenario that inextricably links mesoscale and submesoscale motions.Early evidence of dynamical features much smaller than the mesoscale came from sun-glitter in photographs taken during the 1970s Apollo Mission, which revealed predominantly cyclonic spiral eddies in the ocean, with scales of around 10–25 km136. This forcing is directly balanced by submesoscale symmetric instability, which takes energy mostly from the kinetic energy of the jet, and baroclinic instability, which converts the potential energy of the sloping density surfaces into large meanders and eddies. Associated with these highly energetic processes is a deep vertical velocity structure137 that reaches into the thermocline.Persistent fronts like those associated with the Gulf Stream and Kuroshio are locked in place by the coastal boundary and large-scale atmospheric forcing. Strong winter-time winds are directed nearly parallel to the axis of the jet, driving cold dense water southward across the front through Ekman forcing—a dynamical balance between surface friction, pressure, and Coriolis acceleration that moves upper ocean waters to the right of the wind in the Northern Hemisphere—keeping the density surfaces steep, the stratification low, and strengthening the jet138. In the presence of shallow summer-time mixed layers, these features do not carry much energy and thus have little impact on the local circulation. In the winter, on the other hand, the nearly vertical density surfaces associated with these fronts and filaments extend through the deep mixed layer, and so contain significant potential energy in addition to the intense kinetic energy of their cross-front currents. In the last few years, ample evidence141 indicates that this energy is converted to kinetic energy by mixed layer instability143: a submesoscale baroclinic instability with maximal growth at the mixed-layer deformation scale, LML = NMLhML/f, where NML and hML are, respectively, the mixed-layer buoyancy frequency and mixed-layer depth. In mid-latitudes in winter, with NML~10−3 s−1, hML~200 m and f ~2 × 10−4 s−1, this gives LML ~1 km, and like mesoscale baroclinic instability, the result is the formation of submesoscale vortices with sizes close to this scale143.The ubiquitous submesoscale density fronts and filaments that are continuously created at the ocean’s surface by mesoscale strain differ from persistent fronts like the Kuroshio and Gulf Stream. Unlike their more powerful cousins, submesoscale fronts are continuously forming, moving, and dissipating—they are not in a steady-state balance between forcing and dissipation at a fixed location. These fronts have associated cross-frontal secondary circulations that are generally confined to the vertically well-mixed upper layer of the ocean144. This mesoscale-driven process provides an alternate but potentially important pathway between the surface and interior25.Sufficiently steep density contrasts confined to the mixed layer can generate significant submesoscale energy, as above. But less-steep density surfaces that intersect the surface and reach deep into the interior can also generate significant energy at submesoscales, through a process called Charney-type baroclinic instability, which is likely widespread in the ocean145. The eddy kinetic energy produced in these processes likely enhances lateral turbulent mixing at the submesoscale146. Ultimately, submesoscale turbulent energy undergoes an inverse cascade, coagulating small vortices into larger features and ultimately increasing the energy of the mesoscale147 indirectly modifying the large-scale circulation.In all cases, submesoscale processes act against fronts, reducing mixed-layer depth, increasing stratification, and decreasing vertical mixing12 21, identified through Lagrangian analyses of mesoscale surface currents derived from satellite altimetry. More recently, intense submesoscale chlorophyll features in ocean color images have been statistically connected to the presence of temperature fronts in the North Pacific subtropical gyre22, another piece of indirect evidence for a submesoscale phytoplanktonic growth response to nutrient upwelling at submesoscale fronts.In mid-latitude and high-latitude, wintertime convective mixing brings nutrients into the euphotic zone, and these are consumed when light conditions become favorable, leading to strong seasonality in phytoplankton abundance with a pronounced springtime maximum; it is in only in summer that the environment is oligotrophic, i.e. that the euphotic layer is deprived of nutrients. In contrast, the subtropics are oligotrophic “ocean deserts”—despite having plenty of light year-round, because large-scale downwelling and shallow mixed layers limit nutrient supplies from the deep. In such nutrient-depleted oligotrophic environments, phytoplankton populations respond to upward nutrient inputs into the euphotic zone by submesoscale vertical velocities on time scales of hours to days, exhibiting locally increased growth rates and subsequent increased biomass23  do little besides mix the nutrient-poor surface layer23 Fig. . On the ers Fig. . This up30. This could be interpreted as support for the global importance of active responses to the submesoscale dynamics resolved by the high-resolution models. However, while improved model resolution allows stronger submesoscale fronts, it also leads to stronger persistent fronts that may account for much of the enhanced nutrient flux and increase in basin-integrated productivity  have consistently shown that productivity increased with increased model resolution over the first months to years of model integration31 showed that after more than 50 years the models diverged, with the high-resolution solution showing a deeper nutricline and shallower winter mixed layer in the subtropical gyre. This resulted, counter-intuitively, in less productivity in the subtropics, despite more submesoscale activity. This result illustrates a basin-scale ecosystem response to submesoscale forcing (productivity decrease) in opposition to the submesoscale response .Though they act at small scales, submesoscale dynamics appear to play a role in models of the basin-scale ocean circulation and tracer distribution. For example, comparing solutions from otherwise-identical high-resolution (1/54°) and coarse-resolution (1/9°) models32. However, over vast regions of the ocean, including the subtropical gyres, temperate zones, and high latitudes, wintertime mixed layers are already replete with nutrients through convective mixing. Thus in wintertime, submesoscale vertical velocities may not be effective in driving nutrient transport to the euphotic zone. In summer, shallow mixed layers are nutrient-depleted and phytoplankton growth rates can be enhanced by vertical nutrient fluxes. However, thin surface mixed layers create weaker summer submesoscale vertical velocities that may not penetrate down to the nutricline33. Satellite observations of chlorophyll in the North Pacific subtropical gyre tend to confirm the strong seasonality of the impact of submesoscale dynamics on phytoplankton biomass, showing a negligible effect in summer22. This annual cycle suggests that over large regions of the world’s ocean, submesoscale-driven vertical transport could be out of phase with the seasonal nutrient requirements of phytoplankton.There is also a strong seasonal component to the structure and intensity of submesoscale vertical velocities at higher latitudes: the horizontal buoyancy gradients that underlie vertical velocities at submesoscale fronts are strongest in deep wintertime mixed layers35, and that the presence or absence of high-frequency winds might be a critical factor influencing the depth reached by nutrient fluxes at fronts37. More systematic analysis is required to disentangle the relative contributions and scales of the fluxes associated with different varieties of front38, in presence or absence of winds.The seasonality and shallow penetration of vertical velocities at submesoscale fronts bring into question their efficacy for upward transport of nutrients, particularly in comparison to persistent fronts. Nevertheless, modeling studies suggest that vertical transport at submesoscale fronts could be significantly enhanced in the presence of variable windsN, equivalent to an increase in the number of grid points by a factor of N2, increases the computational cost by N3, because higher resolution also requires smaller time steps31. Since the 1970s when OGCMs were first developed, their horizontal grid resolution has always been constrained by the capacity of supercomputers. This capacity has increased tremendously over the last decade. While ocean grids used for the 5th Coupled Model Intercomparison Project (CMIP5) of the World Climate Research Program (WCRP) ranged between 1° and 2°, ocean grids with ~1/10° resolution are emerging in CMIP6. Mesoscales and submesoscales are thus smaller than the grid size of current ESMs and parameterizations are used to mimic their large-scale effects148. Reducing uncertainties linked to such subgridscale processes is one of the biggest challenges in ocean modeling149.OGCMs are computer codes that estimate solutions to the oceanic primitive differential equations of fluid motion and thermodynamics discretized on a spatial grid that covers the word’s ocean. These models form the ocean core of Earth System Models (ESMs). Their computational cost depends on the number of grid points. A decrease of the horizontal grid size by a factor of 150 is reproduced here: the model equations are solved over a rectangular ocean basin of ~20° × 30° with closed boundaries. The circulation and thermodynamics are forced by seasonally varying winds and heat fluxes at the sea surface. The model equations are integrated on three different horizontal grids of resolution 1°, 1/9°, and 1/54°, and with the same vertical resolution of 30 vertical layers, 10 of which are in the upper 100 m. Common features emerged from the three model solutions including a strong persistent front (marked by the white SST contour) extending toward the northeast, separating a warm subtropical gyre from a cold subpolar gyre. Strong horizontal turbulence emerged as the resolution was increased. At 1/9°, the turbulence appeared as the meandering of the persistent front and in the formation of a few mesoscale eddies. At 1/54°, sharp submesoscale temperature fronts were present and the meandering of the persistent front was more pronounced. In addition, the persistent front was progressively displaced southward when the resolution increased. Thus, resolving small-scale ocean processes can lead to substantial changes in large-scale patterns.Nevertheless, explicit resolution of submesoscale processes is achievable with regional or idealized models, which use the same computer codes as OGCMs but with reduced domains, allowing for finer grid cells. One example taken from Lévy et al.Importantly, the vertical velocity field close to the ocean surface was strongly modified both in its structure and intensity as the resolution increased. While at coarse resolution the main patterns in vertical velocity were coastal upwellings with subsidence in the center of the subtropical gyre, energetic fine structures in vertical velocity became more prominent as the resolution increased. These changes in SST and vertical velocity were also reflected in their spectral slopes , with much flatter spectra at 1/54° than at 1/9° resolution.One might question to what extent submesoscale processes are adequately represented at 1/54° resolution. One indication is provided by the power spectra, which show a sharp decrease of variance at scales smaller than 10 km (gray shading). This is the dissipative range for this model resolution: the effective model resolution is closer to 1/9° when the grid resolution is equal to 1/54°. Thus it appears that a submesoscale-resolving grid enables much better resolution of the mesoscale dynamics, providing the straining and stirring environment favorable for the emergence of submesoscale dynamics. This is clearly seen in the spatial spectra in the 10–100 km range: there is more energy with a 1/54° resolution than with a 1/9° resolution. The submesoscale dynamics, however, are still strongly damped at 1/54° resolution, which explains why this resolution range is often referred to as submesoscale permitting rather than submesoscale resolving.8 and horizontal151 dimensions. This resolution is not yet achievable with present-day computer capacities for regional biogeochemical studies; improved understanding will continue to depend on technological progress in high-performance computing.Recent studies suggest that an order of magnitude increase in resolution is required to adequately capture the full strength of the submesoscale dynamics, both in the vertical39. The downward branch of frontal circulation cells that reach below the base of the euphotic zone may be especially effective in this regard39. In eastern boundary upwelling systems and equatorial regions, for example, nutrients are abundantly supplied to the euphotic zone by large-scale upwelling, sustaining elevated levels of phytoplankton growth. In such systems, model simulations support the suggestion that the observed reduction of biological production in regions of elevated eddy kinetic energy might be due to the downward leakage of both phytoplankton and nutrients from the nearshore to the open ocean41. In the North Atlantic, where seasonal productivity is characterized by the occurrence of a strong spring bloom, the observational and high-resolution modeling study of Omand et al.42 suggests that the most favorable conditions for efficient export are during the transition from winter to spring.Submesoscale vertical velocities may also limit growth by moving phytoplankton and nutrients out of nutrient-rich environments43 by tilting existing horizontal density gradients to increase the vertical stratification of surface mixed layers45. This vertical-shear-driven increase in vertical stratification reduces the local turbulence; in mid and high latitudes (with most observations from the North Atlantic) the increased residence time of phytoplankton in the euphotic zone leads to early local phytoplankton blooms compared to surrounding, actively mixing waters46. The horizontal scale of such changes in vertical turbulence is set by the submesoscale circulation; this leads to submesoscale patches of enhanced phytoplankton growth rates, which can ultimately form submesoscale patches of phytoplankton earlier than the regional average. Such early, local blooms may not change the seasonal productivity budget47 but presumably affect the seasonal species succession and local community structure.Several field and modeling studies have shown that submesoscale dynamics may also increase phytoplankton residence times in the euphotic zone of deep mixing layers5.Finally, submesoscale vertical velocities also have the potential to penetrate into the deep chlorophyll maximum, displacing low-light-adapted cells upward and high-light-adapted cells downward, altering the community structure at the base of the euphotic zone, and potentially altering the net growth rate thereWe now consider the complementary issue of the generation of submesoscale biological features through passive stirring. Stirring by larger-scale currents can readily generate horizontal concentration gradients at scales much smaller than the flow itself Fig. , complicConsider an example of a few smooth mesoscale vortices a few hundred kilometers in diameter, with no dynamic features at smaller scales. A tracer patch in the surface mixed layer stirred by this current will be stretched out in one direction, and laterally compressed in the other by the strain between eddies Fig. . The thi48  indicate more variance at small scales than steeper slopes . The spectrum of passive tracer variance, with no injection or removal and initially spread over a region large relative to the eddy scale, will depend on the spectrum of the velocity field that is stirring it. Mesoscale flows with little variance at submesoscales (thus a steep spectrum) will tend to produce tracer variance spectrum with a slope near k−1—this is the well-known Batchelor cascade52. Counter-intuitively, a velocity field with a great deal of submesoscale variability . Thus, under the assumption of weak biological reactions, spectral slopes of the variance of biological tracers around k−1 could be indicative of stirring by mesoscale flows, while slopes around k−2 might indicate local stirring by submesoscale flows.The rearrangement of spatial gradients by stirring can sometimes be detected in the different slopes of the variance spectra  of the underlying flows and the property being stirred. Oceanic velocity power spectra often exhibit power-law behavior, with spatial variance proportional to 56. Phytoplankton spectra are often found to exhibit power-law scaling, with spectral slopes between k−2 and k−1 over mesoscale to submesoscale length scales , suggesting that passive stirring can create submesoscale phytoplankton variability by deforming large-scale regional gradients61. This is possible because the persistence time scale of phytoplankton surface blooms, 3–6 months on average61, is similar to the physical time over which stirring transfers variance to small scales62. A complexity, however, is that phytoplankton variability can also be created at small scales through active and reactive processes, yet still exhibit power-law scaling of spatial variance63. This complexity is reflected, for instance, in the strong temporal and regional variability of spectral slopes of ocean color variance64; assigning particular mechanisms to specific values of plankton spectral slopes is therefore often ill-advised. Moreover, an important caveat is that the spectrum alone does not contain information about the coherence of the underlying patchiness , gliders, and rapid CTD profilers  has begun to reveal the richness of the three-dimensional structure of biological properties in situone Fig. . The coints Fig. ; the pat69 suggested an origin in the euphotic zone, submesoscale subsurface patches have also been observed originating well below the surface. The formation of a subsurface thin layer, far example, was inferred from an initial phytoplankton/salinity patch at ~125 m depth, with cross-patch and along-patch horizontal scales of ~100 m and 75 km, respectively71. Vertical shearing of the horizontal patch gradients by low-frequency internal waves displaced the top and bottom of the patch relative to each other, forming a layer that tilted and thinned from 25 to 12 m over the course of ~20 h. Though the origin of this low-salinity/high-fluorescence layer is unknown, it is clear that stirring and shearing by the ambient flow created submesoscale horizontal and vertical structure from larger-scale gradients of the original phytoplankton patch72.Though the orientation and vertical gradients of chlorophyll in the submesoscale patches observed by Pietri et al.40. These downward motions will deform tracer gradients—temperature, salinity, nitrate, and phytoplankton—generating interleaved layers. Such interleaved layers in cross-frontal sections, with slopes often steeper than those of isopycnals76, can also form through horizontal deformations of existing plankton patches that extend subsurface, with no need to invoke vertical velocities.It is generally difficult to tease apart the relative contributions of along isopycnal stirring vs. purely horizontal stirring in forming subsurface patches. As with horizontal stirring, by deforming larger-scale gradients, the downward branch of the circulation at submesoscale dynamic fronts Box  will creWhile submesoscale phytoplankton patches can be formed by active increases in growth rate resulting from locally favorable environmental conditions, or passive stirring of existing gradients, not all members of the community respond identically to the underlying physical forcing. We would thus expect to observe altered community structure. These reactions could result from differential growth rates or different behaviors  within the phytoplankton community, or from gradients in mortality rates as predators respond to the phytoplankton distribution, and could thus propagate up the trophic chain to zooplankton and larger predators.One useful measure of the reaction of planktonic communities to physical and biological forcings is their diversity. In terrestrial ecology, diversity is usefully divided into α-diversity and γ-diversity: α-diversity refers to the number of species within a local habitat, while γ-diversity describes the total number of species across multiple habitats in the region. In the ocean it can be difficult to define habitat and region. Here we will consider habitats to be waters that contain similar communities—typically determined by hydrographic properties , light availability, nutrient concentrations, and nutrient fluxes. For example, the colored patches in Fig. 79. However, submesoscale nutrient pulses might be expected to give rise to submesoscale community patchiness  behaviors cause them to accumulate91. For floating organisms, these patches form within submesoscale downwelling regions; the surface patches have subsurface extensions that form stronger horizontal gradients with stronger floating speeds91.Phytoplankton exhibit a variety of behaviors that allow them to move relative to the water, from vertical migration to avoid predators4, plankton motility , diffusion63, and active nutrient fluxes92 can all decorrelate phytoplankton and zooplankton distributions and lead to nonlinear changes in the grazing of phytoplankton by zooplankton95. Similar to phytoplankton, gradients of zooplankton are often  associated with fronts. Composite analyses of hundreds of glider transects across fronts in the California Current System, for example, showed persistently elevated acoustic backscatter  on the cold sides of the fronts98. The abrupt change in acoustic backscatter would seem to be indicative of abutment of two dissimilar zooplanktonic communities at the fronts, suggestive of increased γ-diversity simply through passive stirring of distinct habitats. However, taxon-resolving sampling has shown distinct that submesoscale zooplankton communities form at fronts101, presumably in reaction to the frontal dynamics, indicating front-enhanced zooplankton α-diversity.Stirring102. In general, however, the magnitude of these non-linear interaction effects remains poorly quantified; they are particularly difficult to assess from observations, requiring a synoptic description of phytoplankton and zooplankton distributions, together with spatially and temporally resolved measurements of their growth, grazing, and mortality rates103.In a submesoscale patch in the North Pacific subtropical gyre, lateral stirring led to a large-scale diffusion which decreased the encounter rates of phytoplankton and zooplankton, thereby reducing the grazing pressure on the phytoplankton100 are indicative of locally enhanced zooplankton production, presumably in response to enhanced phytoplankton growth fueled by increased nitrate fluxes at the front83. Though identifying the proximal cause of the enhanced nitrate fluxes is difficult, it is clear that such forcings propagate through the ecosystem, creating distinct local communities with enhanced α-diversity and γ-diversity in the frontal region.The enhanced abundances of eggs, nauplii, and copepodids sometimes observed at fronts104, albacore tuna105, whales106, elephant seals107, frigatebirds109, gannets110). The reasons why predators target frontal structures remain unclear and could have a variety of origins, including foraging and entrainment effects62, and bioenergetics105. One impediment to a better understanding of how submesoscale patchiness extends up the trophic web is the lack of information on the submesoscale distribution of intermediate-level fish that prey upon zooplankton and larval fish, and are foraged by top predators. Frequency-differencing echograms have revealed spatial coherence between top predators and forage fish in the submesoscale range111, and open the way to a better understanding of the reactive responses of ecosystems at fronts.However, while plankton mainly drift with the ocean currents, larger organisms are motile and might be predicted to have a weaker relationship with local physical forcing. Nevertheless, thanks to the development of miniaturized animal tracking devices, associations of top predators with fronts have been reported for many taxa  to contribute significantly to global ocean biological dynamics.Field, laboratory, and modeling studies have provided extensive evidence that submesoscale oceanic currents affect not only phytoplankton concentrations, but also plankton diversity and the entire marine trophic web. Still, the spatial scales of submesoscale phenomena pose an ongoing, observational challenge, particularly when it comes to sampling biodiversity or biogeochemical fluxes. In addition, due to computational limitations, the grid resolution of global models is too coarse to assess the contribution of submesoscale dynamics to biogeochemical budgets. Today, we can only speculate on how much these dynamics affect global biogeochemical cycles, marine productivity, and ocean biodiversity. The categorization of the processes into active, passive, and reactive used in this review, although imperfect, is intended to provide a conceptual framework to guide our speculation and will hopefully open the path for more quantitative approaches in the future. Based on our synthesis, we conclude that submesoscale dynamics might not be as important as previously thought for marine productivity, but might be more important than anticipated for plankton diversity and trophic web dynamics. We want to stress that our arguments, discussed in the following, are more qualitative than quantitative.112. In addition to this modeling bias toward deep-reaching persistent fronts, there may have been a bias toward in situ observations at such fronts because they are more predictable than submesoscale fronts.While passive stirring mainly redistributes constituents, active dynamics have the potential to strongly affect biogeochemical fluxes. This raises the question of how effective submesoscale vertical transport processes are in mediating net fluxes of nutrients within the euphotic zone. Early modeling studies of vertical nutrient transport at fronts explored persistent fronts where vertical velocities reached hundreds of meters below the surface, bringing them well into the deep nutrient pool. Such studies suggested that fronts could make a large (20–50%) contribution to total biogeochemical fluxes32, and their associated vertical velocities tend to confined to the mixed layer25. Such motions are thus strongest when phytoplankton growth could be limited by the lack of light through short residence times in the euphotic zone, and weak later in the season when growth is nutrient-limited; their contribution may be significant during the transition period at the onset of the spring bloom. While this is just one of many possible dynamical processes that characterize the submesoscale, it suggests that the combination of shallow submesoscale vertical fluxes and their phasing relative to phytoplankton growth cycles over vast open ocean oceanic regions may make them inefficient at driving reactive biological responses, and thus less important in global budgets than persistent fronts.A prevalent feature of submesoscale dynamics is their perturbation through mixed-layer instability Box . These i113—is not sufficient to quantitatively evaluate their potential for enhanced nutrient fluxes. Regional surveys using moored arrays, gliders, and high-resolution towed instruments, such as the OSMOSIS project114 have greatly improved our understanding of submesoscale processes; however, one cannot confidently extrapolate the results of a North Atlantic study to the global ocean. The large array (3800 as of today) of profiling Argo floats that populates the word’s ocean providing continuous monitoring of the surface ocean vertical structure is a first step; however, this array undersamples both mesoscale and submesoscale features.Quantifying the importance of vertical nutrient transport at ephemeral and persistent fronts will require better global sampling and statistics. Unfortunately, the surface detection of fronts —which is feasible at the global scale with sea-surface temperature and altimetry satellite data48. However, mesoscale stirring can enhance γ-diversity by bringing formerly geographically distinct habitats and communities close together at frontal regions, increasing the local number of habitats. This simple consideration has started to allow us to detect γ-diversity hot-spots using ocean color satellites116. In addition, the presence of unique communities at fronts—which are sites of enhanced submesoscale physical forcing—may also reflect the effects of submesoscale dynamics on phytoplankton biomass and community structure at fronts. Such active responses of the planktonic community to submesoscale transports will affect both α-diversity and γ-diversity by creating new habitats at the fronts. Again, because of the logistical issues mentioned earlier, most in situ evidence of patterns in α-diversity at fronts comes from measurements at persistent fronts with strong nutrient fluxes. The deployment of continuously sampling underway systems offers the potential to better explore subsurface submesoscale patchiness in planktonic α-diversity.Passive processes such as mesoscale stirring do not, in principle, change planktonic α-diversity, as habitats are simply advected and distorted by the ambient flow117 and associated horizontal diffusivities118 show strong contrasts over broad (>1000 km) regions, suggesting a similar scale of variability for ecosystem diversity. The second characteristic is that stirring and mixing of communities that were initially apart sets them in competition with one another. When the mixing time scale is faster than the competitive exclusion time scale, such stirring may be expected to increase α-diversity and γ-diversity. The degree to which different habitats are being constantly brought together, mixed and modified by the rapidly evolving submesoscale flow will determine the outcome of species competition over longer time and larger space scales.Investigations of the relative roles of the different processes—stirring, mixing, nutrient supply, stratification, swimming—in shaping planktonic biodiversity at the submesoscale are very preliminary, and are areas of active research. Nevertheless, two characteristics lead us to speculate that these processes play crucial roles in shaping biodiversity over much broader spatial and temporal scales than the immediate frontal region. The first characteristic is the constant submesoscale perturbation of marine ecosystems: organisms that succeed in this environment must be adapted to these rapid fluctuations. Thus the environmental variability is a key characteristic, and determinant of the community structure. Geographical variations in eddy stirring119.To distinguish among active, passive, and reactive processes requires high-frequency, high-resolution, 3D sampling of physical, chemical, and biological variables. Measuring down to submesoscale resolution in the field requires significant infrastructure, such as multiple ships, gliders, or large swarms of drifting floats120. The greatest biological oceanographic challenge is to quantify community composition, physiological rates, and trophic interactions with 3D submesoscale resolution.The greatest physical oceanographic challenge is to estimate submesoscale vertical velocities. Direct measurements are difficult due to the presence of inertial motions and internal waves at similar scales. Indirect estimates rely on approximations; these provide limited insight into the vertical extent of submesoscale-driven fluxes that determines their biogeochemical effectiveness124. Real-time estimates of stirring from satellite altimetry can be useful for guiding adaptive sampling strategies during ship-based field campaigns to observe the evolution of tracer fields125. Combined Eulerian/Lagrangian sampling schemes in the field, such as making measurements while following drifters, along with supplementary transect information126, can help in tracking the evolution of biological communities as they are advected away from the submesoscale physical features that formed them. The anticipated 2021 launch of the new, high-resolution Surface Water and Ocean Topography  satellite altimeter mission may provide a significant new remote-sensing tool for resolving Lagrangian trajectories with a better resolution than current altimeters128.Because fronts are regions of strong horizontal shear, vertical transport and horizontal stirring are strongly linked in the upper ocean. Thus, through this phase relationship, passive, active, and reactive processes are highly interconnected. It follows that it is difficult to determine whether a submesoscale phytoplankton patch formed as an active response to submesoscale flow or is simply the result of stirring of a larger patch that formed in response to larger-scale processes. An improved understanding of submesoscale processes will thus rely on our ability to reconstruct the Lagrangian histories of submesoscale patches from observations that are often EulerianThe contributions of submesoscale physical forcing to marine ecosystem dynamics remain unconstrained and uncertain. We are confronted with a problem at the interface of two fields—ocean physics and ecology—that lies at the frontier of knowledge in both fields, with new interaction mechanisms still being identified and their relative importance being evaluated. The strong vertical velocities associated with submesoscale fronts in the upper ocean would appear to position them to have profound biological effects. However, the vertical penetration and seasonal phasing of such dynamics may limit their efficacy in stimulating local phytoplankton growth. The considerable developments in modeling and instrumentation that have occurred over the last decades have helped in quantifying the occurrence of submesoscale biological variability. However, we will require coordinated, well-designed interdisciplinary sampling programs to disentangle the physical and biological dynamics, and in particular, the relative contributions of mesoscale and submesoscale processes. These programs must investigate both the immediate, local biological responses to submesoscale physical forcing, as well as how such responses emerge to affect global processes, such as biogeochemical cycles and biological diversity.


Smoking is a major public health concern. In Japan, a 12-week standard smoking cessation support program is available, however, its required face-to-face visits are a key obstacle in completing the program. Telemedicine is a useful way to provide medical treatment at a distance. Although telemedicine for smoking cessation using an internet-based video system has the potential for ensuring better clinical outcomes for patients with nicotine dependence, its efficacy is unclear.The aim of this study is to determine the efficacy and feasibility of a smoking cessation support program using an internet-based video system compared with a face-to-face program among patients with nicotine dependence.CureApp Smoking Cessation (CASC) for both arms, which consists of the CASC smartphone app for patients and a Web-based patient information management system for clinicians with a mobile carbon monoxide checking device. The primary endpoint will be the continuous abstinence rate (CAR) from weeks 9 to 12. Secondary endpoints will be: (1) the smoking cessation success rate at 4, 8, 12, and 24 weeks; (2) CAR from weeks 9 to 24; (3) changes in scores on the mood and physical symptoms scale and 12-Item French Version Of The Tobacco Craving Questionnaire; (4) Kano Test for Social Nicotine Dependence scores at 8, 12, and 24 weeks; (5) time to first lapse after the first visit; (6) nicotine dependence and cognition scale scores at 12 and 24 weeks; (7) usage rate of the CASC; (8) qualitative questionnaire about the usability and acceptability of telemedicine; and (9) presence of product problems or adverse events.This study will be a randomized, controlled, open-label, multicenter trial. Participants randomized to the intervention arm will undergo an internet-based smoking cessation program, whereas control participants will undergo a standard face-to-face program. We will use the We will recruit 114 participants who are nicotine-dependent but otherwise healthy adults from March to July 2018 and follow up with them until January 2019 (24 weeks). We expect all study results to be available by the end of March 2019.This will be the first randomized controlled trial to evaluate the efficacy and feasibility of an internet-based (telemedicine) smoking cessation support program relative to a face-to-face program among patients with nicotine dependence. We expect that the efficacy of the telemedicine smoking cessation support program will not be clinically worse than the face-to-face program. If this trial demonstrates that telemedicine does not have clinically worse efficacy and feasibility than a conventional face-to-face program, physicians can begin to offer a more flexible smoking cessation program to patients who may otherwise give up on trying such programs.University Hospital Medical Information Network Clinical Trials Registry: UMIN000031620; https://upload.umin.ac.jp/cgi-open-bin/ctr_e/ctr_view.cgi?recptno=R000035975DERR1-10.2196/12701 Smoking is a major public health concern responsible for a diverse range of diseases, such as cancers, heart disease, cerebrovascular disease, and chronic obstructive pulmonary disease . In JapaA smoking cessation support program is widely available in Japan for patients with nicotine dependence. This program is agreed to be a standard program by related academic societies and reimbursed by national health insurance . This 12Recently, telemedicine—or the delivery of health care by remote health care providers via communication technologies—has come to be regarded as a useful method of providing medical care to patients. Telemedicine minimizes a patient’s burden of traveling to a health institution and waiting for consultations with their physicians. In addition, it can lead to improved clinical outcomes for patient quality of life  and overTelemedicine might also be suitable for delivering a smoking cessation support program, as 71.7% of the patients with nicotine dependence in Japan are under 60 years of age and 66.7% of patients are men, both of who are demographics who are unwilling to spend half their day visiting a clinic for treatment . A well-CureApp Smoking Cessation (CASC) is a novel smartphone app paired with a mobile CO checking device that was developed by CureApp Inc, Tokyo, Japan, to improve treatment success of the smoking cessation program for patients with nicotine dependence [The pendence ,20. CASCpendence .Therefore, telemedicine might have the potential to enhance the smoking cessation success rate and other clinical outcomes among patients with nicotine dependence by helping them achieve easier access to smoking cessation programs. However, it remains unclear whether the smoking cessation program using an internet-based video system is effective and safe relative to a conventional face-to-face program.This is a proof-of-concept study aiming to determine the efficacy and feasibility of a smoking cessation support program using an internet-based video system compared with a face-to-face program, both of which use the CASC, among patients with nicotine dependence.This study will be a randomized, controlled, open-label, multicenter trial. The study will be conducted in 4 community clinics located in Tokyo, Japan: Tokyo-Eki Center-building Clinic, Shinjuku Research Park Clinic, Fukuwa Clinic and Miyazaki RC Clinic. Participants in both arms will undergo the smoking cessation support program used in Japan. For the telemedicine arm, the entire program will be conducted remotely via an internet-based video system except for the first registration visit , whereasWe will recruit nicotine-dependent but otherwise healthy adults from March to July 2018. We plan to follow them up until January 2019 . We will include the participants who are diagnosed as nicotine dependent, have smoking history of Brinkman index (BI) >200, and have a determination to quit smoking immediately. Then, we will exclude those participants with severe mental illness and those with any smoking cessation aid, besides prescribed medication at clinics before or after enrollment, based on the subjective questionnaire on the enrollment visit  and historical control groups  is 24% ,23. AccoFor randomization, we will use the block randomization method (with 4 blocks) with a 1:1 allocation ratio. Participants will be allocated in this way to either the intervention (telemedicine) or control (face-to-face) arm. The randomization will be performed at the time of participants’ registration by a staff member using a computer-generated random sequence for each participating clinic.Participants randomized to the intervention  arm will receive an internet-based support program for smoking cessation using the CASC. In contrast, participants randomized to the control (face-to-face) arm will receive the conventional face-to-face standard smoking cessation support program, also using the CASC.The standard smoking cessation support program in Japan consists of 5 clinic visits over 12 weeks, including doctor consultation and exhaled CO check at a registered institution or clinic [Patients in the telemedicine arm will undergo the standard smoking cessation support program with the CASC. However, instead of visiting the clinics, they will meet their physicians to receive counseling via a video-conference system and a standardized telemedicine platform app, in accordance with the guideline for telemedicine in Japan . As in tThe CASC consists of the following: (1) a CASC smartphone app for patients with nicotine dependence, (2) a mobile CO checker for patients, and (3) a Web-based patient management software for health care providers . ParticiThe CASC will be delivered by the study sponsor, CureApp Inc, Tokyo, Japan, and will be carefully managed to avoid being used outside the current study at each institution or clinic. A prescription code specific to each practicing institution or clinic is required to activate the entire system issued by the sponsor, and the sponsor regularly (at least once a year) performs an inventory and confirms the devices are not used outside the research.The primary endpoint of this study will be the CAR from weeks 9 to 12. We hypothesize that the telemedicine group will not show clinically worse CAR from weeks 9 to 12 than the control group (threshold of 15%). The CAR is defined as the percentage of individuals continuously not smoking during the specified period. We will also evaluate the following secondary endpoints: (1) smoking cessation success rate at the points of 4, 8, 12, and 24 weeks; (2) CAR from weeks 9 to 24; (3) changes in the scores on the mood and physical symptoms scale (MPSS) ; (4) KanThe NDCS is a scale for measuring nicotine dependence and cognitive impairment among smokers. It consists of 8 items, each rated on a 4-point scale (ranging from 0 to 3). A higher total score  implies more severe dependency or cognitive impairment.The follow-up schedule is shown in P values from 2-sided tests .We will compare all endpoints between the telemedicine and the face-to-face arms. Baseline characteristics will be described by means and standard deviations, or medians and interquartile ranges (for continuous variables), or proportions . We will analyze the primary outcome using the full analysis set (excluding participants who violate the abovementioned inclusion or exclusion criteria). For all outcomes, summary statistics and group difference measures  will be presented with 95% CIs and Participants in this study were not involved in the design, recruitment, conduct, or assessment of the study.We will conduct this study in compliance with the Declaration of Helsinki, Medical Device Good Clinical Practice guidelines, and all other applicable laws and guidelines in Japan. This protocol and related documents of all the participating clinics were approved by the Tokyo-Eki Center-building clinic institutional review board. We will always use the latest version of the approved documents. We used the SPIRIT reporting guidelines for submitting this protocol to the journal . We willAs of November 2018, 115 participants with nicotine-dependency were already recruited and will be followed up until January 2019 (24 weeks). We expect all study results to be available by the end of March 2019.This will be the first randomized control trial to evaluate the efficacy and feasibility of an internet-based video-assisted smoking cessation support program compared with a face-to-face program in patients with nicotine dependence. We expect that the efficacy of the telemedicine smoking cessation support program (in terms of CAR from weeks 9 to 12) will not be clinically worse than the face-to-face program.Recent advances in mobile technologies have dramatically changed nearly every aspect of our daily lives. Internet services and smartphone apps play a particularly key role because they help us directly communicate with each other even when apart. Nowadays, smartphone and internet-based video communication have been considered useful tools for improving accessibility to smoking cessation programs, thereby improving the outcomes of patients with nicotine dependence. Scott-Sheldon et al demonstrated in their meta-analysis that a mobile phone short messaging service intervention led to substantial benefits for smoking cessation . MoreoveConsidering that the aim of this study is to compare different ways of delivering a standard 12-week smoking cessation program, a CAR for the last 4 weeks of the treatment period would be the ideal endpoint. It would also be appropriate to compare those 2 groups for CAR from weeks 9 to 12 because a previous phase III clinical trial on smoking cessation aid medications, such as varenicline, evaluated CAR for the same period to assess the efficacy .In this study, we will use the CASC for both arms as it serves to complement the standard smoking cessation program. A previous single arm, prospective pilot study showed that the CASC, in addition to the standard program, led to significantly higher CAR from weeks 9 to 24 when compared with a historical control group . CurrentThis study has several limitations. First, this study will be conducted in multiple centers, but participants will be limited to residents in an urban area in Tokyo, Japan, which may limit the generalizability of the study findings. We might need to conduct further investigations to apply the study findings to other cohorts. Second, participants in both groups are going to use the CASC, but this system has not yet been cleared by the Pharmaceuticals and Medical Devices Agency. Therefore, the outcomes for each group must be carefully interpreted because they might be the result of mixed effects of the study intervention and the CASC on the standard smoking cessation program. Nevertheless, since the program in Japan requires evaluation of exhaled CO concentration at each visit, supplying participants with the CASC is the only realistic and validated solution to conduct this study at present. Third, the primary physicians can prescribe treatment drugs, either varenicline or nicotine patch, to support the patients in quitting smoking according to a physician’s discretion. Although the institution is an allocation factor for equal randomization, the baseline characteristics of the drug assignment might not be matched between the 2 arms, which could cause the biased results.In conclusion, we will test whether an internet-based smoking cessation support program does not have clinically worse efficacy and feasibility than a face-to-face smoking cessation program among patients with nicotine dependence. If we obtain the expected findings, physicians can offer a more flexible standard smoking cessation program to patients who might otherwise give up on the idea of trying such programs. In addition, this study could be a milestone to expand the scope of the effective smoking cessation support program, which might contribute to an improvement of public health and reduction of medical expenses.