A study of the simulated climatological January mean upwelling in the northwestern Gulf of Alaska

In this research, we studied the upwelling in the northwestern Gulf of Alaska using the climatological January mean and data from the output of the Ocean General Circulation Model for Earth Simulator (OFES2). Specifically, we analyzed the upwelling in the regions where the Alaska Coastal Current (ACC) flows out of the Shelikof Strait (especially the part to the west of Kodiak Island) and where the ACC and the Alaskan Stream (AS) are confluent. In both regions, strong geostrophic currents and downwelling-favorable wind predominate in winter. Furthermore, there are freshwater discharges along the Alaskan coast and an observed mean current vertical shear in the ACC. We revealed that when the internal water stress is larger than the wind stress inside the study regions, this could be decisive in terms of the local horizontal velocity divergence and further upwelling, even if the region is away from the coast and lacks upwelling-favorable wind conditions. Geostrophic stress is part of the internal water stress and is a product of the geostrophic current shear (due to the thermal wind relation) and the vertical viscosity coefficient. The analysis indicated that a front with a large geostrophic stress may act as a “virtual wall” and contribute to local upwelling within a depth of approximately 100 m in the study regions. This process could provide a heuristic for understanding the distribution of pollock in the areas during February and March, which corresponds to the simulated upwelling region.


Introduction
Coastal upwelling fertilizes the euphotic zone through the food web, which is important for marine ecosystems (Kämpf and Chapman 2016).Its formation is generally explained by the Ekman theory (1905) due to the combination of an upwelling-favorable wind and a unilateral boundary.The northwestern Gulf of Alaska (GOA) is a regime dominated by a downwelling-favorable wind.Ware and Thomson (2005) revealed that in the Kodiak region (Fig. 1), the annual mean chlorophyll-a concentration and the long-term annual yield of resident fish exhibit a high covariation, which implies a rich primary production in this domain.However, the mechanism by which necessary nutrients for primary production (such as iron and nitrogen) advect onto the shelf and upwell to support the spring bloom remains an unresolved question (posed by Stabeno et al. 2004 andLadd et al. 2005).
Up-canyon flow has been observed inside the troughs to the southeast of Kodiak Island (Ladd et al. 2005).In terms of a wind effect, Stabeno et al. (2004) proposed that the wind stress curl associated with a coastal barrier jet (Parish 1982;Loescher et al. 2006) may explain the seaward (primarily inshore of the shelf break) upwelling near the eastern and northern GOA.The intensified wind stress near the coast generates a positive wind stress curl that drives the seaward upwelling.In this case, an average Ekman pumping of approximately 10 m/day could be generated under conditions comprising a nearshore wind speed of 14 m/s ( ∼ 0.3N∕m 2 as a wind stress) and an offshore wind speed of 10 m/s (~ 0.2N∕m 2 as a wind stress)across a width of 20 km.
Although these mentioned studies are helpful in terms of understanding the upwelling to the east and south of Kodiak Island, there are few studies on the upwelling inside the Shelikof Trough, which is to the west of Kodiak Island.
Moreover, it is difficult to collect satellite observations of this region in winter due to the dense cloud coverage.
In this study, two regions located in the western GOA were investigated with a simulated climatological January mean.One of these regions is to the west of Kodiak Island.We mainly focused on regions with a water depth of 100 m around the southern bank and away from the coast.The classic Ekman theory is insufficient in terms of explaining the potential upwelling in this region, in which the Alaska Coastal Current (ACC) dominates and shifts to the southwest of Kodiak Island (please refer to the satellite-tracked drifting buoys in Fig. 10 in Spitz andNof 1991 andStabeno andHermann 1996).Schumacher and Reed (1980) first revealed the ACC, which is driven by the wind and cross-shelf pressure gradient.The other region of interest in our study was the confluence of the ACC and Alaska Stream (AS).The AS is the western boundary current of the Alaskan Gyre, and it responds to the wind stress curl.The current velocity can be as strong as 1m∕s (Reed 1984).The two study regions are marked as A1 and A2 in Fig. 1.
Wind in the studied region is mainly affected by the Aleutian Low.The tracks of this low are changeable, causing variations in the local wind.In the climatological mean, there is a southwestward wind in the winter season and a weak northward wind in the summer and early fall seasons (Fig. 15, Pickart et al. 2009).In winter, the surface wind speed is approximately 2 m/s with an enhanced intensity around the top of the GOA (Fig. 3b, Pickart et al. 2009).
Abundant zooplankton (Ware and McFarlance 1989) and pollock aged ≥ 2 years (Incze et al. 1989, in March) have been observed in the vicinity of the A1 study region.
Here, upwelling could be helpful for local nutrient supply, and pollock distribution is based on the food web.The barrier jet proposed by Stabeno et al. (2004) may not be adequate to explain the possible upwelling in this region due to the wind stress present in winter (~ 0.05N∕m 2 ), which is weaker than that around the northeast (~ 0.2 N ∕m 2 ).Moreover, there is no near-coast amplified wind speed signal (Fig. 5c).
Combining the physical properties introduced in the following section, we consider that the study regions are candidates for adopting the process of reversed Ekman overturning (see Yuan and Mitsudera 2023) and could be responsible for local upwelling.Reversed Ekman overturning is geostrophic current vertical shear due to the thermal wind relation inside a coastal density front that can modify (or reverse) Ekman transport (Cronin and Kessler 2009;Chen and Chen 2017;Yuan and Mitsudera 2023), allowing transport to the left in terms of the wind direction in the Northern Hemisphere.In addition, this process can reshape the upwelling.The stress due to vertical shear of the geostrophic current is termed geostrophic stress, which is part of the internal water stress.To verify this hypothesis and study the upwelling system in the northwestern GOA, we conducted detailed analyses.
At the western end of the Shelikof Strait (Fig. 1), the baroclinicity of the ACC was observed in the climatological winter season, with a surface current of ∼ 0.35m∕s and a vertical current shear u z of ∼ 0.0013s −1 from the surface to a depth of ~ 240 m at the mooring station SS1 (Stabeno et al. 2016).
Across the AS, the observed surface salinity between February and March, 1980(Fig. 6a of Reed 1984), had a range of 32.0-32.6 psu.This was larger than that to the south of Kodiak Island (upstream of the AS), where the surface salinity across the AS ranged from 32.4 to 32.6 psu.This difference in the salinity gradient on the up/ downstream of the AS implies the impact of ACC outflow from the Shelikof Trough on A2 and the existence of a density front.This information is necessary to form a reversed Ekman overturning.
In this study, we explored the impact of internal water stress (partially due to geostrophic current shear) on local upwelling in the two study regions.The remainder of this paper is organized as follows: in Section 2, we introduce the data source and operation.In Section 3, we present the climatological January mean patterns of the ACC and AS and reveal the cross-shelf overturning in these regions.A dynamical interpretation and an analysis are also introduced in this section.In Section 4, we summarize the results and discuss the limitations of the data analysis and possible future advancements.

North Pacific submesoscale-permitting simulation
The OFES2 (Sasaki et al. 2020) is an upgrade of the quasiglobal Ocean General Circulation Model (OGCM) of the OGCM for the Earth Simulator (OFES) based on the Modular Ocean Model (MOM3).The OFES has been widely employed and has effectively elucidated the basin-scale eddy phenomena and the eddy/large circulation interaction (Masumoto et al. 2004;Masumoto 2010).The OFES2 permits submesoscale circulations in the North Pacific (Sasaki et al. 2022) and has a finer regular horizontal grid with a resolution 1∕30 • × 1∕30 • in a domain of 100 • Eto70 • W and 20 • Sto68 • N , which originates from the temperature and salinity fields in 1991 of the quasi-global OFES2 with a resolution 1∕10 • × 1∕10 • .The model has 105 vertical z-levels.
The vertical grid size in a shallow layer (down to ~ 140 m) is 5 m, while that down to ~ 250 m is 10 m.Moreover, the grid's vertical size gradually increases with depth (Sasaki et al. 2020).The turbulence closure scheme proposed by Noh and Kim (1999) was adopted to simulate the eddy viscosity and diffusivity in the mixed layer.The OFES2 includes tidal adjustment mixing parameters, which modify diffusion over rough topography (St. Laurent et al. 2002).According to the simulation, tidal motion amplifies vertical diffusivities over rough bottom topography (Sasaki et al. 2020).The ETOPO1 data are adopted as the model bathymetry.The model also incorporates the monthly climatological river runoff from the Coordinated Ocean-ice Reference Experiments Phase 2 (CORE2, Large and Yeager 2009) and a sea ice module.The three-hourly Japanese 55-year Atmospheric Reanalysis of the driving ocean-sea-ice model (JRA55-do, Tsujino et al. 2018) from 1990 to 2019 was adopted for the atmospheric forcing.
We processed the OFES2 output to a climatological January mean over a period from January 1996 to January 2019 for further analysis.

Geostrophic and ageostrophic current
The pressure ( p ) of each grid point based on the hydrostatic approximation is where is the sea surface height (SSH) with zero pressure on the sea surface, z is an arbitrary vertical layer, and * is the density anomaly relative to the constant reference density 0 ~10 30kg∕m 3 .Here, we define the zonal and meridional geostrophic current u g , v g by pressure p with the Coriolis effect as follows: where the "zonal" and "meridional" denote the east-west and north-south directions, respectively.
Therefore, the ageostrophic currents u a , v a are where (u c , v c ) is the current velocity.Considering the mass conservation of an incompressible fluid, we can retrieve the vertical motion on the z-layer, w (z) , due to the ageostrophic current divergence as follows: where w( ) = 0 is the surface vertical velocity.

Along-isobath averaged variables
To remove the local calculation ambiguity, the along-isobath averaged values inside the study regions are calculated.It should be noted that in the A1 region, due to the topography distribution, the along-isobath averaged variables in areas deeper than 250 m (where the isobath is closed) are removed to present a near-uniform along (cross)-isobath direction.Subsequently, the region is separated into southern and northern halves.The detailed calculation is as follows (Stewart et al. 2019): Here, A is an area selected for conducting the alongisobath average within an isobath range [isobath 1 isobath 2 ] .The two isobath boundaries are selected as the two adjacent model-separated vertical z-layers.The term [•] isobath denotes the integrated variable.After dividing by A, we obtained • , which is an along-isobath averaged variable inside the selected region A. In the following, subscript A denotes a variable incorporated into the above along-isobath average.It should be noted that without special explanation (in this context), the variables presented in a section are along-isobath averaged variables.

Climatological monthly mean wind field
The horizontal grid spacing of the atmospheric forcing JRA55-do is ~ 55km .We processed the 3-h mean 10-m-height wind speed data over a period from January 1, 1958, to December 31, 2019, into the climatological monthly mean.The wind stress � ⃗  s is calculated based on the bulk formula (Large and Yeager 2004), which is expressed as follows: where a ≈ 1.22kg∕m 3 is the near-surface air density, � ⃗ u 10 is the 10-m-height wind vector, and C D ≈ 1.3 × 10 −3 is the air-sea drag coefficient.
It was reported in a modeling study that the ocean surface current can affect the surface wind stress and then the eddy kinetic energy (L Renault et al. 2016).This is because the stress is often estimated by the wind velocity relative to the ocean current velocity.Furthermore, it was observed that the surface current curl affects Ekman pumping (Gaube et al. 2015).The OFES2 adopted the relative wind stress � ⃗  s−ofes (Munday and Zhai 2015).Then, the surface momentum flux is calculated as follows: where � ⃗ u s is the surface oceanic current vector.The results described in Section 3.2 emphasize that the local sea surface current in winter can generally reshape the surface stress in the study regions.

Following the sea surface height (SSH) coordinate
Considering the intricate topography of the GOA, which featured several banks, troughs, valleys, and glaciers created during the Last Glacial Maximum (Zimmermann et al. 2019), the SSH was adopted instead of the isobath as an indicator for establishing an SSH coordinate.This coordinate is adopted in Subsection 3.4.2 to depict a retrieved section.Specifically, the along-and cross-SSH components of a vector variable (using velocity � ⃗ u as an example) are defined as follows: where (x s , ŷs ,ẑ s ) denotes the SSH coordinate obeying the right-hand rule, and xs (ŷ s ) denotes the cross (along)-SSH direction.Term u(v) is the cross (along)-SSH component of the velocity � ⃗ u .The along-SSH current is considered to respond primarily to the geostrophic effect.

Barotropic current
The depth-averaged current is defined as the barotropic current u in the analysis, which is calculated as follows: where H is the entire water column depth.

Simulated flow field in the northwestern GOA
The simulated climatological January mean surface potential density and barotropic current u are presented in Fig. 2. The stronger currents along the coast and the open ocean shelf break are identified as the ACC and the AS, respectively.In the A1 study region, the ACC was concentrated within the Shelikof Trough with a barotropic current of ∼ 0.1m∕s , and the surface potential density range was 25.2 − 25.4kg∕m 3 in terms of .The simulation also reproduced the abrupt shift of the ACC axis, which turned to the left-hand side and moved southward along the 200-m isobath.This result is consistent with the observations introduced in Section 1.The shift of the current axis renavigated the ACC approaching to the southern bank where the water depth was shallower than ~ 50 m.In the AS close to the outflow of the ACC, the surface potential density ranged ( 9) from 25.4to25.8kg∕m 3.Upstream of the AS, the range was 25.6 − 25.8kg∕m 3 .The strongest barotropic current of the AS was ∼ 0.2m∕s and was concentrated in a narrow strip of the open ocean shelf break.
The topography inside the channel of the A1 region monotonically descends from the coast to a depth of ~ 250 m, and the isobath is closed beyond 250 m (Fig. 3a).In the A2 region, there is a broad shoal shallower than 100 m with slight submarine bumps.A steep shelf break is located approximately at the 150-m isobath.The topography between the shoal and the shelf break is gently sloping (Fig. 3b).
The section of the along-isobath averaged potential density and geostrophic current in the A1 region are presented in Fig. 4a.On the southern half, there is a density front ~ 155.2 • W and a strong baroclinicity from the surface to ~ 100 m, where the vertical shear of the geostrophic current | �⃗ u g| z is ∼ 0.00085s −1 .The surface geostrophic current is ∼ 0.17m∕s .Moreover, strong baroclinicity and the current vertical shear at the west end of the Shelikof Strait have been observed year-round (Stabeno et al. 2016).On the northern Fig. 2 OFES2 climatological January mean  barotropic and baroclinic information around the northwestern GOA.The shading and thin white contours represent the sea surface isopycnal, where the isopycnal interval is 0.2kg∕m 3 .The colored thick contours denote the topography, and the isobath values are 50, 100, 200, 250, and 1000 m.The arrows represent the barotropic currents u .The two magenta boxes denote the A1 and A2 study regions, where a variable is incorporated into an alongisobath averaged variable in the analysis described in this paper.The dotted lines denote an averaged section Fig. 3 Zoomed-in topography of the study regions.a The red box encloses the A1 study region, and the color shading and black contours denote the topography.The orange line is the contour of the SSH with a value of − 0.16 m, which divides the region into the southern and northern halves (marked by "N"), and the along-isobath average is calculated in each half region.b The information is the same as that in a, but for the A2 study region half, the current is barotropic with a near-constant geostrophic current and density in the top 120 m.
The section of the along-isobath averaged potential density and geostrophic current in the A2 region are presented in Fig. 4b.Here, there is strong baroclinicity at ~ 54.95 • N from the surface to ~ 100 m, where the surface current is ~ 0.5 m/s and the vertical shear of the geostrophic current | �⃗ u g| z is ∼ 0.00094s −1 .These features are distinguished from the shoal and the deep ocean.In the shoal, the current is weak and the density is near uniform.In the deep ocean, a mixed layer is simulated up to ~ 50 m.The front ends at the shelf break.

Wind field in the northwestern GOA
The northeasterly wind is downwelling-favorable and dominates the domain.� ⃗  s−ofes is ∼ +0.04N∕m 2 in the A1 region and ∼ +0.02N∕m 2 in the A2 region (Fig. 5a).There is a strip of enhanced positive relative wind stress curl between the 200-and 250-m isobaths in A1 associated with the negative sea surface current relative vorticity (Fig. 5b), while the negative relative wind stress curl is presented in areas deeper than the 250-m isobath and shallower than the 100-m isobath and is associated with the positive sea surface current relative vorticity.The positive relative wind stress curl in the A2 study region is also associated with the negative surface current relative vorticity there.For comparison, the climatological January mean absolute wind stress � ⃗  s is presented in Fig. 5c with black arrows, and the shading denotes the curl of � ⃗  s .We revealed that the absolute wind stress curl was one order smaller than the relative wind stress curl in both study regions.
The Ekman pumping due to the relative wind stress curl is presented in Fig. 5d, where it should be reiterated that the OFES2 is driven by the relative wind stress.Compared to the absolute wind stress, the relative wind stress and its Ekman pumping exhibited small structures associated with the oceanic surface current field.Notably, positive wind stress curl and Ekman upwelling were evident along the ACC and AS.

N (a) (b)
Fig. 4 Baroclinicity in the study regions.a The shading and black contours denote the along-isobath averaged geostrophic current inside the A1 region.The magenta contours denote the isopycnal with an interval of 0.1kg∕m 3 .The X-axis is the along-isobath averaged longitude, and the right-hand panel denotes the northern half.The upper panel is for the geostrophic current in the zonal direction, while the lower panel is for the geostrophic current in the meridional direction.b The variables are the same as these, but for the A2 region.In addition, the isopycnal interval is 0.2kg∕m 3 , except for the isopycnal contours of 25.5 and 25.7 kg∕m 3 , which are denoted with the dotted line.The X-axis is the along-isobath averaged latitude

Strong upwelling along the ACC and AS
The model-simulated vertical velocity on the 10-m layer is presented in Fig. 6a.Comparing Figs.6a and 5d, the model-simulated upper layer upwelling had much larger values than the Ekman suction by the relative wind stress.The vertical velocity of the 10-m layer corresponds to the ageostrophic current divergence on the same isobath (Fig. 6b).As described in Sections 3.4 and 3.5, the horizontal divergence of the ageostrophic current around the southern bank of the A1 region (Fig. 6c) and the slope of the A2 region (Fig. 6d) is caused by northward ageostrophic transport, which gradually turns southward with decreasing latitude.This is not expected under the downwelling-favorable wind condition.
Moreover, compared to Ekman pumping (Fig. 5d), the model-simulated downwelling (Fig. 6a) was enhanced along the northern coast due to the blocked onshore Ekman transport (caused by the lateral coastline) under northeasterly winds.

Upwelling in the A1 study region
The sections of the along-isobath averaged vertical velocity and ageostrophic current divergence in the A1 region are presented in Fig. 7c and d.For comparison, the Figure 7c indicates that upwelling predominates in the southern half in the middle trough, where the water depth is deeper than 100 m and is stronger in the lower layer.The maximum upwelling was ~ + 9 m/day at a depth of ~ 180 m.However, we focused on upwelling shallower than 100 m where the wind could drive the upwelling directly, whereas upwelling deeper than 100 m would be discussed in other studies.The downwelling dominates the shallow bank with a magnitude of approximately − 0.5 m/day in the northern half and ~ − 2 m/day in the southern half.For the ageostrophic current on the layer at 10 m (Fig. 6c), there is a bankward current between the 100 and 200-m isobaths in the southern half.The ageostrophic current in the northern half flows toward the northern coast (Fig. 6c).This information corresponds to the surface ageostrophic current divergence (Fig. 7d) and the upwelling (Fig. 7c).
It should be noted that the bank-ward ageostrophic current in the southern half (Figs. 6c and 7b) is opposite to the Ekman transport where the wind is southwest (Fig. 5a).In contrast, the ageostrophic current in the northern half is in the same direction as the Ekman transport.Another feature in these regions is the substantial vertical diffusivity (Fig. 7e) and viscosity (Fig. 7f) coefficient in the top 100 m.In this study, we focused on the processes that cause divergence of the ageostrophic current in the top 100 m between the region 155.25 and 155.35 • W (Fig. 7d) and the associated upwelling.

Contribution from the relative wind stress vorticity
Comparing the along-isobath averaged Ekman pumping (Fig. 7a) to the vertical velocity (Fig. 7c), it is evident that  and 6a, the operation of the along-isobath average ignores some details while this study focused on the region with the 100-200-m isobath around the southern bank where the upwelling dominates.
In the northern half, there was an intensified downwelling along the coast due to the onshore transport blocked by the Alaskan coast.Regarding the surface relative wind stress (Fig. 5a), its value was ~ + 0.04 N/m 2 west of 155.15 • W . Based on the classic Ekman theory, a northward ageostrophic current with a velocity of ~ + 0.005 m/s would be generated if the vertical scale of the Ekman layer was ~ 77 m (estimated by √ 2A v ∕f , where vertical viscosity coefficient A v is ~ 0.3 m 2 ∕s (Fig. 7f)).This value was consistent with the simulated cross-SSH current in the northern half (Fig. 7b).

Adjustment by the geostrophic stress
The geostrophic stress is considered a possible candidate for the dynamical adjustment of the ageostrophic current divergence around the southern half of the trough.The geostrophic stress y p is expressed as x , where g is the acceleration due to gravity and is the density.In this area, there is a large geostrophic current shear due to the thermal wind relation (Fig. 4a) in addition to a large vertical viscosity coefficient (Fig. 7f), resulting in significant geostrophic stress.Since the internal water stress � ⃗  is a combination of the wind-induced ageostrophic stress � ⃗  a and the geostrophic stress � ⃗  p , i.e., � ⃗  = � ⃗  a + � ⃗  p , a large internal water stress can be generated by a large geostrophic stress.
To verify whether reversed Ekman overturning occurs in the southern half of the A1 region, the along-SSH internal water stress y was calculated as follows: where v is the along-SSH current and superscript y denotes the coordinate of the along-SSH direction.The along-isobath averaged y is presented in Fig. 8a.The cross-SSH transport M x e from the surface to a typical layer z is correspondingly obtained after making the vertical integration of the cross-SSH current u a = 1 f 0 y z , as follows: Here, superscript x denotes the coordinate of the cross-SSH direction.The along-isobath averaged M x e is presented in Fig. 8b.
If we presume that the along-isobath averaged M x e is twodimensional in the (x, z) plane, we can consider M x e to be a stream function.Although this presumption is not stringent in the study region, it is still a heuristic for retrieving the ageostrophic overturning according to the following relationships: , where u a1 is the retrieved cross-shelf current and w a is the retrieved vertical velocity.Their along-isobath averaged results are presented in Fig. 8c and d.
Near the southern half of the trough at approximately 155.2° W (where the depth is ~ 50 m), there was a maximum y of ∼ +0.2N∕m 2 , which was larger than the surface wind stress s ∼ +0.04N∕m 2 .Moreover, both the surface wind and internal water stresses were oriented toward the west.Consequently, the transport here is southward according to the modified Ekman overturning, which is in the opposite direction of normal Ekman transport (Fig. 8c).This result was consistent with the simulated southward cross-SSH current (Fig. 7b).In the northern half, the calculated y was smaller than the surface wind stress.Therefore, water transport corresponded to the classical Ekman theory.As a result, there was an upwelling in the top ~ 100 m in the southern half of the trough driven by the transport divergence (Fig. 8d), which was also consistent with the simulated upwelling in that region (Fig. 7c).
The overturning retrieved from M x e reproduces a reversed surface Ekman current on the southern bank and an anticlockwise vertical circulation.However, it should be noted that the retrieved w a > +9m∕day was larger than the model output of ~ + 3-6 m/day.We consider that this result was due to the simulated vertical viscosity coefficient A v of ~ 0.5 m 2 /s being a considerably large value.Therefore, the geostrophic stress x could have an overestimated impact on A linear relation was used to retrieve the transport, and neglecting the nonlinearity could be another reason for overestimation of the upwelling.We estimated the transport ���� ⃗ M′ by considering the impact of the relative vorticity of the geostrophic current g (to simplify the nonlinear equation) as follows: where g = v g x − u g y .The horizontal gradient of transport ���� ⃗ M′ at the top 100 m from 155.25 • W to 155.35 • W was ~ 0.15 m 2 /s smaller than that of the linear estimated M e .As a result, the retrieved upwelling would be 1 m/day smaller than the w a .

Upwelling in the A2 study region
Analogous to the A1 study region, we present the alongisobath averaged vertical velocity and ageostrophic current divergence in the A2 region in Fig. and d.The Ekman suction is presented in Fig. 9a, and the upper layer (vertical It should be noted that in addition to the surface maximum of the vertical diffusivity and viscosity coefficients, there was another maximum at the bottom of the gently sloping shelf at a depth of ~ 150 m in the A2 region (Fig. 9e, f).

Geostrophic stress-modified upper layer overturning
The upwelling in the A2 region involved geostrophic stresscontrolled reversed Ekman overturning similar to that in the A1 region.Figure 10a presents the internal water stress according to Eq. ( 11), Fig. 10b presents the transport according to Eq. ( 12), and Fig. 10c and d presents the retrieved ageostrophic cross-shelf and vertical velocity according to Eq. ( 13).
There was a maximum internal water stress of ~ + 0.2 N/ m 2 at ~ m at ~ 54.95 • N , which was almost 10 times the surface wind stress of ~ + 0.02 N/m 2 .The internal water stress was considered to be regulated by the geostrophic stress, because there is a geostrophic current shear (Fig. 4b) and a large vertical viscosity coefficient of ~ 0.4 m /s in that region (Fig. 9f).As a result, there is a reversed Ekman transport in Fig. 10b and upwelling due to Ekman transport divergence in Fig. 10d.

Lower layer overturning
In the A2 region, there was another maximum internal water stress in the lower layer.Figure 10a presents this other internal water stress maximum of ~ + 0.2 N/m 2 at the bottom of a depth of 150 m.Consequently, there was a transport horizontal divergence (Fig. 10b) resulting in a downslope current (the southward current in Fig. 10c and the downwelling in Fig. 10d).The bottom maximum internal water stress allowed the water to flow over the gently sloping shelf toward the deep open ocean.The bottom stress presented in Fig. 10a was considered to obey the bottom Ekman layer dynamics.The geostrophic current there was ~ 0.3 m/s (Fig. 4b).With an estimation of the bottom stress , where the bottom drag coefficient | was ~ 0.225N/m 2 , which cor- responded to the large internal water stress in that area (Fig. 10a).Therefore, the downslope current responded to the classic bottom Ekman theory.

Summary and discussion
In this study, we primarily analyzed the OGCM OFES2 output to determine whether reversed Ekman overturning is one of the dynamical reasons for the local upwelling around the northwestern GOA, where the downwellingfavorable wind controls all year.The model results indicated that the geostrophic stress could generate a reversed Ekman overturning, including a seaward upwelling in the study regions of up to ~ 100 m.A geostrophic stress-modified internal water stress greater than the surface wind stress was simulated in both regions.Furthermore, the induced surface transport divergence in the area between the normal and reverse Ekman overturnings contributed to the local upwelling, which is away from the coast.Therefore, the analysis implied that a front with a large geostrophic stress could act as a "virtual wall" and contribute to local upwelling within a depth of approximately 100 m in the study regions.The Ekman pumping generated by the relative wind stress curl took part in generating the local upwelling, even though the magnitude of the generated upwelling was far smaller and could not explain the total simulated vertical velocity.
To retrieve the cross-shelf overturning structure, a twodimensional assumption was adopted.Because of the intricate topography of the northwestern GOA and because the water depth is shallower than ~ 350 m, redirection of the upper layer current by the topography should not be ignored.Furthermore, the simulated barotropic current and vertical velocity did not present an along-isobath homogeneous structure, especially in the A2 study region, where there was an undulation of upwelling and downwelling signal on the surface layer (even though the upwelling was dominant).Therefore, the two-dimensional presumption could be an oversimplification because the estimated results presented an upwelling signal that was unmatched to the magnitude of the simulated upwelling, although the results did not lose their essence and were heuristic.A three-dimensional structure should be a future exploration that will potentially reveal more details regarding the formation mechanism of the local upwelling.
In this study, we focused on investigating the roles of geostrophic stress in cross-shelf Ekman overturning in the northwest of GOA, and the following unclarified phenomena were mentioned and will be studied in future work: 1.The shift of the ACC in the A1 study region.A shift in the ACC axis was also observed, which would change the location where the geostrophic stress dominates.2. The connection between the local upwelling, nutrient supply, and primary production.This study provides one possible explanation for the upwelling in a downwellingfavorable alongshore wind domain, while a study that elucidates a further connection between the upwelling and biological production should be necessary to unveil the information required to support the ecosystem of the northwest of GOA.

Fig. 1
Fig. 1 Sketch of the study region (the northwestern Gulf of Alaska).The figure inset depicts the Alaskan Gyre, and the region in the bold black box is the study region.The analyzed regions A1 and A2, the primary currents, and the mentioned locations in the area are marked in the zoom-in figure.The Alaska Coastal Current in this region is primarily concentrated in the Shelikof Trough, and the Alaskan Stream is concentrated in the region near the open ocean shelf break.The orange contour represents the 200-m isobath

Fig. 5
Fig. 5 Climatological January mean wind field and the corresponding Ekman pumping in the study regions.a The color shading and arrows denote the relative wind stress curl.b The color shading and black contours denote the relative vorticity of the surface current.c The

Fig. 6
Fig. 6 Model-simulated current field on the 10 m layer.a The color shading denotes the vertical velocity of the 10 m layer.b The color shading denotes the ageostrophic current divergence on the 10-m layer.The red shading denotes the surface ageostrophic current divergence, and the blue shading denotes the surface ageostrophic current

Fig. 7
Fig. 7 Simulated vertical overturning in the A1 region.a The alongisobath averaged Ekman pumping by the relative wind stress.b The purple line denotes the along-isobath averaged upper layer, vertical average from the surface to a depth of ~ 77 m, cross-SSH current.The figure is drawn only for the region where the water depth of the whole column is deeper than 77 m.The northward current is denoted with a positive value.The green line denotes where the current is equal to

Fig. 8
Fig. 8 Retrieved vertical overturning in the A1 region.a The color shading and contours denote the along-isobath averaged internal water stress that follows the SSH coordinate.The positive value with the greenish shading denotes the westward stress.b The color shad- average from the surface to ~ 77 m) cross-SSH current is presented in Fig.9b.The Ekman suction caused by the positive relative wind stress curl was predominant in the A2 region.However, similar to the A1 region from 55 • N to 55.1 • N , the Ekman suction of ~ + 0.75 m/day could not explain the model-simulated vertical velocity of ~ + 3 m/day higher than ~ 50 m.Combining the upper layer cross-SSH current (Fig.9b) and the vertical velocity, two overturnings were revealed in this area, which are schematically depicted by the purple arrows.The first was an anticlockwise overturning in the upper layer, and the other was a clockwise overturning in the lower layer with a strong bottom downslope current.From the open ocean to 55.2 • N , the surface wind stress (Fig.5a) was ~ + 0.02 N/m 2 , which generated an ageostrophic cross-shelf current of ~ + 0.0026 m/s within a depth of ~ 77 m, as deduced by the Ekman theory.This estimation corresponded to the upper layer cross-SSH current from 55.02 • Nto55.08 • N (Fig.9b).From the open ocean to 55 • N , the cross-SSH current of ~ − 0. 0025 m/s suggests a reversed Ekman transport.

Fig. 9
Fig. 9 Simulated vertical overturning in the A2 region.The variables are the same as those in Fig. 7, although for the A2 study region

Fig. 10
Fig. 10 Retrieved vertical overturning in the A2 region.The variables are the same as those in Fig. 8, although for the A2 study region