The idealized IPUS is contained in a meridionally oriented stretch of continental shelf with constant bathymetry and limited zonally by the coast and the open ocean (Fig. 1). The domain has 300 km of length and width, with a shelf width of 50 km, which is characteristic of the Iberian shelf at 41∘ N. The resolution of the spatial grid is 500 m, allowing for the simulation of summer upwelling seasons up to 90 d duration, with the associated upwelling front dynamics – mesoscale and submesoscale vortices and filaments – within acceptable computing time limits.

The physical–biogeochemical model couples the 3D Regional Ocean Modelling System (ROMS; Shchepetkin, 2015; Shchepetkin and McWilliams, 2005), in its Coastal and Regional Ocean Community (CROCO) version (Debreu et al., 2012), to the low-complexity oxygen–phytoplankton–zooplankton biogeochemical model of Petrovskii et al. (2017) and Sekerci and Petrovskii (2015), hereafter SP2015. Oxygen is used as the main model currency, since it is central for the functioning of marine ecosystems (Breitburg et al., 1997, 2018). Oxygen is also at the heart of the photosynthesis and carbon fixation metabolic pathways for prokaryotic and eukaryotic algae, being a major electron acceptor (Mackey et al., 2008; Zehr and Kudela, 2009) and is needed for many biogeochemical reactions, including those involved in remineralization, which constantly occurs in the oceanic water column. The low-complexity O2PZ model was directly implemented into the CROCO model following one of the already-embedded biogeochemical modules; it allows for maintaining the full capabilities and versatility of this community code while gaining in computing efficiency (allowing for extensive sensitivity studies and the consideration of submesoscale dynamics in oxygen cycling) as compared to the more complex biogeochemical modules already available within CROCO.

ROMS–CROCO is a hydrostatic primitive equation model, formulated in finite differences with time splitting in the barotropic (fast) mode and the baroclinic (slow) mode. It uses a terrain following vertical discretization in σ coordinates with 40 vertical levels. The prognostic variables are the horizontal barotropic and baroclinic momentum components, temperature and salinity. Free-surface displacement and vertical momentum are diagnostic variables. The horizontal advection of momentum and tracers is calculated from a third-order upstream-biased scheme. Horizontal mixing is Laplacian, along iso–σ surfaces, with diffusivity coefficients of 2 and 0.2 m2s-1 for momentum and tracers, respectively. Vertical mixing uses the K-profile parameterization (KPP) scheme of Large et al. (1994). The model is initialized from rest; the initial temperature and salinity distributions are uniform in the horizontal, and the vertical profiles are taken from the World Ocean Atlas 2013 climatology (Boyer et al., 2013). Initial fields of the biogeochemical tracers (O2, P and Z) are also horizontally homogeneous, and their vertical profiles are obtained from a water column (e.g. 1D) model version of the O2PZ model (not shown). The channel is periodic in the meridional boundaries; the eastern boundary (coast) is modelled as a free-slip wall, and the western one (open ocean) is open with radiative boundary conditions for momentum and tracers. Within the westernmost 50 km, a sponge layer is applied with an increased horizontal viscosity of 200 m2s-1 and a nudging timescale of 3 d in order to nudge all prognostic variables to their initial values over the offshore region. The bottom stress formulation is logarithmic with a roughness height of 0.01 m.

The model is forced by a cyclic uniform wind field. To promote the destabilization of the upwelling front, we introduce a small spatial perturbation to the wind field, whose amplitude is less than 1 % of the total wind speed and which has characteristic wavelengths of 10 and 50 km in the alongshore and cross-shore directions, respectively.

In the coupled model, the time evolution of DO, P and Z concentrations are given by, respectively, 1∂[O2]/∂t+u∂[O2]/∂x+v∂[O2]/∂y+w∂[O2]/∂z=kH(∂2[O2]/∂x2+∂2[O2]/∂y2)+∂/∂z(〈[O2]′w′〉-kV∂[O2]/∂z)+Va([O2]-[O2]sat)+AJ(z)f([O2])[P]-ur([O2],[P])-vr([O2],[Z])-m[O2],2∂[P]/∂t+u∂[P]/∂x+v∂[P]/∂y+w∂[P]/∂z=kH(∂2[P]/∂x2+∂2[P]/∂y2)+∂/∂z(〈[P]′w′〉-kV∂[P]/∂z)+l(N)g([O2],[P])-e([P],[Z])-σ[P],3∂[Z]/∂t+u∂[Z]/∂x+v∂[Z]/∂y+w∂[Z]/∂z=kH(∂2[Z]/∂x2+∂2[Z]/∂y)2)+∂/∂z(〈[Z]′w′〉-kV∂[Z]/∂z)+κ([O2])e([P],[Z])-μ[Z], where (u,v,w) is the 3D velocity field, kH and kV are the horizontal and vertical tracer diffusivities, and 〈…〉 are the vertical turbulent fluxes. The biogeochemical model O2PZ (SP2015) defines the source terms of DO, P and Z in the coupled model. It simulates seven biogeochemical reactions between the three compartments (Fig. 2) as follows: in the DO equation (Eq. 1), the term AJ(z)f([O2]) is the rate of O2 production by photosynthesis and is modelled by a Monod parametrization f([O2])=c0/([O2]+c0), where c0 is a half-saturation constant. The term J(z)=1-exp⁡(αPAR(z)/A) represents the light dependency of photosynthesis, with α=30 and the photosynthetically available radiation PAR(z)=PAR(0)exp⁡(-kwz), with PAR(0)=355.19 Wm-2 and kw=0.04 m-1.

We distinguish here the terms “photosynthesis” from “carbon fixation” (Behrenfeld et al., 2008). Indeed, photosynthesis is the production of ATP (adenosine triphosphate) and NADPH (reduced form of NADP+; nicotinamide adenine dinucleotide phosphate) by the photosynthetic-electron-transport (PET) chain, and these two products are referred to as “photosynthate”. By contrast, carbon fixation refers to the use of photosynthate by the Calvin cycle to produce simple organic carbon products independently of light. SP2015 chose to highlight these two stages in their model formulation by decoupling carbon fixation from photosynthesis. The respiration by phytoplankton ur is given by ur([O2],[P])=δ[O2][P]/([O2]+c2), where δ is the maximum per capita phytoplankton respiration rate and c2 is the half saturation constant. Zooplankton respiration is similar: vr([O2],[Z])=ν[O2][Z]/([O2]+c3). The constants ν and c3 have the same functions as δ and c2 in ur. A Monod function is a logical formulation to have respiration depending on oxygen concentration, since if the fluid environment becomes anoxic, then plankton cannot breathe so that respiration terms ur and vr vanish. The fourth term parametrizes bacterial respiration (oxygen loss due to natural depletion, e.g. remineralization). On top of the oxygen that is produced and consumed within marine ecosystems, a considerable part of dissolved oxygen eventually becomes gaseous and is then exchanged at the ocean–atmosphere interface, contributing to the estimations that more than one half of atmospheric oxygen is produced in the ocean (Harris, 1986). The remaining term of Eq. (2) is the air–sea flux of O2, which is the product of the gas transfer velocity Va, which depends on the square of the wind speed and on the Schmidt number (Wanninkhof, 1992), with the difference of the oceanic DO concentration and the solubility of O2 in seawater.

In Eq. (2), phytoplankton growth g([O2],[P]) is given by a linear growth term α([O2])[P] minus intraspecific competition γ[P]2, where γ is the intraspecific competition intensity. The per capita growth rate is a Monod function α([O2])=B[O2]/([O2]+c1), where B is the maximum per capita growth rate in the large [O2] limit and c1 is the half saturation constant. The l(N) term is a Monod function l(N)=k1N(ρ)/(k2+N(ρ)), where N(ρ) is a parametrization of nutrient availability based on the nitrate–density (ρ) relationships measured during an oceanographic cruise which surveyed the IPUS during upwelling season (the 2007 MOUTON – MOdélisation d’Un Théatre d’Opérations Navales – campaign; see also Rossi et al., 2010, 2013). This term is included here to circumvent the absence of nutrient limitation in the original O2PZ model of SP2015. We chose to add a parametrization instead of a new equation for the nutrients because this last option would necessarily increase the complexity of the model.

SP2015 used a formulation where high oxygen increases phytoplankton growth but limits oxygen production by photosynthesis. The Warburg effect (Turner and Brittain, 1962) corresponds to the decrease of the photosynthesis rate at high oxygen concentrations so that the choice of f([O2]) where high [O2] limits [O2] production makes sense. Moreover oxygen stimulates photorespiration which reduces photosynthesis yield. As soon as a water molecule (H2O) undergoes photolysis in the chloroplast of oxygenic photosynthetic organisms, O2 and ATP (adenosine triphosphate) are produced through both photosystems I and II. The products of photosynthesis (ATP) then enter the Calvin cycle to convert carbon dioxide and other compounds into glucose, which is the food that autotrophs need to grow. As such, we can relate the growth term α([O2]) to [O2] with a Monod function so that high [O2] corresponds to a high growth rate. The predation term is e([P],[Z])=β[P][Z]/([P]+h), where β is the maximum predation rate and h is the half saturation constant. Phytoplankton mortality is σ[P]. Regarding zooplankton (Eq. 3), its feeding efficiency is a function of oxygen concentration κ([O2])=η[O2]2/([O2]2+c42), where η is the maximum feeding efficiency and c4 is the half-saturation constant. Zooplankton mortality is given by μ[Z].

The parameters of the O2PZ model were adjusted so that its 0D version (without advection or diffusion; see Table A3) has a steady state at values representative of the IPUS (see Appendix A).

The coupled model is initialized at rest. Biogeochemical tracers are initialized from vertical profiles (Fig. 3a) obtained by a water column 1D model of the O2PZ model that was run for a time long enough to reach stable vertical distributions (not shown). Using these profiles instead of climatological initial conditions allows for reducing the drift of the 3D coupled model (not shown). The initial temperature and salinity profiles (Fig. 3b) were taken from the World Ocean Atlas 2013 (WOA13; Boyer et al., 2013) data at 12∘ W and 41∘ N.

Our set of simulations (Table 1) is designed to investigate the sensitivity of the coastal DO inventory to upwelling duration and community structure (diatom dominated or not). We choose the duration of upwelling-favourable wind instead of its magnitude as a control factor because it has been shown to be a better predictor of coastal hypoxia (Feng et al., 2012; Forrest et al., 2011; Zhang et al., 2018). Community structure is set through the growth regime of the primary producers (phytoplankton) with respect to nutrient input. Thus, a diatom-dominated regime is simulated using enhanced growth rates due to nutrient input, for the (E)nhanced runs, while a non-diatom-dominated regime is simulated with growth rates (N)eutral to and (L)imited by nutrient input. We test the sensitivity of our coupled system to the relative dominance of diatoms in the community, as they have been suggested to decline over the long term, being gradually replaced by dinoflagellates and cyanobacteria (Gregg et al., 2017).

The effects of upwelling season length are studied by running two simulations with four and nine upwelling favourable wind cycles, maintaining a total simulation time of 90 d and considering a diatom-dominated phytoplankton community. The alongshore wind profiles (Fig. 3c) are based on the cyclic wind pulses that are characteristic of the summer–early-fall upwelling favourable conditions in the IPUS, especially those observed during the MOUTON campaign: 10 d pulses with a maximum wind speed of 12 ms-1 (Rossi et al., 2013; Torres et al., 2003). The cross-shore wind component is zero in all cases. Despite the fact that “true” wind patterns observed over western Iberia are undoubtedly more variable (both in terms of direction and magnitude) than our idealized forcing inspired from a specific campaign, it provides the quickest development of a clear upwelling front generating small-scale instabilities. Note that sensitivity tests were performed (not shown) and revealed that the model responses are qualitatively similar among different wind strengths, given that the magnitude is high enough to ensure the development of the unstable upwelling front.

In situ observations of the IPUS, collected during the MOUTON 2007 campaign (Rossi et al., 2010, 2013) and compiled within the WOA13 (Boyer et al., 2013), are used not only to initialize but also to perform a comparison with the outputs of our simulations. The ECC simulation used the wind forcing and phytoplankton growth regimes that most resemble the IPUS region and therefore was chosen as the reference simulation.

We compared the full ranges of densities ρ, DO concentrations [O2] and chlorophyll a concentrations [Chl a] of the reference simulation to all compiled measurements collected during the MOUTON campaign. Given the low complexity of the biogeochemical model and the highly idealized physical setting, a fully quantitative comparison is out of the scope of this paper; however we confirm that the coupled model reproduces qualitatively well the ρ–[O2] and ρ–[Chl a] relationships obtained from in situ observations.

Our coupled model reproduces well the upwelling circulation and the typical biological responses. Indeed, the upwelling of nutrient-rich waters induced by the mean wind-driven circulation promotes the growth of phytoplankton, leading to increased oxygen production by photosynthesis and the subsequent enrichment of oxygen in shelf waters (x<80 km; Fig. 5a), as compared with the lower [O2] found in offshore waters (x>80 km). It also shows a low-[O2] cell (∼50 mmolm-3), at the subsurface over the outer shelf (centred at 40 km and 60 m depth) because of the upwelling of low-O2 waters, consistent with the shelf low-[O2] cell (<200 µmolkg-1) measured during the MOUTON cruise (e.g. Rossi et al., 2013). In a qualitative sense our idealized model results are similar to more realistic model studies, such as Gutknecht et al. (2013), which modelled the Benguela upwelling region and found a low-[O2] plume for the climatological month of December at the shelf edge, and to observational studies such as Hales et al. (2006), which for the Oregon coast, measured [O2] of 70–110 mmolm-3 in upwelled water at the shelf break, about 200 mmolm-3 less than at the surface, which is the same range of the vertical gradient simulated here.

The dynamics of the ECC simulation (Appendix B), are consistent with those documented by Durski and Allen (2005). A mean Ekman upwelling transport is established, moving subsurface waters upwards near the coast. The eddy-induced circulation (Cerovečki et al., 2009; Plumb and Ferrari, 2005) has the opposite sense to the mean circulation and is the strongest in the 50-to-100 km offshore range (Fig. B1). The result of the eddy-induced onshore and downward circulation is mainly seen in the subduction of the oxygen-rich waters just offshore the shelf edge, as suggested by the spatial pattern of the eddy stream function (Fig. B1).

The spatial coincidence between the high-[O2] and high-phytoplankton [P] concentration near the coast (Fig. 5) reflects O2 enrichment caused by photosynthetic production (see Sect. 3.2 for a budget analysis). Since oxygen limits phytoplankton growth in our model, the low-[O2] cell in the coast causes a matching low-[P] cell at the same location. Further offshore, subsurface [P] and [O2] decrease as phytoplankton growth is limited by the lack of nutrients in the euphotic zone.

The subsurface [P] maximum between 60 and 80 m depth results from the trade-off between sufficient oxygen, light levels and nutrients availability. Consequently, the enhanced phytoplankton growth rate due to nutrients appears to compensate for the low oxygen levels, thus promoting phytoplankton growth. Moreover, the low [O2] will maintain the zooplankton stocks at low levels, thus constraining the grazing pressure of zooplankton on phytoplankton.

The dominant length scales, i.e. the inverse of the wave number where the alongshore [O2] anomaly field spectrum has a maximum, vary with time and the distance to the coast (Fig. 6a). After day 30, between 50 and 150 km offshore, we observe the emergence of dominant length scales of 150 km in an intermittent fashion, in a process that agrees with previous studies of the growth and decay of large mesoscale structures in coastal upwelling systems (Durski and Allen, 2005).

Slopes of time-averaged spectra of alongshore [O2] anomalies at three offshore locations (Fig. 6b) show, however, that the submesoscale has also a marked effect on the [O2] field. All spectra are shallower than the k-3 slope of geostrophic turbulence (Charney, 1971), implying that the submesoscale is prominent in our simulations (Capet et al., 2008). The spectrum at x=50 km is the shallowest and the closest to the k-5/3 slope in the range 8.10-4<k<10-4. In the lower k range (k<10-5), the spectra at 50 and 100 km have higher energy than the spectrum at 200 km, as the dominant length-scale plot shows the largest dominant length-scales in the 50–150 km cross-shore region.

The probability density function (PDF) of the [O2] gradient norm (Fig. 6c) has a heavy tail distribution, associated with intermittency (Capet et al., 2008; Castaing et al., 1990). The existence of long tails in all PDFs indicates that sharp [O2] gradients are ubiquitous in the channel.

Turbulence redistributes oxygen through fronts and filaments (strain-dominated regions) as well as vortices (rotation-dominated regions). To analyse this process, we use the Okubo–Weiss criterion γ, which separates turbulent velocity fields in strain-dominated (γ>0) and rotation-dominated (γ<0) regions. More specifically, we compute the daily average surface [O2] for each γ and binned shore distance x.

For day 65, the [O2] distribution by (γ,x) (Fig. 6d) reproduces the cross-shore [O2] gradient of coastal elevated [O2] and lower offshore [O2] (the background gradient; see also Fig. 5a), in the range γ∼0. Deviations from this background gradient are found along the cross-shore direction as we move to larger |γ|, implying that [O2] anomalies with respect to the mean surface field are mainly found in filaments and vortices. Since the highest [O2] levels are found in the shelf region, due to photosynthetic production, their presence further offshore strongly suggests offshore export by turbulent structures. We emphasize that offshore transport of [O2]-rich water results in a net loss of O2 for the continental shelf region.

The [O2] anomalies found offshore in regions of positive and negative γ highlight the transport and dispersion of O2 by (sub-)mesoscale structures from the shelf to the open ocean. We find that although the mean [O2] as a function of γ (averaged over x in each γ bin) remains at ∼200 mmolm-3 (Fig. 6e), the [O2] distribution is biased toward negative γ, as found by Combes et al. (2013) for tracers in the California current. Our results are also in line with those of Lovecchio et al. (2017) that demonstrate the importance of mesoscale processes for the zonal advection of tracers, with a key role of eddies, especially offshore the upwelling front.

The relative importance of the physical vs. the biological processes in controlling coastal oxygen dynamics was analysed in terms of the volume-averaged rate of change of DO due to physics (advection and mixing), biology (photosynthesis, community respiration and remineralization) and air–sea fluxes within a shelf control volume (from the coast to 50 km offshore and from the surface to 140 m depth) and averaged from day 20 to 90. The net enrichment rate, accounting for the physical and biological forcing, is positive (2.26 mmolm-3d-1), and so, over time, the coastal oxygen inventory increases. DO concentrations are increased by biogeochemical processes at a rate of 4.27 mmolm-3d-1 and by air–sea exchange (3.41 mmolm-3d-1) but are limited by physical processes that remove O2 from the coastal region (-5.42 mmolm-3d-1) through lateral advection.

The reference simulation (ECC) has shown three major features: the appearance of subsurface low-[O2] cells because of the upwelling of O2-poor waters, the O2 enrichment of surface levels, and the appearance of an [O2] gradient between the biologically mediated enrichment at the inner shelf and the depleted offshore region. This gradient is, on the one hand, maintained by the upwelling circulation and, on the other hand, smoothed out by the cross-shore transport of O2 by small-scale vortices and filaments. These effects are driven by the wind regime, which controls the upwelling dynamics and instabilities, and by the phytoplankton growth rate, which in turn affects phytoplankton concentrations. We now look at the sensitivity of the coupled model to these two drivers.

The continuous development of filaments and vortices in the ECC run maintains the offshore transport of dissolved oxygen (Fig. 7a). The wind shutdown in the ECS run causes a gradual decrease of turbulence which implies a diminution of the [O2] redistribution by the cross-shore export physical processes, resulting in the creation of a sharper boundary between the oxygen-rich coastal waters and the depleted open ocean (offshore the upwelling front; Fig. 7b).

The phytoplankton growth regime impacts the mean [O2] distribution, since nutrient neutrality (NCC) or limitation (LCC) results in the decrease of [O2], when compared with the ECC run. The largest difference between the NCC and the ECC simulations (Fig. 8a) is observed in the coastal region, with maximum deviations from the ECC run of up to 100 mmolm-3. Offshore the front, on the other hand, we find an increase of [O2] with respect to the ECC run, with the difference reaching ∼50 mmolm-3 at x=250 km. This positive difference is due to the absence of nutrient limitation so that phytoplankton growth and oxygen production persist in the nutrient-depleted surface levels.

The difference between the LCC and ECC cases (Fig. 8b) is also the highest in the shelf region, slightly above 100 mmolm-3. Offshore the front (x>50 km), the difference reduces to less than 50 mmolm-3, above 80 m depth, vanishing below this depth. In both cases, there is a signature of the low-[O2] upwelling over the slope and shelf edge and the eddy-induced subduction just offshore the front (x=50 km).

When analysing O2 budgets in the coastal control volume, from the shore to 50 km offshore and from the surface to 200 m of depth, the short upwelling duration simulation (ECS) results in a slight increase of the shelf [O2] temporal-mean net rate of change by 6 % with respect to the ECC simulation (2.26 to 2.40 mmolm-3d-1; Fig. 9a). Although every term in the oxygen mean budget for ECS is smaller than for ECC, the physical-sink decrease is slightly higher than the combined decrease in the biological source and sink (QO2) and air–sea exchange.

The changes in the physical sink also occur faster than those in the biological terms. The wind cessation at day 40 causes an immediate decrease in the physical term (Fig. 9b, lower panel), while only after day 70 can we observe a significant difference between the biological source and sink terms of both the ECC and ECS simulations.

Changes in the phytoplankton growth regime modify the physical–biological balance of oxygen in the coastal control volume. The coastal region is net autotrophic (QO2>0) for ECC (QO2=4.27 mmolm-3d-1) and ECS (QO2=3.99 mmolm-3d-1) but becomes slightly net heterotrophic (QO2<0) when the phytoplankton growth becomes neutral to (NCC; QO2=-0.11 mmolm-3d-1) or limited by (LCC; QO2=-0.35 mmolm-3d-1) nutrients (Fig. 9a). This modifies the [O2] gradients and the [O2] lateral advective fluxes, and, as a result, the rate of oxygen loss through lateral advection decreases by about 15 % for NCC and LCC, with respect to ECC. The air–sea exchange of O2 is also affected by the growth regime changes, as lower [O2] will result in increased fluxes.

Overall, the phytoplankton growth regime has a stronger impact than the wind regime in the DO inventory in the shelf control volume. The NCC and LCC cases result in net rates of change of dissolved oxygen that are 75 %–80 % lower than in the reference case.