The open-source community- supported 3D physical modeling system SCHISM (Zhang et al., 2016b) is used in this study. SCHISM is a derivative product built from the original SELFE (Zhang and Baptista, 2008) and distributed with an open-source Apache v2 license. SCHISM is a numerically efficient and robust modeling system designed for the effective cross-scale simulation of 3D baroclinic ocean circulation. SCHISM has been used in multiple studies that span from shallow coastal areas to the deep open ocean (Yu et al., 2017; Ye et al., 2020; Wang Z. et al., 2022), as well as in a study of up/downwelling in shelf break canyons (Wang H. et al., 2022).

SCHISM is based on a customizable triangular–quadrangular unstructured horizontal grid. Flexible local refinement of the unstructured grid allows telescoping high horizontal resolution in areas of specific interest, and vice versa a low resolution in other parts of the domain. This feature facilitates high-resolution coupled ocean-ecosystem simulations at reasonable computational costs. The vertical coordinate is discretized with flexible hybrid Localized Sigma Coordinates with Shaved Cells (LSC²; Zhang et al., 2015). The LSC² vertical coordinate effectively reduces the pressure gradient force error (Zhang et al., 2016b). The LSC² vertical coordinate further enables the accurate representation of bathymetry without requiring bathymetry smoothing, which improves model accuracy at steep bathymetric slopes and sites of complex 3D bathymetry (Yu et al., 2017; Ye et al., 2018).

SCHISM solves the Reynolds-averaged Navier–Stokes equations in hydrostatic and Boussinesq approximated form with a semi-implicit finite-element/finite-volume method and an Eulerian–Lagrangian method (ELM) for momentum advection. The transport equations are solved with a robust third-order Weighted Essentially Non-Oscillatory (WENO) solver in the horizontal and an implicit Total Variation Diminishing (TVD) scheme in the vertical dimension. The advanced transport schemes are crucial for the simulation of baroclinic circulation and mesoscale dynamics in cross-scale applications (Ye et al., 2019). Density is calculated with the non-linear International Equation of State for Seawater (Fofonoff and Millard, 1983). Exchange with the atmosphere is computed with a bulk aerodynamic model (Zeng et al., 1998). Bottom drag is parameterized with the log law drag formula by Blumberg and Mellor (1987) and the use of a constant bottom roughness of 0.5 mm in this study. More detailed descriptions of the SCHISM model are given in Zhang et al. (2016a) and Zhang et al. (2016b).

Turbulence in form of eddy viscosities and eddy diffusivities is computed in SCHISM using the Generic Length-Scale formulation (GLS; Umlauf and Burchard, 2003). The specific parameterization of the GLS turbulence closure is set according to the k–kl model with KC94 stability functions (Kantha and Clayson, 1994). In this parameterization, the critical gradient Richardson number is R i C = 0.25 , in accordance with linear stability theory. The background diffusivity is set to 10 − 6   m 2 s − 1 . The maximum cutoff eddy diffusivity is set to 1   m 2 s − 1 .

SCHISM further adds bi-harmonic viscosity to the horizontal momentum equation to effectively remove spurious modes (Zhang et al., 2016b). The domain simulated in this study covers the deep ocean (e.g., eddying regime) and steep bathymetry at the shelf break that particularly exacerbates spurious modes (Yu et al., 2017; Ye et al., 2020). SCHISM augments the dissipation for such conditions by an additional Laplacian viscosity in the form of a spatially variable Shapiro filter (Zhang et al., 2016b; Ye et al., 2020). The local strength of the Shapiro filter is derived as a function of the local bathymetric slope α given by γ = 0.5 tanh ( 2 α / α 0 ) with a reference slope of α 0 = 0.5 .

SCHISM is coupled to the biogeochemical model ECOSMO II (Daewel and Schrum, 2013) via the FABM framework (Bruggeman and Bolding, 2014). ECOSMO II is a further developed version of the ecosystem model ECOSMO first introduced for the North Sea (Schrum et al., 2006). ECOSMO II uses a nutrient–phytoplankton–zooplankton–detritus (NPZD) conceptual model approach, and its extended formulation allows the simulation of lower trophic- level dynamics in a wide range of ecosystems (Daewel and Schrum, 2013; Pein et al., 2021; Yumruktepe et al., 2022).

ECOSMO II solves prognostic equations for a total number of 16 state variables. It simulates three separate nutrient cycles for nitrogen, phosphorous, and silicate. Oxygen is solved as an additional tracer. Primary production in ECOSMO II is divided into three phytoplankton functional groups (diatoms, flagellates, and cyanobacteria) and is limited by either nutrients or light. ECOSMO further includes two zooplankton functional groups (herbivorous and omnivorous) and three functional groups for detritus (particulate organic matter, dissolved organic matter, biogenic opal). Benthic–pelagic coupling is considered, as described in Daewel and Schrum (2013). The model considers three different integrated surface sediment pools for each of the three nutrient cycles, one for opal, one for particular organic material consisting of N and C at a Redfield ratio, and one for iron-bound phosphorous. Sediment processes include sediment nutrient release as well as sinking, deposition, and resuspension of POM depending on a critical bottom shear stress.

Light attenuation in ECOSMO II includes phytoplankton self-shading as well as shading by particulate organic matter (POM) and dissolved organic matter (DOM), as proposed by Nissen (2014) and implemented in Zhao et al. (2019). With this dynamical coupling of turbidity to the seasonal primary production cycle, the model explicitly resolves the competing major bottom-up tidal processes controlling primary production, namely, the reduction of light availability by resuspension and mixing of organic matter into the euphotic zone and the supply of nutrients by tidal mixing.

A detailed description of the ecosystem model as well as a validation against observations are given in Daewel and Schrum (2013). The parameter set used in this study is documented in the Supplementary Material (Table S1) .

The unstructured horizontal grid for the North-West European Shelf-Internal Tide (NWES-IT) model configuration used in this study was constructed with the Surface-water Modeling System software (SMS; Aquaveo, 2019). The NWES-IT domain spans 40°N – 66°N and 20°W – 30°E and thus covers the entire NWES and a part of the northeast Atlantic (see Figure 1 ). The Baltic Sea is included to adequately resolve basin-exchange processes but is not particularly attended to in this study as it does not feature relevant tidal energy. Sea ice, which usually develops seasonally in the Baltic Sea, is neglected for this study.

SCHISM’s cross-scale capabilities are used to achieve telescoping high horizontal resolution in regions affected by internal tide generation at the shelf break and at other extreme bathymetric slopes. The high horizontal resolution of 1.5 km is realized throughout the Celtic Sea and Armorican Shelves and in a 75-km- wide band delimited in an off-shelf direction by the 200-m isobath. The on-shelf extent of 75 km was chosen against the backdrop that most internal tide energy is dissipated within tens of kilometers of their generation site (Pingree et al., 1986; Inall et al., 2011). The horizontal resolution of 1.5 km resolves internal tides with wave lengths of 12–25 km generated by the regionally dominant M2 tide (Guihou et al., 2018). In order to accommodate numerical constraints on model accuracy, the horizontal resolution in the rest of the model domain is determined relative to local water depth and the model time step of 100 s used in this study. This yields a horizontal resolution that smoothly varies from a minimum of ~2.5 km in the shallow coastal zones, or even 500 m at finely resolved areas like the Danish Straits, to a maximum resolution of ~10 km in the deepest parts of the shelf (see Figure 1B ). At the shelf break, defined as the 200-m isobath, horizontal grid size smoothly transitions from 1.5 km to a quasi-uniform horizontal resolution of 10 km in the open Atlantic. The NWES-IT horizontal grid comprises a total number of ~386k grid nodes and ~758k triangular grid elements. A model configuration with a uniform horizontal resolution of 1.5 km would require approximately 2.3 million grid nodes. The coupled SCHISM–ECOSMO NWES-IT configuration runs ~ 170 times faster than real time with 36 CPUs on the Levante HPC-System at the German Climate Computing Center (DKRZ; https://www.dkrz.de, last accessed March 2023).

The coastline for the unstructured horizontal grid was derived from the GSHHS shoreline database at 5-km resolution (Wessel and Smith, 1996). The bathymetry for the domain was interpolated from the EMODnet Digital Bathymetry Digital Terrain Model (version 2018) dataset derived from the EMODnet Bathymetry portal (http://www.emodnet-bathymetry.eu; accessed 04/2020). The bathymetry in the model domain is documented in Figure 1A . The minimum water depth in the domain was set to 10 m to reduce computational demand. The bathymetry was modified at deep fjords along the Norwegian coast to simplify the horizontal and vertical gridding processes. No other bathymetry smoothing was applied.

The LSC² vertical grid designed for the NWES-IT model configuration realizes a high vertical resolution of 2.5–6 m from the surface to ~60-m depth in order to highly resolve the regional thermocline. The number of layers in the vertical grid varies from three layers for the minimum depth of 10 m to 53 layers for water depths larger than 6,000 m.

Model forcing for temperature and salinity, and ECOSMO state variables nitrate, phosphate, silicate, and oxygen, is provided from WOA2018 climatological data (Boyer et al., 2018). Open boundary conditions for the remaining ECOSMO state variables are taken from a HYCOM–ECOSMO hindcast simulation of the North Atlantic (Samuelsen et al., 2022). Dynamic oceanic forcing is provided twofold. Subtidal SSH and horizontal velocities are provided using daily averages from Samuelsen et al. (2022). The harmonic tidal signal is added to both SSH and the horizontal velocities from the FES2014 product (Lyard et al., 2021) for 15 tidal constituents (Q1, O1, P1, S1, K1, 2N2, MU2, N2, NU2, M2, L2, T2, S2, K2, M4). Corrections for multiyear tidal cycles like the lunar nodal and lunar perigee tide are applied. Tidal potential is applied for the partial tides in the model domain; the effects of self-attraction and loading are neglected. We provide daily river forcing in form of river discharge and nutrient loads for the 172 largest rivers in the domain. River discharge and nitrate, ammonium, phosphate, and silicate loads represent daily mean climatological values computed for the period 1986–2015 from a regional river dataset compiled and used by Daewel and Schrum (2013) and further updated as described by Zhao et al. (2019). We assume ambient temperatures for river discharge. At the sea surface, boundary conditions are provided from a hindcast simulation with the regional atmospheric model COSMO-CLM version 5 with 0.11° horizontal resolution (Geyer, 2017). The atmospheric forcing is provided at an hourly time step. A domain wide bias correction of +15% is applied to shortwave radiation in COSMO-CLM to account for a domain- wide sea surface temperature (SST) bias. Surface albedo is globally set to 0.06, and SCHISM light attenuation parameters are set to Jerlov type IA.

A faster coarse resolution SCHISM–ECOSMO NWES-LR configuration was used to run a 10 year spin-up simulation from which the initial conditions for the NWES-IT configuration are interpolated. The separate coarser resolution NWES-LR configuration was co-developed in the same manner as the NWES-IT configuration. Horizontal- grid resolution in the NWES-LR configuration ranges from 4.5 km in shallow coastal regions to approximately 10 km in deep central shelf areas and reaches 15 km in the open ocean ( Supplementary Material Figure S1 ). The LSC² vertical grid in NWES-LR is the equivalent of the one used in NWES-IT. Temperature, salinity, nitrate, phosphate, silicate, and oxygen for the NWES-LR configuration were initialized from WOA2018 (Boyer et al., 2018). ECOSMO sediment fields for NWES-LR were interpolated from long-term ECOSMO simulations provided by F. Werner (in prep.) and Samuelsen et al. (2022). Forcing data for the spin-up simulations is equivalent to the NWES-IT configuration.

We perform two numerical experiments with the NWES-IT model configuration to assess the impact of tides on NWES primary production. The TIDE experiment includes tidal forcing at the lateral open boundaries and tidal potential in the domain. In the NOTIDE experiment, the same model configuration is run completely without tidal forcing. Both experiments are integrated for a period of 6 years from 2010 to 2015 with hourly instantaneous model output. Model output is averaged to daily means and only saved in full temporal resolution for specified months to reduce memory use. The first year of the TIDE/NOTIDE experiments is treated as a secondary spin-up period and omitted from the analysis.

Seasonal stratification on the NWES leads to a quasi two-layer system in spring and summer, with a warm wind-mixed surface layer formed over cold deeper water masses. The pycnocline separates the two layers. Internal tides propagate in the horizontal direction along the pycnocline. In order to achieve realistic bulk mixing, the model needs to adequately represent the properties of the surface and bottom layers, as well as the depth of the layer interface.

We use the potential energy anomaly (PEA, Simpson et al., 1981) to characterize the stratification of the water column. The potential energy anomaly is a measure of the amount of work required to vertically mix the entire water column and is calculated as:

with the depth mean density ρ ¯ =   1 H   ∫ − H η ρ   d z , the mean water depth H, the sea surface elevation η , the actual water depth D = h +   η , and the gravitational acceleration g.

In order to assess stratification in vertical temperature profiles, we define the thermocline depth following Guihou et al. (2018) as a normalized first moment of stratification:

Here, H is the depth of the water column, T t o p and T b e d ( t ) are the surface and bed temperatures at a given time, and T ¯ ( t ) is the depth-averaged temperature. The thermocline depth is represented by δ ( t ) in the limit of a two-layer vertical density structure. The pycnocline depth is derived in the same manner using density instead of temperature.

Internal waves that propagate along the layer interface lead to oscillatory vertical displacements of the pycnocline. We analyze the variability due to tidally generated internal waves with the help of the tidally filtered interface depth 〈 δ 〉 computed with a Doodson X0 filter (Intergovernmental Oceanographic Commission, 1985). The pycnocline depth variability is then defined as:

The standard deviation of the tidal fluctuations in pycnocline depth can then be calculated as an estimate of the internal tide activity on shelf scale:

The standard deviation of δ ˜ is calculated over a moving 3 × 24-h window to avoid aliasing from the spring-neap cycle while retaining sufficient data to isolate a clear signal. The standard deviation of δ ˜ represents a conservative estimate of the tidal variability in the vertical pycnocline displacements (Guihou et al., 2018).

Dissipation of the energy of baroclinic and barotropic tides induces turbulence that mixes nutrients and other tracers in the water column. To assess the ecosystem-relevant turbulent mixing associated with tides, we compute the turbulent nitrate flux in the water column following Sharples et al. (2001) as:

with the (vertical) eddy diffusivity K V   computed by the model turbulence closure, the difference in nitrate concentration between the respective discretized vertical model layers Δ N O 3 , and the vertical model layer thickness Δ z in meters. The turbulent nitrate flux J N O 3 can be used to estimate the potential for new production (Dugdale and Goering, 1967) fueled by allochthonous nitrate from the bottom layer. Assuming full utilization of the vertically mixed nitrate by phytoplankton, we compute potential new production as:

where J N O 3 ( z E ) is the turbulent nitrate flux evaluated at the base of the euphotic zone, R N is the standard N:C Redfield ratio, and M C is the molar mass of carbon.

We evaluate the newly developed NWES-IT configuration’s ability to reproduce general hydrographic and biogeochemical conditions on the NWES and specifically assess its skill in regard to tidal processes. We evaluate the results of the TIDE experiment on the western part of the NWES (i.e., the Celtic Seas and greater North Sea) over the 5-year period from 2011 to 2015.

To facilitate model validation, we divide the NWES into subareas (see Figure 1A ) following a combination of bathymetric, geographic, and physical and ecosystem considerations based on Holt et al. (2012) and the ICES subareas (ICES, 1983). The greater North Sea is divided into the southern North Sea (SNS), the central North Sea (CNS), the northern North Sea (NNS), the English Channel (EC), the Norwegian Trench (NT), and the Kattegat/Skagerrak (SK) subareas. The Celtic Seas are divided into the Armorican Shelf (A), the Celtic Sea (C), the Irish Sea (I), the Inner Seas off the West Coast of Scotland (Sc), and the North-Western Approaches (NWA). The Celtic Sea and the North-Western Approaches are further separated into smaller subareas for a more detailed analysis of tidal impacts. The northeastern inner shelf region (NEC) and the southwestern outer shelf region (SWC) of the Celtic Sea are separated by the approximate 130-m isobath. The North-Western Approaches subarea is divided into the Western Irish Shelf (WI), the Malin Shelf (MS), and the Hebrides Shelf (HS).

The signature of tidal mixing is illustrated in Figure 7A by means of the annual mean Potential Energy Anomaly (PEA; Eq. 1) computed for the period of maximum stratification from mid-June to mid-August (2011–2015). Permanently mixed areas (PEA < 20  Jm − 3 ) are separated from seasonally stratified areas by tidal mixing fronts, e.g., in the southern North Sea, the western approaches of the English Channel or the St. George front separating the Celtic and Irish Seas. PEA magnitude and the positions of the tidal fronts match results of previous studies and observations (Holt and Umlauf, 2008; Pätsch et al., 2017; Graham et al., 2018a) and thus further substantiate the adequate simulation of the mixing-stratification status on the NWES outlined in Sect. 2.5.

The refined horizontal grid resolution in the NWES-IT configuration reproduces pycnocline depth variability at tidal frequencies that suggests the presence of kilometrical-scale internal tides (Sect. 2.5.3). We compute the pycnocline depth tidal standard deviation s t d ( δ ˜ ) (Eq. 4) for a spring tide period from 11 to 14 August 2014 to evaluate the resolved internal tide activity on the entire NWES. We chose a period in early August because the vertical temperature gradients, which mainly control stratification on the NWES, are largest in late July and early August.

The computed s t d ( δ ˜ ) in Figure 7B shows high spatial variability on the NWES; it ranges from 0 to over 8 m at sites along the shelf break. The results from the NWES-IT configuration show high consistency with kilometrical-scale regional model results presented by Guihou et al. (2018). The s t d ( δ ˜ ) along the shelf break of the northern North Sea, where the continental slope is subcritical for internal tide generation (Huthnance et al., 2022), is low. The local horizontal grid resolution (6–10 km; see Figure 1B ) does not resolve kilometrical-scale processes in the central North Sea, and the NWES-IT configuration consequently does not reproduce internal tides in this region. The study of Guihou et al. (2018) shows only very low internal tide activity in the central North Sea, so that the low internal tide activity in the NWES-IT configuration fits with the expected internal tide activity in the region. The s t d ( δ ˜ ) in Figure 7B is significantly elevated along the steep shelf break of the Celtic Sea, in line with multiple observational studies that show high internal tide activity in this region (Pingree and Mardell, 1985; New and Pingree, 1990; Sharples et al., 2007; Green et al., 2008; Inall et al., 2011). The s t d ( δ ˜ ) is also elevated on the Malin Shelf and its continental slope, where on-shelf propagation of internal tides has also been observed (Sherwin, 1988; Rippeth and Inall, 2002). The s t d ( δ ˜ ) is intermediate on the narrow Hebrides Shelf but is elevated on the continental slope close to the Wyville Thomson Ridge known for internal tide generation (Sherwin, 1991; Hall et al., 2019).

The fine-scale structure of s t d ( δ ˜ ) throughout the Celtic Sea further suggests a complex and spatially variable internal tide field with internal tide generation at small-scale bathymetric features like canyon ridges and sea banks. Increases of s t d ( δ ˜ ) at the edge of the permanently mixed areas on the shelf do not indicate increased internal tide activity but reflect reduced stratification. The resolved spatial variability of internal tide activity in the Celtic Sea is consistent with the results of Guihou et al. (2018) and non-hydrostatic simulations in smaller areas of the Celtic Sea (Vlasenko et al., 2013; Vlasenko et al., 2014).

We investigate the impact of tidal forcing on primary production on the NWES by comparing the mean annual primary production (2011–2015) from the NWES-IT experiments with and without tidal forcing. Figure 6A shows mean annual net primary production (NPP) in the TIDE experiment with tidal forcing. Figure 6B shows the respective difference in mean annual NPP between the TIDE experiment and the NOTIDE experiment. Table 2 further documents the NPP response to tidal forcing for the subareas introduced in Sect. 2.5. Note that the Celtic Sea and the North-Western Approaches are separated into smaller subareas for a more detailed analysis of tidal impacts, as described in Sect. 2.5.2 and documented in Figure 1B .

The comparison of mean annual NPP in the two experiments in Figure 6B shows that tidal forcing extensively structures biological productivity on the NWES. Tidal forcing substantially increases mean annual primary production on the shelf by around 16% (~14.47 Mt C; Table 2 ). The tidal response of primary production on the inner shelf found in this study is similar to results obtained by Zhao et al. (2019) for the central and southern North Sea. Tidal impacts on the inner shelf can largely be classified based on stratification characteristics and water depths. Tidal forcing decreases productivity in the majority of the shallow permanently mixed regions of the NWES (see PEA in Figure 7A ). The tidal NPP response is also negative in the tidally energetic North Channel between Ireland and the UK. Shallow stratified areas of the NWES in turn are particularly responsive to tidal mixing of nutrients and show strong productivity increases. The dynamic tidal frontal systems in the southern North Sea, northeastern Celtic Sea, or western English Channel particularly invigorate local primary production in the TIDE experiment.

The tidal NPP response is generally lower in the deep outer shelf regions of the NWES. The northern North Sea shows a minor positive response to tidal forcing (+2%; Table 2 ) but features local reductions of up to − 10   gCm − 2 yr − 1 . Tidal NPP response on the northern North Sea continental slope is neutral or marginally negative. Tidal forcing also locally decreases NPP on the Hebrides shelf, but the HS subarea still shows an aggregated increase of +4%. At around 58°N, tidal forcing locally increases NPP by 10 − 15   gCm − 2 yr − 1   in a patch on the continental slope. The tidal NPP response further increases southward and yields +6% for the Malin Shelf subarea, where NPP is particularly enhanced by tidal forcing in a small region that also features high internal tide activity in Figure 7B . NPP is also increased by 10 − 15   gCm − 2 yr − 1 on the continental slope of the Malin Shelf at around 55.5°N and on the northern flank of the Porcupine Seabank.

The Celtic Sea in the southwest of the NWES stands in stark contrast to the North-Western Approaches, highlighting substantial regional differences in the impact of tidal forcing on primary production along the NWES shelf break. Although the water depth in the southwestern Celtic Sea (SWC) subarea is comparable with, e.g., the NNS (> 130 m), the SWC subarea still shows a substantial NPP increase of +25% with tidal forcing ( Table 2 ). Highest NPP increases (locally up to 50   gCm − 2 yr − 1 ) occur on the continental slope of the Celtic Sea in the English Channel tidal flux window at around 5.5 – 8.5°W. Tidal forcing moreover substantially increases NPP in the deep outer shelf area along the Celtic Sea shelf break (up to 30   gCm − 2 yr − 1 ) and the central Celtic Sea (up to 35   gCm − 2 yr − 1 ). The deep water column limits the impact of the barotropic tide in the region. Figure 7B however indicates high internal tide activity.

We turn to the seasonal cycle of NPP to examine the regional differences of the tidal NPP response in the deep shelf areas along the shelf break in more detail. Figures 6C, D show the mean seasonal cycle of NPP (2011–2015) averaged for the southwestern Celtic Sea (SWC, Figure 6C ) and the Hebrides Shelf (HS, Figure 6D ) subareas. The seasonal cycle of NPP in the TIDE experiment in Figure 6C fits with observations by Joint et al. (2001), who found an extended spring bloom from March to June in the Chapelle Bank region on the Celtic Sea shelf break. Tidal forcing marginally increases spring NPP in the HS subarea in March and then decreases from April to early June ( Figure 6D ). In the Celtic Sea, tidal forcing similarly increases NPP in late March/early April and then reduces NPP until late May. The decrease of spring NPP by tidal forcing is more pronounced in the HS subarea than in the SWC subarea. We attribute the reduction in spring NPP to a delay of the spring bloom that is caused by the deepening of the mean spring surface mixed layer in the TIDE experiment by 8 and 4 m in the HS and SWC subareas, respectively. In a deeper mixed layer, phytoplankton spends less time in favorable light conditions close to the surface, which hinders the buildup of spring bloom biomass in this period. This mechanism was also identified for the northern North Sea in Zhao et al. (2019).

Tidal forcing continuously enhances NPP during the summer bloom period in the southwestern Celtic Sea. The largest tidally induced increase in NPP in the SWC occurs in late spring/early summer; the averaged NPP in the SWC is up to 6 gC m − 2 d − 1 higher in the TIDE experiment in late May/early June. Tidal forcing moreover marginally increases autumn NPP in the SWC. Tidal forcing also increases summer NPP in the HS subarea, but the magnitude of the increase is substantially lower (only up to 2 gC m − 2 d − 1 ) than in the SWC. In the HS subarea, the largest difference between the TIDE and NOTIDE experiment occurs in July.

Tinker et al. (2022) have shown significant tidal impacts on the residual circulation on the NWES, which are reproduced in our study ( Figure S5 Supplementary Material ). Tidal phase-driven transport can locally increase residual shelf circulation. Tides also increase bed friction on the shelf, which in turn can decrease the residual shelf circulation. The latter tidal impact particularly affects regions of freshwater influence (Lin et al., 2022; Tinker et al., 2022). A tidal slowing of river water export may contribute to the decrease in mean (summer) surface nutrient concentrations found in ROFIs along the Dutch and German continental coast or in the English Channel (see Figure 8 ). The (permanently mixed) near-coast areas however are not nutrient limited but light limited (Tett and Walne, 1995) because of intense vertical mixing, high riverine nutrient inputs, and on-shore transport of nutrients and organic matter by estuarine-type circulation (Hofmeister et al., 2017). The reduction of the residual circulation along the continental coast is thus not the decisive factor for the negative near-coast NPP response to tidal forcing. Instead, in line with Zhao et al. (2019), we find that this impact is caused by the degradation of local light conditions due to tidally enhanced resuspension and vertical mixing of POM. Zhao et al. (2019) further established that the major tidal impact on NPP in the seasonally stratified and tidal frontal regions of the North Sea is via vertical mixing of nutrients. We therefore focus our analysis of tidal impacts on vertical mixing in the following sections.

The presented study considers major bottom-up processes controlling the tidal impact on primary production, including the tidal mixing of nutrients and organic matter, as well as the resuspension of POM. The 10-m minimum water depths used in this study however limits the representation of particularly shallow coastal regions, as a wetting and drying scheme is not implemented in the model configuration. River plumes and related near-coastal currents may therefore be underrepresented. Moreover, the identified sensitivity of primary production to tidal forcing could be affected by sediment retention by macrobenthos (Prins et al., 1996; Kamp and Witte, 2005; Le Guitton et al., 2017) and its impact on water column turbidity through reduced POM resuspension. The influence of inorganic suspended particulate matter on tidal impacts on NPP is another source of uncertainty in the presented approach that needs to be addressed in future research.

We investigate the tidal impact on vertical mixing of nutrients to evaluate its role for the tidal NPP response shown in the previous section. In light of the substantial positive NPP responses found in areas of internal tide activity, we will particularly evaluate the impact of internal tides on vertical mixing. We focus on nitrate in the following, as it is the main limiting nutrient for primary production in the stratified regions of the NWES. We compute the mean turbulent nitrate flux J N O 3 ¯ (Eq. 5) during the period of strongest stratification (15 July– 15 August; mean for 2011–2015) to assess how effective turbulence in the water column mixes across the nitrate gradient and replenishes nutrients in the euphotic zone. Figure 9A shows the difference in J N O 3 ¯ between the TIDE experiment and the NOTIDE experiment along a vertical transect that spans from the tidal frontal region in the Irish Sea to the shelf break of the Celtic Sea. The transect is marked in Figure 1B . The corresponding vertical transect of mean eddy diffusivity K V ¯ from the TIDE experiment is shown in Figure 9B .

In shallow regions with strong tidal currents, like the Irish Sea on the left- hand side of Figure 9 , tides and wind generate turbulence in the entire water column ( Figure 9B ). In transitionary tidal frontal areas, the surface and bottom layer strongly interact and wind forcing or the spring-neap tidal cycle can laterally move the tidal front. The persistent competition between tidal mixing and thermal stratification generates intense turbulent mixing of nutrients into the upper water column on the stratified side of the front (e.g., Pingree et al., 1975). Changes in stratification and/or the vertical nitrate gradient by tidal stirring in the bottom boundary layer can also decrease turbulent transports in some regions (see Figure 9A ).

In the stably stratified section of Figure 9 , the pycnocline (marked by the N² contours) suppresses turbulence and acts as a flux barrier. Tidal forcing can however also generate turbulence within the pycnocline, where turbulence has a particularly high mixing efficiency due to stronger vertical gradients (Rippeth, 2005). Figure 9A accordingly shows high tidally generated J N O 3 ¯   at the base of the pycnocline in the northeastern Celtic Sea (water depth< 130m). Pycnocline mixing is elevated at bathymetric features and particularly high at the Jones Bank (approx. 350km in Figure 9 ).

Pycnocline mixing requires shear to be produced in the pycnocline, either directly by the barotropic tide, internal waves, or wind-induced inertial oscillations. Becherer et al. (2022) found the barotropic tide alone to produce sufficient shear at the base of pycnocline to generate observed diapycnal mixing in the shallow southern North Sea. In the Celtic Sea, with its energetic internal tide field, internal wave breaking will contribute as well. The separation of the surface and boundary mixed layers increases in the deeper water column in the southwestern part of the transect shown in Figure 9 (beyond the Jones Bank). Here, the impact of the barotropic tide becomes negligible and pycnocline mixing relies on shear instabilities produced by inertial oscillations and internal waves. Figure 9A shows tidal forcing enhances J N O 3 ¯ within the pycnocline in the deep southwestern section of the transect. Tidal forcing particularly enhances J N O 3 ¯ within the pycnocline in the region close at the shelf break. Turbulent mixing of nitrate across the pycnocline has been observed in the shelf regions along the Celtic Sea shelf break and is attributed to mixing by the energetic internal tide field (Sharples et al., 2007; Sharples et al., 2009). Tidally elevated J N O 3 ¯ in the pycnocline in proximity to the Jones Bank further suggests mixing by internal tides generated at the local extreme bathymetry, which also fits with observations (Palmer et al., 2013; Tweddle et al., 2013).

To obtain a shelf-wide estimate of the turbulent transport that can sustain (new) primary production in the stratified system during summer, we evaluate the mean turbulent nitrate flux at the nutricline (denoted as J N O 3 ( z N ) ¯ in the following). We define the nutricline as the maximum vertical nitrate gradient in the water column. We here follow Sharples et al. (2001) and utilize the condition that primary production sets up the nutricline at the base of the euphotic zone below the subsurface biomass maximum in the pycnocline. We show J N O 3 ( z N ) ¯ averaged for the period of maximum stratification from the 15 July to 15 August for the entire NWES in Figure 10A and for the Celtic Sea in Figure 10C . To understand the impact of tides on vertical mixing, we further compute the difference between J N O 3 ( z N ) ¯ in the TIDE and NOTIDE experiments. The proportional difference between the two experiments, expressed as Δ J N O 3 ( z N ) ¯ , is shown in Figure 10B .

J N O 3 ( z N ) ¯ in Figure 10A, C is zero if there is no vertical nitrate gradient, like in the permanently mixed regions along the coasts. In the northeastern Celtic Sea, the fresh and nutrient-rich river outflow from the Bristol Channel obscures the mixing signal. Figure 10A shows that turbulent transports are high in the tidal frontal regions and weakly stratified shallow regions (delineated by PEA = 50   J m − 3 in Figure 10A ). The high turbulent nutrient supply to the surface sustains particularly high NPP rates in the transitionary regimes, as can be seen by the spatial coherence of high NPP in Figure 6A and the high J N O 3 ( z N ) ¯ found along tidal frontal zones in the NWES (e.g., in the western English Channel or southern North Sea).

Turbulent nitrate fluxes across the nutricline are generally low in the stably stratified regions of the NWES (PEA > 50   Jm − 3 ). Figure 10A shows J N O 3 ( z N ) ¯ <   0.5   mmol N m − 2 d − 1 in most of the central areas of the Celtic Sea and North Sea basins. Observations of diapycnal nutrient fluxes on the NWES are sparse and limited in time, making a direct comparison difficult. Observational estimates suggest a background flux of 1 − 2   mmol N m − 2 d − 1 for the wider Celtic Sea region (Sharples et al., 2001; Williams et al., 2013b). A general underestimation of pycnocline mixing in stratified shelf areas is common for turbulence closures like the GLS k–kl closure used in this study. The deficiency in the representation of pycnocline mixing is attributed to the fact that the parameterizations do not include all physical processes that contribute to pycnocline mixing on the shelf (Simpson et al., 1996; Rippeth, 2005). Observational estimates close to the Norwegian Trench region of the North Sea ( < 0.5   mmol N m − 2 d − 1 ; Bendtsen and Richardson, 2018) and the Western Irish Sea ( 0.31  mmol N m − 2 d − 1 ;   Williams et al., 2013a) however fit better with the mixing reproduced by the model.

The difference in J N O 3 ( z N ) ¯ between the NOTIDE and TIDE experiments in Figure 10B shows that tidal impacts explain almost all turbulent mixing across the nutricline in the shallow stratified regions of the NWES and a relevant proportion of J N O 3 ( z N ) ¯ in the central basins of the North Sea and Celtic Sea. Tidal impacts on J N O 3 ( z N ) ¯ clearly depend on local water depths and mirror the decreasing positive tidal NPP response with water depths in Figure 6B . J N O 3 ( z N ) ¯ decreases with water depths as mixing driven by the barotropic tide loses the potential to affect the euphotic zone. To effectively differentiate between turbulent mixing induced by the barotropic tide and by baroclinic processes like internal tides, we compute the distance Δ Z N B between the nutricline, as a proxy for the euphotic depth, and the depth at which the eddy diffusivity K V ¯ falls below 10 − 3   m 2 s − 1 in the bottom layer as a proxy for the extent of the bottom boundary layer.

Figure 10D shows mean Δ Z N B on the NWES for the period of maximum stratification from the 15 July to 15 August (mean for 2011–2015). The visual comparison with Δ J N O 3 ( z N ) ¯ in Figure 10B indicates that in the North Sea, where there is low internal tide activity, Δ Z N B = 30 m approximately concurs with the extent of positive (i.e., tide-induced) Δ J N O 3 ( z N ) ¯ . The comparison with the tidal NPP response in Figure 6B supports this assumption; here, Δ Z N B = 30 m approximately corresponds to the boundary of the positive tidal NPP response. We use this simplified approximation to define that at Δ Z N B > 30 m , the impact of the barotropic tide on pycnocline mixing becomes negligible and baroclinic processes like internal tides are the dominant drivers of pycnocline mixing.

As already indicated in Figure 9A , turbulent nitrate fluxes across the nutricline are enhanced in a distinct band along the Celtic Sea shelf break ( Figures 10A–C ). The barotropic tide plays a role in the EC tidal flux window (5.5 – 8.5°W), where tidal energy dissipation is very high (Pingree et al., 1982) and Δ Z N B < 30 m extends nearly up to the shelf break ( Figure 10D ). J N O 3 ( z N ) ¯ is particularly high at the shelf break part of the EC tidal flux window (locally up to 5 mmol N / m 2  d ). The remaining area of elevated J N O 3 ( z N ) ¯ along the shelf break shows pronounced separation of bottom and surface mixed layers ( Δ Z N B ≫ 30 m ). In the sector of the Celtic Sea shelf break north of 8.5°W, Figures 10A, C show elevated J N O 3 ( z N ) ¯ with values in the range of ~ 0.5 − 2  mmol N m − 2 d − 1 . Local mixing hotspots with J N O 3 ( z N ) ¯ of up to 5   mmol N m − 2 d − 1 are also evident on the northern sector of the Celtic Sea shelf break. The elevated average turbulent nitrate fluxes fit with the observed range of 1 − 9   mmol N m − 2 d − 1 reported for the northern sector of the Celtic Sea shelf break by Sharples et al. (2007). The area of tidally enhanced nitrate fluxes along the Celtic Sea shelf break in Figures 10A–C extends approximately 10–40 km onto the shelf. This also agrees with the observed dissipation of the majority of baroclinic energy within tens of kilometers of the generation site (Pingree et al., 1986; Inall et al., 2011).

Figure 10C further indicates elevated J N O 3 ( z N ) ¯ at small-scale bathymetric features throughout the Celtic Sea, with mean mixing rates of 0.5 − 3   mmol N m − 2 d − 1 at the respective ridges and sea banks. J N O 3 ( z N ) ¯ shown in Figure 10C reaches values of up to 10   mmol N m − 2 d − 1 at the distinct Jones Bank, which is well within the range of observed mixing rates attributed to local internal lee wave generation (Tweddle et al., 2013; 0.8 − 52  mmol N m − 2 d − 1 ).

Background turbulent nitrate fluxes across the nutricline are overall higher on the narrow North-Western Approaches than in the southwestern Celtic Sea. Figure 10A shows elevated J N O 3 ( z N ) ¯ in some areas along the shelf break of the NWA where the surface and bottom layer are well separated ( Δ Z N B ≫ 30 m ). J N O 3 ( z N ) ¯ is up to 15   mmol N m − 2 d − 1 along the shelf break northwest of Ireland at around 54.5 – 55.5°N, where upper-slope bathymetry is irregular and features a distinct canyon (Huthnance et al., 2022). J N O 3 ( z N ) ¯ is also elevated ( 1 − 4   mmol N m − 2 d − 1 , locally up to 18   mmol N / m 2  d ) along the shelf break of and on the Malin Shelf at around 56 – 57°N, in an area where Figure 7B shows high internal tide activity and mixing by internal tides has been observed (Sherwin, 1988; Rippeth and Inall, 2002). A small area of high J N O 3 ( z N ) ¯ further occurs on the shelf break of Hebrides Shelf at around 7–8°W; here, Figure 10A shows values of up to 20   mmol N m − 2 d − 1 . J N O 3 ( z N ) ¯ on the northern North Sea shelf and shelf break is comparatively low. Small patches of elevated J N O 3 ( z N ) ¯ with up to 5   mmol N m − 2 d − 1 occur at the shelf break north of the Fair Isle Channel and the Shetland islands. A small area at northwestern edge of the Norwegian Trench potentially affected by the low salinity Baltic Sea outflow also shows J N O 3 ( z N ) ¯ of up to 20   mmol N m − 2 d − 1 .

The impact of the barotropic tide in the deep regions along the shelf break of the NWES is negligible ( Δ Z N B ≫ 30 m in Figure 10D ). Figure 10B nevertheless shows that tidal forcing accounts for >60% of locally elevated J N O 3 ( z N ) ¯ in the region along the Celtic Sea shelf break during the investigated period of strongest stratification. Tidal forcing also accounts for >40%–60% of the locally elevated J N O 3 ( z N ) ¯ on the Malin Shelf. Positive Δ J N O 3 ( z N ) ¯ further correlates with elevated J N O 3 ( z N ) ¯ on the northern flank of the Porcupine Bank, the Hebrides Shelf at around 7–8°W and the shelf break section north of the Fair Isle Channel. Sites of positive Δ J N O 3 ( z N ) ¯ generally feature relevant internal tide activity ( Figure 7B ), whereas regions of low internal tide activity along the shelf break of the NWES partially feature low or negative Δ J N O 3 ( z N ) ¯ . The finding that Δ J N O 3 ( z N ) ¯ predominantly explains locally elevated J N O 3 ( z N ) ¯ along the shelf break and the coherence with sites of high internal tide activity shows that the vertical mixing along the shelf break is caused by the resolved kilometrical-scale internal tide field in the region. The dissipation of on-shelf propagating low-mode internal tides vertically mixes nutrients into the euphotic zone and can contribute to the positive tidal NPP response identified for the shelf break regions in Figures 6B–D .

The emergence of substantially tidally elevated pycnocline mixing rates in proximity to internal tide generation sites suggests that resolving kilometrical-scale internal tides locally reduces the mid-water mixing deficiency commonly identified for stratified shelf regimes in ocean models (Simpson et al., 1996; Burchard et al., 2002; Rippeth, 2005). Our results here support Graham et al. (2018a), who suggested that a reduction of a warm SST bias along the Celtic Sea shelf break in their kilometrical-scale AMM15 NEMO model configuration was due to enhanced mixing by resolved internal tides. Pycnocline mixing simulated with a hydrostatic model like SCHISM will still likely underestimate mixing by the fully non-hydrostatic internal wave field (Vlasenko et al., 2014). Our results thus only constitute a lower bound for the impact of internal tides on shelf primary production. An improved representation of the non-linear interaction of wind-generated inertial oscillations and internal tides would also further improve the parameterization of the magnitude and episodic nature of mixing within the pycnocline (Davies and Xing, 2003; Hopkins et al., 2014), with potential impacts in central shelf areas as well. The representation and potentials for such non-linear interaction in kilometrical-scale regional ocean models is particularly interesting in this regard.

We further assess the contribution of tide-induced vertical mixing to the overall tidal NPP response in summer for the shelf areas along the shelf break. We compute tidally generated potential new production (PNP; Eq. 6) using the sum of tide-generated mean turbulent nitrate fluxes across the nutricline, i.e., Δ J NO 3 ( z N ) , over the summer months (JJA; mean for 2011–2015). We only consider stably stratified areas with PEA > 50   Jm − 3 , which explicitly excludes the tidal frontal areas. We further isolate the contribution of the internal-tide field from Δ J NO 3 ( z N ) by masking regions with ΔZ NB < 30 m and only considering the shelf area resolved at kilometrical-scale horizontal resolution. The results are summarized in Table 3 .

Tide-generated potential new production sustained by vertical mixing across the pycnocline explains 20% (0.23 Mt C) of the mean tidal summer NPP response (JJA; 2011–2015) in the SWC subarea, with around 50% of PNP attributable to mixing by the internal tide alone ( Table 3 ). Tide-generated pycnocline mixing in summer therefore only sustains ~ 3% of mean annual primary production in the SWC subarea. The remaining difference in mean summer NPP between the TIDE and NOTIDE experiments in the southwest Celtic Sea (0.92 Mt C; 80%) suggests that other tidally modulated processes are relevant for local primary production as well.

An intensification of regenerated primary production in the surface layer with tidal forcing, potentially associated with the delay of the spring bloom with tidal forcing (see Sect. 3.2) or re-entrainment of organic matter into the surface layer, could also play a role in the tidal NPP response in the Celtic Sea. Huthnance et al. (2022) further showed baroclinic on-shelf transport by internal tides at mooring stations at the Celtic Sea shelf break in summer. Graham et al. (2018b) also found substantial on-shelf transports along the pycnocline and in the surface layer at the Celtic Sea shelf break in late spring and summer and attributed the on-shelf transport at internal depths to internal tides resolved in their kilometrical-scale NEMO AMM15 model configuration. Tide-driven on-shelf transport would explain higher early summer nutrient concentrations in the TIDE experiment found in the outer shelf regions along the Celtic Sea shelf break for both the surface layer (>20 m; Figure 8A ) and at internal depths (20–100 m; Figure 8B ) in our study. In combination, the increased lateral on-shelf transport of nutrients from the tidally enhanced shelf break front ( Figures 6B , 8A ) and vertical mixing by internal tides likely account for the majority of the tidal response of summer NPP in the region. Recent work by Tinker et al. (2022) has also shown an impact of tidal forcing on the residual circulation on the NWES, with a pronounced tidal impact on the continental slope current. Tidal flow can additionally influence local circulation through topographically driven residual eddies, which are resolved at kilometrical-scale horizontal resolution in the Celtic Sea (Polton, 2015). Changes in the residual circulation potentially affect the nutrient distribution and biological productivity in the southwestern Celtic Sea. A detailed analysis of the different tidal impacts on cross-shelf horizontal transports is however beyond the scope of this study.

Analysis of potential new production driven by vertical mixing is more complex on the narrow shelves of the North-Western Approaches. The surface layer on the North-Western Approaches is not nutrient depleted in summer (Savidge and Lennon, 1987; Painter et al., 2017) because of cross-shelf exchange with nutrient-rich North Atlantic current water masses and upwelling at the shelf break (Huthnance et al., 2022). The persistent availability of nutrients in the surface layer throughout summer effectively limits the local NPP response to additional nutrient supply by tidal processes, which is particularly evident in tidal frontal zones (see Figure 6B ). Table 3 nevertheless shows that tide-generated potential new production supplied by vertical mixing across the pycnocline can explain most of the low tidal response of summer NPP in the stratified areas of the Malin Shelf (92%) and Hebrides Shelf (65%). Tide-generated potential new production however only accounts for 30% of the tidal summer NPP response in the northern North Sea, suggesting relevant contributions of other tidally modulated processes here as well.