We assess the temperature and biological control of surface pCO₂ following the approach proposed by Takahashi et al. (2002), which uses a linearization of the temperature dependency of pCO₂ to differentiate between temperature and biologically driven changes of pCO₂. We calculate the effect of temperature and biology on pCO₂ over an annual cycle as

where p C O 2 and T are in-situ pCO₂ and temperature, and p C O 2 ¯ and T ¯ denote annual means. p C O 2 T here estimates the pCO₂ values expected from changes in sea surface temperature alone. The biological signal p C O 2 b i o in this approach inherently comprises all non-temperature related effects on pCO₂ (e.g. also changes in TA).

Again, following Takahashi et al. (2002), the ratio of the effects of temperature and biology on surface pCO₂ was calculated to assess the relative importance of biology and temperature over the annual cycle:

with the seasonal amplitudes of the change in pCO₂ related to temperature and biological effects:

Regions with annually strong biological effects on pCO₂ will show a smaller T / B ratio, while regions with weaker biological effects on pCO₂ show a higher T / B ratio.

We calculate net community production (NCP), i.e. the difference between net primary production and heterotrophic pelagic and benthic remineralization, to evaluate the net change of DIC in the water column evoked by biological processes. We calculate net community production as

where N P P P 1 , P 2 , P 3 is net primary production by the three phytoplankton functional groups, H R P = ϵ D O M C D O M + ϵ P O M C P O M + μ 1 C Z 1 +   μ 2 C Z 2 is pelagic heterotrophic remineralization comprising DOM and POM remineralization and zooplankton excretion (see Equation 1) and F D I C , b e n t h i c is the DIC release from benthic remineralization.

To assess turbulent mixing relevant for the carbonate system, we compute turbulent fluxes of DIC and nitrate following Sharples et al. (2001) and in line with Kossack et al. (2023) as

with the (vertical) eddy diffusivity K V computed by the model turbulence closure, the difference in nitrate and DIC concentrations between the respective discretized vertical model layers Δ N O 3 and Δ D I C , and the vertical model layer thickness Δz in meters. To get the upward diapycnal fluxes from the nutrient-rich deeper water masses into the euphotic zone, we evaluate the diapycnal fluxes at the nutricline z N (defined as the maximum vertical nitrate gradient in the water column) using daily averaged model output. The nutricline z N is here assumed to constitute the base of the euphotic zone.

The turbulent nitrate flux J N O 3 into the euphotic zone can be used to estimate a potential for subsurface primary production, which constitutes a DIC sink that may affect air-sea CO₂ exchange. Assuming full utilization of the vertically mixed nitrate by phytoplankton, we compute potential subsurface primary production as

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

We co-locate the observational DIC and TA samples from the GLODAPv2.2022 data product and daily mean model output in time and space for each subarea to quantitatively assess the model’s consistency with the spatial and temporal variability of the large-scale carbonate system. Data sparsity limits the quantitative validation of DIC and TA to the greater North Sea area (i.e. the SNS, CNS, NNS, SK and NT subareas in Figure 1B ). The direct co-location of observational data and model results is a rigorous test for the model and sensitive to relatively minor spatial and temporal mismatches between model and observations (Allen et al., 2007; Artioli et al., 2012).

Figure 3 shows the normalized and centered statistics of the co-located DIC data for the greater North Sea subareas in form of a Taylor diagram. Correlation coefficients between simulated DIC and observations are > 0.8 for the NNS, NT and SK subareas and 0.79 in the central North Sea. The southern North Sea shows the lowest correlation for DIC (SNS ≈ 0.52 ). The normalized standard deviation for DIC is below 1 in all evaluated subareas and lowest in the CNS, indicating an underestimation of the amplitude of DIC variability (in time and space) in the model. Normalized centered root mean square differences (CRMSD) calculated for DIC in the subareas are between 0.5 and 1, which suggests a good fit between the model data and observations. The SNS shows the highest normalized CRMSD, which again underlines reduced model performance for DIC in the shallow SNS compared to the deeper North Sea areas.

The Taylor plot in Figure 3 illustrates that TA shows poorer agreement with observations than DIC, particularly in the northern North Sea subarea. The correlation coefficient between simulated TA and observations is moderately high for the NT ( ≈   0.77 ) and SK ( ≈   0.71 ) subareas, and ≈ 0.51 for the SNS. Correlation is however low   in the CNS ( ≈ 0.26 ) and statistically insignificant in the deep NNS ( R ≈ 0.05 and p-value > 0.3). The normalized standard deviation for TA is < 0.5 for all subareas except the Skagerrak/Kattegat subarea (NSTD ≈ 0.77 ), which suggests a general underestimation of the amplitude of TA variability in the model. The normalized standard deviation for TA is particularly low for the CNS (NSTD ≈ 0.37 ) and the NNS (NSTD ≈ 0.25 ). Normalized centered root mean square differences for TA are between 0.75 and 1 in the NT, SK, SNS and CNS subareas. The NNS subarea shows the highest normalized CRMSD ( > 1 ).

The evaluation of the percentage bias (i.e. the sum of model error normalized by the data) documented in Table 1 complements the normalized and centered statistics in Figure 3 and provides a measure for systematic over- or underestimation of observations (Allen et al., 2007). The percentage biases for both DIC and TA in Table 1 are ≤ 1 % in all subareas except the SNS, where the percentage bias is 1.7% for DIC and 1.1% for TA. The low percentage bias in Table 1 underlines the good fit between model data and observations demonstrated by the centered statistics in Figure 3 , but suggests a minor overestimation of both DIC and TA concentrations in the model. An additional evaluation of the mean bias of seasonal surface DIC concentrations ( Supplementary Figure S1 in the Supplementary Material ) indicates that the model particularly overestimates surface DIC concentrations in spring (MAM) and summer (JJA). We additionally calculate the cost function (CF) following Holt et al. (2005) as χ 2   =   1 N σ O 2 ∑ n = 1 N ( M n − O n ) 2 , where σ O is the standard deviation of the observations. The cost function gives a non-dimensional value that indicates the goodness of fit between models and observations. Performance levels are categorized following Radach and Moll (2006) as CF< 1 = very good, 1–2 = good, 2–3 = reasonable, > 3 = poor. The cost function values documented in Table 1 thus suggest very good model performance (CF<1) for DIC in all evaluated subareas except the SNS, which is classified as reasonable. The evaluation of the cost function in Table 1 further corroborates generally reduced model performance for TA. The cost function suggests model performance for TA is highest in the SK and NT subareas (CF<1), good in the SNS and NNS subareas (CF<2) but only poor (CF>3) in the CNS.

The evaluation of surface pCO₂ is an important indicator for the representation of air-sea CO₂ exchange on the NWES, and in combination with the validation of DIC and TA, can provide insights on the main processes responsible for limitations in model performance. Errors in the derived carbonate system variable pCO₂ are larger than in TA and DIC, as errors in DIC, TA and the applied parameterizations accumulate (Artioli et al., 2012; Wakelin et al., 2012). Simulated pCO₂ is quantitatively evaluated by co-locating it in time and space against surface in situ measurements obtained from the SOCATv2023 data product for the period 2001-2005. The normalized statistics of the centered co-located pCO₂ data are aggregated for subareas with relevant observational coverage and are shown in the Taylor plot in Figure 3 . Table 1 further shows the annual mean percentage bias and the cost function calculated for the co-located pCO₂ data. Simulated mean seasonal pCO₂ for the period 2001-2005 is additionally qualitatively compared against seasonal averages derived from monthly gridded SOCATv2023 observations (Sabine et al., 2013) in Figure 4 .

The Taylor plot in Figure 3 shows expected poorer model performance for pCO₂ compared to DIC and TA. The correlations between simulated pCO₂ and SOCATv2023 observations are moderate to low. Correlation is highest for the SNS ( ≈   0.59 ) and the NNS ( ≈   0.52 ). The correlation in the CNS subarea is ≈   0.45 , while it is< 0.25 for the remaining SK, NT, E and C subareas. The normalized standard deviation for pCO₂ is< 1 except for the NT subarea (NSTD ≈ 1.02 ), suggesting a general underestimation of the amplitude of pCO₂ variability in the evaluated subareas of the NWES. The normalized standard deviation is particularly low for the SNS (NSTD ≈ 0.19 ) subarea. Normalized CRMSD are between 0.5 and 1 for the SNS, CNS and NNS subareas and between 1 and 1.5 for the SK, NT, E and C subareas.

The percentage bias and cost function for pCO₂ shown in Table 1 suggest reasonable model performance in terms of bulk errors. The percentage bias indicates that the model overestimates pCO₂ over the period 2001-2005 in all evaluated subareas except the southern North Sea (Pbias = -13.6%). The percentage bias for pCO₂ is < 5 % in the CNS, NNS and English Channel, and slightly larger than 10% in the SK, NT and Celtic Sea subareas. The cost function calculated for pCO₂ in the respective subareas indicates highest model performance in the North Sea subareas (CF<1), reduced model performance in the SK and E subareas (CF<2) and poorest model performance in the NT and C subareas (CF ≤ 3).

The additional qualitative comparison of simulated seasonal mean pCO₂ to gridded SOCATv2023 data shown in Figure 4 demonstrates that the model reasonably reproduces the seasonality and spatial variability of surface pCO₂ on the NWES. Figure 4 however also highlights substantial regional differences and temporal variability in the mismatches between simulated pCO₂ and observations.

Simulated mean winter (DJF) pCO₂ compares well against observations in the deeper areas of the North Sea and Celtic Sea. Shallow inner-shelf areas like the English Channel and the southern North Sea in contrast show a strong underestimation of winter pCO₂. The model further moderately underestimates autumn (SON) pCO₂ in parts of the NWES ( Figure 4 ), again particularly in the central and northern North Sea.

The model resolves a strong drawdown of surface pCO₂ in spring induced by biological DIC consumption during the spring bloom, but Figure 4 suggests the model underestimates the magnitude of the spring drawdown in parts of the NWES (i.e. the model overestimates spring pCO₂ compared to the gridded SOCATv2023 data). The overestimation of pCO₂ in spring is particularly high in the shallow southern North Sea, parts of the central North Sea and the Skagerrak. Some shelf regions, for example in the English Channel, however, rather locally underestimate mean spring pCO₂. The higher temperature and heterotrophic remineralization of spring bloom remnants increase surface pCO₂ again in summer, especially in permanently mixed shallow inner-shelf regions. The model captures the increase in surface pCO₂, but overestimates summer pCO₂ nearly everywhere on the NWES. The overestimation of summer pCO₂ is particularly high in the Southern Bight region of the North Sea, the Norwegian Trench and parts of the central North Sea. The underestimation of simulated pCO₂ in autumn/winter and the overestimation of spring/summer pCO₂ predominantly identified for central and inner-shelf regions of the NWES cancel out over an annual mean.

We further assess the overall model performance by comparing the simulated annual mean air-sea CO₂ flux in the TIDE experiment (2001-2005) to the observational product of Becker et al. (2021). The simulated air-sea CO₂ flux is additionally evaluated with observation and model-based literature estimates for the NWES. The annual air-sea CO₂ flux in Figure 5A and Table 2 shows that most regions of the NWES are net sinks of CO₂. Simulated oceanic CO₂ uptake is high in deep outer shelf areas and strongest on the N-W Approaches and in the northern North Sea. Simulated oceanic CO₂ uptake is substantially lower or nearly neutral in shallow inner-shelf areas like the southern North Sea and English Channel. Permanently mixed regions in the Irish Sea and along the German North Sea coast show neutral air-sea CO₂ exchange or weak outgassing. The simulated annual CO₂ flux in the Irish Sea suggests the region is a minor source of CO₂ to the atmosphere over the year (see Table 2 ). ROFIs close to the major rivers on the continental and UK coasts also show outgassing of CO₂ to the atmosphere.

The decrease of the oceanic CO₂ sink from the deep northern North Sea to the shallow southern North Sea qualitatively fits to the spatial structure of observations by Thomas et al. (2004) and the mean air-sea CO₂ flux map for 2001-2005 shown in Figure 5B derived from the data used in Becker et al. (2021). The model shows an increase in CO₂ uptake towards the Fair Isle Channel in the north-east of the North Sea, in agreement with Thomas et al. (2004). Based on an extensive observational campaign in 2001, Thomas et al. (2004) estimate annual oceanic CO₂ uptake of 1.5 − 2.5   m o l   C   m − 2 y r − 1 in the northern North Sea, which compares well to the estimated annual mean flux of 2.1   m o l   C   m − 2 y r − 1 in our simulations. Comparison to Figure 5B suggests the model underestimates annual mean CO₂ uptake in the Norwegian Trench. Our model shows a weak oceanic CO₂ sink in the Southern Bight of the North Sea and the eastern English Channel. Thomas et al. (2004) and Becker et al. (2021) in contrast found the region to be a weak source of CO₂ to the atmosphere (see Figure 5B ). Yet there is large interannual variability in the region and studies from different years and with different methodologies conflict in the direction of the CO₂ flux in the region (Thomas et al., 2004; Schiettecatte et al., 2007; Omar et al., 2010; Kitidis et al., 2019).

Simulated annual mean oceanic CO₂ uptake of 0.8   m o l   C   m − 2 y r − 1 in the north-eastern Celtic Sea and 1.4   m o l   C   m − 2 y r − 1 in the south-western Celtic Sea are higher than respective estimates in Marrec et al. (2015), who proposed 0.6   m o l   C   m − 2 y r − 1 for the north-eastern Celtic Sea and 0.9   m o l   C   m − 2 y r − 1 for the south-western Celtic Sea. Frankignoulle and Borges (2001) however estimated a higher oceanic CO₂ uptake of 1.7 − 2.9   m o l C   m − 2 y r − 1 for the Celtic Sea and Bay of Biscay region. Simulated area-mean weak outgassing of − 0.3   m o l   C   m − 2 y r − 1 in the Irish Sea matches the estimate of − 0.3   m o l C   m − 2 y r − 1 in Marrec et al. (2015).

The overall mean annual oceanic CO₂ uptake on the NWES (delineated by the 200m isobath plus the Norwegian Trench) for the period 2001-2005 is 1.16 T m o l   y r − 1 , compared to the estimated range of 1.3 − 3.3   T m o l   y r − 1 proposed in Legge et al. (2020) based on two observational and two modelling studies. The standard deviation of the simulated annual mean shelf CO₂ uptake, i.e. the interannual variability for the simulation period 2001-2005, is ± 0.08   T m o l   y r − 1 . The overall mean net annual oceanic CO₂ uptake in the North Sea (here defined as the SNS, CNS and NT subareas) is 0.55   T m o l   C   y r − 1 in our simulations, with a standard deviation of ± 0.03     T m o l   C   y r − 1 . Using a slightly larger geographical definition of the North Sea, Thomas et al. (2005a) estimated an annual oceanic CO₂ uptake of 0.794   T m o l   y r − 1 for the North Sea based on observational surveys in 2001 and 2002, with an estimated range of uncertainty of 20-50% related to differences in gas transfer parameterizations (Watson et al., 2009; Meyer et al., 2018).

The strongest tidal imprints on the net carbon budget are found in the carbon enrichment of the shelf waters and the net carbon transfer to the sediments. Tide-induced processes decrease the total pelagic DIC stock (~ 240.5  Tmol C in the TIDE experiment and ~ 240.9  Tmol C in the NOTIDE experiment for 2001-2005), as neglecting tides results in a ~50% stronger DIC enrichment of 0.34  Tmol C yr − 1 , compared to an accumulation rate of 0.23  Tmol C yr − 1 when tides are included. Net carbon sedimentation on the NWES is low in the TIDE experiment ( 0.001  Tmol C yr − 1 ; mean for 2001-2005). Neglecting tides, and therefore primarily the impact of physical resuspension, considerably increases POC deposition and results in an elevated sediment carbon content ( Figure 6 ). Although benthic remineralization returns the bulk of the carbon in the sediments back to the water column in the NOTIDE experiment, the resulting net sedimentation rate is higher by a factor of 10 ( 0.01  Tmol C yr − 1 ). Prescribed riverine carbon input is the same in both experiments ( 2.04  Tmol C yr − 1 )   and the net carbon import from the Baltic Sea is only marginally affected by tidal forcing ( 0.45  Tmol C yr − 1 in the TIDE and   0.41  Tmol C yr − 1 in the NOTIDE experiment). By closing the carbon budget, we infer that ∼ 0.93  Tmol C yr − 1 (or ~80%) of the annual shelf CO₂ uptake in the TIDE experiment ( 1.16  Tmol C yr − 1 ) is exported off-shelf, while ∼ 0.96  Tmol C yr − 1 (or ~73%) of the annual CO₂ uptake ( 1.31  Tmol C yr − 1 ) is exported off-shelf in the NOTIDE experiment.

Tidal forcing has been shown to substantially increase net primary production (NPP) on the NWES (Kossack et al., 2023). Changes in heterotrophic remineralization however also need to be considered to obtain the net tidal impact on biological carbon cycling on the NWES. We directly evaluate tidal impacts on net community production (i.e. the metabolic balance between NPP and heterotrophic remineralization) computed with Equation 7 to assess tidal impacts on biological cycling of carbon. Mean annual NCP in the TIDE and NOTIDE experiments is shown in Figures 7A, B , respectively. The difference in mean annual NCP between the TIDE and NOTIDE experiments is shown in Figure 7C and additionally documented in Table 2 .

Our results suggest that the entire NWES is net heterotrophic ( N C P = − 0.62   T m o l   C   y r − 1 ) in the TIDE experiment (mean for 2001-2005). The North Sea is also net heterotrophic ( N C P =   − 0.32   T m o l   C   y r − 1 ) in the TIDE experiment, with particularly negative NCP (i.e. strong heterotrophy) in the Norwegian Trench. Figure 7C and Table 2 show a spatially heterogeneous tidal response of NCP on the NWES, and suggest that tides make the NWES slightly more heterotrophic (by − 0.04   T m o l   C   y r − 1 ). The difference between the experiments amounts to ~7% (relative to the TIDE experiment). Including tides decreases the burial of POC in the sediment by ∼ 0.009   T m o l   C   y r − 1 (see Sect. 3.2.1). This decrease in the net removal of organic carbon from the NWES carbon cycle explains about ¼ of the increase in heterotrophy (i.e. decrease in NCP) with tidal forcing. As other organic carbon fluxes on the NWES are not changed in the sensitivity experiment without tidal forcing, the remaining increase in heterotrophy with tidal forcing implies higher organic carbon import onto the NWES. We therefore find that although tides substantially increase net primary production on the NWES, this does not move the shelf system closer to autotrophy.

The tidal impact on heterotrophic remineralization is primarily facilitated through the strong tidal impact on benthic-pelagic coupling on the shelf (see Sect. 3.2.1). Higher sedimentation of POC in the NOTIDE experiment redistributes heterotrophic remineralization from the water column into the sediment. Benthic heterotrophic remineralization is also slower than pelagic heterotrophic remineralization (Krumins et al., 2013). The difference in the parameterized remineralization rates (see parameter set in Supplementary Table S1 in the Supplementary Material ) therefore additionally affects the timing of heterotrophic remineralization in the two experiments. Heterotrophic remineralization in the TIDE experiment consequently occurs earlier in the annual cycle than in the NOTIDE experiment. Compared to the TIDE experiment, the NOTIDE experiment is more autotrophic in summer and more heterotrophic in autumn and winter (see Supplementary Figure S2 in the Supplementary Material ).

Tidal impacts on mean annual NCP in Figure 7C show large spatial heterogeneity on the NWES. Tidal impacts on NCP are most pronounced in inner-shelf regions, where Figure 7C shows areas with strong increases of NCP with tidal forcing, but often also directly adjacent areas of strong decreases of NCP. Tidal impacts on NCP in the deeper shelf regions are generally smaller, but also show a pattern of local increases and local decreases. Only the northern North Sea shows a moderate net increase in NCP with tidal forcing ( Table 2 ), particularly in the region east of the Shetland Islands. The observed spatial pattern in the tidal response of NCP in Figure 7C , with local increases and often adjacent local decreases of NCP, is consistent with the strong tidal impact on benthic-pelagic coupling and suggest advective transport of tidally resuspended POM. The tidally resuspended POM is advected downstream, for example with the cyclonic circulation in the North Sea (see Figure 1A ), while the sedimented POM in the NOTIDE experiment remains stationary. Advective transport of POM out of a specific area decreases local heterotrophic remineralization relative to primary production, i.e. it increases local autotrophy. Local increases in heterotrophy in turn suggests tides enhance advective transport of organic matter into the respective area. The substantial reduction of NCP with tidal forcing in the Norwegian Trench ( − 32.8   G m o l   C   y r − 1 ) suggests tides are particularly important for organic matter transport from the North Sea shelf into the Norwegian Trench.

Tidal forcing therefore mainly laterally redistributes organic matter on the shelf, affects the balance of benthic and pelagic heterotrophic remineralization and determines the timing of heterotrophic remineralization. The large mismatches between the tidal impacts on the air-sea CO₂ flux and tidal impacts on NCP shown in Table 2 however suggests there is no direct relationship between the tidal impacts on NCP and air-sea CO₂ exchange. The discrepancies are particularly large in shallow inner-shelf regions like the Irish Sea and English Channel, where tides decrease annual mean oceanic CO₂ uptake even though tidal forcing makes the subareas more autotrophic (which generally facilitates more CO₂ uptake from the atmosphere). This indicates that other tidal processes are the prevailing factor for the tidal impacts on air-sea CO₂ flux in shallow inner-shelf regions.

Tidal mixing partitions the shelf into permanently mixed and seasonally stratified regions, which both constitute distinct biogeochemical regimes with implications for air-sea CO₂ exchange (Thomas et al., 2004). Seasonal stratification enables the drawdown of surface DIC concentrations by means of the biological pump mechanism (Volk and Hoffert, 1985). The drawdown of surface DIC in spring and summer counteracts the effect of seasonal warming, which drives up surface pCO₂, and thus facilitates net oceanic uptake of atmospheric CO₂ over the annual cycle. In permanently mixed regions, primary production and heterotrophic remineralization are not vertically separated and (respired) carbon in the water column can constantly exchange with the atmosphere. Strong tidal resuspension of POM from the sediment additionally increases the organic carbon pool available for pelagic heterotrophic remineralization in spring and summer. Permanently mixed regions consequently generally exhibit weak air-sea CO₂ exchange or show a tendency to weak outgassing of excess carbon to the atmosphere (i.e. from riverine input).

Neglecting tides leads to a larger part of the shallow inner-shelf being seasonally stratified (see Supplementary Figure S3 in the Supplementary Material ), which in turn affects biogeochemical cycling in the region. We investigate the associated tidal impact on air-sea CO₂ exchange by evaluating the tidal impacts on temperature and biological control of surface pCO₂. We use Equations 2, 3 to calculate the effects of temperature and biology on pCO₂ from monthly mean surface pCO₂ and SST (2001-2005). We subsequently use Equations 5, 6 to compute δ p C O 2 T and δ p C O 2 b i o , the respective mean seasonal amplitudes of surface pCO₂ changes related to temperature and biology, and assess the relative importance of temperature and biological effects on pCO₂ over the mean annual cycle by means of the T/B ratio calculated with Equation 4.

The T/B ratio in the TIDE experiment ( Figure 8A ) shows that the temperature effect on surface pCO₂ strongly dominates in inner-shelf areas, while central and outer shelf areas exhibit a stronger biological effect on pCO₂. The tidal impact on the T/B ratio shown in Figure 8B , i.e. the difference between the T/B ratio in the TIDE and NOTIDE experiments, demonstrates that tidal forcing is largely responsible for the relative dominance of the temperature effect on surface pCO₂ in the areas that are permanently mixed in the TIDE experiment. The tidal impact on the T/B ratio in central and outer shelf regions is generally low.

In general, tides affect both temperature and biological control on pCO₂, which in turn determines the tidal impact on the T/B ratio. Tidal mixing affects temperature control of pCO₂ by modulating oceanic heat uptake on the NWES (Arnold et al., 2021), which results in colder summer SST and warmer winter SST in the shallow inner-shelf areas of the NWES ( Supplementary Figure S4 in the Supplementary Material ). Neglecting tides thus results in a larger seasonal amplitude of the temperature effect on pCO₂ ( δ p C O 2 T ; Equation 5) on most of the NWES ( Figure 8C ), which suggests larger temperature control on air-sea CO₂ exchange in the NOTIDE experiment. The tidal impact on δ p C O 2 T is however small compared to the tidal impact on the biological effect on pCO₂ ( δ p C O 2 b i o ; Equation 6) shown in Figure 8D . Neglecting tides results in a larger seasonal amplitude of pCO₂ changes related to biology (i.e. a stronger biological control of pCO₂) on the NWES, particularly in regions that are permanently mixed regions in the TIDE experiment, but are seasonally stratified in the NOTIDE experiment ( Supplementary Figure S3 in the Supplementary Material ). Our results therefore indicate that it is mainly the tidal weakening of the biological effect on pCO₂ that causes the tidal impact on the T/B ratio documented Figure 8B .

Figure 8E exemplifies the tidal impact on surface pCO₂ at a station in the permanently mixed Irish Sea. The strong tidal mixing in the Irish Sea nearly completely offsets the biological buffering of the temperature-driven pCO₂ increase during seasonal warming, and thus leads to temperature-driven net outgassing in the Irish Sea over the annual cycle ( Table 2 ). If tides are neglected, the water column at the station is seasonally stratified and allows the biological buffering of the seasonal warming effect, which draws down surface pCO₂ in summer and enables net oceanic CO₂ uptake in the Irish Sea over the annual cycle.

The analysis of the tidal impact on the T/B ratio demonstrates how the partitioning of the NWES into seasonally stratified and permanently mixed regions plays a key role in controlling surface pCO₂, and thus air-sea CO₂ exchange. Dominance of temperature control on pCO₂ in the permanently mixed shelf regions ultimately entails stronger CO₂ outgassing in summer (Thomas et al., 2004), which limits annual CO₂ uptake or even leads to net outgassing like in the Irish Sea. We find that the permanently mixed regions (as defined in Figure 8B ) alone account for ~40% ( − 0.06   T m o l   C   y r − 1 ) of the difference in oceanic CO₂ uptake on the NWES between the experiments.

Large parts of the deep northern and central North Sea show a moderate increase in mean annual oceanic CO₂ uptake with tidal forcing ( Figure 5D ), which indicates that there is a tidal impact specific to these seasonally stratified central and outer-shelf regions. The evaluation of the annual cycle of surface pCO₂ at a station in the northern North Sea shown in Figure 9A demonstrates that the higher annual oceanic CO₂ uptake in the TIDE experiment predominantly stems from lower surface pCO₂ in winter.

We find that the lower winter pCO₂ at the station in the northern North Sea is the result of a weaker biological mitigation of the seasonal cooling effect on pCO₂ in the TIDE experiment ( Figure 9A ). Heterotrophic remineralization of organic matter produced in summer increases the DIC concentration in the water column in autumn and winter, which constitutes a biological buffering of the effect of seasonal cooling on pCO₂ and controls winter uptake on the shelf. Figure 9C shows that mean winter surface DIC is lower in the TIDE experiment than in the NOTIDE experiment in large parts of the northern and central North Sea, which indicates that the weaker biological mitigation of the seasonal cooling effect on pCO₂ occurs throughout most of the seasonally stratified North Sea.

We find that the difference in the winter DIC concentration in the seasonally stratified North Sea is caused by the tidal impact on benthic-pelagic coupling and associated differences of heterotrophic remineralization between the two experiments (see Sect. 3.2.2). The comparison of the annual cycles of mean DIC in the water column (2001-2005) for the station in the northern North Sea shown in Figure 9E reveals significant tidal impacts on the vertical structure and seasonality of the DIC concentration. In the TIDE experiment, primary production draws down surface layer DIC during the productive season, while vertical POM export and subsequent heterotrophic remineralization increases DIC in the bottom layer ( Figure 9D ). Resuspension and mixing by strong tidal currents retains POM in the water column and limits sedimentation. With seasonal cooling at the end of the summer, surface cooling then convectively mixes the DIC-enriched subsurface water to the surface.

Neglecting tides in contrast redistributes heterotrophic remineralization from the water column into the sediment, where heterotrophic remineralization is slower and only diffusively releases DIC into the bottom layer. Bottom layer mixing is also low in the absence of tides, so that the respired DIC accumulates in a shallow bottom boundary layer and leads to substantially higher bottom layer DIC concentrations in the NOTIDE experiment (up to + 30   m m o l   C   m − 3 ; see Figure 9E ). The entrainment of the DIC-enriched bottom layer into the water column by December results in higher winter DIC throughout the water column in the NOTIDE experiment, which ultimately leads to higher surface pCO₂ ( Figure 9A ) and thus lower oceanic CO₂ uptake during winter compared to the TIDE experiment.

Local increases in NCP in the central and northern North Sea with tidal forcing ( Figure 7C ) imply a reduction of local heterotrophic remineralization relative to local primary production. The local increases in NCP therefore suggest that subsurface advective transport of organic carbon out of the respective shelf areas in the North Sea, predominantly in form of POM (not shown), is more effective in the TIDE experiment than in the NOTIDE experiment. Tidally enhanced advective transport of organic matter in the bottom layer ultimately reduces the magnitude of the biological buffering of the effect of winter cooling on surface pCO₂, and thus contributes to the higher oceanic CO₂ uptake in winter. We find that about 5% ( 8.3   G m o l   C   y r − 1 ; Table 2 ) of the high annual mean oceanic CO₂ uptake in the northern North Sea subarea is related to tides.

Unlike in the North Sea, the majority of the seasonally stratified Celtic Sea shows a decrease in the oceanic CO₂ uptake with tidal forcing ( Figure 5D ). The evaluation of surface pCO₂ at a station in the central Celtic Sea ( Figure 9B ) indicates that the dominant cause for the lower annual mean oceanic CO₂ uptake in the TIDE experiment is higher biologically-driven surface pCO₂ in late autumn/early winter. Figure 9C shows corresponding higher winter surface DIC concentrations in the Celtic Sea in the TIDE experiment. The area of higher surface winter DIC in the TIDE experiment extends from the Armorican shelf in the south across the Celtic Sea to the south-west coast of Ireland.

We find a strong tidal impact on the large-scale residual circulation in the Celtic Sea to be the main reason for the difference in winter DIC that causes the regional reduction of oceanic CO₂ uptake with tidal forcing. The seasonal mean depth-averaged residual circulation (2001-2005) and respective seasonal mean surface DIC fields in the TIDE and NOTIDE experiments are documented in Figure 10 . Tidal forcing evokes a seasonal cyclonic circulation pattern in the Celtic Sea and Western English Channel not present in the experiment without tides. In summer, Figure 10 shows northward residual transport in the Western English Channel tidal frontal zone and along the south-western UK coast, westward flow at the tidal front in the St. George Channel and a tendency to southeastward flow in the south-western Celtic Sea in the TIDE experiment. Winter (DJF) circulation in the TIDE experiment also shows a tendency to southeastward flow in the south-western Celtic Sea, and weak northwestward flow from the Armorican shelf into the Celtic Sea. The NOTIDE experiment in contrast shows very weak residual circulation in summer. In winter, the NOTIDE experiment shows pronounced northwestward flow from the Armorican shelf across the Celtic Sea. A vertical transect of mean summer horizontal velocity across the south-western Celtic Sea reveals that the cyclonic residual circulation in the TIDE experiment is caused by a near-surface baroclinic current generated at the density gradient of a cold pool trapped below the seasonal thermocline ( Figure 11 ). Such a cold pool flanked by sharp density gradients is only set up in the Celtic Sea with tidal forcing.

The tidal impact on the residual circulation is relevant for air-sea CO₂ exchange because it affects the water mass composition in the Celtic Sea. The strong northward transport in the NOTIDE experiment flushes the Celtic Sea with low-DIC waters from the Armorican shelf and Bay of Biscay in the south, while in the TIDE experiment the Celtic Sea is more influenced by DIC-rich waters from the north, and potentially from the Bristol Channel. Mean winter surface DIC in the Celtic Sea is consequently lower in the NOTIDE experiment than in the TIDE experiment, with the largest difference (up to 20   m m o l   C   m − 3 ) occurring in December (not shown). The lower winter DIC concentration in the NOTIDE experiment drives stronger oceanic CO₂ uptake in the Celtic Sea. The seasonally stratified part of the Celtic Sea consequently takes up 49.2   G m o l   C   y r − 1 more atmospheric CO₂ in the NOTIDE experiment than in the TIDE experiment. This makes up more than 90% of the difference in annual mean oceanic CO₂ uptake between the experiments in the Celtic Sea ( ∼ 0.05   T m o l   C   y r − 1 ; Table 2 ), and amounts to ~34% of the difference of the annual mean NWES CO₂ sink between the experiments.