The model domain extends from 15.250∘ W to 14.083∘ E and from 47.583 to 63.983∘ N and comprises the entire North Sea, large parts of the northwestern European continental shelf and parts of the adjacent northeastern Atlantic. The horizontal resolution is 1/5∘ with 82 grid points in latitudinal direction and 1/3∘ with 88 grid points in longitudinal direction. The horizontal grid of the model domain is shown in Fig. . The vertical dimension with a maximum depth of 4000 m is resolved by 31 z-layers with a surface layer of 10 m. The vertical has a resolution of 5 m between 10 and 50 m depth, which is relevant for the calculation of the MLD (Sect. ). Below 50 m, the layer thicknesses successively increase with depth.

The model system was run over the period 1977 to 2012. HAMSOM was initialised with a monthly-averaged climatology based on the World Ocean Atlas WOA;. The meteorological forcing was derived from NCEP/NCAR reanalysis data and provides 6 hourly information for air temperature, cloud coverage, relative humidity, wind speed and direction. Short wave radiation was calculated from astronomic insulation and cloud coverage applying a correction factor of 0.9 . The data were interpolated to the model grid and time step according to and . Daily freshwater run-off data for 249 rivers were provided by Cefas and represent an updated data set of that used by covering the entire simulation period. The same data set encompassed nutrient loads used for the ECOHAM.

At open boundaries, surface elevation was prescribed as a fixed (Dirichlet) open boundary condition (OBC) according to the M2 tide, while for horizontal transport velocities radiation OBCs were applied. For tracers (T and S) radiation and radiative-nudging OBCs were used in the case of inflow and outflow, respectively. A detailed description of the OBCs is provided by . The HAMSOM simulation was carried out with a 10 min time step.

ECOHAM was run off-line with a time step of 30 min using the 24 h averages of the hydrographic and hydrodynamic fields generated by HAMSOM. In the model setup used, short wave radiation is attributed to the first layer (surface) only and the specific effect of light attenuation due to SPM and planktonic self-shading on the thermal structure is not taken into account. A sensitivity study allowing for deeper light penetration and feedback on the thermal structure confirmed this effect to be only of minor importance (not shown).

For the biogeochemical state variables a climatology of depth-dependent monthly averages was prescribed at the boundaries and solely for DIC yearly changing data were provided . To include the effect of SPM on the light climate, a daily climatology from was used. Data for atmospheric N deposition were compiled using a hybrid approach. This was required since the overall simulation period (1977–2012) exceeds the period of data available from the EMEP (Cooperative program for monitoring and evaluation of the long-range transmissions of air pollutants in Europe) model (1995–2012). First, the EMEP results for total deposition of oxidised (NOx) and reduced nitrogen (NH3) were interpolated to the model grid. Second, we calculated the average annual deposition rates for the NOx and NH3 for each grid cell, based on the 1995–2012 EMEP data. The resulting spatially resolved arrays of average deposition rates were subsequently normalised by the spatial average of the entire domain to yield the spatially resolved anomaly fields. Finally, gridded deposition rates for individual years were obtained using (1) the gridded anomaly fields, (2) EMEP's spatially averaged (over our model domain) deposition rates for year 2005, and (3) long-term trends (normalised towards year 2005) for the temporal evolution of European emissions of NOx and NH3 Fig. 2 in. The output of the biogeochemical simulation was stored as daily values (cumulative fluxes, state variable snapshots) for the entire domain and simulation period.

Cefas operates a network of SmartBuoys to provide autonomous in situ measurements of physical, chemical and biological parameters . A SmartBuoy was located directly north of the Dogger Bank (“North Dogger”) at 55∘41′ N, 2∘16.80′ E (see Fig. , region 2) between 24 February 2007 to 15 September 2008 in 85 m water depth . O2 concentrations were continuously recorded with a frequency of 5 Hz at 31 and 85 m. These autonomous O2 measurements were corrected for drift using O2 concentrations determined from discrete water samples to give an accuracy of 0.5 % . For validation purposes the O2 data derived from the sensor at 85 m depth were used. North Dogger data are published and can be accessed according to .

The BSH operates a continuous monitoring station at 54∘10′ N, 6∘21′ E (see Fig. , region 1; hereafter referred to as station “Ems”). The O2 saturation is measured hourly using opto-chemical sensors (optodes). Sensors are located in 6 and 30 m depth, respectively, and the bottom depth is 33 m. The applied sensors have a resolution of 0.03 mgO2L-1 and an accuracy better than 0.26 mgO2L-1. Before deploying the sensors a 0–100 % calibration is conducted, and they are re-calibrated after operation to quantify any drift. In addition, a regular on-site validation takes place using a calibrated fast optode (accuracy of ±2 %) or by applying the Winkler titration (accuracy better than ±1 %).

During the North Sea programme, carried out by the Royal Netherlands Institute for Sea Research (NIOZ) with support from the Dutch Science Foundation (NWO) and the European Union, the North Sea was sampled from 18 August to 13 September 2001, and from 17 August to 5 September 2005 and 2008. The North Sea was covered by an approximate 1∘ × 1∘ grid, sampling approximately 90 stations in each of the years . During each cruise, a total of 750 water samples were collected for dissolved O2. In 2001, the O2 concentrations were determined by the Winkler titration using a potentiometric end-point determination with an accuracy of ±2 µmolO2kg-1 (less than ±0.07 mgO2L-1 depending on T and S). In 2005 and 2008, the O2 concentrations were obtained applying the spectrophotometric Winkler approach with a precision of less than 0.03 mgO2L-1. A detailed description of the measurement system used is given in . The data for the years 2001 and 2005 have been published and can be accessed according to and , respectively.

The data available were gridded to the model grid (Fig. ). In the case of multiple measurements for the same model grid cell and date, the average of these measurements was used for validation. To compare our model results to these data, we calculated the averages and standard deviations of our simulation over the observation period of the corresponding year.

For the development of a regional O2 characteristic, potential controlling factors were analysed in relation to bottom O2. Besides stratification, eutrophication is considered as a major driver for developing low O2 conditions e.g.,. Thus, primary production within the mixed layer and the resulting organic matter export into the layers below the MLD must be considered to be the main source for degradable organic matter. In addition, organic matter can be advected from surrounding waters in the form of phyto- or zooplankton and detritus, subsequently sinking out of the mixed layer.

Another important criterion is the water volume below the thermocline . A smaller volume separated from the surface due to stratification holds a lower initial inventory of O2 than a larger volume even though concentrations can be similar or even higher in the smaller volume. Thus, our set of O2-related characteristics consists of mixed layer primary production (PPmld), horizontal advection of organic matter into and out of the mixed layer (ADHorg,in and ADHorg,out; including phyto-/zooplankton and detritus), vertical organic matter export below the MLD (EXPorg; only detritus) and mixing of O2 below the MLD (MIXO2), and the sub-MLD volume Vsub.

To detect regional characteristics within the North Sea area, we defined four different sub-domains encompassing 4 × 4 model water columns each (see Fig. , red boxes): (A) southern North Sea (SNS) under strong tidal influence, (B) southern central North Sea (SCNS) with high year-to-year variability in stratification, (C) northern central North Sea (NCNS) with a dominant summer stratification each year, and (D) northern North Sea (NNS) with a dominant summer stratification each year and a strong influence of the Atlantic. For all these regions, the parameters described above were calculated for the years 2000–2012 relative to a reference depth Dref, which is defined as the bottom depth of the model layer directly below the annual maximum MLD among all four regions. We decided to use a Dref> MLD to ensure that for the different regions all parameters were determined on a comparable level. This implies that the values for PPmld, ADHorg,in and ADHorg,out are integrated from the surface to Dref, whereas EXPorg and MIXO2 are the vertical fluxes through Dref. The same Dref was applied to all regions, but year-to-year variations were allowed.

To determine the annual maximum MLD, we first calculated the stratification period for the 4 × 4 regions B–D using Eq. (). Region A was excluded from this calculation as no persistent MLD developed due to tidal mixing. In this context, Sstrat(t) of a region is only 1 if Sstrat(x,y,t)=1 for all 16 water columns within a 4 × 4 region. The daily MLD for each water column within a region was calculated by applying Sstrat(t) to Eq. (), and subsequently the daily MLD of the region is defined as the median of these 16 daily values. The annual MLD for each region was then determined as the median of this daily time series. Finally, the annual maximum MLD among all four regions is used to determine the reference depth Dref, which is defined as the bottom depth of the layer directly below this maximum MLD.

The values for these O2-related quantities were calculated for individual years relative to Dref and temporally integrated over the period from 1 April to 30 September (hereafter “summer”). Consequently, the average values over the entire period 2000–2012 are calculated and presented in Table , additionally including the average O2 concentrations at the beginning and end of the summer period as well as the average duration of stratification.

In order to obtain a North Sea wide indicator for O2 deficiency under stratified conditions, it is necessary to extend the regionally confined characteristic described in the previous section. For this purpose, we extract the key factors affecting O2 from this regional information and combine them into a single index – the oxygen deficiency index (ODI). The ODI aims to represent the main spatial and temporal patterns of O2 deficiency in the North Sea under stratified conditions, while being as simple as possible and incorporating only a very limited number of parameters.

Stratification period, organic matter export and sub-thermocline volume are considered as the key parameters controlling the bottom O2 dynamics. Surface primary production can be used as a proxy for organic matter export assuming that most of the exported organic matter is produced locally. Bottom depth can be used as an indicator for the sub-MLD volume assuming only minor fluctuations of the MLD during the summer stratified period. In addition, the bottom depth directly influences the amount of organic matter reaching the bottom layer relative to the amount being produced near the surface, due to the exposure of sinking matter to pelagic remineralisation. Thus, the following key factors are used for the calculation of this index: (longest continuous) stratification period (tstrat; in days), summer surface primary production (PPmld; in gCm-2; 1 April to 30 September), and bottom depth (Dbot; in m).

First, individual dimensionless indices are calculated for each of these quantities. The individual indices range between 0 and 1, indicating conditions counteracting and supporting O2 deficiency, respectively. The calculation of the stratification and production indices, Istrat and Ipp, is based on the work by and reads as IQi(x,y)=min1,max0,Qi(x,y)-Qi,minQi,max-Qi,min, with Q1=tstrat,Q2=Ipp. IQi(x,y) represents the index corresponding to the actual value of the quantity Qi(x,y) with its defined upper and lower thresholds, Qi,max and Qi,min. For tstrat, Qi,max and Qi,min are set to 50 and 150 days, respectively. Stratification periods of less than 50 days are considered to be too short to facilitate the evolution of O2 deficiency, while periods longer than 150 days are considered seasonally well-stratified. The lower threshold for PPmld was set to 120 gCm-2 as PPmld does not reach lower values in most parts of the North Sea. The upper threshold was set to 200 gCm-2 as such high values and even higher are simulated in the southeastern North Sea.

For the depth index, ID, a different definition was chosen as lowest O2 concentrations occur in areas of intermediate depth, where seasonal stratification can develop and the O2 inventory is limited due to a small volume below the thermocline. Therefore, we defined ID as follows: ID(x,y)=max0,Dbot(x,y)-DminDpeak-DminDbot(x,y)<Dpeak1-min1,Dbot(x,y)-DpeakDmax-Dpeakotherwise. Dbot represents the actual bottom depth at location (x,y). Dpeak=40m is the bottom depth we found to be most favourable for O2 deficiency in the North Sea. The lower threshold Dmin=25m corresponds to the maximum MLD we found for the shallower southern North Sea. The upper threshold Dmax=90m was chosen to exclude the areas where the initial O2 inventory is sufficient to prevent O2 deficiency due to the large volume below the thermocline.

Finally, the ODI combines the three individual indices according to the following equation: ODI(x,y)=ID(x,y)⋅∑i=12wQiIQi(x,y), with wQ1=1/4,wQ2=3/4. Here, IQi and wQi represent the index for a quantity and the related weight, respectively. The values for tstrat are referred to by Q1 and those for PPmld by Q2. The equation for ODI implies that it is zero in areas where ID=0. The stronger weighting of PPmld implies that variations in the ODI between different years are more strongly affected by variations in summer surface productivity than by the duration of stratification.

The ODI ranges between 0 (low risk of O2 deficiency) and 1 (high risk) and is calculated for each water column (x,y) within the model domain. By this we obtain a spatially resolved indicator for O2 deficiency in the North Sea, which helps regionalise the North Sea in terms of O2 conditions.

Figure  shows the comparison of simulated bottom O2 against time series data at the Cefas station North Dogger for the years 2007 (a) and 2008 (b) and the MARNET station Ems during 2010 (c) and 2011 (d). The indicated stratification period was derived from the simulated temperature fields using Eq. ().

At North Dogger, observed and simulated bottom O2 concentrations show a steady decrease after the onset of stratification. While stratification according to Eq. () starts a bit earlier compared to that described by , the beginning of the decrease in bottom O2 concentrations coincides well. The simulated and observed O2 concentrations at this time are in good agreement.

Some small-scale fluctuations in the observations are not fully reproduced by the simulation, however, the general evolution is represented well by the model. The average O2 reduction in the simulation is slightly less than in the observations, visible in the difference between the concentrations at beginning and end of the stratified period. Stratification ends a bit earlier in the simulation, with the result that simulated bottom O2 starts to recover while the observed concentrations continue to decline. The observed O2 concentration at the end of the stratified period is about 6.8 mgO2L-1, while the simulation results in about 7.4 mgO2L-1.

In 2008, we can see a similar slight overestimation of simulated O2 concentrations, but less than in 2007. Some minor fluctuations in the observations are again not represented by the model, but the general evolution of bottom O2 is represented well. It should be noted, that the different depths of the time series (76 m for simulation, 85 m for observation) may also affect the difference between simulated and observed O2 concentrations.

At MARNET station Ems the observed bottom O2 concentrations show significantly larger intra-seasonal fluctuations than at North Dogger. This applies to both years 2010 and 2011, and mainly results from the shallower station depth, i.e., sampling depth (sensor in 30 m). As at North Dogger, differences may also relate to different depths of the time series (32.5 m for observation) and the vertical resolution with only six layers.

In 2010, the onset of O2 decline in the observations is in good agreement with that in the simulations. Stratification lasts shorter and is less persistent than at North Dogger. As at North Dogger, intra-seasonal fluctuations in the O2 evolution are not fully reproduced. The model tends to overestimate bottom O2 in 2010, revealing a maximum difference of about 1 mgO2L-1.

In 2011, persistent stratified periods derived from the simulation do not exceed 2 months at station Ems. Consequently, the temporal evolution of bottom O2 represents mainly the temporal evolution of the O2 saturation concentrations. Again large fluctuations of up to ±2 mgO2L-1 can be seen in the observations which are not fully reproduced by the model. Besides these short-term changes, the difference between simulated and observed bottom concentrations is less than 0.8 mgO2L-1 with higher summer values in the simulation.

The validation of bottom O2 at the stations North Dogger and Ems shows that the HAMSOM-ECOHAM model is capable of reproducing the main features of the bottom O2 dynamics at these two stations. The minor differences in the concentrations (<± 0.4 mgO2L-1) at the beginning and end of the year, representing mainly the saturation concentrations, show that the general physical setting provided by the model is reasonable. The slightly slower O2 reduction in the simulation may indicate an underestimation of the biological consumption, e.g., due to benthic remineralisation. Intra-seasonal fluctuations at both stations are not fully reproduced, due to the limited spatial resolution of the model grid. Additionally, the tides may have an effect at station Ems on the short-term. However, they are not resolved due to the daily time step of the simulated current fields.

The generally good agreement between simulation and observation is also shown by the Taylor diagram see Fig. , markers “a” for North Dogger and “b” for Ems, which presents the correlation coefficients (COR), standard deviations (SDs) and centred root-mean-square differences (RMSD) of the simulation relative to the observations. SDs and RMSDs are normalised by the SD of the corresponding observations. For analysis, the data of each data set was merged into a continuous series of data. For both stations, COR is high with values of about 0.95 and the normalised RMSD is less than 0.38. The RMSD values are mainly due to the larger range and higher (seasonal and intra-seasonal) variability in the observed bottom O2, which is also indicated by the normalised SDs of about 0.73 and 0.82 for Cefas North Dogger and MARNET Ems, respectively.

Figure  shows the spatial distribution of the average simulated and observed O2 concentrations in the model bottom layer for the years 2001 (a), 2005 (b) and 2008 (c), and the SD related to the averages in 2005 (d). The averaging period for the simulations corresponds to the complete observation period for each year, listed in the bottom right corner of each panel.

In 2001, the observations show the lowest concentrations of all years with minimum values of 5.9 mgO2L-1 in the area 54–57∘ N, 4.5–7∘ E. This minimum is similarly present in the model yielding 6.96 mgO2L-1. Maximum observed concentrations were found off the southern tip of Norway (9.3 mgO2L-1) and in the deepest parts of the Norwegian Trench (8.7 to 8.8 mgO2L-1). The very high observed value at the northwesternmost sampling site represents an outlier due to the decreasing vertical resolution of the model in greater depth.

In 2005, the observed minimum values are about 0.3 mgO2L-1 higher than in 2001. This relative increase compared to 2001 is reproduced well by the simulation showing a similar increase by about 0.2 mgO2L-1. The observations show lowest bottom O2 a bit north and south of the simulated minimum, but still relatively low values less than 7.2 mgO2L-1 in the centre of the simulated minimum. Highest observed concentrations of 9.3 mgO2L-1 are located in the very deep area at the eastern end of the Norwegian Trench, and in the inner German Bight. In the German Bight, the model indicates only slightly higher values compared to 2001, while in the northern North Sea, the simulation shows lower values compared to 2001, which can be seen in the observations as well.

In 2008, the observations reveal significantly higher bottom O2 concentrations in the area of the 2001 minimum, compared to the previous years. In contrast, observed concentrations in most other parts of the North Sea are lower than in 2001 and 2005. The overall minimum concentration in 2008 of 7.2 mgO2L-1 is reached close to the Dutch coast. In the southern North Sea, the simulation yields lower bottom O2 concentrations, and significantly higher values in the 2001 minimum area. For the western central and northern North Sea the picture is different. Here, the observations result in consistently lower values compared to 2001 and 2005, whereas the simulated O2 shows higher values in most areas, except for the eastern Norwegian Trench.

The simulated SD in 2005 is mainly representative for the years 2001 and 2008 as well. It shows that in most areas of the North Sea the changes in bottom O2 during August/September are very low throughout a period of 3 to 4 weeks, indicated by a SD of less than 0.1 mgO2L-1. The observations also show only small SDs in most areas.

In general, the basin-wide distributions of simulated bottom O2 represent the observed spatial patterns and their year-to-year variations quite well, even though absolute values are not always reflected. Both observed and simulated bottom O2 concentrations show that the 50 m isobath broadly along 54∘ N, 0∘ E to 57∘ N, 8∘ E; marks the separation line between the northern regions unaffected by low O2 conditions and the southeastern parts, which are more vulnerable to low O2 concentrations. In addition, the model demonstrated it is capable of capturing variations in the bottom O2 evolution between different years. In combination with the results of the time series validation (Sect. ), this confirms that the described model setup provides reliable information on the internal physical and biological processes driving the O2 dynamics in the North Sea.

The small SD of simulated bottom O2 confirms that using the averages over a period of up to 4 weeks provides a reasonable measure for most areas. In addition, these small values imply that measurements taken late August/early September (before the breakdown of stratification) can be considered as a representative synoptic picture of the late summer bottom O2 conditions. However, the time series validation showed that in some areas lowest concentrations of bottom O2 may occur remarkably later in the year (see Fig. a). Consequently, the picture obtained from observations taken in August/September does not necessarily reflect the spatial distribution of minimum bottom O2 concentrations, which underlines the importance of choosing the appropriate point in time for the monitoring of low O2 conditions.

The small SD of the observations, which is a result of the data gridding, shows that in most regions vertical O2 gradients near the bottom are negligible. The high values of 0.75 and 0.59 mgO2L-1 southeast of the Dogger Bank and northwest of Denmark, respectively, result from the fact that values above and below the thermocline were taken into account for the averaging.

As for the time series, Fig.  (marker c) shows the statistical measures of the validation for the spatially resolved data. Here, COR reaches only about 0.64 which is also indicated in Fig.  by the variations between year 2008 and the previous years, when the simulation revealed a relative change inverse to that in the observations in the northern North Sea. The normalised RMSD of 0.77 is about twice as high as for the time series, which can be attributed to the greater regional differences in the observed bottom O2 concentrations with higher maximum and lower minimum values. The normalised SD equals 0.67 which indicates the less strong spatial gradients in the simulation. These statistics confirm that the spatial patterns in the observed bottom O2 concentrations are basically reproduced by the model, with only slight shortcomings with respect to the amplitude of the bottom O2 concentrations and year-to-year variations in some regions of the North Sea.

Table  shows the 2000–2012 summer (1 April to 30 September) averages of the quantities considered potentially relevant for O2 for the regions A–D (see Fig. ). The quantities were calculated relative to a Dref of 25 m. In addition, the stratification period (tstrat), average MLD (Dmld), average bottom depth (Dbot) and area of the regions are provided.

The mixed layer net primary production, PPmld, is strongest in the coastal region A and shows decreasing values towards the central North Sea. In the SCNS region B, PPmld accounts for about 87 % of that in the highly productive coastal region A. The corresponding value for the NCNS region C and NNS region D is about 80 and 88 %, respectively.

Despite the highest PPmld in the coastal region A, the SCNS region B shows the strongest contribution of gross advection of organic matter, ADHorg,in and ADHorg,out. Both regions show positive net advection of organic matter, while the two northern regions C and D are characterised by negative net advection, i.e., advective loss in organic matter. The latter regions are located north of the Dogger Bank, thus, they are affected by the northern Atlantic inflow. In this region, net advection results in a loss in organic matter as the recirculated northward flowing water has higher concentrations of organic matter than the incoming Atlantic water.

The vertical export of organic matter, EXPorg, below Dref consistently adds up to about 12–14 % of PPmld, indicating the clear link between these quantities. Region B yields an EXPorg of 75 % of that in the coastal region A, which corresponds to a higher net advective import of organic matter of 6.7 gCm-2 in region A, compared to only 1.6 gCm-2 in Region B. EXPorg in region C and D reach about 69 % and 79 % relative to region A, respectively.

The vertical mixing of O2, MIXO2, is highest within the coastal region A and adds up to 116.1 gO2m-2, which is due to strong tidal mixing. The stratification period, tstrat, of 151 days in region B is shorter than in region C (220 days) and does not cover the entire summer period. Thus, MIXO2 in region B is significantly larger than in regions C and D.

The evolution of the O2 concentrations between the beginning and end of the summer period reveals some interesting aspects in relation to the previously mentioned parameters. The O2 concentrations at 1 April show significant differences between the regions ranging between 9.5 mgO2L-1 (regions C and D) and 10.1 mgO2L-1 (region A). The O2 concentrations at the 30 September yield values between 7.7 mgO2L-1 (region A) and 8.3 mgO2L-1 (region D). This implies a consistently decreasing O2 consumption during summer from region A to D. This spatial gradient in the O2 consumption is opposite to that in tstrat, which shows a steady increase from regions A to D.

In order to give an impression of the impact of EXPorg on the O2 dynamics of the water volume below the MLD, Vsub, we link the amount of exported organic matter to the amount of O2 available within Vsub assuming the organic matter is remineralised completely in the area of settlement. Based on the O2 concentration at the beginning of April, the total amount of O2 available is 1365 kt for region B and 4590 kt for region C. The total amount of exported organic matter is calculated as the product of EXPorg and the total area of the considered region. This calculation yields 130 ktC and 115 ktC for the regions B and C, respectively. As O2 consumption and C release occur with a molar ratio of 1:1 during bacterial remineralisation , we obtain the daily O2 consumption by dividing by the total duration of the considered 6-month period (= 183 days), yielding 0.71 and 0.63 ktO2d-1 for regions B and C, respectively.

The initial O2 mass is calculated as the product of the initial O2 concentration and Vsub. Assuming the daily O2 consumption to be constant for each region, division of this mass by the daily consumption rate calculated above provides an estimate of the amount of time required for the consumption of the entire amount of O2 available in Vsub. This calculation yields a period of about 2 years for region B, whereas the corresponding value for region C is significantly higher with almost 12 years. This great difference between the resulting periods (factor 6), compared to the relatively small difference between the daily consumption rates (factor 1.1), illustrates clearly the large influence of the sub-MLD volume, Vsub, on the temporal evolution of the O2 concentrations below the MLD.

The same calculation based on the threshold of 6 mg O2 L-1 used by OSPAR yields a consumption period of 283 days for region B, which indicates the relatively high potential for O2 deficiency in this region.

This characteristic based on the four different North Sea regions demonstrated that the duration of stratification alone cannot explain the temporal evolution of sub-MLD O2 concentrations. It shows the great importance of the organic matter export which drives the biological O2 consumption. In addition, the volume below the MLD plays a key role as it governs the amount of O2 which is available throughout the stratified period, and in combination with the organic matter export defines whether O2 deficiency may occur or not. Thus, these three quantities can be considered as the key parameters governing the O2 dynamics of the seasonally stratified North Sea.

The ODI resulting from the simulated stratification duration (tstrat), summer surface primary production (PPmld) and model topography for the years 2002 and 2010 is shown in Fig. a and b, respectively. It can be seen that the ODI tends to be higher in 2002 than in 2010 in the region where minimum bottom O2 is lowest in both years (see Fig. ). North of the Doggerbank, the ODI also shows slightly higher values than in the surrounding waters which corresponds to the lowered bottom O2 in this region. The variations of the minimum concentrations between the 2 years in this region are also well-reproduced by the ODI. Especially in 2002, the highest ODI coincides with the lowest concentrations in the entire domain. In 2010, the highest ODI is located a bit south of the minimum O2 concentrations, which is mainly caused by the high surface production in this region. Along the northern British coast, the ODI also shows high values for both years which is in good agreement with the slightly lower minimum bottom O2 in this area. However, ODI values tend to be too high and do not represent the slightly lower minimum O2 concentrations off the eastern Scottish coast around 57–58 ∘N as the bottom depth in this area exceeds 90 m (i.e., ID=0). Directly northwest of Denmark, the ODI also yields high values for both years with higher values in 2002. This corresponds well to the simulated bottom O2 concentrations in this area, even though ODI values are too high, compared to ODI values in the central North Sea.

With respect to the factors selected for the calculation of the ODI, Table  shows that stratification alone is not sufficient to explain the North Sea O2 dynamics. While the reduction in the O2 concentrations is steadily decreasing from regions A to D, stratification duration is characterised by a steady increase from regions A (80 days) to D (226 days). Regarding the PPmld, the strongest O2 reduction occurs in the regions of highest productivity A and B. In the northern regions, the higher PPmld in region D does not correspond to stronger reduction in O2. As tstrat is also higher in this region, a further factor is needed to describe the basic O2 dynamics. The reduced effect of surface production in the northernmost area is likely to result from the dilution effect due to the higher Vsub. Considering the bottom depth Dbot as a proxy for Vsub, it is shown that the strongest decrease occurs in the shallower regions A and B with average depths of about 40 m, while the regions deeper than 90 m (C and D) show a weaker decrease.

Net advection of organic matter, which is not taken into account in the ODI, appears to be of minor importance for subsurface O2 relative to the local surface production as the net advective input of organic matter is significantly less than the local production. The O2 concentrations at the beginning of the stratified period were also not taken into account as they show lower values in regions with higher minimum concentrations and vice versa.

In summary, the ODI represents well the spatial and temporal variations of minimum bottom O2 concentrations despite the small set of controlling factors. This confirms that a simple combination of only stratification duration, organic matter production and bottom depth is sufficient to reproduce the main spatial and temporal patterns of the minimum bottom O2 in the seasonally stratified North Sea. Thus, the findings from Table  can be applied to most parts of the North Sea. In addition, the similarity of the ODI inside the regions analysed in Sect.  and inside the regions selected for the mass balance analyses (see Fig. , regions 2–4) and their surrounding areas shows that these regions can be considered as representative, allowing for a meaningful analysis of the O2 dynamics in these regions.

The comparison of advection (ADVO2; including horizontal and vertical components; dashed light blue) and vertical mixing (MIXO2; turbulent diffusion; dashed dark blue) for the years 2002 and 2010 shows strong variations between the 2 years. ADVO2 regularly changes its influence on the sub-MLD O2 concentrations during stratification in both years. However, considering the temporally integrated effect, ADVO2 causes a net gain of about 25.8 gO2m-2 in 2002, whereas in 2010 it results in a slight net loss in O2. Advection positively affects the O2 concentrations during the last 2–3 weeks of the stratified period in both years and even causes a net O2 increase in 2002.

The vertical mixing of O2 through the mixed layer (MIXO2) adds up to 26.9 gO2m-2 in 2002 (1.5-fold of 2010 value). In late April and late June 2002, two events of enhanced mixing cause a rapid gross increase in the O2 concentrations, in the latter case even resulting in a net increase in O2. During August 2002, MIXO2 even has a negative effect on O2, which coincides with a very shallow MLD of 10 m (= bottom of first model layer). In 2010, this negative effect on O2 is even more persistent. The increased positive net effect of ADVO2 and MIXO2 in 2002 relates to the stronger spatial O2 gradients due to the local O2 minimum in region 3.

The daily rates of change in O2 (averaged over the stratification period) due to these factors for the different years provide a comparable measure of their effect on sub-MLD O2, independent of the duration of stratification. The averages of these daily rates for the entire period 2000–2012 result in 0.008 ± 0.060 gO2m-2d-1 for ADVO2 and 0.153 ± 0.042 gO2m-2d-1 for MIXO2. The small positive average value and the large SD for ADVO2 show that on average advection is only a minor source of O2, however, with large year-to-year variability. The average and SD for MIXO2 show that vertical mixing consistently causes a net increase in sub-MLD O2.

In contrast to the integrated effect of the physical factors, Fig. a and b show that the biological processes cause a net loss in O2. The only source process for O2 is primary production (PP; dashed light blue) which causes a gross increase of about 61.8 gO2m-2 in 2002 (1.4-fold of 2010 value). Considering the biological sink processes, pelagic remineralisation of organic matter (REMpel; dashed light green) has the strongest effect on the sub-MLD O2, accounting for 50 % of the overall biological consumption. Benthic remineralisation (REMsed; dashed yellow) accounts for 18.8 %, while zooplankton respiration (RESzoo; dashed dark green) and nitrification (NIT; dashed red) contribute 22 and 8.8 %, respectively. This order in the relative importance is consistent throughout the entire period 2000–2012 (not shown).

In 2002, REMpel is strongest among all years yielding -103.1 gO2m-2, while 2010 represents the year of weakest REMpel. For RESzoo, 2002 yields a value of -45.1 gO2m-2 (1.8-fold of 2010 value). The 2002 and 2010 values constitute the highest and lowest among all years, respectively. The same applies to REMsed with a 2002 value of -28.5 gO2m-2 (1.2-fold of 2010 value). NIT is also strongest in 2002 resulting in -18.1 gO2m-2, while in 2010 it is about 13 % below the average value of -13.0 ± 2.5 gO2m-2.

The integrated effect of all biological sink processes (REMpel, REMsed, RESzoo and NIT) adds up to -204.8 gO2m-2 in 2002 and to -136.4 gO2m-2 and 2010, i.e., the biological O2 consumption in 2002 is 1.5 times higher than in 2010 and 1.2 times higher than the 2000–2012 average of 169.9 ± 21.2 gO2m-2. The relative contribution of the individual processes to the biological O2 consumption shows only minor variations during the analysed period. REMpel contributes to 53.6 ± 1.7 %, while REMsed accounts for 17.2 ± 0.9 %. For RESzoo and NIT the average contributions result in 21.6 ± 1.5 and 7.6 ± 0.8 %, respectively. The EXPorg below 25 m depth (not presented; calculation analogous to Table ) in 2002 is nearly 1.6 times larger than in 2010, which is in good agreement with the differences in the integrated effect of the biological O2 sinks.

In late April and late June 2002 (Fig. a) two events of enhanced mixing reveal direct and indirect effects on the biological processes. The renewal of the nutrient pool causes short-term increases in PP around the MLD which in turn enhances RESzoo and REMpel. Consequently, only the stronger event in late June causes a net increase in O2. It should be noted that the shown strengthening in the different biological effects is also influenced by the change in the MLD (i.e., integration depth), however, it is also visible when considering a constant MLD (not shown).

PP shows the strongest effects on sub-MLD O2 when the MLD is shallowest which indicates the existence of a deep chlorophyll maximum (DCM). This explains the negative influence of MIXO2 during these periods as O2 concentrations are highest within the DCM due to high PP. The only minor positive or even negative effect of MIXO2 during most of the stratified period emphasises the importance of stratification for the sub-MLD O2 dynamics as it efficiently limits the O2 supply.

The good agreement between the variations in EXPorg and the integrated effect of the biological O2 sinks between the 2 years confirms that the supply of detrital matter to the deep layers is the driving force of sub-MLD O2 consumption. The strong influence of pelagic remineralisation demonstrates its crucial role for the bottom O2 concentrations as it directly affects the potential O2 supply from the mid-water into the bottom layer.