Nemo-Nordic uses a non-linear free surface () with a () option to split the computation of barotropic and baroclinic modes. In comparisons with previous ocean models such as that used by , which used a linear free surface, these features enable Nemo-Nordic to run in regions of high tidal amplitude like the North Sea and the English Channel. Tuning is done in order to obtain an accurate SSH representation. We use a variable bottom roughness () along the cyclonic pathway of barotropic Kelvin waves in the North Sea. This roughness is optimized to obtain the best possible SSH amplitude. Nemo-Nordic runs with a baroclinic time step of 360 s, which proved to be the best compromise between stability and computational speed. The barotropic time step is set to be 30 times smaller.

Vertical and horizontal mixing (and the connections between them) is a critical element when it comes to a Baltic and North Sea configuration. The major difficulty is to simulate the crucial dense water overflows in the Baltic Sea . In order to ease this process, Nemo-Nordic uses a bottom boundary layer parametrization for tracers () in order to reduce the biases of a z coordinate ocean models when it comes to the representation of dense overflows. In NEMO, the bottom boundary layer can be used with an upstream advection scheme or with a purely diffusive scheme or with a mixture of both. For Nemo-Nordic, sensitivity experiments have shown that the use of a purely diffusive scheme results in more realistic deep salinity in the Baltic Sea. Using an advective scheme results in a lower deep salinity, most likely due to a higher entrainment rate during major Baltic inflow events. One could object rightly that using sigma coordinates could have solved this issue without the use of such a parameterization. But using such a coordinate system would, on the other hand, create a strong diapycnal mixing of the Baltic Sea halocline and most likely pressure gradient errors in the steepest places of the North Sea such as the Norwegian trench.

However, the use of the bottom boundary layer parametrization is not enough to achieve a correct representation of the overflows. The tuning of the mixing was a major issue and required a tuning process. Nemo-Nordic includes two basins which have very different dynamical features: the North Sea is strongly influenced by tides, tidal mixing and relatively strong winds. In the North Sea, the stratification is relatively weak, with the exception of a summer thermocline in some regions, regions of freshwater influence and the region of the Norwegian Coastal Current . In contrast, the Baltic Sea has almost no tides, is less exposed to wind forcing and has a strong permanent stratification. Nemo-Nordic uses a two-equation turbulence closure, based on a k-ϵ turbulence scheme (). In addition, the Galperin parameterization is used , in order to preserve the Baltic Sea permanent stratification. This parameterization limits the mixing length computed by the vertical turbulence model in case of low turbulence and high stratification, which fits perfectly with the Baltic Sea halocline environment. This parameterization can be written following Eq. (), in which k is turbulent kinetic energy, N is the Brun–Väisälä frequency, and Cgalp is the Galperin coefficient. Finally, lmax⁡ is the maximum mixing length. lmax⁡=Cgalp2kN

Experiments done on the configuration without this latest parameterization yield a Baltic Sea permanent halocline that vanishes in a few years only. The Galperin coefficient is set to 0.17, which proves to be a good compromise between deep salinity and seasonal thermal stratification. A Galperin coefficient that is too high produces a higher deep salinity but also a very thin and unrealistic seasonal thermocline. In addition to the Galperin parameterization, the background levels of turbulent kinetic energy are turned to their minimum values, the goal being always to limit as much as possible mixing at the level of the Baltic Sea halocline.

Horizontal mixing is based on a Laplacian approach combined with the rotation of the horizontal diffusion tensor (). However, this does not result in a real isopycnal diffusion in the sense that Nemo-Nordic is still based on a z coordinate system and not on isopycnal coordinates. Close to the bottom, sensitivity experiments have demonstrated that the rotation of the diffusion tensor did not enable us to follow dense salt inflows: increasing horizontal diffusivity resulted in lower deep salinity or even no penetration of dense inflows at all, showing that diapycnal mixing is created by horizontal diffusion, even when the rotation of the diffusion tensor is activated. The first versions of Nemo-Nordic used a Smagorinsky approach in order to limit horizontal mixing as much as possible, but this approach finally resulted in very weak Baltic Sea salt inflows and a diffusivity impossible to control. Our final strategy has therefore been to create a viscosity/diffusivity coefficient which is high where model stability requires it the most (i.e. above the halocline), and low where it is crucial for diffusivity to be as low as possible to avoid diapycnal mixing. After a suite of sensitivity runs we decided on using spatially varying values for viscosity and diffusivity. From the surface to a depth of 30 m the viscosity is set to values ranging from 30 to 50 m2 s-1 for the Baltic and the North Sea, respectively, while we set diffusivity to a 10th of this value. Below this depth the values of viscosity is reduced to 0.1 m2 s-1. The same increase was applied to the diffusivity, which is still set to a 10th of the value for viscosity. This feature works as long as the Baltic Sea halocline is located at this precise depth but should be changed if the halocline depth changes. Along the open boundaries, the viscosity is increased to 800 m2 s-1 over the entire water column, decreasing rapidly to standard values within a few grid points inside the domain. This value is huge but prevented the model from ever crashing at the open boundary conditions. Several values were tried, and they proved to have little effect on the sea level variability inside the model domain.

A free slip option is taken for the lateral boundary conditions.

Nemo-Nordic has two open boundaries: a meridional one in the western part of the English Channel and a zonal one set between Scotland and Norway. The setting of the boundary conditions uses the open boundary condition module of NEMO (), as well as the tide module ().

Several settings can be used for boundary conditions. Tidal harmonics are taken from and although further investigation is also being made using the FES tidal model . Harmonical values for SSH are interpolated on the open boundaries of Nemo-Nordic. Harmonical tidal transports (in m2 s-1) are also interpolated in the same manner and then divided by the local depth of the Nemo-Nordic domain. In research mode, temperature and salinity boundary conditions may come from climatological data or from climate simulations, and a simple storm surge model is used. The model itself is corrected by a global ORCA0.25 configuration to take into account seasonal variability due to temperature and salinity variations. In operational mode, Nemo-Nordic uses ECMWF forecast data for its SSH, temperature and salinity boundary conditions.

Nemo-Nordic has been so far used in forced mode using prescribed atmospheric conditions and the CORE bulk formulation .

To cover a long period, the atmospheric forcing is based on different sources. The driving data of the period 1961–1978 are based on downscaled ERA40 data . The ERA40 reanalysis is downscaled with the Rossby Centre regional atmospheric model version 4 (RCA4) with spectral nudging . The downscaling is necessary to improve the horizontal resolution of the global reanalysis data set. Here, we use data from an RCA4 set-up with a horizontal resolution of 11 km. The frequency of the driving data is hourly.

With the beginning of 1979 we change the atmospheric forcing to the SMHI reanalysis product EURO4M which is available until the end of 2013 . The EURO4M data are available 3-hourly and with a horizontal resolution of 22 km. EURO4M incorporates data assimilation which ensures the best quality for our driving data. In operational mode (Nemo-Nordic 1 nm), the simulations were forced by HIRLAM C11 (http://hirlam.org, last access: 17 January 2019).

In forecast mode, Nemo-Nordic uses a combination of hourly ECMWF LL01 (9 km) data and Arome data (2.5 km).

A proper light penetration parameterization proved to be an important feature in order to reproduce the proper thermal structure, and especially the formation of a summer “Cold Intermediate Layer”. The Baltic Sea has turbid waters which prevent deep light penetration, concentrating the summer heat input close to the surface, and hence easing autumn cooling. Nemo-Nordic uses a red–green–blue light penetration parameterization, together with a constant chlorophyll value of 0.5 mg m-3 to represent the turbid Baltic Seawaters. Failing to use chlorophyll concentration results in a cold intermediate layer that is too thin and too shallow. This chlorophyll concentration does not pretend to be realistic from a biogeochemical point of view, it corresponds to a mean value for both basins which allows a realistic light penetration in an area which has a water turbidity higher than that of the global ocean.

The Baltic Sea salinity is sensitive to the accumulated freshwater input since the exchange with the open ocean is very limited e.g.. Freshwater supply to the Baltic Sea in the simulation must therefore be handled with care. Here, we are using data from the HYdrological Predictions for the Environment (HYPE) model . The model simulates a mean runoff to the Baltic Sea of roughly 16 000 m3 s-1 for the period 1981–1998. However, state that the observed runoff for the same period is 15 053 m3 s-1 with an even lower value (14 085 m3 s-1) for the period 1902–1998. Consequently, we reduced the freshwater supply computed by HYPE. We have chosen a general reduction of 10 % which gives more realistic runoff for the Baltic Sea. Moreover, this improved the Baltic Sea salinity (not shown). The freshwater input to the North Sea including the Skagerrak and Kattegat area amounts to 11 515 m3 s-1 after the reduction by 10 %. The river runoff is spread over 424 river mouths in the entire model domain whereas more than 250 are located in the Baltic Sea (excluding the Skagerrak and Kattegat area). The UNESCO equation of state for seawater is used. The reference density is set to 1035 kg m-3, which is most likely overestimated. Further experiments should be done on this point.

Nemo-Nordic benefits from the use of the NEMO ocean engine and of its advanced sea ice model LIM3. Sea ice is a feature specific to the Baltic Sea that is due to the Baltic Sea's low salinity. Being able to represent sea ice dynamics properly is compulsory when it comes to a Baltic Sea ocean model. Models such as do not include this feature. The sea ice in Nemo-Nordic is validated in . Comparison done with suggest that Nemo-Nordic so far reaches the highest accuracy of sea ice representation for the Baltic Sea.

The model reproduces the general cyclonic surface circulation pattern in the North Sea , with a southward flow in the western part of the basin, a northeastward flow along the southern coast and a northward flow along the Norwegian coast in the Norwegian Coastal Current (Fig. ). The strongest modelled southward flow of Atlantic water through the northern boundary occurs just next to the NCC. This flow forms a current that flows south-east and enters the well-known cyclonic circulation pattern in the Skagerrak, in good agreement with the observed surface currents in the North Sea . A part of the southward flow along the British Isles also deviates eastward to directly join the eastward flow towards the Skagerrak. Another part flows further to the south and mixes with inflow from the English Channel. The larger part of inflowing Atlantic water from the northern boundary is restricted to north of 54∘ N and then recirculates mainly following the topography of the Dogger Bank. The southern North Sea is dominated by inflow waters from the English Channel.

In the Baltic Sea and its sub-basins the model reproduces the observed general cyclonic circulation patterns , with a southward flow in its western part and a northward flow in its eastern part. In the Gotland basin the model reproduces the southward flow on both sides of Gotland and the northward flow along the coast of the Baltic, giving rise to the cyclonic structure over the Gotland Deep (Fig. ). In the Kattegat the model simulates a general anticyclonic flow in agreement with and resolves the northward flowing Baltic Current along the Swedish coast, which feeds low-saline waters into the NCC.

The haline vertical structure of the Baltic Sea is in general reproduced well by Nemo-Nordic (Fig. ), with a distinct halocline separating the surface waters from the deeper waters. In the Bothnian Bay and the Kattegat (F9-A13 and Anholt), the modelled depth (50 and 20 m, respectively) and strength of the halocline correspond well to observations. There is a small negative salinity bias over the whole water column in the Bothnian Bay, while the overall salinity is reproduced well in the Kattegat. In the Baltic proper and the Bornholm Basin (BY15 and BY5), the modelled halocline is weaker and shallower than the observed one. The surface water at these stations tends to have a positive bias, while the deeper waters tend to have a negative bias, suggesting too strong a mixing between surface and deep waters. No stronger seasonal cycles exist in the haline structure, except for a freshwater pulse arriving in the surface waters during summer months, which is captured by the model at all stations.

The thermal vertical structure is dominated by the seasonal thermocline. In the Kattegat, Bornholm Basin and the Baltic proper (Anholt, BY5 and BY15), it starts forming earlier than in the Bothnian Bay (F9-A13), both in the model and in the observations (Fig. ). The later formation of the thermocline in the Bothnian Bay is partially due to the lower insolation at higher latitudes but also due to the non-linearity of the equation of state at low salinities. The temperature of maximum density is higher at lower salinities, meaning that the water column has to completely mix before the formation of the thermocline can start, which is reproduced well by the model. The model's development of the seasonal thermocline and its deepening agrees well with observations in the Kattegat, the Bornholm Basin and in the Baltic proper. In the Bothnian Bay no conclusions can be drawn on this aspect due to a lack of measurements between 15 and 40 m, where the thermocline is situated. The break-up of the thermocline is also well represented in the model. The model has, on the other hand, difficulties in representing the colder intermediate waters in the Bornholm Basin and the Baltic proper, which have a warm bias. This might be related to biases in the atmospheric forcing , as these waters are formed during winter convection. Indeed, the simulated winter surface temperatures at BY5 and BY15 tend to have a warm bias. The modelled cold intermediate waters also descend too deep towards the end of the year. This might be related to the weaker halocline, and thus probably stronger mixing, in the model. The deep waters below the halocline are warmer than the intermediate waters, which is reproduced by the model. In the model it is, however, about 0.5∘ warmer than in the observations at the BY15 station.

From the comparison between the observations and their variability (Fig. ), one notices that Nemo-Nordic in general reproduces the variability in the deep-water salinity close to the bottom well, both in the Kattegat and in the Baltic Sea, despite the constant background bias in the salinity. Especially, it is interesting to note from the BY15 salinity that the model is able to reproduce the major Baltic inflows of 1993 and 2003. The mechanisms behind the major Baltic inflows are actually mostly barotropic, although their propagation to the bottom of the Baltic Sea involves mixing processes. Therefore, the representation of sea level variability is a key element in reproducing the variability in the major Baltic inflows. A comparison of the modelled and measured sea level differences during the recorded durations of these inflows shows the model's accuracy to represent the underlying barotropic processes. During the duration of the 1993 major Baltic inflow, the sea level at Landsort increases by 1 m in observations against 1.02 m in the model, while during the 2003 major Baltic inflow, the sea level at Landsort increases by 0.58 m both in the model and in the observations. This further suggests that a misrepresented baroclinic process must be responsible for the negative bias in deep-water salinity in the Baltic Sea. Even though this model uses a bottom boundary layer parameterization , it is still a z coordinate model, which means that the representation of dense overflows is not as accurate as it would be in a sigma or generalized vertical coordinate model. It is also interesting to note that Nemo-Nordic tends to overestimate the variability in deep-water salinity at the Anholt station in the Kattegat, while it slightly underestimates the variability at the BY2 station.

As an example of Nemo-Nordic's performance in the shorter term, we compared the model results to temperature observations from an autonomous Argo buoy. Over 100 profiles were collected during a mission in the Bothnian Sea, which lasted from 13 June to 2 October 2013. The profiles were taken from between 61.57 and 62.47∘ N in latitude and between 19.59 and 20.42∘ E in longitude. This data set has been described in detail by , who also provided an illustration of the buoy route. From a comparison of observed and modelled temperature profiles we see that the seasonal thermocline is visible throughout the summer (Fig. ). The vertical structure of temperature was relatively reproduced well by Nemo-Nordic near the surface. In August the thermocline reached maximum depth and temperature. The model was able to describe well how the mixed layer deepened during the summer. The temperature gradient of the thermocline was also well represented. The surface layer responded to atmospheric forcing in a similar way in observations and model. In layers under the thermocline, model temperatures were somewhat too high. This bias increased in late summer. Deeper, the dicothermal (old winter water) layer was not as pronounced in the model as it was in the observations. In late August, the model predicted larger thermocline depths than were observed. In general, temperature profiles were smoother in the model than in observations. Furthermore, some finer-scale features were not completely reproduced by the model.

Observed and modelled near-surface temperatures, along with estimated thermocline depths, are shown in Fig. . Near-surface temperature was taken to be the temperature of the model point at the depth of the topmost data point in the observations, which was typically around 4 m, depending on the profile. In most cases this is very close to the surface temperature. The location of the thermocline was taken as the place of the maximum temperature gradient along the z axis. Near-surface temperature in the model overall reproduced the seasonal temperature cycle, although in early September surface temperatures were around 1∘ greater in the model than in observations. Thermocline depths were represented quite well in the model, except for the aforementioned time in late August. presented a similar comparison to a different model configuration, derived from an earlier version of Nemo-Nordic. That model used different atmospheric forcing fields taken from an operational HIRLAM forecast from the FMI (Finnish Meteorological Institute), climatological boundary conditions, climatological river runoffs and initial conditions from FMI's operational Baltic Sea forecast. Furthermore, it did not have the light penetration parameterization present in the official Nemo-Nordic configuration described in this paper. Compared to those results, the near-surface temperature in the official Nemo-Nordic results differs more from the observations in autumn but shows less bias in early summer. Thermocline depths were quite similar in both configurations.

In this section we validate the vertical structure and seasonal variability at four stations representative of different hydrological regimes in the North Sea. Two stations are located near the boundaries towards the Atlantic Ocean (Fladen Ground and the Southern Bight). Validating the temperature and salinity structure in these areas also gives a validation of the boundary conditions and the properties of the inflowing water. The open boundary condition fields for tracers (T and S) come from a climatology in this case, so it is interesting to check whether their use with the model enables it to represent measurements. The two other stations (NCC and Frisian Front) are located in areas where there are relatively large horizontal and vertical (only NCC) salinity gradients due to the freshwater forcing from the Baltic Sea and the continental rivers draining into the southern North Sea. The observational data comes from the KLIWAS data set provided by the University of Hamburg . It is composed of all available measurements between 1970 and 2013 in the North Sea, which have been put into a 1×1 grid.

The haline vertical structure at the four stations in the North Sea is displayed in Fig. . The only station with a distinct permanent haline stratification is the NCC station. The vertical haline structure at this station is reproduced well by the model, although the surface waters are less saline than the observations by about 1 PSU. The other stations are rather homogeneous in the vertical with respect to salinity. In the Southern Bight and the Fladen Ground, the model captures the overall mean salinity. At the Frisian Front the modelled salinity is about 1.5 PSU too low, which is probably related to a displacement of the front between coastal waters with lower salinity and offshore waters. At all stations the model simulates a seasonal cycle in the surface salinity with a freshening during the summer months, in agreement with the observations. The timing and the amplitude of this summer freshening is, however, subject to some biases. Because the data set does not contain regular measurements from these positions it can, on the other hand, give rise to biases in the observational estimates of the seasonal cycle.

The thermal vertical and seasonal structure is, as for the Baltic Sea, dominated by the seasonal warming and cooling of the surface waters (Fig. ). In the Southern Bight and at the Frisian Front the waters are well mixed from surface to bottom throughout the year, and no seasonal thermocline develops, which is reproduced well by the model. In the Southern Bight there is a warm bias of the order of 0.5 ∘C (annual mean) in the model throughout the water column. At the Frisian Front there is a warm bias of about 0.3 ∘C in the surface waters. At the two deeper stations, the seasonal development and the depth of the thermocline are reproduced well in the model, although the start of the thermocline formation is somewhat too early in the model. This is the case especially at the Fladen Ground, where it starts almost 1 month too early. Also the winter SSTs are too warm in the model, resulting in too weak a winter convection or temperatures of the convecting water that are too warm, which in its turn gives a warm bias in the deep waters. At both stations there is a warm bias of about 0.5 ∘C (annual mean) in the surface waters.

For biogeochemical processes summer thermal conditions are important when water temperature and light intensity stimulate the growth of phytoplankton. Contemporaneously, thermal stratification develops in the deeper basin of the northern North Sea and the inflow of Atlantic water weakens ; accordingly atmospheric forcing at the surface becomes more important. This leads to substantially better reproduction of interannual variability even in the north (Fig. b). We analyse in the following the modelled thermocline dynamics following previous approaches for the North Sea , which define the presence of thermocline conditions when a certain vertical temperature gradient is exceeded. We here chose a critical gradient of 0.25∘C m-1. The yearly maximum extent of stratified areas is primarily governed by topography and wind stress and varies between 100 000 and 185 000 km2 in 1990 and 2005. Stratified conditions begin to develop in May and reach their maximal intensity during July and August. Already during September wind stress strengthens and temperatures lower, which increases mixing. The thermocline weakens then and is shifted downward. As a result, nutrient-rich water reaches the euphotic zone. During this time, a second phytoplankton bloom can be sometimes observed in the North Sea .

Surface properties are in many cases dominated by local meteorological forcing . Therefore, it is important to also validate subsurface properties, which are also influenced also the by circulation dynamics (like Atlantic inflow). For this, we use the KLIWAS observational data set . We here follow previous approaches and subdivide the North Sea into 1∘×1∘ boxes for which for each month and at each box, standard level Taylor statistics are calculated (for details, see Raddach and Moll, 2006; Gröger et al., 2013). In order to estimate the interannual variability in seasonal signals, we chose January and July as representative of winter and summer as in these month observations were most abundant in the observational data set. The results are shown in Table . In total, 25 619 observations were used for the analysis.

Overall, good correlation with the temperature and salinity observations for summer and winter indicates the model's skill to capture interannual variability and thus the ability to realistically respond to low-frequency modes of climate variations such as decadal variability or the NAO (North Atlantic Oscillation) which likely influence the North Sea hydrography (e.g. Hjøllo et al., 2009; Mathis et al., 2015). The root mean square values lie well within the standard deviation of the observations (with the exception of January salinities where rms is slightly higher; Table ). The model's salinity variability (as indicated by standard deviation) is too high (∼50 %), but the spatial distribution of the observations is much coarser than the model grid, which explains this result.

In the following we compare the modelled SST with a widely used satellite product provided by the Federal Maritime and Hydrographic Agency of Germany, Hamburg (Bundesamt für Seeschifffahrt und Hydrographie; hereafter BSH). By this we are able to investigate how the modelled SST reproduces interannual variability, which is important for the application of the model to climate services and the simulation of various climate scenarios.

In contrast to the warm bias relative to the in situ temperature measurements, the simulated winter SST (Fig. ) is almost everywhere colder than the satellite estimations of SST. Cold biases relative to satellite measurements were also obtained in other ocean models driven by the ERA40 reanalysis data set in and . Given that in situ temperature measurements give a more direct measure than satellite estimations of SSTs and that the atmospheric forcing used for these simulations has a warm bias, especially in the North Sea during winter , it is likely that the satellite underestimates the SST. Despite this, the satellite SSTs can be used for validation of spatial and temporal variability.

Figure a shows an overall good correlation of modelled interannual SST variations with the BSH data set. Likewise the lower correlation in the northern deeper parts could indicate problems with convective and/or wind-induced mixing which would influence the heat transfer from the deeper layers to the surface. In contrast, in the southern and shallower parts, SSTs are dominated largely by the atmospheric forcing , and thus correlation increases. Good correlation is also seen along the Norwegian coast where the effective heat capacity is limited due to haline stratification, which makes SSTs more sensitive to the atmospheric forcing. The same is true for nearly the entire Baltic Sea, where correlation drops below 0.8 almost nowhere.