The Gulf of Finland (GOF) is a 400 km long and 48–135 km wide sub-basin of the Baltic Sea with a mean depth of 37 m and complex bathymetry (see Fig. 1). The large fresh-water input from the Neva River significantly affects the stratification and forms the strong salinity gradient from east to west and from north to south. Sea-surface salinity decreases from 5–6.5 ‰ in the western GOF to about 0–3 ‰ in the easternmost part of the Gulf, where the role of the Neva River is most pronounced (Alenius et al., 1998). In the western GOF, a quasi-permanent halocline is located at a depth of 60–80 m. Salinity in that area can reach values as high as 8–10 ‰ near the sea bed due to the advection of saltier water masses from the Baltic Proper.

The vertical stratification in the GOF as well as in the Baltic Sea is unusual (the thermocline and halocline are usually separated) with a pronounced and relatively stable halocline, whereas the temperature is largely controlled by the seasonal variability of the surface heat fluxes (see, e.g., Hankimo, 1964). During the summer season the water column in the deeper areas of the GOF consists of three layers – the upper mixed layer (UML), the cold intermediate layer, and a saltier and slightly warmer near-bottom layer (see Liblik and Lips, 2012), separated by two pycnoclines – the thermocline at the depths of 10–20 m and the permanent halocline at the depths of 60–70 m. A seasonal thermocline starts to develop in May. The surface mixed layer reaches a maximum depth of 15–20 m by midsummer and an erosion of the thermocline starts in late August due to wind mixing and thermal convection. The bottom salinity also shows significant spatio-temporal variability due to irregular saline water intrusions from the Baltic Proper, as well as from changes in river runoff and the precipitation–evaporation balance. There is no permanent halocline in the eastern GOF, where salinity increases approximately linearly with depth (Nekrasov and Lebedeva, 2002; Alenius et al., 2003).

The simulations of the vertical stratification using three-dimensional (3-D) numerical models are not so reliable yet (Myrberg et al., 2010). This study shows that the most advanced 3-D circulation models are able to simulate the major features of the hydro-physical fields of the GOF. For example, generally the hind-cast temperatures differ from observations by less than 1–2 ∘C and the mean error in salinity is less than 1 ‰. Most of the remaining difficulties are connected with problems in adequately representing the dynamics of the mixed layer. The loss of accuracy is most notable in the simulation of the depth and the sharpness of the corresponding thermo- and haloclines. Despite the application of sophisticated turbulent closure schemes and different schemes for vertical mixing, none of the models, analysed in Myrberg et al. (2010), were able to accurately simulate the vertical profiles of temperature and salinity. The latest experiments with turbulence parameterizations of the 3-D hydrodynamic model COHERENS presented in Tuomi et al. (2013) show that the model still underestimates the thermocline depth. Furthermore, the sensitivity of the modelled thermocline depth to the accuracy of the meteorological forcing was studied by increasing the forcing wind speed to better match the measured values of wind speed in the central GOF. The sensitivity test showed that an increase in the wind speed only slightly improved the performance of the turbulence parameterizations in modelling the thermocline depth.

However, a number of studies have reported important effects of the vertical thermohaline structure on the characteristics and processes in the marine ecosystems of the GOF, such as phytoplankton species composition (Rantajarvi et al., 1998) and sub-surface maxima of phytoplankton biomass (Lips et al., 2010), cyanobacteria blooms (Lips et al., 2008), distribution of pelagic fish (Stepputtis et al., 2011), macrozoobenthos abundance (Laine et al., 2007), and oxygen concentrations in the near-bottom layer (Maximov, 2006).

In summary, prediction of the thermohaline structure is a complex problem for the GOF. The spatial variability of the thermohaline structure encompasses a wide range of physical processes at different scales, some of which are still poorly understood (Soomere et al., 2008, 2009). For example, we hypothesize that the local stratification depends very strongly on the across-GOF movements of water masses and that submesoscale eddies generated by baroclinic instability of fronts in the upper layers of the sea not only play an important role in the heterogeneity of spatial distribution of parameters (temperature, nutrients, phytoplankton), but also can contribute to re-stratify the UML, as described in Gent and McWilliams (1990).

In the ocean, submesoscales are scales of motion equal to or less than the Rossby radius of deformation but large enough to be influenced by planetary rotation (Thomas et al., 2007). Recent studies have shown that increasing the horizontal resolution of the model up to 0.5 km (for the GOF Rossby radius aprox. 2–4 km) enables models to resolve submesoscale eddies. As a result, surface currents and temperatures show highly detailed patterns that qualitatively match well with the expected features (Zhurbas et al., 2008; Sokolov, 2013). However, there has not yet been any consideration of the influence of eddy motions and across-Gulf movements of water masses on vertical re-stratification of the UML of the GOF.

The motivations behind this study are

to provide an insight into the lateral advection processes in the GOF, with particular interest in estimating the contribution of lateral advection processes to the thermocline variations;

The traditional point of view is that the eddy diffusion dominates in the horizontal direction and in the vertical direction mixing due to eddies is limited, and small-scale processes such as turbulence provide the majority of mixing. Based on this idea, most commonly a 1-D approach is used to set up vertical mixing by tuning a turbulent scheme. The GOF, an enclosed basin with complex bathymetry and strong stratification mixed layer dynamics, can be strongly affected by lateral advective processes. To investigate this phenomenon, we present a state-of-the art 3-D model of the GOF with high vertical and two different horizontal resolutions. Shelf sea modelling is characterized by a demand for many different configurations to meet multiple science and user needs. NEMO (Nucleus for European Modelling of the Ocean) gives the capability to rapidly configure shelf sea models using appropriate high resolutions and parameterizations for the representation of coastal dynamics.

The modelling period was chosen from 1 April to 31 August 2011 when pronounced thermocline occurs. The thermocline starts its formation in early May when the surface heating and turbulent mixing are dominant processes. Note that year 2011 was characterized by strong upwelling events in the beginning and in the end of the modelling period.

In Sect. 3.1 the GLS, TKE, and ED mixing parameterizations are compared in a series of sensitivity experiments. The choice of closure scheme and the effects of a varying Galperin limit were investigated against MODIS sea-surface temperature (SST) to get the best reproduction of SST pattern.

In Sect. 3.2 we present results of the model runs compared with available CTD (BED) data to study the performance of the chosen parameterizations to represent the UML evolution. Also, the ability of the model to correctly capture such features as fronts was tested against SST images for different resolutions in beginning of August 2011 when there were cloud-free images.

During the upwelling/downwelling event in May modelled on both grids simulates a substantial re-stratification of the UML. The re-stratification is characterized by a sharpening and at the same time a deepening of the thermocline down to 40 m near the Finish coast and export of cold water to the surface near the Estonian coast (Fig. 6). Figure 6a and b show maps of the turbocline depth on the 16 May 2011. The turbocline depth is defined as the depth at which the vertical eddy diffusivity coefficient falls below a given value (here taken equal to background value of 5 cm2 s-1) and can be interpreted as a maximum penetration depth of the turbulent motion in the surface layer.

According to Fig. 6a and b presenting solutions on 2 and 0.5 km grids respectively, the turbocline depth reaches the maximum in the areas near the Finnish coast where the convection is a dominant factor in vertical mixing. We can note the significant differences in the spatial patterns of the turbocline for fine and rough resolutions. Solution on the 0.5 km grid shows a deeper and more complex thermocline pattern. It can be explained by the fact that small-scale frontal structures induced by strong horizontal gradients and captured by the fine-resolution model lead to convective instabilities (Boccaletti et al., 2007) acting to locally re-stratify UML. The model with 2 km resolution cannot resolve submesoscale frontal features and high values (compare to fine resolution) of lateral diffusion coefficients act to smooth the front in other words decreasing potential energy of the front. Unfortunately, few data are available for validation of these differences. Locations of CTD profiles on 16 May are marked as points I, II, III in Fig. 6a and c. Figure 6 (I, II, III) shows the vertical profiles of temperature at locations near the Finish coast. At panel (I) the UML depth for the 2 km resolution model (dashed black line) is shallower than the observed UML depth (solid black line) by 13 m. At the same time, observations and the 0.5 km resolution model (grey line) temperature are almost collocated, and UML depth reaches 40 m. At panel (II) the modelled UML depth is overestimated, but the misfit reaches 7 m for the 2 km resolution model and only 3 m for the 0.5 km resolution model.

We cannot compare the UML depth from the results presented at panel III since none of the models were able to reproduce lateral intrusions observed. The low model performance at this point can be explained by the proximity of the frontal zone between coastal and deep water masses due to the upwelling. We assume that a small error in the predicted location of the front can lead to a serious misfits in the vertical profile. Note also that point (III) is located in a zone of rapid turbocline depth variations (see Fig. 6a and b). This fact confirms a complex front structure, which is formed by the set of randomly spaced small-scale features. The deterministic model can only predict their appearance but not the exact location.

Figure 7 presents evolution of the thermocline through the season. Left panels present the maximum depth of the turbocline and thermocline for the May when the thermocline was formed. Right panels present the same but for the period from 1 June to 28 July. This period ends just before the upwelling in July–August from which the UML erosion begins. Thermocline depth was defined as the depth of 3.5 ∘C isotherm (see Fig. 4). As seen in the presented data, turbulent mixing during the upwelling in May was the strongest throughout the season (see Fig. 7b). At the same time, the increase in the 3.5 ∘C isotherm depth up to 45 m during June–July is not accomplished by any considerable turbulent activity (maximum turbocline depth during June–July do not exceed 20 m for the most of the area of the GOF). Taking into consideration the low value of the background vertical diffusivity coefficient (10-6 m2 s-1), this fact highlights the importance of the advective processes for the formation of the shape and depth of the thermocline. Advective processes resulting in deepening of the isotherm are initiated by intrusion of warm dense water from the open boundary from the Baltic Proper. The intrusion compensates the general surface outflow from the GOF caused by rivers runoff. Notable differences in the shape of averaged profiles presented at Fig. 4 confirm this hypothesis. The eastern part of the GOF is characterized by sharp and shallow thermocline and halocline. Their depths are approximately equal to the maximum turbocline depth. Turbulent and heating processes are dominant here. Deepening of the thermocline and halocline down to 45 m in the western part of GOF is caused mainly by the GOF–Baltic Sea exchange processes since turbulent mixing does not penetrate at this depth here.

The sensitivity of the model solution to increased horizontal resolution is manifested in the different intrusion propagations to the east (compare the right plots on Fig. 7d and f). Density fronts associated with the intrusion are a source of baroclinic instability, which are resolved differently by the 0.5 km eddy permitting configuration (Fig. 7c ) compared to the 2 km configuration (Fig. 7e).

We used the state-of-the-art modelling framework NEMO, initially developed for the open ocean, to build an eddy-resolving model of the GOF. To evaluate the model skill and performance two different solutions where obtained: a commonly used 2 km grid and 0.5 km eddy-resolving fine grid.

With the resolution of 0.5 km the model starts to resolve submesoscale eddies. In the ocean, submesoscales are scales of motion equal to or less than the baroclinic Rossby radius of deformation. For the GOF the baroclinic Rossby radius varies between 2 and 4 km and we need at least 4 points to resolve the eddy. According to Gent and McWilliams (1990), the eddies can act to re-stratify the UML of the ocean, causing the vertical transport through the thermocline.

By moving from 2 to 0.5 km it is logical to expect an intensification of vertical movements induced by smaller vortices resolution. Figure 8 presents the comparison of vertical velocity absolute values for 2 km and 500 m resolutions. The fields are averaged for the depth of 5 m and a 5-day period in May characterized by high-intensity wind-induced dynamics. The main features of the horizontal distribution of the vertical velocity, including the regions of extreme values are similar in both cases. However, on a finer grid structures resembling meanders, currents, and filaments appeared in the middle of the bay at the Estonian coast as well as near the Finland coast where there is a set of point maxima. Both of these small-scale features are absent at coarse grid. It is important to note that the difference in the vertical velocity field appear mainly in the upper mixed layer of the sea. Below the pycnocline the vertical velocity patterns in both cases are very similar. Thus, marked differences could be attributed to the vortex centres of submesoscale eddies, but this assumption is not confirmed by visual horizontal velocity field analysis: explicit vortices are absent in ultraviolet (UV) horizontal field. An alternative hypothesis links these features with local elevations of the bottom topography.

An additional effect of resolved lateral submesoscale processes was investigated in Sect. 4. It was shown that submesoscale motion affects the plume propagation caused by salty water intrusion to the GOF from the Baltic Sea. Generally speaking this process has found to be dominant in the formation of the shape of termocline through the summer season, while the depth of UML was formed by an intensive mixing during spring upwelling. In both cases advective processes act as the main “driving force”.

The presented model demonstrates a substantial improvement in the basin stratification compared to previous numerical studies. The traditional point of view is that the small-scale processes, such as turbulence, provide the majority of mixing in the vertical direction. Most commonly the 1-D approach is used to set up vertical mixing by tuning a turbulent scheme. The GOF, an enclosed basin with complex bathymetry and strong stratification mixed layer dynamics can be strongly affected by lateral advective processes. Adequate representation of lateral processes by the model let us decrease the role of background constants in a turbulent mixing scheme (we set them to minimum possible values). This simplifies the traditional trade-off between the depth and sharpness of the thermocline. Setting the background values of vertical eddy viscosity and diffusivity to 10-5 and 10-7 m2 s-1 respectively, lets us keep the sharp form of the thermocline and halocline while the UML depth corresponds to observations.

Since the time period of the runs was rather short (less than 1 year) and the model had not been used before, it is obvious that the values of some parameters might have been somewhat improperly chosen for use in this study. Through fine tuning of the model better results could probably be obtained. However, the focus in this study was to examine the differences arising from different horizontal resolutions, the fact that model parameters were similar in each case should be considered to be far more important than the quantitative agreement between observations and model results. Actually, it was shown that the model results for both resolutions are in reasonable agreement with available observations. In some cases the 0.5 km model performs better and at the same time there are areas not covered by observations where we can note more substantial difference between models. It is found that simulations resolving submesoscale are characterized by the deeper UML with more complex structure in the regions of the GOF directly affected by the upwelling/downwelling.

The GOF is a highly dynamic region with lateral currents causing temperature contrasts and/or rapid temporal variations on the surface. From the satellite picture we can identify whether the model properly reproduces the frontal structure at the surface. For example, the temperature drop during an upwelling event and resulting temperature contrast at the surface reached 2.5 ∘C. We assume it to be a considerably more substantial signal compared to known uncertainties of satellite SST measurements (0.4 ∘C; https://podaac.jpl.nasa.gov). The usage of results of hydrodynamic modelling together with SST information can provide an extended analysis and deeper understanding of the upwelling process. Re-stratification of the UML caused by upwelling results in changes of the SST pattern that can be observed from satellites. From the comparison of modelled and observed satellite SST we can identify whether the model reproduces the stratification itself and as a result properly reproduces the frontal structure at the surface.

Refinement of the model resolution below the level of 0.5 km would be of limited benefit in a hydrostatic model. For the purpose of deep investigation of submesoscale processes in GOF such as transport across the UML and on/offshore the non-hydrostatic formulation is needed. It lets us avoid “artificial smoothing” of the velocity field. Other possible improvements of the model performance, which we are planning for the next steps, will include sensitivity tests for the different boundary conditions with higher spatial resolution at the open boundary and surface, and utilization of recently available data with high spatial coverage from the expeditions during the Gulf of Finland Year 2014.

The Baltic Environmental Database – BED – was initiated in 1990 as part of the research project “Large-scale Environmental Effects and Ecological Processes in the Baltic Sea”. The basic idea behind the Baltic Environmental Database has been to make available data sets on the conditions in the Baltic Sea and on forcing functions. Presently, the database is placed at the Baltic Nest Institute (BNI) at the Stockholm University http://www.balticnest.org/bed. MODIS Sea Surface Temperature product generated from the sensors installed on two satellites Terra and Aqua by NASA Goddard Space Flight Center. The gridded global product with spatial resolution 1 km available from http://dx.doi.org/10.5067/TERRA/MODIS_OC.2014.0 and http://dx.doi.org/10.5067/AQUA/MODIS_OC.2014.0.