The BLK-REA model component is the Nucleus for European Modelling of the Ocean (NEMO version 4.0, Madec and the NEMO team, 2019) configured for the domain (Azov and Marmara Seas are not included). NEMO is implemented at a horizontal resolution of 1/40° and 121 vertical geopotential levels. This horizontal resolution provides a spatial discretization of approximately 2.5 km, which conforms to the mesoscale eddy-resolving scale; the Rossby radius of deformation in the Black Sea is approximately 20 km. The model is driven by atmospheric fluxes derived from ECMWF ERA5 reanalysis with spatial and temporal resolutions of 1/4° and 1 h, respectively. The atmospheric forcing considers the following variables: components of 10 m wind, total cloud cover, 2 m air temperature, 2 m dew point temperature, mean sea level pressure and precipitation. The system computes momentum, heat, and water fluxes at the air-sea interface using bulk formulae originally developed for the Mediterranean Sea (Castellari et al., 1998; Pettenuzzo et al., 2010), which have also been employed in other Black Sea systems (Ciliberti et al., 2022; Lima et al., 2021). Additionally, the system applies daily SST relaxation for heat flux corrections based on the ESA-CCI SST-L4 product (Good et al., 2020).

The system assimilates sea level anomaly (SLA) data from the dataset European Seas Along-Track L3 Sea Surface Heights Reprocessed, Tailored for Data Assimilation, available in the Copernicus Marine Service catalog (SEALEVEL_EUR_PHY_L3_MY_008_061, 10.48670/moi-00139; Faugère et al., 2022). To maximize the number and spatial coverage of in-situ observations assimilated into the model, we combine multiple datasets using a predefined priority order, ensuring that duplicate profiles are excluded, as follows:

Global Ocean CORA In-situ Observations – Yearly Delivery in Delayed Mode from Copernicus Marine Service (INSITU_GLO_PHY_ TS_ DISCRETE_MY_013_001; 10.17882/46219) (Szekely et al., 2019; Szekely et al., 2024).

In addition to the standard quality-control procedures applied by the data providers, several supplementary screening steps are implemented to minimize the impact of spurious observations. Only measurements explicitly flagged as good are retained for all variables, and basic physical range checks are applied to temperature and salinity. For CTD profiles, only downcasts are used. For Argo floats and gliders, a vertical-resolution criterion is applied in the upper ocean, excluding profiles with data gaps larger than 40 m in the first 300 m to ensure adequate representation of the thermocline. Finally, in rare cases where the assimilation of specific observations (e.g., T/S profiles or along-track SLA) induces instabilities in the model solution, targeted visual inspection is performed to identify and exclude the problematic data prior to rerunning the assimilation, as neglecting these cases may lead to a model blow-up.

In data assimilation, the in situ instrumental errors assume different values for T and S and vary in the vertical dimension based on statistics derived from Ingleby and Huddleston (2007). The in-situ representation errors are defined as a multiplicative factor applied to the depth-dependent instrumental errors and vary horizontally on the model grid according to previous model–observation statistics. In this component, the same spatially varying factor is applied to T and S, which is a simplification justified by the similar spatial sampling patterns and statistical structure of the T/S in situ observational datasets. Representation errors account for unresolved physical processes, subgrid-scale variability, and model errors that are not part of instrumental uncertainties. Both components of in situ errors are kept constant over time. For SLA observations, the instrumental error is set to 4 cm, and the representation errors vary spatially and monthly following Oke and Sakov (2008). Similar to the previous version, a background quality check is implemented in the data assimilation system to reject observations that deviate significantly from the model prior solution. Rejection by background quality control does not necessarily indicate erroneous data, but often reflects large innovations that would otherwise introduce undesirable shocks in the model state. The quality control procedures and data rejection thresholds are applied as described in Lima et al. (2021), with no changes introduced in BLK-REA.

In contrast to the previous version of the reanalysis (Lima et al., 2021), which used a model-derived mean dynamic topography (MDT), an enhancement in the present version is the use of an observation-based mean dynamic topography MDT to compute the model-equivalent SLA in data assimilation. Sensitivity tests indicated that this choice improves the assimilation skill of SLA, leading to systematically reduced RMSD values. The observation-based MDT field is available in the Copernicus Marine Service catalog: 10.48670/moi-00138 (E.U. Copernicus Marine Service Information (CMEMS), 2024).

The data assimilation system, OceanVar, utilizes a three-dimensional variational (3D-Var) assimilation algorithm. OceanVar was initially developed for the Mediterranean Sea (Dobricic and Pinardi, 2008) and subsequently extended to the global ocean (Storto et al., 2011) and Black Sea (Ciliberti et al., 2022; Lima et al., 2021). The new system utilizes OceanVar, following the same equations outlined in Lima et al. (2021), with particular emphasis on the cost function (J) equation presented as follows: 1J=12δxTB-1δx+12Hδx-dTR-1Hδx-d where δx=xa-xb is the increment, i.e., the difference between the analysis (xa) and background (xb), d=y-H(xb) is the misfit between an observation vector y and its modeled correspondent (in the observation space) where H, the observation operator, maps the model fields to the observation locations. OceanVar is a multivariate scheme, i.e., the state vector x can contain the following model state variables: T, S, SLA, and horizontal velocities (u and v). However, only the first three variables are employed in the present BLK-REA implementation. B and R are respectively the background and observation covariance matrices. R is diagonal in the observation space and includes the sum of instrumental and representation errors, along with an additional error component that depends on the time difference between each observation and the analysis time. The latter component is weighted according to this temporal distance.

In OceanVar, the variational cost function is solved using the incremental formulation (Courtier, 1997), with preconditioning of the cost function minimization achieved through a change-of-variable transformation. Thus, to avoid inverting the B matrix and to precondition the minimization of the cost function, the B matrix is defined as B=VVT where V is decomposed into a sequence of linear operators: V=VηVhVv. The V operator represents the background error covariance matrix, capturing the interdependencies among variables. Furthermore, a new control variable, v=V+x (and thereby δx=Vv), is introduced for the minimization process through the application of a transformation. Thus Eq. (1) becomes: 2J=12vTv+12HVv-dTR-1HVv-d In the present version, the linear operators Vη and Vh follow the same formulation described by Lima et al. (2021). The dynamic height operator in Vη imposes local hydrostatic and geostrophic balance among SLA, temperature, and salinity increments, following Storto et al. (2011), with a level of no motion assumed at 1000 m, where this balance is valid. This restricts SLA assimilation to deep-water regions. Vh represents horizontal correlations, modeled with a first-order recursive filter (Farina et al., 2015) and a fixed correlation length-scale of 20 km. Instead, Vv incorporates background-error T and S vertical covariances that are modelled through 45-mode multivariate Empirical Orthogonal Functions (EOFs) and derives from a previous integration including the assimilation of SLA, T and S profiles, using the full model resolution. In addition, the new approach is non-stationary and a different set of EOFs are applied considering the following decades: 1984–1993, 1994–2003, 2004–2013, and 2011–2020. EOFs are calculated for each month from anomalies estimated from daily T, S and SSH fields with respect to the long-term monthly mean of the corresponding decade.

The experiment is initialized in 1991 with a rest state of temperature and salinity fields derived from the World Ocean Atlas climatology (WOA 2018, Garcia et al., 2019). Following a spin-up of 2 years (1991–1992), the BLK-REA starts in 1993. The data assimilation is applied every 2 d, i.e., if the model initializes at time t, the next data assimilation cycle is performed at the time t+2. The observation window is 4 d centered at the analysis time, so that each cycle assimilates observations from 2 d before until 2 d after the analysis time. Figure 1 shows SST increments (in °C) over the Black Sea on 9 January 2020, overlapped with along-track SLA and in situ profile data assimilated during a single DA cycle in the BLK-REA. The subplot highlights the Marmara Box and its bathymetry, where boundary conditions from U-TSS are applied along faces A, B, and C. In the Black Sea, the limited availability of in-situ observations for assimilation leads to systematic errors in certain variables during specific periods, particularly in the deeper layers. To mitigate this bias, large-scale bias correction (LSBC) toward WOA2018 decadal climatologies is applied below 700 m. The formulation and additional details on the LSBC scheme are described in Lima et al. (2021).

Spatial seasonal maps of reanalysis SST are compared to satellite data in the period 1993–2022 and their difference shows a predominance of model negative biases in winter and spring, and positive biases in summer and fall, with a few exceptions as follows (Fig. 2; left). Positive values of 0.1 up to 0.3 °C are visible in some regions during winter, such as close to the Danube river mouth and along the southwest coast. Negative biases are present adjacent to the Kerch Strait, and the lowest negative biases, of more than 1.0 °C, are exhibited in the upwelling region along the western Anatolian coast in summer. Most of the central-eastern area is covered by negative bias in fall. SST RMSD (Root Mean Squared Difference) maps indicate that errors are generally lower in spring and higher in fall (Fig. 2; right). In general, larger values can be seen close to large river mouths such as near the Dnieper in winter and Danube in winter, spring, and summer. The highest errors, exceeding 1 °C, are observed along the western Anatolian Turkish coast in both summer and fall. In this region, a similar overestimation of upwelling phenomena was observed in the results of the previous Black Sea reanalysis, which was attributed to the influence of stronger winds (Lima et al., 2021). Recent analyses have indicated that the air-sea bulk formulation may be responsible for the intensified upwelling, and we plan to refine this model component in future releases of the Black Sea reanalysis.

The Hovmöller diagram (time-depth) of RMSD for temperature computed as a lateral average, reveals a distinct seasonal cycle in the upper water column (Fig. 3), with lower errors in winter that increase during summer, exceeding 2 °C in the upper 50 m. This summer increase is associated with the model's misrepresentation of the seasonal thermocline, which is partially corrected through data assimilation. Below 100 m, errors remain low, staying below 0.25 °C for almost the whole period. Before the Argo floats era (mid-to-late 2000s), the scarcity of in-situ data limited the effectiveness of data assimilation, compromising both the model correction and the validation process.

The Hovmöller diagram of temperature biases predominantly shows positive values, occasionally exceeding 1 °C near the surface, with intermittent periods of negative biases (Fig. 3). The most pronounced discrepancies are observed within the seasonal thermocline depths. There is a tendency for biases to shift from positive in upper layers to negative values at deeper layers, down to 100 m. This may be related to the misrepresentation of the vertical position of the seasonal thermocline in the BLK-REA results compared to observations over time.

Unlike temperature, the Hovmöller diagram of RMSD for salinity does not exhibit a clear seasonal cycle. Errors exceed 1 psu during short periods (Fig. 3), particularly in the upper layers, where high uncertainties are likely derived from precipitation biases in ERA5, simplified river runoff forcing, and the internal freshwater budget computed via the model's bulk formulae. Apart from these peak values, errors are relatively higher between 50 and 100 m. Within this layer, errors tend to decrease over time, reaching values below 0.25 psu in the most recent years of validation. Once again, the scarcity of observations compromises the validation process before 2004. Below 200 m, errors remain very low, with values consistently below 0.1 psu.

Salinity biases show a predominance of positive values (Fig. 3). The Hovmöller diagram reveals two main characteristics: BLK-REA diverges more from observations in the upper 200 m, with values alternating between positive and negative biases. Below 200 m, biases approach zero and remain predominantly positive. Since 2014, the values tend to be closer to zero, with biases showing a relative reduction in the upper 200 m.

During the validation stage, the elevated T/S errors around 1996 (salinity) and 1998 (temperature) in the Hovmöller diagrams (Fig. 3) may be linked to observations that were not assimilated but included in the quasi-independent validation. These peaks are likely due to such observations, but also sparse coverage, and local model biases.

Figure 4 presents the temporal and spatial averaged RMSD and biases for temperature, comparing the reanalysis results with in-situ observations. For a better spatial analysis, we divide the Black Sea into three different regions: western, central, and eastern. The largest temperature errors occur in the upper layers and are primarily associated with the formation of the seasonal thermocline in summer, as previously shown in the Hovmöller diagrams for temperature (Fig. 3). In this layer, RMSD reaches a maximum of approximately 1.5 °C in the western and eastern regions, and about 1.25 °C in the central region. In the upper water column, temperature biases are negative in the eastern and central regions. In the western region, the bias is positive from the surface down to 50 m, reaching values of up to 0.1 °C, and becomes negative between 50 and 100 m, aligning with the values observed in the central region. The largest errors are observed in the eastern region. Errors gradually decrease with depth, with RMSD reaching values lower than 0.25 °C at 150 m, biases becoming closer to zero.

The same analysis for salinity is shown in Fig. 5. The western region exhibits the highest near-surface RMSD, with values reaching over 0.8 psu in the upper 100 m, despite high observational coverage. In contrast, RMSD values are lower in the central and eastern regions, remaining below 0.2 psu in the upper layers. These high values in the western region are mainly due to limitations in freshwater inputs from major rivers: only the Danube uses monthly varying discharge, while other rivers follow climatologies without intra-annual variability, producing persistent local biases. Prescribed boundary conditions near the Bosphorus Strait improve the physical representation but also introduce uncertainties. Data assimilation can partially improve model representation under these circumstances by incorporating observations with strict quality control, but some errors can still persist. Salinity biases show regional differences. In the western region, positive biases are pronounced near the surface, rapidly transitioning to negative values and reaching about -0.04 psu between 25 and 50 m. In contrast, biases in the surface layers of the central and eastern regions remain closer to zero but increase in the subsurface starting at 50 m, following the pattern observed in the western region. At a depth of around 100 m, all regions exhibit relatively high salinity biases, with the eastern region showing the highest values, reaching up to 0.04 psu. In general, salinity biases decrease beneath 100 m and approach zero at depths greater than 200 m.

In the eastern region, a slight increase in temperature and salinity biases occurs below 700 m (Figs. 4 and 5). This pattern likely arises from sparse deep-layer observations prior to 2003 (as shown in the Hovmöller diagrams, Fig. 3), limitations in model initialization, and unresolved physical processes within the model. The introduction of Argo profiling floats from 2003 increased deep data coverage, revealing biases that were previously undetected and never corrected; below 700 m, LSBC toward WOA2018 climatology is not sufficient to constrain the model. In addition, some observations excluded from assimilation were still included in validation, further contributing to the apparent increase in errors. Even with strict quality control, some measurement errors or inconsistencies may have persisted.

Spatial maps of the SLA RMSD reveal the highest values, ranging from 2.5 to 4 cm, with occasional peaks exceeding 4 cm, predominantly along the basin's periphery (Fig. 6). These elevated deviations are closely linked to the Rim Current and its inherent mesoscale variability. In contrast, SLA RMSD values in the central basin are generally lower, around 2 cm. Notably, areas with large RMSD values align with regions of strong eddy kinetic energy (EKE), which we use to assess mesoscale activity (Fig. 7). This pattern is particularly evident along the Anatolian, Caucasian, and Crimean coasts, where well-known mesoscale characteristics are present (Korotaev et al., 2003). SLA errors show slight variations across seasons, with particular attention given to high values along the Caucasian coast. These values extend further offshore in winter. Additionally, higher SLA errors occupy a larger area around the Batumi eddy region during fall. Error values are relatively high along the Crimean coast, particularly in the western region, where the persistent influence of the Sevastopol eddy contributes to elevated mesoscale variability. However, these errors tend to decrease during summer. Kubryakov and Stanichny (2015) reported that the total number of detected eddies exhibits local maxima in both the Sevastopol and Batumi eddy regions, reflecting the dynamic nature of coastal circulation in these areas. These complex dynamics may not be adequately resolved by the model, potentially contributing to elevated SLA errors in these areas.

This interpretation is further supported by EKE maps (Fig. 7), which consistently show high energy levels in these regions, indicating intense mesoscale activity that aligns with the SLA discrepancies viewed in Fig. 6. EKE maps show elevated values along the Rim Current, particularly along the Caucasian coast. To ensure a clean comparison with altimetry-derived estimates, BLK-REA EKE was computed from the geostrophic component only, using SSH from the model. BLK-REA EKE values generally exceed those derived from altimetry, especially in the Batumi and Sevastopol eddies, where peak values reach about 300 cm² s⁻² in fall and spring, respectively, compared to altimetry-based estimates of around 220 cm² s⁻². This difference likely reflects multiple factors, including the spatial smoothing inherent to the 0.25° Level-4 altimetry product, the reduced capability of altimetry to capture smaller-scale variability due to mapping and interpolation procedures, and possible over-energetic behaviour of the model arising from its higher resolution, physical parameterizations, and potentially insufficient dissipation of mesoscale energy.

We present a set of OMIs computed from the BLK-REA: OHC anomalies, Rim Current interannual variability, and meridional overturning circulation. These indicators are used to monitor key aspects of the Black Sea state and its variability. For the OHC OMI, the evaluation is further supported by a multi-product ensemble analysis combining BLK-REA, GLORYS12, ARMOR3D (Greiner et al., 2025), and CORA5.2 (Szekely et al., 2019), enabling quantitative comparison and uncertainty estimation using independent products. For the remaining indicators, such as the Rim Current index and meridional overturning circulation, ensemble-based analyses are not feasible due to the limited availability of high-resolution velocity data for the Black Sea. Assessments are therefore based on comparisons with studies using earlier versions of the Black Sea reanalysis.