*2.1. Physics*

The Black Sea physical analysis and forecasting system (BS-PHY NRT) as well as the reanalysis system (BS-PHY MY) are free-surface versions of the NEMO ocean general circulation model (Nucleus for European Modelling of the Ocean, [**?** ]), coupled online with a 3D-variational data assimilation scheme, the OceanVar [**? ?** ]. The model's governing equations are discretized over a regular grid with about 3 km of horizontal resolution, using 31 z-levels with partial steps over the spatial domain, as shown in Figure **??**.

The BS-PHY NRT [**?** ] core model is based on NEMO v3.4. The bottom topography was reconstructed from the GEBCO 1 min resolution dataset [**?** ]. It is forced by water, heat, and momentum fluxes, interactively computed by bulk formulae, implemented for the Mediterranean Forecasting System [**?** ] and modified for the Black Sea to account for the Brunt–Berliand formula for the net longwave radiation, as in [**?** ]. It uses monthly climatological precipitation from the GPCP dataset [**? ?** ] and the 3–6 h and 0.125◦ operational analysis and forecast atmospheric fields provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) through the Italian *Aeronautica Militare*.

The model includes 72 rivers, distributed as source points along the Black Sea coastline; major rivers such as the Danube, the Dnieper, and the Dniester are implemented over multi-grid points due to their wide delta and inflow contribution. The river discharge values are provided as monthly climatologies by [**?** ] within the framework of the EU SESAME project, while a zero salinity value is accounted for at the river mouths. Initial conditions for the pre-operational run come from [**?** ] as the climatology for January interpolated on the BS-PHY spatial grid. The model configuration is closed at the Bosporus Strait. Vertical mixing is parameterized according to the turbulent kinetic energy closure scheme.

The assimilation time window is one day. Background error covariances are decomposed into vertical covariances and horizontal correlations through 15-mode multivariate empirical orthogonal functions (EOFs). Observations, assimilated in the BS-PHY NRT, include (Table **??**): (i) in situ temperature and salinity profiles (ARGO floats) from the CMEMS INS TAC. If profiles are disseminated at a high vertical resolution, a vertical thinning is applied to the profile before ingestion in OceanVar; (ii) along-track sea level anomaly L3 data, currently from AltiKa, Cryosat-2, and Jason-2/3, Sentinel3A/3B, distributed by the CMEMS SL TAC; (iii) gridded sea surface temperature SST L4 observations provided by the CMEMS SST TAC. Assimilation of SST satellite data is performed at the first model level. For satellite observations (SLA, SST), a horizontal thinning is also applied to retain approximately one observation only every 6 km.

The BS-PHY NRT processing system consists of two different cycles, run every day. One cycle consists of a 3-day analysis (e.g., a simulation performed with ECMWF analysis atmospheric forcing and assimilation correction), a 1-day simulation (e.g., a run performed with ECMWF analysis atmospheric forcing without assimilation correction), and a 10-day forecast (e.g., a run performed with ECMWF forecast atmospheric fields). The other cycle takes place once a week: the system performs a 14-day analysis in order to ingest a larger number of observations through the data assimilation and produce the best initial condition for the forecasting run. The system produces hourly and daily means of 3D temperature, salinity, and currents as well as 2D sea surface height, mixed layer depth, and bottom temperature, with the nominal start of the forecast at 00:00Z (i.e., averaged daily fields are centered at 12:00Z of each run day).

The BS-PHY MY [**?** ] core model is based on NEMO v3.6 over the same spatial grid as the corresponding NRT. The bottom topography has been improved in relation to the NRT system and is based on a GEBCO 30" resolution dataset [**?** ], with the blending of a high-resolution bathymetric dataset around the Bosporus exit [**?** ] to better represent the connection between the Black Sea and the Marmara Sea, and consequently, the Mediterranean Sea. BS-PHY MY system is forced by ECMWF ERA5 atmospheric reanalysis and GPCP monthly climatological precipitation [**? ?** ].

Similarly to the NRT, the BS-PHY MY system imposes a closed boundary condition at the Bosporus Strait. To account for the Mediterranean water inflow into the Black Sea, the model solution is relaxed to temperature and salinity vertical profiles extracted from the high-resolution time series presented in [**?** ]. The model is coupled online with OceanVar to assimilate (i) in situ temperature and salinity profiles (ARGO floats) pro-vided by the CMEMS INS TAC and the historical SeaDataNet dataset [**?** ], (ii) along-track sea level anomaly L3 data distributed by CMEMS SL TAC. The SST is also relaxed to a gridded sea surface temperature SST L4 product produced by the CMEMS SST TAC. The time series covers the period of January 1993–December 2019 and provides monthly and daily means for the 3D temperature, salinity, current and 2D sea-surface height and mixed-layer depth.
