**1. Introduction**

The circulation in the upper layer of each ocean is in direct contact with the atmosphere and is related to the distribution of meteorological parameters [1–3]. At the same time, the influence of atmospheric forcing on the structure of deepwater circulation is not so clear. For the Black Sea, this problem is complicated by the presence of a strong vertical density gradient (permanent pycnocline) at 50–100 m horizons, which blocks vertical seawater exchange [3].

Regional features of density stratification often arise near the Black Sea continental slope due to the mixing and lowering processes of surface waters along the slope into the deep sea layers [3,4]. The formation of density anomalies here can be caused by external forcing at the boundaries of the basin (including wind, river runoff, etc.), the sinking of denser waters down the continental slope, and the transfer of water with thermohaline characteristics that differ from the ones in eddies [4,5]. These processes are especially important in the northeastern part of the basin due to the narrow and steep continental slope in this region. The seawater density anomalies formed near the slope can lead to the transformation of the velocity field at deep horizons [5]. Thus, the generation of unsteady deepwater undercurrents is found out there [6].

**Citation:** Dymova, O.; Markova, N. Numerical Estimation of the Black Sea Circulation near the Continental Slope Using SKIRON and ERA5 Atmospheric Forcing. *Environ. Sci. Proc.* **2023**, *25*, 61. https://doi.org/ 10.3390/ECWS-7-14305

Academic Editor: Athanasios Loukas

Published: 3 April 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Below the permanent pycnocline, the Black Sea waters become warmer and more saline accumulates towards the bottom [2]. At the same time, anticyclones can form near the shelf edge and then can move along the slope [4,5,7]. In the centers of the anticyclones, subpycnocline waters that are colder and contain less saline deepen, and their movement contributes to the transfer of thermohaline anomalies and the corresponding perturbations of dynamical fields. Such complicated dynamics near the continental slope require a detailed and accurate reconstruction of all hydrophysical characteristics, which is only possible if boundary conditions are correctly specified.

### **2. Materials and Methods**

The Black Sea circulation was reconstructed by an eddy-resolving model from the Marine Hydrophysical Institute (MHI-model) [8]. The model was based on the Navier–Stokes equations in Boussinesq and hydrostatic approximations. Vertical turbulent mixing was described by the Mellor–Yamada closure model 2.5, and horizontal mixing was described using a bilaplacian operator with constant coefficients. The model circulation was driven by atmospheric forcing, including wind stress, heat fluxes, precipitation, and evaporation, on the sea surface. The climatological Black Sea rivers runoff and exchange through the straits were considered. Data assimilation (except for the satellite sea surface temperature data) was not used in the discussed numerical experiments. The MHI-model was implemented on a C-grid with a resolution of (1/48)◦ longitude, (1/66)◦ latitude, and 27 z-levels vertically. The detailed model description is presented in [8].

Basin bathymetry was built from EMODnet data [9]. The initial data were obtained from the Black Sea Physical Reanalysis CMEMS [10]. All initial and input fields were linearly interpolated in the MHI-model grid nodes.

In this work, two numerical simulations with identical model setups but different atmospheric forcing were carried out for the year 2016. In the first simulation (SKIRONexperiment), the forcing included 2 h of data on wind velocity, thermal, latent, sensible, and solar heat fluxes, evaporation, and precipitation provided by the SKIRON/Dust modeling system (Greece), with a spatial resolution of 0.1◦ [11]. In the second simulation (ERA5-experiment), the forcing was based on the freely available hourly data of reanalysis supported by the European Centre for Medium-Range Weather Forecasts for the global climate, with a resolution of 0.25◦ [12].

Comparative analysis of the SKIRON and ERA5 data showed a significant difference in wind forcing in the Black Sea region. As can be seen in Figure 1, the ERA5 wind stress is stronger than SKIRON one by about 25–30%, and the repeatability of NN-E and N-E wind directions (forming surface cyclonic circulation of the Black Sea) is higher. The remaining fluxes in ERA5 and SKIRON are close to each other, with there being some excess (15–20%) ERA5 data on total heat flux during the year and mass flux (precipitation minus evaporation) in autumn and winter.

**Figure 1.** Histograms of the annual mean repeatability of the area-averaged wind directions (digits, %) and wind stress magnitudes (color, 10−<sup>5</sup> N/cm2) for the Black Sea area in 2016: (**a**) by SKIRON; (**b**) by ERA5. Data were calculated from the wind velocity at a height of 10 m.
