In this work the accuracy of reconstructing the Black Sea circulation by using new approximations of nonlinear terms in the transport equations, ensuring the conservation of temperature and salinity to a power greater than two, is analyzed based on the results of forecast calculations. Three numerical experiments with differences in the schemes for calculating temperature and salinity are carried out. In the first experiment – traditional schemes are used to conserve of temperature and salinity in the first and second degrees; in the second one – the temperature is conserved in the first and fifth degrees, salinity in the first and third; in the third one – the temperature in the first and third, salinity in the first and fifth degrees. Calculations are performed on the basis of the MHI model with a resolution of 1.6 km and taking into account realistic atmospheric forcing for 2016. Validation of the results is carried out based on comparison of model fields with in-situ and satellite measurements of temperature and salinity in 2016. Analysis of mean and root mean square errors showed that new schemes for the advection-diffusion equations of heat and salt, ensuring the conservation of predictive parameters to a power greater than two, improve the accuracy of reconstructing the salinity in the Black Sea upper 100m layer throughout the year compared with traditional approximation. The root mean square errors in the salinity field are reduced by 15–20%, the thickness of the upper mixed layer in winter and the depth of the upper boundary of the thermocline layer in summer in the central part of the sea are modeled approximately 10% more accurately. Based on the results of three experiments, the smallest deviations from observational data are obtained when using approximations that ensure the conservation of temperature to the third power and salinity to the fifth power.
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