Modeling Black Sea Circulation Using Heat and Salt Advection–Diffusion Equations with Discrete Nonlinear Invariants

Abstract

In this work, based on the results of predictive calculations, the accuracy of reproducing the Black Sea circulation is analyzed using new approximations of nonlinear terms in the transport equations, ensuring the conservation of temperature and salinity to a power greater than two. Numerical experiments have been carried out that differ in schemes for calculating temperature and salinity. In the first experiment, traditional schemes were used to ensure the conservation of temperature and salinity in the first and second degrees; in the second one, the temperature was maintained in the first and fifth degrees and salinity in the first and third; in the third experiment, the temperature was maintained in the first and third and salinity in the first and fifth degrees. Calculations were performed on the basis of MHI model with a resolution of 1.6 km and accounting a realistic atmospheric forcing for 2016. The validation of results was carried out based on comparison of model fields with data from contact and satellite measurements of temperature and salinity in 2016. An analysis of average and root mean square errors showed that, compared to the traditional approximation, the new difference schemes for the advection–diffusion equations of heat and salt, ensuring the preservation of predictive parameters to a power greater than two, improve the accuracy of reproducing of the Black Sea salinity in the upper 100-m layer throughout the year. Root mean square errors in the salinity field decrease by 15–20%, and the upper mixed layer thickness in winter and the upper boundary depth of the thermocline layer in summer in the central part of the sea are modeled about 10% more accurately. Based on the results of three experiments, the smallest deviations from observational data were obtained when using approximations that ensure the conservation of temperature to the third degree and salinity to the fifth degree.