Volume 61, Nº 3 (2025)

Introductory paper on the issue of the journal Izvestiya, Atmospheric and Oceanic Physics, No. 3, 2025, dedicated to the 100th anniversary of Academician G.I. Marchuk. The main directions of scientific activity of G.I. Marchuk, which had a significant impact on the development of modern geophysical fluid dynamics, are described. These are weather forecasting; modeling of the climate system; application of the theory of adjoint equations to geophysical fluid dynamics problems; computational algorithms. The ideas and mathematical methods of modern geophysical fluid dynamics initiated by G.I. Marchuk and developed by his scientific school over the course of 25 years of the XX and 25 years of the XXI century are discussed. The bright deep mark that he left in science is noted, and the results obtained by him, his disciples and colleagues in the field of geophysical fluid dynamics are highlighted.

The history is described of the Russian sigma-model of oceanic and marine circulation known as INMOM (Institute of Numerical Mathematics Ocean Model). The model was developed for 50 years initially at KCC SB АS USSR, then at INM RAS. The first version of the model was developed under immediate supervision of G.I. Marchuk and was designed for modelling of coupled circulation of global atmosphere and World Ocean. The main method for solving model equations was the multicomponent splitting technique proposed by G.I. Marchuk and evolved by his students and followers. For a half of century, the model’s representation of basic processes, parameterizations and numerical algorithms were improved. The novel period in the model development proceeded in the late 90’s, when it started to be used as the oceanic component of the INM RAS Earth system model. In 2000’s, the range of its application extended essentially. Together with studying Earth climate system, it started to be implemented for simulating circulation of the World Ocean, as well as its separate basins and seas. Currently, the model INMOM is being applied for solving a wide range of fundamental and applied problems concerned with reproducing characteristics of marine and oceanic hydrothermodynamics including their climatic variability. It is used at INM RAS, SOI, IO RAS, Hydrometcenter of Russia, POI FEB RAS and more organizations dealing with study of oceanic and marine hydrothermodynamics. The model is continuing to be evolved by its authors, their colleagues and followers.

This paper discusses some results of the study of eddy heat fluxes in the vicinity of a subtropical jet stream. Many large-scale dynamical phenomena in the Earth's atmosphere are associated with Rossby wave propagation and collapse processes. Here we focus on regions of counter-gradient eddy heat fluxes in the region of the subtropical jet stream in the Northern Hemisphere associated with Rossby wave overturning. In these regions, we observe meridional energy transfer on the northern flank of the jet stream in the equatorial direction from the ERA-5 reanalysis data and simulation data with the INM-CM4-8 climate model of the G.I. Marchuk Institute of Computational Mathematics of the Russian Academy of Sciences. The entropy production due to horizontal heat transfer becomes negative, since heat is transferred against the temperature gradient, but this is not a violation of the second law of thermodynamics, since the main part of entropy production occurs due to the processes of vertical heat transfer, such as convection, and other irreversible processes. Entropy production is sensitive to land cover, the entropy balance being most related to radiation at the surface. Quantifying the thermodynamic balance of entropy and entropy production is a useful metric for evaluating the interactions of the atmosphere-surface system. Some estimates of entropy production by the surface are presented in this paper. The traditional approach to studying the climate system focuses on the dynamic mechanisms and physical processes responsible for the conversion of energy from one form to another, but an approach based on analyzing the entropy balance of the climate system and especially entropy production is also important.

The article is devoted to the discussion of G.I. Marchuk's ideas, which stimulated research in the field of operational oceanography and forecasting of the state of the marine environment in the last 10–12 years at the institutes of the Russian Academy of Sciences and Roshydromet. The methodology developed at the Marine Hydrophysical Institute and research teams in France in reconstructing the temperature and salinity of seawater based on satellite observations is described. The application of the simple algorithm for assimilation of observations based on relaxation of the solution of the numerical forecast model to three-dimensional thermohaline fields reconstructed from satellite data in the basins of Azov – Black seas, Arctic and the World Ocean is demonstrated. Estimates of the standard deviations of the thermohaline fields of the global ocean, calculated using assimilation of observations with the simple algorithm, are compared with similar estimates of CMEMS (Copernicus Marine Environment Monitoring Service) products based on GLO12 v2 and v4. The reasons for the relatively small discrepancies between the estimates of thermohaline field analyses based on a model with a spatial resolution of 0.25° and the simple algorithm for assimilation of observations and the GLO12 v2 and v4 models with a resolution of 1/12° and a much more complex algorithm for assimilation of observations are discussed.

The problem of data assimilation for nonstationary models of impurity transfer and transformation is considered as a sequence of related inverse problems of restoring the spatiotemporal structure of state functions, taking into account the measurement data received during modeling. Data assimilation is carried out together with the identification of an additional desired source function, which we call the uncertainty function of the model. The purpose of the work is a brief historical overview and presentation of an up-to-date version of the data assimilation algorithms for atmospheric chemistry models based on sensitivity operators and ensembles of solutions to adjoint equations. A demonstration of the algorithm for a three-dimensional model with a nonlinear measurement operator is given in a modeling scenario for the Baikal region.