## 1 Introduction
In this paper, the same definitions and notation are used. The current methods for determining biological productivity, based on changes in the concentrations of nutrients, are based on determining the difference between the measured amount of a nutrient and its amount, which \"was in a given volume of water at the time of its physicochemical properties formation in the surface layer of the ocean\" [18]. In some works, these quantities are called preformed concentrations: preformed--phosphates (Ppf), preformed--nitrates (Npf), and preformed--silicates (Sipf). The calculation of preformed concentrations is based on the application of stoichiometric coefficients for phosphorus, nitrogen, and silicon to oxygen and carbon [2; 16; 17; 18]. The preformed concentration is the reference point for the content of the nutrients (maximum concentration), from which the decrease in this value is counted in the process of photosynthesis. This method was used to assess the biological productivity of various water areas of the World Ocean -of the Bering Sea, [16; 17; 18], Antarctic water [19], the Sea of Okhotsk [2], and the Barents Sea [20; 21]. To use this technique, it is necessary to know the winter concentrations of nutrients preceding the spring phytoplankton bloom. In works on the Bering Sea, these concentrations were determined by the concentrations at the lower boundary of the cold intermediate layer, the position of which varied from 40 to 170 m. In works on water areas surrounding Antarctica, this concentration was determined as the weighted average value in the layer of autumn-winter convective mixing. Such approaches are not always applicable for several reasons. In the case when the change in the concentration of nutrients along the vertical is caused not only by the process of photosynthesis but also by the presence in the surface layer of another water mass, with a different initial composition of nutrients, which is typical for the southeastern part of the Barents Sea, as well as for the Kara and Laptev Seas. Changes in oxygen concentrations are caused not only by photosynthesis processes but also by exchange with other layers of water and with the atmosphere. For the transition from the value of nutrient consumption to primary production, i.e., to carbon consumption, current average stoichiometric Redfield-Richards ratios are used; but the use of these ratios for phytoplankton with different species composition can lead to large errors since the ratios of the elements presented differ significantly in different systematic groups; for example, the C:P ratio in diatoms and dinoflagellates differs by 37%, the C:N ratio by 24%, and C:Si by 15 times [13]. The difference shown above is determined not only by the \"productive\" but also by the \"non-productive\" components, which may depend on the element under study input from the bottom layers, as well as on the contribution of other processes. To avoid the above disadvantages, in this paper we propose to use the isotope parameter \(\delta^{18}\)O, which has unique conservative properties. It does not depend on chemical-biological processes and is an ideal tracer for balance estimates. The use of this parameter makes it possible to solve one of the main problems in the assessment of primary production using changes in the concentration of nutrients--to determine the starting point, i.e., the maximum concentration of a nutrients before the start of the photosynthesis process. Determination of the difference between the reference point and the measured nutrient concentration, i.e., consumption values, allows us to move from average stoichiometric ratios to real ones--corresponding to the real composition of the systematic groups of phytoplankton. In this paper, we present in detail the methodology for calculating primary production using the isotope tracer \(\delta^{18}\)O. The results of testing this technique in the Barents Sea are presented.