## 1 Introduction  
The waters of the Barents Sea are highly productive water areas, which account for a significant amount of primary production on the pan-Arctic shelf [1, 2]. Due to its geographical location, and the formation of terrestrial and marine ecosystem features, the Barents Sea is a unique testing ground for studying the entire natural environment responses spectrum of the high-latitude Arctic to external impacts of natural and anthropogenic origin. One of the tasks in such studies is to identify and study areas that are potentially most favorable in terms of the food supply state for fish and other commercial objects, i.e., areas with the highest supply of phytoplankton with nutrients. It is a phytoplankton that plays a decisive role in the formation of the food base of various aquatic organisms, including commercial fish [3]. At the present stage, there are several approaches to assessing phytoplankton production:  
* The first approach is the direct measurements in the summer period. They are presented by conventional methods [4, 5] such as oxygen and radiocarbon [3]. * The second approach is based on the calculation of chlorophyll, both directly measured in seawater samples and obtained from Earth's remote sensing data [6]. * The third is model calculations, including both hydrodynamic and ecosystem models [6]. The fourth involves using traps for solid particles, followed by the removal of inorganic carbon [7]. * The next approach is based on determining nutrient intake and calculating primary production using average stoichiometric ratios. This method is based on research carried out in the last century. The advantage of this approach is that the methods of chemical analysis for the determination of nutrients are quite simple, unified in different countries, and well-developed for their use in the field. In addition, large databases have been accumulated. They contain such values for various areas of the World Ocean. The method for primary production calculation based on nutrient intake estimation is derived from studies carried out in the last century. In the works of [PERSON] [8; 9], [PERSON] [10], and [PERSON] [11; 12], the values of the content of phosphorus and nitrogen in phytoplankton and water are presented. A summary of these studies is presented in the monograph--Ocean Chemistry [13]. When calculating the primary production by carbon mass, as a result of the consumption of nutrients, stoichiometric ratios are used. Usually, Redfield-Richards stoichiometric ratios are used, which in the molar form are C:Si:N:P = 106:23:16:1 [1; 6; 14]. Usually, few forms of primary production are defined [15]. Gross primary production (GPP) is defined as photosynthesis that does not take into account the simultaneous respiration of algae or the metabolism of heterotrophic organisms. Net Primary Production (NPP) is GPP minus algae respiration. Net community production (NCP) is defined as GPP minus autotrophic and heterotrophic respiration. The regeneration of silicon, in comparison with nitrogen and phosphorus, is extremely slow; as a result, the smallest values of production, as a rule, are equivalent to the loss in the euphotic layer of nitrogen and phosphorus, and the largest--to silicon. Moreover, when assessing the production of phytoplankton by changing the content of silicon, the part of the production that is synthesized from the recycling of nitrogen and phosphorus is also taken into account [2; 16; 17]. Nitrates support primary production (new production) and are thought to represent the uptake of nutrients present at the start of the growing season or are carried into the euphotic zone from elsewhere. Summing up the presented analysis following the approach of [PERSON] et al. [16; 17], the NCP calculated silicon production (NCP\({}_{\text{Si}}\)) reflects the total production, while the nitrogen calculation (NCP\({}_{\text{N}}\)) gives the value of \"new\" production. In these works, the definition of \"new\" production corresponds to the definition of \"clean\" production [1].