## 2 Materials and Methods
### Principle Scheme of Primary Production (PP) Calculation (Ecosystem Block)
#### 2.1.3 Calculation of Primary Production  
For the transition from the value of nutrient consumption to primary production, i.e., to carbon consumption, at present, in most cases, the average stoichiometric Redfield-Richards ratios are used, which in the molar form are C:Si:N:P = 106:23:16:1 [1; 6; 13; 14; 26]. However, the application of these ratios for phytoplankton with different species compositions can lead to large errors. Thus, the ratios of the presented elements differ significantly in different dominant divisions of plankton. For example, the change in C:P in the phytoplankton from diatom to peridinium differs by 37%, the change in C:N by 24%, and C:Si by 14 times (Table 2). Accounting for the C:Si ratio variations, change is especially important, since, as mentioned above, the calculation of production for silicon reflects the total production (NCP\({}_{\text{Si}}\)). Figure 3: Example results assessment of the annual cycle nutrient consumption. Dotted line, excluding remineralization (Equation (11)), solid—taking into account remineralization (Equations (12) and (13)). In this figure, \(n\) can take values on the descending branch of the graph (usually 10 or 11). In this case \(n=11\) is November, then \(n-1\)—is October. (\(Kj=(380-220)/380=0.42\)). In this work, an attempt was made to use individual stoichiometric ratios. In this case, it is assumed that all phytoplankton consists of only two systematic groups of phytoplankton--diatoms and dinoflagellates. This assumption also introduces an error in the calculations. However, if we evaluate the entire Barents Sea, then the average sum of the biomasses of these two phytoplankton systematic groups, according to the Biological Atlas of the Barents Sea [27], when analyzing 1000 samples, is 94%. That is, only 6% is the biomass of other systematic groups of phytoplankton. According to the results of some expeditionary field studies, the total biomass of these two groups in the Barents Sea was generally at the level of 99% [28]. The observed measured (real) stoichiometric ratio of carbon to one of the nutrients will be equal to the ratio of the carbon amount to the amount of silicon, nitrogen, or phosphorus (index _J_) involved in the process of photosynthesis:  
\[w_{J}=\frac{(Q_{phyto}^{n})_{C}}{(Q_{phyto}^{n})_{J}} \tag{14}\]  
The numerator is the amount of carbon involved in the process of photosynthesis, and the denominator is the amount of the biogenic element \(J\) involved in the process of photosynthesis. If we assume that all phytoplankton consists of two systematic groups of phytoplankton--diatoms and peridiniums, then we can calculate the value of \(w_{J}\) using the values of the phytoplankton relative chemical composition according to X. Sverdrupat [13] represented in Table 2.  
\[dw_{d}+pw_{p}=w_{j} \tag{15}\]  
where:  
_d_--the relative contribution of carbon in diatom plankton biomass to total primary production;  
_p_--the relative contribution of carbon in peridinium plankton biomass to total primary production;  
_w_\({}_{d}\) and _w_\({}_{p}\)--stoichiometric ratios of carbon to the _j_-th biogenic element for the systematic groups of diatoms and peridinium phytoplankton, respectively, calculated from Table 2.  
Since we made the assumption that we have only 2 systematic groups of phytoplankton, then:  
\[d+p=1 \tag{16}\]  
_w_\({}_{l}\)--stoichiometric ratios which are calculated from the amount of consumption of nutrients in the process of photosynthesis. Index _j_--Si, N, or Ph. In this work, for further calculations, we used the ratios of nutrients Si/Ph and Si/N. \[w_{Si/Ph}=\frac{(Q_{phyto}^{n})_{Si}}{(Q_{phyto}^{n})_{pl}} \tag{17}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Plankton** & **C (by Mass)** & **Si (by Mass)** & **N (by Mass)** & **Ph (by Mass)** \\  & & & & **(Phosphorus)** \\ \hline Diatom & 100 & 93.0 & 18.2 & 2.7 \\ \hline Peridinium & 100 & 6.6 & 13.8 & 1.7 \\ \hline \hline \end{tabular} Note: units of mass (mg, mg, g... ).  
\end{table}