## 2 Materials and Methods
### Principle Scheme of Primary Production (PP) Calculation (Ecosystem Block)
#### 2.1.2 Determining the Values of the Non-Conservative Component (\(\Delta C_{non-con}\))  
The difference between the measured value and the conservative value will determine the value of \"non-conservative\". \[\Delta C_{non-conj}=C_{measj}-C_{conj} \tag{5}\]  
\(j\)--the considered parameter (mineral phosphorus, silicon, nitrogen, or any other). Then, at \(\Delta Gj<0\)--there is a decrease in the concentration of a particular biogenic element due to non-conservative factors (in what follows we will not use the index (non-con). Using Equations (1)-(5), you can calculate the total non-conservative concentration, which is the sum of both production and non-production components. Since the primary production is determined for the volume of a unit area, the obtained values must be integrated from the surface to the horizon, where the measured concentration is equal to the winter concentration. Let us take as the lower limit of integration to the maximum horizon at which, during the year, the saturation of water with dissolved oxygen passes from values of more than 100% to values of less than 100%. In this case, the integration boundary can be any, provided that it is not higher than the maximum horizon at which this transition is observed, otherwise, the obtained values will be underestimated. However, in order to avoid the influence of other processes, it is better than the lower limit of integration to be closer to the above-indicated point. For each calculated point, the position of the transition horizon for the value of water saturation with dissolved oxygen was determined above 100% (_h_). For different areas of the sea, this value varied from 40 (or from the bottom layer) to 100 m.  
For each month, the average monthly integrals value of \(C_{con}\) and \(C_{meas}\) from the surface to the selected horizon \(h\) are calculated, with the _dh_ values presented above. \[Q_{m}^{n}=\int_{0}^{h}C_{meas}^{n}\mathrm{d}h\text{ and }\ Q_{c}^{n}=\int_{0}^{h}C_{con}^{n} \mathrm{d}h \tag{6}\]  
Index \(n\) indicates the month (1, 2,... 12). \begin{table}
\begin{tabular}{c c c c} \hline
**Base Water** & **P-PO4 (\#g/L)** & **N-NO4 (\#g/L)** & **Si-SiO3 (\#g/L)** \\ \hline Atlantic & 23.4 & 114.2 & 135.3 \\ River & 26.2 & 80.6 & 3061 \\ Ice & 11.1 & 24.8 & 30.9 \\ \hline \end{tabular}
\end{table} 
Table 1: Values of the studied parameters (_Caj_, _Crj_, _Cij_) in the initial water masses. For each month, the nonconservative component \(\Delta Q^{n}\) was calculated as the difference between the values of the integrals \(Q^{n}_{m}\) and \(Q^{n}_{c}\). \[\Delta Q^{n}=Q^{n}_{c}-Q^{n}_{m} \tag{7}\]  
This value characterizes the total value of \"non-conservative\"--i.e., the total change in the biogenic element due to all processes of photosynthesis and mineralization of organic matter (productive component) and the processes of exchange of biogenic matter both vertically and horizontally (non-productive component). The plus sign (+) indicates the total amount of expenditure, the minus sign (-) indicates the total amount of income. If the change in the studied biogenic element depended only on the photosynthetic activity course and the mineralization of the formed organic matter, then this value, before the start of the photosynthesis process, would be equal to zero. If it is not equal to zero, then this means the inflow or outflow of this element is due to other processes, such as advection and exchange with underlying layers. The minimum value of the \(\Delta Q^{n}\) for the year, which, before the start of the photosynthesis process (usually for different areas of the sea, this is February-March) will be the value of the non-productive component. \[\Delta Q_{sed}=min(\Delta Q^{n}) \tag{8}\]  
In this paper, we will assume that this value is constant throughout the year, but varies from region to region. If this value is positive, then there is an outflow of the biogenic element from the euphotic layer and vice versa.