= Solution
There are \b[four well-mixed reservoirs]: Mediterranean surface/deep $(M_s,M_d)$ and Black Sea surface/deep $(B_s,B_d)$. Use the actual drawing’s arrow endpoints: $F_2$ leaves $M_s$, $F_5$ enters $M_d$ from $B_s$, and $F_6$ starts in $M_s$ and enters $B_d$. With $F_i$ as positive water-mass transport rates, the four steady <conservation of mass> equations are
$$
\boxed{\begin{aligned}
M_s:&\quad F_1+F_3-F_2-F_4-F_6=0,\\
M_d:&\quad F_4+F_5-F_3=0,\\
B_s:&\quad F_8+F_9-F_5-F_7=0,\\
B_d:&\quad F_6+F_7-F_8=0.
\end{aligned}}
$$
Adding them cancels every internal transport and gives the whole-system requirement \b[$F_1+F_9=F_2$]. There is no stated evaporation, precipitation or other external transport to add.
The schematic endpoints are unusual for the conventional two-layer exchange picture: its Gibraltar outflow is drawn in the surface box, and its Black Sea surface inflow descends into the Mediterranean deep box. Moving $F_2$ to $M_d$, $F_5$ to $M_s$, and the source of $F_6$ to $M_d$ would define a different, more conventional idealization. The displayed equations consistently follow the supplied drawing; the same endpoint convention is used in the following two parts.
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