Past exam of the year 2 of the earth sciences (geology) course of the University of Oxford / 2022 / Paper 1 / 10 / a / ii

Let $S_{Ms},S_{Md},S_{Bs},S_{Bd}$ be salt mass fractions, with reservoir water masses denoted by the corresponding $M$ symbols. Let $S_A$ be Atlantic inflow salinity and $S_D$ the Danube inflow salinity, approximately zero for fresh water. With the diagram endpoint convention from part i, instantaneous mixing givesEvery outgoing salt transport uses the salinity of its donor box. The water masses are constant because the water balances are at steady state, even while the salinities evolve. If reservoir water masses varied, the left side would instead be $d(M_j{S}_j)/dt$.

Summing yields $d({\sum }_j{M}_j{S}_j)/dt=F_1{S}_A+F_9{S}_D-F_2{S}_{Ms}$, a direct whole-system salt check. Fresh water carries essentially no salt, but its dilution effect is still present through the water balance and the resulting transport terms.