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The qualitative behavior of a conceptual ocean box model is investigated. It is a paradigmatic model of the thermohaline ocean circulation of the Atlantic. In a bifurcation study, the two occurring bifurcations, a saddle-node and a Hopf bifurcation, are computed analytically. Using normal form theory, it is shown that the latter bifurcation is always subcritical. The unstable periodic orbit emerging at the Hopf bifurcation vanishes in a homoclinic bifurcation. The results are interpreted with respect to the stability of the thermohaline circulation.
The study examined the summertime behavior of phosphorus (P) and estimated P fluxes in the Inohana Lake Estuary, Shizuoka, Japan through a field observation conducted in the summer of 2007 and a box model approach. The sedimentation flux of P was significantly correlated with the overlying chlorophyll-a concentration. The box model provided a good estimate of the summer-averaged water flux. The P mass balance method yielded the release flux of P, which approximated the observed value. For the P exchange between the Inohana Lake Estuary and Hamana Bay, on the net flux, particulate P flows out into Hamana Bay through the upper layer, while dissolved P (phosphate P) flows into the Inohana Lake Estuary through the lower layer. For the P exchange between the upper and lower layers, the upward transport of P from the lower layer was more than 10 (~100) times greater than the downward transport of P. The results showed that P accumulates in the bottom sediment during the summer. This study indicates the possibility that the P input from Hamana Bay is dominant over the river P input in summer season with significant density stratification.