What causes short-term oscillations in ecosystem models of the ocean mixed layer?

Abstract

An ecosystem model of the oceanic upper mixed layer (UML) that simulates the differences in the annual production cycle observed between the North Atlantic and North Pacific is proposed. It is based on the model of Fasham (1993) modified as follows: (1) the diffusive mixing between the UML and the seasonal pycnocline that is due to internal wave breaking is not included; (2) the nitrate concentration in the seasonal pycnocline is considered to vary with depth rather than be constant; (3) an alternative parameterisation of Zooplankton grazing is used and (4) a number of model parameters are assigned other values. The modelled and observed ecosystem characteristics at Ocean Weather Stations (OWS) I and P are in satisfactory agreement with each other. The model solution obtained shows different regimes of seasonal variability: a periodic regime having a simple annual oscillation and a so-called biharmonic regime that also has oscillations with a period of order one month. The latter oscillations are of interest in that there are observational data showing a succession of phytoplankton blooms at OWS I, although the data are not of sufficient quality to show that the mechanisms causing the oscillations in the model are the same as those producing the oscillations in the data. A qualitative mathematical analysis of the model equations with stationary forcing shows that in the case of entrainment the sole equilibrium solution with non-zero concentrations of all of seven ecosystem components exists, while in the case of detrainment no such solution exists. Analysis of the system of the equations linearised in the vicinity of the former equilibrium state shows it to be stable or unstable and usually corresponds to monotonic changes or damped oscillations at periodic forcing. The model short-term oscillations are connected with feedbacks in the ecosystem initiated by either abrupt changes of the UML thickness in spring or strong deepening of the UML in autumn. A necessary condition of their existence is a combination of intense photosynthetically active radiation, small thickness of the UML, significant mean annual entrainment velocity and a high nitrogen concentration in the seasonal pycnocline. Such combinations are uncommon in the world ocean and this is the reason why such oscillations of the UML ecosystem are only to be expected in some regions.