Stability and predictability of a virtual plankton ecosystem created with an individual-based model

This paper establishes the predictability of a one-dimensional virtual plankton ecosystem created by Lagrangian Ensemble integration of an individual-based model. It is based on numerical experiments for a scenario, in which the surface fluxes have stationary annual cycles, and the annual surface heat budget is in balance, i.e. solar heating equals cooling to the atmosphere. Under these conditions, the virtual ecosystem also followed a stationary annual cycle. We investigate the stability of this ecosystem by studying the statistics of multi-year simulations of the ecosystem in a virtual mesocosm moored off the Azores. The integrations were initialised by a first guess at the state of the ecosystem at the end of the cooling season, when the mixed layer was approaching the annual maximum depth. The virtual ecosystem quickly adjusted to a stable attractor, in which the inter-annual variation was only a few percent of the multi-year mean. This inter-annual variation was due to random displacement of individual plankters by turbulence in the mixed layer. The inter-annual variance is nearly, but not exactly ergodic; the deviation is due to inheritance of zooplankton weight through lineages. The virtual ecosystem is independent of initial conditions: that is the proof of stability. The legacy of initialisation error decays within three years. The form of the attractor depends on three factors: the specification of the ecosystem model, the resource level (nutrients), and the annual cycle of external forcing. Sensitivity studies spanning the full range of model parameters and resource levels demonstrate that the virtual ecosystem is globally stable. In extreme cases the zooplankton becomes extinct during the simulation; the attractor adjusts gracefully to this new regime, without the emergence of vacillation or a strange attractor that would signal instability. At high resource levels, some of the zooplankton produce two generations per year (as was observed by Marshall and Orr [Marshall, S. M., and Orr, A. P. (1955). The biology of a marine copepod. Edinburgh: Oliver and Boyd. 188 pp.]; again the attractor adjusts gracefully to the new regime. Ocean circulation does not disrupt the stability of the virtual ecosystem. This is demonstrated by a 0079-6611/$ see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.pocean.2005.04.004 * Corresponding author. E-mail address: [email protected] (J. Woods). 1 Present address: University of Bremen, D-28334, Germany. 44 J. Woods et al. / Progress in Oceanography 67 (2005) 43–83 numerical experiment in which the virtual ecosystem drifts with the mean circulation on a five-year cycle, following a track in the Sargasso Sea that penetrates deep into the zones of annual heating and cooling. The legacy of initialisation error decays within three cycles of the external forcing. Thereafter the ecosystem lies on a five-year geographicallylagrangian attractor. The stability of virtual ecosystems offers useful predictability with a good sign-to-noise ratio. 2005 Elsevier Ltd. All rights reserved.