Limits to prediction in a size-resolved pelagic ecosystem model

A size-resolved pelagic ecosystem model has been developed based on a continuous (with size) set of model equations and using allometric relationships to specify size-dependent physiological rates. Numerical experiments with identical model equations but different initial conditions and size-class distributions are used to investigate inherent limits to prediction of instantaneous state from an initial condition. The simulations have relatively constant physical forcings, such as solar radiation, to emphasize the dynamical properties of the size-resolved model. Initial condition experiments show that perturbations of 1, 0.1, 0.01, 0.001 and 0.0001% of the initial biomass of individual size-classes from a Hat size spectrum lead to equal spread of model trajectories. The greatest divergence of trajectories occurs when a 2.7 mu m equivalent spherical radius phytoplankton size-class blooms. This divergence has a finite-time Lyapunov exponent of 0.21 day(-1) a prediction time of 33 days for a precision of 10(-3) mol N m(-3). Large member ensembles can approximately halve the effect of growth of initial condition perturbations on prediction. Further numerical experiments are undertaken with the mean body weight at which size-classes are solved perturbed randomly with a standard deviation of 0.15, 0.015, 0.0015 and 0.00015 of the unperturbed body weight. The greatest effect, which dominates the sigma = 0.15 and 0.015 ensembles, occurs when the perturbations of the size-class distribution add and/or remove predator-prey links. These results provide a cautionary warning for the prediction of instantaneous states using complex pelagic ecosystems that are displaced from a stable oscillation and for which biological state is not dominated by physical processes.