On non-linear sensitivity of marine biological models to parameter variations

Marine biological models are usually complex with many free parameters. Parameter prioritization (based on contribution to model output) is important for system management but difficult. A variance-based sensitivity analysis is developed in this paper using the Sobol'-Saltelli sensitivity indices, which measure the relative importance of each parameter (or group of parameters) and range these parameters along their contribution to output variability. To reduce the number of degrees of freedom, the model output is decomposed using the warping functions or irreversible predictability time. A simple three-component [nutrients, phytoplankton and zooplankton (NPZ)] model with 23 parameters for reproducing annual phytoplankton cycle of the Black Sea is taken as the example to show the usefulness and procedure of the sensitivity analysis. Single and total sensitivity indices showed strong sensitivity of the biological model to the light limitation of the phytoplankton growth. This agrees well with physical intuition. However, ranging model parameters along their contributions to model output variability does not follow exactly the physical intuition when model-related errors from large perturbations of the parameters are not small. For example, the model output becomes very sensitive to the nutrient stock parameterization for certain combinations of the light-related factors.