Diagnostic estimation and evaluation of uncertainty of nutrient limitation of phytoplankton growth in Michaelis-Menten functional form

Phytoplankton growth is controlled by temperature, light, and nutrient conditions at a viewpoint of bottom-up control. While temperature and light conditions provide latitudinal gradience of phytoplankton growth at the sea surface in the global view, nutrient limitation characterizes the regional and seasonal complex structures of phytoplankton growth in a relationship between nutrient demand of phytoplankton and stoichiometry of nutrient concentrations in seawater. Michaelis-Menten functional form (MM) is the most widely used relationship of nutrient limitation of phytoplankton growth in large-scale ecosystem models. In MM functional form, the choice of the parameter value of a half-saturation constant is a crucial point for controlling the strength of nutrient limitation. In general, the half-saturation constant increase with the size of the phytoplankton cell depending on the surface-to-volume ratio by diffusive hypothesis, and wide ranges of values are reported from observational studies. On the other hand, most of Plankton Functional Types (PFT) models represent a phytoplankton type as one representative PFT with one global parameter. The parameter value is chosen in the observed range as the most reasonable value that could reproduce observed chl-a or nutrient concentration in each model. As a result, there are uncertainties of the global pattern of nutrient limitation among models. In this study, we diagnostically estimated the nutrient limitation using a various parameter set of different global PFT models from CMIP5 (Coupled Model Intercomparison Project) together with the observation-based nutrient concentrations (World Ocean Atlas for macronutrient and multi-model median for dissolved iron and ammonium concentration). Then we show a climatological view of nutrient limitation as a model ensemble and uncertainties and robustness of estimation of nutrient limitation in the current PFT models with MM functional form. We also diagnostically estimated future changes of nutrient limitation as a multi-model ensemble using future changes of nutrient concentration of CMIP5.