Stochastic estimation of biogeochemical parameters of a 3D ocean coupled physical–biogeochemical model: Twin experiments

Abstract In a 3D ocean coupled physical–biogeochemical model, implemented on the North Atlantic at 1/4° and including six biogeochemical variables, three parameters (phytoplankton maximal growth rate, phytoplankton mortality rate and zooplankton maximal grazing rate) are assumed to be stochastic and have regional variations. Ensemble simulations (200 members, lasting 30 days during the spring bloom) show that the phytoplankton concentration is sensitive to the parameterization, with strong spatial heterogeneity, combined to a nonlinear and non-Gaussian behavior. Within the Kalman filter theory, parameter estimation can be done, in the framework of optimal estimate with Gaussian assumptions and reduced rank approximation, when the state vector is augmented with the uncertain parameters. Twin data assimilation experiments, using surface phytoplankton as observations, were performed either in the linear framework or introducing a nonlinear local transformation (anamorphosis). The anamorphosis is performed using a piecewise linear change of variables (applied to all biogeochemical quantities) remapping the percentiles of the empirical marginal distribution provided by the ensemble on the percentiles of the Gaussian distribution. Nonlinear parameter estimation performed better than linear estimation: on the 39 estimated parameters, there is a reduction in the variance obtained with the nonlinear analysis, compared to the variance obtained with the linear analysis, except for 2 parameters. The reduction is better than 60% in 80% of these cases. The anamorphosis is also useful to define an objective error norm for the biogeochemical variables.