We consider the application of an Ensemble Square Root Filter (ESRF) to a coupled ocean ecosystem model (HYCOM-NORWECOM). Such models, especially the ecosystem models, are characterized by strongly non- linear interactions active in ocean blooms and present important limitations for the use of data assimilation methods based on linear statistical analysis. Besides the non-linearity of the model, one is confronted with physical/biological constraints, the analysis state having to be consistent with the model, especially with the con- straints of positiveness of some variables. Furthermore the non-Gaussian distributions of the biogeochemical variables break an important assumption of the linear analysis, leading to a loss of optimality of the filter. Finally ecosystem models and their coupling with physical ocean models present numerous uncertainties linked to the complexity of the processes that they aim at representing and the parameterizations that they introduce. Indeed these models are sensitive to numerous parameters that are poorly known. We present an extension of the symmetric square root of the Ensemble Kalman filter (EnKF) dealing with these limitations by introducing a non-linear change of vari- ables (anamorphosis function) in order to execute the analysis step in a Gaussian space. We also present the results of a joint state-parameter estimation in a North At- lantic configuration of the HYCOM-NORWECOM cou- pled model issued from the assimilation of SeaWIFS chlorophyll surface concentration data with this non- Gaussian extension of the ESRF.