Twin experiment analysis of data assimilation performance using Gaussian anamorphic transformation for highly skewed ocean model variables

This study investigates the use of Gaussian anamorphic transformations to assimilate non-Gaussian biological state variables in an ensemble Kalman filter framework. The ensemble Kalman filter requires Gaussian errors and state variables, which is not always satisfied for physical and biological processes in the ocean. Hard constraints enforced to ensure non-negativity can lead to bias in state estimates, which is problematic. However, by transforming non-negative or skewed variables into a Gaussian space, the bias can be eliminated and the ensemble Kalman filter can assimilate with improved accuracy. This technique is particularly useful in biogeochemical models that simulate non-Gaussian variables such as phytoplankton, nutrient concentrations or sea ice cover. The present study indicates that implementing Gaussian anamorphosis of state variables that do not conform to the assumptions of the ensemble Kalman filter can lead to a reduction in ensemble bias. This approach is likely to enhance the accuracy of ocean predictions when employed in an ocean observation system that includes variables with non-Gaussian distribution.