Y. Wang, F. Counillon and L. Bertino
This work is based on the Norwegian Climate Prediction Model (NorCPM) which applies the Ensemble Kalman Filter (EnKF) to a fully-coupled Earth System Model (NorESM) with an isopycnic ocean model (MICOM) for climate predictions. An idealised assimilation framework is first developed to identify the origin of assimilation-created bias in the current version of NorCPM. It is found that the bias in ocean heat and salt contents is introduced by the non-negativity constraint of isopycnic layer thickness values. Second, a new and computationally efficient method (referred to as upscaling) is proposed and tested in the idealised framework. In the upscaling method, layers for which analysis yields negative values are iteratively grouped with neighbouring layers, resulting in a probability density function with a larger mean and smaller standard deviation that prevents the appearance of negative layer thickness values. Analysis increments of the grouped layer are then proportionally distributed, which prevents also empty layers to become filled and vice-versa. The upscaling method acts as moderation in the location where the non-negativity constraint is not satisfied and is as such sub-optimal. The upscaling method shows a reduction of heat and salt contents and sea surface height bias by a factor of ten. A small bias remains due to the update of the ensemble anomalies, but the upscaling method would be unbiased for the heat and salt contents with data assimilation methods that utilise a static analysis error covariance matrix (e.g. EnOI). Finally, the upscaling method is demonstrated in a realistic framework with NorCPM by assimilating sea surface temperature observations. Over a 25-year analysis period, the new method does not impair the predictive skill of the system but corrects the assimilation-created bias in the steric sea level rise and provides an estimation in better agreement with IPCC [Bindoff ~al.(2007)Bindoff, Willebrand, Artale, Cazenave, Gregory, Gulev, Hanawa, Le Quere, Levitus, Nojiri, Shum, Talley and Unnikrishnan, IPCC(2013)].