Alleviating the bias induced by the linear analysis update with an isopycnal ocean model

Abstract

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 idealized 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. Secondly, a new and computationally efficient method (referred to as upscaling) is proposed and tested in the idealized framework. In the upscaling method, layers for which analysis yields negative values are grouped iteratively 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 distributed proportionally, which also prevents empty layers from becoming filled and vice versa. The upscaling method acts as a moderation in the location where the non‐negativity constraint is not satisfied and, as such, is suboptimal. The upscaling method shows a reduction in heat and salt contents and sea‐surface height bias by a factor of 10. A small bias remains, due to the update of ensemble anomalies, but the upscaling method would be unbiased for the heat and salt contents with data assimilation methods that utilize a static forecast‐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 steric sea‐level rise and provides an estimation in better agreement with the Intergovernmental Panel on Climate Change.