Impacts on sea ice analyses from the assumption of uncorrelated ice thickness observation errors: Experiments using a 1D toy model

Abstract

Sea ice prediction centres are moving toward the assimilation of ice thickness observations under the simplifying assumption that the observation errors are uncorrelated. The assumption of uncorrelated observation errors is attractive because the errors can be represented by a diagonal observation error covariance matrix, which is inexpensive to invert. In this paper a set of idealized experiments are carried out to investigate the impact of this assumption on sea ice analyses. A background error covariance matrix is generated using a 1D toy model for sea, i.e. forced with idealized models of the ocean and atmosphere. Analysis error covariance matrices are then calculated using this $ \boldsymbol{ \mathrm B } $ matrix for both correlated and uncorrelated observation error covariance matrices, $ \boldsymbol{ \mathrm R } $. The results indicate when the true $ \boldsymbol{ \mathrm R } $ is correlated, using a diagonal approximation results in an analysis that is overconfident at the large scales, in that the analysis error standard deviation at the large scales is underestimated. It is also shown that for the largest observation error correlation length scale tested, 150 km, the analysis error standard deviation for ice thickness is reduced by 10.8% relative to the background error standard deviation when $ \boldsymbol{ \mathrm R } $ has the correct correlation length scale of 150 km, whereas when a diagonal approximation to $ \boldsymbol{ \mathrm R } $ is used in combination with an inflation factor, the reduction is to 6.3%.

Keywords

• data assimilation
• sea ice
• ice thickness
• correlated errors