A State-dependent Error Covariance Model of Surface Atmospheric Forcings over the Arctic Sea Ice

Hee-Sung Jung , Jonathan Poterjoy, Alek Petty 

This paper presents a state-dependent error covariance model of surface atmospheric forcings over Arctic sea ice for constraining atmospheric influences on short-range sea ice forecast errors. Atmospheric influences are argued to be a dominant source of sea ice forecast errors at shorter lead times and thus need to be properly accounted for in generating ensemble sea ice forecasts relevant for operational assimilation systems. The proposed covariance model is built on ensemble perturbations from 10 years of an 80-member atmospheric reanalysis using methods adapted from background error covariance modeling. Specifically, the covariance model consists of a set of matrix operators that each encodes the inter-variable relationships (i.e., balance operators) and the spatiotemporal correlation structures. Comparison of statistics of perturbations from the covariance model with statistics of ensemble perturbations from an atmospheric reanalysis over the validation period reveal good agreement. In particular, balance relationships that are highly state-dependent, such as temperature-humidity balance, are well captured within the error covariance model. Perfect model experiments using the Los Alamos sea ice model (CICE5) show that an atmospheric forcing ensemble generated from the error covariance model can replicate the atmospheric influences on sea ice ensemble forecasts observed when using a reanalysis atmospheric forcing ensemble. These experiments also demonstrate the ability of the covariance model for introducing controllable amounts of forcing error within the sea ice forecast while properly quantifying the error in the ensemble statistics, which can be useful for generating Observing System Simulation Experiments (OSSEs) targeting short-range forecasts.