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Introduction What is this? These pages are a collection of facts (identities, approximations , inequalities, relations, ...) about matrices and matters relating to them. It is collected in this form for the convenience of anyone who wants a quick desktop reference. Disclaimer: The identities, approximations and relations presented here were obviously not(More)
The generation and evolution of eddies in the ocean are largely due to instabilities that are unpredictable, even on short timescales. As a result, eddy-resolving ocean reanalyses typically use data assimilation to regularly adjust the model state. In this study, we present results from a second-generation eddy-resolving ocean reanalysis that is shown to(More)
This paper considers implications of different forms of the ensemble transformation in the ensemble square root filters (ESRFs) for the performance of ESRF-based data assimilation systems. It highlights the importance of using mean-preserving solutions for the ensemble transform matrix (ETM). The paper shows that an arbitrary mean-preserving ETM can be(More)
A simple approach to the estimation of representation error (RE) of sea level (␩), temperature (T), and salinity (S) observations for ocean data assimilation is described. It is assumed that the main source of RE is due to unresolved processes and scales in the model. Therefore, RE is calculated as a function of model resolution. The methods described here(More)
We present a detailed description of TOPAZ4, the latest version of TOPAZ – a coupled ocean-sea ice data assimilation system for the North Atlantic Ocean and Arctic. It is the only operational, large-scale ocean data assimilation system that uses the ensemble Kalman filter. This means that TOPAZ features a time-evolving, state-dependent estimate of the state(More)