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- Kaare Brandt Petersen, Michael Syskind Pedersen, Georg Martius, Glynne Casteel, Jan Larsen, Jun Bin Gao +17 others
- 2004

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)

- PAVEL SAKOV, PETER R. OKE
- 2007

A simple, versatile, computationally efficient ensemble-based method for objectively designing an observation array is described. The method seeks to compute the observation array that minimizes the analysis error variance, according to Kalman filter theory. While most elements of the method have been described elsewhere, this paper attempts to present a… (More)

- Peter R. Oke, Pavel Sakov, Madeleine L. Cahill, Jeff R. Dunn, Russell Fiedler, David A. Griffin +3 others
- 2013

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)

- PAVEL SAKOV, PETER R. OKE
- 2006

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)

- PETER R. OKE, PAVEL SAKOV
- 2007

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)

a r t i c l e i n f o We define the footprint of an ocean observation as the region that is well correlated to the observed variable at zero time-lag. The footprint of observations from an observation array provides an indication of the region that is effectively monitored by that array. This study examines the footprint of moorings that underpin the… (More)

- Marc Bocquet, Pavel Sakov
- 2013

Two main classes of data assimilation methods have taken the lead in geophysical data assimilation [1]. As a nonlinear smoother, 4D-Var is a powerful method found to outperform filters in strongly nonlinear conditions. But its background statistics suboptimally rely on a climatology. Besides, it technically requires the long endeavor of building adjoints of… (More)

This study investigates the relation between two common localisation methods in ensemble Kalman filter (EnKF) systems: covariance localisation and local analysis. Both methods are popular in large-scale applications with the EnKF. The case of local observations with non-correlated errors is considered. Both methods are formulated in terms of tapering of… (More)

- P. Sakov, F. Counillon, L. Bertino, K. A. Lisæter, P. R. Oke
- 2012

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)

The study considers an iterative formulation of the ensemble Kalman filter (EnKF) for strongly nonlinear systems in the perfect-model framework. In the first part, a scheme is introduced that is similar to the ensemble randomized maximal likelihood (EnRML) filter by Gu and Oliver. The two new elements in the scheme are the use of the ensemble square root… (More)