# A multiscale ocean data assimilation approach combining spatial and spectral localisation

Ocean data assimilation systems encompass a wide range of scales that are difficult to control simultaneously using partial observation networks. All scales are not observable by all observation systems, which is not easily taken into account in current ocean operational systems. The main reason for this difficulty is that the error covariance matrices are usually assumed to be local (e.g. using a localisation algorithm in ensemble data assimilation systems), so that the large-scale patterns are removed from the error statistics.

To better exploit the observational information available for all scales in the assimilation systems of the Copernicus Marine Environment Monitoring Service, we investigate a new method to introduce scale separation in the assimilation scheme.

The method is based on a spectral transformation of the assimilation problem and consists in carrying out the analysis with spectral localisation for the large scales and spatial localisation for the residual scales. The target is to improve the observational update of the large-scale components of the signal by an explicit observational constraint applied directly on the large scales and to restrict the use of spatial localisation to the small-scale components of the signal.

To evaluate our method, twin experiments are carried out with synthetic altimetry observations (simulating the Jason tracks), assimilated in a inline-formula $M1inlinescrollmathmlnormal 1/normal 4{}^{\circ }$ 25pt14ptsvg-formulamathimg2ffb54fd47338101d9ca2eed2cade549 os-15-443-2019-ie00001.svg25pt14ptos-15-443-2019-ie00001.png model configuration of the North Atlantic and the Nordic Seas.

Results show that the transformation to the spectral domain and the spectral localisation provides consistent ensemble estimates of the state of the system (in the spectral domain or after backward transformation to the spatial domain). Combined with spatial localisation for the residual scales, the new scheme is able to provide a reliable ensemble update for all scales, with improved accuracy for the large scale; and the performance of the system can be checked explicitly and separately for all scales in the assimilation system.

### Zitieren

Zitierform:

Tissier, Ann-Sophie / Brankart, Jean-Michel / Testut, Charles-Emmanuel / et al: A multiscale ocean data assimilation approach combining spatial and spectral localisation. 2019. Copernicus Publications.

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Rechteinhaber: Ann-Sophie Tissier et al.

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