# Assessment of observational networks with the Representer Matrix Spectra method—application to a 3D coastal model of the Bay of Biscay

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## Abstract

The development of coastal ocean modeling in the recent years has allowed an improved representation of the associated complex physics. Such models have become more realistic, to the point that they can now be used to design observation networks in coastal areas, with the idea that a “good” network is a network that controls model state error. To test this ability without performing data assimilation, we set up a technique called Representer Matrix Spectra (RMS) technique that combines the model state and observation error covariance matrices into a single scaled representer matrix. Examination of the spectrum and the eigenvectors of that matrix informs us on which model state error modes a network can detect and constrain amidst the observation error background. We applied our technique to a 3D coastal model in the Bay of Biscay, with a focus on mesoscale activity, and tested the performance of various altimetry networks and an in situ array deployment strategy. It appears that a single nadir altimeter is not efficient enough at capturing coastal mesoscale physics, while a wide swath altimeter would do a much better job. Testing various local in situ array configurations confirms that adding a current meter to a vertical temperature measurement array improves the detection of secondary variability modes, while shifting the array higher on the shelf break would obviously enhance the model constraint along the coast. The RMS technique is easily set up and used as a “black box,” but the utility of its results is maximized by previous knowledge of model state error physics. The technique provides both quantitative (eigenvalues) and qualitative (eigenvectors) tools to study and compare various network options. The qualitative approach is essential to discard possibly inconsistent modes.

### Keywords

Stochastic modeling Model errors Data assimilation Array design Coastal ocean## Notes

### Acknowledgments

We thank MERCATOR, a GODAE-participating system, for providing the model boundary data used in the nesting. Most of the work was conducted during Matthieu Le Hénaff’s Ph.D. thesis, for which a grant from DGA is gratefully acknowledged. This project also benefited from interactions within the MERSEA and ECOOP European projects, and (in the case of nadir and wide-swath altimetry) within the CNES/NASA OST and SWOT communities. We also thank two anonymous reviewers for their constructive remarks.

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