Tailoring data assimilation to discontinuous Galerkin models

Pasmans, I. ORCID: https://orcid.org/0000-0001-5076-5421, Chen, Y. ORCID: https://orcid.org/0000-0002-2319-6937, Carrassi, A. ORCID: https://orcid.org/0000-0003-0722-5600 and Jones, C. K. R. T. (2024) Tailoring data assimilation to discontinuous Galerkin models. Quarterly Journal of the Royal Meteorological Society. ISSN 0035-9009 doi: 10.1002/qj.4737

Abstract/Summary

In recent years discontinuous Galerkin (DG) methods have received increased interest from the geophysical community. In these methods the solution in each grid cell is approximated as a linear combination of basis functions. Ensemble data assimilation (DA) aims to approximate the true state by combining model outputs with observations using error statistics estimated from an ensemble of model runs. Ensemble data assimilation in geophysical models faces several well-documented issues. In this work we exploit the expansion of the solution in DG basis functions to address some of these issues. Specifically, it is investigated whether a DA–DG combination (a) mitigates the need for observation thinning, (b) reduces errors in the field's gradients, and (c) can be used to set up scale-dependent localisation. Numerical experiments are carried out using stochastically generated ensembles of model states, with different noise properties, and with Legendre polynomials as basis functions. It is found that strong reduction in the analysis error is achieved by using DA–DG and that the benefit increases with increasing DG order. This is especially the case when small scales dominate the background error. The DA improvement in the first derivative is, on the other hand, marginal. We think this to be a counter-effect of the power of DG to fit the observations closely, which can deteriorate the estimates of the derivatives. Applying optimal localisation to the different polynomial orders, thus exploiting their different spatial length, is beneficial: it results in a covariance matrix closer to the true covariance than the matrix obtained using traditional optimal localisation in state space.

Additional Information	Code to reproduce model output and figures is available at https://doi.org/10.5281/zenodo.10647102
Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/116511
Item Type	Article
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO) Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Uncontrolled Keywords	data assimilation, discontinuous Galerkin, localisation, neXtSIM DG , numerical methods
Additional Information	Code to reproduce model output and figures is available at https://doi.org/10.5281/zenodo.10647102
Publisher	Wiley
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