Comparison of Stochastic Parametrization Schemes Using Data Assimilation on Triad Models

In recent years, stochastic parametrizations have been ubiquitous in modelling uncertainty in fluid dynamics models. One source of model uncertainty comes from the coarse graining of the fine-scale data and is in common usage in computational simulations at coarser scales. In this paper, we look at two such stochastic parametrizations: the Stochastic Advection by Lie Transport (SALT) parametrization introduced by Holm (Proc A 471(2176):20140963, 19, 2015) and the Location Uncertainty (LU) parametrization introduced by Mémin (Geophys Astrophys Fluid Dyn 108(2):119–146, 2014). Whilst both parametrizations are available for full-scale models, we study their reduced order versions obtained by projecting them on a complex vector Fourier mode triad of eigenfunctions of the curl. Remarkably, these two parametrizations lead to the same reduced order model, which we term the helicity-preserving stochastic triad (HST). This reduced order model is then compared with an alternative model which preserves the energy of the system, and which is termed the energy preserving stochastic triad (EST). These low-dimensional models are ideal benchmark models for testing new Data Assimilation algorithms: they are easy to implement, exhibit diverse behaviours depending on the choice of the coefficients and come with natural physical properties such as the conservation of energy and helicity.

Full Text

FilePagesSizeAccess
Publisher's official version
331 Mo
How to cite
Lobbe Alexander, Crisan Dan, Holm Darryl, Mémin Etienne, Lang Oana, Chapron Bertrand (2024). Comparison of Stochastic Parametrization Schemes Using Data Assimilation on Triad Models. In Chapron, B., Crisan, D., Holm, D., Mémin, E., Radomska, A. (eds) Stochastic Transport in Upper Ocean Dynamics II. STUOD 2022. Part of the Mathematics of Planet Earth book series (MPE,volume 11). Springer, Cham. Print ISBN 978-3-031-40093-3 Online ISBN 978-3-031-40094-0. https://doi.org/10.1007/978-3-031-40094-0_7. pp.159-191. Springer Nature Switzerland. https://doi.org/10.1007/978-3-031-40094-0_7, https://archimer.ifremer.fr/doc/00856/96755/

Copy this text