Stochastic data-driven model of mesoscale and submesoscale eddies in gyre circulation
Authors: Tucciarone Francesco , Li Long , Memin Etienne 
Published: March 2022

&lt;p&gt;Planetary flows and large scale circulation systems are characterised by an interaction between scales that range over several orders of magnitude, with contributions given by mesoscale and submesoscale dynamics. Resolving numerically &amp;#160;such interactions for realistic configuration is, however, far beyond reach. Any large-scale simulation must then rely on parameterizations of the effects of the small scales on &amp;#160;the large scales. In this work, a stochastic parameterization is proposed based on a decomposition of the flow in terms of a smooth-in-time large-scale contribution and a random fast-evolving uncorrelated small-scale part &amp;#160;accounting for &amp;#160;mesoscales and submesoscales unresolved eddies. This &amp;#160;approach, termed modelling under location uncertainty (LU) [4], relies on a stochastic version of Reynolds Transport Theorem to cast physically meaningful conservation principles in this scale-separated framework. Such a scheme has been successfully applied to several large-scale models of the &amp;#160;ocean dynamics [1, 2, 3, 5]. Here a LU version of the &amp;#160;hydrostatic primitive equations is &amp;#160;implemented within the &amp;#160;NEMO community code (&lt;span role=&quot;link&quot;&gt;&lt;span role=&quot;link&quot;&gt;https://www.nemo-ocean.eu&lt;/span&gt;&lt;/span&gt;) with a data-driven approach to establish the spatial correlation of the fast evolving scales. In comparison to a corresponding deterministic counterpart, this stochastic large-scale representation &amp;#160;is shown to improve, in terms of the eastward jet resolution and variabilities, the &amp;#160;flow prediction of an idealized wind forced double gyre circulation. The results are assessed through several statistical criterion as well as an energy transfer analysis [2,5]. &lt;br&gt;[1] W. Bauer, P. Chandramouli, B. Chapron, L. Li, and E. M&amp;#233;min. Deciphering the&lt;br&gt;role of small-scale inhomogeneity on geophysical flow structuration: a stochastic approach.&lt;br&gt;Journal of Physical Oceanography, 50(4):&lt;span role=&quot;link&quot;&gt;983-1003, 2020&lt;/span&gt;.&lt;br&gt;[2] W. Bauer, P. Chandramouli, L. Li, and E. M&amp;#233;min. Stochastic representation of&lt;br&gt;mesoscale eddy effects in coarse-resolution barotropic models. Ocean Modelling, 151:101646,&lt;br&gt;2020.&lt;br&gt;[3] R&amp;#252;diger Brecht, Long Li, Werner Bauer and Etienne M&amp;#233;min. Rotating Shallow&lt;br&gt;Water Flow Under Location Uncertainty With a Structure-Preserving Discretization. Journal of&lt;br&gt;Advances in Modeling Earth Systems, 13, 2021MS002492.&lt;br&gt;[4], E. M&amp;#233;min Fluid flow dynamics under location uncertainty,(2014), Geophysical &amp; Astrophysical Fluid Dynamics, 108, 2, 119&amp;#8211;146.&lt;br&gt;[5] V. Resseguier, L. Li, G. Jouan, P. D&amp;#233;rian, E. M&amp;#233;min, B. Chapron, (2021), New trends in ensemble forecast strategy: uncertainty quantification for coarse-grid computational fluid dynamics, Archives of Computational Methods in Engineering.&lt;/p&gt;