Abstract
Mathematical and numerical models of the atmosphere and ocean rely on various assumptions, approximations, and simplifications. Over the past decade, significant progress has been made in elucidating their structure and interconnections, particularly for the resolved and reversible fluid components. This advancement has largely been driven by Hamiltonian approaches, encompassing both Hamilton's principle of least action and the associated symplectic structure. Moreover, these insights have influenced the development of numerical methods in production-ready models.
This progress shifts attention toward the unresolved and irreversible processes, where mathematical and theoretical foundations remain scarce-and may continue to be so. I will challenge the notion that partial differential equations are all that is needed, and highlight areas where theoretical progress seems possible. Hopefully, this perspective can shed light on the respective roles of physics-based and data-driven components in comprehensive models.
Thomas Dubos
Thomas Dubos studied mathematics and physics at the École Normale Supérieure (Paris) and obtained his Ph.D. in 2002 at the Laboratoire de Météorologie Dynamique (LMD), focusing on transport through two-dimensional turbulence. As Assistant Professor and then Professor at LMD/École Polytechnique, his research focused on geophysical turbulence and hydrodynamics. More recently, he has used Hamiltonian methods to uncover the structure and connections of existing geophysical models, to derive new models, and to develop numerical methods with desirable physical properties. This fundamental work has contributed to the development of the LMDZ, the atmospheric general circulation model developed at LMD, which is part of the Earth System Model at the Institut Pierre-Simon Laplace (IPSL).
