Effective low-order models for atmospheric dynamics and time series analysis

The paper focuses on two interrelated problems: developing physically sound low-order models (LOMs) for atmospheric dynamics and employing them as novel time-series models to overcome deficiencies in current atmospheric time series analysis. The first problem is warranted since arbitrary truncations in the Galerkin method (commonly used to derive LOMs) may result in LOMs that violate fundamental conservation properties of the original equations, causing unphysical behaviors such as unbounded solutions. In contrast, the LOMs we offer (G-models) are energy conserving, and some retain the Hamiltonian structure of the original equations. This work examines LOMs from recent publications to show that all of them that are physically sound can be converted to G-models, while those that cannot lack energy conservation. Further, motivated by recent progress in statistical properties of dynamical systems, we explore G-models for a new role of atmospheric time series models as their data generating mechanisms are well in line with atmospheric dynamics. Currently used time series models, however, do not specifically utilize the physics of the governing equations and involve strong statistical assumptions rarely met in real data.