I look for a combination of some external periodicities, which period coincides with Chandler's period. My predecessors considered a model of the linear oscillator with a viscosity and several periodic external forces. Necessary and sufficient condition for emergence of a peak in power spectrum at Chandler's period is nonlinearity of the oscillator being considered. The main achievement of my work is the proof that it is necessary to consider the raw nonlinear equations of L. Euler.

This study focuses on the non-Gaussian statistics based on a 10 240-member ensemble data assimilation. The 10 240 members can resolve the detailed structures of the probability density functions (PDFs) and indicates that the non-Gaussian PDF is caused by multimodality and outliers. The results show that the outliers appear randomly and that large multimodality corresponds well with large analysis error, mainly in the tropical regions where highly nonlinear convective processes appear frequently.

Computational models involving adaptive meshes can both evolve dynamically and be remeshed. The remeshing means that the state vector dimension changes in time and across ensemble members, making EnKF unsuitable for the assimilation of observational data. We develop a modification in which the analysis is performed on a fixed uniform grid onto which the ensemble is mapped, with resolution related to the remeshing criteria. The approach is tested on two 1D models proving success.

This paper describes an innovative way to use data assimilation to infer the dynamics of a physical system from its observation only. The method can operate with noisy and partial observation of the physical system. It acts as a deep learning technique specialised to dynamical models without the need for machine learning tools. The method is successfully tested on chaotic dynamical systems: the Lorenz-63, Lorenz-96, Kuramoto-Sivashinski models and a two-scale Lorenz model.

In this work, we conduct the strongly coupled data assimilation (SCDA) experiments using a two-scale Lorenz '96 model with the ensemble adjustment Kalman filter. This is a coupled system composed by two models with different scales. We have developed a new localization strategy for the cross-domain error covariances, which is crucial for the quality of SCDA. The results show that the SCDA with localization could provide much more accurate estimation of the states than the WCDA.

In this paper, we highlight a specific example of large scale flows. We talk about technical developments of how to extract regions of dense mixing in the flow using graph theoretic tools from discrete Mathematics.