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.

I provide a personal view on the role of bifurcation analysis of climate models in the development of a theory of variability in the climate system. By outlining the state-of-the-art of the methodology and by discussing what has been done and what has been learned from a hierarchy of models, I will argue that there are low-order phenomena of climate variability, such as El Nino and the Atlantic Multidecadal Oscillation.

In this paper, we rewrite the adaptive cooperation co-evolution of parallel particle swarm optimization and wolf search algorithm based on principal component analysis (ACPW) and applied it to solve conditional nonlinear optimal perturbation (CNOP) in the WRF-ARW for identifying sensitive areas of typhoon target observations. The experimental results show that the ACPW is meaningful, feasible and effective.

Neural networks are a technique that is widely used to predict the time-evolution of physical systems. For this the neural network is shown past evolution of the system – it is "trained" – and then can be used to predict the evolution in the future. We show some limitations in this approach for certain systems that are important to consider when using neural networks for climate and weather-related applications.

The borehole strain data of the Guza station are used to study the negentropy anomalies before the Wenchuan earthquake. We observed the distribution of anomalies in the skewness-kurtosis domain and accumulated the anomaly frequency over time. Our results show: 1) The earthquake moment is proved to be a critical time during the whole earthquake process. 2) Two cumulative acceleration phases are corresponding to the two crustal stress releases, which may be the precursors to the earthquake.

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.

We design a new nonlinear model to construct the accurate relationship between auroral oval boundaries and 18 space physical parameters, and explore the influence of every single space physical parameter on auroral oval boundary in this paper. As a result, we found the combination of some space physical parameters can strengthen each other’s influence on aurora oval boundary prediction, and this model can achieve the best performance when only partial space physical parameters are used as input.

Forecasting the height of new snow is crucial for avalanche hazard, roads viability, ski resorts and tourism. The numerical models suffer from systematic and significant errors which are misleading for the final users. Here, we applied for the first time a state-of-the-art statistical method to correct ensemble numerical forecasts of the height of new snow from their statistical link with measurements in French Alps and Pyrenees. Thus, the realism of automatic forecasts can be quickly improved.

A generic methodology is developed to estimate the model error and simulate the model uncertainty related to a specific physical process. The method estimates the model error by comparing two different representations of the physical process in otherwise identical models. The found model error can then be used to perturb the model and simulate the model uncertainty. When applying this methodology to deep convection an improvement in the probabilistic skill of the ensemble forecast is found.

A methodology is developed to simplify the mathematical description of activity in a time-dependent driven system. The method describes the response in the system that is most-closely related to the driver. This reduced description has advantages: low noise, high prediction efficiency, linearity in the described system response to the driver, and compactness. The analysis of the Earth’s magnetospheric system is demonstrated.

A popular (variational ensemble smoother) method of data assimilation is simplified. An exact relationship between ensemble linearizations (linear regression) and adjoints (analytic derivatives) is established.

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.