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 Niño and the Atlantic Multidecadal Oscillation.

Negentropy anomalies of borehole strain associated with the Wenchuan earthquake are analysed. The cumulative anomalies are studied on both large and small scales. Through a comparison discussion, we compare the cumulative anomalies of different time periods and stations with those at the Guza station during the study period and preliminarily exclude meteorological factors. We suspect negentropy anomalies at the Guza station to have recorded abnormal changes related to the Wenchuan earthquake.

Neural networks are a technique that is widely used to predict the time evolution of physical systems. For this the past evolution of the system is shown to the neural network – 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.

Atmospheric stably stratified boundary layers display transitions between regimes of sustained and intermittent turbulence. These transitions are not well represented in numerical weather prediction and climate models. A prototype explicitly stochastic turbulence parameterization simulating regime dynamics is presented and tested in an idealized model. Results demonstrate that the approach can improve the regime representation in models.

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.

The chaotic-oscillation inertia weight back propagation (COPSO-BP) algorithm is proposed for transient electromagnetic inversion. The BP's initial weight and threshold parameters were trained by COPSO, overcoming the BP falling into a local optimum. Inversion of the layered geoelectric model showed that the COPSO-BP method is accurate and stable and needs less training time. It can be used in 1-D direct current sounding, 1-D magnetotelluric sounding, seismic-wave impedance and source detection.

The conspicuous feature of the atmosphere–ocean system is the large difference in the masses of the two media. In this respect there is a strong analogy to Brownian motion, with light and fast molecules colliding with heavy and slow Brownian particles. I apply the tools of non-equilibrium statistical mechanics for studying Brownian motion to air–sea interaction.