We have derived exact analytical expressions for the coefficients of evolution equations of long wave motion in the three-layer fluid with arbitrary parameters of the layers and established interrelations of these equations for different interfaces. To our understanding, the core advancement is the clarification and mapping of the regimes of soliton appearance and propagation in this environment that is much more realistic for the description of ocean internal waves.

Long's equation models the steady state of two-dimensional stratified flow over terrain. It has been used extensively to investigate the generation and properties of gravity waves and their impact on the structure constants of the atmosphere. In this paper we derive a time-dependent version of this equation which might be useful in the analysis of experimental data about gravity waves.

The ability of empirical mode decomposition (EMD) to extract multi-decadal variability from sea level records is tested using three simulations, based on sinusoidal oscillations and climate indices. In all cases, the longest-period modes are significantly distorted, with incorrect amplitudes and phases. This affects the estimated acceleration computed from the longest periodic IMF. Additionally, in all cases, extra low-frequency modes uncorrelated with the prescribed variability are found.

The key finding is that an electron beam can be generated in the separatrix region as magnetic reconnection proceeds. This electron beam could trigger the ion-acoustic instability, and a double layer accompanied with electron holes can be found during the nonlinear evolution stage of this instability.

At the Equator, where the heating is larger than that at other latitudes, air rises and diverges poleward in the upper troposphere, descending more or less at 30° latitude; this circulation is the Hadley cell. We studied the impact of different meridional and vertical temperature distributions on a few features of the Hadley cell. Some parameters show a regular dependence on these distributions; others remain rather stable with distributions, but when they change, they do it in an abrupt way.

We consider a dynamic model of the magma-plug system previously derived by Iverson R. M. et al. (2006, Nature, 444) under the influence of stochastic forcing. The effects of noise-induced shifts, pressure stabilization and localization of random trajectories have been revealed by increasing the noise intensity. It is demonstrated that the repetitive stick-slip motions of the magma-plug system in the case of stochastic forcing can be connected with drumbeat earthquakes.

We propose an improved method of data assimilation, in which measured data are incorporated into a physically based model. In data assimilation, one typically seeks to minimize some cost function; here, we discuss a variational approximation in which model and measurement errors are Gaussian, combined with an annealing method, to consistently identify a global minimum of this cost function. We illustrate this procedure with archetypal chaotic systems, and discuss higher-order corrections.

We have developed a fast total-field anomaly inversion to estimate the magnetization direction of multiple sources with approximately spherical shapes and known centres. It requires neither the prior computation of any transformation-like reduction to the pole nor the use of regularly spaced data on a horizontal grid. The method contains flexibility to be implemented as a linear or non-linear inverse problem. Applications to synthetic and field data show the good performance of our method.