This work contributes to the understanding of the interaction between internal waves of different length scales. A key finding is that, when the disparity in length scales between the participating waves is large, the interaction may lead to an almost complete destruction of the waves that have a relatively smaller length scale. This result suggests that the wavelengths of internal waves observed in the coastal oceans are likely to be deficient in short waves.

We employ the Hilbert–Huang transform to study the temporal variability in time series of daily means of the surface solar irradiance (SSI) at different locations around the world. The data have a significant spectral peak corresponding to the yearly variability cycle and feature quasi-stochastic high-frequency "weather noise", irrespective of the geographical location or of the local climate. Our findings can improve models for estimating SSI from satellite images or forecasts of the SSI.

The aim of this review is a comparison of intermittency in the heliosphere and the magnetosphere. We show that turbulence in the heliosheath and even at the heliospheric boundaries is intermittent. Moreover, analysis of turbulence in the magnetosheath shows that for very high Alfvénic Mach numbers and high plasma beta we have non-Gaussian statistics in the transverse directions. However, for directions parallel to the magnetic fields, the plasma is close to equilibrium.

In geophysics, numerical models are generally initialized through so-called data assimilation methods. They require computation of a distance between model fields and physical observations. The most common choice is the Euclidian distance. However, due to its local nature it is not well suited for capturing position errors. This papers investigates theoretical aspects of the use of the optimal transport-based Wasserstein distance in this context and shows that it is able to capture such errors.

In this work we developed a method to obtain a time series named as AE* which is well correlated with the geomagnetic AE index. In this process, wavelet filtering is applied to interplanetary solar wind data from spacecrafts around the L1 libration point. This geomagnetic indicator AE* can be obtained well before the AE index release in its final form, and it can be used to feed models for geomagnetic effects, such as the relativistic electrons, giving forecasts ~ 1 to 2 days in advance.

Kappa distributions are frequently used for modeling space plasmas, but their physical origin remains unknown. Recently we realized that the statistical origin of these distributions is not the classical Boltzmann entropy, but the Tsallis q entropy. Thereafter, the question was about the physical origin of this entropic formula. Here we show that the q entropy can be derived under first principles, i.e., by considering that the energy and entropy are additive quantities under certain conditions.

We have applied tipping point analysis to a large record of ocean acoustic data to identify the main components of the acoustic dynamical system: long-term and seasonal trends, system states and fluctuations. We reconstructed a one-dimensional stochastic model equation to approximate the acoustic dynamical system. We have found a signature of El Niño events in the deep ocean acoustic data near the southwest Australian coast, which proves the investigative power of the tipping point methodology.

We propose a new method to reconstruct the circulation in the Earth's mantle for the last 300 Myr. This method is based on the sequential assimilation of plate layouts obtained from plate tectonic reconstructions into mantle convection models. This method allows us to take into account uncertainties in plate tectonic reconstructions, and provides an estimation of the uncertainties in the final result. We test and validate this method in a controlled environment by using synthetic experiments.

The ensemble forecast sensitivity to observation (EFSO) method can efficiently clarify under what conditions observations are beneficial or detrimental for assimilation. Based on EFSO, an offline assimilation method is proposed to accelerate the development of data selection strategies for new observing systems. The usefulness of this method is demonstrated with the assimilation of global satellite precipitation data.

We develop a general framework for the frequency analysis of irregularly sampled time series. We also design a test of significance against a general background noise which encompasses the Gaussian white or red noise. Our results generalize and unify methods developed in the fields of geosciences, engineering, astronomy and astrophysics. All the analysis tools presented in this paper are available to the reader in the Python package WAVEPAL.

There is so far no general framework for handling the continuous wavelet transform when the time sampling is irregular. Here we provide such a framework with the Morlet wavelet, based on the results of part I of this study. We also design a test of significance against a general background noise which encompasses the Gaussian white or red noise. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.

We present a nonlinear analytic solution for barotropic flow relevant to the oceanographic slope region. A similarity approach is adopted and the solution takes the form of a Lambert W-function. A more general class of linear solutions is also discussed which take the form of error functions. The equations solved are similar to the heat equation and thus the results may be of interest beyond the geophysical community.

Fractals are self-similar objects (which look the same at all scales), whose dimensions can be noninteger. They are mathematical concepts, useful to describe various physical systems, as the fractal dimension is a measure of their complexity. In this paper we study how these concepts can be applied to some problems in space plasmas, such as the activity of the Earth's magnetosphere, simulations of plasma turbulence, or identification of magnetic structures ejected from the Sun.

We have used numerical simulations to investigate the impact that rotation has on large waves existing internally in the ocean. In coastal regions these waves become trapped along the coast because of rotation. We have found that this trapping results in an adjustment of the form of the waves. The adjustment leads to heightened mixing along the coast, which has implications for nutrient and chemical distribution.

The Utsu productivity law, one of the main relationships in seismicity statistics, gives the average number of aftershocks produced by a mainshock of a given magnitude. I demonstrate that the law can be formulated in the solid seismicity theory, where it is parameterized in terms of aftershock density within a geometrical solid, constrained by the mainshock size. This suggests that aftershocks can be studied by applying simple rules of analytic geometry on a static stress field.

We devise a model to investigate the interplay between two common phenomena affecting the evolution of a seismogenic fault: the occurrence of earthquakes on neighbouring faults and the partial degree of anelasticity of rocks in the upper mantle, a feature that is often manifested by a post-seismic process known as viscoelastic relaxation. We show how this process dramatically complicates the way an earthquake may alter the magnitude and timing of a seismic event on the perturbed fault.