In this work, the multiscale dynamics of 38 oceanic and atmospheric pCO₂ time series, sea surface temperature data, and salinity data from fixed buoys recorded with 3 h resolution are considered. The Fourier scaling exponents are estimated. The differences found for three ecosystems – coastal shelf, coral reefs and open ocean  – are discussed. Multifractal properties of pCO₂ difference between ocean and atmosphere are found and characterized over the scale range from 3 h to 1 year.

We explored a simplified climate model based on Earth's energy budget. One advantage of such models is that they are easier to study mathematically. Using a mathematical technique known as boundary integral methods, we present a new way to solve these climate models. This method is particularly useful for modeling climates very different from Earth's current state, such as those on other planets or during past ice ages.

Seismo-electromagnetic (SEM) signals emitted prior to major earthquakes show promise as candidates for short-term earthquake prediction. Analyzing the frequency characteristics of SEM signals provides insights into pre-earthquake processes in the focal zone, such as microfracturing and electrokinetic phenomena. The combined application of fractal and multifractal methods proves to be an effective tool for analyzing these complex signals.

Wind energy exhibits extreme variability in space and time. However, it also shows scaling properties (properties that remain similar across different times and spaces of measurement). This can be quantified using appropriate statistical tools. In this way, the scaling properties of power from a wind farm are analysed here. Since every turbine is manufactured by design for a rated power, this acts as an upper limit on the data. This bias is identified here using data and numerical simulations.

To understand the influence of rainfall on wind power production, turbine power and rainfall were measured simultaneously on an operational wind farm and analysed. The correlation between wind, wind power, air density, and other fields was obtained on various temporal scales under rainy and dry conditions. An increase in the correlation was observed with an increase in the rain; rain also influenced the correspondence between actual and expected values of power at various velocities.

A derivation of discrete dynamical equations for the dry atmosphere without dissipative processes based on the least action principle is presented. For a given set of generally irregularly spaced grid points and a given mode of interpolation, through the minimization of action, the algorithm ensures maximal closeness of the evolution of the discrete system to the motion of the continuous atmosphere. The spatial resolution can be adjusted while executing calculations.

We propose a novel method for the estimation of ocean surface flow properties in terms of its energy and spatial and temporal scales. The method relies on flow observations collected either at a fixed location or along the flow, as would be inferred from the trajectory of freely drifting platforms. The accuracy of the method is quantified in several experimental configurations. We innovatively demonstrate that freely drifting platforms, even in isolation, can be used to capture flow properties.