In the online seminar series "Perspectives on climate sciences: from historical developments to future frontiers" (2020–2021), well-known and established scientists from several fields – including mathematics, physics, climate science and ecology – presented their perspectives on the evolution of climate science and on relevant scientific concepts. In this paper, we first give an overview of the content of the seminar series, and then we introduce the written contributions to this special issue.

Auroral kilometric radiation (AKR) is a radio emission emitted by Earth. Due to the complex mixture of phenomena in the magnetosphere, it is tricky to estimate the time difference between the excitation of two systems. In this study, AKR is compared with indices describing Earth's system. Time differences between the excitation of AKR and the indices are estimated using mutual information. AKR feels an enhancement before the aurora but after more polar latitude features.

The transformation of internal waves at the edge of ice cover can enhance the turbulent mixing and melting of ice in the Arctic Ocean and Antarctica. We studied numerically the transformation of internal solitary waves of depression under smooth ice surfaces compared with the processes beneath the ridged underside of the ice. For large keels, more than 40% of wave energy is lost on the first keel, while for relatively small keels energy losses on the first keel are less than 6%.

The nonstationary kinetic model of turbulence is used to describe the evolution and structure of the upper turbulent layer with the parameters taken from in situ observations. As an example, we use a set of data for three cruises made in different areas of the world ocean. With the given profiles of current shear and buoyancy frequency, the theory yields results that satisfactorily agree with the measurements of the turbulent dissipation rate.