The forecast of weather prediction uncertainty is a real challenge and is crucial for risk management. However, uncertainty prediction is beyond the capacity of supercomputers, and improvements of the technology may not solve this issue. A new uncertainty prediction method is introduced which takes advantage of fluid equations to predict simple quantities which approximate real uncertainty but at a low numerical cost. A proof of concept is shown by an academic model derived from fluid dynamics.

The Hasselmann equation (HE) is the basis of modern surface ocean wave prediction models. Currently, they operate in the black box with the tuning knobs modes, since there is no consensus on universal wind input and wave-breaking dissipation source terms, and require re-tuning for different boundary and external conditions. We offer a physically justified framework able to reproduce theoretical properties of the HE and experimental field data without re-tuning of the model.

A new method of analysing pressure wave dependences is presented and tested against the published experimental data. Upon the results of examination of more than 90 rock samples, it was found that a significant portion of rocks (~ 45 %) exhibit negative Poisson ratios at lower pressures. Such a significant number of naturally auxetic rocks suggests that the occurrence of negative Poisson ratios is not as exotic as assumed previously.

The influence of fluid injection on tectonic fault sliding and generation of seismic events was studied in the paper by a multi-degree-of-freedom rate-and-state friction model with a two-parametric friction law. The considered system could exhibit different types of motion. The main seismic activity could appear directly after the start of fluid injection or in the post-injection phase (after some days or months). Such an influence of injection on seismicity is observed in the real cases.

We have obtained new evidence of the existence of strain waves in the Earth based on a statistical analysis of the dynamics of seismicity along the northern boundary of the Amurian plate and the data derived from in situ GPS experimental observations. Our results (the periodicity of the seismic components, spatial cycles of the seismicity maxima and migration rate of earthquakes) allow us to identify the dynamics of seismicity along the northern boundary of the Amurian plate as a wave process.