Baroclinic and barotropic instabilities are well known as the processes responsible for the production of the most important energy-containing eddies in the atmospheres and oceans of Earth and other planets. Linear and nonlinear instability theories provide insights into when such instabilities may occur, grow to a large amplitude and saturate, with examples from the laboratory, simplified numerical models and planetary atmospheres. We conclude with a number of open issues for future research.

We study a model for the relationship between space plasma and geomagnetic activity, by using an MHD shell model, where its forcing has been replaced by solar wind fluctuation data. We study the fractality of the forcing, its output, and the activity of the model, which may represent the existence of geomagnetic storms. We find correlations between some of these metrics and the solar cycle, suggesting that the complexity of the solar wind may have influence on the level of geomagnetic activity.

A generic methodology is developed to estimate the model error and simulate the model uncertainty related to a specific physical process. The method estimates the model error by comparing two different representations of the physical process in otherwise identical models. The found model error can then be used to perturb the model and simulate the model uncertainty. When applying this methodology to deep convection an improvement in the probabilistic skill of the ensemble forecast is found.

Geophysical flows span a broader range of temporal and spatial scales than can be resolved numerically. One way to alleviate the ensuing numerical errors is to combine simulations with measurements, taking account of the accuracies of these two sources of information. Here we quantify the distribution of numerical simulation errors without relying on high-resolution numerical simulations. Specifically, small-scale random vortices are added to simulations while conserving energy or circulation.

We deduce that after a global thermal perturbation, the Earth's atmosphere would need about a couple of months to come back to equilibrium.

Many applications require wind gust estimates at very different atmospheric altitudes, such as in the wind energy sector. However, numerical weather prediction models usually only derive estimates for gusts at 10 m above the land surface. We present a statistical model that gives the hourly peak wind speed. The model is trained based on a weather reanalysis and observations from the Hamburg Weather Mast. Reliable predictions are derived at up to 250 m, even at unobserved intermediate levels.

We proposed a texture detail enhancement method for seismic section image. Wavelet transform can effectively separate structure information and detail information of an image. High-frequency noise in structural information can be estimated and removed effectively by using bilateral texture filter in a low-frequency sub-band. In the high-frequency sub-band, adaptive enhancement transform can be used to enhance the image edge and texture information and effectively remove the low-frequency noise.

The oceans are losing oxygen, and future changes may worsen this problem. We performed computer simulations of an idealized Iberian Peninsula upwelling system to identify the main fine-scale processes driving dissolved oxygen variability as well as study the response of oxygen levels to changes in wind patterns and phytoplankton species. Our results suggest that oxygen levels would decrease if the wind blows for long periods of time or if phytoplankton is dominated by species that grow slowly.

The soliton vortex two-dimensional solution has been derived for the ionosphere. Why are solitons so important? The advantage of an analytical soliton solution is its localization in space and time as a consequence of balance between nonlinearity and dispersion. One very good example of the balance between nonlinear and dispersive effects is tsunami, a surface gravity one-dimensional wave that can propagate with constant velocity and constant amplitude when it is assured by a parameter regime.

Postprocessing schemes used to correct weather forecasts are no longer efficient when the model generating the forecasts changes. An approach based on response theory to take the change into account without having to recompute the parameters based on past forecasts is presented. It is tested on an analytical model and a simple model of atmospheric variability. We show that this approach is effective and discuss its potential application for an operational environment.

Statistical post-processing of ensemble forecasts is now a well-known procedure in order to correct biased and misdispersed ensemble weather predictions. But practical application in European national weather services is in its infancy. Different applications of ensemble post-processing using machine learning at an industrial scale are presented. Forecast quality and value are improved compared to the raw ensemble, but several facilities have to be made to adjust to operational constraints.

Accurate models of spatial, temporal, and inter-variable dependencies are of crucial importance for many practical applications. We review and compare several methods for multivariate ensemble post-processing, where such dependencies are imposed via copula functions. Our investigations utilize simulation studies that mimic challenges occurring in practical applications and allow ready interpretation of the effects of different misspecifications of the numerical weather prediction ensemble.