We study a model containing the characteristic of self-similarity (invariance under scale) which allows for scaling between lab experiments and geographical-scale seismicity. Particular to this model is the dependency of the earthquake rates on the magnitude difference between events that are causally connected. We present results of a statistical analysis of magnitude correlations for the model along with its implications for the ongoing efforts in earthquake forecasting.

We design a new non-linear model to construct an accurate relationship between auroral oval boundaries and 18 space physical parameters, and explore the influence of every single space physical parameter on auroral oval boundary in this paper. As a result, we found the combination of some space physical parameters can strengthen each other's influence on aurora oval boundary prediction, and this model can achieve the best performance when only partial space physical parameters are used as input.

Statistical post-processing aims to increase the predictive skill of probabilistic ensemble weather forecasts by learning the statistical relation between historical pairs of observations and ensemble forecasts within a given training data set. This study compares four different training schemes and shows that including multiple years of data in the training set typically yields a more stable post-processing while it loses the ability to quickly adjust to temporal changes in the underlying data.

We present a new way to adaptively improve weather forecasts by incorporating last-minute observation information. The recently measured error, together with a statistical model, gives us an indication of the expected future error of wind speed forecasts, which are then adjusted accordingly. This new technique can be especially beneficial for customers in the wind energy industry, where it is important to have reliable short-term forecasts, as well as providers of extreme weather warnings.

This study presents a novel method for reduced-rank data assimilation of multiscale highly nonlinear systems. Time-varying dynamical properties are used to determine the rank and projection of the system onto a reduced subspace. The variable reduced-rank method is shown to succeed over other fixed-rank methods. This work provides implications for performing strongly coupled data assimilation with a limited number of ensemble members on high-dimensional coupled climate models.

Current space weather problems are discussed for young researchers. We have discussed some of the major problems that need to be solved for space weather forecasting to become a reality.

Seasonal prediction of the of the North Atlantic Oscillation (NAO) has been improved in recent years by improving dynamical models and ensemble predictions. One step therein was the so-called sub-sampling, which combines statistical and dynamical predictions. This study generalises this approach and makes it much more accessible. Furthermore, it presents a new verification approach for such predictions.

This paper aims to analyse and simulate correlations between two fields in a scale-invariant framework. It starts by theoretically assessing and numerically confirming the behaviour of renormalized multiplicative power law combinations of two fields with known scale-invariant properties. Then a new indicator of correlation is suggested and tested on rainfall data to study the correlation between the common rain rate and drop size distribution features.