This thesis examines rainfall event characteristics in the Netherlands over a 26-year period (1998–2023) using radar-derived precipitation data. Extreme precipitation is a major contributor to flooding, which impacts human life, infrastructure, and ecosystems. A life-cycle-based tracking approach is employed to analyse rainfall events in terms of spatial extent, duration, and intensity, using 5-minute precipitation data at a 2.4 km resolution.

The study reveals significant increases in the spatial extent and duration of rainfall events, with these trends persisting across most seasons. Intensity trends are more complex: while shorter-duration events show decreasing intensity, a closer look at smaller-scale shorter-duration higher-intensity events indicates an increase in intensity. No significant changes in the shape parameter of extreme event distributions are detected over the study period.

The analysis also finds strong correlations between event duration and area, and between intensity and both duration and dew point temperature, with these relationships evolving over time. This work provides valuable insights into the dynamics of rainfall events in the Netherlands and lays a foundation for future research on refining intensity metrics, distinguishing rainfall types, and improving flood risk assessments.

We consider the game cops and robbers, which is a pursuit-evasion game played on a graph G. The cops and the robber take turns moving across the vertices of G, where the goal for the cops is to eventually catch the robber. Specifically, we study the cop number of G, i.e. the minimum number of cops that is needed to catch the robber on G. We investigate the relation between the cop number of the Erdős-Rényi (ER) random graph G(n, p_n) and compare it to another graph parameter, the domination number. Our goal is to collect results from previous research and create an overview. Throughout this thesis, we provide some examples of graphs for which the cop number is equal to the domination number. Furthermore, we provide proofs for some results on the domination number of the ER random graph. The main takeaway is that the cop number is asymptotic to the domination number for particular values of p_n.