Multivariate motion patterns and applications to rainfall radar data - Svenja Fischer; Marco Oesting; Alexander Schnurr (Stochastic Environmental Research and Risk Assessment, 2024)
The classification of movement in space is one of the key tasks in environmental science. Various geospatial data such as rainfall or other weather data, data on animal movement or landslide data require a quantitative analysis of the probable movement in space to obtain information on potential risks, ecological developments or changes in future. Usually, machine-learning tools are applied for this task, as these approaches are able to classify large amounts of data. Yet, machine-learning approaches also have some drawbacks, e.g. the often required large training sets and the fact that the algorithms are often hard to interpret. We propose a classification approach for spatial data based on ordinal patterns. Ordinal patterns have the advantage that they are easily applicable, even to small data sets, are robust in the presence of certain changes in the time series and deliver interpretative results. They therefore do not only offer an alternative to machine-learning in the case of small data sets but might also be used in pre-processing for a meaningful feature selection. In this work, we introduce the basic concept of multivariate ordinal patterns and the corresponding limit theorem. A simulation study based on bootstrap demonstrates the validity of the results. The approach is then applied to two real-life data sets, namely rainfall radar data and the movement of a leopard. Both applications emphasize the meaningfulness of the approach. Clearly, certain patterns related to the atmosphere and environment occur significantly often, indicating a strong dependence of the movement on the environment.

Implications of modeling seasonal differences in the extremal dependence of rainfall maxima - Oscar E. Jurado; Marco Oesting; Henning W. Rust (Stochastic Environmental Research and Risk Assessment, 2023)
For modeling extreme rainfall, the widely used Brown–Resnick max-stable model extends the concept of the variogram to suit block maxima, allowing the explicit modeling of the extremal dependence shown by the spatial data. This extremal dependence stems from the geometrical characteristics of the observed rainfall, which is associated with different meteorological processes and is usually considered to be constant when designing the model for a study. However, depending on the region, this dependence can change throughout the year, as the prevailing meteorological conditions that drive the rainfall generation process change with the season. Therefore, this study analyzes the impact of the seasonal change in extremal dependence for the modeling of annual block maxima in the Berlin-Brandenburg region. For this study, two seasons were considered as proxies for different dominant meteorological conditions: summer for convective rainfall and winter for frontal/stratiform rainfall. Using maxima from both seasons, we compared the skill of a linear model with spatial covariates (that assumed spatial independence) with the skill of a Brown–Resnick max-stable model. This comparison showed a considerable difference between seasons, with the isotropic Brown–Resnick model showing considerable loss of skill for the winter maxima. We conclude that the assumptions commonly made when using the Brown–Resnick model are appropriate for modeling summer (i.e., convective) events, but further work should be done for modeling other types of precipitation regimes.

Spatial modeling of drought events using max-stable processes - Marco Oesting; Alfred Stein (Stochastic Environmental Research and Risk Assessment, 2018)