Analysis of tornado reports through replicated spatiotemporal point patterns

Understanding the spatiotemporal distribution of tornado events is increasingly imperative, not only because of the natural phenomenon itself and its tremendous complexity but also because we can potentially reduce the risks that they entail. In particular, the US regions are particularly susceptible to tornadoes and they are the focus and motivation of our statistical analysis. Tornado reports can be treated as spatiotemporal point patterns, and we develop some methods for the analysis of replicated spatiotemporal patterns to identify significant structural differences between cold and warm seasons along the years. We extend some existing spatial techniques to the spatiotemporal context to test the null hypothesis that two (or more) observed spatiotemporal point patterns with replications are realizations of point processes that have the same second-order descriptors. In particular, we develop a non-parametric test to approximate the null distribution of the test statistics. We present intensive simulation studies that demonstrate the validity and power of our test and apply our methods to the motivating problem of tornadoes.