Spatio-temporal clustering methodologies for point-event natural hazards

Natural hazards are inherently spatio-temporal processes. Spatio-temporal clustering methodologies applied to natural hazard data can help distinguish clustering patterns that would not only identify point-event dense regions and time periods, but also provide insight into the hazardous process. Here we review spatio-temporal clustering methodologies applicable to point event datasets representative of natural hazards and we evaluate their performance using both synthetic and real life data. We first present a systematic overview of major spatio-temporal clustering methodologies used in the literature, which include clustering procedures  that are (i) global (providing a single quantitative measure of the degree of clustering in the dataset) and (ii) local (i.e. assigning individual point events to a cluster). A total of seven methodologies from these two groups of clustering procedures are applied to real-world (lightning) and synthetic datasets. For (i) global procedures, we explore Knox, Mantel, Jacquez k-NN tests and spatio-temporal K-functions and for (ii) local procedures we consider spatio-temporal scan statistic, kernel density estimation and density-based clustering method OPTICS. The dataset of 7021 lightning strikes is from 1 and 2 July 2015 over the UK, when a severe three-storm system crossed the region with different convective modes producing each of the storms. The synthetic datasets are representative of various topologies of a point-event natural hazard data with a moving source. We introduce a two-source model with input parameters related to the physical properties of the source. Each source has a set number of points events, initiation point in space and time, movement speed, direction, inter-event time distribution and spatial spread distribution. In addition to a base model of two identical moving sources with a set temporal separation, we produce four different topologies of the data by incrementally varying the speed parameter of the source, spatial spread parameters, direction and initiation points, and angle of two sources. With these five synthetic datasets representative of various two-source models, we evaluate the performance of the methodologies. The performance is assessed based on the ability of each methodology to separate the point events produced by the two sources and the sensitivity of these results to changes in the model input parameters. We further discuss the benefits of combining global and local clustering procedures in the analyses as we gain an initial understanding of the spatial and temporal scales over which clustering is present in the data by using global clustering procedures. This information then helps to inform and limit the choice of input parameters for the local clustering procedures.