Spatial threshold exceedance analysis through marked point processes

Indicators of recurrence, persistence and, in general, distribution patterns of extremal events defined by random field threshold exceedances provide relevant information on critical phenomena for risk assessment. Such indicators are directly related to geometrical properties describing the structure of the corresponding excursion sets. Given the intrinsic nature of the latter, spatial marked point processes provide a natural approach to analyze distribution patterns of such extremal events in relation to specific characteristics of interest. In this paper, on the basis of simulations from flexible models separating memory and fractality effects, the structure of threshold exceedances is analyzed in terms of various second-order characteristics. In particular, the study is focused on the variations in size, boundary roughness, and distance heterogeneities in the components of excursion sets, as well as in clustering/inhibition patterns, depending on both the underlying model parameters and the threshold specifications. The methodology proposed is applied to a real data set on surface reflected solar radiation