Diagnostics for Pairwise Extremal Dependence in Spatial Processes

A measure of pairwise extremal dependence for spatial processes, that is marginally invariant, is introduced. This measure enables decisions to be made about whether a spatial process is asymptotically dependent, asymptotically independent or independent for any pair of locations, thus it provides fundamental diagnostic information for understanding or modeling the extreme values of a spatial process. We illustrate the properties and use of this measure through theoretical examples and applications in hydrology and oceanography.