Footprints and footprint analysis for atmospheric dispersion problems

Footprint analysis, also known as the study of Influence areas, is a first order method for solving inverse atmospheric dispersion problems. We revisit the concept of footprints giving a rigorous definition of the concept (denoted posterior footprints and posterior zero footprints) in terms of spatio-temporal domains. The notion of footprints is then augmented the to the forward dispersion problem by defining prior footprints and prior zero footprints. We then study how posterior footprints and posterior zero footprints can be combined to reveal more information about the source, and how prior footprints and prior footprints can be combined to yield more information about the measurements.