The main focus of this paper is on mathematical theory and methods which have a direct bearing on problems involving multiscale phenomena. Modern technology is refining measurement and data collection to spatio-temporal scales on which observed geophysical phenomena are displayed as intrinsically highly variable and intermittant hierarchical structures, e.g. rainfall, turbulence, etc. The hierarchical structure is reflected in the occurrence of a natural separation of scales which collectively manifest at some basic unit scale.