Crossing of scales and non-linearities in geophysical processes

Cross-scale processes, involving both time and space, are common in nature. In this new millennium they are going to play a prominent role in the geosciences. We have discussed the role of cross-scale processes in geophysics and their connection to nonlinearities found in geophysical materials and dynamical phenomena. We have illustrated these points by presenting five case-studies drawn from geophysics. They include: 1) high Rayleigh number convection in air and water and the phenomena of plume-branching; 2) the use of wavelets in characterizing features from large data sets found in high Rayleigh number convection simulations, seismic tomographic model and satellite interferometry data; 3) the nonlinear feedback between mantle rheology and viscous heating; 4) the nonlinear effects caused by variable mantle thermal conductivity; 5) the influence of nonlinear (non-Newtonian) rheology on mantle mixing.