  We investigate the complex spatio-temporal dynamics in avalanche driven
surface growth by means of scaling theory. We study local activity statistics,
avalanche kinetics, and temporal correlations in the global interface velocity,
obtaining different scaling relationships among the involved critical exponents
depending on how far from or close to a critical point the system is. Our
scaling arguments are very general and connect local and global magnitudes
through several scaling relationships. We expect our results to be applicable
in a wide range of systems exhibiting interface kinetic roughening driven by
avalanches of local activity, either critical or not. As an example we apply
the scaling theory to analyze avalanches and roughening of forced-flow
imbibition fronts in excellent agreement with phase-field numerical
simulations.
