Avalanches in the directed percolation depinning and self-organized depinning models of interface roughening

We review the recently introduced Directed Percolation Depinning (DPD) and Self-Organized Depinning (SOD) models for interface roughening with quenched disorder. The differences in the dynamics of the invasion process in these two models are discussed and different avalanche definitions are presented. The scaling properties of the avalanche size distribution and the properties of active cells are discussed.