Recent suggestion and experimental indications that the magnetotail dynamics exhibit self-organized critical behavior have re-motivated interest in sandpile (avalanche) models. Some examples of specific interest for geomagnetic activity have the property that internal avalanches exhibit inverse power law statistics whereas systemwide avalanches have a well-defined mean. Here, we apply the concept of renormalization group to such a model. We demonstrate that invariant analysis based on the renormalization-group theory can explain the power law distribution of energy release by internal avalanches in the large-scale regime of these systems. ¿ 2000 American Geophysical Union