Scale invariance of subsurface flow patterns and its limitation

Abstract

AbstractPreferential flow patterns in the subsurface are of great importance for the availability and the quality of water resources. However, knowledge of their spatial structure is still behind their importance, so that understanding the nature of preferential flow patterns is a major issue in subsurface hydrology. Comparing the statistics of river catchment sizes and spring discharges, we found that the morphology of preferential subsurface flow patterns is probably scale invariant and similar to that of dendritic river networks. This result is not limited to karstic aquifers where the occurrence of dendritic structures has been known at least qualitatively for a long time. The scale invariance even seems to be independent of the lithology of the aquifer. However, scale invariance of river patterns seems to be only limited by the continental scale, while scale invariance of subsurface flow patterns breaks down at much smaller scales. The upper limit of scale invariance in subsurface flow patterns is highly variable. We found a range from thousands of square kilometers for limestone aquifers down to less than 1 km2 in the weathered zone and debris accumulations of crystalline rocks.