Configuration entropy of fractal landscapes

Hydrologic fields like rainfall and river basin topography require the quantitative description of their spatial arrangements. These arrangements can be effectively characterized by the spatial structure of the 2-dimensional images obtained through the intersection with horizontal planes at different heights. We show that configurational entropy clearly displays fundamental aspects of the responsible dynamics. Topography and rainfall depth over a region are found to lack any characteristic length not only in the size of their features but also in their positional arrangements. The spatial arrangement of two-dimensional images is found to be an effective way to characterize fractal landscapes and the configurational entropy of these arrangements imposes demanding conditions for models attempting to represent these fields.