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.