The drainage area is an important, non-local property of a landscape, which controls surface and subsurface hydrologic fluxes. Its role in numerous ecohydrological and geomorphological applications has given rise to several numerical methods for its computation. However, its theoretical analysis has lagged behind.
Recently, an analytical definition for the drainage area was proposed (Gallant & Hutchinson. 2011 Water Resour. Res. 47, W05535. (doi:10.1029/2009WR008540)). However, its validity is limited to regular points of a surface. In our recent paper (Bonetti, Bragg, Porporato. 2018 Proc. R. Soc. A 2018 474 20170693. (doi:10.1098/rspa.2017.0693)), we have extended the theory to critical and singular points of a surface both applying Gauss’ theorem and by means of a dynamical systems approach to define basins of attraction of local surface minima. Our new theoretical description will be used in future work to investigate analytically the properties of landscape evolution and stability.