The distinction between the channel network, the headwater subcatchments, and the lateral subcatchments plays an important role in distributed hydrological and ecohydrological applications. This paper presents some newly found invariance properties of headwater and upstream subcatchments and shows that the invariant morphometric properties characterize only natural networks and virtual networks verifying optimal channel networks (OCN) properties but are not verified for virtual non-OCNs. A model based on self-affine properties was developed in order to calculate the number of headwater catchments N and the total upstream area of headwater catchments U as a function of the cutoff area A used to delineate streams. For 18 French catchments between 43 and 116,450 km2 and for 4 virtual OCNs, results show that U(A)/A0 (with A0 being the catchment area) is independent of A for 0.5 < A < 5 km2 and seems to be constant (0.29 ± 0.03) for various shapes and sizes of channel networks and, consequently, can be considered as an invariant general descriptor of natural channel and virtual OCN networks. On the contrary, this is not the case when the approach is applied on six virtual non-OCNs. Moreover, results show that the knowledge of six morphometric indices enable us to calculate both functions N(A) and U(A) for all values of A < A0. These indices can be considered as geometric and topological properties of headwater and upstream subcatchments and are useful for studying the effects of cutoffs on self-affine river networks or as similarity indices for channel network comparison.
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