A topographic index explaining hydrological similarity byaccounting for the joint controls of runoff formation

Surface topography is an important source of information about the functioning and form of a hydrological landscape. Because of its key role in explaining hydrological processes and structures, and also because of its wide availability at good resolution in the form of digital elevation models (DEM), it is frequently used to inform hydrological analyses. Not surprisingly, several hydrological indices and models have been proposed to link geomorphic properties of a landscape with its hydrological functioning; a widely used example is the Height Above the Nearest Drainage (HAND) index. From an energy-centered perspective HAND reflects the gravitational potential energy of a given unit mass of water located on a hillslope, with the reference level set to the elevation of the nearest corresponding river. Given that potential energy differences are the main drivers for runoff generation, HAND distributions provide important proxies to explain runoff generation in catchments. However, as expressed by the second law of thermodynamics, the driver of a flux explains only one aspect of the runoff generation mechanism, with the driving potential of every flux being depleted via entropy production and dissipative energy loss. In fact, such losses dominate runoff generation in a catchment, and only a tiny portion of the driving potential energy is actually transformed into the kinetic energy of streamflow. In recognition of this, we derive a new topographic index named dissipation per unit length (DUNE) by re-interpreting and enhancing the HAND index. We compare DUNE with HAND, and with the topographic wetness index (TWI), and show that DUNE provides stronger discrimination of catchments into groups that are similar with respect to runoff generation. Our analysis indicates that accounting for both the driver and resistance aspects of flux generation provides a promising approach to linking the architecture of a system with its functioning.