Abstract
Abstract. 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 (DEMs), it is frequently used to inform hydrological analyses. Not surprisingly, several hydrological indices and models have been proposed for linking 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 when rainfall becomes runoff, 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 topographic index called reduced dissipation per unit length index (rDUNE) by reinterpreting and enhancing HAND following a straightforward thermodynamic argumentation. We compare rDUNE with HAND, and with the frequently used topographic wetness index (TWI), and show that rDUNE provides stronger discrimination of catchments into groups that are similar with respect to their dominant runoff processes. Our analysis indicates that accounting for both the driver and resistance aspects of flux generation provides a promising approach for linking the architecture of a system with its functioning and is hence an appropriate basis for developing similarity indices in hydrology.
Highlights
The key role that surface topography plays in hydrology has long been recognized (e.g., Horton, 1945)
Topography provides information about the interplay between uplift, weathering and erosion, and about the past morphological development of a landscape. It provides a strong constraint for future hydrological and geomorphic changes and, importantly for hydrology, is the key driver and control associated with runoff generation and several other hydrological processes
We propose a topographic index that accounts for both the driving potential energy difference and the accumulated dissipative loss along the flow path following straightforward thermodynamic arguments
Summary
The key role that surface topography plays in hydrology has long been recognized (e.g., Horton, 1945). Topography provides information about the interplay between uplift, weathering and erosion, and about the past morphological development of a landscape It provides a strong constraint for future hydrological and geomorphic changes and, importantly for hydrology, is the key driver and control associated with runoff generation and several other hydrological processes. This insight about the past, present and future roles played by topography is surely one reason why almost all key landscape entities in hydrology, such as watershed boundaries, hillslopes and channel networks, are derived from properties of the land-surface topography. Digital elevation models (DEMs) are available at fairly high resolu-. Loritz et al.: A topographic index explaining hydrological similarity by accounting for the joint controls tions across the globe (Farr et al, 2007), helping to fuel the growing popularity of spatially explicit hydrologic models (e.g., Beven, 2001)
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