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

Ralf Loritz, Axel Kleidon, Conrad Jackisch, Martijn Westhoff, Uwe Ehret, Hoshin Gupta, Erwin Zehe

Research output: Contribution to JournalArticleAcademicpeer-review

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.

Original languageEnglish
Pages (from-to)3807-3821
Number of pages15
JournalHydrology and Earth System Sciences
Volume23
Issue number9
DOIs
Publication statusPublished - 18 Sep 2019

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drainage
runoff
potential energy
thermodynamics
catchment
similarity index
hillslope
kinetic energy
digital elevation model
entropy
energy
streamflow
dissipation
hydrology
index
topography
rainfall
river
water
loss

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Loritz, Ralf ; Kleidon, Axel ; Jackisch, Conrad ; Westhoff, Martijn ; Ehret, Uwe ; Gupta, Hoshin ; Zehe, Erwin. / A topographic index explaining hydrological similarity by accounting for the joint controls of runoff formation. In: Hydrology and Earth System Sciences. 2019 ; Vol. 23, No. 9. pp. 3807-3821.
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A topographic index explaining hydrological similarity by accounting for the joint controls of runoff formation. / Loritz, Ralf; Kleidon, Axel; Jackisch, Conrad; Westhoff, Martijn; Ehret, Uwe; Gupta, Hoshin; Zehe, Erwin.

In: Hydrology and Earth System Sciences, Vol. 23, No. 9, 18.09.2019, p. 3807-3821.

Research output: Contribution to JournalArticleAcademicpeer-review

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