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

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.

Surface water and groundwater: Unifying conceptualization and quantification of the two water worlds

“…From the outset, we recognise that flow in both surface water and groundwater systems is controlled by the interplay of potential energy differences, usually expressed as potential gradients, and frictional losses, which dissipate a substantial part of the driving energy difference along the flow path into heat. Overland and channel flows are driven by topographygravitational potential energy differencesand it is well known that only a tiny amount of the driving energy difference is converted into kinetic energy of overland or channel flow (Loritz et al, 2019), while more than 99% is dissipated along the hillslope or in the channel. Frictional losses are essentially turbulent, thus proportional to the square of the fluid velocity, and occur mainly at the contact line between the fluid and the solid (the land surface or the wetted perimeter of the rill or the channel cross section), while internal fluid friction is small.…”

Surface water and groundwater: unifying conceptualization and quantification of the two “water worlds”

“…They particularly allow the exploration of how distributed patterns and their spatial organization jointly control distributed state dynamics and integral behaviour of hydrological systems (Zehe and Blöschl, 2004). Related studies include the investigation of (a) how changes in agricultural practices affect the streamflow generation in a catchment (Pérez et al, 2011), (b) the role of bedrock topography for runoff generation (Hopp and McDonnell, 2009) at the Panola hillslope and the Colpach catchment (Loritz et al, 2017), and (c) the role of vertical and lateral preferential flow networks on subsurface water flow and solute transport at the hillslope scale (Bishop et al, 2015;2014;Zehe, 2011, 2010), including the issue of equifinality. Setting up a physically based model, however, requires an enormous amount of highly resolved spatial data, particularly on subsurface characteristics.…”

“…The residual soil water content is not available for plants, as it is generally stored in fine pores subject to very high capillary forces. Isotopic tracers have been fundamental to unravelling water flow paths in soils, using dual plots (Benettin et al, 2018;Sprenger et al, 2018), and to distinguishing soil water that is recycled to the atmosphere and released as streamflow (Brooks et al, 2010;McDonnell, 2014).…”

“…Before proceeding, we emphasize that our use of the term "two water worlds" throughout this paper is intended to highlight the disparate catchment and groundwater communities, and is not used in the specific context of mobile-immobile water in the root zone (McDonnell, 2014), as discussed at the end of Sect. 3.1.…”

Evaluation of Soil Water Index of distributed Tank Model in a small basin with field data

“…Hence, the use of SWI could be more recommended for the soil moisture representation. Loritz et al (2019) discussed hydrologic similarity in different catchments comparing TWI and HAND performance, and concluded that despite the similarities between these indices, they represent different hydrological aspects, where the modified-HAND version performed better than TWI and HAND approaches. Contrary to their study, the present study showed that HAND was the worst index to represent soil moisture patters.…”