Scale effects on the estimation of erosion thresholds through a distributed and physically-based hydrological model

Abstract

Slope incision and subsequent development of rills, gullies and channels are responsible for significant soil losses and are often irreversible with very high restoration costs particularly in semiarid environments. The location of potential areas of erosion where these processes occur is vital to land management and conservation. The study of the relationship between the local slope (S) and the drainage area (A) through the geomorphological relationship S = αA^b, combined with hydrologic simulation models, has proved to be appropriate for the identification and characterisation of potential areas of incision, especially when it takes into account the spatial distribution of soil properties and the evolution of hydrological processes. However, physical properties of soil, digital elevation models (DEMs) and flow algorithms used may affect the results. This study employs a distributed, physically-based hydrological model to evaluate the infiltration–runoff relationships and their influence on selecting critical area from three DEMs with different resolutions. The results show a significant scale effect on flow distribution and the location of threshold points on slopes. The results obtained from a 30-m DEM significantly differ from those obtained from 10 and 5-m DEMs because the former was unable to capture the spatial variability of geomorphic processes. The selected set of critical points shows high S–A correlations for different values of critical shear stress. The physical model confirmed the dominance of surface runoff in the study site and was validated from field identification of erosion risk areas, although for incision areas < 2 ha, an appreciable error remains in relation to the calculation algorithm used for the drainage network and DEM resolution.

Introduction

Many researchers have studied slope incision resulting from runoff concentration to estimate the volume of erosion and the location of areas at risk. From the first incision in the soil, erosion processes are diverse and develop on different spatial and temporal scales. Depending on various factors such as soil type, vegetation cover, and climate, incision in a certain area can evolve very quickly from rills only a few centimetres wide to permanent gullies and channels. Particularly in semiarid environments, processes such as overland flow, subsurface flow, and small landsliding lead to the formation of large permanent gullies (Vandaele et al., 1996, Bull and Kirkby, 1997), and are responsible for significant soil loss (e.g., Poesen and Hooke, 1997, Poesen et al., 1997, Vandekerckhove et al., 1998, Gallart et al., 2002). In addition, in steep areas with low vegetation cover, these processes can be rapid, resulting in a significant, and in many cases irreversible, alteration of the landscape, incurring very high restoration and correction costs. The prediction of areas susceptible to these processes is important for better land-use planning and management.

The relationship between the local slope of a gully or a channel head, S, and the drainage area, A, has often been used for the identification of erosion thresholds (Montgomery and Dietrich, 1988, Montgomery and Dietrich, 1994, Willgoose et al., 1991, Tarboton et al., 1992, Prosser and Abernethy, 1996, Schoorl et al., 2000, Vandekerckhove et al., 2000, Hancock and Evans, 2006a, Svoray and Markovitch, 2009), mainly due to its potential for describing surface morphology and ability to integrate the major geological, climatic and vegetation-cover features of a basin (Hancock, 2005). This relation can be represented by the power function (Vandaele et al., 1996)

$$S=\text{α}{A}^{\text{b}}$$

where S is the critical slope (m m^− 1), A is the drainage area (ha), α is a coefficient and b is an exponent. This topographic threshold has also been used to identify potential areas of rill and gully development (Moore et al., 1988, Rutherfurd et al., 1997). However, in some cases, weak S–A relationships limit the accuracy of this methodology.

The physical characteristics of soil affect infiltration, subsurface flow and the S–A relation (Montgomery and Dietrich, 1994, Prosser and Slade, 1994, Prosser et al., 1995, Vandaele et al., 1996, Vandekerckhove et al., 2000). In this way, several studies have identified the threshold of erosion using hydrological models of surface runoff based on spatially lumped soil properties such as unsaturated conductivity, matric potential, soil thickness and resistance to surface flow (Dietrich et al., 1992, Prosser and Abernethy, 1996, Schoorl et al., 2000, Massip, 2001). These approaches, however, do not integrate the spatial distribution and temporal evolution of the processes involved in the infiltration–runoff relationship, relevant to the initiation of rills and gullies (Prosser et al., 1995). On the other hand, the resolution of digital elevation models (DEMs) and distributed soil characteristics directly affect the result of hydrological and geomorphological modeling (Moore et al., 1991, Fryer et al., 1994, Zhang and Montgomery, 1994, Quinn et al., 1995, Walker and Willgoose, 1999, Hancock, 2005, Hancock and Evans, 2006a).

This study analyses the influence of DEM resolution on the identification of potential areas of slope incision based on erosion thresholds from the S–A relation, distribution of soil characteristics and the associated processes of runoff, infiltration and subsurface flow during a precipitation event. The physically based, distributed hydrological model, WiMMed (Herrero et al., 2010), was used for a basin where its water balance has already been evaluated in previous studies (Aguilar, 2008, Millares, 2008, Egüen et al., 2010). Precipitation events with different temporal distributions and intensities were used to assess the simulation results.