Slope-area Relationship Research Articles

Thresholds for channel initiation at road drain outlets

Abstract Slope–Area relationships have been widely used to identify channel initiation points in the landscape. More recently, the importance of road-related rill and gully erosion has been highlighted. Previous studies indicate that channel initiation at road drain outlets can be predicted from the contributing road area and hillslope gradient at the drain outlet. In this study the validity and usefulness of channel initiation thresholds for road runoff management has been evaluated using field data from three catchments in south-east Australia. None of these catchments show a clear separation between channelised and non-channelised sites based on contributing road area and hillslope gradient. Many drains without channel have similar contributing road area and slope gradients as drain with a channel at the outlet. This demonstrates a relatively large variability within our dataset and limits the identification of a slope–area threshold for these catchments. Logistic regression using road area and slope gradient shows that both variables contribute significantly to channel initiation in the Albert and Tyers River catchments, while for the Sandy Creek catchment only slope gradient is significant at the 0.05 level. Stepwise logistic regression on a wider range of variables shows the significance of cut-batter height in two of the catchments, indicating that flow interception at cut-and-fill roads may be important. Comparison of road-related channel initiation thresholds to previously published topographic thresholds, indicates that channels at road outlets tend to form at relatively small contributing areas and steep slopes. Current forest management guidelines do not consider the risk of channel initiation at road drain outlets in road design and drain spacing. The slope–area thresholds are still considered useful in minimising the risk of gully erosion, especially in forestry areas where it appears most likely that channel initiation occurs during a significant rainfall event immediately following hillslope disturbance or road construction.

Channel and Perennial Flow Initiation in Headwater Streams: Management Implications of Variability in Source-Area Size

Despite increasing attention to management of headwater streams as sources of water, sediment, and wood to downstream rivers, the extent of headwater channels and perennial flow remain poorly known and inaccurately depicted on topographic maps and in digital hydrographic data. This study reports field mapping of channel head and perennial flow initiation locations in forested landscapes underlain by sandstone and basalt lithologies in Washington State, USA. Contributing source areas were delineated for each feature using a digital elevation model (DEM) as well as a Global Positioning System device in the field. Systematic source area-slope relationships described in other landscapes were not evident for channel heads in either lithology. In addition, substantial variability in DEM-derived source area sizes relative to field-delineated source areas indicates that in this area, identification of an area-slope relationship, should one even exist, would be difficult. However, channel heads and stream heads, here defined as the start of perennial flow, appear to be co-located within both of the lithologies, which together with lateral expansion and contraction of surface water around channel heads on a seasonal cycle in the basalt lithology, suggest a controlling influence of bedrock springs for that location. While management strategies for determining locations of channel heads and perennial flow initiation in comparable areas could assign standard source area sizes based on limited field data collection within that landscape, field-mapped source areas that support perennial flow are much smaller than recognized by current Washington State regulations.

Ultramafic rock weathering and slope erosion processes in a South West Pacific tropical environment

Weathering and erosion processes are investigated using electrical resistivity tomography (ERT) imaging and the quantification of geomorphic patterns at the edges of a lateritic plateau overlying ultramafic rocks in the north western region of the main island of New Caledonia (Southwest Pacific). The obtained ERT images document the structure and long-term evolution of the regolith, while source area parameters such as area ( A) local slope above channel head (tan θ) and longitudinal river profiles allow the characterization of contrasting geomorphic patterns around the plateau. The geo-electrical profiles show a succession of hard rock protrusions and weathering troughs, whose depth varies greatly. The area–slope relationship allows the distinction between saprolite- and ferricrete-mantled source areas. The former could result from a regolith erosion process by shallow landslides; the latter from a secondary ferruginization process of reworked lateritic debris. The deepest troughs underlie saprolite-mantled source areas above channel heads, which are characterized by a low permeability saprolite, relatively high slope gradient, and lower area/slope ratios. Such source areas generate fairly high runoff, sustaining rivers and creeks with relatively high erosion power. The ferricrete-mantled source areas are characterized by higher permeability and area/slope ratios, leading to lower runoff and less erosion but further chemical rock weathering. The ferricrete of those source areas acts as a protective hardcover against mechanical erosion of the underlying regolith. This ferricrete reworks, at least partly, allochtonous lateritic materials inherited from a previous disaggregated ferricrete that suggests past erosion processes driven by hydro-climatic condition changes.

Gully position, characteristics and geomorphic thresholds in an undisturbed catchment in Northern Australia

AbstractGullying is a significant process in the long‐term dynamics and evolution of both natural and rehabilitated (i.e. post‐mining) landscapes. From a landscape management perspective it is important that we understand gully initiation and development, as it is well recognized that catchment disturbance can result in the development of gullies that can be very difficult to rehabilitate. This study examines gully position using geomorphic statistics relating to features such as depth, width and length in a catchment undisturbed by European activity in the Northern Territory, Australia. The results demonstrate that gullying occurs throughout the catchment and that a slope–area threshold does not exist and that gully position broadly follows the catchment area–slope relationship. Simple relationships relating catchment area and slope to gully depth, width and length provide poor results, despite these relationships having been found to apply for ephemeral gullies in cropland. The results suggest that gully initiation thresholds are low as a result of an enhanced fire regime. A threshold model for gully position that uses catchment area and slope to switch between gully and hillslope was evaluated and found broadly to capture gully position. Copyright © 2006 John Wiley & Sons, Ltd.

A comparison of SRTM and high‐resolution digital elevation models and their use in catchment geomorphology and hydrology: Australian examples

AbstractThe recently released Shuttle Radar Topography Mission (SRTM) 3‐arc second digital elevation data set provides a complete global coverage of the Earth's land surface. In this paper we examine the SRTM data for three catchments in Australia over a range of climates, geology and resultant geomorphology. To test this new data set the SRTM data are compared with high resolution digital elevation models. We use basic hydrological and geomorphological statistics and descriptors such as the area–slope relationship, cumulative area distribution and hypsometric curve, along with Strahler and networking statistics. The above measures describe the surface morphology of a catchment, therefore integrating catchment geology, climate and vegetation. The SRTM data were also assessed as input into the SIBERIA landscape evolution and soil erosion model as were runoff properties, using a wetness index. The results demonstrate that the 90 m SRTM data provide a poor catchment representation. Hillslopes appear as a linked set of facets and display little of the complex curvature that is observed in high resolution data. While catchment area–slope and area–elevation (hypsometry) properties are largely correct, catchment area, relief and shape (as measured by the width function) are poorly captured by the SRTM data. Catchment networking statistics are also variable. The large grid size of the SRTM data also results in incorrect drainage network patterns and different runoff properties. Consequently, care must be used for quantitative assessment of catchment hydrology and geomorphology, as in all cases SRTM‐derived catchment area is incorrect and smaller digital elevation grid sizes are required for accurate catchment‐wide assessment. While only a limited number of catchments have been examined, we believe our findings are applicable to other areas. © Crown Copyright 2006. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd.

The impact of different gridding methods on catchment geomorphology and soil erosion over long timescales using a landscape evolution model

AbstractMany digital elevation models are gridded from irregularly spaced data. This study examines differences in catchment geomorphology and hydrology as a result of kriging and Delaunay triangulation gridding methods. Both methods have been widely used as tools for placing irregularly spaced data onto a regular grid. In the past, numerical modelling has been performed with little assessment of model input variability and the variability produced by different gridding methods has not been fully assessed. Given the importance of the impact of digital elevation model error and potential impact on model output, little work has been done to understand the impact of this type of potential error. Examination of the different catchment realizations demonstrates that when using kriging (point or block) or Delaunay triangulation there are subtle differences in catchment area and elevation as well as networking properties. Subtle differences also exist in hillslope profile. Nevertheless, when comparing catchment descriptors such as the hypsometric curve, area–slope relationship and cumulative area distribution there is little hydrological and geomorphological difference between these catchments. Further, when these digital elevation models are used as landscape input in a long‐term landscape evolution model (i.e. SIBERIA) there is little geomorphological difference or hydrological difference between the two digital elevation models after a 50 000 year modelled period. Consequently either method is appropriate for the study catchment. These findings provide confidence in the conversion of irregularly spaced data onto a regular grid using kriging or Delaunay triangulation and that either method can be used. Copyright © 2006 John Wiley & Sons, Ltd.

Development and controlling factors of gullies and gully complexes, East Coast, New Zealand

AbstractSequential aerial photographs of a small headwater catchment in the Waiapu basin, East Coast Region, North Island, New Zealand, were interpreted to measure and analyse temporal changes in active area of gullies and gully complexes for a longer time span (1939–2003) and with higher temporal resolution compared to previous studies. We focus on the conditions leading to the development of gullies and gully complexes under pasture and forest by using topographic thresholds (slope–area relationships) of catchments for the initiation of gullies and gully complexes. In addition, the influence of two different lithologies as well as the occurrence of major rainfall events was related to gully activity.Twenty gullies and four gully complexes (occupying 62·5 ha or 12·5 per cent of the catchment area) occurred in the study catchment between 1939 and 2003. However, the majority of these were not active at all of the dates studied. Gullies developed in the sandstone‐dominated Tapuwaeroa Formation tended to attain their maximum size by 1957 with a mean catchment area of 2·1 ha. Gullies developed in mudstone of the Whangai Formation attained their maximum size in 1939 with a mean catchment area of 4·31 ha. Exceptions are gullies which developed into mass movement deposits or into an earth flow deposit as well as gullies developed under indigenous forest. Topographic threshold values for gullies under pasture and indigenous forest show that values for gullies under forest plot far above the threshold line of gullies under pasture, indicating that the topographical threshold for gully development under forest is higher compared to under pasture. A threshold value of 9·4 ha in catchment area is needed for the development of gully complexes under pasture, all located in the Whangai Formation and with the same orientation as the strike of the mudstones. Gully‐complex area and dominance of mass‐movement erosion increased with larger catchment area. A decreasing distance to the threshold line for gullies under pasture indicates a later development for gully complexes. No gully complexes developed under indigenous forest, indicating that the threshold value for gully‐complex development is higher than for gully complexes under pasture and was not reached in the study area.A model of shifting topographical threshold for gully development for a given catchment is developed which depends on land use. When a catchment has an indigenous forest cover the topographical threshold is very high. After conversion to pasture, threshold values decrease drastically. With the invasion of scrub, the threshold slowly increases and returns to a similar level to that under indigenous forest after reforestation.Development of gullies and gully complexes is a highly dynamic phenomenon, and phases of expansion and inactivity indicate that models describing only unidirectional advancing stages without periods of inactivity are not suitable. Therefore, this study adds more phases to models of gully and gully‐complex development in the East Coast Region. The threshold line for gully initiation under pasture and a value of 9·4 ha in catchment area for gully‐complex initiation permits one to predict which catchments, under similar environmental settings, develop gullies and gully complexes on a physical basis. This enables land managers to implement sustainable land‐use strategies to reduce erosion rates of gullies and gully complexes. Copyright © 2006 John Wiley & Sons, Ltd.

Channel head locations with respect to geomorphologic thresholds derived from a digital elevation model: A case study in northern Thailand

The shape of a catchment is controlled by the interplay of different erosion processes acting within the catchment. It is therefore possible to assess dominant erosion processes, and geomorphologic thresholds that spatially separate those processes, by evaluating catchment form. In this paper, geomorphologic thresholds are detected in a digital elevation model of the Pang Khum Experimental Watershed in northern Thailand and compared to the locations of field mapped channel heads. The intersection of thresholds in the slope–area relationship, the probability distribution of drainage areas, and the probability distribution of energy index produce distinct domains in slope–area space that partition the landscape according to erosion mechanisms. All mapped channel heads plot higher than an energy threshold defined by the product of slope and the square root of drainage area. Above this threshold different types of channel heads are partitioned by independent slope or drainage area thresholds. For example, channel heads formed at groundwater seeps plot higher than a drainage area threshold, independent of slope. Channel heads that originate from landslides and overland flow erosion plot higher than a slope threshold, independent of drainage area. It is our interpretation that the channel heads that did not initiate at groundwater seeps were affected by human disturbance (forest conversion for swidden-based agriculture), as they tend to lay above seeps on highly disturbed hillslopes. This paper explores relationships between the shape of a catchment as defined by a digital elevation model and the distribution of mapped channel heads. These relationships serve as a first-order means to identify locations of potentially unstable areas in a landscape, thereby providing a basis to assess the potential impacts of future catchment disturbances.

Channel head location and characteristics using digital elevation models

AbstractThe drainage network is the conduit through which much surface water and sediment are routed within a catchment. In a catchment, the position of where hillslopes begin and channels end has long been considered the position of transition between diffusive processes upslope and the more incisive fluvial processes downslope. Consequently, understanding channel head location is an important issue in understanding catchment hydrology and geomorphology. This study examines channel head position and characteristics in a catchment in Arnhem Land, Northern Territory, Australia. In this study the position of channel heads was mapped within the catchment and plotted on a reliable digital elevation model of the catchment. It was found that the majority of channel heads have relatively small source areas and that graphical catchment descriptors, such as the area–slope relationship and cumulative area distribution, can provide reliable measures of the field position of the heads of first‐order streams and the transition from hillslope to channel. The area–slope relationship and cumulative area distribution are also shown to be good tools for determining digital elevation model grid size which can capture hillslope detail and the transition from hillslope to channel. Copyright © 2005 John Wiley & Sons, Ltd.

Preserving first and second moments of the slope area relationship during the interpolation of digital elevation models

Accurate representation of terrain with appropriate reproduction of topographic characteristics is important for increasingly sophisticated physically-based models of natural processes. Recently investigators have successfully enforced slope area relationships to interpolate more realistic topographies from the sparse data. The limitation of those procedures is that, for the most part, they preserve only the first moment (the mean), when scaling slope with contributing area. Here we present a simple approach to also enforce the second moment, the variance, during landscape evolution simulations or physically-based spatial interpolations.

The use of digital elevation models in the identification and characterization of catchments over different grid scales

This study examines the ability of well-known hydrological and geomorphological descriptors and statistics to differentiate between catchments with spatially varying geology, size and shape subject to the same climate in the Northern Territory, Australia. The effect of digital elevation model grid resolution on these statistics is also examined. Results demonstrate that catchment descriptors such as the area–slope relationship, cumulative area distribution and hypsometric curve can differentiate between catchments with different geology and resultant morphology, but catchment network statistics are insensitive to differences in geology. Examination of the effects of digital elevation model grid scale demonstrates that while considerable catchment information can be gained at digital elevation grids greater than 10 m by 10 m, hillslope and hydrological detail can be lost. Geomorphic descriptors such as the area– slope relationship, cumulative area distribution, width function and Strahler statistics were shown to be sensitive to digital elevation model grid scale, but the hypsometric curve was not. Consequently, caution is needed when deciding on an appropriate grid resolution as well as the interpretation and analysis of catchment properties at grid scales greater than that for optimal hillslope and area aggregation definition. Copyright  2005 John Wiley & Sons, Ltd.

The design of post‐mining landscapes using geomorphic principles

AbstractNature can provide analogues for post‐mining landscapes in terms of landscape stability and also in terms of the rehabilitated structure ‘blending in’ with the surrounding undisturbed landscape. In soil‐mantled landscapes, hillslopes typically have a characteristic profile that has a convex upper hillslope profile with a concave profile lower down the slope. In this paper hillslope characteristic form is derived using the area–slope relationship from pre‐mining topography at two sites in Western Australia. Using this relationship, concave hillslope profiles are constructed and compared to linear hillslopes in terms of sediment loss using the SIBERIA erosion model. It is found that concave hillslopes can reduce sediment loss by up to five times that of linear slopes. Concave slopes can therefore provide an alternative method for the construction of post‐mining landscapes. An understanding of landscape geomorphological properties and the use of erosion models can greatly assist in the design of post‐mining landscapes. Copyright © 2003 John Wiley & Sons, Ltd.

Slope–area relationships and sediment dynamics in two alpine streams

AbstractThe paper focuses on the channel network of alpine basins, attempting to interpret channel reaches in terms of response to erosion and deposition processes. Two basins in the Dolomites (north‐eastern Italy) were considered: the Rio Cordon (5 km2) and the upper Boite River (163 km2). The channel network was extracted from raster‐type digital elevation models (DEM) using a slope–area threshold criterion. A contribution area index (CAI), which combines drainage area, A, and local slope, S (CAI = A0·5S), was used to identify channel heads. The channel network extracted from the DEM was then analysed to recognize cells showing a value of CAI lower than the threshold adopted for channel initiation. Contiguous cells with low values of CAI define channel reaches with low transport efficiency. Field surveys carried out for some selected cases showed a good agreement between prevailing sediment deposition predicted by the analysis of the channel network and observed channel morphological features. Sediment sources mapped in two study basins were also analysed in relation to the location of channels with high potential for sediment deposition: this made it possible to classify the potential role of different types of sediment sources with regard to basin sediment yield. Topographic characteristics of the channel network, expressed by CAI, were compared with a classification of channel morphology in the Rio Cordon. It was found that cells with low values of CAI frequently occur in the riffle–pool reaches, whereas the percentage significantly decreases in step–pool and bedrock channels. Copyright © 2003 John Wiley & Sons, Ltd.

Deriving drainage networks and catchment boundaries: a new methodology combining digital elevation data and environmental characteristics

Digital data on the position and characteristics of river networks and catchments are important for the analysis of pressures and impacts on water resources. GIS tools allow for the combined analysis of digital elevation data and environmental parameters in order to derive this kind of information. This article presents a new approach making use of medium-resolution digital elevation data (250-m grid cell size) and information on climate, vegetation cover, terrain morphology, soils and lithology to derive river networks and catchments over extended areas. In general, methods to extract channel networks at small scale use a constant threshold for the critical contributing area, independent of widely varying landscape conditions. As a consequence, the resulting drainage network does not reflect the natural variability in drainage density. To overcome this limitation, a classification of the landscape is proposed. The various data available are analysed in an integrated approach in order to characterise the terrain with respect to its ability to develop lower or higher drainage densities, resulting in five landscape types. For each landscape type, the slope–area relationship is then derived and the critical contributing area is determined. In the subsequent channel extraction, a dedicated critical contributing area threshold is used for each landscape type. The described methodology has been developed and tested for the territory of Italy. Results have been validated comparing the derived data with river and catchment data sets from other sources and at varying scales. Good agreement both in terms of river superimposition and drainage density could be demonstrated.

Testing of the SIBERIA landscape evolution model using the Tin Camp Creek, Northern Territory, Australia, field catchment

AbstractThe SIBERIA landscape evolution model was used to simulate the geomorphic development of the Tin Camp Creek natural catchment over geological time. Measured hydrology, erosion and geomorphic data were used to calibrate the SIBERIA model, which was then used to make independent predictions of the landform geomorphology of the study site. The catchment, located in the Northern Territory, Australia is relatively untouched by Europeans so the hydrological and erosion processes that shaped the area can be assumed to be the same today as they have been in the past, subject to the caveats regarding long‐term climate fluctuation. A qualitative, or visual comparison between the natural and simulated catchments indicates that SIBERIA can match hillslope length and hillslope profile of the natural catchments. A comparison of geomorphic and hydrological statistics such as the hypsometric curve, width function, cumulative area distribution and area–slope relationship indicates that SIBERIA can model the geomorphology of the selected Tin Camp Creek catchments. Copyright 2002 © Environmental Research Institute of the Supervising Scientist, Commonwealth of Australia.

Impacts of surface elevation on the growth and scaling properties of simulated river networks

We investigate the connection between surface elevation and the growth and scaling of river networks. Three planar models (Scheidegger, Eden, and invasion percolation) are first considered. These models develop aggregating networks according to stochastic rules but do not simulate erosion because the network growth is independent of the surface elevation. We show that none of these planar growth models produces scaling results consistent with observations for natural river basins. We then modify the models to include elevation, simulating the effects of fluvial erosion by enforcing the slope–area relationship. The resulting configurations have scaling properties that still depend on the model (Scheidegger, Eden, or invasion percolation) but are closer to natural river networks when compared with those from the planar growth rules. We conclude that inclusion of the vertical dimension in these three models is critical for explaining the formation and regularities of fluvial networks.

Estimating uplift rate and erodibility from the area-slope relationship: Examples from Brittany (France) and numerical modelling

We used the local slope/drainage area relationship to derive the basic erosion and tectonic parameters from a topography. Assuming a dynamic equilibrium between uplift and erosion, this relationship is expected to depend quite simply on the rock erodibility, and on the tectonic uplift. This relationship may then be used to quantify independently the effect of lithological variation on the erodibility, and the uplift rate. We tested the method on a computer simulated topography and showed that the uplift information can be precisely calculated from the topographic analysis alone. We then analysed the topography of Brittany (France), and obtained a good agreement with uplift data from comparative levelling studies and river incision analysis.

Two-dimensional modelling of the within-field variation in rill and gully geometry and location related to topography

The topography, rill pattern and geometry were surveyed within a small agricultural field. The rill network and dimensions were converted to a grid-based system and used to calculate the slope gradient and contributing area for each grid cell. A strong correlation was found between the rill cross-sections and a power function of slope gradient and contributing area. The slope and area exponents were 1.28 and 0.89, respectively, for all rill points, and 1.02 and 0.87, respectively, for the rill points not lying in the depositional area. These exponents are within the range reported for field studies in a one-dimensional context. Our data confirmed the potential of an inverse slope-area relationship with an area exponent of 0.5 to predict areas prone to rilling and the location of ephemeral gullies. However, the prediction of individual rill starting points was not possible because of the major influence of small local variations in topography on overland flow discharge. Both the prediction of the rill cross-sections and the prediction of the location of the two ephemeral gullies in the field were significantly improved when the tillage direction was taken into account in calculating the contributing area. Therefore, tillage patterns should be given more attention when developing routing procedures for hydrological and erosion models.

Geomorphic threshold conditions for ephemeral gully incision

Ephemeral gully erosion in cultivated land is an important source of sediment that is frequently being overlooked and not accounted for in soil erosion studies. Furthermore, little is known about the factors controlling ephemeral gully erosion. In this paper the available information on the initiation and location of (ephemeral) gullies is summarised, focusing on the relationship between the upslope drainage area ( A) and the critical slope gradient ( S cr) for ephemeral gully initiation. By plotting the non-linear relationship between critical slope gradient (measured immediately upstream of the incision head) and drainage area (at the incision head) for gullied sites it was possible to draw a straight line on log-log paper through the lower-most points for each of the available datasets, representing a critical slope-area relationship for incision. Consequently, below this line no incision occurs. This line or critical relation can also be written as a power function between critical slope and area. Although many factors vary between the different datasets, the exponent of the drainage area relationship (−0.4) showed very little variation. The observed critical slope-area relationship can be related to a simple model of channel initiation by overland flow. Furthermore, this relationship can be used to identify potentially unstable sites where control measures should be undertaken.