ESURFEarth Surface DynamicsESURFEarth Surf. Dynam.2196-632XCopernicus GmbHGöttingen, Germany10.5194/esurf-3-483-2015Topographic roughness as a signature of the emergence of bedrock in eroding
landscapesMilodowskiD. T.d.t.milodowski@ed.ac.ukhttps://orcid.org/0000-0002-8419-8506MuddS. M.https://orcid.org/0000-0002-1357-8501MitchardE. T. A.https://orcid.org/0000-0002-5690-4055School of GeoSciences, University of Edinburgh, Edinburgh, UKD. T. Milodowski (d.t.milodowski@ed.ac.uk)16October20153448349912March201518May201510September20151October2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://esurf.copernicus.org/articles/3/483/2015/esurf-3-483-2015.htmlThe full text article is available as a PDF file from https://esurf.copernicus.org/articles/3/483/2015/esurf-3-483-2015.pdf
Rock is exposed at the Earth surface when rates of erosion locally exceed
rates of soil production. The thinning of soils and emergence of bedrock has
implications spanning geomorphology, ecology and hydrology. Soil-mantled
hillslopes are typically shaped by diffusion-like sediment transport
processes that act to smooth topography through time, generating the
familiar smooth, convex hillslope profiles that are common in low relief
landscapes. Other processes, however, can roughen the landscape. Bedrock
emergence can produce rough terrain; in this contribution we exploit the
contrast between rough patches of bedrock outcrop and smooth, diffusion-dominated soil to detect bedrock outcrops. Specifically, we demonstrate that
the local variability of surface normal vectors, measured from 1 m resolution
airborne LiDAR data, can be used as a topographic signature to
identify areas within landscapes where rock exposure is present. We then use
this roughness metric to investigate the transition from soil-mantled to
bedrock hillslopes as erosion rates increase in two transient landscapes,
Bald Rock Basin, which drains into the Middle Fork Feather River,
California, and Harrington Creek, a tributary of the Salmon River, Idaho.
Rather than being abrupt, as predicted by traditional soil production
models, in both cases the transition from fully soil-mantled to bedrock
hillslopes is gradual and spatially heterogeneous, with rapidly eroding
hillslopes supporting a patchwork of bedrock and soil that is well
documented by changes in topographic roughness, highlighting the utility of
this metric for testing hypotheses concerning the emergence of bedrock and
adding to a growing body of evidence that indicates the persistence of
partial soil mantles in steep, rapidly eroding landscapes.
Introduction
The geomorphic transition from hillslopes with a continuous soil mantle to
rugged bedrock is a key phase in the evolution of eroding landscapes. Many
slowly eroding landscapes feature sediment transport processes that act to
diffuse and dampen short wavelength features of the topography, generating
smooth, soil-mantled hillslopes (Gilbert, 1909; Carson and Kirkby, 1972).
Bedrock becomes exposed at the surface when the rate of erosion exceeds the
maximum rate of soil production (Carson and Kirkby, 1972; Heimsath et al.,
1997, 2012). This transition is gradual, and spatially variable, reflecting
the fact that both soil production and sediment transport are spatially
heterogeneous, and typically operate via discrete events (Wilkinson et al.,
2005; Strudley et al., 2006a, b; Gabet and Mudd, 2010; Furbish and
Roering, 2013). The emergence of bedrock signifies a fundamental change in
the dynamics of sediment transport, which become increasingly stochastic as
mobile colluvium is stripped away and the hillslope sediment flux becomes
detachment limited (e.g. Binnie et al., 2007). Furthermore, the
establishment of terrestrial ecosystems is dependent on a hospitable
substrate: the mosaic of bedrock and soil that constitutes the hillslope
surface imposes a physical template on the development of terrestrial
ecosystems (Phillips and Marion, 2004; Pelletier and Rasmussen, 2009; Gabet
and Mudd, 2010; Sheffer et al., 2013). The rate of erosion that is
sufficient to completely strip soil may therefore represent a limiting
threshold for ecosystem development (Graham et al., 2010). In addition, the
presence or absence of bedrock outcrop may reveal important information
about the availability of nutrients such as phosphorous in soil parent
material (Hahm et al., 2014). Equally, the transition between deep and
shallower soils, signalled by the appearance of bedrock outcrops, is an
ecological gradient allowing for niche specialisation, driving biodiversity
and diversity within species, influencing ecosystem function, species
creation and adaptability (Smith et al., 1997). Quantifying the spatial
distribution of rock exposure and its relationship to the ecological and
geomorphological characteristics of a landscape thus comprises an important
challenge in understanding critical zone dynamics.
The advent of airborne Light Detection And Ranging (LiDAR) as a remote-sensing technology over the last decade or so has driven a revolution in the
fields of both geomorphology and ecology by providing high-resolution
(< 1 m) observations of both canopy structure and sub-canopy
topography, therefore enabling observations to be made at length-scales
sufficiently small to analyse the geomorphic characteristics of hillslopes
(Roering et al., 2010; Hurst et al., 2012; DiBiase et al., 2012). Higher
resolution still (< 1 cm) is possible using terrestrial LiDAR
systems, permitting the analysis of multi-scale dimensionality from length
scales of centimetres to several metres, enabling the objective
classification of point clouds into specific features, such as vegetation
and bedrock, with a high degree of accuracy (Brodu and Lague, 2012; Lague et
al., 2013). Despite the obvious benefits of high-resolution terrestrial
LiDAR scanning, the greater spatial coverage permitted by airborne surveys
maintains its utility for landscape scale applications, requiring the
development of remote sensing methods with which it is possible to extract
information about the geomorphic characteristics of hillslopes, such as the
extent of rock exposure, from such comparatively low-resolution data.
DiBiase et al. (2012) used airborne LiDAR data to investigate the impact of
increasing erosion rates on hillslope morphology in the San Gabriel
Mountains, CA, demonstrating that slope distributions became increasingly
skewed towards higher gradients, as steep, bedrock slopes became
increasingly abundant. They successfully developed the Rock Exposure Index (REI)
as a topographic metric to map rock exposure in this landscape,
defined as areas in which the local gradient exceeds a threshold steepness
beyond which soil is no longer retained on the hillslope. DiBiase and Lamb
(2013) exploited this metric to quantify sediment storage by vegetation on
steep slopes, and thus assess the likely impact of wild fires on hillslope
sediment fluxes. Marshall and Roering (2014) used a similar slope-based
metric to map erosion-resistant sandstone beds in the Oregon Coast Range.
However, slope-based metrics are not universally applicable. For example,
when long-term rates of erosion exceed the local maximum rate of soil
production, bedrock will be exposed at the surface, irrespective of slope
(Carson and Kirkby, 1972; Heimsath et al., 1997, 2012). Within a given
setting, rates of soil production may be limited by factors such as climate,
vegetation, lithology and soil thickness (e.g. Pelletier and Rasmussen,
2009; Chorover et al., 2011; Goodfellow et al., 2014a). It is evident that
in many landscapes rock exposure emerges in places even at low topographic
gradients, and is particularly common in regions with thin regolith cover,
where tor formation is common (Anderson, 2002; Strudley et al., 2006b), on
ridgelines (Gabet et al., 2015), or where bedrock heterogeneities drive
small-scale variation in weathering rates (Goodfellow et al., 2014b).
Another method by which rock exposure might be mapped from high-resolution
topographic models of hillslopes is through changes in their textural
characteristics. On hillslopes mantled by a veneer of soil, sediment
transport is driven by the time-integrated effect of a suite of local-scale
diffusive processes, including bioturbation, tree throw, dry ravel and rain
splash (e.g. Gabet, 2003; Gabet et al., 2003; Yoo et al., 2005; Furbish et
al., 2007). The net efficiency of these processes in transporting material
increases with topographic gradient – they are diffusion-like (Furbish et
al., 2009) – such that they act to dampen the amplitude of local
topography, particularly when viewed at length-scales greater than those at
which the dominant sediment transport rates operate. The resultant
hillslopes therefore typically exhibit smooth, convex surfaces that are
ubiquitous to many soil-mantled landscapes (Gilbert, 1909; Culling, 1963,
1965; Carson and Kirkby, 1972; McKean et al., 1993). The emergence of
bedrock at the surface potentially drives a significant increase in
roughness, because there is a fundamental change in the dynamics of sediment
transport at this location within the landscape: sediment transport is
detachment limited (Dietrich et al., 2003) and the local relief structure is
governed by the characteristics of the bedrock (fracture density and
orientation, bedding and foliation, weathering behaviour).
In this paper we exploit this idea and develop a new technique to identify
areas of rock exposure from high-resolution LiDAR data, based on
short-wavelength topographic roughness. This method is validated in two
granitoid landscapes by comparing the results to rock exposure mapped
independently from high-resolution orthophotographs, highlighting its
utility and limitations. Finally, as a case study, we apply the algorithm in
two strongly transient landscapes – the first in the Feather River region
of the northern Sierra Nevada, California; the second in the Salmon River
region SW of the Bitterroot Mountains, Idaho – in order to illustrate the
transition from diffusive, soil-mantled hillslopes to rough, bedrock
hillslopes as erosion rates increase in both settings.
Methods – quantifying surface roughness
Sediment fluxes on soil-mantled hillslopes have been shown to be well
approximated by a linear relationship with the topographic slope (Carson and
Kirkby, 1972), becoming non-linear as erosion rates increase and steepen
hillslopes towards a limiting slope beyond which mobile colluvium is
unstable (Roering et al., 1999). The resultant topography is diffusive:
hillslope processes act to dampen the amplitude of local micro-topography
generating characteristically smooth hillslope topography. Our method starts
from the hypothesis that the emergence of bedrock through the soil mantle
should be detectable as an increase in the local roughness of the
topographic surface, due to a geomorphic process transition away from
diffusion-like hillslope processes.
Specifically we analyse surface roughness using the variability of the
orientation of local slope normal vectors, using the eigenvalues of an
orientation tensor, derived from the vectors normal to the topographic
surface. A similar approach has been used in a range of geological
applications, notably in earthquake seismology (Fara and Scheidegger, 1963),
analysing trends in geological structural data (Woodcock, 1977) and more
recently as a method to objectively locate landslides from high-resolution
topographic data (McKean and Roering, 2004). We note here that other metrics
describing surface roughness, such as the standard deviation of slope, have
been used in other geomorphic contexts, such as LiDAR-based mapping of
volcanic deposits (Whelley et al., 2014) and channel bed morphology (Cavalli
et al., 2008).
Initially a second order polynomial surface is fitted to a moving data
window of 3 × 3 pixels (Evans, 1980). This method of surface approximation to
calculate topographic metrics has been widely utilised in the calculation of
surface derivatives, predominately slope and curvature, for the extraction
of geomorphic features such as hilltops (Hurst et al., 2012), channel
networks (Pirotti and Tarolli, 2010; Sofia et al., 2011), landslides
(Tarolli et al., 2010; Lin et al., 2013), and anthropogenic features on
floodplains (Sofia et al., 2014). Using a larger length-scale would dampen
the roughness signal, but may be necessary if the topographic data are noisy
(Sofia et al., 2011). The surface can be described by:
z=ax2+by2+cxy+dx+ey+f,
where z is the surface elevation, x and y are horizontal coordinates, and a, b, c, d, e, and f are
empirical fitting coefficients. A similar approach was employed by Hurst et
al. (2012) to calculate hilltop curvature, who found no significant
difference between the results obtained using six or nine term polynomials
in their surface fitting algorithm. Consequently we use a six term
polynomial as it maximises computational efficiency. The normal to a surface
is given by:
n=∇(f(x,y)-z).
For Eq. (1), using spherical coordinates (r, θ, φ) at
the origin, the unit normal vector becomes:
n=1,tan-1d2-e2,tan-1ed.
For N surface normal vectors, the orientation matrix, T,
can be constructed using the directional cosines li, mi and ni,
as shown below:
T=∑iNli2∑iNlimi∑iNlini∑iNmili∑iNmi2∑iNmini∑iNnili∑iNnimi∑iNni2.
The orientation matrix can be solved to find the three eigenvectors
v1, v2, v3 and their
corresponding eigenvalues, λ1, λ2, λ3, which describe the degree of clustering of the normal
vectors about the principal axes of the distribution (Watson, 1966).
Following Woodcock (1977), we normalise the eigenvalues by the number of
observations (N):
S1=λ1N,S2=λ2N,S3=λ3N.S1 (13≤S1≤1) describes the clustering around the major
axis, S2 (0≤S2≤12) the intermediate axis, and
S3 (0≤S3≤13) the minor axis. These normalised eigenvalues
can be used to describe the morphology of a given surface (Woodcock, 1977):
for a smooth surface, the local surface normal vectors will have similar
orientations, thus they will cluster tightly around the major axis,
v1, and S1 will be large, whereas the degree of clustering
around the minor axis, v3, will thus be very small (low
S3). Conversely, for a rough surface, the normal vectors will be more
randomly orientated; there will be a weaker degree of clustering around
v1 (low S1), whilst the clustering around v3
will be relatively high (therefore high S3).
A moving data kernel is passed over the data set to analyse the variability
of the surface normal vectors within the local (circular) neighbourhood. The
radius of this kernel determines the length-scale over which the roughness
of the surface is quantified. Identifying the correct length-scale in this
case is critical – too large, and long wavelength variations in the
topography (i.e. ridge-valley topography) will dominate, obscuring any
signal from rock exposure; too small, and then the measured roughness will
pick out locally smooth surfaces within an exposure of bedrock. We discuss
determining the optimal length-scale in the Validation section (for results,
see Sect. 3.4).
Summary of data sets used during in this study.
Airborne LiDAR RegionAcquisition dateAreal extent used (km2)Point Density (ptsm-2)Data set acknowledgementRayleigh Peak, COMay 20102310.11Poway Creek, CAJan 20051.41.42Bald Rock Basin, CASep 20084.09.81Harrington Creek, IDAug 201149.04.61Orthophotographs RegionAcquisition dateResolution/mSensor typeData set acknowledgementRayleigh Peak, COMar 20100.30Colour Near-Infrared3Poway Creek, CAMay 20120.15Colour Near-Infrared3
1: National Center for Airborne Laser Mapping (NCALM – http://www.ncalm.org);
2: USGS Center for LiDAR Information Coordination and Knowledge (CLICK – http://lidar.cr.usgs.gov/; via OpenTopography); 3: USGS (via EarthExplorer http://earthexplorer.usgs.gov/).
Field sites used in this study; (a) headwaters of the
Spring Creek catchment, ∼ 2.7 km SW of Rayleigh Peak, in the
Colorado Front Ranges; (b) Poway Creek, California; (c) Bald Rock Basin,
draining into the Middle Fork Feather River, Californian Sierra Nevada;
(d) Harrington Creek, which drains into the Salmon River, Idaho. Sites (a) and
(b) were used to validate our algorithm; sites (c) and (d) were subsequently
analysed to investigate the transition from soil-mantled to bedrock
hillslopes in transient landscapes.
Validation of the surface roughness algorithmValidation sites
In order to test the surface roughness metric described above as a measure
of rock exposure, we selected two validation sites in western USA (Fig. 1)
based on the availability of co-located LiDAR and high-resolution (< 30 cm) orthophotographs. A further requirement for validation sites was that
the degree of vegetation cover was minimal, to permit the objective
classification of rock outcrop in the imagery (Sect. 3.2). All LiDAR
data sets and orthophotographs used in the study are freely available from
either the National Science Foundation's OpenTopography service (www.opentopography.org)
or from the United States Geological Survey (USGS;
earthexplorer.usgs.gov/). Technical details for the data sets
have been collated in Table 1.
Rayleigh Peak, Colorado
The first validation site is located in the headwaters of the Spring Creek
catchment, in the central Colorado Frontal Range, which drains into the
South Platte River ∼ 40 km SSW of Denver (Fig. 1a). The
climate is semi-arid with frequent intense summer storms. Mean Annual
Precipitation (MAP) is 440 mm, and average monthly temperatures varies from
a maximum (minimum) of 27.7 (10.8) ∘C in summer to
6.0 (-9.0) ∘C in winter (http://www.prismclimate.org).
Vegetation comprises grassland and sparse coniferous forest, of which
Ponderosa Pine and Douglas Fir are the principal components, the
distribution of which is dominated by the impact of the 1996 Buffalo Creek
wildfire, in which 79 % of the Spring Creek catchment suffered severe burn
damage (Moody and Martin, 2001), so that forest canopy now covers only a
small proportion of the landscape. The bedrock geology comprises Pikes Peak
Granite (Ruleman et al., 2011), which forms large, blocky outcrops. The
degree of rock outcrop at the site varying from almost full exposure on
hillslopes around Rayleigh Peak, which dominates the topography, to fully
soil-mantled hillslopes that are now predominately covered by grassland.
Poway Creek, California
The second study site is located in the Poway Creek catchment, located just
east of the city of Poway, north of San Diego (Fig. 1b). MAP is 825 mm and
temperatures typically range from 29.1 (14.1) ∘C in summer to
11.5 (-0.2) ∘C in winter (http://www.prismclimate.org). The bedrock geology is principally composed
of granodiorite with dacitic-andesitic extrusive rocks underlying the
eastern margin (Todd et al., 2004). There is a gradient in rock exposure
from predominately soil-mantled, grassy hillslopes that are frequently
gullied, to abundant rock outcrop in the steep, rugged headwaters. Due to
classification errors in the original data set, the LiDAR point cloud was
reclassified using the multi-scale curvature algorithm incorporated within
the MCC-LiDAR tool (Evans and Hudak, 2007).
Validation procedure illustrated for the Rayleigh Peak
site: (a) high-resolution colour near-infrared orthophotograph; (b) results
from the SVM classification procedure – rock = blue, soil
mantled/vegetation = green; (c) classified image following the subsequent
majority filter; (d) map of S3, which we use as a measure of surface
roughness, measured using a neighbourhood window radius of 3 m. Orange pixels
mark areas identified as being channelised.
Objective identification of rock exposure from high-resolution
orthophotographs
The high-resolution orthophotographs were classified using the supervised
classification toolbox available within the ENVI 4.8 processing environment.
Specifically we utilised the Support Vector Machine classification method
(Wu et al., 2004), trained using a series of manually selected sample
Regions Of Interest (ROIs) for each class. The classes used to analyse each
orthophotograph comprised the following: “Rock”, “Vegetation”, “Bare Earth” and
“Shadow”. With the exception of the “Shadow” class, which was not as
spatially extensive, each ROI had a minimum of 10 000 pixels. The SVM
classification was implemented to analyse the imagery at two pyramid levels,
with a Pyramid Reclassification Threshold (i.e. the probability threshold
required to reclassify a pixel, if given a different class at a finer
resolution) of 0.90. As the avoidance of false positives within our
validation data set was of paramount importance, pixels were left
unclassified if the confidence level for the final class fell below 95 %.
Subsequently a 7 × 7 pixel majority filter was employed to reduce the noise in
the classified image Fig. 2. As our focus is on comparing soil-mantled and
rocky hillslopes, we combine the vegetation and bare earth classes, and
treat areas that are in shadow as unclassified.
The quality of the classification scheme for each image was judged based
both with a visual inspection of the classification results to ensure that
there were no systematic errors located away from the training ROIs, and
using the error matrices for each classification, providing a quantitative
assessment of the scheme's ability to correctly reproduce the classification
of the initial ROIs. At the 95 % confidence interval, the SVM scheme
discarded 9.4 % of the ROI pixels as unclassified in the Rayleigh Peak
data set and 12.0 % in the Poway Creek data set. At the Rayleigh Peak site,
the classification scheme was able to replicate the rock ROIs with a
commission error (ratio of non-rock pixels classified as rock to the total
number of pixels in the rock ROI) of 0.23 % and an omission error (ratio
of rock pixels incorrectly classified to the total number of pixels in the
rock ROI) of 0.01 %. At the Poway Creek site, the ROIs were replicated
with a commission error of 0.01 % and an omission error of 0.13 %.
Across the region as a whole, both of our validation sites, the
classification scheme struggled in areas where there are large changes in
the saturation of the imagery (Figs. 3 and 4), due to aspect-driven
differences in illumination: as a result some areas have an increased
proportion of unclassified pixels. This problem is endemic to image
classification in high relief terrain, and is very hard to correct even with
good topographic data and bi-directional reflectance function (BDRF-driven)
models, as there is often no information captured in the brightest and
darkest parts of the image (e.g. Teillet et al., 1982; Colby, 1991; Hale and
Rock, 2003). Again, this highlights the potential advantages of landscape
classification techniques based on the morphological characteristics of the
topographic surface. In addition, it is evident that there are still some
areas where the image classification provides an incorrect classification.
Nevertheless, the classification is sufficiently successful to provide two
large test data sets with which to validate our roughness metric. Errors in
the validation data sets will, if anything, lead to an underestimate of the
accuracy of our topographically derived metric; it is hard to imagine how
errors in the classification could inflate the accuracy of the topographic
roughness metric, as the data sets are entirely independent and any errors
unlikely to be co-located.
Validation maps for the Rayleigh Peak site: (a) high
resolution, colour-near infrared orthophotograph; (b) results from combined
classification procedure: rock = blue, soil mantled/vegetation = green;
(c) map of S3, which we use as a measure of surface roughness, measured
using a neighbourhood window radius of 3 m. To maximise the clarity of the
maps, channelised portions of the landscape have not been masked.
Validation maps for the Poway Creek site: (a) high
resolution, colour-near infrared orthophotograph; (b) results from combined
classification procedure: rock = blue, soil mantled/vegetation = green;
(c) map of S3, which we use as a measure of surface roughness, measured
using a neighbourhood window radius of 3 m. To maximise the clarity of the
maps, channelised portions of the landscape have not been masked.
Validation statistics for Rayleigh Peak site as a
function of the roughness threshold used to delimit rock exposure for three
different neighbourhood window radii: (a) true positive and false positive
rates; (b) commission and omission errors; (c) overall accuracy. These tests
were conducted twice – the red and blue lines illustrate the results from
tests in which the pixels classified as soil-mantled pixels were filtered to
avoid localities proximal to rock exposure (see text), therefore is more
representative of the roughness signature of a pure soil-mantled hillslope;
the grey lines illustrate the same tests, but without this prior filtering
step.
Validation procedure
We used the rock exposure maps from the classifications described above to
perform the validation of the roughness algorithm in each of the four test
landscapes. Since channels are often topographically rough, we first
restricted our analysis to the hillslope domain. Several methods have been
proposed to identify channel pixels in high-resolution topography (e.g.
Lashermes et al., 2007; Passalacqua et al., 2010; Pelletier, 2013); in each
landscape we have used the method of Lashermes et al. (2007), in which the
topography is filtered using a Gaussian filter, and then a curvature
threshold to define the extent of the channel network is obtained
statistically by looking for the departure from the expectations of a
Gaussian distribution. This approach produces visibly satisfactory results
across the range of landscapes used here.
After isolating the hillslopes, we searched through the parameter space for
the S3 eigenvalue, performing a pixel-pixel comparison with the
orthophotograph classifications to ascertain whether the algorithm produced
a true positive (TP), false positive (FP), true negative (TN) or false
negative (FN) for a given roughness threshold. In order to objectively
assess the performance of the algorithm and determine an optimum threshold
value to delineate areas with rock exposure, we calculated five test
statistics: (i) true positive rate (= TP/(TP + FN)); (ii) false positive
rate (= FP/(TN+FP)); (iii) commission error (= FP/(TP + FN)); (iv) omission errors (= FN/(TP + FN));
and (v) the overall accuracy (= (TP+TN)/Total); to objectively assess the performance of the algorithm and
determine an optimum threshold value to delineate areas with rock exposure.
In order to avoid bias in the aforementioned statistics towards either
class, the larger of the two classes was randomly subsampled to the same
number of test pixels as the smaller of the two before proceeding with the
calculations. We repeated this procedure for three neighbourhood radii (3,
5 and 7 m) in each of the two field sites to assess the influence of
neighbourhood size on the measured surface roughness. An important
consideration when interpreting the validation results is that the surface
roughness represents a spatially aggregated metric, representing a blend of
the topographic characteristics within the circumference of the
neighbourhood window. Consequently, it is unlikely that this metric will
discriminate between small areas of patchy soil interspersed between rugged
rock outcrops at length scales smaller than the neighbourhood window. This
effect becomes increasingly significant as the window size increases and is
an inevitable outcome from neighbourhood statistical approaches. As a
result, we eliminate from our validation data set areas that are not classed
as rock exposure that lie within 7 m (the largest neighbourhood radius used)
of mapped rock exposure. For comparison, we also report the same statistics
for the full data set.
Validation results
In both landscapes, the close correspondence between the topographically
derived roughness maps against the rock exposure mapped from the high
resolution orthophotographs attests to a qualitatively good agreement
between the two (Figs. 3 and 4). Hillslopes that are covered by a
continuous mantle of soil map consistently as areas that are topographically
smooth, having locally consistent normal vector orientations; in contrast
the emergence of bedrock drives a significant increase in the roughness of
the affected hillslopes that is clearly picked up by our algorithm.
Validation statistics for Poway Creek site as a function
of the roughness threshold used to delimit rock exposure for three different
neighbourhood window radii: (a) true positive and false positive rates;
(b) commission and omission errors; (c) overall accuracy. These tests were
conducted twice – the red and blue lines illustrate the results from tests
in which the soil-mantled samples were filtered to avoid localities proximal
to rock exposure, therefore is more representative of the roughness
signature of a pure soil-mantled hillslope; the grey lines illustrate the
same tests, but without this prior filtering step.
Summary of validation results
for three different threshold values of the eigenvalue
S3. These represent a subsample from the
data displayed in Figs. 5 and 6. TPR = True Positive
Rate; FPR = False Positive
Rate; CE = Commission
Error; OE = Omission
Error; OA = Overall Accuracy (for definitions see
text). As the surface roughness metric is spatially
aggregated, this pixel-wise
comparison was conducted avoiding soil-mantled pixels
that were located proximal to areas of rock exposure (see
text). Including these results in an increase in the
false positive rate and commission errors, and
corresponding drop in overall accuracy (see also Figs. 4 and
6); however these errors are collocated with areas
of rock exposure, and arise as a consequence of this
proximity.
TPR FPR CE OE OA Neighbourhood3 m5 m7 m3 m5 m7 m3 m5 m7 m3 m5 m7 m3 m5 m7 mWindow RadiusS3,thresholdRayleigh Peak 0.0050.680.760.800.050.110.160.050.110.160.320.240.200.810.830.820.0100.500.590.640.010.030.040.010.030.040.500.410.360.740.780.800.0150.370.460.50<0.010.010.01<0.010.010.010.630.540.490.680.730.75S3,thresholdPoway Creek 0.0050.690.830.880.090.150.230.090.150.230.310.170.120.800.840.830.0100.430.600.680.030.050.070.030.050.070.570.400.320.700.780.810.0150.280.420.500.010.020.030.010.020.030.720.580.500.630.700.73
Illustration of the impact of the effect of changing
neighbourhood window radius on the roughness signal that is measured:
(a) results from combined classification procedure – rock = blue, soil
mantled/vegetation = green; (b–d) maps of S3 using a neighbourhood
window radius of (a) 3 m; (b) 5 m; and (c) 7 m. Orange pixels mark areas
identified as being channelised. Note the increase in the leakage of the
roughness signal into proximal areas as the neighbourhood radius is
increased.
In the Rayleigh Peak example, both areas with widespread rock outcrop and
more isolated exposures are picked out (Fig. 3). The primary area of
discordance lies in the SW corner of the image. Here the roughness algorithm
predicts a much greater extent of rock exposure than the classified image.
Inspection of the orthophotograph in this area reveals significant
vegetation cover, obscuring areas where there is clearly bedrock, thus
severely hampering the optical classification in this location. Areas of
enhanced roughness running laterally along the trunk channel, which flows
from west to east here, provide another potential false positive in the
roughness map; this highly localised roughness signature marks the banks of
the incised channel. The validation statistics similarly show a distinct
difference between soil-mantled hillslopes and areas with rock exposure
(Fig. 5; Table 2). The FPR rapidly decreases as the value of S3 used to
discriminate between the two characteristics increases, with a maximum
accuracy (taking into account both false positives and false negatives) of
> 80 % for ∼ 0.003 ≤S3,threshold≤∼ 0.005. The TPR also decreases across this interval,
which is likely to be driven by areas of rock exposure where the rock
surfaces have a low fracture density, therefore appear smooth, and the fact
that our test data set is not perfect (see discussion in Sect. 3.2). We
stress here that the imperfections in the validation data set derived from
the orthophotographs will lead to a conservative estimate of the true
accuracy of the roughness algorithm. Critically from the perspective of
mapping out areas of rock exposure, the rate at which the TPR decreases with
increasing values of S3,threshold is much lower than that of the FPR.
Increasing the size of the neighbourhood window over which the surface
roughness is characterised acts to increase the number of true positives for
a given threshold, but there is a trade-off, as this improvement is
accompanied by an increase in the number of false positives (Figs. 5 and 7; Table 2).
This is probably due to the “leakage” of the roughness signal
from areas where there is rock exposure into the expanded neighbourhoods of
proximal soil pixels (Fig. 7), and also due to the fact that the longer
wavelength topographic structure imposed by the ridge-valley architecture
starts to influence the variability in the distribution of surface normal
vectors; the latter case is particularly prevalent in areas that are
located close to gullies and channels.
The pattern that emerges from the Poway Creek site is very similar; again,
the maps of rock exposure do a qualitatively good job at locating hillslopes
with rock outcrops, although the visual comparison is hindered by the
spatially variable success of the classification scheme (Fig. 4). Again,
the network of channels and gullies provides additional sources of roughness
in the landscape. The performance in the quantitative tests exhibits very
similar patterns to those obtained for the Rayleigh Peak site (Fig. 6; Table 2).
A comparison of the rock exposure classified from the
orthophotographs against the expected fraction of rock exposure predicted
using different thresholds of the surface roughness metric, S3, for a
series of the validation sites near Rayleigh Peak, Colorado, and Poway
Creek, California. Each data point represents the rock exposure mapped
within a 401 m × 401 m square region within a regularly spaced grid.
(a–c)S3 mapped using a neighbourhood radius of 3 m; (d–f)S3 mapped using
a neighbourhood radius of 5 m. The hollow symbol outlined in blue is from
the SE corner of the Rayleigh Peak site, where the rock exposure mapped from
the orthophotographs significantly under-predicts the true degree of rock
exposure due to a combination vegetation cover and variable insolation
conditions.
Implications for use of topographic roughness in other settings
The fact that the roughness signatures of both validation landscapes display
strikingly similar characteristics (Figs. 5 and 6), suggests that surface
roughness is a promising tool for mapping the extent of bedrock outcrop on
hillslopes. As with existing methods (e.g. REI; DiBiase et al., 2012), an
important caveat is that full calibration is dependent on the a posteriori knowledge of
threshold values, obtained, for example, through comparison against rock
exposure mapped from high-resolution photographs (DiBiase et al., 2012; this
study). This is non-trivial in areas with significant vegetation cover due
to the difficulty in resolving the ground surface; indeed, in areas with
significant tree cover a significant portion of exposed rock is always
hidden. Greater uncertainty will arise in areas where prior calibration
against orthophotographs is not possible. A further element of caution is
required, as our validation sites are limited to low-moderate relief,
granitoid settings, but nevertheless, we expect that the methodology can be
used judiciously in other landscapes. We provide an illustration of the
method in a landscape underlain by layered sedimentary rocks in the
Supplement. A number of important considerations are
necessary in doing so, given that in many scenarios it will not be possible
to use aerial imagery to independently judge the performance of the
algorithm.
Firstly, it is evident from Figs. 3–6 that a minor portion of landscapes
mapped as rock exposure is topographically smooth. Variations in bedrock
morphology present a challenge for the textural classification of
topography. Errors may be introduced in areas where a significant proportion
of the bedrock has been polished, or where the bedrock is massive and
exhibits sparse jointing. The latter case is illustrated by smooth, massive
granitoid domes, where the distribution of fractures is dominated by surface
parallel exfoliation joints (Migon, 2006). In such cases the textural
characteristics of bedrock hillslopes may be indistinguishable from those
with a continuous soil mantle. In the case of layered rocks, slopes parallel
to the structural fabric may be smooth, whereas slopes that cross-cut the
layering will appear rougher. This may drive variable accuracy in the
results of textural classification metrics. However, large areas of smooth
bedrock should be readily visible in satellite/aerial imagery because such
conditions are unlikely to support significant vegetation cover (Graham et
al., 2010; Hahm et al., 2014). Furthermore, where smooth surfaces form steep
structures, a slope-based metric such as the REI (DiBiase et al., 2012) can
easily be employed alongside surface roughness to catch these false
negatives. Combinations of topographic metrics in this way may potentially
permit more robust feature extraction from high-resolution data.
Secondly, bedrock exposure is not unique in adding roughness elements to
landscapes, as surface roughness may potentially be generated by other
processes. At length scales of 11–50 m, topographic roughness may be
dominated by the signature of deep seated landslides, if present (Booth et
al., 2009), while other features associated with landslides may generate
roughness at shorter wavelengths (McKean and Roering, 2004; Tarolli et al.,
2010). Roughness at small length scales (typically < 7.5 m) can also
be generated via tree throw where this process is prevalent (Roering et al.,
2010; Marshall and Roering, 2014). Moreover a degree of familiarity with
target landscapes is likely essential in order to critically evaluate the
results, although this criteria is not unique to this method. Furthermore,
in more complex landscapes with multiple roughness generation mechanisms,
the spatial distribution of roughness generated by different processes may
still allow useful quantitative information to be extracted (for example,
instances of tree throw are likely to be quasi-random, or at least spatially
discrete events, whereas exposure of bedrock in hillslopes is likely to
generate connected “clusters” of roughness), although we do not extend our
analysis in this manner here.
The size of the polynomial surface-fitting window should ideally be
comparable to the feature being extracted. In landscapes where other
roughening elements are present, or when the LiDAR data are noisy, a larger
window can be employed, or the topography can be smoothed, with the
limitation that as the degree of smoothing increases, the textural
information that distinguished bedrock hillslopes from soil-mantled
hillslopes is progressively lost (Albani et al., 2004; Sofia et al., 2013).
Finally, the neighbourhood size used to quantify surface roughness will
dictate the resolution at which you can discriminate between soil and rock
outcrop (Fig. 7).
For many applications, whether making an assessment of shallow landslide
hazard, or testing hypotheses concerning the transition from soil-mantled bedrock topography, avoiding false negatives is of paramount
importance. For neighbourhood radii of 3–5 m, a threshold value of S3= 0.01 limits
the occurrence of false positives to < 5 % (Fig. 5), decreasing to < 2 % for S3= 0.015. Omission errors
decrease substantially by increasing the radius of the neighbourhood window,
but there is a trade-off against an increasing frequency of commission
errors (Figs. 5 and 6).
In Fig. 8, we illustrate an alternative approach to mapping rock exposure
using the surface roughness metric introduced above. Specifically we assess
the fraction of pixels within a local neighbourhood that have a value of
S3 greater than a specified threshold value. Employing a sufficiently
high threshold, we can thus express the expected rock exposure within that
neighbourhood. This provides a conservative estimate of the degree of rock
outcrop for a given portion of hillslope. In all cases, there is a positive
correlation between the rock exposure mapped from the orthophotographs and
the roughness of the topographic surface (Fig. 8). However, when the
S3 threshold is set too low, the frequency of false positives leads to
an overestimation of the rock exposure in a given portion of the landscape,
as expected from our previous analysis (Figs. 4–7). In the Rayleigh Peak
site, there is a good agreement between the degree of rock exposure mapped
by the two methods using an S3 threshold of 0.010, if roughness is
quantified with a neighbourhood radius of 3 m, and 0.015 if quantified with
a neighbourhood radius of 5 m. Again this conforms to the expectations
arising from the validation tests (Fig. 5). In Poway Creek, there appears to
be a systematic over-estimation of the rock exposure. The Poway Creek
catchment presents a more challenging landscape to classify for three
reasons: (i) gullies are common, and many of the channels show evidence of
recent incision; the channel banks in these incised localities generate
false positives due to the sharp break in slope. There may be bedrock
exposed in the terrace walls, but if present may be obscured by overhanging
vegetation. (ii) Changing insolation conditions across the image made
classification using the optical data more difficult (Fig. 5). (iii) The
original LiDAR point cloud was relatively sparse (Table 1), as a consequence
of which discrimination of ground returns from those hitting low lying
shrubs is more difficult. As a general point we emphasise that although the
high-resolution orthophotographs provide the best means of objectively
testing our algorithm, the resulting validation data sets are not perfect,
and classification errors will result in under-estimation of the success of
the roughness metric.
Application of the roughness algorithm to transient landscapes –
investigating the soil-bedrock transition in Bald Rock Basin, California,
and Harrington Creek, IdahoStudy sites
We investigate the variations in hillslope characteristics exhibited in two
landscapes – Bald Rock Basin, in the Californian Sierra Nevada, and the
Harrington Creek catchment, a tributary of the Salmon River, Idaho – which
both exhibit strongly transient states of landscape evolution, under
different climate regimes.
Bald Rock Basin, California
The Bald Rock Basin catchment drains into Middle Fork Feather River, in the
north-western Sierra Nevada Mountains, California (Fig. 1c). The regional
climate in this locality is strongly seasonal, with maximum (minimum)
temperatures range from 30 (12) ∘C in the summer to
9 (-1) ∘C in the winter, and mean annual precipitation typically
∼ 1750 mm, a substantial majority of which falls between
October and April, whereas the summer months are dry (http://www.prismclimate.org). Geologically, the catchment is underlain by
the Bald Rock Pluton, a trondhjemite-tonalite intrusion of mid-late Mesozoic age
(Saucedo and Wagner, 1992). The landscape is close to fully vegetated by
mixed conifer forest that is typical of the mid-elevation Sierra Nevada
(Barbour and Billings, 2000). The notable exception to this is Bald Rock
Dome, which rises precipitously from the Feather River Canyon to form a
broad, smooth, bare bedrock dome to the north of Bald Rock Basin. Although
outside of the study catchment, it hints at the possibility of significant
compositional or structural heterogeneity within the pluton that is imposing
a localised bottom-up restriction on forest growth in some parts of the
landscape (Hahm et al., 2014).
Landscape transience in the Feather River region is driven by a wave of
fluvial incision that is presently propagating up the channel network (Hurst
et al., 2012). The resultant range of erosion rates spans an order of
magnitude, placing fundamental controls on the nature of the hillslopes
(Hurst et al., 2012, 2013a), soils (Yoo et al., 2011; Attal et al., 2014;
Gabet et al., 2015) and biosphere (Milodowski et al., 2015). Rates of
erosion in the inner canyon, driven by fluvial incision along the main-stem
Feather River, reach ∼ 250 mm kyr-1 (Riebe et al., 2000;
Hurst et al., 2012). Bald Rock Basin has not fully adjusted to this elevated
rate of fluvial incision, with a prominent topographic knickpoint marking
the transition to lower relief topography that is eroding much more slowly
at 30–40 mm kyr-1 (Riebe et al., 2000; Hurst et al., 2012).
Moving across this gradient in erosion rates, hillslope form changes from
being low-gradient and convex to steep and planar in the rejuvenated parts
of the landscape below the knickpoint (Hurst et al., 2012), consistent with
the expectations of models of non-linear, diffusion-like sediment transport
(Roering et al., 1999). Within Bald Rock Basin itself, Yoo et al. (2011)
investigated changes in substrate characteristics between a series of
transects across this transition, indicating that the increase in erosion
rate drives a reduction in the residence time of material within the
weathering zone, highlighted by a decrease in the extent of weathering of
both the soil and saprolite. Consistent with these observations, a more
detailed inventory of soil grain size distributions from soil pits
throughout Bald Rock Basin indicate a marked increase in the coarser grain
fraction in more rapidly eroding parts of the basin (Attal et al., 2014). We
use the surface roughness algorithm introduced above to expand on this
earlier work and further characterise changes in the bedrock exposure across
the geomorphic transition.
Harrington Creek, Idaho
The Harrington Creek catchment drains into Main Salmon River, around 40 km
SSW of the Bitterroot Mountains, Idaho (Fig. 1d). The regional climate is
continental, with maximum (minimum) temperatures ranging from
26.2 (6.2) ∘C in the summer to 0.0 (-10.8) ∘C in the
winter, whereas precipitation is more evenly distributed throughout the
year, with mean annual precipitation typically ∼ 630 mm
(http://www.prismclimate.org). Vegetation in the catchment
comprises coniferous forest with variable canopy cover (Barbour and
Billings, 2000). The catchment is underlain by plutonic rocks related to the
Idaho Batholith, with small inclusions of Eocene dykes of rhyolitic-dacitic
composition (Lewis and Stanford, 2002). Analysis of fission tracks in
apatite and zircon grains from the Idaho Batholith suggest that exhumation
rates have varied from 0.03–0.1 mm yr-1 between 50–10 Ma to 0.32 ±0.10 mm yr-1 from 10 Ma-present,
associated with canyon-forming fluvial
incision along the Salmon River (Sweetkind and Blackwell, 1989; Ferrier et
al., 2012). Point measurements of regolith production rates, based on
cosmogenic 10Be concentrations, suggest erosion rates integrated over
103–104 years of up to 0.12 mm yr-1 (Ferrier et al.,
2012). Associated with this fluvial incision are a series of knickpoints
that are propagating up the tributaries of the Salmon River, including
Harrington Creek, which mark the transition from a slowly eroding, relict
landscape to steep, rapidly eroding, rejuvenated topography that is actively
adjusting to the elevated incision rates below the fluvial knickpoint (Wood,
2013). The Harrington Creek region has been subject to significantly less
research relative to Bald Rock Basin; we use the same methods for this site
to investigate changes in the geomorphic characteristics of the hillslopes
across this transition.
Topographic analysis
Changing bedrock exposure across the knickzones was mapped utilising the
surface roughness method as described in Sect. 2, using a circular
neighbourhood with a radius of 3 m, which was shown to perform well, with
limited false positives, in our previous validation (Sect. 3). Topographic
gradient was also measured using the slope of the best fitting six term
polynomial surface, defined by a least squares regression to a circular
neighbourhood with 7 m radius (e.g. Hurst et al., 2012). In order to map
changes in hillslope characteristics along the length of the trunk channel,
we use longitudinal swath profiles, following a similar approach to the
implementation of the generalised swath profile algorithm described by
Hergarten et al. (2014), to map each point on the hillslope to the nearest
location in the channel network. This method allows frequently used swath
profile analysis to be undertaken using curvilinear features, such as river
channels, as the baseline rather than requiring linear features. The trunk
channels themselves were defined using the DrEICH algorithm (Clubb et al.,
2014), which searches for the upstream limit of the topographic signature of
fluvial incision to define the fluvial network within the channelised
domain. To first order, the longitudinal swath profiles should link
hillslopes to the section of channel that sets their lower boundary
condition, enabling us to link geomorphic changes in fluvial incision.
Results
In both Bald Rock Basin (Figs. 9 and 10) and Harrington Creek (Figs. 11 and 12),
there are clearly distinct, contrasting topographic domains
separated by major knickpoints. Moving across this transition, hillslope
morphology changes from low gradient, convex hillslopes (modal gradients
above principal knickpoints are ∼ 0.5 and ∼ 0.4
within the headwaters of Bald Rock Basin and Harrington Creek respectively),
to steep, planar hillslopes downstream of the knickpoints: respective modal
gradients are ∼ 0.9 and ∼ 0.8. However, in
addition to the changes in the hillslope profile across this transition
there are concomitant textural changes to the hillslopes pertaining to the
widespread emergence of bedrock. In both landscapes, the low gradient
headwaters are also characterised by smooth topography indicative of a
continuous soil mantle: within Bald Rock Basin, 1.5 % of hillslope pixels
have S3 > 0.010; < 1 % have S3 > 0.015; within Harrington Creek, 3 % have S3 > 0.010;
1.5 % have S3 > 0.015. In contrast, in the rejuvenated
parts of the landscape, the increased dominance of bedrock is indicated by
elevated topographic roughness: in the lower reaches of Bald Rock Basin
15 % of hillslope pixels have S3 > 0.010; 7 % have
S3 > 0.015, while in the equivalent parts of the Harrington
Creek drainage, 29 % have S3 > 0.010; 19 % have S3 > 0.015.
Critically, the emergence of bedrock is not uniform
across the steeper parts of the landscape. Rather, the steep hillslopes
present a rugged patchwork of bedrock outcrops and discontinuous soil cover.
Likewise, across the upper part of Bald Rock Basin, there are a number of
isolated patches of elevated roughness that can be picked out from the
prevailing smooth terrain (Fig. 9). Field Inspection of these selected
“rough spots” indicated that they corresponded to isolated rock outcrops,
whereas instances of tree throw mounds, which could also generate roughness
at short wavelengths, were comparatively rare.
Maps displaying (a) topographic slope, and (b)S3 for
Bald Rock Basin, Californian Sierra Nevada. The Middle Fork Feather River is
located in the NE corner of each map, flowing from NW to SE.
Changes in topographic characteristics along a
longitudinal swath centred on the trunk channel draining Bald Rock Basin:
(a) surface roughness, S3; (b) topographic gradient; (c) the
longitudinal channel profile. The principal knickpoint has been highlighted,
with the inset histograms summarising the distributions of the topographic
metrics above and below. Upstream of the major knickpoint, smaller
deviations from the typical graded profile indicate a series of smaller
knickpoints. The swath has a half width of 250 m, and has been binned into
50 m intervals. In plates (a) and (b), the median has been plotted with the
shaded intervals bounded by the 25–75th quantiles and
2.5–97.5th quantiles. S3 was calculated using a 3 m radius
neighbourhood window.
Discussion
In both Bald Rock Basin and Harrington Creek, topographic knickpoints mark
the domain transitions between a slowly eroding “relict” landscape, and
rejuvenated topography responding to elevated rates of fluvial incision
(Hurst et al., 2012, 2013a; Wood, 2013). Both landscapes exhibit similar
hillslope responses to this geomorphic forcing. In this contribution we have
deployed our new roughness algorithm to quantify the dynamics of the soil to
bedrock transition. Specifically, in both landscapes the transition from
soil-mantled to bedrock hillslopes is gradual and patchy. Furthermore, the
steep hillslopes do not appear to be completely stripped of soil; the
persistence of topographically smooth areas that manage to sustain a forest
canopy (Milodowski et al., 2015) indicates that patchy soil cover persists
at high erosion rates. In the Feather River Region, aboveground biomass
hosted by the hillslopes has been shown to decrease with increasing erosion
rates (Milodowski et al., 2015), but biogenic soil production is still able
to keep pace with elevated rates of erosion to maintain a partial soil
mantle. This is in agreement with observations from soil depth transects
within the basin that show little difference in soil depths measured above
the knickpoint, ranging from 40–80 cm, to those measured below the
knickpoint, which ranged from 30–60 cm (Yoo et al., 2011).
The nature if the soil-bedrock transition observed at these two sites aligns
closely with the observations from the San Gabriel Mountains in California
(DiBiase et al., 2012). A gradual, patchy transition is significant because
it is at odds with the expectations from widely used models of soil
production, in which the rate of production decays exponentially with depth
from a maximum production rate for a bare bedrock surface (e.g. Heimsath et
al., 1997), which in this framework represents a threshold erosion rate
defining a sharp transition from soil-mantled to bedrock topography. The
patchy transition observed may be driven in part by structural or
compositional controls on the rate at which bedrock breaks down to form
mobile regolith, but can also be rationalised by models of soil production
that consider the processes driving soil production and sediment transport
as occurring in discrete events (Strudley et al., 2006a, b; Gabet and
Mudd, 2010). Understanding whether these patches are stationary in time or
dynamic is important in understanding the longer term evolution of steep
landscapes and how this evolution is shaped by the coupling of geomorphic
and ecological processes. Finally, while clearly important from a hillslope
perspective, there are broader implications for landscape evolution: the
dynamics of sediment transport in bedrock landscapes are very different to
those in soil-mantled landscapes (e.g. Binnie et al., 2007; Dietrich et al.,
2003), impacting on the calibre (Attal et al., 2015; Whittaker et al., 2010)
and temporal variability (Hovius et al., 2000) of sediment supplied to the
channel network; therefore the nature of the soil-bedrock transition impacts
on the nature of hillslope-channel coupling, modulating the fluvial response
to changes in base level.
Maps displaying (a) topographic slope, and (b)S3,
for a sub-catchment of Harrington Creek, Idaho. S3 was
calculated using a 3 m radius neighbourhood window.
Changes in topographic characteristics along a
longitudinal swath centred on the trunk channel draining the principal
tributary to Harrington Creek: (a) surface roughness, S3;
(b) topographic gradient; (c) the longitudinal channel profile. The principal
knickpoint has been highlighted, with the inset histograms summarising the
distributions of the topographic metrics above and below. Upstream of the
major knickpoint, smaller deviations from the typical graded profile
indicate a series of smaller knickpoints. The swath has a half width of 350 m,
and has been binned into 50 m intervals. In plates (a) and (b), the
median has been plotted along with the shaded intervals bounded by the
25–75th quantiles and 2.5–97.5th quantiles.
Overall discussion and conclusions
The structure of topographic relief is controlled by different processes
operating at different spatial scales (Perron et al., 2008): at wavelengths
greater than ∼ 100 m, topography is dominated by the spacing
of ridges and valleys (Perron et al., 2008, 2009); at the sub-hillslope
length-scale, other processes generate detectable topographic signatures
(e.g. McKean and Roering, 2004; Roering et al., 2010). Booth et al. (2009)
exploited spectral analysis to show that areas affected by deep-seated
landslides exhibit significantly greater power at intermediate wavelengths
(∼ 11–50 m), enabling the objective classification of regions
in which deep-seated landslides were prevalent. At shorter length-scales,
Roering et al. (2010) suggested that roughness generated at small
length-scales (< 7.5 m) in the Oregon Coast Ranges could be
attributed to the presence of tree throw mounds; similar analysis of
topographic profiles extracted from contrasting catchments in the same
setting found a lack of spectral power at these short wavelengths for
resistant bedrock hillslopes in comparison to soil-mantled hillslopes,
attributed to a diminished biotic contribution to weathering (Marshall and
Roering, 2014).
We propose that short wavelength surface roughness, quantified using the
same roughness algorithms introduced by McKean and Roering (2004) can be
used to make inferences about hillslope characteristics specifically
pertaining to the exposure of bedrock. Comparison against rock exposure
measured independently and objectively from high-resolution orthophotographs
from multiple landscapes suggests that the emergence of bedrock in
hillslopes produces a detectable topographic signature that distinguishes it
from hillslopes that have a continuous soil mantle. We applied this
technique to forested landscapes in California and Idaho, highlighting the
ability of LiDAR surveys to resolve high-resolution features of the
topography through canopy. For obvious reasons validation is simpler in
un-vegetated terrain but prior to the introduction of below-canopy UAVs for
data collection, we suggest our method is adequate for use in vegetated
terrain. Users should validate using field observations to avoid false
positives from, for example, tree throw mounds. Thus we propose surface
roughness as a new method for mapping rock exposure from LiDAR data that
complements previously published metrics (DiBiase et al., 2012), and is
likely to be of particular benefit in landscapes in which rock outcrops are
present at topographic gradients lower than the angle of repose.
We caveat this finding with the statement that rock exposure is not the only
mechanism of generating topographic roughness at short length-scales; for
example, gullying and slumping provide two mechanisms by which the smooth
parabolic morphology associated with ideal, diffusive soil-mantled
hillslopes may be modified (Tarolli and Dalla Fontana, 2009); likewise
small-scale features associated with deep-seated landslides, such as folds
and scarps, generate a roughness signal at similar length-scales to rock
outcrop (McKean and Roering, 2004; Tarolli et al., 2010). In addition, while
many soil-mantled sediment transport processes act to diffuse topography,
they typically do so through discrete events (e.g. tree throw) (Furbish et
al., 2009; Gabet and Mudd, 2010), and while the fingerprint that these
individual events leave on the landscape is transient, they provide a
potentially important roughness signature at the relevant length-scale for
that mode of disturbance (Roering et al., 2010). An additional factor to
consider is that bedrock morphology is itself variable, and therefore
certain mechanisms of generating rock exposure may not generate significant
roughness; this would be exemplified by, for example, low gradient,
glacially polished surfaces, or by massive granitoid bedrock with very low
fracture density in which jointing is restricted to approximately surface
parallel exfoliation planes. Consequently, interpretation of surface
roughness metrics should critically take into account the presence of other
geomorphic processes that are potentially operating within the landscape and
the characteristics of the bedrock itself. Indeed, this principal applies to
the interpretation of any topographic metric obtained from remotely sensed
data; in complex geomorphic settings, isolation of specific hillslope
characteristics from a single textural attributes may be impossible at the
data resolution presently available from airborne surveys; ultimately a
combination of metrics, covering a broader range of morphological
characteristics may well be necessary.
The characterisation of hillslopes is of importance across a diverse range
of surface processes research, providing a better understanding of controls
on hydrological flow routing, sediment production and transport processes
and ecosystem development. The utility of topographic data to aid this
endeavour is strongly dependent on the resolution of these data sets. In the
case of hillslope characteristics, such as rock exposure, roughness is
expressed at the metre scale; using 1 m resolution digital elevation models, it is possible to
examine variations in hillslope form at sufficient levels of detail that it
is possible to distinguish between soil and bedrock hillslopes; this
information is rapidly lost as the data resolution is coarsened (DiBiase et
al., 2012). However these shorter length scales are particularly susceptible
to noise in the data set (Albani et al., 2004; Sofia et al., 2013). This
highlights the requirement for high quality, high resolution, which permit
accurate classification of vegetation and ground returns prior to surface
creation. LiDAR surveys with higher shot spacing are therefore likely to
provide a disproportionately greater level of detail on hillslope
characteristics (Brodu and Lague, 2012), and this should be taken into
account when planning airborne surveys. In particular, the continued
development of unmanned aerial vehicles (UAVs) as a platform for airborne
LiDAR collection will increasingly make higher resolution surveys accessible
to the research community (e.g. Lin et al., 2011).
Finally, from our analysis of the geomorphic changes associated with
changing rates of erosion in two different landscapes reveals a number of
significant conclusions regarding the nature of the soil-bedrock transition.
In both cases, the transition from soil-mantled hillslopes to bedrock
dominated hillslopes is clearly gradual, with areas of patchy soil coverage
persistent on steep, rapidly eroding hillslopes. A “patchy” transition
from soil-mantled to bedrock hillslopes challenges prevailing modelling
approaches towards soil production, but is in agreement with conclusions
from previous studies of soil production in rapidly eroding landscapes –
the European Alps (Norton et al., 2008), San Gabriel Mountains, California
(Heimsath et al., 2012) and Southern Alps, New Zealand (Larsen et al., 2014)
– each of which observe the coexistence of soil and bedrock on rapidly
eroding hillslopes. This has been attributed in part to efficient biogenic
soil production (Larsen et al., 2014), which facilitates the rapid
generation and stabilisation of soil between landslide events, and
lithological susceptibility to weathering processes (Norton et al., 2008).
The hypothesis of a biogenically mediated soil-bedrock transition is
supported by the observation in these landscapes that patchy vegetation
cover persists on the steeper hillslopes where trees have maintained a
foothold, and is in agreement with expectations from numerical modelling of
soil production by discrete events (Gabet and Mudd, 2010). Capturing the
salient aspects of these models within larger-scale landscape evolution
models represents a key challenge in simulating the evolution of
mixed-bedrock landscapes that are typical of many upland settings.
Software availability
We have made our bedrock detection software available through the community
sediment dynamics modelling system (CSDMS) website; source code may be
downloaded at http://csdms.colorado.edu/wiki/Model:SurfaceRoughness.
The Supplement related to this article is available online at doi:10.5194/esurf-3-483-2015-supplement.
D. T. Milodowski and S. M. Mudd the algorithms and wrote the code. D. T. Milodowski, S. M. Mudd and E. T. A. Mitchard
performed the analysis and wrote the paper.
Acknowledgements
This research was funded by a NERC studentship (NERC DTG NE/152830X/1 and
NE/J500021/1; DTM), in addition to the Harkness Award from the University of
Cambridge (DTM). ETAM is funded by a NERC Fellowship (NE/I021217/1). SMM is
supported by U.S. Army Research Office contract number W911NF-13-1-0478. The
authors would like to thank Emmanuel Gabet, Dimitri Lague, Stuart Grieve,
and Fiona Clubb for valuable discussions that facilitated the development of
this research.
Edited by: J. Willenbring
ReferencesAlbani, M., Klinkenberg, B., Andison, D. W., and Kimmins, J. P.: The choice
of window size in approximating topographic surfaces from Digital Elevation
Models, Int. J. Geogr. Inf. Sci., 18, 577–593,
10.1080/13658810410001701987, 2004.Anderson, R. S.: Modeling the tor-dotted crests, bedrock edges, and
parabolic profiles of high alpine surfaces of the Wind River Range, Wyoming,
Geomorphology, 46, 35–58, 10.1016/S0169-555X(02)00053-3, 2002.Attal, M., Mudd, S. M., Hurst, M. D., Weinman, B., Yoo, K., and Naylor, M.:
Impact of change in erosion rate and landscape steepness on hillslope and
fluvial sediments grain size in the Feather River basin (Sierra Nevada,
California), Earth Surf. Dynam., 3, 201–222, 10.5194/esurf-3-201-2015,
2015.
Barbour, M. G. and Billings, W. D.: North American Terrestrial Vegetation,
edited by: Barbour, M. G. and Billings, W. D., Cambridge University Press,
Cambridge, UK, New York, NY, USA, 2000.Binnie, S. A., Phillips, W. M., Summerfield, M. A., and Fifield, L. K.:
Tectonic uplift, threshold hillslopes, and denudation rates in a developing
mountain range, Geology, 35, 743–746, 10.1130/G23641A.1, 2007.Booth, A. M., Roering, J. J., and Perron, J. T.: Automated landslide mapping
using spectral analysis and high-resolution topographic data: Puget Sound
lowlands, Washington, and Portland Hills, Oregon, Geomorphology, 109,
132–147, 10.1016/j.geomorph.2009.02.027, 2009.Brodu, N. and Lague, D.: 3D terrestrial lidar data classification of complex
natural scenes using a multi-scale dimensionality criterion: Applications in
geomorphology, ISPRS J. Photogramm., 68, 121–134,
10.1016/j.isprsjprs.2012.01.006, 2012.
Carson, M. A. and Kirkby, M. J.: Hillslope form and process, Cambridge
University Press, Cambridge, UK, 1972.Cavalli, M., Tarolli, P., Marchi, L., and Dalla Fontana, G.: The
effectiveness of airborne LiDAR data in the recognition of channel-bed
morphology, CATENA, 73, 249–260, 10.1016/j.catena.2007.11.001, 2008.Chorover, J., Troch, P. A., Rasmussen, C., Brooks, P. D., Pelletier, J. D.,
Breshars, D. D., Huxman, T. E., Kurc, S. A., Lohse, K. A., McIntosh, J. C.,
Meixner, T., Schaap, M. G., Litvak, M. E., Perdrial, J., Harpold, A., and
Durcik, M.: How Water, Carbon, and Energy Drive Critical Zone Evolution: The
Jemez–Santa Catalina Critical Zone Observatory, Vadose Zone J., 10,
884–899, 10.2136/vzj2010.0132, 2011.Clubb, F. J., Mudd, S. M., Milodowski, D. T., Hurst, M. D., and Slater, L.
J.: Objective extraction of channel heads from high-resolution topographic
data, Water Resour. Res., 50, 4283–4304, 10.1002/2013WR015167, 2014.
Colby, J.: Topographic Normalization in Rugged Terrain, Photogramm. Eng.
Rem., 57, 531–537, 1991.
Culling, W.: Soil Creep and the Development of Hillside Slopes, J. Geol.,
71, 127–161, 1963.
Culling, W. E. H.: Theory of Erosion on Soil-Covered Slopes, J. Geol.,
73, 230–254, 1965.DiBiase, R. A., Heimsath, A. M., and Whipple, K. X.: Hillslope response to
tectonic forcing in threshold landscapes, Earth Surf. Proc. Land.,
37, 855–865, 10.1002/esp.3205, 2012.DiBiase, R. A. and Lamb, M. P.: Vegetation and wildfire controls on sediment
yield in bedrock landscapes, Geophys. Res. Lett., 40, 1093–1097,
10.1002/grl.50277, 2013.
Dietrich, W. E., Bellugi, D. G., Sklar, L. S., Stock, J. D., Heimsath, A. M., and Roering, J. J.: Geomorphic transport laws for predicting landscape form
and dynamics, Geophys. Monogr.-Am. Geophys. UNION, 135, 103–132, 2003.
Evans, I. S.: An integrated system of terrain analysis and slope mapping, Z.
Geomorphol, 36, 274–295, 1980.Evans, J. S. and Hudak, A. T.: A Multiscale Curvature Algorithm for
Classifying Discrete Return LiDAR in Forested Environments, IEEE T. Geosci.
Remote, 45, 1029–1038, doi:10.1109/TGRS.2006.890412, 2007.
Fara, H. D. and Scheidegger, A. E.: An eigenvalue method for the statistical
evaluation of fault plane solutions of earthquakes, B. Seismol. Soc. Am., 53, 811–816, 1963.Ferrier, K. L., Kirchner, J. W., and Finkel, R. C.: Weak influences of
climate and mineral supply rates on chemical erosion rates: measurements
along two altitudinal transects in the Idaho Batholith, J. Geophys.
Res.-Earth, 117, F02026, doi:10.1029/2011JF002231, 2012.Furbish, D. J., Hamner, K. K., Schmeeckle, M., Borosund, M. N., and Mudd, S.
M.: Rain splash of dry sand revealed by high-speed imaging and sticky paper
splash targets, J. Geophys. Res.-Earth, 112, F01001,
10.1029/2006JF000498, 2007.Furbish, D. J., Haff, P. K., Dietrich, W. E., and Heimsath, A. M.:
Statistical description of slope-dependent soil transport and the
diffusion-like coefficient, J. Geophys. Res., 114, F00A05, 10.1029/2009JF001267, 2009.Furbish, D. J. and Roering, J. J.: Sediment disentrainment and the concept of
local vs. nonlocal transport on hillslopes, J. Geophys. Res.-Earth, 118,
937–952, doi:10.1002/jgrf.20071, 2013.Gabet, E. J.: Sediment transport by dry ravel, J. Geophys. Res.-Sol. Ea.,
108, 2049, 10.1029/2001JB001686, 2003.
Gabet, E. J., Reichman, O. J., and Seabloom, E. W.: The effects of
bioturbation on soil processes and sediment transport, Annu. Rev. Earth Pl. Sc., 31, 249–273, 2003.Gabet, E. J. and Mudd, S. M.: Bedrock erosion by root fracture and tree
throw: A coupled biogeomorphic model to explore the humped soil production
function and the persistence of hillslope soils, J. Geophys. Res.,
115, F04005, 10.1029/2009JF001526, 2010.Gabet, E. J., Mudd, S. M., Milodowski, D. T., Yoo, K., Hurst, M. D., and
Dosseto, A.: Local topography and erosion rate control regolith thickness
along a ridgeline in the Sierra Nevada, California, Earth Surf. Proc. Land., 40, 1779–1790, 10.1002/esp.3754, 2015.
Gilbert, G.: The convexity of hilltops, J. Geol., 17, 344–350, 1909.Goodfellow, B. W., Chadwick, O. A., and Hilley, G. E.: Depth and character of
rock weathering across a basaltic-hosted climosequence on Hawai'i, Earth
Surf. Proc. Land., 39, 381–398, doi:10.1002/esp.3505, 2014a.Goodfellow, B. W., Skelton, A., Martel, S. J., Stroeven, A. P.,
Jansson, K. N., and Hättestrand, C.: Controls of tor formation, Cairngorm
Mountains, Scotland, J. Geophys. Res.-Earth., 119, 2013JF002862,
doi:10.1002/2013JF002862, 2014b.Graham, R., Rossi, A., and Hubbert, R.: Rock to regolith conversion:
producing hospitable substrates for terrestrial ecosystems, GSA
Today, 20, 4–9, doi:10.1130/GSAT57A.1, 2010.Hahm, W. J., Riebe, C. S., Lukens, C. E. and Araki, S.: Bedrock composition
regulates mountain ecosystems and landscape evolution, P. Natl. Acad. Sci. USA, 111,
3338–3343, 10.1073/pnas.1315667111, 2014.Hale, S. R. and Rock, B. N.: Impact of topographic normalization on
land-cover classification accuracy, Photogramm. Eng. Rem. S., 69, 785–791,
doi:10.14358/PERS.69.7.785, 2003.Heimsath, A., Dietrich, W., Nishiizumi, K., and Finkel, R.: The soil
production function and landscape equilibrium, Nature, 388, 358–361,
10.1038/41056, 1997.Heimsath, A. M., DiBiase, R. A., and Whipple, K. X.: Soil production limits
and the transition to bedrock-dominated landscapes, Nat. Geosci., 5,
210–214, 10.1038/ngeo1380, 2012.Hergarten, S., Robl, J., and Stüwe, K.: Extracting topographic swath profiles
across curved geomorphic features, Earth Surf. Dynam., 2, 97–104, 10.5194/esurf-2-97-2014, 2014.
Hovius, N., Stark, C. P., Hao-Tsu, C., and
Jiun-Chuan, L.: Supply and removal of sediment in a landslide-dominated
mountain belt: Central Range, Taiwan, J. Geol., 108, 73–89, 2000.Hurst, M. D., Mudd, S. M., Walcott, R., Attal, M., and Yoo, K.: Using hilltop
curvature to derive the spatial distribution of erosion rates, J. Geophys.
Res.-Earth, 117, F02017, 10.1029/2011JF002057, 2012.Hurst, M. D., Mudd, S. M., Yoo, K., Attal, M., and Walcott, R.: Influence of
lithology on hillslope morphology and response to tectonic forcing in the
northern Sierra Nevada of California, J. Geophys. Res.-Earth, 118,
832–851, 10.1002/jgrf.20049, 2013a.Hurst, M. D., Mudd, S. M., Attal, M., and Hilley, G.: Hillslopes Record the
Growth and Decay of Landscapes, Science, 341, 868–871,
10.1126/science.1241791, 2013b.Lague, D., Brodu, N., and Leroux, J.: Accurate 3D comparison of complex
topography with terrestrial laser scanner: Application to the Rangitikei
canyon (N-Z), ISPRS J. Photogramm., 82, 10–26,
10.1016/j.isprsjprs.2013.04.009, 2013.Larsen, I. J., Almond, P. C., Eger, A., Stone, J. O., Montgomery, D. R., and
Malcolm, B.: Rapid Soil Production and Weathering in the Western Alps, New
Zealand, Science, 343, 637–640, 10.1126/science.1244908, 2014.Lashermes, B., Foufoula-Georgiou, E., and Dietrich, W. E.: Channel network
extraction from high resolution topography using wavelets, Geophys. Res.
Lett., 34, L23S04, 10.1029/2007GL031140, 2007.Lewis, R. S. and Stanford, L. R.: Geologic map compilation of the western
half of the Nez Perce Pass 30 × 60 min
quadrangle, Idaho Geological Survey, Idaho, USA, 2002.Lin, Y., Hyyppa, J., and Jaakkola, A.: Mini-UAV-Borne LIDAR for Fine-Scale
Mapping, IEEE Geosci. Remote S., 8, 426–430, doi:10.1109/LGRS.2010.2079913, 2011.Lin, C.-W., Tseng, C.-M., Tseng, Y.-H., Fei, L.-Y., Hsieh, Y.-C., and
Tarolli, P.: Recognition of large scale deep-seated landslides in forest
areas of Taiwan using high resolution topography, J. Asian Earth Sci., 62,
389–400, 10.1016/j.jseaes.2012.10.022, 2013.Marshall, J. A. and Roering, J. J.: Diagenetic variation in the Oregon Coast
Range: Implications for rock strength, soil production, hillslope form, and
landscape evolution, J. Geophys. Res.-Earth, 119, 1395–1417,
10.1002/2013JF003004, 2014.McKean, J. A., Dietrich, W. E., Finkel, R. C., Southon, J. R., and Caffee, M.
W.: Quantification of soil production and downslope creep rates from
cosmogenic 10Be accumulations on a hillslope profile, Geology, 21,
343–346, 10.1130/0091-7613(1993)021<0343:QOSPAD>2.3.CO;2, 1993.McKean, J. and Roering, J.: Objective landslide detection and surface
morphology mapping using high-resolution airborne laser altimetry,
Geomorphology, 57, 331–351, 10.1016/S0169-555X(03)00164-8, 2004.
Migon, P.: Granite Landscapes of the World, Oxford University Press,
Oxford, UK, 2006.Milodowski, D. T., Mudd, S. M., and Mitchard, E. T. A.: Erosion rates as a
potential bottom-up control of forest structural characteristics in the
Sierra Nevada Mountains, Ecology, 96, 31–38, 10.1890/14-0649.1,
2015.Moody, J. A. and Martin, D. A.: Initial hydrologic and geomorphic response
following a wildfire in the Colorado Front Range, Earth Surf. Proc. Land., 26, 1049–1070, 10.1002/esp.253, 2001.Norton, K. P., von Blanckenburg, F., Schlunegger, F., Schwab, M., and Kubik,
P. W.: Cosmogenic nuclide-based investigation of spatial erosion and
hillslope channel coupling in the transient foreland of the Swiss Alps,
Geomorphology, 95, 474–486, 10.1016/j.geomorph.2007.07.013, 2008.
Passalacqua, P., Trung, T. D., Foufoula-Georgiou, E., Sapiro, G., and
Dietrich, W. E.: A geometric framework for channel network extraction from
lidar: Nonlinear diffusion and geodesic paths, J. Geophys. Res., 115, F01002, doi:201010.1029/2009JF001254, 2010.Pelletier, J. D.: A robust, two-parameter method for the extraction of
drainage networks from high-resolution digital elevation models (DEMs):
Evaluation using synthetic and real-world DEMs, Water Resour. Res., 49,
75–89, 10.1029/2012WR012452, 2013.Pelletier, J. D. and Rasmussen, C.: Quantifying the climatic and tectonic
controls on hillslope steepness and erosion rate, Lithosphere, 1, 73–80,
10.1130/L3.1, 2009.Perron, J. T., Kirchner, J. W., and Dietrich, W. E.: Spectral signatures of
characteristic spatial scales and nonfractal structure in landscapes, J.
Geophys. Res.-Earth, 113, F04003, 10.1029/2007JF000866, 2008.Perron, J. T., Kirchner, J. W., and Dietrich, W. E.: Formation of evenly
spaced ridges and valleys, Nature, 460, 502–505,
10.1038/nature08174, 2009.Phillips, J. D. and Marion, D. A.: Pedological memory in forest soil
development, Forest Ecol. Manag., 188, 363–380,
10.1016/j.foreco.2003.08.007, 2004.Pirotti, F. and Tarolli, P.: Suitability of LiDAR point density and derived
landform curvature maps for channel network extraction, Hydrol. Process.,
24, 1187–1197, 10.1002/hyp.7582, 2010.
Riebe, C. S., Kirchner, J. W., Granger, D. E., and Finkel, R. C.: Erosional
equilibrium and disequilibrium in the Sierra Nevada, inferred from
cosmogenic 26Al and 10Be in alluvial sediment, Geology, 28, 803–806,
2000.Roering, J. J., Kirchner, J. W., and Dietrich, W. E.: Evidence for nonlinear,
diffusive sediment transport on hillslopes and implications for landscape
morphology, Water Resour. Res., 35, 853–870, 10.1029/1998WR900090,
1999.Roering, J. J., Marshall, J., Booth, A. M., Mort, M., and Jin, Q.: Evidence
for biotic controls on topography and soil production, Earth Planet. Sc.
Lett., 298, 183–190, 10.1016/j.epsl.2010.07.040, 2010.Ruleman, C. A., Bohannon, R. G., Bryant, B., Shroba, R. R., and Premo, W. R.:
Geologic Map of the Bailey 30′× 60′
Quadrangle, North-Central Colorado, US Geological Survey, Denver, Colorado, USA, 2011.
Saucedo, G. J. and Wagner, D. L.: Geologic Map of the Chico
Quadrangle, California Department of Conservation, Division of Mines and
Geology, Sacramento, California, USA, 1992.Sheffer, E., von Hardenberg, J., Yizhaq, H., Shachak, M., and Meron, E.:
Emerged or imposed: a theory on the role of physical templates and
self-organisation for vegetation patchiness, Ecol. Lett., 16, 127–139,
10.1111/ele.12027, 2013.Smith, T. B., Wayne, R. K., Girman, D. J., and Bruford, M. W.: A Role for
Ecotones in Generating Rainforest Biodiversity, Science, 276,
1855–1857, 10.1126/science.276.5320.1855, 1997.Sofia, G., Tarolli, P., Cazorzi, F., and Dalla Fontana, G.: An objective approach
for feature extraction: distribution analysis and statistical descriptors for
scale choice and channel network identification, Hydrol. Earth Syst. Sci., 15,
1387–1402, 10.5194/hess-15-1387-2011, 2011.Sofia, G., Pirotti, F., and Tarolli, P.: Variations in multiscale curvature
distribution and signatures of LiDAR DTM errors, Earth Surf. Proc. Land., 38, 1116–1134, 10.1002/esp.3363, 2013.Sofia, G., Fontana, G. D., and Tarolli, P.: High-resolution topography and
anthropogenic feature extraction: testing geomorphometric parameters in
floodplains, Hydrol. Process., 28, 2046–2061, 10.1002/hyp.9727,
2014.Strudley, M. W., Murray, A. B., and Haff, P. K.: Emergence of pediments,
tors, and piedmont junctions from a bedrock weathering–regolith thickness
feedback, Geology, 34, 805–808, 10.1130/G22482.1, 2006a.Strudley, M. W., Murray, A. B., and Haff, P. K.: Regolith thickness
instability and the formation of tors in arid environments, J. Geophys. Res.-Earth, 111, F03010, 10.1029/2005JF000405, 2006b.Sweetkind, D. S. and Blackwell, D. D.: Fission-track evidence of the
Cenozoic thermal history of the Idaho batholith, Tectonophysics, 157,
241–250, 10.1016/0040-1951(89)90142-X, 1989.Tarolli, P. and Dalla Fontana, G.: Hillslope-to-valley transition
morphology: New opportunities from high resolution DTMs, Geomorphology,
113, 47–56, 10.1016/j.geomorph.2009.02.006, 2009.Tarolli, P., Sofia, G., and Fontana, G. D.: Geomorphic features extraction
from high-resolution topography: landslide crowns and bank erosion, Nat.
Hazards, 61, 65–83, 10.1007/s11069-010-9695-2, 2010.
Teillet, P. M., Guindon, B., and Goodenough, D. G.: On the slope-aspect correction of
multispectral scanner data, Can. J. Remote Sens., 8, 84–106, 1982.Todd, V. R., Alvarez, R. M., and Techni Graphic Systems, Inc.: Preliminary
geologic map of the El Cajon 30′× 60′ quadrangle, southern California,
US Geological Survey, Menlo Park, California, USA, 2004.
Watson, G. S.: Statistics of orientation data, J. Geol., 74, 786–797, 1966.Whelley, P. L., Glaze, L. S., Calder, E. S., and Harding, D. J.:
LiDAR-Derived Surface Roughness Texture Mapping: Application to Mount St.
Helens Pumice Plain Deposit Analysis, IEEE T. Geosci. Remote,
52, 426–438, 10.1109/TGRS.2013.2241443, 2014.Whittaker, A. C., Attal, M., and Allenn, P. A.: Characterising the origin,
nature and fate of sediment exported from catchments perturbed by active
tectonics, Basin Res., 22, 809–828,
10.1111/j.1365-2117.2009.00447.x, 2010.Wilkinson, M. T., Chappell, J., Humphreys, G. S., Fifield, K., Smith, B., and
Hesse, P.: Soil production in heath and forest, Blue Mountains, Australia:
influence of lithology and palaeoclimate, Earth Surf. Proc. Land.,
30, 923–934, 10.1002/esp.1254, 2005.Woodcock, N. H.: Specification of Fabric Shapes Using an Eigenvalue Method,
Geol. Soc. Am. Bull., 88, 1231–1236,
10.1130/0016-7606(1977)88<1231:SOFSUA>2.0.CO;2,
1977.Wood, R.: Transient hillslope response to an incision wave sweeping up
a watershed: a case study from the Salmon River, Masters Theses, available
at: http://scholarworks.sjsu.edu/etd_theses/4322 (last access: 14 October 2015), 2013.
Wu, T. F., Lin, C. J., and Weng, R. C.: Probability estimates for multi-class
classification by pairwise coupling, J. Mach. Learn. Res., 5, 975–1005, 2004.Yoo, K., Amundson, R., Heimsath, A. M., and Dietrich, W. E.: Process-based
model linking pocket gopher (Thomomys bottae) activity to sediment transport
and soil thickness, Geology, 33, 917–920, 10.1130/G21831.1, 2005.
Yoo, K., Weinman, B., Mudd, S. M., Hurst, M., Attal, M., and Maher, K.:
Evolution of hillslope soils: The geomorphic theater and the geochemical
play, Appl. Geochem., 26, S149–S153, 2011.