Introduction
Landscapes are shaped by competition between crustal processes such as
tectonic plate motion or dynamic topography and deposition or erosion at the
Earth's surface. This competition, if unperturbed, tends toward a topographic
steady state at which vertical motions are counterbalanced by erosion
e.g.. In unglaciated landscapes, the main
driver of erosion is the river system , which incises the
landscape to remove and transport material from uplands to active basins. The
analysis of river long profiles has been a key method to interpret landscape
evolution e.g., from the early recognition
of graded rivers e.g. to the generalised
recognition that river profiles reflect varying erosion processes
e.g..
In a river system, topographic steady state requires spatially stable rock
uplift and climatic conditions over a long period of time
. In most landscapes, however, these conditions are
unlikely . Many processes have been
suggested to result in both spatial and temporal variations in uplift rate,
such as varying tectonic stress e.g., complex mantle
processes inducing vertical motions e.g.,
uplift driven by differential rock density and base-level
variations linked to eustatic variations
e.g.. River
systems affected by these processes respond by transmitting signals upstream
through the channel network
e.g., eventually driving
drainage network reorganisation and resulting in additional transient signals
e.g..
Moreover, river profiles are also affected by intrinsic landscape properties,
such as fracture density e.g or differential lithology
e.g., which can also lead to morphological
adjustment of the channel e.g.. The most direct and
widely observed expression of river adjustment to transient or intrinsic
perturbations is a discrete change in river gradient, commonly referred to as a
“knickpoint”.
Changes in channel gradient linked to different lithologies have been
recognised in geomorphological studies for centuries.
suggested that these changes may represent “successive reaches” with
different base levels, hypothesising that these reaches somehow migrate
upstream. recognised the tectonic genesis of some of these
signals, describing how landscapes experience erosion cycles with periods of
“rejuvenation” followed by periods of gradual adjustment and thus
transience. However, these early studies did not name such morphologies as
distinct entities. The term knickpoint was first introduced into the
geomorphological literature by , borrowing the word from
chemical sciences to “denote an abrupt change in direction from a gentle
concave curve to a curve that is convex upward” (p. 636).
Based on earlier observations on the topography and geology of the
Appalachians e.g.,
described a knickpoint as a migrating steepened boundary between two river
reaches. She went on to state that the downstream reach should flow with a
gradient determined by the present-day balance between uplift and erosion,
and the upstream reach should flow with a gradient representing an older such
balance. The recognition of knickpoints and their significance in transient
landscapes has driven much research into interpreting topography
e.g., as
well as using river profiles to extract past uplift histories
e.g..
The diverse nature of knickpoint formation means that these features have
been used to investigate many geomorphological problems. For example, retreat
rates have been used to link knickpoints with tectonic events and faulting
e.g. or climatically triggered
base-level fall e.g.. Although
migrating knickpoints are commonly associated with base-level variations,
highlighted the role of differential lithologies in the retreat
rates of vertical knickpoints within tectonically and climatically stable
landscapes. Furthermore, and
noted the importance of sediment supply and hydraulic conditions in waterfall
retreat, providing a quantitative interpretation of the early observations of
on waterfall migration. observed an
important correlation between knickpoint retreat and bedload transport,
further highlighting the importance of sediment transport.
demonstrated that considering the role of resistant lithologies is crucial
when studying landscape evolution, as they can considerably slow down
landscape response time to transient signals. Other studies have linked
knickpoints directly to landscape characteristics such as heterogeneous
lithology e.g.. Recent
analogue experiments on knickpoint retreat e.g. have
highlighted the interconnectivity of all these processes and the need to
consider both internal and external landscape characteristics.
These examples demonstrate the importance but also the diversity of transient
and lithologic signals in landscapes and highlight the fact that different processes
can generate remarkably similar channel morphology. It is therefore crucial
to define knickpoints morphologically before drawing interpretations about
their significance in terms of processes or genesis. In this contribution, we
aim to provide a method for reproducibly and systematically extracting
knickpoints within real landscapes based on river profile morphology.
Knickpoint morphology and detection
Morphological description
Knickpoints can be defined as discrete changes in river gradient
. proposed two endmember knickpoints:
break-in-slope knickpoints expressed by an abrupt change in river gradient
and break-in-elevation knickpoints characterised by a step in the elevation, such as
a waterfall, with similar gradients on both sides of the knickpoint. These
knickpoints are now commonly referred to as slope-break knickpoints and
vertical-step knickpoints e.g..
suggest that although vertical-step knickpoints tend to be
linked to discrete heterogeneities along the river profile (e.g. caused by
geological boundaries), both morphologies can either be fixed or mobile and
each style of knickpoint may be generated by a range of processes.
As discussed in and , both morphologies
can be detected using a slope–area plot (Fig. ) or a
slope–distance plot. It has long been observed that channel gradients vary
systematically as a function of drainage area. For example,
stated the following: “In general we may say that,
ceteris paribus, declivity bears an inverse relation to quantity of
water” (p. 114). How do we then find anomalous channel gradients? In the
mid-twentieth century, authors such as and
found systematic, quantitative
relationships between channel gradient and drainage area that are often used as a
proxy for discharge. and later
recognised that channel gradients often declined
systematically downstream in a trend that could be described by a power law:
S=ksA-θ,
where θ is referred to as the concavity index since it describes how
concave a profile is: the higher the value, the more rapidly a channel's
gradient decreases downstream. The term ks is called the
steepness index, as it sets the overall gradient of the channel, and a number
of authors have noted that ks frequently scales with erosion rate
in lithologically homogeneous landscapes
e.g.. A knickpoint might manifest itself
as an abrupt change in slope–area scaling and lead to local variations in
ks (Fig. a).
Different methods to detect knickpoints. (a) Cartoon
showing how vertical-step and slope-break knickpoints appear in slope–area
plots; adapted from . (b) A slope–area plot
derived from SRTM 30 m resolution data in Romania; the catchment's outlet
coordinates are 45.252842, 26.375697 (WGS84). Different colours represent
different tributaries, small “+” symbols are individual data points and
circles are logarithmically binned data. A single slope-break knickpoint can
be interpreted but minor knickpoints are more difficult to extract.
(c) The same basin represented in a χ-elevation plot using
θ=0.15.
![]()
However, using slope–area data derived from digital elevation models (DEMs)
suffers from noise in channel slopes, leading to scattering of gradient data,
as discussed in . proposed
methods to reduce the effect of noise and extract trends from slope–area
plots. These recommendations include regular sampling of elevations to
extrapolate artefact-free contour lines or logarithmic binning by drainage
area. Smoothing induces inexorable data loss and may result in difficulties
detecting subtle but important features such as knickpoints
(Fig. b).
Alternatively, we can integrate Eq. (), since S=dz/dx where z is elevation and x is distance along the
channel e.g., resulting in
z(x)=z(xb)+ksA0θ∫xbxA0A(x)θdx,
where A0 is a reference drainage area introduced to non-dimensionalise the
area term within the integral in Eq. ().
We can then define a longitudinal coordinate, χ
:
χ=∫xbxA0A(x)θdx.
χ has dimensions of length and is defined such that at any point in the
channel,
z(x)=z(xb)+ksA0θχ.
The χ approach to represent normalised long profiles
(Eqs. and ) can serve as an
alternative method to explore the slope–area relationship within a drainage
network. The χ coordinate integrates information about drainage area,
while requiring less smoothing and lumping than log(S)–log(A) plots
(Fig. c). This approach has been widely used in recent studies
e.g..
Existing algorithms
Traditional knickpoint identification from DEMs relied upon user-based
selection along river long profiles
e.g.. Several computational
methods have been proposed for extracting knickpoints from DEM-derived
datasets. The first (semi-)automated methods taking advantage of digital
topographic data used long-profile geometry to isolate knickpoints or
knickzones. proposed a semi-automated extraction method
based on decreasing gradient with increasing length. This method involved
the use of ArcGIS and spreadsheet software to process the outputs for each
river. Recognising the need for automated regional knickpoint mapping methods
in geomorphological studies, proposed an
automated algorithm to map abrupt changes in river gradient using slope,
profile and plan-view curvature. used systematic changes
in profile convexity over given thresholds (>20 m in elevation drop
coupled with a slope threshold ≥0.1) to isolate knickpoints in
fluvially dominated channels with the aim of reconstructing rejuvenation
events, both climatically and tectonically driven, in the southern
Appalachians. A similar method has been implemented in ArcGIS by
. More recently, published an ArcGIS
toolset (called KET) that automates and optimises the
method. These methods are based on the direct use of channel elevation,
gradient and curvature, and they are therefore susceptible to the previously described
limitations related to noise. Furthermore, the method
does not incorporate drainage area information, which is an important
parameter to consider when studying knickpoints over large spatial scales or
when interpreting the retreat rates of these features.
Another set of methods exploits the use of ks from
Eq. () (or ksn when calculated using a fixed
value of θ) to extract knickpoints from slope–area plots, as reviewed
by . These methods suffer from limitations linked to
slope–area scattering, noise sensitivity and difficulty in precisely locating
knickpoints because of the stepped nature of drainage area (increasing
instantaneously downstream when a new tributary reaches the river channel).
To ameliorate problems with noise and data scattering,
devised a method that first calculates ksn on channel profiles
smoothed using the algorithm of . This derives
ksn either from the regression of slope–area plots or using the
first-order derivative of χ plots. The method selects a knickpoint for
which
the ratio between downstream and upstream ksn, averaged with
two 2 km long serial windows, exceeds a factor of 2.
developed an algorithm focused on knickzone detection
(KZ-Picker). Knickzones are selected from normalised profiles (using the
approach of ) by comparison with a reference profile
calculated for a defined concavity index (θ in
Eq. ). This reference profile is a line in
χ-elevation space between the outlet and headwaters of the channel, and
knickzones are then defined based on the deviation of the χ profile from
the reference. After initial detection, knickzones are quantified by their
relief (elevation drop) and adjusted using several filters or lumping-window
parameters. This method is well adapted to detect knickzones that are
composed of a base and a lip separating a steepened reach. An example of output
produced by this algorithm and compared to ours is presented in
Sect. .
Another method for extracting knickpoints has recently been implemented using
TopoToolbox . Although unpublished, the code is
available and also aims to reproducibly extract knickpoint locations from
river profiles. It selects knickpoints by creating reference channel profiles
that are concave up and then selecting knickpoints for which the actual channels
are the most different from the reference channels. Although not based on the
slope–area relationship, this method is perhaps the closest algorithmic
attempt to match the knickpoint definition of early workers
e.g.. A sensitivity parameter defines the number of
iterations and indirectly the number of knickpoints detected. After
knickpoint extraction, a value is attributed to each identified knickpoint
quantifying the divergence of the long profile from the reference profile. We
discuss the similarities and differences of this method compared to our
method in Sect. .
Motivation for a new method
Despite the large number of past approaches to selecting knickpoints, we have
developed a new method because (i) many authors still select knickpoints
based on qualitative interpretation of channel long profiles or slope–area
data and we desired an open-source, reproducible method that has no reliance
on proprietary software such as ArcGIS e.g. or
MATLAB e.g.. (ii) Channel erosion is
modelled to scale with discharge, and therefore we wished to use a method
that includes discharge (or its proxy drainage area). (iii) Existing
slope–area approaches make it difficult to pinpoint knickpoint locations
(Fig. ), and therefore we choose to use a χ-based
approach. (iv) We wished to develop a method that not only selected
knickpoint locations but also included metrics of changes in normalised channel
steepness, as that metric is frequently used in tectonic geomorphology, and
(v) we aimed to create a method allowing for differentiation between
different knickpoint morphologies (e.g. slope break vs. vertical step).
Although the newest methods meet a subset
of these criteria, they both only describe a specific morphology of a
knickpoint and/or knickzone and use indirect methods to quantify their magnitude
(e.g. derived from comparison with a reference profile). Our aim here is
to provide a method that selects locations, styles (e.g. vertical step,
slope break) and magnitudes (e.g. main features or secondary ones) of
knickpoints and knickzones that is free of manual selection in order to
complement these existing methods that are more focused on identifying
locations of a particular style of knickpoint and knickzone (e.g.
waterfall).
We provide comparisons with two existing methods in Sect. . These have been chosen for the
following reasons: (i) the knickpoint-extracting algorithms are open source
(with the limitation of MATLAB licences), (ii) the methods are objective,
reproducible and provide a quantification of knickpoint magnitude in order
to compare it with ours, and (iii) is purely based on
channel morphology, while use the slope–area relationship
and χ, thus providing a reasonable comparison of our algorithm with the
range of existing methods.
Methods
An overview of our knickpoint identification method can be found in Fig. .
Flowchart of the knickpoint detection
algorithm.
![]()
DEM preprocessing and river network extraction
Firstly, we fill the DEM using the filling algorithm of to
make sure that each cell has a flow direction and to avoid internal basins
generated by DEM noise e.g.. This approach is suitable
for cases in which no feature is spuriously damming the DEM. Spurious damming
can occur when vegetation, bridges or other features lead to high elevations
over the channel when in fact the channel sits at a lower elevation. The
filling process will create flat surfaces behind such spurious dams and will
therefore hinder channel profile analysis.
If features that lead to spurious damming are present, we give users the
option to use a breaching or carving algorithm. This excavates through
spurious dams to avoid overfilling. The depression-breaching algorithm in our
code is that created by and adapted from
within our method. It is also possible to supply the
algorithm with preprocessed DEMs e.g..
From the preprocessed, carved or filled DEM, we provide several methods of
extracting the river network, including the DrEICH method ,
a curvature method proposed by and a method that uses
a Wiener filter that combines elements of
the methods of and
first implemented by and .
found this latter method least sensitive to DEM
resolution. Finally, we include extraction based on a drainage area
threshold more suitable for low-resolution DEMs (e.g. SRTM, ASTER) or
large-scale studies in which the location of channel heads is less important. We
also ensure during the preprocessing that no catchments are beheaded by the
edge of the DEM, as the χ coordinate is a function of drainage area and
therefore incomplete basins will have incorrect χ values.
<inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">sn</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> extraction
Following channel extraction, we then calculate the χ coordinate for the
resulting network. A key parameter that must be constrained prior to
calculation of χ is the concavity index (θ). Changing the
concavity index significantly affects values of the χ coordinate
e.g. and therefore
subsequent knickpoint extraction. We select the concavity index using a
method developed by . This method calculates the χ
coordinates for a range of concavities within each watershed and determines
the most likely concavity index by directly comparing the collinearity of
points on each tributary with the trunk channel .
This approach does not assume linearity in χ-elevation space and is
therefore applicable in transient landscapes .
Once we determine θ values for each basin, we calculate χ and
then use χ-elevation profiles to determine changes in
ksn, which is the gradient of the χ-elevation profile
when we set A0=1 (see Eq. ).
Theoretical work by suggested that in eroding
landscapes changes in erosion rates would be represented by changes in
χ-elevation gradient between segments of channels that would be linear
in χ-elevation space, which called slope
patches. devised a statistical method that identified the
most likely linear segments in χ-elevation space. This technique
searched all possible combinations of channel pixels and used the corrected
Akaike information criterion (AIC) to balance
the goodness of fit of linear segments against overfitting the data. Here we use
this same algorithm to search for breaks in slope within the profile
corresponding to knickpoint locations.
Knickpoints will manifest themselves as changes in the slope of these
patches equivalent to the slope-break knickpoints of ,
whereas knickzones will be represented by patches with locally high
gradients. That is, knickpoints and knickzones result in either changes in or
locally high values of ks (or ksn if calculated
with a fixed concavity index). The segmentation algorithm casts the profile
as a series of linear segments, and each segment has a gradient and an
intercept. The gradient reflects ks of the segment and the
intercept can be used to detect vertical-step knickpoints, as it detects
elevation jumps between adjacent slope patches.
The method developed by subsamples underlying topographic
data iteratively: on each iteration nodes from the channel network are chosen
randomly and segmentation is applied to this subset of nodes. The number of
iterations is called nMC. This iterative approach was taken
because it significantly reduces the sensitivity of the results to user
parameters . The computational expense of the segmentation
scales highly non-linearly with the number of nodes, so channel profiles are
broken into subsections of length ntg (called the “target nodes” in
). The sampling of the underlying data on each iteration is
random: after sample nodes are “skipped” randomly, the number of nodes
skipped varies with a uniform distribution from zero to twice a parameter
nsk such that the mean “skip” is nsk. We explore the sensitivity
of the method to these parameters in the discussion.
The final ksn values are an average of many iterations using
different channel profiles subsampled from the raw data, as are intercepts of
local segments. These averaged values are used to build segmented elevation.
Each node then represents an average of the best-fit segments for every
iteration of the segmentation routine (Fig. a):
zsegi=Mχi×χi+bχi,
where i is the given node, zseg its elevation on the segment,
Mχ the average gradient of the segments and bχ the averaged
intercept of the segments. Mχ can be expressed with the following
equation:
Mχ=EK×A0m1/n.
We note here that Mχ is the same as ksn if χ is
calculated using A0=1 m2.
Extraction of normalised channel steepness (ksn) from
a river profile. (a) Example of best-fit segmentation
where + symbols are individual data points and the
coloured lines are the segments. (b) The associated plot of
ksn plotted as a function of χ coordinate. The
segmentation output results in some noise due to iterative sampling of the
channel network (+ symbols). A total variation denoising filter
is then applied on the signal to extract the main
variations in ksn.
![]()
Knickpoint extraction from <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mi mathvariant="normal">sn</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> data
Change point detection
Change point detection is a common technique used within many fields (e.g.
time series analysis) and a number of statistical tools have been developed
to identify change points, reviewed and described by . In
our case, the signal (ksn) is by definition piecewise stationary, and
abrupt changes occur between each segment (i.e. knickpoints).
Change point detection algorithms aim to estimate and isolate the exact
location of these boundaries between stationary patches. Method choice
depends on the nature of the original dataset (e.g. noise
intensity) and the number of changes we aim to extract (e.g.
predetermined or unknown). In our case, although the segmentation algorithm
of can result in very sharp segment boundaries, in many
cases the transitions between segments is fuzzy. We therefore have an unknown
number of change points to detect from a variably noisy signal. We therefore
choose to use a signal processing filter to flatten the
piecewise ksn patches and discretise all potential change points. This
algorithm identifies where ksn and elevation are statistically
varying the most within any transition zones. It also combines segments that
have very small changes in ksn relative to the noise in the
data (Fig. b).
We denoise the data using a one-dimensional total variation denoising (TVD) filter,
a signal processing filter adapted from an optimised algorithm by
solving the following equation:
minimisex∈ℜN12∑k=1Ny[k]-x[k]2+λ∑k=1N-1x[k+1]-x[k],
where N represents the number of samples (nodes) per population (in this
case a river channel from source to the next higher-order stream or the outlet),
y represents the raw signal y1,y2,y3,…yN, in this case
ksn ordered by ascending χ within each river, x the
denoised signal x1,x2,x3,…xN, referred to as denoised
ksn, and λ is a regularisation parameter
. This method minimises variations, whereby the parameter
λ must be real and greater than zero. Greater λ values result
in less variation in the processed signal, and λ→+∞
results in no variation in the processed signal whatsoever. The selection and
sensitivity of this parameter are discussed in Sect. .
After denoising the data, our method then iterates through all nodes in each
channel and identifies change points as any variation in the denoised
ksn data. These represent first-order knickpoints that we
quantify by their change in denoised ksn, which we call Δksn. Δksn is a quantitative measure of the
magnitude of the slope-break component of the knickpoint
(Fig. a). We refer to change points as knickpoints
in the rest of the paper.
Combining knickpoints
Denoised ksn data can still contain closely clustered steps in
ksn values, which may in fact represent a single knickpoint. We
therefore use an algorithm to determine which of these clusters can be
combined. Iterating through each river, the algorithm tests the neighbouring
nodes of each raw knickpoint in a window that we call the “combining
window”. If two knickpoints in the denoised ksn data are
within the combining window and both have the same sign of Δksn, the two knickpoints are merged and their magnitude summed.
This process is repeated using newly merged knickpoints until no nodes are
within the combining window or until a change in knickpoint sign
(Fig. b). The combined knickpoint is then centred
between the combined nodes. The width of the combining window (which we
denote rcomb and is defined by a number of nodes rather than a flow
distance) is a user-defined parameter, the selection of which we address in
Sect. .
Knickpoint extraction from the denoised ksn profiles.
(a) The first step extracts all variations of ksn,
quantifying each with Δksn, which we call the “raw”
knickpoint dataset. Negative and positive changes represent decreases or
increases in ksn, respectively. (b) After the detection of
changes in ksn, knickpoints are combined. All knickpoints
within a node window will be combined, summing their values (i.e. a sum of
Δksn). This process is repeated as long as the subsequent
raw knickpoint is within a node window and as long as the polarity (i.e.
if it is negative or positive) does not change.
![]()
Vertical-step knickpoint detection
Small variations between segments with similar ksn values may
be ignored by denoising, which may seem trivial if the aim is to isolate the
main variations in channel steepness. However, this may lead to vertical-step
knickpoints being missed if channel segments above and below the
vertical-step knickpoint have similar ksn values despite a jump
in zseg. We therefore use a second approach to extract
knickpoints, allowing us to identify both slope-break and vertical-step
knickpoints.
The algorithm calculates changes in zseg using
Eq. () in order to isolate the main jumps in profile
elevation. We differentiate this value along the river nodes (Δzseg) to detrend the elevation signal and focus on the stepped
variations. For each node in the channel, the mean and standard deviation of
Δzseg is calculated within a window of surrounding nodes;
the window width in nodes is called rW. The nodes within the first and
last half-windows are calculated using the first and last
window, respectively. Δzseg is then compared to the standard deviation
of the nodes within the corresponding window multiplied by a coefficient
(which we call Tσ), and the node is selected as a vertical-step
knickpoint if Δzseg is greater
(Fig. b). This approach ensures that the selected
vertical-step knickpoints show an anomalous increase in elevation. The
selection of the window width and the coefficient is discussed in Sect. . We can then use Δzseg as a
quantitative measure of the size of each vertical-step knickpoint.
Extraction of knickpoints from the segmented elevation
(Eq. ). (a) Expression of a vertical-step knickpoint
in a χ-zseg profile compared to a slope-break knickpoint.
(b) Representation of the identification window and the
corresponding standard deviation around the reference node (in red). μ is
the mean and Tσ the coefficient applied to the standard deviation.
This process is repeated for each node. Reference nodes outside their own
window are considered to be outliers.
![]()
Accuracy metrics
The accuracy of the method is assessed using a true positive (TP), false
positive (FP) and false negative (FN) approach. This comparison method is
often use to test algorithm performances on point data, such as channel heads
e.g. or knickzone locations
e.g.. We test the algorithm with these accuracy metrics
using two sites where locations of hand-picked knickpoints based on field
observations and river profiles are available. Knickpoints were identified at
Santa Cruz Island (California, USA) by , and we introduce a
new dataset in the Quadrilátero Ferrífero, Minas Gerais, Brazil.
We define as TP a reference knickpoint detected by the algorithm, as FP a
knickpoint detected by the algorithm that is not a reference knickpoint, and
as FN reference knickpoints not detected by the algorithm.
propose a fourth kind of prediction called “mixed” to assess the knickzone
base and lip detection, whereby only one of the two knickzone boundaries is
detected. We chose not to use this approach as we define a knickpoint as a
point location showing an increase or decrease in ksn or
Δzseg, which is more applicable to varying knickpoint
morphologies. The definition of the different knickpoint predictions allows
for the calculation of sensitivity, s, reliability, r, and metrics. We also
add an overall quality metric, q, described in . The
sensitivity can be expressed as
s=∑TP∑TP+∑FN,
where ∑TP and ∑FN are the sum of TP and FN. This metric
measures the method's ability to detect a knickpoint that a user would have
manually picked. s=1 implies the detection of all the locations of
reference knickpoints. The reliability can be expressed as
r=∑TP∑TP+∑FP,
where ∑TP and ∑FP are the sum of TP and FP. This metric
measures the occurrences of the method identifying knickpoints that a user
would not have picked. The overall quality metric can be expressed as
q=∑TP∑TP+∑FP+∑FN.
A q value of unity implies perfect agreement between algorithmically and
hand-picked knickpoints. We focus on these metrics instead of the knickpoint
magnitude, as it is more difficult to predict and is dependent on many
parameters within the extraction of the Δksn values.
Test locations
In order to test the performance of our method, we extract knickpoints from
two field sites with independently mapped knickpoint and knickzone locations.
The first of these sites is Smugglers Basin on Santa Cruz Island (California,
US), where knickpoints and knickzones were mapped by using
a combination of fieldwork and supervised selection from river long profiles.
Smugglers Basin is undergoing transient adjustment to climatic and tectonic
signals . The second field site is located in the
Quadrilátero Ferrífero (Minas Gerais, Brazil), where we present a
new dataset of extracted knickpoint and knickzone locations from field
observations and river profiles. Quadrilátero Ferrífero represents a
more stable site in terms of climate and tectonics e.g., and therefore knickpoints in this landscape have been linked
instead to changes in lithology.
Santa Cruz Island, USA
The first calibration test site is the headwaters of the Smugglers Cove
catchment, located in the SE of Santa Cruz Island, the largest of the
California Channel Islands (California, USA; Fig. 6a). Lidar data at 1 m resolution
are available in the basin via the 2010 US Geological Survey Channel Islands
Lidar Collection, available from OpenTopography (opentopography.org).
The basin has a total relief of approximately 550 m and drains to the Pacific
Ocean. Previous work has estimated uplift rates of ≈1 mm yr-1
using dated terraces and fault activity e.g.,
and the site has experienced regional sea-level variations
e.g.. This, along with bedrock
heterogeneity, has led to numerous knickzones in the catchment which have
been mapped and tested against a previous knickzone extraction algorithm by
. A total of 18 knickzone bases and lips have been reported based on
topographic expression and field observations across the whole catchment. As
the algorithm is targeted specifically at knickzones, we
compare the mapped knickzone bases and lips with those picked by our
algorithm. Knickzone bases and lips are the equivalent of increases and
decreases in ksn, respectively.
We extracted channel heads using a curvature-based method of channel
extraction, following and . This
method has an estimated accuracy of ≈10 m horizontally along
drainage paths . Before extracting channel steepness, we
calculated the best-fit concavity index for the basin by maximising
collinearity between the main-stem channel and the tributaries in
χ-elevation space using the bootstrapping method of :
the best-fit θ at the site is 0.25.
Quadrilátero Ferrífero, Minas Gerais, Brazil
The second calibration test site is located in the eastern part of the
Quadrilátero Ferrífero (QF, Brazil), in a basin draining the Caraça
Range (Fig. ). The QF is an area of relatively high
elevation in southeastern Brazil, and the Caraça Range is its most
pronounced topographic feature with a maximum elevation of ≈2100 m
and maximum relief of ≈1500 m. Tectonic activity is thought to have
ceased by ≈500 Ma e.g..
Upstream areas are primarily underlain by resistant rocks (e.g. quartzites
and banded iron formations), whereas less resistant rocks often underlie
downstream areas (e.g. schists and phyllites). The association of
mountainous topography and long-term tectonic stability have led to
controversy in the post-orogenic evolution of the QF . The
most accepted hypothesis is that differential denudation of lithologies with
different resistance to denudation has led to a geomorphic differentiation
whereby the uplands, underlain by strong rocks, are high because they have been
denuded less and more slowly than their surroundings
e.g.. An
alternative hypothesis is that the relief of the QF results from a
complicated history of geographic cycles interrupted by epeirogenic uplift
e.g..
Knickpoints are common features in the rivers flowing away from the Caraça
Range (Fig. ). These rivers have headwaters at high
elevations (≈2000 m), and their long profiles display many
convexities associated with substantial elevation drops (up to 1.4 km of
descent over ≈15 km of downstream distance) and steep channel and
hillslope gradients. These rivers flow over quartzite terrains,
transitioning in their distal part to schists (see Supplement Sect. S5.2).
The origin of these knickpoints is unresolved, being possibly the result of
spatial variations in rock resistance or alternatively resulting from
transient uplift signals that have failed to progress beyond quartzite units
. We used a TanDEM-X DEM with 12 m resolution to extract
knickpoints from the QF. Before extracting channel steepness, we estimated
the best-fit concavity index as 0.15 using the methods presented in
.
Results
Performance at Santa Cruz Island
We carried out knickpoint extraction on Santa Cruz Island (Fig. 6b) initially with
parameters detailed in Table ; the full parameter
file is available in the Supplement. As explained in Sect. , extraction prior to post-processing thinning generates a
dense dataset of knickpoints both within and outside knickzones identified by
the calibration dataset (see Supplement Sect. S5.1). Therefore, we
apply a threshold approach to thin the dataset by removing small knickpoints.
We set cut-off values of |Δksn|>0.8 and Δzseg>2.1, whereby knickpoints smaller than these thresholds are
ignored. These values are set for this case study with the specific aim of
isolating the main knickpoints while matching with the calibration dataset.
This approach is fully reproducible and does not involve manual picking of
knickpoints.
Parameter values used for the two field sites. Differences in
parameter values between the two sites are due to differing DEM resolution
(1 m for Santa Cruz Island and 12 m for the Ribeirão Caraça).
Sensitivity to these parameters is described in Sect. .
Note that although the parameter values have been carefully optimised for
knickpoint analysis, we suggest the values below as defaults for each of
these two data resolutions in order to allow for a rapid initial knickpoint
extraction for other landscapes.
Parameter
Santa Cruz
Ribeirão Caraça,
name
Island, USA
Brazil
ntg
30
50
nsk
1
1
nMC
100
100
λ
1.7
0.3
rcomb
10
30
Tσ
7
7
rW
120
100
Our thinning procedure reduced the number of slope-break knickpoints from 398
to 160 and the number of vertical-step knickpoints from 40 to 17. This is a
relatively high number of knickpoints compared to the calibration bases and
lips (18 pairs). However, this disparity can partly be explained by the
differences in methods: our algorithm details discrete changes in channel
morphology, whereas the calibration knickzones are identified over longer
channel reaches. Therefore, one mapped knickzone may contain several
algorithmically identified knickpoints.
propose an error radius of 50 m around each base and
lip in order to test the performance of their algorithm: we used the same
approach when comparing our extracted knickpoints to the calibration
data (Fig. 6b). A
TP is determined as any knickpoint within the calibration knickzone or the
corresponding 50 m radius. An FP
is determined as any knickpoint which does
not lie within this radius, and an FN is determined as a base or a lip which
is not identified by our algorithm. The reliability, sensitivity and overall
quality metrics are presented in Table .
High sensitivity (s=0.93) but lower reliability (r=0.53) and overall
quality (q=0.51) suggest that the algorithm detects the bulk of
human-selected knickpoints, but also a significant amount of other knickpoint
features. The implications of these results are discussed below.
Accuracy metrics for calibration site I (Smugglers catchment,
California, USA).
Source
TP
FP
FN
Total
key
detected
0
26
15
4
41
11
0
15
0
15
41
4
5
0
9
121
2
5
1
7
127
17
15
1
32
210
17
9
0
26
263
11
13
0
24
313
10
4
1
14
759
4
5
0
9
Total
91
81
7
177
s=0.93, r=0.53 and q=0.51
Performance at Quadrilátero Ferrífero, Minas Gerais, Brazil
The application of our method in the Ribeirão Caraça basin resulted in a
dense dataset of knickpoints (n=252); see
Table for parameter values and the Supplement for the full parameter file. To thin this dataset, we removed
knickpoints with attributes lower than the cut-off values of |Δksn|>0.8 and Δzseg>2.1 for the
slope-break and vertical-step knickpoints, respectively. This filtering
procedure decreased the number of slope-break knickpoints from 252 to 108,
whereas the number of vertical-step knickpoints diminished from 44 to 23. We
tested the performance of our method compared to human-selected knickpoints
for the Ribeirão Caraça basin using the metrics TP, FP and FN
(Table ). We used the same error radius as was
used on Santa Cruz Island for consistency. These metrics (see Sect. ) indicate that the sensitivity of our method is high for
the Ribeirão Caraça basin (s=0.89), and thus the bulk of human-selected
knickpoints are captured by our algorithm. On the other hand, the reliability
(r=0.60) and the overall quality (q=0.56) are lower because the
number of false positives is high, indicating that our algorithm determines a
relatively high number of knickpoints compared to human selection. In
summary, our algorithm captures knickpoints that are visually selected for
the Ribeirão Caraça basin and many knickpoints that are not
recognised by traditional field mapping of knickpoints, but are
morphologically similar as defined by our algorithm.
Accuracy metrics for calibration site II (Ribeirão Caraça
basin, Caraça Range, QF, Brazil).
Source
TP
FP
FN
Total
key
detected
0
17
13
2
32
1
6
5
1
12
5
9
1
0
10
22
4
2
0
6
37
3
2
1
6
56
4
2
1
8
88
9
7
1
17
114
5
2
1
9
139
8
5
0
14
151
4
4
1
10
252
6
8
0
15
Total
75
51
8
139
s=0.89, r=0.60 and q=0.56
Sensitivity to algorithm parameters
One important parameter in our method of knickpoint detection is the
concavity index (θ). The concavity index controls the magnitude of
ksn because it determines the values of χ
(Eq. ), and a higher concavity index will produce higher
ksn values for the same channel. We ran the algorithm on Santa
Cruz Island for θ values ranging from 0.05 to 0.95 in steps of 0.05.
Because the value of θ affects the ksn order of magnitude,
λ must be adapted to keep denoising the signal. We therefore tested a
wide range of λ values for each θ value. From these tests (see
Supplement Sect. S4.1) we determined default λ values
appropriate for a range of θ values. These default values are
implemented internally in the code, but can be modified if needed.
The sensitivities of knickpoint locations to θ using default λ values are presented in Fig. . This analysis shows
that the general spread of the data, represented by its zscore
(difference between the data point and the mean normalised by the standard
deviation), is not significantly impacted by different θ values.
However, the relative magnitude of each knickpoint, measured by changes in
ksn, depends on the chosen value of θ. Therefore, if the
intention of the user is to find the spatial distribution of the largest
knickpoints then it is essential that θ is picked with care (see
Supplement Sect. S4.2 for more illustrations).
Because ksn values are sensitive to the value of the concavity
index, θ, it is important to note that basins with different θ values should be
analysed separately to isolate knickpoint locations. Δksn values are therefore also dependent on the value of θ, so the relative magnitudes of knickpoints and knickzones should only be
compared amongst basins with the same θ value. On the other hand, the
locations of knickpoints and knickzones are relatively insensitive to
θ so the method can be used to determine the spatial distribution of
knickpoints across large areas even in the event that the concavity index may
vary spatially.
The extraction of channel steepness will also be influenced by parameters in
the segment fitting algorithm : the number of target nodes
(noted ntg) and the average number of nodes skipped (noted nsk). We
therefore ran sensitivity analyses on these parameters testing every
combination for the following ranges of values: from 5 to 120 ntg and
values of 1 to 4 for the nsk parameter. Our results show that both of these
parameters affect the segment lengths. Increasing either the number of
ntg or the nsk parameter leads to longer segments (see
Supplement Sect. S4.3 for more details). This affects the number of
knickpoints detected. We also tested the number of Monte Carlo iterations
(nMC) processed for each segment from 5 to 500 and find that
the results become insensitive to nMC when nMC>50.
The results of the vertical-step knickpoint detection can change with the
size of the moving window that detects sudden changes in zseg
compared to neighbouring nodes (Sect. ). We tested the
following combination of parameters for vertical-step knickpoint detection:
rW from 10 to 200 nodes over intervals of 10 nodes and Tσ from
5 to 10 over intervals of 0.5. Our results show that the extraction is
insensitive to rW above a threshold minimum value of around 80 in our case.
Below this value, the algorithm begins to identify steep channels as a
succession of steps and will detect each node in the steep section as a
knickpoint. We find that the number of extracted knickpoints becomes much
higher if Tσ<6, whereas Tσ>8 results in very few
knickpoints being detected. We therefore suggest selecting a value of 6≤Tσ≤8.
The resolution of the DEM may also affect the location of extracted
knickpoints and knickzones. We conducted a sensitivity analysis on raster
resolution by resampling the original 1 m lidar-derived DEM into coarser
grids to represent commonly available resolutions of 5 m (e.g. NED or NetMap),
10 m (e.g. NED or TanDEMX) and 30 m (ASTER or SRTM). Our results (see
Supplement Sect. S4.7) show a decreasing number of detected knickpoints at
coarser grid resolutions. This is directly linked to the amount of nodes in
each river profile: as the resolution decreases, the number of nodes per
river also decreases, meaning that fewer segments are used to extract
ksn. Therefore, fewer knickpoints are detected as knickpoints
tend to be located near the segment boundaries. Furthermore, with lower-resolution grids the knickpoints that are detected tend to represent
larger-scale variations in the channel profile. Vertical-step knickpoints
also tend to be identified as steepened reaches rather than purely vertical
regions of the channel profile, as the grid resolution prohibits
the identification of small waterfalls. In order to show an overview of the
algorithm performance in different field sites and DEM datasets, we extracted
knickpoints from an additional test site using a 30 m DEM derived from SRTM
(Supplement, Fig. S21).
Discussion
Selecting parameter values
Ideally our method for knickpoint detection could proceed without any human
supervision. Due the method's sensitivity to grid resolution, roughness
and the intrinsically heterogeneous nature of landscapes, the method
does, however, retain some user-defined parameters. The sensitivity analysis
performed on the Santa Cruz Island data (Sect. )
indicates which of these must be selected with care.
We found that changing the concavity index does not change the location of
the knickpoints substantially, but it does control their relative magnitude
(Sect. ), and therefore if the user is interested in
knickpoint magnitude then θ should be selected carefully
e.g.. The parameters linked to segmenting the
χ-elevation profiles that affect results are the
ntg and nsk parameters (Sect. ). Increasing
both of these increases the length of the segments, whereby setting these
parameters to smaller values result in a large number of detected changes in
ksn which must thereafter be thinned. The one potential
advantage of smaller segments is that more vertical-step knickpoints can be
detected (i.e. waterfalls). Smaller segments also affect the relative values
of knickpoint magnitude because short, steep reaches can be extracted and
will generate high-magnitude Δksn knickpoints. If high
values for the ntg and nsk parameters are used, the resulting
knickpoint dataset will be sparser but will not necessarily detect local
changes in ksn due to local layers of hard rock or a
change in erosion processes, for example. Larger segments are also less
sensitive to topographic noise. After running sensitivity analyses, we
recommend default parameters of ntg=80 and nsk=1.
Once segmentation is performed, we use the TVD routines to isolate changes in
ksn, which require an additional parameter (λ) to
control the degree of denoising (Eq. ). As the relative
magnitude of ksn is controlled by the θ value, we also
determine the λ value for each value of θ that best isolates
changes in ksn based on our sensitivity analysis (Sect. ). However, some landscapes that are either very gentle
or steep may require changes to the λ value: low-relief landscapes
may require a smaller λ value, whereas the opposite is true for steep
landscapes. The user can check the efficacy of the selected λ value
by plotting ksn and denoised ksn against χ
or the flow distance. Guidance on the selection of λ is described in
greater detail in the Supplement Sect. S4.1.
We also explored the possibility of using the TVD routine to denoise the
river profile before extracting knickpoints in order to avoid dependency on
the θ parameter. We applied the denoising routine on Δelevation in order to reduce the amount of variation. The intensity
λ of denoising has to be manually selected and controls the amount of
change from original data. Results from these tests are available in the
Supplement (Figs. S18–S20). We found that additional denoising
is still required during the Monte Carlo segment determination of
. We suggest that prior smoothing of river profiles needs to
be carefully considered, as it unavoidably leads to some modification of the
existing profile. Users of our software may, if they wish, apply a technique
for denoising river profiles prior to applying our method
e.g..
The test location on Santa Cruz Island, CA, USA. (a) Map of
channel network extracted with the Pelletier method
and coloured by ksn value calculated with .
(b) Extracted knickpoints plotted after thinning the dataset as
described in Sect. . The purple and green circles
respectively represent the calibration knickzone bases and lips with the
50 m radius used for assessing algorithm performances. Stars and associated
numbers are source numbers, which can be compared to
Fig. . Topographic data are 1 m precision lidar
DEM (see Supplement Sect. S1 for metadata) reprojected in WGS84 UTM zone
11N.
![]()
The width of the combining window can also be an important factor. As
explained in Sect. , segment boundaries can still be fuzzy
after the denoising process, generating successions of low-magnitude
slope-break knickpoints. The combining window solves this issue by merging
adjacent knickpoints within a certain radius. However, underestimating
rcomb could result in retaining some of these low-magnitude knickpoints.
Overestimating its size would possibly result in shifted knickpoint locations
and misrepresentation of their magnitude if unrelated knickpoints are merged.
In the case in which the DEM resolution is high enough to represent a close
succession of knickpoints, we recommend carefully choosing a combining window
smaller than the spacing between these features in order to avoid merging
them.
Vertical-step knickpoint detection is controlled by two parameters: the
window radius (rW) and the standard deviation threshold for detecting
anomalies (Tσ). Section details the combined
sensitivity analysis on these parameters and allows us to determine a set of
values suitable for this analysis. However, if the user's specific aim is to
detect vertical-step knickpoints (assuming that the DEM precision allows it),
we recommend that users precisely constrain the standard deviation
coefficient, the window size and the segment size in order to make sure that
vertical-step knickpoints are extracted rather than slope break.
Although parameters in the method may be tuned and therefore the method can
be supervised, it is reproducible. Workers using the method can report on the
parameter values used and others can use these to reproduce the original
results. One advantage of these adjustable parameters is that users can
visually inspect outputs and change parameters such that the algorithm
selects “obvious” knickpoints. However, we emphasise that
this is not hand-picking of knickpoints: the algorithm output is a dense dataset of
knickpoints. While sorting the dataset, once a threshold or statistical
criterion is selected, all knickpoints and knickzones matching the selection
are chosen. This means that one cannot eliminate knickpoints that
qualitatively appear to be in the “wrong” place. As highlighted in
Fig. , human-selected knickpoints and knickzones
frequently produce biased knickpoint datasets that both include and exclude
knickpoints and knickzones that have the same magnitude. We note that because
the segmentation algorithm uses a Monte Carlo sampling routine
there may be minor differences in results between two users,
but by using a reasonable nMC (>50) the results from one run to
the next are nearly identical.
Knickpoint extraction for Santa Cruz Island, CA, USA, shown for the
channel long profiles. These are the same knickpoints depicted in
Fig. b. The stars and associated numbers correspond to
the source numbers, and green and mauve circles correspond to the lips and
bases of mapped knickpoints from .
![]()
Knickpoint extraction on the Ribeirão Caraça basin
(Caraça Range, QF, Brazil). (a) Map of knickpoints extracted
with the algorithm after thinning the dataset as described in
Sect. . Most of the calibration knickpoints are expressed
by a succession of knickpoints detailing along-channel increases and/or decreases in
ksn. Streams depicted in panel (b) are shown as thick
blue lines. (b) Longitudinal profile of the trunk stream (the
Ribeirão Caraça river) highlighting the performance of the algorithm
in picking along-channel breaks in steepness. (c) Example of a known
waterfall (i.e. waterfall with a name) in the field: the
Cascatinha waterfall. This waterfall features an elevation break of 40 m.
Other known waterfalls include the Cascatona, Bocaina, Brumadinho and
Quebra-ossos waterfalls.
![]()
Sensitivity of the knickpoint extraction to the concavity index
(θ). As different values of θ result in different values of
ksn, we use a normalised zscore (i.e. the
difference to the mean normalised by the standard deviation) to compare the
overall spread of Δksn. The plot shows probability
distributions of the zscore of Δksn
represented by violin plots calculated with a kernel density estimation
(bandwidth 0.20). The outliers and their relative magnitudes are affected
by this parameter, whereas the general data distribution remains similar. The
“min” and “max” stated above and below the violin plots respectively
represents the minimum and maximum ΔMχ for each run.
![]()
Quantification and selection of knickpoints
The aim of extracting knickpoints is mainly to link knickpoint location and
magnitude to a specific event resulting in landscape transience
e.g.. Therefore, an important step is to isolate the
most significant knickpoint features from the dense raw dataset in order to
interpret landscape evolution, which can be done using knickpoint magnitude.
Knickpoint magnitude may be affected by the calculation of ksn
using the gradient of segments in χ-elevation space. Depending on the
relief, particularly with a high value of θ, the absolute values
of χ coordinates and associated elevation can differ by an order of
magnitude. If the values of χ are low compared to the values for
elevation, any changes in elevation at a knickpoint will result in a much
higher segment gradient than if the χ values are of a similar magnitude
as the elevation. This can result in the exaggeration of knickpoint magnitude
in high-relief landscapes, for example, where it is more likely that χ values will be
lower than the elevation values, eventually resulting in a
bias during the sorting. We therefore suggest that, in such cases, A0
from Eq. () should be set such that the value of the
χ coordinate is the same order of magnitude as the elevation. However,
if A0≠1, then the gradient of the segment corresponds to Mχ
in Eq. () rather than to ksn. We wish to
emphasise that this does not change the relative ordering between
knickpoints. We illustrate this relationship by running a simple sensitivity
analysis on the Santa Cruz Island dataset, with a range of A0 varying
from 1 to 500 (Fig. ). This sensitivity analysis shows that, as
A0 is increased, the extreme values of Δksn within the
dataset are reduced so that the effect of low absolute χ values on the
gradient calculation is diminished. As for θ (see Sect. ), knickpoint absolute magnitude (i.e. the
direct value of Δksn and Δzseg) cannot be
compared if calculated with different A0 from
Eq. (). However, the location of the isolated main
knickpoints can still be compared.
The effect of varying A0 on knickpoint extraction
(Eq. ). The reference area (A0) will affect knickpoint
magnitude and can be increased to reduce exaggerations in χ-elevation
gradients. Changing A0 does not affect the relative order of knickpoints:
the largest knickpoints remain the largest for all values of A0.
Increasing A0, however, reduces the spread in the zscore of
the changes in channel steepness. This value has to be set only if necessary
(e.g. if the high-gradient effect is important): A0≠1 implies that
the magnitude is not Δksn but ΔMχ from
Eq. (). Moreover, overestimating A0 can mask knickpoints
that would be detected with A0=1 m2. The “min” and “max”
stated above and below the violin plots represent the minimum and maximum
ΔMχ for each run.
![]()
Our sensitivity analyses suggest that two different approaches may be used to
select knickpoints. The first of these is that a single θ and A0
can be fixed for an entire landscape: the knickpoint magnitudes can directly
be used to isolate the main knickpoint locations and relative importance.
However, this approach may lead to some errors due to inevitable landscape
heterogeneity over larger scales. The second approach is to calculate
θ and A0 values separately for individual basins, which allows
knickpoints to be extracted with greater precision than if a single value is
set for the entire landscape. However, this approach means that the
knickpoint extraction has to be processed independently for each catchment,
and only the location (e.g. latitude, longitude, elevation) is comparable
between different catchments. Which approach is taken is dependent on the
aims of each particular study and should be carefully considered on a
case-by-case basis.
Knickpoint and knickzone morphology
Along with the calculation of knickpoint magnitude, our algorithm allows for the
characterisation of knickpoint morphology. We can identify different
knickpoint or knickzone types by (i) identifying locations where
ksn increases downstream (positive slope-break knickpoints) or
(ii) identifying locations where ksn decreases (negative slope-break knickpoints) and (iii) identifying locations where a sudden change in
elevation occurs (vertical step knickpoints). This approach is suitable to
identify the most common morphologies described in the literature
e.g.. However, we wish to emphasise that this
algorithm can also be used to focus on one particular knickpoint morphology.
For example, the classical convex-upwards knickpoint expression
e.g. can be isolated by only displaying the knickpoints
with a drop in Δksn (Fig. b). In
order to examine steepened reaches or knickzones, we can also isolate
locations where Δksn increases. Finally, waterfall
detection can be achieved, if the resolution of the DEM allows it, by
focusing on locations with a jump in zseg. We provide all these
different knickpoint types for the Smugglers catchment in the Supplement
(Fig. S12).
Comparison with other knickpoint extraction techniques
For each of our two study sites, we have presented performance metrics of our
method compared to knickpoints selected by humans. We find that our method
has a high sensitivity, meaning that nearly all human-identified knickpoints
were selected by the algorithm, but a lower reliability. This suggests that
our algorithm also identifies many changes in channel steepness which are not
selected as knickpoints through field mapping techniques. This raises the
question of whether the algorithmic selection of knickpoints is more or less
trustworthy than those selected by humans.
Comparison of results from the Smugglers catchment for our algorithm
and the most recent similar ones. (a) Results for a single source
from KZ-Picker and our results. The results from
are directly taken from their study to ensure objectivity.
Only the slope-break knickpoints are displayed to make the comparison valid.
(b) Basin-wide comparison between our algorithm outputs and the one
recently implemented in using a tolerance of 5. We
only display the knickpoints showing a decrease in ksn in
order to provide a relevant comparison with the knickpoint morphology
detected by . Differences in channel length are due to
different methods for extracting channel heads between the two techniques.
![]()
Knickpoints identified for geomorphic studies should be reproducible, in that
two workers should be able to select the same locations and magnitudes from
the same river profile. This is challenging when mapping features in the
field, as different workers may have different criteria for what constitutes
a knickpoint. Furthermore, knickpoint selection should be objective: the same
morphological criteria should be used to identify all features in the
dataset. A common problem with field mapping by humans is that some specific
features are picked in order to interpret a signal, whereas others with a
similar morphology may be omitted. Our approach allows for the production of an
objective dataset of knickpoint locations and magnitudes that can later be
correlated by the user with process-based interpretations. Algorithmic
extraction also allows for coverage of much larger areas compared to field
mapping that can later be calibrated with additional data
e.g.. As illustrated by our accuracy metrics, our
algorithm produces datasets significantly denser than hand-picked knickpoints.
However, it is possible to thin the number of knickpoints by applying
threshold metric values selected based on statistical criteria and making
the number of identified features similar to human-picked datasets. Such a
process is objective in the sense that no hand selection is involved; only
the morphology drives the thinning.
To provide a full assessment of our methods, we compare the output to that
generated by two other algorithms as explained in Sect. :
TopoToolbox and KZ-Picker . Figure a expresses
the differences between KZ-Picker and our
algorithm for a single channel, whereby KZ-Picker identifies the main knickzone
(in red) and quantifies its magnitude by the difference in elevation between
the toe and lip of the knickzone. The purpose of the KZ-Picker is to find
broad zones of steepened channels and is less granular than our method (e.g.
Sect. ). It is also not constructed to identify
discrete vertical-step knickpoints. Because the raw output from our algorithm
is denser than the KZ-Picker, the main knickpoints from our algorithm
require more sorting based on their magnitudes, which results in extra steps
to explore the data.
Figure b provides a basin-wide comparison of our outputs
with those from TopoToolbox , with the tolerance
parameter of the TopoToolbox method fixed to 5. In order to ensure that the
comparison is valid we only compare it to our negative Δksn knickpoints, which should quantify similar features. The
TopoToolbox method effectively identifies the main knickpoints expressed by
the difference to an idealised profile that is concave up. However, reducing
the tolerance parameter increases the number of knickpoints detected (e.g.
10: 12 knickpoints, 5: 44 knickpoints, 1: 343 and 0.1: 2234), meaning that the
TopoToolbox method can result in a network of knickpoints that has a similar
density to our method. However, the TopoToolbox method relies on profiles in
elevation plotted against flow distance, so further processing is required
to analyse changes in channel steepness using this method. Because the selection
of knickpoints in this method is not normalised for drainage area, the
largest knickpoints selected may not correspond to the largest changes in
channel steepness. However, it has fewer parameters and is more
computationally efficient than our method.
While the KZ-Picker and the TopoToolbox methods are well adapted for
identifying specific types of knickpoint, neither allows for the separate
identification and quantification of positive slope-break, negative
slope-break and vertical-step knickpoints. Each method produces slightly
different data products that can be used to interpret different components of
the channel network, making these methods complementary.
Finally, we chose to build our change point detection method using the TVD
routine . However, as explained in Sect. , alternative methods could
be used. The algorithm therefore
provides the raw data before the TVD routine, meaning that these data can be
ingested by other change point detection techniques, e.g. the
methods reviewed in and the associated open-source code.