High-relief great escarpments at passive margins present
a paradoxical combination of high-relief topography but low erosion rates
suggesting low rates of landscape change. However, vertical erosion rates do
not offer a straightforward metric of horizontal escarpment retreat rates,
so we attempt to address this problem in this paper. We show that detrital
cosmogenic nuclide concentrations can be interpreted as a
directionally dependent mass flux to characterize patterns of non-vertical
landscape evolution, e.g., an escarpment characterized by horizontal retreat.
We present two methods for converting cosmogenic nuclide concentrations into
escarpment retreat rates and calculate the retreat rates of escarpments with
published cosmogenic
Passive continental margins exhibit a characteristic morphology with a high-relief escarpment separating a low-relief inland high plateau and the low, flat coastal plain (Fig. 1). The edge of an escarpment often coincides with a major, even a continental, water divide. The escarpment that separates the plateau and the coast plain often exhibits local relief of over 1 km, even reaching heights exceeding 2 km. These great escarpments extend hundreds of kilometers parallel to the coast along rift margins and are typically found 30–200 km inland from the coastline (Linari et al., 2017; Persano et al., 2002). Examples of passive margin escarpments and their age of formation include the Red Sea margin (10–5 Ma), the Western Ghats in India (84 Ma) (Eagles and Hoang, 2014), the Serra do Mar escarpment in Brazil (125 Ma), the Drakensberg escarpment (130 Ma) in South Africa, the Queensland escarpment in Australia (150 Ma) and the Blue Ridge escarpment in the US (200 Ma) (Matmon et al., 2002).
The absence of active tectonics at old rift margins makes the formation and
persistence of escarpments a long-debated problem. One major dispute is
whether an escarpment is geomorphologically static or dynamic in the sense
of rates of change of erosion or back-cutting or retreat of the escarpment
away from the coast. Most researchers agree that an escarpment originates
from rifting-related processes, forming at the edge of a rift graben, and
subsequently migrates inland to its modern position (Sacek et al., 2012;
Tucker and Slingerland, 1994; Gilchrist and Summerfield, 1990), but it is
still debated as to whether this happens as a continuous process or occurs
rapidly following rifting with subsequent slowing or stalling, so that the
modern geomorphic feature is static (Beauvais et al., 2016; Bonnet et al.,
2016; Beauvais et al., 2008). The hypothesized evolution towards relatively
static escarpments is supported by the observation of low time-averaged
denudation rates. Apatite fission track (AFT) ages and (U-Th)
Alternatively, numerical studies of escarpment topography evolution suggest
a much more dynamic and long-lived geomorphic evolution (Braun, 2018;
Willett et al., 2018; Sacek et al., 2012; van der Beek et al., 2002; Tucker
and Slingerland, 1994; Kooi and Beaumont, 1994). Braun (2018) presented a
parameterization of erosion and retreat of an escarpment based on fluvial
erosion and diffusion, and showed that this would lead to a constant rate of
retreat over time. Willett et al. (2018) also argued that escarpment
processes should evolve to maintain a constant form of an escarpment with a
constant rate of backward retreat where escarpment slope maintains a balance
with rock advection driven by retreat. Given a constant rate of escarpment
retreat and formation during rifting, a retreat rate of order
Testing of these models is difficult in that measuring a horizontal retreat
rate of a geomorphic feature is quite difficult. Direct evidence for
escarpment retreat comes from terrace deposits found atop of the Blue Ridge
escarpment crest and beheaded drainages on the plateau side of the
escarpment (Prince et al., 2010). Erosion rates are easier to measure and
have been estimated from sediment budgets measured in the offshore
(Campanile et al., 2008) and from concentrations of cosmogenic radionuclides
(e.g., de Souza et al., 2019; Linari et al., 2017; Salgado et al., 2014).
Detrital cosmogenic nuclide (DCN)
The lack of post-rift thermochronometric cooling ages and the very low rates
of erosion derived from
In this paper, we present a new, systematic method for interpreting detrital
cosmogenic isotope concentrations in terms of horizontal retreat rates of an
escarpment. The method is based on the physical principle of the models of
Braun (2018) and Willett et al. (2018) that argued that an escarpment should
evolve into a morphology that drives horizontal retreat at a constant rate.
We demonstrate that these conditions are exhibited by the Western Ghats
escarpment in India, which shows channel profiles consistent with the
concept of a steady, retreating escarpment with occasional river capture
from the upper plateau. Under conditions of steady horizontal escarpment
retreat, we demonstrate that in situ detrital cosmogenic nuclide
concentrations can be interpreted directly in terms of an average horizontal
retreat rate of a catchment. We present two methods for the calculation of
horizontal retreat rates and demonstrate these methods using published
detrital
Conceptual diagram showing two scenarios of escarpment evolution:
a retreating escarpment or a downcutting escarpment with stationary water
divide. The gray surface denotes the surface of an elemental
escarpment-draining catchment. Inset is the mathematical representative of
the two scenarios as motion relative to the rock.
High-relief escarpments along rifted continental margins pose a stark morphologic contrast with their neighboring low-relief plateau and coastal plain. The typical width of an escarpment normal to the margin is 5 to 20 km, implying enough drainage area in which a well-developed river network is present and dominates the erosional processes. Normal scaling relationships between slope and area predict high normalized channel steepness for most escarpments, so the observed rates of erosion, which are low, are surprising.
To maintain generality, one can consider two evolution scenarios in terms of river incision: downcutting of the topography with a stationary escarpment (Gunnell and Fleitout, 1998) and back-cutting or retreat of the escarpment with migration of the water divide (Tucker and Slingerland, 1994) (Fig. 1). The downcutting model can be driven by base-level fall or it can involve a change in relief with a fixed base level and a stationary water divide and escarpment. In the stationary escarpment and water divide scenario, the position of an elemental catchment remains stationary. Assuming that erosion rates on the plateau are negligible, the surface of the catchment will downcut only if the escarpment front becomes steeper and shorter. Without a change in the coastal elevation, erosion is focused on the escarpment. In the retreating escarpment scenario, the escarpment front retreats towards the inland plateau. Headward erosion of escarpment rivers drives retreat of the escarpment, widening the coastal plain and enlarging the escarpment-draining basins, although the overall height and morphology of the escarpment remain constant, neglecting the increase in elevation of the base of the escarpment as the coastal plain increases in length (Willett et al., 2018).
These models can be described in terms of a surface moving in either a vertical or horizontal direction with respect to its underlying rock (Fig. 1). Although, as argued by Gunnell and Harbor (2010), the geometry of an escarpment cannot remain strictly self-similar or uniform during its evolution at geological timescales, we assume that morphologic changes are small, and an instantaneous erosion or retreat velocity is characteristic of the average change over longer timescales. For vertical erosion, this is essentially the assumption made in treating cosmogenic isotope concentrations, converting concentration to catchment average erosion rate. Here, we propose that the retreat velocity should be treated in the same manner, representing it as a horizontal motion of the catchment surface. In this case, the change of the surface can be characterized by a vector in which the magnitude represents the retreat velocity and the direction represents the retreat direction, taken with respect to the solid earth. In this paper, we will investigate the implications of these end-member models for erosional fluxes.
The escarpment on the west margin of India is a well-recognized escarpment.
It extends parallel to the coast for 1500 km and defines the mountainous
region of the Western Ghats (Fig. 2). The western margin of India rifted
from Madagascar at
Escarpment rivers in the SWG are bedrock rivers cutting into the Precambrian
metamorphic basement. The morphology of the rivers draining the escarpment
differs primarily due to their initiation on the escarpment or landward of
the escarpment on the plateau (Fig. 3). Rivers initiating on the escarpment
are characterized by a long, low-slope reach on the coastal plain and abrupt
steepening at the escarpment front (Fig. 3a). This is particularly evident
in transformed
River profiles and corresponding transformed
In order to calculate a scaled river profile, it is necessary to assume or estimate the concavity of the profile (Perron and Royden, 2013). We evaluated the slope–area scaling of escarpment-draining rivers (Fig. 4). The channel slope and drainage area data were extracted with the MATLAB-based software TopoToolBox 2 (Schwanghart and Scherler, 2014). We calculated the average slope and drainage area over predefined river segments. River segments were defined with a length of 1 km but break at confluences and were limited by both a threshold slope and drainage area. Recognizing that there were two sets of data, corresponding to the escarpment and the coastal plain, we searched for an optimal break point in slope–area space, searching within the red-dashed-line box in Fig. 4b.
We found concavities of 0.3 to 0.6 for the SWG rivers from a slope–area plot
with a mean value of 0.42, which is typical for bedrock rivers (Snyder et
al., 2000). Conventionally, normalized steepness index is taken as a proxy
for erosion rate (Kirby and Whipple, 2012). However, for an escarpment,
uplift rate is likely to be limited to the isostatic response to erosion,
and the erosion rate should be reflective rather of the erosion associated
with the escarpment retreat. Willett et al. (2018) analyzed this problem and
demonstrated that the slope–area scaling for a river retreating in a
direction opposite to its flow should scale according to
The segmented form of the escarpment-draining rivers is consistent with
models of escarpment retreat with a lower reach on the coastal plain, where
the gradient is sufficient to transport eroded sediment, but is not incising
bedrock. On the upper reach, incision rates are high but have a pattern
that results in horizontal retreat of the escarpment as well as the drainage
divide. The normalized steepness indices derived from slope–drainage area
plots or from the normalized channel profiles show a constant value for the
escarpment reaches, consistent with a constant rate of erosion but also
consistent with a constant horizontal retreat rate (Willett et al., 2018).
Furthermore, river profiles have the same form, but the lengths of the
various reaches are highly variable, even scaled into
Rivers that include plateau reaches (Fig. 3c and d) are scattered throughout the study area, intermixed with the escarpment rivers. This suggests that they are not the response to temporal variations in uplift rate; i.e., they are not moving knickpoints in response to base-level changes, or they would be clustered together spatially and have common chi profiles, at least within single drainage basins. Rather they appear to be the response to capture of river reaches from the plateau to the coastal plain (Giachetta and Willett, 2018).
The values of the normalized steepness on the escarpment reaches are relatively high compared to other rivers globally but particularly for the observed erosion rates (Fig. 5). In fact, the values of channel steepness from the Western Ghats are amongst the highest in the world at the observed erosion rates. Although the bedrock is relatively resistant to erosion, rainfall is also relatively high, so there is no obvious reason for these high values in a region where the tectonic uplift rates are likely to be low and not localized to the escarpment.
Taken together, these observations suggest that the Ghats escarpment is
actively retreating to the east. The high relief is likely to be old and
inherited rather than the result of recent uplift, and erosion is focused
on the escarpment, driving the escarpment horizontally rather than eroding
the entire landscape downward. This suggests that the
Normalized channel steepness index and cosmogenic
The use of cosmogenic isotope concentrations to derive erosion rates makes a
key assumption of continuous and steady removal of rocks from the Earth's
surface (Lal, 1991). As production of cosmogenic isotope nuclides is fast
with respect to erosion rates, steady erosion implies that the concentration
profile of a cosmogenic nuclide with depth is also time invariant (Niemi et
al., 2005). Catchment-wide detrital cosmogenic-based erosion rates relax
this assumption and require only that equilibrium is maintained between the
catchment-integrated quantities of production and removal. The appropriate
secular equilibrium state implies that over an appropriate timescale, the
number of cosmogenic isotope atoms produced is equal to the number lost by
erosion, as integrated over the entire catchment. The total rate of
production is predictable according to the geographic location, topology and
exposed lithology of the catchment (Stone, 2000; Lal, 1991). If we assume
well-mixed sediment derived from the entire catchment surface, the measured
concentration of a cosmogenic nuclide within these sediments is equal to the
total catchment production divided by the total volume of eroded rock, or
more precisely, the volume of the target mineral bearing the cosmogenic
nuclide, e.g., quartz (von Blanckenburg, 2005). Production divided by volume
can be expressed as the erosional mass flux out of the catchment surface. As
a flux, this requires the area of the surface, and in practice this area is
calculated from the surface projected onto a horizontal plane, as is done
with any standard digital elevation model. This implicitly defines the
erosional flux vector to be vertical. However, in general, the mass flux
does not need to be treated as a purely vertical flux. In many geomorphic or
tectonic settings such as the escarpment problem described above, the change
of the surface is better described with a component in the horizontal
direction with respect to the underlying rock, thus defining a flux in a
non-vertical direction. At rift escarpments, the mass flux of an
escarpment-draining basin can be approximated as purely horizontal and the
mass flux is determined by the rate of escarpment retreat with no vertical
component. This suggests a need to redefine the expressions describing
erosion rates in terms of
In the following section, we derive a model for catchment-wide mass flux based on the production of cosmogenic nuclides and concentrations measured from river sediments but for the case where the average motion of rock with respect to the Earth's surface is in a horizontal rather than a vertical direction. We then present two methods for calculation of mass flux and velocity from the measured detrital concentration and the catchment-wide nuclide production.
Cosmogenic nuclide (CN) concentration of river sediment at a basin outlet
represents the basin-integrated production of CNs and the basin-integrated
erosion of the rock (Granger et al., 2013):
Radioactive decay is only a factor if erosion rates are low. For CN
Shielding of cosmic rays on an individual surface is a function of the
surrounding topography on the skyline, as well as by local slope effects.
Cosmic ray shielding generally reduces surface production rate
This conventional calculation of basin-averaged erosion rates from CNs concentrations is widely used in many geological studies and can be done using standard software algorithms (e.g., CRONUS) (Balco et al., 2008) to calculate the basin-averaged erosion rate.
DCN concentrations as expressed above can be thought of as representing a
balance between two fluxes. The flux of cosmic rays into a catchment
determines the total production in the basin as given by Eq. (4). With a
steady state, this production is balanced by the export of the CNs within
eroded sediment. The flux of sediment out of the basin determines the mass
through which the CN is distributed and thus the concentration.
Concentration can be expressed in terms of the total production over a time
interval divided by the total volume of sediment produced over that time
interval (von Blanckenburg, 2005):
This concept can be generalized if we think of the rock within the Earth as
moving at a constant velocity,
Depiction of the flux of mass through the surface of a drainage
basin from the coastal escarpment of the Western Ghats, India. Basin
position is indicated as basin D in Fig. 2. Spatial surface of drainage
basin and its projection in the vertical and a horizontal direction.
Projected areas are
It is important to note that changing the assumed direction of the rock with
respect to the surface does not change any of the basic physical processes.
Production of a CN is unaffected as it is still produced within the same
depth range,
Escarpment retreat or other non-vertical motion of Earth's surface can be
regarded as being simply a result of spatially variable surface lowering. To
illustrate this point, consider the example shown in Fig. 7. A land surface
is represented by a one-dimensional profile represented by an exponential
function. This surface is back-cutting or retreating to the right,
maintaining its form. That motion can be represented by a vertical erosion
rate that is variable in space (Fig. 7b) or by a horizontal back-cutting at
a constant rate,
In two dimensions, the concept of horizontal motion of Earth's surface with respect to the underlying rock is somewhat more complicated. The complex geometry (Fig. 7e) of any catchment surface implies that there will never be perfect horizontal motion of that surface. Any given catchment has facets that dip in all directions (Fig. 7e), so pure, uniform, steady horizontal motion of a catchment is impossible. However, much as the catchment-averaged erosion rate is an average of a spatially variable quantity, the horizontal velocity can also be regarded as an average, where individual facets of the surface lower and retreat at different rates, but the net result can be characterized by an average horizontal velocity. For example, Fig. 7e shows a catchment from the Western Ghats draining the great escarpment. Although the drainage dips dominantly to the SW, there are both channel reaches and hillslopes that dip in all directions, including north or east. If erosion rates in this catchment are higher in the steep escarpment regions in the NE, individual slopes might retreat in any direction or not at all, but the catchment as a whole will expand to the NE, thereby “retreating” in this direction. The “average horizontal velocity” describes the regional motion of the surface by averaging all the individual slope changes. By parameterizing the problem in terms of a horizontal velocity of the surface with respect to its underlying rock, rather than a vertical erosion rate, we do not change any assumptions regarding geomorphic processes, or cosmogenic nuclide production and transport, but we do characterize the change in the landscape with a more representative metric. One important remaining assumption is that all points within the catchment are eroding fast enough that radioactive decay does not contribute significantly to secular equilibrium.
Relationship between mass flux through a surface and the velocity
for a retreating escarpment.
We assume that there is no distortion of the surface or rock and that the relative motion can be described as a single Euclidian vector without rotation. We present two methods for the calculation of mass flux and velocity from the measured detrital concentration and the catchment-wide nuclide production.
In the analysis above, we showed that the measured concentration of
Basin projection method Consider a representative escarpment-draining basin (e.g., the basin in Fig. 6);
if the erosion is completely efficient along the escarpment face, the
escarpment would form a planar surface retreating horizontally, leaving a
flat featureless coastal plain. However, erosion is not completely efficient
and although the channel profiles (Fig. 3) show most relief on the
escarpment face, lateral variations are significant and catchments show
considerable variability in morphology and, presumably, erosion rate. The
assumption in the calculation of an average is that inefficiencies in
escarpment erosion are balanced by the continued erosion of remnant
topography between the escarpment and the coastline. During a unit time
period, the mass of rock that is removed from the basin surface can be
calculated from the retreat rate Local scalar product method As an alternative to full surface projection, we can also calculate the
local surface projection. The dot product of the rock velocity and the
catchment surface To put this method into practice, we discretize the basin surface into
triangular elemental surfaces. The three vertexes of a triangular surface
are With a complex catchment surface and a horizontal velocity, there are many
local surfaces which dip towards the direction of rock motion, which implies
a local scalar product and a local mass flux
Local mass flux of elemental surfaces of an escarpment-draining
basin in the Western Ghats. Basin location is indicated as basin D in Fig. 2
and is also shown in Fig. 6. The basin surface is discretized into elemental
surfaces and color-coded with the relative magnitude of the local mass flux
for a horizontal rock velocity in the direction indicated. Flux is
normalized to the catchment-averaged mass flux. Thick white lines are
channels extracted from the DEM for a minimum drainage area of 1 km
In both the basin projection and local scalar product methods, it is necessary to select a direction for the velocity or mass flux vector. For the escarpment retreat problem, we can assume that this direction is purely horizontal but with an unknown azimuth. It is practical to sweep through a range of horizontal directions to determine the range of velocities associated with a range of directions. We pick channels that drain through the escarpment but do not appear to be recent captures and take the orientations of these channel segments as an estimate of the potential range of escarpment retreat directions. We then sweep through all possible azimuths within this range. This is visualized by plotting the resulting vector magnitudes as a function of directional azimuth.
An example of the calculation of horizontal retreat rate from
The local scalar product method has the characteristic that the inferred velocity increases rapidly as the direction rotates towards parallel with the dominant catchment flow direction. This is an artifact of the ability of a scalar product to take negative values. A typical catchment has a bowl-shaped geometry, open at the outlet, but as the basin is rotated, the horizontal view eventually sees only the side of the bowl, and with further rotation, would provide a view of only the back of the basin. Through this rotation, the effective area thus goes to zero or even negative, so that the flux goes to infinity for these orientations.
Escarpment retreat rate as a function of azimuth of a horizontal
mass flux vector using
As a demonstration as to how CN data can be used to constrain the geomorphic
evolution of a great escarpment, we use the cosmogenic
Mandal et al. (2015) report an average erosion rate of all
escarpment-draining basins in the southern Western Ghats to be
We evaluated all catchments draining the escarpment for which there are
reported detrital
The two methods yield broadly consistent results (Table 2, Fig. 10). However, the local scalar product method is much more sensitive to azimuth. It always shows a distinct minimum value of velocity, but velocity increases rapidly for other azimuths of velocity. For oddly shaped basins or for flux azimuths oblique to the dominant river direction, there is a strong influence of the negative values from the sides of a basin, and inferred velocities become large and deviate from those obtained from the basin projection method.
Comparison of retreat rates from the basin projection method and
the local scalar product method applied to the data from the Western Ghats
escarpment of India.
The basin geometry can play a large role in the inferred retreat rate.
Basin (a1) in Fig. 11 shows an almost symmetrical basin, with a clear flow
direction. The retreat rate is between 500 and 600 m/Myr and only weakly
dependent on azimuth for the basin projection method. The local scalar product
method gives a similar result for the most likely retreat direction
of N80E but deviates quickly for other azimuths. In particular, a more
northerly azimuth gives very high retreat rates, because high topography on
the south margin of the basin provides many negative pixels, reducing the
projected area and thus increasing the flux. Basin (c1) in Fig. 11 is
strongly asymmetric, with high topography (above
Example basins from the Western Ghats showing the retreat rate as
a function of azimuth of a horizontal mass flux vector using
In order to compare basins within the Western Ghats, we selected a common retreat direction and calculated retreat rates for all basins in this direction. We selected a direction that is normal to the regional coastline, which is estimated to be trending at N158W. Escarpment retreat rates calculated from both methods vary from 171 m/Myr to 2427 m/Myr and are shown in map view in Fig. 12.
The average value of the retreat rates is close to the retreat rate expected
from steady retreat of the escarpment from the coast to its present location
since the time of rifting of the margin (Fig. 13). The age of rifting of
India from Madagascar is constrained to be between 120 and 100 Ma
(Thompson et al., 2019). The important event for the formation of the
escarpment is the initial continental rifting that would have formed the new
water divides at the crest of escarpments on each margin, so an earlier age
is more likely. This event might have even predated other indications of
rifting. The majority of retreat rates from
Escarpment retreat rates in the normal direction of the reference
coastal line on the topography base map of the southern Western Ghats.
Topography is from SRTM 90 m DEM (Jarvis et al., 2008). Rates from
Current distance from the coastline against inferred retreat rate
of the Western Ghats escarpment basins from detrital
We also investigated the relationship between channel steepness of
escarpment reaches, escarpment elevation and escarpment retreat rate
(Figs. 14 and 15). Steepness is correlated with relief or total height of the
escarpment (Fig. 14). Such a relationship was predicted by Willett et al. (2018)
for escarpments retreating at a constant velocity; steepness would
need to increase with height in order to maintain the higher velocity
associated with higher remnant topography. We also plot the predicted
relationship between steepness and retreat rate from Eq. (2) for two values
of slope exponent,
Relationship between channel steepness and escarpment height in the Western Ghats. The channel steepness is calculated from slope–area plots using a uniform concavity of 0.42. Correlation is consistent with the theory that morphology has evolved to erode pre-existing topography at a constant rate of retreat. See Table 1 for the data.
Channel steepness against escarpment retreat rates with
Cosmogenic
One effect not accounted for in our horizontal flux calculation is the vertical uplift and flux that results from flexural compensation of the mass eroded from the escarpment face. Retreat of the escarpment generates a flexural isostatic uplift centered at the escarpment front but spread over a distance that encompasses the nearby plateau and lowland coastal plain. Approximately half of the flexural uplift occurs on the plateau side of the escarpment. This uplift is manifested as surface uplift, not exhumation, and therefore raises the height of the plateau edge above where it would be in the absence of an isostatic response. This increase in the height of the escarpment is accounted for in the projected basin area and thus is accounted for in the horizontal retreat calculation (Fig. 16a). However, uplift of the coastal plain is not part of the horizontal retreat calculations and if this uplift is eroded, it represents a vertical component to the erosional flux that we have not accounted for. Not accounting for this eroded mass implies that we have overestimated escarpment retreat rates, so we assess how large this effect is here.
The flexural uplift rate due to escarpment erosion can be quantified with
the isostatic deflection of a simple line load centered on the escarpment.
The magnitude of the line load is expressed as
The effect on our calculations depends on the uplift between the escarpment
and the point at which a DCN sample is taken. In Fig. 16b, we show this at
the coast, but in practice this will be closer to the escarpment. Assuming
complete erosion of uplifted rock, isostatic uplift results in a mass flux
through the surface. Mass flux is obtained by integrating the uplift from
the escarpment to the sample point at
Figure 16b shows the flux ratio
The calculation of a horizontal escarpment retreat rate is based on
recognition that the concentration of
In practice, there are some disadvantages to the local scalar method. The primary of these is the strong effect of blocking of flux by neighboring basins. If the flux direction is such that the sides of the basin overlap with neighboring basins, a negative flux results from these sides, canceling the corresponding flux from the escarpment surface. This is the “edge of the bowl” problem discussed above, where if one viewed the basin in the direction of the flux vector, one could see only the outside of the basin. This is not necessarily an error, depending on the geometry of the basins and the erosive role of the neighboring basin, so this approach may or may not be correct, but the basin projection method is less sensitive to this effect, and so gives a more robust, if not more accurate, result.
Within a given escarpment-draining basin, the dependence of retreat rate on
retreat direction (e.g., Fig. 9) comes directly from the geometry of the
basin surface. Isolated buttes, inselbergs or other topography internal to
the drainage basin such as escarpment-normal interfluvial ridges, define a
type of remnant topography due to inefficient retreat of the escarpment.
Buttes are generally regarded to be part of the ancient escarpment but now
are erosion residuals (Gunnell and Harbor, 2010). Their existence attests to
some inefficiency in the past escarpment erosion, such that a portion of the
high topography is not removed as the escarpment passes. If the erosional
efficiency of the escarpment is variable along strike, we would expect the
low efficiency segments of the escarpment to lag and potentially become
isolated from the escarpment forming a butte. An important question for our
analysis is how this impacts the
By calculating the mean retreat rate, we are implicitly assuming that
anomalously slow-retreating escarpment segments, including incipient buttes,
are balanced by segments elsewhere in the same catchment that have higher
retreat rates. As with vertical erosion rate calculations, spatial variation
will not impact the mean unless it has an extreme variation that affects the
assumptions regarding production or radioactive decay. This is also valid
for the formation of remnant topography. For example, a butte forms because
part of the escarpment was eroding at a retreat rate slower than the
average. After a butte has formed as an isolated topographic feature, it
continues to erode, thus contributing sediment (and
Pure horizontal mass flux is an end-member flux direction; the other end-member is purely vertical. Horizontal flux requires assuming an azimuth direction. Both methods for calculating a purely horizontal mass flux have an important azimuthal dependence. The local scalar product method is more sensitive than the basin projection method to the assumed direction. Drainage basins have surfaces dipping in all directions but dominant directions are evident (e.g., Fig. 7e). A perfect escarpment basin would have rivers and hillslopes dipping nearly normal to the escarpment, in which case the direction of propagation is easy to determine, but most basins have geometry that is more complex (Fig. 7e) and this leads to sensitivity to the selected azimuth. Inferred rates deviate if the azimuth varies far from the dominant direction, particularly with the local scalar product method. The basin projection method displays less azimuthal sensitivity. At the largest scale, a rift margin escarpment is sinuous, implying variations in its average long-term retreat rate and local direction. The Western Ghats is assumed to be retreating at N57E, but locally, there is likely to be considerable variation in retreat direction.
Retreat rates from our analysis are on the order of 100 m/Myr to 1 km/Myr. The
retreat rates are horizontal, but the dominant physical process is still
vertical incision of rivers (Fig. 7a–c). As we use DCN
Using the current coastline and the rifting age as reference position and
time also gives an average retreat rate of hundreds to thousands of meters per Myr
since continental break-up. For this calculation, the modern coastline is
assumed to represent the locus of the break-up structures, which may not
always be true, although the western margin of India shows that the
structural hinge between uplift and subsidence is close to the modern coast
(Campanile et al., 2008; Chaubey et al., 2002). Average retreat rates are in
the same range but systematically higher than DCN
Although offshore sedimentation records are difficult to interpret given that basins are open to sediment export and recycling of sediment by subsequent erosion, records do not generally support steady rates of sediment supply with time since rifting. The offshore Konkan and Kerala basins abutting the Western Ghats record two pulses of intensive sedimentation: a Paleocene phase and a Pliocene phase (Campanile et al., 2008). If these sediment records are correct reflections of sediment supply from the eroding escarpment, they suggest that the correspondence between modern and long-term retreat rates might be fortuitous. However, the cause of the variations in erosion rate remains unclear. Escarpment relief might have changed over time if there has been significant continental uplift or tilting due to mantle dynamic flow, but there is no evidence for this aside from the variations in offshore sediment volume. The consistency in escarpment morphology and lack of along-strike variations in height, morphology or distance from the coast suggests that escarpment retreat has been the dominant process since rifting and any dynamic uplift would need to affect the entire margin nearly uniformly. A role for dynamic uplift, however, does remain possible and would affect the temporal variability of escarpment retreat. The other possibility is climate change; changing precipitation rates through the Cenozoic would also affect the erosional efficiency and thus retreat rate of the escarpment. Given India's migration from the tropics to its current midlatitude position and global climate changes over the Cenozoic (Kent and Muttoni, 2008), climate change certainly occurred and some impact on temporal variations in retreat rate is likely.
Large escarpments such as those that occur on many passive margins represent
disequilibrium landscapes that have a long timescale of response and are
characterized by erosion rates localized onto the escarpment, thereby
driving retreat of the escarpment inland. Erosion rates are strongly
variable in space, so an average erosion rate, as derived from detrital
cosmogenic nuclides for catchments draining the escarpment, does not give an
effective characterization of the rates of landscape change. We have
addressed this issue by showing how
Study of the Western Ghats demonstrates that the morphology of the escarpment rivers is consistent with evolution of the escarpment to a form driving escarpment retreat at a constant rate with a low-steepness coastal reach keeping up with sediment transport and isostatic uplift, and a steep-escarpment reach driving landward retreat. Escarpment retreat leads to episodic capture of plateau rivers, and we found numerous examples of rivers with high flat reaches characteristic of capture. These examples were distributed randomly along the escarpment, inconsistent with the alternative model of constant catchment geometry and transient uplift.
The general conclusion of this study is that great escarpments on passive margins are dynamic features with significant rates of retreat and high local rates of mass removal by erosion. Although rates are likely to be variable in time, escarpment retreat appears to be active from the time of rifting to the modern with current and average rates at hundreds to thousands of meters per million years, and these rates can be estimated by analysis of cosmogenic isotope concentrations.
Related codes are available at
Data used in this paper are available at
YW and SDW conceptualized and designed the research. YW analyzed morphological features, developed the theory, developed the codes, conducted calculations, analyzed the data, wrote the manuscript and prepared the figures. SDW contributed to theory development and data interpretation, and provided input on the manuscript.
The authors declare that they have no conflict of interest.
We thank Maarten Lupker for valuable discussions.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This paper was edited by Jens Turowski and reviewed by Greg Balco and one anonymous referee.