Earth and Planetary Science Letters 416 (2015) 12–20
Contents lists available at ScienceDirect
Earth and Planetary Science Letters
www.elsevier.com/locate/epsl
Sea-level responses to erosion and deposition of sediment
in the Indus River basin and the Arabian Sea
Ken L. Ferrier a,b,∗ , Jerry X. Mitrovica b , Liviu Giosan c , Peter D. Clift d
a
School of Earth and Atmospheric Sciences, Georgia Institute of Technology, United States
Department of Earth and Planetary Sciences, Harvard University, United States
c
Department of Geology and Geophysics, Woods Hole Oceanographic Institution, United States
d
Department of Geology and Geophysics and Coastal Studies Institute, Louisiana State University, United States
b
a r t i c l e
i n f o
Article history:
Received 17 July 2014
Received in revised form 20 January 2015
Accepted 23 January 2015
Available online xxxx
Editor: G.M. Henderson
Keywords:
sea level
sediment
Indus River
a b s t r a c t
Changes in sea level are of wide interest because they shape the sedimentary geologic record, modulate
flood-related hazards, and reflect Earth’s climate. One driver of sea-level change is the erosion and
deposition of sediment, which induces changes in sea level by perturbing Earth’s crust, gravity field, and
rotation axis. Here we use a gravitationally self-consistent global model to explore how sediment erosion
and deposition affected sea level during the most recent glacial–interglacial cycle in the northeastern
Arabian Sea and the Indus River basin, where fluvial sediment fluxes are among the highest on Earth. We
drive the model with a widely used reconstruction of ice mass variations over the last glacial cycle and a
sediment loading history that we constructed from published erosion and deposition rate measurements.
Our modeling suggests that sediment fluxes from the Indus River are large enough to produce meterscale changes in sea level near the Indus delta in as little as a few thousand years. These sea-level
perturbations are largest closest to the center of the Indus delta, and they grow larger over time as
sediment deposition increases. This implies that the elevation of sea-level markers near the Indus delta
will be significantly altered by sediment transfer over millennial timescales, and that such deformation
should be accounted for in studies that use paleo-sea-level markers to infer past ice sheet volume or
explore local processes such as sediment compaction. Our analysis highlights the role that massive fluvial
sediment fluxes play in driving sea-level changes over >1000-yr timescales from the Indus River, and, by
implication, from other rivers with large sediment fluxes.
© 2015 Elsevier B.V. All rights reserved.
1. Introduction
Small increases in sea level prime coastlines for huge disasters. The flooding generated by Hurricane Sandy in November
2012, for instance, was responsible for tens of billions of dollars
(US) of damage and the loss of ∼250 lives (Aerts et al., 2013;
McNally et al., 2014). Flood-related damages of this scale will
likely grow more frequent as a result of the anticipated changes
in sea level over the coming century. Global mean sea level is projected to rise by 19–83 cm by 2100 relative to that in 1985–2005
(Church et al., 2013), which will reduce the size of the storm sufficient to inundate coastal cities and increase the frequency with
which storms do so (e.g., Fitzgerald et al., 2008). With ∼10% of the
world’s population living at elevations of <10 m (McGranahan et
*
Corresponding author at: School of Earth and Atmospheric Sciences, Georgia Institute of Technology, United States.
E-mail address: [email protected] (K.L. Ferrier).
http://dx.doi.org/10.1016/j.epsl.2015.01.026
0012-821X/© 2015 Elsevier B.V. All rights reserved.
al., 2007), these increases in sea level pose a particularly acute hazard. Such hazards motivate continued efforts to fully understand
the physics of sea-level change.
In this paper we focus on sea-level responses to erosion and
deposition of sediment over the most recent glacial–interglacial
cycle (∼120 ka to the present). While sea-level change on short
timescales (seconds to decades) is dominated by waves, tides, currents, thermosteric effects, and water fluxes between the oceans,
ice sheets, atmosphere, and continents (e.g., Cazenave and Llovel,
2010), sea-level change on longer timescales (103 –106 yr) is dominated by ice sheet growth, tectonics, and changes in surface loads,
which perturb Earth’s crustal elevation, its gravity field, and its rotation axis (e.g., Mitrovica et al., 2001; Mitrovica and Milne, 2002).
This includes perturbations due to changes in sediment loads.
It has long been known that the transfer of sediment from
continents to oceans affects sea level by perturbing the elevation of the seafloor (e.g., Bloom, 1964; Watts and Thorne, 1984;
Simms et al., 2007, 2013; Ivins et al., 2007; Blum et al., 2008;
Wolstencroft et al., 2014), but only recently have these and related
K.L. Ferrier et al. / Earth and Planetary Science Letters 416 (2015) 12–20
effects been incorporated into a gravitationally self-consistent
framework for modeling global sea-level variations (Dalca et al.,
2013; Wolstencroft et al., 2014). Incorporating the impact of sediment redistribution in a gravitationally self-consistent fashion is
complex because the associated redistribution of sediment and
water alters Earth’s shape and gravity field, which in turn induces
further redistribution of water. Modeling sea-level changes thus requires accounting for water’s gravitational attraction to itself (e.g.,
Farrell and Clark, 1976). In this paper we adopt the treatment of
Dalca et al. (2013) to predict sea-level responses to the combined
changes in ice, ocean, and sediment loads.
In considering the impact of sediment transfer on sea level, we
focus on responses that occur over timescales of ∼103 –105 yr, because the viscoelastic deformation of the Earth is slow enough that
sea level takes tens of thousands of years to completely equilibrate
to changes in surface loads (e.g., Cathles, 1971; Peltier, 1974). Fully
understanding sea-level variations at any moment in Earth’s history thus requires accounting for changes in surface loads over
the preceding tens of thousands of years. One implication of this
is that sea level today is responding to sediment transfer that
happened over ten thousand years ago, and that a complete understanding of what is driving modern sea-level changes requires
quantifying how much past erosion and deposition continue to influence modern sea level.
Our goal in this study is to explore sea-level responses to erosion and deposition of sediment in the northeastern Arabian Sea
and the Indus River basin. We choose this as a study area because
sediment-driven effects on sea level in this area are large – fluvial sediment fluxes in the Indus River are among the highest on
Earth (Milliman and Farnsworth, 2011) – and because the modeled
sea-level history can inform studies of the response of local midHolocene human civilizations to changes in sea level (e.g., Giosan
et al., 2012).
In this paper, we review the theory underlying sediment-driven
changes in sea level and describe how we constructed a sediment loading history for the study area. Our analysis suggests that
sediment fluxes from the Indus River are large enough to generate meter-scale sea-level perturbations near the Indus delta over
timescales as short as a few thousand years, and that these perturbations grow larger over time. This implies that any paleo-sea-level
markers older than a few thousand years near the Indus delta are
likely to be significantly deformed by sediment fluxes, and that accurately inferring paleo-ocean water (or, equivalently, ice) volume
from such markers requires accounting for the deforming effects of
sediment transfer.
2. A brief review of static sea-level theory and model
implementation
2.1. Theory
Modern theories for post-glacial sea-level change are built on
the work of Farrell and Clark (1976), who derived expressions
for the gravitationally self-consistent redistribution of water during the growth and melting of ice sheets. These expressions were
based on an equilibrium sea-level theory in which the redistribution of water is determined by perturbations in the elevation of
the Earth’s crust and the gravitational equipotential that defines
the sea surface. This equilibrium sea level is commonly known as
static sea level, and may be understood as the background sea level
upon which short-term perturbations caused by waves, tides, and
currents are superimposed.
Farrell and Clark (1976) developed their static sea-level theory
for a viscoelastic non-rotating Earth with fixed shorelines, a theory
that has since been generalized to include sea-level responses to
changes in Earth’s rotation (e.g., Milne and Mitrovica, 1996, 1998),
13
Fig. 1. Schematic of sea level in the presence of sediments and ice. Changes in sediment thickness, H , and ice thickness, I , produce changes in the elevation of the
sea surface equipotential (G) and the crust ( R), and thereby induce changes in
sea level (SL), as defined in Eq. (2). Modified from Dalca et al. (2013).
shoreline migration (e.g., Johnston, 1993; Mitrovica and Milne,
2003; Kendall et al., 2005), and sediment transfer (Dalca et al.,
2013). Extensive descriptions of the sea-level theory and its numerical implementation may be found in Dalca et al. (2013). Here
we briefly describe the central aspects of the sea-level theory.
We first define what we mean by sea level. Consider the
schematic in Fig. 1. Sea level in ice age theory is defined as the elevation difference between two globally defined surfaces. The first
is the equipotential height G, which is the elevation above an arbitrary datum of the gravitational equipotential that defines the sea
surface. The second is Earth’s solid surface, which is defined as
the sum of the crustal elevation R above the same arbitrary datum, the sediment thickness H , and the grounded ice thickness I
(Fig. 1). Thus, sea level is given by:
SL = G − R − H − I .
(1)
Because each term on the right side of Eq. (1) is defined over
the whole planet, the sea-level field SL is also defined globally.
That is, sea level is defined over continents as well as over oceans.
At a site in the ocean, for example, sea level is the thickness of sea
water, while at a continental site with no sediment or grounded
ice, sea level is the elevation difference between the sea surface
equipotential and the surface of the crust. Following Eq. (1), sea
level is the negative of the topography, under the usual definition
of topography as the elevation of the crustal surface relative to the
local sea surface equipotential.
Eq. (1) follows the traditional geological definition of sea level.
It is useful for interpreting the sedimentary rock record because it
considers the sea surface elevation relative to the ground, which
is where the sedimentary record is formed. It is also useful for
studies that use past indicators of global ocean water volume to
infer ancient ice volumes, because the global ocean water volume
is the thickness of the water column – i.e., sea level in Eq. (1) –
integrated over the ocean area. This definition differs from geodetic
studies that define sea level as the elevation of the sea surface
equipotential relative to another datum, such as satellite ranging
measurements of sea surface height.
The sea-level theory developed by Farrell and Clark (1976) computes the total change in sea level, SL, in response to changes in
mass loading on the Earth’s surface between an initial time and a
later time. Using Eq. (1), we may write:
SL = G − R − H − I ,
(2)
where H and I are changes in the thickness of sediment and
grounded ice, respectively, since the onset of loading, and G and
R are the resulting perturbations in the elevation of the sea surface equipotential and crust, respectively.
Eq. (2) is commonly known as the sea-level equation, and it is
what we use to compute changes in sea level in this paper. The
changes in sea level in Eq. (2) are driven by changes in surface
loading L, which we compute as the total change in water, sediment, and ice mass loads:
L = ρw S + ρs H + ρI I
(3)
14
K.L. Ferrier et al. / Earth and Planetary Science Letters 416 (2015) 12–20
Here ρw , ρs , and ρI are the densities of water, sediment, and ice,
respectively, and S is the change in the thickness of seawater.
Eqs. (2) and (3) are characterized by a circularity that reflects
an important aspect of the physics of sea-level change. That is,
changes in ice and sediment loads perturb the elevations of the
crust and sea surface equipotential, and thereby drive changes in
sea level. However, the resulting redistribution of water represents
a change in the surface load that induces further perturbations
in the elevations of the crust and sea surface equipotential. In
other words, computing changes in sea level requires computing
changes in the elevations of the crust and sea surface equipotential, which are themselves dependent on changes in sea level.
Mathematically, G and R in Eq. (2) depend on S through the
expression for the total surface mass load, Eq. (3), such that computing SL requires S. Thus, Eq. (2) is, in its detailed form, an
integral equation, and its solution generally requires an iterative
scheme in which a first guess to S is successively improved.
It will also be useful to define relative sea level. Relative sea
level at some arbitrary time t is defined as the sea level at time t
relative to sea level at present day, t p . Using Eq. (2) above, we can
write
RSL(t ) = SL(t ) − SL(t p ) = SL(t ) − SL(t p ).
(4)
At a specific site, RSL(t ) represents the predicted elevation of a
sea-level marker (e.g., a shoreline or a coral reef) of age t relative
to present sea level.
The definitions in Eqs. (2) and (4) include the change in sea
level associated with the direct topographic changes resulting from
sediment erosion or deposition (i.e., H ). It will be useful, in the
discussions below, to consider slightly altered definitions that ignore these contributions. In particular, we can write
SLGR = G − R ,
(5)
and
RSLGR (t ) = SLGR (t ) − SLGR (t p ).
(6)
We emphasize that these equations include crustal deformations
and the associated gravity perturbations driven by the changing
sediment load (i.e., Eq. (3) is adopted in computing G and R
in Eq. (5)) and it is only the direct effect of the sediment height
on crustal elevation that is ignored in Eqs. (5) and (6). Moreover,
in this study, we only consider sites with no changes in local ice
cover, and thus only this direct effect of changes in sediment thickness on crustal elevation contribute to the difference between SL
and SLGR or between RSL and RSLGR .
Because Eqs. (5) and (6) ignore direct changes in topography
associated with sediment deposition and erosion, the fields they
describe isolate changes in sea level that arise from isostatic adjustment and perturbations in Earth’s gravity field in response to
the surface mass loading from ice, ocean, and sediment. In the discussion below we focus in large part on SLGR and RSLGR .
2.2. Numerical implementation
Sea-level responses to changes in ice and sediment loads are
governed by the viscoelastic and density characteristics of the
Earth. In our numerical model, we adopt, for the purpose of illustration, a spherically symmetric Earth with an elastic lithosphere
90 km thick and a viscosity profile given by a model known as
VM2 (Peltier, 2004), and profiles for density and elasticity parameters given by the Preliminary Reference Earth Model (PREM;
Dziewonski and Anderson, 1981). We use the ETOPO2 global topographic data set for the modern topography (United States Department of Commerce, 2001).
We drive the model by imposing time series of changes in
sediment thickness H and ice thickness I over one glacial cycle, from 122 ka to the present. These are cumulative changes
since the onset of the model run. Given these inputs for H
and I , the calculation of sea-level changes using Eq. (2) requires
computing perturbations in the sea surface equipotential G and
crustal elevation R. In the case of 1-D (i.e., depth varying) viscoelastic structure, we follow the usual approach and compute G
and R using a viscoelastic Love number theory (Peltier, 1974;
Kendall et al., 2005; Dalca et al., 2013).
We prescribe the ice load history I using version 1.2 of the
global ICE-5G model for the last glacial cycle (Peltier, 2004). The
model is characterized by a glaciation phase that begins at 122 ka,
a glacial maximum extending from ∼26 to 21 ka, and an end to
deglaciation (and start of the present interglacial) at 4 ka. The
ICE-5G model includes variations in the major ice sheets that existed during the last glacial cycle (i.e., the Greenland, Laurentide,
Fennoscandian, and West and East Antarctic ice sheets, etc.), but it
does not include variations in Himalayan alpine glaciation, which
are capable of perturbing sea level in our region of study (e.g.,
Mitrovica et al., 2001; Lambeck and Purcell, 2005), although the
glacial advance in the western Himalaya at the LGM was relatively
modest because of the dry climate (Owen et al., 2002). In the next
section, we describe how we constructed a sediment load history
H .
3. Methods: generating a sediment history for the Indus River
and northeastern Arabian Sea
To calculate sea-level responses to sediment transfer, the sealevel model must be fed a time series of global grids, each containing the cumulative change in sediment thickness since the beginning of the model run ( H in Eq. (2)). In this paper we call such
a time series of grids a sediment transfer scenario. Here we briefly
describe how we constructed a sediment transfer scenario for the
region around the Indus basin and the northeastern Arabian Sea
(more details may be found in Supplementary Information). The
scenario is based on published measurements of erosion and deposition rates, and represents our best estimate for the sediment
redistribution in the region over the most recent glacial cycle.
We began by using published measurements to create a grid
of modern erosion and deposition rates at 0.01◦ resolution (Fig. 2;
Table S1). Nearly all erosion rates in this compilation were derived
from fluvial sediment flux measurements, and therefore are averaged over the basin’s area and the duration of monitoring, which
varied from 11 to 39 yr among the studies we considered. Our
analysis neglects mass redistribution associated with solute fluxes,
which modern fluvial measurements suggest total 10 Mt/yr in the
Indus River (Milliman and Farnsworth, 2011), or <3% of the total
mass flux from the Indus River (Table S1).
Most deposition rates were derived from dated sediment cores,
and therefore are averaged over the age of the core. 94% of the
sedimentation rate measurements in this compilation are averaged over <18 000 yr, and the remaining 6% are averaged over
<127 000 yr. In the Arabian Sea, we used an inverse distance
weighted interpolation scheme to estimate deposition rates between the point measurements of deposition rates. For terrestrial
drainage basins without measured erosion rates, we assigned erosion rates based on published erosion rate measurements from
nearby basins.
We next resampled the rates onto a global grid with 512 rows
and 1024 columns suitable for input to the numerical sea-level
model. We multiplied the erosion and deposition rates by the densities of the eroded and deposited material: 1900 kg m−3 on the
Indus plain (Farah et al., 1977) where the material is relatively
unconsolidated sediment, 2700 kg m−3 everywhere else on land
where the material is assumed to be bedrock, and 1750 kg m−3
(Clift and Giosan, 2014) in the ocean. We then rescaled the marine
deposition rates downward by a factor of 4.37 to ensure that the
K.L. Ferrier et al. / Earth and Planetary Science Letters 416 (2015) 12–20
Fig. 2. Locations of erosion rate and deposition rate measurements used to construct
the sediment transfer scenario discussed in the main text and supplementary file
(see Table S1). Dots in the Arabian Sea show sites of sediment cores with published
sedimentation rates. Terrestrial regions with published erosion rate or sedimentation rate data are shaded gray, and basins without published erosion rate measurements are colored white with black outlines. Terrestrial regions without published
erosion rates were assigned rates based on rates in neighboring regions (Table S1).
Shaded regions in the Arabian Sea have published areally-averaged estimates of sedimentation rates (Table S1).
integrated rate of continental erosion equaled the integrated rate
of marine deposition by mass. We assigned the resulting grid to
the time period 10–0 ka (Fig. 3E).
There are few empirical constraints on erosion and deposition
rates for times earlier than ∼10 ka. The constraints that exist are
in the Indus plain, the Indus delta, and the Indus fan. For continental regions outside these regions – i.e., everywhere else in the
Indus basin and all other drainage basins – we set erosion rates between 122–10 ka to be equal to those in the 10–0 ka period. Using
this assumption, and adopting available constraints, we divided the
sediment transfer scenario from 122–10 ka into four time periods
(Fig. 3).
During 14–10 ka, ocean water volume increased rapidly as the
global ice sheets collapsed. Sediment cores suggest that the Indus upper plain was depositional prior to 10 ka (Clift and Giosan,
2014), but do not provide strong constraints on the average deposition rate in this region over the entire glacial period. In
the absence of detailed control, we assigned deposition rates on
the Indus upper plain such that the integrated volume of sediment deposited since the Last Interglacial (that is, from 122 to
10 ka) matched the integrated volume of sediment eroded during
10–0 ka.
As ocean water volume increased from 14 ka to 10 ka, parts
of the continental shelf that had been subaerial became submerged, which affected patterns of sediment deposition. The edge
of the continental shelf is ∼50–130 km from the modern shoreline within most of the study region, and is as much as ∼260 km
from the modern shoreline off the Gulf of Cambay. We assigned
15
Fig. 3. A timeline of erosion and deposition rates used to create the sediment transfer scenario discussed in Section 3. A: At the onset of the model run (122 ka, at
the end of the previous interglacial), we set erosion and deposition rates equal to
those in the present interglacial (panel E). B: One representative frame of the transition period from 120–110 ka, for which we modified deposition rates on the Indus
shelf and fan as the shoreline migrated seaward. C: We assigned temporally constant rates during the bulk of the glacial period (110–14 ka). D: One representative
frame of the transition period from 14–10 ka, for which we modified deposition
rates on the Indus shelf and fan as the shoreline migrated landward. E: Rates assigned to the modern interglacial (10–0 ka) are based on measurements in the
literature (Table S1). In each panel, the plotted shoreline is the present shoreline,
and the integrated marine deposition flux (t yr−1 ) has been set equal to the integrated terrestrial erosion flux (t yr−1 ). As shown at bottom right, red colors indicate
areas of deposition whereas blue colors indicate areas of erosion. (For interpretation of the references to color in this figure legend, the reader is referred to the
web version of this article.)
deposition rates on the Indus shelf at 14–10 ka based on the
shoreline location computed at each time step from a preliminary, no-sediment redistribution scenario. For submarine regions
on the Indus shelf, we assigned deposition rates identical to those
in the 10–0 ka rate grid. For subaerial regions on the Indus shelf,
we assigned deposition rates given by the nearest subaerial grid
cell in the Indus delta at 10–0 ka. For times when the Gulf of
Kutch was above water, we assigned that region a deposition rate
of zero because most modern sediment deposition in the Gulf of
Kutch is derived from alongshore transport of Indus River sediment, which was disconnected from the Gulf of Kutch at those
times (e.g., Ramaswamy et al., 2007).
Although the compiled measurements imply that modern deposition in the deep Arabian Sea is slow (Table S1; Fig. 3E; see also
Prins et al., 2000), the existence of a large sedimentary fan that
extends from the Indus delta as far south as ∼9◦ N in the deep
Arabian Sea requires that much of the Indus River’s sediment is
transported to the deep ocean over million-year timescales (e.g.,
Kolla and Coumes, 1987; Clift et al., 2001). Much of this transport
may occur during glacial periods, when the shoreline is farther
seaward and less Indus River sediment is trapped on the continental shelf. To mimic deposition on the Indus fan during glacial
periods, we assigned deposition rates that are fastest at the northern end and decline exponentially with distance from the shelf
with an e-folding length of 300 km. We scaled deposition rates
on the fan such that the integrated mass deposition rate on the
fan matched the integrated eroded mass flux from the Indus basin
minus the deposited mass flux on the Indus shelf and the Gulf
of Kutch. One representative grid from 14 to 10 ka is shown in
Fig. 3D.
16
K.L. Ferrier et al. / Earth and Planetary Science Letters 416 (2015) 12–20
Fig. 4. Cumulative changes in inputs to and outputs from the sea-level model over
the 122 kyr model run, driven by ICE-5G (Peltier, 2004) and the sediment transfer
scenario discussed in Section 3 (see Fig. 3). A: The input change in sediment thickness, H . B: The change in computed sea surface elevation, G, multiplied by a
factor of ten to make its variations visible in this color scheme. C: The computed
change in the elevation of the crust immediately underlying the deposited or eroded
sediment, R. D: The computed change in sea level not including direct changes
in crustal elevation associated with sediment deposition or erosion (i.e., SLGR =
G − R; Eq. (5)). E: The computed change in sea level, SL = G − R − H
(Eq. (2)).
For the period 110–14 ka, sediment cores suggest that the Indus lower plain was erosional (Clift et al., 2008), so we assigned
deposition rates on the Indus lower plain such that the integrated
volume of sediment eroded over 110–14 ka matched the integrated volume of sediment deposited during the remainder of the
simulation. In all other regions, we assigned rates the same way
we did during the 14–10 ka period. Because the shoreline was relatively stable during this period, we assigned temporally constant
rates over the period 110–14 ka (Fig. 3C).
For 120–110 ka, the shoreline migrated rapidly as the ice sheets
grew. We assigned rates to this transition period the same way we
did during the 14–10 ka transition period. One representative grid
from this period is shown in Fig. 3B.
For 122–120 ka, almost no empirical constraints on erosion and
deposition rates are available. We assigned to this period the same
rates we assigned to the 10–0 ka period (Figs. 3A, 3E), under the
assumption that erosion and deposition rates during the previous
interglacial were similar to those during the present interglacial.
4. Results
4.1. Changes in sea level, crustal elevation, sediment thickness, and sea
surface height over the 122-kyr simulation
We ran the sea-level model using the imposed ice mass variations (ICE-5G; Peltier, 2004) and the sediment mass redistribution
summarized in Fig. 3. Fig. 4 shows a snapshot of the cumulative sediment redistribution and various outputs at the end of the
model run.
Figs. 4A–C show the cumulative changes in sediment thickness H , the height of the sea surface equipotential G, and the
crustal elevation R, respectively, over the 122 kyr simulation.
(Note that G in Fig. 4B is amplified by a factor of ten to render its spatial variations visible under the color scheme in Fig. 4.)
Fig. 5. Relative sea-level predictions in scenarios with and without sediment transfer. Positive values (red colors) indicate that sea level at 4 ka was higher than at
the present; negative values (blue) indicate that it was lower. Frames A–C are based
on the definition of relative sea level in Eq. (6), which shows the contribution from
changes in the elevation of Earth’s crust and gravitational equipotential (i.e., RSLGR ).
Frames D–F are analogous to A–C but use the definition of relative sea level in
Eq. (4), which includes the direct topographic contribution from erosion and deposition of sediment (i.e., RSL). A, D: A snapshot of relative sea level at 4 ka in response
to changes in ice loading (ICE-5G; Peltier, 2004) and the sediment transfer scenario
discussed in Section 3 (see Fig. 3). White squares show locations of Karachi (K;
24.81◦ N, 67.02◦ E), Lothal (L; 22.52◦ N, 72.25◦ E), and South Saurashtra (S; 20.90◦ N,
70.37◦ E). B, E: Relative sea level at 4 ka in response to ice mass variations alone,
with no sediment redistribution. C: Difference in relative sea level between panels
A and B. F: Difference in relative sea level between panels D and E.
Figs. 4D and E show two estimates of the cumulative change
in sea level calculated from the quantities in Figs. 4A–C. Fig. 4D is
the change in sea level calculated from Eq. (5) (i.e., SLGR ). As discussed above, this field does not include the direct effect of erosion
or deposition on topography, and thus reflects the contribution of
isostatic and gravitational adjustments to the sea-level change. Alternatively, it may be interpreted as the total sea-level change at a
point on the Earth’s surface that experienced negligible erosion or
deposition during the simulation, such as an erosionally resistant
rock outcrop standing above any deposited sediment. In contrast,
Fig. 4E shows the change in sea level as defined by Eq. (2) (i.e.,
SL). This field represents the total change in height of the sea
surface equipotential relative to the sea bottom, or solid surface,
where the latter includes direct topographic changes caused by
erosion or deposition. For example, at a marine site, this quantity represents the change in the thickness of the water column at
that site.
We note that at sites where | H | exceeds |G − R − I |,
the direct effect of changes in sediment thickness on crustal elevation determines the sign of local sea-level change. A comparison of
Figs. 4D and 4E provides examples of sites where changes in sediment thickness exert minimal direct influence on changes in sea
level and sites where H dominates predicted changes in local sea
level.
4.2. Relative sea-level responses in simulations with and without
sediment transfer
Fig. 5A shows a map of RSLGR (Eq. (6)) at 4 ka (i.e., the start
of the interglacial) over the study area in a simulation driven by
the combined changes in ice and sediment. Fig. 5B shows the
analogous response for a simulation in which no sediment transfer occurs, and sea-level changes are driven only by ice mass
changes. Fig. 5C shows the difference between the sediment and
no-sediment simulations (Fig. 5A minus Fig. 5B). Figs. 5D–F are
K.L. Ferrier et al. / Earth and Planetary Science Letters 416 (2015) 12–20
17
Fig. 6. Modeled relative sea-level histories (calculated as RSLGR ; Eq. (6)) at Karachi, Lothal, and South Saurashtra (Fig. 5). Panels A–C show the predicted responses to the
combined ice and sediment loading (solid line) and to ice loading only (dashed line) over the past 10 000 yr. Panels D–F are identical to panels A–C except that they cover
the entire model run, which spans the last glacial cycle. Panels G-I show the difference between the responses in panels D–F computed with and without sediment loading.
analogous to Figs. 5A–C, with the exception that they include the
direct topographic changes due to erosion and deposition (RSL;
Eq. (4)). Fig. 5B and 5E are identical since there is no sediment
redistribution in this particular simulation and no local ice mass
changes.
Figs. 6A–F show predicted relative sea-level histories (calculated
as RSLGR ) at the three sites marked in Fig. 5A: Karachi (K), on the
western side of the Indus delta at the modern coast; Lothal (L),
∼40 km north of the northern tip of the Gulf of Cambay; and
South Saurashtra (S), on the modern coast between the Gulfs of
Cambay and Kutch. The dashed lines are RSL predictions in the
case of a simulation with ice mass variations only. The solid lines
are relative sea-level predictions following the definition in Eq. (6),
in a simulation that includes both ice mass variations and sediment redistribution. Figs. 6G–I show the differences between predictions based on the simulations that include sediment redistribution and those that do not.
4.3. Effects of sediment redistribution on modern rates of sea-level
change
In Fig. 7 we turn our attention to the predicted rate of sealevel change over the most recent 100 yr of the simulation. Fig. 7A
shows the difference between a simulation that includes sediment
redistribution and one that does not, where the sea-level change
is defined as in Eq. (5) (i.e., SLGR ). Fig. 7B is analogous to Fig. 7A,
with the exception that the sea-level change is computed using
Eq. (2) (i.e., SL).
5. Discussion
The results in Fig. 4 indicate that the cumulative regional sealevel change since the start of loading (Fig. 4E) is dominated by
changes in crustal elevation, R, and sediment thickness, H .
Both R and H are significantly larger than changes in the
height of the sea surface equipotential, G. At the end of the
122 kyr model run, for instance, the peak value of G in Fig. 4B is
1.4 m, or less than 4% of the maximum value of R in the same
region (Fig. 4C).
The perturbations G and R vary smoothly over distances
of several hundred km, which reflects the damping of short-
Fig. 7. Sedimentary effects on the modeled rate of sea-level change over the past
100 yr. Positive values (red colors) indicate sea-level rise; negative values (blue) indicate sea-level fall. A: Difference in the rate of sea-level change in a simulation
driven by the combined variations in ice and sediment loads (Section 3) and a simulation driven only by variations in ice loads. This frame shows rates of sea-level
change computed as SLGR /t (Eq. (2)), which neglects direct topographic changes
due to erosion and sedimentation. B: Identical to Fig. 7A except that the rate of sealevel change is computed as SL/t (Eq. (5)), which includes direct topographic
changes due to erosion and sedimentation. (For interpretation of the references to
color in this figure legend, the reader is referred to the web version of this article.)
wavelength variations by the elastic lithosphere and the highviscosity mantle. In contrast, erosion and deposition rates can vary
by orders of magnitude over distances as short as a few kilometers (Fig. 3E), which imprints the predicted sea-level changes in
Fig. 4E with the same fine-scale structure via the contribution of
H to SL in Eq. (2). This raises an important point. In areas
subject to significant sediment redistribution, site-specific sea-level
histories (SL, as defined in Eq. (2)) may be characterized by large
spatial gradients, which means that predictions such as those in
Fig. 4E may be subject to large errors if the deposition and erosion
histories are not known to high spatial and temporal resolution.
In contrast, an accurate prediction of the isostatic contribution to
the sea-level change, SLGR (Fig. 4D), does not require such an
accurate spatio-temporal model for the local sediment redistribution. For this reason we focus, in the remainder of this section,
on predictions of SLGR and RSLGR , with the understanding that
the accuracy of any prediction of the total sea-level signal (SL or
RSL) will be governed by the accuracy with which H is known in
areas of significant sediment redistribution.
18
K.L. Ferrier et al. / Earth and Planetary Science Letters 416 (2015) 12–20
5.1. The impact of sediment redistribution on sea level along the
northeastern Arabian Sea coast
In Figs. 4D and 5C, the largest variations in sea level are, not
surprisingly, predicted to occur near the greatest sediment redistribution. In Fig. 5C, the peak amplitude of RSLGR (i.e., the relative
sea level change not including the direct effect on topography associated with erosion and deposition; Eq. (6)) at 4 ka is ∼1.9 m. This
is comparable in magnitude to the relative sea-level change over
the past 4 kyr computed with no sediment redistribution (Fig. 5B).
In regard to the three sites identified in Fig. 5A, the perturbation
is highest at the site nearest the Indus delta (Karachi), where deposition is greatest, and smallest at Lothal, which is farthest from
the Indus delta and characterized by relatively little local sediment
redistribution (Fig. 4A).
In the absence of sediment loading or unloading, the physics
of interglacial sea-level change at sites in the far field of the late
Pleistocene ice sheets is well understood (e.g., Mitrovica and Milne,
2002). At sites near coastlines, ocean loading associated with the
collapse of grounded ice since the Last Glacial Maximum (LGM)
acts to tilt the crust upward toward the continent (contributing
a sea-level fall) and down toward the ocean (contributing a sealevel rise) in a process known as continental levering. Moreover,
migration of water from the far field oceans toward zones of subsidence at the periphery of ancient ice cover produces a regional
fall in sea level termed ocean syphoning. Together, these processes
lead to the spatially variable pattern of sea-level change evident
in Fig. 5B, and they produce predicted relative sea-level histories
(dashed lines) that differ among the three sites in Figs. 6A–C.
How are these predictions impacted by loading due to sediment
redistribution? At sites subject to significant sediment deposition
(see Fig. 3C), crustal subsidence contributes a sea-level rise. Conversely, at sites subject to erosion, crustal uplift contributes a sealevel fall (Fig. 5C). Karachi and South Saurashtra are examples of
the former. At these sites the crustal subsidence induced by sediment deposition contributes a sea-level rise that partially counters
the sea-level fall associated with continental levering and ocean
syphoning (compare the dashed and solid lines in Figs. 6A–C over
the past 4 kyr).
The relative sea-level histories in Fig. 6 highlight an important
difference between the sea-level signals associated with sediment
loading and those associated with ice plus water loading. That is,
sea-level changes driven by ice mass fluctuations wax and wane
through a glacial cycle, whereas sea-level changes driven by sediment transfer grow larger over time. For example, at Karachi, on
the western edge of the rapidly depositing Indus delta, the predicted rise in sea level due to the loading effect of sediment redistribution is ∼7 m from LGM to present day, and nearly ∼15 m
from the Last Interglacial (LIG) at 120 ka to the present day.
This has implications for studies of paleo-sea level. For example, if one were to use a geological record of relative sea level at
Karachi to estimate past ocean water volume, the estimate at LGM
would be biased by ∼7 m of equivalent eustatic sea level if the
effects of sediment transfer were neglected. This is comparable to
the amplitude of the bias at LGM introduced by neglecting strong
lateral variations in mantle viscosity near convergent plate margins
(Austermann et al., 2013). At the LIG, the bias introduced by neglecting the loading effect of sediment transfer is even larger. In
the simulation in the present study, incorporating this loading effect brings down predicted relative sea level at the LIG by ∼7 m
at South Saurashtra and twice this much at Karachi (Figs. 6G, I). As
a point of comparison, the total ice volumes above local sea level
in the current Greenland and West Antarctic Ice Sheets are ∼7.3 m
and ∼5 m, respectively, in units of equivalent eustatic sea-level
rise (Lemke et al., 2007). In other words, if one were to neglect the
loading effect of sediment transfer in attempting to fit an observed
sea-level highstand at these sites, one would underestimate ice
sheet collapse at the LIG. (As a caveat, we remind the reader that
the solid lines in Fig. 6 do not include the direct effect on sea level,
and topography, of changes in the local height of sediments.) This
indicates that estimating paleo-ice volumes from paleo-sea-level
markers will, in general, be more robust at sites far from rivers
with large sediment fluxes, where sediment-driven changes in sea
level are likely to be small relative to sea-level changes driven by
glacial isostatic adjustment.
5.2. Modern rates of sea-level change
Because sediment continues to erode from the continents and
deposit on the seafloor, modern rates of sea-level change reflect
Earth’s instantaneous elastic response to ongoing deposition and
erosion. And, because Earth’s viscous mantle takes time to fully
respond to changes in surface loading, modern rates of sea-level
change also reflect Earth’s viscous response to sediment transfer
over the previous tens of thousands of years. The total sedimentdriven contribution to modern rates of sea-level change is the sum
of the elastic and viscous responses.
Fig. 7A shows that sediment transfer near the Indus delta perturbs the predicted rate of sea-level change over the past 100 yr by
as much as ∼0.5 mm/yr. As expected on the basis of Figs. 6A–C,
sediment deposition causes Late Holocene sea level to fall more
slowly than it would if it were driven only by ice mass variations.
The predicted perturbation in Fig. 7A is significant in the sense
that it is as much as ∼40% of the globally averaged rate of sealevel change over the 20th century driven by thermosteric effects
and the recent melting of ice sheets and glaciers (Hay et al., 2015).
This underscores the importance of accounting for sedimentary effects on modern sea level at sites near areas with high rates of
sediment deposition or erosion.
5.3. Sensitivity of the modeled sea-level responses to uncertainties
in sediment transfer
The sediment deposition and erosion history described in Section 3 is characterized by uncertainties at nearly every spatial and
temporal scale. Many drainage basins have no erosion rate measurements, and large patches of the Arabian Sea have no sedimentation rate measurements. Furthermore, some measurements are
averaged over only a few years, while others are averaged over
thousands of years and provide no indication of how rates varied over that time. The degree to which anthropogenic activity has
perturbed modern sediment fluxes likely varies among tributaries,
but is unquantified. One indication of the size of these uncertainties is the nearly seven-fold range of published estimates for the
modern sediment flux from the Indus River to the Arabian Sea
(100–675 Mt/yr; Ali and De Boer, 2007).
As we noted above, the uncertainties in H map directly into
predictions of the total sea-level change SL (Eq. (2)). They also
impact the accuracy of predictions of the isostatic and gravitational
effects of sediment redistribution embodied in SLGR (Eq. (5)) and
driven by L (Eq. (3)). In the supplementary file, we present
numerical experiments that repeat the predictions of SLGR in
Fig. 6D–I for a suite of additional sediment transfer scenarios (see
Section S.6 and Fig. S1). These calculations indicate that if the
geometry of sediment redistribution is held fixed, the predicted
isostatic effect on sea level has a quasi-linear dependence on the
adopted rates of deposition and erosion. This illustrates that sealevel responses to sediment transfer depend on the magnitude of
the sediment fluxes, and not just their spatial pattern.
K.L. Ferrier et al. / Earth and Planetary Science Letters 416 (2015) 12–20
6. Final remarks
The extended sea-level theory derived by Dalca et al. (2013)
incorporates viscoelastic crustal deformation driven by the sediment load, the perturbation to the gravitational field associated
with this deformation and the sediment redistribution, and the
feedback into sea level of load-induced changes in the orientation
of Earth’s rotation axis. The theory also includes a gravitationally
self-consistent redistribution of the ocean, including water entering
or leaving the ocean driven by changes in the volume of grounded
ice and any water displaced by the evolving sediment load.
We conclude, on the basis of our results, that estimating global
ice volumes since the LIG using paleo-sea-level markers from sites
near the Indus delta – or regions with comparable fluvial sediment
fluxes – requires that these markers be corrected for the effects
of sediment erosion and deposition. The Indus River has one of
the highest sediment fluxes on Earth, and the perturbations in sea
level evident in Figs. 4–7 would have implications for any effort
to use geological records from this region in a variety of common
ice age applications. These include inferences of excess ice volume
at the LGM, minimum ice volumes at the LIG, and ongoing late
Holocene melting beyond the end of the main deglaciation phase.
The perturbation to present-day rates of change of sea level due to
sediment transfer in the area is also non-negligible, and must be
corrected for if geodetic observations are to be used to estimate
ongoing eustatic sea-level rise due to modern climate change.
On longer timescales, the elevation of sea-level markers may
be significantly deflected by erosion and deposition even in areas
with slow sediment fluxes, because the integrated sea-level perturbation continues to grow larger over time. Potentially important
examples include analyses aimed at inferring minimum ice volume, or equivalently maximum eustatic sea level, during earlier
interglacials such as MIS11 (Raymo and Mitrovica, 2012) and during the mid-Pliocene climate optimum at ∼3 Ma (e.g., Rowley et
al., 2013).
Significant uncertainties exist in the history of sediment redistribution in the Indus River basin and adjacent Arabian Sea. One
possible route to improving these constraints would be the acquisition of more sediment cores, dated with a high temporal resolution, in areas with the highest sedimentation rates, including the
Indus delta, both on land and offshore, and the Gulf of Cambay.
In this regard, it would also be helpful to obtain improved erosion rate measurements over longer time scales and finer spatial
scales within the Indus basin. At present, nearly all erosion rate
measurements in western India and the Indus basin are based on
fluvial sediment flux measurements averaged over no more than a
few decades. In contrast, cosmogenic nuclide measurements in fluvial stream sediment could provide erosion rate estimates averaged
over the past several thousand years and more robust estimates of
the mean sediment fluxes that drive sea-level responses.
As a final point, we note that our application of the Dalca
et al. (2013) sea-level theory assumes that the sediment density
is temporally constant. Specifically, the model does not treat the
compaction of sediment over time, which can be fast in freshly
deposited sediment in big deltas (e.g., 1–10 mm/yr in the Mississippi River delta; Blum et al., 2008). Extending the numerical
predictions to incorporate the effects of spatially variable sediment
compaction (e.g., Brain et al., 2012), will be the focus of future
work.
Acknowledgements
We thank Richard Meadow for comments on an early version
of this manuscript and for many insightful discussions about the
history of human civilizations in the Indus basin. We also thank
19
the two anonymous reviewers for constructive comments that improved this manuscript. K.L.F. was supported in this work by a
Global Scholar fellowship with the Canadian Institute for Advanced
Research (CIFAR). J.X.M. was funded by Harvard University and
CIFAR.
Appendix A. Supplementary material
Supplementary material related to this article can be found online at http://dx.doi.org/10.1016/j.epsl.2015.01.026.
References
Aerts, J.C.J.H., Wouter Botszen, W.J., de Moel, H., Bowman, M., 2013. Cost estimates
for flood resilience and protection strategies in New York City. Ann. N.Y. Acad.
Sci. 1294, 1–104.
Ali, K.F., De Boer, D.H., 2007. Spatial patterns and variation of suspended sediment
yield in the upper Indus River basin, northern Pakistan. J. Hydrol. 334, 368–387.
Austermann, J., Mitrovica, J.X., Latychev, K., Milne, G.A., 2013. Barbados-based estimate of ice volume at Last Glacial Maximum affected by subducted plate. Nat.
Geosci. 6, 553–557.
Bloom, A.L., 1964. Peat accumulation and compaction in a Connecticut coastal
marsh. J. Sediment. Petrol. 34, 599–603.
Blum, M.D., Tomkin, J.H., Purcell, A., Lancaster, R.R., 2008. Ups and downs of the
Mississippi Delta. Geology 36, 675–678.
Brain, M.J., Long, A.J., Woodroffe, S.A., Petley, D.N., Milledge, D.G., Parnell, A.C., 2012.
Modelling the effects of sediment compaction on salt marsh reconstructions of
recent sea-level rise. Earth Planet. Sci. Lett. 345–348, 180–193.
Cathles, L., 1971. The viscosity of the Earth’s mantle. PhD thesis. Princeton University, Princeton, NJ.
Cazenave, A., Llovel, W., 2010. Contemporary sea level rise. Annu. Rev. Mar. Sci. 2,
145–173.
Church, J.A., Clark, P.U., Cazenave, A., Gregory, J.M., Jevrejeva, S., Levermann, A.,
Merrifield, M.A., Milne, G.A., Nerem, R.S., Nunn, P.D., Payne, A.J., Pfeffer, W.T.,
Stammer, D., Unnikrishnan, A.S., 2013. Sea level change. In: Stocker, F., Qin, D.,
Plattner, G.-K., Tignor, M., Allen, S.K., Boschung, J., Nauels, A., Xia, Y., Bex, V.,
Midgley, P.M. (Eds.), Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge and New
York.
Clift, P.D., Giosan, L., 2014. Sediment fluxes and buffering in the post-glacial Indus
Basin. Basin Res.. http://dx.doi.org/10.1111/bre.12038.
Clift, P.D., Shimizu, N., Layne, G.D., Blusztajn, J.S., Gaedicke, C., Schlüter, H.-U., Clark,
M.K., Amjad, S., 2001. Development of the Indus Fan and its significance for
the erosional history of the Western Himalaya and Karakoram. Geol. Soc. Am.
Bull. 113, 1039–1051.
Clift, P.D., Giosan, L., Blusztajn, J., Campbell, I.H., Allen, C., Pringle, M., Tabrez, A.R.,
Danish, M., Rabbani, M.M., Alizai, A., Carter, A., Lückge, A., 2008. Holocene erosion of the Lesser Himalaya triggered by intensified summer monsoon. Geology 36, 79–82.
Dalca, A.V., Ferrier, K.L., Mitrovica, J.X., Perron, J.T., Milne, G.A., Creveling, J.R., 2013.
On postglacial sea level – III. Incorporating sediment redistribution. Geophys. J.
Int.. http://dx.doi.org/10.1093/gji/ggt089.
Dziewonski, A.M., Anderson, D.L., 1981. Preliminary reference Earth model. Phys.
Earth Planet. Inter. 25, 297–356.
Farah, A., Mirza, M.A., Ahmad, M.A., Butt, M.H., 1977. Gravity field of the buried
shield in the Punjab Plain, Pakistan. Geol. Soc. Am. Bull. 88, 1147–1155.
Farrell, W.E., Clark, J.A., 1976. On postglacial sea level. Geophys. J. R. Astron. Soc. 46,
647–667.
Giosan, L., Clift, P.D., Macklin, M.G., Fuller, D.Q., Constantinescu, S., Durcan, J.A.,
Stevens, T., Duller, G.A.T., Tabrez, A.R., Gangal, K., Adhikari, R., Alizai, A., Filip,
F., VanLaningham, S., Syvitski, J.P.M., 2012. Fluvial landscapes of the Harappan
civilization. Proc. Natl. Acad. Sci. USA, E1688–E1694.
Hay, C.C., Morrow, E., Kopp, R.E., Mitrovica, J.X., 2015. Probabilistic reanalysis of
twentieth-century sea-level rise. Nature. http://dx.doi.org/10.1038/nature14093.
Ivins, E.R., Dokka, R.K., Blom, R.G., 2007. Post-glacial sediment load and subsidence
in coastal Louisiana. Geophys. Res. Lett. 34, L16303.
Johnston, P., 1993. The effect of spatially non-uniform water loads on predictions of
sea level change. Geophys. J. Int. 114, 615–634.
Kendall, R.A., Mitrovica, J.X., Milne, G.A., 2005. On post-glacial sea level – II. Numerical formulation and comparative results on spherically symmetric models.
Geophys. J. Int. 161, 679–706.
Kolla, V., Coumes, F., 1987. Morphology, internal structure, seismic stratigraphy, and
sedimentation of Indus Fan. Am. Assoc. Pet. Geol. Bull. 71, 650–677.
20
K.L. Ferrier et al. / Earth and Planetary Science Letters 416 (2015) 12–20
Lambeck, K., Purcell, A., 2005. Sea-level change in the Mediterranean Sea since
the LGM: model predictions for tectonically stable areas. Quat. Sci. Rev. 24,
1969–1988.
Lemke, P., Ren, J., Alley, R.B., Allison, I., Carrasco, J., Flato, G., Fujii, Y., Kaser, G., Mote,
P., Thomas, R.H., Zhang, T., 2007. Observations: changes in snow, ice and frozen
ground. In: Solomon, S., Qin, D., Manning, M., Chen, Z., Marquis, M., Averyt, K.B.,
Tignor, M., Miller, H.L. (Eds.), Climate Change 2007: The Physical Science Basis.
Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge University Press, Cambridge
and New York. 996 pp.
McGranahan, G., Balk, D., Anderson, B., 2007. The rising tide: assessing the risks of
climate change and human settlements in low elevation coastal zones. Environ.
Urban. 19, 17–37.
McNally, T., Bonavita, M., Thépaut, J.-N., 2014. The role of satellite data in the forecasting of Hurricane Sandy. Mon. Weather Rev. 142, 634–646.
Milliman, J.D., Farnsworth, K.L., 2011. River Discharge to the Coastal Ocean. Cambridge University Press. 392 pp.
Milne, G.A., Mitrovica, J.X., 1996. Postglacial sea-level change on a rotating Earth:
first results from a gravitationally self-consistent sea-level equation. Geophys. J.
Int. 126, F13–F20.
Milne, G.A., Mitrovica, J.X., 1998. Postglacial sea-level change on a rotating Earth.
Geophys. J. Int. 133, 1–19.
Mitrovica, J.X., Milne, G.A., 2002. On the origin of postglacial ocean syphoning. Quat.
Sci. Rev. 21, 2179–2190.
Mitrovica, J.X., Milne, G.A., 2003. On post-glacial sea level: I. General theory. Geophys. J. Int. 154, 253–267.
Mitrovica, J.X., Tamisiea, M.E., Davis, J.L., Milne, G.A., 2001. Recent mass balance of
polar ice sheets inferred from patterns of global sea-level change. Nature 409,
1026–1029.
Owen, L.A., Finkel, R.C., Caffee, M.W., 2002. A note on the extent of glaciation
throughout the Himalaya during the global last glacial maximum. Quat. Sci.
Rev. 21, 147–157.
Peltier, W.R., 1974. The impulse response of a Maxwell Earth. Rev. Geophys. Space
Phys. 12, 649–669.
Peltier, W.R., 2004. Global glacial isostasy and the surface of the ice-age Earth:
the ICE-5G (VM2) model and GRACE. Annu. Rev. Earth Planet. Sci. 32,
111–149.
Prins, M.A., Postma, G., Cleveringa, J., Cramp, A., Kramp, N.H., 2000. Controls on
terrigenous sediment supply to the Arabian Sea during the late Quaternary: the
Indus Fan. Mar. Geol. 169, 327–349.
Ramaswamy, V., Nagender Nath, B., Vethamony, P., Illangovan, D., 2007. Source and
dispersal of suspended sediment in the macro-tidal Gulf of Kachchh. Mar. Pollut.
Bull. 54, 708–719.
Raymo, M.E., Mitrovica, J.X., 2012. Collapse of polar ice sheets during the
stage 11 interglacial. Nature 483, 453–456. http://dx.doi.org/10.1038/nature
10891.
Rowley, D.B., Forte, A.M., Moucha, R., Mitrovica, J.X., Simmons, N.A., Grand, S.P.,
2013. Dynamic topography change of the eastern United States since 3 million
years ago. Science 340, 1560–1563.
Simms, A.R., Lambeck, K., Purcell, A., Anderson, J.B., Rodriguez, A.B., 2007. Sea-level
history of the Gulf of Mexico since the Last Glacial Maximum with implications for the melting history of the Laurentide Ice Sheet. Quat. Sci. Rev. 26,
920–940.
Simms, A.R., Anderson, J.B., DeWitt, R., Lambeck, K., Purcell, A., 2013. Quantifying
rates of coastal subsidence since the last interglacial and the role of sediment loading. Glob. Planet. Change 2013. http://dx.doi.org/10.1016/j.gloplacha.
2013.10.002.
United States Department of Commerce National Oceanic and Atmospheric Administration National Geophysical Data Center, 2001. 2-Minute gridded global
relief data (ETOPO2). http://www.ngdc.noaa.gov/mgg/fliers/01mgg04.html. Accessed 2006.
Watts, A.B., Thorne, J., 1984. Tectonics, global changes in sea level and their relationship to stratigraphical sequences at the US Atlantic continental margin. Mar.
Pet. Geol. 1, 319–339.
Wolstencroft, M., Shen, Z., Törnqvist, T.E., Milne, G.A., Kulp, M., 2014. Understanding subsidence in the Mississippi Delta region due to sediment, ice and ocean
loading: insights from geophysical modeling. J. Geophys. Res., Solid Earth 119,
3838–3856. http://dx.doi.org/10.1002/2013JB010928.