More extensive land loss expected on coastal deltas due to
rivers jumping course during sea-level rise
Austin J. Chadwick
a,1
, Sarah Steele
a
, Jose Silvestre
a
, and Michael P. Lamb
a
Edited by Andrea Rinaldo, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland; received October 22, 2021; accepted June 9, 2022
River deltas are home to hundreds of millions of people worldwide and are in danger of
sinking due to anthropogenic sea-level rise, land subsidence, and reduced sediment sup-
ply. Land loss is commonly forecast by averaging river sediment supply across the entire
delta plain to assess whether deposition can keep pace with sea-level rise. However, land
loss and deposition vary across the landscape because rivers periodically jump course,
rerouting sediment to distinct subregions called delta lobes. Here, we developed a
model to forecast land loss that resolves delta lobes and tested the model against a scaled
laboratory experiment. Both the model and the experiment show that rivers build land
on the active lobe, but the delta incurs gradual land loss on inactive lobes that are cut
off from sediment after the river abandons course. The result is a band of terrain along
the coast that is usually drowned but is nonetheless a sink for sediment when the lobe is
active, leaving less of the total sediment supply available to maintain persistent dry
land. Land loss is expected to be more extensive than predicted by classical delta-
plain
–
averaged models. Estimates for eight large deltas worldwide suggest that roughly
half of the riverine sediment supply is delivered to terrain that undergoes long periods
of submergence. These results draw the sustainability of deltas further into question
and provide a framework to plan engineered diversions at a pace that will mitigate land
loss in the face of rising sea levels.
land loss
j
sea-level rise
j
river deltas
j
river avulsions
j
river diversions
River deltas host natural resources, ecosystem services, and coastal megacities home to
over 300 million people worldwide (1, 2). Because deltaic plains are maintained by sed-
iment deposition in areas at or near sea level, they are vulnerable to land loss as sea level
rises (Fig. 1
A
) (3, 4). Anthropogenic interference is endangering deltas worldwide:
climate change drives global sea-level rise at an accelerating pace (5), groundwater and
hydrocarbon extraction induce coastal subsidence (6), and dams and levees restrict the
deposition of sediment (7, 8). These pressures are escalating globally, and projections
for land loss in the coming century are dire (1, 9, 10).
Land-loss projections are commonly based on sediment-mass-balance models aver-
aged over the entire landscape (3, 10
–
14). Rivers supply sediment to deltas at a volu-
metric rate (
Q
s
) that is partitioned between vertically accreting the delta plain at the
rate of relative sea-level rise (
σ
) and laterally expanding the delta-plain area (
A
),
Q
s
c
0
¼
A
σ
þ
H
b
dA
dt
,
[1]
where
H
b
is the basin depth offshore and
c
0
is the solids fraction in the sediment
deposit (1
porosity) (Fig. 1
B
) (13, 14). Eq.
1
does not consider additional offshore
and biogenic sources of sediment (15
–
17) or wave erosion (18, 19) for simplicity.
Given projected rise rates, many densely populated deltas do not have enough sediment
to sustain their current area (10). To sustain their current area (
dA
dt
¼
0), rivers need at
least enough sediment to vertically accrete the delta-plain area at pace with sea-level
rise,
Q
s
,
need
¼
c
0
A
σ
,
[2]
where
Q
s
,
need
is the needed sediment supply (13, 14).
These landscape-averaged models are based on the simplifying assumption that rivers
evenly distribute sediment across the delta plain. However, coastal rivers typically parti-
tion sediment intermittently among four to six subregions called delta lobes (Fig.1
C
)
(18, 20, 21). Sediment supply is primarily deposited on the lobe hosting the active
river channel. Other lobes may remain inactive
—
without their main supply of riverine
sediment
—
for tens to thousands of years (Fig. 1
C
). Deposition shifts to a new lobe
when the river jumps course, in naturally occurring river diversions called avulsions (22).
Signi
fi
cance
Deltaic land is valuable and at risk
of drowning due to relative sea-
level rise. Forecasts for the next
century suggest sediment
deposition by rivers can help
counteract land loss, but
estimates have yet to account for
deposition patterns as rivers
change course over time. We
present a model and a laboratory
experiment that resolve these
patterns. Results show deltaic land
is in more danger than previously
anticipated. Repeated changes in
river course temporarily build land
that later drowns for decades to
centuries. This process leaves less
of the river
’
s sediment supply
available to sustain persistently
dry and habitable land. Revised
forecasts suggest deltas
worldwide will require more
sediment
—
or frequent
engineered river diversions
—
to
sustain land through the coming
century.
Author af
fi
liations:
a
Division of Geological and Planetary
Sciences, California Institute of Technology, Pasadena,
CA 91125
Author contributions: A.J.C. and M.P.L. designed research;
A.J.C., S.S., J.S., and M.P.L. performed research; A.J.C., S.S.,
J.S., and M.P.L. analyzed data; and A.J.C., S.S., J.S., and
M.P.L. wrote the paper.
The authors declare no competing interest.
This article is a PNAS Direct Submission.
Copyright © 2022 the Author(s). Published by PNAS.
This article is distributed under
Creative Commons
Attribution-NonCommercial-NoDerivatives License 4.0
(CC BY-NC-ND)
.
1
To whom correspondence may be addressed. Email:
austin.chadwick23@gmail.com.
This article contains supporting information online at
http://www.pnas.org/lookup/suppl/doi:10.1073/pnas.
2119333119/-/DCSupplemental
.
Published July 25, 2022.
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RESEARCH ARTICLE
|
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Avulsions are abrupt, reoccurring events
—
like earthquakes
—
with a characteristic frequency that varies from delta to delta
(23). For instance, avulsions on the Mississippi River have
occurred every 2,000 y (21) (Fig. 1
C
), whereas avulsions on the
Yellow River have taken place every decade (20, 24).
River avulsions are important for building new land and sus-
taining existing land in the face of relative sea-level rise (25). At
the same time, avulsions necessarily involve abandonment of
the old lobe, leaving it deprived of sediment and vulnerable to
land loss (26). The implications are unclear: Land losses and
gains among lobes could have an unforeseen impact on delta-
plain evolution, or alternatively losses and gains could poten-
tially compensate one another such that the delta plain evolves
according to landscape-averaged models. Regardless, land loss
on inactive lobes could persist for centuries (Fig. 1
C
), rendering
coastal zones effectively uninhabitable.
Engineering on some deltas has eliminated avulsions altogether
through dams and levees (27). Anthropogenic interference has
come at a high cost: many delta lobes are now permanently cut
off from their source of sediment, resulting in catastrophic land
loss (8, 26). Ongoing billion-dollar efforts aim to restore natural
avulsion bene
fi
ts through engineered diversions (11, 25, 28),
which may reroute the river completely (e.g., the Yellow River
Delta) (25, 26, 29) or partially (e.g., the 1963 Atchafalaya diver-
sion of the Mississippi River at the Old River Control Structure;
Fig. 1
A
)(30
–
32). Coastal management leaders face decisions
regardingwhenandwherediversionsshouldbemadeandwhere
land can be intentionally left to drown (11, 27). Some efforts
have proven successful (31, 33), and scientists agree that multiple
large-scale diversions are so effective at combating land loss that
the question is not if, but rather how, such diversions will be
implemented in the future (11, 12, 34). A predictive framework
is needed to understand the extent to which diversions can restore
sinking land and how diversions should be implemented to maxi-
mize the land-building potential of sediment resources.
Whether through natural avulsions or engineered diversions,
the cycles of sediment delivery among lobes determine where
coastal land is built and where it is lost. Here, we present a
model to forecast land loss that accounts for river avulsion
among lobes. We then validate the model against a scaled labo-
ratory experiment, and we compare how its predictions for
future land loss on densely populated deltas differ from that of
classical landscape-averaged models.
Accounting for Avulsions and Delta Lobes in
Land-Loss Forecasts
Landscape-averaged models (Eqs.
1
and
2
) are based on the
idea that a river evenly distributes its sediment supply across
the subaerial delta plain. Model forecasts can be improved by
accounting for potential land loss on inactive delta lobes due to
intermittent sediment delivery. Rivers build land on the active
delta lobe, but after avulsion, the majority of the sediment sup-
ply is diverted elsewhere and some of this land will be lost as
sea level rises. Lost land may be rebuilt during the later reoccu-
pation of the delta lobe, but lobes spend most of their time
A
Q
s
B
H
b
O
f
f
s
h
o
r
e
d
e
p
o
s
i
t
i
o
n
DELTA PLAIN
A
DROWNED
DE
LTA PLAIN
DRY
DELTA PLAIN
New
Orleans
Baton
Rouge
Old River
Control Structure
Mississippi Delta
200 km
C
Avulsion site
Delta lobes:
Natural diversion frequency:
f
A
~ 2000 yr
7500-5000 yrs BP
5500-3800 yrs BP
4000-2000 yrs BP
2600-800 yrs BP
1000 yrs BP to present
50 yrs BP to present
σ
Fig. 1.
(
A
) Satellite view of the Mississippi River delta (Google Earth) outlining the delta plain (white line) (21) and the modern shoreline (dashed yellow lin
e)
(51), which is retreating due to relative sea-level rise. (
B
)De
fi
nition sketch of a landscape-averaged model (Eqs.
1
and
2
). (
C
) Same as
A
, here showing that
the delta plain is composed of multiple lobes (gray-shaded regions bounded by dotted lines). Each lobe was built by a different path of the Mississippi
River,
which has naturally diverted its course every 2,000 y (see
Inset
). The drowned delta plain is primarily found along older, inactive delta lobes.
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inactive and thus partially drowned (Fig. 2
A
). To account for
drowning on inactive lobes, the total delta-plain area (
A
in Eq.
1
) should be subdivided into the intermittent land area that is
gradually lost during lobe inactivity (
A
lost
) and the persistent
land area that remains dry regardless of lobe state (
A
dry
),
A
dry
¼
A
A
lost
:
[3]
Intermittent land area is approximated by a band of terrain
along the coastal perimeter (
P
) that progresses landward where
lobes are inactive (Fig. 2
A
). For simplicity, we estimate a char-
acteristic perimeter by the square root of the dry delta-plain
area (
P
¼
ffiffiffiffiffiffiffiffi
A
dry
p
) (13), which should hold for a variety of delta
symmetries and basin geometries, and we adopt a characteristic
seaward slope
S
for all lobes. Furthermore, we assume inactive
lobes are completely deprived of sediment and do not consider
additional sources of sediment (15
–
17) or erosion (18, 19).
Inactive lobes passively drown as the shoreline retreats at a
velocity given by the ratio of the rise rate and the seaward slope
(
σ
=
S
; Fig. 2
B
). The intermittent land area is determined by
integrating shoreline retreat velocity across the coastal perimeter
until a given lobe is reactivated,
A
lost
¼
σ
S
P
n
f
A
,
[4]
where the term in parentheses is the rate of land loss on inactive
lobes and the second term is the average time before avulsions
reroute the river back to the same lobe, where
f
A
is the avulsion
frequency,
n
¼
N
þ
1
2
, and
N
is the number of lobes (35).
Previous work shows
f
A
scales inversely with the time it takes
the river to deposit sediment to a thickness comparable to the
river channel depth (
H
c
) on the active-lobe delta plain; at this
point,
fl
ow in the channel is rendered gravitationally unstable,
and overbank
fl
oods can trigger avulsion (22, 24, 36). Avulsion
frequency can be estimated by sediment mass balance, similar
to Eq.
1
but here averaged across a delta lobe (Fig. 2
C
) (37),
Q
s
c
0
¼
f
A
L
A
1
2
D
BH
þ
f
A
DB H
b
þ
1
2
z
,
[5]
where the
fi
rst term on the right-hand-side represents sediment
deposition on the delta plain and the second term represents
offshore deposition;
z
¼
n
σ
f
1
A
is the height of sea-level rise
before a lobe is reactivated;
D
¼
H
z
ðÞ
S
H
H
z
S
is the nonnega-
tive distance the active lobe builds seaward (where
H
is the
Heaviside step function); and
H
and
B
are the active lobe
’
sthick-
ness and width of deposition. The lobe length is the avulsion
length
L
A
, i.e., the distance up-river from the sea where avulsions
occur (Fig. 2
C
). On lowland deltas,
L
A
can extend hundreds of
kilometers up-river to a distance approximately equal to the back-
water length-scale,
L
b
≡
H
c
=
S
(23, 38). Together, Eqs.
3
–
5
.pro-
vide a means to forecast land loss that resolves intermittent
sediment delivery due to switching of the active lobe.
Land Loss on an Experimental Delta
To test the landscape-averaged and lobe-averaged models, we
conducted a scaled laboratory experiment. The experiment con-
sisted of a 7-m-long, 14-cm-wide
fi
xed-width
fl
ume connected
to a 5-m-long, 3-m-wide ocean basin (Fig. 3
A
and
B
). Water
and sediment were supplied at the upstream end, and sea level
was controlled using a programmable standpipe at the down-
stream end. The basin was initially 4.5 cm deep and free of sed-
iment, and over the course of 105 h, water
fl
ow naturally built
a river delta. We designed the experiment to replicate realistic
backwater-scaled avulsions (
L
A
∼
L
b
) over length scales of
∼
1 m, achieved by oscillating input water and sediment supply
such that the river experienced persistent backwater effects (39)
while maintaining subcritical
fl
ow (
Fr
<
1), channel depths of
H
c
¼
7
:
5 mm, and gentle bed slopes of
S
¼
0
:
0042 (
L
b
¼
H
c
=
S
¼
1
:
8m;
SI Appendix
, Table S1
). We systematically raised
sea level at four different speeds during four phases of the
experiment, lettered A to D (Fig. 3
C
). Sea-level rise rates were
scaled in terms of a dimensionless sea-level rise rate,
σ
¼
σ
Q
s
=
nL
b
Bc
0
,
[6]
where the denominator represents the maximum possible depo-
sition rate averaged across the active-lobe delta plain. Rise rates
A
B
C
Fig. 2.
(
A
)De
fi
nition sketch of the lobe-averaged model (
SI Appendix
, Eqs.
S3
–
S5
) for a delta with four lobes delineated by dotted lines. The dashed
line shows the upstream extent of intermittent land, which is gradually lost
during lobe inactivity and periodically regained when a lobe is reactivated.
(
B
) Cross-section view of an inactive lobe where sea-level rise causes inter-
mittent land loss (Eq.
4
). (
C
) Cross-section view of an active lobe, where the
river deposits sediment on both persistent and intermittent land (Eq.
5
).
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covered the range 0
<
σ
<
1 common to natural deltas (37,
40). To isolate the effect of sea-level rise and river avulsions
from other factors that in
fl
uence land loss, the experiment fea-
tured no ocean waves, tides, storms, vegetation, or cohesive sed-
iment (17, 41, 42). Overhead images were collected every
minute of the experiment and used to map the area of dry and
drowned land and identify avulsions (Fig. 3
A
and
B
;
Materials
and Methods
).
The experimental delta evolved through repeated river avul-
sions (Fig. 3
A
and
B
). Without sea-level rise (Phase A;
σ
¼
0;
Fig. 3
C
), there was no land loss; the entire delta plain was per-
sistently dry (Fig. 3
D
and
E
). Land area gradually increased at a
rate of
∼
840 cm
2
=
h, in close agreement to models averaged
over both the landscape (Eq.
1
in Fig. 3
D
) and lobe (Eq.
3
in Fig. 3
D
). Avulsions occurred once per 2 h on average
(
f
A
¼
0
:
50
:
2, 1
:
0
½
h
1
, where terms in brackets represent the
maximum and minimum;
SI Appendix
, Table S2
) and focused
land-building near the active river mouth.
Withtheonsetofsea-levelrise(PhaseB;
σ
¼
0
:
08; Fig. 3
C
),
the delta plain lost land in inactive areas cut off from the riverine
sediment supply (Fig. 3
A
and
B
). Inactive coastlines retreated by
∼
20 cm, forming a band of drowned terrain along the coast. The
shapeofthedrownedzonevariedovertimedependingon
local slopes (43) and the time since an area was last supplied with
A
CE
DF
B
Fig. 3.
Land loss on an experimental delta. (
A
) Overhead photograph showing mapped shoreline (yellow line) and delta-plain extent (white line) de
fi
ning
the dry and drowned delta-plain areas at 87.5 h. The river channel is labeled in blue. (
B
) Overhead photograph captured 1.1 h later, showing mapped avul-
sion (blue star) and measured avulsion length
L
A
and frequency
f
A
. Dashed lines show the shoreline and delta-plain extent from
A
, and white arrows high-
light land building near the active channel and gradual land loss on inactive plains. (
C
) Sea-level curve for the experiment, showing labeled Phases A through
D. (
D
) Area of the entire delta plain (crosses) and the dry delta plain (circles) over the experiment, alongside predictions from the landscape-averaged m
odel
(Eq.
1
) and the lobe-averaged model (Eq.
3
), with the shaded envelope showing propagated uncertainty from Eqs.
4
and
5
.(
E
) Drowned fraction of the delta
plain as a function of dimensionless rise rate
σ
(Eq.
6
), showing experimental results (yellow box plots) and predictions from the landscape-averaged model
(red;
SI Appendix
, Eq.
S6
) and lobe-averaged model (magenta; Eq.
4
). The magenta-shaded envelope shows propagated uncertainty in the predicted avulsion
frequency (Eq.
5
). Dotted lines show
σ
values for deltas in nature (37). (
F
) Lobe-averaged model predictions for how dimensionless sea-level rise
σ
affects
sediment partitioning between the persistently dry delta plain (light gray),
the intermittently drowned delta plain (medium gray), and farther off
shore (dark
gray) (
SI Appendix
). The landscape-averaged model (Eq.
1
) does not differentiate between persistent and intermittent delta plain.
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riverine sediment, and maintained a roughly constant size of
∼
0
:
9m
2
, which was
∼
25% of the entire delta plain (Fig. 3
E
).
Avulsions were more frequent (
f
A
¼
0
:
9
½
0
:
2, 1
:
8
h
1
;
SI
Appendix
,TableS1
) and land building outpaced land loss on aver-
age, leading to net land-area gain at
∼
570 cm
2
=
h(Fig.3
D
). The
lobe-averaged model accurately captures the amount of land loss
(Eq.
4
in Fig. 3
E
)andthetrajectoryofthedrylandarea(Eq.
3
in
Fig. 3
D
).Theinitial,suddendropindrydelta-plainarea
(43
:
5
48 h) may re
fl
ect transient sedimentation of the trunk
channel upstream of the delta lobes
—
a process that can temporar-
ily increase lobe thickness
H
and delay avulsion (40), thereby
reducing dry-land area (Eqs.
3
–
5
).
The lobe-averaged model reproduces the increase in avulsion
frequency (Eq.
5
), which arises because the river responds to
rising sea level by partitioning a greater fraction of sediment to
delta-plain deposition (
∼
13%, as compared to
∼
8% during sta-
ble sea-level; Fig. 3
F
), which destabilizes channels more quickly
(44). In contrast, the landscape-averaged model predicts no
land loss (
SI Appendix
, Eq.
S6
in Fig. 3
E
), overestimating
the dry-land area and more closely following the trajectory of
the total delta plain (Eq.
1
in Fig. 3
D
). This is because the
landscape-averaged model does not differentiate between persis-
tent and intermittent land; the area
A
in Eq.
1
pertains to the
delta plain where deposition occurs, and not necessarily the
delta plain that is persistently dry. Intermittent land was usually
submerged, but was emersed when revisited by the river such
that it accreted roughly at pace with persistent land. Thus, the
sediment deposited in intermittent zones is a sediment sink not
accounted for by landscape-averaged predictions, which leaves
less sediment available to build persistently dry land.
More rapid sea-level rise during Phase C (
σ
¼
0
:
33; Fig.
3
C
) caused more extensive land loss and a long-term reduction
in the dry-land area (Fig. 3
A
–
C
). Inactive shorelines retreated a
distance of
∼
45 cm before being replenished by the active
channel, resulting in a drowned area of
∼
2
:
5m
2
, which was
∼
50% of the total delta-plain area (Fig. 3
E
). Importantly,
despite a fourfold increase in rise rate compared to Phase B,
land loss increased by only a factor of 2; this is because avul-
sions were more frequent (
f
A
¼
1
:
00
:
6, 2
:
1
½
h
1
;
SI Appendix
,
Table S2
), partially mitigating land loss by limiting the dura-
tion of sediment starvation. Similar to Phase B, the lobe-
averaged model accurately predicts the observed experimental
land loss (Eq.
4
in Fig. 3
E
) and the trajectory of dry-land area
(Eq.
3
in Fig. 3
D
), whereas the landscape-averaged model over-
estimates dry-land area by a factor of 2 (Eq.
1
in Fig. 3
D
) and
erroneously predicts negligible land loss (
SI Appendix
, Eq.
S6
in
Fig. 3
E
). By the end of Phase C, the landscape-averaged model
predicts that the delta-plain area should have reached its maxi-
mum size in the experiment (
∼
5m
2
); in reality, over half the
delta plain had drowned (Fig. 3
D
). By taking the ratio of terms
in Eq.
5
(
SI Appendix
, Eqs.
S1
–
S3
), we estimate that
∼
30%
of the sediment supply during Phase C was deposited on the
delta plain as a whole (the other 70% was deposited on the delta
foreset offshore; Fig. 3
F
). The
∼
30% provided to the delta plain
wassplitroughlyevenlybetweenpersistentlydrylandand
intermittent land, such that only
∼
15% of the total sediment
supply contributed to deposition on persistent land. This is
only
∼
8% greater than the amount partitioned to persistent
land during Phase B despite a fourfold increase in sea-level
rise rate (Fig. 3
F
).
During Phase D, sea-level rise was further increased to exceed
the maximum possible sedimentation rate (
σ
¼
1
:
33
>
1; Eq.
6
;
Fig. 3
C
). As a result, shorelines retreated even at the active river
mouth; land was lost at a rate of
∼
9000 cm
2
=
h, and the delta
plain was completely submerged within 2 h (Fig. 3
D
). Both
models predict land loss in this phase (Fig. 3
D
and
E
), but the
landscape-averaged model overestimates the amount of dry land at
any given time, similar to earlier phases. The lobe-averaged model
provides reliable estimates, until the point the entire delta was
entirely submerged and avulsions ceased. Nearly the entire sedi-
ment supply during this phase was partitioned to the delta plain,
consistent with previous studies (37, 45), with the majority
(
∼
65%) being delivered to intermittent land (Fig. 3
F
)
Discussion and Conclusions
River deltas receive substantial sediment deposition on terrain
that is intermittently exposed subaerially as land but is usually
submerged. The lobe-averaged model and experimental results
demonstrate how, at a given time, the river builds land on the
active lobe, and inactive lobes are drowned to an extent that
depends on the time since they were last supplied with sedi-
ment (Figs. 3
A
and
B
and 4
A
), creating a zone of intermittent
land. After avulsion, deposition shifts to a new lobe where
intermittent land is replenished with sediment. At the same
time, the previously active lobe commences drowning and the
zone of intermittent land on the oldest lobes approaches full
submergence (Fig. 4
B
). This process continues for each avul-
sion cycle (Fig. 4
C
), maintaining an approximately constant
area of intermittent land delta-wide because the delta is com-
posed of multiple lobes with staggered histories of active sedi-
ment supply and inactivity (Fig. 4
A
–
D
). In terms of sediment
mass balance, deposition in intermittent zones is a sediment
sink that leaves less sediment available to nourish persistently
dry land (Fig. 3
F
). In consequence, land loss on deltas is more
extensive than predictions from landscape-averaged models
(Fig. 3
D
and
E
) that have classically relied on the assumption
that all available riverine sediment can be deposited on persis-
tently dry land (i.e.,
A
¼
A
dry
in Eq.
2
).
To assess the effect of deltaic avulsions on land loss globally,
we revised previous sediment budgets by evaluating Eq.
2
accounting for deposition in both persistent and intermittent
land areas (
A
¼
A
dry
þ
A
lost
) (Fig. 4
E
) using available data (
SI
Appendix
). These revised estimates support that deltas are in
more danger of land loss than previously anticipated. For exam-
ple, we
fi
nd the Mississippi River delta will need more than
three times greater sediment supply than previously estimated
to sustain its current dry-land area (Fig. 4
E
), an amount total-
ing
Q
s
,
need
¼
201 Gt. This is more than
fi
ve times the sediment
available by some estimates (46), although others have estimated
that greater sediment supply is possible (47). Similarly, we esti-
mate that the Orinoco and Parana deltas in South America need
roughly triple the sediment than estimated previously to main-
tain current dry-land area. In Europe, the Rhone and Rhine-
Meuse deltas need more than
fi
ve times the sediment, and the
Danube needs more than 10 times the sediment compared to
previous estimates
—
all far beyond the estimated riverine sedi-
ment supply available. Not all deltas are predicted to drown; riv-
ers like the Yellow and Brahmaputra have enough sediment to
maintain their current land area. The fate of many other deltas is
uncertain (Fig. 4
E
) because revised estimates require quanti
fi
ca-
tion of the avulsion frequency, which is dif
fi
cult to constrain
and is unavailable for many deltas.
The fate of river deltas depends upon the frequency of river
avulsions (Fig. 4
F
). In our experiment, river avulsions occurred
more frequently as sea-level rise increased (
SI Appendix
, Table
S1
), partially mitigating land loss through a negative feedback.
As captured in Eq.
4
, as rise rate increases, the rate of land loss
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(
σ
S
P
) increases, but at the same time more frequent avulsions
reduce the amount of time (
n
f
A
) that lobes spend inactive with-
out riverine sediment supply. This change of pace in lobe activ-
ity reduces the area of intermittent land and the volume of
sediment lost to intermittent land, leading to a relative increase
in sediment supply to persistently dry land. As a result, an
order-of-magnitude increase in rise rate (
σ
¼
0
:
1 to 1), like
that in our experiment, should incur only a doubling of lost
land (
A
lost
A
¼
28% to 60%; Fig. 3
E
). This negative feedback
helps mitigate land loss on deltas, which are also expected to
avulse more frequently in the coming century (Fig. 4
F
) (37).
However, there is a limit to the feedback: If rise rate increases
beyond
σ
>
1(Eq.
6
), avulsion frequency ceases to naturally
increase and land loss accelerates with rise rate (Eq.
4
in Fig.
3
E
). Anthropogenic interference is pushing many deltas beyond
this limit (5, 37). For example, the Mississippi was built over the
last eight millennia with
σ
∼
0
:
3 (40), but anthropogenic sea-
level rise and coastal subsidence may have already forced the Mis-
sissippi into
σ
>
1 conditions (37). Our model suggests that the
σ
>
1 scenario could render the entire delta plain as intermittent
land (
A
lost
A
¼
100%; Fig. 3
E
), implying imminent drowning as far
as
∼
500 km inland to the avulsion site near Baton Rouge (21,
38) (Fig. 1
A
and
C
). Where natural avulsions are not suf
fi
cient or
prevented by manmade infrastructure, mitigating land loss will
require frequent engineered diversions.
Our results indicate that sediment supply is most ef
fi
ciently
leveraged as a land-building resource when engineered diversions
commit
fl
ow to different delta lobes regularly, maintaining an
inland zone of persistent dry land similar to natural avulsions
(Fig. 4
A
–
D
). Such an approach has already proven successful on
10
2
10
3
10
4
10
5
10
6
Sediment needed to elevate the delta plain
by 1 meter in 100 years [Mt]
10
2
10
3
10
4
10
5
10
6
Sediment available [Mt]
Ebro
Yellow
Rhine-Meuse
Brahmaputra
Mississippi
Amazon
Niger
Lena
Parana
Orinoco
Rhone
Nile
Magdalena
Danube
E
NOT ENOUGH SEDIMENT TO SUSTAIN
CURRENT DRY-LAND AREA (
Q
s
< Q
s,need
)
Sediment needs estimated assuming all sediment is deposited
on persistent land (Eq. 2 with
A = A
dry
)
Revised estimation after accounting for sediment deposition
on intermittent land (Eq. 2 with
A = A
dry
+A
lost
; Table S4)
Q
s
= Q
s,need
10
-2
10
-1
10
0
10
1
10
2
Number of river avulsions or diversions
in 100 years [-]
10
2
10
3
10
4
10
5
10
6
Sediment available [Mt]
Yellow
Danube
Rhine-
Meuse
Brahmaputra
Mississippi
Parana
Orinoco
Rhone
Natural avulsion frequency (before
anthropogenic interference; Table S3)
Predicted avulsion frequency in the next cen
tury (Eq. 5; Chadwick et al., 2020)
F
NOT ENOUGH SEDIMENT TO SUSTAIN
CURRENT DRY-LAND AREA (
Q
s
< Q
s,need
)
Q
s
= Q
s,ne
ed
Q
s
= Q
s,need
for smaller
management area
(50% delta area)
Intermittent
land area
Time
Avulsion
Avulsion
Increased
diversion frequency
Increased
sea-level rise rate
D
Panel (b)
Panel (c)
Panel (d)
Intermittent land area remains
constant for a given sea-level rise
rate and diversion frequency.
Drowned
Intermittent
land
Offshore
B
Inactive
Inactive
Active
Inactive
Intermittent
land
Offshore
Drowned
Inactive
Inactive
Active
Inactive
Persistent
land
Intermittent
land
Offshore
Drowned
Inacti
ve
Inactive
Active
Deposition
Sea-level rise
Inactive
Avulsion
Avulsion
AC
Fig. 4.
(
A
–
D
) Schematic of intermittent land dynamics. (
A
) On inactive lobes (dark gray), intermittent land is deprived of riverine sediment and gradually
drowns due to sea-level rise (blue arrows). (
B
–
C
) As the river experiences avulsions over time, lobes are periodically reactivated (light gray) and sediment
deposition (green arrows) accretes both intermittent land and persistent land. (
D
) The area of intermittent land is persistent until changes in sea-level rise
rate or diversion frequency are introduced (Eqs.
3
–
5
). (
E
) Sediment budgets for deltas in the face of 1 m of sea-level rise in the next century. The shaded
region highlights conditions where the sediment available is insuf
fi
cient to sustain the modern delta plain. Gray circles are estimates for different deltas
based on the landscape-averaged model (Eq.
2
with
A
¼
A
dry
; Giosan et al., ref. 10). Black circles are revised estimates using the lobe-averaged model (Eq.
2
with
A
¼
A
dry
þ
A
lost
), which accounts for sediment deposition on intermittently drowned land (Eq.
4
; effect indicated by empty black circles and arrows). (
F
)
The effect of river diversion frequency on sediment budgets. Boundary of the shaded region was calculated by combining Eqs.
2
–
4
(
SI Appendix
, Eq.
S7
). The
dashed red line and arrow show predicted shift in the shaded boundary for management strategies that focus diversion efforts within a smaller, target
ed
management area covering only 50% of the delta plain. Gray circles show natural diversion frequency before anthropogenic interference, and black ci
rcles
show predicted diversion frequency in the face of 1 m of sea-level rise over the next century (Eq.
5
). Revised estimates in
E
and model predictions in
F
are
not possible for deltas where diversion data are unavailable.
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