Upstream migration of avulsion sites on lowland deltas with river-mouth retreat

a Key Laboratory of Tectonics and Petroleum Resources (China University of Geosciences), Ministry of Education, Wuhan 430074, China b Key Laboratory of Theory and Technology of Petroleum Exploration and Development in Hubei Province, Wuhan 430074, China c Department of Geography, University of California Santa Barbara, Santa Barbara, CA, USA d Department of Earth Science, University of California Santa Barbara, Santa Barbara, CA, USA


Introduction
River deltas are dynamic depositional landscapes that host biodiverse ecosystems, fertile farmlands and approximately 339 million people worldwide (Edmonds et al., 2020;Giosan et al., 2014;Syvitski et al., 2009;Vörösmarty et al., 2009). They are extremely low-lying areas that are sustained by the intricate balance between fluvial sediment supply, sea level rise, and land subsidence. Climate change and human activities are, however, accelerating sea level rise and land compaction rates (Erban et al., 2014;Higgins et al., 2013;Levermann et al., 2013;Meehl et al., 2005;Nicholls and Cazenave, 2010), and diminishing fluvial sediment supply (Best and Darby, 2020;Syvitski et al., 2005;Vörösmarty et al., 2003)-changes that are drowning many river deltas world- Schematic planform of a river delta constructed through repeated cycles of lobescale avulsions that occur at a consistent distance upstream of the river mouth (L A ). (B) Schematic longitudinal profile view showing how the natural flood discharge variability and nonuniform flows within the backwater zone lead to the preferential location for avulsions (yellow star), i.e., the backwater hypothesis. Low flows (blue line) cause a depositional wave to propagate downstream (dashed blue line) within the backwater zone, and floods (red line) cause an erosional wave to propagate upstream from the river mouth (dashed red line). The imbalance between these zones of erosion and deposition lead to sediment accumulation and preferential avulsions within the backwater zone Chatanantavet et al., 2012;Ganti et al., 2016a). (C) Under the geometric hypothesis, the avulsion length scales with the typical progradation length during an interavulsion period, which scales with the backwater lengthscale. Delta-lobe progradation causes riverbed aggradation and the disconnect between the rates of sedimentation within the channel and the floodplain causes avulsion sites to be associated with a slope-break in distal floodplain profiles (Ratliff et al., 2021). (D) Accelerated relative sea-level rise and storm surges will cause the drowning of coastal areas and the upstream retreat of the river mouth. Under the backwater and geometric hypotheses, the avulsion location is tied to the river mouth and should translate upstream in concert with the river mouth (gray star to yellow star) such that the avulsion length remains constant. (For interpretation of the colors in the figures, the reader is referred to the web version of this article.) der and Liu, 2017; Slingerland and Smith, 2004). Avulsions are a consequence of preferential riverbed aggradation that causes the river to become unstable and perched above its surrounding floodplain (Ganti et al., 2016b;Jerolmack and Mohrig, 2007;Mohrig et al., 2000). Historical avulsions on lowland deltas have occurred at a persistent location within the backwater zone of coastal rivers (Chatanantavet et al., 2012;Ganti et al., 2014;Jerolmack and Swenson, 2007) (Figs. 1A, 1B): the lowermost part of alluvial rivers characterized by nonuniform flows caused by the effect of a constant water-surface elevation at the river mouth   (Fig. 1B). The upstream extent of the nonuniform flows can span a few hundred meters to hundreds of kilometers based on the size of the river, and is approximated by the backwater lengthscale, where h c and S are the bankfull flow depth and the riverbed slope within the normal flow reach, respectively (Paola and Mohrig, 1996).
Theory and physical experiments indicate that the preferential avulsion site on deltas emerges because of the morphodynamic feedbacks within the backwater zone caused by the natural flood discharge variability Chatanantavet et al., 2012;Ganti et al., 2016a) (Fig. 1B). Low flows cause flow deceleration and a wave of sedimentation that propagates downstream through the backwater zone; however, large floods are accompanied by flow acceleration through the backwater zone and the upstream propagation of an erosional wave from the river mouth (Chatanantavet and Lamb, 2014;Lamb et al., 2012) (Fig. 1B). Over multiple floods, the spatial imbalance between the regions of erosion and deposition causes a peak in sediment accumulation within the backwater zone that leads to avulsions Chatanantavet et al., 2012;Ganti et al., 2016aGanti et al., , 2016b (Fig. 1B). Field observations support the backwater hypothesis for avulsions on deltas with the avulsion length-streamwise distance of the avulsion site to the river mouth-ranging from 0.2L b to 1.3L b on large, lowland deltas Chatanantavet et al., 2012;Ganti et al., 2019Ganti et al., , 2016aJerolmack, 2009;Moodie et al., 2019).
Recent numerical models also indicate that the backwater scaling of avulsion sites can emerge from purely geometric considerations, even in the absence of natural flood-discharge variability Ratliff et al., 2021). Under this geometric hypothesis, the critical amount of sedimentation needed to trigger an avulsion, which scales with h c (Mohrig et al., 2000), is achieved when a delta-lobe progrades by a distance that scales with the backwater lengthscale, leading to the correlation between the avulsion length and the backwater lengthscale ( Fig. 1C) Ratliff et al., 2021). In this scenario, the preferential avulsion location arises from the differential rates of sedimentation in the channel and the surrounding floodplains, and avulsion sites coincide with an abrupt topographic slope-break in the distal floodplain profiles (Fig. 1C) (Ratliff et al., 2021).
The backwater and geometric hypotheses have important untested predictions for how avulsion sites on deltas will respond to river-mouth retreat Ratliff et al., 2021). The landward retreat of the river mouth is expected to cause a commensurate shift in the backwater zone, and river-mouth retreat should be accompanied by a predictable landward migration of avulsion sites Ganti et al., 2016a;Ratliff et al., 2021) (Fig. 1D). This theoretical prediction is yet to be tested because avulsions reoccur on centennial to millennial timescales on most large, lowland deltas (Ganti et al., 2014;Jerolmack and Mohrig, 2007), limiting the observations of natural avulsions. Consequently, it is uncertain how historical avulsion sites will change on river deltas in response to relative sea-level rise.
Deltas formed near inland lakes provide a natural laboratory to test the key prediction of how avulsion hazards will respond to river-mouth retreat. Climate change and human impacts are already altering the extent of global lakes (Adrian et al., 2009;Ma et al., 2010;Woolway et al., 2020), mimicking the effect that coastal inundation and accelerated sea-level rise will have on large, lowland deltas. Here, we combined time series analysis of satellite imagery, spaceborne digital elevation models, and field measurements of river morphometry to identify and analyze the response of lobe-scale avulsions on a low-gradient river draining into a lake in the Qaidam Basin, China, to river-mouth retreat caused by the expansion of the lake area.

Study area: Sulengguole River, Qaidam Basin, China
We focused on the lower reach of the Sulengguole River, which drains into the North Huoluxun Lake in the Qaidam Basin, China (Fig. 2). The Qaidam Basin is an internally drained basin at the northeastern margin of the Qinghai-Tibetan Plateau ( Fig. 2A). The Qaidam basin has three major lakes: the Huoluxun, the Taijinaer and the Dabuxun Lakes. Reduction in the areal extent of glaciers, human activities, and precipitation changes have caused substantial variations in the extent of the lakes in the Qaidam Basin over the last five decades (Duan, 2018;Li et al., 2019). Owing to the hyper-arid climate, the lake areas also show seasonal variations (Figs. 3,4), where extreme precipitation and snowmelt is accompanied by the seasonal flooding of the low-lying areas surrounding the lakes. The Sulengguole River is a low-gradient, singlethreaded perennial river in the Qaidam Basin (Figs. 2, S1)-fed by seepage water in the piedmont area-that drains into the North Huoluxun Lake in the southeast part of the basin ( Fig. 2A). The North Huoluxun Lake was a permanent lake before an upstream dam construction in 2010 C.E., which gradually dried the lake. The dam construction led to the river running dry in the distal part after 2010 C.E. (Figs. S2). Before this time, the Sulengguole River delta experienced multiple cycles of natural lobe-scale avulsions, which are the focus of our study.

Identification and quantification of lobe-scale avulsions
We tracked the planform evolution of the distal Sulengguole River from 1973 C.E. to 2010 C.E. using Landsat multispectral imagery, including Landsat 1-5 MSS and Landsat 4-5 TM data (Fig. 3, Supplementary Movie S1). Detailed analysis could only be made from 1986 C.E. with the Landsat TM data because Landsat MSS sensor had a coarse spatial resolution. We defined an avulsion as a permanent change (abrupt or gradual) in the river course, and located the avulsion site using a combination of visual interpretation of the time series of Landsat imagery and water masks derived using a Modified Normalized Difference Water Index (MNDWI) (Figs. 3, S3). The MNDWI is widely used to extract water bodies due to stronger absorption by water of solar radiation in shortwave infrared bands than in near infrared and visible bands (Xu, 2006) (Figs. S1 to S3). MNDWI is computed as: where for Landsat TM data, ρ green is reflectance in Band 2 and ρ S W I R is reflectance in Band 5. MNDWI mapping results in an image with values between 1 and −1, whereby pixels with high inundation probability have a high (positive) MNDWI. These timeseries images were employed to generate water maps using the method of Otsu (1979), where single pixels were classified as wa- ter if the computed MNDWI was greater than a dynamic threshold value. Overall, these water maps allowed for the identification of the abrupt changes in river course through time and aided the visual interpretation of time series of satellite images (Fig. S3). High-resolution satellite imagery on Google Earth Pro was further used to validate the avulsions by cross-cutting relationships (Fig. S7).
We identified the avulsion site as the location where an avulsion was initiated. The avulsion location remained fixed during the process of the formation of a new channel for the avulsions analyzed here (Supplementary Movie S1). We located the avulsion site and the river mouth just before an avulsion occurred for all identified avulsions and evaluated the avulsion length, L A , as the streamwise distance between the two locations (Figs. 1, 3A-F, S3). To quantify the temporal evolution of the river mouth and avulsion site, a fixed point was selected at the confluence of Sulengguole River with two anabranches (36 • 50.011'N, 96 • 5.518'E; gray asterisk in Fig. 2B). This location is hereafter referred to as the fixed reference point. Satellite imagery revealed that the fixed reference point remained spatially consistent during the observation period. Distances between the fixed reference point and avulsion sites, and the fixed reference point and river mouth were measured along Sulengguole River course. We computed the streamwise distance of the river mouth from the fixed reference point at least 3 times during each year to quantify the seasonal variability. In addition, we also measured the streamwise distance of the river mouth from the fixed reference point on the satellite image that best captured the avulsion.
Finally, we visualized the distinct deltaic lobes of the Sulengguole River by analyzing the Landsat images during dryer periods of a year when the water level was low after the abandonment of the lobe (Fig. S5). Given the water persistence maps generated from Landsat imagery, we used visual interpretation to draw the boundaries of the individual lobe areas and exported them as shapefile to ArcGIS to generate a map of deltaic lobes.

Temporal evolution of the North Huoluxun Lake
We quantified the changes in the areal extent of North Huoluxun Lake for the contemporaneous period of observation of lobescale avulsions on the Sulengguole River. We used Global Surface Water datasets, which categorized surface water areas into three classes: permanent waters, seasonal waters and ephemeral seasonal surfaces (Pekel et al., 2016). Pekel et al. (2016) defined permanent waters as surfaces that are underwater throughout the year, and seasonal waters are surfaces that are underwater for less than 12 months in a year. We estimated the areal extent of the permanent and seasonal waters by computing the area enclosed within continuous boundaries that demarcate these areas. We manually excluded any sporadic or discrete water bodies, and the surface waters that corresponded to the river water by visual inspection for the computation of the areal extent of the lake. Ephemeral seasonal surfaces are flood event-based areas with moisture, also called wet lands (Li et al., 2018), and are not the focus of this study. All the data were processed through Google Earth Engine and ArcGIS.

Morphometry of the Sulengguole River
We used the TDX-12 m digital elevation data to estimate reachscale slope, S, of the Sulengguole River. The TanDEM-X mission was carried out by German AeroSpace Centre and Airbus deployed TerraSAR-X and TerraSAR-X equipped with Synthetic Aperture Radar (SAR) for Digital Elevation Measurement (TanDEM) on a global scale (Wessel et al., 2018;Zink et al., 2014). The mission launched a global, 12-m TanDEM-X product, which covered all land surfaces with a spatial resolution of 0.4 arc seconds (∼12 m). The absolute vertical accuracy of TDX-12 m could be up to 2 m (Hawker et al., 2019;Wessel et al., 2018;Zink et al., 2014). A recent study demonstrated that TDX-12 m data enabled the characterization of topographic features in the dryland low-gradient, unvegetated Rio Colorado terminus system with accuracy of < 0.5 m (Li et al., 2020). We validated the TDX-12 m data for the Sulengguole River with differential Global Positioning System (dGPS) field surveys (Fig. S9, Table S1). Due to speckle noise, TDX-12 m data were smoothed using a feature preserving filter, which has been previously tested in low-gradient river systems (Li et al., 2020;Lindsay et al., 2019). Longitudinal river profile was extracted from TDX-12 m data, and we evaluated the slope over 7 km windows by fitting a linear regression line between elevation and the streamwise distance ( Fig. 2C; Supplementary text).
We used an empirical width-to-depth relationship developed for single-threaded rivers in unvegetated basins to estimate the bankfull flow depth upstream of the avulsion sites (Ielpi and Lapôtre, 2020). To test the validity of this empirical relationship to our field site, we compared the estimated bankfull flow depths from the empirical relationship with field-measured bankfull flow depths at 11 locations along a 2.5 km long reach of the Sulengguole river (Figs. 2C, S10; Supplementary Text). The surveyed reach is located ∼70 km upstream of the permanent lake boundary (Fig. 2C), which is significantly upstream of the avulsion sites, and hence, could not be directly used to estimate the backwater lengthscale of the Sulengguole river.

Evolution of the Sulengguole River delta
The evolution of the distal Sulengguole River was characterized by river-mouth progradation and construction of delta lobes, which were punctuated by lobe-scale avulsions ( Fig. 3; Supplementary Movie S1). We identified six lobe-scale river avulsions on the Sulengguole River within the observation period (Figs. 3A-F). All observed avulsions were full avulsions, where the parent channel was completely abandoned and the new daughter channel captured all the flow (Fig. 3). We observed the channel relocation for 5 avulsions that were initiated in 1989, 1997, 2003, 2007 and 2008 C.E., which occurred when seasonal waters intruded landward beyond the permanent lake boundary (Fig. 3). We could not locate the time of the oldest avulsion; however, we constrained the occurrence of this avulsion between 1977 C.E. and 1986 C.E. (Fig. S4). We assigned 1982 C.E. as the time of the oldest avulsion-average of the constrained duration for the avulsion.
The six lobe-scale avulsions resulted in the Sulengguole River feeding water and sediment to distinct deltaic lobes (Fig. 3G). The lobe-scale avulsion cycles on the Sulengguole River displayed similar characteristics. The new channel path was typically shorter than the parent channel length before avulsion (Fig. 3), similar to experimental observations of deltaic evolution (Ganti et al., 2016b). Channel abandonment was gradual, typically lasting one to two years when both the old and new channel paths were active (Fig. S6). During the avulsion cycle, we observed river-mouth progradation, river bifurcation, intralobe avulsions, and crevasse splays (Fig. S6). The intralobe avulsions and crevasse splays are also evident as channel cross-cutting relationships within delta lobes on high-resolution satellite imagery (Fig. S7).
We quantified the avulsion length, L A , for the six avulsions from satellite imagery (Fig. 3A-F). For avulsions that occurred after 1986 C.E., we chose the satellite image that best captured the avulsion (Figs. 3B-F); however, we used the satellite image from 1986 C.E. to evaluate L A for the oldest lobe-scale avulsion that occurred before 1986 C.E. (Fig. 3A). The avulsion lengths were consistent across the 6 avulsions with a mean and standard deviation of 3.48 km and 1.60 km, respectively. The minimum and maximum avulsion lengths were 1.90 km and 5.91 km, respectively. We did not find a statistically significant temporal trend in the measured avulsion lengths (Fig. S8).

Landward retreat of river mouth and avulsion sites
Our results indicate that the North Huoluxon Lake expanded during the observation period (Fig. 4). The areal extent of the permanent water was stable during the observation period with a mean of 45.2 km 2 , and maximum and minimum values of 48 km 2 and 38.2 km 2 , respectively. We did not observe a statistically significant temporal trend in the areal extent of the permanent waters with a rate of change of −0.12 ± 0.19 km 2 /yr at a 95% confidence level (Fig. 4E). However, the areal extent of the seasonal lake water near the Sulengguole River terminus showed substantial variation (Figs. 3, 4; Supplementary Movie S1). The mean area of the seasonal water was 26.8 km 2 with maximum and minimum values of 54.2 km 2 and 0.8 km 2 , respectively. We observed a statistically significant temporal trend in the area of seasonal waters with a rate of change of 1.94 ± 0.68 km 2 /yr at a 95% confidence level (Fig. 4E). The combined areal extent of the permanent and seasonal waters of the lake also showed a statistically significant temporal trend with a rate of change of 1.82 ± 0.75 km 2 /yr at a 95% confidence level (Fig. 4E). These results demonstrate that the areal extent of the North Huoluxun Lake increased during the observation period (Fig. 4), likely due to the increase in precipitation extremes or glacial snowmelt (Duan, 2018;Li et al., 2019), which caused the progressive downstream drowning of the river delta.
The increase in the areal extent of the lake waters caused the Sulengguole river mouth to retreat landward (Fig. 3G). The streamwise distance of the river mouth from the fixed reference point revealed both the variability in the river-mouth location caused by the seasonal variation of the lake level, and also the river-mouth progradation over avulsion cycles (Fig. 5A). Avulsions caused river- Fig. 4. Expansion of the North Huoluxun Lake. Surface water maps of the permanent waters (dark blue) and seasonal waters (light blue) of the North Huoluxun Lake derived from the Global Surface Water dataset (Pekel et al., 2016) in the year (A) 1987, (B) 1992, (C) 2005, and (D) 2007 C.E. (E) The temporal evolution of the areal extent of the permanent lake waters (royal blue circles), seasonal lake waters (cyan circles), and the combined lake waters (orange squares). The solid and dashed lines indicate the best fit linear trend and their 95% confidence bounds, respectively. length shortening, which manifested as a sharp decline in the distance of the river mouth from the fixed reference point (Fig. 5A). To quantify the average rate of river-mouth retreat, we measured the distance of the river mouth just before avulsion from the fixed reference point and found that the river mouth retreated upstream by 7.80 km over the 6 avulsion cycles at a rate of 0.31 ± 0.17 km/yr at a 95% confidence level (Fig. 5A).
Results show that the avulsion sites retreated upstream in concert with the river mouth (Figs. 3G, 5A). The avulsion sites retreated upstream by 6.28 km over the 6 avulsion cycles, similar to the river-mouth retreat distance. The average rate of upstream retreat of the avulsion sites is 0.22 ± 0.07 km/yr, consistent with the river-mouth retreat rate (Fig. 5A).

Backwater scaling of the avulsion length
Results indicate that the avulsion sites were not coincident with a topographic slope-break (Fig. 2C), consistent with lobe-scale avulsions on large, lowland river deltas (Ganti et al., 2014). We computed the backwater lengthscale of the Sulengguole River to test if the measured avulsion lengths, L A , scaled with the backwater lengthscale (Fig. 1). The estimated channel-bed slope upstream The temporal trend of the landward retreat of the river mouth (blue squares) and avulsion site (gray circles) as measured from the fixed reference point (gray asterisk in Fig. 2B) at the time of avulsion. The solid and dashed lines indicate the best-fitting linear regression line and the 95% confidence bounds, respectively. The small blue circles show the variations in the river mouth location annually, where the river-mouth location was measured at least 3 times during a year. The error bars show the seasonal variations in river-mouth location to the lake-level fluctuations, and the larger trends in the blue circle markers highlight river-mouth progradation and river-length shortening by avulsion (time of avulsions are marked by red arrows). (B) Ratio of the measured avulsion length to the estimated backwater lengthscale for the lobe-scale avulsions on the Sulengguole River. The red shaded area denotes the mean and standard deviation of the dimensionless avulsion length (L A /L b = 0.60 ± 0.27) for the Sulengguole River. The shaded green area denotes the range of dimensionless avulsion length for a global compilation of large, low-gradient river deltas (Brooke et al., 2020;Chadwick et al., 2019;Ganti et al., 2019). of the avulsion sites was S = 1.75 × 10 −4 (95% confidence bounds of 1.72 × 10 −4 and 1.77 × 10 −4 ) (Fig. 2C). Results indicated that the empirical width-to-depth scaling of Ielpi and Lapôtre (2020) is applicable to our field site, with the predicted bankfull flow depth and the measured bankfull flow depth showing good agreement at a location that is ∼70 km upstream of the permanent lake boundary (Fig. S10). Therefore, we applied this empirical relation to estimate the bankfull flow depth upstream of the avulsion site. The bankfull channel width between the fixed reference point and the avulsion sites, estimated using 175 independent measurements from Google Earth Pro imagery, is 15.8 ± 2.7 m (mean and standard deviation), which yielded h c = 1.02 ± 0.26 m (mean and standard deviation). Together, the estimated S and h c yielded a backwater lengthscale of L b = 5.85 ± 0.86 km (mean and standard deviation) for the Sulengguole River.
Results demonstrate that L A scales with L b for all 6 lobe-scale avulsions on the Sulengguole River. The dimensionless avulsion length Ganti et al., 2019), defined as the ratio of L A to L b , is L A /L b = 0.60 ± 0.27 (mean and standard devi-ation; Fig. 5B). This value is similar to the reported dimensionless avulsion length for large, lowland deltas of L A /L b = 0.84 ± 0.32 (mean and standard deviation), with a minimum and maximum value of 0.20 and 1.30, respectively (Fig. 5B) (Brooke et al., 2020;Chadwick et al., 2019;Ganti et al., 2019). These results demonstrate that, despite significant river-mouth retreat, avulsions occurred within the backwater zone of the Sulengguole River (Fig. 1B).
Our results also demonstrate that the avulsion sites on the Sulengguole River were not coincident with an abrupt break in the topographic slope of the surrounding floodplain profiles (Fig. S11)-a key prediction under the geometric hypothesis for backwater-scaled avulsions (Ratliff et al., 2021). These results suggest that the difference between in-channel and floodplain sedimentation rates is small in Sulengguole River basin, and the origin of the avulsion sites is likely tied to the morphodynamic feedbacks arising from natural flood-discharge variability.

Discussion and conclusions
Our results provide field evidence for how avulsion sites on lowland deltas will respond to the landward retreat of the river mouth. Results demonstrate that river-mouth retreat will necessarily cause the avulsion sites on deltas to translate upstream at a commensurate rate such that the avulsion length will remain constant and scale with the backwater lengthscale (Figs. 5A, 5B). Theory indicates that this landward shift in the avulsion sites should occur because the morphodynamics that lead to preferential sediment accumulation within the backwater zone is fundamentally tied to the river-mouth location Ganti et al., 2016a). Results also indicate that backwater hydrodynamics play a primary role in setting the location of lobe-scale avulsions on low-gradient rivers draining into lakes (Fig. 5B), similar to lowgradient coastal rivers Chatanantavet et al., 2012;Ganti et al., 2016aGanti et al., , 2014Jerolmack, 2009). The future fate of lowland deltas has received considerable attention (Blum and Roberts, 2009;Chadwick et al., 2020;Syvitski et al., 2009;Vörösmarty et al., 2009); however, global lakes are already responding rapidly to environmental stressors (Woolway et al., 2020). Our results indicate that the contraction and expansion of lakes that have occurred in the last five decades (Ma et al., 2010;Woolway et al., 2020) may already have led to the lakeward and landward translation of the historical avulsion sites on deltas formed at the lake margins (Fig. 5).
The results have substantial implications for future flood risk management on large, low-gradient deltas. Theory indicates that large deltas such as the Paraná and the Rhine-Meuse are sediment starved to the point that river-mouth retreat and land loss are inevitable under historical rates of relative sea-level rise . While other major deltas such as the Mississippi, Amazon, Orinoco, and Nile have kept pace with the relative sealevel rise through the Holocene, they are also likely to experience river-mouth retreat with storm surges and the ongoing and projected acceleration in the relative sea-level rise rates Edmonds et al., 2020). The extremely low slopes that characterize large river deltas make them especially vulnerable to flooding, with >100,000 km 2 of deltaic land less than 2 m above mean sea level . Thus, even a small magnitude rise in relative sea level and storm surges on sediment-starved deltas can potentially cause kilometer-scale river-mouth retreat.
Our results indicate that river-mouth retreat on these large deltas can cause avulsion sites to migrate inland by tens to hundreds of kilometers, given consistent supply of water and sediment that control the backwater lengthscale (Fig. 5). For example, the Old River Control Structure prevents the avulsion of the Mississippi River into the Atchafalaya River at the historical avulsion site; how-ever, our results indicate that river-mouth retreat will create a new preferential location for lobe-scale avulsions upstream (Fig. 5), rendering the existing engineering structure ineffective. Our results also bolster the notion that the backwater lengthscale is a reliable, first-order predictor of future lobe-scale avulsions on deltas (Fig. 5B), which could inform management actions for flood mitigation.
The results add to the growing recognition that climate change and human activities will make avulsions a serious and frequent future flood hazard on deltas (Brooke et al., 2020;Chadwick et al., 2020). Changes in frequency and magnitude of flood extremesan expected consequence of climate change (Hirabayashi et al., 2013)-and the fining of fluvial sediment supply by the trapping of coarse sediment behind dams are expected to cause the avulsion sites on lowland deltas to occur further upstream of the backwater zone (Brooke et al., 2020). Our results indicate that the reduction in sediment supply, acceleration of sea-level rise rates and storm surges will exacerbate this flooding risk because avulsion sites will translate further inland with river-mouth retreat (Fig. 5B), affecting upstream communities that have historically seldom experienced avulsion-induced flood hazards.
Our results also have implications for paleoenvironmental interpretation of fluvial deposits on Mars. Multiple stacked depositional lobes with spatially distributed avulsion sites are a diagnostic feature of rivers draining into lakes and seas (Figs. 3G,5), which is in contrast to lobe-scale avulsions on alluvial fans that are tied to abrupt topographic changes (Ganti et al., 2014). These results suggest that spatially distributed avulsion sites can serve as a tool to distinguish fan deposits from delta deposits, thus, enabling the interpretation of paleolakes and seas on Mars and other planetary bodies (Adler et al., 2019;DiBiase et al., 2013).
Ultimately, results suggest that the drowning of river deltas from accelerated relative sea-level rise and coastal inundation will result in the upstream translation of the historical avulsion sites. This phenomenon will expose new inland communities to the risks of catastrophic flooding, and the manner in which the avulsion sites will migrate inland is predictable and consistent with the backwater hypothesis for lobe-scale avulsions on deltas.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.