Accelerated river avulsion frequency on lowland deltas due to sea-level rise Austin J. Chadwicka,1, Michael P. Lamba, and Vamsi Gantib,c aDivision of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA 91125; bDepartment of Geography, University of California, Santa Barbara, CA 93106; and cDepartment of Earth Science, University of California, Santa Barbara, CA 93106 Edited by Andrea Rinaldo, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, and approved June 3, 2020 (received for review July 17, 2019) Sea-level rise, subsidence, and reduced fluvial sediment supply are delta during Holocene sea-level rise (21). Similarly, numerical causing river deltas to drown worldwide, affecting ecosystems and model predictions differ on whether avulsions on the Mississippi billions of people. Abrupt changes in river course, called avulsions, and Trinity Rivers were more or less frequent during the Ho- naturally nourish sinking land with sediment; however, they also locene period (22, 23) despite their geographic proximity (24). create catastrophic flood hazards. Existing observations and models Sequence stratigraphic models (25) and physical experiments conflict on whether the occurrence of avulsions will change due to (26) predict sea-level fall causes valley incision preventing avul- relative sea-level rise, hampering the ability to forecast delta re- sion, whereas the Goose River delta (27) represents an example sponse to global climate change. Here, we combined theory, numer- where avulsions persisted during sea-level fall. ical modeling, and field observations to develop a mechanistic Previous work documented that the characteristic avulsion framework to predict avulsion frequency on deltas with multiple frequency, fA, scales with the rate that the riverbed aggrades to a self-formed lobes that scale with backwater hydrodynamics. Results height comparable to its channel depth, show that avulsion frequency is controlled by the competition be- v tween relative sea-level rise and sediment supply that drives lobe f = a [1] progradation. We find that most large deltas are experiencing suf- A H, ficiently low progradation rates such that relative sea-level rise en- p hances aggradation rates—accelerating avulsion frequency and where va is the in-channel aggradation rate, H = H Hc is the associated hazards compared to preindustrial conditions. Some del- aggradation thickness necessary for avulsion, and Hc is the bank- p tas may face even greater risk; if relative sea-level rise significantly full channel depth (28, 29). The avulsion threshold, H , is a di- EARTH, ATMOSPHERIC, AND PLANETARY SCIENCES outpaces sediment supply, then avulsion frequency is maximized, mensionless number between 0.2 and 1.4 on lowland deltas (30). delta plains drown, and avulsion locations shift inland, posing new Aggradation rates, in contrast, span orders of magnitude hazards to upstream communities. Results indicate that managed (va = 0.5 to 100 mm=y; ref. 29). Thus, river avulsions may occur deltas can support more frequent engineered avulsions to recover as frequently as every decade (e.g., the Huanghe; Fig. 1A and ref. sinking land; however, there is a threshold beyond which coastal 31) or as rarely as each millennium (e.g., the Mississippi; Fig. 1B land will be lost, and mitigation efforts should shift upstream. and ref. 32), and Eq. 1 is only useful insofar as aggradation rate can be predicted. sea-level rise | river deltas | river avulsion Analytical models are often used to approximate va through spatial averaging of sediment mass balance. A common approach oastal cities and wetlands are drowning due to global sea- Clevel rise, accelerated subsidence from fluid extraction, and Significance reduced fluvial sediment supply (1–3), with significant implica- tions for the global economy, carbon cycle, and diverse ecosys- River deltas host large cities and ecosystems and are sinking tems (4–6). Most estimates of coastal inundation for the coming under global sea-level rise and land subsidence from ground- century do not consider the land-building potential of riverine water and hydrocarbon extraction. Coastal rivers naturally sedimentation (7–9). Rivers naturally distribute sediment across build land by distributing sediment through abrupt shifts in deltaic plains through avulsions—catastrophic shifts in the river river course, known as avulsions, which also have caused some course—which occur every 10 to 1,000 years on different deltas of deadliest flood disasters in human history. We show that (Fig. 1 A and B) (10, 11). However, it is unknown what sets modern rates of relative sea-level rise should cause avulsions avulsion timescales and how avulsion occurrence will change to occur more frequently on deltas, and in extreme cases with increasing rates of relative sea-level rise caused by climate avulsion locations will shift farther inland. Our results provide and land-use changes (12, 13). River avulsions counter land loss a quantitative framework to predict delta response to future by nourishing wetlands with sediment (14) but also have caused sea-level rise, which is valuable for planning engineered di- some of the deadliest floods in human history (10, 15, 16). On versions to nourish deltas and prevent catastrophic hazards. densely populated fluvial systems, dammed reservoirs trap sedi- ment and engineered levees prevent avulsions, with the un- Author contributions: A.J.C., M.P.L., and V.G. designed research; A.J.C. and M.P.L. per- formed research; A.J.C. and M.P.L. analyzed data; and A.J.C., M.P.L., and V.G. wrote intended consequence of heightened land loss (8, 9). Engineered the paper. river diversions are now important parts of future billion-dollar The authors declare no competing interest. coastal restoration plans (17). Despite their global importance, This article is a PNAS Direct Submission. we lack a predictive framework for avulsion reoccurrence on deltas, which is imperative to mitigate catastrophic flood hazards Published under the PNAS license. and design effective diversions on engineered deltas (8, 9). Data deposition: The data and model code underlying this study are publicly available in the SEAD Repository (http://doi.org/10.26009/s0FSLKFK) and GitHub (https://github.com/ Existing observations and models produce conflicting results achadwick2323/Accelerated-river-avulsion-frequency-on-lowland-deltas-due-to-sea-level- as to whether avulsion frequency will increase or decrease with rise), respectively. relative sea-level rise. For example, avulsion frequency on the 1To whom correspondence may be addressed. Email: [email protected]. Rhine–Meuse delta increased during late Holocene sea-level rise This article contains supporting information online at https://www.pnas.org/lookup/suppl/ (19), consistent with observations in fan-delta experiments (20). doi:10.1073/pnas.1912351117/-/DCSupplemental. In contrast, avulsion frequency decreased on the Mitchell River www.pnas.org/cgi/doi/10.1073/pnas.1912351117 PNAS Latest Articles | 1of7 Downloaded by guest on September 28, 2021 historic Huanghe delta Mississippi River delta ABchannels TRUNK avulsion modern node DELTA channel DELTA avulsion SEA node drowned SEA TRUNK 40 km 100 km C 2 avulsion node B Bc 3 LA 4 (5) TRUNK CHANNEL DELTA 1 SEA D DED TRUNK TRUNK L LA A S shoreline shoreline σ avulsion avulsion node H node H z Hb Hb Fig. 1. Natural and modeled deltas. (A) Huanghe delta, China and (B) Mississippi River delta, United States, showing modern (solid line) and abandoned (dotted line) channel pathways and avulsion node (yellow star) (Google Earth). The thin dashed line in B indicates approximate shoreline before human management (18). (C) Model conceptualization, showing channels of width Bc that occupy lobes of width B (shaded regions) and length LA (yellow line). Shaded regions are deposits created during avulsion cycles 1 through 4. Once the channel avulses from the active lobe 4 to the space 5, all lateral accom- modation is filled, and the avulsion node moves downstream in tandem with progradation. (D) Model conceptualization in cross-section for constant relative sea level and (E) relative sea-level rise rate of σ, showing lobe length LA, lobe-progradation distance D, topset slope S, basin depth Hb, relative sea-level rise magnitude z, and aggradation height H in a single avulsion cycle on the active lobe (gray shaded region). to estimate va is a radially averaged model, in which the delta apex balance for a channel. For example, Reitz et al. (43) found is geographically fixed and relative sea-level rise causes the delta avulsions occurred in a fan-delta experiment at the rate the 1 QsTA = HBcLA radius to shrink until sediment supply is sufficient to keep delta- sediment supply could fill the channel: (1−λp) ,where top aggradation at pace with sea level (8, 11, 33–38). At steady TA is the time between avulsions, Bc is channel width, and LA 1 Qs AΔ = Qs is delta lobe length—the distance upstream from the shore- state, the delta land area is given by (1−λp) σ , where is the volumetric sediment supply, σ is the relative sea-level rise rate, and line where avulsions occur (Fig. 1C). Combined with Eq. 1 =f ≡ T λp is the deposit porosity (8, 11). Aggradation rate is given by and 1 A A, aggradation rate is given by Q 1 Qs v = 1 s = σ [2] va = . [3] a . (1 − λp) LABc ()1 − λp AΔ 3 B B For the radially averaged model, aggradation is enhanced during In Eq. , c can be substituted by an effective delta lobe width, , to approximate lateral distribution of sediment across a delta marine transgression because, with a fixed delta apex and – sediment supply, the delta land area is reduced (33, 39). Eq. 2 lobe, for example due to bifurcations (35, 44 48). While the shows agreement with steep experimental deltas where the delta channel-averaged model considers sedimentation within a dis- apex was geographically fixed by a canyon-fan transition or flume crete channel or lobe, it does not account for backwater hydro- inlet (20, 37).