Cellular automata to understand the prograding limit of deltaic tidal flat

Deltaic tidal flat is an important ecosystem that supports the livelihoods of millions of people globally. Due to the complexity and stochastic nature of tidal flat development, it is a challenging task to predict the tidal flat prograding limit accurately. In this study, we fill out this gap from the perspective of numerical simulation by focusing on the tidal flat extension limit of Nanhui Shoal (NHS), the largest marginal shoal of the Changjiang Estuary. Our results suggest that the tidal flat of NHS extended 29.16 m/y seaward in 1989–2002, had a rapid progradation of 158.08 m/y in 2002–2012 and a retreat rate of 26.88 m/y in 2012–2019, while the fluvial sediment supply decreased 56.78% from 1989–2002 to 2003–2012 and another 20.68% from 2003–2012 to 2013–2019. During the 1989–2002 period, the advancing rate of the −5 m isobaths followed a Gaussian frequency distribution, in agreement with simulation results of cellular automata. We suggest that in the absence of human perturbations, as the sediment input to NHS declines to the threshold of 0.01 × 108 t/y, the seaward advance of tidal flats may significantly slow down. However, human interferences generated large uncertainties on the development tendency of the NHS.


Introduction
Located between the marine and terrestrial environment, deltaic tidal flats (DTF) are natural buffer against the impact of storms and offer several ecosystem services (Temmerman et al., 2013;Anthony et al., 2015).A holistic understanding of the morphological evolution of DTF is of great significance to the development of related conservation and restoration measures (Lotze et al., 2006;Murray et al., 2019).However, it is a challenging task to predict the tidal flat evolution process accurately due to its complexity and stochastic nature (Caldwell & Edmonds, 2014).
Recent progress has been made through the use of numerical models to unravel how hydrodynamics, sediment deposits and channel features shaping the delta morphologies.For example, Edmonds et al. (2010) simulate the response of river-dominated delta channel network to permanent changes in river discharge and suggested that deltas in areas of increased drought will be more likely to experience significant rearrangement of the delta channel network.Nardin and Edmonds (2014) investigated deposition in a river delta with varying vegetation characteristics and water discharge through CONTACT Xuefei Mei xfmei@geo.ecnu.edu.cnState Key Laboratory of Estuarine and Coastal Research, East China Normal University, Shanghai, People's Republic of China Supplemental data for this article can be accessed here.https://doi.org/10.1080/19942060.2023.2234038hydrodynamic numerical model simulations and showed that intermediate vegetation height and density are optimal for enhancing both sand and mud deposition.Caldwell and Edmonds (2014) indicated that dominant grain size and percent cohesive sediment of the incoming sediment load controls deltaic processes and planform morphology using numerical experiments.Fagherazzi et al. (2015) reviewed the initial hydrodynamics and morphodynamic stages leading to deltas formation with focus on mouth bars and subaqueous levees.Li et al. (2021) established a one-dimensional numerical model for watersediment coupling to analyze the water-sediment erosion and deposition characteristics in the water diversion channel and reservoir of an injection-water supply project.Li and Yang (2022) improved the accuracy of suspended sediment load forecasting in river flows by Bayesian optimized machine learning methods.Jia et al. (2022) visualized the vortex processed in a partly-obstructed canopy channel using a validated depth-averaged large-eddy simulation model.
The evolution of DTF is closely related to the sediment input to the coastal system (Hu et al., 2018;Anthony, 2016;Leonardi et al., 2021).Over the past half century, sediment supply to the coastline has been subject to a worldwide decline caused by human perturbations (e.g.dams, dredging, and land reclamation), which has been particularly detrimental for the river delta and translated into the loss of several tidal flat areas (Murray et al., 2019).For instance, the entire Nile Delta tidal flat is retreating landward because the construction of dams has cut off the fluvial sediment supply (Syvitski, 2008).The once strongly advancing tidal flat of the Mekong River also experienced large-scale erosion and land loss during 2003-2012 due to a decreasing river sediment supply to the coast caused by dam retention and sand mining (Anthony et al., 2015).However, there are also a number of estuaries, such as Mississippi River, Pearl River and Red River, indicate DTF progradation in response to the diminishing fluvial sediment (Wagner et al., 2017;Zhang et al., 2015;Besset et al., 2019).In comparation with DTF retreating, DTF gaining in sediment-starved environment brings forward more doubts since the fluvial sediment delivery into the estuary is the main source for deltaic progradation (Syvitski & Saito, 2007;Rao et al., 2010), in particular for the mega Changjiang River.
Following the establishment of the Three Gorges Dam (TGD) in 2003 (Figure 1A), currently the world's largest hydraulic engineering project, fluvial sediment supply from Changjiang River to the estuary has been declining substantially by 70% in comparison to the period of 1955-2002(Mei et al., 2018)).In response to this drastic decline, earlier research showed that the Changjiang Estuary revealed recession at the delta front and expected that the Changjiang subaqueous delta will experience continuous erosion in the near future (Yang et al., 2007(Yang et al., , 2017;;Luo et al., 2017), while the recent studies detected high accumulation in the tidal flat and submerged delta and further revealed that siltation will stop when the shore slope reach a threshold (Dai et al., 2014;Wei et al., 2019).Above discrepancies can be explained by the fact that these studies were carried out in different areas or during different periods, which, also reflect the complexity of delta evolution.Most importantly, above works were conducted based on the historical bathymetric data and hydrodynamic observations only, which rely too heavily on the survey and has deficits in a clear quantitative prediction of the future evolution tendency of the delta and its linkage to the available sediment supply.
In this study, we would like to fill out this gap from the perspective of numerical simulation by focusing on the Nanhui Shoal (NHS).NHS is the largest tidal flat in the Changjiang Estuary that lies in the main delivery channel of fluvial sediment and discharge to the East China Sea (Figure 1B).The main aims of this study are: (1) quantifying the morphodynamic evolution of NHS tidal flats in the context of diminished fluvial sediment discharge using field data; (2) detecting the delta shoreline development limit under a sediment decline condition through cellular automata (CA).

Study area
Over the past millennia, the Changjiang Estuary developed a three-order bifurcation and four outlets configuration.The South and North Branch are the first order bifurcations, followed by the South Channel and North Channel as second order, and the South and North Passages as third order (Figure 1B).Sediment distribution among the bifurcations of Changjiang Estuarine is uneven.Specifically, the North Branch discharges neither water nor sediment to the East China Sea.North Channel is the main conduit by transporting ∼ 50% of riverine sediment to the sea, followed by the South Passage and North Passage, respectively with a delivery ratio of ∼ 28% and ∼ 22% (Dai et al., 2018b).Sediment through the South Passage feeds the NHS, the largest marginal shoal of the Changjiang Estuary (Milliman et al., 1985), which serves as an important land reserve resource for the mega-Shanghai City.
Located at the transitional zone between the Changjiang Estuary and Hangzhou Bay, NHS is dominated by fluvial, tidal and wave forces (Figure 1B).The shoal is characterized by a meso-tide, with a mean tidal range of 3.2 m and a relatively intense wave, with a mean wave height of 1 m (Wei et al., 2017).NHS exhibits a unique hook-like shape, with the tidal flat width increasing from the upstream edge to the spit, and then gradually decreasing (Figure 1B).It has advanced southeastwards over the past 2000 years, with its shoreline annually extending 20 m, consisting with the evolution tendency of the Changjiang Delta (Luo et al., 2017).In the recent 50 years, NHS has entered a high extension period, when the annual progradation rate reached hundred meters due to large scale of land reclamation for urban development (Kuang et al., 2013).

Data collection
Our data consists of four groups.The first group includes bathymetric data of the NHS in 1989NHS in , 2002NHS in , 2012NHS in and 2019, which , which were collected from different sources to extract the −5 m isobath information of NHS.Specifically, the bathymetric map in 1989 was obtained from the Navigation Guarantee Department of the Chinese Navy Headquarters (http://hydro.ngd.gov.cn/Default_e.aspx/).Bathymetric data in 2002, 2012 and 2019 were obtained from the Changjiang Estuary Waterway Administration Bureau, Ministry of Transportation (http://www.cjkhd.com/).Depth information were obtained using Line echo sounders in 1989 and through DESO-17 echo sounders in 2002DESO-17 echo sounders in , 2012DESO-17 echo sounders in and 2019.The vertical error of the measurement is 0.02-0.05m for water depths less than 5 m, which may generate a maximum error of 1% for the −5 m isobaths.The horizontal error for positioning through GPS is 1 m, introducing a measurement error of 1% for every 100 m of isobaths movements.Above small depth and position error guarantee the quality of the collected data.Besides, the map scale ranges from 1:25, 000-1: 10,000, having a high investigation density of 40-100 survey points/km 2 , which further improve the data accuracy.The second group includes yearly sediment loads at Datong station, the tidal limit of the Changjiang Estuary (Figure 1A), which were obtained from the Changjiang Water Resources Commission (www.cjw.gov.cn) for the period from 1989 to 2019 to indicate the fluvial sediment supply from the river to the estuary.The third group includes sediment diversion ratio at the three bifurcations during ebb tide of flood season, namely, the percentage of sediment enters the South Branch, South Channel and South Passage between 1989 and 2019, which were acquired from the Changjiang Estuary Waterway Administration Bureau to calculate how much sediment finally is transport into the South Passage.The fourth group includes hourly flow velocity and suspended sediment concentration (SSC) around the NHS were measured during flood tide and ebb tide of the flood seasons (18-20 August, 2006, 14-15 August 2011, 21-22 September 2017 and 2-3 August 2019) (Figure 1B, Supplementary information).Specifically, flow velocity was recorded through an acoustic Doppler current profiler (Teledyne RD Instruments), which are for the generation of surficial tidal current rose diagram around the NHS and thus to estimate the surrounding hydrodynamic characteristics.Water samples were collected using a horizontal water sampler.SSC was extracted as dry masses through per unit water volume, which are for the assessment of possible sediment transport pattern around the NHS.

Isobaths extraction and change detection
The 4 bathymetric charts were firstly transformed into depth points relative to Beijing 54 coordinates and calibrated into 'Wusong Datum' through ArcGIS.Thereafter, the bathymetric point data from each survey were extracted through the Kriging scheme into a 50 × 50 m resolution to produce a digital elevation model (DEM) (Burrough & McDonnell, 1998, Figure S1).The −5 m isobaths, corresponding to the lower boundary of the tidal flat, were extracted to further characterize the evolution of the tidal flat (Figure 1C).
The movement of each isobath is analyzed through Digital Shoreline Analysis System (DSAS) in a Geographic Information System (GIS).DSAS generates a certain number of transects that intersect the isobaths and a user-created baseline (Thieler et al., 2009).The advancing rate of any transect between any two isobaths can be calculated based on the elapsed time and their linear distance.In this study, transects were cast at a 100 m interval along the baseline for the −5 m isobaths (Figure 1C).

Cellular automata model
The linkages between sediment supply and delta geomorphology can be difficult to identify because of the physical complexities of the system.While both processbased and empirical models have been established to estimate the tidal flat evolution (Hu et al., 2015), this study adopt an alternative conceptual model that can simulate complex systems and extract universal features of the tidal flat progradation based on few rules governing the interaction among individual components.
It has been suggested that both deltaic systems and salt marshes are relatively constant in space and time (e.g.Pranzini, 2001;Fagherazzi, 2008;Leonardi & Fagherazzi, 2014, 2015;Dai et al., 2018a).Theoretically, 'stable' deltaic systems have been found to maintain themselves through time by reorganizing the sedimentation patterns and by leading to channels being close to the silting threshold (Fagherazzi, 2008).Here we used a stochastic model based on cellular automata rules to reproduce the selfprogradation of the tidal flat under different sediment supply scenarios.Different from the process-based model that works more on the physical process deduction on the basis of relatively clear physical mechanisms, CA cares more about the entire system by expressing the complex system behaviors through data analysis and CA rules (Stevens et al., 2007;Fagherazzi et al., 2012).This type of model has been found to be effective in reproducing the emerging behavior and universal features of natural systems (Goldenfeld & Kadanoff, 1999;Murray, 2007;Wagner et al., 2017).
We use a variation of the model proposed by Leonardi andFagherazzi (2014, 2015), which was initially developed to simulate wetlands erosion.We modified the model to represent the advancement, rather than retreat, of tidal flats.The model consists of a two-dimensional grid of square cells.For each cell, i, it has an advancement rate A i depending on the cell resistance and sediment input to the system: where A i is the seaward advancing rate, S is the sediment input (t/y), and γ i is a randomly distributed value between 0 and 1 that represents local geomorphic and hydrodynamic variabilities within the tidal flat.According to the formulation, the probability of each element to prograde is proportional to the amount of sediments which are inputted in the system (first part of equation 1).The seaward growing rate is proportional to a randomly distributed value which account for the variety of geomorphologic processes affecting each portion of the isobaths, this could include biogeomorphy processes promoting tidal flat stability, and local hydrodynamic processes (second part of equation 1).Our hypothesis, is that the development of NHS is inherently linked to the volume of sediment that deposits in the shoal (Li, 1991;Milliman & Farnsworth, 2011;Besset et al., 2019).Furthermore, we hypothesize that the local variability in isobaths characteristics (exponential part of equation 1) is particularly relevant when the sediment supply is low.In contrast, when the sediment input increases, local geomorphologic characteristics play a secondary role and different isobaths elements grows at a similar rate because factors influencing differential accretion rates have a reduced influence in comparison to the external input of sediments (Leonardi & Fagherazzi, 2014).
In the CA model, a cell's neighborhood refers to the four cells adjoining its four faces (Figure 2).The behavior of the cells on the grid is governed by the follows restrictions: (1) only neighbors of previously advanced cells can develop seawards.Therefore, only cells having at least one face in common with previously advanced elements are susceptible to progradation; (2) At each time step interval, one element on the grid is occupied at random with a probability of P i = A i A i ; (3) A cell is occupied from the domain automatically if it is surrounded by the land (full of neighbors).The time interval t in the CA simulation is set as t = 1 A i because the progradation rates of individual sites are independent to each other.Model results will be qualitatively compared with the analyzed data and used for a first order prediction on the amount of sediment input below which significant changes in system behavior might be expected.Sediment input that directly contributes to the shoal prograding is estimated by comparing the bathymetric maps of different years, which considers a combined effect of accretion due to sediment supply and erosion due to wave, storm surge and sea level rising (Supplementary information).

Tidal flat morphological evolution
During 1989-2002, the entire NHS experienced an overall accretion, with medium accretion ranges between 0.1 and 1 m/y around the −5 m isobaths, which resulted in a volume increase of 9.55 × 10 6 m 3 (Figure 3A and D).Similar scale of deposition was observed in the subsequent 10 years from 2002 to 2012, when NHS on the whole gained another 9.86 × 10 6 m 3 volume of tidal flat (Figure 3D).In this period, the −5 m isobaths indicated a much more intensive deposition, with most areas showing a high siltation magnitude over 0.5 m/y (Figure 3B).Morphological variation of NHS during 2012-2019, however, is inconsistent with the previous two periods, with alternating erosion and deposition and an overall erosion of 5.44 × 10 6 m 3 and obvious retreat of the −5 m isobaths in the northern region (Figure 3C).

Tidal flat shoreline changes
From 1989 to 2012, the −5 m isobath was characterized by a pronounced seaward progradation.Specifically, it experienced seaward advancement at an average rate of 29.16 m/y during the 1989-2002 period with the two edges of the tidal flat showing a maximum mobility of 95.85 and 56.65 m/y, respectively (Figure 4).The expanding trend continued in the following decade from 2002 to 2012, when the annual advancing rate increased more than 4 times with respect to the 1989-2002 period and went up to 158.08 m/y.In addition, the advancing trend for the 2002-2012 period was characterized by a multibell-shape, with the expanding peak shifting to the central area of each bell (Figure 4).The variation tendency of the −5 m isobath during 2012-2019, however, showed a completely different pattern with respect to the previous periods, with a retreat rate of 26.88 m/y.Despite large scale of erosion, expansion of the isobaths was detected in the downstream lateral cross-sections during 2012-2019, with a maximum expanding rate of 30.63 m/y, when the entire advancing rate series were characterized by a bellshape (Figure 4).
The mobility of −5 m isobath of the NHS for each time interval is further described by establishing frequencymagnitude distributions for transect advancing rates along the shoal, namely, calculating the frequency of advancing rates of different magnitudes (Figure 5).It is found that the frequency of the transect advancing rates during 1989-2002 followed a Gaussian distribution with most of the advancing rates in the range of 15-25 m/y (Figure 5A), indicating a uniform rate of advancing along the shoal.As for the period during 2002-2012 and 2012-2019, the advancing rates of their transect didn't indicate observable frequency distribution pattern and the scattered points were distributed randomly over various ranges (Figure 5B and C).

Simulated tidal flat progradation
The CA was used to test the progradation rate of the tidal flat in NHS for different sediment input concentrations in the absence of human perturbation on the seafront.The magnitude of a progradation event is evaluated as the number of progradation cells (Figure 6).The observed and modeled advancing magnitude during the period of 1989-2002 are transformed to no-dimensional form to verify the model performance.specifically, they are normalized by the magnitude of the maximum advancing event (Figure 7).When ignoring the extreme low scatter points, the correlation coefficient between the bathymetric data from survey and the simulations from CA is as high as 0.82, suggesting the CA model can well reflect the main statistical characteristics of the −5 m isobaths prograding of the NHS.
When the yearly sediment input to the NHS is high at 0.15 × 10 8 t/y, the same as that during 1989-2019, the profile of the tidal flat is relatively smooth since each cell has similar resistance compared to the strong external driver and most of the cells propagate at same magnitude of rate (Figure 6A).The frequency magnitude distribution of progradation events therefore approaches a Gaussian distribution (Figure 8A).As the sediment input decreases, there is an observable system transition with the initial part of the Gaussian distribution getting shorter (Figure 8B and C).Eventually, when the sediment supply is extremely low, such as 0.01 × 10 8 t/y, the tidal flat has a jagged boundary since each cell has different scale of advancing rates which are significantly different with respect to the external supply, thus the frequency distribution of the progradation events becomes characterized by a power-law distribution (Figure 8D).In summary, as the sediment supply declines, the frequency distribution gradually shifts from a Gaussian distribution to a power-law distribution in natural scenarios.The passage from a Gaussian to a power-law distribution suggests the transition from a condition when the advance rate is predictable and scatters around an average value to a condition when the seaward advance is significantly slow down and unpredictable, i.e. very frequent low advancing rates and occasional high magnitude seaward expansion are mediated by local systems characteristics.

Discussion
According to the historical sediment records at Datong and sediment diversion ratio of the South Branch, the  South Channel and the South Passage, both sediment transport from the Changjiang River to the estuary and the fluvial sediment enters to the South Passage decreased dramatically following the construction and regulation of TGD (Figure 9).The significant decrease of fluvial sediment input, however, was not immediately followed by a slower growth rate of the −5 m isobath (Figure 4).This can be explained by considering the complex local hydrodynamic characteristics of the system and the interferences of local human activities.

Local hydrodynamic characteristics in the estuary
By modelling wave dynamics around the NHS, Wei et al indicated that the maximum significant wave height  over the shoal ranges between 0.22 and 0.58 m during a tidal cycle between 2002 and 2012 (Wei et al., 2019).Such a wave motion may significantly promote sediment transport along the shallow foreshore, like 1 m below the surface, but has limited effect on the area around −5 m isobaths.The evolution of −5 m isobath therefore is dominated by other hydrodynamic forcing.
At the interface between terrestrial and ocean environment, NHS is a highly hydrodynamic area, with its −2 m and −5 m isobaths being respectively shaped by flood and ebb currents due to the Coriolis (Li et al., 2007;Wei et al., 2019).Rose diagrams define the magnitude and direction of the surficial tidal flow velocity over the NHS of flood seasons (Figure 10A).This demonstrates that the marginal areas are predominantly driven by bidirectional flow while a rotatory flow zone is generated in the middle zone that covers the −5 m isobaths.Under the interaction between flood and ebb currents, the shallower region suggests relatively lower coefficient of dominant sediment less than 50%, preferentially sediment delivered to the tidal flat, while that in the deeper region indicates larger coefficient of dominant sediment over 50%, preferentially seaward sediment transport, thus a clockwise sediment transport pattern forms around the −5 m isobaths that favorites sediment settling over a tidal cycle (Figure 10B; Li et al., 2010).This deposition zone is prone to extension seaward in a rich sediment supply environment.As the fluvial sediment decreases, the interaction between flood current and fluvial runoff increases, which firstly thwarts the sediment deposition along the shallow tidal flat but favors sediment siltation in the deeper area around −5 m.Note that once the fluvial sediment decreases to the threshold, when the flood tidal forces are considerable strong to generate flood tide channels (Figure 3C), shoal line retreat and deltaic land lose can be expected.

Interferences of local anthropogenic activities
Land reclamation is becoming increasingly popular in many areas worldwide (Murray et al., 2019).Shanghai City, the world's largest city by population, has reclaimed over 800 km 2 of land since 1985 (Tian et al., 2016).One of the typical land reclamation projects in Shanghai is Nanhui New Town, a 133 km 2 new city adjacent to the NHS.Before 2002, land reclamation along NHS mainly interested depths above the 0 isobaths, which may affect the −2 m isobaths, but hardly influence the evolution of −5 m isobaths.However, starting from 2002, when the lands above the 0 isobaths are already reclaimed, land reclamation projects started to interest tidal flats below the −2 m isobaths, which can severely interfere the natural develop of −5 m isobaths.
To create more land, Shanghai Government carried out a series of measures, such as the construction of dikes and riprap, to increase sediment deposition (Figure 11).While land reclamation near the NHS has led to the creation of rich agricultural, urban and industrial area, the artificial siltation pushed the system far from its historical natural features.For instance, in a natural scenario, the north side of NHS would be dominated by river runoff with fluvial sediment generally depositing along the upstream area and then gradually spreading downstream (Figure 1B; Wei et al., 2015).This led to a great expansion of the upstream area for −5 m isobaths during the 1989-2002 period (Figure 4).However, following the implementation of reclaiming projects, the middle area of NHS was characterized by a more pronounced seaward advancing during 2002-2012 (Figure 4; Dai et al., 2018a).

Comparation of observed and modelled tidal flat progradation
The evolution of NHS tidal flat can be divided into two phases according to the occurrence of intensive human interference since 2002.Specifically, during 1989-2002, the tidal flat evolution is dominated by sediment input only when CA model performs well with a high correlation coefficient (Figure 7), thus we conclude that CA can provide a reliable simulation of the tidal flat development in natural scenario under the control of sediment supply only (Figure 12).For the period 2002-2019, the CA model fails to capture the feature of tidal flat development because of the intervention of anthropogenic interferences.As the effect of different sediment supply magnitudes can be simulated by the CA, we suggest that as a first approximation the effect of anthropogenic activities can be assessed by comparing observed and modelled morphological changes (Figure 12).
By using CA to simulate the tidal flat evolution under a variety of natural scenarios with sediment input only, it is found that the seaward advance of the NHS would significantly slow down if the sediment supply declines to 0.01 × 10 8 t/y, when the isobaths mobility may approach the power-law distribution and a quasi-steady state without any significant progradation (Figure 8D; Leonardi & Fagherazzi, 2015).Below this value, in the presence of power-law distribution for the seaward advancement rate, the progradation of the tidal flat would be less predictable.According to the bathymetric maps of NHS in 1989, 2002 and 2012, annual sediment input to the NHS is respectively 0.15 × 10 8 t/y and 0.16 × 10 8 t/y during 1989-2002 and 2002-2012.However, in response to the similar sediment input magnitude, the two periods present completely different prograding characteristics in the −5 m isobaths, with the advancing rates of 1989-2002  well following a frequency magnitude distribution close to Gaussian, while those of 2002-2012 suggest insignificant regular pattern (Figure 5A and B).The lack of a regular pattern might be attributed to human disturbances, which have caused the tidal flat development significantly off its natural course and reach the growth threshold in advance (Dai et al., 2018b).

Comparation with previous work and implications
DFT is constructed by a number of variables, like the fluvial, wave and tidal energies, sediment characteristics and channel pattern (Edmonds et al., 2010;Geleynse et al., 2010;Nardin & Edmonds, 2014).Previous research has made great efforts to understand the connection between these properties and DFT development from the point of physical mechanism through pross-based modelling.However, the full breadth of DFT development is hard to capture due to the complexity and stochastic nature of tidal flat evolution.In this study, we provide a new sight to reproduce the self-progradation of the tidal flat by focusing on the entire system through data analysis and CA rules.We demonstrate that the CA is a reliable option for accurate prediction of tidal flat progradation, thus performance can be explored to explore tidal flat retreat behaviors.However, the CA model only works for the one-way DTF develop.It fails to simulate the scenario with tidal flat progradation and recession occurring simultaneously as this option is not included in the formulation.In addition, while the CA model successfully reproduces the emerging behavior, it doesn't capture the spatial variation features along the tidal flat.It is anticipated that this can be realized in follow-up research by coupling with the pross-based modelling.Furtherly, the evolution of NHS during 2012-2019 is inconsistent with the previous prediction that suggests NHS will experience a seaward growth over the period of 2005-2025 based on the topographical data from 2002-2005(Kuang et al., 2013)).This disagreement further indicates the complexity of delta evolution and brings forward the necessity for follow-up studies.
Our results suggest that in the absence of human perturbations on the seafront, as the sediment input to NHS declines to the threshold of 0.01 × 10 8 t/y, the seaward advance of tidal flats may significantly slow down.Given that there is a significant number of mega deltas subject to sediment starvation, the model has a great applicability in the understanding of tidal flat evolution behavior in estuarine systems.Such investigations could provide new insight on the evolution tendency of deltas, especially on whether a delta is or about to in transition from progradation to recession, and so it can have engineering and management usefulness.

Conclusions
The morphological development of tidal flats in response to available sediment supply has been estimated using the tidal flats of NHS in the Changjiang Delta as a test case in this work.We used site-specific data coupled with a stochastic cellular automaton model which provides an effective mean to assess the tidal flat development under a variety of scenarios.The main conclusions can be summarized as: 1.For the NHS tidal flats, following the construction of TGD, the annual seaward growth of the

Figure 1 .
Figure 1.(A) Location of Three Gorges Dam and Changjiang Estuary in Changjiang River; (B) Changjiang Estuary and the location of Nanhui Shoal; (C) −5 m isobaths of the Nanhui Shoal, isobaths also indicated as dashed line C into panel B. The remote sensing image of Changjiang Estuary on March 12th, 2015 is from USGS.

Figure 2 .
Figure 2. Cellular automate modelling of tidal flat progradation.(A)To start the CA simulation, row 1 with blue cells is set as land that has been occupied by seaward growth of tidal flat (A 1 , A 2 , A 3 , A 4 ), thus any cell belonging to the second row (A 5 , A 6 , A 7 , A 8 ) is susceptible to occupancy because it has one face in common with previously advancement cells.Here the weaker cell with small resistance, let A 6 , will be occupied at t = 0.As a consequence, A 5 , A 10 , A 7 , A 8 are susceptible to progradation in the next time step; (B) Possible domain configuration after growth of one more cell (A 10 ) at t = 1; (C) One more cell develops seaward (A 9 ) at t = 2; and (D) the cell that is closed by the blue elements automatically grow seaward (A 5 ) at t = 3.

Figure 4 .
Figure 4. Seaward advancing of the Nanhui Shoal for the −5 m isobaths.Cross sections on the horizontal axis are also indicated in Figure 1C.

Figure 7 .
Figure 7.Comparison of bathymetric data and model simulation results during the period of 1989-2002.

Figure 9 .
Figure 9. (A) Suspended sediment discharge at Datong; and (B) Suspended sediment discharge enters into the South Passage.

Figure 10 .
Figure 10.Hydrodynamic characteristics and land reclamation around the Nanhui Shoal, with (A) tidal flow rose diagram; and (B) coefficients of dominant flow and dominant sediment.The remote sensing image of the Nanhui Shoal on March 12th, 2015 is from USGS.

Figure 11 .
Figure 11.Artificial riprap projects along the Nanhui Shoal for siltation promotion.

Figure 12 .
Figure 12.Diagram showing the drivers of NHS tidal flat evolution over the period of 1989-2019.
−5 m isobath increased significantly from 29.16 m/y during 1989-2002 to 158.08 m/y during 2002-2012, but experienced a net retreat of 26.88 m/y during 2012-2019 while the riverine sediment experienced a continuous decrease from 3.37 × 10 8 t/y during 1989-2002 to 1.45 × 10 8 t/y between 2003-2012 and further to 1.15 × 10 8 t/y during 2013-2019.2. During the 1989-2002 period, the seaward advancement for the −5 m isobaths followed a Gaussian frequency magnitude distribution, while during the 2002-2012 and 2012-2019 periods, the frequency distribution followed a disordered pattern.3. Local hydrodynamic interactions between flood and ebb current induced rotatory flow and land reclamation should be responsible for the instant shoal line propagation during 2002-2012, which, however, also lead the NHS system away from the equilibrium of natural development.