An Analysis of the Periodic Evolution of the Jingjiang Sandbank in the Tidal Reach of the Yangtze River

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Article An Analysis of the Periodic Evolution of the Jingjiang Sandbank in the Tidal Reach of the Yangtze River

Ying Hu 1,2,3,* , Minxiong Cao 1,3, Aixing Ma 1,3, Xiping Dou 1,3 and Yuncheng Wen 1,3

1 River and Harbor Engineering Department, Nanjing Hydraulic Research Institute, Nanjing 210029, China; [email protected] (M.C.); [email protected] (A.M.); [email protected] (X.D.); [email protected] (Y.W.) 2 College of Harbor, Coastal and Oﬀshore Engineering, Hohai University, Nanjing 210098, China 3 State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Nanjing 210098, China * Correspondence: [email protected] or [email protected]

Received: 12 April 2020; Accepted: 5 June 2020; Published: 9 June 2020

Abstract: The Jingjiang Sandbank (JJS) is located on the bank of the tidal reach in the Yangtze River. It experiences a periodic evolution process of increase, split, migration, and dissipation, which affects the current direction, fish habitat, navigation safety, etc. In this paper, the periodic evolution of the JJS is investigated based on 17 field bathymetric measurements of the river from 1999 to 2017. Firstly, six cycles of the evolution process of the sandbank are described, and the evolution pattern of the split detached bar and the main body of the sandbank are analyzed according to the migration tracks of the detached bars and the historical volume-change of the JJS, respectively. Then an empirical orthogonal function (EOF) is conducted on the historical measurements of the bathymetry. The first four eigenfunctions correspond to the time-averaged bathymetry, the long-term change of the pattern of bathymetry, the periodic change of the JJS, and the downstream migration of the split detached bar, and the periodic change of the rip at the back of JJS. It is pointed out that the construction of two waterway regulation projects might have changed the evolution pattern of the JJS permanently.

Keywords: sandbank; multi-branching river; tidal reach; Empirical Orthogonal Functions; human projects

1. Introduction A sandbank, defined as a large under-water deposit of sand, can be found in coastal areas [1,2], out of estuaries [3], and attached to the riverbanks. The sandbanks attached to riverbanks, hereinafter mentioned as marginal sandbanks, affect the direction of the mainstream in dry seasons, habitat of fish and other benthic animals [4], navigation safety, levee safety, and other aspects. The marginal sandbanks are also mentioned as alternative bars [5,6], point bars [7,8], and marginal shoals [9]. It can be defined as the lateral accumulation of sediment, experiencing complex interaction of erosion and deposition along its length [10]. One of the explanations of the marginal sandbanks is the change of erosion and deposition caused by river flood [11,12]. Meanwhile, the hydrodynamic conditions under low water levels also play important roles in the formation of the marginal sandbanks [13]. Due to the differences in hydrodynamic, sedimental and morphology conditions, marginal sandbanks show different behaviors [14,15]. Meanwhile, human activities, such as the construction of water conservancy projects, soil conservation, and channel regulation, change the water and sediment target of the rivers [16–18], and further affect the evolution process of the marginal sandbanks. Therefore, it is of great significance to reveal the mechanism of the sandbank evolution. Located in the tidal reach of the Yangtze River which is the longest river in China, the Jingjiang Sandbank (JJS), a marginal sandbank, is at the entrance of a multi-branching reach, with the complex hydrodynamic environment and sediment transportation. In this paper, first, the evolution pattern of

Water 2020, 12, 1652; doi:10.3390/w12061652 www.mdpi.com/journal/water Water 2020, 12, x FOR PEER REVIEW 2 of 15 hydrodynamic environment and sediment transportation. In this paper, first, the evolution pattern of the JJS is studied based on the measurements of the bathymetry during the period from 1999 to 2017 and the historical record from 1960 to 1998. Affected by the runoff, tidal current, and human constructions, the JJS has been experiencing a periodic evolution process of increase, split, migration, and dissipation for several decades as illustrated in Figure 1. Generally, the scale of the JJS keeps increasing due to the sediment deposition, and then a piece of the sandbank splits away from the main body and forms a detached bar, which migrates downstream and dissipates gradually. The pattern of the evolution of the JJS might be influenced by human project activities constructed in nearby areas, and it would affect the morphology feature, the channel depth, the levee safety and Waterother2020 aspects, 12, 1652 of the natural evolution, navigation function, and safety of the river channel. Then2 of an 15 empirical orthogonal function (EOF) analysis, a mathematical method of multivariate statistical analysis, is conducted on the bathymetric dataset of the JJS and adjacent riverbed to investigate the theprincipal JJS is studied modes basedof the oncomplex the measurements evolution and of theexplore bathymetry the main during control the factors. period Empirical from 1999 o torthogonal 2017 and thefunction historical (EOF) record analysis from 1960is a tomathematical 1998. Affected method by the of runo multivariateff, tidal current, statistical and human analysis. constructions, It can be theregarded JJS has as been an application experiencing or aan periodic extension evolution of principal process component of increase, analysis split,migration, (PCA). It has and been dissipation widely forused several in structural decades dynamics as illustrated, meteorology in Figure1,. geophysics Generally, the, coast scaleal ofengineering the JJS keeps, etc. increasing In this study due, to more the sedimentthan 96% deposition,of the data variation and then is a piececaptured of the by sandbank the first four splits eigenfunctions away from the, which main bodycorrespond and forms to the a detachedtime-averaged bar, which bathymetry migrates, the downstream long-term change and dissipates of the pattern gradually. of bathymetry The pattern, the of periodic the evolution change of theof the JJS JJS might and bethe influenced downstream by human migration project of the activities split detached constructed bar, inand nearby the periodic areas, and change it would of the aff ripect theat the morphology back of JJS feature,. The major the channelcomponents depth, of thethe levee evolution safety of and the other JJS are aspects further of discussed the natural on evolution, the base navigationon the features function, of the andfour safetyeigenfunctions. of the river channel. Then an empirical orthogonal function (EOF) analysis,Due ato mathematical complex dynamic method conditions, of multivariate evolution statistical process analysis,es of river is morphology conducted on, especially the bathymetric in tidal datasetreaches ofimpacted the JJS andby the adjacent coupling riverbed of runoff to investigate and tidal current, the principal always modes show ofstrong the complexnonlinear evolution, and are andalways explore analyzed the main qualitative controlly factors. and synthetically Empirical orthogonal in general function. In this (EOF) paper, analysis the periodic is a mathematical evolution methodprocess of multivariate increase, split, statistical migration analysis., and dissipation It can be regarded of the JJS as an is firstlyapplication analyzed or an by extension long-term of principalbathymetric component measurements. analysis The (PCA). EOF Itanalysis has been is firstly widely employed used in structural to study dynamics,the evolution meteorology, of the JJS geophysics,and adjacent coastal riverbed, engineering, helping identify etc. In and this quantify study, more the dominant than 96% patterns of the data of the variation evolution is captured process byin space the first and four time eigenfunctions, from the measured which dataset correspond, which to provide the time-averaged further understanding bathymetry, of thethe long-termprocess of changeriver morphology of the pattern evolution. of bathymetry, It is important the periodic to note change that the of thehuman JJS and projects the downstream might have migrationchanged th ofe theevolution split detached pattern of bar, the and JJS permanently. the periodic change Besides of, possible the rip at explanations the back of JJS.of the The change major of components the evolution of thepattern evolution of the ofJJS the and JJS adjacent are further riverbed discussed are given. on the base on the features of the four eigenfunctions.

Figure 1. DiagrammaticDiagrammatic sketch sketch of of the the periodic periodic evolution evolution process process of of the Jingjiang Sandbank ((JJS)JJS) including increase, split, migration,migration, and dissipation.dissipation. ( (aa)) increase increase process process of of the sandbank; ( b) split process of the sandbank; (c) generally migrationmigration and dissipation of the split detached bar; ( d) totally dissipation of the split detached bar and deposition again of the sandbank.sandbank.

Due to complex dynamic conditions, evolution processes of river morphology, especially in tidal reaches impacted by the coupling of runoff and tidal current, always show strong nonlinear, and are always analyzed qualitatively and synthetically in general. In this paper, the periodic evolution process of increase, split, migration, and dissipation of the JJS is firstly analyzed by long-term bathymetric measurements. The EOF analysis is firstly employed to study the evolution of the JJS and adjacent riverbed, helping identify and quantify the dominant patterns of the evolution process in space and time from the measured dataset, which provide further understanding of the process of river morphology evolution. It is important to note that the human projects might have changed the evolution pattern of the JJS permanently. Besides, possible explanations of the change of the evolution pattern of the JJS and adjacent riverbed are given. Water 2020, 12, 1652 3 of 15

2. Study Area The Yangtze River has a total length of 6300 kilometers and a basin area of 1.8 million square kilometers. Diﬀerent types of sandbanks are distributed along the Yangtze River, due to the diﬀerence of hydrodynamic and sediment conditions. Large-scale hydraulic works, such as the constructions of the Three Gorges Dam and the 12.5 m Deep-water Channel Project (DWC Project) of the Yangtze River, have been carried out to support the social development of the national economy, transportation and residents’ safety living along the river. In addition, some local hydrodynamic constructions, such as river damming, ports are distributed along the river. JJS is located at the entrance of Fujiangsha (FJS) Reach, a multi-branching reach, in the tidal reach of the Yangtze River, as seen in Figure2. FJS Reach is divided into two branches by FJS Shoal (shown in Figure2) with the diversion ratios of discharge are 80% for the north branch and 20% for the south branch, and then divided into two branches by Shuangjiansha (SJS) Shoal (shown in Figure2). WaterThe north2020, 12 branch, x FOR PEER is the REVIEW main channel with about 3 km wide and 19 km long. 4 of 15

(a)

(b)

Figure 2. 2. ((aa)) Location Location of of the the study study area area and and the the tidal tidal current current limit limit in in Yangtze Yangtze River River,, and ( (b)) l layoutsayouts of thethe t twowo major projects in the s studytudy a area.rea.

3. Data and Methods

3.1. Data Studies on the evolution of the sandbank are based on the 17 bathymetric measurements from 1999 to 2017 provided by the Construction Headquarters of Deep-water Channel Project of the Yangtze River. Hydrological data in this paper are collected from the Hydrologic Data Year Book of China and Sediment Bulletin of China, including the tidal water level and tidal range of Jiangyin tide station from 2003 to 2015, and the runoff and the sediment discharge at Datong hydrometric station, a key hydrological station reflecting the runoff of downstream of Yangtze River, from 2001 to 2018.

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Previous studies have shown that, influenced by the coupling of runoff and tidal current, the location of the tidal current limit of the Yangtze River can be traced back to Zhenjiang (Figure2) in dry seasons and moved down to the Xijie Port in flood seasons, and FJS Reach is located between the two positions. According to statistics, the location of the tidal current limit varies in the study reach with the discharge of the runoff between 10,000 m3/s and 40,000 m3/s. According to the measurements at Jiangyin tidal station (Figure2), the tidal level ranges from 1.11 m to 6.67 m with the maximum − tidal range of 3.36 m and mean tidal range of 1.78 m, and the maximum flood and ebb velocities are about 0.5 m/s and 1.8 m/s, respectively. According to the sampling of the riverbed material in recent years, the medium grain size in the FJS Reach ranges from 0.15 to 0.25 mm, which is larger in the deep channel than that in shallows in general. The sediment in the SJS Shoal is finer, with the medium grain size smaller than 0.1 mm. The medium grain size of suspended sediment in the study area ranges from 0.006 to 0.017 mm. In dry seasons, the average suspended sediment concentration (SSC) ranges from 0.043 to 0.226 kg/m3 in flood tides and 0.045 to 0.117 kg/m3 in ebb tides, while in flood seasons, the values are 0.039 to 0.233 kg/m3 in flood tides and 0.061–0.207 kg/m3 in ebb tides. In the past 10 years, two major projects, including the SJS Project and the spur dikes of DWC Project, have been carried out in the FJS Reach. The SJS Project started at the end of 2010 and finished in May 2012. It includes the construction of three long submerged breakwaters that aims to protect the SJS Shoal from erosion (Figure2). The DWC Project is a large-scale hydraulic work which covers 283 km from Nanjing to Yangtze Estuary in Yangtze River in China, with a long construction period from 2011 to 2018. Additionally, a series of regulation measures have been carried out in six reaches along Yangtze River to deal with the navigation obstruction problem, one of which is the FJS Reach where the study area is. The engineering measures in the FJS Reach include the construction of a series of spur dikes in the north bank of the FJS Shoal and both sides of the submerged breakwaters of SJS Project (Figure2) from 2015 to 2018 to improve the flow condition for navigation.

3. Data and Methods

3.1. Data Studies on the evolution of the sandbank are based on the 17 bathymetric measurements from 1999 to 2017 provided by the Construction Headquarters of Deep-water Channel Project of the Yangtze River. Hydrological data in this paper are collected from the Hydrologic Data Year Book of China and Sediment Bulletin of China, including the tidal water level and tidal range of Jiangyin tide station from 2003 to 2015, and the runoff and the sediment discharge at Datong hydrometric station, a key hydrological station reflecting the runoff of downstream of Yangtze River, from 2001 to 2018.

3.2. Method First, a digital elevation model [19] (DEM) of the river section was established to study the general pattern of sandbank evolution. Series of typical parameters were extracted over the years, including the shape of the typical cross-section, the volume of the sandbank, location of the bar peak, etc. Then, an empirical orthogonal function (EOF) analysis was conducted on the bathymetric dataset to investigate the major evolution patterns of the JJS and the detached bar and to explore the functions of corresponding impacts. EOF analysis has been widely used in ocean science and coastal engineering to investigate the changing patterns of beach profile [20–22], coastal sandbank [23], surface temperature [24], sea surface height [25], current profiles [26], terrestrial water storage [27], etc. The methodology of EOF analysis is to seek an expansion of the dataset in terms of a series of eigenfunctions with the same size of the data samples. In this case, the eigenfunctions are derived from the data of historical elevation data to find both time series and spatial modes. Each of the eigenfunctions consists of a contribution to the water depth as a function of a planimetric position. The 2-dimensional water depth field could be written as Water 2020, 12, 1652 5 of 15

XN h(X, t) = cn(t)en(X) (1) n=1 where h is the water depth, X is the planimetric position, t is the time of each measurement, en is the nth eigenfunction, cn is the corresponding temporal coeﬃcient, and N is the total number of eigenfunctions. The eigenfunctions should be independent of each other as

enem = δnm (2) where em is the mth eigenfunction, δnm is the Kronecker delta, where δnm = 1 if n = m and δnm = 0 otherwise. One of the approaches to calculate the eigenfunctions is the Lagrange multiplier approach [28] as

Aen(X) = λnen(X) (3) where λn is the eigenvalues. The matrix A can be calculated by

1 A = HHT (4) nxnt where nx is the number of water depth points in data sample, nt is the number of the measurement, H is made up of the individual elements of h(X,t), and HT is the transpose of H. The temporal coefficient cn can be calculated with XnX cn(t) = h(Xi, t)en(Xi) (5) i=1 Each eigenfunction indicates a description of the data accounting for a certain percentage of the data variance. These eigenfunctions functions are usually ranked in descending order of the magnitude of the corresponding eigenvalues which are proportional to the data variance. In this way, the first few eigenfunctions describe the most significant variations.

4. Results and Discussion

4.1. Periodic Evolution of the Sandbank In this section, the historical evolution of the JJS was analyzed based on 17 bathymetric measurements of the FJS Reach from 1999 to 2017. The earliest bathymetric measurement used in the analysis was measured in 1999, before which some documentation can be found to record the events of the earlier splitting of the JJS. These events are introduced before the data analysis as a historical comparison.

4.1.1. Documented Splitting Events of the JJS before 1999 From 1960 to 1999, there were eight documented splitting events of the JJS which vary in the scale of the detached bars [29]. The splitting location was usually between Pengqi Port and Liuzhu Port. The splitting times and the scales of the detached bars are listed in Table1. As seen, the periods between the splitting events ranges between two years to seven years. The widths are about 0.5 km and the lengths range from 0.5 to 5 km. Water 2020, 12, 1652 6 of 15

Table 1. Documented splitting events of the Jingjiang Sandbank (JJS) before 1999.

No. Time Scale of the Detached Bar (Length Width) × 1 November 1966 5 0.6 km × 2 June 1970 multiple detached bars, 3 0.5 km (largest one) × 3 March 1975 5 0.6 km × 4 March 1980 3 0.4 km × 5 September 1987 multiple detached bars, 0.5 0.5 km (largest one) × 6 August 1989 4 0.6 km × 7 July 1994 0.5 0.5 km × 8 October 1998 1.5 0.5 km ×

4.1.2. Analysis of the Evolution of the JJS during 1999 to 2017 From 1999 to 2017, the JJS generally experienced a periodic evolution mode with the stages of increase, split, migration, and dissipation. Nine out of 17 of the bathymetric measurements used in the analysis are plotted in Figure3 and supplementary information is recorded in Table2. From 1999 to 2017, the JJS went through six evolution cycles, which can be divided into two categories, complete cycle and splitting cycle, and the periods of the cycles ranged from two years to eight years. A complete cycle means that the detached bar migrates the whole way to SJS Shoal and merged into it, while the splitting cycle means that the detached bar dissipates after splitting away from the JJS. The complete cycles occurred during the period from 2002 to 2010 and 2006 to 2015, and the splitting cycles occurred before 2002 and in 2009, respectively. Overlapping of time can be overserved between two adjacent cycles, i.e., new splitting happens before the dissipation of the last detached bar. The processes of each evolution cycle can be described as follows. The splitting of the detached bar of the first cycle happened before 1999. The detached bar was found to migrate downstream with a scale of about 2.5 km (length) 0.5 km (width). The migration × speed was about 0.56 km/y. The splitting of the second cycle took place during 1999 and 2002, after which the detached bar continued to migrate downstream with a speed of about 1.04 km/y, and then merged into the SJS Shoal in 2010. The third cycle started with an inward curving shape formed in the upstream side of JJS in 2006. The splitting finished in 2010 and formed a detached bar with a scale of about 3 km (length) 0.6 km (width). The detached bar migrated downstream with a speed of × 1.25 km/y, and then merged into SJS Shoal in 2015. The fourth and fifth cycles occurred from 2012 to 2016, during which the detached bars dissipated rapidly after splitting from the JJS. The sixth cycle started at the end of 2016 and the splitting process was not yet finished in the last measurement in 2017, (see the half-splitting block of the sandbank in Figure3). A typical cross-section at JJS is chosen to see the evolution process during the period from 1999 to 2017 (Figure4). It can be seen obviously that the shape of the sandbanks changed significantly above elevation 16 m, with the top three scales of the sandbank in January 2001, June 2006, and May 2017 − respectively, while the morphology rarely changed in channel. Water 2020, 12, 1652 7 of 15 Water 2020, 12, x FOR PEER REVIEW 7 of 15

Figure 3. Nine out of 17 of the digital elevation models (DEMs) based on the bathymetric Figure 3. Nine out of 17 of the digital elevation models (DEMs) based on the bathymetric measurements measurements showing the six evolution cycles with overlapping of time, in which (a) to (b) show 1st showing the six evolution cycles with overlapping of time, in which (a) to (b) show 1st cycle, (b) to (e) cycle, (b) to (e) show 2nd cycle, (d) to (g) show 3rd cycle, (f) to (g) show 4th cycle, (g) to (h) show 5th show 2nd cycle, (d) to (g) show 3rd cycle, (f) to (g) show 4th cycle, (g) to (h) show 5th cycle, and (h) to (cyclei) shows, and 6th (h) cycle. to (i) shows 6th cycle.

A typical crossTable-section 2. Periodic at JJS change is chosen and splittingto see the events evolution of the JJSprocess from 1999during to 2017. the period from 1999 to 2017 (Figure 4). It can be seen obviously that the shape of the sandbanks changed significantly No. Period Time Splitting Time Scale of the Detached Bar (Length Width) above elevation −16 m, with the top three scales of the sandbank in January 2001, June 2006× , and May 1 before 1999 to 2002 1998 2.5 km 0.5 km 2017 respectively, while the morphology rarely changed in channel. × 2 before 2002 to 2010 before 2002 5 0.5 km × 3 2006 to 2015 2009 3 km 0.6 km × 4 2012 to 2015 2014 dissipated rapidly after splitting 5 2014 to 2016 2016 dissipated rapidly after splitting 6 2016 to 2017 Not happened yet Not happened yet

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Figure 4. Shapes of the typical cross section with the maximum width of JJS based on the Figure 4. Shapes of the typical cross section with the maximum width of JJS based on the bathymetric bathymetric dataset. dataset. To investigate the feature of the migration of the detached bars, they were distinguished from To investigate the feature of the migration of the detached bars, they were distinguished from the bathymetryTo investigate measurements the feature of from the migration 1999 to 2017. of the A detached total of sixbars individual, they were detached distinguished bars werefrom the bathymetry measurements from 1999 to 2017. A total of six individual detached bars were distinguished,the bathymetry and measurements the migration tracks from of1999 them to are 2017. plotted A total in Figure of six5, inindividual which the detached Y-axis indicates bars we there distinguished, and the migration tracks of them are plotted in Figure 5, in which the Y-axis indicates distancedistinguished from, the and peak the ofmigration the detached tracks bar of them to the are reference plotted point in Figure in the 5, upstream in which ofthe the Y- JJSaxis (Figure indicates2). the distance from the peak of the detached bar to the reference point in the upstream of the JJS (Figure Asthe seen,distance most from of thethe peak splitting of the process detached occurs bar to between the reference Pengqi point Port in and theLiuzhu upstream Port, of the and JJS only (Figure the 2). As seen, most of the splitting process occurs between Pengqi Port and Liuzhu Port, and only the second2). As seen and, thirdmost detachedof the splitting bars reached process SJSoccurs Shoal between before Pengqi the disappearance. Port and Liuzhu It can P alsoort, and be seen only that the second and third detached bars reached SJS Shoal before the disappearance. It can also be seen that thesecond overlapping and third of detached time is common bars reached between SJS S adjacenthoal before cycles. the Anotherdisappearance. interesting It can ﬁnding also be is seen that that the the overlapping of time is common between adjacent cycles. Another interesting finding is that the periodthe overlapping of the evolution of time cycle is common seems to between reduce toadjacent about twocycles. to three Another years interesting after 2012, finding and the is detached that the period of the evolution cycle seems to reduce to about two to three years after 2012, and the detached barsperiod tend of the to disappearevolution cycle quickly seems after to splitting reduce to away about from two theto three JJS. Theyear timings after 2012 is consistent, and the detached with the bars tend to disappear quickly after splitting away from the JJS. The timing is consistent with the constructionbars tend to ofdisappear the SJS Projectquickly and after the splitting following away spur from dikes the of JJS DWC. The Project, timing sois oneconsistent of the possiblewith the construction of the SJS Project and the following spur dikes of DWC Project, so one of the possible reasonsconstruction for the of shortening the SJS Project of the and period the of following the evolution spur cycledikes and of DWC the rapid Project dissipation, so one ofof thethe detached possible reasons for the shortening of the period of the evolution cycle and the rapid dissipation of the barreasons is the for construction the shortening of the of projects. the period If this of the explanation evolution is cycle right, and it means the rapid that thedissipation pattern of the the detached bar is the construction of the projects. If this explanation is right, it means that the pattern evolutiondetached cyclebar is hasthe beenconstruction changed of permanently the projects. by If thethis construction explanation ofis theright two, it projects.means that However, the pattern the of the evolution cycle has been changed permanently by the construction of the two projects. existingof the evolution three observed cycle evolution has been cycles changed are inadequate permanently to bydraw the a convincingconstruction conclusion, of the two and projects. future However, the existing three observed evolution cycles are inadequate to draw a convincing worksHowever are, expected.the existing three observed evolution cycles are inadequate to draw a convincing conclusion, and future works are expected.

FigureFigure 5.5. MigrationMigration trackstracks of of the the detached detached bars, bars including, including two two complete complete cycle, cycle three, three splitting splitting cycle cycle and oneand unﬁnishedone unfinished cycle. cycle.

Except for the migration of the detached bars, the periodic evolution of the sandbank itself is Except for the migration of the detached bars, the periodic evolution of the sandbank itself is also concerned. To investigate the change of the scale of the JJS, the historical volumes of the JJS also concerned. To investigate the change of the scale of the JJS, the historical volumes of the JJS were calculated and are plotted in Figure 6. The volume of the JJS is defined as the volume of the sediment that is above −16 m in the area of the JJS. From 1999 to 2017, the volume change of the JJS seemed to

Water 2020, 12, 1652 9 of 15

WaterwereWater 20 calculated202020, 1,2 1, 2x, FORx FORand PEER PEER are REVIEW REVIEW plotted in Figure6. The volume of the JJS is defined as the volume of9 of9 the of 15 15 sediment that is above 16 m in the area of the JJS. From 1999 to 2017, the volume change of the − haveJJShave seemed two two periodic periodic to have cycles cycles two, periodic during, during each cycles,each of of which during which the eachthe volume volume of which of of the the the JJS JJS volume experienced experienced of the a JJS adecreasing decreasing experienced-and-and- a- increasingdecreasing-and-increasingincreasing process. process. However However process., the, the scope scope However, of of the the volume thevolume scope change change of the seemed seemed volume to to changedecrease decrease seemed significantly significantly to decrease after after 2012.significantly2012. Like Like the the after change change 2012. of of Likethe the evolution the evolution change pattern pattern of the evolutionof of the the detached detached pattern bar bar of, thethe, the detacheddecrease decrease of bar, of the the scope scope decrease of of the the of volumethevolume scope change change of the volumeof of the the sandbank change sandbank of can the can sandbank also also be be explained canexplained also be by by explained the the construction construction by the construction of of the the two two of projects. theprojects. two Howeverprojects.However,However, ,this this ex explanationplanation this explanation is is given given is tentatively tentativelygiven tentatively due due to to due limited limited to limited field field data field data, data,,and and future and future future works works works are are expected.areexpected. expected.

Figure 6.Figure The historical 6. The historical volumes volumes of the of main the main body body of JJS of above JJS above elevation elevation −1616 m m.. Figure 6. The historical volumes of the main body of JJS above elevation −16− m. 4.2. Major Patterns of the Sandbank Evolution 4.2.4.2. Major Major P atternsPatterns of of the the S andbankSandbank E volutionEvolution To investigate the major patterns of the complex evolution of JJS, an empirical orthogonal function ToTo investigate investigate the the major major patterns patterns of of the the complex complex evolution evolution of of JJS JJS, ,an an e mpiricalempirical o rthogonalorthogonal (EOF) analysis was conducted on the bathymetric dataset of the JJS and adjacent riverbed. The area of functionfunction (EOF) (EOF) analysis analysis wa was sconducted conducted on on the the bathymetric bathymetric dataset dataset of of the the JJS JJS and and adjacent adjacent riverbed riverbed. . EOF analysis is illustrated in Figure7. The area contains the JJS and its downstream reach. The spur TheThe area area of of EOF EOF analysis analysis is is illustrated illustrated in in Figure Figure 7 .7 The. The area area contains contains the the JJS JJS and and its its downstream downstream reach. reach. dikes are excluded to reduce the variance impact near artiﬁcial structures. TheThe spur spur dikes dikes are are excluded excluded to to reduce reduce the the variance variance impact impact near near artificial artificial structures. structures.

Figure 7. The area for empirical orthogonal function (EOF) analysis. The spur dikes are excluded to FigureFigure 7. 7. TheThe area area for for e empiricalmpirical o orthogonalrthogonal f functionunction ( (EOF)EOF) analysis analysis.. The The spur spur dikes dikes are are excluded excluded to to reduce the variance impact near artificial structures. reducereduce the the v varianceariance impact impact near near artificial artiﬁcial structures structures..

AAA total totaltotal of ofof 17 1717 bathymetric bathymetricbathymetric measurements measurements from from from 1999 1999 1999 to to to2017 2017 2017 we we wererere interpolated interpolated interpolated onto onto onto a aregular regular a regular 50 50 m50m × m ×50 50 m50 m grid mgridgrid using using using linear linear linear and and andthen then then used used used in in the the in EOF the EOF EOF analysis. analysis. analysis. The The result The result result shows shows shows that that more that more morethan than 96% than 96% × (96%T(ableTable (Table 3 )3 of) of 3the) the of data thedata datavariation variation variation is is captured captured is captured by by the the by first thefirst four ﬁrst four foureigenfunctions. eigenfunctions. eigenfunctions. A Additionally,dditionally, Additionally, the the fir thefirstst four ﬁrst four eigenfunctionseigenfunctions are are plotted plotted together together with with the the corresponding corresponding historical historical changes changes of of the the temporal temporal coefficientscoefficients in in Figure Figure 8 .8 .

TableTable 3. 3. Percentage Percentage of of the the total total variability variability represented represented by by the the first first four four eigenfunctions eigenfunctions of of EOF EOF analysis analysis. .

Water 2020, 12, 1652 10 of 15 four eigenfunctions are plotted together with the corresponding historical changes of the temporal coeﬃcients in Figure8. Water 2020, 12, x FOR PEER REVIEW 10 of 15 Table 3. Percentage of the total variability represented by the ﬁrst four eigenfunctions of EOF analysis. EOF 1 EOF 2 EOF 3 EOF 4 Remain EOF 1 EOF 2 EOF 3 EOF 4 Remain 86.45% 7.16% 2.02% 1.25% 3.12% 86.45% 7.16% 2.02% 1.25% 3.12%

Figure 8. First four eigenfunctions (spatial modes) and the corresponding temporal coefficients in theFigure upper 8. First left four corner. eigenfunctions The dotted line(spatial indicates modes) the and approximate the corresponding area of thetemporal JJS. The coefficients color indicates in the theupper values left corner. of the corresponding The dotted line eigenfunctions, indicates the approximate which is the samearea of size the of JJS. the The EOF color analysis indicates area, the unitvalues is meter,of the corresponding which is the same eigenfunctions, as the analyzed which data, is the i.e., same the bathymetry. size of the EOF (a) theanalysis first eigenfunctionarea, the unit andis meter the, correspondingwhich is the same temporal as the coeanalyzedfficient; data, (b) i.e., the the second bathymetry. eigenfunction (a) the andfirst theeigenfunction corresponding and temporalthe corresponding coefficient; temporal (c) the coefficient third eigenfunction; (b) the second and the eigenfunction corresponding and temporalthe corresponding coefficient; temporal (d) the fouthcoefficient eigenfunction; (c) the third and theeigenfunction corresponding and temporal the corresponding coefficient. temporal coefficient; (d) the fouth eigenfunction and the corresponding temporal coefficient. 4.2.1. Sensitivity Analysis of EOF 4.2.1.To Sensitivity study the A sensitivitynalysis of ofEOF the results of EOF analysis to the number of samples, the eigenfunctions were also calculated with different numbers (15 and 16) of bathymetric measurements, and deviations To study the sensitivity of the results of EOF analysis to the number of samples, the eigenfunctions were also calculated with different numbers (15 and 16) of bathymetric measurements, and deviations of the eigenfunctions to the eigenfunctions calculated with all 17 bathymetric measurements are calculated. The deviations are calculated by the following formula:

푁 2 1 퐷푒푣𝑖푎푡𝑖표푛 = √ ∑[푒푘(푋) − 푒17(푋)] (6) 푁 푛 푛 푖=1

Water 2020, 12, 1652 11 of 15 of the eigenfunctions to the eigenfunctions calculated with all 17 bathymetric measurements are calculated. The deviations are calculated by the following formula: v tu N Water 2020, 12, x FOR PEER REVIEW 1 Xh i2 11 of 15 Deviation = ek (X) e17(X) (6) N n − n 푘 i=1 where 푒푛 (푋) is the nth normalized eigenfunction calculated with k bathymetric measurements, N is the totalk number of grid points in the analysis area. where en(X) is the nth normalized eigenfunction calculated with k bathymetric measurements, N is the Results show that, compared with the eigenfunctions calculated with all 17 measurements total number of grid points in the analysis area. 푒17(푋), the deviations of the eigenfunctions maintain in a small level, i.e., the deviation of 푒16(푋) 푛 Results show that, compared with the eigenfunctions calculated with all 17 measurements e171 (X), ranged from 0.037% to 0.56%, the deviation of 푒16(푋) ranged from 1.19% to 2.57% the deviationn of the deviations of the eigenfunctions maintain in a2 small level, i.e., the deviation of e16(X) ranged from 푒16(푋) ranged from 0.32% to 1.36%, the deviation of 푒16(푋) ranged from 0.21%1 to 10.82%, the 0.037%3 to 0.56%, the deviation of e16(X) ranged from 1.19%4 to 2.57% the deviation of e16(X) ranged deviation of 푒15(푋) ranged from 0.46%2 to 0.88%, the deviation of 푒15(푋) ranged from3 1.74% to 3.30% from 0.32% to1 1.36%, the deviation of e16(X) ranged from 0.21% to2 10.82%, the deviation of e15(X) the deviation of 푒15(푋) ranged from 1.42%4 to 1.50%, and the deviation of 푒16(푋) ranged from 0.68%1 ranged from 0.46%3 to 0.88%, the deviation of e15(X) ranged from 1.74% to 3.30%4 the deviation of e15(X) to 11.40%. The deviations are plotted in Figure2 9. As seen, for most of the cases the deviation is smaller3 ranged from 1.42% to 1.50%, and the deviation of e16(X) ranged from 0.68% to 11.40%. The deviations than 3.5%, for only one case of 푒16(푋) and one case4 of 푒15(푋) the deviations were between 10% and are plotted in Figure9. As seen, for4 most of the cases the deviation4 is smaller than 3.5%, for only one 12%. The reason of the relatively large deviations in these two cases is the remove of a data (the case of e16(X) and one case of e15(X) the deviations were between 10% and 12%. The reason of the measurement4 in May 2009) that4 made significant contribution to the variance. Generally, removing relatively large deviations in these two cases is the remove of a data (the measurement in May 2009) one or two data measurements yields limited influence on the eigenfunctions, indicating that the that made significant contribution to the variance. Generally, removing one or two data measurements results of the EOF analysis based on existing bathymetric measurements can reflects the evolution yields limited influence on the eigenfunctions, indicating that the results of the EOF analysis based on pattern of the JJS and adjacent riverbed. existing bathymetric measurements can reflects the evolution pattern of the JJS and adjacent riverbed.

(a) (b)

FigureFigure 9.9. TheThe deviations deviations of of eigenfunctions eigenfunctions induced induced bbyy differentdiﬀerent numbers of the the bathymetric bathymetric measurements,measurements, comparingcomparing withwith thethe resultsresults ofof thethe totaltotal 1717 bathymetric measurements:measurements: ((aa)) thethe deviationdeviation ofof EOFEOF 1;1; ((bb)) thethe deviationdeviation ofof EOFEOF 2;2; ((cc)) thethe deviationdeviation ofof EOFEOF 3;3; andand ((dd)) thethe deviationdeviation ofof EOFEOF 4.4.

4.2.2. The First Four Major Patterns As noted in most of the existing studies, the first eigenfunction corresponds to the time-averaged bathymetry, and it can be labeled as the mean elevation function with the corresponding temporal coefficient basically unchanged. It represented 86.45% of the data variance. The second eigenfunction corresponds to the long-term change of the pattern of elevation, representing 7.16% of the data variance. As it can be seen, the temporal coefficient turned from positive to negative after 2012, indicating that the detached bar that split from the JJS became strongly active. In addition, the disappearance of the sand ridge in the east part of the study area and the

Water 2020, 12, x FOR PEER REVIEW 12 of 15

Water 2020, 12, 1652 12 of 15 siltation in the north of the sand ridge indicates that sand ridge shifted north. The sand ridge can be found existing in Figure 3a to Figure 3d during the period from 1999 to 2006, and disappearing in 4.2.2.Figure The 3e in First 2009. Four In MajorFigure Patterns3f to Figure 3i from 2012 to 2017, the sand ridge cannot be found. A highly possible explanation of this pattern is the construction of the SJS Project and the spur dikes of the As noted in most of the existing studies, the first eigenfunction corresponds to the time-averaged DWC Project, which indicates that the human projects might have changed the evolution pattern of bathymetry, and it can be labeled as the mean elevation function with the corresponding temporal the JJS permanently. Spur dikes at the north side of the FJS Shoal increase the waterpower outer edges coefficient basically unchanged. It represented 86.45% of the data variance. of the heads the spur dikes, forcing the mainstream moving to the north. In addition, the influence of The second eigenfunction corresponds to the long-term change of the pattern of elevation, the LZ port can also be reflected in the second eigenfunction. As seen in Figure 8b, a significant large representing 7.16% of the data variance. As it can be seen, the temporal coefficient turned from vale of the second eigenfunction can be found at and downstream of the LZ port. positive to negative after 2012, indicating that the detached bar that split from the JJS became strongly The third eigenfunction reflects the long-term periodic change of the JJS itself and the detached active. In addition, the disappearance of the sand ridge in the east part of the study area and the bar with a period of 18 years, representing 2.02% of the data variance. A trough can be found in the siltation in the north of the sand ridge indicates that sand ridge shifted north. The sand ridge can be middle of the JJS and an obvious wave of the water depth can be found in the downstream of the JJS. found existing in Figure3a to Figure3d during the period from 1999 to 2006, and disappearing in According to the long-term periodic change of the temporal coefficient, the JJS itself experiences a Figure3e in 2009. In Figure3f to Figure3i from 2012 to 2017, the sand ridge cannot be found. A highly siltation–erosion–siltation process, while the wave of the water depth propagates downstream, which possible explanation of this pattern is the construction of the SJS Project and the spur dikes of the DWC reflects the periodic splitting-away and downstream movement of the detached bar. Those changing Project, which indicates that the human projects might have changed the evolution pattern of the JJS patterns of the shape of the JJS can be confirmed in the historical measurements of the elevation permanently. Spur dikes at the north side of the FJS Shoal increase the waterpower outer edges of the shown in Figure 3, e.g., the middle of the JJS had a relatively large width in 1999 and 2010, while the heads the spur dikes, forcing the mainstream moving to the north. In addition, the influence of the LZ width was smaller after 2012. The temporal coefficient of the third eigenfunction turned from port can also be reflected in the second eigenfunction. As seen in Figure8b, a significant large vale of negative to positive around 2003 and changed significantly after 2012, which implies closely the second eigenfunction can be found at and downstream of the LZ port. associated with the runoff conditions, including discharge and sediment. Statistics from the The third eigenfunction reflects the long-term periodic change of the JJS itself and the detached hydrometric station of Datong show a decrease of suspended sediment discharge since 2003 and a bar with a period of 18 years, representing 2.02% of the data variance. A trough can be found in the significant change around 2011 after the reservoir filling of the Three Gorges Dam, which indicates a middle of the JJS and an obvious wave of the water depth can be found in the downstream of the JJS. promotion of sediment carrying capacity (Figure 10). However, sediment conditions upstream of the According to the long-term periodic change of the temporal coefficient, the JJS itself experiences a JJS should have a more immediate effect. Future works are expected to confirm the impact of the siltation–erosion–siltation process, while the wave of the water depth propagates downstream, which runoff. reflects the periodic splitting-away and downstream movement of the detached bar. Those changing The fourth eigenfunction shows a rip adjacent to the north bank of the river and between the JJS patterns of the shape of the JJS can be confirmed in the historical measurements of the elevation shown and downstream area, representing 1.25% of the data variance. In addition, an obvious wave of the in Figure3, e.g., the middle of the JJS had a relatively large width in 1999 and 2010, while the width water depth can be found in the downstream of the JJS. With the periodic change of the corresponding was smaller after 2012. The temporal coefficient of the third eigenfunction turned from negative to temporal coefficient, the wave of the water depth propagates downstream, which reflects the periodic positive around 2003 and changed significantly after 2012, which implies closely associated with the splitting-away and downstream movement of the detached bar, with a period of eight years. As runoff conditions, including discharge and sediment. Statistics from the hydrometric station of Datong shown in Figure 11, the temporal coefficient of the fourth eigenfunction shows a similar trend to the show a decrease of suspended sediment discharge since 2003 and a significant change around 2011 change of the annual maximum tidal range which partially reflects the interannual variability of the after the reservoir filling of the Three Gorges Dam, which indicates a promotion of sediment carrying tidal current. Therefore, the fourth eigenfunction might be related to the tidal current. However, due capacity (Figure 10). However, sediment conditions upstream of the JJS should have a more immediate to a limited time range of measurement, the relationship between the fourth pattern and tidal current effect. Future works are expected to confirm the impact of the runoff. is expected to be confirmed in future works.

FigureFigure 10.10. Annual runorunoffﬀ and and suspended suspended sediment sediment load load recorded recorded at at the the hydrometric hydrometric station station of of Datong. Datong. The fourth eigenfunction shows a rip adjacent to the north bank of the river and between the JJS and downstream area, representing 1.25% of the data variance. In addition, an obvious wave of the water depth can be found in the downstream of the JJS. With the periodic change of the corresponding

Water 2020, 12, 1652 13 of 15 temporal coefficient, the wave of the water depth propagates downstream, which reflects the periodic splitting-away and downstream movement of the detached bar, with a period of eight years. As shown in Figure 11, the temporal coefficient of the fourth eigenfunction shows a similar trend to the change of the annual maximum tidal range which partially reflects the interannual variability of the tidal current. Therefore, the fourth eigenfunction might be related to the tidal current. However, due to a limited time range of measurement, the relationship between the fourth pattern and tidal current is expected Water 2020, 12, x FOR PEER REVIEW 13 of 15 to be confirmed in future works.

Figure 11. 11. AnnualAnnual maximum maximum tidal tidal range range of flood of andflood ebb and respectively ebb respectively,, and the andfourth the temporal fourth coefficienttemporal coe. fficient. 5. Conclusions 5. Conclusions The JJS is a marginal sandbank located on the left bank of the FJS Reach in the Yangtze River. The JJS is a marginal sandbank located on the left bank of the FJS Reach in the Yangtze River. It It experiences a periodic evolution process of increase, split, migration, and dissipation, which affect experiences a periodic evolution process of increase, split, migration, and dissipation, which affect the morphology feature, the channel depth, the levee safety, and other aspects of the FJS Reach. In this the morphology feature, the channel depth, the levee safety, and other aspects of the FJS Reach. In paper, the periodic evolution of the JJS was investigated on the base of 17 field measurements of the this paper, the periodic evolution of the JJS was investigated on the base of 17 field measurements of elevation of the FJS Reach from 1999 to 2017. the elevation of the FJS Reach from 1999 to 2017. The evolution pattern of the JJS and the adjacent riverbed was firstly discussed according to the The evolution pattern of the JJS and the adjacent riverbed was firstly discussed according to the measured elevation changes. The six cycles of the evolution process of the JJS and adjacent riverbed measured elevation changes. The six cycles of the evolution process of the JJS and adjacent riverbed and during 1999 to 2017 were described. It was found that the overlapping of time is common between and during 1999 to 2017 were described. It was found that the overlapping of time is common adjacent evolution cycles. The detached bars were distinguished from the elevation measurements between adjacent evolution cycles. The detached bars were distinguished from the elevation and the migration tracks were discussed. It was found that after 2012 the period of the evolution cycle measurements and the migration tracks were discussed. It was found that after 2012 the period of the reduced to about two to three years and the detached bars seemed to disappear quickly after splitting evolution cycle reduced to about two to three years and the detached bars seemed to disappear away, the reason of which might be the construction of the SJS Project and the spur dikes of DWC quickly after splitting away, the reason of which might be the construction of the SJS Project and the Project. The volumes of the JJS in each measurement of elevation were calculated and the historical spur dikes of DWC Project. The volumes of the JJS in each measurement of elevation were calculated change of the volumes was discussed. The scope of the volume change also decreased significantly andafter the year historical of 2012, change which of can the also volumes be explained was by discussed. the construction The scope of the of two the projects. volume According change also to decreasethe changesd significantly of the evolution after featurethe year of of the 2012 detached, which barcan andalso thebe explained JJS itself, the by constructionthe construction of the of twothe projectstwo projects. might According have changed to the the changes evolution of the pattern evolution of the feature JJS permanently. of the detached However, bar dueand tothe the JJS limited itself, thetime construction range of measurement of the two projects after the might construction have changed of the the two evolution projects, pattern future of works the JJS are permanently. expected to Howeverinvestigate, due the to eff ectsthe limited of the two time projects. range of measurement after the construction of the two projects, futureEOF works analysis are expected was conducted to investigate on the historicalthe effects elevation of the two of projects. the JJS and adjacent riverbed. The first four eigenfunctionsEOF analysis wa corresponds conducted tothe on meanthe historical elevation, elevation the long-term of the changeJJS and ofadjacent the pattern riverbed of bathymetry,. The first foura periodic eigenfunctions change of the correspond JJS itself and to thedownstream mean elevation migration, the of the long split-term detached change bar of with the a pattern period of 18bathymetry years, and, a the periodic periodic change change of of the the JJS rip itself at the and back downstream of JJS with amigration period of of eight the years.split deta Theched last twobar withof the a eigenfunctionsperiod of 18 years with, and the the corresponding periodic change temporal of the coe ripffi atcient theindicate back of properJJS with runo a periodff-dominated of eight years.and tide-dominated The last two of changes the eigenfunctions of the JJSs, with respectively, the corresponding which are expectedtemporal tocoeffi be furthercient indicate confirmed proper in runofffuture- works.dominated In addition,and tide- accordingdominated to chang bothes the of historical the JJSs, analysisrespectively and, EOFwhich analysis, are expected the current to be workfurther also confirmed highlights inthat future the works. construction In addition of two, waterwayaccording regulationto both the projects historical in the analysis multi-branching and EOF analysis, the current work also highlights that the construction of two waterway regulation projects in the multi-branching reach might have changed the evolution pattern of the JJS permanently. However, due to a limited time range of measurement after the construction of the two projects, future works are expected to investigate the effects of the two projects.

Water 2020, 12, 1652 14 of 15 reach might have changed the evolution pattern of the JJS permanently. However, due to a limited time range of measurement after the construction of the two projects, future works are expected to investigate the eﬀects of the two projects.

Author Contributions: Conceptualization, Y.H. and M.C.; methodology, Y.H.; software, Y.H.; validation, Y.W., A.M.; formal analysis, Y.H.; investigation, A.M. and Y.W.; resources, A.M.; data curation, Y.H.; writing—original draft preparation, Y.H.; writing—review and editing, Y.H., M.C. and X.D.; visualization, Y.H.; supervision, M.C. and A.M.; project administration, M.C.; funding acquisition, M.C. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by National Key R&D Program of China, 2016YFC0402107. Acknowledgments: We would like to thank the Construction Headquarters of Deep-water Channel Project of the Yangtze River for providing bathymetric dataset and other technical support. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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