Modelling sediment transport processes in macro-tidal estuary

Science in China Series E: Technological Sciences©2009 SCIENCE IN CHINA PRESSModelling sediment transport processes in macro-tidal estuaryMA FangKai 1†, JIANG ChunBo 1, Rauen William B.2 & LIN BinLiang 21 State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China;2Hydro-environmental Research Centre, School of Engineering, Cardiff University, Parade, Cardiff CF24 3AA, UKThis paper outlines a numerical modeling study to predict the sediment transport processes in a macro-tidal estuary, namely the Mersey Estuary, UK. An integrated numerical model study is conducted to investigate the interaction between the hydrodynamic, morphological and sediment transport proc-esses occurring in the estuary. The numerical model widely used in environmental sediment transport studies worldwide, namely ECOMSED is used to simulate flow and sediment transport in estuary. A wetting and drying scheme is proposed and applied to the model, which defines “dry” cells as regions with a thin film of fluid O (cm). The primitive equations are solved in the thin film as well as in other regular wet cells. A model for the bed load transport is included in the code to account for the dynamics of the mobile bed boundary. The bed evolution due to bed load transport which is calculated according to van Rijn (1984a) is obtained by solving the sediment mass-balance equation. An estuary-related laboratory flume experiment is used to verify the model. Six sets of field measured hydrodynamic data are used to verify the corresponding predictions of the model, with the model-predicted water eleva-tions and salinity levels generally agreeing well with the field measurements. The numerical model re-sults show that in the Mersey Estuary both the tidal level and river discharge affect significantly the sediment transport. Reasonable agreement between the model results and field data has been obtained, indicating that the model can be used as computer-based tool for the environment management of estuarine system.hydraulic modelling, sediment transport, estuary, ECOMSED, flooding and drying1 IntroductionIn estuarine delta, tidal energy, sedimentation, river dis-charges and topography determine the development and characteristics of the wetland ecosystem. In recent years, significant advances with respect to field measurements, data analysis, and numerical modeling have allowed high-resolution simulation of many coastal processes including waves, currents, sediment transport and bathymetric change [1]. However, as the detail of these simulations improves, knowledge of specific boundary conditions, particularly with respect to the bottom boundary, becomes more critical [2]. A number of flood-ing and drying schemes have been implemented in coastal models [3,4], and a flooding and drying schemehas been applied to the Princeton Ocean Model (POM)[5]. The sediment transport along a natural bed of the same sediment material is a complex [6]. Over the past three decades, a large number of computational hydrodynamic /sediment transport models have been developed [7−11]. This paper describes a numerical modelling study to acquire a better understanding of the sediment transport processes in the Mersey Estuary, UK. This is a part of a series of studies of the environmental impact mechanismReceived July 8, 2009; accepted July 29, 2009 doi: 10.1007/s11431-009-0351-6 †Corresponding author (email: mfk@)Supported by the National Basic Research Program of China (“973” Project) (Grant No. 2006CB403304), the State Key Laboratory of Hydroscience and Engineering of Tsinghua University (Grant No. 2008-ZY-5) and the National Natural Science Foun-dation of China (Grant No. 90610028)Ma F K et al. Sci China Ser E-Tech Sci | Nov. 2009 | vol. 52 | no. 11 | 3368-33753369and its integral model for wetland system. Details of the numerical model used in this study are given in Section 2, the models are tested by two flume experimentalcases in Section 3, and Section 4 presents the model simulation result of the Mersey Estuary. Finally, the main conclusions drawn from this investigation are given in Section 5. 2 Mathematical model2.1 Hydrodynamic modelECOMSED is a numerical model of the 3-D hydrody-namic, wave, sediment and contaminant transport proc-esses in shallow water environments, such as rivers,bays, estuaries and coastal and oceanic waters. An or-thogonal curvilinear coordinate system in the horizontal plane and a sigma coordinate system in the vertical di-rection allow an accurate representation of a simulated domain. The 3-D hydrodynamic equations for incom-pressible and unsteady turbulent flows are [12],0211221=∂∂+∂∂+∂∂+∂∂σηξςwh h Dv h Du h t h h (1) where,11221⎟⎠⎞⎜⎝⎛∂∂+∂∂−⎥⎦⎤⎢⎣⎡⎟⎟⎠⎞⎜⎜⎝⎛∂∂+∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂+∂∂−=t tD D v h D u h h h W ςσηςησξςξσω (2) 2122112211220220212201d 2H M h h Du h Du h Duv wuh h t h h Dv v u h h f gD h D gDh D Dh h h h P u u K A D D h σξησξηςρσρσξρξξσρξσσξξ∂∂∂∂++++∂∂∂∂∂∂⎛⎞−+−⎜⎟∂∂⎝⎠⎛⎞∂∂∂∂=−−⎜⎟∂∂∂∂⎝⎠⎛⎞∂∂∂∂∂⎛⎞−++⎜⎟⎜⎟∂∂∂∂∂⎝⎠⎝⎠∫12,M M h u v A D A D h ηηηξ⎛⎞⎛⎞∂∂∂∂++⎜⎟⎜⎟∂∂∂∂⎝⎠⎝⎠ (3)2122112211220110d h h Dv h Duv h Dv wvh h t h h Du v u h h f gD h D gDh D σξησξηςρσρσηρηησ∂∂∂∂++++∂∂∂∂∂∂⎛⎞−+−⎜⎟∂∂⎝⎠⎛⎞∂∂∂∂=−−⎜⎟∂∂∂∂⎝⎠∫ 1121022H M Dh h h h P v v K A D D h ρησσηξ⎛⎞∂∂∂∂∂⎛⎞−++⎜⎟⎜⎟∂∂∂∂∂⎝⎠⎝⎠ 21,M M h v u A D A D h ξηξη⎛⎞⎛⎞∂∂∂∂++⎜⎟⎜⎟∂∂∂∂⎝⎠⎝⎠ (4),212112211221⎟⎠⎞⎜⎝⎛∂∂∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂∂∂=∂∂+∂∂+∂∂+∂∂σσηηξξσηξc K D h h c D h h A c D h h A wch h Dvc h Duc h t Dc h h H M M (5)where D =ς+H , total water depth; ς, water elevation; H , water depth below datum; t , time; ε, η and σ, the longi-tudinal, lateral and vertical directions with u , v and w being the corresponding velocity components; h 1, h 2, distance in ε and η direction at center of grid; f , Coriolis parameter; ρ0, the reference density; ρ, water density; P , pressure; W , vertical velocity; A M and K H are the hori-zontal and vertical diffusivity coefficients respectively; C , the water temperature or salinity.Details about the numerical model, including the boundary conditions, the full set of governing equations and the discretisation scheme can be found in the users manual [13]. The 3-D hydrodynamic governing equations are solved with the hydrostatic pressure distribution as-sumption. The second order k-ℓ scheme of Mellor and Yamada [14] is used for turbulence closure, where equa-tions for the turbulence kinetic energy (k ) and a turbu-lence macro scale (ℓ) are solved. The bed shear stress provides a link between the hydrodynamics and sedi-ment transport calculations and is computed using the log law method.A flooding and drying scheme has been implemented into the Princeton Ocean Model (POM)[5]. The scheme can be easily applied to ECOMSED which shares POM’s features: sigma-coordinate, time-splitting and C-grid. To invoke these conservation laws, a thin water film is defined with thickness H dry =0 (cm) at dry cells, to solve the primitive equations of ECOMSED in these cells as well as in other regular water cells. A separate time-dependent mask, ‘‘WETMASK’’, is defined as WETMASK = 0 at dry cells and = 1 at wet cells. At each time step, the velocity is set to zero if the water depth at cells’ interfaces drops below H dryUA i , j =0 if (D i , j +D i −1, j )/2 ≤ H dry ,VA i , j =0 if (D i , j +D i , j −1)/2 ≤ H dry . (6)3370Ma F K et al. Sci China Ser E-Tech Sci | Nov. 2009 | vol. 52 | no. 11 | 3368-3375The out flow is set to zero if the water depth at cells center drops below H dry. .0and 0WETMASK ,or ,0and 0WETMASK if 0,,,,1,<=>==−j i j i j i j i j i UA UA UA )7(.0and 0WETMASK ,or ,0and 0WETMASK if 0,,,1,,<=>==−j i j i j i j i j i VA VA VANo vertical (baroclinic) velocity structures cross cells’ interfaces if the water depth at cells’ interfaces drops below H dry . U i ,j ,k =UA i ,j if W ETMASK i , j * WETMASK i -1, j =0, and,V i ,j ,k =VA i ,j if W ETMASK i , j * WETMASK i , j −1=0. (8) The ECOMSED model with flooding and dryingscheme has been verified against a two-dimensional testcase with analytical solution of free oscillations in aparabolic basin, which has been discussed in anotherpaper as we focus on the sediment transport processeshere.2.2 Sediment transport modelThe transport and fate of cohesive and non-cohesivesediments have been simulated in the numerical model. The model calculates the total suspended load transport,which includes the bed load transport component. The 3-D advection diffusion equation that governs the trans-port of cohesive and non-cohesive sediments is solved separately for each sediment size class and is given by,)(212112211221⎟⎠⎞⎜⎝⎛∂∂∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂∂∂+⎟⎟⎠⎞⎜⎜⎝⎛∂∂∂∂=∂−∂+∂∂+∂∂+∂∂σσηηξξσηξc K D h h c D h h A c D h h A c w w h h Dvch Duc h t Dc h h H M M s (9)where c is the suspended sediment concentration, t is time, ξ,η, and σ, the longitudinal, lateral and verti-cal directions with u , v and w being the corresponding velocity components; w s is the settling velocity; h 1, h 2, distance in ξ and η directions at center of grid; and A M and K H are the horizontal and vertical diffusivity coeffi-cients respectively. The boundary conditions for eq. (9) include specification of the Dirichlet and Neumann con-ditions at the inlet and outlet boundaries respectively, while the zero flux condition is applied at lateral walls. The surface and bottom boundary conditions are),surface at the (0=∂∂σCD K H (10)bed bed (at the end),H K CE D D σ∂=−∂ (11) where E bed and D bed are re-suspension and deposition fluxes respectively, calculated at the interface between the water column and sediment bed. For non-cohesivesediments, these fluxes are computed following the van Rijn [15] formulation, based on the calculated values of the bed shear stress, sediment settling velocity and sus-pended sediment concentrations. Bathymetric changes are calculated from the predicted net fluxes of sedimenterosion and deposition.The bed load transport is not considered in the currentpublicly available ECOMSED modelling framework. Ascheme for the bed load transport is included in themodel to account for the dynamics of the mobile bedboundary. The bed evolution due to bed load transport which is calculated according to van Rijn [16] is obtainedby solving the sediment mass-balance equation: b b b b b bed bed ()(1)0,yx q z c q p D E t t x yδ∂∂∂∂′−++++−=∂∂∂∂(12) where q b x and q b y are the components of the bed-load transport q b in the x and y directions, respectively; z b ,local bed level above datum; p ′, porosity of the bed ma-terial; b c , concentration in the bed-load layer averaged over the layer thickness; δb , the bed-load layer thickness.The equation determining the bed-load transport q b reads [17] :b *b bed bed b b s1()0,y x q q D E q q x y L ∂∂++−+−=∂∂ (13) where L s , is the nonequilibrium adaptation length for bed-load transport; q b *, bed-load transport under equilib-rium conditions:*b q = (14)where s is the specific density; g , acceleration of gravity; D *, particle size parameter; T , nondimensional excess bed shear stress; d 50, median diameter of the bed mate-rial.Ma F K et al. Sci China Ser E-Tech Sci | Nov. 2009 | vol. 52 | no. 11 | 3368-3375 33713 Model validation3.1 Suspended sediment transport models test caseVan Rijn [18]reported a flume experiment with initially clear water that flowed over a loose sand bed and en-trained sediment into suspension until the full transport capacity was reached. The development of the sus-pended sediment concentration profiles in this case was already calculated by many researchers [17, 19−21]. Figure 1 shows the experimental configuration. The water depth is 0.25 m with the mean inflow velocity 0.67 m/s. The bed material consisted of sand with D 50 = 0.23 mm and D 90 = 0.32 mm. Figure 2 compares the predicted and measured concentration profiles at various locations (X/H = 0, 4, 10, 20, 40). The agreement can be seen to be good.Figure 1 Vertical view experimental configuration.Figure 2 Comparison of the predicted and measured concentration pro-files at various locations (X /H = 0, 4, 10, 20, 40).3.2 An estuary-related laboratory flume experiment studyAn estuary-related laboratory flume experiment was taken in the Hyder Hydraulics Laboratory, at Cardiff University [22]. As illustrated in Figure 3, the model had three main reaches, namely an upstream channel, a di-verging channel and a downstream channel. The water depth H = 0.3 m with the inflow Q = 45 L/s. Fine uni-form silica sand (D 50 = 0.133 mm) was used to fill thebottom of the model, up to an initial height h = 10 cm. The key sediment transport parameters were calculated using the formulations of Soulsby [23], with w s = 1.2 cm/s, D * = 3.3, θcr = 0.065 and u *cr = 1.2 cm/s, for the settling velocity, dimensionless grain size, critical Shields pa-rameter and critical friction velocity respectively.Experimental results show that erosion occurred at upper straight channel of the flume, and the erosion rate was slowing down after eight hours reaching equilib-rium condition. Most of the sediment deposition hap-pened near the mouth of the diverging channel, and the bed form of the downstream straight channel changed less with less deposition. Figure 4 depicts the experi-mental and numerical model bed level change obtained at t = 4.0 h and t = 8.0 h. It can be noted in this figure that the predictions obtained with the modified code were in good agreement with the data.Figure 3 Plan view experimental configuration.Figure 4 Comparison of the experimental and numerical model bed level changes.3372Ma F K et al. Sci China Ser E-Tech Sci | Nov. 2009 | vol. 52 | no. 11 | 3368-33754 Application to Mersey Estuary4.1 Studying areaThe Mersey Estuary is hugely important to the economy of the region, but it is also valuable from an environ-mental perspective. Historically, the Estuary has been seriously polluted by industrial discharges and adjacent sea dumping [24]. The Mersey Basin Campaign has been focusing on improving the water quality in the rivers and waterways of the Northwest of England for almost 20 years, with the aim being to encourage high quality wa-ter front regeneration in the region, with a comprehen-sive programme of actions currently being undertaken to improve water quality [25]. The Mersey Estuary is a macro-tidal estuary, with typical spring-neap cycle tidal ranges varying between about 10.5 and 3.5 m. Freshwa-ter inflow from the Mersey River into the Mersey Estu-ary varies from about 412 to 29520 ML/d. The Upper Estuary (upstream of Runcorn) is a narrow meaning channel of about 15 km in length. In the downstream of Runcorn, the estuary opens up into a large shallow basin to form the Inner Estuary, of about 20 km in length, with extensive inter-tidal banks and salt marshes on its south-ern margins. Further downstream of the Inner Estuary, the Estuary converges to form the Narrows, a straight narrow channel of up to 30 m depth, at low water. In the seaward of the Narrows, the channel widens again to form the Outer Estuary, consisting of a large area of in-ter-tidal sand and mud banks [26]. Figure 5 is a map of the Mersey Estuary showing the location of sampling sites. 4.2 Model setupThe topographic dataset was interpolated onto a 386×22 grid (approximately along and across-inlet) in the Mer-sey Estuary from Gladstone (seaward) to Fiddlers Ferry(landward) which was shown in Figure 6. Grid sizesFigure 5 Map of the Mersey Estuary.Figure 6 Map of the Mersey Estuary bottom elevation and the location of sections.vary from 1 to 2 km in the lower inlet to less than 0.05 km in the upper inlet. The water elevation recorded at the Gladstone tide gauge was chosen as the seaward boundary condition to drive the tidal currents and the daily flow rate recorded at Fiddlers Ferry was used for the upstream flow boundary condition.The integrated model was calibrated against six sets of data provided by the UK Environment Agency, as listed in Table 1. Four of these data sets were collected during spring tides and two were collected during neapTable 1 Six sets of field dataCase Tide type Date Tide range (m)High water (m)Flow rate (ML/d)1 Spring 18-09-1989 9.36 10.07 10502 Spring 28-03-1990 9.79 9.94 19003 Spring 18-03-1991 8.99 9.59 27604 Spring 15-07-1991 8.45 9.36 1070 5 Neap 21-03-1990 3.27 7.15 2000 6 Neap 13-09-19904.297.29570Ma F K et al. Sci China Ser E-Tech Sci | Nov. 2009 | vol. 52 | no. 11 | 3368-33753373tides. The freshwater input from the Mersey River forthese sets of data covered both wet and dry season conditions. All model runs started at high water with the initial velocities being set to zero. The time step was set to 1 s, and the model was run for six tidal cycles, to re-duce the effect of the initial conditions, before predic-tions were considered. 4.3 Hydrodynamic resultsAt the beginning as the water level is the lowest at the mouse of estuary, the whole slope along the Mersey Es-tuary SPA is about 0.2‰. The water levels of the main channel from upper reaches to the estuary are more than 2 m when the water level at the mouth is above 4 m. Figure 7 shows the water level change with high tidal at the cross sections.Only the selected results are shown herein for the calibration undertaken using the survey data collected. However, these data sets and comparisons are typical of a wide range of comparisons. Comparisons of the ob-served and predicted water elevations were made at Wa-terloo, Eastham and Runcorn, with the calibration details given for a spring tide of Case 3. Figure 8 shows a comparison between the model predicted and surveyed water levels at Waterloo, Eastham and Runcorn. Good agreement was obtained between the model predictedFigure 7 Water level change at cross sections (18-03-1991). (a) Section A; (b) section B.water levels and field data at Waterloo and Eastham. At Runcorn the difference between the model predicted water levels and field data proceeded from the flooding and drying processes. By inspection of the comparisons between recorded and predicted water elevations above, it can be seen that the percentage error is always less than 15% and generally considerably less than this value and that the times of high water are almost coincidental. Figure 9 shows a comparison between the model pre-dicted and surveyed salinities at Waterloo, Eastham and Runcorn. By inspecting the comparisons between the recorded and predicted salinity levels, it can be seen that at Runcorn, the agreement between the recorded and predicted salinity levels are not as good as at the other locations. At Runcorn there are large variations of salin ity throughout the tidal cycle, recorded values range from circa 25‰ to 0. Salinity levels at Runcorn are relatively strongly influenced by freshwater flows. How-Figure 8 Water levels change with time (18-03-1991). (a) Waterloo; (b) eastham; (c) runcorn.Figure 9 Salinities change with time (18-03-1991). (a) Princes Pier; (b) eastham; (c) runcorn.ever, model inputs of freshwater for the Mersey River are based on 10 day average flow values which will ob-viously miss storm events and their effect on salinity predictions.4.4 Sediment transport resultsWhen the comparisons are made directly between model predictions and recorded data it is shown that the model represents the major sediment transport processes during the ebb and flood tides quite well, and the discrepancies are observed (Figure 10). The main reason for the dis crepancies lies in the fact that the bed sediment particle size distribution is taken as an average of the recorded data throughout the estuary at one instance in time. The sediment particle size distribution is then assumed con-stant throughout the estuary, whereas in reality this is not the case. Another reason for the discrepancies may lie in the fact that the transition zone from non-cohesive to cohesive sediments cannot be accurately determined from available recorded data.Figure 10 Suspended sediment concentration change with time (18-03-1991). (a) Princes Pier; (b) runcorn.5 ConclusionsThe salt marshes in Mersey Estuary are an important habitat for wintering and migratory waterfowl within the estuary both for feeding and for high tide roosting. The salt marshes on the southern side of the estuary can be totally buried in the high tidal condition (spring tide) with a topographic elevation of about 8 m. By inspecting the comparisons between the recorded and predicted water elevations of the Mersey Estuary, it can be seen that the percentage error is always less than 15% and generally considerably less than this value, and the times of high water are almost coincidental.Although there are discrepancies between model pre-dictions and recorded data, it is felt that throughout the model domain, as a whole, it is possible for the model to predict suspended sediment concentrations well with the available data. The model appears to represent the transport of suspended sediments quite well throughout the estuary with the timing of high and low values of the model being compared well with the recorded data.The dynamic distribution of bottom friction coursed by salt marsh wetlands which is important to inundation physics will be coupled with the new model. The future work can study the impact of the heavy metal transport process in the Mersey Estuary EPA.3374Ma F K et al. 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