Three dimensional sediment transport model of the Belgian coastal zone: application of the CART theory

-Plymouth

Three dimensional sediment

transport model of the Belgian

coastal zone

Application of the CART theory

C. Mercier and E.J.M. Delhez University of Li`ege, Li`ege, Belgium

-Plymouth

Study Area

0 20 40 60 80 100 0 10 20 30 40 50 60 Distance (km) Distance (km) 5 10 15 20 25 30 N S • Dunkerque • Nieuwpoort _• Oostende • Zeebrugge • Westkapelle Scheldt River 51°00´ | 2°30´ | 3°00´ | Depth (m)

• _{Shallow and irregular bathymetry.}

•

Hydrodynamic dominated by tides, winds and

waves.

•

Intense mixing of the water column during the

entire year.

•

Exchanges with offshore waters limited.

• _{Sediment distribution influenced by the complex sand banks system.}

• _{Sediments consist of fine to medium sand with a fining trend to the east.}

• _{Large mud fields (concentration of SPM > 400 mg/l) occur between}

-Plymouth

Study Area

0 20 40 60 80 100 0 10 20 30 40 50 60 Distance (km) Distance (km) 5 10 15 20 25 30 N S • Dunkerque • Nieuwpoort _• Oostende • Zeebrugge • Westkapelle Scheldt River 51°00´ | 2°30´ | 3°00´ | Depth (m)

• _{Shallow and irregular bathymetry.}

• _{Hydrodynamic dominated by tides, winds and waves.}

• _{Intense mixing of the water column during the entire year.}

• _{Exchanges with offshore waters limited.}

• _{Sediment distribution influenced by the complex sand banks system.}

• _{Sediments consist of fine to medium sand with a fining trend to the east.}

• _{Large mud fields (concentration of SPM > 400 mg/l) occur between}

-Plymouth

Study Area

0 20 40 60 80 100 0 10 20 30 40 50 60 Distance (km) Distance (km) 5 10 15 20 25 30 N S • Dunkerque • Nieuwpoort _• Oostende • Zeebrugge • Westkapelle Scheldt River 51°00´ | 2°30´ | 3°00´ | Depth (m)

• _{Sediment distribution influenced by the complex sand banks system.}

• _{Sediments consist of fine to medium sand with a fining trend to the east.}

• _{Large mud fields (concentration of SPM > 400 mg/l) occur between}

-Plymouth

Hydrodynamic model

• _{3D, baroclinic (T,S), k turbulence closure.}

• _{Horizontal resolution 500 × 500 m, 10 unequally spaced} σ_-levels.

• _{Forcings: 21 tidal components and NCEP meteorological data.}

• _{Finite volume method, Arakawa C grid, mode-splitting method.}

• _{Semi-implicit vertical advection and turbulent diffusion.}

• _{TVD advection scheme with superbee flux limiter used for advection of}

scalar quantities.

• _{Grid parallel to the coast.}

• _{Flooding and drying algorithm.}

• _{Coupled with a large scale model presenting the same characteristics}

-Plymouth

Sediment transport model (1)

• _{Only mud is considered (grain size < 62.5 µm)}

• _{4 classes of suspended sediments to take in account the variability of}

their dynamic properties.

• _{Sediment processes:}

Neglected Considered

Bedload tranport Sedimentation Sand-mud interactions Erosion of the seabed

Fluidization Deposition

Liquefaction Consolidation (partly) Changing in material properties

Biological Processes Flocculation

-Plymouth

Sediment transport model (1)

• _{Only mud is considered (grain size < 62.5 µm)}

• _{4 classes of suspended sediments to take in account the variability of}

their dynamic properties.

• _{Sediment processes:}

Neglected Considered

Bedload tranport Sedimentation Sand-mud interactions Erosion of the seabed

Fluidization Deposition

Liquefaction Consolidation (partly) Changing in material properties

Biological Processes Flocculation

-Plymouth

Sediment transport model (1)

• _{Only mud is considered (grain size < 62.5 µm)}

• _{4 classes of suspended sediments to take in account the variability of}

their dynamic properties.

• _{Sediment processes:}

Neglected Considered

Bedload tranport Sedimentation Sand-mud interactions Erosion of the seabed

Fluidization Deposition

Liquefaction Consolidation (partly) Changing in material properties

Biological Processes Flocculation

-Plymouth

Sediment transport model (2)

Non-consolidated layer

Consolidated bed layer

Water body

Non-consolidated layer

Consolidated bed layer

Water body Sedimentation ∂Ci ∂t +∇·[ v +w i s
Ci −_{K ·}∇_Ci] | {z } = 0

Average particle Settling velocities

sizes [µm] [mm/s] 2 0.005 6 0.05 10 0.1 35 1 Non-consolidated layer

Consolidated bed layer

Water body ∂_Ci ∂t +∇·[ v + w i s
Ci −_{K ·}∇_Ci] | {z } = 0 ∂C_si ∂t = z }| { F_depi −F_eroi Erosion Deposition Non-consolidated layer

Consolidated bed layer

Water body ∂_Ci ∂t +∇·[ v + w i s
Ci −K ·∇Ci] | {z } = 0 ∂C_si ∂t = z }| { F_depi −F_eroi z }| {  v+ wi_s
Ci −K ·∇Ci·_n = F_depi −_Feroi | {z }

-Plymouth

Sediment transport model (2)

Non-consolidated layer

Consolidated bed layer

Water body Sedimentation ∂Ci ∂t +∇·[ v +w i s
Ci −_{K ·}∇_Ci] | {z } = 0

Average particle Settling velocities

sizes [µm] [mm/s] 2 0.005 6 0.05 10 0.1 35 1 Non-consolidated layer

Consolidated bed layer

Water body ∂_Ci ∂t +∇·[ v + w i s
Ci −_{K ·}∇_Ci] | {z } = 0 ∂C_si ∂t = z }| { F_depi −_Feroi Erosion Deposition Non-consolidated layer

Consolidated bed layer

Water body ∂_Ci ∂t +∇·[ v + w i s
Ci −_{K ·}∇_Ci] | {z } = 0 ∂C_si ∂t = z }| { F_depi −F_eroi z }| {  v+ wi_s
Ci −K ·∇Ci·n = F_depi −F_eroi | {z }

-Plymouth

Sediment transport model (2)

Non-consolidated layer

Consolidated bed layer

Water body ∂_Ci ∂t +∇·[ v + w i s
Ci −_{K ·}∇_Ci] | {z } = 0 ∂C_si ∂t = z }| { F_depi −_Feroi Erosion Deposition Non-consolidated layer

Consolidated bed layer

Water body ∂_Ci ∂t +∇·[ v + w i s
Ci −_{K ·}∇_Ci] | {z } = 0 ∂C_si ∂t = z }| { F_depi −_Feroi z }| {  v+ wi_s
Ci −K ·∇Ci·n = F_depi −F_eroi | {z }

-Plymouth

Sediment transport model (2)

Non-consolidated layer

Consolidated bed layer

Water body ∂_Ci ∂t +∇·[ v + w i s
Ci −_{K ·}∇_Ci] | {z } = 0 ∂C_si ∂t = z }| { F_depi −_Feroi z }| {  v+ wi_s
Ci −K ·∇Ci·n = F_depi −F_eroi | {z }

-Plymouth

Deposition

• _{Deposition is controlled by turbulent processes near the seabed.}

• _{Krone (1962):} F_depi = P_sedi |{z} sedimentation threshold wi_s C_bi |{z} near bottom concentration • _{Krone (1962):} F_depi = P_sedi |{z} sedimentation threshold wi_s C_bi |{z} near bottom concentration P_sedi =         1 − τb τi crd  if τ_b < τi_crd 0 if τ_b ≥ τi_crd • τ

crd is the critical bottom shear stress for deposition = 0.5 Pa.

• τ

b is the bottom shear stress calculated under the combined effects of

-Plymouth

Deposition

• _{Deposition is controlled by turbulent processes near the seabed.}

• _{Krone (1962):} F_depi = P_sedi |{z} sedimentation threshold wi_s C_bi |{z} near bottom concentration • _{Krone (1962):} F_depi = P_sedi |{z} sedimentation threshold wi_s C_bi |{z} near bottom concentration P_sedi =         1 − τb τi crd  if τ_b < τi_crd 0 if τ_b ≥ τi_crd • τ

crd is the critical bottom shear stress for deposition = 0.5 Pa.

• τ

b is the bottom shear stress calculated under the combined effects of

-Plymouth

Deposition

• _{Deposition is controlled by turbulent processes near the seabed.}

• _{Krone (1962):} F_depi = P_sedi |{z} sedimentation threshold wi_s C_bi |{z} near bottom concentration P_sedi =         1 − τb τi crd  if τ_b < τi_crd 0 if τ_b ≥ τi_crd • τ

crd is the critical bottom shear stress for deposition = 0.5 Pa.

• τ

b is the bottom shear stress calculated under the combined effects of

-Plymouth

Erosion

• _{Ariathurai (1974):} F_eroi = P_eroi |{z} erosion threshold Mifi where fi = C i s

∑

j C_sj • _{Ariathurai (1974):} F_eroi = P_eroi |{z} erosion threshold Mi fi where fi = C i s

∑

j C_sj P_eroi =       _τ b τi cre −1  if τ_b >τi_cre 0 if τ_b ≤τi_cre • τ

cre is the critical bottom shear stress for erosion. It is set to 0.5 Pa for

freshly deposed mud (in the non-consolidated layer) and to 2 Pa for erosion in the parent bed layer.

• _{Erosion of the parent bed only occurs when the upper non-consolidated}

-Plymouth

Erosion

• _{Ariathurai (1974):} F_eroi = P_eroi |{z} erosion threshold Mi fi where fi = C i s

∑

j C_sj P_eroi =       _τ b τi cre −1  if τ_b >τi_cre 0 if τ_b ≤τi_cre

• τ_{cre is the critical bottom shear stress for erosion. It is set to 0.5 Pa for}

freshly deposed mud (in the non-consolidated layer) and to 2 Pa for erosion in the parent bed layer.

• _{Erosion of the parent bed only occurs when the upper non-consolidated}

-Plymouth

Erosion

• _{Ariathurai (1974):} F_eroi = P_eroi |{z} erosion threshold Mi fi where fi = C i s

∑

j C_sj P_eroi =       _τ b τi cre −1  if τ_b >τi_cre 0 if τ_b ≤τi_cre

• τ_{cre is the critical bottom shear stress for erosion. It is set to 0.5 Pa for}

freshly deposed mud (in the non-consolidated layer) and to 2 Pa for erosion in the parent bed layer.

• _{Erosion of the parent bed only occurs when the upper non-consolidated}

-Plymouth

Validation

0 20 40 60 80 100 0 10 20 30 40 50 60 Distance (km) Distance (km) 5 10 17.8 31.6 56.2 100 178 316 N S • _Dunkerque • Nieuwpoort _• Oostende • Zeebrugge • Westkapelle Scheldt River 51°00´ | 2°30´ | 3°00´ |

Tide average SPM concentration (mg/l) 0 20 40 60 80 100 0 10 20 30 40 50 60 Distance (km) Distance (km) 5 10 17.8 31.6 56.2 100 178 316 N S • Dunkerque • Nieuwpoort _• Oostende • Zeebrugge • Westkapelle Scheldt River 51°00´ | 2°30´ | 3°00´ |

-Plymouth

Validation

0 20 40 60 80 100 0 10 20 30 40 50 60 Distance (km) Distance (km) 5 10 17.8 31.6 56.2 100 178 316 N S • _Dunkerque • Nieuwpoort _• Oostende • Zeebrugge • Westkapelle Scheldt River 51°00´ | 2°30´ | 3°00´ |

-Plymouth

CART: sediment (1)

• _{New state variables:}

   αi _{= C}i_ai αi s = Csiais • _{Differential equations:} ∂αi ∂t +∇·[ v + w i s
αi_{] = C}i_{+∇· K ·∇α}i
∂αi s ∂t = C i s+ Fαi,sed −Fαi,ero

• _{Sediments are eroded and deposed with their ages:}

F_αi_,ero = ai_sF_eroi and F_αi_,dep = aiF_depi

• _{Equations coupled through the boundary condition:}



-Plymouth

CART: sediment (1)

• _{New state variables:}

   αi _{= C}i_ai αi s = Csiais • _{Differential equations:} ∂αi ∂t +∇·[ v + w i s
αi_{] = C}i_{+∇· K ·∇α}i
∂αi s ∂t = C i s+ Fαi,sed −Fαi,ero

• _{Sediments are eroded and deposed with their ages:}

F_αi_,ero = ai_sF_eroi and F_αi_,dep = aiF_depi

• _{Equations coupled through the boundary condition:}



-Plymouth

CART: sediment (1)

• _{New state variables:}

   αi _{= C}i_ai αi s = Csiais • _{Differential equations:} ∂αi ∂t +∇·[ v + w i s
αi_{] = C}i_{+∇· K ·∇α}i
∂αi s ∂t = C i s+ Fαi,sed −Fαi,ero

• _{Sediments are eroded and deposed with their ages:}

F_αi_,ero = ai_sF_eroi and F_αi_,dep = aiF_depi

• _{Equations coupled through the boundary condition:}



-Plymouth

CART: sediment (1)

• _{New state variables:}

   αi _{= C}i_ai αi s = Csiais • _{Differential equations:} ∂αi ∂t +∇·[ v + w i s
αi_{] = C}i_{+∇· K ·∇α}i
∂αi s ∂t = C i s+ Fαi,sed −Fαi,ero

• _{Sediments are eroded and deposed with their ages:}

F_αi_,ero = ai_sF_eroi and F_αi_,dep = aiF_depi

• _{Equations coupled through the boundary condition:}



-Plymouth

CART: sediment (2)

• _{Study of resuspension-deposition events}

⇒ _{age of a particle = the time elapsed since the last time}

that particle left the bottom layer

• _{Quantification of the transport rate of mud across the BCZ}

⇒ _{age of a particle = the time elapsed since that particle}

passed through a source region S

⇒ Advantages : circumvents the difficulties of diffusion

process and implementation of a Lagrangian approach

-Plymouth

CART: sediment (2)

• _{Study of resuspension-deposition events}

⇒ _{age of a particle = the time elapsed since the last time}

that particle left the bottom layer

• _{Quantification of the transport rate of mud across the BCZ}

⇒ age of a particle = the time elapsed since that particle

passed through a source region S

⇒ _{Advantages : circumvents the difficulties of diffusion}

process and implementation of a Lagrangian approach

-Plymouth

CART: Computation procedure

1. Mark the suspended sediments crossing the source region. 2. Compute simultaneously the dynamic of mud for both marked and

non-marked sediment because of the non linearity of the erosion term:

• _{New variables C}˜i _{and C˜}i

s

• _{Additional conditions: C}˜i _{= C}i _{and C˜}i

s = Csi in S

• _{At inflow open boundaries: C}˜i _{= 0 and C˜}i

s = 0 • _F˜i ero = ˜ C_si C_si F i

ero and F˜depi =

˜ Ci Ci F

i dep

3. Compute the age contents of marked sediments ˜αi_s and ˜αi where

˜ F_αi_,ero = α˜ i s C_si F i

ero and F˜αi,dep = ˜ αi

CiF

i dep

4. Compute the age using the relations α˜i _{= ˜}Cia˜i and α˜i_{s = ˜}C_sia˜i_s

-Plymouth

CART: Computation procedure

1. Mark the suspended sediments crossing the source region.

2. Compute simultaneously the dynamic of mud for both marked and non-marked sediment because of the non linearity of the erosion term:

• _{New variables C}˜i _{and C˜}i

s

• _{Additional conditions: C}˜i _{= C}i _{and C˜}i

s = Csi in S

• _{At inflow open boundaries: C}˜i _{= 0 and C˜}i

s = 0 • _F˜i ero = ˜ C_si C_si F i

ero and F˜depi =

˜ Ci Ci F

i dep

3. Compute the age contents of marked sediments ˜αi_s and ˜αi where

˜ F_αi_,ero = α˜ i s C_si F i

ero and F˜αi,dep = ˜ αi

CiF

i dep

4. Compute the age using the relations α˜i _{= ˜}Cia˜i and α˜i_{s = ˜}C_sia˜i_s

-Plymouth

CART: Computation procedure

1. Mark the suspended sediments crossing the source region.

2. Compute simultaneously the dynamic of mud for both marked and non-marked sediment because of the non linearity of the erosion term:

• _{New variables C}˜i _{and C˜}i

s

• _{Additional conditions: C}˜i _{= C}i _{and C˜}i

s = Csi in S

• _{At inflow open boundaries: C}˜i _{= 0 and C˜}i

s = 0 • _F˜i ero = ˜ C_si C_si F i

ero and F˜depi =

˜ Ci Ci F

i dep

3. Compute the age contents of marked sediments ˜αi_s and ˜αi where

˜ F_αi_,ero = α˜ i s C_si F i

ero and F˜αi,dep = ˜ αi

CiF

i dep

4. Compute the age using the relations α˜i _{= ˜}Cia˜i and α˜i_{s = ˜}C_sia˜i_s

-Plymouth

CART: Computation procedure

1. Mark the suspended sediments crossing the source region.

2. Compute simultaneously the dynamic of mud for both marked and non-marked sediment because of the non linearity of the erosion term:

• _{New variables C}˜i _{and C˜}i

s

• _{Additional conditions: C}˜i _{= C}i _{and C˜}i

s = Csi in S

• _{At inflow open boundaries: C}˜i _{= 0 and C˜}i

s = 0 • _F˜i ero = ˜ C_si C_si F i

ero and F˜depi =

˜ Ci Ci F

i dep

3. Compute the age contents of marked sediments ˜αi_s and ˜αi where

˜ F_αi_,ero = α˜ i s C_si F i

ero and F˜αi,dep = ˜ αi

CiF

i dep

4. Compute the age using the relations α˜i _{= ˜}Cia˜i and α˜i_{s = ˜}C_sia˜i_s

-Plymouth

CART: Computation procedure

1. Mark the suspended sediments crossing the source region.

2. Compute simultaneously the dynamic of mud for both marked and non-marked sediment because of the non linearity of the erosion term:

• _{New variables C}˜i _{and C˜}i

s

• _{Additional conditions: C}˜i _{= C}i _{and C˜}i

s = Csi in S

• _{At inflow open boundaries: C}˜i _{= 0 and C˜}i

s = 0 • _F˜i ero = ˜ C_si C_si F i

ero and F˜depi =

˜ Ci Ci F

i dep

3. Compute the age contents of marked sediments ˜αi_s and ˜αi where

˜ F_αi_,ero = α˜ i s C_si F i

ero and F˜αi,dep = ˜ αi

CiF

i dep

-Plymouth

Conclusion

• _{The model was applied successfully to reproduce the mud behaviour in}

the Belgian coastal zone.

• _{The CART theory is a useful diagnostic tool to investigate the different}

behaviours of mud during deposition-resuspension events and transport. Future developments:

• _{Pollutants and nutrients are transported preferentially in an}

absorbed state and tend to bind to the sediments

⇒ Their transport outside the coastal zone highly dependent

on the sediments’ dynamic.

⇒ _{Use this tool to quantify the transfer rate of contaminants}

-Plymouth

Contents

•

_{Study Area}

•

_{Hydrodynamic model}

•

_{Sediment transport model (1)}

•

_{Sediment transport model (2)}

•

_Deposition

•

_Erosion

•

_Validation

•

_{CART: sediment (1)}

•

_{CART: sediment (2)}