Suspended Particle Matter ( SPM) model

C.1 Suspended Particle Matter ( SPM) model

For the SPM modelling we used the 2D Water Quality module of Sobek. The water quality module in Sobek uses the Delwaq-processes library as the central core. In this way the distribution of SPM between channels, inundated areas, torrents and sand fangs can be simulated. The SPM model considers one fraction of inorganic matter (IM1): clay-sand mix. This fraction has its own sedimentation characteristics. In Delwaq, the SPM transport is modelled with a Krone-Partheniades approach for resuspension – sedimentation. The bed shear stress ( ) is the determining parameter for resuspension and sedimentation. The bed shear stress is a function of the flow velocity, the roughness of the river bed and the water depth. At low bed shear stresses, sedimentation of suspended particles prevails ( c,sed ). At intermediate bed shear stresses, sedimentation and resuspension are in a state of equilibrium ( c,sed < c,res ). When the flow velocity and bed shear stress exceed a certain threshold level, the sediment layer goes into resuspension ( c,res ).

The sedimentation velocity and the critical shear stress for sedimentation are different for each suspended solids fraction. The resuspension velocity and the critical shear stress for resuspension, on the other hand, apply to all sediment fractions. The SPM fraction is assumed to be mixed within the sediment layer. The resuspension flux of SPM fraction depends on the relative amount of the particular fraction in the sediment layer.

sedimentation

equilibrium

resuspension

crit, sed

crit, res

flow velocity

Figure C.1 Schematic representation of the Krone-Partheniades approach for resuspension

The following table summarises the output variables of the SPM model.

Table C.1

output variables of the SPM model

g/m 3 IM1S1

mineral fraction 1: clay-sand mix

mineral fraction 1 in sediment

g/cell

IM1S1M2 2 amount of mineral fraction 1 in sediment g/m fSedIM1

g/m 2 ,d fResS1IM1 resuspension flux of mineral fraction 1 from the sediment

sedimentation flux of mineral fraction 1

g/m 2 ,d

Tau 2 bottom shear stress N/m ActThS1

actual thickness of sediment

C.1.1 Boundary conditions and initial conditions

In order to study the sedimentation en accumulation of fresh SPM in the study area, the sediment layer contains no sediments at the start of the simulation. In other words, IM1S1 equal zero.

No recent data of SPM concentrations was available in the study area. Only data could be found for the years 1986 and 1987 (see Figure C.2 , station Papendrecht – blue dots). We neither could find data at the closest measurement stations Hardinzverld (1974-1992) or Vuren (1953–1992) (see for available data Figure C.2 and Figure C.3 for location). Although in the case of the latter’s, data was available

In this study the peak discharge is around 2500 m 3 /s. According to Fioole (1999), the discharge of the Beneden Merwede is about ¼ of the discharge at Lobith. Because of the limitations in the availability of data of discharges and SPM concentrations, we decided to simulate two different concentrations of SPM as boundary conditions for the study area: 1) 50 mg SPM/l and 2) 100 mg SMP/l

Table C.2

Boundary and initial conditions

variable Scenario 1 Scenario 2 units

IM1S1

0 0 g/cell 0 0 g/cell

arg ntra e

isch D onc

Jan-94 Jan-95

Time

Hardinxveld (kilometer 962)

Papendrecht (kilometer 972.5)

Vuren

Discharge Lobith

Figure C.2 Concentration of SPM (mg/l) in the period 1985 – 1995 at Papendrecht (blue dots), Hardinxverld (red dots) and Vuren (black dots). The discharge (m 3 /s) at Lobith (line) is

also presented.

Figure C.3 Location of measurement stations of SPM as found in Waterbase. A) Papendrecht (km

972.5), B) Hardinxverld (km 962), C) Vuren

C.1.2 Process coefficients

The number of process coefficients in the SPM model is limited. For the fraction IM1 the density of the material, the sedimentation velocity and the critical shear stress must be defined. The resuspension velocity and the critical shear stress for resuspension are two coefficients that apply to all sediment fractions.

The porosity applies to the entire sediment layer. The model assumes that the IM1 fraction is completely mixed within the sediment layer. The density of the sediment particles and the porosity of the sediment layer determine the simulated thickness of the sediment layer (ActThS1).

Heise and Förstner (2004) present results of sediment sampling and field investigation conducted in the Dutch part of the river Rhine at Hollandsch Diep. Critical shear stress for resuspension at this location was in the range of 2-7 N/m 2

for cohesive material, and below 1 N/m 2 for sand. The shear stress changes with the time and the depth as result of consolidation and chemical effects. According to Winterwerp and van Kesteren (2004), the values for critical shear stress for erosion

are in general between 0.1 and 5 N/m 2 for not consolidated material to heavy consolidated material. For this study we decided to use a value of 4 N/m 2 , which higher than the average of the above mention values for the critical shear stress for resuspension, since we expect to find in the study area mainly mud with some percentage of sand.

Asselman and van Wijngaarden (2002) developed a one-dimensional (1D) floodplain sedimentation model that estimates average sediment accumulation over floodplain sections in the river Rhine in the Netherlands and that can be used for estimation of changes in floodplain sedimentation caused by landscaping measures. They found that a settling velocity of the SPM of 7 x 10 -5 m/s (about 6

m/day) and a critical bed shear stress for sedimentation of 1.8–2.0 N/m 2 produced the most accurate estimates. This combination of parameter values was confirmed by the model validation.

Since this study focuses manly on the sediment distribution during a flooding event we decided to extend both scenarios to an average situation (scenario 1) and en extreme situation (scenario 2). The following table gives the required process coefficients in the model for both scenarios.

Table C.3

Name and values of the process coefficients used in the model

Value coefficient

name

units Scenario 1 Scenario 2

10 m/day TauScIM1 critical shear stress sedimentation

VSedIM1

sedimentation velocity IM1

500 1/day TauRS1DM critical shear stress resuspension

first order resuspension velocity

4 4 N/m 2 RHOIM1 3 density IM1 2600 2600 g/m

PORS1

0.25 0.25 - MinDepth

porosity sediment layer 1

minimum water depth for

0.01 0.01 m

sedimentation

C.1.3 Results SPM model

The modelling of SPM under the 2 scenarios was done for the three planning possibilities:

• Palmboom •

Vloedfront •

Wantij Figure C.4 to Figure C.9 show the thickness of the sediment layer (m).

Figure C.4 Thickness of the sediment layer (m) for planning Palmboom in scenario 1

Figure C.5 Thickness of the sediment layer (m) for planning Palmboom in scenario 2

Figure C.6 Thickness of the sediment layer (m) for planning Vloedfront in scenario 1

Figure C.7 Thickness of the sediment layer (m) for planning Vloedfront in scenario 2

Figure C.8 Thickness of the sediment layer (m) for planning Wantij in scenario 1

Figure C.9 Thickness of the sediment layer (m) for planning Wantij in scenario 2