A dynamic 2DH flocculation model for coastal domains

Abstract

A dynamic two-dimensional depth-averaged (2DH) parameterization for flocculation of cohesive sediments is proposed based on the kinetic model by Winterwerp (J Hydraul Res 36:309–326, 1998). The aim is to achieve a realistic representation of the suspended sediment field by accounting for flocculation, also taking into consideration its dependence on advection, turbulent diffusion, and turbulent shear. This formulation is evaluated in a sand-mud model of the Belgian Coast and the Western Scheldt. Results indicate that it can reproduce known sediment transport patterns: modelled floc size and suspended sediment concentrations are in the range of measurements. When evaluating the model results spatially, the extent and shape of the coastal sediment plumes are similar to the observed suspended particle matter (SPM) maps from the PROBA-V satellite. Therefore, the use of the presently proposed flocculation model has added value to improve sediment transport calculations in coastal areas.

Appendices

Appendix A: Flocculation and sediment model calibration

A total of 19 Simulations were run with the flocculation equations activated. These simulations start on 01/03/2009 00:00 and have a duration of 45 days. The initial 25 days are considered warm-up time and discarded from any analysis. Only the remaining time interval was used.

Table 2 Parameter values of the “standard” simulation, which was the baseline throughout the calibration process

The first simulation was called “standard”. It used the parameter values listed in in Table 2. The ensuing simulations consisted on progressive but not cumulative variations of the parameter values of the standard simulation (Table 2). The characteristic parameters of each of these simulations are listed on Table 3, column “Characteristic parameters”. The suspended sediment concentration and the mean floc size variables, at the MOW1 station, were extracted from all simulations’ results and used for sensitivity analysis and for choosing the best performing set of parameters.

Table 3 Sensitivity analysis. Calibration runs are qualitatively compared with the standard simulation. The characteristic parameters are the changes relative to the standard, the arrows indicate an increase ($\uparrow$) or decrease ($\downarrow$) relative to the standard parameters. The response column evaluates the results relative to the standard, the arrows indicate an increase ($\uparrow$) or decrease ($\downarrow$) relative to the standard results

The sensitivity analysis consisted of qualitative comparisons of the calibration simulations with the standard. These results can be seen in Figs. 14 and 15. The summarized patterns are listed in Table 3 (column “Response”). In general, the suspended sediment concentration is more sensible to parameters that are directly linked to sediment availability and erodibility. For example, increasing values of the bottom layer thickness and the Partheniades constants lead to larger overall concentrations. Conversely, larger values of the constant a, and lower values of the thresholds for non-cohesive and cohesive erosion, lead to lower sediment concentration values. The parameters associated with the mean floc size are less sensible regarding the suspended sediment concentration, but they do cause some important variations. Large values of the aggregation constant and the relaxation time decrease the suspended sediment concentration.

Fig. 14

Model calibration simulations in direct connection with the suspended sediment concentration. $\tau _{ce,m}(1)$ and $\tau _{ce,m}(2)$ are the critical bed shear stresses for erosion of mud for the top and bottom sediment layers respectively. The arrows on the figure legend indicate an increase ($\uparrow$) or decrease ($\downarrow$) in the parameter values relative to the standard simulation. LISST-measurements (black solid line) are included for reference

Fig. 15

Model calibration simulations in direct connection with the floc size. The arrows on the figure legend indicate an increase ($\uparrow$) or decrease ($\downarrow$) in the parameter values relative to the standard simulation. LISST-measurements (black solid line) are included for reference

The mean floc size is more responsive to parameters linked directly to the aggregation source term. The aggregation constant plays a major role, and increasing its value causes the floc size to increase. Raising values of the relaxation time also lead to larger flocs and a slightly less peaked floc size curve. On the other hand, directly-related sediment parameters are only sensible if they cause acute decreases on the sediment concentration. That is, large values of a and low thresholds for non-cohesive and cohesive erosion cause larger floc sizes.

Regarding the critical bed shear stress, the results were not conclusive and it is difficult to assign a straightforward sensitivity to this parameter. The reason for this is that by having two vertical sediment layers, the model response to variations is consequence of the combination of critical bed shear stresses of both layers. For example, in simulations “tau ce m0015” and “tau ce s001” the critical bed shear stresses of the top layer decreased, either because the critical bed shear stress of the mud or the sand fractions were reduced. This caused the top layer to wash away and only the bottom layer remained. However, this resulted in lower suspended sediment concentrations because the bottom layer had larger critical bed shear stresses for the mud fraction.

Table 4 Calibration performance in relation to measurements at the MOW1 station. The bold text highlights the best performing simulation based on the RMSE obtained both for the suspended sediment concentration and the floc size

The best performing simulation was chosen by ranking the RMSE of both the suspended sediment concentration and the mean floc size, which were calculated for each simulation and with respect to measurements at the MOW1 station (see Table 4). The best simulation was “Tr3600 ka1800 E0S0008”, and its parameter values were used in Sections 3.1 and 3.2.

Fig. 16

Comparison of tide measurements and results of the BCG model at the Scheur Wielingen (top), Wandelaar (middle) and A2 (bottom) measuring stations. The right column shows the ensemble averages of the times series (left colum), the solid lines are temporal means and the shaded areas are the standard deviation

Fig. 17

Comparison of current velocity measurements and results of the BCG model at the Scheur Wielingen station

Fig. 18

Comparison of wave measurements and results of the BCG model at the Scheur Wielingen station. The black solid lines are measurements from the Flemish Banks Monitoring Network, and the blue lines are results from the BCG model

Fig. 19

Comparison of wave measurements and results of the BCG model at the Wandelaar station. The black solid lines are measurements from the Flemish Banks Monitoring Network, and the blue lines are results from the BCG model

Fig. 20

Comparison of wave measurements and results of the BCG model at the A2 station. The black solid lines are measurements from the Flemish Banks Monitoring Network, and the blue lines are results from the BCG model

Appendix B: Hydrodynamics-waves model assessment

The performance of the BCG model hydrodynamics are assessed for the month of March 2009. The comparison with measurements was done according to data availability, thus not all measuring stations have the same variables.

Simulated tides are in agreement with the measurements data (see Fig. 16). The maximum RMSE is 0.20 m, at the Scheur Wielingen station. Wandelaar and the A2 stations had have RMSE values of 0.17 m and 0.18 m respectively.

The flow velocities are overall on the same range of measurements, although there are noticeable phase mismatches during slack waters, both from ebb to flood and from flood to ebb tides (see Figs. 17 and 6). The RMSE at the Scheur Wielingen is 0.22 m/s, and at Bol van Heist it is 0.21 m/s (Fig. 6).

Modelled wave integrated variables are well in agreement with the measurements. The RMSE at Scheur Wielingen (Fig. 18), Wandelaar (Fig. 19) and A2 (Fig. 20) are 0.17 m, 0.15 m, and 0.16 m respectively. The mean wave period is slightly overestimated, with RMSE values of 0.64 s, 0.67 s, and 0.61 s.