Calibration suspended sediment model Markermeer

Calibration suspended sediment model Markermeer

Thijs van Kessel, Gerben de Boer, Pascal Boderie

© Deltares, 2008

Prepared for: Waterdienst


Thijs van Kessel, Gerben de Boer, Pascal Boderie

Report May 2009

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Calibration suspended sediment model

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Markermeer

May 2009

Klant

Waterdienst

Titel


Samenvatting In deze studie is een computermodel voor het Markermeer opgezet, ingeregeld en gevalideerd. Het model beschrijft dynamisch de stroming van water, waterpeilen, golven en slib in het water en in de bodem. Het model is gecalibreerd voor de periode augustus 2007 - april 2008 en gevalideerd voor de periode daarna tot september 2008. In deze periode zijn hoogfrequente meetgegevens voor twee meetpalen in het Markermeer beschikbaar. Onafhankelijke daarvan is het model gevalideerd aan de hand van remote sensing beelden voor het jaar 2006. Tijdens de calibratie bleken met name de windaandrijving en de ruwheid van de bodem van groot belang. De verdeling van de windrichtingen van het KNMI station Berkhout blijkt representatief voor het midden van het Markermeer. Station Lelystad blijkt minder geschikt, aanbevolen wordt om een windmeter op meetpalen in het meer te installeren. Bodemruwheid werd afgeleid uit beschikbare veldmetingen en gegevens over het voorkomen van (mossel)schelpen. Het modelresultaat voor het percentage slib in de bodem komt goed overeen met de gemeten verdeling. Het is aan te bevelen om de actuele bodemruwheid in het veld te meten. Ook wordt aanbevolen om dynamische ruwheidsmodellering te onderzoeken om het model op dit punt voorspellend te maken. Het slibmodel levert een realistische beschrijving van de dynamiek van het slib in het Markermeer en geeft voor een tijdsduur van enkele jaren een betrouwbare weergave van slibgehaltes van het water en van de opwerveling, sedimentatie en vastlegging van slib; zowel voor de bestaande situatie als voor toekomstige situaties met extra inrichtingsmaatregelen. Het blijkt dat slibconcentraties in de huidige situatie sterk variëren in plaats en tijd. Inrichtingsmaatregelen kunnen deze variatie versterken. Voor de robuustheid en toekomstbestendigheid van inrichtings-maatregelen geeft het model wèl aanwijzingen, maar geen directe modelresultaten. Extra model-ontwikkeling is nodig zijn voor het doorrekenen van deze langetermijnprocessen.

Referenties

Contractnummer WD-4927/BIO/916

Ver

Date 7 november 2008

Auteur Kessel, de Boer Kessel, de Boer, Boderie

Project nummer

3 december 2008

Remarks

Review Boderie

Approved by

Winterwerp

Aantal bladzijden

Q4612 3D,model, slib, Markermeer, calibratie, validatie, meetpaal, remote-sensing, bodemruwheid 89

Classsificatie

None

Status

Final

Trefwoorden

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Contents 1

Introduction ......................................................................................................... 1

2

Data overview...................................................................................................... 1

3

4

2.1

MWTL-data............................................................................................... 1

2.2

Data from rigs FL41 and FL42. ................................................................ 4

2.3

Remote sensing data ............................................................................... 5

2.4

Bed data ................................................................................................... 7

2.5

Additional data:......................................................................................... 7

Set-up of 3D hydrodynamic model ................................................................... 8 3.1

Model grid and bathymetry....................................................................... 8

3.2

Simulation periods.................................................................................... 9

3.3

Model settings ........................................................................................ 10

3.4

Coupling wave and flow ......................................................................... 10

3.5

Hydrology: water inflows and water levels ............................................. 11

3.6

Wind forcing............................................................................................ 13

Calibration of hydrodynamic model ............................................................... 18 4.1

Calibration of the water levels ................................................................ 18 4.1.1 Available stations ....................................................................... 18 4.1.2 Calibration procedure................................................................. 18 4.1.3 Result of calibration ................................................................... 18

4.2

Calibration of the Wave model ............................................................... 25 4.2.1 Methods to obtain wave heights from field measurements....... 25 4.2.2 Wave model results (SWAN) compared to measurements....... 26 4.2.3 Alternatives to save computational burden ............................... 28

5

Set-up of 3D fine sediment model................................................................... 31

6

Calibration of suspended sediment model.................................................... 34

7

6.1

Introduction............................................................................................. 34

6.2

1DV approach......................................................................................... 34

6.3

3D approach ........................................................................................... 38

Results ............................................................................................................... 41 7.1

Hydrodynamics....................................................................................... 41

7.2

Suspended sediments............................................................................ 41

8

Validation on remote sensing data ................................................................. 47

9

Conclusions and recommendations............................................................... 52

10

References......................................................................................................... 53

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Introduction

Fine suspended sediments are considered to be an important pressure on the foodweb the Markermeer. A foodweb that is not functioning optimally may have caused a decline in bird populations in the area. Some of the bird species are protected under the Natura 2000 act. In a seach for effective measures to increase water transparancy in the lake, the interest in suspeded sediments Markermeer has grown over the years. The aim of this study was to further develop a mathematical model that was made in 2007 (Hulsbergen and Kuijper). The improved model is then to be used for scenario simulations to access the impact of measures such as dams, island or deep pits on typical suspended sediment concentrations. These measures aim at reducing the resuspension and distribution of sediments in the Markermeer. The application of the model is described in a separate report (Vijverberg and Boderie, 2008). In 2007 a field measurement campaign was initiated to collect the requied data to calibrate the model. Measurements are now available for the period October 2007 – September 2008. Field measurements and remote sensing data will be used to validate the model. Improving the confidence in the model predictions is an important objective of the validation task in this study.

2

Data overview

In this chapter an overview is given of the data used to calibrate the fine sediment model of the Markermeer. It is stressed that this chapter is not a comprehensive overview of all data gathered in this area. For this we refer to Noordhuis (2008). The following data is discussed in some detail: 1 2 3 4

MWTL data on TSM and turbidity (www.waterbase.nl) Data from measurement poles FL41 and FL42 (Blok, 2008) Remote-sensing data (VU-IVM; Kamps et al., 2007) Bed sampling data (RWS-IJG)

Some additional data is shortly described at the end of this chapter.

2.1

MWTL-data

The MWTL-data is acquired within the framework of the standard monitoring programme of RWS. MWTL-data cover a long history, measurement series are available from 1974 onward. Also, measurements have been made at a number of locations in Markermeer. However, these measurerments have the disadvantage that the measurement frequency is once in 14 days only, at most. This frequency is much too low to evaluate the short-term response of total suspended matter (TSM) to changes in wind conditions. Also, the number of measurement locations has reduced substantially since 1982 (4 locations left). After 1992, the only MWTL observation point for TSM left in Markermeer is a location named ‘Markermeer Midden’ (MKM), which is situated in the South-western part of the lake, see Figure 2.1. It is noticed that location

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MKM (indicated with an arrow in Figure 2.1) is indicated at the wrong position in www.waterbase.nl.

Figure 2.1: Mean TSM values (mg/l) at MWTL locations, period 1974 – 2006. Location Markermeer Midden is number 55. The black arrow indicates the shift of location MKM in Waterbase.

Figure 2.2: 10-percentile (left) and 90-percentile (right) TSM values (mg/l) at MWTL locations; period 1974 – 2006.

The long-term average TSM concentration in Markermeer is about 50 mg/l (Figure 2.1). The long-term distribution of TSM is quite uniform, but values are much lower in the IJmeer (about 20 mg/l). The 10-percentile value is just under 10 mg/l, whereas the 90percentile values are well above 100 mg/l (Figure 2.2). Again much lower values are observed in the IJmeer. Figure 2.3 shows all measurements for Markermeer Midden, the only station at which monitoring has been continued, for the period 1/1/1982 – 1/1/2008. The TSM values exhibit a large scatter in the range 0 – 300 mg/l in response to the different wind conditions during sampling. The Secchi depth observations show a similar scatter, but for this parameter a decreasing trend is noticed. Before 1992 at some instances a Secchi depth over 1 m is observed; after 1992 Secchi depth remains always below 1 m.

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Markermeer

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Markermeer midden 300

20 Secchi TSM Linear (TSM) Linear (Secchi)

18 16

250

200 12 150

10 8

TSM (mg/l)

Secchi depth (dm)

14

100 6 4 50 2 0 1/1/82

0 1/1/84

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1/1/94

1/1/96

1/1/98

1/1/00

1/1/02

1/1/04

1/1/06

1/1/08

date

Figure 2.3: Overview of all TSM (mg/l) and Secchi depth (dm) observations at Markermeer Midden in the period 1/1/1982 – 1/1/2008. MWTL-data.

Markermeer midden 4 Secchi TSM Linear (TSM) 14 per. Mov. Avg. (TSM) Linear (Secchi) 14 per. Mov. Avg. (Secchi)

normalised Secchi depth (-)

3.5

3

2.5

3

2.5

2

2

1.5

1.5

1

1

0.5

0 1/1/82

3.5

normalised TSM (-)

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0.5

0 1/1/84

1/1/86

1/1/88

1/1/90

1/1/92

1/1/94

1/1/96

1/1/98

1/1/00

1/1/02

1/1/04

1/1/06

1/1/08

date

Figure 2.4: Overview of all TSM and Secchi depth observations at Markermeer Midden in the period 1/1/1982 – 1/1/2008. MWTL-data. Values normalised for 6h average wind speed prior to sampling.

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In order to reduce scatter, both TSM and Secchi depth data have been normalised with averaged wind speed prior to the sampling time (a 6-hour average is used). The procedure is as follows. First, all TSM and Secchi values are plotted against the 6h average wind speed prior to observation. Secondly regression lines are determined for these plots: TSM = 10.7 uwind and Secchi = 15 / uwind, with uwind the wind speed in m/s. Finally, each observation is normalised with the value computed from the regression equations and the 6h average wind speed prior to each observation. From Figure 2.4 an decreasing trend in Secchi depth and an increasing trend in TSM levels is observed (dashed lines). Note that an increasing trend in TSM level was not observed for the raw data uncorrected for wind speed (Figure 2.3). However, on a shorter timescale other trends can be observed. From the solid lines in Figure 2.4, which represent year-average values, it can be observed that in the period 1990 – 1999, normalised Secchi depths decrease strongly from over 2 to under 0.5, whereas normalised TSM levels increase markedly from just over 0.5 to just under 2. However, in the period 1999 – 2007, both the normalised Secchi depth and normalised TSM level, recover to a value of about 1. A concept of a continuously decreasing transparency and a continuously increasing mud concentration in Markermeer is therefore too simple. 2.2

Data from rigs FL41 and FL42.

To overcome the limitations of MWTL-data with regard to sampling frequency, two semi-permanent observation stations have been installed in the Markermeer. Figure 3.2 shows their locations. Station FL41 is positioned close to the island of Marken, whereas station FL42 is positioned in the middle of the Markermeer. In the framework of another project, another station (FL40) was installed in the Eemmeer. Details of the set-up, instrumentation, calibration and servicing of the rigs is reported by Blok (2008). Here only the most relevant issues for the calibration are discussed. The following parameters were measured, amongst others: • • •

Wave height Current velocity Turbidity

The first two parameters are used to calibrate the hydrodynamic model. The last parameter is used to calibrate the mud model. Turbidity sensors (OBS) were mounted at two levels, one about 1 m from the surface, another 0.2 – 0.4 m above the bed. Precise levels are shown in Table 2.1, including local bed levels. The OBS sensors were cleaned at an interval of 14 days, but is summer this turned out to be not always sufficient. Therefore some data gaps exist in the period discussed in this report, 1/8/2007 until 1/4/2008. Table 2.1

Vertical position of OBS sensors at locations FL41 and FL42 in m NAP

FL41 Water level (summer) Water level (winter) Top sensor Bottom sensor Bed level

4

-1.19 -2.49 -2.92

FL42 -0.20 -0.40 -1.39 -4.08 -4.25

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The measurement frequency was set at 10 min in order to be able to monitor the shortterm TSM response to short-term changes in wind forcing. This yields valuable information indispensable to calibrate the mud model. Figure 2.5 and Figure 2.6 show the observed TSM concentration from 1/8/2007 until 1/4/2008. The observed concentration at FL42 can be compared with MWTL-observations at Markermeer Midden, which is fairly close to location FL42. Figure 2.6 demonstrates how much more information is retrieved on the fine sediment dynamics of Markermeer from the highfrequency observations compared with the MWTL observations. The vertical concentration gradient (i.e. the difference in TSM level between top and bottom sensors) in combination with the local current conditions yields information on the settling velocity. However, the vertical concentration gradients for both FL41 and FL42 turn out to be small, only revealing an upper limit for the settling velocity. To get some impression of the horizontal variability, observed near-surface TSM concentrations at FL41 and FL42 are also plotted in the same figure (see Figure 2.7). TSM levels at FL42 exceed those of FL41 most of the time, but for short periods this is the other way around. 2.3

Remote sensing data

As two observation points are insufficient to get a good impression of the spatial variability of TSM levels in the Markermeer, also remote-sensing data are used. For 2006 (Kamps et al., 2007), 30 images are available for varying wind conditions. Here two examples are shown, one on 16 July 2006 (NE wind, 4 m/s), another at 17 April 2006 (W wind, 8 m/s). These examples (see Figure 2.8) demonstrate that a distinct spatial variability exist which changes in wind direction.

Figure 2.5: Observed near-surface and near-bottom TSM concentration (mg/l) at location FL41 in the period 1/8/2007 – 1/4/2008.

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Figure 2.6: Observed near-surface and near-bottom TSM concentration (mg/l) at location FL42 in the period 1/8/2007 – 1/4/2008. MWTL data points Markermeer Midden (Ma mi, in red crosses) are also shown.

Figure 2.7: Observed near-surface TSM concentration (mg/l) at locations FL41 and FL42 in the period 1/8/2007 – 1/4/2008.

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Figure 2.8: Observed near-surface TSM distribution (mg/l) from remote sensing data. Left: at 17/4/2006 (wind W, 8 m/s); right: at 16/7/2006 (wind NE, 4 m/s) (Kamps et al., 2007).

2.4

Bed data

The data described so far deal with the water column. However, also the composition and properties of the lake bed are important, as resuspension of fine sediment is not only determined by the stress exerted by waves and currents on the bed, but also by the strength of the bed and the availability of sediment for resuspension. The following data have been used: • • •

Data on the thickness composition of the top layer of the bed from Noordhuis (2008) and Vijverberg (2008); Data on the shell distribution on the bed acting as a proxy for roughness height (Noordhuis, 2008); Data on the bed composition of subsurface layers from the Geological Atlas Markermeer (Lenselink and Menke, 1995).

These maps are not shown here, but in Chapter 7 (see Figure 7.4) together with the computed bed composition from the mud model.

2.5

Additional data:

Additional data on near-bed TSM concentration measured with ALTUS turbidity sensors mounted on a bed frame is reported by Vijverberg (2008). In Novermber 2007, a number of 41 grab samples and 13 sediment cores were taken and analysed by IHEstudents (Rozari, 2008 and Ang’weya, 2008). They also placed sediment traps and analysed their contents. The PhD-thesis by Van Duin (1992) contains valuable datasets acquired in the late eighties and early nineties, e.g. on settling velocities and sedimentation fluxes. Some of these data are discussed later in this report, when appropriate.

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Markermeer

Set-up of 3D hydrodynamic model

3.1 Model grid and bathymetry A curvilinear grid was constructed (see Figure 3.2 ). The grid shows especially high resolution in the Markermeer study area whereas the resolution in the Gooi-Eeemmeer is less. The high(er) resolution in the Markermeer area (200 to 300m) is required because the model is later to be used to evaluate the effect of measures in the area, thus the grid has to be fine enough to allow realistic representation of those measures in the grid, for this reason the resolution in the eastern part of the Markermeer is finer than in other parts of the Markermeer (less than 150m). Especially small or thin structures such as dams, islands and shipping channels require a fine grid. A typical grid size is 200 ± 50m, the frequency distribution in Figure 3.1 shows that 90% of the grid cells are smaller than 250m, 40% smaller than 150m. The course schematisation of the Gooi-Eemmeer ensures correct storage of water and resulting water levels. However, the resolution for the Gooi-Eemmeer is insufficient to obtain reliable results, for that reason the simulation results for this part of the grid will not be used. In the vertical dimension we used 7 layers (sigma layers), each covering arount 15% of the local depth. Figure 3.3 shows the bathymetry used in the model. The total area of the Markermeer is 730 km 2 and it’s averaged depth is around 3.5 m. Gridcell size distribution

frequency (%)

120% 100% 80% 60% 40% 20% 0% 0

50

100

150

200

250

300

size (m)

Figure 3.1

8

Frquency distribution of the size (m) of the grid cells of the model grid represented in (Figure 3.2).

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Simulation periods

Two types of simulations have been performed: short simulations with stationary wind and long simulations with variable wind. The simulations with stationary wind forcing run for a 2-day period. After a period of 1.5 days the simulations reach a stationary result for the coupled flow-wave model. The stationary flow-wave conditions of the last three hours of the 2-day simulation are stored and used as forcing for the suspended sediment model. The simulation period for the dynamic simulations is 13 months and comprises of a calibration period (August 1st 2007 to April 1st 2008 followed by a validation period (April 1st 2008 to September 1st 2008 ). Dynamic simulations start 4-days prior to the simulation period of interest to be sure the model is sufficiently conditioned to the actual conditions and it’s results are not affected by the initial flow and wave conditions. Based on the results of the stationary runs, a 2-day period would probably also suffice to reach adequate ‘spin up’ of the model. Krabbersgat

Markermeer

Edam

Houtribsluizen

IJmeer Schellingwouderbrug

Gooimeer

Eemmeer

Figure 3.2

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Model grid for the Markermeer-IJmeer model. The positions of the three fixed field measuring sites (measuring poles in red), the water level stations (in blue) are indicated in red

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legenda

Figure 3.3

3.3

Model bathymetry

Model settings

The following model settings were used: • • • • •

3.4

The turbulence model used is kThe bed roughness formulations of White-Colebrook are used with equivalent geometrical roughness ks in both flow directions 0.05 m Uniform horizontal eddy viscosity is set to 0.5 m 2 s-1 The model simulation time step is 2.5 minutes, files for the off-line water quality (TSM) model are written every 6 hours The simulation timestep equals 2.5 minutes

Coupling wave and flow

There are two fundamentally different methods in Delft3D to simulate waves. Initially we used the on-line-coupling of the FLOW module using the SWAN module for the calculation of wave characteristics (see left pane of Figure 3.4). The on-line coupling yields correct results at fairly high computational costs though. On-line wave calculations are used for the stationary flow calculations in this study. In an attempt to speed up the simulation time we compared the on-line method with an alternative method to simulate wind induced waves offline in WAQ using the Bretschneider formulas (see right pane of Figure 3.4). An algorithm to calculate wind fetch offline (in various wind rose directions) from the D3D grid was developed. This offline WAQ method proved to be equally accurate at far less computational cost. This helped us to carry out the scenario simulations in time. This successful application of the offline WAQ wave growth for the Markermeer is no guarantee for similar success in other situations. Only after comparing both methods a founded choice can be made.

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D3D-Flow

D3D-WAQ Waves

Golfmodule

module Golfmodule

SWAN Wind Fetch

Figure 3.4

3.5

Model set-up for simuation of waves: on-line coupling of Flow/Swan (left) compared to use of the waves module in D3D-WAQ.

Hydrology: water inflows and water levels

The water balance for lake Markermeer was constructed from measurements of: Daily water levels in the middle of the lake, the so called “middenstand”. Data are obtained from RWS website (http://www.rijkswaterstaat.nl/ijg/water/waterkwantiteit/peilbeheer/) and from RWS-IJG (Oude Voshaar, pers. comm.) Daily precipitation and evaporation time series Note the average lake water level (middenstand) is calculated by RWS using a weighing method using various high frequency water level measurements in the lake. In order to construct a closed water balance for the lake, the daily variations in water level in the middle of the lake (representing time variable storage volume) are transformed to a corresponding waterflow (unit m 3/s) using the time derivative of the water level multiplied by the horizontal surface area of the lake. This corresponding flow is presented in Figure 3.6 (thin green lines in lower panel of the figure). This flow is prescribed to the model, equally distributed over the two sluices near the Krabbersgat and the Southern part of the Houtribdijk (see Figure 3.5). For numerical reasons, the flows are schematised as discharges (alternatively they could be schematised as waste loads) as they can be rather big (up to 100 m 3/s). As can be seen in the upper panel of Figure 3.6 there is a fairly strong deviation from the water targeted winter water level (black line, so called “streefpeil”) compared to the actual water level fluctuations (green line). This implies that actual measurements are preferred over targetted values, which was our initial approach.

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Figure 3.5

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Study area showing Houtribdijk, sluices of Krabbersgat and S. Houtribdijk.

By definition (as a result of the approach), the model exactly simulates the daily water level variations in the middle of the lake. Actual (momentarily measured) water levels may, and normally do, vary as a result of wind, both in time as well as in space. The model response for water levels in the lake is calibrated using actual water level recordings at various positions in the lake, see section 4.1

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Figure 3.6

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The average lake water level (“middendstand”) of the IJsselmeer areas (upper pane) showing elevated water levels (m NAP) in summer and lowed water levels in winter (nonnatural water level control). Flows (m3/s) corresponding to the water level variations for the whole lake (lower pane). The thin green line represents daily flows used as model forcing, the thick green line is the 15 day moving average of the same. The black line represents flows corresponding with the targeted water level (“streefpeil”) for Markermeer (corresponding to the thick black line in the upper pane).

Wind forcing

Wind is the dominant forcing function for suspended sediment model in the Markermeer. The choice of the wind station, the measurement frequency and period are important choices which are discussed in this section. The wind station must be representative for the middle of the Markermeer (near to the measurement station), it is therefore recommend to have a station in the middle of the lake for future use. In this study data were available for three land stations relatively close to the lake: Lelystad, Berkhout and Schiphol. Lelystad, being the nearest and thus the first choice. The wind distribution for the middle of the lake is unknown but strong anomalies (wind from some directions being over or under represented) are unlikely as

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the middle of the lake is surrounded by water from all sides. For illustration: Terschelling (mostly uniformly surrounded by open water) and Schiphol (mostly uniformly surrounded by land) show no anomalies in their long term averaged wind roses (Figure 3.7). For station Lelystad on the other hand winds form the south west seem to be over represented because of open water form that direction and winds form the southeastern part seem underrepresented because of presence of land. To make a choise between Berkhout and Schiphol we compared the windroses for the last 7 years. Figure 3.8 shows the average wind characteristics for te period (20012008) for the three stations around the Markermeer, viz. Schiphol, Berkhout and Lelystad. Also for this period station Lelystad shows an anomaly for certain wind directions. The wind roses for Berkhout and Schiphol resemble each other quite well and both are uniform and in principle representative for the Markermeer. Because station Berkhout is closer to the Markermeer wind data for this study are obtained from Berkhout. The expected differences in wind speed compared to a (non existing) open water station in the middle of the lake will be subject of the calibration of the wind drag coefficient (see section 4). The suspended sediment model will be calibrated, amongst others, using bottom sediment data (see paragraph 7.2). Accumulation of bottom sediments is a long-term process (many years). It is thus important to verify that the wind forcing during the simulation period is representative for longer periods also. Figure 3.9 shows that the wind characteristics for station Berkhout in the relatively short calibration period differs somewhat from the previous 7 years. South western winds seem to be over represented, probably because of of the fact that the calibration period coincides with the winter period. We translated the wind climate for both periods (2001-2008 and the calibratioin period) to average bottom shear stress in the lake, as bottom shear stress is an important parameter for sediment erosion and sedimentation. The procedure to this is as follows. Stationary simulations of the bottom shear stress were made for eight wind directions using a constant wind speed (10 m.s-1). A representative average bottom shear stress for each of the two periods (2001-2008 and the calibration period) is composed using weight factors for each wind direction derived from the statistics of the wind direction for the two periods (see Figure 3.10). The bottom shear stress maps for 10 m.s-1 stationary direction-weighted winds are presented in Figure 3.11. The bottom shear stress values for the calibration and the long-term term period do not differ much. We checked that the method is sensitive enough to show such differences.

Figure 3.7

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Climatic (KMMI) wind roses for a typical land station, a typical open water station and Lelystad.

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Figure 3.8

Long time (2001-2007) wind speed (m.s-1) and wind direction for three meteorological stations, viz. Schiphol, Berkhout and Lelystad.

Figure 3.9

Wind statistics for a long year period January 1st 2001 – April 1st 2008 (left) compared to the statistics in the simulation period for the calibration period October 1st 2007 – April 1st 2008 (right).

Figure 3.10 Statistics (frequency distribution) of the wind direction for winds of one velocity class (10 m.s-1) during a longer period viz January 2001 – April 2008 (left) compared to the calibration period 1st October 2007 – 1 April 2008 (right).

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We have repeated the procedure using two rather than one wind class using wind speeds of 5 and 10 m.s-1. The graphs are shown in Figure 3.12 and Figure 3.13. The conclusion is the same as the conclusion based on the method using only one wind velocity class (see Figure 3.10). We conclude that the eight month calibration period is considered representative for longer periods as well and that it is thus likely that model results for accumulated bottom sediments can be extrapolated to represent accumulation over longer time periods.

Figure 3.11 Representative maps of the bottom shear stress (N.m-2) based on stationary simulations in eight wind directions at a wind speed of 10 m.s-1. The weighing factor per wind direction is equal for each direction (left), valid for the long-term period 2001-2008 (middle) and valid for the calibration period (October 2007- April 2008).

Figure 3.12 Statistics (frequency distribution) of the wind direction for winds of two velocity classes (5 and 10m.s-1) during a longer period viz January 2001 – April 2008 (left) compared to the calibration period 1st October 2007 – 1 April 2008 (right).

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Figure 3.13 Representative maps of the bottom shear stress (N.m-2) based on two sets of stationary simulations in eight wind directions at a wind speeds of 5 and at 10 m.s-1. The weighing factor per wind direction is equal for each direction (left), valid for the long-term period (middle) and valid for the calibration period (October 2007- April 2008).

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4

Calibration of hydrodynamic model

4.1

Calibration of the water levels

4.1.1

Available stations


Besides the FL41 and FL42 measuring stations there are four other measurement sites in the lake where the water level is measured continuously. These four stations are Edam, Houtribsluizen, Krabbersgat and Schellingwouderbrug (see Figure 3.2). At the fictive station in the middle of the Markermeer the water level (‘actual peil’) is calculated from these four stations using weighing factors using data provided by RWS-IJG. The FL42 station is close to the middle of Markermeer. Water levels are recorded every 10 minutes at these stations and are converted to a 30-minute signal using a moving average. 4.1.2

Calibration procedure

The interfacial drag coefficient is a dimensionless coefficient that quantifies the drag or resistance at the wind to water interface. The drag coefficient determines the ‘hold’ the wind has on the water surface. The drag coefficient thus determines how strong the model predicted water levels react to wind. During the calibration of the drag coefficient the aim is to get optimal model results with respect to: sloping of water levels in the lake short term fluctuations of water levels around the average water level Starting from the default drag coefficient (0.00063) we doubled the value to 0.0013 which is uniformly distributed over the Markermeer. This value is used in the calibrated model, and the results presented herein. 4.1.3

Result of calibration

Results of the calibrated water levels are shown in Figure 4.1 to Figure 4.5 for the stations FL42, Edam,Houtribsluizen, Krabbersgat and Schellingwouderbrug respectively (see Figure 3.2 for their locations) for the month of August, selected randomly. The figure show 4 lines, viz.: • • • •

The blue line is the average lake waterlevel (“middenstand”) which is constant over the lake and was forced to the model through in- outflows as described in 3.5 The thin grey line is the actually measured water levels at the five locations in the lake. (4 regular stations and FL42) The black line (‘actual, imposed’) is the weighted average from the 4 water level measuring stations The red line is the water level as predicted by the model

The amplitude of the variations in water level of the four stations away from the middle of the lake, viz. Edam, Houtribsluizen, Krabbersgat and Schellingwouderbrug, increases in the order mentioned. At the FL42 station (close to the virtual station MarkermeerMidden) the average water level is close to the target water level (streefpeil). With increasing distance from the middle of the lake the water levels are occasionally tilted

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resulting in larger deviations from the water levels in the middle of the lake (tilted water levels do not affect the Markermeer Midden level too much as this is the centre of the oscillation). Increasing the drag coefficient increases the water level amplitudes. A higher drag coefficient improved the model simulation results for three of the four measurement stations. For station Schellingwouderbrug the calibrated model underpredicts water levels now. In the model the water is driven too much towards the northeast resulting in too low water levels near Amsterdam. Our expert opinion is that the enhanced drag coefficient is most likely correct but the wind velocity used in the model is too high compared to the actual wind speed near Schellingwouderbrug where the overland wind which will have less velocity. Application of a non-uniform wind field may improve the waterlevel simulation results in this area. The result of the calibration is that the model correctly simulates the high-frequency water levels at all measurement stations. At station FL42 the absolute water level is overestimated by 3 cm. The uniform wind and uniform wind forcing make the model less suitable for accurate predictions of water levels in the southwestern area of the lake. The small model error in predicted water levels in the actual study area of the lake makes the model suitable to serve as a sound basis for the suspended sediment model. It is recommended to have a constant wind monitoring station in the middle of the lake.

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Figure 4.1

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Upper part: Water levels at measurement station FL42 (see Figure 3.2) after calibration of the drag coefficient from wind to water. The solid black line is the middenstand (constant over the lake) as forced to the model. The blue line is the target water level (streefpeil) which is also constant over the lake. The thin grey line is the high frequency measured water level at FL42. The thick grey line is the water level as predicted by the model .Lower part: wind speed and wind direction.

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Figure 4.2

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Upper part: Water levels at measurement station Edam (see Figure 3.2) after calibration of the drag coefficient from wind to water. The solid black line is the middenstand (constant over the lake) as forced to the model. The blue line is the target water level (streefpeil) which is also constant over the lake. The thin grey line is the high frequency measured water level at Edam. The thick grey line is the water level as predicted by the model. Lower part: wind speed and wind direction.

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Figure 4.3

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Upper part: Water levels at measurement station Houtribsluizen (see Figure 3.2) after calibration of the drag coefficient from wind to water. The solid black line is the middenstand (constant over the lake) as forced to the model. The blue line is the target water level (streefpeil) which is also constant over the lake. The thin grey line is the high frequency measured water level at Houtribsluizen. The thick grey line is the water level as predicted by the model. Lower part: wind speed and wind direction.

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Figure 4.4

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Upper part: Water levels at measurement station Krabbersgat (see Figure 3.2) after calibration of the drag coefficient from wind to water. The solid black line is the middenstand (constant over the lake) as forced to the model. The blue line is the target water level (streefpeil) which is also constant over the lake. The thin grey line is the high frequency measured water level at Krabbersgat. The thick grey line is the water level as predicted by the model. Lower part: wind speed and wind direction.

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Figure 4.5

Upper part: Water levels at measurement station Schellingwouderbrug (see Figure 3.2) after calibration of the drag coefficient from wind to water. The solid black line is the middenstand (constant over the lake) as forced to the model. The blue line is the target water level (streefpeil) which is also constant over the lake. The thin grey line is the high frequency measured water level at Schellingwouderbrug. The thick grey line is the water level as predicted by the model. Lower part: wind speed and wind direction.

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4.2 Calibration of the Wave model The wave model (SWAN) is calibrated and validated using wave characteristics as measured for station FL42 (see Figure 3.2). 4.2.1 Methods to obtain wave heights from field measurements At station FL42 two different methods were used to measure the wave height. The first method is an acoustic method which measures water level fluctuations which directly determine the height of the waves (Hmo). The second method is called the spectral method and is an indirect method that uses a pressure transducer installed at about 0.3 m above the bed (Blok, 2008). The recorded high frequency pressure data were converted to water level fluctuations using a spectral method (Doorn and Eysing, 2004). The calculated waterlevel fluctuations determine wave height (Hs). The second method correctly represents the water levels although the method is quite insensitive for shallow waves (=high frequency waves). Figure 4.6 shows that waves of less then 20 to 15 cm height are not picked up by the pressure transducers. When shallow waves are left out of the calculation method, the wave height based on the this spectral method (Hs) shows good resemblance with the wave height from the direct acoustic method (Hm0). We performed an analysis to determine the sensitivity of the pressure transducers in more detail. In Figure 4.7 the relation between the calculated wave period and wave height is shown. Normally the wave period decreases (higher frequency) as the wave height decreases. The figure shows that for smaller waves (green vertical line in the figure) this does not hold anymore as the wave period then increases. From Figure 4.7 we conclude that the pressure transducers in FL42 can detect waves > 15 cm only.

Figure 4.6

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Measurement data for FL42 for an arbitrary period (one data file). Blue line represents Hm0 from the acoustic method. The black line represents Hs based on the pressure transducer and the spectral method. The red line also represents Hs from the spectral method where wave heights lower than 15 cm are not processed.

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Figure 4.7

Measurement data for FL42 for an arbitrary period (same as in Figure 4.6). The average wave period (y-axis) and wave height (x-axis) are calculated with the spectral method from pressure transducer data (black dots). The red dots are results of the spectral method discarding waves < 15 cm.

4.2.2

Markermeer

Wave model results (SWAN) compared to measurements

Figure 4.8, Figure 4.9 and Figure 4.10 show the results of the calibration of the SWAN model using data from the central part of the lake (FL42 data). The measurements form FL41 (see Figure 3.2) are not used for the calibration. The reason is that for station FL41 waves are only measured indirectly using pressure transducers. This method is less reliable than the direct method (see 4.2.1). Moreover the pressure recordings at FL41 are disturbed by ship induced waves which complicates the translation to reliable wave characteristics. Wave heights simulated with SWAN are compared with wave heights measured by bothe the direct (Hm0) and indirect (Hs) measuring methods. Initially the wave model overestimated the wave heights. After changes in parameters for the white capping formulations in SWAN (van Westhyusen, 2007) the model fits better to the data (Figure 4.8 and Figure 4.9). After calibration especially the higher waves are more in line with the measurements. The height of the lower waves is decreased after the calibration (Figure 4.9).

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Figure 4.8

Measured wave heights (Hm0, acoustic method) on the y-axis compared the modelled wave height on the x-axis for the full calibration period (1st August. 2007 – 1st April. 2008. Left with the standard SWAN white capping method and right after calibration with the new white capping method of SWAN.

Figure 4.9

Time series of measured and modelled wave height for an arbitrary period (November 2007) comparing the standard (up) and calibrated (Figure 4.10) “white capping” method of SWAN.

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Figure 4.10 Time series of measured and modelled wave height for an arbitrary period (November 2007) comparing the standard (Figure 4.9) and calibrated (up) “white capping” method of SWAN. The period between two wave computations is doubled compared to Figure 4.9.

4.2.3

Alternatives to save computational burden

SWAN computations take several days (6 to 7) to simulate one year. Given the number of scenarios to calculate we explored options to reduce the computation time. First we doubled of the period between two wave computations (from 3 to 6h). It is clear from Figure 4.10 that the model cannot follow the fast variations in wave height anymore, further increasing the period would result in loosing too much detail. Simulation time with a period of 6h was still not feasible given the timeframe of the project. There for we decided to use the method available in Delft3D-WAQ as explained in section 3.4 . In this method for each point in the model grid the distance to the shore or land boundary, the so called fetch, is calculated for 8 wind directions. This calculation is done once and prior to the simulation (Figure 4.11). During the suspended matter simulation in WAQ the wave characteristics are then calculated using the Brettschneider formula’s that calculate wave height and period as a function of the local wind speed and fetch. This method is much faster, gives accurate wave dynamics in time but compromises on spatial detail of wave patterns and neglects processes such as wave propagation and decay. The results of the wave computation using Delft3D-WAQ’s fetch approach are shown in Figure 4.12 and Figure 4.13. We conclude that the method exceeds expectations in this particular Markermeer application and at some points performs better then SWAN.

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Figure 4.11 Example of fetch for 4 wind directions calculated off-line for calculation of wave characteristics using WAQ. The arrows indicate the windsector.

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Figure 4.12 Time series of measured and modelled wave height for an arbitrary period (November 2007) using the fetch approach in WAQ. The time step between the wave calculations is equal to the time step of the suspended sediment model (30 minutes) but plotted every hour for comparison with Figure 4.9 and Figure 4.10.

Figure 4.13 Measured wave heights (Hm0, acoustic method) on the y-axis compared the modelled wave height on the x-axis using the fetch approach in WAQ for the full calibration period (1st August. 2007 – 1st April. 2008. Compare to Figure 4.8.

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Markermeer

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Set-up of 3D fine sediment model

The fine sediment model is a continuation and further improvement of the sediment model developed in 2007 (Hulsbergen and Kuijper, 2007). The model consists of 7 horizontal -layers representing the water column and 3 layers representing the bed. The layer distribution is illustrated schematically in Figure 5.1. The arrows represent sediment fluxes, which are discussed sequentially below. 1 2 3 4 5 6 7 S1

A S

M

Dis Dep E1

S2

B1 E2 B2

S3

Figure 5.1

P

Schematic representation of sediment fluxes in model.

In the vertical of the water column, a dynamic balance exist between sediment settling and mixing. At equilibrium, a Rouse-type vertical concentration profile results. The vertical mixing coefficient is derived from FLOW. The settling flux S is computed according to S = ws C, with ws is settling velocity and C is sediment concentration. A concentration-dependent settling velocity is applied according to ws = ws0 C/C0. With ws0 the settling velocity for C = C0. Two sediment fractions are applied with the following properties: ws01 = 2.3 10-5 m/s (2 m/d); ws02 = 4.6 10-6 m/s (0.4 m/d) and C0 = 25 mg/l. These settling velocities are within the range reported by Van Duin (1992) and are chosen in order to a) reproduce observed vertical sediment concentration gradients and b) reproduce observed sediment concentration decay rates during calm weather after a period of rough weather. This is further discussed in Chapter 6. The deposition flux from water layer 7 to bed layer S1 is expressed by: Dep = ws CL7. Note that no critical shear stress for deposition is applied. At equilibrium, the deposition flux is balanced by the erosion flux, which may act on both bed layers S1 and S2: E1 = M1 (

crit1

E2 = p2 M2 (

– 1) = M1

crit2

e1

– 1)3/2 = p2 M2

e2

Layer S1 is characterised by its critical shear stress for erosion crit1 and resuspension coefficient M1. Layer S2 is characterised by its critical shear stress for erosion crit2 and resuspension constant M2. Typically, layer S1 is easier erodible than layer S2: crit1 < crit2. Conceptually, layer S1 represents the thin fluff layer on top of the sediment bed, whereas layer S2 represent the sediment bed itself, in which fines may be stored. The

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mud fraction p2 in layer S2 is computed from m2, the total sediment mass per m 2 in layer S2, according to p2 = m2 / d(1-n , where n is the bed porosity, d the thickness of layer S2 and the solids density. The maximum mud fraction p2 is unity. If necessary, excess material is buried in the deep bed layer S3 (term B2 in Figure 5.1) to maintain this upper limit, as d is constant. It is noted that for parameters describing bed properties, subscripts 1 and 2 refer to layers S1 and S2, respectively. However, for parameters describing suspended sediment properties (such as ws), subscripts 1 and 2 refer to the first and second fraction, respectively. The resuspension coefficient M1 depends on the thickness of fluff layer S1. If the thickness remains below the typical roughness height of the bed, no space-covering layer is expected to form. In this case, it is unrealistic to assume a zero-order resuspension flux, i.e. a flux that does not depend on the amount of sediment available. A first-order resuspension flux is then more realistic, i.e. a flux that scales linearly with m1, the amount of sediment per m 2 in layer S1. This results in the following expression for M1: M1 = min(m1 M1’, M0), where M1’ and M0 are the first and zeroth order resuspension parameters, respectively. Transition between both erosion modes occurs for m1 = M0/M1’. With M0 = 10-6 kg/m 2/s and M1’ = 2.5 10-7 s-1 this occurs for m1 = 4 kg/m 2, which is equivalent of a fluff layer of 2 cm thickness assuming a fluff layer concentration of 200 kg/m 3. Typically, the fluff layer will erode faster than the second bed layer. Only when the fluff layer becomes depleted (such as during a storm), erosion from the second bed layer becomes the dominant term. Therefore a constraint for the parameter settings is that integrated over time, E1 > E2 or M1 e1 > p2 M2 e2. Transfer of sediment from layer S1 towards S2 takes place by burial. This term (B1) is expressed as: B1 = m1 Vbur. The burial rate from S1 towards S2 scales linearly with the available sediment mass m1. No digging term from S2 towards S1 is applied, as upwards sediment transport from layer S2 is accounted for by the erosion process (term E2). Finally, a constant production term P is applied, transferring sediment from the deep layer S3 towards S2. This term can be used to take into account the slow erosion of geological deposits (such as Zuiderzee clay). At short time scale, this term plays a minor role, but at long times scales it may become significant: gradually the sediment mass in the model domain (and with that the suspended sediment concentration) will increase of decrease until term P equals term B2 (burial of sediment from layer S2 towards deep layer S3). For the Markermeer model, term P is set at 1 kg/m 2/year, resulting in a total production of 730 kton/year. Apart from vertical fluxes, also horizontal fluxes are important, resulting in the dispersion of sediment along the lake. Horizontal fluxes are either caused by advection A = UC or dispersion Dis = –Dhor dC/dx. Both current velocity U and horizontal dispersion Dhor are derived from the hydrodynamic model and vary in time and space. It is envisaged that the processes and formulations described above capture the most essential processes involved with fine sediment transport in the Markermeer. However, they are a simplification of a much more complex reality. Also, some processes are not included at all. For example, no sediment-density coupling is applied, which may play a role during periods with high concentrations (Vijverberg, 2008). If the fluff layer has a

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sufficient thickness and a sufficiently low strength, it may flow under gravity. Flocculation is only taken into account a basic form, assuming a linear relationship between total suspended sediment concentration and settling velocity. No production and decay of organic matter is taken into account. A number of other limitations remain unmentioned here.

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Calibration of suspended sediment model

6.1 Introduction The objective of the calibration of the fine sediment model is to arrive at a set of parameter settings that capture the fine sediment dynamics in the Markermeer in a satisfactory way, both in a qualitative and quantitative sense. Important characteristics are: 1 2 3 4 5 6 7 8 9 10 11

Average TSM levels Typical TSM levels during storms Typical TSM levels during calm weather Time-scale for TSM increase for increasing wind conditions Time-scale for TSM decrease for decreasing wind conditions Typical ratio of near-surface and near-bed TSM levels Spatial distribution of TSM concentration for various wind directions Spatial distribution of equilibrium bed composition Magnitude of net deposition flux in deep pits or navigation channels Location and extent of areas exhibiting net deposition Sediment budget of Markermeer

The number of parameters which may be optimised during the calibration is quite extensive: wsi M1i crit1i

M2 crit2

Vbur d P ks

settling velocity of fraction i resuspension constant for bed layer S1 (combination of M0i and M1i’) critical shear stress for erosion for layer S1 reuspension constant for bed layer S2 critical shear stress for erosion for layer S2 burial rate from S1 towards S2 thickness of layer S2 production contributing to the sediment pool of layer S2 bed roughness

Note that resuspension characteristics may be different for different sediment fractions in layer S1, whereas they are identical for layer S2. The reason for this is that erosion of layer S2 is steered by the bulk properties of this layer, consisting of a sand matrix with a variable percentage several fractions of fines. However, for the sake of simplicity, in the present study the erosion characteristics of layer S1 are kept the same for both sediment fractions. The only difference between both fractions is the settling velocity. 6.2

1DV approach Set-up of balance equations

In view of the quite extensive number of parameters, a trial-and-error calibration procedure is cumbersome and may not lead to optimal parameter settings. Therefore a more rational step-by-step procedure is adopted, starting with a 1DV approach. Neglecting horizontal advection (A) and dispersion (Dis), production (P) and deep burial (B2), the total sediment mass per unit area will remain constant. However, the vertical

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distribution of sediment over the water column and bed layers S1 and S2 will vary according to the local bed shear stress climate. For this simplified case, analytical expressions can be derived for this vertical distribution. Three simple balance equations form the foundation for these analytical expressions. The first is an overall mass balance: mtot = m1 + m2 + Ch

(1)

where h is the local water depth, C is time-average TSM concentration and m1 and m2 the mass per unit area in bed layers S1 and S2, respectively. The second balance equation is based on the assumption of long-term equilibrium between sedimentation and erosion: ws C = m1 M1’

e1

+ p2 M2

(2)

e2

where ei is the long-term time-averaged excess bed shear stress for fraction i defined as e1 = t / crit1 – 1) dt and e2 = t / crit2 – 1)3/2 dt. Note that (2) is invalid for areas with net deposition, such as deep pits, but for these areas deep burial (B2) will occur, which we assume to be negligible. The third balance equation is based on the assumption of long-term equilibrium between burial towards layer S2 and erosion from layer S2: m1 Vbur = p2 M2

(3)

e2

The relationship between mud fraction p2 and sediment mass per unit area m2 is: m2 = p2 (1-n) d

(4)

with d is layer S2 thickness and n is the bed porosity. The residence time tres2 in layer S2 is expressed as: tres2 = m2 / (p2 M2

e2)

= (1-n) d / (M2

e2)

For a storm with duration tstorm and excess bed shear stress concentration increase in the water column will be: C = (tstorm/h) (p2 M2

e2s

+ m1 M1’

e1s)

(5) e1s

and

e2s,

the

(6)

Note that the maximum contribution of layer S1 to the storm concentration peak is limited to m1/h kg/m 3, as layer S1 then becomes depleted. Layer S2 contains so much sediment that it will never become depleted. The excess bed shear stress depends on the values of crit1 and crit2. The lower they are, the higher the excess bed shear stress and the larger the concentration increase. From the above set of equations, the parameter settings can be computed from the desired values for C, C, tres2 and m1 (or tres1) for chosen settings for p2 and d (i.e. m2). It is advised to set p2 at a level representative for the typical mud fraction observed in the field (anywhere between 0 and 1) and d at a value representative for the typical mixing depth observed in the field (typically in the order of 0.1 m). Target values for C and C are derived from TSM observations. The value of m1 is proportional to the fluff layer thickness dfluff: dfluff = m1/Cgel, with Cgel the gelling concentration, i.e. the concentration at which a space-filling network is formed and mud flocs start to support each other. Typically, Cgel > 50 g/l for inorganic mud, but Cgel < 50 g/l for organic mud.

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The residence time tres2 determines the response time of the mud model to changes in forcing (wind climate), sediment supply or geometry (scenarios). Unfortunately, little is known on the average residence time (or even better: residence time distribution) of fines on the lake bed of the Markermeer. For the present study, we assume one year. From a practical point of view, a longer time would make the simulation time and CPU time required to reach equilibrium too long. Note that already for a residence time of 1 year, a simulation period of 3 years is required to bridge 95% of the difference between the initial and the equilibrium conditions. A much shorter time appears to be unrealistic based on the little experimental evidence available. However, the setting of tres2 has only a small influence on the short term mud dynamics. Also, tres2 has no influence on the final equilibrium concentrations. It only influences the time scale required to reach this equilibrium. Therefore, the setting of tres2 is of minor importance for the objectives of the present study. Computation of parameters From the balance equations (1-3) and target settings for C, C, tres2, p2 and m1, the parameters settings are computed as follows: m2 = p2 (1-n) d

(7)

mtot = m1 + m2 + Ch

(8)

Vbur = m2/(m1 tres2)

(9)

M1 = (ws C – m1 Vbur) / ( M2 = (1-n) d / (tres2

e1

m1)

e2)

(10)

(11)

The value for ws is optimised independently to reproduce typical observed vertical concentration gradients and the rate of concentration decrease after a storm event. The former is obtained from the Rouse profile: C(z) = ([a(h-z)]/[z(h-a)])

C(z=a)/C(z=h-a) = Cbot / Csurf = (h/a-1)

where is the Rouse coefficient defined as = ws / U*,U* = b ) = U g/Chézy, h is water depth and a is a distance from the bed in the order of the roughness height. Typical conditions for the Markermeer are: U = 0.1 m/s and Chézy = 60 m 0.5/s, U* = 5 mm/s. Assuming ws = 0.1 mm/s, h = 4 m and a = 0.1 m, = 0.05 and Cbot / Csurf = 1.4. Sediment with a settling velocity below 0.1 mm/s will therefore show hardly any vertical stratification under typical conditions. Coarser sediment suspensions are stratified, however. Note that as the settling velocity is assumed to increase with concentration, the water column will tend to be more stratified during periods of strong winds. Also, the coarser tail of the particle size spectrum can be more easily resuspended in these conditions, thereby changing the average suspended sediment composition.

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The deposition flux is related to the near-bed sediment concentration. In areas where resuspension is negligible, such as deep pits, the gross deposition flux equals the net deposition flux. The former is computed from Dep = wsC. For example, for ws = 0.1 mm/s and Cbot = 100 mg/l, Dep = 1 10-5 kg/m 2/s = 0.86 kg/day. The computed deposition rate should match the observed one. Data on sediment traps and the infilling of deep pits can be used as calibration material. Note that the contribution of the coarser sediment fractions (having a higher settling velocity) tends to dominate the total deposition flux. The time scale for concentration decay after a wind event can be approximated with: tdecay = h/ws. After t = 3tdecay, 95% of the difference between storm concentration and the equilibrium quiet weather concentration has been bridged. For h = 4 m and ws = 0.1 mm/s, tdecay = 0.5 day only. This demonstrates that a finer fraction is required for a slower transition between high-wind and low-wind events. High-frequency TSM observations from measuring poles FL41 and FL42 will provide the essential calibration data for the settling velocity (amongst other parameters). At least to fractions need to be defined in order to attain a satisfactory reproduction of observations both during calm periods and storm events. Let us consider the typical distribution of sediment over the vertical. Under quit conditions, the typical concentration is 10 mg/l only, equivalent with a sediment mass of 0.04 kg/m 2 at a water depth of 4 m. A fluff layer thickness of 0.01 m is equivalent with a sediment mass of m1 = 1 kg/m 2, assuming Cgel = 100 kg/m 3. A thickness of layer S2 of 0.05 m with a mud fraction of 0.2 is equivalent with a sediment mass of m2 = 15.6 kg/m 2. Nearly all sediment is therefore stored in layer S2. Under storm conditions, the fluff layer will be completely resuspended (m1 = 0 kg/m 2). The concentration in the water column may be up to 500 mg/l, equivalent with an eroded mass of 2 kg/m 2 at a water depth of 4 m. The remaining sediment mass in layer S2 is 14.6 kg/m 2, still by far the larger contribution to the total sediment mass. Integrated over the lake area (about 730 km 2), the active fine sediment mass is in the order of 10 MT. The next parameter to consider is the critical shear stress for erosion, crit. Depending on its setting in relation to the local bed shear stress climate, either one of two conditions will occur: 1 M2 e2 > m1Vbur: no net accumulation will occur, layer S2 will reach an equilibrium mud fraction p2 = m1 Vbur / M2 e2, or 2 M2 e2 < m1Vbur: to avoid p2 > 1; excess sediment is buried towards the deep bed layer S3 and net sediment accumulation will occur. Condition 1 will occur in areas with a moderate to rough bed shear stress climate, whereas condition 2 will occur in areas with a mild bed shear stress climate such as deep pits. These areas will act as a net sediment sink. In reality, areas 1 may be in dynamic equilibrium indeed or act as a net sediment source by the gradual erosion of old deposits. In the present model, this source is implemented as a constant, spatially uniform term, however. For the present study, sinks to and sources from the deep bed are of minor importance, as they hardly change the active sediment mass at the short time scale considered (order of 1 year). As the source term is uncertain, it is chosen such to match the net sink term, which is computed by the model. If sink and source terms are not in equilibrium, the active sediment mass will increase or decrease (and concurrently also the suspended sediment concentration) until an equilibrium is reached. The time scale to reach such equilibrium is at least tres2, but at the spatial scale of the whole lake amounts to the ratio Meq/P, which may be of the order of 10 years or more. Herein Meq is defined as the active sediment mass in the whole lake at

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equilibrium (order 10 MT) and P the source term integrated over the lake (order 1 MT/y). In the calibration procedure, crit2 is chosen such that net deposition does occur in known sink areas such as deep pits and channels, but does not occur in areas in which the observed bed composition is not predominantly muddy. Note that the exact value for crit is unimportant in highly dynamic areas: it is the product of M e that matters, not the individual terms. Parameter crit1 is set at a value that results in an onset of resuspension of the fluff layer at a wind speed of 4 m/s (Bft 3). For such a wind speed, the wave-induced bed shear stress is typically 0.02 Pa. 6.3 3D approach After the above analytical considerations, the parameter settings are applied to the 3D numerical model, in which also horizontal advective and dispersive transport are taken into account. Locations with identical bed shear stress climates but with a different advective and dispersive sediment supply will have a different equilibrium sediment mass per m 2. Starting from a uniform initial sediment distribution, areas with a rough bed shear stress climate will act as a sediment source for areas with a mild bed shear stress climate. This redistribution will continue for a time scale of 3tres2, until an equilibrium bed composition has (nearly) been reached. The only residual transport left is from the source areas (in the present model chosen spatially uniform) towards the sink areas (such deep channels and pits). It is stressed that by definition, these source and sinks do not originate from or are not stored in bed layers S1 and S2, but originate from or are stored in deep bed layer S3. Layers S1 and S2 only show temporal fluctuations, fluff layer S1 on a time scale of hours to days, layer S2 on a time scale of months. Short term fluctuations in layer S2 do occur (induced by bed shear stress fluctuations), but are much dampened owing to the large sediment buffer in layer S2 and its higher resistance to erosion. It is obvious that the settings derived for the case of vertical sediment exchange only need some modification when applied to the full 3D model, as horizontal advection and dispersion is now taken into account. However, the analytical expressions still give good guidance on which parameter to change if the average concentration is too low or if modelled peak concentrations during storm are too high, for example. Starting from uniform initial conditions, all modelled spatial patterns of suspended sediment concentration, bed composition and net deposition are computed by the fine sediment model and not steered by the model user. Spatial patterns are caused by the interaction of wind forcing, lake geometry, lake bathymetry and bed roughness. To keep the model as simple as possible, all parameters are defined to be spatially uniform. However, the modelled bed composition in this case does not agree with the observed bed composition in the Markermeer. The computed bed has a too low mud content in the deepest part near Lelystad, whereas it has a too high mud content along the east coast near Hoornsche Hop. As the deposition pattern is primarily steered by the time-integrated bed shear stress distribution, more attention has been paid to this shear stress distribution. Two potential culprits can be identified: 1. the wind climate and 2. the bed roughness. If the wind climate in the calibration period (1/8/2007 – 1/4/2008) would deviate significantly from the long-term average wind climate, also a deviation of the bed composition would be expected. Note that the simulation time required to approach an equilibrium bed composition is at least 5 times the calibration period; the wind forcing of the calibration period is therefore also repeated at least 5 times (> 3 years).

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Although the wind climate in the calibration period does slightly deviate from the longterm average climate (see Section 3.6), it does not cause the mismatch between the computed and observed bed composition. This has been verified by constructing an equilibrium bed composition from 16 weighed stationary fine sediment computations (based on 2 speeds and 8 directions). The 16 stationary simulations are weighed according to their frequency of occurrence according to the long-term wind climate. As the initial assumption of uniform bed roughness may deviate too much from reality, it is decided to use a spatially variable bed roughness (Figure 6.1). Nikuradse roughness heights for waves are derived from the observed shell distribution in Markermeer. Areas with a high shell density are attributed a higher Nikuradse roughness height R than areas with a low shell density according to: R = max(0.003, 0.07pshell) (Van Leeuwen, 2008), where pshell is the shell fraction varying between 0 (no shells) and 1 (completely covered with shells). As a result, the roughness height varies between 3 mm (no shells) and 7 cm. At the Gooi- en Eemmeer, where no data on shell density are available, the roughness height is set at a uniform value of 2 cm. By applying this spatially varying bed roughness, the model reproduces the observed bed composition pattern quite well. Further fine-tuning may be required when additional field observations become available. As a local reduction in bed shear stress also results in a reduction in resuspension, also the suspended sediment concentration above a smooth area tends to decrease. This is indeed what the model results do show. A comparison with remote sensing data will provide additional validation material. It is remarked that while adopting a non-uniform bed roughness, the wave modelling has been simplified. This has no theoretical, but practical grounds. To avoid recomputation of the hydrodynamics for each new roughness field, the variable roughness is not applied in the FLOW computations, but in the WAQ computations. To compute the wave-induced bed shear stress in WAQ, a fetch length approach is implemented (see Section 4.2.3). The SWAN wave fields coupled to the FLOW simulations are therefore not used. However, there is no limitation to do FLOW simulations with a variable bed roughness height at a later stage and use the combined current- and wave-induced (from SWAN) bed shear stress in WAQ. It is noted that the fetch length approximation is demonstrated to work well for location FL41 (Markermeermidden).

Figure 6.1: Left: observed shell distribution (%); Right: Nikuradse roughness height (m) derived from shell distribution.

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As remarked in Chapter 5, the present model contains two sediment fractions with the following properties: ws01 = 2.3 10-5 m/s (2 m/d); ws02 = 4.6 10-6 m/s (0.4 m/d) and C0 = 25 mg/l. The first fraction is suspended during periods with moderate to strong wind, whereas the second fraction also remains partly in suspension during calm weather. These two fractions are required to reproduce satisfactorily the observed concentration variations during both calm and rough weather conditions. Applying a single fraction only would either result in too low computed TSM levels during calm weather or too little variability during rough weather. In theory, the application of more than two fractions may result in a more accurate model compared with a two-fraction model, but the requirements on data become also higher, as more parameters need to be set. For the present model, two fractions is judged to be the optimum between simplicity and accuracy. The initial mass ratio between the fractions is 3:1, i.e. the coarser fraction is 3 times more abundant than the finer fraction. With regard to the computation of bed shear stress, the current-induced bed shear stress is computed according to the Manning formulations (nMa = 0.024 m1/3/s). The wave-induced bed shear stress in computed according to the Soulsby et al. (1993) formulations. As discussed above, a space-varying Nikuradse roughness height for waves has been applied, ranging between 0.3 and 7 cm according to the observed shell distribution. The total bed shear stress is approximated with the scalar sum of the waveand current-induced bed shear stress. Model settings according to analytical expressions (1D case) and after calibration of the 3D fine sediment model are listed in Table 6.1. It is noticed that most parameter settings of the 1D and 3D cases are equal, implying that the analytical approach neglecting advection is successful. Only the resuspension coefficients M1 and M2 and burial rate Vbur have been changed within a range of a factor 2–5 (indicated in bold in Table 6.1). Table 6.1

parameter ws01 ws02 C0 M0 M1 M2 c1 c2

n d2 Vbur P nMa

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Parameter setting based on a) (second column): analytical expressions for 1D case using the bed shear stress climate of FL41 and assuming tres2 = 1 year; m1 = 0.5 kg/m2; mtot = 23.4 kg/m2 (equivalent with p2 = 0.3); C = 60 mg/l; C = 50 mg/l; h = 4 m; and b) (third column): after calibration of 3D fine sediment model.

value 1D 2.31 10-5 4.63 10-6 0.025 1.0 10-6 8.8 10-7 2.24 10-8 0.05 0.1 0.4 0.05 1.44 10-6 0.024

value 3D 2.31 10-5 4.63 10-6 0.025 1.0 10-6 2.49 10-7 4.12 10-9 0.05 0.1 0.4 0.05 9.06 10-7 3.17 10-8 0.024

unit m/s m/s kg/m 3 kg/m 2/s 1/s 1/s Pa Pa m 1/s kg/m 2/s m 1/3/s

explanation st settling velocity 1 fraction nd settling velocity 2 fraction reference concentration for ws 0th order resuspension flux S1 1st order resuspension flux S1 1st order resuspension flux S2 critical shear stress erosion S1 critical shear stress erosion S2 porosity thickness bed layer S2 burial rate from S1 towards S2 production rate Manning roughness factor

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Results

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Results on water level and wave height are discussed in Chapter 4. The hydrodynamic model is demonstrated to reproduce observations on these parameters well. Validation on current patterns is pending. Although no synoptic data exist on spatial current distribution in the Markermeer, validation is possible at measuring poles FL41 and FL42, on which ADCP current profilers were mounted. However, such validation has not yet been carried out because of time constraints. It is expected that the present 3D hydrodynamic model is able to reproduce large-scale current patterns satisfactorily, as the physics driving these patterns is well described in the model. Also, the successful reproduction of observed suspended sediment distribution discussed in the next section would not be possible without realistic current patterns. Local deviations of the current pattern may be caused by variations in bed roughness. If synoptic data would be available, this aspect could be calibrated and validated in detail.

7.2

Suspended sediments

Following the calibration procedure, we will now present the results. Both results with uniform bed roughness with waves computed by SWAN and results with spatially varying bed roughness with waves based on the Brettschneider approach are presented, see Figure 7.1 and Figure 7.2. Although the results based on a uniform roughness are convincing regarding the reproduction of observed TSM levels and variations herein caused by wind forcing, two problems are noted: 1 2

The computed equilibrium bed composition does not agree with observations. With a proper reproduction of typical TSM levels at location FL41, computed levels at FL42 are too high. For slightly changed parameter setting, the computed levels are FL42 are right, but in this case the computed levels at FL41 are too low.

With variable roughness and Brettschneider approach, the first problem is solved to a large extent, see Figure 7.3 and Figure 7.4. The computed bed composition is similar to the observed bed composition. The observed high mud content in the SE corner of the Markermeer is reproduced reasonably well by the model, although high mud contents near the Houtrib dike are not reproduced. Apparently, the low roughness area more to the North catches so much sediment that the water column becomes partially depleted towards the Houtrib dike. Indeed, this is observed from the remote sensing images, showing a significant concentration decrease towards the Houtrib dike. However, for the applied bed roughness distribution this effect is probably exaggerated. A further optimization of the roughness distribution may result in a closer match between model and observations. The second problem is only partly solved. Although the computed difference between FL41 and FL42 becomes smaller (on average 19 mg/l difference instead of 28 mg/l), it is not yet according to observations (which show a difference of 7 mg/l only).

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Figure 7.1:

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Observed and computed near-surface TSM concentration (mg/l) at location FL41. The line ‘cb012opt’ represents the final calibration settings with non-uniform bed roughness and fetch length approximation. The line ‘swan’ represents the simulation with uniform bed roughness and with waves computed with SWAN.

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Figure 7.2:

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Observed and computed near-surface TSM concentration (mg/l) at location FL42. The line ‘cb012opt’ represents the final calibration settings with non-uniform bed roughness and fetch length approximation. The line ‘swan’ represents the simulation with uniform bed roughness and with waves computed with SWAN.

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Figure 7.3:

Computed mud fraction. Left: uniform bed roughness; Right: variable bed roughness according to Figure 6.1.

Figure 7.4:

Left: observed thickness (m) of mud layer on bed (Vijverberg, 2008). Right: mud percentage in seabed (%) (sampling campaign 2000, RWS).

Markermeer

Figure 7.5 shows the gross sedimentation flux at locations FL41 and FL42. The modelled flux ranges between 100 and 700 g/m 2/day, which is in agreement with the estimate by Van Duin (1992) of 350 g/m 2/day. The major contributor to the gross sedimentation flux is the coarser sediment fraction, notably during rough weather periods. Recent sediment trap data by IHE (2008) suggest a 2 to 3 times higher sedimentation rate in the upper part of the water column. To achieve this in the model, a higher settling velocity would be required (maintaining present TSM levels), or the introduction of a third coarser sediment fraction (ws about 10 m/d). It is noted that in the period 1/1/2008 – 1/2/2008, the computed TSM concentration is about 50% too high at location FL42 (Markermeer Midden), whereas it is about 50% too low at location FL41 (near Marken) (see Figure 7.1 and Figure 7.2, lower panels). In this period SW winds prevail. The observed concentration gradient between FL41 and FL42 is small: both stations show similar TSM levels in January 2008. The observed concentration in FL41 sometimes even exceeds that of FL42. This is unexpected, as for

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SW wind location FL41 is more sheltered than FL42. Therefore also the observations should be interpreted with care. Sensor fouling or optical properties of the suspended sediment different from the samples on which the sensor calibration is based may introduce bias. Without changing the hydrodynamics, the simulated spatial distribution of SPM can be influenced in two ways: 1 2

By changing the spatial roughness distribution By changing the settling velocity and/or the relative availability of sediment fractions. sedimentation flux FL41 and FL42 800

700

600

g/m2/day

500

400

FL41/STB FL42/STA

Van Duin (1992)

300

200

100

0 1

2

3

4

5

6

7

period

Figure 7.5:

Computed gross sedimentation flux (g/m2/day). Van Duin (1992) reports a rate of 350 g/m2/day. Period 1 = 22/11–4/12; 2 = 4/12–18/12; 3 = 18/12–2/1; 4 = 2/1–16/1; 5 = 16/1– 29/1; 6 = 29/1–12/2; 7 = 12/2–26/2.

The first method is discussed earlier in the report. TSM concentration in areas with a low roughness tends to be lower. The second method is based on the dispersion behaviour of fines: the lower the settling velocity, the more uniform the distribution of TSM tends to be, as horizontal exchanges becomes more important at the expense of vertical exchange. This is illustrated in Figure 7.6, showing that both the distribution in the water column (a ‘snapshot’) and in the bed (being a response to the shear stress history) is of the fraction with ws1 = 2 m/d is distinctly different from the fraction with ws2 = 0.4 m/d. The spatial distribution may be further calibrated using remote-sensing data by tuning the fraction distribution, settling velocity and roughness. However, too much detail should not be aimed at, as a) modelled relative impacts of system changes such as dams or deep pits are not very sensitive to changes in parameter settings and b) in the model some processes are strongly simplified or even completely missing, so even if a close reproduction of observed TSM patterns would be possible, such a reproduction is based on a partly reproduction of the underlying physical mechanisms only, giving a false sense of accuracy for conditions deviating from the calibration conditions. A comparison with remote sensing data is discussed in the next chapter of this report.

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Figure 7.6:

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Top: surface concentration (mg/l) of fine fraction IM2 (0.4 m/d) at 28/1/2008 midnight; Middle: surface concentration (mg/l) of coarser fraction IM1 (2 m/d) at same date and time; Bottom: fraction (-) of IM2/IM1 in bed layer (wind: 3.2 m/s Bft 2-3, direction WSW, following a period of Bft 6 direction W the previous day).

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Validation on remote sensing data

The second phase of the fine sediment model development project consist of validation on data not used for calibration. This data consist of: 1 2

Station FL41 and FL42 turbidity data for the period 1 April – 1 September 2008. Remote sensing data for the year 2006.

For the second comparison, the hydrodynamic and mud model was re-run with 2006 wind forcing and water balance. All model settings remained identical to those for the 2007/2008 simulation. Figure 8.1 and Figure 8.2 show the modelled and observed TSM concentration at locations FL41 and FL42, respectively. In general, the model performance is similar in the period after April 1 to that before this date. Trends and concentration peaks are often well reproduced, although peak amplitude are regularly over- or underestimated and some periods exist with a bias in the modelled average concentration compares with observations. However, it should be realised that also the OBS data will contain errors because of sensor fouling and the inherently difficult translation from turbidity to solids concentration. For example, data after August 1, 2008 at FL42 may be less reliable, as the concentration levels of the top and bottom sensor start to diverge significantly, which contradicts with the complete 1 year period before this date. Appendix A.1 shows a comparison between the modelled and remotely sensed suspended sediment distribution at Markermeer for a number of dates and times in 2006. Note that these are comparisons of momentarily states, which is more ambitious than a comparison of time-averaged concentrations. The modelled and observed distributions compare remarkably well. Compared with the 2007 version of the mud model, which has been used to compile the Suspended Matter Atlas Markermeer 2006, a clear step forward has been made (see Appendix A.3). A new edition of the atlas is therefore recommended. Only the comparison between the new model and remote sensing data at very low wind speeds is not convincing: in the model the concentration drops to a level typically between 10 and 20 mg/l, whereas the remote sensing data suggests levels below 10 mg/l. The cause for this is that in the calibration data for the model (i.e. OBS data at FL41 and FL42 in the period 01/08/2007 – 01/04/2008) concentrations below 10 mg/l does hardly occur. It is recommended to make also remote sensing data for 2007/2008 available, as this would make possible a comparison between remote sensing and OBS data. The model calibration would benefit from such comparison. The only date that the model results really contradict remote sensing data is on 11 June 2006 (SE wind Bft. 3). The model shows resuspension in the NW corner of Markermeer, whereas resuspension is not visible on the remote sensing image. The simulated image of 10 June shows a much better agreement (see Figure 8.3). Either the model simulates the presence of a fluff layer at a time and place when and where it is apparently not there, or the critical shear stress for erosion should be slightly increased, avoiding resuspension at Bft. 3. An important conclusion from both remote sensing data and the model simulations is that the Markermeer is far from a homogeneous turbid lake: suspended sediment

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concentration varies strongly in space and time. Also for strong winds, low turbidity areas may persist in some parts or corners of the lake, depending on wind direction.

Figure 8.1:

Observed and computed near-surface and near-bed TSM concentration (mg/l) at location FL41 for the period 01/08/2007. Results until 01/04/2008 are identical to those presented in Figure 7.1.

Figure 8.2:

Observed and computed near-surface and near-bed TSM concentration (mg/l) at location FL42 for the period 01/08/2007 – 01/09/2008. Results until 01/04/2008 are identical to those presented in Figure 7.2.

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Figure 8.3: Remotely sensed (left) and modelled (right) near surface TSM concentration mid-June 2006 at Markermeer. Mean concentrations and 10 and 90 percentile values are also shown. The wind history of the previous 24h is indicated with gray arrow, with the more recent winds in darker gray. The inset shows the time series of modelled TSM concentration (in mg/l) at station FL42 from 18 days before until 9 days after the date indicated. When available, also MWTL data at Markermeer Midden is indicated with an * herein.

Finally, a simulation has been made in an effort to further improve the model performance compared to FL41 and FL42 OBS data. It is noticed that location FL41 will be more difficult to reproduce than FL42, as the remote sensing data and model results show that the spatial concentration gradients in the vicinity of location FL41 are stronger than at location FL41. This is logical, as FL41 is much closer to the shore and wave and current conditions will be very sensitive to wind direction. At FL42, in the middle of Markermeer, this is less so. Changes made to the model are: • • • •

Settling velocity of 1st fraction increased from 2 to 3 m/day Settling velocity of 2nd fraction decreased from 0.4 to 0.3 m/day Mass in system of 2nd fraction reduced with 30% Lowest bed roughness increased from 3 mm to 5 mm.

Figure 8.4 and notably Figure 8.5 demonstrate that the model performance in improved indeed with respect to OBS data. At FL42, the modelled concentration becomes higher in the period November – December 2007 and is in better agreement with OBS data. In the period January – February 2008, the modelled concentration becomes lower and also is in better agreement with OBS data. Also the modelled concentration peak near the end of May 2008 is less exaggerated compared with data.

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The effect of the changes in parameters settings on the spatial distribution of suspended sediment is shown in Appendix A.2. The concentration peaks during storms reduce in amplitude owing to the higher settling velocity of the first fraction. The concentration minima during calm weather become less pronounced (note that the impact on the spatially-averaged concentration level during calm weather is only small because of the applied 30% reduction of the total sediment mass of the finest fraction). The average concentration in the SE corner of the Markermeer, where the local bed roughness has been increased from 3 to 5 mm is increased, as more often resuspension is possible due to a higher bed shear stress. However, spatial gradients tend to become too small compared with remote-sensing data, resulting in a slightly less favourable comparison with these data. This result (i.e. an improvement with respect to OBS data, but a deterioration with respect to remote sensing data) suggests that the present model settings result in a model performance that approximates the optimal performance that can be reached with the present process based 3D mud model, in which only the most essential processes have been included with relatively simple formulations.

Figure 8.4:

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Observed and modelled near-surface and near-bed TSM concentration (mg/l) at location FL41 for the period 01/08/2007. Results until 01/04/2008 are identical to those presented in Figure 7.1.

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Figure 8.5:

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Observed and modelled near-surface and near-bed TSM concentration (mg/l) at location FL42 for the period 01/08/2007 – 01/09/2008. Results until 01/04/2008 are identical to those presented in Figure 7.2.

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Conclusions and recommendations

Based on the results presented and discussed in this report, it is concluded that the Markermeer mud model in its present state is able to capture the essentials of the observed dynamics of suspended matter. Computed typical concentration levels are in agreement with observed typical levels and also the observed temporal variability forced by wind is reproduced satisfactorily. The computed equilibrium bed composition resembles the observed one. However, to arrive at this result it is required to apply a spatially varying bed roughness based on the observed shell distribution. The model compares favourably against remote sensing images of 2006. For most images available, the model reproduces typical features of the suspended sediment distribution. However, the modelled concentration levels at low wind speeds remain substantially higher than suggested by remote sensing data. This is caused by limitations of the calibration dataset, as such low concentrations do not occur in the 2007/2008 OBS calibration data at locations FL41 and FL42. Concurrent remote sensing and OBS data are required to solve this issue. Based on this validation, recommendations are made on the range of applicability and further possible development. Based on a preliminary judgement, they include: • More focus on settling distribution to improve both the horizontal suspended sediment distribution and the net sediment deposition flux. The properties and availability of both the finest and coarsest classes may need some modification; • Focus on production and loss terms relevant for long-term behaviour; • More sophisticated modelling of flocculation and near-bed processes; For some applications, such as the relative impact assessment of measures to reduce the suspended sediment concentration in Markermeer, the present model is suitable for application at short time scales (up to a few years). However, it is stressed that the model is not calibrated to properly reproduce the long-term fine sediment balance. Also, the model is not designed to describe near bed processes such as sediment-driven flow. These aspects require both more field data on bed roughness and composition, sediment sources and sinks and the inclusion of additional processes. Also, it is recommended to measure wind speed and direction in the middle of the Markermeer at future measurement poles.

Acknowledgements Deltares would like to thank IVM for supplying remote sensing data, KNMI for wind data, RWS for SPM data from Waterbase and RWS IJG for water level data.

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References

Ang’weya, Rose Aluoch (2008). Sediment characteristics of Lake Markermeer, The Netherlands. UNESCO-IHE MSc-thesis ES 08.34, Delft, The Netherlands. Blok, B.W.G. (2008). Monitoring markermeer. Data rapport on measurement program FL41/FL42 at Markermeer, August 2007 – September 2008. Deltares report no. G0200.10. Deltares, Delft, The Netherlands. Brettschneider, C.L. (1954). Generation of wind waves over a shallow bottom. US Army Corps of Engineers, Beach Erosion Board, Tech. Memorandum no. 51. Coastal Engng. Conf., Honolulu, ASCE, 1976, 202. Duin, E.H.S. van (1992). Sediment transport, light and algal growth in the Markermeer : a two-dimensional water quality model for a shallow lake. PhD-Thesis Wageningen University, The Netherlands. Doorn N. en W.D. Eysink, 2004. Golfmeting met drukopnemers. WL rapport H 4318 voor Rijkswaterstaat, IJsselmeergebied Hulsbergen, R. and M. Kuijper (2007). Modellering slibhuishouding Markermeer. WL | Delft Hydraulics Report Q4408, Delft, The Netherlands (in Dutch). Kamps, R., E. Koster, M. Eleveld, M. Kuijper, M. Laanen (2007). Zwevend stof atlas Markermeer 2006. RWS IJG report 2007-3. ISBN 9789036914611. Leeuwen, B. van (2008). Modeling mussel bed influence on fine sediment dynamics on a Wadden Sea intertidal flat. MSc-thesis Twente University. Lenselink G. and U. Menke (1995). Atlas Geology and Soil of the Markermeer. Rijkswaterstaat, Directie IJsselmeergebied, Lelystad. ISBN 90-369-1148-6. Noordhuis, R. (2008). Data overview of Markermeer. Waterdienst, Lelystad, The Netherlands. (In prep.) Rozari, P. de (2008). Sediment Dynamics in Lake Markermeer, The Netherlands. MScthesis WM 08.02, UNESCO-IHE, Delft, The Netherlands. Soulsby, R.L., L. Hamm, G. Klopman, D. Myrhaug, R.R. Simons and G.P. Thomas (1993). Wave-current interaction within and outside the bottom boundary layer. Coastal Engineering, Vol. 21, pp. 41–69. Vijverberg, T. (2008). Mud dynamics in the Markermeer. MSc-thesis Delft University of Technology, Delft, The Netherlands. Vijverberg, T en P. Boderie (2008). Analyse Scenario berekeningen Markermeer. Deltares report Q4613, Delft, The Netherlands (in Dutch). Westhyusen, A.J. van, 2007. Advances in the spectral modelling of wind waves in the nearshore. PhD thesis Delft University of technology.

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