# Modeling Storm Surge Attenuation by an Integrated Nature-Based and Engineered Flood Defense System in the Scheldt Estuary (Belgium)

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Case

#### 2.1.1. The Scheldt Estuary

^{3}[37]. The part upstream the border until Merelbeke (located at 170 km from the mouth) is called Sea Scheldt and is characterized by a single channel bordered by much smaller intertidal flats and marshes. In Merelbeke, the tide is blocked by locks and a weir. For clarity, because water flows in both directions in an estuary, downstream depicts the direction towards the sea and upstream is directed towards the inflow of fresh water.

^{3}/s) is very small compared to the tidal volume [32,38].

#### 2.1.2. FCAs and CRT

#### 2.2. TELEMAC-3D Model: SCALDIS

#### 2.3. Model Implementation of Culvert Flow

#### 2.3.1. Different Types of Flow

#### 2.3.2. Reformulation of the Equations for Model Implementation

_{D}) for each flow type, depending on a number of geometric properties of the culvert [46]. The discharge coefficients can vary from 0.39 to 0.98. A different approach is proposed by Carlier [47] using a non-dimensional coefficient, also referred to as a discharge coefficient that, for hydraulic structures made of only one culvert, can be written as follows:

_{1}is the head loss coefficient at the entrance of the culvert, C

_{2}is the head loss coefficient inside the culvert, and C

_{3}is the head loss coefficient at the exit of the culvert. Then, if the general expression for the discharge equation through a culvert proposed by Carlier [47]:

_{D}, and the continuous and local head losses. ΔH is the head for each type of flow. The equations of Bodhaine in Table 1 can be rewritten according to the format proposed by Carlier [47] and can in this form be implemented in the TELEMAC code. The equations following Carlier [47] and the conditions of when to use which equation are summarized in Table 2.

#### 2.3.3. Different Head Loss Coefficients

- (1)
- The entrance head loss represents the head loss due to the contraction of the flow at the entrance of the culvert. An abrupt contraction at the culvert entrance causes a head loss due to the deceleration of the flow immediately after the vena contracta. A head loss coefficient C
_{1}, of which the value is a function of the diameter ratio after and before the contraction, is proposed by [48]. For a culvert between a river and a floodplain, the contraction can be seen as very large, estimating the entrance head loss coefficient to be 0.5 according to [48]. Bodhaine [46] noticed that the entrance head loss coefficient C_{1}for flow type 5 had to be lowered comparatively with the other flow types. The calculated discharge seemed to be overestimated when the default equation was used. Therefore, a correction coefficient C5 is multiplied with entrance head loss coefficient C_{1}when flow type 5 occurs. An exact value for C5 is not given but according to Bodhaine [46] this coefficient lies in the following interval: 4 ≤ C5 ≤ 10. - (2)
- The head loss due to pillars inside the culvert: Sometimes, at the entrance of culverts, the flow is divided into two sections by a pillar. This pillar causes additional head loss and is taken into account. According to [48], the head loss coefficient C
_{p}to account for a pillar is given by:$${C}_{p}=\beta {\left(\frac{{L}_{p}}{b}\right)}^{4/3}\mathrm{sin}\text{}\theta $$_{p}is the thickness of the pillar; b is the distance between two consecutive pillars; and β is a coefficient dependent on the cross-sectional area of the pillar and according to Bodhaine [46] β equals 2.42 for rectangular pillars and 1.67 for rounded pillars; θ stands for the angle of the pillar with the horizontal plane. In most cases, this angle will be 90° and sin θ will be equal to 1. - (3)
- The head loss due to internal friction: The head loss coefficient C
_{2}takes the head loss inside the culvert due to internal friction into account and is calculated according to [49]:$${C}_{2}=\frac{2gL{n}^{2}}{{R}^{4/3}}$$ - (4)
- The exit head loss: C
_{3}represents the head loss coefficient due to expansion of the flow exiting the culvert. It is calculated according to [49]:$${C}_{3}={\left(1-\frac{{A}_{s}}{{A}_{s2}}\right)}^{2}$$_{s}and A_{s}_{2}are the sections just in- and outside the downstream end of the culvert. - (5)
- The head loss due to non-return or one-way valve: All outflow culverts have non-return valves on the estuary side to prevent water from entering the FCA (see number 1 in Figure 2). Depending on the opening, the valve will cause more or less head loss. C
_{V}represents the head loss coefficient due to the presence of a non-return valve. For a flap gate valve rotating around hinges at its upper edge, values for C_{V}were obtained experimentally by [48]. Four values for C_{V}are given in Table 3 according to the opening of the valve.like for head loss coefficient C_{1}, a correction coefficient C_{V}5 is multiplied with the head loss coefficient C_{V}to take into account the increase of the head loss when applying flow type 5. Through a number of laboratory experiments with a physical scale-model at Flanders Hydraulics Research, the value for this coefficient was determined to be 1.5 [45]. - (6)
- The head loss due to the presence of a trash screen: Trash screens in front of the inflow and outflow culverts prevent garbage, drift wood, and plant debris from clogging the culverts (indicated by number 4 in Figure 2). The head loss due to the presence of these screens can be estimated by its relationship with the velocity head through the net flow area. The head loss coefficient C
_{T}accounting for the presence of a trash screen can be calculated according to [50]:$${C}_{T}=\left(1.45-0.45{A}_{T}-{{A}_{T}}^{2}\right)$$_{net}, to gross rack area, A_{gross}, is given by A_{T}:$${A}_{T}=\frac{{A}_{net}}{{A}_{gross}}.$$ - (7)
- Wooden beams in front of the inflow culvert to function as a small weir: The height of these wooden beams is used to fine tune the moment the flow enters the FCA during flood in the estuary (indicated by number 2 in Figure 2). This structure will not be taken into account with the head loss. Instead, on the side where this wooden weir structure is present, the bottom level of the culvert will be set equal to the top of this wooden weir. For the entrance diameter or opening of the culvert, the height of the small weir will be subtracted from the height of the culvert. This structure makes the overall modelling of the culvert discharge more complicated. However, this assumption provides the correct time of water inflow in an FCA with CRT in the calculations.
- (8)
- Downward sliding valves to close the culvert: Sliding valves were designed to close the culvert for maintenance or to prevent inflow in an FCA with CRT in case of a storm surge. However, in practice, these valves are often used to smother the inflow of the culverts (indicated by number 3 in Figure 2). No additional head loss coefficient is defined for these valves. The length over which these valves are let down is subtracted from the culvert height in the calculations.

#### 2.4. FCA with CRT Bergenmeersen: Detailed 3D Hydrodynamic Model

#### 2.4.1. FCA with CRT Bergenmeersen

#### 2.4.2. Detailed 3D Hydrodynamic Model

^{3}/s discharge. In September 2014, a 13-h measurement campaign was executed (13 h to capture one full tidal cycle), measuring the in- and outflow discharges with a StreamPro ADCP. Divers measured the water level in- and outside the FCA. These measurements are used to calibrate the input parameters for the culverts of FCA Bergenmeersen. A detailed description of all model parameters needed to model the discharge through culverts is given in Appendix A. An overview of the culvert parameter values after calibration is given in Appendix BTable A1. This 3D model of FCA Bergenmeersen is also available in the TELEMAC-MASCARET software package as a validation case.

_{1}was chosen equal to 0.5 according to [48] when a large contraction is assumed going from the river to the culvert. The correction factor for the entrance head loss coefficient for flow type 5 was chosen equal to 6 after calibration and given the interval proposed by Bodhaine [46]. The inflow culverts have squared pillars in the middle and C

_{p}is calculated according to Equation (3) where L

_{p}equals 0.35 m; b equals 1.35 m; and β equals 2.42 for rectangular pillars. The angle between the pillar and the horizontal is 90° so that sin θ equals 1. With these values, C

_{p}equals 0.4. In the TELEMAC code, there is no variable foreseen for C

_{p}, so its value will be added to the entrance head loss coefficient for the entrance of the inflow culverts at the river side only. The head loss due to internal friction within the culvert is calculated by the model by giving the length of the culvert and a Manning Strickler friction coefficient to solve Equation (4). The length of the culvert construction is 18 m, but given the specific construction type, this value is brought back to 1 and 9 m for the in- and outflow culverts, respectively. For the Manning Strickler coefficient, a value of 0.015 s/m

^{1/3}is taken corresponding to smooth concrete. For the exit head loss coefficient, Equation (5) suggests that for a very large expansion, the coefficient would be close to 1, but taking the neighboring outflow culverts into account, the same value as the entrance head loss was chosen: 0.5. The value 1 was kept for the inflow culverts. Non-return valves are present on the outflow culverts. These are relatively lightweight high density polyethylene (HDPE) valves rotating around hinges on the top. The angle of opening was measured in the field for this type of valve and the measurements showed a maximum opening angle of 70° [52]. This corresponds to a head loss coefficient C

_{v}equal to 1 according to Table 3 and [48]. For the trash screens, the ratio A

_{T}is equal to 0.8, which makes C

_{T}equal to 0.45 according to Equation (6). This value was rounded to 0.5. Trash screens can sometimes have a lot of debris on them, creating more head loss. Therefore, the head loss coefficient for trash screen is usually used for calibration of the total head loss. In this calibration case, a day before the measurements the screens were cleaned, and thus the value of 0.5 was kept here. To differentiate between flow type 5 and 6, a coefficient C56 is chosen equal to 10 according to [46]. The width of the inflow culverts is 2.7 m. The width of the outflow culverts is 1.35 m. The level at which flow enters the inflow culverts depends on the bottom level of the inflow culvert and the height of possible stacked wooden weir logs in front of it. The total inflow area is further restricted possibly by the height of how far the sliding valves were let down. For the three older outflow culverts, the same parameters were chosen, but their geometric values were changed accordingly: Their width and height is 1.5 m. Their length is 30 m and their bottom level lies at 2.5 m TAW for the two in the East and 3.0 m TAW for the one in the West (for locations see Figure 1b).

^{3}/s and for the outflow discharges the RMSE was 0.57 m

^{3}/s.

#### 2.4.3. Validation of the Bergenmeersen Culverts Flow Model

#### 2.5. Physical Scale Model

#### 2.5.1. Scale Model Geometry

#### 2.5.2. Scale Model Tests Setup

#### 2.5.3. Culvert Parameters

^{1/3}was chosen. The exit head loss coefficient was set to 0.2 as there is not a big expansion downstream of the culvert in the flume. The width of the culvert was 0.087 m and the height was 0.147 m. The bottom level of the inflow culverts was constructed at 0.313 m from the flume bottom. The length of the inflow culverts was 0.6 m. To differentiate between flow type 5 and 6 the parameter C56 was equal to 10 according to [46]. C5 was chosen equal to 6 according to the value taken for the Bergenmeersen culverts as both structures are very similar.

#### 2.6. Hindcast of Storm Surge and Impact of FCA in the Scheldt Estuary

- (1)
- Scenario 1 will hindcast the storm surge of 6 December 2013 as it was. All FCAs that were active at that time are active in the model. This scenario will tell how well the model can simulate this storm surge and it will be used as a reference to compare the other two scenarios with.
- (2)
- Scenario 2 starts from scenario 1 for which the largest intertidal marsh area in the estuary (the so-called Drowned Land of Saeftinghe, for location see Figure 1) is removed from the model domain. Its effect on storm surge attenuation was already demonstrated in [19,55]. This scenario is added to compare the impact of a large natural marsh on storm surge attenuation within the estuary with the impact of several smaller FCAs. This marsh was removed from the model domain by increasing its bottom level to a point where it cannot be flooded anymore.
- (3)
- Scenario 3 starts from scenario 2 for which all FCAs are removed from the model domain.

## 3. Results

#### 3.1. Bergenmeersen Detailed 3D Model Validation

#### 3.2. Physical Scale Model Tests

#### 3.3. SCALDIS Estuary Scale Storm Surge Simulations

## 4. Discussion

#### 4.1. Storm Surge Height Reduction by FCAs

#### 4.2. Culvert Flow Implementation in TELEMAC

#### 4.3. Detailed 3D Model FCA Bergenmeersen

#### 4.4. Physical Scale Model

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Practical Implementation of the Culvert Equations into TELEMAC

- I1: mesh node number of culvert on side 1;
- I2: mesh node number of the culvert on side 2;
- CE1: entrance head loss coefficient for the culvert on side 1 (this corresponds to the head loss coefficient C
_{1}); - CE2: entrance head loss coefficient for the culvert on side 2 (this corresponds to the head loss coefficient C
_{1}); - CS1: exit head loss coefficient for the culvert on side 1 (this corresponds to the head loss coefficient C
_{3}); - CS2: exit head loss coefficient for the culvert on side 2 (this corresponds to the head loss coefficient C
_{3}); - LARG: the width of the culvert;
- HAUT1: height of the culvert on side 1;
- CLP: coefficient to restrict the flow direction (0 both directions are possible; 1 = only flow from side 1 to 2; 2 = only flow from side 2 to 1; 3 = no flow);
- L: linear head loss coefficient used only when OPTBUSE = 1; If OPTBUSE = 2, L is calculated;
- RD1: culvert bottom elevation on side 1 (z
_{1}); - RD2: culvert bottom elevation on side 2 (z
_{2}); - CV: head loss coefficient when a valve is present;
- C56: factor to differentiate between flow types 5 and 6;
- CV5: correction factor for C
_{V}when flow type 5 is used; - C5: correction factor for CE
_{1}and CE_{2}with flow type 5; - TRASH: head loss coefficient when trash screens are present;
- HAUT2: height of the culvert on side 2;
- FRIC Manning Strickler friction coefficient;
- LONG: length of the culvert;
- CIR: indicates whether the culvert is rectangular (=0) or circular (=1); in case of a circular culvert the height is taken to calculate the wet section.

_{c}) inside the culvert is assumed to be equal to two thirds of the culvert height. Secondly, when a wooden weir log is present in front of a culvert, an equivalent culvert bottom elevation is used replacing both the bottom elevations z

_{1}and z

_{2}in the equations itself (not in the conditions to determine when which type of flow is occurring). The mean between z

_{1}and z

_{2}is taken as equivalent bottom elevation of the culvert. The diameter of the culvert used in the equations will be the one corresponding to the side were the flow enters the culvert. For the wet section of the culverts, the shape of the culverts is taken into account. Rectangular and circular shapes are both possible. Other shapes are not foreseen in the code.

**Figure A2.**Different flow types for flow through culverts during spring tide at FCA with CRT Bergenmeersen.

## Appendix B. Model Parameters Culverts

Parameter | Inflow Culverts | Outflow Culverts | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 1 | 2 | 3 | 4 | 5 | 6 | |

CE1 | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.9 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

CE2 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

CS1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

CS2 | 1 | 1 | 1 | 1 | 1 | 1 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

LARG | 2.7 | 2.7 | 2.7 | 2.7 | 2.7 | 2.7 | 1.35 | 1.35 | 1.35 | 1.35 | 1.35 | 1.35 |

HAUT1 | 0.35 | 0.35 | 0.35 | 0.45 | 0.25 | 0.35 | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 |

CLP | 0 | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 2 | 2 | 2 | 2 |

RD1 | 4.5 | 4.5 | 4.35 | 4.2 | 4.2 | 4.2 | 2.7 | 2.7 | 2.7 | 2.7 | 2.7 | 2.7 |

RD2 | 4.2 | 4.2 | 4.2 | 4.2 | 4.2 | 4.2 | 2.7 | 2.7 | 2.7 | 2.7 | 2.7 | 2.7 |

CV | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |

C56 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |

CV5 | 0 | 0 | 0 | 0 | 0 | 0 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 | 1.5 |

C5 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |

TRASH | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 |

HAUT2 | 1.6 | 1.6 | 1.6 | 1.6 | 1.6 | 1.6 | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 | 1.1 |

FRIC | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 | 0.015 |

LONG | 1 | 1 | 1 | 1 | 1 | 1 | 9 | 9 | 9 | 9 | 9 | 9 |

CIR | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Parameter | Inflow Culverts | |||
---|---|---|---|---|

1 | 2 | 3 | 4 | |

CE1 | 0.5 | 0.5 | 0.5 | 0.5 |

CE2 | 0.5 | 0.5 | 0.5 | 0.5 |

CS1 | 0.2 | 0.2 | 0.2 | 0.2 |

CS2 | 0.2 | 0.2 | 0.2 | 0.2 |

LARG | 0.087 | 0.087 | 0.087 | 0.087 |

HAUT1 | 0.147 | 0.147 | 0.147 | 0.147 |

CLP | 1 | 1 | 1 | 1 |

RD1 | 0.313 | 0.313 | 0.313 | 0.313 |

RD2 | 0.313 | 0.313 | 0.313 | 0.313 |

CV | 0 | 0 | 0 | 0 |

C56 | 10 | 10 | 10 | 10 |

CV5 | 0 | 0 | 0 | 0 |

C5 | 6 | 6 | 6 | 6 |

TRASH | 0 | 0 | 0 | 0 |

HAUT2 | 0.147 | 0.147 | 0.147 | 0.147 |

FRIC | 0.012 | 0.012 | 0.012 | 0.012 |

LONG | 0.6 | 0.6 | 0.6 | 0.6 |

CIR | 0 | 0 | 0 | 0 |

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**Figure 1.**Map of the Scheldt estuary in 2013 (i.e., the year of the simulated storm surge, see text) with names of all active flood control areas (FCAs). (

**a**) The SCALDIS model domain located in W-Europe; (

**b**) model domain and bathymetry of the detailed model of FCA Bergenmeersen with Q indicating the upstream discharge input and SL indicating the downstream surface level boundary (TAW is the Belgian vertical reference plane where 0 m TAW corresponds to low water level at sea).

**Figure 2.**Cross section of flood control area (FCA) with controlled reduced tide (CRT) Bergenmeersen also showing the internal structure of the in- and outflow culverts. TAW is the Belgian vertical reference plane where 0 m TAW corresponds to low water level at sea.

**Figure 3.**Helicopter photo of FCA Bergenmeersen on the morning of 6 December 2013, one hour after high water level of the ‘Sinterklaas’ storm surge (6/12/2019 09:25 local time). The thin white line indicates the location of the flood protecting dike and the thicker black dashed line indicates the location of the overflow dike. The panel in the top left corner gives a closer view on the in- and outflow culvert construction seen from within the FCA when the water level is low. The trash screens are visible.

**Figure 4.**Calibrated modeled discharges compared to measured discharges through the in- and outflow culverts of FCA with CRT Bergenmeersen.

**Figure 5.**Side view photo of the actual scale model in the flume (

**a**) and flume and scale model dimensions with side and top view plan (

**b**). Water flows from left to right.

**Figure 6.**Comparing modeled and measured water level variations inside the FCA with CRT Bergenmeersen for the storm surge on 6 December 2013.

**Figure 7.**Water levels scenario simulations SCALDIS 2013 with indication of flood protecting dike and overflow dike levels.

**Table 1.**Summary of the different flow types through a culvert by Bodhaine [46], how to calculate the discharge, and when to use which equation.

Flow Type | Discharge Equation | Occurs When |
---|---|---|

1 | $Q={C}_{D}{A}_{c}\sqrt{2g\left({h}_{1}-z-{h}_{c}-{h}_{f12}+\alpha \frac{{V}_{1}^{2}}{2g}\right)}$ | $\frac{{h}_{1}-z}{D}<1.5;\frac{{h}_{4}}{{h}_{c}}<1.0;{S}_{0}>{S}_{c}$ |

2 | $Q={C}_{D}{A}_{c}\sqrt{2g*\left({h}_{1}-{h}_{c}-{h}_{f12}-{h}_{f23}+\alpha \frac{{V}_{1}^{2}}{2g}\right)}$ | $\frac{{h}_{1}-z}{D}<1.5;\frac{{h}_{4}}{{h}_{c}}<1.0;{S}_{0}<{S}_{c}$ |

3 | $Q={C}_{D}{A}_{3}\sqrt{2g\left({h}_{1}-{d}_{3}-{h}_{f12}-{h}_{f23}+\alpha \frac{{V}_{1}^{2}}{2g}\right)}$ | $\frac{{h}_{1}-z}{D}<1.5;\frac{{h}_{4}}{D}\le 1.0$ |

4 | $Q={C}_{D}{A}_{0}\sqrt{\frac{2g\left({h}_{1}-{h}_{4}\right)}{1+29{{C}_{D}}^{2}{n}^{2}L/{R}^{4/3}}}$ | $\frac{{h}_{1}-z}{D}>1.0;\frac{{h}_{4}}{D}>1.0$ |

5 | $Q={C}_{D}{A}_{0}\sqrt{2g\left({h}_{1}-z\right)}$ | $\frac{{h}_{1}-z}{D}\ge 1.5;\frac{{h}_{4}}{D}\le 1.0$ |

6 | $Q={C}_{D}{A}_{0}\sqrt{2g\left({h}_{1}-{d}_{3}-{h}_{f23}\right)}$ | $\frac{{h}_{1}-z}{D}\ge 1.5;\frac{{h}_{4}}{D}\le 1.0$ |

_{D}, the discharge coefficient; A

_{c}, the flow area at the critical water depth; g, the gravitational constant; h

_{1}, the upstream water depth; z, the elevation of the culvert entrance; h

_{c}, the critical water depth; h

_{f}

_{12}, the head loss due to friction from the approach section to the culvert entrance; α, kinetic energy correction coefficient for the approach section; V

_{1}, the average flow velocity at the approach section of the culvert; h

_{f}

_{23}, the head loss due to friction inside the culvert; A

_{3}, the flow area at the culvert outlet; d

_{3}, water depth at the culvert outlet; A

_{0}, flow area at the culvert entrance; h

_{4}, the downstream water depth; n, the Manning friction coefficient; L, the length of the culvert; R, the hydraulic radius; S

_{0}, the culvert slope; S

_{c}, the critical slope.

**Table 2.**Summary of the discharge equations for the different flow types through a culvert following Carlier [47].

Flow Type | Discharge Equation | Occurs When |
---|---|---|

2 | $Q=\mu {h}_{c}W\sqrt{2g*\left({S}_{1}-\left({z}_{2}+{h}_{c}\right)\right)}$ | $\frac{{S}_{1}-{z}_{1}}{D}<1.5;\text{}{S}_{2}-{z}_{2}{h}_{c}$ |

3 | $Q=\mu \left({S}_{2}-{z}_{2}\right)W\sqrt{2g\left({S}_{1}-{S}_{2}\right)}$ | $\frac{{S}_{1}-{z}_{1}}{D}<1.5;\frac{{S}_{2}-{z}_{2}}{D}\le 1.0$ |

4 | $Q=\mu DW\sqrt{2g\left({S}_{1}-{S}_{2}\right)}$ | $\frac{{S}_{1}-{z}_{1}}{D}>1.0;\frac{{S}_{2}-{z}_{2}}{D}>1.0$ |

5 | $Q=\mu DW\sqrt{2g{h}_{1}}$ | $\frac{{S}_{1}-{z}_{1}}{D}\ge 1.5;\frac{{S}_{2}-{z}_{2}}{D}\le 1.0;\text{}\frac{L}{D}\le C56$ |

6 | $Q=\mu DW\sqrt{2g*({S}_{1}-({z}_{2}+D\left)\right)}$ | $\frac{{S}_{1}-{z}_{1}}{D}\ge 1.5;\frac{{S}_{2}-{z}_{2}}{D}\le 1.0;\text{}\frac{L}{D}C56$ |

_{1}, water level on side 1, S

_{2}, the water level on side 2, h

_{1}, the water level above the culvert bottom on side 1, h

_{2}, the water level above the culvert bottom at side 2, h

_{c}, the critical water level inside the culvert, z

_{1}, level of the bottom of the culvert at side 1, z

_{2}, the level of the bottom of the culvert at side 2, L, the culvert length, C56, coefficient to differentiate between flow type 5 and 6.

**Table 3.**Values for the head loss coefficient C

_{V}depending on the opening of a flap gate valve according to [48].

Valve Position | Wide Open | ¾ Open | ½ Open | ¼ Open |
---|---|---|---|---|

C_{V} | 0.2 | 1. | 5.6 | 17 |

Set # | Upstream Water Level | Downstream Water Level | Upstream Water Level | Downstream Water Level |
---|---|---|---|---|

(Reality) | (Reality) | (Model) | (Model) | |

[m TAW] | [m TAW] | [m] | [m] | |

1 | 4 | 3 | 0.361 | 0.293 |

2 | 5 | 3 | 0.429 | 0.291 |

3 | 6 | 3 | 0.494 | 0.293 |

4 | 7 | 3 | 0.559 | 0.291 |

5 | 8 | 3 | 0.626 | 0.292 |

6 | 7 | 6 | 0.560 | 0.492 |

Set # | Upstream Water Level | Downstream Water Level | No Trash Screen | Trash Screen | ||||
---|---|---|---|---|---|---|---|---|

Model [m] | Model [m] | Measured Q [m^{3}/s] | Calculated Q [m^{3}/s] | Difference [%] | Measured Q [m^{3}/s] | Calculated Q [m^{3}/s] | Difference [%] | |

1 | 0.361 | 0.293 | 0.006 | 0.006 | 0 | 0.005 | 0.005 | 0 |

2 | 0.429 | 0.291 | 0.025 | 0.025 | 0 | 0.023 | 0.022 | −4.3 |

3 | 0.494 | 0.293 | 0.050 | 0.049 | −2 | 0.046 | 0.043 | −6.5 |

4 | 0.559 | 0.291 | 0.063 | 0.063 | 0 | 0.060 | 0.060 | 0 |

5 | 0.626 | 0.292 | 0.076 | 0.071 | −6.6 | 0.073 | 0.068 | −6.8 |

6 | 0.56 | 0.492 | 0.061 | 0.062 | 1.6 | 0.057 | 0.054 | −5.2 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Smolders, S.; João Teles, M.; Leroy, A.; Maximova, T.; Meire, P.; Temmerman, S.
Modeling Storm Surge Attenuation by an Integrated Nature-Based and Engineered Flood Defense System in the Scheldt Estuary (Belgium). *J. Mar. Sci. Eng.* **2020**, *8*, 27.
https://doi.org/10.3390/jmse8010027

**AMA Style**

Smolders S, João Teles M, Leroy A, Maximova T, Meire P, Temmerman S.
Modeling Storm Surge Attenuation by an Integrated Nature-Based and Engineered Flood Defense System in the Scheldt Estuary (Belgium). *Journal of Marine Science and Engineering*. 2020; 8(1):27.
https://doi.org/10.3390/jmse8010027

**Chicago/Turabian Style**

Smolders, Sven, Maria João Teles, Agnès Leroy, Tatiana Maximova, Patrick Meire, and Stijn Temmerman.
2020. "Modeling Storm Surge Attenuation by an Integrated Nature-Based and Engineered Flood Defense System in the Scheldt Estuary (Belgium)" *Journal of Marine Science and Engineering* 8, no. 1: 27.
https://doi.org/10.3390/jmse8010027