Impacts of Coastal Structures on Sediment Transport: A Case Study of Damietta, Egypt

2.1. Study area description / Opis područja proučavanja

The study area encompasses a 10 km coastal segment, within which DP is situated. Constructed in 1981, DP is an inland port with a depth of 15 m (see Figure 2) designed to accommodate the increasing demands of international trade in the Eastern Mediterranean region [40]. To mitigate sediment entrapment, the port was equipped with two jetties. It is located 9.7 km west of the Damietta Branch [41].

Notably, the site selected for DP has low susceptibility to waves and currents, making it an accreting zone [42,43]. However, the sediment patterns in the area were significantly altered following the construction of the Aswan High Dam [44]. Despite these changes, DP’s location remains characterized by accretion [45].

Several coastal protection measures have been implemented along the coastal line. These include two jetties along the Damietta Branch, a seawall, a revetment, three additional jetties, and eight detached breakwaters parallel to the shoreline. Furthermore, between 2016 and 2019, four detached breakwaters, each 200 m long with 240 m gaps, were constructed over a 1.5 km stretch to protect DP. These defense structures, along with the port, have altered the wave refraction patterns, leading to new erosion and deposition patterns in the region [46].

Figure 2 Study area, monitoring buoy, and location of the coastal structures

Slika 2. Područje proučavanja, nadzorna plutača i lokacija obalnih struktura

2.2. Data collection / Prikupljanje podataka

Various datasets describing the study area were collected from multiple sources to ensure a comprehensive analysis. Specifically, the observed data were sourced from the Egyptian Coastal Research Institute (CoRI), previous research conducted in the study area. While the bathymetric information was derived from two distinct surveys. The first survey, conducted in 2010, provided a detailed bathymetric map of the area (Figure 3). While, the second survey, completed in 2011, produced profiles used for calibration and verification purposes. Additionally, nearshore wave data were gathered through a buoy positioned near DP at coordinates 31°30.43' N and 31°45.6' E, located at a depth of 12 m. However, in regions with limited buoy measurements, methods are employed to extend the time series [47]. To complement this, long-term deep-water wave data covering 81 years (1940–2020) were obtained from the ECMWF-ERA5 reanalysis dataset. This buoy recorded data over the period 2003–2004, capturing wave measurements every four hours.

Frihy et al. [48] conducted a grain size analysis using a standard Ro-Tap sieving system, which employed whole phi sieve intervals. Their findings indicated a gradual decrease in mean grain size offshore. Specifically, the mean grain size of beach sediments fluctuates between 0.14 mm and 0.58 mm, with an average of 0.25 mm. However, offshore sediment (i.e. up to 6 m depth) varies between 0.08 and 0.22 mm, where the mean grain size varies between 0.08 and 0.22 mm with an average of 0.11 mm, where the closure depth was designated to be 8 m (approximately 1.3 km offshore).

Tidal data was accumulated to feature that the tidal range is 14 cm with a daily mean sea level variation of 60 cm at Port Said [49]. Additionally, currents data were augmented, where they mainly flow eastwards (i.e. NE-E sector) and westward (i.e. WSW-WNW sector). However, in winter (i.e. November to February), the highest current velocity occurred in January (i.e. 100 cm/s), where the average occurred in winter within the range between 15 and 20 cm/s [48,50].

Figure 3 Bathymetric survey of the study area by CoRI, 2010

Slika 3. Batimetrijski pregled područja proučavanja s pomoću CoRI, 2010

2.3. Numerical modeling / Numeričko modeliranje

In this study, the MIKE 21 SM was employed to simulate the LST dynamics along the Damietta coast, both before and after the construction of Damietta Port. MIKE 21, a well-established numerical modeling tool, is recognized for its accuracy in simulating sediment transport, hydrodynamic processes, and shoreline evolution. To evaluate the impact of Damietta Port on LST, MIKE 21 SM has proven to be particularly effective due to its ability to model complex coastal dynamics with high precision. In particular, the software has been successfully applied in several coastal studies, demonstrating its reliability in predicting changes in sediment transport patterns [51-58].

2.3.1. Theoretical background / Teoretska pozadina

MIKE21 SM, developed by the Danish Hydraulic Institute (DHI), is a shoreline morphology tool designed to model coastal dynamics. As part of the MIKE21 program framework, it integrates hydrodynamic and sediment transport functionalities. MIKE21 was chosen for this study due to its global acceptance and proven effectiveness in various applications. Its flexible grid-based structure excels in simulating two-dimensional dynamics, such as waves and sediment transport in coastal areas and estuaries.

MIKE21 is a comprehensive software package that simulates coastal processes through several modules. It includes four main modules: Spectral Wave (MIKE21 SW), Hydrodynamic (MIKE21 HD), Sand Transport (MIKE21 ST), and Shoreline Morphology. MIKE21 HD addresses the conservation of mass and momentum, while MIKE21 SW employs a cell-centered finite-volume technique to solve the differential equations governing wave dynamics. The governing equations in MIKE21 SW are available in both Cartesian and Polar coordinates [59,60], as follows:

[TeX:] \frac{S}{\sigma} = \frac{\partial N}{\partial t} + \nabla\left( \overrightarrow{v}N \right)$\frac{S}{\sigma }=\frac{\partial N}{\partial t}+\nabla \left(\vec{v}N\right)$ (1)

Where:

Where: [TeX:] N(\sigma,\ \theta,\ x,\ t)$N(\sigma ,\theta ,x,t)$ represents the action density, with t as the time. (x, y) denotes the Cartesian coordinates x, while [TeX:] v = (c_{\sigma},\ c_{\theta},\ c_{x},\ c_{y})$v=(c_{\sigma },c_{\theta },c_x,c_y)$ are the group propagation velocity in four dimensions. ∇ is a four-dimensional differential operator in space (v, σ, and θ).

On the other hand, MIKE21 ST calculates sediment transport due to wave-current interaction and other factors (i.e. turbulence and sediment concentration). MIKE21 ST calculates bed- and suspended-load-transport, using flow velocity Shields parameter, where the vertical variation in the sediment concentration is estimated by a diffusion equation. MIKE21 ST provides the littoral drift gradient, shape shoreline morphology by the continuity equation of MIKE21 SM via the implementation of the one-line theory, which divides the shore into perpendicular strips to calculate the changes in shoreline position due to the volumetric relationship of each strip, as follows:

[TeX:] \frac{\text{ΔN}}{\text{Δt}} = \frac{\text{vol}}{dA_{z}}$\frac{\mathrm{\text{ΔN}}}{\mathrm{\text{Δt}}}=\frac{\mathrm{\text{vol}}}{d{A}_z}$ (2)

Where: Δt: time increment, ∆𝑁 is the distance the shoreline moves perpendicular to its orientation and 𝑑𝐴𝑧 is the vertical area of the active coastal profile in each shoreface strip over which MIKE21 SM uniformly distributes.

For a detailed description of MIKE21 SM and its applications, refer to [53,61–64]. These sources offer comprehensive insights into the model's framework and its implementation for sediment transport analysis.

2.4. Calibration-verification processes / Procedure kalibracije-verifikacije

The calibration and verification results were analyzed by implementing statistical metrics, including average ([TeX:] \overline{x}$\overline{x}$), correlation coefficient (CC), Root Mean Square Error (RMSE), bias, Scatter Index (SI), where bias quantifies is the disparity between the measured and computed values, as follows:

[TeX:] \overline{x} = \ \frac{1}{n}\sum_{i = 1}^{n}x$\overline{x}=\frac{1}{n}{\sum }_{i=1}^{n}x$ (3)

[TeX:] \text{CC} = \frac{\sum_{i = 1}^{n}{\left( x_{i} - \overline{x} \right)\left( y_{i} - \overline{y} \right)}}{\sqrt{\sum_{i = 1}^{n}\left( x_{i} - \overline{x} \right)^{2}\sum_{i = 1}^{n}\left( y_{i} - \overline{y} \right)^{2}}}$\mathrm{\text{CC}}=\frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{\sqrt{{\sum }_{i=1}^n{(x_i-\overline{x})}^2{\sum }_{i=1}^n{(y_i-\overline{y})}^2}}$ (4)

[TeX:] \text{RMSE} = \sqrt{\frac{1}{n}\sum_{i = 1}^{n}\left( y - x \right)^{2}}$\mathrm{\text{RMSE}}=\sqrt{\frac{1}{n}{\sum }_{i=1}^n{(y-x)}^2}$ (5)

[TeX:] \text{BIAS} = \frac{1}{n}\sum_{i = 1}^{n}\left( y - \overline{x} \right)$\mathrm{\text{BIAS}}=\frac{1}{n}{\sum }_{i=1}^n(y-\overline{x})$ (6)

[TeX:] \text{SI} = \frac{\sqrt{\frac{1}{n}\sum_{i = 1}^{n}\left( y - x - BIAS \right)^{2}}}{\frac{1}{n}\sum_{i = 1}^{n}\left| x_{i} \right|}$\mathrm{\text{SI}}=\frac{\sqrt{\frac{1}{n}{\sum }_{i=1}^n{(y-x-BIAS)}^2}}{\frac{1}{n}{\sum }_{i=1}^n\left|x_i\right|}$ (7)

Where: n represents the number of data, x is the measured value, y is the simulated value, and [TeX:] \overline{x}$\overline{x}$ represent the average values.

2.4.1. Calibration / Kalibracija

Model calibration is an important phase of numerical modeling, through which the model parameters are tuned to force the model to produce output data similar to observed data. Accordingly, MIKE 21 was calibrated in terms of wave height, wave period and bed level (i.e. H, T and d). During the calibration process, ERA5 deep wave data for the year 2003 were implemented and the output (i.e. near-shore wave data) was contrasted against the measured near shore wave data of 2003. During the calibration process, 2 profiles of the 2011 bathymetrical survey were implemented and the output was analogized against the bathymetrical survey data of 2011.

2.4.2. Verification / Verifikacija

Model verification is a crucial stage in numerical modeling, during which the tuned model parameters are implemented (i.e. together with input data for an interval different from that implemented during the calibration process) to produce output data similar to observed data during the same interval. Accordingly, MIKE 21 was verified in terms of wave height, wave period and bed level (i.e. H, T and d). During the verification process, ERA5 deep wave data for the year 2004 were implemented and the output (i.e. near shore wave data) was contrasted against the measured near shore wave data of 2004. During the verification process, another 2 profiles of the 2011 bathymetrical survey were utilized and the output was compared to the bathymetrical data of 2011.

2.5. Simulations / Simulacije

Confident with the calibration and verification results, MIKE 21 was implemented to simulate a time interval of 81 years. Primarily, data was introduced to the model, where they encompassed the wave data of ERA5 during 1940-2020 and the bathymetrical data of 2010. Simultaneously, all the structures were introduced to the model upon their construction year (i.e. DP and all the protective structures).

MIKE 21 was operated, where its internal computation utilized the input data. During the internal computation, the deep waves were transformed to near shore waves. Also, during the internal computation, MIKE 21 calculated GLST and NLST for the pre- and post- construction of DP with its protective measures. It is of significance to mention that DP was constructed in 1982. Accordingly, the pre-construction condition prevailed before 1982, while the post-construction condition reflects the duration after 1982.

3.1. Calibration-verification results analysis and discussion / Analiza rezultata kalibracije-verifikacije i rasprava

During the calibration process, using equations 3 through 7, the model demonstrated high correlation values with the measured data for all parameters. Specifically, the Correlation Coefficient for wave height and water depth were 0.93 and 0.99, respectively. Additionally, the Root Mean Square Error values were relatively low, indicating a strong agreement between the computed and measured data. However, a slight bias was observed in some cases, such as a negative bias in wave height (i.e., -0.03). In the subsequent verification process, as described by equations 3 through 7, the model continued to show a high correlation with the measured data. Nevertheless, some parameters exhibited slightly higher RMSE values, as detailed in Table 1. Despite this, the data presented in Table 1 clearly demonstrate the model’s capability to effectively predict crucial parameters for the study area. This verification highlights the model’s potential for providing valuable results in future applications.

The verification results from this study align with previous research in the Mediterranean Sea using ERA5 data. Amarouche et al. [19] reported Bias, RMSE, and SI values for Hs of 0.04m, 0.31m, and 0.3%, respectively. Similarly, Abu Zed et al. [65] using the SWAN model, found Bias, RMSE, and SI values for Hs of 0.06m, 0.22m, and 0.33%, and for Tp of 0.43s, 1.34s, and 0.18%. Elkut et al. [66] also found comparable values for Hs, with Bias, RMSE, and SI of -0.28m, 0.29m, and 0.31%.

Table 1 Statistical metrics of the model calibration and verification processes

Tablica 1. Metrička statistika modela procesa kalibracije i verifikacije

3.2. Wave climate results analysis and discussion / Analiza rezultata klimatskih valova i rasprava

The computed wave data obtained from MIKE 21 are presented in Figure 4, where the figure represents the long term wave distribution, in terms of direction and height simulated over 81-year.

From the figure, it is evident that the dominant wave along Damietta is propagating from the North-North West sector (i.e. N-NW) sector. The obtained rose indicates that H_s is less than 1 m during 90% of the year, with an annual average of around 0.9 m. However, H_s ranges between 1.5 and 4.9 m during 10% of the year.

Moreover, Figure 4 indicates that the predominant wave direction originates from the north-northwest (NNW), where 40% of waves approach from the sector of 320 to 340 degrees. However, the maximum wave height reach 4.98 m from the North direction, while throughout the year, the waves predominantly approach from the NW 87% of the year.

Figure 4 Wave rose of significant wave height at a depth of 14 m (1940-2020)

Slika 4. Ruža valova značajnih visina valova na dubini od 14 m (1940. – 2020.)

3.3. Longshore sediment transport results analysis and discussion / Analiza rezultata nanosa sedimenta na obali i rasprava

The model results indicated that the major annual LST moves from West to East, as the waves originate from the NW. This section elaborates the results of the annual LST, monthly GLST and monthly NLST, as follows:

3.3.1. Annual longshore sediment transport / Godišnji nanos sedimenata na obali

The annual LST (i.e. NLST and GLST) was analyzed and presented on figures 5 and 6. The figures provide the computed values pre- and post-DP construction (i.e. 1940-1981 and 1982-2020), respectively.

During the pre-DP construction, GLST ranged between 0.87 and 1.5 x10⁶ m³/yr with an average of 1.1 x10⁶ m³/yr. During the pre-DP construction, NLST ranged between 0.49 and 1.04 x10⁶ m³/yr, with an average of 0.73 x10⁶ m³/yr. These values agree to previous findings in the study area, where researchers estimated the transport to be 0.66 x10⁶ m³/year to the East and 0.26 x10⁶ m³/year to the West with NLST of 0.4x10⁶ m³/year to the East [43]. However, other researchers estimated NLST to be 0.8x10⁶ m³/year [67], while [68] estimated it to be 0.6-1.8x10⁶ m³/year.

During the post-DP construction, GLST ranged between 0.75 and 1.07 x10⁶ m³/yr with an average of 0.9 x10⁶ m³/yr. During the pre-DP construction, NLST ranged between 0.25 and 0.65 x10⁶ m³/yr, with an average of 0.42 x10⁶ m³/yr. A similar estimate was previously documented. However, Frihy et al. [48] employed fluorescent tracers to designate the annual LST. The study revealed that GLST was 0.85x10⁶ m³/year, while NLST was 0.49x10⁶ m³/year.

Based on figures 4 and 5, apparent was the following:

Human intervention resulted in LST alterations, where GLST was 1.1 x10⁶ m³/yr, pre-human-intervention, and decreased to 0.9 x10⁶ m³/yr, post-human-intervention, with a decrease of 18%. Similarly, the average NLST was 0.73 x10⁶ m³/yr, pre-human-intervention, and decreased to 0.42 m³/yr, post-human-intervention, with a decrease of 42%.

Figure 5 Annual LST pre- DP construction in x10⁶ m³/yr (1940-1981)

Slika 5. Godišnji LST prije izgradnje DP u x 10⁶ m³/godišnje (1940. – 1981.)

Figure 6 Annual LST post-DP construction in x10⁶ m³/yr (1982-2020)

Slika 6. Godišnji LST nakon izgradnje DP u x 10⁶ m³/godišnje (1982. – 2020.)

3.3.2. Monthly gross longshore sediment transport / Mjesečni bruto nanos sedimenata na obalu

The monthly GLST was analyzed and presented on figure 7, where the figure provides the monthly GLST alteration of pre- and post-human-intervention (i.e. DP construction and establishment of the protection measures) in 10⁵ m³/yr.

Pre-human-intervention, the GLST was 1.45 x 10⁵ m³ in January, while this value was reduced to be 1.15 x 10⁵ m³ with 21% reduction. February value experienced 10% reduction, in terms of January value. March and April indicated a significant increase of 28% and 25%, in terms of February and March, respectively. May recorded a marginal increment of 1%, in terms of April. June, July, August and September marked an increase of 18, 27, 35 and 22% in terms of May, June, July and August, respectively. October, November and December reflected minor decrease of 2, 3 and 11%, in terms of August, October and November, respectively. This indicated that GLST decreased by 2 to 21%, while NLST increased by 1 to 35%.

Figure 7 GLST monthly alteration pre- and post-human intervention (10⁵ m³/yr)

Slika 7. GLST mjesečne alteracije prije i nakon intervencija čovjeka (10⁵ m³/godišnje)

3.3.3. Monthly net longshore sediment transport / Mjesečni neto nanos sedimenta na obalu

The monthly NLST was analyzed and presented on figure 8, where the figure provides the monthly NLST alteration of pre- and post-human-intervention (i.e. DP construction and establishment of the protection measures) in 10⁵ m³/yr.

Post-human-intervention, NLST exhibited a decrease throughout the year, in terms of pre-human-intervention. The average decrease was 37%, in terms of pre-human-intervention. Pre-human intervention, NLST was 0.96 x 10⁵ m³, while post-human-intervention it decreased to be 0.49 x 10⁵ m³, with a reduction of 49%. This reflects the immediate impact of human intervention on sediment transport. February, March, April, May decreased by 34, 47, 43 and 9%, in terms of January, February, March and April, respectively. June, July, August, September, October, November and December witnessed an increase of 28, 34, 43, 27, 46 and 37% in terms of May, June, July, August, September, October and November, respectively. These results underscored the dynamic changes in NLST, which emphasized the significance of monitoring sediment transport within the framework of human intervention.

Figure 8 NLST monthly alteration pre- and post-human intervention (10⁵ m³/yr)

Slika 8. NLST mjesečna alternacija prije i poslije čovjekove intervencije (10⁵ m³/godišnje)