Spatio-Temporal Analysis of Shoreline Changes and Wave Modeling: Case of Mostaganem Bay, Algeria

3.1.Data Sources / Izvori podataka

Shoreline changes were analyzed using aerial imagery acquired in 2003 and QuickBird satellites imagery from 2014 and 2023, with a spatial resolution of 0.5 m (Table 1). Mosaic processing, geodatabase creation, and overlay techniques were applied using ArcGIS 10 software (ESRI) to facilitate shoreline extraction analysis.

Table 1 Data used to measure shoreline evolution between Sidi Madjedoub and Oureah

Tablica 1. Podaci korišteni za mjerenje evolucije obale između Sidi Madjedouba i Oureaha

3.1.1. Image treatment / Obrada slika

The technique for processing aerial photographs involves three main steps: digitizing, rectifying, and mosaicing the images. The aerial photos were digitized and scanned using an A3 scanner with a resolution of 1000 dpi. However, these images can exhibit various distortions that may introduce errors of several meters.

Geometric corrections were applied to the aerial photographs using ERDAS Imagine 9.2 software [29] to reduce distortions caused by tilt, scale, and orientation. These operations were conducted by the National Institute of Cartography and Remote Sensing (INRS) and relied on the use of Ground Control Points (GCPs). A total of 35 GCPs were selected to georeference the aerial photographs. The images were georeferenced using the projection system UTM, WGS 1984, Zone 31 [21]. The resulting images were then combined into a single image and stored in TIFF format.

Our study area is located in a micro-tidal zone, where the tidal variation between low and high tide generally ranges from 60 to 70 cm. To minimize errors associated with tidal variations, multi-date images were collected during periods of high tide [30-31].

3.1.2. Shoreline Extraction and error estimation / Ekstrakcija obalne linije i procjena pogreške

The annual rates of shoreline change in our study area over the past twenty years were assessed using the Digital Shoreline Analysis System (DSAS), developed by the United States Geological Survey (USGS), and incorporated into ArcGIS 10. This approach allowed us to evaluate both short-and long-term variations in the shoreline [32].

The Digital Shoreline Analysis System (DSAS) estimates the shoreline position for each transect by generating 720 cross-shore transects, each 250 m long, spaced every 20 m along the baseline. (Figure 3).

For our analysis, we utilize two statistical outcomes generated by the DSAS model [33]: (1) the Endpoint Rate (EPR) and (2) the Net Shoreline Movement (NSM).

Figure 3 Transect mapping

Slika 3. Mapiranje transekata

The End Point Rate (EPR) is determined by dividing the distance between the old and recent shorelines by the time interval between them (Eq. 1). The EPR is expressed in meters per year (m/year) and is a technique commonly employed by researchers [34].

[TeX:] EPR\ (\frac{m}{year\ )} = \ \frac{D_{1} - D_{2}}{t_{1} - t_{0}}\text{\ \ \ \ \ \ }$EPR(\frac{m}{year)}=\frac{D_1-D_2}{t_1-t_0}$ (1)

The second technique, the Net Shoreline Movement (NSM) method, measures the distance between the most recent and oldest shorelines for each transect [35]. After calculating the accretion and erosion rates for our study area, we created seven classes [35] (Table 2).

Table 2 Classification of shorelines change according to EPR [36]

Tablica 2. Klasifikacija promjene obalnih linija prema EPR-u (stopi krajnje točke)

According to [37], the results of shoreline changes are not reliable without assessing and measuring error margins (uncertainties). These uncertainties include the geo-referencing error (U_g), pixel error (U_p) [38], digitization error (U_d), and the error related to the tide level at the time the aerial photograph was taken (U_pd). The total uncertainty (U_t) is calculated as the square root of the sum of the squares of these variables (Eq. 2) [39-40].

[TeX:] U_{t}\left( m \right) = \sqrt{U_{g}^{2}{+ U}_{p}^{2}{+ U}_{d}^{2} + U_{\text{pd}}^{2}}\text{\ \ \ \ }$U_t\left(m\right)=\sqrt{U_g^2{+U}_p^2{+U}_d^2+U_{\mathrm{\text{pd}}}^2}$ (2)

The total weighted uncertainty [TeX:] U_{a}$U_a$ [TeX:] \left( \frac{m}{\text{year}} \right)$\left(\frac{m}{\mathrm{\text{year}}}\right)$ is computed by weighting the uncertainties [TeX:] U_{t1}$U_{t1}$,[TeX:] U_{t2}\text{\ and\ }U_{t3}$U_{t2}\mathrm{\text{and}}{U}_{t3}$,… according to the length of the periods [TeX:] L_{1},L_{2}\text{\ and\ }L_{3}$L_1,L_2\mathrm{\text{and}}{L}_3$. The weights [TeX:] {(w}_{i})${(w}_i)$ are defined as (Eq. 3):

[TeX:] w_{i} = \frac{L_{i}}{_{1}^{n}L_{j}\text{\ \ }}$w_i=\frac{L_i}{1_n^{}{L}_j}$ (3)

where:

[TeX:] L_{i}\ $L_i$is the length of the period ([TeX:] L_{1}$L_1$=2014−2003, [TeX:] L_{2}$L_2$= 2023 – 2014 and [TeX:] L_{3}$L_3$= 2023 – 2003).

[TeX:] _{1}^{n}L_{j}\ $1_n^{}{L}_j$is the total length of all periods (20 years).

The total weighted uncertainty [TeX:] U_{\text{total}}$U_{\mathrm{\text{total}}}$ is then calculated as: (Eq. 4):

[TeX:] U_{\text{total}} = \sqrt{w_{1}*U_{t1} + w_{2}*U_{t2} + w_{3}*U_{t3}}\text{\ \ }$U_{\mathrm{\text{total}}}=\sqrt{w_1*U_{t1}+w_2*U_{t2}+w_3*U_{t3}}$(4)

In this study, the annualized degree of uncertainty ([TeX:] U_{a}$U_a$) over a period of twenty years is equal to 0.29 m/year (Table 3).

Table 3 Evaluation of measurement errors for each source of coastal data

Tablica 3. Procjena pogrešaka mjerenja za svaki izvor obalnih podataka

3.2. Waves Modeling / Modeliranje valova

In this study, we analyze the effects of wave climate on shoreline stability. Wave propagation modeling is used to examine wave dynamics in shallow water [41]. The spectral wave model MIKE 21-SW was employed to simulate wave propagation and evaluate the pattern of wave energy distribution along the coast. This model includes one land boundary and three open boundaries [42].

The data input for the MIKE 21 spectral wave model (SW) includes significant wave height (Hs), tide, peak wave period (T_p) (Table 4), directional standard deviation, bathymetry data, wind direction [42].Two parameters were considered to configure the SW module: bottom friction and breaking wave. The bottom friction was set to a value of 0.04, while the breaking wave parameter was set to 0.8.

MIKE21 SW uses a cell-centered finite-volume method to solve the differential equations that govern wave dynamics. The governing equations in MIKE21 SW are presented in both polar and Cartesian coordinates [43-44], as detailed below: Eq. (5).

[TeX:] \frac{S}{\sigma} = \frac{\partial N}{\partial t} + \nabla(\overrightarrow{\nu}N)$\frac{S}{\sigma }=\frac{\partial N}{\partial t}+\nabla (\vec{\nu }N)$ (5)

Where [TeX:] N\ $N$represents the action density over time t, expressed as [TeX:] N = \frac{E}{\sigma}$N=\frac{E}{\sigma }$ , where 𝐸 represents the wave energy density and 𝜎 is the wave frequency. [TeX:] S$S$ is the source term accounting for energy changes due to wind input, non-linear interactions and dissipation. The expression [TeX:] \nabla(\overrightarrow{\nu}N)$\nabla (\vec{\nu }N)$ represents the divergence of wave action flux.

Bathymetric variation is a crucial factor in the propagation of swell and the dissipation of wave energy. The bathymetric data used for MIKE 21-2D was obtained from GEBCO and a digital bathymetric map from Navionics for the year 2020, using the WGS84 coordinate system with UTM projection in Zone 31. This data was processed in Mike Zero under the "Mesh Generator" module from the Danish Hydraulics Institute (DHI); it was interpolated onto unstructured triangular meshes. A fine mesh was employed near the coastline, while a larger mesh was used for the offshore zone (Figure 4).

By analyzing the annual wave rose (Figure 2) and the orientation of Sidi Madjedoub coast’s, extending from the east to Oureah in the west, the studied coastline is principally exposed to waves from the north-northeast (22.5°), northwest (315°), and west (270°) (Table 4).

Table 4 Forcing conditions and Boundary input

Tablica 4. Prisilni uvjeti i granični parametri

Figure 4 Triangular mesh of the study area

Slika 4. Trokutasta mreža područja istraživanja

4.1. DSAS Results / DSAS rezultati

This study analyzes the evolution of the shoreline along the coast from Sidi Majdoub to Oureah Beach using automated calculation methods. The results obtained are presented in Figures 5, 6, and 7 for the following periods: 2003-2014, 2014-2023, and 2003-2023, additionally, the shoreline evolution rates along the coast are listed in Table 5.

DSAS generated 720 transects perpendicular to the baseline, spaced at 20-meter intervals along a 15-kilometer stretch of coastline. For a comprehensive diachronic analysis, the study area is subdivided into three segments: (east, center, and west).

The first sector, located between Sidi Madjedoub Beach and Metarba Beach, includes 181 transects. The second sector, situated between Corniche Cliffs and Crique Beach, comprises 165 transects. Finally, the last sector, extending from Sablette Cliffs to Oureah Beach, comprises 304 transects.

Period 2003-2014 / Razdoblje 2003. – 2014.

During the period between 2003 and 2014 (11 years), the coastal zone between Sidi Madjedoub Beach to Oureah Beach experienced important erosion, affecting over 85% of the study area (Figure 5). The global evolution of shoreline indicated that all transects in the studied region (west, centre, and east) were exposed to high erosion, with a mean rate of -0.8 m/year. During this period, the most important regression was registered on the sandy beaches of the region (Sidi Madjedoub, Metarba, Salamander, Crique, and Sablette west), reaching rates of up to -20 m/year.

During the period between 2014 and 2023 (09 years), the coastal zone between Sidi Madjedoub Beach to Oureah Beach indicated a situation of progression-regression-progression compared to the period from 2003 to 2014 (Figure 6). The progression of the shoreline is more important in the eastern segment of the study area (East Sidi Madjedoub), with a range of variation between -23 and + 24 meters and an annual rate ranging from -2.65 to +2.73 m/year. A maximum accretion rate is noted on Metarba East beach. This state of accretion can be explained by the impact of coastal protection structures (breakwaters and groins) installed in the central part since 2012, which have resulted in the formation of "tombolos."

The results obtained from the analysis of the global evolution of shoreline changes over the last 20 years (2003–2023) indicate that almost all the transects in the studied region (west, center, and east) have been exposed to relatively rapid erosion (Figure 7).

In the eastern part, the average rates of erosion calculated using the EPR method vary between -12.01 m/year and +2.8 m/year, with a mean erosion rate of -0.28 m/year. The highest erosion rate is registered at Sidi Madjedoub beach, with an EPR rate of -4 m/year.

In the central part, between the Corniche cliffs and Crique beach, the shoreline fluctuates between accretion and retreat, with a rate of change of -0.29 m/year, along with a maximum erosion rate observed at the Corniche cliffs.

In the western part, between Crique beach and Stidia beach, the shoreline shows a relatively stable situation compared to the eastern and central parts, with an average rate of -0.13 m/year.

Figure 5 Analysis of the shoreline change between 2003 and 2014 in the study area

Slika 5. Analiza promjene obalne linije između 2003. i 2014. na području istraživanja

Figure 6 Analysis of the shoreline change between 2014 and 2023 in the study area

Slika 6. Analiza promjene obalne linije između 2014. i 2023. na području istraživanja

Figure 7 Analysis of the shoreline change between 2003 and 2023 in the study area

Slika 7. Analiza promjene obalne linije između 2003. i 2023. na području istraživanja

Table 5 Long-term shoreline change rates

Tablica 5. Stope dugoročnih promjena obalne linije

4.2. Numerical modelling of waves / Numeričko modeliranje valova

This part aims to show the wave propagation towards the coast to show their contribution on the shoreline morphology; the three relevant sector discussed before are analysed.

Analysis of the results shows that north-northeast (22.5°) waves (Figure 8) have the highest amplitude, particularly apparent during spring storms in the study area. These waves grow toward the coast at a diagonal angle. These waves do not keep their initial energy due to the addition of refraction and depth-induced breaking phenomena. The wave heights decrease to low values in the shallow water, ranging from 0.42 meters to 1.2 meters on sandy beaches and from 0.1 m to 2.2 meters in front of the harbor’s jetty and cliffs area. The refraction coefficients vary between 0.08 and 0.7; these waves generate rip currents.

Figure 9 shows the propagation of waves from the northwest sector, the wave heights values near the coast vary between 0.8 and 1.6 meters, and refraction coefficients vary between 0.11 and 0.37. In front of the studied area, refraction is less important because the crests of the northwesterly waves run parallel to the bathymetric contours. However, in front of the cliffs area and jetties significant wave heights reach 3.2 m; in this case, the energy dissipation is principally caused by diffraction phenomena.

The waves from the western sector (270°) (Figure 10) are generally winter waves. Significant wave heights decrease considerably, with values ranging between 0.2 meters and 1.5 meters and refraction coefficients varying between 0.08 and 0.83 across the study area. The lowest wave heights are observed along sandy coasts such as Sablette and Oureah while the highest values are observed approximately harbor’s jetty.

Figure 8 Propagation of north-northeast waves offshore (22.5°) simulated by Mike 21_SW model.

Slika 8. Širenje sjeverno-sjevernoistočnih valova od obale (22,5°) simulirano modelom Mike 21_SW

Figure 9 Propagation of northwest waves offshore (315°) simulated by Mike 21_SW model

Slika 9. Širenje sjeverozapadnih valova od obale (315°) simulirano modelom Mike 21_SW

Figure 10 Propagation of west waves offshore (270°) simulated by Mike 21_SW model

Slika 10. Širenje zapadnih valova od obale (270°) simulirano modelom Mike 21_SW