Study of the hydrodynamics and morphodynamics of the Óbidos lagoon, Portugal Diogo Silva Mendes

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1 EXTENDED ABSTRACT Study of the hydrodynamics and morphodynamics of the Óbidos lagoon, Portugal Diogo Silva Mendes Instituto Superior Técnico, University of Lisbon, Lisboa, Portugal. Abstract: In the Óbidos lagoon, waves and tidal currents induce rapid morphological changes driving its inlet to closure. Dredging solutions are frequent in order to reposition the inlet in a central location and to deepen the main channels, therefore, preventing the inlet s closure. However, less is known about the effect of dredging solutions on the inlet s behaviour, especially the addition of transverse channels to the main dredged channels in dredging solutions. Waves induce important changes in the hydrodynamics inside the Óbidos lagoon. The effect of wave characteristics in the water levels inside the lagoon was studied using a fully-coupled hydrodynamic and wave model. The water levels increased with growing wave peak periods (up to 5 cm) and with the mean wave direction perpendicular to the coastline. The impact of the full interaction between waves and currents on the sediment dynamics in the Óbidos lagoon was also investigated. This study concludes that the sediment transport during the flood towards the lagoon increases 30% if the previous interaction was considered by the numerical model. The three dredging plans were assessed by implementing and exploiting a morphodynamic model. The new dredging plans increased the tidal prism and reduced the differences between the ebb and flood durations mainly due to the southern and northern main channels. The transverse channels increased the accretion of the southern main channel and promoted the stability of the northern main channel. However, due to the shallow depths and the very energetic wave regime, dredging solutions are unable to permanently stabilize the Óbidos lagoon. Keywords: Morphodynamic model, Dredging, Wave-induced processes, Tidal inlets, Transverse channels, Dredging equilibrium depth Introduction The strong influence of waves and tidal currents on the Óbidos lagoon is evidenced by the morphodynamic changes that are presented in its inlet. This lagoon has a limited tidal prism and displays a flood dominant behaviour, as a result, its inlet is mainly driven by the sediment transport induced by waves. Due to its fragile equilibrium, along the years, the inlet frequently shoals (Oliveira et al. 2006). The shoaling to the northern and southern margins in the last decades puts in risk the neighbour constructions. Dredging solutions were implemented to prevent further shoaling and to maintain the lagoon opened to the sea (Oliveira et al. 2006). However, the dredging solutions were not sufficient to prevent the inlet closure in January This study aims at contributing to the coastal management decisions, with a major focus on the hydrodynamics, by studying the influence of waves on the Óbidos lagoon, and on the morphodynamics, by assessing the morphological evolution of three dredging plans. To achieve the previous goals and due 1

2 to the complexity of the coastal systems it was decided to use a morphodynamic model that works in an unstructured grid and makes its computations in parallel. This study is divided into seven sections besides this introduction. Section 2 characterizes the Óbidos lagoon. Section 3 describes the morphodynamic model used in this study and verifies the morphodynamic model against wave, water level and bathymetry measurements. Section 4 studies the influence of waves on the Óbidos lagoon. Section 5 assesses two dredging plans, comparing both with the dredging plan used in the last decade. This study ends with section 6 which summarizes the main conclusions. 1. Study site the Óbidos lagoon 2.1 Geomorphological setting The Óbidos lagoon is a shallow coastal system located in the western Portuguese coast with a small (less than 100 m) wave-dominated inlet which comprises the connection between the lagoon and the open-sea (Figure 1 - I). The average depth of this lagoon is 4,5 m below the mean sea level, it has a maximum width of 1,8 km and a total length between its inlet to the main tributaries of 4,5 km (Freitas et al., 1992). Morphologically, the Óbidos lagoon is divided in two zones: the upper zone and the lower zone (Figure 1 - II). The upper zone is constituted by cohesive sediments, while in the lower zone, the vast majority of sediments are sands with a sediment median grain diameter (d 50 ) ranging 0,4 to 0,8 mm (Fortunato et al., 2011). 2.2 Hydrodynamic setting Besides the Óbidos lagoon main tributaries, Vala do Ameal, Arnóia and Cal (A, B and C in Figure 1 I), the freshwater input is generally small as it represents less than 5% of the average tidal prism scaled by the M 2 period (Oliveira et al., 2006). In this region the wave regime is characterized by a significant wave height (Hs) larger than 1 m during 88% of the time, reaching 6 m in the maritime winter. The most frequent mean wave direction (Dir) is 315º N and the wave peak period (Tp) varies between 5 and 20 s (Bertin et al., 2009). The tidal regime is semidiurnal with amplitudes ranging between 2 to 4 m at the coast and 1 to 2 m inside the lagoon after the damping caused by the inlet (Oliveira et al. 2006). I II III Figure 1 - I General location of the study site; II Lower zone of the Óbidos lagoon; III Proposed solution for the Óbidos lagoon by Fortunato and Oliveira (2007a) 2.3 Past engineering solutions In such wave and tidal conditions, the inlet had displayed a fragile equilibrium during the last decades. Engineering solutions composed by traditional jetties had been proposed but were never implemented because they interrupt the littoral drift and cause a high visual impact. Fortunato and Oliveira (2007a) 2

3 proposed an innovative solution to stabilize wave-dominated inlets composed by a partially submerged guiding wall and an innovative dredging plan (Figure 1 - III). This dredging plan was constituted by two main dredged channels and seven transverse channels dredged over the tidal flats. The purposes of these transverse channels are: reduce the ebb duration, optimize the tidal asymmetry and increase the capacity of removing sediments from the flood-delta. This study assesses the morphological evolution through the comparison between three dredging plans: the dredging plan used in the last two decades proposed by the DHI (1997) (DP1), the dredging plan proposed by Fortunato and Oliveira (2007a) (DP2) and the dredging plan similar to (DP2) but with only one transverse channel (DP3). 2. The modelling system 3.1 General outline The morphodynamic model used in this study includes a hydrodynamic model SELFE (Zhang and Baptista, 2008), a wave model WWM-II (Roland, 2009) and a sediment transport and a bottom evolution model SED2D (Dodet, 2013) and its purpose is to simulate the sediment transport for noncohesive sediments in coastal areas considering the full interaction between waves and currents (Figure 2 - I). The unstructured grid used in this study was shared by the previous models and was derived from previous studies (Bruneau et al., 2011). The grid has elements and nodes with a spatial resolution between 1600 m on the sea boundaries and 6 m at the inlet (Figure 2 - II). Hydrodynamic boundary conditions are provided by the regional applications of the wave model WaveWatch3 (WW3) (Dodet et al., 2010), which gives the 2D wave spectrum (white stars in Figure 2 - II), and the tidal model (Fortunato et al., 2014), which computes the amplitude and phase for twenty harmonic constituents (white crosses in Figure 2 II). The initial bathymetry was measured in July 2001 (IH, 2001) and represents the bathymetry after the dredging plan implemented in May/June 2001 proposed by DHI (1997). I II Figure 2 I Morphodynamic numerical scheme; II Unstructured grid and bathymetry of July

4 3.2 The wave module WWM-II The WWM-II (Roland, 2009) is a phase-average wave model that solves the wave action density balance equation and was used in this study in a quasi-steady mode with a time step of 5 min to simulate the wave propagation from the ocean to the shoreline. In this study, the deep-water source terms were disregarded, the spectral discretization was done according to 12 frequencies from 0,2 and 0,05 Hz, the directional discretization was done according to 12 directions in a 180º window centred at the inlet, the bottom friction source term was set to 0,067m 2 s -3 (Hasselman et al., 1973) and the depth-induced breaking coefficient took the constant value of 0, The hydrodynamic module SELFE The SELFE (Zhang and Baptista, 2008) is a circulation model and in this study was used the depthaveraged barotropic version with the Boussinesq approximation which solved the 2D shallow water equations with a time step of 20 s. The coupling between SELFE and WWM-II was achieved through the radiation stresses that forced SELFE and by the currents that induced the wave shoaling in WWM-II. The bottom drag was done according to a quadratic friction law using a Manning coefficient variable in space (0,025-0,04 m -1/3 /s) followed the values in Bruneau et al. (2011) with a small increase at the inlet. A constant eddy viscosity of 1 m 2 s -1 was set in the domain to account for horizontal turbulence. The water depth threshold for drying was set on 0,01m and the Manning formulation threshold depth in 0,10 m. 3.4 The sediment transport and bottom evolution module SED2D The SED2D (Dodet, 2013) is a sediment transport and a bottom evolution model which simulates the sand transport using one of several semi-empirical formulae (in this study was used Van Rijn (2007a,b)) and computes the resulting bed-changes through the Exner equation with a time step specified on 20 s. Due to the empirical sediment transport formulas which originate spurious bathymetric developments, this model has three filters to prevent numerical oscilations: an extrema filter (Fortunato and Oliveira, 2000), a slope filter (Roelvink et al., 2009) and a diffusive filter (Fortunato and Oliveira, 2007b). In this study, the boundary conditions of SED2D were modified due to the continuously spurious bathymetries that were simulated at the northern coast. In resume, the entire boundary nodes were not updated each time step, this way, the waves will not reach the land grid boundaries and the spurious morphological developments were prevented. The d 50 variable in space (0,3-2 mm) followed Bruneau et al. (2011) with small modifications inside the lagoon, in the open-sea and at the inlet. 3.5 Verification of the morphodynamic model The models which constitute the building blocks of the morphodynamic model were individually verified against measurements. The wave model was verified during the period between 4 July and 21 October 2001 against three wave parameters: Hs, Tp and Dir recorded by an ADCP (black star in Figure 2 - II) placed at a bathymetric depth of 25 m (IH, 2001). The statistical error analysis showed the good performance of the wave model. The scatter index (SI) was 44% for Hs and 17% for the Tp while the root-mean square error for Dir was 19,8º. The hydrodynamic model simulations were compared through statistical error measures with the water elevations recorded by three tidal gauges (IH, 2001) located inside the Óbidos lagoon (yellow stars in Figure 2 - II) during twenty days (between 18 July and 6 August 2001). The comparisons illustrate the 4

5 accuracy of the coupled hydrodynamic-wave model with values of Skill between 0,91 (Cais do arelho - northern tidal gauge in Figure 2 - II) and 0,94 (Braço da Barrosa - eastern tidal gauge in Figure 2 - II). In what the concerns the remaining tidal gauge (Bico dos Corvos - southern tidal gauge in Figure 2 - II), the mean error was 0,42 m and this suggests a large error in this tidal gauge. Although, the comparison between the measured mean sea levels (MSL) between the three tidal gauges allows concluding that the measured reference level in the Bico dos Corvos was incorrect, thereby, the performance of the coupled numerical model was verified. The bathymetry simulated (Figure 3 I) between July and November 2001 with the morphodynamic model was compared with the measured one (Figure 3 II) in November 2001 (IH, 2001). The accuracy of this model was verified with the statistical error measure brier-skill score (BSS) (Sutherland et al., 2004) and with the comparison between the time series of M 2 amplitudes simulated and measured in Cais do Arelho tidal gauge similar to Bertin et al. (2009). The obtained BSS value of 0,47 clearly verifies the model s ability to represent complex morphological evolutions of the Óbidos lagoon. Qualitatively, the model could reproduce the shoaling of the transitional channel southwards, its final orientation northwards and the channels meandering inside the lagoon, although, the sand spit in the southern barrier island and the full shoaling of the northern barrier island were not reproduced (Figure 3 I and II). The comparison between the measured and simulated evolution of the M 2 amplitude in Cais do Arelho suggests that this morphodynamic model is able to reproduce the inlet enlargement until November and the further infilling. I II Figure 3 Simulated (I) and measured (II) bathymetries in November The effect of waves in the Óbidos lagoon 4.1 The influence of the wave peak period and the mean wave direction Regarding the coupling between SELFE and WWM-II it was investigated the influence of the wave parameters on the water levels inside the Óbidos lagoon. The simulations were performed during twenty days and the wave forcing was computed with a JONSWAP spectrum, constant in space and time. The amplitudes and phases of twenty harmonic constituents were computed with the regional model of Fortunato et al. (2014) and the water levels inside the lagoon were obtained near Cais do Arelho (northern 5

6 tidal gauge in Figure 2 - II). The forcing Hs was kept constant with a value of 2 m and the forcing Tp and Dir were changed between: 6, 9 and 12,5 s and 270, 315 and 360º N, respectively. I II Figure 4 - Top: Hs simulated in front of the inlet (5 (I) and 10 (II) m depth); Middle: SSE for a simulation without waves in front of the inlet; Bottom: Differences on SSE with a constant Hs of 2 m and Dir of 315º N (I) and constant Hs of 2 m and Tp of 9 s (II) when comparing with a simulation without waves The results show that a higher Tp will increase the water elevations inside the Óbidos lagoon (Figure 4 I). An explanation for this phenomenon is the group velocity, which corresponds to a term of the radiation stresses equations. A higher wave period will increase the group velocity. As group velocity increases, the radiation stresses increase too, and more momentum will be transferred to the water column which increases the MSL (Figure 4 I; bottom). Another explanation concerns the breaking type induced by different Tp. An analysis of the surf similarity parameter showed that for the same beach slope (β) and the same offshore wave height (H 0 ), the increase of the Tp will induce a different breaking type, therefore, the Hs in front of the inlet varies with Tp (Figure 4 I; top). In what concerns the Dir, the waves coming from 315º N had the higher Hs in the breaking zone and induced the higher increase on the SSE inside the lagoon (Figure 4 II). One of the phenomena subjected to waves when they travel to the coastline is the wave refraction. The waves with Dir of 315º N are less sensible to this phenomenon because more energy was concentrated in the breaking zone (Figure 4 II; top), therefore, the MSL will increase outside and further inside the lagoon (Figure 4 II; bottom). 4.2 The influence of waves on the sediment dynamics The combined effect of waves and currents plays a major role on the sediment dynamics of wavedominated inlets. When waves are propagating toward the lagoon, the ebb-currents can partially or totally block the wave motion. Besides analysing the wave blocking phenomenon in the Albufeira lagoon, Dodet et al. (2013) showed that if the numerical model takes into account the full interaction between waves and currents, the sediment transport towards the lagoon will increase during the flood. There are two coupling options between the hydrodynamic and the wave models: fully coupled (1) and partially coupled (2). In option (1), SELFE is forced with the radiation stresses from WWM-II, and the currents obtained by SELFE are considered by the WWM-II in order to reproduce the wave shoaling induced by currents. In the option (2), only the radiation stresses of WWM-II are considered by SELFE. To verify the wave blocking phenomenon in the Óbidos lagoon, the wave model was forced by a JONSWAP spectrum with a constant Hs, Tp and Dir of 2 m, 9 s and 315º N, respectively. The wave 6

7 blocking phenomenon will be addressed with two simulations of five days, each one with a different coupling option. The sediment discharge was computed with the Soulsby-Van Rijn (Soulsby, 1997) sediment transport formulation, which considers the wave-current interaction for the sediment transport. fully-coupled partial coupled Figure 5 - Comparison between a simulation with the coupling option (1) (red lines) and with the coupling option (2) (blue lines) for the Hs, sea surface elevations (SSE), wave orbital velocity (WOV) and sediment discharge (qtot) between the third and fourth days at the beginning of the flood delta The results (Figure 5) showed: the total wave blocking phenomenon as the Hs equals zero with the coupling option (1), the smaller wave orbital velocity during the flood for the coupling option (2) and the increase on the sediment transport during the flood towards the lagoon. Therefore, the wave blocking phenomenon was also experienced in the Óbidos lagoon which increases the importance of the full interaction between waves and currents in the numerical model to simulate realistic morphological evolutions. 4. Morphodynamic simulations for the three dredging plans 5.1 Qualitative comparison between the three dredging plans The DP2 and DP3 clearly change the behaviour and the morphological evolution of the inlet after five months (Figure 6). In average, the transitional channel depth, width and area become 25, 40 and 60% higher when compared with the DP1. These evidences reflect the characteristics of a more stable and ebbdominated inlet where the ebb-currents are the main agents that transport sediments seawards. (DP1) (DP2) (DP3) Figure 6 Bathymetries simulated for the three dredging plans over five months 5.2 Analysis of the tidal prisms and differences between ebb and flood durations The tidal prism is the volume of water that enters inside a lagoon during half of the tidal cycle and, in this study, was calculated in order to compare quantitatively the three dredging plans. The higher depths of the DP2 and DP3 lead to an average increase of 30% on the tidal prism volume during the simulated period (Figure 7 - I). The tidal prism is also associated with the inlet stability through the PA relationship (O Brien, 1969) and the results suggest that the DP2 and DP2 promoted the inlet stability comparing to DP1. 7

8 I DP1 DP2 DP3 II DP1 DP2 DP3 Figure 7 I Tidal prism time series for the DP1, DP2 and DP3 (black, red and blue lines, respectively); II Time series of the differences between ebb and flood durations for the DP1, DP2 and DP3 (black, red and blue lines, respectively) near Cais do Arelho tidal gauge Sediments deposited inside the lagoon are mainly transported seawards by the ebb currents. The differences between ebb and flood durations give a quantitative measure of the magnitude of the ebb currents because these currents will be stronger if the ebb durations decreased. The DP2 and DP3 also promoted faster ebb when compared with the DP3 (Figure 7 - II). In average, the differences during the study period were 60% smaller than the DP1, thereby, the DP2 and DP3 increased the sediment transport capacity seawards. 5.3 Balance of the sediment volumes during five months The calculation of the differences between the initial and final bathymetries for each dredging plan allows understanding the volumes of sediments that crossed the inlet (Table 1) and the eroded (blue) or accreted zones (red) inside the Óbidos lagoon (Figure 8). Table 1 Sediment volumes that crossed the inlet for each dredging plan Volumes (x10 4 m 3 ) DP1 DP2 DP3 Inside the lagoon (accretion) 19,3 24,1 22,0 Outside the lagoon (erosion) -24,9-26,3-24,6 Net balance -5,5-2,2-2,7 (DP1) (DP2) (DP3) Figure 8 - Differences between the initial and the final bathymetries for each dredging plan The results show that with the DP2 and DP3 the incoming sediments were mainly accreted in zones adjacent to the transitional channel. In DP2 the low efficiency of the western transitional channel lead to 8

9 it infilling during five months and the transverse channels addition improved the capability of the Óbidos lagoon to export sediments seawards by 6% when compared with the other two dredging plans. Overall, the differences between sediment net balances for the three dredging plans suggest that the accretion rate will decrease asymptotically until an the coastal system reach an equilibrium depth or the natural equilibrium profile, as suggested by Vicente and Uva (1985). 4.4 The application of the PA relationship to the Óbidos lagoon inlet Several empirical relationships are used to predict or to evaluate the stability of an inlet based, for example, on the tidal prism and on the area of the inlet cross-section. In this study, it was decided to perform the application of the PA relationship (O Brien, 1966) to evaluate the stability of the Óbidos lagoon inlet for the different dredging plans during the studied period. The spring tidal prisms and the cross-sectional areas were obtained at the inlet for each dredging plan with two bathymetries: July 2001 and November The stability curve presented in Figure 9 was made with the Jarret (1976) empirical coefficients of 5,02x10-4 for C and 0,84 for n and the right dot for each dredging plan represents the bathymetry of July 2001, while the left dot represents the bathymetry of November Figure 9 - Tidal prism-cross-section relationships for the three dredging plans The persistent behaviour displayed by the DP2 and DP3 with the same distance to the Jarret s stability curve and also the displacement of the DP1 dot in November 2001 suggest that the equilibrium curve for the Óbidos lagoon inlet is above the one draw with the coefficients of Jarret (1976). In this study, is therefore proposed an equilibrium curve (PA relationship) for the Óbidos lagoon inlet with the values of 2,9x10-3 for C and 0,75 for n. 5. Conclusions This study allows improving the present knowledge limitations in terms of the hydrodynamics and morphodynamics of the Óbidos lagoon and the conclusions are therefore enumerated: (I) inside the lagoon the SSE increased with growing Tp and this effect is explained by the dependence of the radiation stresses on the group velocity and also by the different wave breaking type induced by different Tp, (II) inside the lagoon the tidal SSE had their maximum when waves are coming from 315º N - up to 5 cm 9

10 when compared with other incidences and this increase is explained by wave refraction as more energy are concentrated in the breaking zone, (III) the wave blocking phenomenon in the Óbidos lagoon was verified and this phenomenon enhances the importance of the numerical models to take into consideration the full interaction between waves and currents, (IV) the application of the PA relationship to the different dredging plans suggest the equilibrium curve to the Óbidos lagoon has a value for C PA of 2,9x10-3 and 0,75 for n, and in the case of implementing the proposed dredging plan by DHI (1997), inlet cross-section should be increased by 100 m 2 to be closer to the previous proposed curve, (V) the higher depths of the new dredging plans (DP2 and DP3) increased the tidal prism and reduced the differences between ebb and flood durations, mainly due to the northern and southern main channels. Therefore, these channels must be included in future applications in the Óbidos lagoon with the configurations proposed by Fortunato and Oliveira (2007a) except for the bathymetric depth at the inlet which must be +0,0 m (HZ), (VI) the transverse channels in the southern main channel increased the accretion while the transverse channels located in the northern main channel enhanced the erosion. Hence, three transverse channels must be placed in the northern main channel with the configuration proposed by Fortunato and Oliveira (2007a). 6. Acknowledgements The author would like to thank the developers of SELFE, WWM-II and SED2D for making their source codes available. This work makes use of results produced with the support of the Portuguese National Grid Initiative; more information in 7. References Bertin, X., A. B. Fortunato, and A. Oliveira, (2009a). A modeling-based analysis of processes driving wave-dominated inlets, Continental Shelf Research, 29 (5 6). Bruneau, N., Fortunato, A. B., Dodet, G., Freire, P., Oliveira, A., & Bertin, X. (2011). Future evolution of a tidal inlet due to changes in wave climate, sea level and lagoon morphology (Óbidos Lagoon, Portugal). Continental Shelf Research, 31(18), Danish Hydraulic Institute, (1997). Projecto para a Fixação da Aberta da Lagoa de Óbidos. Hydraulic and Sedimentologic Studies. Design of a Dike/Channel System. Relatório Final. Dodet, G., Bertin, X., & Taborda, R. (2010). Wave climate variability in the North-East Atlantic Ocean over the last six decades. Ocean Modelling, 31(3), Dodet, G., Bertin, X., Bruneau, N., Fortunato, A. B., Nahon, A., & Roland, A. (2013). Wave-current interactions in a wave-dominated tidal inlet. Journal of Geophysical Research: Oceans, 118(3), Dodet., G., (2013). Morphodynamic modelling of a wave-dominated tidal inlet: the Albufeira Lagoon. PhD thesis, Université de la Rochelle. Fortunato, A. B., & Oliveira, A. (2000). On the representation of bathymetry by unstructured grids. Computational Methods in Water Resources XIII, 2, Fortunato, A. B., Bruneau, N. and Freire, P., (2011). Dragagem e defesa da margem Sul da lagoa de Óbidos. Resposta às questões levantadas em sede de declaração de impacte ambiental: Aplicação de 10

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