Beach response to multi-scale wave forcing and sea level variations 

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Wave-induced currents and undertow

Waves approaching the shoreline cause secondary fluid motions such as undertow and wave-induced currents, namely longshore and rips currents. All have the potential to contribute to sediment transport and lead to complex horizontal beach structures (Castelle, 2004).

Longshore currents

When the incidence of the swell is oblique, the waves induce a longshore current (Church and Thornton, 1993; Reniers and Battjes, 1997; Lippmann and Thornton, 1995; Kuriyama and Nakatsukasa, 2000) that can move large volumes of sediment from one location to another along the coastline. The amount of sediment transported by longshore currents is known as the littoral drift. Longshore current velocity depends primarily on the angle of the wave crest to the shoreline. But, the volume rate of flow of the current and transport rate depend on the breaker height (CERC, 1984). Longshore current velocity varies both across the surf zone and in the longshore direction (CERC, 1984). There are several formulations for the calculation of the longshore sediment transport associated with longshore current, e.g. of three of the most widely used: the Coastal Engineering Research Center CERC (CERC, 1984), Kamphuis (Kamphuis, 1991), Bayram (Bayram et al., 2007).

Rip currents

In the review by Castelle et al. (2016), rips currents are defined as « narrow and concentrated seaward-directed flows that extend from close to the shoreline, through the surf zone, and varying distances beyond ». Rip current flows are driven by alongshore variations in alongshore variations in breaking wave height that result from a number of different causes among which are the alongshore-variable surf-zone bathymetry, the wave energy focusing enforced by wave refraction over offshore bathymetric anomalies and the wave shadowing by a rigid boundary. Rip currents contribute to cross-cutting bars and thus to the instability of the bars along the coast, creating important sedimentary exchanges between surf zone and deep water. Rip currents can driven by swash processes, usually leading to small-scale rips (Castelle et al., 2016). In the surf-zone, Castelle et al. (2016) described six fundamental surf-zone rip current types based on the dominant controlling forcing mechanism. Hydrodynamically-controlled rip currents (shear instability rips and flash rips) are spatially and temporally variable in occurrence and exist solely due to hydrodynamic forcing mechanisms. Bathymetrically-controlled rip currents (channel rips and focused rips) are, for a given wave regime and tidal elevation, relatively persistent in space and time. Boundary controlled rip currents (Shadow rips and Deflection rips) are dominated by the influence of rigid lateral boundaries, such as natural headlands or anthropogenic structures (groynes, jetties), on their hydrodynamic forcing.

Undertow

The undertow is caused by shoreward movement of water and setup. The water that piles up at the shoreline is returned along the bottom (Davidson-Arnott, 2010a). The undertow can induce intense sediment transport offshore, especially during storms. This can expose the beach to erosion and cause significant movement of bars perpendicular to the shoreline.

Sediment budget

According to Davidson-Arnott (2010a) and Rosati (2005), the littoral sediment budget is a technique for estimating the amount of all inputs (called sources) and outputs (sinks) of sediment to a stretch of shoreline, in order to assess its long-term variability (interannual to decades).

Littoral cell

The coastal zone can be seen as a morphodynamic system composed of various sub-areas (cells), each with its own spatial and temporal scales. A sediment cell operates with alongshore wave energy gradients coupled with sediment availibility (Davidson-Arnott, 2010a). The shore-line erodes under negative longshore sediment balance, and advances when the sediment balance is positive.
The concept seems to have been applied first to the California coast (Inman and Frautschy, 1966; Bowen and Inman, 1966). In the Bight of Benin, West Africa, this concept has been applied by Laibi et al. (2014) and Anthony et al. (2019) to understand the erosion trend affecting the entire coast of this region. Littoral cells may often be largely isolated from adjacent one with boundaries such as headlands that are easily demarcated and cells. However, there can be exchange of sediment between adjacent littoral cells as the boundaries between them may be quite fuzzy, unlike coastal compartments. Littoral cell boundaries can be convergent, divergent or interruptive and it is possible to recognise sub-cells within major littoral cell units.
Before collecting information on sediment inputs, the starting point for the determination of a littoral sediment budget might be the identification of the cells and direction of net longshore sediment transport (Davidson-Arnott, 2010a). This approach provides a systematic framework for research on coastal processes and coastal evolution, and for the establishment of coastal management plans (Davidson-Arnott, 2010a).

Sediments sources and sinks

Inputs from rivers are probably the most important source, followed by cliff erosion, and in the tropics biogenic inputs from coral reefs may dominate. Many rivers around the world release large amounts of sediment at the coast. Although river bed transport is still difficult to measure, there are a number of good predictive equations for the total sediment discharges, e.g. Logah et al. (2017) for Volta river in the Bight of Benin. It is then easy to obtain an estimate of the order of magnitude of supply. However, this requires accurate measurements of sediment concentrations and river flows in the water column before the mouth. Other natural sources of sediment (dunes, inlets,lagoons, etc.) will be less important depending on the study site. In addition to the natural sources, human actions can have also contribute through activities such as jetty and seawall construction, and through dredging, beach mining and beach nourishment (Fig. 1.3).

Sea level variations at the coast

Understanding large-scale coastal evolution requires consideration of the sediment budget and sea-level changes as the dichotomy between their respective roles in coastal evolution be-comes blurred when they are weak and act in tandem (see Roy and Thom (1994), p.169). This section details the latest advances in understanding sea level dynamics on the coast.

Global mean sea level

Since mid- and late 19th century, tide gauges have been used to measure mean sea level along continental and island coasts (Cazenave and Le Cozannet, 2013). Since the early 1990s, high-precision altimetry satellites have been providing regular measurements (orbital cycle of a few days to a few weeks) with almost global sea level coverage: Topex/Poseidon (1992-2006), Jason-1 (2001-2013), Envisat (2002-2011), Jason-2 (2008-), Cryosat-2 (2010-), HY-2A (2011-), SARAL/Altika (2013-), Sentinel-3A (2016-), Jason-3 (2016-), CFOSAT (2018-), Sentinel-3B (2018-). Tide gauges measure relative sea level variations with respect to the ground, while satel-lite altimetry measures « absolute » sea level variations in a geocentric reference frame (Cazenave and Le Cozannet, 2013).
Direct observations of sea level available from tide gauges and satellites show that sea level is rising (Jevrejeva et al., 2008; Nerem et al., 2010; Mitchum et al., 2010; Church et al., 2011). And it has doubled in the last two decades compared to the average rise in the 20th century as observed by Merrifield et al. (2009). They suggested that this cannot be attributed to decadal variations but rather reflects a recent acceleration in the global average rise (since the early 1990s). The main factors behind this rise in global mean sea level are the thermal expansion of sea water due to ocean warming, land ice loss and fresh water mass exchange between oceans and land water reservoirs. These contributions vary according to natural climate variability and global climate change induced by anthropogenic green house gas emissions (Cazenave and Le Cozannet, 2013).
Satellite altimetry has also revealed that sea level is not rising uniformly (Cazenave and Le Cozannet, 2013). Observations show that the rate of rise displays strong regional variations (Lombard et al., 2005; Meyssignac and Cazenave, 2012). Observed spatial patterns in sea level trends mainly result from changes in the density structure of the oceans associated with temper-ature, wind stress and salinity variations (Bindoff et al., 2007). The largest contribution comes from ocean temperature variations, except for the Arctic region. Salinity also plays a role (in particular in the Arctic) and, in many regions, partly offsets thermal expansion (Wunsch et al., 2007; Stammer et al., 2013). Tropical climate modes are often responsible of sea level variations at seasonal and interannual while coastally-trapped waves can be caused by wind stress vari-ability, atmospheric disturbances and variations in the intensity of oceanic currents (Polo et al., 2008; Ding et al., 2009).
Future projections based on physical processes indicate that global average sea level will almost certainly accelerate during the 21st century (Church and al., 2013). However, the magni-tude of this rise and its spatial variations remain uncertain due to uncertainties related to GHG emissions. In addition, the representation of climate change by more or less approximate models (due to the uncertainty inherent in the chaotic nature of climate variability) is still a scientific issue. Meyssignac et al. (2017) studied regional sea level variations between 1900 and 2015 us-ing a set of 12 climate model simulations. Their results showed that coastal tide gauge records contain contributions from many coastal and local processes that are either absent from the climate models or not properly resolved by them. These processes include wind-trapped coastal waves, local flooding, the hydrological influence of nearby river flows, and others. This remains an important issue, as coastal communities need reliable projections to prepare adaptation plans for future sea-level rise (Slangen et al., 2017; Meyssignac et al., 2017).

Local and short-term contributors to sea level at the coast

Variations in total water levels at the coast result from the superposition of variations in global mean sea level, regional sea level and local sea level (McInnes et al., 2016; Melet et al., 2016, 2018a; Slangen et al., 2017). As indicated in the previous section, changes in global mean sea level are driven by ocean global warming and the transfer of water mass from the cryosphere and land to the ocean. Regional-scale variations are mainly the result of changes in ocean circulation and associated ocean heat, variability in wind stress, atmospheric disturbances and variations in oceanic current intensity, salinity and regional mass distribution. Mass redistri-bution also leads to geoid changes that further impact regional sea-level variations (Tamisiea, 2011).
Other processes make additional substantial contributions to total water-level changes in the coastal ocean: astronomical tides, atmospheric surges, wind stress, oceanic currents and wave transformations in the surf zone (Melet et al., 2016, 2018a; Slangen et al., 2017). The atmospheric surges can be defined as changes due to surface atmospheric pressure and the displacement of surface waters by the wind, called wind set-up. Wave transformations in the surf zone include wave set-up, which is the time-mean sea-level elevation onshore the wave breaking point due to wave energy dissipation, and swash, which corresponds to the vertical fluctuation of the water line above the still water level induced by individual waves. Wave set-up and swash are particularly responsible for the overtopping or overflowing, occuring when individual waves pass over coastal defences or dunes because of swash, and when the mean water level is greater than the level of the land or defences, respectively, resulting in a continuous spillage of sea water on land (Melet et al., 2016, 2018a). And recent works showed that waves are dominant contributors to extreme sea levels at the coast (Serafin et al., 2017; Rueda and et al., 2017; Vitousek and et al., 2017) and can strongly modify the coastal effects of thermal expansion and land ice loss on coastal water-level changes at interannual-to-multidecadal timescales (Melet et al., 2016, 2018a).
Taking all of these contributions into account, it remains difficult to predict sea level variabil-ity over shorter periods (season to decade) on the coast (Melet et al., 2016), as little attention has been focused on it. Only few locations in the western equatorial Pacific Ocean are available for statistically based operational prediction schemes of sea level anomalies at of interannual and seasonal scales (Chowdhury et al., 2007; Chowdhury and Guard, 2014). Nevertheless, some work (McIntosh et al., 2015) has shown the capability of physical-based models to address the challenge of providing skillful forecasts of seasonal sea level fluctuations for coastal communities over a broad area.

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Monitoring sea level at the coast

Observations from tide gauges, satellite altimetry and less developed methods such as new radars are essential for sea level monitoring. However, these devices are not adapted to the same environments and does not measure the same sea level components.
• Altimetry: Sea level variations are now well quantified by satellite altimeters, both in terms of global mean and geographical distribution. However, satellite altimetry, optimised for the open ocean, is poorly performing at less than 10 km from the coasts because land masses disturb the radar signal (Cipollini et al., 2017). New processing schemes (Marti et al., 2019), combining ALES retracked altimetry data (Passaro et al., 2018a,b) and geophysical corrections dedicated to coastal areas (Birol et al., 2017) allow to get a little closer to the coasts (up to 3 km). But, undergoing transformations of waves and sea level within depths of less than 10 m stil remain out of range.
• Tide gauges: There are several technologies used in tide gauges: pressure, acoustic and radar systems (Intergovernmental Oceanographic commission (IOC), 2006). Tradi-tionally, tide gauges around the world have been mainly devoted to tide and mean sea level applications. This implies that any oscillation between wind waves and tides has not been considered a priority, and in fact has not been properly monitored, due to the standard sampling time of more than 5-6 minutes. And most tide gauges are limited to deep water or sheltered harbors and omit part of the natural total sea level variability at open coasts (Melet et al., 2016). The new radar gauges have capabilities to monitor wave contribution to sea level variations, but there is still a challenge in understanding wave effects on these sensors.
• Field experiments: One of the best solutions for monitoring water level variations along the continental shelf to the coast remains field experiments. However, intensive nearshore field experiments with high spatial and temporal sampling rates are limited and expensive. Bathymetric surveys with echo sounders are time consuming and often contain data gaps between the bathymetry and the topography, especially in the micro-to mesotidal regimes.
There is still an observational gap in our knowledge of total sea level propagation across the shelf to the shore (Cipollini et al., 2017). One of the objectives of this thesis is to make a contribution to this knowledge gap. This gap is in the region that represents the main interface between our society and the ocean, i.e. the coastal zone. It is therefore very important to be able to link altimetry observations from the open sea to measurements made on the coast (tide gauges, radar, etc.). This generally holds for most major recent studies dealing with sea level at the coast (Melet et al., 2016; Idzanovic et al., 2018a; Birol et al., 2017; Melet et al., 2018a; Marti et al., 2019).
Sea level rise variations can have significant impacts on coastal zones. The most immediate impact of sea-level rise and local extreme sea level events is the increased risk of coastal flooding and submergence (Nicholls and Cazenave, 2010). Longer-term effects to sea level rise also occur as the coast adapts to new conditions, including increased erosion and saltwater intrusion into groundwater. In particular, sandy beaches are receiving particular attention, due to their po-tential sensitivity to sea level variations and at least 24% and up to 70% of the world’s beaches are already chronically eroding, albeit with large regional and local differences (Le Cozannet et al., 2019). Coastal wetlands such as salt marshes and mangroves will also decline if the sedi-ment supply remains insufficient to keep pace with sea-level rise (Nicholls and Cazenave, 2010). However, the response of coastal systems to sea level rise is highly dependent on local natural and human settings.
There are two main classes of models that can be used to study and predict the impact of sea level rise on the coast: the Bruun rule (and improvements) and the Probabilistic Coastline Recession (PCR). The Bruun rule and its variants are the most commonly used and histori-cal approach to assess sea-level rise impacts on shorelines (Bruun, 1962b; Shand et al., 2013; Le Cozannet et al., 1962; Dean and Houston, 2016; Atkinson et al., 2018). It assumes a landward translation of the beach profile as sea level rises. The PCR model is a recently introduced ap-proach that quantifies sediment losses at the dune toe during storms, as well as the nourishment of the dune by aeolian sediment transport processes between storms (Ranasinghe et al., 2012a). Over multi-decadal timescales, the superimposition of unchanged storms with rising mean sea levels results in more frequent and larger sedi-ment losses in the PCR model. The Brunn rule and the PCR models are not only based on different assumptions regarding the physical pro-cesses guiding the response of sandy shorelines to sea-level rise, but they also provide different results (Ranasinghe et al., 2012a; Toimil et al., 2017). For instance, Le Cozannet et al. (2019) showed that for most of the world’s beaches, structural uncertainties due to the choice of coastal impact model can be expected to have a significant impact on projections of shoreline change.
There are many studies in the literature on the response of coastlines and beaches to sea level rise (Nicholls and Cazenave, 2010; Cazenave and Le Cozannet, 2013; Le Cozannet et al., 2014; Le Cozannet et al., 2017; Leatherman et al., 2017). But, the literature on the impact of short-term sea level variations (10s-days to years) on coasts is scarce, as it is thought that at these time scales, waves, tides, sedimentary processes, and anthropogenic factors drive beach changes that surpass sea level impact (Stive, 2004; Ranasinghe, 2016). However, the coastal impact of short-term sea level variations may not be negligible and must be taken into account (Komar and Enfield, 1987). But, how they operate in the coastal zone is still a scientific issue (McInnes et al., 2016). There are only a few pioneering studies that showed the importance of short timescale variations in sea level on the coast, e.g. Segura et al. (2018) which studied the impact of seasonal sea level variations on a reef-fringed beach. Such studies are necessary and need to be intensified, especially since coastal environments are very different from one to another. That’s part of what’s going to be done in this thesis.

Table of contents :

1 Background 
1.1 Introduction
1.2 Contributors to beach changes
1.2.1 Waves and beach morphology
1.2.2 Storms
1.2.3 Wave-induced currents and undertow
1.2.4 Sediment budget
1.2.5 Sea level variations at the coast
1.3 Measuring beach changes and profile
1.3.1 Several techniques for measuring beach morphology
1.3.2 Altimetry and video for continuous coastal monitoring
1.4 Shoreline model review
1.4.1 Modeling shoreline changes driven by longshore transport
1.4.2 Modeling shoreline changes driven by cross-shore transport
1.4.3 Longshore and cross-shore integrated model
1.5 Conclusion
2 Study area, methods and data 
2.1 Introduction
2.2 The Bight of Benin, Gulf of Guinea
2.2.1 Location and general overview
2.2.2 Oceanic forcing
2.2.3 Harbors and coastal infrastructure
2.2.4 River discharges
2.2.5 Grand Popo beach, Benin
2.3 Data
2.3.1 The Grand Popo 2014 field measurements
2.3.2 Waves from Era-Interim global reanalysis
2.3.3 Tide gauge and FES2014 model
2.3.4 Satellite measurements
2.3.5 Video-based station, images and processing
2.4 Conclusion
3 Depth inversion and sea level from video 
3.1 Introduction
3.2 New approach in the temporal method of estimating wave celerity
3.2.1 Approach statement
3.2.2 Validation of video-derived depths
3.3 Error proxies in video-based depth inversion: temporal celerity estimation
3.3.1 Background
3.3.2 Depth Error Estimates
3.3.3 Kalman filter
3.3.4 Results
3.3.5 Discussion
3.3.6 Conslusion
3.4 Sea level at the coast from video-sensed waves
3.4.1 Background
3.4.2 Water level estimation
3.4.3 Results
3.4.4 Discussion
3.4.5 Conslusions
3.5 Conclusion
4 Beach response to multi-scale wave forcing and sea level variations 
4.1 Introduction
4.2 Beach response to wave forcing from event to inter-annual time scales
4.2.1 Background
4.2.2 Methods
4.2.3 Results
4.2.4 Discussion
4.2.5 Conclusions
4.3 Beach adaptation to intra-seasonal sea level changes
4.3.1 Background
4.3.2 Sea Level Data
4.3.3 Intra-seasonal sea level forcing
4.3.4 Detection algorithm for intraseasonal sea level event and Kelvin waves
4.3.5 Intra-seasonal beach response
4.3.6 Influence of intraseasonal sea level variations on beach morphology
4.3.7 Conclusions
4.4 Conclusion
5 The Bight of Benin coast evolution from 1990 to 2015
5.1 Introduction
5.2 Sedimentary cell dynamics in the Bight of Benin
5.3 Trends in shoreline evolution
5.4 Causes of shoreline mobility in the Bight of Benin
5.4.1 EOF Analysis
5.4.2 Longshore sediment transport, coastal infrastructures and rivers sand supply
5.4.3 Influence of South Atlantic climate dynamics
5.4.4 Localized sand mining
5.4.5 Outer shoreface/inner shelf sand supply
5.4.6 Future management and climate change
5.5 Conclusion
6 Modeling regional coastal evolution 
6.1 Introduction
6.2 Data form employed
6.3 Modeling regional coastal evolution
6.3.1 Background and theoretical formulations
6.3.2 Model set-up
6.3.3 Model calibration
6.3.4 Model validation
6.4 Simulation results for selected scenarios
6.4.1 Overview
6.4.2 Transport pattern without harbor structures
6.4.3 Nourishment to remedy downdrift erosion
6.4.4 Influence of reduced boundary transport
6.5 Discussion
6.6 Conclusions
Conclusions and Future Research

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