The Maldives archipelago, shown in Fig. a, is located to the south-west of the Indian subcontinent. Bounded by the 2000 m bathymetric contour of the Chagos–Laccadive ridge, the archipelago ranges over approximately 1000 km from north to south and 150 km from east to west. The 22 atolls that form the Maldives archipelago each have their own unique characteristics and range in size from a few kilometres to tens of kilometres , encompassing thousands of individual reefs and more than 1200 low-lying islands . None of the islands exceed more than a few metres in height above current sea level. The most prominent feature of the Maldives archipelago is the arrangement of the double chain of atolls in the central zone of the archipelago separated by the Maldives inner sea with depths typically in the range 300–500 m . Even though there have been a limited number of studies, the geological features of Maldives coral atolls and their formation have been discussed since observations obtained from field expeditions in the late 19th and early 20th centuries e.g. as well as more recent studies in the past few decades e.g..

Located in the doldrums, the Maldives does not generally experience major storms, and the climate is primarily influenced by the seasonal fluctuations of the South Asian monsoonal wind patterns, with the wind speed averaging 5 m s-1 for both the north-eastern and south-western monsoons. The archipelago experiences a semidiurnal microtidal regime with a tidal range of approximately 1 m . The combined tidal- and wind-driven currents can exceed speeds of 2 m s-1, particularly in the channels separating the atolls, along the ocean-facing flanks of atoll rims and through gaps in atoll rims . The absence of major storms and relatively low wind speeds across the archipelago suggest that the currents across the archipelago, particularly in areas of deeper water, are mainly driven by tides.

The impact of wind-driven sediment transport has been discussed in several studies, as presented in Sect. , particularly with respect to attempts to understand the formation of the Maldives, and the presence of faros in the atolls of the Maldives being attributed to the influence of changes in monsoonal wind patterns. However, studies such as that of , which attempted to statistically correlate the presence of geomorphological features in the atolls of the Maldives with various different geological parameters, found that wind speeds do not have a significant statistical correlation with the abundance of faros and lagoon reefs within the larger atoll basin. Further, the correlation between both the number of lagoonal faros and marginal faro areas with the wind stress were found to be statistically insignificant. Additionally, studies also show that the island shape influences the morphological change of the islands more than wave exposure . This provides more support to the argument that while winds dominate sediment transport processes in shallow areas of the atoll (which overall constitute a small area of the wider, deeper atoll basin, as illustrated in grey in Fig. b) the influence of wind decreases in deeper areas, with the tides being the major driver for sediment transport processes at these depths.

Malé atoll is an administrative unit in the Maldives archipelago located on the north-eastern side of the double chain of atolls of the Maldives archipelago and is comprised of the geographic atolls of Kaashidhoo, Gaafaru, and North and South Malé atolls. Kaashidhoo atoll, classified as an oceanic platform reef, is separated from the other parts of the administrative unit by deep channels exceeding 500 m separating the atoll on all sides. Due to the distance from the main geographical areas of the administrative atoll and its distinct nature, Kaashidhoo atoll was not included in this study.

Gaafaru atoll, seen in Fig. b, also classified as an oceanic faro , is a small atoll 15 km in width and 8 km in length with a surface area of 88.50 km2. The atoll, similar to other atolls classified as oceanic faros across the country, is significantly smaller than the larger more complex atolls. The outer rim of Gaafaru atoll has no major openings besides two channels in the north of the atoll. The only island in the atoll is Gaafaru island to the south-east, and no other lagoon or faro exists in the atoll. The atoll is separated from North Malé atoll by the narrow, deep channel Hani Kandu which is 3 km wide with depths of up to 160 m in the central region of the channel . We include Gaafaru atoll in the simulations conducted here because field studies suggest that smaller atolls of the archipelago have different characteristics compared to the larger more complex atolls in terms of their response to changes in tides and wind patterns.

North Malé atoll and South Malé atoll, seen in Fig. b, are both large complex atolls making up the bulk of the area of the administrative unit of Malé atoll. The larger North Malé atoll measures 60 km in length and 40 km in width with a surface area of ∼1623.92 km2. The atoll contains more than 189 individual reefs for a total reef area of 349 km2 . The atoll has numerous faros, particularly concentrated in the southern and the northern regions of the atoll, with the faros found in the southern zone being more shallow and prominent. The atoll also consists of numerous islands, both natural and reclaimed. The southern islands of the atoll, which include the major islands of Malé (the capital island of the country), Hulhulé, Hulhumalé and Vilingilli, are home to more than 150 000 people, which represents more than a third of the population of the entire country. To accommodate the socio-economic changes that have occurred over the past few decades, fuelled largely by the tourism industry, almost all islands in the atoll have experienced coastal modifications in terms of both harbour construction and land reclamation activities, with nearly half of all the currently existing land being reclaimed . This makes the location an ideal setting within which to consider the impact of such anthropogenic modifications.

South Malé atoll is separated from North Malé atoll by a 5 km wide channel Vaadhoo Kandu, with depths of close to 400 m in its central regions . South Malé atoll has a surface area of ∼558.31 km2. The atoll also has numerous reefs with 112 individual reefs identified , with a combined area of ∼175.60 km2. However, unlike North Malé atoll where the outer rim is cut with numerous channels, the outer rim of South Malé atoll is more continuous with fewer channels separating the outer rim. While South Malé atoll has also seen extensive land reclamation, these activities at large scale have occurred only in the last few years, and the changes are thus not included in this study. However, sediment grain size data available for the atoll were used as the main source of observational data to derive the grain size tidal proxy.

The bed sediment of the coral atolls of the Maldives archipelago has been examined by several studies at the local scale across individual reefs, as well as at a regional scale spanning one or more atolls, mainly for the purposes of better understanding the formation of the archipelago . However, the correlation between bed sediment type and flow patterns in the Maldives archipelago has been known since . With the sediment entirely devoid of terrigenous input due to the distance from major landmasses over the past 55 Myr , most bed sediment studies in the archipelago have focused on identifying the biological composition of the benthic surface, with a minimal number of studies focusing on sedimentary dynamics, especially at regional (atoll) scales e.g..

In this study we use the Thetis coastal ocean model, a 2D and 3D flow solver constructed using the Firedrake finite-element solver framework . Here we use the 2D implementation of Thetis which solves the depth-averaged nonlinear shallow water equations in non-conservative form, given by 1∂η∂t+∇⋅(Hdu)=0,2∂u∂t+u⋅∇u-ν∇2u+fu⟂+g∇η=-τbρHd, where η is the free surface displacement (m), Hd is the total water depth (m), u is the depth-averaged velocity vector (m s-1) comprising u and v in the x and y directions respectively, and ν is the kinematic viscosity of the fluid (m2 s-1). The term fu⟂ accounts for the Coriolis force, where f=2Ωsin⁡(ζ), with Ω the angular rotation of the Earth, ζ the latitude and u⟂ the velocity vector rotated 90∘.

The model uses a discontinuous Galerkin-based finite-element discretisation (DG-FEM), specifically the P1DG–P1DG finite-element pair where piecewise-linear discontinuous function spaces are used to represent both the velocity and the free surface prognostic fields. For time-stepping, a Crank–Nicolson approach is applied with a constant time step of Δt=45 s. The model treats wetting and drying according to the formulation of , which introduces a modified bathymetry h̃=h+f(Hd) to always ensure a positive total water depth, with f(Hd) defined as 3f(Hd)=12Hd2+α2-Hd, where H is the water height, and α is a tunable constant. Bed shear stress τb is implemented through the Manning's n formulation 4τbρ=gn2|u|uHd1/3.

All simulations were carried out for the period of 00:00 1 January 2018 to 24:00 5 January 2018, which corresponded to a spring tide in the region. A further 2.5 d of simulation was included at the start to allow for the model dynamics to spin up from a state of rest. The wetting and drying constant α parameter was set to 0.5 m, and the tidal model was forced with 11 tidal constituents (M2, S2, N2, K2, O1, P1, Q1, M4, MS4 and MN4) at the open boundaries interpolated from the TPXO database . Harmonic analysis of long-term tide gauge data of the region have identified these constituents as having significant contributions to the combined tidal amplitude in the region .

In order to select the most appropriate domain extent (i.e. distance to the open forcing boundary) and mesh resolution pattern in space, a sensitivity study for these choices was conducted through a series of numerical experiments, using the meshes in the configurations summarised in Table . The correlation of the simulation data to observations and between simulations was studied through the use of the correlation coefficient R defined as 5R=∑n=1N(On-O‾)(Mn-M‾)∑n=1N(On-O‾)2∑n=1N(Mn-M‾)2, where N is the number of data points, On and Mn are the observed and modelled values, and O‾ and M‾ are the means of the observed and modelled values respectively. As described below, we used the correlation coefficient to identify the appropriate resolution for the mesh in order to represent the bathymetry within the domain and also to investigate the sensitivity of the simulated tidal amplitude to mesh resolution and distance to the open (i.e. forcing) boundary.

The correlation coefficient is indicative of the linear least squares fit between the modelled and observed values and has been used widely for sensitivity studies of ocean models . The square of the coefficient, R2, provides a measure of the variation between the observed and modelled values ranging from 0 for no correlation up to 1 for perfect correlation.

Field data , illustrated in Fig.  and described in Sect. , were further analysed using the GRADISTAT software to calculate the d50 values, following the procedure adopted by . The d50 value, which represents the particle diameter representing the 50 % cumulative percentile value, is often used as a representative particle diameter for larger particle groups. Due to the limited number of field points (38 in total), all field points were used.

To develop the grain size tidal proxy, the modelled peak bed shear stress in floods was calculated using Eq. () and is shown in Fig. a. Due to the absence of a large inland mass to obstruct the flow, it is difficult to define the flood and ebb simply in terms of the reversal of tidal current patterns in coral atolls of the Maldives archipelago; rather we find the rise and fall of water elevations to be more appropriate. While previous studies have used different Manning coefficients for the numerical model and for calibrating bed shear stress for sediment e.g., here we find that the same Manning coefficient of 0.025 s m-1/3, which provides drag coefficients described in Sect. , gives results which are comparable to field observations. Next, shear stress values from the model, interpolated at the locations of field data points, were plotted against the calculated d50 values from field data; this is shown in Fig. . Due to the limited number of field observations, a line was fit through the maximum of the bed shear stress values obtained for the simulation. The corresponding peak stress value for the maximum grain size for each sediment class was then obtained as summarised in Table , following the grain size classification scheme used in earlier field studies . However, given the large values obtained at larger grain sizes in two different clusters, larger grain sizes in the range exceeding 2 mm were further split into two classes.

While it is clear that global mean sea level is rising e.g., the extent and rate of sea level rise is the subject of significant ongoing research. Analysis of long-term tide gauge data at Hulhulé Island harbour indicates a current local mean sea level rise of ∼ 4.46 mm yr-1, with an accelerating trend, which is in line with recent studies which quote a SLR rate of 3.93 mm yr-1 over the period 1993–2018 for the Indian Ocean and the South Pacific obtained from observations of sea level . Some sources predict a global rise of 0.75 to 1.9 m by 2100 , while others predict much larger increases in sea level . The Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC) proposes that a SLR of 1.0 m is unlikely before 2100 . Additionally, studies of glaciological conditions leading to sea level rise indicate that a rise of more than 2 m is unlikely . Reflecting this, studies incorporating sea level rise scenarios have used varying rates of increase when studying impacts using numerical models. used a 5 m rise in sea level to study the response of shelf seas to SLR, used a SLR of 2 m to study the response of tides in the Bohai Sea, and used successive rates of SLR up to 2 m to study the response of tides to SLR in a tidal bay. In line with these studies as well as , which suggests the use of a global total SLR of 2 m for planning purposes in the 21st century, in this work we also consider a SLR of 2 m. This is an important figure as the islands of the Maldives generally have maximum heights of just over 2 m above sea level. Here we make the simplifying assumption that coastlines remain unchanged during the SLR process. This assumption holds true for many of the current coastlines of North Malé atoll, which are completely or partially protected by artificial barriers. While at other locations this assumption is admittedly hard to justify, we feel this is a reasonable and reproducible choice that avoids the addition of further uncertainties over how the coastlines will respond naturally and anthropologically to SLR.

The bed shear stress values obtained in the tidal model, and their classification into the dominant sediment classes using the bed shear tidal proxy developed above, are shown in Fig. .

Qualitatively, the model results compare well with the previous studies described in Sect. . Model results show that the atoll basin is primarily composed of sand. In contrast, regions experiencing high-flow velocities, particularly the outer flanks of the atoll rim, the inter atoll channels, openings along the atoll rim (channels), and the flanks of the steep oceanic lagoons inside the atoll, are comprised of coarser sediment; this is consistent with observations by , and others.

At this resolution, the model also distinguishes sediment particle sizes within individual lagoons, with shallow exposed areas of the lagoons consisting of coarse particles, while the deeper, less exposed areas of individual lagoons are predicted to be comprised of fine particles, in line with observations of Felidhé atoll . Additionally, the presence of sand on the eastern side of Gaafaru atoll is captured by the model as a region of medium and fine sand pits surrounded by particles of coarser grain size. The absence of such sand pits on the western side of the island, where the bed sediment is predicted by the model to be dominated by particles of a larger size, correlates well with satellite data. However, as the sediment processes at these relatively shallow depths are influenced by a variety of other factors , further work is required to determine the origin of the discrepancy.

In addition, a qualitative comparison with bed sediment data gathered from environmental impact assessment surveys , which provide a limited bed sediment assessment of the region, indicates that the predicted grain sizes compare well with field data. Comparison of bed sediment type with field data at 56 locations around North Malé atoll shows that the model predictions match observations across all locations except for fine sand pits located around the vicinity of islands. This can be attributed to the fact that the model does not incorporate wave-driven sediment patterns which dominate sediment transport in these shallow areas .

Next, we classified the bottom bed sediment for the simulations carried out using the 1997 coastline scenario, as well as under SLR of 2 m. The same procedure described earlier was adopted and the changes in grain size were compared for each of the scenarios. Due to the vast majority of the coastal modifications occurring in North Malé atoll we focus on results for this region.

Satellite imagery indicates that the landmass of North Malé atoll has more than doubled from 10.85 km2 composed of 75 individual islands in 1997, to 26.51 km2 and 88 islands in 2018. Model results, shown in Fig. , predict that significant changes in grain sizes across the domain will have occurred as a result of coastline modification over the two decades. In general, the absolute difference in grain size class increase significantly in the immediate vicinity of areas where significant reclamation has taken place, including the lagoons of reclaimed islands. Significant differences in grain size class can also be seen around channels adjacent to major coastline modifications, arising from increased flow rates. Further, at this scale the model predicts large changes in bed sediment type at the island scale. For example, increased erosion patterns around the island of Kudabandos, observed since the large-scale reclamation of Hulhumalé island , is predicted well in the simulation (Fig. a1). The model simulation shows that increased flow rate in the channel between the artificial island of Hulhumalé and the island of Kanifinolhu is the major contributor to the increased erosion, arising from further reclamation of Hulhumalé Island in 2016 completely blocking the flow across the lagoon and forcing the flow through the channel only. This provides confidence in the model results which predicts similar patterns of change in bed sediment arising from coastline modification. The results also highlight that the location of the reclamation area is important in influencing the erosion and accretion patterns, and the impact of reclamation locations needs to be further studied in major reclamation projects to minimise future damage.

In addition to sediment change driven by artificial reclamation, the results also indicate that tidal sediment in the atoll can be driven by natural changes in the lagoons which are influenced by seasonal wind patterns. Figure  shows that the formation of sand banks (Fig. b) in the Maabadhi lagoon of the Dhiffushi channel, which are present in the 2018 satellite images but absent in the satellite image captured in 1997, causes changes in bed sediment in the vicinity of the lagoon. These results predict that natural changes arising from the monsoon wind patterns in the region can influence tidal sediment of the atoll basin in the vicinity of the locations.

Similar to the difference in grain size associated with coastline modification, a significant change in bed shear stress is observed with a SLR of 2 m, as seen in Fig. . No change is predicted by the model at the channel entrances because the bed sediment at the entrances is already at the coarsest level, but the dominant bed sediment class in the proximity of the major channels does change, as fine particles are swept away leaving more coarse sediment. The model also predicts widespread changes to sediment class at the rims of the lagoons and faros of the inner atoll basin. It is also interesting to note that areas of significant reclamation such as the southern regions of North Malé atoll are predicted by the model to show an increased response with SLR. However, this requires further study to be verified and could arise from the change in flow across the region which has a higher concentration of faros.

A comparison of the spatial extent of the predicted change in grain size from the two scenarios, shown in Fig. , indicates that artificial coastline change over a period of decades produces changes in bed sediment type which are comparable in magnitude to those due to long-term sea level rise. However, while changes associated with coastline change are more restricted to the vicinity of the modification itself, the predicted changes associated with SLR are more widespread.

These results agree with studies of other coral atolls around the world e.g., which highlights that the main changes driving morphological changes to islands are purely anthropogenic. Further, through the use of a high-resolution hydrodynamic model the results of this study predict that the effects of anthropogenic modifications to island coastlines are not only felt in the vicinity of the lagoons and island coastlines but are felt across the atoll with potentially far-reaching consequences. This provides further support to existing studies which show that coastal modification can severely weaken the ability of islands in coral archipelagos to naturally adjust to pressures, increasing their vulnerability to future changes in ocean and climate.

The main limitation of this study is the sparsity of available field data. While field data describing grain size for the domain were accessible, the data are relatively scarce. Availability of more field data would enhance the results. Furthermore, tide gauge data were only available for one location within the considered domain and this was located within a sheltered harbour. Additional tide gauge data would help to further validate the model results and increase confidence in the model set-up and corresponding simulation results.

Additionally, the model results as well as the bed shear stress are highly sensitive to the bathymetry. While this study was made possible by the newly available high-resolution bathymetry dataset , which contains data from a variety of sources collected over decades, it is likely that the bathymetry data will contain some errors which impact the final grain size approximation. Further, the inclusion of the changes to coastlines with SLR also needs to be included in the model to fully understand the impacts of SLR. This need is further demonstrated in this study, in that coastline modification at the island scale is shown to have a large impact across the atoll. To facilitate accurate studies, additional detailed bathymetry and coastline data for the region would be beneficial.

Finally, this study focuses on tidally driven large-scale bottom sediment classification within the larger atoll, with model performance comparable to observational data. To account for the shallow lagoon areas, wind-driven sediment can be incorporated into the model in future works; however, this requires field data currently not available for model set-up and calibration.