Evaluating dynamic mechanisms and formation process of freshwater lenses on reclaimed atoll islands in the South China Sea

Journal of Hydrology 584 (2020) 124641

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Evaluating dynamic mechanisms and formation process of freshwater lenses on reclaimed atoll islands in the South China Sea

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Chong Shenga,b,c,d, Dongmei Hane,f, Hehua Xua,b,c, , Fucheng Lia,b,c, Yunfan Zhanga,b,c, Yongqiang Shena,b,c,d a

CAS Key Laboratory of Ocean and Marginal Sea Geology, South China Sea Institute of Oceanology, Guangzhou 510301, China Innovation Academy of South China Sea Ecology and Environmental Engineering, Chinese Academy of Sciences, Guangzhou 510301, China c Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), Guangzhou 511458, China d University of Chinese Academy of Sciences, Beijing 100049, China e Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographical Science and Natural Resources, Chinese Academy of Sciences, Beijing 100101, China f College of Resources and Environment, University of Chinese Academy of Sciences, Beijing 100049, China b

A R T I C LE I N FO

A B S T R A C T

This manuscript was handled by Huaming Guo, Editor-in-Chief, with the assistance of Fereidoun Rezanezhad, Associate Editor

Groundwater on remote coral atoll islands in tropical oceans occurs in the form of freshwater groundwater lenses (FGLs) that serve as an important water resource for local inhabitants and ecosystems. Continuous recharge of freshwater from rainfall can flush out salt water and eventually create a FGL beneath the natural or reclaimed island. However, the process whereby a FGL grows in reclaimed islands, and the dynamic mechanisms and formation process are unclear. This study used numerical modeling for a reclaimed island in the South China Sea to evaluate the process of mixing between freshwater and saltwater, dynamic mechanisms, and the formation process of FGLs influenced by tidal action. Our results revealed that the long-term average flow lines of FGLs were superimposed by short-term tidal fluctuations beneath the atoll island. The tidal signals move rapidly inland from the lower aquifer and are then propagated upwards to drive the water level in the Holocene sediments. This causes an oscillation of the FGLs and increased mixing between salt and fresh water. The formation of the FGLs can be divided into three stages: preparatory, formation, and pseudo steady-state. Yongshu Island (a reclaimed island) was used as a case study. The island’s preparatory phase lasted approximately 2.5 years, and will take 20 years to form a stable FGL (with a thickness of about 15 m). Recharge rates, and the nature of the contact between the Holocene and the underlying Pleistocene aquifers, determine the shape of the FGLs beneath the island. Abstraction during the formative period of the FGLs will increase the time required to reach a stable state. The results obtained enhance the understanding of the formation of FGLs, and can provide a reference for the management of freshwater resources on atoll islands.

Keywords: Freshwater lens Reclaimed island Numerical simulation Yongshu Island Dynamic mechanism Formation process

1. Introduction Atolls are typically ring-shaped reefs surrounding, or partly surrounding, a relatively shallow seawater lagoon or a sinking volcano, and are usually associated with one or more small coral islands (Werner et al., 2017). Available information indicates that there are approximately 425 atolls in the world (Falkland, 1992), and most of them are located in the Indian Ocean, Pacific Ocean and Atlantic Ocean between 30° N and 30° S (Fig. 1a). Furthermore, over one million people live on these atolls (Falkland, 1991; Barnett and Adger, 2003; UNESCO, 2016). These tropical coral islands usually have a low elevation. When the recharge from rainfall exceeds the losses through evapotranspiration,

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discharge into the ocean and lagoon, mixing with underlying seawater, and groundwater abstraction for human use, a fresh groundwater lens (FGL) may form (Post et al., 2018a,b), and float above the denser, saline groundwater originating from sea water origin (Werner et al., 2017). These FGLs are a vital source of freshwater for terrestrial ecosystems and domestic consumption, especially during frequent (and sometimes lengthy) dry seasons. Therefore, it is important to understand the formation process and the internal dynamic mechanisms of FGLs (Underwood et al., 1992; Griggs and Peterson, 1993; Bryan et al., 2016). In the field survey undertaken by Falkland’s (1994) in the South Cocos (Keeling) atolls in the Indian Ocean, the smallest island with a

Corresponding author at: CAS Key Laboratory of Ocean and Marginal Sea Geology, South China Sea Institute of Oceanology, Guangzhou 510301, China. E-mail address: [email protected] (H. Xu).

https://doi.org/10.1016/j.jhydrol.2020.124641 Received 21 October 2019; Received in revised form 29 December 2019; Accepted 28 January 2020 Available online 04 February 2020 0022-1694/ © 2020 Elsevier B.V. All rights reserved.

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Fig. 1. Regional distribution of published FGLs in coral islands of the world (a), including the maximum thickness of the FGLs of different islands; (b) the distribution of major reclaimed islands in the South China Sea.

boundary conditions, which are crucial for the formation of FGLs (Dose et al., 2014; Stoeckl et al., 2015). Usually, no rivers or streams are found on atoll islands, and atmospheric rainfall is the only replenishment source for the FGLs. During the rainwater seepage, fresh water will flow to the island edge under the influence of the hydraulic gradient and continuously push the saltwater outward, enabling the persistence of the FGLs. Dose et al. (2014) and Stoeckl et al. (2015) verified FGL velocity field characteristics by using physical experiments combined with tracer tests. Underwood et al. (1992) used a variable-density numerical model (finite difference model) to further explore the effect of tidal action, and focused on the transition zone. They concluded that the vertical component of longitudinal dispersion, coupled with the vertical oscillations through the Pleistocene aquifer, will significantly affect the thickness of the transition zone. However, the larger longitudinal dispersion will intensify the mixing of fresh and salt water, and result in a thinner FGL, which is different from the behavior noted for continental coastal aquifers. For continental aquifers, longitudinal dispersion and transverse dispersion usually have the same contribution to the width of the transition zone (Abarca et al., 2007). Therefore, in many subsequent works on non-tidal atoll models, the dispersivity parameters were adjusted to compensate for the lack of tidal effects on the transition zone width (Ghassemi et al., 2000; Alam et al., 2002; Comte et al., 2014). Atoll islands are generally composed of two overlying aquifer formations, which comprise unconsolidated Holocene sediments deposited unconformably on Pleistocene limestone reef deposits (Ayers and Vacher, 1986; White and Falkland, 2010). This can be termed a “binary geological structure” (BGS). The contact between the Holocene and Pleistocene aquifers typically occurs at a depth of 10–25 m, and is known as the “Thurber discontinuity” or “Holocene–Pleistocene

FGL was about 270 m wide, under a recharge (W) of 1938 mm/y; if the island width is less than this value, the precipitation will quickly flow into the ocean and cannot form a FGL. Underwood et al. (1992) used numerical simulation to analyze the scale effect and concluded that if a threshold thickness of 2–3 m is required to maintain a developable lens, the minimum viable island width was about 250 m for a recharge rate of 2.0 m/yr. A series of surveys and studies about barrier islands have been also carried out in the East Frisian Barrier Island Chain in northwestern Germany recently (Röper et al., 2013; Holt et al., 2017; Post et al., 2019). The researchers found that a shallow freshwater lens can also be formed in such a barrier island and changed during the development of geomorphology. However, on such small islands, the FGL is connected to the sea water through the pores or karst caves, and the effects of tidal fluctuation on the FGL are direct and obvious. In coastal aquifers, tides influence the groundwater flow pattern, salinity distribution, and characteristics of groundwater flow to the sea (Werner et al., 2013). When a tidal signal travels inland, the amplitude reduction is quantified by the tidal efficiency (ε ), which is the ratio of the tidal amplitude of the groundwater to that of the sea (Hunt and Peterson, 1980). The time difference between high or low tide in the ocean and the peak or trough of the groundwater fluctuation is referred to as tidal lag (t τ ) (Hunt and Peterson, 1980). Both ε and t τ can reflect the characteristics of the groundwater velocity field and the stratigraphic structure of atoll islands (e.g., Carr and Kamp, 1969; Herman et al., 1986; Erskine, 1991; Underwood et al., 1992). The impacts of geological heterogeneity, spatially variable groundwater recharge, and rising sea levels on the geometry of FGLs has been addressed by Schneider and Kruse (2003), , Chui and Terry, (2013) and Gulley et al. (2016). However, few studies have considered the detailed flow processes within the FGLs, especially under tidal 2

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Fig. 2. Map showing the location of the Yongshu Island (a). The red points in the illustration are observation wells, (b) and (c) depict the typical drilling holes and geological cross section on Yongshu Island (modified from Sun et al., 2003; Zhu et al., 2014).

maximum volume and formation time of fresh groundwater that can occur beneath reclaimed islands. However, this study is more theoretical and the stratigraphic structure of the model was set randomly, which is in conflict with the actual situation for coral islands. In addition, limited by data availability and high computation requirements, the study also did not consider tidal boundaries and the shape of islands. On the basis of analytical models of islands proposed by Fetter (1972) and Vacher (1988). Hu and Jiao (2014) obtained steady-state analytical solutions for groundwater levels and the thickness of FGLs, assuming the reclamation site of a single zone of uniform hydraulic parameters. Previous studies mainly focused on natural islands, including the influence of climate factors, human factors, and sea level rise on the already formed freshwater lens (Alam and Falkland, 1997; Bailey et al., 2009; Chui and Terry, 2013; Bailey and Jenson, 2014). However, the formation process and dynamics mechanisms of FGLs remain poorly understood, especially in the case of reclaimed islands (Werner et al., 2017; Post et al., 2018a,b). While some works on the formation of island freshwater lenses have studied them physically, analytically, and numerically in detail (Fetter, 1972; Vacher, 1988; Dose et al., 2014; Stoeckl et al., 2015; Post et al., 2018a,b; Yao et al., 2019), few investigations have considered the effect of the tidal boundary during the formation process of the FGLs, particularly in the cases of some reclaimed islands. Furthermore, most of these previous works were conceptual and did not involve any realistic aquifer data or observation data. In order to overcome these limitations, it is also necessary to verify them using a practical case. As the pressure induced by climate change and population increase intensifies, the construction of reclaimed islands will become an increasingly popular method in the Small Island Developing States (SIDS). Furthermore, a systematic and comprehensive analysis of the formation process of FGLs can provide further information for future studies (Barnett and Adger, 2003). This study is the first to comprehensively characterize the groundwater flow system and formation process of FGLs for a reclaimed island in the South China Sea based on the previously-unpublished

unconformity” (Ayers and Vacher, 1986; Buddemeier and Oberdorfer, 2004; Werner et al., 2017). A report made by Cox (1951) on the Arno Atoll in the Marshall Islands, provided a comprehensive description of an atoll island dual-aquifer system. Vacher (1988) considered four general non-homogeneous cases including the BGS (Case C) and developed analytical models for each of them, which was verified by Dose et al. (2014). Therefore, a more reliable conceptual hydrogeological model can be considered a dual-aquifer system subjected to laterally and vertically propagated tidal signals. Examples of atoll islands with dual-aquifer systems include those in the Majuro Atoll (Marshall Islands), the Cocos (Keeling) Islands, the Diego Garcia Atoll, as well as the Yongxing Island (Xisha Islands) and the Yongshu Atoll (Nansha Islands). At present, many extensive islands have been created by filling the sea, and these artificial islands not only provide valuable space for urban development, but also can serve as valuable aquifers (Hu and Jiao, 2014; Yao et al., 2019). Examples of reclaimed land include, the largest artificial island, Palm Island, and its adjacent islands in Dubai that span a recreational area of about 80 km2; the rectangular reclaimed island of Kansai International Airport (38 km2) in Japan; about 76 km2 of reclaimed island in Singapore constructed for supporting its economic growth (Van Ginkel, 2015; Donchyts et al., 2016; Yao et al., 2019). Recently, reclaimed islands have also been constructed for others purposes in the South China Sea (Fig. 1b). Groundwater lenses beneath these reclaimed islands are analogous to those beneath natural islands (Werner et al., 2017), but differences exist. The difference between artificial islands and natural islands is manifested in their shape and the geological structure (artificial sedimentary sequence) created by multiple sources of filling materials and compaction technology (Yan et al., 2013; Alzaylaie and Abdelaziz, 2016; Yao et al., 2019). Van Ginkel (2015) discussed three artificial aquifers designs while constructing reclaimed islands and evaluated the efficiency of different mining methods. Yao et al. (2019) used a series of 3-D density-dependent flow and transport conceptual models (SEAWAT) to investigate the mixing process of fresh and salt water, and to quantify the potential 3

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observation and field data. A numerical model of variable-density flow and solute transport was established for the Yongshu Island, which is an exemplar system of reclaimed atoll islands (reclamation based on a dual-aquifer system) worldwide (Zhu et al., 2014). The main objectives were to (1) describe the dynamic mechanisms and formation process of the FGL of the Yongshu Island, (2) evaluate the impact of hydrogeological factors and abstraction on the formation process of the FGL, and (3) to compare the difference between tidal and non-tidal models, and further analyze the adaptability of different models. 2. Study area The study area is located on the Yongshu Atoll of the Nansha Islands (Latitude 9°37′ N, Longitude 112°58′ E) in the South China Sea. The Yongshu Island is a typical coral island (Fig. 2), but has been modified: its surface layer (3–4 m) is composed of artificially filled coral sand. The Yongshu Island reclamation project began in August 2014 and was finished in September 2015. Before reclamation, the land area, mainly located in the southwest region, was less than 0.2 km2. After reclamation, the Yongshu Island had a length of 3.71 km and a maximum width of 0.99 km, and had an area of 2.23 km2. The topography is flat and the elevation of the land surface is usually 3–4 m above the mean sea level (MSL). The construction project for reclaimed islands in the South China Sea adopted the overall technical routes of “natural simulation”. The building techniques used in the Yongshu Island generally involved cutter suction dredging (CSD) and/or trailing hopper dredging (THD). Large cutter suction dredgers were used to cut, pump loose coral gravel excavated in the surrounding lagoon or other parts of the reef, and fill or accumulate on the objective reef flat through a duct to form a foundation platform (Fig. 2a). Please find more details of this process in the website: https://amti.csis.org/maps/. Generally speaking, this process is very similar to the formation of natural coral islands, which mainly depends on storm or tidal waves to move and carry coral debris to form the island (Werner et al., 2017), but reclaimed islands have accelerated this process. Therefore, the permeability properties of the artificial coral sand for reclaimed islands is very similar to those of natural sands (Zhu et al., 2014; Jiang, 2018). In 1990, the Nanyong-1 engineering geological borehole was drilled on the reef flat in this small atoll. Having a depth of 152.1 m, it reached up to the early Pleistocene of the Quaternary Period (Zhao et al., 1992). Later, in 1994, the Nanyong-2 engineering geological borehole was drilled, reaching a depth of 413.7 m and progressing to the Miocene of the Tertiary Period (Zhu et al., 1997). According to drilling information (Fig. 2b), a seismic reflection time profile, and a borehole section (Fig. 2c) obtained for the island, the unconformity surface of the upper Holocene and lower Pleistocene aquifer is approximately 20 m below mean sea level (MSL) (Sun et al., 2003; Zhu et al., 2014). There are some sub-aquifers in the Holocene aquifer, caused by the transport of deposits by waves and tides. Although it differs in granularities and shapes, the lithology and hydrological properties do not change much across the region. Therefore, we regard them as a hydrogeological units (HGU). Furthermore, the upper artificial layer is mainly composed of coral sand, excavated from the lagoon and reef flat and shows some similarities to natural coral sand (Zhu et al., 2014; Jiang, 2018). The average temperature of the Yongshu Atoll is above 28.0 ℃ and the average daily or monthly variations and the difference between winter and summer temperatures are small. The lowest annual temperature (26.7 °C) is recorded in January, and the highest temperature (29.6 °C) appears in May. The average relative humidity of the Yongshu Island is 81%, and the extreme minimum is 51%, which occurs in January (Zhao, 1996). According to our groundwater monitoring data, variation in the groundwater temperature with time at different depths (−2 m, −5 m, −8 m, −20 m) is shown in Fig. 3 below. With the increase in depth, fluctuation in the water temperature becomes smaller and the temperature remains mainly between 26.5 °C and 28.5 °C. In addition, the temperature variation at different depths at the same time

Fig. 3. Variation of groundwater temperature with time at different depths of Yongshu Island (−2 m, −5 m, −8 m, and −20 m).

is less than 0.8 °C. Therefore, the effect of temperature on mixing between seawater and fresh water at different depths can be considered negligible. This is also the reason that we ignore the temperature boundary in our actual numerical simulation. The distribution of rainfall and evapotranspiration in the study area is shown in Fig. 4a. There is a small meteorological station on the island, and monitoring records were available for the monitoring period from September 2016 to June 2018. It can be seen that annual rainfall is abundant at the Yongshu Atoll but the distribution among the months is extremely uneven. The mean annual rainfall for this period was 2972 mm and the rainfall mainly concentrated from August to January of the following year, when 67% of the annual rainfall occurred. From February to May, there was a very little rainfall, which accounted for only 15.3% of the annual rainfall: thus, this period can be considered as the dry season on the island. In addition, the spatial distribution of rainfall was also uneven (Fig. 4b), because of some rainfall-catchment system on the airport runway and some buildings. The actual recharge of these region was established by referring to the report made by Gingerich et al. (2017). Due to equipment constraints, the potential evaporation data here were the surface evaporation data. The diameter of the surface evaporator was 618 ± 2 mm and a depth of 600 mm (look like Fig. 4a) and the accuracy of the water surface micrometer was 0.1 mm. The potential evaporation was calculated by the difference in the water level. Under the influence of monsoon and high temperature, the monthly average evaporation in the study area was only about 100 mm. 4

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Fig. 4. Monthly rainfall and potential evaporation (a) for Yongshu Island from September 2016 to June 2018. The potential evaporation data here obtains by the surface evaporator. (b) Tidal water level of Yongshu Island, the monitoring period here is over 2 880 h (120d).

Fig. 2c), the salinity of the groundwater at the depth of 2 m decreased to about 22.5 g/L in October 2016 (1 year later after completion of the land reclamation), while the observed salinities of the three wells at the depth of 5 m were 33.5 g/L, 27.7 g/L, and 23.6 g/L respectively. Two years after the reclamation project of the Yongshu Island, the salinities of the groundwater at the depth of 2 m of the wells N8, N7, and N6 were 18.2 g/L, 7.7 g/L, and 6.3 g/L respectively. Overall, the salinity of all observation wells on the Yongshu Island suggested brackish water, and no freshwater has been produced so far. At present, there are few residents on the island, and their drinking water is mainly obtained using a desalinator. Additional sources of potable water are rainwater–harvesting devices near the airport runway and on some rooftops. In addition, there are several pumping wells on the island, but the amount of abstraction is limited by the high salinity of the groundwater. Therefore, the Yongshu Island is an ideal island for studying the dynamic mechanisms and formation process of fresh groundwater lenses.

In general, the groundwater recharge to a coral island is not equivalent to the rainfall. The relationship between recharge and rainfall can be expressed as follows (Falkland and Woodroffe, 2004; Comte et al., 2014; Werner et al., 2017; Post et al., 2018a,b):

R = P − ET − ΔV

(1)

where R is the recharge [mm]; P is the rainfall [mm]; ET is the actual evapotranspiration [mm], and ΔV is the change in storage within the soil moisture zone [mm]. The water budget is calculated using long time steps (≥1 month) and the coarse nature of sandy material ensures that the field capacity is very low and does not allow water retention. Therefore, the available water content of the soil ΔV was usually neglected (Hunt and Peterson, 1980; Falkland, 1991; Comte et al., 2014; Werner et al., 2017; Gingerich et al., 2017). In addition, because the Yongshu Island is an artificial refill island, therefore the vegetation on the island is currently sparse. Surface runoff was neglected because of the high infiltration capacity of the soils, the flat topography, and the lack of surface flow features on the island. Roupsard et al. (2006) reported an excellent correlation between the actual evapotranspiration ET and the Penman–Monteith potential evapotranspiration ET0 for the Vanuatu Island, South Pacific (15° 26.6′ S, 167° 11.5′ E), which was verified by Comte et al. (2014) for Grande Glorieuse, according to the following equation.

ET = 0. 5086 × ET0 + 0. 6203 (R2 = 0.98)

3. Numerical model 3.1. Model set-up The numerical simulation used in the present study was carried out using SEAWAT ver. 4 (Langevin et al. 2008), a finite difference model developed by the US Geological Survey (USGS), which combines MODFLOW and the MT3DMS to simulate variable-density groundwater flow and solute transport and has been verified and used widely for simulating seawater intrusion. We used this code to solve the following coupled flow and transport equations (Langevin et al., 2008):

(2)

Using Eqs. (1) and (2), the monthly recharge R [mm] was calculated from the average monthly rainfall P [mm] (Fig. 4a). From the rainfallrecharge formula, the infiltration recharge was calculated to be 2150 mm per year, which is 72% of the rainfall. The study area is affected by the tropical weather system all year round. The most important wind field is characterized by the monsoon, which is characterized by the prevailing winter wind of the NE and the summer wind of the prevailing wind direction of the SW. In addition, it is also affected by the tropical cyclone, but it is mainly concentrated at 10° N. The tidal phenomena in the Yongshu atoll area are mainly dominated by tidal waves carried into the South China Sea by the Bashi channel in the western Pacific Ocean. The variation in the tidal fluctuation is generally no more than 1.6 m, and results in an irregular fulldiurnal tide (there is a high tide level and a low tide level every day) (Fig. 4b). Under the control of seasonal risk, the surface current has a prevailing NW direction in winter and a prevailing NE direction in the summer. The waves also show obvious seasonal changes. NE waves prevail in winter and S and SW waves prevail in the summer (Zhao, 1996). Our groundwater monitoring work started in October 2016, with data recording intervals of 30 min. At the time of investigation, the reclamation project had been completed for one year. In terms of the observation salinity data of the wells N8, N7, and N6 (shown as the

ρ − ρf ⎤ ⎞ ∂hf ∂ρ ∂C ⎛ ⎡ − ρs qs +θ ∇∙ ρKf ⎢∇hf + ∇z⎥ = ρSf ⎟ ⎜ ρf ∂C ∂t ∂t ⎣ ⎦ ⎠ ⎝

(3)

and

∂ (θC ) = ∇∙ (θD∇C ) − ∇ (θvC ) + qs Cs ∂t −3

(4)

where ρ is the fluid density (ML ), Kf is the equivalent fresh water hydraulic conductivity (LT−1), hf is the equivalent fresh water head (L), z is the elevation (L), Sf is the equivalent fresh water specific storage (L−1), t is the time (T), θ is the porosity (dimensionless), C is the dissolved salt concentration (ML−3), ρs is the fluid density in the source/ sink, qs is the source/sink flow rate (T−1), D is the hydrodynamic dispersion tensor (L2T−1), v is the pore water velocity (L/T), and Cs is the salt concentration in the sources/sinks. Long-term time series (i.e. decadal) of tidal boundaries are often not available where FGL studies are needed. This makes it difficult to calibrate 3-D models. Because when we want to simulate tidal boundaries, we usually need to split the time period into small intervals (e.g., 0.021 5

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Fig. 5. Modeling domain for the profile A–A′, discretized into a mesh comprising 6731 active cells. The specified head was expressed using a step function instead of the tidal boundary (Mulligan et al., 2011). The specified head can only change at the beginning of each stress period, and each stress period’s length was about 0.021 d (30 min).

d), so the model can “feels” the change of boundaries. This incurs a large computation time and requires high storage capacity. The other reason is that building and calibrating 3D models require substantial observation and aquifer data, if we don't have so much data, it will reduce the accuracy of numerical models. Therefore, the present study opted to work with a 2D model based on the profile A–A′ (Fig. 2) to provide an understanding of the main processes occurring in the FGL (Fig. 5). The cross-section had a width of 1400 m, including the island and reef flat. In the vertical plane, three distinctive geological structures were recognized: an upper layer of 20 m of coarse coral-derived carbonate sands, artificial coral sand, and an underlying cemented reef limestone. The model domain was mainly discretized into uniform finite-difference grids (10 m × 1 m), with 140 columns and 50 layers and 6731 active cells. The thickness of the first layer varied according to the surface topography.

3.2.2. Boundary conditions Fig. 5 shows the boundary conditions of the numerical model. The topmost layer was assigned to the specified flux boundaries and depended on the calculated recharge rate. In contrast, the boundary fluid pressure was specified along the reef and lagoon basement to simulate the presence of sea water, with source water at the nodes along these boundaries assigned a salt concentration of 35.0 g/L to represent sea water. The approach used for the addition of tidal boundaries is of note. The tidal model has very large computational requirements because of the short length of the time steps, which may be no more than 1.5 h so that the system can sense the effects of the tidal fluctuations (Underwood et al., 1992). Therefore, we chose the tidal signal measured for 2880 h (120 d) as the specified head condition (shown as Fig. 4b), and each stress period was 0.5 h. The specified head can only change at the beginning of each stress period, and therefore a step function was used to fit the tidal curve (look like Fig. 5) (Mulligan et al., 2011). Specifically, the complete tidal cycle was divided into 20 stress periods, each with a duration of 0.021 d (30 min). In addition, no-flow boundaries were assigned to the bottom of the mesh domain.

3.2. Initial and boundary conditions 3.2.1. Initial conditions FGLs usually form over long periods (20–150 years) (Comte et al., 2014; Holding and Allen, 2015), and it is difficult to conduct tidal simulation for such a long time without parallel computing clusters. Therefore, we used an iterative algorithm here to achieve a long-timescale simulation of tidal action: the simulation results (concentration and head distribution) of one stage were considered as the initial conditions of the next stage. As for the initial stage, before the FGL was formed, the initial concentration for the entire model was 35.0 g/L, and the initial head of the model was the mean sea level (0 m). After running the model for 120 d in the first stage with the tidal boundary, the second stage was reached, for which the steady-state salinity and water head distribution obtained from the previous operation were set as the new initial conditions (shown in Table 1). The model was then run until it reached a pseudo steady state was attained (where in salinity and water head of the FGL showed little changes, and these changes were periodic and tide-induced) (Underwood et al., 1992; Holding and Allen, 2015).

3.3. Model parameters Model parameters were mainly obtained by field or laboratory tests and from literature (Bailey et al., 2009; Bailey et al., 2014; Deng and Bailey, 2017; Jiang, 2018). Because the artificial coral sand is mainly above the groundwater table, the hydrologic parameters of this aquifer were obtained through laboratory experiments. However, the horizontal and vertical K of the Holocene aquifer were obtained by the pumping test undertaken by Jiang (2018). Parameters for the lower Pleistocene layer are difficult to obtain using pumping tests because of the extremely high K. Therefore, the initial K of the lower aquifer was based on results from a previous study on Maldives Atoll (Bailey et al., 2009; Bailey et al., 2014; Deng and Bailey, 2017), which was based on the considerations that the Yongshu Island is at the same latitude as the Maldives and the type of coral reef and genetic environment at these two locations are similar. Therefore, the hydrogeological parameters of the lower Pleistocene layer have certain similarities in both cases. The hydrogeological parameters assigned to the numerical model are

Table 1 Main features of the different model stages. Model Stages

1st stage 2nd stage 3rd stage Other stage

Initial conditions

Boundary conditions

Simulation time [d]

Initial heads [m]

Initial Conc. [g/L]

Specified head [m]

Conc. boundary [g/L]

0.0 Simulation results of 1st stage Simulation results of 2nd stage …

35.0 Simulation results of 1st stage Simulation results of 2nd stage …

Tide Tide Tide Tide

35.0 35.0 35.0 35.0

6

120.0 120.0 120.0 120.0

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Table 2 Hydrogeological parameters and solver setting for the SEAWAT numerical model. Steps

Parameter

Units

Value

Sources

Model setup

Domain length Domain height Porosity Specific yield Specific storage Recharge Artificial aquifer horizontal K Artificial aquifer vertical l K Holocene aquifer horizontal K Holocene aquifer vertical K Pleistocene aquifer horizontal K Pleistocene aquifer vertical K Longitudinal dispersivity ∂L Transverse dispersivity ∂T Advection solution schemea Reference fluid density (Freshwater) Seawater density Density/Concentration slopeb

m m \ \ \ mm/yr m/d m/d m/d m/d m/d m/d m m \ kg/m3 kg/m3 \

1400 50 0.3–0.4 0.12 1 × 10−5 2150 5 5 30 15 3000 1000 0.5 0.05 TVD 1000 1025 0.7143

\ \ Calibration Calibration Holding and Allen, (2015) Calibration Calibration Calibration Calibration Calibration Recalibrated c Recalibrated c Mulligan et al., (2011) Mulligan et al., (2011) Langevin et al. (2008) Yao et al. (2019) Yao et al. (2019) Langevin et al. (2008)

Flow model

Transport model

Density-dependent model

a b c

This is specified by SEAWAT. The slope of linear equation of state that relates fluid density to solute concentration. From Bailey et al. (2009), Bailey et al. (2014), Deng, et al. (2017).

square error (RMSE); b) verification of the error of tidal effects (tidal efficiency ε & tidal lag t τ ); c) comparison of concentrations of the multilevel observation wells were compared to the model-calculated concentrations in the cells corresponding to the location and depth of the measurement point; d) ensuring thickness of the FGLs are approximately the same as or smaller than the values of the analytic solution.

summarized in the Table 2. 3.4. Model output and calibration Water-level loggers were installed at different sites as shown in Fig. 2c. We used the LTC Levelogger (Solinst, Canada), with specific observation depths at −2 m, −5 m, and −8 m beneath the water surface, and a monitoring interval of 30 min. The monitoring records were available for the monitoring period of October 2016–December 2017. The water level, electrical conductivity, and temperature were recorded. For comparison with the modelled total dissolved solid (TDS) concentrations, the measured electricity conductivity (EC) values (in units of mS/cm) were converted to TDS (in units of kg/m3) by multiplying by 0.72. The EC–TDS conversion was obtained by comparison between EC and TDS values when water chemistry data were available (Galvis-Rodriguez et al., 2017). The model output results include the concentration distribution of different stages and the velocity fields under different stress periods. We used a TDS concentration of ≤0.875 kg/m3 (2.5% of the sea water) to distinguish between potable fresh water and non-potable sea water, and to represent the boundary of the FGL (Bailey et al. 2014). In addition, tidal effects at different depths and locations on the island were also calculated. These effects included the tidal efficiency (ε ), which is the ratio of the groundwater tidal amplitude to that of the sea; and tidal lag (t τ ), which is the time difference between high or low tide in the ocean and the corresponding peak or trough of the groundwater fluctuation (Hunt and Peterson, 1980). The total simulation time was subdivided into a calibration period from October 2016 to December 2017, and a prediction period from December 2017 to the time when the FGL of the Yongshu Island reached a pseudo steady state. The calibrated parameters were the horizontal and vertical hydraulic conductivities (KH and KV, respectively), porosity (n), and dispersivity (horizontal longitudinal, ∂L ; and transverse, ∂T ). When the shape of the FGL reached a steady state, we also used the analytical model (Case C) proposed by Vacher (1988), which was corrected by Dose et al. (2014), to verify the numerical solution. Due to the limitations of the analytical solution, we had to undertake some generalizations of the aquifer to make the aquifer boundary more regular, such that a probable result can be obtained (shown in Fig. 5). Therefore, there were four calibration indicators for model accuracy: a) comparison of the curve of the water level for the simulation and observation results and calculation the root-mean-

4. Results 4.1. Calibration results Fig. 6 shows the comparison of the water level fluctuation and salinity of the multi-level observation wells with the modeled results for the part of calibration and validation periods. Due to the equipment limitations, we only obtained the water level fluctuation data at a depth of −5 m in observation wells N8, N7, and N6 and a depth of −2 m in the observation well N8 in the same period. Other depth observation data were incomplete for this same period. The difference between the simulated water level and the observed water level was small, with the final root-mean-square error (RMSE) being 9.2 m, 7.9 m, 6.5 m, and 24.5 m during the validation period, respectively. This represents scaled-RMSE values of 7.1%, 12.1%, 9.8%, and 18.7% respectively, indicating an acceptable level of model–measurement mismatch for the proposed application of the model, particularly considering the heterogeneous nature of the island’s subsurface, the high temporal dynamics, and the manual approach to model calibration. It is not sufficient for the model calibration to be based only on water levels. Therefore, we also calibrated the model using groundwater salinity data. Fig. 6e and f show the calibration of the groundwater salinity for the Yongshu Island after one and two years of reclamation. Although our monitoring period was limited, there was a significant decrease in the salinity of the groundwater during this period, and the salinity of groundwater at a depth of 2 m was approximately 20% of that of sea water in October 2017. Moreover, the calculated values of tidal lag and tidal efficiency based on the water level fluctuation data are shown in Fig. 7. As the distance from the coast increased, the tidal efficiency gradually decreased while the tidal lag time increased in the same direction. However, in the center of the island, the tidal lag and efficiency remained essentially the same, and at values of 35% and 2.4 h, respectively. The model values match the geometry of the salinity distribution for the measured data reasonably 7

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Fig. 6. Modeled versus observed water levels for (a), (b) and (c) the depth of −5 m of observation well N8, N7 and N6, and (d) the depth of −2 m of the observation well N8 for the calibration period 13 Dec. 2016–14 Apr. 2017. (e) and (f) show the calibration of the groundwater salinity for Yongshu Island after one and two years of reclamation.

caused by tidal effects can be neglected. The velocity characteristics under such conditions are shown in Fig. 8-a6. The particle-tracking code MODPATH (Pollock, 2012) here was used for this evaluation. A total of 102 particles were placed across the model domain to track flow paths. This artificial groundwater system receives recharge from rainfall on the land surface with subsequent discharges to the sea. In conclusion, the present study showed that the dynamic mechanisms involved in the formation of FGLs beneath an atoll island have two different timescales: long-term average flow lines that are superimposed by short-term tidal fluctuations (Underwood et al., 1992; Yao et al., 2019). 4.3. Formation process of FGL of Yongshu Island Fig. 9 shows the predicted formation process for the Yongshu Island’s FGL. The maximum simulation time was 50 years. Within 2.5 years after reclamation, no fresh water accumulated (Fig. 9b1). We regard this stage as a preparatory phase: the coral sand is leached to remove the salt. With continual infiltration from rainfall recharge, the FGL gradually forms and increases in thickness. Five years after the reclamation project was completed on Yongshu Island, the maximum thickness of the FGL was about 7.5 m (Fig. 9b2). By approximately 2035, the FGL will reach a steady state, and the maximum thickness of the FGL will be 15 m (Fig. 9b5). The thickness of FGL is not evenly distributed in space: the thickness on the northwest side is high (the maximum thickness is 15 m), and that on the southeast side is small, reflecting the relationship between the freshwater lens and the hydrogeologic structure. At the same period, with continual infiltration of rainfall recharge, the transition zone of the FGL gradually became thinner and the final thickness was 17 m at the center of the island. Besides, we also compared the results between analytical and numerical solutions at the steady state, it can be seen that there is a big difference between them. The maximum thickness gave by the analytical solution is about 28 m, which is much larger than the numerical result. However, this is acceptable that the analytical solution assumes that the system is in hydrostatic equilibrium and that freshwater and seawater

Fig. 7. Modeled versus observed tidal efficiency and lag at depth of −5 m (a) for calibration period and salinities (b) for profile A–A′ at October 2017. From the tidal efficiency and lag (a) along profile A–A′, it can be seen that tidal efficiency and tidal lag have changed little in the central area of the island.

well.

4.2. Dynamic mechanism of FGL Based on the verification of the accuracy of the model, the dynamic mechanisms of the FGL on the Yongshu Island was predicted, as shown in Fig. 8. In terms of velocity fields (Fig. 8a1–a5), the propagation pattern of tidal signals based on the simulated flow path can be clearly seen. Because the permeability of the lower aquifer is much larger than that of the upper unconsolidated sediments, the tidal signal was propagated laterally very rapidly through the highly permeable Pleistocene layer, and then moved vertically into the upper aquifer. If the timescale is long (the time step was 10 days), the velocities over short time scales 8

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Fig. 8. The dynamic mechanisms of Yongshu Island’s FGL with tidal boundary. The short-term tidal fluctuations (a1–a5) are superimposed on the long-term average flowlines (a6). Color bar indicates effective flow velocity (m/d), whereby the size also depicts size of the velocity and direction depicts direction of flow.

are immiscible fluids, separated by a sharp, continuous interface of equivalent pressure (Vacher, 1988; Werner et al., 2017; Post et al., 2018a,b), which will have a overestimate result sometimes. We will discuss this phenomenon in more detail below. In order to better realize the freshwater lens of the Yongshu Island, we also carried out the establishment of a 3D model. Fig. 10 shows the 3D shape of the FGL during a stable period for the Yongshu Island. Underwood et al. (1992), Ghassemi et al. (2000), and Comte et al. (2014) have shown that non-tidal models of atoll islands require modification of the dispersivity parameters to compensate for the lack of tidal effects on the mixing-zone width. Alam et al. (2002) compared their tidal model of Bonriki Island (Kiribati) to the previous non-tidal model proposed by Alam and Falkland (1997), and found that the tidal and non-tidal variants required calibrated ∂T values of 0.05 m and 1 m, respectively. In the present study, we calibrated the 3D non-tidal model based on the simulation results of profile A–A′ by adjusting the dispersivity parameters. It can be seen that topography also plays an important role in the formation of the FGL. The thickness of the FGL varies at different positions, and the maximum thickness of the FGL was near the profile A–A′.

5. Discussion 5.1. Dynamic mechanism and tidal effects As a reclaimed island, the Yongshu Island provides study opportunities that other (natural) islands do not provide. Specific attention has been paid to how FGLs are formed, and how large it is. The changes with time and space in the FGL formation were captured reasonably well by the numerical model, although our assessment of the formation process was largely subjective due to the limitation of the field data. The calibration results and the use of model input parameters that fall within the range of expected values suggest that the model is an adequate tool for exploring FGL behavior under various boundary conditions. Our application of the model provided new insights into FGLs compared to previous studies (Dose et al., 2014; Stoeckl et al., 2015; Yao et al., 2019). These insights are important for understanding the physical processes that occur within atoll island settings. Tidal efficiency and average tidal lags were calculated for the upper and lower aquifer, and these computations provided a means for analyzing the relation between tidal effects and depth or distance from a shoreline. Generally, tidal effects are transmitted from the shoreline

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Fig. 9. The simulated formation process of Yongshu Island’s FGL based on profile A-A′. The FGL on Yongshu Island is predicted to reach a steady state about 20 years after the completion of the reclamation project. At this time, the difference between the analytical and numerical solutions were also compared.

Fig. 10. (a) 3-D grid model of Yongshu Island, and (b) steady-state 3-D distribution of a FGL with a non-tidal boundary. The total number of grid active cells is 122218.

below the MSL. In terms of distance, the ε of the central area of the island remains basically the same, about 5%, but at the coastal zone it was above 60%. Due to the permeability of the Pleistocene aquifer being very high (~102–103 m/d), the tidal signals rapidly moved inland from the lower aquifers and then propagated upward to drive the water level in the Holocene sediments, causing the FGLs to oscillate and thus increasing the mixing between salt and fresh water, unlike the numerical simulation results without tidal boundary obtained by Griggs and Peterson (1993) and Stoeckl et al. (2015). More generally, all four velocity-field drawings (Fig. 8a1–a5) serve to illustrate the dominant presence of

toward the center of the island, and thus tidal efficiencies decrease inward, whereas tidal lags increase in the same direction. However, in the present study, the tidal effects in the central area of the island remained essentially unchanged, which are consistent with the actual observation data obtained for some coral islands (Hunt and Peterson, 1980; Herman et al, 1986; Ghassemi et al., 2000; White and Falkland, 2010). For example, a relationship between the tidal response and depth on Enjebi Island (Enewetak Atoll) obtained by Herman et al. (1986) showed that the ε varied from 5% to 10% near the water table, but increased to 70% at a depth of 10 m below the MSL. Similarly, tτ decreased from 3.5 h at the water table to nearly 0.5 h at the 10 m 10

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Fig. 11. (a) Conceptual 3-D block diagram of an atoll island groundwater system, modified from Post et al. (2018a,b); (b) the FGL formation process on Yongshu Island, which can be divided into three stages.

vertical groundwater flow in the central portion of the island. However, if the timescale is longer (time step is 10 d), those velocity over short timescales caused by tide is no longer obvious. The flow path looks like the Fig. 8–a6, where the groundwater system receives recharge from rainfall on the land surface with subsequent discharges to the sea. This process mainly depends on the recharge rate and the density difference between seawater and fresh water. These two scale velocity characteristics exist simultaneously and affect each other.

model, it was unclear whether this approach (modification of dispersivity parameters) suitably compensates for the lack of tidal effects in a non-tidal model and this issue requires further study. Our model did, however, show that tidal action plays a major role in the dynamic mechanisms and formation process of FGLs. The tidal model simulates short-term vertical fluctuations that are superimposed upon the longterm flow regime (Fig. 8). The non-tidal model simulates only the longterm flow regime. Another shortcoming of the non-tidal model is that it cannot calibrate vertical permeabilities (Underwood et al., 1992). Pool et al. (2015) studied the effects of tidal fluctuations and spatial heterogeneity on mixing and spreading in spatially heterogeneous coastal aquifers. They found that once tidal oscillations boundary was included, as the degree of heterogeneity increases, the combined effect of heterogeneity and tidal oscillations on mixing and spreading of the interface reduces. They also identified that the mixing behavior induced by tidal oscillations in heterogeneous coastal aquifers is controlled by e the effective tidal mixing number (ntm ) which depends on the amplitude, the period, the storativity, and the effective horizontal permeability. However, if the transition zone of the FGLs is wide, the analytical solution seems not suitable. As stated in Section 4.3 above, the analytical solution assumes that the system is in hydrostatic equilibrium and that freshwater and seawater are immiscible fluids, separated by a sharp, continuous interface of equivalent pressure (Fetter, 1972; Vacher, 1988; Post et al., 2018a,b). As a matter of fact, this does not accord the fact especially for those tidal models. Because the broad transition zone that exists beneath the island is produced by the oscillating flow velocities that cause mixing between the fresh water and salt water on each tidal cycle. Ignoring tidally driven flow would mean ignoring this mixing mechanism and could lead to gross overestimation of the amount of potable water (≤2.5% seawater) that might be available. This could lead to unrealistic responses when the model is later used in a predictive mode (Oberdorfer et al., 1990). The GhijbenHerzberg principle usually thought that the maximum FGL thickness is 40 times than the highest FGL water-table elevation above MSL (Post et al., 2018a,b). However, according to our research result, this ratio seems a bit high especially for those thicker transition zone. Therefore, we may need to modify this ratio in practical problem, such as 20–40, we regard it as the “Effective Ghijben-Herzberg Ratio (EGHR)”. Vandenbohede and Lebbe (2007) evaluated the influence of tides on groundwater dynamics and propagation of the tidal wave. They provided an exhaustive insight in that there are two interfering flow cycles on the sloping shore. The first is a shallow tidally fluctuating flow cycle on the shore due to the interaction of the gently sloping shore and the tidally oscillating sea level. The second is a deeper flow cycle from the dunes towards the sea. However, this flow cycle is rarely found in coral

5.2. Stages of FGL formation On the whole, the formation of a FGL can be divided into three stages (Fig. 11). Taking the Yongshu Island for example, in the first stage (about 2.5 years), coral sand is leached and the salt is removed thus enabling a FGL to form. This can be regarded as the preparatory phase. With continual infiltration of rainfall recharge, the FGL gradually forms and increases in thickness. We refer to this as the formation stage. This is the most important stage of FGL formation and may be affected by many factors. For example, if groundwater was abstracted from the FGL during this period, the time needed for the FGL to reach a steady state will be extended. The formation phase of a FGL usually takes 20–50 years (Comte et al. 2014; Holding and Allen 2015; Yao et al., 2019). Finally, the FGL will reach a pseudo steady state. At this stage, the thickness of the FGL will fluctuate with the seasons and tides, but the average thickness of the FGL does not change. Irrespective of whether natural islands or artificial islands models are used, the formation process of FGL can be divided into these three stages. If the concentration range of the transition zone is defined by salinities between 2.5% and 95% of seawater concentration. It can be seen that the thickness of the transition zone is gradually reduced during the formation process. This is mainly affected by two factors: (1) The contact between the Holocene and underlying Pleistocene sediments, known as the Thurber discontinuity, plays a vital influence here that restricts the further development of a freshwater lens. Due to the permeability coefficient of Pleistocene aquifer being very large (102–103 m/d), the mixing between seawater and fresh water is severe so that freshwater is hard to preserve. (2) With continual infiltration of rainfall recharge, the FGL gradually forms and increases in thickness, while the position of the underside of the transition zone does not change. Therefore, the thickness of the transition zone is gradually reduced and finally reaches a steady state. 5.3. Comparison of tidal and nontidal models Although we used an iterative algorithm to realize the long-term simulation of a 2D tidal model and compared with the 3D nontidal 11

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islands, because the coral island is surrounded by the reef flat, which are flat and also not wide compared to the continental shore (shown in Fig. 2). In addition, the attenuation and time lag of the wave would be influenced by the large difference in storage (S) or specified yield (Sy) change of the aquifer in tidal model because the fluctuation of the water level will cause the elasticity of the aquifer and of the water (Carr and Kamp, 1969; Erskine, 1991; Vandenbohede and Lebbe, 2007; Liu et al., 2012). However, in the non-tidal model, no matter how we change these two parameters (S & Sy) within reasonable limits, they both play an insensitive role in the model, because the water table acts as a constant head boundary during the whole simulation phase and does not influence the elastic release quantity. The addition of tidal boundary also plays an important role in some hydrogeological events simulation. Underwood et al. (1992) evaluated the effects of a drought event on FGLs by the tidal model and non-tidal model respectively. After a steady-state lens condition was reached, the recharge was stopped for a 1-year simulation period. However, they found that during the drought period the transition zone thickness of the tidal model increased by approximately 20%, with the greatest response occurring in the upper part of the transition zone. However, in the nontidal model, the simulated transition zone thickness actually decreased by about 10%. Yang et al. (2013) analyzed the effects of tides and storm surges on coastal aquifers groundwater and found that tidal activity would intensify for the formation of the recirculating zone beneath the upper part of intertidal zone but does not affect the position of the seawater–freshwater interface. The tidal model retains the true tidal boundary conditions and best describes the atoll island groundwater flow system and the transition zone thickness, including the average permeability distributions, permeability contrasts, and estimates of freshwater storage. However, the large computational requirement is undesirable sometimes. In addition, groundwater modeling necessarily involves generalizations and simplifications, and specific problems need specific solutions. Consequently, more detailed analyses are needed to further improve our understanding of the responses of atoll FGLs to tidal action.

making it possible for a FGL to form. The second stage was the formation stage: with continuous infiltration of rainfall recharge, the FGL gradually formed and became thicker. This stage usually lasts longer than the preparatory stage. The third stage was the pseudo steady-state phase. The FGL reached a long-term equilibrium thickness and was in a pseudo steady-state. The recharge and the Thurber discontinuity determined the thickness. The preparatory stage clearly lasted 2.5 years. With continual rainfall infiltration, the FGL on the Yongshu Island will reached a pseudo stable-state in approximately 20 years, and the maximum thickness of the FGL was approximately 15 m. Although our monitoring period was mainly focused on the two years after the completion of the reclamation project on the Yongshu Island, it is of great significance for studying the formation of FGLs and overcome the shortcomings of the previous conceptual model. Largescale island reclamation projects similar to those undertaken in the South China Sea are rare in the rest of the world, and this is also the natural experimental site for studying the formation of FGLs. Our results demonstrate the potential of retaining large volumes of freshwater in the aquifers of reclaimed islands, as long as sufficient rainfall and island area can be ensured. CRediT authorship contribution statement Chong Sheng: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing - original draft, Writing - review & editing. Dongmei Han: Conceptualization, Formal analysis, Methodology, Validation, Writing original draft, Writing - review & editing, Supervision. Hehua Xu: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing - original draft, Writing - review & editing, Supervision, Funding acquisition. Fucheng Li: Conceptualization, Writing - original draft. Yunfan Zhang: Investigation, Validation. Yongqiang Shen: Data curation, Visualization. Declaration of Competing Interest

6. Conclusions The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Reclaimed islands not only provide valuable land for urban development (e.g., industrial base, national defense and commercial ground or residential area), but can also be important freshwater aquifers for retaining rainfall and store fresh water. The reported study investigated the formation process of a freshwater lens on a reclaimed island (Yongshu Island, whose reclamation project was completed in 2015). Based on a comprehensive data set of meteorological, geological, and groundwater data, a numerical model was constructed, which was used to perform a series of numerical simulations to reveal the dynamic mechanisms and formation process of a shallow FGL on an atoll island. The prediction of thickness and formation time of the FGL have also been discussed. The results clearly show that there are two time-scale dynamics that affect the formation of FGLs. On a short-time scale (about 0.5–1 h), the tidal dynamics are dominant. Because lower Pleistocene aquifers have a high conductivity, tidal signals will rapidly move inland through the lower aquifers and will then be propagated upwards to influence the water level in the Holocene sediments. This causes FGL oscillations and increased mixing between the salt water and fresh water. At long timescales, the time step is longer and the boundary conditions are simplified to hydrostatic sea water conditions. At this scale, the groundwater system receives recharge from rainfall infiltration, and groundwater is subsequently discharged to the sea. The two time-scales for FGL dynamics beneath an atoll island thus comprise short-term tidal fluctuations superimposed on long-term average flow lines (Fig. 11). We divided the formation of a FGL on a reclaimed island into three stages. In the first stage, the preparatory stage (approximately 2–5 years), coral sand was leached and the salt was removed, thus

Acknowledgements This research was supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant XDA13010303), Key Special Project for Introduced Talents Team of Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou) (GML2019ZD0104) and the National Natural Science Foundation of China (Grants 91428205 and 41376061). The authors appreciate the helpful field work and data collection made by Dr. Mingjian Hu from the State Key Laboratory of Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, and the suggestions on the structure and content of the manuscript by Dr. Chunhui Lu from Hohai University. We would also like to thank the editor Huaming Guo and two anonymous reviewers for their constructive comments, which significantly improved the manuscript quality. References Abarca, E., Carrera, J., Sanchez-Vila, X., Dentz, M., 2007. Anisotropic dispersive Henry problem. Advances in Water Resources 30, 913–926. https://doi.org/10.1016/j. advwatres.2006.08.005. Alam, K., Falkland, A., Mueller, N., 2002. Sustainable yield of Bonriki and Buota freshwater lenses, Tarawa. SAPHE Project, Hydrogeology Component. ECOWISE Environmental Pty Ltd, Tarawa, Republic of Kiribati. Alam, K., Falkland, A.C., 1997. Vulnerability to Climate change of the Bonriki Freshwater Lens, Tarawa. Ministry of Environment and Social Development Republic of Kiribati.

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