Processes Controlling Formation of Salt Efflorescence in Coastal Salt Flats

Salt flats are bare soil surfaces with elevated salinity levels which inhibit vegetation. They are commonly found in areas of coastal wetlands where salt in surface soil accumulates due to evaporation from the shallow saline water table. The expansion of these vegetation‐free zones may severely affect the bio‐ecological function of these coastal wetland systems. In this study, sand flume experiments and numerical modeling were carried out to investigate the mechanisms underpinning the development of salt flats in the elevated areas of coastal wetlands. We found that salt precipitation occurred on the soil surface where water content is low, but the hydraulic connection to the saline groundwater table is maintained. This connection is required for evaporation to promote upward porewater flow and bring salt to the surface. However, the surface salinity level decreases with increasing surface saturation due to the density‐driven removal of salt. As a result, salt efflorescence is absent on the surface with higher water saturations, despite strong evaporation. Density‐driven flows can be triggered by the evaporation‐induced upward salinity gradient and transfer salt from the surface back to the water table. Numerical simulations confirmed this salt removal process and suggested the intensity of the density‐driven flow is mainly dictated by the soil permeability in the unsaturated zone. The findings from this study increase understanding of the processes involved in the formation and evolution of salt flats.

are influenced by water saturation and salinity at the soil surface, which is dependent on the surface elevation, the depth of saline groundwater table, and the tidal regime (Shen et al., 2018;Wang et al., 2007;Xin et al., 2017).
The evaporation rate is affected by water saturation and salinity.The correlation between water saturation and evaporation was described by both empirical (Camillo & Gurney, 1986;Griend & Owe, 1994;Kondo et al., 1990;Mahfouf & Noilhan, 1991;Passerat de Silans, 1986;Shu, 1982) and physical based models (Schlünder, 1988;Shahraeeni et al., 2012;Suzuki & Maeda, 1968;C. Zhang et al., 2015).These models classify evaporation into three stages dependent on water saturation of the top soil layer: (a) Evaporation rates are close to potential evaporation in the high water saturation range; (b) Evaporation rates decline rapidly when the water saturation reduces to near the residual level; (c) Evaporation rates become very low when the surface dries, as it can only be sustained by water vapor generated below the surface.At the same water saturation level, higher porewater salinity results in lower evaporation rates because the salts in water reduce osmotic potential and hence lower saturated vapor pressure near the water surface (Al-Shammiri, 2002;El-Dessouky et al., 2002;Gran et al., 2011;Kelly & Selker, 2001;Oroud, 2001).If the salinity exceeds the solubility limit, the excess salts will precipitate in the top soil layer, blocking soil pores and reducing vapor flux, or form a salt crust on the soil surface, exerting mulching resistance to evaporation (Eloukabi et al., 2013;Fujimaki et al., 2006;Gupta et al., 2014;Nachshon et al., 2011;Shokri-Kuehni et al., 2017;C. Zhang et al., 2014).Both effects lead to a decrease in evaporation rates.Moreover, evaporation and salinity are largely dependent on the depth to watertable, which determines whether the hydraulic connection between the soil surface and the watertable can be maintained (Gran et al., 2011;Lehmann et al., 2008;Or et al., 2013;Shokri & Salvucci, 2011).If soil surface is hydraulically connected to the watertable due to a shallow depth, evaporation is mainly supported by the capillary-driven liquid flows, and salt is transported as a solute with the capillary water, from the watertable to the soil surface, causing an increasing salinity at the surface until salt precipitates (Hillel, 2003).However, if the hydraulic connection is cut off due to deeper depth to watertable, the liquid flows cannot reach the soil surface.In this situation, evaporation can only be contributed by vapor generated under the surface, and salt can only accumulate at depth, leading to a surface free of salt precipitation (Rose et al., 2005).
The salt accumulation near the surface results in water with higher density overlying porewater with lower density.Such an upward density gradient is unstable and may trigger density-driven flows, forming salt fingers or plumes below the soil surface (Simmons, 2005;Simmons et al., 2002).This phenomenon has been observed in salt lakes (induced by evaporation of surface or ground water in the lakes) (Lasser et al., 2021(Lasser et al., , 2023;;Wooding, Tyler, & White, 1997;Wooding, Tyler, White, & Anderson, 1997), coastal aquifers (due to seawater intrusion) (Van Dam et al., 2009), tidal wetlands (due to dissolution of surface precipitated salts during tidal inundation) (Geng & Boufadel, 2015a;Shen et al., 2018;Stevens et al., 2009;Xiao et al., 2019;Xin et al., 2017;J. Zhang et al., 2021), and agricultural lands (caused by irrigation) (Jambhekar et al., 2015).Such salinity-driven convection process has attracted wide attention, with most studies focusing on the formation mechanism of density-driven flow under saturated conditions (Bringedal et al., 2022;Simmons et al., 2001;Slim, 2014;Weatherill et al., 2004;Wooding, Tyler, & White, 1997;Wooding, Tyler, White, & Anderson, 1997).In these studies, the denser water was either introduced directly to the water-saturated surface or produced by dissolving salt precipitated on the surface.The density contrast led to density-driven flows that modified the local porewater flow and enhanced downward salt transport, thus contributing to the reduction of surface salinity.Besides density (salinity) contrasts, the ambient horizontal flow velocity, dispersion, and permeability of the soil also affect the formation and development of these flows (Oostrom et al., 1992).A few studies related to density-driven flow in unsaturated zone have typically introduced dense water at the surface of unsaturated soils with less dense pore water (e.g., Boufadel et al., 1999;Dane et al., 1994;Oostrom et al., 1992;Simmons et al., 2002).In these study cases, the matrix potential gradient, rather than the water density contrast, dominates the porewater flow in the soil given these studies mainly focused on the infiltration process.To authors' knowledge, there are very limited studies that investigate the salt dissipation effect caused by density-driven flows in the unsaturated zone Boufadel et al. (1999) numerically investigated the effect of capillary on density-driven flows and found totally different flow patterns in the porous domain between saturated and unsaturated flow cases.When capillarity effects are presented, the upwelling regions observed under saturated flow conditions transform into downwelling areas.However, evaporation was also ignored in this study.That is, in the studies of density-driven flows, researchers generally adopted predefined density contrasts as initial conditions to simplify the analytical process.However, evaporation, a process that generates the unstable density gradient, was ignored and the density-driven flows were triggered by a prescribed upward density gradient as an initial condition.The interaction between evaporation and density-driven flows plays a crucial role in influencing salt dynamics and surface salinity distribution, yet they remain poorly understood.The primary objective of this study is to investigate how evaporation leads to density gradients, subsequently inducing density-driven flows under variable water saturation conditions.By understanding these mechanisms, we aim to elucidate how they govern the distribution of surface salinity and the formation of salt efflorescence in salt flats.We conducted 2-D sand flume experiments to study the formation of salt efflorescence in unsaturated soil under evaporation and a shallow saline watertable.A 2-D numerical model considering variable-density, variable-saturation pore water flow, solute transport, and evaporation was adopted to simulate the development of salt efflorescence according to the laboratory experiments and explore the relationship between evaporation, salt accumulation, and density-driven flows in unsaturated zone.

Laboratory Experiments
A glass-walled sand flume with a size of 1,200 mm (length) × 600 mm (height) × 100 mm (width) was constructed to conduct the experiments (Figures 1a and 1b).The flume has a sealed bottom and an open top to allow evaporation.A water outlet was installed in the lower section of the glass panel on the right side (referring to Figure 1) and was connected to a Mariotte bottle for controlling the groundwater level in the flume.The Mariotte bottle was filled with a saline solution, prepared by dissolving sodium chloride in deionized water to a salinity of 35 ppt (mass fraction, parts per thousand).The Mariotte bottle was placed on a digital scale (Ohaus NVL20000, capacity 20 kg, resolution ±1 g) to record the water loss from evaporation.The digital scale was placed on a lab jack to adjust the groundwater level in the flume.
Gravels with a d 50 of 10 mm were laid at the bottom of the flume to a thickness of 50 mm for enhancing the hydraulic connectivity between the overlying sand and saline water reservoir controlled by the Mariotte bottle.Geotextile fabric was placed between the gravel and sand to prevent sand from mixing with gravel or blocking the water inlet valve.The gravel zone provided a stable water head from the bottom of the flume through its connection to the Mariotte bottle.Sand was poured and compacted into the flume in layers with an incremental thickness of 50 mm.The heights of the sands at the left and right boundaries were 405 and 300 mm, respectively, forming a surface slope of 5°.The particle size distribution of the coarse silica sand used in this experiment is relatively uniform with a d 50 of 0.8 mm and a d 60 /d 10 of 1.5.Prior to packing, the sand was rinsed with deionized water to remove impurities and then washed four times using the saline water, following the method detailed by Shen et al. (2015).Other properties of the sand are given in Table 1.
After packing, the gravel and sand were saturated by the saline water from the bottom up to minimize air bubbles trapped in the pore space.The saline water completely submerged the sand and then the water level was lowered to 240 mm above the flume base by adjusting the lab jack under the Mariotte bottle.The flume was then left for 24 hr with the sand flume covered by a plastic film to allow the equilibration of the free water level and the porewater in the unsaturated zone, and to avoid evaporation before the start of the experiment.With reference to Figure 1a, an electric fan was installed on the left side above the flume to enhance air circulation and evaporation from the sand.Temperature and humidity sensors (Xiaomi NUN4126GL, measuring range 0°C-60°C and 0%-99% relative humidity (RH), resolution 0.1°C and 1% RH) were installed on the top of the flume.Cameras (Logitech HD Pro Webcam C920, resolution 1,920 × 1,080) were installed above the flume to monitor the formation of salt efflorescence.
The experiment started after removing the plastic film and switching on the electric fan.The water saturation of the soil surface varied with vertical distance to the groundwater level, resulting in different evaporation rates.Salt accumulated at the soil surface due to evaporation, precipitating when the salinity exceeds the solubility limit, forming efflorescence.If only the efflorescence salt thickness increases, and not its area, for three consecutive days, it is assumed the location and extent of the salt precipitation zone have reached a steady state.
At the end of the experiment, three 120 mm long soil cores were extracted by pushing a cylinder with a radius of 20 mm into the sand surface at the lowest surface elevation (right side, referring to Figure 1), the middle elevation (flume center), and the highest surface elevation (left side, referring to Figure 1).Each core was cut into four sections depending on the depth: 0-30 mm, 30-60 mm, 60-90 mm, and 90-120 mm.Porewater saturation and salinity of each section were measured.The porewater saturation was measured gravimetrically (Reynolds, 1970).The porewater salinity was calculated by weight difference (water mass) and salt mass.To obtain the salt mass, the electrical conductivity (EC) was first measured by a handheld salinity probe (Hanna, HI98194) from an unfiltered 1:5 (mass ratio) dry sand: distilled water suspension for each section (Hardie & Doyle, 2012).The solution salinity (ppt) was then converted from the EC value using the equation: Salinity (ppt) = 0.4665 × EC (mS/cm) 1.0878 (Williams, 1986).The salt mass was then obtained from salinity using the determined water mass.

Numerical Simulations
A modified version of SUTRA (developed by USGS) was used to carry out the numerical analysis.The original SUTRA (Provost & Voss, 2019) simulates variably saturated, density-dependent porewater flow and solute transport processes.Additional modules were added to consider evaporation, salt efflorescence (America et al., 2020;Shen et al., 2018), and vapor transport (C.Zhang et al., 2014).A summary of the governing equations of the model is provided in Text S1 and Table S1 of Supporting Information S1.
As shown in Figure 1c, the domain used for the numerical model follows the dimensions of the sand section in the flume.The left and right boundaries were set as no flux boundaries.Evaporation was implemented on the sand surface (America et al., 2020;Shen et al., 2018;C. Zhang et al., 2014), removing porewater while leaving salt behind.A potential evaporation rate of 8.9 mm/d was applied.The actual evaporation rate may be affected by porewater saturation, salt accumulation, and salt efflorescence (Fujimaki et al., 2006;Rose et al., 2005;C. Zhang et al., 2014).A constant pressure head with a salinity of 35 ppt was applied at the bottom boundary to maintain a saline groundwater table 240 mm above it.
The model domain consisted of 14,701 nodes and 14,400 elements.The horizontal mesh was uniform with a Δx of 5 mm.The vertical mesh size from the soil surface to a depth of 100 mm was refined with a Δz of 5 mm to better characterize the water and salt transport near the soil surface, while Δz ranges from 5 to 7.6 mm as the depth is greater than 100 mm.This mesh resolution is a trade-off between the computation times required and the simulation accuracy.The values of model parameters are listed in Table 1.The model simulated 600 days with a time step of 200 s, and the simulation results of the first 11 days were compared with the experimental results.A reduced time step (10 s) and finer mesh (with 54,691 nodes and 54,000 elements) were tested, and the simulation results were shown to be independent of these parameters.Sensitivity analysis was also conducted on the dispersion coefficient and presented in Text S3 and Figure S2 of Supporting Information S1.
It should be noted that the constant head implemented at the bottom boundary of the numerical model allowed salt to leave the domain.However, the constant head maintained by the Mariotte bottle in the laboratory setup prevented salt from exiting the flume.The impact of such boundary condition difference on the salt transport and distribution was examined and presented in Text S2 and Figure S1 of Supporting Information S1.The analysis suggests that the presence of the no-flow bottom boundary increased the background salinity with time due to the continuous evaporation, but did not affect the salt dynamics under the formation of the salt efflorescence and the location of it.In field conditions, the accumulated salts in the unsaturated zone are less likely to significantly change the salinity level of the underlying groundwater connected to the sea.Therefore, we adopted the simulation case with a constant head at the bottom to be more representative of the expected field condition.

Salt Efflorescence Patterns and Porewater Salinity in Experiments
Figure 2a shows the development of salt efflorescence on the soil surface, while the location of the photographed area in Figure 2a in relation to the entire soil surface is marked with a green line in Figure 2b.After the location and extent of the salt efflorescence had reached a steady state (Day 11 in Figure 2a), three zones can be visually identified according to the distribution of surface salt precipitation.The high efflorescence zone (abbreviate as HEZ hereafter) was the whitest part of the surface (x ≈ 0.35-0.78m, depth to watertable ≈ 97-134 mm) by the end of the experiment, where the salt precipitated at the soil surface and formed salt crusts.The left to the HEZ (x < 0.35) was low efflorescence zone (abbreviate as LEZ hereafter) where the salt precipitated at the surface but did not form salt crusts.The no efflorescence zone (abbreviate as NEZ hereafter) was located to the right of the HEZ (x > 0.78), with no salt precipitation at the surface.
Salts started to precipitate in the LEZ and HEZ on Day 3 and thickened in the HEZ afterward, with the main area of salt efflorescence at x ≈ 0.35-0.70m.The upper boundary of the HEZ remained stable thereafter, while the lower boundary continued to expand toward lower elevation surfaces until it reached x ≈ 0.78 m on Day 8.The extent of the HEZ remained unchanged after Day 8.In the LEZ, evaporation occurred initially, allowing salt to accumulate at the surface, while it ceased around Day 3 as the hydraulic disconnection between the soil surface and the groundwater table cut off the water supply, thus inhibiting further salt accumulation (Shen et al., 2018;Wang et al., 2007).Salts did not precipitate in NEZ during the whole process, despite a strong hydraulic connection and continuous evaporation in that area.The evaporation rate fluctuated between 1.33 mm/ day and 3.36 mm/d during the experiments due to the changes in RH and temperature (T) as shown in Figure 2c.
The average evaporation rate throughout the experiment was 2.23 mm/d, with an average RH of 57.3% and an average temperature of 23.9°C.
The salinity and water saturation of the soil samples taken from these cores are shown in Table 2.The salinity at a depth of 0-30 mm from the highest (313.4 ppt) and middle elevation (376.6 ppt) of the soil surface exceeded the solubility limit of sodium chloride (∼265 ppt), implying the presence of solid salts.For the soil core collected at the highest elevation, which is in the LEZ, the water saturation at the surface was low (0.01) but increased with the distance from the surface, while the salinity decreased with the depth.This nearly zero surface saturation suggests the hydraulic connection between the soil surface and the water source below was cut off (Shen et al., 2018), so the evaporation was driven by vapor flow across a dry surface soil layer (Griend & Owe, 1994;C. Zhang et al., 2015).The elevated salinity at the surface was caused by the evaporation of the residual water at the start of the experiment.The soil core collected from the soil surface in the middle of the tank was located within the HEZ, where continuous evaporation brought water to the surface and accumulated salts, resulting in high salinity and further thickening of solid salt near the surface.The salinity below the surface decreased sharply as the water saturation increased, returning to near the initial salinity when the water saturation was above 0.67.For the soil core at the lowest elevation of the surface (in the NEZ), despite continuous hydraulic connection and evaporation, the salinity at the surface and at depth were both close to the initial salinity, indicating that the salt accumulated near the surface by evaporation was not retained there.
It is worth noting that salt efflorescence continued to thicken at only a section of the soil surface.In the LEZ, the water saturation was below the residual level and the evaporation could not be sustained, thus cutting off the salt supply.The surface saturation in the HEZ was relatively low but was able to support continuous evaporation, resulting in the accumulation of salt at the surface and the thickening of the salt efflorescence over time.In contrast, the NEZ had higher water saturation and continuous evaporation, but there was no salt efflorescence.

Salt Transport and Distribution in Numerical Simulation
Figure 3 compares the transient results of the numerical.Corresponding to the surface partitioning of the experimental results, the same three zones are divided based on the surface salinity of the simulation results: (a) HEZ (0.34 < x < 0.7 m), (b) LEZ (x < 0.34 m), and (c) NEZ (x > 0.7 m).The HEZ had a stable surface saturation of around 0.1, a surface salinity reaching the solubility limit, and a relatively low evaporation rate.The thickness of solid salt in the HEZ gradually decreased with decreasing surface elevation (and thus depth to groundwater table ).Salt efflorescence on the soil surface of this zone thickened with time due to continuous evaporation, but the rate of the thickening process decreased over time (Figures 3c-3f).The increasing solid salt thickness led to the increase of the mulching resistance to evaporation (Fujimaki et al., 2006), which in turn reduced evaporation and salt precipitation.Salt fingers induced by density-driven flows (see salinity distribution in Figure 3) initially formed near the right boundary and develop to the HEZ on Day 11.These downward flows carried the salt accumulated by evaporation out of the domain through the bottom boundary, reducing the salt level near the surface soil layer.The exit of salt fingers formed transient water and salt outflow (negative flux) at the bottom boundary dominated by stable evaporation-driven inflow (positive flux).The upward-moving porewater from the bottom boundary may either reach the surface and then evaporate, increasing the local salt levels, or not reach the surface due to the downward density-driven flows (see the porewater flow lines).The LEZ was located to the left of the HEZ, with a higher surface elevation and a lower surface saturation (less than residual saturation).The surface salinity increased slowly during the first 30 days with evaporation.However, the hydraulic disconnection between the surface and the water source below cut off the water and salt supply, inhibiting further evaporation and salt accumulation.Density-driven flows also formed underneath the LEZ, but on a smaller scale than those that occurred in the HEZ.With a lower surface elevation and thus higher surface water content, the NEZ was located to the right of the HEZ.Although high evaporation was sustained here, the surface of this zone was free of solid salts and the surface soil had a relatively low salinity.This is due to the occurrence of density-driven flows close  LIU ET AL. 10.1029/2022WR034279 9 of 14 to the surface that remove salt from this zone.The high evaporation rate and the magnitude of the density-driven flow also enhanced local salt transport and mixing, inducing more salt fingers of larger size, and greater water and salt fluxes at the bottom boundary of this zone.
Figure 4 shows the average and cumulative evaporation rate across the soil surface, the water and salt mass in the soil, and the cumulative flux across the bottom boundary during the simulation.The average evaporation rate across the soil surface kept steady at around 2.32 mm/d, close to the experimental results of 2.23 mm/d.The stable evaporation rate led to almost a linear rise in cumulative evaporation over time (Figure 4a).This constant average evaporation rate at the surface suggested that despite surface saturation and salinity level varied temporally and spatially over 600 days, they posed only minimal impact on the average evaporation rate.The total water mass reached a quasi-steady state soon after the start of the simulation (around Day 7) (Figure 4b), because the evaporative loss equaled the water influx from the bottom boundary.By contrast, the total salt mass in the soil reached the quasi-steady state after nearly 400 days (Figure 4b), as it took a long time for the salt dissipation to be equal to the salt accumulation in the HEZ.The cumulative water flux across the bottom boundary corresponded to the cumulative evaporation, attributed to the total water mass in the soil reaching a steady state at the early stage (Figure 4c).The cumulative salt flux across the bottom boundary oscillated around 0.2 kg/m 2 after 400 days, since the salt brought in constantly from the bottom boundary by evaporation was comparable to that carried out intermittently through salt fingers (Figure 4c).

Boundary Effect of the Sand Flume
As indicated by the porewater flow lines in Figure 3, the right-side no flux boundary appeared to force the flow downward and inhibit its lateral development.This boundary effect may artificially enhance the density-driven flow in the NEZ, thus altering the salt distribution at the surface.
To examine the impact of the right-side boundary, we carried out additional simulations (referred to as the extended model, hereafter) by extending the length of the soil domain from 1.2 to 1.8 m.The configuration of the left boundary stayed the same while the height of the right boundary was set to 250 mm to keep the 5° slope of the soil surface.All other parameters including the grid size remained the same as the original model described in Section 2.2.  the right side became fully saturated due to the short distance to the groundwater table, resulting in higher evaporation rates.More salt fingers formed in the NEZ compared to other zones, especially in the extended domain (x > 1.2 m), reducing the surface salinity close to the background level (35 ppt).

Rayleigh Number and the Conditions Triggering Density-Driven Flows
Previous studies have identified that under fully saturated conditions, the occurrence of density-driven flows can be characterized by the Rayleigh number (Ra), defined as the ratio of buoyancy-driven forces to resisting forces caused by diffusion (Gilman & Bear, 1996;Simmons, 2005;Simmons et al., 2001;Weatherill et al., 2004;Wooding, Tyler, & White, 1997).A high Rayleigh number suggests solute transport is dominated by free convection while a low number represents the dominance of diffusion.The previously defined Rayleigh number may not be applicable to this study where density-driven flow was initiated from the unsaturated zone.We found in the simulation results that salt fingers tended to initiate and be more intense where the surface is at a higher water saturation.The magnitude of water saturation and relative permeability in the unsaturated zone appears to have a significant impact on the density-driven flows.To consider the impact of the unsaturated conditions, we revised the Rayleigh number to include relative permeability (Mualem, 1976;van Genuchten, 1980) and water saturation, and applied it to the soil surface layer.The thickness of this surface layer was set to 0.01 m to avoid too much saturation difference within this unsaturated layer.As the dispersion is assumed independent of convective flow velocity (Gilman & Bear, 1996;Simmons et al., 2001;Weatherill et al., 2004), the revised Rayleigh number can be given by: where ρ 0 (kg/m 3 ) is freshwater density (kg); g (m/s 2 ) is gravitational acceleration; k s (m 2 ) is intrinsic permeability, while k r (−) is relative permeability which can be obtained from the average liquid water saturation S l (−) of the soil surface layer with a thickness of 0.01 m.Due to the upward salinity gradient, C max (−) and C min (−) were the  Among all the factors in Equation 1, only (k s k r )/(θS l ) and (C max − C min ) varied at the surface.(k s k r )/(θS l ) dictates the permeability for convection in unsaturated zone, so we defined it as the actual permeability K (m 2 ).In saturated condition, K equals to k s /θ.The difference between C max and C min provides the salinity contrast to trigger free convection.Figure 6 shows the development of permeability K, salinity difference ∆C (−) (=C max − C min ), and Rayleigh number Ra of the surface soil layer on Day 1, 6, and 11, and compares them to the results under fully saturated condition.Overall, the profile of K and Ra on the soil surface did not change over time (solid lines), due to the relatively stable surface saturation and evaporation rate.K (solid lines) tended to be larger toward the rightside boundary due to the high water saturation level.∆C plateaued at the HEZ and gradually decreased toward both sides.The actual permeability K has a larger impact on Ra than ∆C, as they both have almost the same profile (Figures 6a and 6c) over the entire soil surface.According to the distribution of Ra, the density-driven flows are more intense at NEZ, which is consistent with the simulation results.In contrast, assuming that the surface is fully saturated, K (dotted lines) keeps constant while the value of Ra (dotted lines) stabilizes at a high level.Therefore, in HEZ and LEZ, the low soil permeability at the surface layer limited the occurrence of density-driven flows.As a result, the salt dissipation mechanism was dominated by diffusion/dispersion rather than free convection, causing a much lower salt dissipation rate and a higher salinity.In contrast, the higher permeability at the surface layer of the NEZ enhanced the effect of density-driven flows, resulting in lower surface salinity.

Conclusions
Previous studies on salt flats ignored the importance of the relationship between evaporation and density-driven flows in the unsaturated zone.We conducted sand flume experiments with saline groundwater to monitor the formation of salt efflorescence due to evaporation from an unsaturated soil surface, as well as corresponding numerical simulations to examine the pore water and salt transport.The experimental results suggest that salt precipitated only at the surface zone having continuous evaporation and lower water saturation.The increase in surface saturation at lower surface elevation resulted in a rapid drop in salinity despite intense evaporation.The numerical simulations revealed that the evaporation-induced upward salinity gradient can trigger density-driven flows, forming salt fingers which carried the accumulated salt downward and reduced the surface salinity.These salt fingers tended to form at the soil surface with higher water saturation and permeability.At higher surface elevation, the surface saturation declined, and so the density-driven flows weakened, allowing the continuous evaporation to accumulate salt on the soil surface and forming salt efflorescence.Above a threshold surface elevation (and thus distance to groundwater), the hydraulic connection between the soil surface water and the groundwater below was lost, cutting off the evaporation and inhibiting salt accumulation.
While previous studies attributed the main processes of dissipating accumulated salts to tidal flushing and infiltration (Hsieh, 2004;Morris, 1995;Shen et al., 2018;Wang et al., 2007), our study suggests that besides tidal effects, density-driven flows induced by salinity contrasts can also reduce the surface salinity.Due to the infrequent tidal inundation around the supratidal line, these density-driven flows may play an important role in shaping the salinity distribution near salt flats.This finding may help to better explain the salt transport not only in salt marsh systems but also in other regions with shallow saline groundwater.Future study is encouraged to explore the correlation between evaporation and density-driven flows under different soil properties and environmental conditions, and their influence on the development of salt flats.Data from the experiments and analysis can be obtained by sending a request to the corresponding author.The research project has been funded by the Australian Research Council Discovery Project Grant (DP180104156).Xiaocheng Liu acknowledges the financial support from China Scholarship Council.

Figure 1 .
Figure 1.(a) Schematic of the sand flume and other parts of the experimental apparatus.(b) Photo of the experimental setup taken in the laboratory.(c) Laboratory-scale numerical model setup with descriptions of boundary conditions.

Figure 2 .
Figure 2. (a) Time lapse of salt efflorescence development on the soil surface.The depth to water table (DTW) indicates the distance from the soil surface to the constant groundwater level.(b) Location of the photographed area (green line) in relation to the entire soil surface in the flume.Three zones including low efflorescence zone, high efflorescence zone, and no efflorescence zone are divided by two purple dash lines.Black boxes indicate the locations of three samples collected at the conclusion of the experiment.(c) Relative humidity (black line), temperature (orange line), evaporation rate (blue line), and cumulative evaporation (green line) during the experimental process.

Figure 3 .
Figure 3. (a-f) Surface saturation (green lines), surface evaporation rate (abbreviated as E) (blue lines), surface salinity (purple lines), surface solid salt thickness (red lines), salinity distribution in the soil (colors), porewater flow lines (white lines with arrows), and transient bottom boundary flux (positive value indicates influx) including water flux (yellow lines) and salt flux (black lines) on Day 1, Day 6, Day 11, Day 30, Day 100, and Day 200.Numbers on flow lines represent the travel time (in days) of each flow.Dotted line indicates the water table.
Figures 5a and 5bshow the transient results of the extended model on Day 1 and 11.The results estimated by the extended model (solid lines) almost coincided with that of the original model (dot-dash lines) between x = 0 and 1.2 m, suggesting that the change of right-side boundary location had almost negligible impact on water and salt flow in the flume (and therefore the area of HEZ and LEZ).The NEZ (x > 0.7 m) widened due to the extension of the domain, and the travel time for flowlines in this zone, either those terminating at the surface or those returning to the bottom boundary, was shorter than for the flowlines in the HEZ and LEZ.The soil surface near

Figure 4 .
Figure 4. Time series of (a) average evaporation rate (yellow line) and cumulative evaporation (blue line) on the whole surface, (b) total water mass (purple line) and total salt mass (green line) in the domain, and (c) cumulative water flux (black line) and salt flux (red line) through the bottom boundary (positive value indicates influx).

Figure 5 .
Figure 5. (a and b) Surface saturation (green lines), surface evaporation rate (blue lines), surface salinity (purple lines), surface solid salt thickness (red lines), salinity distribution in the soil (colors), porewater flow lines (white lines with arrows), and transient bottom boundary flux (positive value indicates influx) including water flux (yellow lines) and salt flux (black lines) on Day 1 and Day 11.Numbers on flow lines represent the travel time (in days) of each flow.Solid lines and dot-dash lines represent the results of the extended model and the original model, respectively.Gray dash lines indicate the right-side boundary of the original model.Dotted line indicates the water table.
salinity at the surface and at the depth of 0.01 m, respectively.β (−) is the linear expansion coefficient of density/ concentration (=   −1 0 (∕) ), and the factor ∂ρ/∂C is approximately 700 kg/m 3 for NaCl; H (m) is the layer thickness considered in the calculation of Ra and set to 0.01 m in our case; θ (−) is porosity; μ 0 (≈1 × 10 −3 kg/m/s) is the dynamic viscosity of fluid; D m (m 2 /s) is the molecular diffusivity of solute in water, which is 1 × 10 −9 m 2 /s for NaCl at 20°C; R a0 (−) is Rayleigh number under fully saturated condition, since both k r and S l are equal to 1 in saturated zone.

Figure 6 .
Figure 6.(a) Actual permeability K, (b) concentration difference ∆C, and (c) Rayleigh number Ra along the soil surface on Day 1 (blue lines), Day 5 (red lines), and Day 11 (green lines).Solid lines indicate the results considering the change of relative permeability k r with surface saturation.Dotted lines represent the K and Ra assuming that the surface is fully saturated.

Table 1
Properties of the Sand for Experiments and Values of Model Parameters Adopted in the Numerical Simulations

Table 2
Measured Salinity and Water Saturation of Soil Samples From Three Locations