An integrated modelling approach to reconstruct complex solute transport mechanisms – Cl and δ37Cl in pore water of sediments from a former brackish lagoon in The Netherlands

A one-dimensional transport model was developed to reconstruct historical conservative transport of chloride and δ 37 Cl in pore water of sediments from a former brackish lagoon in The Netherlands, an area now covered by the freshwater Lakes IJssel and Marken. Knowledge of the mechanism of historical solute transport in the sediments and environmental conditions during transport is critical in understanding observed pore water chemistry and will form a basis for simulating effects of changing environmental (climate change) conditions. The model synthesizes present knowledge of geology and historical information on storm surges in the area and takes into account processes such as erosion of sediments, mixing of pore water, sedimentation, and diffusion (EMSD). The chemistry of pore water from one particular boring in the area was found to be mainly controlled by alternating seawater and freshwater diffusion. Models with a constant (averaged) porosity ( ϕ = 0.55) and tortuosity factor ( τ = 0.3) showed similar results as models incorporating the measured bulk porosity variations ( ϕ = 0.4–0.8) and variable tortuosity factors calculated with Archie’s law, τ = ϕ . The relatively small tortuosity factor either results from anion exclusion or from the heterogeneous build-up of the profile in which a peaty layer in the middle part may obstruct diffusion. Diffusion of 35 Cl − was found to be 1.0017 times faster than of 37 Cl − . Seawater diffusion into the sediments started at least 400 years ago and refreshening took place since the lagoon was isolated from the sea by a dam in 1932. 1 Introduction During Holocene times the area in The Netherlands now covered by Lakes IJssel and Marken ( Fig. 1 ), had sedimentation occurring under alternating brackish and saline conditions. Chloride profiles in these lake sediments were first examined by Volker (1942, 1961) with the objective of calculating seepage to nearby, low-lying, reclaimed areas. He showed how diffusive transport of saltwater into the sediments from overlying surface water changed pore water salinity over a period of approximately 700 years before isolation of the brackish/saline lagoon (Zuiderzee) from the North Sea by a dam in 1932. The closure of the lagoon induced freshening in the upper few metres of the lake sediments. Chloride concentrations deviating from those predicted by ideal diffusion behaviour were interpreted as being influenced by upward or downward groundwater flow ( Volker and Van der Molen, 1991 ). The aim of the present study is to reconstruct the transport mechanism which explains salinity changes in Lake Marken sediments within the context of geology and history of the area. This reconstruction is based on detailed analysis of a 14 m cored borehole (D) using chloride and chlorine isotopes. Knowing the transport mechanism in historic times is of prime importance in explaining present-day pore water chemistry and forms a basis for the prediction of future changes. 1.1 Chloride and chlorine isotopes Chlorine is one of the most conservative elements. It is mostly found in the I oxidation state and the lack of changes in redox state means that only little variation in its stable isotope composition is found. Most large reservoirs on Earth have δ 37 Cl values very close to 0‰ vs. Standard Mean Ocean Chloride (SMOC) which suggests that variations found in natural materials are the result of secondary fractionation processes. Processes that produce variations of the chlorine isotope ratios include salt precipitation ( Eggenkamp et al., 1995 ), anion exchange ( Musashi et al., 2004, 2007 ), and diffusion ( Desaulniers et al., 1986; Beekman, 1991; Beekman et al., 1992; Eggenkamp et al., 1994; Groen et al., 2000; Eggenkamp and Coleman, 2009 ). Isotope fractionation as the result of diffusion is related to the reduced masses of the colliding species in solution. The reduced mass is defined as: (1) μ i = m i M m i + M where m i and M are the masses of the colliding species (in an aqueous solution of chloride, m i is a hydrated chloride ion and M is a water molecule). Although the kinetic theory is developed for gases ( Tabor, 1991; Bird et al., 2002 ) it is also valid for species in aqueous solution (e.g. Jähne et al., 1987 ). The definition of isotope fractionation as a result of diffusion ( L/H α) is: (2) L / H α = D L D H = μ H μ L = m H ( m L + M ) m L ( m H + M ) where D L and D H are the diffusion coefficients of the light and heavy isotopes ( Richter et al., 2006 ). Calculation of 35/37 α requires knowledge of the hydration number n of the diffusing chloride ion [ Cl ( H 2 O ) n - ]. This number is generally assumed to be ⩽ 6 ( Powell et al., 1988 ). Impey et al. (1983) defined a dynamic hydration number which is 2.6 at 287 K, whereas Marchese and Beveridge (1984) suggested a ninefold hydration. Samoilov (1957) even assumed a negative hydration on the basis of calculations which showed that a H 2 O molecule stays next to a chloride ion for a shorter period than next to another H 2 O molecule. Based on the experimentally known 35/37 α (1.0012–1.0022, with an average value of about 1.0017; Eggenkamp and Coleman, 2009 ) the hydration number n of Cl would be 3: [ Cl ( H 2 O ) 3 - ] and this number is the same as the number suggested by the Debye-Hückel å parameter ( Appelo and Postma, 2005 ). Although the above results in an acceptable hydration number for the diffusing chloride ion, experiments by Richter et al. (2006) with MgCl 2 revealed that a shell of 140–900 water molecules would be needed for the Mg 2+ diffusing ion which suggests an unrealistically high hydration number. Richter et al. (2006) proposed that fractionation due to diffusion can be described by the inverse power relation: (3) 35 / 37 α = D 35 D 37 ∝ m 37 m 35 - β where β is a dimensionless exponent ( β = 0.025 based on diffusion experiments by Richter et al. (2006) ). Molecular dynamics simulation ( Alder et al., 1974; Impey et al., 1983; Nuevo et al., 1995; Willeke, 2003 ) as applied by Bourg and Sposito (2007) gave results which are similar to those experimentally determined by Richter et al. (2006) . Further investigations by Bourg and Sposito (2008) and Bourg et al. (2010) revealed β values between 0 and 0.2 for different noble gas atoms and mono- and divalent ions in solution. β is dependent on the strength of the solute–solvent interaction which is defined as the average residence time of water molecules in the first solvation shell of ions. β varies from ∼0.00 to ∼0.01 for divalent ions; from ∼0.01 to ∼0.06 for monovalent ions and from ∼0.05 to ∼0.19 for noble gases ( Bourg et al., 2010 ). Determination of diffusion coefficients and fractionation is straightforward for simple systems with no or little sedimentation and variation in salinity, such as in Kau Bay sediments ( Eggenkamp et al., 1994 ) where saline ocean water diffuses into freshwater sediments or in experiments as conducted by Eggenkamp and Coleman (2009) . In these studies the diffusion coefficients could easily be obtained by solving Fick’s diffusion laws ( Fick, 1855 ). In more complex systems, however, such as described by Beekman (1991) and Groen et al. (2000) , simulated and observed chloride diffusion profiles do not easily match, due to variations in sedimentation rate and (irregular) alternating freshwater and salt water influxes. For these cases there are no simple analytical solutions available, hence the need for application of numerical techniques. In the present study we will apply numerical techniques and will demonstrate that the use of both chloride concentration and chlorine isotope composition will significantly enhance our understanding of a complex diffusion dominated system in which sedimentation as well as changing environmental conditions (alternating freshwater and seawater) have taken place. 1.2 Hydrogeological setting Marine influence ceased in the Lake IJssel and Marken areas and the eastern area of West-Friesland about 3400 before present (BP); tidal channels silted up and salt-marshes and reed swamps were formed. A complex of freshwater lakes and peat bogs developed and the area was called Lake Flevo according to the Roman historians Pomponius Mela (Anno Domini (AD) 43, Chorographia, book 3) and Plinius (AD77, Naturalis historia, no. 4) . Between 3200 and 2000 BP detritus-gyttja accumulated in the lakes. Inflow of freshwater to the lakes by the river IJssel was probably small ( Ente et al., 1986; Makaske et al., 2008 ) and drainage of the lakes may have taken place via a northern connection with the North Sea or via a new (seawater) inlet in the south–west, the Oer-IJ, which formed several centuries after closure of the Bergen Inlet (around 3300 BP). The lakes expanded by erosion of the peat. The lakes became brackish during the period 0–1570 AD (Almere phase), particularly since their connection with the North Sea (Inlet Marsdiep) was further widened by the storm surge of 1170 AD ( Gottschalk, 1971; Zagwijn, 1986 ). Several other storm surges and concomitant land losses followed in the 13th and 14th century and contributed to the development of the Almere lagoon. The lower discharge of the river IJssel at the end of the 16th century and a severe storm surge in 1570 (Allerheiligenvloed) may have caused the rapid salinisation of the lagoon ( Ente et al., 1986 ). The saline phase of the lagoon, now called Zuiderzee, ended in 1932 after completion of the Afsluitdijk, the dam which isolated the lagoon from the North Sea. The Zuiderzee then became Lake IJssel. Within a few years the enclosed water became fresh and remained so until present. The total surface area of the former Zuiderzee was successfully reduced from about 3700 to about 1230 km 2 by reclamation ( Hoeksema, 2007 ): Wieringermeer 1927–1930; North–East Polder 1937–1942; Eastern Flevoland 1950–1957; Southern-Flevoland 1959–1968 and the isolation of Lake Marken from Lake IJssel by a dam in 1975 ( Fig. 1 ). Fig. 2 shows cross-sections through five borings with Cl profiles from Volker (1942) and our cored boring D in relation to geological strata. The distribution of Holocene deposits in the cross-sections is based on data from Ente (1976) and Winkels (1991) and lithological descriptions of borings in the area (Rijkswaterstaat, Directie Flevoland; unpublished). The Holocene deposits can be divided into three units according to their (relative) degree of permeability to groundwater flow. From top to bottom these are: I. Zuiderzee deposits (Zu; middle to coarse sand): permeable. II. Almere deposits (Al C1 ; fine sand): semi-permeable. III. Almere deposits (Al C2+3 ; humic, clayey), Lake Flevo deposits (Fl; detritus-gyttja), Holland Peat (Hp), Calais deposits (Om; “old” marine sea-clay, detritus-gyttja, Cardium-clay) and Lower Peat (Lp): low permeability. The overall thickness of these units at site D is 10.3 m and the hydraulic resistance is about 100 years ( RGD et al., 1991 ). The thick line at the base of the third unit represents the boundary between Holocene and Pleistocene deposits. Maximum chloride concentrations are generally found in the second unit. The lake bottom relief, bottom currents (still operating after completion of the Afsluitdijk) and bioturbation may have enhanced refreshening in the more permeable upper unit (Zuiderzee deposits) to a greater depth at several places in the area during the Lake IJssel phase. 2 Materials and methods Coring of sediments below Lake Marken at site D was carried out from a ship (“Heffesant”, RWS) by Delft Geotechnics at location 52°39′24.48N/5°21′27.72E ( Beekman, 1991; Appelo and Beekman, 1992; Beekman et al., 1992 ). After hydraulically pushing a stainless steel tubing into the sediment, a corer (1 m length and internally lined with a cleaned PVC tube, Appelo et al. (1990) ) with a sediment catcher at its end is driven out of the steel tubing into undisturbed sediment. Upon recovery, the PVC tube with the sediment core is taken from the corer and immediately frozen in a bath of liquid nitrogen to prevent oxidation of labile sulphides and ferrous iron by oxygen from the air. During and after transportation the sediment was stored at −20 °C. The lake bed was at 2.4 m – Dutch Ordnance Level (DOL ∼ mean sea level) and the coring could be carried out down to 14 m below lake bed, cutting through Holocene deposits and the upper few metres of sandy Pleistocene deposits. For each 1 m depth interval, a 6 cm diameter core segment with minimum sediment thickness of ca. 70 cm was obtained. From each core segment two deeply frozen samples (pre-cooled in a liquid nitrogen bath), each of 12 cm length (near the top and bottom), were cut by diamond saw at the Institute of Earth Sciences (IES) in Amsterdam, The Netherlands. The samples were stored in liquid nitrogen filled boxes, transported to the Laboratory of Geochemistry (LGU; Utrecht University, The Netherlands) and placed in Reeburgh-type squeezers ( Reeburgh, 1967 ) inside a glovebox filled with gaseous nitrogen (O 2 < 0.003%). Detailed description of apparatus and experimental procedures are given by De Lange (1992) . Pore water was extracted by pressure filtration after thawing of the core segments. Part of the original pore water from a few sediment samples was extracted by an anaerobic column elution procedure ( Beekman, 1991 ). Chemical and stable isotope analysis of pore water was carried out at the LGU laboratory and sediment characteristics were determined at the IES laboratory. 2.1 Pore water chemistry and δ 37 Cl determination Pore water chemistry comprised pH measurement, alkalinity and major cation and anion analyses. For the reconstruction of conservative solute transport described in this paper, we used Cl; analysis was carried out by Mohr’s titration with AgNO 3 ( Vogel, 1961 ). δ 37 Cl was determined using positive ion gas mass spectrometry on chloromethane (CH 3 Cl, Taylor and Grimsrud, 1969; Long et al., 1993; Eggenkamp, 1994 ). An amount of sample containing about 80 μmole of chloride is mixed with a 1 M KNO 3 solution to reach an ionic strength of at least 0.4 ( Taylor and Grimsrud, 1969 ), and a citric acid-phosphate buffer to produce a pH of at most 2.2 to avoid a precipitate of Ag 2 S ( Kaufmann, 1984 ). This mixture is heated to approximately 80 °C and AgNO 3 is added to precipitate AgCl. The precipitate is filtered and brought into a capsule together with 100 μL of CH 3 I. The CH 3 I reacts with the AgCl to CH 3 Cl, which is separated from the remainder of CH 3 I by gas chromatography. The isotopic composition of the pure CH 3 Cl is then measured on a VG SIRA 24 isotope ratio mass spectrometer ( Eggenkamp, 1994 ). δ 37 Cl is defined as ( Kaufmann et al., 1984 ): (4) δ 37 Cl = R sample - R SMOC R SMOC ∗ 1000 where R sample is the 37 Cl/ 35 Cl-ratio of the water sample and R SMOC is the 37 Cl/ 35 Cl-ratio of the standard. The internationally accepted standard is ocean water (Standard Mean Ocean Chloride, SMOC), which is, within error, a homogeneous reservoir and could thus be used as a reference standard ( Godon et al., 2004 ). 2.2 Sediment characterisation In addition to chemical analysis of pore water, determination of sediment characteristics is essential for reliable transport description and simulation. X-radiography was carried out on frozen core segments and thin sections were made to examine in detail the sediment characteristics and environmental conditions during deposition. Grain-size analysis of sediment, after removal of organic matter by addition of H 2 O 2 and dissolution of carbonates in HCl, was carried out with a Fritsch® Laser Particle Sizer: Analysette 22, for the range 0.12–1166 μm. The clay fraction (<2 μm; precision ±1.0%) was determined according to the Robinson Pipet method ( Hofstee, 1980 ) and was included in calculation of grain size distributions from 0 to 1166 μm. Bulk porosity was calculated from gravimetrically determined moisture content, corrected for precipitated salts (sediment dried at 60 °C oven temperature), and volumetric measurement of the frozen sediment slice. The effective porosity, calculated from the breakthrough curve of Cl − in a column displacement experiment with a clayey sample from the core, was found to be comparable with the bulk porosity. Total carbonate content (precision ±0.5%) was determined by gas-volumetric analysis of CO 2 according to the Scheibler method (detection limit 0.3 wt.%; Hofstee, 1980 ). Organic matter or humus (a product of decayed, condensated and polymerized organic matter) content (wt.%) was derived from a “loss on ignition” determination (precision ±0.8%) which must be corrected for CO 2 -loss, chemically bound water and evaporation of precipitated salts from pore water due to ignition of the sediment at 950 °C ( Hofstee, 1980 ). 3 Historical transport and model construction Changes in sedimentation pattern, environmental conditions (e.g. variation in salinity of overlying surface and bottom waters), solute transport mechanism and water–rock interaction, all affect pore water chemistry. Knowing the historical transport mechanism is therefore of prime importance when simulating the distribution of water quality, since the concentration distribution of a conservative tracer in pore water may reflect past transport phenomena ( Appelo and Willemsen, 1987; Appelo et al., 1990 ). A one-dimensional finite difference model (forward in time and central in space) was constructed to simulate the concentration distribution of a conservative tracer (Cl) under a variety of hydrogeologically controlled initial and boundary conditions: the EMSD-model (Erosion-Mixing-Sedimentation-Diffusion-model, Beekman, 1991 ). The model is based on the transport equation of a single solute under conditions of saturated, unsteady-state flow in a heterogeneous and isothermal porous medium ( Bear, 1972; Berner, 1980 ): (5) ∂ ( ϕ C ) ∂ t = ∂ ∂ z ϕ D l ∂ C ∂ z - ∂ ( ϕ v z C ) ∂ z where C is the solute concentration [ML −3 ], D l is the longitudinal dispersion coefficient [L 2 T −1 ], v z is the average linear pore water velocity in the z -direction [L T −1 ] (Darcy velocity/effective porosity), t is the time [T], z is the space coordinate or distance along a flow path [L] and ϕ is the volume fraction or porosity of the saturated porous medium [L 3 L −3 ]. It is assumed in the model that solute concentration is constant in a direction perpendicular to the local flow direction and that solution density ( ρ l [ML −3 ]) is constant over time and space. The numerical solution for one dimensional vertical, conservative, solute transport was based on the explicit method (see e.g. Richter, 1987; Appelo and Postma, 2005 ). In Eq. (5) , D 1 is given by ( Bear, 1972, 1979 ): (6) D l = D m + v z a i where D m is the molecular diffusion coefficient [L 2 T −1 ] of a species in porous media and a i is the longitudinal hydrodynamic dispersivity [L], which is a medium characteristic. The molecular diffusion coefficient D m of a species in a porous medium is related to its coefficient in the free liquid phase D 0 ( Bear, 1972; Berner, 1980 ): (7) D m = D 0 τ where τ is a correction factor accounting for the tortuosity ( θ ; [L L −1 ]) of the porous medium (0 < ( τ = θ 2 ) < 1). D m may be obtained by estimating tortuosity from resistivity measurements ( Klinkenberg, 1951; McDuff and Gieskes, 1976 ) or by solving the transport Eq. (5) for measured C ( z , t ) from diffusion experiments under appropriate initial and boundary conditions ( Berner, 1980; Robin et al., 1987; Appelo et al., 2010 ). D 0 depends on temperature, viscosity and pressure of the liquid. For most natural groundwater systems, the pressure effects on viscosity and D 0 are negligible, and, with temperatures ranging from 0 to 100 °C, the Stokes–Einstein relation can be used to estimate the temperature- and viscosity-dependence of D 0 : (8) D 0 η T T 1 = D 0 η T T 2 where T is the absolute temperature and η [ML −1 T −1 ] is the viscosity. Volker (1942) and Volker and Van der Molen (1991) showed that observed Cl concentration profiles in Lakes IJssel and Marken, when not affected by advective transport, are easily simulated by downward diffusion of seawater from a fixed boundary plane into sediments containing freshwater. Their calculations used a single constant diffusion coefficient: D m = 4.63 × 10 −10 m 2 /s and did not take into account the variation of the diffusion coefficient with depth due to changes in lithology and salinity, nor did they take into account sedimentation/erosion of deposits during the diffusion period. However, the simple procedure proved inadequate for the detailed analyses of δ 37 Cl that we made, and two scenarios were considered in our simulations: (1) in which diffusion into the sediments takes place from a fixed boundary plane: diffusion without sedimentation (A: Volker’s scenario) and (2) in which diffusion takes place from an upward moving boundary plane: diffusion combined with sedimentation (B: EMSD scenario). Advective mixing of surface water and pore water at a particular time and to a certain depth, as a result of storm/erosion events (=intermediate mixing), was included as an option in the model. In both scenarios groundwater movement resulting from reclamation of lakes in North Holland since the 17th century was neglected. The model input comprises data on: – initial and boundary conditions, including time periods of diffusion with corresponding input Cl concentrations, – diffusion coefficients for Cl ( D m ) and – sedimentation rate and intermediate mixing. Cl concentration and δ 37 Cl were calculated simultaneously. First, concentrations of both light and heavy isotopes were calculated and then δ 37 Cl was calculated according to Eq. (4) ( Eggenkamp and Coleman, 2009 ). 3.1 Initial and boundary conditions The sediment sequence of boring D ( Figs. 1 and 2 ) was divided into a number of cells, each representing a depth interval of uniform length Δ z = 0.5 m. A smaller size, taking the distribution of small-scale sedimentary structures into account, barely improved the results of the simulations. All cells of the sequence below a boundary plane of diffusion at depth z d (in metres below present lake bottom) were filled initially with the same chloride content: (9) C z , 0 = 65 mM for z ⩾ z d where z (in metres) represents the depth below present lake bottom. These initial Cl concentrations were assumed to have no fractionation and thus δ 37 Cl = 0. The initial Cl concentrations are close to the observed concentration for the deepest water sample and are well within the range of minimum pore water chloride contents directly below Holocene deposits reported from drillings in the vicinity of site D: 40 < Cl < 85 mM ( Volker, 1942; Gieske, 1989 ). Volker (1961) and Thijsse (1972) suggested that pore water salinity in the upper part of the Pleistocene deposits is derived from underlying Eem deposits by upward diffusion of saltwater. However, observations by Hebbink and Schultz (1984) of groundwater flow in the first aquifer below Holocene deposits indicate that the present pore water salinity in the aquifer may also originate from other sources, notably from infiltration through the Zuiderzee bottom, induced by large scale reclamation in North Holland since the 17th century ( Thijsse, 1972 ). For scenario A (diffusion without sedimentation), z d was fixed at 1 m below the present lake bottom, and the pore water above this level was assumed to be mixed completely by storms and bioturbation. Because sedimentation of the Almere Member is not included in this type of scenario, the maximum duration of saltwater transport in the bottom sediments is limited to the 362 years duration of the Zuiderzee phase. It should be noted that this scenario, with a fixed boundary plane from which diffusion proceeds at the (1940) depth of the lake bottom: – downward diffusion of saltwater from 1238 to 1932 and freshwater from 1932 to 1987 and – if necessary, upward or downward groundwater movement to match observed Cl concentrations, leaves a very short time for sediment build-up of the Al C1 member. Sedimentation from 5.8 to 1.5 m below the lake bed would have happened in approximately 40 years in the first half of the 13th century. The initial Cl concentrations represent the environmental condition for pore water in sediments at the end of the Almere phase (1570 AD). The concentration of chloride at the lower boundary of the sediment sequence was fixed at its initial level: (10) C z 1 , t = C z 1 , 0 = 65 mM for t ⩾ 0 where z 1 is the depth of the lower boundary; taken here as 14 m below present lake bottom (about 3 m below the Holocene-Pleistocene boundary). The Cl concentration at this depth was thus assumed to have no fractionation for t ⩾ 0. For scenario B (diffusion combined with erosion and sedimentation) the diffusion boundary plane shifts with time from 5.5 m to 1 m below present lake bottom. The initial depth of the plane at 5.5 m coincides with the deepest level in the Al C1 unit above the Holland Peat Member where the beginning of sand-influx is observed. Based on the sand-influx, which was dated at the end of the 12th century in the NE-polder ( Ente, 1973 ), the period for brackish/saltwater transport was set at 700 ± 50 years (thus, twice longer than in scenario A). The initial Cl concentrations for this scenario represent the environmental conditions of pore water for the first half of the 13th century, during the brackish/saline Almere period Al C1 . The diffusion boundary plane during the Zuiderzee phase was kept at z d = l m as in scenario A. This depth is ca. 0.5 m above the deepest level where the marine fossil Mya arenaria is found. Thus, it is assumed that the bottom water salinities during the Zuiderzee phase are averaging above the diffusion boundary plane (upper metre of the sediment sequence) for calm periods and storm surges alike by frequent erosion and sedimentation events and by bioturbation. Because the observed Cl concentrations are relatively low in the upper metre of the sequence and cannot be explained by either diffusive transport alone, or by vertical groundwater movement, the depth of the diffusion boundary plane for the fresh Lake IJssel phase (55 years) was also set at 1 m below the present lake bottom. A Cl concentration of 25 mM at the diffusion boundary plane, representing an average concentration of Lake IJssel bottom water and pore water at 1 m below the present lake bottom, provided the best fit for the observed Cl concentrations. Groundwater movement resulting from reclamation activity during the Lake IJssel phase was neglected. Core inspection did not reveal direct evidence for compaction of sediments above the Holland Peat Member. Porosities ( ϕ ) and diffusion coefficients ( D m ) were therefore assumed to be time-invariant for the whole sediment sequence: (11) ∂ ϕ ∂ t = ∂ D m ( z ) ∂ t = 0 We have used Archie’s law to relate the pore water and free water diffusion coefficients: (12) D m = D 0 ϕ n Two different types of calculation were performed during the simulations, first with constant porosity and n = l (implying a constant correction factor τ in Eq. (7) ), second with the actual porosity distribution and 1 ⩽ n ⩽ 2. 35/37 α factors ranging from 1.0012 to 1.0022 were used to obtain D m values for lower Cl mobility and to calculate δ 37 Cl. 3.2 Sedimentation and intermediate mixing In scenario B, sedimentation was simulated by adding a new layer with thickness Δ z on top of existing layers, the rate of average net sedimentation (minimal 1 cm/year) being determined by the period of diffusion from the new boundary plane. The build-up of the sediment pile in the Almere lagoon and Zuiderzee at site D was certainly affected by storm events ( Gottschalk, 1971, 1975, 1977 ). North–south directed gullies in the Enkhuizerzand bear witness to tidal activity in the past ( Ente et al., 1963; Winkels, 1991 ). 3.3 Historical chloride concentrations Diatom analysis revealed relatively fresh and saline intervals in the sediment sequence. At least eight intervals of increased bottom water salinity can be interpreted from information on severe storm events during the Al C1 period 1250–1570 AD: about one severe storm every 40 years ( Gottschalk, 1971, 1975 ). Zuiderzee surface water contained saltwater from the Atlantic Ocean (Cl concentration about 540 mM and freshwater, mainly from the river Rhine (Cl concentration of about 1.5 mM before 1935: Thijsse, 1972 ). At the inlet of the Zuiderzee to the north (Inlet Marsdiep) annual Cl concentration of surface water was about 490 mM during the period 1860–1932 ( Van der Hoeven, 1982; Van Aken, 2007 ); approximately 86.5% derived from ocean water and 13.5% from freshwater, mainly from discharge of the river Rhine into the North Sea via the delta in south–west Netherlands. At site D the annual Cl concentration of Zuiderzee surface water for the period 1894–1932, estimated from salinity data for three observation stations in the vicinity, was 260 ± 40 mM: 53 ± 7% was derived from the North Sea (46 ± 7% from the ocean and 7 ± 1% from river Rhine discharge into the North Sea), 30 ± 5% from inflow of the river IJssel (a branch of the river Rhine) into the Zuiderzee and 17 ± 3% from other freshwater inflow into the Zuiderzee (based on data from Van der Hoeven, 1982 ). Although it is expected that bottom water salinity increased during storm events, Cl concentration of bottom water at site D during the Zuiderzee phase must have been generally much lower than 540 mM. The following cycle of events was developed for each sedimentation step and is illustrated in Fig. 3 : 1. Relatively strong bottom currents during a storm event, originating from the open sea in the north with higher salinity erode the sediments or mix/displace pore water with bottom water to a certain depth: z d 0 + m d ( m d is the thickness of the erosion/mixing zone below the diffusion boundary plane ( z d 0 ) for the previous calm diffusion period). The Cl concentration in the erosion/mixing zone becomes identical to the average Cl concentration for bottom water during the storm. δ 37 Cl = 0 as a result of mixing. 2. After the erosion/mixing event, the current activity and salinity decrease gradually, and sediment is deposited until the new depth of the diffusion boundary plane becomes z df = z d 0 − Δ z . As a result, the Cl concentration decreases upwards and δ 37 Cl = 0. 3. Diffusion starts again from the new boundary plane until bottom currents from a new storm erode the sediments or mix/displace pore water. 4 Results and discussion 4.1 Pore water Cl and δ 37 Cl We measured the δ 37 Cl values of 22 pore water samples. In addition, five sediment samples were leached with distilled water and also measured for δ 37 Cl. The squeezed pore water samples have sample numbers which end with T or B, indicating that the sample is from the top or the bottom of the core section. The leached pore waters have TB added to their sample number to indicate that the sample has been taken between the T and the B sample (see table 1 ). A water sample from the river IJssel near the town of Deventer and a sample of lake bottom water at the location of the sediment core were also measured. From the bottom of the sediment core a regular increase in Cl − concentration from about 70 to 285 mM (2500–10,100 ppm) was found. This is followed by a sharp decrease in Cl − concentration in the upper 2.5 m of the core. δ 37 Cl values are negative in the lower half of the core and positive in the upper half. From bottom to top, the δ 37 Cl values regularly increase towards a maximum that is positioned slightly above the maximum Cl − concentration, after which they sharply decrease in the upper 2.5 m of the core. The δ 37 Cl values of the leached pore water analysis generally agree with those of the squeezed pore water analyses (with the exception of the low value of 14TB). As expected, δ 37 Cl of the IJssel River and the Lake IJssel bottom water are close to 0‰. 4.2 Sediment characteristics Fig. 4 shows the major lithostratigraphic and sedimentary characteristics of Holocene deposits at site D. From bottom to top the sequence consists of the Lower Peat Member (Lp: 10.0–10.3 m below lake bed): reed peat and wood fragments; Old Marine deposits of Calais transgression phases (Om: 7.3–10.0 m): clay; Holland Peat Member (Hp: 5.8–7.3 m): peat and peat-detritus; Hiatus; Almere deposits (Al C1 : 1.5–5.8 m): silt (2–63 μm grain-size) to medium sand (150–300 μm) and Zuiderzee deposits (Zu: 0–1.5 m): fine (63–150 μm) to medium sand. Bulk porosities of the sediments at site D (determined by volumetric and gravimetric analysis) range from 40% to 80% and reflect the lithological changes (e.g. changes in dry solid phase density ρ s ). Macroscopic observations, thin sections (one for each core segment from M-4 to M-10) and the relatively high porosities of up to 80% in the Holland Peat Member at 6–7 m below the lake bed indicate that compaction of the sediments is either small or nonexistent. 4.3 Results of transport modelling The first objective was to find combinations of a constant tortuosity factor (Eq. (7) ) and a Cl concentration of bottom water during the Al C1 period and/or Zuiderzee phase which explained the observed Cl concentrations. Data for Cl concentrations during these phases are scarce but could be deduced from different sources such as diatom analyses (see Section 3.3 ). It was assumed that during relatively calm periods of the Al C1 period (for scenario B) the bottom water was less saline than during the Zuiderzee phase, and only for storm events during the Al C1 period did bottom water salinity rise above that during Zuiderzee times. There was no difficulty in obtaining a good fit between calculated and observed Cl concentrations for both scenarios A and B. Thus, if only Cl concentrations were considered, the relatively simple type A scenario would be preferred. However, type A scenario requires an unreasonably high salinity of Zuiderzee bottom water (up to 540 mM Cl). More importantly, δ 37 Cl could not be explained by scenario A, not even when mixing to 1 m depth below the diffusion boundary plane during Zuiderzee storms was assumed in the model. The best fit for the scenario proposed by Volker and Van der Molen (1991) ; D m = 4.63 × 10 −10 m 2 s −1 ; z d = 1 m below lake bed) was obtained for a hypothetical downward groundwater movement of 0.5 cm/year since 1638 and lower Cl concentrations for Almere and Zuiderzee bottom water of 350 mM. However, the δ 37 Cl fit remained poor ( Fig. 5 ). Table 2 shows the parameter values that provide the best fit between calculated and observed values for both Cl and δ 37 Cl for scenarios A and B, neglecting groundwater movement other than resulting from erosion/sedimentation. Note that the best fit fractionation factors 35/37 α for scenario B are in very good agreement with the fractionation factors obtained from recent experimental studies ( Eggenkamp and Coleman, 2009 ). Fig. 5 compares observed and calculated data and illustrates that scenario A is inadequate for explaining the observed δ 37 Cl values. The sign of δ 37 Cl in diffusive transport is controlled by differences in Cl content. Diffusion of saltwater in fresh pore water gives negative δ 37 Cl values, and out-diffusion of salt water leads to positive δ 37 Cl values. The point of intersection for zero δ 37 Cl and depth (6.5 m below lake bed) is controlled mainly by the deepest level at which the first pore water mixing and/or displacement takes place ( m 0 = 4.5 m below present lake bottom) and by the corresponding mixing depth ( m d = 1 m). The fractionation factor 35/37 α determines the absolute level of δ 37 Cl, with a higher 35/37 α value giving larger deviations of δ 37 Cl from zero. Fig. 6 shows several stages in the development of the Cl and δ 37 Cl profile for scenario B with τ = 0.30. Each stage represents the end of a (calm) diffusion period. The Cl concentration of bottom water during the Al C1 period (1250–1570) was set at 100 mM and at 425 mM for storm events. The lower Cl concentration for bottom water during the third and fourth calm period of 75 mM represents relatively “fresh” conditions in the Al C1 period (3.5–4.5 m below present lake bottom), in line with the diatom analysis. The inclusion of this relatively “fresh” interval barely affected the results. A constant concentration level for Cl of 350 mM was used at the diffusion boundary plane from the Allerheiligen storm surge in 1570 ( z d = 1 m) until the Zuiderzee closure in 1932. A well mixed reservoir from present lake bottom to 1 m depth was thus assumed during the Zuiderzee phase (tidal activity, which was more pronounced during the Zuiderzee phase than during the Al C1 period and bioturbation enhanced the mixing process). The higher Cl concentration at the diffusion boundary plane compared with the estimated Cl concentration of surface water during the period 1894–1932 (260 ± 40 mM) is explained by the contribution of severe storms to the salinity of bottom- and pore water. Small deviations between calculated and observed δ 37 Cl are seen in the interval 3–6 m below present lake bottom. These result from a combination of the long diffusion time which was used for the Zuiderzee phase and the difference between Cl concentration of bottom water during Al C1 storms and the Zuiderzee phase. The Cl concentration of pore water above 1 m depth was set to 25 mM after closure of the Zuiderzee in 1932 and mixing may explain the observed positive δ 37 Cl values (0.47‰ and 0.39‰) in this part of the sediment sequence. For δ 37 Cl (river IJssel) = 0‰ and δ 37 Cl (observed) ∼ 0.43‰, δ 37 Cl (Zuiderzee pore water) is calculated to be ∼0.53‰ (={25 × 0.43–0.942 × 5 × 0}/{0.058 × 350}) which more or less agrees with the observed value at 2 m depth ( Fig. 6 ). However, such a linear mixing in the upper zone implies non-zero δ 37 Cl values at the diffusion boundary plane at the end of the Zuiderzee phase and thus, is not in agreement with the constraints used to calculate δ 37 Cl below this boundary. Other processes and events such as (partial) diffusion, nature of linear mixing (horizontal/vertical, e.g. by bioturbation), timing and duration of mixing and a shifting diffusion boundary plane may also affect δ 37 Cl in the upper zone, but these were not examined in detail. If in scenario B models the porosity and tortuosity factor are kept constant, it results in τ = 0.30, which gives an exponent n = 2 in Archie’s law (Eq. (12) ) for the average ϕ = 0.55. If the measured bulk porosities are incorporated in scenario B, the calculations also give the best results for n = 2. Fig. 7 illustrates this for a single diffusion coefficient D m ( τ = 0.30) and depth dependent diffusion coefficients with τ = ϕ n , for n = 1 and n = 2. To obtain a fit for variable ϕ and n = l, the bottom water salinity during the Zuiderzee phase must be adapted to unrealistic values of Cl (Zuiderzee) ∼ 540 mM and Cl (AlC1-storm) ∼ 250 mM. The calculation with variable ϕ and n = 2 slightly improves the fit with observed δ 37 Cl at 12 m depth, but gives otherwise quite similar results as with a constant porosity and D m (and τ = 0.30). The optimal tortuosity factor is lower than often reported for unconsolidated sand and clay with similar porosities; e.g. in a clay with ϕ = 0.57, τ = 0.55 ± 0.04 ( Li and Gregory, 1974 ; D 0 = 1.4 × 10 −9 m 2 /s at 10 °C), in other clays with ϕ ≈ 0.37, 0.25 < τ < 0.40 ( Johnson et al., 1989; Iversen and Jørgensen, 1993 ). Also, Van Loon et al. (2007) found n = 0.9 in Archie’s law for bentonite compacted to three different densities. However, Van Loon et al. (2007) used the anion-accessible porosity in Archie’s law, whereas we used the total (bulk) porosity, as did Li and Gregory (1974), Johnson et al. (1989), and Iversen and Jørgensen (1993) . Accordingly, the lower tortuosity that we found could be explained by anion exclusion in diffuse double layers which closes off pores when they overlap, forcing the anions to circumnavigate the obstacle via a longer route ( Appelo and Wersin, 2007; Appelo et al., 2010 ). It would be in line with the smaller tortuosity factor for Cl − than for CH 4 that Iversen and Jørgensen (1993) observed, although we find a larger effect when expressing it in the terms of the exponent of Archie’s law. The larger effect may be related to the lower salinity in the Zuiderzee, which can be expected to increase the anion exclusion more than in the profile studied by Iversen and Jørgensen. The simple Volker scenario (A) yields a tortuosity of 0.6 ( Table 2 ) for the Cl − measurements. It gives an exponent of 0.85 in Archie’s law, which would appear to be in line with the other data in which also the bulk porosity is used to calculate the tortuosity. However, the Volker scenario must be discarded since it cannot explain the δ 37 Cl measurements. Assuming that the relatively high exponent in Archie’s law that we obtained is due to anion exclusion of part of the porespace, and taking the exponent n = 1 that was noted by Van Loon et al. (2007) , the anion accessible porespace is calculated to be 0.3, or slightly more than half of the bulk porespace Other effects may play a role in lowering the diffusion in the profile, such as the peaty layer in the middle part of the profile, with relatively large reed- and wood fragments. 5 Conclusions Solute transport of fresh- and seawater was examined in sediments from a boring in Lake Marken, The Netherlands. Pore water chemistry was found to be mainly controlled by diffusion, seawater or brackish water starting to diffuse at least 400 years ago into sediments of a lagoon previously containing pore water of lower salinity. Refreshening of the upper few metres has taken place since isolation of the lagoon from the sea by a dam in 1932. Simulation of historical conservative transport revealed good agreement between predicted and observed pore water Cl and δ 37 Cl only when erosion of sediments, pore water mixing and sedimentation were taken into account together with diffusion. The EMSD (Erosion-Mixing-Sedimentation-Diffusion) model developed to include these processes synthesizes present knowledge of geology, particularly at site D, and historical information on storm surges in the area. The results imply that Volker’s hypothesis (republished by Volker and Van der Molen, 1991 ) for historical transport is incomplete and incorrect with respect to geological and historical data. Simulations using depth dependent diffusion coefficients which are related to porosity changes did not improve the results. This is mainly due to heterogeneity of the sediments; a combination of variable lithology and sediment structures smoothed the effect of porosity on the diffusion coefficient. This study clearly demonstrates the value of δ 37 Cl for reconstruction of complex historical transport mechanisms in environments where fresh-seawater interaction dominates. Modelling of δ 37 Cl, and comparison of the model diffusion coefficient with data based on Archie’s law, suggests that either the Cl − accessible porespace in the studied profile is half of the bulk porespace, or that the peaty character of part of the profile is obstructing diffusion. Since the bulk and effective porosities were found to be similar in a column experiment with a clayey sample from the profile, the latter option is the more likely one. Acknowledgements We thank Dr. Orfan Shouakar-Stash, two anonymous reviewers and the Executive Editor, Prof. R. Fuge for their comments to improve the manuscript. We would like to thank the Dutch Waterboard (RWS) and Delft Geotechnics for sampling the core at site D. J. Middelburg sampled the River IJssel water sample near Deventer, P.v.d. Klucht (RGD) made X-ray exposures of the frozen core samples, and H. van Egmond (IES) prepared thin sections. D. Schoonderbeek (Wijnants Staring Centre) carried out micromorometric measurements on the sediments, diatom analysis was done by H. de Wolf (RGD), and M. Geluk (RGD), S. Kars (IES) and J. Dormans (RIVM) assisted with microscopic observations on thin sections. G. Hamid extracted water samples from the sediments for chemical and isotope analysis and R. Kreulen (RUU) assisted with the Cl isotope measurements. This study was supported by the IES and the Netherlands Foundation for Earth Science Research (AWON) with financial aid from the Netherlands Organization for the Advancement of Pure Research (NWO), Grant 755.355.014 (HE). 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