# Introducing a water activity coefficient to account for abundance and isotopic compositions of gypsum and halite in the Mediterranean's salt giant deposit

William B.F. Ryan, Fadl Raad

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William B.F. Ryan, Fadl Raad. Introducing a water activity coefficient to account for abundance and isotopic compositions of gypsum and halite in the Mediterranean's salt giant deposit. Sedimentary Geology, 2025, 481, pp.106876. 10.1016/j.sedgeo.2025.106876. hal-05086922

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# Introducing a water activity coefficient to account for abundance and isotopic compositions of gypsum and halite in the Mediterranean's salt giant deposit

William B.F. Ryan<sup>a,*</sup>, Fadl Raad<sup>b</sup>

## ARTICLE INFO

Editor: Dr. Massimo Moretti

**Keywords:**

Mediterranean

Messinian

Gypsum

Halite

Water activity coefficient

## ABSTRACT

A simple box model is developed to access the astronomical-modulated exchange of ocean seawater with the Mediterranean during the Late Miocene salinity crisis. The model differs from previous ones by using a unidirectional portal as the method to get salinity to increase to saturation for gypsum and halite. Flow through the entry portal switches in direction as climate oscillates from arid to wet during each precession cycle. The calculations incorporate a water activity coefficient that reduces the rate of evaporation as salinity increases. As a result, the accumulation rate of gypsum and halite declines with time. The sodium, sulfate, potassium and magnesium ions observed from fluid inclusions in gypsum and halite are replicated in the model. The reduction in input from the exterior ocean and eventual closure of the gateway conforms with the sedimentological and geochemical behavior of the gypsum deposits on margins and halite in salt mines and reflection profiles. By showing that rain and rivers supply eight times more water to the Mediterranean brine than seawater during the hypersaline stage of the Late Miocene salinity crisis, the calculations resolve the geochemical riddle of "low salinity gypsum". The sulfur isotopes in gypsum derive from ocean seawater and the oxygen and hydrogen isotopes in the gypsum hydration water from atmospheric precipitation.

## 1. Introduction

The Mediterranean Sea experienced a major episode of evaporation during the Messinian stage of the Miocene epoch. This episode was initially called a *crisi di salinità* (Selli, 1954) and is now referred to as the Messinian Salinity Crisis (MSC). On the basis of seismic reflection profiles, the volume of the precipitated gypsum and salt and their interbedded sediments is estimated to be 0.8 to 1.0 million km³ (Ryan, 1973; Haq et al., 2020). The enormous size makes the Mediterranean evaporites one of the largest saline giants in the geologic past (Hsü, 1972a; Hübscher and Netzeband, 2007; Camerlenghi and Aloisi, 2020).

The presence of buried salt was first deduced by the observation of seabed knolls (Alinat and Cousteau, 1962; Hersey, 1965; Menard, 1965; Leenhardt, 1968) and subsequently by the observed flowage of an acoustically-transparent sub-bottom layer into anticlines and diapirs (Mauffret, 1969; Montadert et al., 1970; Lofi et al., 2008; Dal Cin et al., 2016). Beneath the floor of the Liguro-Provençal basin in the western Mediterranean, this ductile layer, also known as the Mobile Unit (MU) of

Lofi (2018), has an overall thickness ranging from 450 to 500 m. In the Albero-Balearic basin the MU thickness increases to 600–800 m (Blondel et al., 2022, 2023). The total calculated volume of this layer across both basins is approximately 120,000 km³ (Heida et al., 2022). In the Caltanissetta Basin in central Sicily salt thickness reaches 1000 m in the Braemi well (Valenti, 2010). In the eastern Mediterranean the thickness of the MU approaches 2 km in the Levant Basin (Ryan, 1978; Bertoni and Cartwright, 2006; Hübscher and Netzeband, 2007; Hübscher et al., 2008; Gvirtzman et al., 2013), 2.5 km in the Antalya Basin (Güneş et al., 2018), 3 km beneath the Herodotus Abyssal Plain (Kirkham et al., 2020) and > 3 km beneath the Mediterranean accretionary ridge (Polonia et al., 2002). Accordingly, the MU thickness is significantly bigger in the Eastern Mediterranean Basin. Indeed, there are three to four times more salt in the eastern basins than in the western basins, presumably due to the intervening Siculo-Tunisian sill (Topper and Meijer, 2013), greater surface area, stronger rates of evaporation, and further distance from the source of ocean saltwater (Schmalz, 1969; Debenedetti, 1982; Schmalz, 1991; Kirkham et al., 2020).

<footnote><sup>a</sup> Lamont-Doherty Earth Observatory of Columbia University, Palisades, NY 10964, USA</footnote>

<footnote><sup>b</sup> Géosciences Montpellier, CNRS, Université de Montpellier, Montpellier Cedex 05 34095, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: billr@ldeo.columbia.edu (W.B.F. Ryan).</footnote>
Following the first sampling of the Mediterranean evaporites by deep-sea drilling (Ryan et al., 1970; Ryan, 1971; Hsü, 1972b) and publication of the initial reports (Ryan et al., 1973), intense discussion arose about the most appropriate scenario for their formation (Drooger, 1973): “deep desiccated basin” (Cita, 1973; Hsü, 1973; Hsü et al., 1973a), “shallow water desiccated basin” (Nesteroff, 1973), and “deep non-desiccated basin” (Richter-Bernberg, 1973; Selli, 1973). In subsequent years progress has been advanced on the elevation of the basin floors relative to global sea level during the MSC (Ryan, 1976; Watts and Ryan, 1976; Steckler and Watts, 1978; Bessis, 1986; Heida et al., 2022), biostratigraphic assignment of the Messinian Stage (Cita and Gartner, 1973; Cita, 1975; Cita and Colombo, 1979; Colalongo et al., 1979; Hilgen and Krijgsman, 1999; Sierro et al., 2001; Hüsing et al., 2009), the impact of fluvial erosion (Barr and Walker, 1973; Chumakov, 1973; Clauzon, 1973, 1978; Barber, 1981; Clauzon, 1982; Lofi et al., 2005; Urgeles et al., 2011; Bowman, 2012), the depositional environment for the sampled gypsum, anhydrite and dolomitic marls (Friedman, 1973; Schreiber, 1973; Garrison et al., 1978; Rouchy, 1982a; Marsaglia and Tribble, 1999; Lugli et al., 2008) and chronology (Hilgen, 1991; Gautier et al., 1994; Hilgen and Langereis, 1988; Krijgsman et al., 1999a,b; Hilgen, 2000).

It became apparent after investigations of the evaporites in circum-Mediterranean terrestrial outcrops and in industrial mines that the MSC needed to be viewed in successive stages beginning with a hypersaline sea (stage 1) and ending with a hyposaline lake (Ruggieri and Sprovieri, 1976; van Couvering et al., 1976; Hsü et al., 1977; Ruggieri,

1978; Roveri et al., 2008b, 2014a). In the Vena del Gesso composite section of the northern Apennines (Vai and Ricci Lucchi, 1977; Krijgsman et al., 1999a,b; Lugli et al., 2007), the margins of the Caltanissetta Basin in Sicily (Decima and Wezel, 1971, 1973), and the Sorbas Basin in Spain (Dronkert, 1976; Riding et al., 1998; Krijgsman et al., 2001), the initial stage 1 deposit contains the Primary Lower Gypsum (PLG) consisting of up to 16 cycles of alternating selenitic gypsum and euxinic shale accumulating in a hypersaline environment from 5.97 to 5.60 Ma. Everywhere in terrestrial outcrops the PLG is separated by stratigraphic hiatus from overlying stage 3 deposits with 7 to 9 cycles consisting of gypsum or limestone or continental deposits belonging to a subsequent brackish lacustrine environment between 5.55 and 5.33 Ma (Manzi et al., 2009; Roveri et al., 2014a; Andreetto et al., 2021).

Disagreement has occurred with the stratigraphic placement of the thick halite observed in the reflection profiles. Most researchers have placed the 400 to 800 m thick halite in the Caltanissetta basin in Sicily above the PLG gypsum (Decima and Wezel, 1973; Krijgsman et al., 2007; Roveri et al., 2008c, 2008b, 2008a, 2008d, 2014b; Ryan, 2009), whereas others (Richter-Bernberg, 1973; Selli, 1973; van Couvering et al., 1976; Hsü et al., 1977; Garcia-Veigas et al., 1995; Rouchy and Caruso, 2006; Ryan, 2011; Ryan, 2023) envisaged a lateral transition between gypsum on margins and halite on basin floors.

Although there is a widely-adopted consensus (CIESM, 2008) that the halite layer succeeds the PLG, drill cores in the Caltanissetta Basin of Sicily show the Halite Member of the Gessoso Solfifera Formation rests on a thin anhydrite layer (a few meters thick), which in turn directly

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** A: Representative section of the Messinian sediments in the Caltanissetta basin in Sicily that places the Stage 1 Cattolica Gypsum Mb. of the MSC on basin edges and the Cattolica Halite Mb. in the basin axis (modified from Garcia-Veigas et al., 1995). B: Stratigraphic column of the Realmonte mine in Sicily showing the position and thickness of the MSC halite units (modified from Lugli et al., 1999). C: The MSC salt at the Realmonte Mine showing the exposure surface at the top of the K-Mg salts in Unit B with the desiccation cracks and the passage to halite in Unit C containing truncated chevron crystals indicative of repeated shoaling and periodic desiccation. D: A drawing of the contact between Units B and C showing the sets of fissures initiating from the salt layers (modified from Lugli et al., 1999).</figcaption></figure>
covers pre-MSC Messinian-Tortonian marls (Garcia-Veigas et al., 1995). The Halite Mb. is confined to the narrow axis of the basin. The Gypsum Mb. with its 16 beds of PLG is found on the margins of the basin where it overlies the Calcare di Base Mb. evaporative limestone, and the Tripoli Fm. diatomite (Fig. 1).

An identical downward succession of halite, a single thin anhydrite bed and the pre-MSC Messinian-Tortonian Lakhish Formation is encountered in the Dolphin, Yam 1 & 2, and Hof Ashdod 1 wells in the deep offshore of the Levant margin in the eastern Mediterranean (Fig. 2). Recent IODP drilling in the Tyrrhenian Basin also showed the same configuration with a halite layer resting on a thin anhydrite layer that overlays the pre-MSC sediments (Zitellini et al., 2024).

The simultaneous onset of the PLG in the terrestrial outcrops in Spain, Greece and Italy has now been found in the offshore of Spain where the PLG rests directly on marls with the last ten of the biostrati- graphic events definitive of the pre-evaporative interval of the Messinian stage of the late Miocene (Ochoa et al., 2015). Reflective layers within the halite have acoustic velocities too low to be beds of solid gypsum or anhydrite (Dal Cin et al., 2016), but their absence does not rule the presence of sulfate in the MU. Indeed, XRD elemental analyses on halite samples from the Dolphin well in the eastern Mediterranean reveal the presence of micro-crystals of CaSO₄ within cavities of the larger and more common halite crystals (Meilijson et al., 2019). Accordingly, gypsum and anhydrite are an integral part of the thick MU layer.

Each of the successive beds of selenite in the PLG is separated from the one above by non-evaporitic marly or shaly layer (Vai and Ricci Lucchi, 1977; Lugli et al., 2007, 2008). Therefore, the environment had to have either changed from sufficiently hypersaline for the growth of gypsum to hyposaline in order to stop the growth, or the supply of new salt ions from the exterior ocean had to cease.

During the preceding Pliocene and Pleistocene epochs ocean seawater entered into the Mediterranean through the Strait of Gibraltar. Its salinity increased from evaporation as it passed to its eastern ex- tremity where the seawater became saltier, sank to an intermediate depth, before exiting out of the Strait as an undercurrent. Evaporation (E) minus precipitation (P) and river discharge (R) remained positive despite millennial climate variations (Bethoux, 1984; Castellari et al., 1998; Hopkins, 1999). Late Miocene climate may have been somewhat warmer and wetter than the present day as indicated by the available proxy reconstructions and modelling studies (Fauquette et al., 2006; Bradshaw et al., 2012, 2015; Marzocchi et al., 2015), yet it was on an overall cooling trend with a dip to near-modern values between 7 and 5.4 Ma (Herbert et al., 2016).

The post-Messinian Pliocene and Pleistocene sediments in the eastern Mediterranean contain organic-carbon-rich sapropels that appeared at times of African monsoon run-off (Rossignol-Strick, 1983, 1985; Rossignol-Strick and Planchais, 1989; Lourens et al., 1996; Larrasoana et al., 2003). The timing of the freshening has been linked to the Earth's orbital cycles of precession and eccentricity (Hilgen, 1991; Lourens et al., 1996). The freshening of the Mediterranean happened every 21 to 24 kyr at times of maxima boreal summer insolation and minima of the precession index. The increase in atmospheric precipita- tion and fluvial discharge is credited mostly to greater seasonal contrast (Rohling, 1994) and to a lesser degree to northern hemisphere ice sheet melt (Troelstra et al., 1991). The calcite tests of upper water column planktonic foraminifera in the Mediterranean sapropels have δO¹⁸ sig- natures 2 to 4‰ lighter than the entering ocean seawater (Thunell et al., 1977; Vergnaud-Grazzini et al., 1977; Thunell and Williams, 1989; Emeis et al., 2000; Casford et al., 2003). Despite the significant fresh- ening, the formation of Mediterranean sapropels in both the eastern and western Mediterranean always took place under an anti-estuarine type of circulation comparable to the present (Rohling, 1994). An estuarine circulation would have produced a west to east decrease is sea surface temperatures that is not observed in alkenone unsaturated ratios (Emeis et al., 2000).

The onset of the MSC is thought to have been initiated by the

tectonically-driven narrowing and shoaling of the two main straits that connected the Mediterranean with the exterior ocean: the Betic Strait through southern Spain, and the Rifian Corridor through northern Morocco (Benson et al., 1991; Krijgsman et al., 1999a,b; Van Assen et al., 2006; Martín et al., 2009; Hüsing et al., 2010; Martín et al., 2014; Flecker et al., 2015; Achalhi et al., 2016; Capella et al., 2018; Krijgsman et al., 2018). As long as there was substantial return flow to the exterior ocean, the salinities in the Mediterranean basin attained a steady state. To achieve gypsum saturation, the ocean exchange coefficient (m³/s/ (kg/m³)⁻⁰.⁵) would need to be reduced by 4 orders of magnitude from present values (Meijer, 2006; Rohling et al., 2008; Raad et al., 2023; Ebner et al., 2024).

The absence of any evidence of subaerial exposure of the PLG beds (Roveri et al., 2008d) precludes closure of the Atlantic–Mediterranean connection during the first 370 kyr of the MSC, which, if it had occurred, would have initiated a recognizable drop in the brine surface (Blanc, 2000; Meijer and Krijgsman, 2005). A basin not completely closed, but still sufficiently restricted to prevent outflow, would receive a contin- uous supply of seawater leading to a storage of all incoming sulfate, sodium chloride and the more soluble potassium and magnesium chlo- rides and sulfates in pre-existing depocenters (Meijer, 2006). With constant inflow for 370 kyr and without outflow, the volume of accu- mulating salt would become 4 to 6 times larger than the volume observed (Debenedetti, 1976; Blanc, 2000, 2006; Krijgsman and Meijer, 2008; Raad et al., 2023).

## 2. Conceptual model

To satisfy the observed periodic interruptions of the PLG gypsum beds without signs of dissolution and the requirement to limit an amount of salt to the volume observed, we have developed a novel box model for the MSC. The model incorporates a water activity coefficient to reduce the rate of evaporation with rising salinity, which significantly decreases the amount of salt precipitated. The model is purposely kept algebraic. Its objective is to discover that when using a water activity coefficient for the evaporating brine and an oscillating one-way inflow and outflow, to what degree do the budgeting of the molarity of the incoming and outgoing solutes successfully mimic the observations and measurements of the Mediterranean gypsum and halite. In our model, evaporite deposition occurs only when new saltwater is supplied in each dry in- terval (Fig. 3). Shale and marl become deposited when the supply of water is only from precipitation and rivers during each wet interval.

The ratio of seawater inflow and brine outflow (leakage) to the external ocean is set at levels to limit the evaporite accumulation to the magnitude of the halite observed in the Mediterranean's mobile layer (Haq et al., 2020). This leakage delays the precipitation of the more- soluble potash and magnesium salts until closure of the ocean entryway and the onset of evaporative drawdown (Maiklem, 1971). The replacement of high-salinity brine lost by leakage with low-salinity new seawater has the effect of not only reducing the salinity in the Medi- terranean's brine reservoir during the wet periods but also changes the relative proportion of the various ions in the brine reservoir (Sanford and Wood, 1991).

### 2.1. Boundary conditions and chemical components

For simplicity, the late Miocene Mediterranean is considered a single large receptor for evaporites with a volume and surface area similar to today (Meijer and Krijgsman, 2005; Ryan, 2008). Using the same initial conditions of Meijer and Krijgsman (2005), the salinity of incoming Atlantic seawater is set to 35 kg m⁻³ (=g/l). The calculations account for the number of moles of each ion (Cl, Na, Ca, SO₄, K, Mg, Sr, Br) intro- duced with each cubic meter of incoming seawater and accumulate these ions in the brine. Precipitation of gypsum and halite remove ions from the brine reservoir. Leakage returns ions to the external ocean. The combined charges of positive and negative ions remain balanced.
<figure><img src="image_5.png" /><figcaption>**Fig. 2.** Four wells of descending depth (left to right) on the Levant Margin of the eastern Mediterranean where the Mavqiim Fm. halite layer overlies a thin bed of anhydrite that in turn rests directly on marine marls of the Lakhish Fm. The marls contain the planktonic foraminifera assemblage of the *Globorotalia conomioizea* group attributed to pre-evaporite interval of the Messinian stage of the late Miocene (Cohen, 1993; Derin, 2000; Meilijson et al., 2019).</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Fig. 3. The periodic switching during MSC stage 1 between inflow of Atlantic saltwater and outflow of the accumulated Mediterranean brine.</figcaption></figure>

Gypsum saturation occurs when the brine salinity reaches 145 kg m⁻³. As brine concentration increases beyond 145 kg m⁻³, CaSO₄ in excess of saturation becomes gypsum (CaSO₄·2H₂O) with a density of 2310 kg m⁻³. Since the amount of SO₄ in seawater is greater than Ca, the excess SO₄ accumulates in the brine reservoir. Halite (NaCl) saturation starts at a salinity of 350 kg m⁻³. The excess Cl also accumulates in the Mediterranean brine reservoir since the amount of Cl in seawater is greater than the Na. Halite solidifies with a density of 2160 kg m⁻³.

The rate of evaporation is represented in the model calculations as a water activity coefficient. The rate of evaporation depends not only on temperature, humidity, atmospheric vapor pressure and wind speed (Stumm and Morgan, 1981), but to an even greater extent on salinity because higher concentrations of dissolved salts lower the free energy of the water molecules (Salhotra et al., 1985). The relationship between saturation vapor pressure and salinity is also contingent with the particular ions in solution. For example, solutions of KCl have a higher water activity coefficient than solutions of NaCl at the same concentration whereas solutions of MgCl₂ have a lower water activity coefficient than NaCl.

Wet-dry cycles in the model are represented in a sinewave that mimics in timing the eccentricity-modulated precession cycles during the first 370 kyr of the MSC (Fig. 4). Atmospheric precipitation and river input are amplified by 33 % during wet periods and reduced by 20 % in the dry periods to reflect the Pliocene-Pleistocene δ¹⁸O records during insolation maxima and minima (Fig. 4). A similar adjustment to the sinewave amplitude is applied to enhance evaporation rates during dry periods and decrease evaporation rates during wet periods. The values for initial values of E, P and R come from Castellari et al. (1998) and are listed in Table 1.

At times of inflow (i.e., dry interval of precession; Fig. 4) gypsum (CaSO₄·2H₂O) is created by subtracting equal numbers of moles of Ca and SO₄ equivalent to each kg of entering seawater and the twice number of moles of H₂O from the brine reservoir per unit time. The remaining unused ions are added to the Mediterranean brine which increases its salinity. The number of moles per cubic meter of seawater for the various ions including bromine and strontium are listed in Table 2. The molecular weights of the evaporites are in Table 3.

At times of return flow to the exterior ocean during wet periods, ions in the Mediterranean brine are returned to the ocean in the same

<figure><img src="image_7.png" /><figcaption>Fig. 4. Simplified periodic input of freshwater from precipitation and rivers, amplified by 33 % in wet periods and reduced by 20 % in dry periods in synchronization with summer insolation at 65°N (Laskar et al., 2004) for the first 370 kyr of the MSC between 6.0 and 5.6 Ma. Red in panel 2 indicates drier climate.</figcaption></figure>

**Table 1**

Water sources and their equivalent rate from Castellari et al. (1998).

<table><thead><tr><td>Water source</td><td>Rate (m/y)</td></tr></thead><tbody><tr><td>Evaporation</td><td>-1.32 to -1.57</td></tr><tr><td>Precipitation</td><td>0.55 to 0.70</td></tr><tr><td>Rivers</td><td>0.21</td></tr><tr><td>Gibraltar exchange</td><td>0.56 to 0.66</td></tr></tbody></table>
<table><caption>**Table 2**
Composition of seawater.</caption><thead><tr><th>Constituent</th><th>Moles per kg</th><th>Grams per liter</th></tr></thead><tbody><tr><td>H<sub>2</sub>O</td><td>53.6</td><td>965.0000</td></tr><tr><td>Cl<sup>-</sup></td><td>0.546</td><td>19.2500</td></tr><tr><td>Na<sup>+</sup></td><td>0.469</td><td>10.76000</td></tr><tr><td>Mg<sup>++</sup></td><td>0.0528</td><td>1.2920</td></tr><tr><td>SO<sub>4</sub><sup>-</sup></td><td>0.0282</td><td>2.7120</td></tr><tr><td>Ca<sup>++</sup></td><td>0.0103</td><td>0.4200</td></tr><tr><td>K<sup>+</sup></td><td>0.0102</td><td>0.3990</td></tr><tr><td>Br<sup>-</sup></td><td>0.000844</td><td>0.0673</td></tr><tr><td>Sr<sup>++</sup></td><td>0.000091</td><td>0.0079</td></tr><tr><td>CO<sub>3</sub><sup>-</sup></td><td>0.000283</td><td>0.0002</td></tr><tr><td>Total salts</td><td></td><td>34.8352</td></tr></tbody></table>

<table><caption>**Table 3**
Mineral, formula and density.</caption><thead><tr><th>Mineral name</th><th>Mineral formula</th><th>Density (gm/ cc)</th><th>Molecular weight (gm/ mol)</th></tr></thead><tbody><tr><td>Anhydrite</td><td>CaSO<sub>4</sub></td><td>2.97</td><td>136.14</td></tr><tr><td>Bischofite</td><td>MgCl<sub>2</sub>·6H<sub>2</sub>O</td><td>1.6</td><td>203.30</td></tr><tr><td>Calcite</td><td>CaCO<sub>3</sub></td><td>2.71</td><td>100.90</td></tr><tr><td>Carnalite</td><td>KClMgCl<sub>2</sub>·6 (H<sub>2</sub>O)</td><td>1.6</td><td>277.85</td></tr><tr><td>Gypsum</td><td>CaSO<sub>4</sub>·2H<sub>2</sub>O</td><td>2.32</td><td>172.17</td></tr><tr><td>Halite</td><td>NaCl</td><td>2.16</td><td>58.43</td></tr><tr><td>Kainite</td><td>KMgClSO<sub>4</sub>·3H<sub>2</sub>O</td><td>2.17</td><td>248.97</td></tr><tr><td>Kieserite</td><td>MgSO<sub>4</sub>·H<sub>2</sub>O</td><td>2.57</td><td>138.38</td></tr><tr><td>Polyhalite</td><td>K<sub>2</sub>MgCa<sub>2</sub>(SO<sub>4</sub>)<sub>4</sub></td><td>2.85</td><td>602.94</td></tr><tr><td>Sylvite</td><td>KCl</td><td>1.99</td><td>74.55</td></tr><tr><td>Bicarbonate</td><td>HCO<sub>3</sub></td><td>1.67</td><td>61.02</td></tr><tr><td>Epsomite</td><td>MgSO<sub>4</sub>·7H<sub>2</sub>O</td><td>1.67</td><td>246.48</td></tr><tr><td>Hexahydrite</td><td>MgSO<sub>4</sub></td><td>2.66</td><td>220.46</td></tr><tr><td>Glauberite</td><td>Na<sub>2</sub>Ca(SO<sub>4</sub>)<sub>2</sub></td><td>2.75</td><td>278.20</td></tr><tr><td>Dolomite</td><td>CaMg(CO<sub>3</sub>)<sub>2</sub></td><td>2.84</td><td>184.40</td></tr></tbody></table>

proportion of their concentrations in the brine reservoir at that time. The salinity of the remaining brine is thereby momentarily reduced and the water activity coefficient increased. Strontium is added to the Mediterranean with its late Miocene marine $^{87}$Sr/$^{86}$Sr isotopic composition (0.7090) only during times of ocean inflow, whereas the river water adds its strontium with its continental isotopic signature (<0.7088) at all times and with lower abundance. Sulfate is added with its marine $^{34}$S/$^{32}$S composition (~21 ‰) and $^{18}$O$_{SO4}$/$^{16}$O$_{SO4}$ composition (8 ‰) (Rees et al., 1978; Böttcher et al., 2007). Since bromine does not precipitate, it increases in the brine reservoir.

### 3. Model results

The decrease in the water activity coefficient with rising salinity in the Mediterranean brine has the effect of reducing the evaporation rate and hence the amount of entering ocean seawater necessary to keep the Mediterranean filled (Fig. 5). Since freshwater is added continuously during both wet and dry periods and ocean seawater only in dry periods, a much greater amount of freshwater is supplied to the Mediterranean compared to saltwater. The consequence of using a water activity coefficient is to allow the Mediterranean to switch from a negative to a positive water budget during wet intervals, in contrast to the permanent negative water budget before and after the MSC.

The mass of gypsum and halite increases stepwise during the 370 kyr interval with pauses in the wet periods (Fig. 6). The accumulation produces a salt deposit beginning with gypsum and followed by halite. The PLG is confined to margins at elevations above an anoxic interior (de Lange and Krijgsman, 2010) where it grows on the bottom in discrete beds (Natalicchio et al., 2022) except during the wet periods.

During the arid phase of each precession cycle, an equal number of moles of Ca and SO$_{4}$ per kyr is consumed in the crystallization of gypsum and the excess moles of SO$_{4}$ are added to the brine reservoir. The excess

moles of Cl not added to halite and all the moles of the K and Mg accumulate in the reservoir (Fig. 7). This leads to an evolving reservoir composition with proportions and abundances of Na, SO$_{4}$, Mg, K substantially different from those of seawater (Fig. 8).

### 4. Compatibility of observations with the evaporative model

#### 4.1. Strontium isotopes

The $^{87}$Sr/$^{86}$Sr isotope ratio measured on seven individual beds of the PLG in the Vena del Gesso Basin of the northern Apennines (Fig. 9, top panel) shows a gradual departure from the late Miocene coeval global ocean value to those of rivers (Reghizzi et al., 2018). This departure is replicated in the model calculations (Fig. 9, middle panel) and is produced by a reduction of periodic ocean inflow in comparison to a constant supply of river water. The computed $^{87}$Sr/$^{86}$Sr values show the same brief increase in $^{87}$Sr/$^{86}$Sr observed in each of the seven Vena del Gesso gypsum beds (Reghizzi et al., 2018). This pulse towards the oceanic signature reflects the addition of seawater with its more abundant dissolved strontium during each arid phase.

#### 4.2. Sulfate isotopes

The sulfate isotopes also fit with the model. For example, the $\delta^{34}$S (ratio of $^{34}$S/$^{32}$S) measured on Primary Lower Gypsum (PLG) from the Sorbas Basin in Spain (Fig. 9, bottom panel) displays an overall trend from 24 ‰ in the earliest beds to the 22 ‰ value of sulfate minerals precipitated from evaporated Late Miocene seawater in the youngest beds (García-Veigas et al., 1995; García-Veigas et al., 2018). Superimposed on the trend are measurements of $\delta^{34}$S from 12 individual PLG beds that each show a 0.5 to 1.5 ‰ change towards the lighter seawater composition. The individual shifts and the overall trend towards the expected seawater composition are attributed to the accumulation of new seawater accompanying each arid phase. During the euxinic conditions of each wet period bacterial sulfate reduction (BSR) consumed lighter $^{32}$S and thereby left the reservoir enriched in $^{34}$S. The trend initiating with heavier $\delta^{34}$S at the commencement of Stage 1 is attributed to precursor oxygen-deprived environments with increasing salinity starting as early as 6.4 Ma (Kouwenhoven et al., 2006).

The $\delta^{18}$O$_{SO4}$ from the gypsum in the Sorbas Basin shows a similar shift in each PLG bed towards the lighter value of the incoming seawater (Rees et al., 1978; Böttcher et al., 2007). However, the overall trend is instead directed towards more positive values (García-Veigas et al., 2018). The alignment to more positive values of the $\delta^{18}$O$_{SO4}$ is also attributed to bacterial sulfate reduction (BSR) that results in the lighter $^{16}$O isotope being depleted during the reoxidation of reduced sulfur compounds. The fractionation leaves increasing amounts of the heavier $^{18}$O isotope in the remaining sulfate-rich reservoir.

The observed periodic shift from heavy to light isotopic compositions in the Sorbas Basin PLG beds and the return from light to heavy during the deposition of the interbedded euxinic shale is a consequence of the climate-driven oscillation between saltwater inflow and brine outflow (Fig. 3) incorporated in the model computations.

#### 4.3. Gypsum hydration isotopes

The $\delta^{18}$O and $\delta$D of the gypsum hydration water (CaSO$_{4}$ • 2H$_{2}$O) have been measured on one cycle (PLG Bed 6) of gypsum–marl deposition from the Messinian Yesares Member in Sorbas Basin, Spain (Evans et al., 2015). The relatively low $\delta^{18}$O and $\delta$D values in the hydration water indicate a significant influence of meteoric water supplied from the larger freshwater supply. Bed 6 occurs at 5.86 Ma in Fig. 5 where the proportion of freshwater approaches 100 %.

The PLG Bed 6 gypsum bed begins with a “nucleation zone” (Dronkert, 1985) followed by swallow-tailed selenite crystals with size decreasing upwards (Fig. 10A). As the crystal size decreases, it becomes
<figure><img src="image_8.png" /><figcaption>**Fig. 5.** The effect of the decreasing water activity coefficient on evaporation rate, ocean seawater inflow rate and percent of freshwater addition to saltwater addition. The most significant change occurs at the eccentricity minimum, aligning with the precipitation of PLG bed 6, where the activity coefficient is least effective, freshwater input peaks, and Atlantic saltwater input is at its lowest. At this point, the salinity of the Mediterranean brine also reaches its maximum.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 6. The progressive accumulation of gypsum and followed by halite.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Fig. 7. The progressive storage of SO₄ and Cl in the Mediterranean brine reservoir.</figcaption></figure>

“banded selenite” (Lugli et al., 2010; Natalicchio et al., 2021). Further upwards the “banded selenite” takes on the appearance of giant cauliflower-shaped “supercones” (Dronkert, 1985).

Closely-spaced isotopic measurements of the mother water for gypsum growth (Fig. 10B) show an upward increase of δ¹⁸O₂>O₂O from -2.0 ‰ to +3.8 ‰ and δD₂>O₂O from -16 ‰ to +18.4 ‰ in the massive elongated swallow-tailed selenite. The passage from lighter to heavier compositions is followed by a decrease in the “banded selenite” and eventually a return to the starting values at the end of the “supercone” interval (Evans et al., 2015). The trend to more positive values has been attributed to increasing aridity at the time of precession maxima and the reversed trend to wet conditions during precession minima (Evans et al., 2015).

The curve of percent freshwater in Fig. 5 conforms with the isotopic behavior in the PLG 6 gypsum bed represented in Fig. 10. Minima in percent freshwater and maxima in saltwater are coincident with the positive δ¹⁸O₂>O₂O and δD₂>O₂O in the tall swallow-tailed selenite crystals.

The beginning of the maxima in percent freshwater water is coincident with the end of the “supercone” growth and the onset of euxinic marl. The marl beds separating the gypsum beds have δ¹⁸O₂>O₂O descending from +2.0 ‰ directly above the “supercone” to -3.9 ‰ beneath the next gypsum bed. The shale corresponded to times of outflow to the ocean. River and rain freshen the surface water, inhibiting the supply of oxygen to the interior.

4.4. Fluid inclusions

Samples from the Messinian gypsum of the Sorbas Basin were also subject to micro-thermometric analysis (Evans et al., 2015). Fluid inclusions in the gypsum crystals were first frozen to shrink the vapor bubble and turn the liquid to ice. The inclusions were then gradually reheated. During heating, the first melting of the ice took place between -42 °C and -32 °C and the final melting between -5.2 °C and -0.2 °C. Equations and tables of the freezing point depression of H₂O-NaCl in
<figure><img src="image_11.png" /><figcaption>**Fig. 8.** Changes in the proportion of various salt ions in the Mediterranean brine reservoir, starting from left to right with the precipitation of gypsum, followed by halite, PLG Bed 6 when salinity approaches maximum and at the beginning of evaporative drawdown. Ca is consumed in the growth of gypsum, Na decreases during the growth of halite, leaving an enrichment of SO₄, K and Mg at the conclusion of Stage 1.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Fig. 9.** Top 2 panels: comparison of model output trends (bottom) to measured $^{87}$Sr/$^{86}$Sr isotope trends (top) on seven PLG gypsum beds from the Vena del Gesso section in the northern Apennines (from Reghizzi et al., 2018). Bottom panel: $^{δ^{34}}$S isotopes measured on the PLG beds in the Sorbas Basin of SE Spain (trends extracted from Fig. 8 of García-Veigas et al., 2018). The gray bar indicates the $^{δ^{34}}$S composition of Late Miocene seawater.</figcaption></figure>

solutions (Bodnar, 1993) indicate that the final melting temperatures for the passing of ice to liquid corresponds to a salinity between 35 and 81.4 kg/m³ which is significantly below the 145 kg/m³ threshold for crystallization from normal seawater. The highest salinities deduced from the inclusions are from the swallow-tailed selenite and the lowest are from measurements in the “supercone” above and from the “nucleation cone” below.

A similar analysis on fluid inclusions has been performed on the PLG from Calabria (Costanzo et al., 2019). Salinities are reported in the range of 0.18 to 11.34 wt% NaCl equivalent and are interpreted once again to be from a brine with a significant proportion of non-marine waters.

Fluid inclusions in Messinian selenite crystals from the Piedmont

Basin in northwest Italy have comparable salinities of 1.6 wt% NaCl equivalent. These low values have been explained as a hybrid mixture of seawater with Ca and SO₄ derived from solution of nearby older gypsum deposits that have been recycled in the PLG (Natalicchio et al., 2014).

The PLG is widespread on Mediterranean continental margins and is present at depths exceeding 600 m offshore of Spain far from continental sources (Ochoa et al., 2015; Raad et al., 2021). If once present to such depths on all margins, the PLG volume could have been as large as 5 % of the size of the halite layer. A mass of gypsum as large as 5 × 10¹⁶ kg (Fig. 6) vastly exceeds whatever amount that could have been recycled from previous evaporites.
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Diagram of δ¹⁸O>H₂O vs. δD>H₂O measured from the gypsum hydration water (adapted from Evans et al., 2015). The values (enclosed with a dashed ellipse) are distributed midway between rainwater (lower left) and modern gypsum precipitated from concentrated seawater (upper right). The values from the tall swallow-tailed selenite crystals lie closer to modern gypsum, and those from the “nucleation zone” are closer to rainwater. The values from the “banded selenite” and “supercone” are midway and close to Standard Mean Ocean Water. Insert is from Evans et al. (2015) and displays the δ¹⁸O>H₂O of the gypsum hydration water change upwards from the nucleation zone to the top of the “supercone” in PLG Bed 6.</figcaption></figure>

### 4.5. Geochemical riddle of “low-salinity gypsum”

The longstanding discussion of whether the Messinian gypsum was precipitated from seawater at elevated salinity or seawater at substantially reduced salinity (Longinelli, 1979; Müller and Mueller, 1991; Attia et al., 1995; Playà et al., 2000; Lu et al., 2001; Flecker et al., 2002; Lugli et al., 2010; Natalicchio et al., 2014; Evans et al., 2015; Kirkham et al., 2020) has been presented as a geochemical riddle (Aloisi et al., 2022). According to the model calculations rain and river water was continuously supplied to the Mediterranean during the MSC, but saltwater only during the arid phase and at rates reduced with increasing salinity. Hence the Mediterranean brine acquired a geochemical signature resembling meteoric water rather than ocean water, even with high salinity in the residual brine.

### 4.6. Evidence confirming high salinity in the Piedmont Basin

Carlo Sturani (1973) investigated the PLG 6 cycle gypsum bed and its bounding euxinic shales in the Monticello d'Alba region of the Piedmont Basin of northern Italy (Dela Pierre et al., 2011), where the fluid inclusions in the gypsum had indicated low salinity (Natalicchio et al., 2014). Indeed, Sturani found many features indicative of fresh to brackish water (i.e., dragon fly larva, spiders, leaves of deciduous trees, freshwater reeds and turtles). In the sulfate-rich, euxinic clays above and below the gypsum bed were imprints of fish: Cyprinodontoids (Pachy-lebias sp.), herring (Spratelloides lemoinei), sole (Microchirus bassanianus), Goby (Gobius sp.), and eel (Anguilla attributed by Carnevale and Schwarzhans (2022) to the genus Lepidopus) (Fig. 11). Sturani considered that the fish lived in a surface layer above a deeper and more saline anoxic layer in which, after death, the fish became remarkably-well preserved.

The backbones of the eel and fish were wrinkled in a zig-zag pattern caused by post-mortem shrinkage of the soft tissues. Shrinkage was extreme and specimens were reduced to one fourth of their original length. Sturani surmised that the shrinkage was the consequence of

dehydration during extraction of water from inside the body to the surrounding brine by osmotic pressure. Out of 100 specimens, only one was fossilized without a severely deformed spine. In order to produce the required magnitude of osmatic pressure to complete the dehydration, the salinity in the deeper anaerobic water of the Piedmont Basin must have been far above the salinity deduced from the fluid inclusions and in the range of the salinity from the model calculations. Indeed, fish remains have also been found within the ‘balatino’ facies of gypsum at Racalmuto Sicily (Carnevale and Schwarzhans, 2022).

### 4.7. Evolution of the gypsum facies with increasing salinity

Branching selenite (Lugli et al., 2008, 2010) appears throughout the Mediterranean in the 6th PLG bed, There, the gypsum consists of branching selenite interwoven with laminar gypsum facies called ‘balatino’ (Ogniben, 1957). The ‘balatino’ gypsum is thought to be a cumulate deposit composed of crystals formed either at the water/air surface or at the oxic/anoxic interface in the water column and settled on the seabed from a “pelagic rain” (Hardie and Lowenstein, 2004; Lugli et al., 2015; Natalicchio et al., 2021). The change from vertically-oriented swallow-tail selenite to banded selenite is credited by Natalicchio et al. (2021) to an intensification of water column stratification and by Lugli et al. (2010) to the passage from a low-degree of super saturation allowing crystals to grow large to an increase in supersaturation that enhances the nucleation of crystals and therefore creates more competition for space among the nuclei. The laminar “balatino” gypsum appears at the highest level of supersaturation and favoring the formation of new nuclei while inhibiting them from growing larger (Alimi et al., 2003; Alimi and Gadri, 2004; Reiss et al., 2017).

The increase in water column stratification is analogous to the increase in supersaturation of the brine reservoir compared to a less-saturated surface layer. Although the contorted skeletons of fish and eels were more commonly observed in bituminous sediments above and below the laminar “balatino” gypsum, fish remains have been also found within the laminated gypsum. This observation implies that even when
<figure><img src="image_14.png" /><figcaption>**Fig. 11.** A sketch modified from Figs. 1 (top) and 2 (bottom) of Sturani (1973) showing the laminated microcrystalline primary gypsum Bed 6 ('balatino' facies) and the overlying thinly-laminated shale containing the imprint of fossilized shrunken fish (Round Herring: *Spratelloides*) and eel (*Anguilla* attributed to the genus Lepidopus sp.). Upon death, the eel sank into an underlying hypersaline brine, causing water to be pumped by osmotic pressure from inside its body into the surrounding brine. The soft tissues shrank and the backbone wrinkled. Fish and other fossils are occasionally founded within the laminated gypsum. The laminated gypsum comprising PLG Bed 6 is 7 m thick. The eel length is 5 cm.</figcaption></figure>

the interior became supersaturated, the surface lens remained habitual for fish particularly in regions such as the lagoon and estuary setting in the Monticello d'Alba region of the Piedmont Basin.

The continuously rising salinity derived from the model calculations during each arid phase is replicated with the evolution of the gypsum facies from tall swallow-tail selenite, to bedded selenite and then to laminar gypsum, interpreted to reflect progressively increasing levels of supersaturation. The oscillation of ocean inflow and outflow as the climate fluctuates from arid to wet is evident in the changing isotopic composition of the individual gypsum beds. The model computations offer a mechanism for the fluctuations of salinity that is alternative to prior hypotheses of falling and rising sea level as the primary agents of changing salinity (Vai and Ricci Lucchi, 1977; Rouchy, 1982b; Lugli et al., 2010). In fact, Krijgsman et al. (2024) showed that there is no direct relationship between the gypsum occurrence of the PLG beds and the sea-level curve during the MSC.

Since the euxinic shales between the gypsum beds contain stenohaline fish and marine diatoms, their presence requires either a connection with the external ocean or refuge in estuaries. Incoming ocean seawater with salinity below the concentrating Mediterranean brine would be expected to be distributed in a widespread upper layer as did the incoming ocean water during the Pliocene and Pleistocene. A

pronounced vertical density stratification is an important component of the deep-water model of evaporite sedimentation. The sufficiently lower salinity surface layer during wet periods would allow marine fish and diatoms to recolonize the Mediterranean each precession cycle (Carnevale and Schwarzhans, 2022). Fish are abundant in Bahama brine reservoirs at concentrations up to 1.75 times seawater (McCaffrey et al., 1987). Halophilic Archaea live in extreme salinities up to 70 times seawater (Hallsworth et al., 2007).

### 4.8. The succession to more soluble salts

Only upon closure and the subsequent further concentration of solutes remaining in a shrinking reservoir do the more soluble salts precipitate from the brine in the reservoir. Kainite (KMg(SO4)Cl·3H2O) appears first and followed by bischofite (MgCl2·6H2O) as the volume of the reservoir shrinks.

The salts from mines and boreholes in Caltanissetta Basin in Sicily have a facies succession similar to the model calculations. The succession begins with a basal anhydrite a few meters thick (Fig. 1). Above are four consecutive units of halite named A, B, C and D (Decima and Wezel, 1973; Decima, 1976). Unit A begins with laminated halite and interbedded nodular anhydrite followed by halite with thin anhydrite
laminae and then thick homogeneous halite (>98 % NaCl). The halite crystals in Unit A show no evidence of bottom overgrowth, current structures, or dissolution with or without truncation surfaces and point to a substantial water depth (Lowenstein and Hardie, 1985). Unit B has halite intercalated with beds of kainite, sylvite (KCl), kieserite (MgSO₄·H₂O), and bischofite (MgCl₂·6H₂O). Unit B shows evidence of decreasing water depth that resulted in an exposure surface with desiccation cracks filled by red mud (Lugli et al., 1999).

Where Unit C is present, it is relatively thin with coarse halite intercalated with anhydrite laminae and polyhalite (K2Ca2Mg(SO₄)₄·2H₂O). Unit D begins with anhydrite marls and ends with halite containing frequent anhydrite laminae. Vertically elongated chevron crystals truncated by dissolution surfaces in Units C and D indicate shoaling and periodic desiccation (García-Veigas et al., 2018). Units C and D consist of Ca, SO₄, Na, Cl, K and Mg dissolved from exposures of Units A and B on margins of desiccated regions of the Mediterranean interior at elevations below the external Atlantic surface (García-Veigas et al., 1995).

Microanalysis of fluid inclusions in the halite samples from the Caltanissetta Basin in Sicily and from the Lorca Basin in SE Spain show that the halite below the exposure surface contains brines concentrated during advanced stages of seawater evaporation (McCaffrey et al., 1987; García-Veigas et al., 1995; Brennan et al., 2013; García-Veigas et al., 2018). The residual brines in the Catollica Mb. halite inclusions had evolved to high Mg, K and SO₄, decreasing Na, and negligible Ca, similar to the compositions derived from the calculations in our evaporative model (Fig. 8). Inclusions in halite above the exposure surface contain less concentrated brine with lower Mg, higher Na and some Ca enrichment indicative of the recycling of previously precipitated salt and gypsum (García-Veigas et al., 1995; Cendón et al., 2004).

The bromine measurements in halite show a comparable evolution of the Mediterranean brine (Decima, 1976; García-Veigas et al., 1995; García-Veigas et al., 2018). In the Caltanissetta Basin, the Br content increases from <13 ppm in the base of Unit A to >150 ppm prior to the first kainite bed in Unit B. The Br then drops precipitously to 25 ppm where laminae of sylvite, kieserite, and bischofite appear (Lugli, 1999). The presence of potassic and magnesian salt minerals announces an extreme hypersaline environment (Yoshimura et al., 2016). The drop in Br in Unit B is interpreted to be the result of the closing of the ocean

portal, cessation of seawater arriving with new bromine, and commencement of evaporative drawdown that led to the precipitation of ions stored in the residual brine. The bromine in the recycled halite above the exposure surface is below detection because the introduction of ocean saltwater had ceased. In the absence of seawater, evaporation in arid intervals led to drawdown of the brine surface. Complete desiccation is observed in the Realmonte mine by an erosion surface truncating the deformed salt layer (Figs. 1 and 12).

## 4.9. Absence of early evaporites beneath the mobile salt layer

The high-amplitude reflectors observed at the base in the mobile salt layer (MU) in the western Mediterranean (Montadert et al., 1970; Mauffret et al., 1973; Shipboard Scientific Party, 1973; Bache et al., 2009) have been attributed to a Lower Evaporite (LE) interval of the MSC that purportedly comprises the first 370 kyr (Montadert et al., 1978; Lofi et al., 2008; Raad et al., 2021, 2023). However, these reflectors are not observed in the adjoining central and southern Balearic and Algerian basins (Camerlenghi et al., 2008; Dal Cin et al., 2016; Camerlenghi et al., 2018; Blondel et al., 2022, 2023). Where these reflectors are observed their sonic velocities are well below those of gypsum and anhydrite (Geletti et al., 2014; Dal Cin et al., 2016).

In the Tyrrhenian Sea these pre-MU high-amplitude reflectors have been sampled by deep-sea drilling at ODP Sites 652 and 654. There, the reflectors coincide with the euxinic shale and diatomite belonging to the Tripoli Formation that directly preceded the gypsum and salt (Shipboard Scientific Party, 1987, 1987b; Cita et al., 1990; Ryan, 2023). The absence of the PLG or its equivalent euxinic shale beneath the mobile salt layer in the eastern Mediterranean (Bertoni and Cartwright, 2007; Solem, 2014; Lofi, 2017; Güneş et al., 2018; Camerlenghi et al., 2020) adds further support to the timing in our calculations with halite precipitation in deeper regions at the same time as the PLG on margins.

## 4.10. Ductile and rigid salt layers

The MU salt layer is acoustically transparent and only interrupted by faint internal reflectors. In a typical refraction profile from the western Mediterranean (Fig. 13) the Mobile Unit (MU) begins with a ductile sublayer (DL) that under the weight of its overburden has flowed into

<figure><img src="image_15.png" /><figcaption>**Fig. 12.** Revised schema of the deformed halite of Units A and B based on mine shafts, tunnels (horizontal lines) and boreholes (vertical lines) (Butler et al., 1995). Drawn to true scale: vertical and horizontal distances are the same. The halite (yellow) is mobile whereas the kainite beds (black) are more rigid. Erosion surface #1 is the Intra-Messinian Truncation Surface (Gvirtzman et al., 2017; Kirkham et al., 2020) separating the hypersaline salt Units A & B halite from the Stage 3 hyposaline Pasquasia Fm. Halite Units C and D were removed by the erosion after the Stage 2 evaporative drawdown. The Pasquasia Fm. corresponds to the Stage 3 Lago-Mare interval.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>**Fig. 13.** Seismic profile SPBAL01-04 highlighting the MSC sublayers in the northwestern Mediterranean which show salt flowage confined to the earliest halite ductile layer (DL) comprising the lower part of the Mobile Unit (MU). RL is the more Rigid Layer thought to contain the equivalents of Units B, C and D in Sicily. The Upper Unit (UU) contains the MSC hyposaline evaporites. TS: Top Surface; DL: Ductile Layer; BS: Bottom Surface; VE: Vertical Exaggeration.</figcaption></figure>

the observed anticlines. Above is a more rigid sublayer (RL) of relatively uniform thickness with stronger internal reflectors. On top is the upper unit (UU) belonging to the MSC Stage 3 evaporites with the highest amplitude internal reflectors. Based on thickness, ductility and reflectivity the DL sublayer could be equivalent to Unit A of the Cattolica halite in Sicily (Fig. 10) with its 98 % pure NaCl. Sublayer RL would then match to Units B, C and D of the Cattolica halite in Sicily with its more abundant clastics, anhydrite and re-precipitated salts contributing to greater rigidity. UU the Upper Unit accumulated in the hyposaline stage 3 of the MSC and corresponds to the Pasquasia Fm.

Potash and magnesium salts interbedded with sandstone at the top of the MU were encountered by deep-sea drilling at Site 134 in the western Mediterranean (Hsü et al., 1973b) and at Sites 374 and 376 in the eastern Mediterranean (Kuehn and Hsü, 1978). Brines from the disso-lution of bischofite are present in the Discovery Basin in the Ionian Sea (Wallmann et al., 1997).

The halite Unit A in Sicily is devoid of clastics. The model's increase in brine salinity and hence density would assert hydrostatic pressure against the pore waters in the basin margin's sediments. Brine at satu-ration for halite reaches a density of 1.215 kg/m³ and brine at saturation for kainite a density > 1.3 kg/m³ (McCaffrey et al., 1987). The resulting hydrostatic pressure against pore waters in pre-MSC margin sediments with a density of 1.024 kg/m³ could have allowed the brine to act as a buttress and hold the margin sediments in place, until the onset of evaporative drawdown.

The gamma ray log and XRD of cuttings from the Dolphin well in the easternmost Mediterranean show the 1-km thick seismo-stratigraphic Units 1, 2, 3 and 4 to be essentially clastic free followed by abundant clastics with anhydrite in Unit 5 (Meilijson et al., 2019). This super-position suggests that the Mediterranean remained full of brine until the onset of evaporative drawdown at the time of Unit 5. Seismo-stratigraphic Unit 5 in the Levant Basin has high internal reflectivity that corresponds to bundles of thin layers of clastic materials, mainly claystone (Feng et al., 2016).

### 4.11. Extrapolations from the model calculations

Our model shows a progressive increase in chloride in the Mediter-ranean brine reservoir (Fig. 7). The Cl entering from the external ocean

has two stable isotopes: ³⁵Cl (75.77 %) and ³⁷Cl (24.23 %). Evaporation in the Mediterranean sequesters the heavier ³⁷Cl isotope in halite and leaves more abundant lighter ³⁵Cl to accumulate in the brine reservoir. As a consequence, the ⁶³⁷Cl in the Mediterranean halite becomes more positive than Standard Marine Ocean Chloride. Upon closure and evaporative drawdown, the ratio ³⁷Cl/³⁵Cl decreases as the much greater amount of ³⁵Cl stored in the shrinking reservoir is available to the halite.

In the model, gypsum precipitates simultaneous with halite. In the MSC evaporites, gypsum is observed as bottom-growth selenite on margins and either as scattered anhydrate nodules (Decima and Wezel, 1971) or small-sized laths (Garcia-Veigas et al., 1995) in the halite. Based on hypsometry where basin floors cover substantially more sur-face area than slopes, there is perhaps an under-appreciated proportion of SO₄ sequestered within the mobile unit (Aloisi et al., 2024). The presence of gypsum microcrystals within cavities of the larger and much more common halite crystals is observed in SEM-EDS imagery and element maps of halite samples from the Dolphin well in the eastern Mediterranean (Meilijson et al., 2019).

The rate of gypsum growth lessens with time as the result of a decreasing water activity coefficient as salinities steadily rise in corre-spondence with the reduction of the ocean inflow. The evaporative model's decline in the Atlantic-Mediterranean exchange conforms with the upward reduced thicknesses of the PLG beds beginning after the PLG Bed 6 (Fig. 14).

## 5. Model sensitivity

Because the rate of evaporation is reduced with increasing salinity, there is less demand for saltwater from the ocean as the brine concen-trates in the Mediterranean. Using published water activity coefficients (Myers and Bonython, 1958; Salhotra et al., 1985; Mor et al., 2018) the rate of evaporation eventually becomes insufficient once salinities approach the saturation levels for Mg and K salts. Therefore, in order for these minerals to appear in the Mediterranean salt layer, salinity is driven into the range of their saturation by shrinkage of the brine reservoir. The drop in Br in halite Unit B in Sicily signifies the closure of the ocean seaway. Drawdown exposes the PLG on the margins and ter-minates further growth.
<figure><img src="image_17.png" /><figcaption>**Fig. 14.** Progressive decrease in the thickness of the PLG gypsum beds. Measurements for Maiella composite from Schildgen et al. (2014), Vena del Gesso composite from Lugli et al. (2007) and Calpe, La Malta and Los Molinios-Sorbas offshore wells from Ochoa et al. (2015). The abrupt decrease in the Vena del Gesso occurs at the time of PLG Bed 6 when the contribution of freshwater exceeds the saltwater supplied from the exterior ocean.</figcaption></figure>

The model also needs to be tuned so that the amount Na, K and Mg stored in the reservoir does not produce a volume of salt greater than the volume calculated from the thickness of the MU in reflection profiles. This requires adjusting the magnitude of the leakage from the reservoir back to the ocean during wet intervals.

The model uses a less-saline surface layer supplied by rain and rivers for the molecular composition of the leakage brine. A reduced molarity of the surface layer is supported by the presence of well-preserved planktonic diatoms and mid-chain alkanes interbedded with halite in the Dolphin well from the eastern Mediterranean (Meilijson et al., 2019) and the aforementioned eels and fish in the euxinic shales between the individual beds of PLG in the Piedmont Basin of northern Italy (Sturani, 1973). Marine planktonic diatom taxa in the Piedmont Basin (e.g., Coscinodiscus sp. and Thalassionema longissimi) are closely related to species within the Dolphin assemblage (Dela Pierre et al., 2014; Meilijson et al., 2019). Nano-sized planktonic diatoms are found in the reentrant angle of the selenitic twins of the PLG. Upon sinking from the sun-lit surface layer the siliceous tests became entombed in the gypsum. Diatoms belonging to the genus Thalassiosira thrive in marine to brackish waters (Hoppenrath et al., 2007) and do not tolerate hypersaline conditions. Their presence suggests that the PLG gypsum formed from a saturated brine at water depths far below a fresher photic zone (Pellegrino et al., 2021).

To obtain a compatibility between the calculated halite mass and the observed volume of subsurface Mediterranean halite layer it becomes necessary to reduce the duration of the periodic ocean inflow of salt-water to less than half of the sine-wave cycle illustrated in Fig. 4. Using spectral analyses, the thin laminations in the twinned selenite and laminar gypsum have been interpreted as annual layers (Manzi et al., 2012). If the laminae are indeed of annual origin, their thickness suggests that solutes from the ocean were supplied to the Mediterranean for less than half of each precession cycle (Raad et al., 2023), rather than during the full half of the precession cycle as assumed by Schildgen et al. (2014).

Adjusting the magnitudes of the inflow of seawater and outflow of brine is therefore subjective. The goal of the exercise is to find out to what degree can budgets of the incoming ions and their loss through

precipitation and leakage reproduce the composition of the PLG and halite that has been investigated in numerous regions of the circum-Mediterranean margin and its deep interior.

## 6. MSC Stage 1 halite versus Stage 2 halite

As previously mentioned, there is a widely-adopted hypothesis that the halite comprising the entire MU in reflection profiles postdates the Stage 1 PLG and occurred only in the brief Stage 2 window of 50 kyr (CIESM, 2008; Roveri et al., 2014a). However if the salinification of the Mediterranean had only risen to the level for gypsum precipitation in Stage 1, only a fraction of the observed salt in the Mediterranean would have been precipitated during a single Stage 2 evaporative drawdown. The 370 kyr duration for the elevation of salinity to the level for potash and magnesium salts allows for a significantly high brine concentration such that when saltwater from the ocean ceases, evaporative drawdown results in a sizable portion of the observed salt.

Researchers promoting the Stage 2 halite hypothesis do not provide an explanation for the preceding strontium and sulfur isotope evolutions in the PLG during Stage 1, nor for the elevation in the transformation of columnar to laminated to branching selenite, and no reasoning for the low levels of Ca and Na in the molecular composition of brine entrapped in selenite.

## 7. Conflicting evidence

The low salinities inferred from fluid inclusions in gypsum need further elucidation. The equations and tables of the freezing point depressions are only for H2O-NaCl solutions. According to the model calculations the accumulating Mediterranean brine becomes enriched in Cl at the expense of Na (Fig. 8). Solutions with this mixture and at high concentrations have yet to be measured for their freezing point temperatures. Might the first melting temperatures of -42 and -32 °C of the gypsum fluid inclusions be an indication of brine of extreme salinity and an entirely different composition than seawater.

Carnevale and Schwarzhans (2022) argue for "a persistent continuity of marine stenohaline fish taxa throughout most of the interval between
5.97 and 5.33 Ma". According to them, "the record of articulated fish skeletons is unquestionably autochthonous, thereby providing unambiguous evidence of the occurrence of open marine environments in the MSC preceding the 'Lago-Mare' phase". As discussed, earlier, when seawater periodically enters the Mediterranean in Stage 1 it feeds a low-density surface layer resting above a denser hypersaline brine reservoir. Consequently, fish could enter, survive and even reach distal locations such as the Piedmont Basin, Crete and Cyprus. However, the occurrence of fish remains does not indicate that the entire Mediterranean was filled with marine water and preclude the existence of an underlying brine reservoir. The fish bearing localities investigated are at settings considered by most researchers to have been shallow silled basins. For example, the PLG Bed 6 of gypsum investigated by Sturani (1973) was deposited in a near-shore environment as shown by the remains of twigs, leaves, frogs and spiders. Even in this setting the water in which the frogs and fish lived overlay a brine in which they became preserved.

Carnevale et al. (2008, 2018) report 'Lago Mare' fish assemblages from seven Italian localities. These fish assemblages are dominated by taxa characterized by a "strict marine affinity", thereby suggesting that the Mediterranean was filled by marine waters. The material investigated consists of the otoliths (ear bones) of extant fish. Measurements of the oxygen and carbon isotope signatures on the otoliths from four fish species are distinct from measurements on marine planktonic foraminifera from earliest marine Pliocene sediments. Furthermore, the range of the strontium $Sr^{87}/Sr^{86}$ measurements on the Lophiiform and *Gobius* sp. otoliths (0.70856-0.70879) is confined to the range of $Sr^{87}/Sr^{86}$ from Lago-Mare ostracods diagnostic of fresh to brackish water and distinct from the range of earliest Pliocene foraminifera from Capo Rossello, Sicily (0.70898-0.709004).

## 8. Conclusions

The algebraic calculations applied in our model determine the number of moles of the various ions entering the Mediterranean and those lost to gypsum, halite and leakage. They reveal that the $SO_4$ in the PLG from Sorbas Basin in SE Spain, the Vena del Gessso in the Northern Apennines, the Piedmont Basin in northern Italy and the Caltanissetta Basin in Sicily was supplied by ocean seawater, whereas the water of hydration in the gypsum was meteoric in origin. The model illuminates the geochemical riddle of "low-salinity gypsum" (Aloisi et al., 2022).

The periodic inflow of seawater is confirmed by the observed increase in $^{87}Sr$/$^{86}Sr$ for each of the seven investigated PLG beds of the Vena del in the Gesso towards the oceanic value when superimposed on an overall decreasing trend towards the river's continental value (Reghizzi et al., 2018).

Similarly, the periodic inflow of seawater is revealed by $^{87}Sr$/$^{86}Sr$ progressing towards the Late Miocene oceanic value during each arid phase (García-Veigas et al., 2018). The overall $^{87}Sr$/$^{86}Sr$ enrichment took place in the brine reservoir with bacterial sulfate reduction of the $SO_4$. The consumption of the lighter $^{32}S$ in the reservoir left the Mediterranean with increasing amounts of the heavier $^{34}S$.

The consumption of Na from the incoming seawater as it crystallizes into halite accounts for the low Na relative to Mg in the remaining brine and thus the observed low Na relative to Mg in fluid inclusions (García-Veigas et al., 1995). The paucity of Ca in the residual brine accounts for the absence of polyhalite in Units A and B in the Caltanissetta Basin (García-Veigas et al., 1995) and in the eastern Mediterranean Dolphin well (Meilijson et al., 2018, 2019).

The decreasing water activity coefficient as salinity increases explains the progressive decrease in the thickness of the PLG beds. The drop in Br in Unit B provides the timing of the closure of the gateway from the external ocean. The halite, kainite and bischofite in Unit B are the products of the shrinking brine reservoir that accompanied evaporative drawdown.

The calculations succeed in showing a simultaneous precipitation of gypsum and halite during the hypersaline stage 1 of the MSC (Richter-

Bernberg, 1973; van Couvering et al., 1976; Hsü et al., 1977; Rouchy and Caruso, 2006; Meilijson et al., 2018, 2019). They unexpectedly reveal that >80 % of the water supplied to the Mediterranean in the course of 16 precession cycles came from rain and rivers. From the large contribution of fresh water one might reason that the "Messinian salinity crisis" could be re-framed as the "Messinian fresh-water crisis" (Longinelli, 1979).

## CRediT authorship contribution statement

**William B.F. Ryan:** Writing – review & editing, Writing – original draft, Software, Project administration, Data curation, Conceptualization. **Fadl Raad:** Writing – review & editing, Methodology, Investigation.

## Declaration of competing interest

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.

## Acknowledgements

The initiation of this investigation was funded by US National Science Foundation grants OCE-76-21964 and OCE 02-41964. The preparation of the model code, writing of the first draft and preparation of the figures occurring during the first author's appointment as Special Scientist at the Lamont-Doherty Earth Observatory of Columbia University. The authors wish to thank the three anonymous reviewers for the constructive comments. We also would like to express our sincere gratitude to Angelo Camerlenghi, Johanna Lofi, Athina Tzevahirtzian and Ronja Ebner for their valuable insights that contributed to the development of the ideas presented in this manuscript.

## Data availability

No new data was used for the research described in the article.

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