Volume 129, Issue 2 e2023JE008036
Research Article
Open Access

Ice-Ocean Interactions on Ocean Worlds Influence Ice Shell Topography

J. D. Lawrence

Corresponding Author

J. D. Lawrence

Honeybee Robotics, Altadena, CA, USA

Cornell University, Ithaca, NY, USA

Correspondence to:

J. D. Lawrence,

[email protected]

Contribution: Conceptualization, Methodology, Software, Validation, Writing - original draft, Writing - review & editing, Funding acquisition

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B. E. Schmidt

B. E. Schmidt

Cornell University, Ithaca, NY, USA

Contribution: Conceptualization, Methodology, Writing - review & editing, Supervision, Project administration, Funding acquisition

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J. J. Buffo

J. J. Buffo

Dartmouth College, Hanover, NH, USA

Contribution: Conceptualization, Methodology, Writing - review & editing

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P. M. Washam

P. M. Washam

Cornell University, Ithaca, NY, USA

Contribution: Conceptualization, Methodology, Writing - review & editing

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C. Chivers

C. Chivers

Woods Hole Oceanographic Institute, Woods Hole, MA, USA

Contribution: Conceptualization, Methodology, Writing - review & editing

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S. Miller

S. Miller

Cornell University, Ithaca, NY, USA

Contribution: Conceptualization, Writing - review & editing

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First published: 13 February 2024

Abstract

The freezing point of water is negatively dependent on pressure; therefore in any ocean without external forcing it is warmest at the surface and grows colder with depth. Below floating ice on Earth (e.g., ice shelves or sea ice), this pressure dependence combines with gradients in the ice draft to drive an ice redistribution process termed the “ice pump”: submerged ice melts, upwells, and then refreezes at shallower depths. Ice pumping is an exchange process between the ocean and overhead ice that results in unique ice compositions and textures and influences the distribution of sub-ice habitats on Earth. Here, we scale recent observations from Earth's ice shelves to planetary conditions and find that ice pumping is expected for a wide range of possible sub-ice shell pressures and salinity at other ocean worlds such as Europa and Enceladus. We show how ice pumping would affect hypothetical basal ice shell topography and ice thickness under varying ocean conditions and demonstrate how remote sensing of the ice shell draft can be used to estimate temperature gradients in the upper ocean ahead of in situ exploration. For example, the approximately 22 km gradient observed in Enceladus' ice shell draft between the south pole and the equator suggests a temperature differential of 0.18 K at the base of the ice shell. These concepts can extend the interpretation of observations from upcoming ocean world missions, and link ice shell topography to ice-ocean material exchange processes that may prove important to overall ocean world habitability.

Key Points

  • When ice is submerged, a melting and freezing exchange process termed the “ice pump” can affect ice composition, texture, and thickness

  • We find that ice pumping is likely beneath the ice shells of several ocean worlds in our solar system

  • The ice pump concept enables inversion between ocean world ice shell thickness and ice-ocean interface temperature ranges

Plain Language Summary

The freezing point of water depends on pressure. As pressure increases, the freezing point decreases, which can influence the melting or freezing of ice in an ocean. A helpful way to conceptualize this dependency is to recall that water expands as it freezes. As pressure increases, this expansion requires more work to displace the higher pressure surroundings, so the water must be even colder to freeze—a decrease in the freezing point. If ice is submerged, the deeper ice where the freezing point is colder can melt faster. This forms freshened meltwater that may rise to shallower depths where it is now colder than the shallower, lower pressure freezing point and can refreeze underwater. This process is referred to as an “ice pump”, because it acts to equilibrate topography in submerged ice. In ice-covered oceans on Earth, the ice pump is an important process that influences the composition and texture of the ice, and therefore the sub-ice ecosystems. Here, we find that ice pumping is also likely at other ocean worlds in our solar system where it may similarly influence potential sub-ice ecosystems and show how observations of planetary ice shell thicknesses can be used to bound ocean conditions.

1 Introduction

Geologic and magnetic evidence suggest that Jupiter's moon Europa has a saline subsurface ocean below its icy exterior (Kivelson et al., 1997, 2000; Pappalardo et al., 1999). Radiolytic oxidant production at the surface of Europa's ice shell may couple with reduced species generation via rock-water reactions at the seafloor below, suggesting that Europa could support life (Carlson et al., 2009; Chyba, 2000; Hand et al., 2009; Vance et al., 2018; Zolotov & Kargel, 2009). This potential makes Europa a priority target in NASA's mission to explore habitable environments in our solar system (Board & Council, 2012; Hendrix et al., 2019; National Academies of Sciences and Medicine, 2022). However, the factors that would mediate material exchange between the ice shell and ocean in support of long-term habitability—like Europa's ice shell thickness, ocean depth, and salinity (ionic composition and relative concentration)—are not yet well constrained (Schmidt, 2020; Soderlund et al., 2020). Other worlds with observed or theorized subsurface oceans include another Jovian moon Ganymede, and Saturn's moons Enceladus and Titan (Lunine, 2017). Independent lines of evidence indicate that these bodies also have global ice-ocean interfaces, which, like Europa's, may act as gateways for the transfer of heat and material between the surface and subsurface.

Ongoing efforts to develop global ocean circulation models for Europa accordingly span a broad spectrum of possible regimes from fast, tidally driven flow and convection-driven circulation (Soderlund, 2019; Soderlund et al., 2014, 2020) to slower, rotationally dominated flow (Ashkenazy et al., 2018; Ashkenazy & Tziperman, 2021), with varying implications for melting and freezing processes (ice-ocean interactions) at the base of the ice shell. Similar ocean circulation dynamics have been modeled for Enceladus (Bire et al., 2022; Kang et al., 2022; Soderlund, 2019; Zeng & Jansen, 2021). The upper water column below Europa's ice shell may be at similar temperatures and pressures to the oceans beneath Earth's polar ice shelves (Schmidt, 2020; Soderlund et al., 2020; Vance & Goodman, 2009; Wolfenbarger, Fox-Powell, et al., 2022), and so bounding regimes of physical interactions at relevant conditions can serve as a powerful tool for developing understanding of Europa's distant ocean. Both Earth-based analog observations and theoretical arguments can provide these constraints. Here, we extrapolate processes observed in sub-ice shelf oceans on Earth to constrain different ice-ocean interaction regimes and explore how sub-ice shell topography would evolve at Europa and other ocean worlds.

1.1 Terrestrial Ice Shelves and the Ice Pump

Earth's ice shelves form as snow compressed into glacial ice flows from land into the ocean. The shoreline, or coastal transition zone between grounded and floating ice, is referred to as the grounding zone (GZ). The GZs of large ice shelves lie hundreds to thousands of meters below sea level. Ice shelves generally thin seaward due to the combined effects of surface mass balance, basal melting, and extensional strain. Ice-ocean interactions (melting and freezing) along the base of an ice shelf are tied to the freezing point (Tf), which is negatively pressure dependent (Tf decreases as pressure increases). This means that the temperature of a water parcel (Tw) relative to the freezing point can vary adiabatically (i.e., by a change in pressure alone, without the exchange of heat or salt). The difference between the water temperature and in situ freezing point (Tw − Tf) is termed thermal driving (i.e., Haumann et al., 2020), where positive values mean the water is above the freezing point and negative values mean the water is below the freezing point. The latter condition is also referred to as supercooling. Thermal driving can switch from positive at deeper ice drafts (melting) to negative values at shallower ice shelf drafts (freezing) due to the pressure dependence of the freezing point alone, without any external heat sources or sinks.

For example, some ice shelf cavities are filled with water masses formed at the surface freezing point by sea ice generation in polynyas (∼35 ppt salinity High salinity shelf water [HSSW]). When this water reaches the deep GZ, the higher pressure and commensurately lower Tf increase thermal driving such that even water formed at the surface freezing point (HSSW) can melt deep GZ ice. The resultant meltwater is generated at the pressure depressed in situ Tf (colder than the surface freezing point), which freshens and cools the ambient seawater upon mixing. As the meltwater-modified parcel (termed Ice Shelf Water) is made less dense than the surrounding seawater, it rises along the ice shelf base. The pressure reduction during upwelling raises Tf above Tw such that thermal driving becomes negative and supercooling results. Supercooled water then forms buoyant crystals of frazil ice (see Haumann et al., 2020; Hoppmann et al., 2020), which accumulate beneath the meteoric ice shelf. This cycle (Figure 1) where deep ice melts, upwells, and re-freezes at shallower depths was first described by Robin (1979) and termed the “ice pump” by Lewis and Perkin (1986).

Details are in the caption following the image

Thermohaline ice pump circulation below a generalized ice shelf. (1) High salinity shelf water (HSSW) forms at the surface freezing point (Tf = −1.9°C) as the brine rejected from sea ice growth mixes into the water column. (2) HSSW is dense relative to the surrounding seawater, so it sinks and a portion circulates beneath the ice shelf to the grounding zone, where it is now warm compared to the pressure-depressed freezing point (positive thermal driving) and drives melting. (3) Fresh meltwater generated at the colder, in situ freezing point mixes with HSSW, generating fresher, colder, and relatively buoyant Ice Shelf Water (ISW). (4) ISW upwells, the freezing point increases, and thermal driving commensurately decreases. With a sufficient pressure decrease, supercooling occurs and frazil ice forms, which can accumulate into hundreds of meters thick layers of marine ice at the ice shelf base. Modified from Soderlund et al. (2020), see also Lewis and Perkin (1986), MacAyeal (1984), Nicholls et al. (1991), and Robin (1979).

The mechanism by which ice forms in the ocean determines its physical properties such as composition, conductivity, liquid fraction, grain size, density, and mechanical strength, and viscosity (Dierckx & Tison, 2013; Glasser & Scambos, 2008; Jansen et al., 2013; Kulessa et al., 2014, 2019; Lange & MacAyeal, 1986; Larour et al., 2005; Matsuoka et al., 2009; McGrath et al., 2014; Rignot & MacAyeal, 1998). Marine ice formed through the accumulation and consolidation of frazil ice resulting from supercooling has a texture, salinity, temperature, and fabric distinct from sea ice formed by conductive heat loss to the atmosphere, or from sub-shelf congelation ice formed by conductive heat loss to an overhead meteoric ice shelf (Craven et al., 2004, 2009; Fricker et al., 2001; Hoppmann et al., 2020; Jeffries et al., 1993; Moore et al., 1994; Tison et al., 1993; Wolfenbarger, Buffo, et al., 2022; Zotikov et al., 1980). Both marine ice and congelation ice can host and entrain ocean-derived organisms (Arrigo et al., 2009; Roberts et al., 2007), although marine ice more effectively excludes solutes (Moore et al., 1994; Tison et al., 1993) and gasses (Oerter et al., 1992) during the formation. Marine ice layers on Earth have bulk salinity typically between 0.01 and 5 ppt and can exceed hundreds of meters in thickness (Craven et al., 2009; Jansen et al., 2013; Khazendar et al., 2001; Morgan, 1972; Robin, 1979; Wolfenbarger, Buffo, et al., 2022).

1.2 Relevance to Ocean Worlds

Pressure-dependent ice-ocean interactions are an important driver of regional ocean circulation (e.g., MacAyeal, 1984; Stevens et al., 2020), which influences sub-ice ecosystem structure and distribution (Azam et al., 1979; Horrigan, 1981; Martínez-Pérez et al., 2022; Post et al., 2014; Riddle et al., 2007; Vick-Majors et al., 2016). While there are important physical and compositional differences between Earth's freshwater, terrestrially-sourced ice shelves and Europa's global and saline ice shell (Buffo et al., 2020; Trumbo et al., 2019; Wolfenbarger, Buffo, et al., 2022; Zolotov & Kargel, 2009), the pressures, temperatures, and salinity of sub-ice oceans on Earth fall within observationally bounded ranges for the oceans at Europa, Enceladus, and other ice-ocean worlds (Soderlund, 2019; Soderlund et al., 2020; Vance & Goodman, 2009; Wolfenbarger, Buffo, et al., 2022). During the Neoproterozoic era, Earth also experienced periods of total or partial glaciation, and the study of Earth's past “icy ocean world” periods can also provide insight into dynamics on other ocean worlds (Soderlund et al., 2020).

Recent work is beginning to incorporate parameterizations developed for ice-ocean interactions below ice shelves (e.g., Dinniman et al., 2016; D. M. Holland & Jenkins, 1999) into ocean world models (e.g., Ashkenazy & Tziperman, 2021; Miller, 2022). Understanding how these processes may operate on Europa helps to constrain potential mechanisms of material exchange between the ocean and ice shell, which in turn influence intra-shell geologic processes and may enable long-term habitability (Cockell et al., 2016; Schmidt, 2020; Soderlund et al., 2020; Vance et al., 2018). For example, the ice pump represents a mechanism that may introduce relatively low-density ice into the shell that could contribute to convective overturning (Buffo et al., 2020; Wolfenbarger, Buffo, et al., 2022).

Buoyancy-driven circulation strongly impacts ocean mixing and ice-ocean material exchange on Earth such that scaling observed dynamics on Earth to ocean worlds informs links between ice shell structure, ice thickness, basal topography, and ocean conditions. Here, we leverage recent observations of ice-ocean interactions and exchange beneath Antarctic ice shelves (Lawrence et al., 2023; Schmidt et al., 2023) and theoretical arguments to define expected regimes and evolution of ocean world basal ice shell topography from pressure-driven ice pumping. This work builds upon prior theoretical considerations of ocean and ice shell interactions at Europa (Ashkenazy et al., 2018; Ashkenazy & Tziperman, 2021; Melosh et al., 2004; Soderlund et al., 2014, 2020; Vance & Goodman, 2009; Zhu et al., 2017) and other ocean worlds such as Saturn's moons Enceladus (Bire et al., 2022; Kang et al., 2022; Soderlund, 2019; Zeng & Jansen, 2021) and Titan (Kvorka et al., 2018).

2 Methods and Assumptions

Throughout this work we calculate thermodynamic properties of water using the Python3 Gibbs Seawater Toolbox (GSW; v3.4.0) (Firing et al., 2021; McDougall & Barker, 2011) implementation of the International Thermodynamic Equation of SeaWater—2010 (TEOS-10) (IOC, 2010; McDougall et al., 2013). The GSW Toolbox is valid over the “Neptunian” or standard oceanographic range of 0 ≤ SA ≤ 42 g kg−1, Tf < T < 40°C, and 0 < P ≤ 100 MPa (Feistel, 2008).

We focus on ice-ocean interactions at Europa, but consider a range of pressures from 0 to 6,000 dbar (0–60 MPa) and salinities from 0 to 42 g kg−1 to include conditions relevant to other ocean worlds like Enceladus and Titan. Europa's ice shell thickness may range from 3 to 40 km (Billings & Kattenhorn, 2005; Howell, 2021), and the ocean salinity from 5 to 12 g kg−1 (Zolotov & Shock, 2001) although there are limited observational constraints and Europa's ocean may also be hypersaline (Hand et al., 2007). Enceladus' ice shell thickness may range from 2 to 50 km (Beuthe et al., 2016; Čadek et al., 2016; Hemingway & Mittal, 2019; Thomas et al., 2016), and the ocean salinity from 2 to 40 g kg−1 (Glein et al., 2018; Hsu et al., 2015; Postberg et al., 2009, 2011; Zolotov, 2007), although the bulk ocean salinity could be higher if the plumes sampled by Cassini are sourced from relatively low salinity polar water (Lobo et al., 2021; Zeng & Jansen, 2021). Titan's ice shell may be 10s to 200 km thick and the ocean salinity <100 g kg−1 (Hemingway et al., 2013; Soderlund et al., 2020; Vance et al., 2018).

We note that at higher pressures the GSW toolbox has been fit to minimize errors in a smaller salinity range (as the majority of salinity variability in Earth's oceans is near the surface), and as such some higher pressure calculations here lie outside of the optimized range (i.e., “the funnel,” see Blanc et al., 2020; McDougall et al., 2013). TEOS-10 is also developed from seawater with a relative ionic composition (thalassohaline) that may (Hand & Carlson, 2015; Trumbo et al., 2019) or may not (Vance et al., 2018; Zolotov & Kargel, 2009; Zolotov & Shock, 2001) be similar to Europa's bulk ocean ionic composition; although other work has shown that the thermodynamic properties of other theorized compositions would be expected to have similar pressure-dependent behaviors (Chang et al., 2022; Vance & Goodman, 2009). This study could be extended in the future with empirically derived equations of state in development for additional ocean-world relevant ocean compositions (Chang et al., 2022; Journaux et al., 2020a, 2022; Vance, 2021).

We further assume the ice shell to be in quasi-equilibrium, neither freezing nor melting on the global average. We presume a freshwater ice density for the shell, as even though the bulk salinity of Europa's ice shell may vary from 0.1% to 10% of the ocean salinity (Buffo et al., 2020; Wolfenbarger, Buffo, et al., 2022; Wolfenbarger, Fox-Powell, et al., 2022) ice melt will always freshen the upper ocean. It is also worth considering that at other ocean worlds, the hydrosphere can be a more significant fraction of the planetary radius than Earth's. For example, gravitational acceleration at Europa varies by ∼10% between the surface and seafloor (Leighton et al., 2008), but here we only consider processes at the basal ice shell-ocean interface. Gravity varies from approximately 1.31 m s−2 at Europa's surface to 1.33 m s−2 at the base of a 20 km thick ice shell (<1.4% difference). Calculated over the same pressure range of 0–2,400 dbar, ocean density (ρw) would vary from approximately 999.8 to 1,011.7 kg m−3 (<1.2% difference). We therefore use constant values for ocean density (ρw = 1,000 kg m−3), ice density (ρi = 917 kg m−3), and gravitational acceleration when determining pressure and depth variations. All calculations are available (Lawrence, 2023) as a Jupyter Notebook (Granger & Pérez, 2021).

3 Freezing Point Pressure Dependence and Ice Pumping Regimes

3.1 Ocean World Ice-Ocean Regimes

To constrain the drivers of an ocean world ice pump, we explore the effects of pressure and salinity on the freezing point. Figure 2a shows that the freezing point pressure dependence, T f P $\frac{\partial {T}_{f}}{\partial P}$ , is only weakly dependent on absolute pressure and minimally dependent on salinity for the ranges considered. The pressure-driven change in the freezing point is also generally an order of magnitude greater than the pressure-driven change in temperature (the slope of the adiabat, i.e., McDougall & Feistel, 2003), so we consider it to be the dominant factor controlling thermal driving near an ice base away from sources of heat (Figures 2b and 2c). We focus our initial calculations on Europa and adopt a constant value of −0.85 mK dbar−1 for T f P $\frac{\partial {T}_{f}}{\partial P}$ going forward (see also Melosh et al., 2004), which is calculated at ∼2,400 dbar (Figure 2a) consistent with pressures below a 20 km European ice shell and Earth's thickest ice shelves.

Details are in the caption following the image

Comparison between the pressure and salinity -dependence of Tf compared to the adiabatic lapse rate. Panel (a) shows minimal dependence of T f P $\frac{\partial {T}_{f}}{\partial P}$ on (thalassohaline) salinity (see also Vance & Goodman, 2009, §8). Compared to the adiabat (temperature increase due to compression with increasing pressure) in Panel (b), the pressure-driven change in Tf is generally at least an order of magnitude greater for the ranges considered here, shown in Panel (c) as the ratio of the adiabat to T f P $\frac{\partial {T}_{f}}{\partial P}$ .

We therefore expect the same change in thermal driving in either Earth's or Europa's ocean for a given pressure change (∆P). Working in terms of thermal driving instead of water temperature can be thought of as canceling out the unknown absolute freezing point and enables us to quantitatively consider ice-ocean dynamics without knowledge of ocean salinity or ice shell thickness.

Pressure change (∆P, Pa) for a given depth change (∆H, m) scales with gravity as ∆P = ρi gH. In Earth's oceans where gravitational acceleration is ∼9.8 m s−2, 1 dbar (1 × 104 Pa) of pressure change is nearly equivalent to a 1 m change in depth, or a −0.85 mK m−1 change in Tf. For less massive Europa where gravitational acceleration is ∼1.3 m s−2 (13.4% that of Earth's) the value for the freezing point depression per meter becomes −0.1 mK m−1. The freezing point depression per meter of depth change on Earth is equivalent to a ∼8.5 m change in depth on Europa. Europa's ice shell basal interface may exhibit topographic disequilibria ranging from hundreds of meters to kilometers (Nimmo et al., 2007; Vance & Goodman, 2009; Walker et al., 2021), equivalent to tenths of a degree of pressure-dependent Tf variability. This magnitude of topography could be sufficient to induce ice pumping given predictions for Europa's ocean to be very near the freezing point at the ice interface (Melosh et al., 2004; Vance & Goodman, 2009).

Next, we seek to quantitatively bound specific pressure and salinity regimes that support ice pumping, which is determined primarily by (a) the initial thermal driving magnitude, (b) the topographic relief of the submerged ice, and (c) whether the water produced by melting ice is buoyant.

The first two factors determine whether the pressure gradient is sufficient to result in negative thermal driving and induce marine ice formation, as the pressure-dependent change in Tf upon upwelling must be larger than the initial thermal driving magnitude or positive thermal driving will remain after upwelling and no supercooling occurs. In some cases, the upwelling-induced reduction in thermal driving can still prime waters for refreezing through conductive heat loss through the overlying ice even if no in situ supercooling occurs. For example, Zotikov et al. (1980) report a 6 m thick layer of “sea ice” accreted below 410 m of fresh glacial ice at the J9 site on Ross Ice Shelf. This porous and saline ice formed by the direct freezing of seawater very near the local freezing point onto the base the ice shelf, and grew at a rate in agreement with modeled rates due to heat conduction through the ice shelf. If the seawater at the basal interface at J9 were instead in situ supercooled, frazil ice formation and accumulation in turbulent waters would have instead occurred resulting in accretion of saline ice with a different and distinct morphology (e.g., Robinson et al., 2017; Smith et al., 2001; Wolfenbarger, Buffo, et al., 2022).

The third factor, relative buoyancy, is perhaps most important to bound regimes where ice pumping is expected. The density of a meltwater mixture is determined by the change in both temperature and salinity, and the net effect varies depending on initial seawater salinity, temperature, and pressure. The relative importance of changes in temperature and salinity to density is given by the ratio of the thermal expansion coefficient (α) to the haline contraction coefficient (β), α β $\frac{\alpha }{\beta }$ . For the ranges considered here β is always positive (increasing salinity decreases volume and increases density), but α increases from negative (contraction, where density increases upon warming) to positive (expansion, density decreases upon warming) with increasing pressures and salinity. While α is positive in terrestrial sub-ice shelf oceans and cooling with meltwater addition causes contraction (increased density), ice pumping still occurs because α β $\frac{\alpha }{\beta }$ is generally ≪1 and the freshening effect dominates, causing meltwater to rise (e.g., Figure 1).

At the endmember condition of a freshwater ocean, there is no change in salinity upon melting to consider. For lower pressures where α is negative, Tf is colder than the temperature of maximum density (Tmd) and the coldest waters are less dense (i.e., why freshwater surface lakes freeze from the top down). Ice pumping can occur as melt-cooled water mixtures are buoyant. However, for freshwater near the freezing point at higher pressures (approximately 2,800 dbar or 28 MPa for water at −2°C) α is positive, Tf is warmer than Tmd, and the coldest waters are now most dense (see also Melosh et al., 2004; Thoma et al., 2010; Wüest & Carmack, 2000). Above this critical pressure, cooling through meltwater input makes the resultant admixture negatively buoyant and no ice pumping can occur.

At Europa, predictions for ocean salinity (Zolotov & Shock, 2001) and ice shell thicknesses (Billings & Kattenhorn, 2005) vary—if the ocean is fresh and the ice shell draft is greater than ∼23 km, meltwaters would sink and we would not expect ice pumping. Given the hypothesis that ice pumping may be an important mechanism in the exchange of material between an ice shell and ocean, this motivates the question: For a given ocean world ice shell draft (basal interface pressure), at what ocean salinity should we expect ice pumping?

3.2 Ice Pump Regimes

We consider the product of α β $\frac{\alpha }{\beta }$ and the relative change in temperature and salinity upon the addition of meltwater, T S $\frac{{\increment}T}{{\increment}S}$ , for a range of initial ocean salinities and pressures. We expect ice pumping when α T β S $\frac{\alpha {\increment}T}{\beta {\increment}S}$  < 1 as below Earth's ice shelves, but no ice pumping in lower salinity oceans at higher pressures where the T S $\frac{{\increment}T}{{\increment}S}$ upon melting becomes large enough that α T β S $\frac{\alpha {\increment}T}{\beta {\increment}S}$  > 1 (see also Ashkenazy & Tziperman, 2021; Kang et al., 2022; Zhu et al., 2017). The resultant properties of a mixture of fresh meltwater and seawater can be described by the slope of the Gade line (Gade, 1979; Wåhlin et al., 2010; Washam et al., 2018),
T m S m = T ocean + L f c p 1 S ocean S m ${T}_{m}\left({S}_{m}\right)={T}_{\text{ocean}}+\frac{{L}_{f}}{{c}_{p}}\left(1-\frac{{S}_{\text{ocean}}}{{S}_{m}}\right)$ (1)
where ( T , S ) ocean ${(T,S)}_{\text{ocean}}$ are the initial bulk ocean temperature and salinity, ( T , S ) m ${(T,S)}_{m}$ are the resultant salinity and temperature of the mixture of ocean water and ice meltwater, L F ${L}_{F}$ is the latent heat of fusion for ice, and C P ${C}_{P}$ is the specific heat capacity of water at ( S , T ) ocean ${(S,T)}_{\text{ocean}}$ . We calculate Gade line slopes, T m S m $\frac{{\increment}{T}_{m}}{{\increment}{S}_{m}}$ , across the pressure and salinity range of interest and multiply with α ( T , S , P ) β ( T , S , P ) $\frac{\alpha (T,S,P)}{\beta (T,S,P)}$ (approximating T as Tf for a given salinity and pressure) across the same range to identify the interface pressures and ocean salinities that would preclude ice pumping ( α T β S > 1 ) $(\frac{\alpha {\increment}T}{\beta {\increment}S} > 1)$ :
α T β S $\frac{\alpha {\increment}T}{\beta {\increment}S}$ (2)

In the pressure and salinity space, this relationship delineates three regimes (Figure 3). One is a “lacustrine” regime at lower salinities and pressures where α is negative α T β S < 0 $\left(\frac{\alpha {\increment}T}{\beta {\increment}S}< 0\right)$ and colder meltwater upwells akin to surface freshwater lakes (e.g., Wüest & Carmack, 2000). A second is a “marine” regime at increased salinities where α is now positive, but 0 <  α T β S $\frac{\alpha {\increment}T}{\beta {\increment}S}$  < 1 as in Earth's familiar sub-ice shelf ocean regime. Finally, there is a third low salinity, high pressure regime where no ice pumping occurs because α is negative and the ocean is too fresh for the freshening effect upon melting to overcome the temperature change α T β S > 1 $\left(\frac{\alpha {\increment}T}{\beta {\increment}S} > 1\right)$ .

Details are in the caption following the image

Three different circulation ice-ocean interaction regimes are determined by the temperature of maximum density (Tmd, red shaded contours where Tmd > Tf, blue shaded and given as the freezing point where Tmd < Tf) and combined heat and salt flux, α T β S $\frac{\alpha {\increment}T}{\beta {\increment}S}$ , upon meltwater mixing. In the lacustrine regime, α is negative and both the ∆T and ∆S upon melting contribute to positive buoyancy and ice pumping occurs. In the marine regime α is positive, but β dominates and the freshening effect upon melting causes ice pumping. The white shaded rectangle indicates observed pressure and salinity ranges for Antarctic sub-ice shelf oceans in the marine regime (Ross and Amery Ice Shelves; RIS and AIS). At higher pressures and lower salinity where α is positive (dark gray region at bottom left), however, the ocean is too fresh for the dilution from melt input to overcome the temperature change, and no ice pumping occurs. Falling in this regime is “SGL Vostok,” denoting the approximate pressure of the ice interface in subglacial Lake Vostok beneath the East Antarctic Ice Sheet. The upper dotted line indicates equivalence between the freezing point and temperature of maximum density. The lower line indicates where, for a given pressure, the initial water salinity is now high enough for the density contrast between ambient water and meltwater to allow the meltwater to upwell and ice pumping to occur. Possible ranges for basal ice shell interface pressures and ocean salinity are approximated with boxed regions for Enceladus, Europa, Ganymede, and Titan (Soderlund et al., 2020), collated in Vance et al. (2018) and Wolfenbarger, Buffo, et al. (2022). This diagram continues from the work of Melosh et al. (2004, Figure 2), and Vance and Goodman (2009, Figure 8).

The overlay of theorized pressure and salinity bounds for ocean worlds in our solar system in Figure 3 suggests that European ocean circulation is likely to fall in either the lacustrine or marine regime—in either case, the admixture of ice melts and ocean water is relatively buoyant and would upwell into regions of shallower ice shell basal topography. If Europa's ice shell is thicker (drafts exceeding ≳35 km) and the ocean is nearly fresh, then freshening from melting could be insufficient to overcome the density increase due to cooling, and in this case no ice pumping would be expected. However, the majority of predictions for Europa's ice shell thickness (Billings & Kattenhorn, 2005; Howell, 2021) suggest that the interface falls in the marine regime, such that Earth's ice shelves can serve as system analogs to inform European ice-ocean interactions.

Predicted salinity and pressure ranges for Titan or Ganymede's upper ocean (Journaux et al., 2020b; Vance et al., 2018) also suggest that ice pumping is probable, except for lower salinity ranges where bulk ocean salinity may be too low for melt-induced freshening to overcome positive α. Enceladus' ocean is predicted to fall nearly entirely within the “lacustrine” regime, where both negative α and melt-induced freshening contribute to ice pumping.

Subglacial Lake Vostok in East Antarctica is an interesting example which falls into the “no ice pump” regime because it is relatively fresh and lies below 3,750–4,200 m of ice. Pressure within the lake is sufficiently high for α to be positive, meaning the temperature of maximum density is below the freezing temperature (Wells & Wettlaufer, 2008; Wüest & Carmack, 2000). Vostok's waters are generally thought to be at the freezing point, and the slope of the ice overhead leads to a difference in the freezing point of 0.31 K between the roof such that freezing occurs below the thinner ice in the south and melting occurs at the thicker ice flowing in from the north (Wüest & Carmack, 2000). These melting and freezing processes occur via an overturning circulation where geothermal heatflux causes upwelling and colder melt waters downwell (Siegert et al., 2001; Wüest & Carmack, 2000), instead of ice pumping as it occurs below ice shelves where colder melt waters upwell along a sloping ice-ocean interface and refreeze at shallower depths (Lewis & Perkin, 1986). Wüest & Carmack (2000) suggest that the latter ice pump process would equilibrate ice ceiling slopes faster in freshwater subglacial lakes at lower pressures (where α is negative). Laboratory experiments have similarly found that overturning circulation dominates Vostok circulation (Wells & Wettlaufer, 2008).

Other studies have estimated Vostok salinity at 0.4–1.2 ppt from ice cores of accreted ice collected over the southern end of the lake (Souchez et al., 2000). This led to suggestions that even this low salinity (seawater salinity is ∼35 ppt) is sufficient to drive ice pumping as is observed in marine regimes below ice shelves, where melting in northern Vostok drives upwelling along the sloped ice ceiling, which leads to supercooling and frazil ice accretion in the southern region of the lake (Siegert et al., 2001; Souchez et al., 2000, 2004). Some modeling efforts for Vostok circulation at 1.2 ppt salinity supported this finding (Mayer et al., 2003); however, these efforts do not account for the dilution of the melt water upon mixing into the lake water. Here we show that the low salinity predicted for Vostok are insufficient to drive ice pumping through upwelling of melt waters due to a salinity contrast.

4 Theorized Ice-Ocean Interactions Below Europa's Ice Shell

We now consider how four hypothetical topographic features at the base of an ice shell would evolve for an ocean with ice pumping (Figure 4). The first three cases consider topography hypothesized to form using geologic processes within the ice shell with an equilibrium ocean: (a) brittle fracture (a basal crevasse), (b) ice shell thinning, and (c) downwelling or downdipped ice. In each case, we assume no sources of sensible heat and a well-mixed upper ocean within ∼50 mK of the freezing point at the mean ice base (similar order to sub-ice shelf oceans on Earth, e.g., Lawrence et al., 2023). For a fourth case, we consider ocean-driven melting where warm, buoyant plume results in localized ice thinning. We do not describe the processes that initiate the topography in each case and instead focus on how an understanding of the ice pump informed by analogous features below terrestrial ice shelves can be bound to the evolution of basal ice shell topography.

Details are in the caption following the image

The evolution of ice-ocean interactions is related to four basal ice shell topographic features. Each case is indexed to vertical profiles comparing the adiabat (red line) to the freezing point (black dashed line), illustrating how thermal driving changes with depth from the prescribed initial condition of +50 mK at the ice base. Black arrows indicate ice dynamics driving ice pumping, gray arrows indicate ice flow resulting from ocean driven-processes, cross hatching and green shading indicates marine ice formation. Case 1 depicts ice pumping following brittle fracture and crevasse opening at the base of the ice shell. Case 2 illustrates ice pumping following tensile strain thinning. Case 3 illustrates how downwelling ice melts as thermal driving increases with depth, which could also drive marginal ice pumping marine ice accretion because the melt input additionally cools the water and reduces the ∆H requires for supercooling to occur. In Case 4, an upwelling warm plume melts upward until thermal driving decreases to 0, although a melt-freshened lens (e.g., as discussed in Melosh et al. (2004) and Zhu et al. (2017)) in the melt case can insulate the ice base while horizontal melting continues on the sidewalls (as observed below ice shelves by Dutrieux et al. (2014) and Schmidt et al. (2023)).

We also work in terms of thermal driving to be able to quantitatively relate basal ice topography to ice-ocean interactions without knowledge of ice shell thickness or ocean composition (the latter two are required to calculate the absolute freezing point). For a given initial thermal driving and topographic gradient (∆P), the change in Tf with depth controls when thermal driving of upwelling water becomes negative and refreezing begins (and melting ceases). The hydrostatic equation describes the change in pressure for a given change in depth, assuming constant ρ w ${\rho }_{w}$ and g $g$ ,
P ( dbar ) = ρ w kg m 3 g m s 2 H ( m ) 10 4 dbar Pa 1 ${\increment}P(\text{dbar})={\rho }_{w}\left(\text{kg}\,{\mathrm{m}}^{-3}\right)\ast g\left({\mathrm{m}\,\mathrm{s}}^{-2}\right)\,\ast \,{\increment}H\,(\mathrm{m})\,\ast \,{10}^{-4}\left(\text{dbar}\,{\text{Pa}}^{-1}\right)$ (3)
which we can equate with the pressure change required to null an initial thermal driving magnitude (TD),
P ( dbar ) = TD ( mK ) T f P mK dbar 1 ${\increment}P(\text{dbar})=\frac{\text{TD}(\text{mK})}{\frac{\partial {T}_{f}}{\partial P}\left(\text{mK}\,{\text{dbar}}^{-1}\right)}$ (4)
to yield the depth change in meters that would result in supercooling for some initial thermal driving magnitude (the difference between the water temperature and in situ freezing point, Tw − Tf):
H ( m ) = TD ( mK ) ρ w kg m 3 g m s 2 T f P mK dbar 1 10 4 dbar Pa 1 ${\increment}H(\mathrm{m})=\frac{\text{TD}\,(\text{mK})}{{\rho }_{w}\left(\text{kg}\,{\mathrm{m}}^{-3}\right)\ast g\left({\mathrm{m}\,\mathrm{s}}^{-2}\right)\ast \frac{\partial {T}_{f}}{\partial P}\left(\text{mK}\,{\text{dbar}}^{-1}\right)\ast {10}^{-4}\left(\text{dbar}\,{\text{Pa}}^{-1}\right)}$ (5)

Below, we use this relation to consider how basal topography may evolve on Europa.

4.1 Case 1—Brittle Fracture

On Earth, the presence of marine ice has been inferred or observed within ice shelf basal crevasses, suture zones, and rifts from remote sensing techniques or oceanographic profiles (Fricker et al., 2001; Grosfeld et al., 1998; Hillebrand et al., 2021; P. R. Holland et al., 2009; Jansen et al., 2013; Khazendar & Jenkins, 2003; Khazendar et al., 2001; Kulessa et al., 2019; Matsuoka et al., 2009; Orheim et al., 1990; Tison et al., 1993). In situ observations of marine ice formation made by the remotely operated underwater vehicle (ROV) Icefin below Antarctica's Ross Ice Shelf show local-scale ice pumping occurring within a 40 m tall basal crevasse (Lawrence et al., 2023). At the base of the crevasse, thermal driving was +30 mK such that melt-modified water upwelling into the crevasse became supercooled after rising ∼35 m. This elevation also corresponded to the visual onset of marine ice (Figure 5).

Details are in the caption following the image

Supercooling and ice growth in a basal crevasse below the Ross Ice Shelf, modified from Lawrence et al. (2023). Green shading indicates observed marine ice; hatching indicates marine ice accumulation. The background contour shows thermal driving, which switches from positive in the lower body of the crevasse (red shades) to negative in the crevasse roof (blue shades) where refreezing occurred. Insets (a)–(h) (labeled in order of initial observation) show the resultant gradient in ice composition and morphology. (a) Melting, dimpled meteoric (fresh) ice base. (b) The transition from meteoric ice to refreezing ice at the supercooling horizon. (c–e) The evolution of marine ice morphologies as supercooling increases. (f) The supercooling horizon on the opposite crevasse wall, at approximately the same height. (g–h) Melting meteoric ice below the supercooling horizon. Discussion of the scale of features in each inset can be found in Lawrence et al. (2023).

These observations support models (Jordan et al., 2014) that show how marine ice can form in basal rifts or crevasses on Earth filled with supercooled waters. Marine ice accumulation rates below ice shelves have been observed at 2 m year−1 (Jansen et al., 2013), with seasonally higher rates possible below sea ice (observed by the authors during late winter into early spring beneath McMurdo Sound). Marine ice can also compact and further consolidate through congelation style growth (Bombosch & Jenkins, 1995; Craven et al., 2009; Dempsey et al., 2010; Hoppmann et al., 2020; Hubbard et al., 2012; Lewis & Perkin, 1986) to form a distinct lower salinity ice layer (Matsuoka et al., 2009; Moore et al., 1994).

At the base of Europa's ice shell, stresses may open water-filled basal fractures that penetrate hundreds of meters to kilometers upward, depending on the overall ice shell thickness (Walker et al., 2021). The freezing point at Europa increases (warms) with height by 0.1 mK m−1 (as compared to 0.85 mK m−1 on Earth), which along with the initial thermal driving of the water that upwells to fill the newly opened fracture determines the depth change required before refreezing will occur. For example, if thermal driving at the base of Europa's ice shell was +50 mK and a 1 km tall crevasse formed, supercooling would occur in water flowing up into the crevasse after a ∆H of ∼500 m (e.g., Figure 4, Case 1). This would generate buoyant frazil ice that would accumulate above that height in the crevasse ceiling. Europa's ocean is thought to be at or very near the freezing point (Melosh et al., 2004), so basal fractures are unlikely to remain open due to infilling by refreezing ice and the taller the initial fracture, the faster it will refreeze. Lower magnitudes of initial supercooling in the ocean would require smaller increases in the freezing point (or, smaller ∆H) to become supercooled, lowering the supercooling horizon where refreezing could begin. Conversely, higher initial thermal driving magnitudes (warmer waters) require greater changes in pressure for the freezing point to warm above the water temperature.

Refreezing through sensible heat flux to the adjacent ice can also occur along the crevasse sidewalls where buoyant frazil ice does not accumulate (Buffo et al., 2020), although conduction is generally a relatively small fraction of the ocean heat flux budget compared to the latent heat flux of melting or freezing, as observed by Arzeno et al. (2014) and Washam et al. (2020). Melting below the supercooling horizon during upwelling could also further reduce thermal driving and lower the refreezing horizon depth in a crevasse.

4.2 Case 2—Ice Shell Thinning

In the second case, we consider how a thinned region at the base of Europa's ice shell interacts with the ocean. We again assume an isothermal upper ocean near the freezing point, such that the localized thinning is the result of ice shell processes (e.g., extensional strain and viscous deformation, or localized upwelling). As in Case 1, if the topographic gradient from the ice base to the top of the negative topography/concavity is sufficient to warm the freezing point greater than the initial thermal driving at the same rate of approximately 10 m mK−1, supercooling and ice pumping results (Figure 4, Case 2). We would expect ice pumping to continually produce relatively less dense ice in a locally thinned area if the thinning was persistently maintained by upwelling or extensional processes in the ice shell. Refreezing of warmer, less saline, less dense ice in these regions could contribute to localized ice upwelling and diapir formation. Even if the ∆H of the thinned region is not sufficient to null the initial thermal driving, the reduction of the total thermal driving with height could still favor increased rates of congelation ice growth at the ice interface through conductive heat loss to the overhead ice, as has been observed below the Ross Ice Shelf (Zotikov et al., 1980).

4.3 Case 3—Ice Downwelling

On Europa, assuming an isothermal ocean near the freezing point as in Cases 1 and 2, the ocean will work to erode any positive (convex/downward) basal ice features. Just as thermal driving decreases as water rises into a basal crevasse or concavity, thermal driving increases with depth (Figure 4, Case 3) by 0.1 mK m−1 and is higher under deeper ice. The pressure-driven increase in thermal driving with depth such that melt rates are highest where the ice is deepest, and acts as a negative feedback on locally thickened ice such as downwelling ice or keels.

Near the GZ of the Ross Ice Shelf, positive thermal driving of approximately +50 mK drove melt rates of 0.26 m year−1, or ∼3 × 10−9 m s−1 (Lawrence et al., 2023), which exceeds meridional ice transport rates at Europa suggested to be on order 1 × 10−11 m s−1 (Zhu et al., 2017) by two orders of magnitude. Presuming that Europa's sub-ice ocean is similarly near the freezing point, these relative rates show that ice-ocean interactions can respond quicker than viscous ice flow within the shell, as suggested by Soderlund et al. (2014) and Wolfenbarger, Buffo, et al. (2022) and act against the formation of ice shell topography. Any observed basal ice shell topography may then represent an equilibrium condition where the melt rate (primarily a function of thermal driving, current speed, and the transfer efficiency of heat and salt) is balanced by a continuous flux of downwelling ice due to ice shell dynamics.

If a positive topographic feature also represents the maximum draft of the ice shell, melting there will generate the coldest possible meltwater because the lowest Tf occurs at the highest pressure ice interface (assuming constant salinity). Water masses generated at the base of thickened/deepened ice features may then represent the lower limit for the ocean temperature. Meltwater input also reduces thermal driving, which could result in supercooling and marine ice growth as the mixture rises to the mean ice base draft at the margins of the feature (Figure 4, Case 3). Observations below Arctic sea ice also illustrate the above mechanism where locally deepened ice keels preferentially melt and induce frazil ice formation and accretion onto the underside of the shallower ice base adjacent (Katlein et al., 2020).

4.4 Case 4—Melt Thinning

In Case 4, we consider ocean-driven melting as a source of regionally thinned ice. Upwelling ocean plumes with elevated thermal driving impinging upon the ice base may result from eddies such as those expected near the equator in rapidly rotating models (e.g., Soderlund et al., 2014). In the case of ocean-driven ice shell thinning, the maximum height of a melt feature/negative topography is determined by the initial positive thermal driving in the ocean. In the simplest case, melting can proceed upward until the positive thermal driving falls to zero at the same rate 0.1 mK m−1. Other processes such as cooling through meltwater entrainment and conductive heat loss to the ice during upwelling can also reduce the thermal driving of the upwelling ocean plume, reducing the height of the melt feature.

Depending on flow speeds and positive buoyancy of the upwelling plume, melting can produce a freshened and cold upper lens along the ceiling of the feature (e.g., Melosh et al., 2004; Zhu et al., 2017). This freshened lens and density gradient can slow the transfer of heat to the ice base and inhibit upward melting. Such suppression of vertical melting due to stratification is observed in quiescent regions even in warm-cavity ice shelves such as Thwaites Glacier where thermal driving is more than 2 K, while flow through these regions permits horizontal melting by the advection of warm water directly to sloped or vertical ice-ocean interfaces. This effect permits widening of negative topography and steepens slopes along positive topography (Schmidt et al., 2023). Similar processes were observed in melting basal terraces into ice keels at Pine Island Glacier and Petermann Gletscher (Dutrieux et al., 2014). The degree of melt suppression depends on the stability of the stratification, which could be eroded by rapid currents or variability in the warm plume (e.g., Soderlund et al., 2014). Melt-thinned regions may then switch between melting and refreezing (behaving akin to Case 2 in the latter situation), resulting in spatially variable basal ice composition and roughness.

5 Other Ocean Worlds

Ice pumping scales with gravity and so may prove important to dynamics at the ice shell-ocean interfaces of other similarly massive ocean worlds such as Ganymede or Titan (see also Kvorka et al., 2018). Enceladus' sub-shell ocean also falls within an ice pumping regime (Figure 3), but Enceladus' gravity is 10 times less that of Europa and so would require 10 times greater ∆H for the same pressure-driven change in the freezing point. Ocean waters 50 mK above the freezing point at Titan or Europa (which have similar gravity at 1.352 and 1.315 m s−2, respectively) would begin to refreeze within a concave region or fracture taller than 500 m; the same feature would need to be 5 km on Enceladus for supercooling to occur. Accordingly, lower gravity at Enceladus should permit higher gradients in basal ice topography to persist.

In the assumption that the ice topography is generally in equilibrium with ocean forcing (i.e., mass flux through ice pumping occurs faster than viscous ice flow), any observed or inferred spatial variation in ice shell topography can provide an estimate of maximum ocean thermal driving. For example, Enceladus' ice shell thickness could vary from approximately 5 km at the south pole to 30 km at the equator (Beuthe et al., 2016; Hemingway & Mittal, 2019). If the ice is assumed to be in hydrostatic equilibrium, this ∆H of ∼22.5 km is equivalent to a pressure differential of approximately 250 dbar or a 200 mK difference in the freezing point at the ice shelf base between the pole and the equator. Supercooling is difficult to measure on Earth, but is generally limited to magnitudes between 1 and 100 mK due to frazil formation (Haumann et al., 2020). This suggests that even at ∼1% of Earth's gravity, the topographic gradient below Enceladus' ice shell may result in ice pumping.

Thermal driving can then be converted to ocean temperature and inform broader sub-shell ocean circulation dynamics, which enables a first order inversion between ice shell draft and ocean properties. We can estimate the ice-ocean temperature range at Enceladus using observations from NASA's Cassini mission, which indicates an NaCl-dominated (similar to Earth's oceans) upper bound of ∼20 g kg−1 (Glein et al., 2018; Postberg et al., 2009), although we note a few caveats on this upper bound. The plume material observed by Cassini may have been sourced from an upper lens of relatively fresh water in a stratified ocean case (Lobo et al., 2021), or the solute abundances in the ice grains may have been modified from the original fluid composition due to different freezing processes and rates (Buffo et al., 2021). With an estimate of 20 g kg−1, below the thinnest regions of the ice shell at a draft of 4.5 km, the maximum freezing point would be −1.095°C. At the interface below the thicker, equatorial ice at a draft of 27 km, the minimum freezing point would be −1.272°C. We can use this concept to bound the ocean temperature range for ocean worlds with known ice shell drafts (ice-ocean interface pressure), and with additional constraints on ocean salinity composition and spatial variability can then determine the absolute freezing point at a given ice-ocean interface depth. NASA's upcoming Europa Clipper mission is expected to improve knowledge of both European ice shell thickness variation and ocean salinity which will enable estimates of the ocean temperature below the ice shell and ice pump dynamics.

Supercooling and frazil formation processes could also be expected to modify intra-shell fluids, for example, within melt lenses (Buffo et al., 2020; Chivers et al., 2021) or upwelling water in plume conduits at Europa (Fagents, 2003; Quick & Marsh, 2016; Rhoden et al., 2015; Sparks et al., 2017; Vorburger & Wurz, 2021; Wolfenbarger, Buffo, et al., 2022). At ocean worlds more massive than the moons in our solar system, such as tidally locked water-rich exoplanets (Del Genio et al., 2019; Yang et al., 2019), the change in freezing point is greater for the same change in depth and ice pumping may be an even more important process to consider in global ocean circulation models (e.g., Cullum et al., 2016).

6 Conclusion

We show that ice pumping can occur for a range of ocean salinity and ice thicknesses relevant to ocean worlds, and that ice pumping is an important process linking ice shell dynamics, ocean circulation, and basal ice shell topography. Ice pumping provides insights into material exchange between the ice shell and the ocean (e.g., Allu Peddinti & McNamara, 2015). Areas of consistent freezing and marine ice accumulation (Cases 1 and 2) would act to export entrained ocean materials into the ice shell and at potentially lower salinity than the surrounding ice shell. Regions of relatively lower density marine ice formed by ice pumping could contribute to convective upwelling and ice overturn in the shell (Wolfenbarger, Buffo, et al., 2022). Deepened or downwelling ice regions (Cases 3 and 4) could be areas where exogenic materials or radiolytically generated oxidants (Chyba, 2000; Hand et al., 2007; Johnson et al., 2003) are delivered from the ice shell into the ocean, eroded by higher thermal driving at the deeper draft ice. This is analogous to how melting meteoric ice creates oxygen fluxes into sub-ice shelf oceans and subglacial lake water columns, and subglacial outflows can “subsidize” the sub-shelf ecosystem (Vick-Majors et al., 2020).

This work highlights a mechanism for the generation of heterogeneity in ice properties and compositions within the ice shells of ocean worlds. We show that the relationship between ice-ocean interactions and ice topography establishes a link between variability in ocean temperature and ice shell thickness that potentially makes constraining ocean temperatures possible in the absence of in situ ocean observations. Measuring ice shell thickness is a priority goal of NASA's upcoming Europa Clipper mission and may be constrained by limb profiles, gravity measurements, or via ice penetrating radar. The concepts described here will enable the thermal state of Europa's upper ocean to be constrained from ice shell thickness.

Acknowledgments

This work was supported by the Future Investigators in NASA Earth and Space Science and Technology (FINESST) program (J. D. Lawrence) Grant 80NSSC19K1544, NASA Grants NNX14AC01G, NNX16AL07G, and 80NSSC19K0615, as well as NSF Grants 1739003 and 2152742. This work is motivated by planetary analog and climate research and was inspired by several seasons of Antarctic field work exploring ice-ocean interactions on Earth. Portions of the work benefitted from discussions leading up to and during the 2019 Ocean Worlds Meeting IV, the 2022 Princeton Center for Theoretical Science workshop on Ice-Ocean Interactions on Icy Moons in the Solar System organized by Nicole Shibley, as well as many more discussions with Krista Soderlund, Natalie Wolfenbarger, Inga Smith, Natalie Robinson, Craig Stevens, Christina Hulbe, Mike Williams, Huw Horgan, Steve Vance, and Alex Robel.

    Data Availability Statement

    All figures were generated using the Python3 Gibbs Seawater Toolbox (GSW; v3.4.0) (Firing et al., 2021; McDougall & Barker, 2011) implementation of the International Thermodynamic Equation of SeaWater—2010 (TEOS-10) (IOC, 2010; McDougall et al., 2013). Code is available as a Jupyter Notebook (Granger & Pérez, 2021; Lawrence, 2023).