Massive Ice Sheet Basal Melting Triggered by Atmospheric Collapse on Mars, Leading to Formation of an Overtopped, Ice-Covered Argyre Basin Paleolake Fed by 1,000-km Rivers

Abstract

Near the Noachian-Hesperian boundary (∼3.6 billion years ago), most of Mars' near-surface water inventory was likely frozen in large southern ice sheets and Mars' CO₂ atmosphere had eroded enough that it began to periodically collapse. Here, I report model results showing that thermal blanketing of a southern H₂O ice sheet by a CO₂ ice cap formed during atmospheric collapse would produce melt equivalent to ∼0.2–2.0 × Mars' present-day global near-surface H₂O inventory. I then model downstream flow, demonstrating the likely development of an ice-covered fluviolacustrine system with 1,000s-of-kilometer-long rivers, an overtopped Mediterranean-Sea-sized lake in Argyre Basin, and substantial water delivery into Margaritifer Terra and potentially Chryse Planitia. This study shows that a steady-state hydrologic cycle driven by pole-to-equator melt and equator-to-pole sublimation and atmospheric transport lasting 10⁵–10⁷ year could occur multiple times throughout a ∼10⁸-year window during which atmospheric pressure was low enough to collapse yet CO₂ and H₂O inventories and geothermal heat output were high enough to produce substantial meltwater. The nature of this proposed hydrologic cycle is consistent with estimates of the timing, duration, and intermittency of Noachian-Hesperian fluvial activity. Thus, meltwater release triggered by atmospheric collapse potentially played an important role in the intense pulse of Noachian-Hesperian fluvial activity: directly so for the Argyre-Margaritifer-Chryse system and perhaps indirectly for other catchments. Finally, this study demonstrates that large amounts of water can mobilize in a cold climate, driven by the same atmospheric collapse process occurring on Mars today, without invoking late-stage warming processes.

Key Points

• Collapsing Mars' atmosphere onto an ice sheet ∼3.6 billion years ago can melt and liberate about half of Mars' water inventory

• Meltwater feeds an ice-covered fluviolacustrine system with 1,000s-km-long rivers and a breached Mediterranean-Sea-sized Argyre Basin lake

• This hydrologic process was likely important for Mars' intense Noachian-Hesperian fluvial period and does not require late-stage warming

Plain Language Summary

Approximately 3.6 billion years ago, most of Mars' water was likely frozen in large southern ice sheets and Mars' atmosphere had thinned to the point that it began to collapse, periodically forming a massive south polar CO₂ ice cap. I model the thermal blanketing effect of the CO₂ ice cap overlying the water ice sheets, demonstrating that it leads to massive meltwater liberation. I also model downstream meltwater, showing that it flowed through 1,000-km-long, ice-covered rivers, filling and then overtopping an ice-covered lake in Argyre Basin with approximately the volume of the Mediterranean Sea, eventually emptying 8,000 km away into the northern plains. This is the first model that produces enough water to overtop Argyre, consistent with decades-old geologic observations. Basal melting events likely occurred multiple times, 0.1-to-10 million years at a time, during a one-hundred-million-year era about 3.6 billion years ago. Water sublimed downstream likely returned to the south polar cap, perpetuating a pole-to-equator hydrologic cycle that may have played an important role in Mars' enigmatic pulse of late-stage intense fluvial activity. Finally, this study demonstrates that large amounts of water can mobilize in a cold climate without invoking the fraught paradigm of late-stage climatic warming.

1 Introduction

Mars' atmosphere is primarily CO₂ (Jakosky, 2021). Since the beginning of the Noachian (∼4.1 billion years ago; Carr & Head, 2010), Mars' atmospheric pressure has declined from a pressure that was initially ∼1-to-3 bar (Forget et al., 2013; Hu et al., 2015; Jakosky, 2021; Kite, 2019; Kurokawa et al., 2018). Once below ∼0.6 bar, periodic atmospheric collapse began to occur whenever Mars' sinusoidally evolving obliquity (spin-axis tilt; Laskar et al., 2004) fell below ∼30° because latitudinal heat transport was insufficient to prevent runaway deposition of the atmosphere into polar CO₂ ice sheets (Forget et al., 2013; Soto et al., 2015). The decline below ∼0.6 bar likely happened ∼3.6 billion years ago (Hu et al., 2015; Kite, 2019), at which time most of Mars' surface water was likely frozen in an extensive south polar cap (Figure 1a; Fastook et al., 2012; Head & Pratt, 2001).

Figure 1

Overview of proposed model and relevant geography. (a) MOLA (Smith et al., 1999) elevation and hillshade map of Mars (blue, low = −5,000 m; red, high = +6,000 m) in south polar projection with geologic units (Tanaka et al., 2014), eskers (Scanlon et al., 2018), and Argentea Planum proglacial paleolake (Dickson & Head, 2006). CO₂ ice sheet extent assumes a constant 660 m depth. Note the correspondence between model-predicted domains, that is, CO₂ ice sheet extent, and location of eskers. (b) Schematic overview of proposed model, with ∼100× vertical exaggeration of ice column.

This study uses modeling to show that a thick CO₂ ice layer burying the H₂O ice cap would insulate geothermal heat conducting from Mars' interior (Solomon et al., 2005), liberating massive amounts of meltwater. I then analyze downstream meltwater movement through ∼1,000-km-long rivers into an Argyre Basin paleolake (Hiesinger & Head, 2002), all beneath ice cover (Figure 1b). Notably, no previously identified mechanism can deliver enough water to fill Argyre, even though morphologic evidence is consistent with equatorward breach outflow flooding into the Uzboi-Ladon-Morava Valles system (Figure 1a; Grant & Parker, 2002; Hiesinger & Head, 2002). I show that the modeled meltwater liberation and fluviolacustrine transport is amply sufficient to overtop Argyre Basin, delivering water into Margaritifer Terra (Salvatore et al., 2016) and perhaps all the way to Chryse Planitia (Moore et al., 1995) in a cold, steady-state collapsed environment, without the need for any warming episodes. Finally, I discuss the potential implications of the hydrologic cycle proposed here for Mars' enigmatic intense terminal pulse of fluvial activity near the Noachian-Hesperian boundary (e.g., Fassett & Head, 2011; Irwin et al., 2005; Kite, 2019).

2 Methods

2.1 Modeling Overview

I model equilibration between CO₂ in the atmosphere, CO₂ adsorbed in the regolith (a pervasive CO₂ film coating martian soil) and polar CO₂ ice (Buhler and Piqueux, 2021a) to calculate the CO₂ ice cap mass that collapsed onto a pre-existing south polar H₂O ice cap (Section 2.2). Ice thermal structure is modeled using a one-dimensional conduction scheme accounting for geothermal heat, H₂O ice strain heating, latent heats of sublimation and fusion, mass balance, and the formation of CO₂ hydrate clathrate (a cage-like H₂O structure enclosing CO₂; e.g., Mellon, 1996), with appropriate interfacial temperature bounds (Section 2.3), including a consideration of glacial flow (Section 2.4). I then model the downstream fate of the meltwater using Moore et al.’s (1995) 1-dimensional model for ice-covered lake development and then adapt the model for ice-covered river flow; the fluviolacustrine model balances liquid water input, ice freezing, and ice surface sublimation (Section 2.5). Appendix A provides a table of all model variables.

2.2 CO₂ Collapse Model

CO₂ collapse mass is calculated with a regolith adsorption and atmospheric mass equilibration model (Buhler & Piqueux, 2021a) as a function of geothermal heat (Ojha et al., 2020; Solomon et al., 2005), atmospheric pressure, obliquity, regolith thermal conductivity, and regolith albedo drawn from equal probability distributions and regolith specific surface area and depth drawn from probability distributions in Buhler and Piqueux (2021a; their Figure 4) over the ranges in Table 1. Exchangeable regolith in the model extends between 60°S and 60°N, consistent with the inferred extent of H₂O and CO₂ Noachian-Hesperian polar ice caps at 30° obliquity (Fastook & Head 2015; Forget et al., 2013; Head & Pratt 2001; Wordsworth et al., 2013).

Table 1. Range of Regolith Adsorption Parameter Space

Quantity	Range	Units
Regolith Thermal Conductivity (kreg)	8.37 × 10^−2–2.0	Wm^−1K^−1
Regolith Albedo (Areg)	0.1–0.3	Unitless
Average Geothermal Flux (Fgeo)	0.03–0.08	Wm^−2
Regolith Specific Surface Area (aS)	10^2–10^5	m^2kg^−1
Active Regolith Depth (zreg)	1–1,000	m

In brief, the regolith is divided into a grid of 2°-latitude (e.g., Fanale & Cannon, 1971) and depth, with numerically stable adaptive depth spacing (Buhler & Piqueux, 2021a). CO₂ mass adsorbed in each grid box depends upon pressure, temperature, and specific surface area (Zent & Quinn, 1995). Temperature is determined from the one-dimensional energy balance between absorbed solar flux, emitted thermal flux, and subsurface conductive flux calculated in 30-min time steps to a depth of 50 m (>10 annual skin depths). Below 50 m, the temperature is set according to: $$\frac{dT}{dz}=-\frac{{F}_{\text{geo}}}{{k}_{\text{reg}}}$$, where T is temperature, z is depth, F_geo is geothermal flux, and k_reg is regolith thermal conductivity. The total adsorbed CO₂ reservoir is the sum of all grid boxes.

Atmospheric pressure after collapse is determined from vapor pressure equilibrium with cap surface temperature T_cap = $${\left((1-A)\times \frac{{S}_{0}}{{\epsilon}{\sigma }_{B}}\right)}^{\tfrac{1}{4}}$$, for CO₂ emissivity ϵ = 0.8 (Buhler et al., 2020; Hayne et al., 2012), Stefan-Boltzmann constant σ_B, insolation-dependent albedo A (Equation 4 of Buhler et al., 2020), and mean annual insolation S₀ calculated in 30-min time steps with modern solar flux of 586 W m⁻² assuming a circular orbit at 30° obliquity. The corresponding vapor pressure equilibrium pressure P_cap is calculated from the empirical relation presented in Span and Wagner (1996). Assuming instead a faint young Sun with 0.75× present flux (Gough, 1981) yields T_cap = 141 K and P_cap = 3 mbar (cf. Section 3.2). Basal melt volumes and rates assuming a faint young Sun are within 3% of those using modern flux because potential melt enhancement from increased CO₂ cap mass (due to lower P_cap) is closely offset by the effect of lower T_cap.

The CO₂ cap deposition location depends upon local elevation and thermophysical conditions (Buhler et al., 2020). Collapse across this parameter space is not well explored (Forget et al., 2013; Soto et al., 2015), but south polar CO₂ ice caps are favored in early Mars climate modeling (Forget et al., 2013) and the modern climate (Buhler et al., 2020; Gary-Bicas et al., 2020). CO₂ migrates to the region of highest thermodynamic stability faster than Mars' obliquity evolution, precluding multiple permanent CO₂ caps (Buhler et al., 2020). Therefore, CO₂ exclusively forms a south polar cap in the model.

The initial, inflated atmosphere is taken from prior modeling, which predicts the initial onset of collapse for Mars' atmosphere to be 600 mbar at 30° obliquity (Forget et al., 2013). Adding H₂O greenhouse effects to the Forget et al. (2013) model increases temperatures by at most a few K (Forget et al., 2013; Wordsworth et al., 2013), changing collapse onset by <∼1° obliquity, which is negligible compared to the 15° amplitude oscillations sampled by Mars on 10⁵-year timescales (Laskar et al., 2004). Including more powerful Noachian greenhouse effects, such as CO₂-H₂ collision-induced absorption (Ramirez et al., 2020), would still yield atmospheric collapse once H₂ concentrations dropped below ∼1%, which would occur on ∼10⁴–10⁵-year timescales (Haberle et al., 2019; Tarnas et al., 2018; Tosca et al., 2018) after punctuated release events or even a debatably (Wordsworth et al., 2021) long-term volcanically sustained H₂-rich atmosphere (Ramirez et al., 2020). Thus, the inclusion of greenhouse warming does not affect the conclusions of this work.

Modeled CO₂ adsorption after collapse accounts for the difference in pressure between P_cap and mean regolith surface pressure P₀ (i.e., at the global 0 m datum), assuming cap base elevation of +1 and 3 km H₂O and 660 m CO₂ ice column thickness (Figure 2c), using an isothermal atmospheric approximation with scale height H = 11.1 km. This yields P₀ = $${P}_{\text{cap}}\times \mathrm{exp}\,(4.66\,\text{km}/\mathrm{H})$$ = 17 mbar.

Figure 2

Atmospheric collapse and CO₂ cap formation model output. (a) Maximum likelihood (black line) and ±1σ (purple region) mass of combined atmospheric and adsorbed CO₂ reservoirs as a function of atmospheric pressure. (b) CO₂ collapse area as a function of partially collapsed pressure assuming initial inflated pressure of 600 mbar and depth to melting from surface temperature defined by vapor pressure equilibrium (Figure 3a) for maximum likelihood (black line) and ±1σ (purple region) mass of combined atmospheric and adsorbed CO₂ reservoirs. (c) Depth to reach CO₂ melting (217 K) as a function of heat flux (i.e., geothermal plus shear heating) for CO₂ deposits in surface vapor pressure equilibrium with atmospheric pressures indicated in the legend.

The regolith vapor diffusion skin depth d_vap on ∼10⁴ yr timescales relevant to atmospheric collapse (Forget et al., 2013; Soto et al., 2015) ranges from 300 m (P₀ = 10 mbar) to >>1 km (P₀ = 600 mbar) (Table 2), as calculated from Equation 7 of Toon et al. (1980) with a low-end estimate of 1–10 μm pores (Clifford, 1991; Jakosky, 1986; Morgan et al., 2018; Toon et al., 1980); larger pores would increase d_vap. Most obliquity-driven CO₂ exchange occurs in the upper few hundred meters of regolith (Buhler & Piqueux, 2021a), so the model assumes no kinetic hindrance to CO₂ desorption. The model neglects changes to the regolith temperature profile during collapse because obliquity changes by <∼1° in 10⁴ yr (Laskar et al., 2004). CO₂ collapse onto the south pole is not kinetically hindered in the model because the magnitude of seasonal CO₂ ice cycling between poles exceeds the net annual CO₂ collapse deposition rate (Forget et al., 2013). The assumed presence of thick south polar H₂O ice sheets (Fastook et al., 2012) during atmospheric collapse is consistent with latitudinal H₂O transport equilibration rates exceeding obliquity variation rates (Wordsworth et al., 2015).

Table 2. Vapor Diffusion Skin Depth d_vap for 10⁴ yr and Various Pressures and Pore Sizes

	1 μm pores	10 μm pores
$${P}_{0}$$ = 10 mbar	$${d}_{vap}\sim 3\times {10}^{2}\,\mathrm{m}$$	$${d}_{vap}\sim 1\times {10}^{3}\,\mathrm{m}$$
$${P}_{0}$$ = 100 mbar	$${d}_{vap}\sim 1\times {10}^{3}\,\mathrm{m}$$	$${d}_{vap}\sim 1\times {10}^{4}\,\mathrm{m}$$
$${P}_{0}$$ = 600 mbar	$${d}_{vap}\sim 2\times {10}^{5}\,\mathrm{m}$$	$${d}_{vap}\,\sim 1\times {10}^{8}\,\mathrm{m}$$

2.3 Polar Cap Ice Column Model

2.3.1 Initial H₂O Ice Cap Conditions

Previous studies indicate that a ∼2–4 km-thick south polar H₂O ice cap extended to ∼60°S near the Noachian-Hesperian boundary (Figure 1b; Fastook et al., 2012; Head & Pratt, 2001; Scanlon et al., 2018) and that the present-day H₂O cap is almost 4 km thick (Plaut et al., 2007). Model H₂O column melt volume and flux are calculated by assuming a starting H₂O ice thickness of 2-to-4 km and subtracting the remaining H₂O thickness when the threshold for model melt halting is reached, that is, once the ice column basal temperature equals the H₂O melting temperature (Figure 3a). The vertical structure of the ice column is assumed to be identical throughout the entire lateral model domain, with ∼660 m CO₂ thickness and H₂O thickness initially 2-to-4 km (depending on the model run). This study explores a range of 2-to-4 km initial H₂O ice thickness, a range entirely encompassed by the large uncertainties in Mars' early near-surface exchangeable H₂O inventory mass and distribution (Carr & Head, 2015; Jakosky, 2021) when considering a column thickness governed by cross-latitude ablation-deposition cycling and H₂O glacial flow (Section 2.4.2).

Figure 3

Thermodynamic and physical property phase space of CO₂, H₂O, and CO₂ structure-I clathrate hydrate. (a) Phase diagram of CO₂–H₂O–CO₂ structure-I clathrate hydrate system, with sublimation, melting, and vaporization curves for H₂O (Wagner et al., 2011) and CO₂ (Span & Wagner, 1996), triple and critical points for CO₂, decomposition curve for clathrate (Ohgaki & Hamanaka, 1995; Yasuda & Ohmura, 2008), and pressure-temperature relation with depth for pure CO₂ ice columns in surface equilibrium with atmospheres of 10, 100, and 600 mbar. (b) Density of liquid CO₂ and clathrate as a function of temperature. Clathrate density from Ohgaki and Hamanaka (1995) at 4 MPa and with full CO₂ site occupancy (pink circles; least-squares fit: pink dash-dot) and 75% occupancy (pink x's; least-squares fit: pink dashed). The black dotted line demarcates 217 K, approximately the CO₂ melt temperature for all runs. Liquid CO₂ density along vaporization pressure curve (black solid; Span & Wagner, 1996) and at higher pressures from Klimeck et al. (2001) (red = 12 MPa, yellow = 18 MPa, green = 24 MPa, blue = 30 MPa, solid lines) extended with cubic extrapolation (same colors, dotted).

2.3.2 Thermal Model

The 1-dimensional temperature profile through the polar deposit column is determined from $$\frac{dT}{dz}=-\frac{F}{k}$$, where F is column heat flux (sum of polar geothermal flux F_pol and strain heating flux F_strain) and k is the thermal conductivity of the appropriate species. Model F_pol ranges from 40 to 60 mW m⁻², nominally (Ojha et al., 2020; Solomon et al., 2005) 50 mW m⁻². In the model, F_geo (which controls global adsorption; Section 2.2) can be different from F_pol within a given run because of likely regional geothermal gradient variations (McGovern et al., 2002). Allowing F_geo ≠ F_pol yields a negligible (∼1%) uncertainty increase in modeled net desorbed regolith mass (Figure 2a); input uncertainty in regolith thickness and specific surface area dominate this aspect of model output uncertainty (Buhler and Piqueux, 2021a).

For runs with CO₂ ice, the zero-flux surface temperature boundary is set to T_cap = 152 K (i.e., modeled $${T}_{\text{cap}}$$ following collapse, see Section 3.2) and the basal CO₂ temperature is set to the melting temperature $${T}_{\text{melt},\mathrm{C}{\mathrm{O}}_{2}}$$ (∼217 K for all runs; Figure 3a). The thickness of CO₂ within the column is set by the condition that CO₂ accumulates until its base melts at temperature 217 K because the accumulation rate far exceeds modeled lateral CO₂ glacial flow (Section 2.4.1; Table 3). Note that CO₂ basal melt would likely kinetically enhance clathrate formation (Section 2.3.3), with residual liquid CO₂ escaping laterally and quickly evaporating or refreezing under thinner CO₂ near the cap edge. For bare H₂O ice runs, the surface temperature is a typical Noachian 195 K mean average south polar temperature (Scanlon et al., 2018).

Model thermal conductivity (CO₂ ice) $${k}_{\mathrm{C}{\mathrm{O}}_{2}}$$ = $$93.4/\mathrm{T}\,\mathrm{W}\,{\mathrm{m}}^{-1}\,{\mathrm{K}}^{-1}$$ (Mellon, 1996) and (H₂O ice) $${k}_{i}=651/\mathrm{T}\,\mathrm{W}\,{\mathrm{m}}^{-1}\,{\mathrm{K}}^{-1}$$ (Petrenko & Whitworth, 1999); because they depend on T, the temperature profile is calculated iteratively until the cumulative temperature difference is <0.001%. Prior study indicates a reasonable structure-I CO₂ hydrate clathrate thermal conductivity $${k}_{\text{clath}}$$ is 0.4 $$\mathrm{W}\,{\mathrm{m}}^{-1}\,{\mathrm{K}}^{-1}$$ (Jiang & Jordan, 2010).

Annual e-folding thermal relaxation depth $$D=\sqrt{Pk/\pi \rho c}$$ for clathrate, CO₂, and H₂O are, respectively, D_clath = 1.5 m, $${D}_{\mathrm{C}{\mathrm{O}}_{2}}$$ = 1.6 m, and $${D}_{{\mathrm{H}}_{2}\mathrm{O}}$$ = 4.4 m, where period P = 1 year, ρ is density (ρ_clath = ∼1,100 kg m⁻³; Henley et al., 2014; Kondori et al., 2020), and c_clath = ∼1,800 J kg⁻¹ K⁻¹, $${c}_{\mathrm{C}{\mathrm{O}}_{2}}$$ = 1,200 J kg⁻¹ K⁻¹, and c_i = 1,400 J kg⁻¹ K⁻¹ are clathrate, CO₂, and H₂O ice heat capacity, respectively (Giauque & Egan, 1937; Giauque & Stout, 1936; Ning et al., 2015). The deposition rate of CO₂ onto the cap is smaller, ∼10 cm yr⁻¹ (Forget et al., 2013; Soto et al., 2015). Thus, the model thermal profile remains in conductive equilibrium throughout the collapse.

Strain heating is calculated from F_strain = 2A_T(ρgh tan α)⁴ with gravity g, depth h, surface slope α = 4 × 10⁻³ (representative of 3-dimensional Noachian polar cap model profiles; Fastook et al., 2012) and A_T an empirical constant (Cuffey & Paterson, 2010). Strain heating is calculated iteratively; CO₂ ice, clathrate, and H₂O ice column thicknesses adjust to the previous iteration of strain heating until the strain heating power difference is <1 × 10⁻⁴ mW m⁻² between iterations. Low values of A_T are 24 × 10⁻²⁵ and 3.5 × 10⁻²⁵ s⁻¹ Pa⁻³ m⁻¹, for H₂O ice at 273 and 263 K, respectively, and high values of A_T are 93 × 10⁻²⁵ and 8.7 × 10⁻²⁵ s⁻¹ Pa⁻³ m⁻¹, for H₂O ice at 273 and 263 K, respectively (Cuffey & Paterson, 2010). In H₂O ice colder than 263 K A_T decreases exponentially by a factor of 10 for every 10 K decrease. In practice, this is approximately equivalent to neglecting strain heating in H₂O ice colder than 263 K because >99% of model strain heating power occurs in H₂O ice warmer than 263 K. As a test of functionality, the model predicts that a bare H₂O ice cap basally melts at a thickness of ∼3.5–4.5 km, given 40–60 mW m⁻² geothermal flux (Solomon et al., 2005) and H₂O ice strain heating (Cuffey & Paterson, 2010), consistent with previous 3-dimensional modeling (Fastook & Head, 2015; Fastook et al., 2012).

Basal melt volume V_melt is calculated as the difference between the initial H₂O column thickness $${h}_{{\mathrm{H}}_{2}\mathrm{O},\text{init}}$$ and depth to H₂O melting $${h}_{{\mathrm{H}}_{2}\mathrm{O},\text{melt}}$$ after CO₂ burial, according to:

$$${V}_{\text{melt}}=\left(\left({H}_{{\mathrm{H}}_{2}\mathrm{O},\text{init}}-{h}_{{\mathrm{H}}_{2}\mathrm{O},\text{melt}}\right)\times {\rho }_{i}\times {A}_{\text{cap}}-{m}_{{\mathrm{H}}_{2}\mathrm{O},\text{clath}}\right)/{\rho }_{w}$$$ (1)

Here ρ_i is H₂O ice density (917 kg m⁻³), ρ_w is H₂O liquid density (1,000 kg m⁻³), and $${m}_{{\mathrm{H}}_{2}\mathrm{O},\text{clath}}$$ is the column mass of H₂O contained in clathrate. A_cap is the CO₂ cap area calculated by dividing the model CO₂ ice cap mass by the depth to CO₂ melting (Figures 2b and 2c) and the 1,600 kg m⁻³ density of CO₂. H₂O basal melting flux depends on the available basal heat flux once the thermal gradient has risen to allow basal H₂O melting (e.g., Clifford, 1987).

The model is conservative in producing basal melting. There is no contribution of CO₂ strain heating in the model because empirical constants for CO₂ ice strain heating are not available. The model also neglects thermal flux from sliding at the base of both the CO₂ and H₂O ice because models of sliding velocity have difficulty accurately reproducing observation—even for modern glaciers on Earth—because sliding velocity depends on substrate, is nonlinear, and highly spatially variable (Cuffey & Paterson, 2010). There are even greater uncertainties for ancient martian ice flow, especially for CO₂ ice. Nevertheless, CO₂ basal sliding may potentially enhance clathrate formation (Section 2.3.3) and H₂O ice basal sliding might contribute a factor of ∼10% increase to the column heat flux for basal sliding velocities of ∼0.1 m yr⁻¹ (Clifford, 1987), velocities that are plausible based on observed terrestrial (Cuffey & Paterson, 2010; Rignot & Mouginot, 2012; Rignot et al., 2011) and modeled Mars (Fastook & Head, 2015) ice sheets. Additionally, the model does not include entrained dust within the H₂O ice, which would lower the column thermal conductivity and add column mass that would increase shear heating, nor does it include freezing point depression due to the presence of salts in the H₂O ice, which is appropriate because basal melting should quickly purge salts (Fastook et al., 2012). Finally, the ice column model does not consider the fate of H₂O ablated downstream of basal melting, some of which would likely recycle through the atmosphere and become cold-trapped onto the cap, providing additional mass loading and insulation that could perpetuate basal melting (Section 4.3.1).

2.3.3 Clathrate

Clathrate formation is thermodynamically favored over the formation of pure liquid CO₂ and H₂O melt under model conditions at the CO₂-H₂O ice interface (Figure 3a; Longhi, 2005) and has been observed to form in laboratory experiments (Bollengier et al., 2013) directly between CO_2(s) and H₂O_(s). Thus, clathrate is included in the model despite no definitive detection of martian clathrate (Longhi, 2006; Phillips et al., 2011), which likely arises from kinetic hindrance to formation on the surface of modern Mars (under conditions not applicable to the present model) and difficulty in distinguishing spectroscopically between clathrate and H₂O ice (Ambuehl & Madden, 2014; Anderson, 2003).

Clathrate formation enthalpy is important for assessing whether clathrate forms in the column but is not reported directly in the literature, so I calculate it here. Clathrate formation (Anderson, 2003) from $$\mathrm{C}{{\mathrm{O}}_{2}}_{(\mathrm{g})}$$ and $${\mathrm{H}}_{2}{\mathrm{O}}_{(\mathrm{s})}$$ has an enthalpy of $${\Delta }{H}_{f,C{O}_{2(g)}+{H}_{2}{O}_{(s)}}$$ = 23.8 $$\pm $$ 0.4 kJ mol⁻¹, from:

$$$\mathrm{C}{{\mathrm{O}}_{2}}_{(\mathrm{g})}+{\mathit{n}}_{0}{\mathrm{H}}_{2}{\mathrm{O}}_{(\mathrm{s})}\to \mathrm{C}{\mathrm{O}}_{2}\cdot {\mathit{n}}_{0}{\mathrm{H}}_{2}{\mathrm{O}}_{(\mathrm{s})}+\text{Heat}$$$ (2)

Here n₀ is a constant equal to 5.75 when CO₂ is completely accommodated. However, some sites are typically unoccupied, yielding (Ferdows & Ota, 2006) n₀ ∼6. Thus, n₀ = 6 in the model. Clathrate formation enthalpy from $$\mathrm{C}{{\mathrm{O}}_{2}}_{(\mathrm{l})}$$ and $${\mathrm{H}}_{2}{\mathrm{O}}_{(\mathrm{s})}$$ can be determined from Equation 2 by subtracting CO₂ vaporization enthalpy (Shen et al., 2017) $${\Delta }{H}_{\text{vap},\mathrm{C}{\mathrm{O}}_{2}}$$ = 16.5 kJ mol⁻¹, yielding $${\Delta }{H}_{f,C{O}_{2(l)}+{H}_{2}{O}_{(s)}}$$ = 7.3 $$\pm $$ 0.4 kJ mol⁻¹ (exothermic). Likewise, $${\Delta }{H}_{f,C{O}_{2(s)}+{H}_{2}{O}_{(s)}}$$ = −2.1 $$\pm $$ 0.4 kJ mol⁻¹ (endothermic) is determined using CO₂ sublimation enthalpy (Shen et al., 2017) $${\Delta }{H}_{\text{sub},\mathrm{C}{\mathrm{O}}_{2}}$$ = 25.9 kJ mol⁻¹.

$${\Delta }{H}_{f,C{O}_{2(s)}+{H}_{2}{O}_{(s)}}$$ is smaller than H₂O and CO₂ melting enthalpy (−6.0 and −9.4 kJ mol⁻¹, respectively) and will thus proceed more readily than the formation of pure H₂O and CO₂ liquid melt. Given 25 mW m⁻² of flux, clathrate molar mass of 147.5 g mol⁻¹, and sufficient mixing, clathrate formation at the CO₂-H₂O interface should proceed at a rate of 0.5 m yr⁻¹, with a CO₂ uptake of ∼0.1 m yr⁻¹, balancing net annual CO₂ deposition during collapse (Section 2.3.2).

Heat production explicitly accounted for in the model is from F_pol and F_strain, which are localized near the bottom of the column. However, there will likely also be some strain heating and slide heating localized near the base of the CO₂ ice column. CO₂ strain heating constants are not available, so no estimation of CO₂ strain (or slide) heating is attempted. However, even if no heat is generated near the CO₂-H₂O interface, heat from F_pol and F_strain would diffuse upward within ∼10² year (for $${D}_{{\mathrm{H}}_{2}\mathrm{O}}$$ = 4.4 m; see above). Thus, if H₂O basal melting ceases, clathrate formation should initiate, adjusting the column thermal profile to reinitiate basal melting within ∼10² year, which is <<10⁴ yr minimum timescale relevant to atmospheric collapse. For a formation rate of >∼0.5 m yr⁻¹ (as above), a clathrate layer hundreds of meters thick could form in <<10³ year. Thus, clathrate formation is not kinetically or energetically limited in the model.

H₂O—CO₂ mixing through a growing clathrate layer must occur in order to form layers of clathrate thick enough to meaningfully affect H₂O basal melting. Mixing may be buoyancy-limited because the density of liquid CO₂ is highly temperature dependent (Figure 3b). The density of fully occupied (n₀ = 5.75) clathrate is fairly uncertain, between ∼1,100 and 1,200 kg m⁻³ (Kondori et al., 2020) and also depends on n₀ (Ferdows & Ota, 2006). The exact choice of ρ_clath within that range has a small (<<1%) effect on basal melting from a thermal conduction and strain heating perspective. However, if CO₂ mixing through the clathrate layer is buoyancy-limited, the density of ρ_clath will affect the clathrate layer thickness. Liquid CO₂ is denser than clathrate for temperatures <∼225–245 K (Figure 3b). Thus, the nominal range of clathrate basal temperature T_base,clath is 225–245 K (∼60–220 m thickness for a 50 mW m⁻² heat flux; Figure 4). However, models with T_base,clath ranging from $${T}_{\text{melt},\mathrm{C}{\mathrm{O}}_{2}}$$ (no clathrate) to 273 K (leading to melting of H₂O ice directly beneath the clathrate) are performed for completeness (Figure 5).

2.4 Glacial Flow

2.4.1 CO₂ Glacial Flow

It is important to consider the rates of CO₂ ice cap vertical subsidence and lateral flow due to viscous creep relative to other model rates. Glacial movement depends on a flow law (e.g., Cross et al., 2020):

$$$\dot{\varepsilon }={A}_{D}{\sigma }^{n}{d}^{-m}\,\mathrm{exp}(-Q/RT)$$$ (3)

Here $$\dot{\varepsilon }$$ is strain rate, A_D is an empirical constant (Table 3; Cross et al., 2020; Durham et al., 1999; Nye et al., 2000), σ is differential stress, d is grain size, Q is creep activation energy, R is the gas constant, and n and m are stress and grain size exponents, respectively. Laboratory measurements of CO₂ are compatible with a wide variety of flow law dependencies from n = 1 at low stress and high temperature to n = 8 (or higher) at high stress and low temperature (Table 3; Cross et al., 2020; Durham et al., 1999; Nye et al., 2000). I adopt empirically derived values of Q and A_D for flow laws with n > 1 from Table 1 of Nye et al. (2000) and Table 1 of Cross et al. (2020), which do not depend on grain size (i.e., m = 0). Flow laws with n = 1 depend on grain size and A_D is not explicitly provided in the literature for these laws (Cross et al., 2020). However, A_D can be estimated from Table S1 of Cross et al. (2020) for their experiment PIL208 (with T = 212.5 K) using Equation 2 and d = 30 μ m, Q = 212 kJ mol⁻¹, and m = 2 (Nabarro-Herring creep) or m = 3 (Coble creep) (Table 3).

Table 3. Empirical Constants (Cross et al., 2020; Nye et al., 2000) and Calculated Timescales and Rates for Various CO₂ Glacial Flow Models

Quantity	n = 1, m = 2	n = 1, m = 3	n = 2	n = 4.5	n = 7	n = 8
Log10AD (MPa^−ns^−1)	14.1	9.57	−2.02	3.64	11.1	13.0
Q (kJ mol^−1)	112	112	15	31	59	67
t0 (yr)	4.3 × 10^9	1.4 × 10^14	6.9 × 10^3	1.5 × 10^7	5.4 × 10^11	6.5 × 10^13
$$\dot{h}$$ (m yr^−1)	1.7 × 10^−9	5.1 × 10^−14	1.6 × 10^−4	1.4 × 10^−9	8.4 × 10^−16	<1 × 10^−16
$$\dot{r}$$ (m yr^−1)	1.3 × 10^−6	3.9 × 10^−11	1.3 × 10^−1	1.0 × 10^−6	6.5 × 10^−13	<1 × 10^−16

The characteristic relaxation timescale t₀ and 10⁴-yr-average deposit central height decay rate $$\dot{h}$$ and outer rim expansion rate $$\dot{r}$$ can be calculated from Equations 14 to 16 of Nye et al. (2000) for an idealized smooth, radially symmetric CO₂ ice cap with nominal central height 660 m and radius 1.0 × 10⁶ m (from nominal area 3.2 × 10¹² m²) at temperature 212.5 K (near melting) with surface slope 3 × 10⁻⁴ (assuming approximately equal-thickness CO₂ ice draping over an idealized H₂O ice cap) (Table 3). A maximum vertical subsidence of 1.6 × 10⁻⁴ m yr⁻¹ ensues under the n = 2 flow law, which is ∼2 orders of magnitude lower than the net annual deposition of CO₂ during collapse (Forget et al., 2013; Soto et al., 2015). However, the n = 1 flow laws are likely more appropriate to the high (near melting) temperature and low (<1 MPa) shear stress regime of the CO₂ cap considered here (Cross et al., 2020), which yield subsidence rates 7-to-12 orders of magnitude lower than CO₂ surface deposition. Thus, viscous glacial flow is likely to be negligible relative to both the size of the cap and net annual CO₂ deposition rates. Therefore, in the thermal column model, CO₂ accumulates to a thickness at which its basal temperature equals $${T}_{\text{melt},\mathrm{C}{\mathrm{O}}_{2}}$$.

2.4.2 Consideration of H₂O Glacial Flow

Glacial flow of the H₂O ice would tend to distribute H₂O ice to lower latitudes and thin the H₂O ice column. Under a latitudinally integrated ablation-deposition atmospheric water cycle, H₂O ice column thickness is expected to be <∼13% thinner when experiencing glacial flow than if the column were static, depending on the exact assumption of subsurface heat flux heat and total available near-surface exchangeable water inventory (Fastook & Head, 2015). This effect on column thickness is much smaller than the uncertainty on the available near-surface global water budget and its distribution near the Noachian-Hesperian boundary (Carr & Head, 2015; Jakosky, 2021) and so is encompassed by the factor of two exploration of the potential starting ice column between 2 and 4 km thick (Section 2.3.1); thus, H₂O glacial flow is not explicitly calculated in the model.

2.5 Lake and River Ice Cover Model

2.5.1 Lake Ice Model

The lake ice model is a 1-dimensional time-marching model that balances liquid water input at the bottom, ice freezing at the ice-water interface, and ice sublimation at the top with 1-year time steps (Figure 6). Note that infiltration is not explicitly considered in the model because the sub-ice-sheet and sub-lake aquifers will likely quickly saturate and a permafrost aquitard will rapidly form beneath the rivers (Section 4.3).

Figure 6

Ice-covered lake and river models. (a–h) Lake ice model output for various ice albedo A_w, water influx and sublimation scenarios, with ice thickness (light blue) and liquid thickness (dark blue). Runs terminate when lake breaches (a–d, f–g) or maximum column thickness is reached (e). Horizontal black line indicates breach elevation. Note the log-scale time axis. (i) Argyre area-depth relation. (j) Ice thickening rate for model-predicted median and interquartile range of river ice basal heat fluxes for A_w = 0.3, compared to a typical geothermal-only flux (0.045 Wm⁻²). Lines truncate when equilibrium ice thickness is reached. The solution for A_w = 0.6 is nearly identical except for a time-constant shift toward a faster thickening rate and so is not shown for clarity.

The rate of vertical infill of Argyre Basin depends on the lake surface area, which was measured for Argyre Basin at 100-m contours in Mars Orbiter Laser Altimeter (MOLA) 1/128 pixel per degree gridded data (463 m/px) (Smith et al., 2001) using Esri® ArcMap® 10.8.1 (Figure 6i); the lowest point (ignoring a crater with negligible volume) is ∼−3,500 m, which I take to be the bottom of Argyre Basin. At each model time step, growth of the vertical liquid column is calculated by dividing the incoming flux by the basin contour area at the elevation of the top of the liquid column from the previous time step (found by linear interpolation between the measured 100-m contour areas).

Surface sublimation E₀ (kg m⁻² s⁻¹; equivalently z_sub (m yr⁻¹)), ice lid thickening rate $$\frac{d{z}_{i}}{dt}$$, and ice lid equilibrium thickness z_eq,i are determined using the 1-dimensional model of Moore et al. (1995) originally developed for 25°N in Chryse Planitia. The sublimation and freezing model routines employed here adopt the same setup and parameters as Moore et al. (1995), except at Argyre's mean latitude (50°S) and with 50% higher F_geo = 0.045 W m⁻² (Solomon et al., 2005) based on improved F_geo estimates performed after Moore et al. (1995). The difference in elevation between Chryse and Argyre is small (<1 km) and accounting for the pressure difference does not affect the analysis, that is, the Schmidt number and atmospheric kinematic viscosity, important to calculating E₀, still fall in the range considered by Moore et al. (1995).

In the interest of space, the reader is referred to Moore et al. (1995) for a full model description for calculating E₀, particularly their Equations 1–11 and their Figure 5. In brief, water vapor flux from the surface is determined by eddy diffusion governed by the water-vapor density gradient within various sublayers of the atmospheric boundary layer, including convective and advective flow. E₀ is determined primarily by mean annual surface temperature T_S, wind speed u_wind, and surface roughness z_rough; for the model-relevant parameter range, z_sub varies by ∼3 orders of magnitude for T_S = 160-to-200 K, ∼1 order of magnitude for u_wind = 3-to-30 m s⁻¹ and tens of percent for z_rough = 0.03-to-1.0 cm (Figure 5 of Moore et al., 1995).

$${T}_{S}$$ (Table 4) is calculated using the Buhler and Piqueux (2021a) thermal model assuming albedo $${A}_{w}$$ = 0.3 and 0.6, based upon dark and bright Antarctic ice-covered lakes, respectively (McKay et al., 1985), and ice thermal conductivity $${k}_{w}$$ = 3.5 J m⁻¹ K⁻¹ s⁻¹, emissivity = 1.0, density $${\rho }_{i}$$ = 917 kg m⁻³, and heat capacity $${c}_{w}$$ = 1400 J kg⁻¹ K⁻¹ (Piqueux & Christensen, 2009a, 2009b), and a circular orbit with obliquity $$\varepsilon $$ = 30$${}^{\circ}$$. Sublimation during warm months dominates $${E}_{0}$$, due to the approximately exponential nature of $${E}_{0}$$ dependence on temperature (figure 5 of Moore et al., 1995). Thus, $${E}_{0}$$ is enhanced by a factor of $$\left[1+0.2\times \mathrm{exp}\left(\frac{{\Delta }T}{a}\right)-1\right]\times {E}_{0}\left({T}_{S}\right)$$, with $$a$$ = 6.56 K and $${\Delta }T$$ the amplitude of the annual $${T}_{S}$$ wave (Moore et al., 1995). Each calculation of $${E}_{0}$$ is performed at minimizing ($${z}_{\text{rough}}$$ = 0.03 cm, $${u}_{\text{wind}}$$ = 3 m s⁻¹) and maximizing ($${z}_{\text{rough}}$$ = 1 cm, $${u}_{\text{wind}}$$ = 30 m s⁻¹) model parameters, as in Moore et al. (1995).

Table 4. Modeled T_S, E₀, and z_sub for Various Latitudes and Albedos

Albedo	Latitude (deg)	TS (K)	E0 min (kg m^−2 s^−1)	E0 max (kg m^−2 s^−1)	zsub min (m yr^−1)	zsub max (m yr^−1)
0.3	0	214.5	1.61E-06	1.68E-05	5.55E-02	5.81E-01
0.6	0	186.9	2.08E-08	2.76E-07	7.15E-04	9.48E-03
0.3	25	206.7	4.42E-07	7.25E-06	1.52E-02	2.49E-01
0.6	25	180.2	8.21E-09	8.84E-08	2.82E-04	3.04E-03
0.2	50	197.7	1.24E-07	1.48E-06	4.26E-03	5.08E-02
0.3	50	191.6	4.80E-08	5.60E-07	1.65E-03	1.92E-02
0.4	50	184.7	1.60E-08	1.64E-07	5.50E-04	5.63E-03
0.5	50	176.9	4.00E-09	4.08E-08	1.37E-04	1.37E-03
0.6	50	167.8	8.00E-10	8.11E-09	2.75E-05	2.75E-04
0.3	55	186.5	1.60E-08	2.36E-07	5.50E-04	8.11E-03
0.6	55	163.8	2.68E-10	2.76E-09	9.21E-06	9.48E-05
0.3	60	181.4	9.60E-09	1.00E-07	3.30E-04	3.44E-03
0.6	60	159.8	1.48E-10	1.52E-09	5.08E-06	5.22E-05
0.3	65	177.4	4.07E-09	4.45E-08	1.37E-04	1.51E-03
0.6	65	156.6	6.43E-11	6.89E-10	2.20E-06	2.34E-05

• Note. Minimum and maximum E₀ and z_sub models assume u_wind = 3 and 30 m s⁻¹ and z_rough = 0.03 and 1.0 cm, respectively.

Lake ice thickness grows according to (e.g., Moore et al., 1995):

$$$\frac{d{z}_{i}}{dt}=\lambda \sqrt{\frac{{\kappa }_{i}}{t}}$$$ (4)

This is the solution to the well-known Stefan problem, where $${\kappa }_{i}$$ is the ice thermal diffusivity, $$t$$ is time, $${z}_{\text{i}}$$ is ice thickness and $$\lambda $$ is a constant determined by the condition:

$$${\mathrm{exp}(-\lambda )}^{2}/(\lambda \hspace*{.5em}\mathrm{erf}(\lambda ))=\frac{{L}_{f}\sqrt{\pi }\hspace*{.5em}}{{C}_{p,w}\left({T}_{m}-{T}_{0}\right)}$$$ (5)

Here $${L}_{f}$$ is water latent heat of fusion and $${c}_{p,w}$$ is water specific heat. $${T}_{0}$$ is the near-surface temperature below the depth at which all sunlight is substantially absorbed (nominally ∼a few m, practically approximated as $${T}_{S}$$), and $${T}_{m}$$ is the melting temperature of H₂O.

The equilibrium ice lid thickness z_eq,i over stagnant water (e.g., a lake) is achieved when the energy lost at the surface due to sublimation matches the rate of energy input into the base of the ice, which comes from the flux of latent heat F_l from ice freeze-out on the bottom of the lid plus geothermal flux F_geo and is given by (Moore et al., 1995):

$$${z}_{eq,i}=\frac{b\,\mathrm{ln}\left(\frac{{T}_{m}}{{T}_{S}}\right)+c\,\left({T}_{S}-{T}_{m}\right)-{h}_{ex}\left[1-\mathrm{exp}\left(-\frac{{z}_{eq,i}}{h}\right)\right](1-A)\,{S}_{0}}{{F}_{l}+{F}_{\text{geo}}}$$$ (6)

Here, $${F}_{l}=\frac{d{z}_{i}}{dt}{\rho }_{w}{L}_{f}$$; ρ_w is water density. Constants b = 780 W m⁻¹ and c = 0.615 W m⁻¹ K (McKay et al., 1985). The extinction path length h_ex is set equal to 1 m, similar to Antarctic lakes (McKay et al., 1985). S₀ is the mean annual solar flux for a circular orbit with 30° obliquity at 50°S (Argyre Basin), calculated using the Buhler and Piqueux (2021a) model. T_m is the melting temperature.

Once meltwater input into the basin ceases, model lakes completely freeze and then sublime away. Reported freeze-out and sublimation timescales (Section 3.5) assume abrupt water input cessation immediately after breaching for concreteness. Continued input after breaching would cause the ice lid to thicken until reaching z_eq,i, and ultimately lead to longer sublimation timescales (by <∼30%).

Table 5. Valley Measurements and Statistics

Name	Channel 1	Surius	Dzigai	Doanus	Palocopas
Valley Width Mean (m)	2,520	2,826	1,528	2,502	2,243
Valley Width Standard Deviation (m)	715	1,213	650	1,213	1,524
Channel Width Mean (m)	454	509	275	450	404
Channel Width Standard Deviation (m)	202	226	122	200	179
Length (m)	6.80E+05	7.60E+05	9.10E+05	1.00E+06	1.10E+06
Maximum elevation (m)	1,100	900	1,200	1,500	1,600
Slope to 0-m global elevation	0.00162	0.00118	0.00132	0.00150	0.00145
Minimum elevation (m)	−2,300	−2,400	−2,700	−2,700	−2,800
Slope to minimum elevation	0.00500	0.00434	0.00429	0.00420	0.00400
Most poleward extent (deg S)	64.8	64.8	67.5	62.6	56.0

For the high flux case, during the first 100 years the paleolake areal increase rate is <1% year⁻¹ and, by ∼1 kyr, is <0.1% year⁻¹, and tenfold lower for the low flux case, justifying a 1-dimensional model treatment. Additionally, the lake ice surface elevation is always less than that of the south polar ice sheet, so the potential flow direction is always into Argyre. Note that unconfined ice above the breaching contour would likely undergo viscous flow, a process beyond the model scope. However, isostatic compensation at the ice-water interface would likely prevent the formation of an appreciable ice surface slope, substantially diminishing the effect of viscous flow. Finally, as a test that the model is functioning correctly, note that the calculated T_S, E₀, z_eq,i, z_sub and lake freeze out and sublimation timescales are comparable to previous solutions presented in the literature (e.g., Haberle et al., 2003; Madeleine et al., 2009; McKay et al., 1985; Moore et al., 1995).

2.5.2 River Ice Model

Similar to lake ice modeling, the surface sublimation boundary condition is calculated using the Moore et al. (1995) model. However, sensible heat transfer to the ice base from underlying moving water is well known in the Earth-based literature to be an important effect governing river ice growth (e.g., Leppäranta, 1993; Shreve, 1972). Thus, for rivers, $$\frac{d{z}_{i}}{dt}$$ and z_eq,i is substantially diminished, compared to stagnant water ice formation, by additional heat input from the heat flux due to fluid friction in turbulent flow, following the well-known bulk formula (e.g., Leppäranta, 2010) $${F}_{\text{fric}}={C}_{{H}_{w}}{\rho }_{w}{c}_{p,w}\left({T}_{w}-{T}_{m}\right){U}_{w}$$.

Here, U_w is the flow velocity and $${T}_{w}$$ is the water temperature. The heat exchange coefficient $${C}_{{H}_{w}}$$ (a.k.a. turbulent Stanton number) is typically of order several ×10⁻³ (the model uses 5 × 10⁻³, for definitiveness; McPhee, 1992; Shirasawa & Ingram, 1997; Shirasawa et al., 2005; Sirevaag, 2003, 2009). Although $${C}_{{H}_{w}}$$ has a theoretical dependence on the Reynolds number, observations show that this dependence is weak and $${C}_{{H}_{w}}$$ is similar across a wide range of Reynolds number (McPhee et al., 1999), including those considered in this study. In all model runs, flow has a turbulent Reynolds number (>3 × 10⁴). $${T}_{w}$$ is set by the balance between input sensible heat from the release of gravitational potential energy as the river flows downhill F_pot = ρ_wz_wgsU_w (W m⁻²; cf. Shreve, 1972) and F_fric (e.g., Komar, 1979).

Here g is gravity, s is slope, and z_w is the flow depth. z_w is typically deeper for ice-covered rivers than open water rivers by a few tens of percent due to increased hydraulic resistance from turbulence due to roughness on the bottom of the ice lid and is given by (Prowse & Beltaos, 2002):

$$${z}_{w}=1.32{\left[\frac{{Q}_{w}{n}_{c}}{1.49B\sqrt{s}}\right]}^{\tfrac{3}{5}}$$$ (7)

Here, $${Q}_{w}$$ is the discharge flux, $$B$$ is the channel width, and $${n}_{c}$$ is the composite Manning coefficient, which accounts for frictional drag both on the channel bed and on the underside of the ice, according to (Prowse & Beltaos, 2002):

$$${n}_{c}={\left[\frac{{n}_{i}^{\tfrac{3}{2}}+{n}_{b}^{\tfrac{3}{2}}}{2}\right]}^{\tfrac{2}{3}}$$$ (8)

Majewski (2003) measured $${n}_{i}$$ (ice Manning coefficient) values ranging from 0.040 to 0.077 (average 0.056) under rough (i.e., laden with frazil and refrozen ice pans) ice cover and 0.012 to 0.073 (average 0.040) under solid crystalline ice with no frazil deposits, with a typical $${n}_{b}$$ (bed Manning coefficient) ∼0.03. Hoque (2009) reports lower values: $${n}_{b}$$ = 0.0251 ± 0.004 and $${n}_{i}$$ = 0.0196 ± 0.060. White and Daly (1997) suggest $${n}_{c}$$ = 0.02 for smooth ice and 0.15 for very rough ice, with an average across all ice cover of 0.066 ± 0.023. Thus, reasonable $${n}_{c}$$ values are 0.035–0.056 and 0.022–0.537 for rough ice and smooth ice, respectively (Majewksi, 2003), 0.020–0.026 (Hoque, 2009), or 0.043–0.089 (1-$$\sigma $$ range; White & Daly, 1997). I thus model across a range of $${n}_{c}$$ = 0.020–0.089.

Flow velocity U_w is determined by continuity according to Q_w = U_wBz_w for flow through an ice-covered rectangular channel (e.g., Prowse & Beltaos, 2002). Note that hydraulic pressure from the flow acts to increase channel depth and lifts ice, compensating for freezing and thereby maintaining sub-ice flow (e.g., Beltaos, 2021). Models are run for a range of Q_w = 66–3,000 m s⁻¹. Low Q_w corresponds to minimum modeled melt flux divided amongst five channels and high Q_w to maximum modeled melt flux in a single channel. s and B are determined from MOLA 1/128 pixel per degree gridded data (463 m/px) and Thermal Emission Imaging System (THEMIS; Christensen et al., 2003) measurements using Esri® ArcMap® 10.8.1 (Table 5). s = 1.1–1.6 × 10⁻³ was calculated as the average slope from the elevation of the valley head to the 0-m global elevation (Argyre breaching) contour, divided by the valley length measured from the head to the 0-m global contour elevation along the thalweg at THEMIS scale (∼18 m/px). B was calculated by taking minimum-length wall-to-wall transects every 10 km where the valley was sufficiently well preserved (range of number of transects: 31 (“Channel 1”) to 90 (Palacopas)). Martian inner channel widths are typically much smaller than their host valleys, at a ratio of 0.18 ± 0.08 in the nearby Margaritifer Sinus quadrangle (Buhler et al., 2014; see also Penido et al., 2013, who measure a mean ratio of 0.14 for inner channels in valleys across a broad range of the southern highlands). B for each valley is calculated by multiplying the mean measured width of each valley by the valley-to-channel ratio; model runs span the low-one-sigma B of the smallest channel (153 m) to the high-one-sigma B of the largest channel (735 m), where the one-sigma uncertainty is the quadrature addition of the standard deviation of the valley-to-channel-width ratio and the standard deviation of transect width measurements.

Table 6. Equilibrium Ice Thickness z_eq,i (Meters) Over Rivers Calculated for Various Albedos and Latitudes for Calculated F_pot

Aw	0°S	25°S	50°S	55°S	60°S	65°S
0.3	3.2 (1.1–11.2)	7.7 (2.7–27)	16 (5.5–58)	18 (6.4–66)	21 (7.2–76)	23 (7.9–84)
0.6	19 (6.3–67)	23 (7.9–83)	30 (10–110)	32 (11–117)	35 (12–125)	36 (12–131)

• Note. The difference between assuming high and low u_wind and z_rough is negligible (<∼1%). Reported in median (interquartile) format.

If the flow is steady and uniform, a reasonable assumption at steady state, then the gravitational acceleration is balanced by frictional drag forces (e.g., Komar, 1979), that is, F_fric = F_pot. Thus, (a) the heat flux into the ice is equal to F_pot and (b) an equilibrated T_w can be calculated, which is done recursively until the temperature converges within <0.001%. Temperature homogenization at the length-scale of the flow depth is achieved rapidly, with an e-folding length on the order of the flow depth divided by the flow velocity, that is, meters (see Section 3.5), by turbulent mixing (e.g., Obukhov, 1949; Warhaft, 2000), a scale much smaller than the valley lengths, so the temperature is homogenized at the macroscale of the river along essentially its entire course. Across all model parameters, the equilibrated model T_w ranged from 4 × 10⁻⁵ to 3 × 10⁻³ K above freezing.

$${z}_{eq,i}$$ is substantially affected by the addition of basal heat flux from $${F}_{\text{pot}}$$, which modifies the denominator of Equation 6 as follows:

$$${z}_{\text{eq},i}=\frac{b\,\mathrm{ln}\left(\frac{{T}_{m}}{{T}_{S}}\right)+c\,\left({T}_{S}-{T}_{m}\right)-{h}_{\mathit{\text{ex}}}\left[1-\mathrm{exp}\left(-\frac{{z}_{\text{eq}}}{h}\right)\right](1-A)\,{S}_{0}}{{F}_{l}+{F}_{\text{geo}}+{F}_{\text{pot}}}$$$ (9)

Because $${F}_{\text{pot}}$$ dominates $${F}_{\text{geo}}$$ for the parameters considered in this study, $${z}_{\text{eq},i}$$ is several orders of magnitude smaller over rivers than over lakes (e.g., Tables 6 and 7).

The Stefan solution for $$\frac{d{z}_{i}}{dt}$$ (Equation 4) can be modified for the case when there is substantial heat flux (compared to $${F}_{l}$$) from below, for example, Leppäranta (1993):

$$$\frac{d{z}_{i}}{dt}=\frac{1}{{\rho }_{i}{L}_{f,i}}\left[\frac{{\kappa }_{i}\left({T}_{m}-{T}_{s}\right)}{{z}_{i}}-\left({F}_{\text{below}}\right)\right]$$$ (10)

Here $${F}_{\text{below}}$$ = $${F}_{l}+{F}_{\text{geo}}+{F}_{\text{pot}}$$. Equation 10 does not generally admit analytical solution, but in the case of constant $${T}_{s}$$, which is reasonable for growth averaged over many years, the implicit solution is (Leppäranta, 1993), where $${\rho }_{i}$$ is ice density:

$$${-}\frac{{z}_{i}}{{z}_{eq,i}}-\log \left(1-\frac{{z}_{i}}{{z}_{eq,i}}\right)={F}_{\text{below}}\times \frac{t}{{\rho }_{i}\times {L}_{F}\times {z}_{eq,i}}$$$ (11)

The river ice model assumes that all the sensible heat is conveyed to the ice (as is common practice for subglacial flow calculations, e.g., Shreve, 1972). Nevertheless, at least ∼half of the heat should transfer to the ice (i.e., the ice-covered hydraulic radius in the modeled rectangular channel is ∼equal to the wetted bed radius because B ≫ z_w and n_i ≳ n_b), so the uncertainty in how heat transfers to the ice versus surrounding bedrock contributes a potential factor of <∼2× to the heat flux (i.e., lower heat flux if heat is not effectively transferred to the ice) and therefore also <∼2× uncertainty to z_eq,i (i.e., thicker z_eq,i), because z_eq,i depends dominantly on the inverse of F_pot (Equation 9). Median and quartile statistics are reported for river-related calculations because they more accurately reflect the non-Gaussian (skewness ≈ +1) characteristic range of results for the selected range of input parameters. Notably, this model treatment of martian ice-covered rivers substantially advances over previous literature (cf. Wallace & Sagan, 1979), especially the consideration of F_pot, which allows calculation of ice cover thickness.

3 Results

3.1 Qualitative Model Effects of Burying an H₂O Ice Sheet With a CO₂ Ice Cap

Adding CO₂ ice atop the H₂O ice cap has three principal model effects, which can collectively melt up to several kilometers of H₂O ice (Figure 4). First, CO₂ ice thermally insulates the column. Second, adding CO₂ ice mass increases shear stress and thus strain heating in the underlying H₂O ice. Third, CO₂ clathrate hydrate forms at the CO₂-H₂O ice interface, where it is thermodynamically favored over pure H₂O and CO₂ ice (Figure 3a; Mellon, 1996). Clathrate has a low thermal inertia, increasing thermal insulation (Section 2.3.3). Clathrate is also stable at higher temperatures than pure CO₂ ice (Figure 3a) and thus accommodates additional CO₂ mass (that would otherwise exit the column via melting), increasing shear stress and thus strain heating.

Figure 4

Stratigraphic columns depict the threshold at which basal melting halts in the model, showing temperature profiles and layer thicknesses. Dotted black line indicates thickness at which melting halts in a pure H₂O ice column with 195 K surface temperature for comparison. Colors as shown in key (except black text for clathrate thickness). Subpanels show columns with polar geothermal fluxes of 40, 50, and 60 mW m⁻². Nb. The vertical column is the same throughout the entire lateral extent of the model domain (purple circle in Figure 1b). (a) Low shear, no clathrate. (b) Low shear, clathrate to temperature 225 K. (c) Low shear, clathrate to 245 K. (d) High shear, no clathrate. (e) High shear, clathrate to 225 K. (f) High shear, clathrate to 245 K.

3.2 Atmospheric Collapse and CO₂ Ice Sheet Formation

The model predicts T_cap = 152 K and P_cap = 11 mbar for a collapsed atmospheric state at 30° obliquity, yielding a modeled collapsed CO₂ ice cap mass of $${3.4}_{-0.7}^{+0.8}\times {10}^{18}$$ kg (1-σ uncertainty), given an initially inflated 600 mbar atmosphere (Section 2.2), with ∼400 mbar CO₂ desorbed from the regolith (Figure 2a). For a nominal 50 mW m⁻² basal polar heat flux F_pol, modeled CO₂ basal melting occurs at 660 m depth (Figures 2b and 2c), yielding a collapse area of $${3.2}_{-0.6}^{+0.8}\times {10}^{12}\,{\mathrm{m}}^{2}$$ (Figure 1). Heat flux (geothermal plus shear) across model runs spans ∼45–100 mW m⁻², yielding ∼3× variance in CO₂ melting depth and collapse area (Figures 2 and 4).

3.3 H₂O Basal Melting Volume, Flux, and Timescale

Model H₂O melt volumes are on the order of 10¹⁵–10¹⁶ m³ (Figure 5a), produced in one to a few ×10⁵ yr. H₂O basal melting flux depends upon heat flux (Section 3.2), yielding column melt rates of 4.3–9.7 mm year⁻¹. Multiplying by the CO₂ ice sheet area yields 3.3 ×10²–3.0 × 10³ m³ s⁻¹ melt fluxes (Figure 5b). Model melt volume and flux is higher for initially thicker H₂O ice, larger CO₂ inventories, thicker clathrate layers, higher geothermal flux, and larger strain heating constants (Figures 4 and 5).

Figure 5

Modeled H₂O basal melt volume and rate. (a) Volumes. Subpanels indicate low (2.7 × 10¹⁸ kg), nominal (3.4 × 10¹⁸ kg), and high (4.2 × 10¹⁸ kg) CO₂ collapse mass from inflated 600 mbar atmospheric pressure (Figure 2). Shaded regions indicate the range of melt for polar geotherms of 40, 50, and 60 mW m⁻² (labeled) bounded by assumptions of low and high shear heating. Colors indicate the original H₂O ice column thickness at collapse onset. Argyre volume up to 0 m contour (Figure 1) provided for reference. Nb., maximum considered clathrate thickness exceeds Figure 2 values due to inclusion of models for which clathrate formation is not buoyancy limited at temperatures exceeding 245 K. (b) Basal H₂O melt rate as a function of H₂O column thickness for various scenarios. Green, blue, and red regions indicate the range of melting rates for low to high shear heating and polar geothermal fluxes of 40, 50, and 60 mW m⁻², respectively. Nb., variation in melt rate from varying clathrate thickness (not shown) is small compared to variation from modeled range of shear heating. A lower bound melt discharge rate estimate from eskers (Scanlon et al., 2018) is provided for reference.

The greatest sources of model uncertainty for calculating meltwater output considered in this study are, in order of importance (Figure 5a): uncertainty in initial H₂O ice column thickness (2–4 km range), yielding several ×10¹⁵ to <∼1 × 10¹⁶ m³ meltwater uncertainty, dependent on the range of other parameters considered; CO₂ collapse mass (1-σ range; Sections 2.2 and 3.2), several × 10¹⁵ m³ uncertainty; geothermal heating (40–60 mW m⁻²), several ×10¹⁵ m³ uncertainty; clathrate formation thickness (Section 2.3.3), ∼1–2 × 10¹⁵ m³ uncertainty; strain heating (24–93 × 10⁻²⁵; Section 2.3.2), <∼1 − 2 × 10¹⁵ m³ uncertainty. Uncertainty due to other variables is dominated by the uncertainty in these five input parameters.

3.4 Meltwater Transport Through Ice-Covered Rivers

Across the entire input parameter range considered (meltwater flux = 66–3,000 m s⁻¹, slope = 1.1–1.6 × 10⁻³, channel width = 153–735 m, ice albedo A_w = 0.3–0.6, wind speed u_wind = 3–30 m s⁻¹, and ice surface roughness = 0.03–1.0 cm; Section 2.5) the median (interquartile range) model flow depth is 1.5 (0.73–3.0) m; flow velocity is 1.0 (0.57–1.7) m s⁻¹; basal heat input from flow friction is 8.8 (2.4–26) W m⁻²; and equilibrium ice cover thickness z_eq,i is, for A_w = 0.3, 18 (6–58) m, and A_w = 0.6, 32 (11–117) m. The time to reach z_eq,i for A_w = 0.3 is 118 (14–1,400) year and for A_w = 0.6 is 209 (24–2,800) year. Once ice thickness approaches z_eq,i, ice thickening substantially slows, and the final ∼25% thickening takes about 10× longer than the initial ∼75% (Figure 6j). Varying across latitude 50°–65°S (the range spanned by the input valleys) varies z_eq,i by <30% (Table 6). Flow influx (>9 kg m⁻² s⁻¹ for all models) is much greater than the maximum model surface sublimation rate z_sub (6 × 10⁻⁷ kg m⁻² s⁻¹), so the modeled river neither completely freezes (cf. Wallace & Sagan, 1979) nor completely sublimes.

3.5 Ice-Covered Lake Development

Figures 6a–6h shows the results of lake modeling across the full range of input parameters. Meltwater influx is modeled over the full calculated meltwater flux range (i.e., 3.3 × 10²–3.0 × 10³ m³ s⁻¹) because infiltration (Section 4.3) and river ice sublimation (Section 3.4) are likely negligible. For the lowest ∼100 m, the paleolake area is <∼10¹⁰ m², implying an initial fill rate $$\frac{d{z}_{\text{liq}}}{dt}\sim 1-10\,\mathrm{m}\,\mathrm{y}{\mathrm{r}}^{-1}$$ (for minimum and maximum fluid flux input, respectively); $$\frac{d{z}_{\text{liq}}}{dt}$$ drops tenfold by 400 m depth, and tenfold again by 2.5 km depth (Figure 6i).

For A_w = 0.3: mean annual surface temperature T_S = 191.6 K and surface sublimation rate z_sub = 1.7–19 mm yr⁻¹; for A_w = 0.6: T_S = 167.8 K and z_sub = 0.3–0.03 mm yr⁻¹ (Table 4). The z_sub at which loss over Argyre's entire breaching contour area (1.7 × 10¹² m²) would exceed minimum and maximum modeled basal melt flux $$\frac{d{V}_{\text{melt}}}{dt}$$ is 6.5 mm yr⁻¹ and 62 mm yr⁻¹, respectively. Thus, model flux into Argyre is always net positive for maximum modeled $$\frac{d{V}_{\text{melt}}}{dt}$$ (Figure 6) and for most parameter space for minimum modeled $$\frac{d{V}_{\text{melt}}}{dt}$$, that is, {A_w = 0.3 and u_wind ≤ 10 m s⁻¹} or {u_wind = 30 m s⁻¹ and A_w ≥ 0.39} (see Section 4.2.3). When sublimation outpaces input, for example, for maximum z_sub and minimum $$\frac{d{V}_{\text{melt}}}{dt}$$ (Figure 6e), the total column thickness reaches the elevation at which the contour area × z_sub equals $$\frac{d{V}_{\text{melt}}}{dt}$$.

After ∼1–20 model years, z_i = 2–20 m thick (range across all models) and liquid water increases stably underneath the ice (see also Section 4.2.1). The rate of ice thickening decreases as the inverse square root of time, reaching <0.01 m yr⁻¹ at 12 and 53 kyr for A_w = 0.3 and 0.6, respectively (Figure 6, Equation 4). Equilibrium ice thickness z_eq,i is not reached prior to basin breaching in any lake model run (Table 7). For A_w = 0.3 or 0.6 and high and low meltwater influxes, respectively, model Argyre breaches after 34–480 or 38–557 kyr at which point z_i = 0.4–1.5 or 0.9–3.4 km (Figure 6; Table 7).

Table 7. Lake Model Outputs (See Figures 6a–6h)

	A = 0.3				A = 0.6
	Low zsub		High zsub		Low zsub		High zsub
dVmelt/dt input	High	Low	High	Low	High	Low	High	Low
Overflow time (kyr)	34	480	44	Inf^a	38	535	38	557
zi at overflow (m)	405	1,522	463	Inf^a	891	3,365	893	3,433
zeq,i (m)	2,360		621		5,921		5,622
Freeze out time (kyr)	1,010	1,280	155	39	815	1,122	786	1,100
zi at freeze-out (m)	2,240	2,920	982	610	4,369	6,819^b	4,177	6,532^b
Time to sublime after freeze-out (yr)	1.36E+06	1.77E+06	5.11E+04	3.18E+04	1.59E+08	2.48E+08	1.51E+07	2.38E+07
Argyre + ice lid volume (10^15 m^3)	2.9	4.8	3.0	–	3.7	7.9	3.7	8.0

• Note. Argyre plus ice lid volume assumes vertical edges at 0-m breach contour.
• ^a Model lake does not breach in this run; freeze out time, z_i at freeze-out, and complete sublimation time are given for a lake that fills to its maximum height (i.e., final state in Figure 6e).
• ^b Note that z_ice at freeze-out is larger than z_eq,i, so the model column does not completely freeze immediately, but instead maintains some liquid water beneath the ice until the column sublimes to a thickness of z_eq,i.

4 Discussion

4.1 Polar Ice Column and Basal Melt Discussion

4.1.1 Consistency With Observations

Previous literature supports the presence of a ∼0.6 bar (atmospheric) CO₂ inventory, as utilized in the model, near the Noachian-Hesperian boundary. For example, Kite (2019; their figure 9) presents a comprehensive collection of 11 literature results constraining Mars' atmospheric pressure history (from cosmochemistry, mineralogy, atmosphere and meteorite trapped-gas isotopic ratios, geomorphology (bomb sag, dune wavelengths), present-day CO₂ inventory, and extrapolation of modern atmospheric escape-to-space), indicating that Mars' atmospheric pressure dropped from >∼1 bar to below ∼0.6 bar somewhere between ∼3.5-and-4.1 Gyr. All 26 southern highlands valley networks dated by Fassett and Head (2008) have median best-fit ages from 3.45 to 3.81 Gyr with a typical 2-σ uncertainty of a few hundred Myr (combined from Poisson counting statistics and isochron uncertainty). Thus, there is strong evidence that Mars had a sufficiently large mobile CO₂ reservoir to drive the atmospheric-collapse-driven melting scenario described in this manuscript, with collapse occurring at a time commensurate with Valley Network formation during Mars' intense, Late Noachian/Early Hesperian terminal pulse of intense fluvial activity.

Total modeled basal melt production is ∼0.2–2.0× Mars' present-day estimated global near-surface H₂O inventory, equivalent to 4%–40% of the likely maximum Noachian-Hesperian inventory, with the upper Noachian-Hesperian limit (5× present) based upon model predictions that larger inventories would produce substantial low-latitude basal ice sheet melting, for which there is no observational evidence (Fastook & Head, 2015). Additional continued melting is likely once cycling of downstream sublimation returns H₂O to the polar ice column (Section 4.1.2).

Modeled basal melt production (3.3 × 10²–3.0 × 10³ m³ s⁻¹) is consistent with previous melt production estimates (2.9 × 10²–3.0 × 10⁴ m³ s⁻¹) from dimensions of Noachian-Hesperian-aged south polar eskers (long, winding deposits left by subglacial rivers; Figure 1a; Head & Pratt, 2001; Scanlon et al., 2018). Notably, previous mapping found an unexpected lack of association between eskers and volcanic edifices, disfavoring a volcano-driven subglacial melting hypothesis for esker formation (Scanlon et al., 2018). Other attempts to create basal melting by increasing geothermal input or thickening the H₂O ice (Scanlon et al., 2018), or including a firn layer (Cassanelli & Head, 2015) or other thermal blanketing material (Section 4.1.2) all either yield insufficient melt, melt in locations inconsistent with observed eskers, and/or require ad hoc addition of substantial (>20–50 K) surface warming (e.g., by a “gray gas” greenhouse, Fastook & Head, 2015; Scanlon et al., 2018). Thus, the proposed basal melting mechanism of burial of H₂O ice by CO₂ has several advantages over previous models because it can produce (a) sufficient melt (Figure 5) (b) in locations corresponding to eskers (Figure 1a) (c) without requiring the ad hoc addition of surface warming (d) by a well-established atmospheric process (i.e., atmospheric collapse) (e) likely to occur at ∼3.6 Gyr (f) without invoking mechanisms that would be stronger earlier in Mars' history that would likely produce earlier (not observed) episodes of basal melt.

The model proposed here predicts basal melting only poleward of ∼70°S (where the model CO₂ cap forms and eskers are observed; Figure 1a), consistent with the lack of widespread glacial and periglacial landforms at lower latitudes (e.g., Grau Galofre et al., 2020). Note, however, that such landforms—if they ever existed—may have been obscured or obliterated poleward of ∼30°, and especially ∼60°, by mantling and reworking by younger ice (Kreslavsky and Head, 2000, 2002; Levy et al., 2014). The lack of direct geomorphic evidence for an ancient (∼3.6 Gyr) CO₂ ice cap is consistent with the expected <∼10 Myr survival time of CO₂ ice cap remnant morphologies (Buhler, 2023; Buhler & Piqueux, 2021a), the ablation of H₂O ice over 3 Gyr, and obscuration by a much younger (∼100 Myr), present-day H₂O ice surface (Herkenhoff & Plaut, 2000).

4.1.2 Consideration of Alternative Thermal Blanketing Materials

CO₂ is Mars' only volatile that is sufficiently abundant to generate basal melting via thermal insulation (e.g., Jakosky, 2021). Refractory (“rocky”) material has intrinsic thermal conductivity of ∼2–20 W m⁻¹ K⁻¹ (Clauser & Huenges, 1995)), higher than CO₂ ice (∼0.5 W m⁻¹ K⁻¹) and similar to $${k}_{{\mathrm{H}}_{2}\mathrm{O}}$$ (∼3.5 W m⁻¹ K⁻¹). However, porosity decreases conductivity and, in the extreme case, hyper-desiccated unconsolidated soil in relevant environments (e.g., at the Phoenix landing site [68.22°N, 234.25°E]) can reach k_soil = 0.085 W m⁻¹ K⁻¹ due to poor thermal contact between grain surfaces (Piqueux & Christensen, 2009a; Zent et al., 2010). k_soil is extremely sensitive to cementation (e.g., pore ice); only ∼0.02% pore ice can double k_soil and ∼0.3% pore ice can increase k_soil equal to $${k}_{\mathrm{C}{\mathrm{O}}_{2}}$$ (Piqueux & Christensen, 2009b), so refractory material must completely desiccate to reach ultra-low k_soil. No other known abundant martian refractory material has thermal conductivity lower than $${k}_{\mathrm{C}{\mathrm{O}}_{2}}$$. Because k_soil/$${k}_{\mathrm{C}{\mathrm{O}}_{2}}$$ = 0.17, a lag layer of desiccated refractory material covering the ice sheet would need to be ∼82–127 m thick (=0.17 × 480–747 m-thick CO₂ ice; Figure 4) to produce a similar amount of melt volume as that produced by CO₂ ice burial.

Most eskers lie between ∼70° and 80°S with equator-heading orientations (Figure 1a; Scanlon et al., 2018). Thus, the basal melting recorded by these eskers occurred poleward of 70°S. The mean annual temperature poleward of 70°S is lower for all obliquities ε ≤ 60° (Haberle et al., 2003) than for the region of stable present-day (ε = 25°) lag-covered ice poleward of ∼55° latitude (Bramson et al., 2017; Schorghofer & Forget, 2012); Mars likely experienced <∼1 Myr in a mean ε > 60° state integrated over its entire history (Holo et al., 2018; Laskar et al., 2004). Higher mean annual polar temperatures (but still in the range of lag-covered ice stability) occur at higher ε, but atmospheric vapor pressure also increases with ε (e.g., Chamberlain & Boynton, 2007; Schorghofer, 2010). Both lower temperature and higher atmospheric vapor pressure increase stability, so sufficiently lag-covered ice poleward of 70°S may, in fact, always be stable. The depth to stable ice is always <∼1 m for Mars conditions (Schorghofer, 2010; Schorghofer & Forget, 2012). Thus, a lag-covered Late Noachian Icy Highlands ice sheet poleward of 70°S would likely persist stably beneath <∼1 m of lag, much thinner than that required to produce substantial basal melt. Note that an ice sheet would still efficiently sublime without basal melting if insubstantial lag forms and/or lag is removed (e.g., by wind) (Bramson et al., 2019; Haberle & Jakosky, 1990).

However, even if such a lag-covered ice sheet were unstable, basal melting due to lag formation would still be too slow to account for the observed eskers (Scanlon et al., 2018). Maximum modeled lag growth rates atop remnant Arcadia Planitia ice sheets [38°–50°N] are <1.5 × 10⁻⁶ m yr⁻¹ (Bramson et al., 2017). The column basal melting rate depends upon $$\frac{{dz}_{\text{melt}}}{dt}=\frac{d{z}_{\text{lag}}}{dt}\left(\frac{{k}_{{\mathrm{H}}_{2}\mathrm{O}}}{{k}_{\text{soil}}}-\frac{\left({1-\phi }_{\text{lag}}\right)}{{f}_{\text{dust}}}\right)$$, with lag porosity ϕ_lag (∼25–60%; Cull et al., 2010), dust fraction f_dust, and zero-porosity lag liberation rate $$\frac{d{z}_{\text{lag}}}{dt}$$. Thus, basal melting cannot even occur for H₂O ice with less than a critical dust fraction f_crit = $$\frac{\left({1-\phi }_{\text{lag}}\right)\times {k}_{\text{soil}}}{{k}_{{\mathrm{H}}_{2}\mathrm{O}}}$$ = ∼1% to 2% because of the H₂O ice loss (and attendant thermal insulation loss) required to form the lag. Using the most favorable values for ϕ_lag = 60% and f_dust = 10% (cf. f_dust <10% for midlatitude Lobate Debris Aprons (Holt et al., 2008); ∼3% for bulk Polar Layered Deposit ice (e.g., Grima et al., 2009; Lalich et al., 2019); ∼3% for Arcadia Planitia ice (Bramson et al., 2017); and <1% for Phoenix landing site ice (Cull et al., 2010)), and the driest published atmospheric vapor parameters (those of Schorghofer & Forget, 2012; see Bramson et al., 2017) yields $$\frac{{dz}_{\text{melt}}}{dt}=$$ 5.5 × 10⁻⁵ myr⁻¹. Multiplying by the entire area poleward of 70°S (9.6 × 10¹² m²) yields a basal melting rate of 5.4 × 10⁰ m³ s⁻¹, still two orders of magnitude lower than the minimum melt rates required to form the observed eskers (3.4 × 10² ms⁻¹; Scanlon et al., 2018). As discussed in the previous paragraph, an ice sheet poleward of ∼70°S would likely experience lower mean annual temperature and higher atmospheric vapor pressure and thus even slower lag formation (and basal melt) rates than this. Thus, thermal insulation due to the development of lag layers is not a plausible candidate for basal melt leading to the observed eskers.

4.2 Ice-Covered Lakes and Rivers

4.2.1 Initial Conditions

During initial fluviolacustrine development, surface freezing will likely form enclosed pockets of liquid surrounded by a downhill-advancing ice crust, similar to solid-crusted lava flows (e.g., Griffiths, 2000; Stasiuk et al., 1993). The volume of water plus ice in a single channel with equilibrium ice cover is ∼10⁶ m (length) × <10³ m (width) × <∼10² m (depth) = <∼10¹¹ m³, (Tables 5 and 7), equivalent to <∼1–10 years of basal melt production (Section 3.3). Likewise, an ice-covered paleolake 100 m deep would form in Argyre in ∼10–100 years (Figure 6). Thus, a steady-state ice-covered fluviolacustrine system should develop in ∼10–100 years, or perhaps less if an initially high fluid pulse occurs, for example, due to outburst flooding of a liberated subglacial melt pool (cf. Shreve, 1972) or breach of a proglacial paleolake (e.g., Argentea Planum paleolake; Dickson & Head, 2006; Figure 1a). The modeled steady-state system is analogous to Arctic and Antarctic ice-covered fluviolacustrine systems, where ice-covered rivers flow >1,000-km distances and lakes and seas are fed by rivers beneath ice cover year-round (e.g., Costard et al., 2007; McKay et al., 2005; Vincent et al., 2008). Notably, modeled river ice equilibrium thickness is on the order of tens of meters, less than the valley depths (∼100 m) and is reached within 10–1,000 years across the modeled interquartile range (Section 3.4; Table 6; Figure 6j).

4.2.2 End State

Once meltwater input ceases, model lakes freeze in 1.5 × 10⁵–1.3 × 10⁶ yr for all breached runs, leaving a remnant ice column 980–2,920 m thick that sublimes in 5 × 10⁴–1.8 × 10⁶ yr for runs with A_w = 0.3 and 4,180–6,820 m thick that sublimes in 1.5 × 10⁷–2.5 × 10⁸ yr for runs with A_w = 0.6 (Table 7). The total volume to breach Argyre (basin fill plus ice lid) is 2.9–4.8 × 10¹⁵ m³ for A_w = 0.3 and 3.7–8.0 × 10¹⁵ m³ for A_w = 0.6, well within the range of modeled V_melt (Figure 5a; Table 7), especially for the A_w = 0.3 cases.

4.2.3 Favored Lake and River Ice Scenario

I favor models with A_w = 0.3, similar to present-day polar ice (Byrne et al., 2008; Titus et al., 2003) and multi-year Antarctic Lake ice (which have albedo = 0.3–0.4) (McKay et al., 1994). I favor low-intermediate u_wind (few-to-<∼10 m s⁻¹), as does Moore et al. (1995), because Viking Lander 1 and 2 site observed u_wind is ∼2–7 m s⁻¹ (Hess et al., 1977) and Phoenix Landing site observed u_wind is 6.94–9.68 m s⁻¹ (Sullivan et al., 2000) and simulations suggest u_wind ≈ few-to-10 m s⁻¹ near Argyre/50°S (Basu et al., 2004; Fenton & Richardson, 2001) and south polar ice sheet u_wind ≈ 10 m s⁻¹ (Smith et al., 2015). Thus, I consider the most likely scenario that meltwater from basal melting was conveyed to Argyre by 1-to-5 ∼100s-m-wide rivers covered by ∼6–58 m of ice with flow depth ∼1.5 m and flow velocity ∼1 m s⁻¹, feeding an Argyre paleolake that develops an ice lid ∼400–1,500 m thick by the time the lake breaches at 3 × 10⁴–5 × 10⁵ yr and which, following meltwater cessation, freezes out completely in ∼1 Myr and sublimes away after another ∼1 Myr.

4.3 Subsurface Water Infiltration

Subsurface water is not explicitly considered in the model because subsurface infiltration is substantially insufficient to drain terrestrial ice sheet melt (Flowers, 2015). On Mars, near-surface (∼1 km) megaregolith permeability is likely ∼10⁻¹¹ − 10⁻¹³ m² (increasing with depth), equivalent to hydraulic conductivity k_hyd ∼ 2 × 10⁻⁵ − 2 × 10⁻⁷ m s⁻² for near-freezing water on Mars (Hanna & Phillips, 2005). Directly comparable terrestrial model scenarios, that is, a 1,000-km-scale sheet with 6 mm yr⁻¹ basal melting and k_hyd = 4 × 10⁻² − 9 × 10⁻⁵ m s⁻² (Breemer et al., 2002), show that modeled terrestrial sub-ice-sheet aquifers saturate within ∼1 kyr (much less than modeled basal melt timescales in this study), bounded at depth by development of a counteracting hydraulic head and along lateral margins by permafrost sealing (Figure 1b), after which meltwater overwhelmingly drains along the ice-ground interface (Breemer et al., 2002). Once overlying water and ice in an Argyre paleolake raise the subsurface geotherm to temperatures above the melting point of water, a similar process of aquifer saturation and sealing would likely occur. Infiltration beneath rivers would likely create a permafrost aquitard within ∼days, as in Arctic rivers (e.g., Streletskiy et al., 2015), even for initially dry regolith (Clifford, 1993), stopping further infiltration.

4.4 Global H₂O Cycle Implications

4.4.1 Steady-State Hydrologic Cycle and Climatic Timescales

The model reaches the H₂O melt halting threshold that produces the volumes shown in Figure 5a on a timescale of a few ×10⁵ years and predicted Argyre breaching can occur in a few ×10⁴–10⁵ yr (Figure 6; Table 7). Atmospheric collapse duration timescales range from 10⁴–10⁷ years, depending on whether collapse occurred via a dip to <∼30° obliquity during a generally high obliquity state or entry into a persistently <∼30° obliquity state (Laskar et al., 2004). All reported modeled melt volumes, fluxes, and fluviolacustrine results can occur during a single atmospheric collapse period driven by ice sheet basal melting due to steady-state geothermal input (notably not variable insolation forcing), although maximal melt production may not be reached for short-duration (<few × 10⁵ yr) atmospheric collapse events in models with low-end basal melt rates. During a plausible low obliquity period lasting up to one-to-several × 10⁷ years (Laskar et al., 2004), a steady-state cycle of mass loading and insulation from H₂O atmospherically recycled to the cap surface could sustain basal H₂O melt (Clifford, 1993; Fastook et al., 2012).

Calculated sublimation rates integrated over the entire breaching contour of Argyre yield a H₂O source of 5.1 × 10⁷ to 3.2 × 10¹⁰ m³ yr⁻¹. Sublimed water from Argyre would likely eventually cycle back to the pole (Wordsworth et al., 2013). Such H₂O cycling may cause enhanced clathrate formation (Section 2.3.3) or CO₂ melting or sublimation if CO₂ becomes buried to a depth below where the temperature gradient surpasses its melting temperature (∼217 K). Melted or sublimed CO₂ would then refreeze higher in the column or exit the column and return to the atmosphere, causing an atmospheric overpressure and subsequent redeposition of CO₂ ice onto the surface, effectively moving recycled H₂O vertically down the ice column. Such addition of H₂O back into the column and interbedding (Buhler, 2023; Buhler et al., 2020) of CO₂ and H₂O would perpetuate basal melting in a manner quantitatively equivalent to directly thickening the basal H₂O layer because the column-integrated thermal conductivity of a layered heterogeneous ice stack depends on the cumulative fractional path length through each species regardless of the number of layers (Mellon, 1996). Thus, replenishment of H₂O into the ice column would generate additional melt water beyond that which is modeled here. Equatorward meltwater flow at longitudes outside the Argyre catchment may have also occurred, given the broad longitudinal distribution of eskers wherever the surface is not obscured by younger polar deposits (Figure 1a; Scanlon et al., 2018), but evidence of such flow may have been obscured by ubiquitous ice-mediated degradation and mantling that occurs at latitudes >∼30° (e.g., Kreslavsky & Head, 2000, 2002; Levy et al., 2014).

Notably, the proposed pole-to-equator hydrologic system could persist in steady-state for the entire duration of atmospheric collapse because polar melt is driven by bottom-up geothermal-driven melting and not top-down insolation-driven melting. Moreover, due to Argyre's mid-latitude location, its mean annual temperature T_S is insensitive to obliquity, with <∼5 K T_S variation between ε = 0 and 40° (e.g., Haberle et al., 2003). Thus, a hydrologic cycle driven by polar basal melt flow to Argyre and Argyre sublimation return to the pole would be insensitive to orbital forcing in a collapsed atmosphere climate. Such a long-term climate with substantial basal melt and ice-covered rivers and lakes may have been habitable inasmuch as the presence of liquid water is a prerequisite for life and life inhabits perennially ice-covered, autochthonous Antarctic fluviolacustrine ecosystems (e.g., McKay et al., 2005) and terrestrial ice sheet basal melt ecosystems (e.g., Hodson et al., 2008).

Transition from atmospheric collapse onset (∼0.6 bar) to inflated atmospheric pressures at which collapse-induced melt volumes were insufficient to breach Argyre Basin (∼0.2 bar) likely occurred in ∼10⁸ years (i.e., from ∼3.6 to ∼3.5 billion years ago) based upon rates of decline in geothermal flux (Solomon et al., 2005) and near-surface CO₂ and H₂O inventory (Hu et al., 2015; Jakosky, 2021; Kite, 2019). Notably, such a ∼10⁸-year total duration hydrological cycle with intermittent fluvial activity is consistent with estimates of timescales of the duration and style of Noachian-Hesperian fluviolacustrine activity (e.g., Buhler et al., 2014; Fassett & Head, 2011; Kite, 2019). Low obliquity state recurrence intervals are comparable to their duration (Laskar et al., 2004). Thus, given the statistical distribution of Mars' historical obliquity (Laskar et al., 2004), this model predicts up to ∼100 short (∼10⁵-year) and/or ∼ tens of medium (∼10⁶-year) and/or a few (<∼10) long (∼10⁷-year) basal melting cycles. Over time, meltwater production potency during collapse would decline (potentially abruptly).

4.4.2 Regional Hydrologic Implications

No previously identified mechanism is capable of delivering enough water to fill Argyre Basin, even though morphologic evidence is consistent with equatorward breach outflow flooding (Grant & Parker, 2002; Hiesinger & Head, 2002). Basal melt from the model proposed here is capable of filling and breaching Argyre Basin.

Argyre lake breaching occurs in ∼3–4 × 10⁴ yr (high basal melt scenario) or ∼5 × 10⁵ yr (low basal melt), substantially shorter than the ∼10⁷ yr timescale of plausible entry into a long epoch of low obliquity (Section 4.4.1). Once Argyre breached, equatorward flow output into the extensive Uzboi-Ladon-Morava valley system would ensue (Figure 1a; Grant & Parker, 2002), at fluxes reduced by a few-to-tens of percent relative to input flux to Argyre Basin (due to balancing surface sublimation loss in Argyre; Section 3.5), although the initial breach would likely release a short pulse of much higher flux.

The entire length of the Uzboi-Ladon-Morava plus Ares Vallis system is ∼8,000 km long (e.g., Salvatore et al., 2016; Figure 1a) and spans from latitude ∼35°S to past the equator, terminating in Chryse Planitia. Equilibrium ice thickness over rivers for these latitudes is of order 10 m for typical intermediate model runs (Table 6) and thus an equilibrium ice cover could form along its entire length in 8 × 10⁶ m (length) × <∼10³ m (width) × <10² m (depth) = <∼8 × 10¹² m³, equivalent to <∼10–100 years for the range of modeled melt fluxes. Ice sublimation at lower latitudes is more rapid than at the higher latitude rivers sourcing Argyre (Tables 4 and 6). For a length of 8,000 km, and an estimated width of 1 km (assuming steady-state flow widths on the same scale as the input paleorivers poleward of Argyre because the tens-of-kilometer Uzboi-Ladon-Morava and Ares Valles widths are likely set during outbreach flooding; e.g., Grant & Parker, 2002), the river ice surface area would be ∼8 × 10⁹ m² and, assuming the highest model sublimation rate (at the equator = 1.68 × 10⁻⁵ kg m⁻² s⁻¹; Table 4) along its entire length, yields a total sublimation rate of 1.3 × 10² m³ s⁻¹, about one-third the minimum basal melt flux predicted by the model. Thus, steady-state flow underneath the ice cover from Argyre to Chryse Planitia through the Uzboi-Ladon-Morava plus Ares Valles system is plausibly predicted for the entire melt range predicted by the model.

Geologic observations indicate evidence of multiple Uzboi-Ladon-Morava discharges (Grant & Parker, 2002), which can be explained by the polar basal meltwater hypothesis proposed here if multiple episodes of entry into a collapsed atmosphere environment occurred during the ∼10⁸ year period during which geothermal flux and the near-surface CO₂ and H₂O inventory were sufficient to produce melting capable of breaching Argyre (Section 4.4.1). In the long term, Moore et al. (1995) propose that fluid delivery to the Chryse Basin could have led to subsurface fluid infiltration in regions susceptible to magmatic heating (thus eliminating the formation of a permafrost aquitard), charging the regional aquifer and preparing a cycle of Hesperian outflow channel megaflooding around Chryse Planitia, for example, through Ares Vallis (see Moore et al. (1995) for additional discussion). Such an aquifer charging mechanism could also have been active in various locations throughout the Margaritifer Basin (cf. Salvatore et al. (2016) observations).

4.4.3 Implications for Mars' Late, Intense Terminal Epoch of Fluvial Activity

Mars experienced a unique, intensive, late-stage pulse of fluvial erosion near the Noachian-Hesperian boundary (∼3.6 Gyr) characterized by regionally integrated incision (i.e., valley networks), distinct from the comparatively gentler and deeper fluvial erosion style of the Early/Middle Noachian (∼3.9–3.7 Gyr), followed by an abrupt cessation and transition to scarce fluvial activity in the Hesperian and Amazonian (<∼3.4 Gyr) (Fassett & Head, 2011; Goudge et al., 2021; Irwin et al., 2005; Kite, 2019; Matsubara et al., 2018). The paradigm for explaining this pulse at ∼3.6 Gyr is a singular period of climate warming (e.g., Kite, 2019). Under this paradigm, the geologic record implies that more intensive warming occurred near the Noachian-Hesperian boundary than in the Early/Middle Noachian.

Recent climate models can produce wet conditions on early Mars (e.g., Ito et al., 2020; Ramirez & Craddock, 2018; Wordsworth et al., 2021) that can potentially explain the diffusive style of fluvial erosion typifying Mars' Early Middle Noachian period (e.g., Kite, 2019). However, models seeking to create a warmer, wetter early Mars climate utilize mechanisms (volcanism, impacts, thicker atmospheric mass, and greenhouse gases) that decline over time, implying higher erosive power during the earlier Noachian (Fassett & Head, 2011). Late warming typically invokes greenhouse gas release based upon processes not observed today (e.g., CH₄ clathrate release; Kite et al., 2017) or nonspecific gray-gas greenhouse warming (e.g., Scanlon et al., 2018). Other late warming proposals also face difficulties. For example, proposed volcanic activity from a late Tharsis Formation (Bouley et al., 2016) is inconsistent with the observed lack of large-scale stress fractures (Ehlmann et al., 2016). Moreover, late-Tharsis-induced true polar wander would dislocate the center of the Dorsa Argentea Formation (well-established as expansive remnant Noachian-Hesperian polar deposits) 19° off the pole during its glacially active period (Scanlon et al., 2018) and is also not necessary to explain the distribution of valley networks (e.g., Kite et al., 2022). Thus, late warming models have difficulty explaining geomorphic evidence of a unique, intense, late, terminal fluvial pulse near the Noachian-Hesperian boundary with a topographically superficial erosion style distinct from that of the Early Middle Noachian, after which neither the Early Middle Noachian nor Noachian-Hesperian erosive styles reoccurred (Irwin et al., 2005), without invoking special processes not observed today (Kite, 2019).

The collapsed-atmosphere, steady-state hydrologic cycle extending from the pole to Margaritifer Terra, and perhaps Chryse Basin (Section 4.2.2), with major polar (melt) and Argyre Basin (sublimation) water sources (Section 4.4.1) proposed here was likely an important global-scale hydrologic process operating solely near the Noachian-Hesperian boundary and should thus be considered when attempting to understand this uniquely geomorphically potent period of Mars' fluvial history. For example, meltwater debouched to lower latitudes was likely longitudinally distributed by atmospheric processes (e.g., Madeleine et al., 2009; Wordsworth et al., 2013). Such distribution could potentially have sourced water into catchments beyond Argyre Basin, Margaritifer Terra, and Chryse Planitia, with fluvial activity in other catchments occurring either during a period of atmospheric collapse itself or during a reinflated atmospheric period, sourced from liberation of frozen reservoirs seeded during atmospheric-collapse-driven hydrologic activity (e.g., Kite et al., 2020).

Mars' geologic observables indicate several periods of fluvial activity and climatic transitions (e.g., Kite, 2019; Kite & Conway, 2024). Thus, the novel hydrologic mechanism proposed here is consistent with and complementary to other models that seek to produce climates amenable to the fluvial erosive style recorded from the Early and Middle Noachian. However, the results presented here show that large amounts of water can mobilize near the Noachian-Hesperian boundary in a cold climate in response to the same CO₂ atmospheric collapse process that occurs today (Buhler et al., 2020)–given the well-established larger inventories of CO₂ and H₂O and higher rates of geothermal heating near the Noachian-Hesperian boundary (Jakosky, 2021; Solomon et al., 2005)–without appealing to special late climatic warming conditions typically assumed by the currently prevailing archetype.

5 Conclusions

This study uses modeling to investigate the implications of combining two of the most robust results of late-Noachian climate science arising during the past decade: the well-vetted Late Noachian Icy Highlands model (e.g., Fastook et al., 2012; Wordsworth, 2016) and the well-established onset of atmospheric collapse near the Noachian-Hesperian boundary (e.g., Forget et al., 2013; Soto et al., 2015). Model results presented here demonstrate that thermal insulation of the Late Noachian Icy Highlands due to burial by a CO₂ ice cap would release massive amounts of meltwater, equivalent to ∼0.2–2.0 × Mars' present-day global near-surface H₂O inventory (Sections 3.1-3.3), at rates of 3.3 × 10²–3.0 × 10³ m³ s⁻¹, consistent with geologic observations (Section 4.1).

Modeling of downstream meltwater, including freezing, sublimation, and infiltration, demonstrates the viability–for almost all plausible parameter space–of the development of an ice-covered fluviolacustrine system with 1,000s-of-kilometer-long rivers, an overtopped Mediterranean-Sea-sized lake in Argyre, substantial water delivery into Margaritifer Terra, and potential debouchment all the way into Chryse Planitia (Sections 3.4, 3.5, 4.2, 4.3, 4.4.2). Notably, the model produces the first self-contained and self-consistent prediction for a paleolake completely filling and overtopping Argyre Basin, which has been supported on observational grounds for decades (Section 4.4.2), and the first calculation of martian river ice thickness (Sections 2.5.2 and 3.4).

All reported model results of basal melt and fluviolacustrine transport occur in a cold, steady-state, collapsed-atmosphere environment, without the need for warming episodes or multiple collapse events. Such a steady-state hydrologic cycle between pole-to-equator melt and equator-to-pole sublimation could occur multiple times, each time lasting 10⁴–10⁷ year (depending on Mars' exact orbit history) over a ∼10⁸-year window during which atmospheric pressure was low enough for collapse yet CO₂ and H₂O inventories and geothermal heat output were high enough to produce massive basal meltwater releases (Section 4.4). Notably, the timing and duration of this proposed hydrologic cycle are consistent with estimates of the timing, duration, and intermittency of the observed pulse of Noachian-Hesperian fluvial activity. Thus, the large-scale release of meltwater triggered by atmospheric collapse may have played an important role in the intense pulse of Noachian-Hesperian fluvial activity: directly so for the Argyre-Margaritifer-Chryse system and perhaps indirectly for other catchments (Section 4.4). Finally, this study demonstrates that large amounts of water can mobilize in a cold climate driven by the same atmospheric collapse process observed today, without needing to invoke late stage warming processes near the Noachian-Hesperian boundary (Section 4.4.3).

Acknowledgments

I thank Sylvain Piqueux for helpful discussions and Tim Goudge and Mike Sori for thoughtful reviews. Funding: NASA Solar System Workings Program Grant 80NSSC21K0212 and NASA Mars Data Analysis Program Grants 80NSSC21K1088 and 80NSSC23K1160.

Conflict of Interest

The author declares no conflicts of interest relevant to this study.

Appendix A: Notation Table

This section provides Table A1, which lists all variables used in calculations throughout the text.

Table A1. Symbol Notation and Explanation

Symbol	Description	Value	Units
a	Inverse wind-driven temperature slope	6.56	K
A	CO2 albedo	variable	Unitless
α	Ice sheet surface slope	4 × 10^−3	m m^−1
Acap	CO2 cap area	variable	m^2
Log10AD	CO2 glacial strain constant	variable	MPa^-ns^−1
Areg	Regolith albedo	0.1–0.3	unitless
aS	Regolith specific surface area	10^2–10^5	m^2kg^−1
AT	Empirical strain heating constant	3.5–93 × 10^−25	s^−1 Pa^−3 m^−1
Aw	Lake and river water ice albedo	0.3–0.6	Unitless
b	Constant for determining zeq,i	780	W m^−1
B	River channel width	153–735	m
c	Constant for determining zeq,i	0.615	W m^−1 K
cclath	Clathrate heat capacity	1,800	J kg^−1 K^−1
$${c}_{\mathrm{C}{\mathrm{O}}_{2}}$$	CO2 ice heat capacity	1,200	J kg^−1 K^−1
ci	H2O ice heat capacity	1,400	J kg^−1 K^−1
$${C}_{{H}_{w}}$$	Heat exchange coefficient, a.k.a. turbulent Stanton number	5 × 10^−3	Unitless
d	CO2 glacial grain size	variable	m
D	e-folding thermal relaxation depth	variable	m
$${\Delta }{H}_{f,C{O}_{2(s)}+{H}_{2}{O}_{(s)}}$$	Clathrate formation enthalpy	−2.1 ± 0.4	kJ mol^−1
$${\Delta }{H}_{sub,C{O}_{2}}$$	CO2 sublimation enthalpy	25.9	kJ mol^−1
ΔT	Annual temperature wave amplitude	variable	K
dvap	Regolith vapor diffusion skin depth	variable	m
$$\frac{d{V}_{melt}}{dt}$$	Polar cap basal melt rate	3.3 × 10^2–3.0 × 10^3	m^3 s^−1
ε	Obliquity	30	Degree
$$\dot{\varepsilon }$$	CO2 glacial strain rate	variable	s^−1
ϵ	CO2 emissivity	0.8	Unitless
E0	Water ice surface sublimation	variable	kg m^−2 s^−1
F	Column heat flux (sum of Fpol and Fstrain)	variable	W m^−2
fcrit	Critical polar cap dust fraction	0.01–0.02	Unitless
fdust	Polar cap dust fraction	0.01–0.10	Unitless
Ffric	Frictional turbulently dissipated heat flow	variable	W m^−2
Fgeo	Geothermal flux	0.04–0.06 (cap), 0.045 (Argyre), 0.3–0.8 (global average)	W m^−2
Fl	Latent heat of ice freeze-out	variable	W m^−2
Fpol	Polar geothermal flux	0.04–0.06	W m^−2
Fpot	River water gravitational potential energy release	variable	W m^−2
Fsol	Solar flux	variable	W m^−2
Fstrain	Glacial strain heating flux	variable	W m^−2
g	Gravitational force	3.71	m s^−2
h	Ice sheet depth	variable	m
hex	Ice lid light extinction path length	1	m
$$\dot{h}$$	CO2 glacial central height decay rate	variable	m yr^−1
H	Atmospheric scale height	11.1	km
$${h}_{{\mathrm{H}}_{2}\mathrm{O},\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}}$$	Initial H2O2 polar cap column thickness	variable	m
$${h}_{{\mathrm{H}}_{2}\mathrm{O},\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t}}$$	H2O2 polar cap melting depth after CO2 burial	variable	m
kclath	Clathrate thermal conductivity	0.4	Wm^−1K^−1
$${k}_{\mathrm{C}{\mathrm{O}}_{2}}$$	CO2 ice thermal conductivity	93.4/T	Wm^−1K^−1
ki	H2O2 ice thermal conductivity	651/T	Wm^−1K^−1
khyd	Hydraulic conductivity	2×10^−5-2×10^−7	m s^−2
κi	Water ice thermal diffusivity	1 × 10^−6	m^2 s^−1
kreg	Regolith thermal conductivity	8.37 × 10^−2 — 2.0	Wm^−1K^−1
kw	Water ice lid thermal conductivity	3.5	J m^−1 K^−1 s^−1
λ	Ice lid growth constant	variable	unitless
Lf	Water latent heat of fusion	3.34 × 10^5	J kg^−1
m	CO2 glacial grain size exponent	2–3	Unitless
mbasal	Basal melt mass	variable	kg
$${m}_{{\mathrm{H}}_{2}\mathrm{O},\mathrm{c}\mathrm{l}\mathrm{a}\mathrm{t}\mathrm{h}}$$	Column mass of H2O2 contained in clathrate	variable	kg
n	CO2 glacial stress exponent	1–8	Unitless
n0	Clathrate occupation state	6	Unitless
nb	River bed Manning coefficient	0.0247–0.03	Unitless
nc	Composite Manning coefficient	0.02–0.089	Unitless
ni	River ice Manning coefficient	0.012–0.077	Unitless
P	Annual period to calculate D	5.94 × 10^7	sec
P0	Mean regolith surface pressure at the global 0 m datum	17	mbar
Pcap	CO2 cap surface pressure	11	mbar
ϕlag	lag porosity	0.25–0.60	Unitless
Q	CO2 glacial creep activation energy	variable	kJ mol^−1
Qw	River discharge flux	66–3,000	m s^−1
$$\dot{r}$$	CO2 glacial outer rim expansion rate	variable	m yr^−1
R	Universal gas constant	8.314	J mol^−1 K^−1
ρclath	Clathrate density	1,100	kg m^−3
$${\rho }_{\mathrm{C}{\mathrm{O}}_{2}}$$	CO2 ice density	1,600	kg m^−3
ρi	Water ice density	917	kg m^−3
ρw	Liquid water density	1,000	kg m^−3
s	River slope	1.1–1.6 × 10^−3	m m^−1
σ	CO2 glacial differential stress	variable	kg m^−1 s^−2
S0	Mean annual insolation	variable	W m^−2
σB	Stefan-Boltzmann constant	5.67 × 10^−8	W m^−2 K^−4
t	Time	variable	s
T	Temperature	variable	K
t0	CO2 glacial characteristic relaxation timescale	variable	yr
T0	Near-surface temperature at depth below which all sunlight is absorbed	variable	K
Tbase, clath	Clathrate basal temperature	225-245 (nominal); 225–273 (complete)	K
Tcap	CO2 cap surface temperature	152	K
Tm	Water melt temperature	273.15	K
$${T}_{\mathrm{m}\mathrm{e}\mathrm{l}\mathrm{t},\mathrm{C}{\mathrm{O}}_{2}}$$	CO2 melting temperature	217	K
TS	Mean annual surface temperature	variable	K
Tw	Water temperature	variable	K
Uw	River water flow velocity	variable	m s^−1
uwind	Wind speed over ice lid	3–30	m s^−1
Vmelt	Polar meltwater volume	variable	m^3
z	Depth	variable	m
zeq,i	Equilibrium ice thickness	variable	m
zi	Lake/river ice lid thickness	variable	m
zlag	Polar cap lag thickness	variable	m
zmelt	Polar cap basal melting rate	variable	m
zreg	Active regolith depth	1–1,000	m
zrough	Ice lid surface roughness	0.03–0.1	cm
zsub	Water ice surface sublimation	variable	m yr^−1
zw	River flow depth	variable	m

Open Research

Data Availability Statement

Numerical code for CO₂ adsorption (Buhler & Piqueux, 2021b) and ice column thermal model calculations and machine-readable versions of data presented in all figures are publicly available (Buhler, 2021).