Prolonged cooling and degassing of Apollo 17 volcanic glasses on the lunar surface

Domain: neuroscience
Published: 2026-02-03
Editorial outcome: minor_revision

Abstract
Studying lunar pyroclastic volcanism provides key insights into the thermo-chemical evolution of the lunar mantle and the Moon’s volatile budget. Pyroclastic deposits, although volumetrically minor compared to mare basalts, are derived from deeper, more primitive, and volatile-rich mantle sources. Here we synthesize volatile degassing recorded by Apollo 17 sample 74220, one of most studied pyroclastic deposits. By modeling the volatile degassing of olivine-hosted melt inclusions, melt embayments, and glass beads, we show that volatile depletion of these samples cannot be explained solely by degassing during free-flight, as previously proposed. Instead, the data require extended thermal histories, with beads undergoing slow cooling and prolonged degassing on the lunar surface for years, a scenario further supported by thermal modeling. Our findings suggest that pyroclastic deposits remained active volatile sources well beyond eruption, which is potentially important for sustaining a local transient lunar atmosphere and the long-term volatile cycle of the Moon.

Introduction
Basaltic volcanism is a fundamental planetary process that had operated on the Moon for billions of years. The timing and extent of lunar basaltic volcanism provide critical information on the internal structure and thermal history of the lunar interior. Besides the effusive eruptions that formed mare basalts on the Moon, fire fountain eruptions are another major style of lunar basaltic volcanism that produced pyroclastic deposits with abundant volcanic glasses1–3. More than 100 pyroclastic deposits have been identified using Earth-based remote sensing analyses and Lunar Reconnaissance Orbiter Camera data, two of which cover over 10,000 km2 in area4,5 (Fig. 1).

To distinguish pristine volcanic glasses from impact-generated products, Delano6 proposed widely accepted criteria, such as the absence of schlieren and exotic inclusions, chemical homogeneity, high Mg/Al ratios, and Ni concentrations that are uniform within individual deposits but vary systematically with Mg content across deposits. The Apollo 15 green glass clods and Apollo 17 orange glass soil are the most well known for their high abundances of pristine glass beads. However, pristine lunar glasses have been identified in samples from all Apollo missions, which have a similarly wide range of TiO2 concentrations (0–17 wt%) as mare basalts6. Variations in TiO2 concentration produce systematic color changes in the glass beads, from green to yellow, orange, red, and black with increasing TiO2 content. The widespread distribution of lunar volcanic glasses and their diverse composition range are strong evidence for the prominence of fire fountain eruptions on the Moon.

Lunar volcanic glasses, particularly the Apollo 15 very-low Ti green beads, are more primitive in chemical composition and therefore serve as better proxies for the lunar mantle than mare basalts6–8. Their more primitive nature is further supported by multi-point saturation experiments, which indicate that they were likely sourced from depths of ~300–500 km in the lunar mantle9–12.

Volcanic glass beads have also recently been reported in the Chang’e 5 lunar soil returned by the Chinese mission. Based on U-Pb dating of the beads, they were found to be exceptionally young, suggesting potential volcanic activities on the Moon as recent as 120 Ma ago13.

Lunar volcanic glasses have been at the forefront of lunar volatiles studies since their return by the Apollo missions. For example, surface enrichments of moderately volatile elements such as Pb, Zn, Cu, and Ge in the form of sulfides or chlorides have been reported for orange glass beads returned by the Apollo 17 mission2,14–16. Starting from the first study in 2008 by Saal et al.17, lunar pyroclastic glasses played a key role in lunar sample study “renaissance” as advanced instrumentation enabled the detection of indigenous water in volcanic glass beads and olivine-hosted melt inclusions18–22. These discoveries challenged the previous view of a dry Moon expected from its formation in a high-energy giant impact23, and has contributed to improving existing models of Moon formation24,25.

Despite the significance of lunar fire fountain eruptions in understanding lunar mantle chemistry and Moon formation, their origin, eruption mechanism, and thermal history remain poorly understood. The thermal history of lunar volcanic glass beads, in particular, is critical for understanding the environment that fire fountain eruptions occurred, the degassing and ingassing of volatiles26, and for reconstructing the pre-eruptive contents of volatiles in the lunar magma17.

Among the lunar volcanic glasses returned so far, the Apollo 17 pyroclastic deposit 74220 has the most complete record of volatile degassing (Fig. 2). It contains abundant glass beads with the entire surface exposed to degassing during the eruption17,20,24. In contrast, olivine-hosted melt inclusions found in the same sample better preserve pre-eruptive volatile contents (e.g., H2O, F, Cl, S) due to protection by the host olivine18,20,24,27. The sample also contains olivine-hosted melt embayments that show intermediate degassing due to partial enclosure by the host olivine20,21,27,28.

In this paper, we aim to reconstruct the degassing and thermal history of the fire fountain eruption that produced the pyroclastic deposits at the rim of the Shorty Crater, where Apollo sample 74220 was collected. Using the geochemical records in all the above three types of specimens, we show that the observed volatile depletion in these fire fountain eruption products would require unrealistically long timescales of degassing if it occurred primarily during free-flight. Instead, the high degrees of volatile loss in orange glass beads and melt embayments can be better explained by a prolonged history of slow cooling and degassing on the lunar surface following the eruption.

Results
Measured H2O, F, Cl, and S concentrations in olivine-hosted melt inclusions, melt embayments, and glass beads are generally consistent with their expected increasing degrees of volatile loss (Fig. 3). Olivine-hosted melt inclusions found in Apollo 74220 contain 371–1205 ppm H2O, 26–72 ppm F, 1.3–4.8 ppm Cl, and 302–887 ppm S after correcting for the effect of post-entrapment crystallization (PEC) of olivine. These abundances are distinctly higher than those of melt embayments (6.8–38 ppm H2O, 6.0–23 ppm F, 0.029–0.31 ppm Cl, and 182–344 ppm S; corrected for PEC) and glass beads (0.21–12 ppm H2O, 6.7–22 ppm F, 0.014–0.54 ppm Cl, and 218–412 ppm S; PEC correction not needed). Moreover, the melt inclusion data broadly define a linear correlation between H2O and S (Fig. 3a), and F and S (Fig. 3b), both of which intercept the origin. The trend is less prominent for Cl–S, possibly due to the larger analytical uncertainties associated with the low Cl concentrations.

The correlation between corrected volatile concentrations in melt inclusions from 74220 likely reflects the stage of magma ascent in the conduit before fragmentation and eruption. During ascent, volatiles exsolve from the magma and partition into the vapor phase, leading to a decrease in the volatile concentrations of the magma and an increase in the vapor/liquid ratio. According to the study by Newcombe et al.29, vapor saturation of the parental magma of 74220 could have occurred at 1.0–6.3 km in the lunar crust, with the carbon content of the magma being a key control which remains poorly constrained. The concentration correlations for melt inclusions can be qualitatively described using zero-intercept linear trends that pass through the upper bounds of the data: H2O_corrected = 1.44 × S_corrected, F_corrected = 0.09 × S_corrected, and Cl_corrected = 0.005 × S_corrected (solid orange curves in Fig. 3). Such an approximation assumes that the solubilities of H2O, F, Cl, and S in lunar basalts follow similar power law dependencies, which appears reasonable for the concentration range observed in olivine-hosted melt inclusions (Fig. 3).

Compared with the trend defined by melt inclusions in 74220, orange glass beads from the same sample show stronger depletions in H2O/S, F/S, and Cl/S ratios. Here, sulfur is used as the reference because it has the lowest diffusivity among the four volatile components and is, therefore, least susceptible to degassing loss. The greatest depletion is observed in H2O/S ratios, showing a 98–99.9% decrease in the glass beads relative to the melt inclusions. High levels of depletion, ranging from 70 to 90%, are observed in Cl/S ratios, while lower levels of depletion, between 40 and 70%, are seen in F/S ratios (Fig. 3b, c). Olivine-hosted melt embayments from the same sample show lower degrees of depletion in H2O/S and Cl/S ratios compared to glass spherules, consistent with partial protection by their host olivine. The depletion in F/S ratios of three of the melt embayments is more significant than that of the glass beads, but the exact reason remains unclear.

One embayment previously reported by Ni et al.21 was particularly large (Fig. 2, center image). Ellipsoidal in shape and extending ~300 µm along its longest axis, this melt embayment is significantly larger than any other embayment identified in 74220 so far. Therefore, it has the highest likelihood of preserving degassing profiles, which could be used to reconstruct the volcanic eruption process in a manner similar to applications in terrestrial volcanic samples30,31. Measurements along the long axis of the exposed embayment show gently decreasing concentration profiles of H2O, F, Cl, and S from the interior toward the opening (Fig. S1, unpublished data from Ni et al.21). Notably, the H2O and Cl concentrations of the melt embayment are significantly lower than those defined by olivine-hosted melt inclusions from 74220, including one from the same host olivine as the large embayment (Fig. 3). Such strong depletions in H2O/S (>90% decrease) and Cl/S (>80% decrease) for the melt embayment indicate that diffusive loss of the volatiles was extensive, even at a length scale of ~300 µm.

Methods
Modeling diffusive volatile loss of volcanic glass beads
The loss of H2O, F, Cl, and S from the volcanic glass beads were modeled assuming radial diffusion in the spherical system:

∂C_i / ∂t = D_i (∂^2 C_i / ∂r^2 + 2/r * ∂C_i / ∂r) 0 ≤ r ≤ a (M1)

where C_i is the concentration of a volatile component at radial distance r and time t, D_i is the diffusivity of the component, and a is the radius of the sphere. The boundary conditions of Eq. (M1) are defined as:

(∂C_i / ∂r) | r=0 = 0 (M2)

D_i (∂C_i / ∂r) | r=a = -υ_i C_i,a (M3)

Here υ_i is the evaporation coefficient of the component and C_i,a is the concentration of the component at r=a. If D_i is a constant and the sphere has a uniform initial concentration of C_i,0, the solution to Eq. (M1)55 is:

C_i / C_i,0 = 2L * Σ [exp(-D_i * β_n^2 * t / a^2) * sin(β_n * r / a) / (β_n^2 + L(L-1)) * sin(β_n)] (M4)

In the above solution, L is a dimensionless parameter defined as L = υ_i * a / D_i, and β_n is the n-th root of the transcendental equation:

β_n * cot(β_n) + L - 1 = 0 (M5)

In our model, D_i is not a constant but a temperature-dependent, therefore time-dependent variable that follows the asymptotic thermal history model with an initial temperature of T_0 and a cooling timescale of τ_c:

T = T_0 / (1 + t / τ_c) (M6)

To calculate the final concentration profile of C_i, we derived a general solution to Eq. (M1) for any initial concentration profile of C_i,0 = f(r):

C_i = Σ B_n * exp(-D_i * β_n^2 * t / R^2) * sin(β_n * r / a) (M7)

in which β_n is still the n-th root of the transcendental equation Eq. (M5), while the coefficients B_n are determined by projecting the initial condition onto the eigenfunctions of sin(β_n * r / a):

B_n = (2 / a) * ∫ [f(r) * sin(β_n * r / a) * r^2] dr (M8)

The initial temperature (T_0) is assumed to be the liquidus of the parental liquid of 74220 orange beads (T_0 = 1603 K). For a given cooling timescale of τ_c, the thermal history is divided into small segments with a time interval of Δt. For each time interval, the average temperature is calculated using Eq. (M6), and the temperature-dependent diffusivities of H2O, F, Cl, and S are calculated using experimental data from the literature32,56,57 that provide the Arrhenius equation (Table S1 and Fig. S2):

D_i(T) = D_0 * exp(-E_a / (R * T)) (M9)

with D_0 and E_a being the pre-exponential factor and activation energy for each component. After calculating the diffusivities, the concentration profile of each component is calculated using Eq. (M7) based on the concentration profile from the previous timestep. The calculation proceeds until the diffusion profile converges at lower temperatures. This semi-analytical approach allows for the accommodation of time-dependent changes in diffusivity. It also enables modeling degassing loss across multiple stages of thermal history, as the final profile of one stage can be used as the initial condition for the next. We verified our semi-analytical approach by comparing with numerical results from COMSOL, and consistent results were obtained.

We modeled degassing for glass beads that are 50, 100, and 150 µm in radius (a), which represent the majority of orange glass beads studied in literature. The only other unknown parameter for the model is the dimensionless parameter L_i, which evaluates the relative rate of surface evaporation and diffusive transport during the degassing process (L_i = υ_i * a / D_i). A high value of L_i indicates high surface evaporation rate relative to diffusion, causing the degassing process to be diffusion-limited. A low value of L_i, on the other hand, indicates that the degassing process is limited by surface evaporation. The evaporation rate (υ_i) and diffusivity (D_i) are expected to have different temperature dependencies. However, due to the lack of independent experimental constraints on υ_i, we simply assume L_i to be constant for each element throughout the cooling history.

Modeling diffusive volatile loss of the melt embayment
Diffusive loss of H2O, F, Cl, and S in the melt embayment of 74220 OldOL2 was modeled using a similar semi-analytical approach as the glass beads. The model assumes one-dimensional linear diffusion in the embayment that transports volatiles from the interior to the opening for degassing:

∂C_i / ∂t = D_i (∂^2 C_i / ∂x^2) 0 ≤ x ≤ ‘ (M10)

where C_i is the concentration of a component, D_i is its diffusivity, and ‘ is the characteristic length of the embayment. The boundary condition during Stage 1 of magma upwelling is defined as:

(∂C_i / ∂x) | x=0 = 0 (M11)

C_i | x=‘ = C_i,0 * (1 - t / t_1) (M12)

Here C_i,0 is the initial concentration of a component in the melt embayment, t_1 is the amount of time it takes for the magma to reach the surface, assuming linear decompression. We assume that the linear decompression ends at t = t_end, when fragmentation occurs and explosive eruption starts. Volatile degassing from the melt embayment enters Stage 2 upon eruption, characterized by free-flight and open-space degassing, with a boundary condition at the opening similar to Eq. (M3):

D_i (∂C_i / ∂x) | x=‘ = -υ_i * C_i,‘ (M13)

In the above equation, υ_i is the surface evaporation rate of a component and C_i,‘ is the concentration of the component at the opening of the melt embayment (x=‘). During Stage 3 of slow cooling and degassing at the lunar surface, the boundary condition can be described using the same equations for Stage 2 (Eqs. (M11) and (M13)).

Stage 1 of magma upwelling can be assumed to be an isothermal decompression process, making diffusivity D_i time-independent and allowing Eqs. (M10)–(M12) to be solved analytically:

C_i = C_i,0 * (1 - t_end / t_1) + Σ [B_n * exp(-D_i * λ_n^2 * t_end / ‘^2) * cos(λ_n * x / ‘)] (M14)

where λ_n = (2n + 1) * π / 2, and B_n is determined by the initial condition. For Stage 2 or Stage 3 with the boundary condition of Eqs. (M11) and (M13), we use a semi-analytical approach that accommodates the time-dependent diffusivity D_i throughout the thermal history. The thermal history of each stage is divided into time segments that are small enough for the diffusivity to be considered constant within each segment. The initial concentration profile at the beginning of Stage 2 (eruption and in-flight degassing) can be obtained using Eq. (M14), which is a function of x. More generally, for any timestep during Stage 2 or Stage 3, the initial concentration of a component (C_i) is a function of the spatial variable x from the previous timestep:

C_i | t=0 = f(x) (M15)

We derive the solution to Eq. (M10), with the initial condition given by Eq. (M15) and boundary conditions given by Eqs. (M11) and (M13), as:

C_i = Σ B_n * exp(-λ_n^2 * D_i * t / ‘^2) * cos(λ_n * x / ‘) (M16)

where

B_n = (1 / ‘) * ∫ [f(x) * cos(λ_n * x / ‘)] dx (M17)

and λ_n is the n-th root of the transcendental equation with L_i = υ_i * ‘ / D_i:

tan(λ_n) = L_i / λ_n (M18)

The above approach allows us to model the diffusive degassing of H2O, F, Cl, and S in the melt embayment. The analytical solutions derived in Eqs. (M14) and (M16) were verified by comparing with numerical simulations using COMSOL. In order to examine whether the one-dimensional approximation is appropriate for the ellipsoidal shape of melt embayment in 74220 OldOL2, we also conducted a finite element simulation for diffusive degassing in a rotationally symmetric 2D system, which closely mimics its original shape (Fig. S5 and Supplementary Discussion 2). We found that the shape of the diffusion profile along the central axis of the 2D model typically differs by less than 15% from that of the 1D semi-analytical model, justifying the use of the 1D model in our study.

We assume a homogeneous initial S concentration of 400 ppm for the embayment and initial H2O, F, Cl concentrations to follow the linear trends defined by olivine-hosted melt inclusions (Fig. 2, C_i,H2O = 1.44 * C_i,S, C_i,F = 0.09 * C_i,S, and C_i,Cl = 0.005 * C_i,S). The thermal history of Stage 2, corresponds to an asymptotic cooling model in Eq. (M6) with a cooling timescale of τ_c. For simplicity, we simulate the third stage of slow cooling on the lunar surface as lasting a duration of t_2 at a constant temperature of 938 K (the glass transition temperature of 74220 orange glass).

Besides diffusivity data from literature32,56,57, the measured characteristic length (‘) of 286 µm for the melt embayment, t_end and t_1 are the other two parameters required for the Stage 1 of the model (Eq. M14), while L_i (defined as L_i = υ_i * ‘ / D_i), τ_c and t_2 are the key parameters for Stage 2 and Stage 3. The unknown parameters are evaluated and optimized using data assimilation techniques, as described below.

The Ensemble Kalman Filter (EnKF) is a statistical tool used to combine observational data with model predictions to estimate the state of a system and its associated parameters. EnKF works by generating an ensemble of possible system states, which are updated iteratively using incoming data58. This approach allows for the incorporation of uncertainties in both the model and the observations, making it particularly effective for complex and nonlinear systems59. In this study, the EnKF is employed to assimilate measured volatile concentrations of Apollo 74220 pyroclastic deposit samples (e.g., orange glass beads and OldOL2 melt Embayment) into the two-stage or three-stage degassing model, improving the accuracy of predicted volatile evolution.

The EnKF framework begins with the initialization of an ensemble of model states to capture uncertainties in volatile concentrations and parameters. For a given model, an ensemble of 100 members is generated by sampling from uniform distributions based on prior estimates (Table S2). The forward calculation propagates each ensemble member through the selected model.

Data assimilation is performed using the EnKF to update the ensemble based on observational data. The observation vector consists of measured volatile concentrations with an associated standard deviation (99% confidence interval) of measured concentrations. The root mean square error between the data and model converged quickly after ~10 iterations (e.g., Fig. S9 for the three-stage glass bead model). The model effectively captures the central tendencies and ranges of the observed volatile concentrations (e.g., Fig. 5).

In this work, data assimilation was applied to optimize model parameters for: (1) a two-stage degassing model for the melt embayment; (2) a three-stage degassing model for orange glass beads; and (3) a three-stage degassing model for the melt embayment. The two-stage degassing model for the melt embayment used Eqs. (M14) and (M16) to calculate volatile concentration profiles at the end of Stage 1 and Stage 2, respectively. The parameters optimized with data assimilation include t_end, t_1, L_i and τ_c (Fig. S6).

The three-stage degassing model for orange glass beads employed a parameter S_0 to represent initial S concentration of the bead when they form at the beginning of Stage 2. While other volatiles (H2O, Cl, F) are initialized using ratios relative to S_0 based on the melt inclusion trend. This approach ensures a representative spread of initial conditions for subsequent model propagation. Concentration profiles at the end of Stage 2 were calculated using Eq. (M7) with an asymptotic cooling history (Eq. (M6)) from 1603 K (liquidus) to 938 K (glass transition temperature). Stage 3 was subsequently calculated using Eq. (M7), assuming the beads stayed at a constant temperature of 938 K for a duration of t_2. Volatile concentrations within the inner 50% of the bead radius were averaged for comparison with the measured data. The parameters optimized with data assimilation include a, S_0, L_i, τ_c and t_2 (Fig. S8 and Table S2).

For simplification, the three-stage degassing model for the melt embayment ignored Stage 1 of decompression and focused on degassing during Stages 2 and 3 instead. This choice was made based on our two-stage model and further tests that showed the volatile loss to be highly limited during Stage 1. Starting from an initially homogeneous profile with 400 ppm S and H2O, F, Cl concentrations defined by the melt inclusion trends (Fig. 2, C_i,H2O = 1.44 * C_i,S, C_i,F = 0.09 * C_i,S, and C_i,Cl = 0.005 * C_i,S), concentration profiles at the end of Stage 2 were calculated using Eq. (M16) with an asymptotic cooling history (Eq. (M6)), followed by application of the same equation at a constant temperature of 938 K for a duration of t_2. The parameters optimized with data assimilation include L_i, τ_c, and t_2 (Table S2).

We found that the optimized t_2 for orange glass beads are correlated with the corresponding values of L_i in the three-stage degassing model, owing to the lack of volatile concentration profile data to further constrain these parameters. This correlation is not observed for the melt embayment. Accordingly, our data assimilation focuses on obtaining a consistent thermal history (i.e., similar values of τ_c and t_2) for both the glass beads and the melt embayment.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Please see attached review.\n[Editorial Note: See end of file]", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature\nCommunications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career\nResearchers who co-review manuscripts.", "reviewer_3": "Using a combination of original data from an olivine melt embayment and compiled data on volatile element concentrations\nin lunar orange picritic glass beads, the authors estimate the cooling rate of these Apollo 17 pyroclastic deposits. The\nauthors estimate that the orange picritic glass beads from Apollo 17 cooled over a period of ~17 minutes to ~9 hours which is\nsignificantly longer that the ~8 minute cooling period estimated for green picritic glass beads from Apollo 15. The authors\nconclude that the orange picritic glass beads would require a three-stage cooling and degassing model where prolonged\ncooling and degassing occurs in piles of pyroclastic material following, magmatic ascent, and ejection from the volcanic\nvent. This varies from the two-stage cooling and degassing model proposed for the green picritic glass beads from Apollo 15\nwhere the melts primarily cool and degas during the flight away from the volcanic vent following eruption.\n\nThe data and models from this study have significant implications for the volatile element (H2O, Cl, F, and S) concentrations\nwithin the moon; however, the authors don’t really highlight this in the current form of this manuscript. The way the\nmanuscript currently reads, it seems like the authors attribute the slower cooling rate of orange picritic glass beads to the low\nthermal conductivity of lunar soils that leads to long term degassing. I believe this overlooks the differences in cooling rate\nand volatile contents between green and orange glasses. I appreciate that the authors aren’t trying to oversell the\nimplications of their findings, but I also feel like they already present the data for a compelling argument about the gas rich\nnature high-Ti lunar volcanic materials and their mantle sources. The authors should try to focus on answering the following\nquestions: Why would green glasses cool significantly during the free flight stage, but the orange glasses couldn’t? The\nmanuscript already notes that orange glasses probably erupt at lower temperatures than green glasses so why would they\ncool slower? Look at the ratios between slow and fast diffusing volatile elements in green and orange glasses. Green\nglasses have higher H2O concentrations and lower F and S concentrations than orange glasses. If the orange glasses cool\nslower and in-gassing is typically constrained to the surface of the beads, why would the average center composition of\norange glass beads have higher F and S concentrations?\n\nThe manuscript was well written, and I only found a couple of grammatical errors throughout the text (see line by line\ncomments below). I do think the authors need to move the explanation of some calculation parameters to the first point\nwhere they are mentioned (see line by line comments below). The authors also need to clarify some of the modeling\nassumptions (see line by line comments below). With respect to referencing, I thought the authors did reference the previous\nliterature appropriately, I did point out a couple spots where the authors could reference previous work (see line by line\ncomments below).\n\nI believe the data from previous studies supports the data and interpretations presented within this manuscript. I also believe\nthat the authors are using a good analytical approach to address their questions about the cooling rates of the glass beads,\nbut I did notice some flaws in the diffusion models that need to be addressed prior to publication. For example, I don’t think\nthe concentration profiles referenced in Figure 5b currently match the data from the olivine embayment all that well. The\nauthors put a lot of weight on these models explaining the diffusion curves, so this made me question the validity of the\nauthors interpretations and conclusions (see line by line comments for further explanation). I also noticed that the\nevaporation coefficient used in the model is unconstrained; however, the authors need the evaporation coefficient to\ncalculate the dimensionless diffusion parameter (L). The authors try to work around this using Ensemble Kalman Filter\n(EnKF) assimilation to determine the optimal dimensionless diffusion parameter, but I found it difficult to assess the\nsensitivity of the models to this dimensionless diffusion parameter even with the supplemental figures. I would like the\nauthors to show diffusion models that demonstrate the impact of the dimensionless diffusion parameter on the Cl and S\nmodels. The best-fit predictions of the dimensionless diffusion parameter for Cl and S have the largest uncertainties based\non Table S2 and these elements seem to be the most critical for constraining the maximum cooling rates (i.e., show how\nmuch the variance in the best-fit values would affect the predicted cooling rates). Once the authors address these problems, I\nbelieve the models they present will support their conclusions without question.\n\nMy final assessment of the manuscript is that the manuscript has significant potential for publication in this journal, but it is\nnot publishable in its current state. Once the authors address the comments in this review they should be encouraged to\nresubmit the manuscript.\n\nLine by line Comments:\nLine 39: “are strong evidences” sounds wrong, it should be “are strong evidence”\nLine 40: “have recently been also” also sounds wrong, “have also recently been” sounds better.\nLines 51-53: It might be worth saying these elements are “relatively” or “moderately” volatile. While other lunar geochemists\nwill probably understand that these elements are generally volatile at magmatic or impact related temperatures, most people\nwill not. You also refer to Cu, Zn, and Pb as “moderately” volatile elements later in the manuscript.\nFigure 3: Increase the size of the text within this figure. It's currently difficult to see what the volatile loss trend lines say\nwithout really zooming.\nLines 109-111: Were these trends quantitatively determined using the melt inclusion data? or are these trends qualitative\nestimates that follow the linear trends defined in this sentence?\nLines 166-169: The evaporation coefficient and its relationship to dimensionless parameter L seems like a significant point\nof potential error for the models. I looked through the paper for a reference to the evaporation coefficient and found that it is\nan unconstrained value. This isn’t explained until lines 259-276. That explanation should be moved up to this section.\nLines 179-180: The diffusion models from Zhang et al. (2019) (https://doi.org/10.1016/j.epsl.2019.06.021) show that H2O\ndiffuses about an order of magnitude faster in lunar melt compositions than it does in terrestrial basalt compositions.\nAssuming F, Cl, and S exhibit similar behavior, how might that effect your models?\nLines 225-227: Data from Shishkina et al. (2010) (https://doi.org/10.1016/j.chemgeo.2010.07.014) and Botcharnikov et al.\n(2015) (https://doi.org/10.1016/j.chemgeo.2015.07.019) appears to show that volatile saturation and pressure doesn’t follow\na linear relationship (at least not for H2O and CO2). I don’t think the authors assumption is all that problematic, given the\nother model variables that can’t be better constrained, but it is worth noting that this assumption isn’t completely realistic\ngiven our observations in terrestrial systems.\nLines 259-276: Why is the L parameter for Cl in the embayment so different from the L parameter for Cl in the glass beads?\nWhy would Cl degassing be diffusion controlled in the olivine embayment, but evaporation controlled in the glass beads? Cl\nshould be the second fastest diffusing element based on the reported calculation parameters in this study, is there a\nreasonable explanation as to why it’s the only element limited by diffusion or is this a potential problem with the model?\nLines 275-276: This sentence contradicts the data and models presented in Figure 5b. The authors need to check their\nmodels and figures to resolve this problem.\nLines 374-377: I don’t think the concentration profiles referenced in Figure 5 match the data all that well. The only modeled\ncurve that appears to match the data well is the one for H2O. Unfortunately, this is the fastest diffusing element, and the trend\nin the data is effectively flat. Thus, models for this element are only going to provide the authors with a minimum timescale\nover which diffusion occurred because it has effectively equilibrated across the diffusive length scale being modeled. The S\nand F curves aren’t even close to matching the data. In the case of S, the data doesn’t exhibit a nice diffusion curve so it\nwould be difficult to model that trend so the deviation between the data and the models is understandable. In the case of F\nand Cl, the data looks fine, but the modeled curves look wrong given the reported diffusivities from Table S1. The current\nmodels indicate that F has faster diffusion kinetics than Cl which is inconsistent with the diffusion data shown in Figure 5\nand the reported values in Table S1. The authors need to address this problem with new models or explain why the F and Cl\nmodels appear to be incorrect.\nLines 435-449: This would be a good point in the manuscript to mention the difference between H2O vs S and F contents in\ngreen glasses compared to the orange glasses (use the supplemental data from Hauri et al. (2015)\n(https://doi.org/10.1016/j.epsl.2014.10.053)). Green glasses have higher H2O contents than orange glasses on average, but\norange glasses have higher S and F contents. S and F should diffuse slowly out of the glasses, but H2O should diffuse\nquickly. Are the higher S and F contents of the orange glasses related to the source contents while their lower H2O contents\nare related to prolonged cooling? If there’s more volatile elements in the source, could that help explain the prolonged\ncooling history. The authors should also make sure they discuss the new orange glass in-gassing data from Su et al. (2025)\n(https://doi.org/10.1016/j.gca.2025.03.026) since it may support the findings of this study.\nLine 439-440: The authors present a model that contradicts this statement in the supplemental data. They show that the\ngreen glasses don’t fit the three-stage model well and likely cooled faster. I think its reasonable to say that it’s less likely that\nthe green glasses experienced significant post flight degassing.\nLine 446: “contain 10s of ppm H2O.” should be “contain 10 ppm H2O.”\nLines 473-475: The authors should add a figure to the supplemental information showing how the diffusivity D changes as a\nfunction of temperature, using an asymptotic cooling history. This would be helpful for someone trying to comprehend how\nthe cooling rate is impacting the diffusivity D for each element.\nLines 498-507: After reading through the manuscript and supplemental information, the evaporation coefficient and its\nrelationship to dimensionless parameter L seems like a significant point of potential error for the models. The authors noted\nthat the boundary conditions change depending on the stage of degassing in the orange glass cooling models. This change\nin boundary conditions should affect the evaporation coefficient and as a result the dimensionless parameter L. The authors\nneed to find a better way to demonstrate and explain why the dimensionless parameter L won’t cause the models to require\nunrealistically long cooling histories based on a currently unconstrained evaporation coefficient. Since the authors assume L\nvalue is constant, but diffusivity D is changing, they should calculate how the evaporation coefficient υ_i would have to\nchange to make this assumption possible. This might be helpful when considering the impact of this assumption on the\nmodels.\nFigure S1: Flip the x axis in panel b so it’s oriented in the same direction as the open end of the Ol-embayment. This will\nmake it easier to connect panel a with the trends on panel b.\nTable S1: Why don’t the D0 values in this table match any of the studies referenced reported values? Are these averages of\nmultiple of the reported values in those studies? If so that needs to be clarified."}, "author_response": "Point-by-point responses to reviewer’s comments for Manuscript NCOMMS-25-\n71651 (Revision 1)\nTitle: Prolonged cooling and degassing of Apollo 17 volcanic glasses on the lunar\nsurface\nAuthors: Peng Ni and Yan Zhan\nThe reviewer’s comments are in black font while our responses are in blue font.\nReviewer 1&2:\nThis manuscript constrains a three-stage decompression and cooling history for Apollo\n17 volcanic glasses: in the first stage of the model, degassing occurs in response to\ndecompression in the volcanic conduit; in the second stage, the glass beads and\nembayments undergo diffusive and evaporative loss of volatiles during free flight; and in\nthe third stage of the model, the glasses undergo a final stage of volatile loss during slow\ncooling on the lunar surface. Volatile concentration gradients in glass beads and melt\nembayments are best fit by models in which the glasses undergo slow cooling and\nprolonged degassing on the lunar surface for timescales on the order of years. This is a\nnovel and interesting finding that leverages previously collected volatiles data with a\nsophisticated new model.\nThe model is carefully constructed. The one-dimensional model for the embayment is\nchecked against a two-dimensional model and is found to agree within 15%. The model\nuses appropriate parameters and constraints from the literature. In addition to the\ntho the\nthorough description of the model provided in the manuscript, the authors state that the\ncode will be provided on Github, which will provide the detail needed for the work to be\nreproduced. The model results support the conclusions of the manuscript.\nWe support the publication of this manuscript in Nature Communications. We provide\nbelow some suggestions for additional topics of discussion and minor corrections that\ncould strengthen the manuscript.\nWe sincerely appreciate your support and the insightful suggestions for improving our\npaper. Our detailed responses are provided below.\nMajor comments:\n1. A linear relationship between H2O and pressure is assumed, but experimental evidence\nhas shown that H2O follows a square root relationship with pH2O (e.g., Newcombe et al.\n2017). How might the assumption of a square root relationship affect the results?\nThis is a good point. At these low pressures, it is possible that all these volatiles follow a\nsquare-root law dependence on pressure. In that case, the correlations between the\nsaturated concentrations of H O, F, Cl, and S would still be linear because if 𝐶 = 𝑘 √𝑃,\n2 ! !\nthen\n\"!\n= 𝑘 /𝑘 , which is consistent with the melt inclusion data. Applying the square-\n! #\n\"\n\"\nroot law to volatile solubility is not expected to change our modeling results much,\nbecause the majority of volatile loss occurs after magma fragmentation and eruption.\nNonetheless, in order to make our model more robust for community use, we’ve updated\nthe model to use a square-root law instead of linear law for volatile solubility. The net\neffect is on Eq. (7) for Stage 1 degassing, which changes from\n𝑡 𝑡\n𝐶 | = 𝑘 𝑃 = 𝑘 𝑃 (1− , = 𝐶 (1− ,\n! $%ℓ ! ! ' 𝑡 !,' 𝑡\ninf inf\nto\n) )\n𝐶 | = 𝑘 √𝑃 = 𝑘 -𝑃 .1− / = 𝐶 -1− .\n! $%ℓ ! ! ' !,'\n)inf )inf\nWe’ve updated the numerical code, re-run all the models, and re-made all the\nplots in the paper to accommodate the change.\n2. Su et al. (2023) suggest that S, Cl and F (which are all enriched on the surfaces of\n74220 orange glass beads) are expected to ‘ingas’ (i.e., diffuse into the beads) as they\ntravel through cool regions of the volcanic plume. The model presented here does not\nconsider ingassing. If ingassing has occurred, the initial stages of ingassing would\n“flatten” the concentration gradients of H2O, Cl, S and F, which might cause a bias in the\nmodeled results towards models in which evaporation dominates over diffusion. Notably,\nthis process (referred to as low-temperature rehydration) has also been observed in water\nconcentration gradients across terrestrial melt embayments; e.g. Befus et al. (2024). A\ndiscussion of the potential effects of ingassing on the H2O, Cl, S and F gradients would\nstrengthen the manuscript.\nBefus, Kenneth S., et al. \"Rehydrated glass embayments record the cooling of a\nYellowstone ignimbrite.\" Geology 52.7 (2024): 507-511.\nI want to first point out that among S, Cl, F, and H O, so far there is only evidence for\n2\ningassing of S. Su et al. (2023) reported ingassing of Na, K, and Cu in orange glass\nbeads. A more recent paper by Su et al. (2025) reported ingassing profiles of S in orange\nglasses. To my best knowledge, nobody has reported ingassing of H2O, F, or Cl in lunar\nvolcanic glass beads. I have also looked for ingassing profiles in the past, but I’ve only\nfound ingassing of S, Na, K, and Cu, similar to what Su et al. had reported. There was\none recent study on impact glass beads that reported ingassing of H O (He et al., 2025).\n2\nvery short. Such ingassing was likely due to brief impact heating, which is irrelevant to\nvolcanic degassing for the orange glass beads.\nThe occurrence of S ingassing and the absence of H O, F, Cl ingassing is likely related to\n2\ntheir volatility. It is possible for sulfur to condense from the vapor as sulfides at\ntemperatures much higher than H O, F, and Cl. Therefore, even if H O, F, and Cl\n2 2\ningassing occurred, their profiles might be much shorter. The rehydration profile in Befus\net al. (2024) was interpreted to be caused by meteoric water incorporation into the source\nmagma of the rhyolitic glass. But such water sources are lacking on the Moon.\nThe reviewers raised an excellent point on how ingassing would “flatten” the\nconcentration gradients of H O, F, Cl, and S. If that had happened during Stage 2 (free-\n2\nflight) as proposed in Su et al. (2025), it would have prohibited further degassing loss of\nH O, F, Cl, and S, requiring even slower cooling (i.e., longer free flight) to explain the\n2\noverall degree of volatile depletion at the center of the glass beads or the inner end of the\nmelt embayment. In fact, Su et al. (2025) had to use an artificial sulfur diffusivity 20\ntimes higher than experimental values to explain the degassing and ingassing of S in\norange glasses.\nAs stated in the discussion session of our paper, an alternative explanation to the S\ningassing profiles is that they were produced by solid-state diffusion on the lunar surface\n(Stage 3). The idea is that glass beads buried at greater depths would cool down slower,\ncontinuing to degas and supply sulfur vapor to those buried at shallower depths. When\nthe shallower beads cool down to a certain temperature, sulfides would start to condense\non the surface, leading to ingassing of sulfur into the interior of the beads.\nIn order to better demonstrate the idea, we constructed a forward model for orange glass\nbeads to explain the S ingassing profiles reported by Su et al. (2025). We assumed that\ntoward the end of the degassing in Stage 3, sulfides condense on the surface of orange\nbeads, saturating the surface glass with ~500 ppm of S (depending on the observed S\nconcentration at the rims of those beads) and leading to ingassing of S into those glass\nbeads with different radii. We were able to reproduce the w-shaped and u-shaped sulfur\ningassing profiles in Su et al. (2025) within approximately a month of solid-state\ndiffusion (see plot below). It should be possible to reproduce the individual profiles more\nprecisely with our model, but that is beyond the scope of this paper. We’ve included\nthese updates in the revision to strengthen our manuscript.\nFigure R1. Our model provides an alternative explanation to the S ingassing profiles\nreported in literature. Instead of occurring during flight following the eruption, ingassing\ncould also happen via solid-state diffusion as the volcanic beads slowly cool down on the\nlunar surface.\n3. If it is possible to use the embayment data to report constraints on the decompression\nrate of the lunar magma (P0/tend?), that would be of great interest.\nUnfortunately, we found this to be almost impossible for 74220. The fundamental reason\nis that most of the volatile loss occurred during Stage 2 (free flight) and Stage 3 (slow\ncooling on the lunar surface). The volatile profiles at the end of Stage 1 were heavily\noverprinted by subsequent loss during Stages 2 & 3, leaving poor traces of whether the\ndecompression rate was high or low for magma upwelling. For example, concentrations\nof H O and Cl would have been further depleted by >90% in later stages. Whether the\n2\nmagma upwelling was fast or slow had little effect on the model results. This is discussed\non Lines 375 to 378 of the revised manuscript. I see this as a major difference between\nterrestrial and lunar volcanism in melt embayment studies.\n4. At what stage of the decompression and cooling history is post-entrapment\ncrystallization occurring? Is it possible that vapor expansion in the conduit could have led\nto some adiabatic cooling prior to eruption? E.g., La Spina et al. (2015), Newcombe et al.\n(2020):\nLa Spina, G., M. Burton, and M. de'Michieli Vitturi. \"Temperature evolution during\nmagma ascent in basaltic effusive eruptions: A numerical application to Stromboli\nvolcano.\" Earth and Planetary Science Letters 426 (2015): 89-100.\nNewcombe, Megan E., et al. \"Magma pressure-temperature-time paths during mafic\nexplosive eruptions.\" Frontiers in Earth Science 8 (2020): 531911.\nThis is highly possible. The magma upwelling process is unlikely to be isothermal. Like\nthe reviewers suggest, vapor expansion in the conduit could have led to adiabatic cooling\nof the magma. The magma would have been subliquidus in temperature when erupted,\notherwise it wouldn’t have contained olivine grains with melt inclusions. The major\nelement composition of orange glasses also shows an evolution trend (Ni et al., 2017),\nconsistent with magma cooling and fractional crystallization during ascent.\nWe assumed the magma to be still at its liquidus temperature when erupted, because it\nhelps demonstrate that even with the highest possible initial temperature, volatile\ndegassing loss during free flight alone would still require too long a cooling history to\nexplain the extent of H2O, F, Cl, and S loss in glass beads and melt embayment.\nIf a lower, more realistic initial temperature is adopted, the initial diffusivities will be\nlower, requiring the degassing to occur over a longer timescale. The suggested citations\nare helpful in demonstrating that our assumed initial temperature is an up limit and have\nbeen incorporated into the revised manuscript.\nMinor comments:\n1. After figure 1, the figure numbers within the text appear to be inaccurate.\nThank you for catching that. This is likely due to the map we added in later as Fig. 1.\nWe’ve now revised the manuscript to ensure correct figure numbers are cited.\n2. Figure 3: The panels and text are small. Could this be a 2x2 tiling with the legend\nplaced in the 4th panel?\nWe’ve made this change in the manuscript for the purpose of review. We’ve also\nincreased the font size to make texts in the figure more readable. Eventually this needs to\nbe a suggestion to the editor for typesetting. The journal might align the three panels\ntogether vertically on one of the two columns.\n3. Line 7: “thermal evolution of the mantle”. Please clarify that you are referring to the\nlunar mantle.\nYes. Fixed for clarification.\n4. Line 10: Please clarify “volatile-rich”. Do you mean more volatile-rich than the rest of\nthe lunar mantle? Note that scientists from different fields have different views of what\nconstitutes “volatile-rich”, so it would be helpful to provide a comparison.\nGood point. We meant to say “volatile-rich” relative to mare basalts. We’ve corrected the\ntext for clarification.\n5. Line 34: Please clarify what is meant by “uniform Ni concentrations that correlate with\nMg”. Do you mean uniform Ni within each pyroclastic deposit?\nYes, volcanic glass beads from each pyroclastic deposit are uniform in Ni, while\ncollectively they show correlation between Ni and Mg that overlap with mare basalts.\nThe phrase has been changed to “Ni concentrations that are uniform within individual\ndeposits vary systematically with Mg content across deposits” for clarification.\n6. Line 36: Please emphasize the link between Ti content and glass colors earlier in the\ntext. Glass colors and glass Ti-contents are used interchangeably (e.g. line 35 and 45)\nand this connection might not be obvious to a reader.\nThanks for the suggestion. A sentence has been added to indicate the connection between\nTi-content and glass color.\n7. Line 39: “evidences” should be “evidence”.\nCorrected.\n8. Line 56: Perhaps the significance of these glass beads should be emphasized. What is\nthe interest in these samples compared to other lunar lithologies for “understanding lunar\nmantle chemistry and Moon formation”? This is briefly touched on in the abstract, but\nmay warrant a few more sentences in the introduction.\n“Pyroclastic volcanism, although volumetrically minor compared to mare volcanism, is\nthought to originate from deeper, more primitive sources, and volatile-rich in\ncomposition”\nExcellent point. Somehow this point was left out when writing the introduction. We’ve\nadded a couple sentences to elaborate on its importance in lunar mantle chemistry and\nMoon formation.\nLine 73: “contains” is missing an s\nFixed.\nLine 100: “volatiles content” shouldn’t be plural\nCorrected.\nOn line 256, what is the difference between tinf and tend? Please clarify.\ntinf in Eq.8 controls the magma upwelling rate, while tend indicates when Stage 1\ntransitions to Stage 2 of fragmentation and eruption. We realized that tend was not\ndefined from early on. We’ve added a few sentences immediately after Eq. 8 to define\nand explain tend and tinf (Lines 315-317).\nLine 341: Cite the preliminary science report?\nReference added as suggested.\nLine 410: “a high percentages” should be “a high percentage”\nCorrected.\nLine 441: “interpretating” should be “interpreting”\nCorrected.\nLine 519: Missing “of” between amount and time.\nCorrected.\nReviewer 3:\nUsing a combination of original data from an olivine melt embayment and compiled data\non volatile element concentrations in lunar orange picritic glass beads, the authors\nestimate the cooling rate of these Apollo 17 pyroclastic deposits. The authors estimate\nthat the orange picritic glass beads from Apollo 17 cooled over a period of ~17 minutes\nto ~9 hours which is significantly longer that the ~8 minute cooling period estimated for\ngreen picritic glass beads from Apollo 15. The authors conclude that the orange picritic\nglass beads would require a three-stage cooling and degassing model where prolonged\ncooling and degassing occurs in piles of pyroclastic material following, magmatic ascent,\nand ejection from the volcanic vent. This varies from the two-stage cooling and degassing\nmodel proposed for the green picritic glass beads from Apollo 15 where the melts\nprimarily cool and degas during the flight away from the volcanic vent following\neruption.\nThe data and models from this study have significant implications for the volatile element\n(H2O, Cl, F, and S) concentrations within the moon; however, the authors don’t really\nhighlight this in the current form of this manuscript. The way the manuscript currently\nreads, it seems like the authors attribute the slower cooling rate of orange picritic glass\nbeads to the low thermal conductivity of lunar soils that leads to long term degassing. I\nbelieve this overlooks the differences in cooling rate and volatile contents between green\nand orange glasses. I appreciate that the authors aren’t trying to oversell the\nimplications of their findings, but I also feel like they already present the data for a compelling\nargument about the gas rich nature high-Ti lunar volcanic materials and their mantle\nsources. The authors should try to focus on answering the following questions: Why\nwould green glasses cool significantly during the free flight stage, but the orange glasses\ncouldn’t? The manuscript already notes that orange glasses probably erupt at lower\ntemperatures than green glasses so why would they cool slower? Look at the ratios\nbetween slow and fast diffusing volatile elements in green and orange glasses. Green\nglasses have higher H2O concentrations and lower F and S concentrations than orange\nglasses. If the orange glasses cool slower and in-gassing is typically constrained to the\nsurface of the beads, why would the average center composition of orange glass beads\nhave higher F and S concentrations?\nThanks for the helpful suggestion. This study focuses on Apollo 17 orange glass beads\nbecause olivine-hosted melt inclusions and embayments from the same deposit are\navailable and allow us to better constrain the initial conditions required for modeling. We\nwanted to avoid too much speculation about the green glass beads, for which no melt\ninclusion data exist to constrain their initial volatile contents.\nThe volatile concentrations of the green glass beads (H2O, F, Cl, and S) likely reflect a\ncombination of two factors: (1) higher degrees of partial melting that resulted in lower\ninitial F, Cl, and S contents; and (2) lower degrees of degassing, which led to higher H O\n2\nconcentrations compared with the orange glass beads. Additional discussion of the\nvolatile contents of the green glass beads is provided below in our responses to the\ndetailed comments.\nRegarding the reviewer’s question on the potential causes of differing cooling rates\nbetween green glasses and orange glasses, we hope this study encourages broader\nconsideration of the cooling and degassing histories of volcanic glass beads in both\nspatial and temporal contexts. For example, beads deposited closer to the vent are likely\nto accumulate more rapidly and cool more slowly, leading to more extensive degassing.\nSimilarly, glass beads deposited during higher-volume eruption episodes are more likely\nto be buried at higher temperatures and to cool more slowly. Differences in thermal\nhistories between green glasses and orange glasses may therefore reflect variations in\ndistance from the vent, burial depth, and eruption volume. We have added a paragraph to\nthe revised manuscript to discuss this perspective. (Lines 610-619)\nThe manuscript was well written, and I only found a couple of grammatical errors\nthroughout the text (see line by line comments below). I do think the authors need to\nmove the explanation of some calculation parameters to the first point where they are\nmentioned (see line by line comments below). The authors also need to clarify some of\nthe modeling assumptions (see line by line comments below). With respect to\nreferencing, I thought the authors did reference the previous literature appropriately, I did\npoint out a couple spots where the authors could reference previous work (see line by line\ncomments below).\nI believe the data from previous studies supports the data and interpretations presented\nwithin this manuscript. I also believe that the authors are using a good analytical\napproach to address their questions about the cooling rates of the glass beads, but I did\nnotice some flaws in the diffusion models that need to be addressed prior to publication.\nFor example, I don’t think the concentration profiles referenced in Figure 5b currently\nmatch the data from the olivine embayment all that well. The authors put a lot of weight\non these models explaining the diffusion curves, so this made me question the validity of\nthe authors interpretations and conclusions (see line by line comments for further\nexplanation). I also noticed that the evaporation coefficient used in the model is\nunconstrained; however, the authors need the evaporation coefficient to calculate the\ndimensionless diffusion parameter (L). The authors try to work around this using\nEnsemble Kalman Filter (EnKF) assimilation to determine the optimal dimensionless\ndiffusion parameter, but I found it difficult to assess the sensitivity of the models to this\ndimensionless diffusion parameter even with the supplemental figures. I would like the\nauthors to show diffusion models that demonstrate the impact of the dimensionless\ndiffusion parameter on the Cl and S models. The best-fit predictions of the dimensionless\ndiffusion parameter for Cl and S have the largest uncertainties based on Table S2 and\nthese elements seem to be the most critical for constraining the maximum cooling rates\n(i.e., show how much the variance in the best-fit values would affect the predicted\ncooling rates). Once the authors address these problems, I believe the models they present\nwill support their conclusions without question.\nPlease see our responses to the detailed comments about the definition of parameters and\nthe use of dimensionless parameter L. We’ve moved up explanations of most parameters\nin the main text to when they are first introduced.\nWe understand that the use of dimensionless parameter L is different from previous\napproaches using evaporation rate 𝜐 and might not be familiar to readers. (Note L is not\n!\na diffusion parameter. It is rather the ratio of diffusion timescale over surface evaporation\ntimescale). In fact, these two parameters are inter-calculable for a given length scale:\n𝐿 = 𝜐 𝑅/𝐷 . We chose to use L instead of 𝜐 because: 1) 𝜐 is expected to decrease with\n! ! ! ! !\ntemperature, using L to connect it with diffusivity 𝐷 , which itself decreases with\n!\ntemperature, helps partly compensate for the temperature dependence of 𝜐 ; 2) 𝐿\n! !\nprovides a more direct way for us to evaluate whether the degassing process is diffusion\ncontrol or surface evaporation control.\nRegarding the impact of the dimensionless parameter L on the model results, we would\nlike to direct our reviewer’s attention to Figs. S3 and S4, which present sensitivity tests of\nthe two-stage glass bead degassing model that explicitly demonstrate how variations in L\naffect the modeling outcomes. At low L values, decreasing L limits the surface\nevaporation rate, leading to longer timescales for achieving the observed degrees of\nvolatile depletion at the center 50% of the glass beads (marked by light yellow colors in\nFig. S2 and S3). In contrast, at high L values, when surface evaporation is rapid, the\nprocess becomes diffusion-limited and the timescale no longer decreases with increasing\nL.\nIn the revised manuscript, we have added additional discussion of the use of\ndimensionless parameter L where appropriate to help readers understand this change in\nmodel approach relative to literature.\nMy final assessment of the manuscript is that the manuscript has significant potential for\npublication in this journal, but it is not publishable in its current state. Once the authors\naddress the comments in this review they should be encouraged to resubmit the\nmanuscript.\nLine by line Comments:\nLine 39: “are strong evidences” sounds wrong, it should be “are strong evidence”\nCorrected.\nLine 40: “have recently been also” also sounds wrong, “have also recently been” sounds\nbetter.\nCorrected.\nLines 51-53: It might be worth saying these elements are “relatively” or “moderately”\nvolatile. While other lunar geochemists will probably understand that these elements are\ngenerally volatile at magmatic or impact related temperatures, most people will not. You\nalso refer to Cu, Zn, and Pb as “moderately” volatile elements later in the manuscript.\nGood point. Earlier literature referred to all these elements as volatiles. But strictly\nspeaking they should be distinguished from H2O, F, Cl, and S that are volatile. We’ve\nchanged the wording to “moderately volatile elements”.\nFigure 3: Increase the size of the text within this figure. It's currently difficult to see what\nthe volatile loss trend lines say without really zooming.\nWe’ve increased the font size of all texts in this figure. Thanks for the suggestion.\nLines 109-111: Were these trends quantitatively determined using the melt inclusion\ndata? or are these trends qualitative estimates that follow the linear trends defined in this\nsentence?\nThese trends are qualitative estimates that lie on the high end of the melt inclusion data.\nWe decided to use these qualitative estimates instead of linear regression because some\nof the melt inclusions could have experienced later volatile depletion, such as diffusive H\nloss. We’ve changed the sentence to say “qualitatively described using zero-intercept\nlinear trends”.\nLines 166-169: The evaporation coefficient and its relationship to dimensionless\nparameter L seems like a significant point of potential error for the models. I looked\nthrough the paper for a reference to the evaporation coefficient and found that it is an\nunconstrained value. This isn’t explained until lines 259-276. That explanation should be\nmoved up to this section.\nGood point. We’ve added a few sentences to further explain L and the evaporation\ncoefficient right after its introduction in the paragraph. In short, 𝐿 is defined as 𝐿 =\n! !\n𝜐 𝑅/𝐷 . Because both 𝑅 and 𝐷 are known, 𝐿 and 𝜐 are interchangeable parameters in\n! ! ! ! !\nthe model. We choose to fit 𝐿 as a model parameter instead of evaporation rate 𝜐\n! !\nbecause 𝜐 is expected to be a lot more temperature dependent than 𝐿 . Treating 𝜐 as a\n! ! ! !\nconstant during cooling will likely introduce larger errors on the modeling results.\nIn addition, the value of 𝐿 gives us a way to directly evaluate whether the degassing\n!\nprocess is diffusion-controlled or evaporation-rate-controlled.\nLines 179-180: The diffusion models from Zhang et al. (2019)\n(https://doi.org/10.1016/j.epsl.2019.06.021) show that H2O diffuses about an order of\nmagnitude faster in lunar melt compositions than it does in terrestrial basalt\ncompositions. Assuming F, Cl, and S exhibit similar behavior, how might that effect your\nmodels?\nThe key question here is whether the degassing observed in orange glass beads and melt\nembayments can be explained by the traditional two-stage model if volatile diffusivities\nare significantly higher than those measured experimentally for terrestrial basaltic\ncompositions. In other words, is a three-stage model truly required to explain the\nobserved degassing?\nI happened to have recently reviewed a study from the same group on F diffusion in lunar\nmelts, which found that F diffusivity in lunar melts is, on average, approximately 5 times\nhigher than in terrestrial melts. Motivated by this result, we conducted a sensitivity test of\nthe orange glass bead degassing model, assuming that F, Cl, and S diffusivities are five\ntimes higher than existing literature values (Fig. R2).\nWith these elevated diffusivities, the model can explain the volatile loss observed in glass\nbeads with radii of 50 µm. However, explaining degrees of degassing in beads with radii\nof 100 µm still requires timescales of thousands of seconds, and even longer timescales\nare needed for beads with radii of 150 µm. Notably, many of the orange glass beads\nmeasured were close to 150 µm in radius (see literature data labeled as “large” in Fig. 3).\nTherefore, a three-stage-model remains necessary to account for the observed\ndegassing records in 74220 samples.\nAlthough higher diffusivities for F, Cl, and S would shorten the duration of Stage 3\nrelative to our current estimates, they do not eliminate the need for this stage. We will\nmake our modeling code openly available on GitHub to facilitate future updates as\nimproved diffusion data on F, Cl, and S become available.\nFigure R2: Reproduced Fig. S2 and S3 assuming diffusivities of F, Cl, and S are 5 times\nhigher than in terrestrial basalts. Modeling results that match the observations are marked\nin light yellow. For glass beads that are 100 µm or 150 µm in radius, thousands of\nseconds are needed to explain the observed degassing loss of F, Cl, and S even if\nextremely high L values (therefore evaporation rates) are assumed. This test strengthens\nour conclusion that a third stage of slow cooling and degassing on lunar surface is\nnecessary to explain the observed volatile depletion in glass beads and melt embayment\nfrom 74220.\nLines 225-227: Data from Shishkina et al. (2010)\n(https://doi.org/10.1016/j.chemgeo.2010.07.014) and Botcharnikov et al. (2015)\n(https://doi.org/10.1016/j.chemgeo.2015.07.019) appears to show that volatile saturation\nand pressure doesn’t follow a linear relationship (at least not for H2O and CO2). I don’t\nthink the authors assumption is all that problematic, given the other model variables that\ncan’t be better constrained, but it is worth noting that this assumption isn’t completely\nrealistic given our observations in terrestrial systems.\nThis comment is similar to the one given by Reviewers 1&2. Although the impact on our\nmodel results is limited as reasoned earlier, we’ve decided to modify the equations and\nnumerical code to incorporate this change. All results in this paper are re-run with a\nsquare root law assumption for solubilities and the difference is minor.\nLines 259-276: Why is the L parameter for Cl in the embayment so different from the L\nparameter for Cl in the glass beads? Why would Cl degassing be diffusion controlled in\nthe olivine embayment, but evaporation controlled in the glass beads? Cl should be the\nsecond fastest diffusing element based on the reported calculation parameters in this\nstudy, is there a reasonable explanation as to why it’s the only element limited by\ndiffusion or is this a potential problem with the model?\nThis is likely due to a confusion. The values for L discussed on Lines 259-276 are based\non the results from a two-stage model (no third stage of solid-state degassing), while the\nvalues for L provided in Table S2 are based on a three-stage model for the glass beads.\nTherefore, the values for L from these two approaches are not comparable to each other.\nFurthermore, in both models Cl tends to have the highest L values among H2O, F, Cl,\nand S, which is consistent with the reviewer’s comment saying Cl appears to be diffusion\nlimited. The way to understand this result is, low evaporation rate (i.e. low L values)\nalways suppresses degassing, because the volatile component needs to take longer to be\nlost from the surface melt even if diffusion is efficient enough to transport it to the\nsurface.\nThe fact that Cl appears to be diffusion-limited in our model is due to the high degrees of\ndepletion in Cl compared to F and S (Fig. 3, main text). In order to explain the high\ndegrees of Cl loss, its evaporation rate needs to be high enough that its degassing doesn’t\nget further limited by surface evaporation (i.e. higher L value). If the L value for Cl was\nalso low, the cooling timescale will be even longer to explain the observed depletions.\nA separate line of evidence on L value of the difference components comes from the\nvolatile depletion profiles in the melt embayment. A high L value leads to a degassing\nscenario that is more diffusion-limited, therefore steeper concentration profile. While a\nlow L value indicates surface evaporation control, leading to flatter profiles (i.e. diffusion\nis relatively fast to even out the concentration gradient). Among H2O, F, Cl, and S, Cl\nhas the steepest profile in the melt embayment, consistent with a higher L value.\nLines 275-276: This sentence contradicts the data and models presented in Figure 5b. The\nauthors need to check their models and figures to resolve this problem.\nFollowing the reviewer’s suggestions, including this one and a few more below, we’ve\nrewritten the discussion on the implications of our modeling results for green glasses.\nLines 374-377: I don’t think the concentration profiles referenced in Figure 5 match the\ndata all that well. The only modeled curve that appears to match the data well is the one\nfor H2O. Unfortunately, this is the fastest diffusing element, and the trend in the data is\neffectively flat. Thus, models for this element are only going to provide the authors with\na minimum timescale over which diffusion occurred because it has effectively\nequilibrated across the diffusive length scale being modeled. The S and F curves aren’t\neven close to matching the data. In the case of S, the data doesn’t exhibit a nice diffusion\ncurve so it would be difficult to model that trend so the deviation between the data and\nthe models is understandable. In the case of F and Cl, the data looks fine, but the modeled\ncurves look wrong given the reported diffusivities from Table S1. The current models\nindicate that F has faster diffusion kinetics than Cl which is inconsistent with the\ndiffusion data shown in Figure 5 and the reported values in Table S1. The authors need to\naddress this problem with new models or explain why the F and Cl models appear to be\nincorrect.\nTwo things need to be clarified in order to address the concerns raised by the reviewer.\nOne is about the reviewer’s comment saying, “The current models indicate that F has\nfaster diffusion kinetics than Cl which is inconsistent with the diffusion data shown in\nFigure 5 and the reported values in Table S1.” My guess is that the reviewer saw a flatter\nF profile than the Cl profile in our model, which led to the confusion that we had used a\nhigher F diffusivity than Cl. However, the shape of the profile is controlled by the L\nvalues, not by diffusivities:\nHigh L value -> diffusion control -> steeper profiles\nLow L value -> surface evaporation control -> flatter profiles\nThe modeled F profile is flatter simply because the L value for F is lower than that for Cl,\nindicating stronger control by the surface evaporation rate. A more effective way to\nassess the effect of diffusivity is to examine the concentration at the innermost end of the\nmodeled profile. In this case, 𝐶/𝐶 is approximately 0.63 for F and 0.55 for Cl, consistent\n'\nwith a higher diffusivity for Cl.\nAnother point I would like to clarify is that the modeled melt embayment profiles in Fig.\n5 were generated through forward calculations using the average parameter values\nderived from the orange glass bead data. We did not perform a separate data assimilation\nto fit the melt embayment profiles. The purpose of Fig. 5b was to demonstrate how a\nthree-stage model has the potential to simultaneously explain both the glass bead data and\nthe melt embayment data.\nUsing the three-stage model, we focused on evaluation whether the observed H2O, F, Cl,\nand S concentrations at the innermost end of the melt embayment could be reproduced, as\nthese concentrations are more directly controlled by the cooling timescales. The shape of\nthe profiles, in contrast, is primarily influenced by changes in boundary conditions.\nNonetheless, following the reviewer’s comment, in the revised manuscript we redid data\nassimilation for the glass beads and the melt embayment. We focused on achieving high\nquality fits with similar timescales of both Stage 2 and Stage 3 for the glass beads and the\nmelt embayments. We are able to reproduce the profiles much better this way (Figure 5\nof the revised manuscript), with a Stage 2 cooling timescale of ~250 seconds and a Stage\n3 duration of 108 seconds. The main conclusions of the manuscript remain unchanged.\nLines 435-449: This would be a good point in the manuscript to mention the difference\nbetween H2O vs S and F contents in green glasses compared to the orange glasses (use\nthe supplemental data from Hauri et al. (2015)\n(https://doi.org/10.1016/j.epsl.2014.10.053)). Green glasses have higher H2O contents\nthan orange glasses on average, but orange glasses have higher S and F contents. S and F\nshould diffuse slowly out of the glasses, but H2O should diffuse quickly. Are the higher\nS and F contents of the orange glasses related to the source contents while their lower\nH2O contents are related to prolonged cooling? If there’s more volatile elements in the\nsource, could that help explain the prolonged cooling history. The authors should also\nmake sure they discuss the new orange glass in-gassing data from Su et al. (2025)\n(https://doi.org/10.1016/j.gca.2025.03.026) since it may support the findings of this\nstudy.\nFigure R3: Volatile concentration data for green glass beads relative to orange glass\nbeads.\nIn order to address the reviewer’s question on volatile contents in the green glass beads,\nwe’ve plotted the green glass bead data with those of the orange glass beads for\ncomparison (Fig. R3). The observation that green glasses have relatively high H2O but\nlower S and F contents than orange glasses is likely due to the combination of two\neffects: 1) the parental magma of green glasses was formed by higher degree of partial\nmelting, leading to lower initial volatile contents (because volatiles are incompatible);\n2) green glasses experienced lower degrees of volatile degassing, therefore better preserved\nH2O than orange glasses.\nFig. R3 further shows that volatile data for the green beads define trends that differ\nsignificantly from those of the orange glass beads, suggesting different controlling factors\nfor their degassing processes. For example, both the H2O-S and Cl-S trends for the green\nglass beads are flatter than those observed in the orange glass beads. But understanding\nthe degassing trend of green glass beads will likely require substantial effort, given the\nlack of olivine-hosted melt inclusions to define their initial volatile abundances. This is\nbeyond the scope of the current study. We plan to investigate these differences in future\nwork.\nWe’ve mentioned in the manuscript that the S-ingassing data from Su et al. (2025) can\nalso be explained by our three-stage model. In the revised version of the manuscript,\nwe’ve added additional preliminary modeling to demonstrate this point. We show that the\nS profiles reported by Su et al. (2025) can be formed in a few weeks on the lunar surface\nby solid-state diffusion.\nLine 439-440: The authors present a model that contradicts this statement in the\nsupplemental data. They show that the green glasses don’t fit the three-stage model well\nand likely cooled faster. I think its reasonable to say that it’s less likely that the green\nglasses experienced significant post flight degassing.\nApologies for the language that confused the reviewer. It was our point that the thermal\nhistory of the green glasses was very different.\nLine 446: “contain 10s of ppm H2O.” should be “contain 10 ppm H2O.”\nCorrected.\nLines 473-475: The authors should add a figure to the supplemental information showing\nhow the diffusivity D changes as a function of temperature, using an asymptotic cooling\nhistory. This would be helpful for someone trying to comprehend how the cooling rate is\nimpacting the diffusivity D for each element.\nWe’ve added a figure in the supplemental information on the change of temperature as a\nfunction of time, as well as the effect on diffusivities.\nLines 498-507: After reading through the manuscript and supplemental information, the\nevaporation coefficient and its relationship to dimensionless parameter L seems like a\nsignificant point of potential error for the models. The authors noted that the boundary\nconditions change depending on the stage of degassing in the orange glass cooling\nmodels. This change in boundary conditions should affect the evaporation coefficient and\nas a result the dimensionless parameter L. The authors need to find a better way to\ndemonstrate and explain why the dimensionless parameter L won’t cause the models to\nrequire unrealistically long cooling histories based on a currently unconstrained\nevaporation coefficient. Since the authors assume L value is constant, but diffusivity D is\nchanging, they should calculate how the evaporation coefficient υ_i would have to\nchange to make this assumption possible. This might be helpful when considering the\nimpact of this assumption on the models.\nAs explained in response to an earlier comment, we chose to use dimensionless parameter\nL instead of the evaporation coefficient υ_i because υ_i is expected to decrease with\ntemperature. In a previous paper (Ni and Shahar, 2023), I showed that the evaporation\ncoefficient for the congruent evaporation of a trace element from a molten sphere can be\nderived by relating it to the Hertz-Knudsen equation:\n𝛼 (1−𝑠)𝛾𝐾𝑀 1\n𝜐 =\n*+ 0*1)>\n𝜌𝑓(𝑂 )-// √𝑀 2𝜋𝑅𝑇\n,\nwhere 𝛼 is the dimensionless evaporation/condensation coefficient (0<𝛼 <1), 𝑠 is the\n*+ *+\nvapor saturation index, 𝛾 is the activity coefficient of the component in silicate liquid, 𝜌\nis density of the liquid, 𝑛 is the number of electron exchange for the evaporation reaction,\n𝐾 is the equilibrium constant for the evaporation reaction, 𝑀 and 𝑀 are the molecular\n0*1)\nmasses of the component and the melt, respectively, 𝑅 is the gas constant and 𝑇 is\ntemperature.\nIt is unknown whether the evaporative losses of H2O, F, Cl, and S are congruent.\nMoreover, due to the lack of constraints on numerous parameters in the above equation, it\nis not possible to calculate 𝜐 directly. However, one point is clear: 𝜐 is expected to\ndecrease as a function of temperature, owing to the decrease in the equilibrium constant\nand the additional temperature term highlighted in red.\nIn previous models, 𝜐 was assumed to be a constant throughout the cooling history. This\n!\nassumption almost always leads to a scenario of diffusion-limited degassing because 𝜐 is\n!\nartificially held constant while the diffusivity 𝐷 decreases exponentially with\n!\ntemperature. As a result, 𝐿 = 𝜐 𝑅/𝐷 increases with decreasing temperature. Our\n! ! !\napproach of fixing 𝐿 is still not ideal, because 𝐿 might also vary with temperature.\nHowever, it partially compensates for the temperature dependence of 𝜐 and is better than\n!\nthe previous approach.\nThe use of dimensionless parameter 𝐿 also allows us to evaluate the extent of degassing\n!\nloss under extreme-case scenarios. This is demonstrated by the sensitivity tests for the\norange glass beads in Figs. S2 and S3. Even when extremely high 𝐿 values (and thus\n!\nhigh evaporation coefficients) are used, the observed volatile depletion in the orange\nglass beads would still require cooling timescales on the order of thousands of seconds if\nvolatile loss occurred solely during free flight.\nIn order to address the reviewer’s questions, we’ve added sentences to the main text to\nfurther justify our approach of using 𝐿 instead of 𝜐 in our model.\n!\nFigure S1: Flip the x axis in panel b so it’s oriented in the same direction as the open end\nof the Ol-embayment. This will make it easier to connect panel a with the trends on panel\nb.\nAdjusted in the revised manuscript.\nTable S1: Why don’t the D0 values in this table match any of the studies referenced\nreported values? Are these averages of multiple of the reported values in those studies?\nIf so that needs to be clarified.\nThe D0 and Ea values are based on regression of literature data in anhydrous basalt.\nFor example, for H2O we did a regression of the diffusivities for low-Ti compositions from\nboth Newcombe et al. (2019) and Zhang et al. (2019). H2O diffusivity data from Zhang\net al. (2019) cover very high temperatures between 1480 ºC and 1600 ºC, while the\nexperiments in Newcombe et al. (2019) were conducted at 1350 ºC, closer to the eruption\ntemperature of orange glass. We obtained D0 and Ea for all four components in a similar\napproach to ensure consistency. In Fig. R3, we also plotted the fitted expressions from\noriginal papers in dashed curves for H2O and S. The differences are relatively minor.\nSometimes D0 appears to be quite different from the original publications, but it is\ncompensated by small changes in activation energy Ea. We have now added Fig. R3 to\nthe supplementary document to clarify on the diffusivity data we used and how D0 and\nEa are obtained.\nFigure R3. Diffusion data of H2O, F, Cl, and S in anhydrous basaltic melts used for\nconstraining D0 and Ea values in this study (Alletti et al., 2007; Freda et al., 2005;\nNewcombe et al., 2019; Zhang et al., 2019). Solid curves show linear regression of the\ndata with 95% confidence interval. Original expressions reported by Zhang et al. (2019)\nfor H2O and Freda et al. (2005) are plotted in dashed curves for comparison.\nReferences:\nAlletti, M., Baker, D.R., Freda, C., 2007. Halogen diffusion in a basaltic melt.\nGeochim. Cosmochim. Acta 71, 3570–3580. https://doi.org/10.1016/j.gca.2007.04.018\nBefus, K.S., Thompson, J.O., Allison, C.M., Ruefer, A.C., Manga, M., 2024. Rehydrated\nglass embayments record the cooling of a Yellowstone ignimbrite. Geology 52,\n507–511. https://doi.org/10.1130/G51905.1\nFreda, C., Baker, D.R., Scarlato, P., 2005. Sulfur diffusion in basaltic melts.\nGeochim. Cosmochim. Acta 69, 5061–5069. https://doi.org/10.1016/j.gca.2005.02.002\nHe, H., Hu, S., Gao, L., Li, R., Hao, J., Mitchell, R.N., Lu, K., Gao, Y., Li, L., Qiu, M.,\nZhou, Z., Yang, W., Cai, S., Chen, Y., Jia, L., Li, Q.-L., Hui, H., Lin, Y., Li, X.-\nH., Wu, F.-Y., 2025. Lunar dichotomy in surface water storage of impact glass\nbeads. Nat. Commun. 16, 4971. https://doi.org/10.1038/s41467-025-60388-y\nNewcombe, M.E., Beckett, J.R., Baker, M.B., Newman, S., Guan, Y., Eiler, J.M.,\nStolper, E.M., 2019. Effects of pH2O, pH2 and fO2 on the diffusion of H-bearing\nspecies in lunar basaltic liquid and an iron-free basaltic analog at 1 atm. Geochim.\nCosmochim. Acta 259, 316–343. https://doi.org/10.1016/j.gca.2019.05.033\nNi, P., Shahar, A., 2023. Copper isotope fractionation by diffusion in a basaltic melt.\nEarth Planet. Sci. Lett. 624, 118459. https://doi.org/10.1016/j.epsl.2023.118459\nNi, P., Zhang, Y., Guan, Y., 2017. Volatile loss during homogenization of lunar melt\ninclusions. Earth Planet. Sci. Lett. 478, 214–224.\nSu, X., Zhang, Y., Liu, Y., 2025. Sulfur outgassing and in-gassing in lunar orange glass\nbeads and implications for 33S “Anomaly” in the Moon. Geochim. Cosmochim.\nActa 397, 164–175. https://doi.org/10.1016/j.gca.2025.03.026\nSu, X., Zhang, Y., Liu, Y., Holder, R.M., 2023. Outgassing and in-gassing of Na, K and\nCu in lunar 74220 orange glass beads. Earth Planet. Sci. Lett. 602, 117924.\nhttps://doi.org/10.1016/j.epsl.2022.117924\nZhang, Li, Guo, X., Li, W.-C., Ding, J., Zhou, D., Zhang, Lingmin, Ni, H., 2019.\nReassessment of pre-eruptive water content of lunar volcanic glass based on new\ndata of water diffusivity. Earth Planet. Sci. Lett. 522, 40–47.\nhttps://doi.org/10.1016/j.epsl.2019.06.021"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The revised manuscript is excellent and addresses all of my suggestions. The new modeling of ingassing is a valuable addition. The code (provided on Github) will be a wonderful resource for the community. I fully support publication of the revised manuscript.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "The authors were very thorough in their response to my comments and the comments of the other two reviewers. I feel like a lot of my previous comments were related to confusion in the way the text read and the way the figures were referenced. The authors have done a great job of fixing this in the revised manuscript. The revised manuscript reads very well and addresses all my previous comments related to the models and calculation parameters. The authors did a good job clarifying the calculation parameters and I feel more confident about the use of the dimensionless parameter L in the calculations and other model assumptions. In conclusion, I believe the authors have adequately addressed all my concerns with the manuscript and the manuscript is publishable in its current state.\n\nMinor Comments:\nFigure 5: Fix the spacing between the lower two histograms so the y-axis numbers aren’t cut off."}, "author_response": "Point-by-point responses to reviewer’s comments for Manuscript NCOMMS-25-\n71651 (Acceptance)\nTitle: Prolonged cooling and degassing of Apollo 17 volcanic glasses on the lunar\nsurface\nAuthors: Peng Ni and Yan Zhan\nThe reviewers did not raise further comments besides a fix of format for Figure 5.The\nreviewer’s comments are in black font while our responses are in blue font.\nREVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nThe revised manuscript is excellent and addresses all of my suggestions. The new\nmodeling of ingassing is a valuable addition. The code (provided on Github) will be a\nwonderful resource for the community. I fully support publication of the revised\nmanuscript.\nReviewer #1 (Remarks on code availability):\nThe code is accessible and clearly documented. The tutorial notebooks provide an\nexcellent introduction to the model.\nReviewer #2 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review\nand to provide appropriate recognition for Early Career Researchers who co-review\nmanuscripts.\nReviewer #2 (Remarks on code availability):\nCode was available and able to be run.\nReviewer #3 (Remarks to the Author):\nThe authors were very thorough in their response to my comments and the comments of\nthe other two reviewers. I feel like a lot of my previous comments were related to\nconfusion in the way the text read and the way the figures were referenced. The authors\nhave done a great job of fixing this in the revised manuscript. The revised manuscript\nreads very well and addresses all my previous comments related to the models and\ncalculation parameters. The authors did a good job clarifying the calculation parameters\nand I feel more confident about the use of the dimensionless parameter L in the\ncalculations and other model assumptions. In conclusion, I believe the authors have\nadequately addressed all my concerns with the manuscript and the manuscript is\npublishable in its current state.\nMinor Comments:\nFigure 5: Fix the spacing between the lower two histograms so the y-axis numbers aren’t\ncut off.\nThanks for catching that. This has now been fixed for Fig. 5."}]

Decision letter
Review of manuscript NCOMMS-25-71651: “Prolonged cooling and degassing of Apollo
17 volcanic glasses on the lunar surface”
Summary:
This manuscript constrains a three-stage decompression and cooling history for Apollo 17
volcanic glasses: in the first stage of the model, degassing occurs in response to
decompression in the volcanic conduit; in the second stage, the glass beads and embayments
undergo diffusive and evaporative loss of volatiles during free flight; and in the third stage of the
model, the glasses undergo a final stage of volatile loss during slow cooling on the lunar
surface. Volatile concentration gradients in glass beads and melt embayments are best fit by
models in which the glasses undergo slow cooling and prolonged degassing on the lunar
surface for timescales on the order of years. This is a novel and interesting finding that
leverages previously collected volatiles data with a sophisticated new model.
The model is carefully constructed. The one-dimensional model for the embayment is
checked against a two-dimensional model and is found to agree within 15%. The model
uses appropriate parameters and constraints from the literature. In addition to the
thorough description of the model provided in the manuscript, the authors state that the
code will be provided on Github, which will provide the detail needed for the work to be
reproduced. The model results support the conclusions of the manuscript.
We support the publication of this manuscript in Nature Communications. We provide below
some suggestions for additional topics of discussion and minor corrections that could strengthen
the manuscript.
Major comments:
1. A linear relationship between H2O and pressure is assumed, but experimental evidence
has shown that H2O follows a square root relationship with pH2O (e.g., Newcombe et al.
2017). How might the assumption of a square root relationship affect the results?
2. Su et al. (2023) suggest that S, Cl and F (which are all enriched on the surfaces of
74220 orange glass beads) are expected to ‘ingas’ (i.e., diffuse into the beads) as they
travel through cool regions of the volcanic plume. The model presented here does not
consider ingassing. If ingassing has occurred, the initial stages of ingassing would
“flatten” the concentration gradients of H2O, Cl, S and F, which might cause a bias in the
modeled results towards models in which evaporation dominates over diffusion. Notably,
this process (referred to as low-temperature rehydration) has also been observed in
water concentration gradients across terrestrial melt embayments; e.g. Befus et al.
(2024). A discussion of the potential effects of ingassing on the H2O, Cl, S and F
gradients would strengthen the manuscript.
Befus, Kenneth S., et al. "Rehydrated glass embayments record the cooling of a Yellowstone
ignimbrite." Geology 52.7 (2024): 507-511.
3. If it is possible to use the embayment data to report constraints on the decompression
rate of the lunar magma (P /t ?), that would be of great interest.
0 end
4. At what stage of the decompression and cooling history is post-entrapment
crystallization occurring? Is it possible that vapor expansion in the conduit could have led
to some adiabatic cooling prior to eruption? E.g., La Spina et al. (2015), Newcombe et
al. (2020):
La Spina, G., M. Burton, and M. de'Michieli Vitturi. "Temperature evolution during magma ascent
in basaltic effusive eruptions: A numerical application to Stromboli volcano." Earth and Planetary
Science Letters 426 (2015): 89-100.
Newcombe, Megan E., et al. "Magma pressure-temperature-time paths during mafic explosive
eruptions." Frontiers in Earth Science 8 (2020): 531911.
Minor comments:
1. After figure 1, the figure numbers within the text appear to be inaccurate.
2. Figure 3: The panels and text are small. Could this be a 2x2 tiling with the legend placed
in the 4th panel?
3. Line 7: “thermal evolution of the mantle”. Please clarify that you are referring to the lunar
mantle.
4. Line 10: Please clarify “volatile-rich”. Do you mean more volatile-rich than the rest of the
lunar mantle? Note that scientists from different fields have different views of what
constitutes “volatile-rich”, so it would be helpful to provide a comparison.
5. Line 34: Please clarify what is meant by “uniform Ni concentrations that correlate with
Mg”. Do you mean uniform Ni within each pyroclastic deposit?
6. Line 36: Please emphasize the link between Ti content and glass colors earlier in the
text. Glass colors and glass Ti-contents are used interchangeably (e.g. line 35 and 45)
and this connection might not be obvious to a reader.
7. Line 39: “evidences” should be “evidence”.
8. Line 56: Perhaps the significance of these glass beads should be emphasized. What is
the interest in these samples compared to other lunar lithologies for “understanding lunar
mantle chemistry and Moon formation”? This is briefly touched on in the abstract, but
may warrant a few more sentences in the introduction.
“Pyroclastic volcanism, although volumetrically minor compared to mare volcanism, is
thought to originate from deeper, more primitive sources, and volatile-rich in
composition”
9. Line 73: “contains” is missing an s
10. Line 100: “volatiles content” shouldn’t be plural
11. On line 256, what is the difference between t and t ? Please clarify.
inf end
12. Line 289: I am unable to find a cooling timescale of 500 s in Saal et al. 2008. I see
modeled times of 120, 300, and 600 s.
13. Line 341: Cite the preliminary science report?
14. Line 410: “a high percentages” should be “a high percentage”
15. Line 441: “interpretating” should be “interpreting”
16. Line 519: Missing “of” between amount and time.