Main

The current composition of Jupiter is strongly coupled to the formation mechanisms of the planet. Its compositional make-up is diagnostic of both the location of Jupiter’s formation in the solar nebula and the processes that governed the planet’s accretion and subsequent evolution. Measurements of thermochemically active species, such as water and ammonia, provide crucial insight into the planet’s accretion rate and its proximity to relevant ice lines during formation1. Furthermore, the chemistry of Jupiter’s atmosphere is inextricably tied to its dynamics. Previous works used one-dimensional (1D) diffusion-kinetic modelling to constrain the thermochemistry of the planet while simplifying the parameterization of the atmospheric dynamics by using the vertical (or eddy) diffusion coefficient Kzz as a free parameter2,3,4,5. This approach captures the complexity of atmospheric thermochemistry but ignores most of the dynamical effects that the constituent species undergo in Jupiter’s atmosphere, such as convective inhibition6. Despite this limitation, such approaches have provided key insights into the nature of disequilibrium chemical species in Jupiter’s atmosphere, such as carbon monoxide (CO), germane (GeH4) and phosphine (PH3). Ground-based observations7,8 as well as those made with the Jovian infrared auroral mapper instrument onboard the Juno spacecraft9 have detected these chemical species, highlighting the role of disequilibrium thermochemistry in Jupiter’s atmosphere.

One of the primary objectives of the Juno mission is to ascertain Jupiter’s overall water content. This was largely motivated by the Galileo probe’s low water abundance measurement in the atmosphere at the 22 bar level10. Since that measurement, no true consensus has been reached regarding how representative the Galileo probe value is of the bulk atmospheric water content. Several subsequent measurements point to the water content being supersolar2,11, meaning that the value is greater than what would be expected for the protosolar nebula from which Jupiter formed, or subsolar12, implying the opposite. Whether or not the Jovian deep water abundance is sub- or supersolar is a crucial component of our understanding of the processes that have shaped Jupiter’s formation and evolution.

As the name implies, disequilibrium chemical species exist in a quasi-steady state. Ground-based telescopes and orbiting spacecraft have observed these species at altitudes in the atmosphere where the temperatures and pressures are not conducive for their thermochemical equilibrium. These gases are seen in much greater abundance than expected, which suggests that Jupiter’s vertical motions sufficiently replenish the ever-depleting gases through vertical mass transport2,13. Therefore, the observed abundances represent a balance between the chemical destruction of these species and the dynamical processes in the deep atmosphere that churn them aloft.

Atmospheric vertical transport depends on several parameters, including the deep water content, internal heat flux and assumed cloud structure. Sugiyama et al.14 showed that the conventional three-layer cloud structure is an overly simplistic picture of Jupiter’s troposphere, as it neglects the long-term effects of cloud microphysical processes and precipitation. Compositional boundaries play a critical role in inhibiting vertical motions due to molecular weight gradients15. Water plays the key role in modulating the thermal stratification at the cloud level because of its phase change at the lifting condensation level (LCL)16. Due to its coupling with carbon at higher temperatures and pressures, the subsequent abundance of CO is dependent on the microphysics of the LCL and the water hydrological cycle.

Thermochemically, CO has been extensively modelled due to its relevance in combustion chemistry and industrial uses17,18. As such, its chemical reaction networks are well known in oxygen-rich atmospheres but less so in hydrogen-dominated atmospheres. The abundance of carbon in Jupiter is traced by the dominant carriers of the element in its atmosphere. The main carrier of Jovian carbon is methane, CH4, which is well mixed in the envelope19. The second largest carrier of elemental carbon, however, is carbon monoxide. CO also functions as a sensitive parameter for atmospheric diffusive processes and has been used to constrain the vertical eddy diffusion coefficient Kzz, in the context of 1D chemical-diffusion modelling.

Recent 1D chemical-diffusion models have produced a variety of estimates for Jupiter’s deep water abundance. Wang et al.2 used a H/C/N/O reaction network to constrain the behaviour of CO sensitivity to the diffusive strength and water enrichment. They based their reaction network on the chemical model from Venot et al.20 (hereafter referred to as V12), which produced results different from those of several other CO–CH4 reaction networks. This has been attributed to the reaction from Hidaka et al.21, which has notable differences in hydrogen-rich atmospheres relative to laboratory measurements2,22. A more recent 1D chemical-diffusion model from Cavalié et al.12 used the Venot et al.23 reaction network (hereafter referred to as V20), from which they explicitly removed the reaction from Hidaka et al.21. Their findings suggest a subsolar water enrichment of ~0.3 times solar based on the CO abundance at the cloud levels, which is in stark contrast to the ~3 times solar enrichment determined by Li et al.11.

A fundamental limitation of the 1D chemical-diffusion models is that they are unable to simulate the effects of cloud microphysics. As observations of disequilibrium species are primarily limited to the tropospheric pressure levels, the behaviour of cloud condensates in relation to the system’s overall water content becomes relevant in ascertaining the planet’s deep water abundance3. Sugiyama et al.14 found that the presence of a moist convective layer substantially alters long-term cloud behaviour and structure due to the presence of dynamical boundaries at the water LCL. Compositional changes and layers associated with condensation function as effective barriers against vertical mixing. As 1D chemical-diffusion models are unable to resolve dynamic mixing, the interplay of chemical tracers and water at the LCL remain unexplored.

Hydrodynamic modelling of planetary atmospheres has greatly added to our understanding of Jupiter’s formation and the subsequent evolution of its gaseous envelope. It provides insight into the nature of moist convection, mass and momentum transport, and the overall energy cycle of Jupiter’s atmosphere. Results from the Juno mission have provided important observational constraints on the various dynamical processes that occur on the planet, such as the myriad of storms at its poles24, possibly deep jets seated at the lower latitudes25 and a wide array of atmospheric waves26. As the dynamics of Jupiter’s atmosphere are influenced by its gaseous constituents, neglecting the effects of molecular weight gradients limits the applicability of such ideal models to the complex behaviour of the planet’s troposphere and, thus, tells only a portion of the story.

Here we used the Simulating Non-hydrostatic Atmospheres on Planets (SNAP) code16 to model the local atmospheric behaviour of Jupiter down to 103 bars with temperatures reaching up to 1,200 K. The temperature and pressure of these regions are high enough to contain the quench levels—the regions in the atmosphere where the chemical destruction timescale is equal to the vertical-mixing timescale—of disequilibrium chemical species. The observed abundances are representative of the abundances at the quench level, and the values were said to be ‘frozen’ in ref. 8. As the quench level is dependent on the rate of chemical depletion for a given disequilibrium species along with the expected dynamical timescales, the choice of reaction network is important in constraining the pressure levels where the oxidized form of said species is more dominant. Our model focuses on the dynamical consequence of including water condensation at the cloud level, where subsequent changes in mixing strength can yield compositional trends across the LCL for CO, PH3 and GeH4.

Results

Our model set-up and experimental design are described in Methods. We tested both the V12 and V20 reaction networks (with the Hidaka et al. reactions removed21) using the chemical timescale approach. Here we discuss the main results from our hydrodynamic simulations.

Chemical timescale approach

The chemical timescale of CO has been attributed to the oxidation of CH4 (refs. 27,28,29). Although the rate of CH4 destruction may be sensitive to the assumed temperature versus pressure profile, we explored the effects of increased water enrichment on CO, PH3 and GeH4 mole fractions in the presence of strong condensation. We first tested the original V12 network coupled with water condensation. Figure 1 shows several important features that emerge from the inclusion of vapour and cloud microphysics. In Fig. 1a, the time-averaged CO mole fractions are shown as a function of pressure. As the diffusion coefficient is no longer explicitly set to capture all the dynamics, the emerging diffusive trends in the deep atmosphere are produced over time. The higher enrichment values, particularly \({E}_{{{\rm{H}}}_{2}{\rm{O}}}\ge 5\), show the typical ~1 part per 109 (ppb) value below the cloud domain (shaded region), where \({E}_{{{\rm{H}}}_{2}{\rm{O}}}\) is the water enrichment level as defined in Methods. Across the LCL, however, there is a substantial decrease in the CO abundance. The associated cloud layers and corresponding rainfall across the LCL are shown in Fig. 1b. As expected, cloud activity and the associated precipitation are substantially larger with a supersolar water enrichment. Very little cloud formation is seen for the subsolar cases. Importantly, CO mole fractions around 10 bars tend to increase by a factor of ~2 for every doubling of the deep water abundance.

Fig. 1: Trends across the cloud decks for CO mole fractions \(\langle \overline{X_\mathrm{CO}} \rangle\) for different water enrichment levels \({E}_{{{\rm{H}}}_{2}{\rm{O}}}\).
figure 1

a, Mean vertical CO mole fraction profiles shown as solid lines. The dotted lines signify the initial thermochemical equilibrium. The dashed dotted lines signify the final states. The grey region denotes the general extent of the water cloud decks, ranging from 4 to 10 bars. The overplotted triangle shows the ground-based observation of CO (ref. 50) with associated uncertainties from recent literature7. The colour scheme is the same as that in b. b, Associated water particle density (solid lines for cloud and dotted lines for rain). c, Temporally and horizontally averaged \(\langle \overline{{X}_{{\rm{CO}}}}\rangle\) values (squares) at different pressure levels (P) for various \({E}_{{{\rm{H}}}_{2}{\rm{O}}}\) values with their 1σ error bounds (vertical lines). Pink squares correspond to abundances deeper than the CO quench level. Green squares correspond to a range from 60 to 80 bars. Grey squares correspond to the LCL abundances. d, Difference between mean diffusive domain abundance and mean LCL abundance with the 1σ standard deviations.

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Figure 1c shows the specific \(\langle \overline{{X}_{{\rm{CO}}}}\rangle\) values in the quench region (pink), inertial region (green) and the LCL (grey) with their 1σ errors. The overbar and angle brackets denote temporal and horizontal averaging, respectively. We define the inertial region to be the domain below the water LCL but above the quench region. The deep atmospheric regions exhibit a power-law relation with increasing water enrichment. Across the LCL, the larger enrichment exhibits a downturn due to the intense condensation that occurs in the \({E}_{{{\rm{H}}}_{2}{\rm{O}}}=7\) simulation, which inhibits further CO deposition. However, there is still an increase in delivered CO, as seen in Fig. 1d, which shows the difference in CO mole fractions between deep regions (100 bars) and the LCL. It demonstrates a clear power-law relation between \(\Delta \langle \overline{{X}_{{\rm{CO}}}}\rangle\) and H2O, highlighting a steady rise in the difference between deep CO abundances and values that dominate the cloud decks. Notably, there is an upper limit on the CO abundance at the LCL due to the associated convective inhibition. That is, the CO abundance does not increase monotonically with the deep water abundance as indicated by the grey squares in Fig. 1c.

A distinct feature of the simulations with supersolar water content is their dynamic barrier. Figure 2 shows the mean static stability, or the square of the Brunt–Väisälä frequency (N2), of the atmosphere over the cloud decks. The corresponding mean XCO values are tabulated in Table 1. Increasing the water content results in increased inhibition of vertical convection due to increases in condensation. The associated water cloud layers can be inferred from Fig. 1b, where the corresponding LCL peaks increase in height with decreasing oxygen enrichment. This occurs because the increased stability can support denser clouds. Such dense, water-laden clouds are generally hosted in low-altitude higher-pressure regions, whereas wispy cloud formations with a low density of condensibles are typically in the high-altitude lower-pressure regions. The increase in static stability is linked to the enrichment of heavy metals30. Thus, in systems with supersolar oxygen enrichment, vertical motion is more inhibited near the LCL, as opposed to their subsolar counterparts. Furthermore, the increase in static stability is directly related to the vertical mean tracer gradient: high supersolar oxygen enrichment tends to result in a stronger CO vertical gradient across the cloud decks, whereas no such gradient is evident in low oxygen enrichment simulations. Such convective inhibition also affects PH3 and GeH4 abundances (Extended Data Fig. 1). As the vertical mean tracer flux is not linearly related to the vertical mean tracer gradient, the tropospheric abundance of a disequilibrium species in Jupiter’s atmosphere may not be representative of its quench-level abundance, which is a fundamental assumption of 1D models but not true in more realistic hydrodynamic modelling.

Fig. 2: Mean static stability or square of the Brunt–Väisälä frequency (N2, [1/s2]) of the atmosphere across the LCL for different \({\boldsymbol{E}}_{{{\bf{H}}}_{\bf{2}}{\bf{O}}}\) values, signified by the colours.
figure 2

The solid lines signify the spatially and temporally averaged profiles for each case. Higher water enrichment leads to substantially more condensation near the LCL, resulting in a stronger inhibition of convection. The peaks of the stability occur at higher pressures with increased water content due to the lower LCL. The shaded regions signify the 1σ standard deviation for each simulation.

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Table 1 Mean XCO values for different atmospheric levels and water enrichments in units of ppb with 1σ uncertainties
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Effect of CO timescale on the subsolar case

Recent updates to 1D thermochemical modelling of Jupiter’s atmosphere using H/C/N/O chemical networks have led to notably different water enrichment estimates for Jupiter’s atmosphere. Although coupling a full reaction network to our cloud-resolving model is not yet possible, we studied the bulk characteristics of slowed CH4 destruction with a wide-ranging timescale, which approximates the removal of the Hidaka et al. reactions21. We tested the \({E}_{{{\rm{H}}}_{2}{\rm{O}}}=0.3\) case with varying timescales by using Wang’s functional form of the CO interconversion time from V1229. We modified this temporal function with a scaling factor to approximate the gross effect of accelerated or decelerated CH4 destruction.

The decelerated destruction of CH4 in Jupiter’s atmosphere would lead to a noticeable variation in the quench pressure estimate for CO, as identified by Venot et al.23. A slower CH4 to CO conversion timescale leads to a higher tropospheric CO abundance, as it is representative of deeper atmospheric regions than previously expected (Fig. 3). Note that the decelerated timescale increases the CO abundance at the LCL, in agreement with Cavalié et al.12.

Fig. 3: CO mole fraction profiles calculated using the hydrodynamic model with various timescale scaling factors for the ×0.3 water enrichment case.
figure 3

The different colours signify the corresponding scaling factors. The variation in the profile due to timescale changes is substantial. However, the nominal value estimated by Cavalié et al.12 is unlikely to fit the observed CO abundance near the LCL.

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To better constrain the overall modification of the timescale from the V12 network, we used a simplified 1D model (Methods) to examine the space of Kzz and the chemical timescale. The 1D results show that a scaling factor for the timescale of about 500 is sufficient to reach the minimum bounds of uncertainty in the CO measurement using \({E}_{{{\rm{H}}}_{2}{\rm{O}}}=0.3\) (Supplementary Fig. 1). As the agreement is also dependent on the assumed mixing in the deeper atmosphere, we used the conventional value of 1 × 108 cm2 s−1 to remain consistent with other 1D models. By applying this scaling factor for \({E}_{{{\rm{H}}}_{2}{\rm{O}}}=2.5\) in our hydrodynamic model, we attained CO mole fractions close to the measured value of 1 ppb (Table 1). The ×0.3 case falls short of the measured CO value due to the decreased mixing. We show the full evolution of the horizontally averaged CO mole fractions for both cases in Fig. 4. Our results demonstrate that even though \({E}_{{{\rm{H}}}_{2}{\rm{O}}}=0.3\) results in 〈XCO〉 ≈ 1 ppb in the 1D formulation, it fails to do so in a hydrodynamic model. Our simulations suggest that mixing simulated by hydrodynamics is weaker than what has been assumed in 1D models, possibly due to the inhibition of moist convection in hydrogen atmospheres. When the updated timescale is implemented within the hydrodynamic framework, \({E}_{{{\rm{H}}}_{2}{\rm{O}}}=2.5\) is needed to fit the observational bounds of tropospheric CO, which corroborates the value inferred from Li et al.31.

Fig. 4: Comparison of sub- and supersolar oxygen enrichment cases using the updated CO/CH4 interconversion timescale.
figure 4

Left: time evolution of the horizontally averaged CO mole fraction for ×0.3 solar oxygen enrichment with the updated timescale from our 1D model, assuming a deep eddy mixing of 1 × 108 cm2 s−1. Right: same as left but for ×2.5 solar enrichment. The supersolar enrichment reaches the measured value of the CO mole fraction (marked by the grey triangles) using the modified interconversion timescale for CO/CH4. The dashed lines show the mean value in time for each case.

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Further constraints on the deep water abundance

Our simulations with different chemical timescales do not support \({E}_{{{\rm{H}}}_{2}{\rm{O}}}=0.3\). Furthermore, we highlight the possibility of an observable correlation that is exclusive to supersolar oxygen enrichment when the CH4 destruction rate is high, as favoured by the V12 network. In Fig. 5, we highlight the mechanism that delivers CO across the water cloud decks despite the strongly inhibited vertical mixing. Panels associated with supersolar oxygen enrichment show examples of moist convective events that occur in our simulations at various times. Moist convective events, indicated by the overplotted relative humidity contours, occur in regions where CO is locally enhanced relative to the background. Importantly, this occurs only for simulations with high water enrichment levels. No such correlation between local CO enhancement and moist convection exists for the subsolar enrichment cases, although moist convection occurs in the subsolar cases as well.

Fig. 5: Logarithmic CO mole fractions for different oxygen enrichment levels.
figure 5

a–g, Oxygen enrichment levels are 10 (a), 7 (b), 5 (c), 2.5 (d), 1.25 (e), 0.6 (f) and 0.3 (g). White contours highlight the relative humidity of water to show where moist convective events occur. A relative humidity of 1.0 signifies saturation. For cases above solar enrichment, the humidity contours are limited to the range 0.8–1.0, whereas for subsolar cases they are limited to 0.75–1.0. For supersolar oxygen enrichment, saturation occurs where CO is locally enhanced due to updrafts from moist convective cells. No such saturation and underlying CO enhancement is seen in the subsolar cases.

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This is due to the occurrence of a large molecular weight contrast in simulations with supersolar oxygen enrichment. In such cases, the dynamical barrier imposed on the vertical mixing due to the phase change of water is much larger. However, even when vertical mixing is strongly inhibited, occasional strong moist convective events overcome the barrier and burst through. Such events are concomitant with higher particle densities in water clouds and subsequent rainfall in the simulations. Once the barrier breaks locally, CO mixes across the LCL much more efficiently. For subsolar oxygen enrichment, the vertical mixing faces a weaker barrier across the LCL due to the lack of dense water clouds, allowing for a more homogeneous mixing of CO across the domain. Thus, on timescales associated with moist convective storm activity, systems with supersolar oxygen enrichment should exhibit local enhancements of CO whereas no such correlation should hold in subsolar cases.

Specific regions in Jupiter’s atmosphere exhibit stronger moist convective activity than others32. Lightning is generally associated with such storm formation, although shallow lightning has also been observed on the planet33. If, however, future observations show a correlation between CO and moist convection, as possibly indicated by lightning, then only supersolar oxygen enrichment would be possible, suggesting a large heliocentric distance for Jupiter’s formation.

The PH3 and GeH4 steady-state abundances are provided in Extended Data Fig. 1. Both species exhibit very similar values for the low water enrichment cases across different pressure levels. However, beyond about ×5 solar oxygen, convective inhibition prevents the gases from reaching ~4.5 bar pressure regimes, suggesting an upper limit to the Jovian water content (see Methods for further discussion).

Discussion

Our work resolves the apparent discrepancy between the inference of oxygen abundance on Jupiter based on the thermochemical modelling of disequilibrium species using Juno observations. We demonstrate that any inference on the oxygen abundance from disequilibrium chemistry has to be examined under a hydrodynamic model that can calculate transport and mixing. Our results show that hydrodynamics can substantially affect the short-term behaviour of CO across the water clouds and that increased condensation in supersolar cases leads to a notable decrease in CO abundance across the LCL. This is due to increased inhibition of vertical mixing as the change of mean molecular weight provides a dynamical barrier to the vertical advective motions. As such, the CO mass flux across the water clouds tends to decrease for supersolar cases, in general, although ascertaining a steady-state representative Kzz profile from a mesoscale model such as ours is difficult34.

This work suggests the recent estimate of ×0.3 solar12 for the Jovian deep water abundance using CO might be too low. However, using the updated chemical timescale in our hydrodynamic model, the \({E}_{{{\rm{H}}}_{2}{\rm{O}}}=2.5\) case can satisfy the uncertainty bounds of the tropospheric CO mole fraction, although PH3 and GeH4 demonstrate less sensitivity to the low oxygen cases. Also note the emergence of observable trends that would be exclusive to high water enrichment cases, which highlights the interplay of chemistry and dynamic mixing in Jupiter’s atmosphere. Due to increased inhibition of convective activity near the water cloud for systems with large water content, the vertical mixing of CO is decelerated. In such cases, the primary mode of transport for CO across the LCL is strong and stochastic moist convective events, which we show in the Hovmöller diagrams in Extended Data Fig. 2. As moist convective activity exhibits some degree of latitudinal preference and is strongly related to lightning strikes, as observed by several of Juno’s instruments32,35, we conjecture that if Jupiter hosts a supersolar water abundance in the deep atmosphere, there must be correlations between such regions and locally enhanced CO. Such behaviour would be akin to that of an entrainment zone, which is a typical feature of convective boundary layers.

Our result highlights a correlation between CO and moist convection. If future studies observe such a trend, that would limit the parameter space of Jovian deep water abundance to supersolar values only. Even with a deep, statically stable radiation layer36, the estimate of the oxygen enrichment would only increase, as demonstrated by Cavalié et al.12. This further corroborates our conclusion that the deep O/H ratio must be supersolar, as our current estimate of ×2.5 solar enrichment for oxygen was without a radiation layer. Our results for PH3 and GeH4 further suggest an upper limit to the oxygen abundance, as enrichment ≥5 times solar would require lower mixing ratios for these species than are observed, constraining the Jovian deep water abundance to 2.5–5.0 times solar, which is consistent with the most recent estimates of the deep water abundance from Li et al.31 derived for Jupiter’s equatorial region. Such supersolar enrichment would favour the formation of Jupiter through the accretion of clathrate-rich material, indicative of formation near the H2O ice line37,38.

Methods

Full chemical reaction networks cannot be included in hydrodynamic models due to their stiffness, which means that some of the chemistry occurs extremely fast whereas the rest occurs slowly39. A robust approach that circumvents this problem is that of linear chemical relaxation time40, which has the form:

$$\frac{\mathrm{d}{q}_{i}(T,P)}{\mathrm{d}t}=-\frac{{q}_{i}(T,P)-{q}_{i,\mathrm{eq.}}}{{\tau }_{i}},$$
(1)

where \(\mathrm{d}/\mathrm{d}t=\partial /\partial t+(\mathbf{v}\cdot \nabla )\). Here, qi(T, P) is the mass fraction of species i as a function of temperature and pressure, qi,eq. is its equilibrium value, τi is the associated chemical disequilibrium timescale and \(\mathbf{v}=({v}_{x},{v}_{y})\) is the velocity vector. The linear approach is well established for certain species and has been shown to produce results consistent with full chemical-kinetic modelling4,39. Although we have largely focused on CO, we also provide results from PH3 and GeH4 thermochemistry and apply the chemical relaxation scheme in the context of cloud microphysical processes.

The SNAP code models the atmosphere by solving the Euler equations using the finite-volume method41. The complete details of the dynamical solver are outlined in ref. 16, along with dynamical benchmarks. We describe tests of several numerical parameters relevant to our work in the Supplementary Information. Here we discuss only the modifications to the primary equations and how they are integrated into the dynamic core of SNAP. The general tracer transport equation is

$$\rho \frac{\mathrm{d}{q}_{i}}{\mathrm{d}t}=\frac{\partial }{\partial t}(\;\rho {q}_{i})+\nabla \cdot ({q}_{i}\rho \mathbf{v})={S}_{i},$$
(2)

where ρ is the total density and v is the velocity field. The forcing or source term, Si, is given using the linear chemical relaxation time approach in equation (1). For the analysis, everything is converted to mole fractions to facilitate comparison with previous work.

The computational domain is two-dimensional, spanning 1,200 km horizontally and 500 km vertically, with a spatial resolution of about 4 km in both directions. We used a doubly periodic horizontal boundary condition. For the vertical boundaries, a spatially homogeneous and constant cooling was applied at the top. The cooling rate was maintained at −10 W m−2. Cloud microphysical processes occur over short timescales, and thus, the integration period was kept short, provided that the tracer kinetic energy stabilized over that duration. As there was no bottom heating, this set-up captured the real evolution of the short-term dynamics better, as the initial heat reservoir cooled down freely without an artificial heat source applied at the lower boundary. Although this means that the model never reached a true steady state, it evolved to sufficient tracer kinetic energy stabilization (Supplementary Fig. 3), and it is appropriate for integration over hundreds of days. Supplementary Fig. 5 compares the effects of adding bottom heating of the same magnitudes, demonstrating that there was no dynamical difference over the timescale of interest.

Constraining the parameter space

One-dimensional models are typically computed with vast chemical networks due to the assumed simplicity of the dynamics. Although we used a dynamic model with simplified thermochemistry, we limited the overall parameter space by first exploring it in a simplified 1D chemical-diffusion framework. In the same way that the thermochemistry is handled in the primary simulation suite, the chemical terms were simplified using a relaxation term with a timescale given by τCO (‘Experimental design’).

The 1D chemical-diffusion equation can be written in terms of the CO mole fraction X as

$$\frac{\partial X}{\partial t}={K}_{zz}\frac{{\partial }^{2}X}{\partial {z}^{2}}-\frac{X-{X}_\mathrm{eq.}}{{\tau }_{{\rm{CO}}}}.$$
(3)

Casting equation (3) into the fully implicit form, we get:

$$\frac{{X}_{j}^{\;n+1}-{X}_{j}^{\;n}}{\Delta t}={K}_{zz}\frac{{X}_{j+1}^{\;n+1}-2{X}_{j}^{\;n+1}+{X}_{j-1}^{\;n+1}}{\Delta {z}^{2}}-\frac{{X}_{j}^{\;n+1}-{X}_{j,\mathrm{eq.}}}{{\tau }_{{\rm{CO}},\;j}},$$
(4)

where n and j are the temporal and spatial indices, respectively. Using the fully implicit formalism allows the 1D models to remain unconditionally stable for any choice of Δt. We can rearrange the above equation as follows:

$$-\frac{{X}_{j}^{\;n}}{\Delta t}-\frac{{X}_{j,\mathrm{eq.}}^{\;n}}{{\tau }_{{\rm{CO}},\;j}}=\frac{{K}_{zz}}{\Delta {z}^{2}}{X}_{j-1}^{\;n+1}-\left[\frac{1}{\Delta t}+\frac{1}{{\tau }_{{\rm{CO}},\;j}}+\frac{2{K}_{zz}}{\Delta {z}^{2}}\right]{X}_{j}^{\;n+1}+\frac{{K}_{zz}}{\Delta {z}^{2}}{X}_{j+1}^{\;n+1}.$$
(5)

The implicit formalism results in a simple tridiagonal matrix in \({\mathbf{X}}^{n+1}\) where \({\mathbf{X}}^{n}=\langle {X}_{0}^{\;n},{X}_{1}^{\;n},\ldots ,{X}_{j-1}^{\;n},{X}_{j}^{\;n}\rangle\). The coefficients on the left-hand side of equation (5) form a matrix that can be inverted once the appropriate boundary conditions are provided. As in ref. 29, we used a constant mole fraction for CO at the bottom and a zero-flux boundary condition for the top of the atmosphere. This allowed us to determine the appropriate scaling for τCO that would approximate the updated CO/CH4 interconversion time without needing a full chemical sensitivity analysis of the newer network. Although this is a simplification, it yielded important constraints that were relevant for mesoscale, cloud-resolving and general circulation models.

We approximated the updated chemical timescale using various scaling factors for τCO. This approach was motivated by the recipe outlined in ref. 40, where changes to the chemical network can be approximated by variations to the mixing length scale and timescale. Simultaneously, we varied the turbulent eddy mixing for the atmosphere, Kzz, and let each simulation reach a steady state. We used the ×0.3 solar enrichment case in the 1D framework to determine what scaling factor was needed to get within 25% of the observed CO value, assuming a deep Kzz = 1 × 108 cm2 s−1. We show the contours of the CO mole fractions at the top of the atmosphere in Supplementary Fig. 1.

Experimental design

The primary focus of this work was to study the effects of water condensation near the cloud decks on the modelled CO abundance. Thus, the parameter space was largely a function of the water enrichment level, which was explicitly set by the mass mixing ratios for each simulation. We defined the water enrichment level relative to solar as \({E}_{{{\rm{H}}}_{2}{\rm{O}}}={q}_{{{\rm{H}}}_{2}{\rm{O}},{\rm{planet}}}/{q}_{{{\rm{H}}}_{2}{\rm{O}},{\rm{solar}}}\), where \({q}_{{{\rm{H}}}_{2}{\rm{O}},{\rm{planet}}}\) is the planetary water mixing ratio and \({q}_{{{\rm{H}}}_{2}{\rm{O}},{\rm{solar}}}=9.61\times 1{0}^{-4}\) (ref. 42). Water was varied from subsolar to supersolar values between 0.3 and 10 times enrichment relative to solar.

The chemical timescale uses the functional form determined by Wang et al.29:

$${\tau }_{{\rm{CO}}}\approx 5\times 1{0}^{-6}\exp (2.8\times 1{0}^{4}/T\;)\,{P}^{-1.29}\,{\rm{s}},$$
(6)

where P is given in bars. This form uses the timescale from the V12 network and adequately captures the behaviour of CO without needing the full capabilities of its thermochemical reaction network. It has been shown to produce results consistent with Wang’s 1D approach29. Recent kinetic updates have modified the H/C/N/O reaction network by excluding Hidaka’s methanol reaction21. Several studies have shown that the Hidaka et al.21 reaction overestimates the destruction rate of CH4 into CO (refs. 4,12,23). However, the resulting variations in CO abundance are strongly dependent on the assumed temperature and pressure profiles, as demonstrated by case studies of several exoplanets4,23.

To quantify the expected effect on CO abundance at the cloud level, we tested one of our simulations \(({E}_{{{\rm{H}}}_{2}{\rm{O}}}=0.3)\) with (0.1, 1.0, 10.0, 500.0) × τCO. Although this cannot capture the full complexity of the updated reaction networks, it was sufficient to highlight the temporal effect on the expected quenching of CO, and its behaviour near the LCL in the context of microphysical processes due to water condensation. In contrast to ref. 3, which appropriately captured the effect of latent heat release due to water condensation, our model captures the dynamical effect of water on the wind field, which subsequently affects the tracer advection.

We emphasize that translating updates to the chemical destruction rates of CH4 in terms of CO–CH4 interconversion times is not a linear process. Although our approach captures the general rate change of CH4 oxidation due to kinetic updates, whether or not the full chemical timescale can be updated with the same scaling factor remains to be seen. Despite these limitations, our work highlights specific trends that can be used to estimate the deep atmospheric water content.

CO equilibrium

The overall reaction that governs the behaviour of CO equilibration is

$${\rm{CO}}+3{{\rm{H}}}_{2}\leftrightarrow {{\rm{CH}}}_{4}+{{\rm{H}}}_{2}{\rm{O}}.$$
(7)

Thus, the equilibrium value for CO can be determined as

$${X}_{{\rm{CO}},{\rm{eq.}}}=\frac{{X}_{{{\rm{CH}}}_{4}}{X}_{{{\rm{H}}}_{2}{\rm{O}}}{K}_{{\rm{CO}},{\rm{eq.}}}}{{X}_{{{\rm{H}}}_{2}}^{3}{P}^{2}},$$
(8)

where X denotes volumetric mole fractions and P is the atmospheric pressure in bars. The equilibrium constant KCO,eq. can be written as

$${K}_{{\rm{CO}},{\rm{eq.}}}=\exp \left[-\frac{{\Delta }_\mathrm{f}{G}_{{\rm{CO}}}-{\Delta }_\mathrm{f}{G}_{{{\rm{CH}}}_{4}}-{\Delta }_\mathrm{f}{G}_{{{\rm{H}}}_{2}{\rm{O}}}}{RT}\right],$$
(9)

where ΔfGi is the Gibbs free energy of formation for the species i and R = 8.314 J mol−1 K−1 is the universal gas constant. We obtained the Gibbs functions from the JANAF database as NASA polynomials43. The model calculates the local CO equilibrium mole fraction using the water vapour content of a grid cell and local thermodynamic values. The choice of water enrichment \({E}_{{{\rm{H}}}_{2}{\rm{O}}}\) sets the appropriate CO equilibrium as the simulation evolves.

As CH4 is well mixed, we set \({X}_{{{\rm{CH}}}_{4}}=2.37\times 1{0}^{-4}\) (ref. 44), which was kept constant. We used the conventional hydrogen value to set the H2 mole fraction, \({X}_{{{\rm{H}}}_{2}}=0.864\) (ref. 45). In this framework, the forcing of the chemical tracer is realistic, as all local changes are taken into consideration. Thus, the primary differences that emerged in our simulations as we varied the water vapour content were driven by phase change behaviour near the cloud decks. Subsequent dynamical effects were then reflected in the behaviour of CO abundance across the LCL, which conventional 1D chemical-kinetic models are unable to explore.

PH3 and GeH4 thermochemistry

For PH3, we assumed the following net reaction:

$${{\rm{PH}}}_{3}+4{{\rm{H}}}_{2}{\rm{O}}\leftrightarrow {{\rm{H}}}_{3}{{\rm{PO}}}_{4}+4{{\rm{H}}}_{2}.$$
(10)

This assumes that the dominant form of oxidized phosphorus in Jupiter’s atmosphere is H3PO4, which has been shown to be energetically more favourable than the alternative, P4O6 (ref. 2). Moreover, the thermodynamics of H3PO4 are better constrained than that of P4O6, as there are significant variations in the enthalpy data for the latter46. Assuming that PH3 and H3PO4 are the dominant phosphorus-bearing species in the atmosphere, the equilibrium mole fraction for PH3 can be simplified to

$${X}_{{{\rm{PH}}}_{3},{\rm{eq.}}}=\frac{{X}_{{\rm{P}}}{X}_{{{\rm{H}}}_{2}}^{4}}{{X}_{{{\rm{H}}}_{2}}^{4}+{K}_{{{\rm{PH}}}_{3},{\rm{eq.}}}{X}_{{{\rm{H}}}_{2}{\rm{O}}}^{4}},$$
(11)

where \({K}_{{{\rm{PH}}}_{3},{\rm{eq.}}}\) is the equilibrium constant for the phosphine net reaction and is defined in a similar manner as equation (9). XP is the Jovian phosphorus content, which was set to \(7\times 1{0}^{-7}\,{X}_{{{\rm{H}}}_{2}}\). Using the rate-limiting step identified by Wang et al.2, the chemical timescale can be written as

$${\tau }_{{{\rm{PH}}}_{3}}=\frac{{P}^{3/2}{X}_{{{\rm{H}}}_{2}}^{7/2}}{{k}_{{{\rm{PH}}}_{3}}{K}_{{{\rm{PH}}}_{3},{\rm{eq.}}}n{X}_{{{\rm{H}}}_{2}{\rm{O}}}^{3}},$$
(12)

where n is the number density of the atmosphere. \({k}_{{{\rm{PH}}}_{3}}\) is defined by the rate-limiting step of the full phosphorus reaction network and was set to \(2.35\times 1{0}^{-12}\exp (-1.067\times 1{0}^{4}/T)\,{{\rm{cm}}}^{3}\,{\rm{s}}^{-1}\).

Compared to CO and PH3, the chemical kinetics of GeH4 are highly uncertain. No reaction network is known for the species and its kinetics are largely approximated using the behaviour of silane, SiH4. The primary assumption is that the sulfurization of germane to GeS is similar in nature to the oxidation of silane to SiO. The net reaction that we used for GeH4 in our model is

$${{\rm{GeH}}}_{4}+{{\rm{H}}}_{2}{\rm{S}}\leftrightarrow {\rm{GeS}}+3{{\rm{H}}}_{2},$$
(13)

which represents the principal thermochemical destruction pathway for germane gas27. As can be seen from the net reaction for GeH4, there is no explicit dependence on the water mole fraction. We used the chemical equilibrium estimated by Fegley and Lodders47 for Jupiter’s atmosphere and scaled it to the updated values of Jupiter’s germanium enrichment as employed by Wang et al.2, such that \({X}_{{\rm{Ge}}}=3.93\times 1{0}^{-8}\,{X}_{{{\rm{H}}}_{2}}\). As the reaction network for this gas is unknown, the chemical interconversion timescale for GeH4 was approximated by the rate-limiting step from the reaction network of SiH4. The chemical timescale can be written as

$${\tau }_{{{\rm{GeH}}}_{4}}=\frac{P{X}_{{{\rm{H}}}_{2}}}{{k}_{{{\rm{SiH}}}_{2}}{K}_{{{\rm{GeH}}}_{2},{\rm{eq.}}}n{X}_{{{\rm{H}}}_{2}{\rm{S}}}},$$
(14)

where \({X}_{{{\rm{H}}}_{2}{\rm{S}}}=8.9\times 1{0}^{-5}\,{X}_{{{\rm{H}}}_{2}}\) (ref. 44). \({k}_{{{\rm{SiH}}}_{2}}\) is the rate coefficient from the silane reaction network and was set to \(3.57\times 1{0}^{-14}{T}^{\,0.7}\exp (-\text{4,956}/T\;)\,{{\rm{cm}}}^{3}\,{\rm{s}}^{-1}\). The equilibrium constant \({K}_{{{\rm{GeH}}}_{2},{\rm{eq.}}}\) is a state function that assumes GeH4 = GeH2 + H2 (ref. 47). Obtaining the correct thermodynamic properties for this reaction requires a calibrated enthalpy of formation for GeH2. Although there are substantial variations of this value in the literature, we found that its impact on the chemical timescale of GeH4 was negligible. As such, we set it to 238 kJ mol−1 (refs. 48,49).

Extended Data Fig. 1 shows that both species lose sensitivity to the Jovian deep water abundance if the enrichment is too low. For an enrichment between 0.3 and 2.5 times solar, both gases exhibited little variation between the 1σ level for both the steady-state mean mixing ratios and the final mean mixing ratios. However, there was an important trend in the mean vertical tracer gradient as the enrichment was increased. The convective inhibition continued to increase due to more condensation at the LCL, and the same behaviour as was seen for CO was observed for these disequilibrium gases as well, leading to a larger variation in the mixing ratios as a function of pressure.

Recent observations of PH3 and GeH4 in the 4.5–6 bar region9 suggest values reasonably close to what our models produce. Given that these observations depend on the assumed cloud structure8 and that there are flux contributions from deeper pressure levels, our results from the 6–10 bar pressure levels are in agreement with data from the Jovian infrared auroral mapper instrument and ground-based observations7. As the PH3 and GeH4 mixing ratios are insensitive to the Jovian deep water abundance below ×5 solar enrichment, we used the CO results to constrain the water enrichment to ≥2.5 times solar. We found that the mean GeH4 mixing ratio was lower than the observed value beyond the 1σ range for an oxygen enrichment of ×7 solar and above. Thus, an oxygen enrichment greater than ×5.0 solar would require lower mean mixing ratios for PH3 and GeH4 than what are observed, suggesting a nominal range of 2.5–5.0 times solar enrichment for the Jovian deep water abundance.