Modelling Non-Condensing Compositional Convection for Applications to Super-Earth and Sub-Neptune Atmospheres

TL;DR

The paper addresses how vertical compositional gradients modify atmospheric convection in exoplanetary contexts, focusing on non-condensing tracers. It combines 3D convection-resolving CM1 simulations with stability analyses (Ledoux criterion, virtual adiabat, CAPE) to characterize the final state after mixing and to develop a practical convective adjustment scheme. Key findings include the frequent formation of compositional staircases and a final state that is marginally stable per Ledoux criteria and close to a virtual adiabat, with the extent of mixing highly sensitive to the scale of initial perturbations. The resulting CAPE-based adjustment framework enables more physically grounded representation of non-condensing compositional convection in GCMs, with plans to incorporate condensation and radiative forcing in future work to better connect to observable exoplanet atmospheres.

Abstract

Compositional convection is atmospheric mixing driven by density variations caused by compositional gradients. Previous studies have suggested that compositional gradients of atmospheric trace species within planetary atmospheres can impact convection and the final atmospheric temperature profile. In this work, we employ 3D convection resolving simulations using Cloud Model 1 (CM1) to gain a fundamental understanding of how compositional variation influences convection and the final atmospheric state of exoplanet atmospheres. We perform 3D initial value problem simulations of non-condensing compositional convection for Earth-Air, $\rm H_2$, and $\rm CO_2$ atmospheres. Conventionally, atmospheric convection is assumed to mix the atmosphere to a final, marginally stable state defined by a unique temperature profile. However, when there is compositional variation within an atmosphere, a continuous family of stable end states is possible, differing in the final state composition profile. Our CM1 simulations are used to determine which of the family of possible compositional end states is selected. Leveraging the results from our CM1 simulations, we develop a dry convective adjustment scheme for use in General Circulation Models (GCMs). This scheme relies on an energy analysis to determine the final adjusted atmospheric state. Our convection scheme produces results that agree with our CM1 simulations and can easily be implemented in GCMs to improve modelling of compositional convection in exoplanet atmospheres.

Figures (13)

• Figure 1: Buoyancy for finite adiabatic displacements from pressure $p_0$ in an ambient profile. The atmosphere is a mixture of $\mathrm{H_2}$ with water vapour, with water vapor profile $q_v(p) = 10 (p/p_0)$, where $p_0$ is the surface pressure. (a) The ambient profile is the virtual adiabat passing through $\rm p= 5\cdot 10^4$ Pa and T = 300 K, and the parcel is lifted from $\rm p_0=10^5$ Pa. (b) The ambient profile is the Ledoux-stable profile $\rm T_{v,ad}(p,\frac{1}{2}p_0)$, with $T_{v,ad} = 300 \; \mathrm{K}$ at $\rm p = \frac{1}{2}p_0$, and the parcel is lifted from the various $p_0$ given in the legend.
• Figure 2: 2D plots showing vertical cross sections of mass mixing ratio taken in the middle of the y-domain for CM1 Case 1 and Case 4 which have an Earth Air Atmosphere. The top panel shows the $\rm q_v$ cross sections for Case 1, isothermal Earth air atmosphere, while the bottom panel shows the $\rm q_v$ cross section for Case 4, Earth-Air atmosphere with initial temperature and mass mixing ratio step profile. Within each panel, the top row shows the results when using only initial random perturbations to trigger convection, while the bottom row shows the results when using the initial perturbation given by Eqn. \ref{['eq:3d_wave']} in conjunction with random perturbations. The mass mixing ratio is shown for seven different time steps during the CM1 simulation. The color bar indicates the value of $\rm q_v$. The plots show the formation, growth, and mixing of convective plumes. Eventually, the atmosphere reaches a marginally stable state where discrete layers of varying composition form. The observed "compositional staircases" are analogous to the compositional staircases presented in compositional convection modelling for stellar atmospheres Garaud2015.
• Figure 3: Same as Fig. \ref{['fig:air_2d_mass_mixing_ratio']} but for the $\rm H_2$ atmosphere test cases. The top panel shows 2D vertical cross sections of the mass mixing ratio taken in the middle of the y-domain for Case 2, while the bottom panel shows the results for Case 5.
• Figure 4: Same as Fig. \ref{['fig:air_2d_mass_mixing_ratio']} but for the $\rm CO_2$ atmosphere test cases. The top panel shows 2D vertical cross sections of the mass mixing ratio taken in the middle of the y-domain for Case 3, while the bottom panel shows the results for Case 6. Note that in Case 6, $\rm q_v,s = 0.3$ kg/kg, and thus the color bar for Case 6 is not equivalent to the color bar shown for Case 3.
• Figure 5: Vertical profiles from left to right of $\rm \theta (p)$, $\rm \theta_v(p)$, $\rm T(p)$, $\rm T_v(p)$, and $\rm q_v(p)$ with respect to pressure for Case 1, isothermal Earth-air atmosphere with an initial non-condensing $\rm H_2O$ in the lower half of the atmosphere. The vertical profiles for $\rm \theta (p)$, $\rm T(p)$, and $\rm q_v(p)$ are determined by taking the horizontal average of the output 3D CM1 data. $\rm T_v(p)$ and $\rm \theta_v(p)$ are calculated using horizontally averaged $\rm T(p)$ and $\rm q_v(p)$ profiles. The coloured lines represent the atmospheric vertical profiles at different four time steps during the CM1 simulation where the initial state is given by a blue line and the final state is the red line. The blacked dashed lines show uniform composition dry adiabats, calculated using Eqn. \ref{['eq:DryAdiabat']},in the temperature panel, and virtual adiabats, calculated using Eqn. \ref{['eq:VirtualAdiabatExact']}, in the virtual temperature panel. The blue-green shaded region shows the predicted mixing zone from a CAPE analysis performed on the initial atmospheric sounding state using Eqn. \ref{['eq:cape']}. Finally, the top row shows the vertical profiles when CM1 Case 1 was run using only random perturbations to trigger convection, while the bottom row shows the results when convection is triggered with both random perturbations and a large sinusoidal wave given by Eqn. \ref{['eq:3d_wave']}. Case 1 version 2 shows the least agreement of where convection occurred to the predicted mixing zone.