Virga: Python Cloud Modeling for Exoplanets

Updated 3 July 2026

Virga is a Python-based cloud modeling framework that applies the Ackerman & Marley eddysed parameterization to simulate vertical cloud profiles in exoplanet and brown dwarf atmospheres.
It solves the steady-state condensate transport by balancing upward turbulent diffusion with gravitational sedimentation, supporting both constant and altitude-dependent sedimentation efficiency.
The tool integrates with radiative transfer and GCM frameworks, supports fractal aggregate physics, and has been validated against detailed microphysical models and JWST observations.

Virga refers to a suite of Python-based cloud modeling codes and frameworks implementing the Ackerman & Marley (2001) "EddySed" (eddysed) cloud–sedimentation parameterization, designed for exoplanet and brown dwarf atmospheric studies. Virga’s core function is to predict vertical profiles of cloud condensate mass, particle size, and resulting optical properties in 1D atmospheric columns, balancing upward turbulent mixing against gravitational settling. Critically, Virga generalizes the classic scheme to allow for both constant and altitude-dependent sedimentation efficiency, supports a wide range of condensates, and interfaces with state-of-the-art radiative transfer and retrieval pipelines.

1. Theoretical Foundations and Governing Equations

Virga models the steady-state, vertical transport of condensate in substellar atmospheres by solving upward turbulent diffusion of condensables against sedimentation of cloud particles. The governing equation, inherited from Ackerman & Marley (2001), is

$-\,K_{zz}(z)\,\frac{\partial q_t}{\partial z}\;-\;f_{\rm sed}(z)\,w_*(z)\;q_c(z)\;=\;0$

where $K_{zz}$ is the eddy diffusion coefficient, $q_t = q_v + q_c$ is total mixing ratio (vapor plus condensate), $w_*$ is the convective velocity or mixing length updraft, $q_c$ the condensate mixing ratio, and $f_{\rm sed}$ the dimensionless sedimentation efficiency. $f_{\rm sed}$ relates mass-weighted particle settling velocity to $w_*$ as $f_{\rm sed} = \langle v_{\rm fall}\rangle / w_*$ . The equilibrium condensation framework ensures that everywhere above the cloud base, gas vapor does not exceed local saturation; the excess instantly forms condensate.

This ODE is discretized layerwise, yielding analytic solutions for $q_t(z)$ and, by subtraction of vapor, $K_{zz}$ 0. Particle size is assigned so that the imposed $K_{zz}$ 1 matches the velocity scaling and mass flux. A lognormal size distribution describes particle radii, and the layer mean effective radius $K_{zz}$ 2 is computed as the ratio of third to second moment of the size distribution. The condensing species is governed by a prescribed condensation curve (saturation vapor pressure as a function of local T).

The sedimentation efficiency parameter $K_{zz}$ 3 is central: lower values generate vertically extended, optically thick clouds of small particles, while higher values concentrate mass into thin decks of large particles (Rooney et al., 2021, Batalha et al., 20 Aug 2025, Mang et al., 25 Feb 2026, Mang et al., 2022).

2. Model Architecture and Capabilities

Virga is implemented as an open-source Python package and serves as a standalone microphysics/optics module or as a component in atmospheric modeling frameworks (e.g., radiative-convective equilibrium, retrievals, GCM post-processing). Key architectural features include:

Inputs: pressure-temperature profiles, Kzz(z), condensate species, vapor boundary conditions, and, optionally, user-defined $K_{zz}$ 4(z) profiles (Rooney et al., 2021, Batalha et al., 20 Aug 2025).
Species Support: Virga-v1 supports ≳15 condensate species (e.g., KCl, MgSiO3, H2O, NH3, SiO2, Fe, Al2O3), with up-to-date vapor-pressure and optical constant databases (Batalha et al., 20 Aug 2025).
Particle Morphology: Initially assuming spherical particles with Mie scattering, Virga-v2 extends to fractal aggregate physics, allowing for arbitrary fractal dimensions, monomer sizes/numbers, and aggregates’ optical properties using Modified Mean-Field (MMF) theory (Moran et al., 8 Sep 2025).
Vertical Resolution: Atmosphere discretized into thin layers; output includes $K_{zz}$ 5, $K_{zz}$ 6, optical depth, single scattering albedo, and asymmetry parameter per layer and wavelength.
Numerics: Analytical solution for constant or any $K_{zz}$ 7 profile with a closed-form anti-derivative; Numba acceleration enables thousands-fold speedup over explicit microphysical solvers (Rooney et al., 2021).

This modularity allows rapid parameter scans and coupling to retrieval and radiative-transfer frameworks (e.g., PICASO, petitRADTRANS, POSEIDON) (Batalha et al., 20 Aug 2025, Mang et al., 25 Feb 2026).

3. Sedimentation Efficiency: Constant vs. Variable Formulations

Traditional eddysed implementations fix $K_{zz}$ 8 with height. However, microphysical models and laboratory data support vertical variation (e.g., CCN-limited growth, supersaturation-induced nucleation), which is now supported in Virga:

Constant $K_{zz}$ 9:

$q_t = q_v + q_c$ 0

where $q_t = q_v + q_c$ 1.

Altitude-dependent $q_t = q_v + q_c$ 2:

$q_t = q_v + q_c$ 3

where $q_t = q_v + q_c$ 4 are tunable; the analytical solution remains tractable provided the anti-derivative exists in closed form (Rooney et al., 2021).

Comparisons to microphysics codes (notably CARMA) show that introducing realistic $q_t = q_v + q_c$ 5 enables Virga to match the curvature and extent of CCN-limited microphysical cloud profiles, which constant $q_t = q_v + q_c$ 6 cannot reproduce (Rooney et al., 2021, Mang et al., 2022). In regimes dominated by homogeneous nucleation, both constant and variable forms converge in performance.

4. Extension to Fractal Aggregates

Virga-v2 offers explicit treatment for fractal and aggregate morphologies, reflecting rigorous evidence for non-spherical aerosol particles in both solar system and exoplanet atmospheres. Users specify fractal dimension $q_t = q_v + q_c$ 7, monomer radius $q_t = q_v + q_c$ 8, aggregate size, and select between fixed monomer or fixed aggregate-number growth modes. The dynamical impact is encoded by scaling fall speeds with aggregate structure, and the optical properties are computed using MMF tables (Optool).

Key scaling relations for aggregates are:

Number of monomers: $q_t = q_v + q_c$ 9
Aggregate density: $w_*$ 0
Fall speed adjustment: $w_*$ 1 (free molecular regime)

Application to KCl clouds on GJ 1214b demonstrates that lower fractal dimension (fluffier aggregates) produces larger, less-dense particles with reduced settling velocities, impacting cloud-top pressure, column density, and transmission spectral slopes. This new physics enables rapid exploration of aggregate morphologies' imprint on observables, unachievable with previous models (Moran et al., 8 Sep 2025).

5. Model Validation and Benchmarking

Virga has been benchmarked against a range of published models and observations:

CARMA Microphysics: Virga reproduces major trends but only matches detailed vertical structure when variable $w_*$ 2 is adopted; the fit remains imperfect due to the eddysed approach’s neglect of explicit nucleation and coagulation kinetics (Mang et al., 2022).
Brown Dwarf and Exoplanet Spectra: Consistency was demonstrated with Sonora Diamondback brown dwarf grids and patchy/cloudy models for hot Jupiters, recovering both $w_*$ 3- $w_*$ 4 profiles and cloud optical depths within ≲5% (Batalha et al., 20 Aug 2025, Mang et al., 25 Feb 2026).
JWST Observations: Application to WASP-17 b, WASP-107 b, VHS-1256 b, and YSES-1 c constrains settling efficiency and, in microphysical intercomparisons, suggests the high-altitude nanocluster-sized silicate grains inferred by JWST require $w_*$ 5 or sticking $w_*$ 6 (Kiefer et al., 13 Mar 2026). The ability to flexibly tune cloud vertical extent and integrate laboratory-derived haze optical constants (pre/post-UV irradiation) enables direct modeling of JWST spectral signatures (Huseby et al., 4 Jun 2026).

6. Applications: Coupling with Radiative Transfer, Retrieval, and GCMs

Virga is fully integrated into open-source frameworks such as PICASO for climate, emission, and transmission modeling:

Self-consistent RCE Solvers: Virga rapidly generates cloud profiles within the thermal iteration loop, updating cloud opacity and feedback effects (PICASO 4.0), handling supersaturation, rainout/cold trap effects, and multiple condensate species (Mang et al., 25 Feb 2026).
GCM Post-processing: By mapping 3D GCM T–P outputs and eddy mixing onto Virga’s 1D columns, users can generate phase-resolved spectra and thermal phase curves; computation remains tractable over large grids (Robbins-Blanch et al., 2022).
Retrieval Frameworks: Variable $w_*$ 7 adds flexibility in representing realistic cloud vertical structures necessary for unbiased multi-wavelength retrievals (Rooney et al., 2021, Kiefer et al., 13 Mar 2026).
Experimental Laboratory Data: Laboratory haze optical constants (including post-UV irradiation) are ingested to directly generate transmission spectra for sub-Neptune and water-world exoplanets—impacting JWST observability and compositional inference (Huseby et al., 4 Jun 2026).

7. Limitations and Future Developments

Virga’s current architecture is “equilibrium condensation” and “parameterized microphysics.” Limitations include:

Instantaneous saturation equilibrium: neglects time-dependent nucleation, supersaturation, or explicit kinetics.
No self-consistent microphysical evolution of particle sizes, coagulation, or fragmentation.
Spherical or fixed-morphology particle assumption is only relaxed for fractal aggregates in v2.
1D vertical columns independent of horizontal/3D effects (except by GCM post-processing).
Atmospheric mixing parameter $w_*$ 8 and convective velocities must be externally supplied.

Future directions highlighted in recent works include GPU acceleration, terrestrial climate extension (PICASO 6.0), microphysics/GCM coupling, and direct integration with photochemistry modules and dynamic turbulent mixing (Mang et al., 25 Feb 2026, Batalha et al., 20 Aug 2025, Moran et al., 8 Sep 2025). There is also an explicit effort toward community-driven development with open-source code, extensible optical databases, and modular architecture for rapid model improvement and new physical processes.

In summary, Virga is a modular, extensible, and computationally efficient cloud modeling tool based on the eddysed paradigm. Its incorporation of vertically variable sedimentation, fractal aggregate physics, and transparent data/model interfaces positions it as a reference framework in substellar atmospheric sciences for connecting microphysics, radiative transfer, and observational constraints (Rooney et al., 2021, Batalha et al., 20 Aug 2025, Mang et al., 25 Feb 2026, Moran et al., 8 Sep 2025, Mang et al., 2022, Kiefer et al., 13 Mar 2026, Robbins-Blanch et al., 2022, Huseby et al., 4 Jun 2026).