notus-gcm 1.0.0

A spectral-transform General Circulation Model in JAX.

Notus

A spectral-transform General Circulation Model written from scratch in Python/JAX.

Named after Νότος (Notus), the Greek god of the south wind.

What is this?

Notus is an atmospheric GCM built for learning and experimentation. It implements a pseudo-spectral dynamical core using spherical harmonics on a Gaussian grid, with moist physics, radiation, and interactive surface models.

The model is planet-agnostic — it can simulate any rotating planet with an ideal-gas atmosphere.

Architecture

• Spectral transform: spherical harmonic decomposition (FFT in longitude, Legendre transform in latitude)
• Vertical coordinate: sigma (p/ps) on a Lorenz grid
• Time stepping: IMEX leapfrog with Robert-Asselin filter + semi-implicit 3D Helmholtz solver (with virtual temperature linearization for moist dynamics)
• Implicit physics: surface fluxes (sensible + latent heat), Rayleigh friction, and Betts-Miller convection treated with backward Euler for unconditional stability
• Filtering: exponential spectral filter (Hou & Li 2007) + del-8 hyperdiffusion
• Physics: Held-Suarez forcing, Frierson (2006/2007) simple physics (Betts-Miller convection, large-scale condensation, bulk surface fluxes), pluggable via Forcing protocol
• Moisture: specific humidity as optional spectral tracer, surface evaporation, condensation with latent heating, virtual temperature feedback in both dynamics and semi-implicit solver
• Radiation: three schemes available — Frierson gray LW, Byrne/Isca semi-gray (humidity-dependent), and SPEEDY multi-band (4-band LW with temperature-dependent fractions + 2-band SW with near-IR H₂O absorption + diagnostic clouds). Seasonal insolation with orbital parameters. CO₂ sensitivity knob.
• Boundary layer: Monin-Obukhov surface layer (Louis 1979 stability functions), spatially varying roughness lengths
• Surface models: slab ocean (implicit, prescribed Q-flux) + bucket land surface (Frierson 2006 / Manabe 1969: soil energy balance, P-E-R hydrology, evaporation resistance)
• Clouds: diagnostic cloud scheme (SPEEDY-style) — RH + precipitation-based cloud cover, stability-dependent stratiform clouds, SW reflection and LW absorption
• Computation: JAX (JIT compilation, GPU support, autodiff)

Installation

Requires Python 3.13 or newer.

Install from PyPI:

pip install notus-gcm

The PyPI package becomes available after the first tagged release is published.

For local development:

uv sync --group dev

Usage

from notus import GaussianGrid, SpectralTransform, EARTH, PlanetaryConstants

# Create a T42 grid (standard Held-Suarez resolution)
grid = GaussianGrid(truncation=42)

# Set up spectral transforms
transform = SpectralTransform(grid, EARTH.radius)

# Or define your own planet
my_planet = PlanetaryConstants(
    name="Arrakis",
    radius=6.0e6,
    rotation_rate=8.0e-5,
    gravity=9.1,
    gas_constant=287.0,
    specific_heat_cp=1005.0,
)

Held-Suarez benchmark

Run the standard dry dynamical core intercomparison:

# Quick demo (T21, 300 days, ~45s)
uv run python examples/held_suarez.py --days 300 --spinup 100 --truncation 21 --dt 1200

# Full benchmark (T42, 1200 days)
uv run python examples/held_suarez.py

# Generate diagnostic plots
uv run python examples/plot_held_suarez.py

Frierson aquaplanet (dry)

Run the gray-radiation aquaplanet with surface fluxes (Frierson et al. 2006):

# Quick demo (T21, 300 days)
uv run python examples/dry_aquaplanet.py

# Generate diagnostic plots
uv run python examples/plot_dry_aquaplanet.py

Moist aquaplanet

Run the moist aquaplanet with condensation, Betts-Miller convection, and surface evaporation:

# Quick demo (T21, 300 days, Frierson gray radiation)
uv run python examples/moist_aquaplanet.py

# With SPEEDY multi-band radiation + clouds
uv run python examples/moist_aquaplanet.py --scheme speedy --clouds

# Byrne two-band radiation
uv run python examples/moist_aquaplanet.py --scheme byrne --days 300

# Generate diagnostic plots (U, T, q, EKE, spinup, surface pressure)
uv run python examples/plot_moist_aquaplanet.py

Slab ocean + land

# Slab ocean with seasonal cycle (Byrne radiation, default)
uv run python examples/slab_ocean_aquaplanet.py

# Slab ocean with SPEEDY radiation + clouds
uv run python examples/slab_ocean_aquaplanet.py --scheme speedy --clouds

# Land-ocean aquaplanet with bucket hydrology
uv run python examples/land_ocean_aquaplanet.py --scheme speedy --clouds

Radiation validation

# Validate radiation energy conservation (SW column closure, TOA balance)
uv run python examples/validate_radiation.py --scheme speedy --clouds --days 300

# Coupled slab ocean validation (Q-flux diagnosis + coupled integration)
uv run python examples/validate_radiation_coupled.py --scheme speedy --clouds

Tests

uv run pytest tests/ -v

References

Built with guidance from:

• SpeedyWeather.jl — clean modular spectral GCM in Julia
• Dinosaur — differentiable spectral dycore in JAX (Google)
• SPEEDY — simplified atmospheric GCM (ICTP)
• Held & Suarez (1994), A Proposal for the Intercomparison of the Dynamical Cores of Atmospheric General Circulation Models, BAMS
• Frierson et al. (2006), A Gray-Radiation Aquaplanet Moist GCM, JAS
• Frierson (2007), The Dynamics of Idealized Convection Schemes and Their Effect on the Zonally Averaged Tropical Circulation, JAS