SPEEDY Physics Package

Overview

The SPEEDY (Simplified Parameterizations, primitivE-Equation DYnamics) physics package provides intermediate-complexity atmospheric parameterizations suitable for climate modeling and machine learning applications. SPEEDY was originally developed by Franco Molteni at ICTP and has been widely used for studying atmospheric dynamics and climate variability.

JAX-GCM’s implementation is a pure JAX translation that maintains the physical fidelity of SPEEDY while adding full differentiability and GPU/TPU acceleration.

Key Characteristics

• Computational Efficiency: Simplified physics allows for fast simulations

• Physical Realism: Captures essential atmospheric processes despite simplifications

• Vertical Resolution: Designed for 8 vertical levels (can work with other configurations)

• Time-Varying Forcing: Supports daily climatological or constant boundary conditions

• Differentiability: Fully compatible with JAX automatic differentiation

Physics Parameterizations

The SPEEDY physics package includes the following components, executed in sequence:

1. Convection (Simplified Tiedtke Scheme)

2. Large-Scale Condensation

3. Cloud Diagnostics

4. Shortwave Radiation

5. Longwave Radiation

6. Surface Fluxes

7. Vertical Diffusion

Each parameterization is described in detail below.

Convection

Type: Simplified mass-flux scheme based on Tiedtke (1993)

Description: Represents subgrid-scale moist convection using a bulk mass-flux approach. The scheme diagnoses convectively unstable grid boxes where saturation moist static energy decreases with height.

Key Features:

• Primary and secondary mass fluxes

• Entrainment and detrainment

• Convective precipitation

• Temperature and moisture tendencies

Activation Criteria:

Convection activates when:

1. Conditional instability exists (saturation moist static energy decreases upward)

2. Either:

   • Actual convective instability (moist static energy decreases upward), OR

   • Relative humidity exceeds threshold in boundary layer

Configurable Parameters (ConvectionParameters):

Parameter	Description	Default
psmin	Minimum surface pressure for convection	0.8
trcnv	Relaxation time toward reference state (hours)	6.0
rhil	RH threshold for secondary mass flux	0.7
rhbl	RH threshold in boundary layer	0.9
entmax	Maximum entrainment fraction	0.5
smf	Secondary to primary mass flux ratio	0.8

Large-Scale Condensation

Description: Represents stratiform precipitation and clouds through a relaxation scheme toward saturated conditions when relative humidity exceeds a threshold.

Process:

1. Check if relative humidity exceeds threshold

2. Relax specific humidity toward saturation

3. Convert excess moisture to precipitation

4. Release latent heat

Vertical Variation: RH threshold varies from rhlsc at the surface to rhlsc + drhlsc at model top, ensuring more precipitation in upper levels.

Configurable Parameters (CondensationParameters):

Parameter	Description	Default
trlsc	Relaxation time for specific humidity (hours)	4.0
rhlsc	Maximum RH threshold at surface	0.9
drhlsc	Vertical range of RH threshold	0.1
rhblsc	RH threshold for boundary layer	0.95

Clouds

Description: Diagnostic cloud cover based on relative humidity and precipitation. Two types of clouds are diagnosed:

Convective Clouds:

• Based on relative humidity

• Weight applied to square root of precipitation

• Cloud cover increases with RH and precipitation

Stratiform Clouds:

• Additional component based on static stability

• Diagnosed from vertical gradient of dry static energy

• Higher over land (minimum cover clsminl)

Cloud Top: Determined as the highest level with significant cloud cover.

Configurable Parameters (in ShortwaveRadiationParameters):

Parameter	Description	Default
rhcl1	RH for zero cloud cover	0.30
rhcl2	RH for full cloud cover	1.00
qacl	Specific humidity threshold	0.20
wpcl	Precipitation weight (mm/day)⁻⁰·⁵	0.2
pmaxcl	Maximum precipitation contribution (mm/day)	10.0
clsmax	Maximum stratiform cloud cover	0.60
clsminl	Minimum stratiform cover over land	0.15

Shortwave Radiation

Description: Two-band shortwave radiation scheme (visible and near-IR) with explicit treatment of:

• Rayleigh scattering

• Water vapor absorption

• Cloud albedo and absorption

• Aerosol absorption

• Surface albedo (land, ocean, ice, snow)

Process:

1. Compute solar zenith angle and TOA insolation

2. Calculate atmospheric absorption by water vapor and aerosols

3. Account for cloud reflection and absorption

4. Compute surface albedo (varies by surface type)

5. Calculate multiple reflections between surface and clouds

6. Distribute absorbed radiation to atmospheric layers

Radiation Frequency: Computed every nstrad timesteps (typically every 3 hours) to save computation.

Configurable Parameters (ShortwaveRadiationParameters):

Parameter	Description	Default
albcl	Cloud albedo	0.43
albcls	Stratiform cloud albedo	0.50
absdry	Dry air absorptivity (visible)	0.033
absaer	Aerosol absorptivity (visible)	0.033
abswv1	Water vapor absorptivity (band 1)	0.022
abswv2	Water vapor absorptivity (band 2)	15.0
abscl1	Cloud absorptivity (visible, max)	0.015
abscl2	Cloud absorptivity (band 2)	0.15

Surface Albedo (ModRadConParameters):

Parameter	Description	Default
albsea	Ocean albedo	0.07
albice	Sea ice albedo	0.60
albsn	Snow albedo	0.60

Longwave Radiation

Description: Three-band longwave scheme representing:

• Window region (transparent to water vapor)

• Water vapor band 1 (weak absorption)

• Water vapor band 2 (strong absorption)

Process:

1. Compute blackbody emission at each level

2. Calculate water vapor absorptivity in each band

3. Account for cloud emissivity

4. Integrate upward and downward fluxes separately

5. Apply surface emissivity

Band Weights: Fixed fractions of blackbody spectrum allocated to each band.

Configurable Parameters (ShortwaveRadiationParameters):

Parameter	Description	Default
ablwin	Window band absorptivity	0.3
ablwv1	Water vapor absorptivity (band 1)	0.7
ablwv2	Water vapor absorptivity (band 2)	50.0
ablcl1	Thick cloud absorptivity (window)	12.0
ablcl2	Thin cloud absorptivity	0.6

Surface Parameters (ModRadConParameters):

Parameter	Description	Default
epslw	PBL emission fraction	0.05
emisfc	Surface emissivity	0.98

Surface Fluxes

Description: Bulk aerodynamic formulation for turbulent fluxes of momentum, heat, and moisture between the surface and atmosphere.

Separate Treatment:

• Land: Prognostic skin temperature from energy balance; moisture availability factor

• Ocean: Prescribed SST; unlimited moisture availability

Stability Correction: Adjusts exchange coefficients based on static stability (Richardson number approach).

Energy Balance (land only):

• Solves for skin temperature satisfying: Net radiation = Sensible heat + Latent heat + Ground heat flux

• Includes diurnal cycle correction

• Heat conduction to soil layer

Configurable Parameters (SurfaceFluxParameters):

Parameter	Description	Default
cdl	Momentum drag coefficient (land)	2.4×10⁻³
cds	Momentum drag coefficient (sea)	1.0×10⁻³
chl	Heat exchange coefficient (land)	1.2×10⁻³
chs	Heat exchange coefficient (sea)	0.9×10⁻³
vgust	Subgrid wind gust speed (m/s)	5.0
dtheta	Potential temp gradient for stability	3.0 K
fstab	Stability correction amplitude	0.67
ctday	Daily cycle correction	0.01
clambda	Soil heat conductivity	7.0
lfluxland	Compute land surface temperature	True
lskineb	Redefine skin temp from energy balance	True
lscasym	Use asymmetric stability coefficient	True

Vertical Diffusion

Description: Represents subgrid-scale vertical mixing by:

1. Shallow Convection: Moisture redistribution in marginally unstable conditions

2. Moisture Diffusion: Removes sharp vertical RH gradients

3. Dry Convective Adjustment: Removes super-adiabatic lapse rates

Process:

• Shallow convection diagnosed where moist static energy is nearly neutral

• Reduced in regions of deep convection

• Moisture diffusion applied where RH gradient exceeds threshold

• Super-adiabatic adjustment maintains stability

Configurable Parameters (VerticalDiffusionParameters):

Parameter	Description	Default
trshc	Shallow convection time scale (hours)	6.0
trvdi	Moisture diffusion time scale (hours)	24.0
trvds	Super-adiabatic adjustment time scale (hours)	6.0
redshc	Shallow convection reduction factor	0.5
rhgrad	Maximum RH gradient (d_RH/d_σ)	0.5
segrad	Minimum dry static energy gradient	0.1

Forcing and Boundary Conditions

Description: Manages time-varying and constant boundary conditions including:

• Sea surface temperature (SST)

• Sea ice concentration

• Snow cover

• Soil moisture

• Surface albedo

• Orographic parameters

CO₂ Forcing: Optional increasing CO₂ concentration over time.

Configurable Parameters (ForcingParameters):

Parameter	Description	Default
increase_co2	Enable time-varying CO₂	True
co2_year_ref	Reference year for CO₂	1950

Using Custom Parameters

To customize physics parameters:

from jcm.physics.speedy.speedy_physics import SpeedyPhysics
from jcm.physics.speedy.params import Parameters
from jcm.model import Model

# Get default parameters
params = Parameters.default()

# Modify convection parameters
params = params.copy(
    convection=params.convection.copy(
        trcnv=8.0,  # Slower convection relaxation
        rhbl=0.85   # Lower RH threshold
    )
)

# Modify radiation parameters
params = params.copy(
    shortwave_radiation=params.shortwave_radiation.copy(
        albcl=0.50  # Higher cloud albedo
    )
)

# Create physics with custom parameters
physics = SpeedyPhysics(parameters=params)

# Use in model
model = Model(physics=physics)

Viewing All Parameters

To see all parameter values:

from jcm.physics.speedy.params import Parameters

params = Parameters.default()
print(params)

Scientific References

The SPEEDY physics parameterizations are based on the following key publications:

1. Molteni, F. (2003). Atmospheric simulations using a GCM with simplified physical parametrizations. I: Model climatology and variability in multi-decadal experiments. Climate Dynamics, 20, 175-191. https://doi.org/10.1007/s00382-002-0268-2

2. Tiedtke, M. (1993). Representation of clouds in large-scale models. Monthly Weather Review, 121(11), 3040-3061.

3. Original SPEEDY Documentation: SPEEDY User Guide

4. Fortran 90 Implementation: Our JAX implementation references the speedy.f90 version by Sam Hatfield and Leo Saffin.

Assumptions and Limitations

Vertical Resolution:

• Designed for 8 vertical levels with specific σ-coordinates

• Performance may vary with different vertical resolutions

• Some parameters are tuned for the standard 8-level configuration

Simplifications:

• Two-band shortwave radiation (more sophisticated schemes use 4+ bands)

• Simplified cloud microphysics (no explicit ice/liquid separation)

• Bulk mass-flux convection (no explicit cloud dynamics)

• No aerosol indirect effects on clouds

• No chemistry or interactive trace gases (except optional CO₂ trend)

Time Steps:

• Recommended time step: 30 minutes for T31 resolution

• Shorter time steps needed for higher resolutions

• Radiation computed less frequently (typically every 3 hours)

Forcing Data:

• Requires either daily climatological or constant boundary conditions

• Assumes 365-day year for climatological forcing

• SST and other boundary conditions are prescribed (not predicted)

Domain:

• Global model (no regional capability)

• Assumes spherical geometry

Performance Characteristics

Computational Cost: SPEEDY is designed to be ~10-100× faster than state-of-the-art physics packages while maintaining reasonable climatology.

Physical Realism:

• Captures large-scale circulation patterns well

• Reasonable representation of tropical variability (e.g., MJO-like features)

• Mean climate biases comparable to some comprehensive GCMs

• Best suited for dynamics studies, sensitivity experiments, and ensemble applications

Use Cases:

• ✓ Large ensemble simulations

• ✓ Parameter sensitivity studies

• ✓ Dynamics and variability research

• ✓ ML/AI training data generation

• ✓ Educational purposes

• ✗ Detailed process studies (e.g., cloud microphysics)

• ✗ High-accuracy climate projections

Comparison with Other Physics Packages

Feature	SPEEDY	ICON (future)	Comprehensive GCMs
Complexity	Intermediate	High	Very High
Speed	Fast	Medium	Slow
Vertical Levels	8 (typical)	Flexible	30-100+
Radiation Bands	2 (SW), 3 (LW)	Multi-band	10-100+
Cloud Scheme	Diagnostic	Prognostic	Prognostic+Microphysics
Aerosols	Fixed climatology	Interactive	Fully interactive
Use Case	Dynamics, ML	Research	Climate projections

Next Steps

• See Getting Started for examples of running models with SPEEDY physics

• See API for detailed API documentation of individual parameterizations

• See Developer Guide for information on implementing custom physics packages