1983

Efficient Three-Dimensional Global Models for Climate Studies: Models I and II

J. Hansen, G. Russell, D. Rind, P. Stone, A. Lacis, S. Lebedeff, R. Ruedy & L. Travis

Observation and Context

By the early 1980s, numerical climate modeling based on the fundamental conservation equations was highly limited by extreme computing costs. Traditional General Circulation Models (GCMs) required fine horizontal resolutions and substantial artificial smoothing or numerical viscosity to maintain computational stability. However, this approach tended to damp out real atmospheric motions alongside numerical noise.

Observations indicated that the main features of global atmospheric circulation could be defined at a coarse resolution of 1000 km. Climate researchers recognized that if a model could remain numerically stable at this coarse scale without explicit horizontal diffusion, it would achieve an order-of-magnitude reduction in computing time, allowing for decades of long-range climate simulation.

Hypothesis

The researchers hypothesized that a global atmospheric model could realistically simulate the major features of the Earth’s climate at a very coarse horizontal resolution (~1000 km). They proposed that by utilizing potential enstrophy-conserving and momentum-conserving spatial differencing schemes (based on the work of Akio Arakawa), the model could maintain strict numerical stability without requiring artificial viscosity, thereby preserving essential eddy kinetic energy and transport processes.

Experiment and Methodology

The scientists developed a grid-point global atmospheric model designed with highly flexible horizontal and vertical resolutions. The primary testing configurations used horizontal resolutions of 12°×15°, 8°×10°, and 4°×5°, combined with 7-layer and 9-layer vertical spans under a normalized Phillips σ coordinate system.

The experimental matrix was conducted across multiple evolutionary model iterations:

• Model I Baseline: The initial core model solved prognostic equations for mass, energy, momentum, and water vapor. It utilized a semi-implicit spectral integration for radiation, explicit subgrid-scale moist convection, and basic ground hydrology.
• Sensitivity Matrix: The team conducted 60 distinct climate sensitivity experiments with integration run times lasting from 3 months up to 5 years. These tests systematically isolated the impacts of horizontal gridding (Arakawa B vs. C schemes), time-stepping methods, explicit horizontal diffusion, cloud nucleation physics (liquid vs. ice phase points), and vegetation-dependent ground hydrology.
• Model II Upgrade: Armed with the sensitivity data, the researchers created Model II by modifying key sub-grid physics. Notable changes included implementing an interactive Ekman boundary layer wind formulation with computed cross-isobar angles, placing an active friction layer in the stratosphere to eliminate unphysical wave reflection, expanding vertical resolution to 9 layers, and linking ground hydrology directly to regional vegetation files.

Results and Data

The coarse-resolution experiments demonstrated robust physical capabilities and generated three core insights:

1. Resolution Independence: The 8°×10° coarse horizontal grid (approx. 1000 km) successfully captured the primary global structures of temperature, jet streams, and wind fields, while running ten times faster than fine-mesh models.
2. Boundary Layer and Eddy Transformations: Implementing the interactive Ekman wind formulation in Model II drastically reduced unphysical surface friction, driving a massive ~50% increase in transient eddy kinetic energy. This enhanced wave activity boosted winter poleward energy transports, raising high-latitude tropospheric temperatures by up to 10 °C to match observed data.
3. Hydrological and Cloud Realism: Transitioning to a 5-hour time step for large-scale precipitation and introducing a −40 °C threshold for ice saturation optimized the cloud integration, raising global cloud cover to a realistic 52% and cleanly resolving severe dry desert features in the Sahara.

Conclusion and Climate Impact

The experiment successfully proved that coarse horizontal grid architectures can achieve high-fidelity climate simulations provided that their underlying numerical schemes conserve fundamental integral properties. By demonstrating that a 1000-km resolution model remains stable and dynamically active without explicit horizontal diffusion, Hansen and his team removed the supercomputing barrier to long-range modeling.

This study introduced the world to the GISS GCM (Goddard Institute for Space Studies General Circulation Model). By shifting GCM development toward computational efficiency, this landmark breakthrough enabled complex climate experiments, laying the direct technical foundation for modern transient climate change projections, volcanic aerosol forcing studies, and historical global temperature reconstructions.