1969c

A Global Climatic Model Based on the Energy Balance of the Earth-Atmosphere System

William D. Sellers

Observation and Context

In the late 1960s, a major focus in atmospheric science was estimating how planetary temperatures react to large-scale changes like solar variations, albedo shifts, or industrial air pollution. Early research in Russia, notably by M. I. Budyko and L. R. Rakipova, suggested that removing the arctic ice sheet would dramatically warm the polar region. However, their models primarily focused on local energy balances and completely omitted heat transfer by ocean currents.

Concurrently, scientists like Erling Eriksson observed that if global ice cover grows and reaches a critical lower latitude, the ice-albedo loop could trigger an explosive, rapid transition to an entirely ice-covered planet. This underscored a strong need for holistic, global frameworks capable of capturing regional interactions before a stable climate equilibrium is reached.

Hypothesis

William D. Sellers hypothesized that the steady-state, annual latitudinal distribution of surface temperature could be modeled as a direct function of incoming solar energy, infrared atmospheric transparency, planetary albedo, and horizontal heat and water vapor transport by both atmospheric and oceanic currents. He proposed that localized climate updates would have global repercussions and that accounting for variable albedo would reveal extreme sensitivity to small fluctuations in solar intensity.

Experiment and Methodology

Sellers constructed a relatively simple, steady-state numerical climate model where the primary dependent variable was the average annual sea-level temperature across 10° latitude belts. The methodology included several specialized parameters:

• The Energy Equation: The framework calculated energy balance by matching a belt’s net radiation against the poleward flux of water vapor, atmospheric sensible heat, and oceanic sensible heat.
• Dynamic Albedo Feedback: The model utilized a critical equation allowing planetary albedo to increase by 0.009 for every 1 °C drop in temperature below 10 °C to realistically simulate expanding snow and ice cover.
• Transport Dynamics: Transport was calculated using a combination of a mean meridional circulation and horizontal eddy thermal diffusivities for both the atmosphere and the oceans.
• Simulation Experiments: Boundary conditions dictated zero energy transfer across the poles. The model was run iteratively to assess the global impacts of four scenarios: artificially dropping polar albedo (melting the ice caps), changing the solar constant, altering infrared transmissivity, and adding industrial waste heat from human activities.

Results and Data

The model successfully recreated Earth’s present temperature zonation before revealing three major predictive insights:

1. Polar Ice Modification: Artificially removing the north polar ice cap and fixing the albedo to 0.50 raised temperatures poleward of 70 °N by no more than 7 °C. However, due to global coupling, this localized change increased tropical temperatures by 1 °C and warmed the south pole by 1 °C to 3 °C.
2. Solar Constant Vulnerability: When albedo was permitted to vary with temperature, a mere 2% to 5% decrease in the solar constant was sufficient to initiate a severe ice age, pushing glacier lines down to 30° latitude. Any drop beyond this limit triggered a runaway freeze to a completely ice-covered planet sitting at an equilibrium temperature of −100 °C.
3. Anthropogenic Heating: Spreading projected industrial waste heat across latitude belts — assuming a 4% annual compounding increase over the next 200 years — resulted in a massive global warming trend averaging 15 °C. Polar regions warmed by up to 27 °C, completely eliminating permanent ice caps.

Conclusion and Climate Impact

Sellers concluded that Earth’s climate equilibrium is highly sensitive to variations in solar radiation and albedo due to powerful, interconnected thermal feedback mechanisms. The model demonstrated that modifying the climate in one region inevitably shifts the steady-state thermal profile of the entire globe. Furthermore, it confirmed that unabated human industrial output could eventually become a dominant climate-forming factor, potentially generating a planet entirely devoid of polar ice.

Published in parallel with similar findings by M. I. Budyko, this work is celebrated as the co-origin of the Budyko-Sellers Energy Balance Model (EBM). It introduced computationally efficient, highly accurate thermodynamic parameterizations that allowed climate scientists to isolate specific feedback loops, laying the groundwork for modern climate sensitivity metrics and tipping-point analysis.