I modeled mathematically the thermal imbalance of our biosphere, which we call global warming, so as to gain my own quantitative understanding of the interplay of the two major effects that give rise to this phenomenon. This is a “toy model,” an abstraction of a very complicated planetary phenomenon that teams of scientists using supercomputers have been laboring for decades to enumerate in its many details, and to predict its likely course into the future.
The result of my model is a formula for the history of the rise of average global surface temperature. The parameters of the model are ratios of various physical quantities that affect the global heat balance. Many of those physical quantities are set by Nature and the laws of physics. A few of those parameters characterize assumptions I made about physical processes, specifically:
the degree of increase in Earth’s reflectivity of light because of an increase of cloud cover with an increase of temperature,
the degree of decrease in Earth’s reflectivity of light because of a decay of ice cover with an increase of temperature,
the rate of increase in Earth’s reflectivity of light because of the steady emission of air pollution particles,
the rate of increase of the infrared radiation absorptivity — heat absorptivity — of the atmosphere because of the steady emission of greenhouse gas pollution.
The parameters for the four processes just mentioned were selected so that a calculated temperature rise history from 1910 to 2020 matched the trend of the data for average global surface temperature rise during that period. That average temperature rise was 1°C between 1910 and 2020.
The two major effects involved in the dynamics of the current global heat imbalance are: heating because of the enhanced absorptivity by the atmosphere of outbound infrared radiation — which is heat; and cooling because of the enhanced reflectivity of the atmosphere to inbound sunlight.
The biosphere is in thermal equilibrium — existing at a stable average global temperature — when the rate of absorbed inbound sunlight is matched by the rate of heat radiated out into space.
Greenhouse gases emitted into the atmosphere capture a portion of the infrared radiation — heat — rising from the surface of the Earth, and retain it. They are able to do this because the nature of their molecules makes them highly efficient at absorbing infrared radiation. The molecules involved are primarily those of carbon dioxide (CO2), water vapor (H2O), and methane (CH4).
This captured heat is then redistributed to the rest of the atmosphere by molecular collisions between the greenhouse gas molecules and the molecules of the major constituents of our air: nitrogen (N2) and oxygen (O2). The excess atmospheric heat evaporates more seawater, makes more clouds, drives stronger winds and causes more intense rainstorms — such as hurricanes, typhoons and tornadoes — and more frequent and severe flooding.
That excess atmospheric heat is gradually absorbed by the oceans, which as a unit is the most massive and heat retentive component of the biosphere. The biosphere encompasses: the atmosphere, the oceans, and the land surface down to a depth of perhaps 10 meters, below which the temperature variations due to the seasons and the weather do not penetrate significantly. The oceans are the “heat battery” of Planet Earth.
The biosphere naturally emits a portion of the greenhouse gases contained in the atmosphere, but humanity has been adding massively to that load, and at an increasing rate since the beginning of the 20th century. So, global warming is an anthropogenic — human caused — effect.
Natural emissions of greenhouse gases and aerosols include: evaporation from the surfaces of the oceans to form clouds; the ejection of sulfur dioxide gas (SO2) and ash particles by volcanic eruptions; the rising of smoke from wildfires with their loads of carbon dioxide gas and soot; the rising of windblown dust; and the bubbling up of methane gas from the rotting of organic matter on land and at the ocean bottom.
Anthropogenic emissions of greenhouse gases include: carbon dioxide gas (CO2) and soot particles from the combustion of liquid fossil fuels, coal, and biomass; and the emission of organic vapors like methane from industrialized agriculture, mining, and oil and natural gas drilling; and ozone-depleting gases evaporated from cleaning fluids, solvents, and refrigerants.
Prior to significant anthropogenic emissions, there was a long-term balance between the natural emissions of greenhouse gases and aerosols, and their being rained-out and reabsorbed by the land and ocean surfaces. In particular, carbon dioxide gas is absorbed by green plants, which combine it with water to form sugar — used to supply the metabolic energy for plant growth, and of the animals that feed on plants — in a process called photosynthesis, and which is powered by sunlight.
About 30% of the sunlight incident on the Earth is reflected back into space. This light reflectivity by Planet Earth is called the albedo. Droplets of water in the atmosphere — often condensing around particles of soot, ash or dust — form into clouds, which are very efficient light reflectors, and are responsible for 24% of Earth’s reflectivity.
The other 6% of the Earth’s albedo is due to the overall light reflectivity of the surface of the Earth, which is the combined effect of reflections from the surfaces of the ice caps, oceans and lands. The rejection of a portion of the inbound solar light energy is a cooling effect.
The Earth’s albedo increases with a rise in the average global surface temperature, and with an increase in the load of aerosols in the atmosphere. Higher average temperature enhances evaporation and atmospheric humidity, creating more reflective cloud cover. A larger load of aerosols provides a greater number of light scattering particles to interfere with the influx of sunlight.
Aerosols tend to fall out and rain out of the atmosphere within a short period of weeks to months. So their contribution to the albedo — and thus to global cooling or “global dimming” — would be short-lived were they not being continuously replenished in the atmosphere by natural processes like the rainwater cycle, volcanic eruptions and wildfires; and by anthropogenic emissions of gas and aerosol pollution from the industrial activities of civilization.
Despite the slightly greater cooling effect of Earth’s albedo being increased by the introduction of anthropogenic pollution that scatters light, the biosphere is steadily warming because the greenhouse gases also included in that anthropogenic pollution have the dominating influence.
The only way to slow global warming is to reduce — and ideally eliminate — anthropogenic emissions of greenhouse gas and aerosol pollution.
Temperature History, Past and Future
Figure 1 shows the average global surface temperature rise, relative to the temperature in 1910, for the 110 years between 1910 and 2020. This calculated history matches the trend of the observational data. The temperature rise shown in Figure 1 is 1°C. The Earth in 1910 was experiencing a spatially and temporally averaged global surface temperature that I take to have been 13.75°C (56.75°F). The Earth in 2020 is experiencing a spatially and temporally averaged global surface temperature that I take to be 14.75°C (58.55°F).
Figure 1: Average Global Surface Temperature Rise between 1910 and 2020 (°C of temperature rise vs. relative time in years)
Figure 2 shows the average global surface temperature rise, relative to the temperature in 1910, for the 210 years between 1910 and 2120. Obviously, the temperature history beyond 2020 is a projection, and it is based on a continuation of the same conditions — which are reflected in a constancy of the parametric values used in my model calculation for between 1910 and 2020 — beyond 2020 for another 100 years. This is a projection of the consequences of “business as usual.”
Figure 2: Average Global Surface Temperature Rise between 1910 and 2120 (°C of temperature rise vs. relative time in years)
Three points to be observed in Figure 2 are the temperature rises of:
1.5°C (2.7°F) by 2047 (in 27 years),
2.0°C (3.6°F) by 2070 (in 50 years),
3.2°C (5.76°F) by 2120 (in 100 years).
A temperature rise of 2°C has been declared as the must-never-exceed “redline” on our global thermometer because it is seen by the widest range of climate scientists, earth scientists, biologists, ecologists and evolutionary biologists, as a threshold beyond which the Earth’s climate would run away to conditions inimical to human and non-human habitability and survival, without any possibility of alteration by human restraint or human action.
A temperature rise of 1.5°C has been declared as the realistic upper limit humanity could allow itself to tolerate if it still wished to slow the rate of subsequent global warming, by the drastic reduction of its anthropogenic emissions of atmospheric greenhouse gas and aerosol pollution.
Responsiveness of Earth’s Climate System
By my calculation, if magically all emissions of greenhouse gases and pollution grit ceased immediately today, it would take a minimum of 9,000 to 11,000 years for the excess 1°C in the biosphere to dissipate and thus return Earth to the climate we had for 10,000 years up to about 1910. The actual recovery time could be much longer. (This estimate is based on the thermal diffusivity of seawater.)
Because the Earth’s biosphere and its climate are immense systems with immense inertia, Earth’s recognition of our hypothetically abrupt cessation of greenhouse gas emitting, and Earth’s reaction to that cessation with a climatic response — a slowing of global warming — could take over 200 years to become noticeable. (This estimate is based on my calculated e^-1 exponential decay time of 240 years.)
The timescales of the planetary processes whose interactions produce climate are much longer than those of individual human attentiveness or of current societal preoccupations.
How Should We Respond?
The physics is clear, whether reflected by my simple analytical toy model, or by the immensely intricate state-of-the-art supercomputer numerical models by the many climate science institutes.
How global warming — as a complex of interrelated physical phenomena — will affect us can be estimated by climate scientists from their models. What we should do about the present and anticipated effects of global warming remains an open question that is beyond physics, and whose answer rests entirely on human choice.
What aspects of human and non-human life do we consider essential to protect and preserve? What degree of commitment are we willing to make to strategies for the continuation of civilization that require an equitable sharing of the new burdens imposed on human activity by increases of global temperature? In short, what kind of people do we want to be as we all live out our lives in a globally warming world?
It is easy to imagine many utopian or dystopian responses to global warming. We — as a species — are completely free to choose the type of cooperative or uncooperative collective future that we wish to inhabit, for as long as Planet Earth allows us to enjoy its hospitality.
If you wish to examine my global warming model for yourself, you can take a copy of it from:
A Simple Model of Global Warming
26 May 2020