Warming model

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; and 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.

Excerpted: 'Living With Global Warming'.

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