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Joseph Fourier

February 7, 2012 by Tony Noerpel filed under Columns, Sustainable Planet No Comments

Jean Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French Physicist and Mathematician who is well known among scientists and engineers for developing “Fourier transforms”, Fourier Series” and “Fourier’s Law”. The latter is the law of heat conduction and describes the rate of heat flow through a material. He is also considered to be the discoverer of the Earth’s atmospheric greenhouse effect.

Fourier was orphaned at the age of eight, but received a good education and yet was disqualified for a commission to the French army scientific corps because he was not born to nobility. Such was pre-revolutionary France. He supported the revolution and was rewarded with scholastic appointments. In 1798, he accompanied Napoleon Bonaparte on his expedition to Egypt and served as governor until the defeat of the French in 1801.

After the war, he made his contributions to the theory of heat transfer.

Wikipedia claims “Fourier believed that keeping the body wrapped up in blankets was beneficial to the health. He died in 1830 when in this state he tripped and fell down the stairs at his home.” We all make mistakes.

First in 1824 and in a revised version in 1827, he published a paper establishing the concept of energy balance whereby the heat energy radiated into space by the earth had to equal the energy incident on the earth from the sun. He calculated that the Earth was about 33 degrees Celsius warmer than it should be based on the estimated energy our home planet receives from the sun. He correctly estimated that the geothermal heat energy was very small when compared with solar radiation. Geothermal energy includes the kinetic energy left over from all the collisions of planetesimals 4 billion years ago which formed the Earth, the gravitational energy of the earth mass compressing the core, and radioactive decay of uranium and other radioactive elements of which the earth was formed.

This energy balance equation is the simplest model of a planet’s climate, albeit inaccurate, and is derived from the Stefan-Boltzmann Equation:

T = [(1-?)S/(4?)]1/4

In this equation T is the temperature of the planet’s surface, ? is the albedo, S is the incoming solar radiation, ? is the emissivity, and ? is the Stefan-Boltzmann constant, 5.67 X 10-8 Watts/meter squared / K 4. The albedo is the reflectivity of the planet surface to incoming short wave (visible light and ultraviolet) solar radiation. On average the Earth surface reflects about 30% of this radiation. The incoming solar radiation is 1366 Watts per meter squared and is nearly constant over millennial times. Figure 1 shows the value of S over the last thirty years. Fourier did not use this equation exactly as it was not to be discovered for another 50 years. But he came to the correct conclusion however. Using the more recent equation and the values given for Earth, we compute the surface temperature of -18 degrees Celsius or 0 degrees Fahrenheit. The average Earth surface temperature is about 55 degrees F and Fourier correctly surmised that the atmosphere must be acting as an insulating blanket retaining the radiated heat energy of the surface. He likened this to a greenhouse. This natural greenhouse effect makes life possible here on Earth because without the insulating effect of the atmosphere the Earth would be too cold for life except perhaps for the deep ocean near geothermal vents.
What Fourier did not know was which of the atmospheric components were responsible for the greenhouse effect. These remained to be discovered. In the meantime 1837 Louis Agassiz proved that ice ages or periods of glaciations in Europe and North America had occurred. The cause of the ice ages fascinated scientists and the hunt for this cause intersected the hunt for an explanation of the greenhouse effect. We will examine these phenomena in future articles. Fourier’s results suggest that if the Earth were ever to lose its greenhouse gases, it would freeze like a snowball. In fact, this phenomenon has occurred at least six times in our planet’s past. We will discuss this as well.

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