By Doug Criner

The above dubious observation was written by Thomas Jefferson, an amateur meteorologist, in the early 1800s. It seems that global warming is not a new concern.

The study of global warming is a specialty of climatologists and atmospheric scientists, not engineers. However, engineers' knowledge of heat transfer and thermodynamics can provide a rudimentary understanding of global warming.

Heat Balance Equation

Consider a heat balance equation for Earth. Ignoring geothermal, fossil, nuclear, and tidal energy, which are negligible, the planet is heated by incident solar radiation and loses heat by radiating infrared energy back into space. At equilibrium, these two heat flows are equal, i.e.:

πr²S_c (1 – α) = 4πr²σT_e⁴

where,

r = Earth’s radius

S_c = solar irradiance = 1.37 kW/m²

α = the earth’s albedo (fraction of incident solar energy reflected by clouds, etc. 0.3

σ = Stephan-Boltzmann constant = 5.67 x 10 ^{– 11} kW/m² K⁴

T_e = average effective global temperature

The left side of the above equation represents the incident solar energy; it includes the term πr² because solar energy is effectively intercepted by a circular disc equal in area to the earth’s cross-sectional area. The right side of the above equation represents the thermal energy radiated by the earth's surface; this is proportional to the earth’s surface area, 4πr².

The above heat-balance equation may be solved for T_e, the earth’s average temperature. The  solution is a rather inhospitable 225 K (-18 ˚C, 0 ˚F ).  The answer cannot be correct:  the measured average temperature of the earth’s surface is a pleasant 15 ˚C (59 ˚F).

The 33 C˚ disparity arises because the right-hand side of our energy balance equation did not account for the infrared energy reflected back to earth by the atmosphere—i.e., the greenhouse effect. Naturally occurring greenhouse gasses are more transparent to shortwave solar radiation that to the long-wave radiation emitted by Earth. Much of Earth’s long-wave radiation is absorbed by the atmosphere and returns to Earth’s surface, and then must be re-radiated. For the equation to balance, the earth’s surface must assume a higher temperature than predicted by our overly simplified model.

The following figure shows a simplified schematic of Earth’s energy flows. The net energy flows across each boundary between space, atmosphere, and Earth sum to zero.

What are the constituents of the atmosphere that cause the greenhouse effect? The concentration of CO₂, the most significant, has increased by about 25% since pre-industrial times. Other greenhouse gasses include methane (CH₄), nitrous oxide (NO₂), chlorofluorocarbons (CFCs), and other synthetic halocarbons. All of these gasses, including CO₂, occur only in trace amounts:  the two major constituents of the atmosphere, nitrogen and oxygen, comprise over 99% of the total.

Historical Perspective

There is scientific consensus that significant global warming is in process. It is interesting, though, that the last period of glaciation, with glaciers covering much of North America and northern Europe, occurred only about 15,000 years ago—a mere snap of the fingers in geological time and even in the history of human existence. In fact, geological evidence suggests that Earth is now in a brief, geologically speaking, interglacial period in the midst of a general ice age. The previous interglacial period occurred about 130,000 years ago and lasted but 10,000 years.

Although an aberration, it’s interesting to note that in 1816, a severely cold summer occurred in higher latitudes. In New England, for example, it snowed in June and killing frosts continued through August. This unusual weather was attributed to volcanic eruptions in Indonesia, with volcanic dust in the upper atmosphere, reducing the solar radiation reaching earth.

The context of natural climatic cooling does not necessarily provide solace to us, the current residents of Earth, and our near-term progeny. If some of the projections for global warming within the current century occur, the rate of climatic change could be more rapid than any other such episode in Earth’s history, at least since the emergence of humans. On the bright side, humankind has never been better situated, technologically, to cope with such a challenge. Engineering solutions will be needed to minimize global warming and to deal with warming that occurs.

© 1996 Doug Criner