where I©(t) is the luminosity of the Sun at time t and t© is the current age of the Sun, usually taken as 4.6 billion years. This formula was originally proposed to describe the younger Sun, but it continues to be reasonably accurate out to times 4 billion years in the future as well.
It follows from Eq. 1.1 that 4 billion years ago the Earth received solar energy at only 75% of the rate it does today. All other things being equal - atmospheric composition in particular - that means the Earth would have been colder than it is today. How much colder? We will learn how to do this calculation in the simplest way in Chapter 3, and add sophistication to the calculation in Chapter 4. It turns out that if the atmospheric composition were the same as today's atmosphere throughout Earth's history, then Earth should have been completely frozen over 4 billion years ago, and given that ice reflects sunlight so well, it should still be completely frozen over today. However, we know that incidents of global ice coverage are rare in Earth history, if indeed they happened at all; we know with rather more certainty that the Earth is not solidly frozen over today. This contradiction is generally known as the Faint Young Sun Paradox, though of course, like most paradoxes it is not paradoxical at all once one understands what is going on. Calling it a "paradox" is just a way of starkly bringing home the fact that to account for the basic facts of
Earth's climate history, the atmosphere must indeed have undergone massive changes - changes of a sort that could substantially affect climate. How much would we need to increase CO2 or CH4 in order to make up for the faintness of the young Sun? This is another one of the big questions. It will be answered in Chapter 4. A related Big Question is the extent to which CH4 (or some other long-lived greenhouse gas) substituted for CO2 in maintaining the Earth's warmth during the Archaean. There is scattered evidence from mineral composition of fossil soils that during some periods of the Archaean the CO2 concentration might not have been high enough to offset the Faint Young Sun. This has led some researchers to jump to the conclusion that CH4 played the decisive role throughout the Archaean, but such a viewpoint rests on exceedingly shaky evidence. It matters a great deal whether CO2 or CH4 did the trick, since the long term control of the two gases is governed by very different processes, with very different time scales. The matter, at present, must be considered unresolved.
A corrollary to the above resolution of the Faint Young Sun Paradox is that any atmosphere that would be sufficient to keep the Early Earth unfrozen would make it uninhabitably hot with the present Solar output. The atmosphere must have somehow changed in lock step with the brightening Sun, in precisely such a manner as to keep the Earth in a habitable temperature range - one where liquid water exists at or near the surface, but where the water never gets hotter than about 100C - or indeed, even hotter than about 50C if cyanobacteria are to survive. It defies belief that the required co-evolution of atmosphere with solar output could maintain the required temperature range purely by coincidence, so it seems likely that some sort of temperature-regulating mechanism is in operation. In Chapter 8 we'll see how the Urey reaction can participate in a geochemical thermostat for the Earth and similar planets. The Snowball episodes represent temporary, and evidently rare, breakdowns of the temperature-regulating mechanism. Whatever the regulating mechanism may be, it must be sufficiently fail-safe to allow for recovery from global or near-global glaciations.
Given what we laid out earlier concerning the myriad processes churning out turmoil in atmospheric composition, the reader should quite rightly feel it a bit silly to make the stipulation "all other things being equal" in the statement of the Faint Young Sun Paradox. Indeed, even if the solar output were constant over time, any number of the aspects of atmospheric evolution we discussed earlier would have been sufficient to freeze or fry the Earth, so the gradual increase in solar output has no special claim on our attention in this regard. To be fair, when the "paradox" was first laid out, much less was known about the ways the Earth's atmosphere evolved, and with much less certainty. From the standpoint of current science, however, the traditional framing of the Faint Young Sun Paradox leaves a lot to be desired. It would be more satisfactory to refer to the Habitability Problem, which could be stated as follows: How can the temperature of a planet be maintained in the habitable range for billions of years, in the face of geological, geochemical and biological turmoil in atmospheric greenhouse gas composition, and in the face of gradual increase in solar output?. This is indeed one of the grandest of questions. The material discussed in Chapter 8 provides a plausible solution, but the book is far from closed on the Habitability Problem.
The history of the Faint Young Sun problem reveals something magnificent and deeply inspiring about the nature of discovery in Earth and planetary climate. The basic physics underpinning the energy source of stars was worked out by Hans Bethe by 1939, and the existence of benign conditions on the Early Earth was known (or at least inferred) even earlier. Yet, it was not until 1972 that Carl Sagan and George Mullen put the two bits together and inferred that there was indeed a big problem, requiring a profound answer 4. This insight sparked a revolution
4Sagan and Mullen proposed accumulation of atmospheric ammonia as a resolution to the paradox, but later work on atmospheric chemistry showed that sunlight destroys ammonia too rapidly to allow it to build up to the required concentrations. Attention later shifted to CO2 and CH4.
in thinking about planetary climate, that was in its own way as earthshaking as the discovery of DNA was in its own domain. This history highlights a lovely thing about our subject: The most profound new phenomena are often discovered by putting together a few bits of basic physics and chemistry in creative new ways. For the most part, new ideas come from playing with simple models, not from enormous incomprehensible computer simulations that take huge teams to put together. The entire goal of this book is to teach students to think the way Carl Sagan and other innovators did, and to provide the tools needed to build the simple models needed to turn a bright idea into real science.
The problem of maintaining long-term climate stability is not just an issue for Earth. Planets that could support some form of life are naturally of special interest, and while other forms of life than those we know of might prefer quite different conditions than prevail on Earth, the long-term maintainence of climate in a fairly narrow "habitable" range clearly would make it easier for life to evolve and persist. Any potentially life-bearing planet in any solar system anywhere must negotiate a way to maintain long-term habitability in the face of the gradual increase of the brightness of its sun and gradual or not-so-gradual changes in the composition of its atmosphere. Naturally, such considerations apply to the evolution of the climates of other planets in our very own solar system. Venus and Mars did not manage to maintain their habitability, or perhaps were never in a habitable state. How close did we come to the same fate?
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