The relationship of CO2 to temperature


Is temperature a function of CO2 or is CO2 a function of temperature i.e.

Is T=f(CO2) or CO2=f(T) ?

The answer according to Richard Betts is both, because increasing CO2 warms the planet but levels in the atmosphere also respond to ENSO cycles. However for the last 50 million years until now, CO2 levels have only ever reacted to changes in temperature rather than being the cause of temperature change. Glacial cycles are driven by regular variations in the earth’s orbit around the sun. The most important of these are changes to the tilt of the  earth’s rotation axis to its orbital plane which determines the distribution of solar energy with latitude and with season. During a glacial cycle CO2 levels rise in synch with temperature but fall out of synch with reducing temperatures, never exceeding 290ppm. The Biosphere seems to regulate maximum CO2 levels at ~280ppm for as long as possible into the next glaciation. Eventually spreading ice sheets destroy this Biosphere balance and CO2 levels then fall rapidly, reaching as low as 190ppm at LGM.

Today though we have a totally different situation. Human emissions of CO2 since 1900 are artificially increasing CO2 levels during an otherwise fairly cool interglacial. CO2 has rapidly increased beyond 280 ppm ahead of any associated increase in  temperature. So now we are studying the T = f(CO2) dependence. Yet such a situation has only occurred once before, some 55 million years ago (PETM), when the earth’s climate was already far warmer than today.

Artificially increasing CO2 must reduce slightly the IR radiation escaping to space from the atmosphere. This results in a sudden energy imbalance causing the surface to warm slightly in compensation, thereby restoring energy balance. The reduction in outgoing IR energy with more CO2 is because the effective height of emission rises to a colder level. All layers in the atmosphere, including the surface, are in local thermodynamic equilibrium at the appropriate lapse rate temperature. Of course if the surface warms up a bit then there will also be a bit more evaporation and more clouds because 70% of the earth is covered by oceans. This is where it gets complicated and no-one really knows how much it really will warm if we double CO2. Climate models may claim to take all these feedbacks into account but at the end of the day they are just guesses, which is also why there is such a large spread in resultant climate sensitivity.

During Glacial cycles climate change is induced by changes in orbital insolation and CO2 comes along for the ride as a feedback. Interglacials begin with a burst of very fast warming. Initially increases in CO2 are due to outgassing from warmer oceans. However the biosphere then flourishes in this new warmer and wetter climate. This seems to limit the increase in CO2 such that levels never exceed 280 – 300 ppm independent of how warm the interglacial gets. There is not a simple one to one relation between temperature and CO2. CO2 ne f(T) when the climate is driven by orbital cycles. Interestingly though 280ppm also happens to be the peak for the atmosphere to radiate heat to space for the current climate.

280ppm is optimised for radiative cooling of the atmosphere by CO2 in today’s climate. This cooling then drives convection, generates the lapse rate and bootstraps the greenhouse effect.

To understand better what happens if CO2 suddenly increases while everything else  remains constant we need to look at PETM 55 million years ago. The climate conditions then were radically different than those of today.  CO2 levels were 1000ppm and temperatures  8-10C warmer than today. The Arctic ocean was isolated and warm. The Himalayas had yet to form, and Antarctica was joined to South America and still ice free. The Atlantic ocean was expanding and North America was about to split from Eurasia.

Up to 6000 GTC was emitted into the atmosphere during in a short period of time at PETM.  For comparison, human emissions to date are 500 GTC and if we were to burn all known reserves of fossil fuels they would become 2000GT. The source of the carbon for  PETM is not known but may be connected to volcanism associated with the opening of the Atlantic ocean

This is a reconstruction from ocean core proxy measurements of PETM (taken from the book ‘Paleoclimate’ by Michael Bender).

Temperatures rose by about 5C and both CO2 levels and temperatures recovered within about 100,000 years. Does this tell us what will happen if humans double CO2 levels ? The main difference today is that the natural climate is much colder than the Eocene with regular 100k glacial cycles. The temperature falls by over 5C between an interglacial as now and a glacial minimum. The likely effect in the Holocene would be that an anthropogenic warming of  ~4C would be reduced back to zero as the earth’s tilt reduces, allowing the earth to  skip the next ice age, which I estimate will start in 15000 years time.

Orbital parameters today are very similar to the Anglian interglacial with low eccentricity suppressing precession of the equinoxes. For this reason the Holocene would naturally have lasted longer than normal. However a minimum obliquity will occur in 12000 years time, and this always heralds a new glaciation.

Near term global warming is not to be welcomed and will surely have near term negative effects. However, such an AGW spike peaking in 2100 would have a silver lining by making the next glacial cycle habitable for North Americans and Europeans !

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