# The Atmosphere is getting heavier

The earth’s atmosphere is gaining mass due to fossil fuel burning.  When we burn coal we add extra carbon atoms to the atmosphere in the form of CO2. For every O2 molecule that we take out of the atmosphere we simply release back an extra carbon atom tacked on. The net effect of this is to increase the total mass of the atmosphere, resulting in a net  increase in atmospheric pressure. How large is this effect and  are there any long term consequences? I decided to look into this after a twitter exchange. All estimates  and any errors are all my own fault. First some facts.

• Molar mass of CO2 is 41 44g/mol
• Molar mass of O2 is 32g/mol
• Mean molar mass of air is 29g/mol

CO2 levels have increased by about 43% since 1750. This means that about 0.14% of atmospheric oxygen has been converted to CO2. This is also confirmed by measurements.

O2 levels are falling by about 19 parts per million each year. This has no effect on nature or on human health, but it is still significant.

So the net fractional increase in mass for the oxygen component is 0.0014*(44-32)/32 = 0.0005. Oxygen is 20% of the atmosphere but makes up 28% of its mass. Therefore the increase in atmospheric mass caused so far by fossil fuel burning is 0.0011 0.0014%. This works out at ~ 5.7 7.2 x 10^14 kg

This figure is nearly half of the annual variation in atmospheric mass of 1.5 x 10^15 kg due to water vapor (1.5 x 10^15 kg). So it is certainly not negligible. This increase in mass m implies a proportional increase in surface pressure $P_s$ through the hydrostatic relationship
$P_s = mg$
Therefore average surface pressure has increased by ~ 0.011 mb. Does such a small increase matter? What effects if any will this extra mass have?

• Firstly the slight increase in surface pressure combined with a 40% increase in CO2 density will increase the absorption of CO2 in the world’s oceans.
• Secondly the extra CO2 molecules will lead to an enhancement in the dissociation of CO2 by UV to CO and O2 in the stratosphere.
• Thirdly a higher concentration of CO2 will lead to enhanced rock weathering through the dissolving of CO2 in rainwater.

All these tend to increase the natural sinks that remove CO2 from the atmosphere over the long term.  The retention of CO2 emissions is stable at about 42%, so about half of the excess is absorbed each year. This fraction has not noticeably changed for several decades. More subtle effects I can think of are as follows.

• Barometric pressure falls as $P = P_0 \exp{- \frac{M_ag}{RT}z}$ There has been a very small increase in M_a (molecular weight of air) which therefore will slightly decrease the scale height. The troposphere shrinks a little.
• There would also be a very small increase in the Dry adiabatic lapse rate $\Gamma = -\frac{g}{C_p}$ because $C_p$ for CO2 is 16% smaller than ‘air’.

The first effect would tend to offset the enhanced CO2 greenhouse effect, whereas the second would enhance it further, although this lapse rate change (1 part in a thousand) is essentially negligible.  In any case, I doubt whether any of this is included in any climate model.

Update: corrected for Molar mass of CO2 (44 not 41)

PhD High Energy Physics Worked at CERN, Rutherford Lab, JET, JRC, OSVision
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### 24 Responses to The Atmosphere is getting heavier

1. Ron Graf says:

“The retention of CO2 emissions is stable at about 42%, so about half of the excess is absorbed each year. This fraction has not noticeably changed for several decades. “

Clive, do you have some good references for determining the ocean and other sinks’ rate of uptake and what the kinetics are as the concentrations shift further off equilibrium? I am guessing the equilibrium is dynamic with the rate of ocean overturning, particularly at the arctic down-welling zones. Judging from the paleo record of range I am guessing the current equilibrium is with a ~300ppm atmosphere. When fossil fuel emissions stop or the temperature gets cooler this level should slowly sink and thus speed the kinetics of the carbon sink, especially if there is carbon fixing biological elements in the oceans.

Do you think the CMIP models accurately model ocean uptake of CO2 for the RCP8.5 and other simulations?

• Clive Best says:

Ron,

I have the book by David Archer – The Carbon Cycle which is good because not only does it describe what we do know it also highlights just how much we still don’t know. The basic premise is that over geological times the carbon cycle acts to stabilize and regulate the earth’s climate. This is mainly because the weathering of rocks is temperature dependent. This means that no matter how much CO2 humans emit the atmosphere and climate will recover over a period of tens of thousands of years. However we are in a glacial cycle so there is no single stable value for CO2 levels.

About 50 million years ago there was a sudden release of CO2 roughly equal to the burning of all known reserves of fossil fuels. This is the Paleocene-Eocene Thermal Maximum – PETM.

Currently half our emissions are seemingly absorbed in the surface zone of the oceans and this doesn’t seem to have saturated yet. If we can just stop increasing emissions and either hold them constant at some (reduced) level then (I think) CO2 levels will eventually stabilize.

I suspect all CMIP5 models use the BERN model which has 3 independent lifetimes and a constant value. This constant term implies that 22% of emissions will remain forever which is clearly incorrect as the PETM shows. With a single lifetime you can show that levels must stabilize. see : https://clivebest.com/blog/?p=2391

2. Javier says:

We tend to believe that conditions on Earth are ideal just when modern civilized man showed up a few centuries ago. This is pure anthropocentrism. Everything indicates that conditions on Earth have deteriorated progressively to the sorry state of the Quaternary.

Over the last 30 million years plants have had to evolve numerous times a mechanism to survive the low CO2 levels of the atmosphere, resulting in plants that can increase their internal CO2 pressure and thrive in the harsh low CO2 levels of glacial periods.

We know there has been a continuous reduction in terrestrial animal size also. The planet cannot support the giants of the past. Mammals reached their maximum size between 50-30 million years ago and it has been downwards since.

We know the atmosphere must have changed too. Not only the large pterosaurius, like Quetzacoatlus, but also the giant flying birds of the Eocene-Oligocene, like Argentavis magnificens and Pelagornis sandersi, with a wingspan of 6-7 meters (20-23 feet) could not fly today according to modern flight theory. They were over twice the size of the largest flying birds today. Some scientists speculate that a CO2 richer atmosphere was also denser and supported larger flying animals. A higher oxygen content could also allow higher metabolic rates for larger animals.

Atmospheric CO2 content appears to have been on a downward trend for the last 600 million years at least. If this trend continues in the future, as vulcanism diminishes, very small animals will be the norm, and later just bacteria. A geologically brief explosion of complex life thanks to atmospheric CO2.

• Clive Best says:

Javier,

You’re right and in some senses the Pleistocene has been a far tougher environment for life to thrive than previous epochs. Certainly plants have had to evolve leaves with small stomata to cope with lower levels of CO2.

There is something of a mystery (at least to me) as to why the natural level in an interglacial should be 280 ppm. Why not 400 ppm? There is something very subtle going on which keeps CO2 levels low but not quite low enough to kill plant life.

One clue might be due to CO2 radiative cooling of the atmosphere for Tsurf=288K. 280ppm turns out to be about optimum for the atmosphere itself to radiate heat to space. Too little and the surface radiates directly to space. Too much and the atmosphere radiates only from cold regions.

• Javier says:

It is not only the stomata, Clive. C4 photosynthesis with its associated morphological and biochemical modifications evolved numerous times within different higher plant taxa in response to low CO2 concentrations in the Paleogene-Neogene transition. C4 plants concentrate CO2 internally in bundled sheath cells even when atmospheric CO2 is low, allowing the plant to continue growing. Although only 3% of plant species are C4, they represent above 15% of plants today, indicating a huge advantage. They have radically altered many of the Earth’s ecosystems, manifesting the profound effect of low CO2 concentrations.

Also agriculture was not possible until CO2 raised from 200 to 270 ppm between 15-10,000 years ago, and then it was almost simultaneously and independently discovered in every adequate region. Much of the success of modern agriculture is due to the further increase to 400 ppm.

Gerhart, L. M., & Ward, J. K. (2010). Plant responses to low [CO2] of the past. New Phytologist, 188(3), 674-695.

• Alan Poirier says:

Point well taken. We live in a CO2 starved epoch and our climate is far from hospitable for both flora and fauna. Humans, to be sure, have adapted. Ironically our adaptability has been a boon for the world, returning fossilized CO2 to the atmosphere.

• Frank says:

Javier: You exaggerate when you say that agriculture was simultaneously discovered in every adequate region between 15-10,000 years ago (see below) and suggest that rising CO2 levels were critical to this process. If high CO2 levels were all that were critical, then agriculture could have begun during the Eemian interglacial.

If you think about it, the key factor probably was the behavior of man. AFAIK, crops were accidentally bred when man began living in one location for long enough to accidentally breed (select) strains that were superior for use by man rather than survival in the wild. And the FOXP2 mutation that made speech more practical apparently occurred during the last glacial period, perhaps making permanent settlement on fertile ground more practical.

From Wikipedia: From around 9500 BC, the eight Neolithic founder crops, emmer and einkorn wheat, hulled barley, peas, lentils, bitter vetch, chick peas and flax were cultivated in the Levant. Rice was domesticated in China between 11,500 and 6,200 BC, followed by mung, soy and azuki beans. Pigs were domesticated in Mesopotamia around 13,000 BC, followed by sheep between 11,000 and 9,000 BC. Cattle were domesticated from the wild aurochs in the areas of modern Turkey and Pakistan around 8,500 BC. Sugarcane and some root vegetables were domesticated in New Guinea around 7,000 BC. Sorghum was domesticated in the Sahel region of Africa by 5000 BC. In the Andes of South America, the potato was domesticated between 8,000 and 5,000 BC, along with beans, coca, llamas, alpacas, and guinea pigs. Cotton was domesticated in Peru by 3,600 BC. In Mesoamerica, wild teosinte was domesticated to maize by 4,000 BC.

• daveburton says:

Clive wrote, “There is something of a mystery (at least to me) as to why the natural level in an interglacial should be 280 ppm. Why not 400 ppm? There is something very subtle going on which keeps CO2 levels low but not quite low enough to kill plant life.”

It’s because at 400 ppmv CO2 plants (and calcifying coccolithophores in the ocean) grow faster, and drive down the CO2 level.

Mankind’s fossil fuel use adds about 35 Gt of precious air fertilizer to the atmosphere each year, but the IPCC estimates that, each year, either 27% or 29% of anthropogenic CO2 emissions are removed from the atmosphere through “greening,” otherwise known as the “fertilization effect” of CO2, which causes accelerated plant growth. It’s a “negative feedback” mechanism: as CO2 levels go up, plants remove CO2 from the atmosphere faster, reducing CO2 levels, and thus attenuating the effect of CO2 emissions. On p. 6-3 of AR5 they give these numbers:

“During 2002–2011, atmospheric CO2 concentration increased at a rate of 2.0 ± 0.1 ppm yr–1 (equivalent to 4.3 ± 0.2 PgC yr–1 54 ); the ocean and the natural terrestrial ecosystems also increased at a rate of 2.4 ± 0.7 PgC yr–1 and 2.5 ± 1.3 PgC yr–1 55, respectively.”

That would work out to:
4.3 / (4.3+2.4+2.5) = 4.3 / 9.2 = 47% remained in the atmosphere
2.5 / 9.2 = 27% went into the biosphere (“greening”)
2.4 / 9.2 = 26% went into the ocean

Their figure 6.1 gives slightly different numbers:

2.6 / (7.8 + 1.1) = 2.6 / 8.9 = 29% went into the biosphere (“greening”)
2.3 / 8.9 = 26% went into the ocean
(8.9 – (2.6+2.3)) / 8.9 = 45% remained in the atmosphere

If mankind weren’t burning fossil fuels, the CO2 level wouldn’t stay at 400 ppmv. At 400 ppmv, plants use so much more CO2 than is produced by animal respiration (+ natural combustion + decay processes) that atmospheric CO2 levels would be falling about 1 ppmv per year, even if the oceans weren’t also absorbing CO2.

Have you ever wondered about the anomalously high level of free oxygen in the Earth’s atmosphere?

On Venus and Mars nearly all the oxygen in the atmosphere is in the form of CO2. O2 is nearly non-existent, because it is more reactive, and combines with other elements to make less-reactive, more stable molecules, like CO2, H2O, SO2, etc.

But on Earth, other than water vapor, 99.8% of the oxygen in the atmosphere is in the form of O2. Only 0.2% is in CO2, despite animal respiration (& fires, etc.) which constantly produce CO2 from O2.

Have you ever wondered why?

It’s because Venus and Mars are dead planets, and Earth is not.

On Earth, CO2-hungry living things have stripped nearly all the CO2 from the atmosphere, to get the carbon, releasing the O2 as a waste product. That’s why, although 21% of the Earth’s atmosphere is oxygen, carbon dioxide levels are measured in parts-per-million.

The CO2/O2 balance is determined by a race between plants and animals. Animals use O2 and produce CO2; plants use CO2 and produce O2. But there are a lot more plants than animals, and in the tug-o-war between plants and animals the plants have won. They’ve tugged the CO2-O2 tug-of-war rope all the way to the end. Animals are relatively scarce, compared to photosynthetic plants, and the plants have used up nearly all the CO2. The animals just can’t produce enough CO2 to keep up.

The plants would use much more CO2, but they ran out of it. The chronic shortage of CO2 in the Earth’s atmosphere is the primary limit on plant growth. That’s why anthropogenic CO2 emissions, which have increased atmospheric CO2 from about 0.03% in the 1940s to about 0.04% today, are directly responsible for 15%-20% of current agricultural productivity.

If CO2 were still at 0.03% instead of the current 0.04% of the atmosphere, we’d need 18-25% more land under cultivation, just to maintain current agricultural output. If all the world’s rain forests were put under cultivation, that would almost, but not quite, make up the deficit. The rain forests can thank anthropogenic CO2 for their continued existence!

• Ron Graf says:

Life in the oceans is limited by dissolved iron.
https://en.wikipedia.org/wiki/Iron_fertilization

“In an article in the scientific journal Nature (February 1988; 331 (6157): 570ff.), John Gribbin was the first scientist to publicly suggest that the upcoming greenhouse effect might be reduced by adding large amounts of soluble iron compounds to the oceans of the world as a fertilizer for the aquatic plants.

Martin’s famous 1988 quip four months later at Woods Hole Oceanographic Institution, “Give me a half a tanker of iron and I will give you another ice age”, drove a decade of research whose findings suggested that iron deficiency was not merely impacting ocean ecosystems, it also offered a key to mitigating climate change as well.

Perhaps the most dramatic support for Martin’s hypothesis was seen in the aftermath of the 1991 eruption of Mount Pinatubo in the Philippines. Environmental scientist Andrew Watson analyzed global data from that eruption and calculated that it deposited approximately 40,000 tons of iron dust into the oceans worldwide. This single fertilization event generated an easily observed global decline in atmospheric CO
2 and a parallel pulsed increase in oxygen levels.”

• daveburton says:

The fertilization of the oceans with iron is key to a recently hypothesized negative (stabilizing) feedback mechanism:
http://www.sealevel.info/feedbacks.html#iceiron

However, I thought the flattening of CO2 growth following the Mt Pinatubo eruption was because it cooled the oceans, and cooler water absorbs CO2 faster:

• Ron Graf says:

If the oxygen analysis is accurate then one can parse both effects, the delta in CO2 uptake from equilibrium shift in solubility and the delta in photosynthesis.

• clivebest says:

The 21% oxygen in the atmosphere is exactly equal to all the buried carbon mainly in sedimentary rocks. Fossil fuels are a tiny quantity in comparison.

Most of the CO2 absorbed by plants is soon liberated to the atmosphere when they die or are eaten by animals, while only a tiny amount of carbon is buried in sediments. Even by including this recycling effect we still find CO2 depletion of the atmosphere by plants takes a mere 13,000 years while phosphorous depletion takes only 29,000 years. So what are we doing wrong?

The incredible story is that these trapped sediments are not lost from the environment for ever because plate tectonics recycles material over very long timescales today. Subduction, mountain building and sea level change continuously re-exposes the raw materials for life through weathering. This recycles phosphorous and CO2. Plate tectonics is essential to re-cycle the raw materials for life on earth !

3. Chic Bowdrie says:

CO2 = 44 g/mol

• Clive Best says:

Thanks! Corrected it now. Increases values by about 25%.

4. daveburton says:

Clive wrote, “There would also be a very small increase in the Dry adiabatic lapse rate (gamma = g/Cp) because Cp for CO2 is 16% smaller than ‘air’. … this lapse rate change (1 part in a thousand) is essentially negligible.”

I get 1 part in about 50,000, rather than 1 part in 1000.

I might have goofed. See if you spot an error:

We’re contrasting Cp (specific heat capacity) of air w/ 280 ppmv CO2 to Cp of air w/ 400 ppmv CO2.

The increase in CO2 is 120 ppmv.

If Cp of Air is 1.01 at 280 ppmv CO2 then, and Cp of CO2 is 0.844 (ref), then:

Cp of Air at 400 ppmv CO2 is ((1 – 0.000120) * 1.01) + (0.000120 * 0.844) = 1.00998008.

So Cp decreases from 1.01 at 280 ppmv CO2 to 1.00998008 at 400 ppmv CO2.

Lapse rate gamma = g/Cp increases from g/1.01 to g/1.00998008.

The ratio of gamma at 400 ppmv CO2 to gamma at 280 ppmv CO2 is:

(g / 1.00998008) / (g/1.01) = 1.01 / 1.00998008 = 1.0000197,

which an increase of about one part in 50,000 rather than one part in 1000.

• Clive Best says:

Dave,

You are quite correct. I simply estimated the decrease in Cp as 1.2 x10^-4 x 0.84 as if it were added to the atmosphere. So I should have written 1 in 10,000 NOT 1 in a thousand !

I think it also depends slightly on whether you assume that the extra 120 ppm of CO2 is in addition to pre-industrial air, or whether it is instead a conversion of O2 molecules to CO2 molecules.

Does the slight increase in surface pressure also cause more O2 to be dissolved in the oceans? Is atmospheric pressure stabilized as a result ?

• daveburton says:

I had always heard that it was believed that the Earth’s atmosphere is very slowly losing mass, on multi-million-year time scales. But a recent article says the opposite: that the early Earth had a much thinner atmosphere:
http://www.livescience.com/54709-early-earth-atmosphere-was-half-as-thick.html

There are a lot of processes going on which add and subtract from the atmosphere. For instance, nitrogen-fixing bacteria, in symbiosis with clover and legumes, remove nitrogen from the atmosphere. Most oxygenation processes, other than the oxygenation of carbon, remove oxygen from the atmosphere.

I don’t have good intuition about the relative scales of those various processes, compared to effect of adding carbon to the atmosphere by burning fossil fuels, except that I suspect that, over time scales relevant to humanity, those changes in atmospheric pressure are dwarfed by the change in atmospheric pressure when you walk up the stairs to the 2nd floor of your house. (I haven’t done the arithmetic, though.)

5. daveburton says:

(Sorry about the botched /a tag in the previous comment; please just delete that comment.)

Clive wrote, “There would also be a very small increase in the Dry adiabatic lapse rate (gamma = g/Cp) because Cp for CO2 is 16% smaller than ‘air’. … this lapse rate change (1 part in a thousand) is essentially negligible.”

I get 1 part in about 50,000, rather than 1 part in 1000.

I might have goofed. See if you spot an error:

We’re contrasting Cp (specific heat capacity) of air w/ 280 ppmv CO2 to Cp of air w/ 400 ppmv CO2.

The increase in CO2 is 120 ppmv.

If Cp of Air is 1.01 at 280 ppmv CO2 then, and Cp of CO2 is 0.844 (ref), then:

Cp of Air at 400 ppmv CO2 is ((1 – 0.000120) * 1.01) + (0.000120 * 0.844) = 1.00998008.

So Cp decreases from 1.01 at 280 ppmv CO2 to 1.00998008 at 400 ppmv CO2.

Lapse rate gamma = g/Cp increases from g/1.01 to g/1.00998008.

The ratio of gamma at 400 ppmv CO2 to gamma at 280 ppmv CO2 is:

(g / 1.00998008) / (g/1.01) = 1.01 / 1.00998008 = 1.0000197,

which an increase of about one part in 50,000 rather than one part in 1000.

6. Frank says:

Clive: If it were important to know how exactly much heavier the atmosphere has become, there are other factors to investigate. When natural gas is burned, far more oxygen is consumed than when coal is burned. Nor is coal pure carbon, it is about 4-6% hydrogen by weight and 80-90% carbon. (Methane is 75%C and 25%H.) So burning fossil fuels has consumed some oxygen.

The amount of CO2 in the atmosphere is partially limited by the concentration of calcium and magnesium in the ocean and the insolubility of calcium and magnesium carbonates. Most of the ocean near the surface is super-saturated with respect to calcium carbonate, which apparently is slowly “raining” onto the bottom of the ocean. From there, it becomes sedimentary rock, transported via plate tectonics to a volcanic area and returned to the atmosphere. As the planet has weathered, the concentration of calcium and magnesium in the ocean has increased with time. Although the rise of photosynthetic micro-organisms was responsible of converting most of the CO2 in our atmosphere to O2 more than a billion years ago, I assume that the increase in these ions – perhaps in addition to the rise in plants – was responsible for the subsequent long-term downward trend in CO2.

This biggest change in the weight of our atmosphere might come from water vapor. Saturation vapor pressure increases about 6-7% per degK and is 0.4% of the atmosphere. Mean global temperature rises about 3.5 degK seasonally every year (which is masked by taking anomalies) and about 6 degK during interglacials. These changes are on the order of 0.1% of the atmosphere. (Liquid water and water vapor are not in equilibrium in our atmosphere, so I dislike the assumption that relative humidity must remain constant with rising temperature in the upper atmosphere where its GHE is important. However, the bulk of the water vapor is near the surface where constant relative humidity is a more reasonable assumption

• clivebest says:

Frank,

These are all very good points !

Sedimentary rocks contain 99.9% of the carbon extracted from the atmosphere over billions of years. I also agree that on average the largest changes in ‘weight’ of the atmosphere is due to the water vapour seasonal cycle.

7. J Martin says:

If temperature is proprtional to pressure, then an increase in pressure of 0.11 mb gives an increase in temperature of nearly one third of a degree centigrade. ? A not insignificant proportion of the increase we’ve had since co2 went from 280 ppm to 400 ppm.

• J Martin says:

0.011 mb

8. daveburton says:

Re: ” Oxygen is 20% of the atmosphere but makes up 28% of its mass.”

32/29 * .21= 0.23

So I think the correct statement is, “Oxygen is 21% of the atmosphere by volume, but makes up 23% of its mass.”

9. Charles Crumpton says:

Increase in CO2 is warming atmosphere allowing it to hold more water vapor a greenhouse gas that will warm the atmosphere. More heat will release ocean carbon and slow rate of co2 from air to oceans Oceans are rapidly loosing ability to convert CO2 as phytoplankton is decreasing 1% a year. It seems impossible to reverse global warming by cutting back on fossil fuels alone. 50years too late. Water vapor is increasing faster than carbon could be reduced. Cars and energy production cannot be changed over the next 10 years enough to make a dent in CO2. Electric cars are using fossil fuels to charge batteries