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From a comment in another question here,

Oh, and a third factor: the added atmospheric CO2 does not magically go away once all the fossil fuels are burned. It will stay in the atmosphere for thousands of years, if not more, and will keep on heating things up. Currently the ocean absorbs a lot of the increased heat, and since the circulation time to the deep ocean is 100 years or more, heating will keep on for quite a while.

How much could Earth's temperature increase by the time we run out of oil reserves?

But recent reports from ESA satellite and others says,

Air pollution over Italy is seeing a drop after the country introduced a nationwide lockdown in response to the novel coronavirus outbreak

New data from the European Space Agency’s (ESA) Copernicus Sentinel-5p satellite, which can measure concentrations of greenhouse gases and pollutants in the atmosphere, shows that between Jan. 1 and March 11, concentrations of nitrogen dioxide over Italy fell dramatically

China has also shown a sharp reduction in pollution and greenhouse gas emissions after travel bans and quarantines

Italy sees drop in pollution

Now with this, you still could interpret that by reduction of pollution they only meant Nitrogen dioxide and excluded CO2, but from here,

Italy emissions Coronavirus

This will have just a minor effect of global concentrations of CO2, unless it leads to a really long depression of the world economy

Would pollution / greenhouse houses really take a lot of years to disappear from the atmosphere once people stop producing them?

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    $\begingroup$ It depends on the substances you are talking about. That makes your question awfully broad - can you edit it and ask about one specific (group of) substance(s) - especially in the title? $\endgroup$
    – Jan Doggen
    Commented Mar 17, 2020 at 16:29
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    $\begingroup$ Pollution is really the wrong word to use here. What you want to look at is the residence times (equivalent to radioactive half-life) for different chemicals. Some are unstable and decompose quickly, others (like CO2) have much longer residence times. What you're seeing in those measurements is a drop in the emissions. If particular chemicals decompose or react quickly, you also see a drop in atmospheric concentration. With CO2, since it's long-lived, the most you would see is a halt to the increase. $\endgroup$
    – jamesqf
    Commented Mar 17, 2020 at 18:53
  • $\begingroup$ Faintly I recall that an atmospheric researcher assembled his colleagues to monitor the decrease of air pollution in the days just past 9/11 where basically all air traffic with and within the U.S.A. shutdown for once and for all. (Which may differ from the current situation of banning flights across the oceans on one, but gradual thinning e.g., liasons within Europe / domestic liasions in the U.S.A, on the other side). Maybe some of you may indicate a citeable reference to this study. $\endgroup$
    – Buttonwood
    Commented Mar 17, 2020 at 20:58
  • $\begingroup$ Note the use of the word "emissions". In means that the output to the atmosphere decreased, but it doesn't mean that the stuff we put there a year ago is gone. $\endgroup$
    – Gimelist
    Commented Mar 17, 2020 at 22:02
  • $\begingroup$ This post lacks clarity. Specify the pollutant you are interested in and make your question clear. Every pollutant has a different atmospheric process. Voting to close. $\endgroup$
    – f.thorpe ♦
    Commented Mar 18, 2020 at 0:23

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[I apologise for this long & somewhat scrappy answer. It may contain significant errors, for which I apologise as well.]

How long something persists in the atmosphere once it's there depends, obviously, on how it gets removed from the atmosphere and also if anything is adding it to the atmosphere. Different things we might consider pollutants will have different lifetimes, often very different, and it's confusing to lump them together as 'pollution'.

However there is a very important distinction to be made:

  • one thing we could care about is 'how long do we expect an individual atom/molecule/particle of $x$ to remain in the atmosphere before it leaves it?'
  • another thing we might care about is 'how should we expect the concentration of $x$ to behave in the atmosphere over time?'

These two things are not the same. They are not the same because, even considering only 'natural' processes (which we might define as 'processes not resulting from the burning of fossil fuels or industrial activity') absorption is not all that happens: emission also happens.

The thing that is interesting to know is generally the second: 'how does the concentration of $x$ go over time?' That's because no-one actually cares whether a given unit of something stays in the atmosphere for long: they care about how much of it there is in the atmosphere: I don't care whether I'm breathing some particular oxygen molecules, I care that there is enough oxygen in the atmosphere that I can breathe.

Removal mechanisms

There are at least three mechanisms for removing something from the atmosphere.

  • It may not be stable in the atmosphere. A good example of this is methane, which gets turned into other things over a few years. If methane emissions (including natural ones) stopped it would essentially all disappear within a few decades at most.
  • It may leave the atmosphere by falling out of it or by being involved in precipitation. This is true for aerosols (particulates) in the atmosphere: aerosols with large particle sizes really fall out of the atmosphere, aerosols with very small particle sizes get removed by precipitation and intermediate size ones experience both processes.
  • It may get actively absorbed by something on the surface.

A fourth mechanism is 'it may escape to space' but this is not a significant process anything interesting here, so I'll ignore it. There may be other mechanisms I have not remembered.

Addition mechanisms

There are, I think, two significant mechanisms for creating stuff in the atmosphere:

  • it may be emitted by something on the surface;
  • it may be created by some process in the atmosphere.

(And again, it may arrive from space, but I'll ignore that.)

How long things persist in the atmosphere

So, now, how long things persist in the atmosphere depends on what they are: the term 'pollution' bundles together things which have radically different characteristics.

  • Human-generated aerosols (smoke, other aerosols) have relatively short lifetimes in the atmosphere and are not created by processes in the atmosphere, and so will fairly quickly decline in concentration once emission stops.
  • Aerosols of water – clouds – are created in the atmosphere, from water vapour which will continue to be emitted from the surface, and are also removed from the atmosphere as rain, but these processes balance out over time and so clouds will persist in the atmosphere. Clouds are not a pollutant of course: I just wanted to add them as another type of aerosol with another lifecycle in the atmosphere.
  • $\mathrm{NO_x}$ has a relatively short lifetime in the atmosphere as it's not stable: its lifetime in the lower atmosphere is hours, and in the upper is not more than few weeks. Some $\mathrm{NO_x}$ is created in the atmosphere by lightning, but I think the quantities are rather small compared to the amounts created by human emissions. So the amount in the atmosphere will decline pretty quickly once emission from the surface stops.
  • and so on.

The elephant in the room: $\mathrm{CO_2}$

$\mathrm{CO_2}$:

  • is pretty much chemically stable and so does not decay in the atmosphere (it does undergo processes of being dissolved in water droplets and then evaporating from them, and perhaps others);
  • is not an aerosol and so does not leave the atmosphere by the mechanisms which affect aerosols, unless it is dissolved in aerosols of water;
  • is absorbed by several processes on the surface;
  • is also emitted by several natural processes on the surface.

The things which absorb $\mathrm{CO_2}$ on the surface are, among others (not necessarily in order):

  • plants, which absorb $\mathrm{CO_2}$ and turn it into plant and oxygen;
  • the oceans, which dissolve $\mathrm{CO_2}$;
  • rock weathering;
  • other things.

The natural (see above definition!) processes which emit $\mathrm{CO_2}$ are (not in order):

  • plants and animals which respire;
  • plants (and animals) which die & decay or catch fire, releasing $\mathrm{CO_2}$ back to the atmosphere;
  • the oceans, which release dissolved $\mathrm{CO_2}$ back to the atmosphere;
  • vulcanism;
  • other things.

So in order to know how $\mathrm{CO_2}$ behaves over time we need to understand how the various processes work: how fast is $\mathrm{CO_2}$ cycled through the atmosphere and how fast does the concentration change.

Understanding this is not simple, and it's why people write big climate and earth system models. But it's possible to give ballpark numbers.

The answer to the first question: 'how long does an individual $\mathrm{CO_2}$ molecule spend in the atmosphere' is 'a few years'.

The answer to the second question: 'how long would it take for $\mathrm{CO_2}$ concentrations to decline to preindustrial levels if fossil-fuel burning stopped, is 'from a few hundred to a few thousand years'.

The reason for the large difference between these numbers is that the natural processes that absorb and emit $\mathrm{CO_2}$ are very close to being in balance. This is easy to see because we know that the concentration of $\mathrm{CO_2}$ in the atmosphere was not zero before we started burning fossil fuels.

Just to give some figures (these are not meant to be accurate):

  • plants absorb about $120\,\mathrm{GtC/y}$ through photosynthesis;
  • plants emit about $60\,\mathrm{GtC/y}$ through respiration;
  • about $60\,\mathrm{GtC/y}$ is emitted from decay of plant matter;
  • the oceans absorb about $90\,\mathrm{GtC/y}$;
  • the oceans emit about $90\,\mathrm{GtC/y}$.

As it stands this is completely balanced. Well, these figures are approximate, and there are other processes both of absorption and emission. But it's close to being in balance.

This is why the concentration of $\mathrm{CO_2}$ would fall only rather slowly if fossil-fuel burning stopped.

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    $\begingroup$ Good answer. Just one nitpick: Some NOx is created in the atmosphere, by lightning, which is part of the natural nitrogen cycle. (Human-created NOx pollution is, I think, a problem mostly localized to urban areas.) See e.g. en.wikipedia.org/wiki/Nitrogen_cycle for more. $\endgroup$
    – jamesqf
    Commented Mar 18, 2020 at 18:53
  • $\begingroup$ @jamesqf: I've reworded that bit to be better I hope – mentioning it is created in the atmosphere (which I didn't know but should have). Thank you $\endgroup$
    – user18801
    Commented Mar 19, 2020 at 9:41
  • $\begingroup$ This article claims different, it says "Global emissions would need to fall by more than 6% every year this decade – more than 2,200MtCO2 annually – in order to limit warming to less than 1.5C above pre-industrial temperatures" carbonbrief.org/… $\endgroup$
    – Pablo
    Commented Apr 10, 2020 at 13:02
  • $\begingroup$ @Pablo: that's very possible: I think the usual figure for 1.5K is we need to halve human emissions by 2030, and 6% a year is about that (and then of course we need to keep decreasing them after that). Doing that leaves enough excess $\mathrm{CO_2}$ in the atmosphere to raise average temperatures by 1.5K over preindustrial, and that excess would then presumably very slowly decline back to somewhere near preindustrial levels. $\endgroup$
    – user18801
    Commented Apr 11, 2020 at 9:38
  • $\begingroup$ Another article on the matter "Keeling estimated that global fossil fuel use would have to decline by 10% for a full year to show up in carbon dioxide concentrations" climatechangenews.com/2020/03/26/… $\endgroup$
    – Pablo
    Commented Apr 12, 2020 at 13:55

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