Finding a hair in the swimming pool: The signal of changed fossil emissions in the atmosphere

24 April 2020

First published in 24.04.2020

Translations of this text are available: Nederlands, Français, Deutsch, Suomi, Italiano, Czech

Werner Kutsch, Alex Vermeulen and Ute Karstens

When carbon dioxide (CO2) is released into the atmosphere, it will be mixed by the winds and distributed over the whole globe, with time. This process of mixing takes one-to-two months for the northern or southern hemisphere and more than a whole year for the globe, as northern and southern hemisphere only mix slowly. The atmosphere already contains a lot of CO2;  plants need it to grow, and many different processes take up and release CO2, adding to the changes in time and space.  

How fossil fuel emissions influences the CO2 signal of the atmosphere, can be best explained by a simple analogy or model: Let’s assume we have a swimming pool, where the water stand for carbon dioxide in the atmosphere, thus the water level represents the CO2 content of the atmosphere. Rain dripping into the pool stands for the natural emissions of CO2, evaporation of water from the pool represents the uptake of CO2 by plants, and a leak in the bottom of the pool the uptake by oceans. Finally, fossil fuel emissions of CO2  are pictured with an additional tap filling the pool with water.

If one peta-gram  (=1015 g =1,000,000,000,000,000 g) carbon translates into 1 m3 of water, we are talking about a 25 x 15 m pool of 1.57 m depth. There is a natural stream of rainfall going into the pool, that brings every year about 110 m3 fresh water into the pool, about the same amount flows out because of discharge through the leaky bottom and evaporation. Despite the seasonal variation in evaporation and rainfall, the water table is on average stable. However, inflow and outflow are not absolutely in phase, which means the water table is a bit higher in winter and a bit lower in summer. The fluctuation may be +/- half a centimetre, thus in summertime the water table is 1.565 m and in winter time 1.575 m. This means the daily change in the water table may be maximum -0,1 mm (which is the same as 100 µm) per day in spring and early summer and +0,1 mm in autumn and early winter. 

A model of "atmospheric swimming pool" without human influence.
Figure 1: Without any human influence the fluctuation in the ‘atmospheric swimming pool’ would look like this.  This is a theoretical 5-year period with highest values in January and in February, and lowest in July and in August. The reason is that in the norther hemisphere, the terrestrial ecosystems fix carbon dioxide in summer, which they release again during winter.



About 200 years ago someone has installed a second inflow that has increased over time and adds nowadays about 10 extra m3 of water per year to the pool. This has also changed the outflow, about 5.7 m3 of the additional input are flowing out, but 4.3 m3 stay in the pool. The additional water has already caused an increase of 64 cm to an actual water table of 2.21 m. Every year the water table increases currently by 11 mm, on average this is 30 µm per day. This is the diameter of a very thin hair.

Figure 2. The model of how human influence is changing the "atmospheric swimming pool".
Figure 2: The human influence is changing the ‘atmospheric swimming pool’. The annual variations and the additional source combine to a curve that shows ups and downs but also a very clear trend. The increase by about 6 cm in five years is clearly detectable.


The effect of the Covid-19 shutdown – almost impossible to see

The Covid-19-related shutdown has now reduced the additional net inflow from 4.3 to 3.8 m3 per year or the daily increase from 32 to 28 µm. This is the difference between a very thin hair and an even thinner hair. However, it adds up over time and increases with the duration of the shutdown.

Model: The influence of the Covid-19 shutdown distributed equally over 6 months.
Figure 3: The influence of the Covid-19 shutdown(reduction of emissions by 2000 Mt CO2 distributed equally over 6 months): the water table in the ‘atmospheric swimming pool’ would only change a tiny little bit compared to the business as usual scenario.   Blue line: business as usual.    Red line: lower emissions due to the shutdown


Figure 4: Difference between the "business as usual" and the "lower emissions during the shutdown" models.
Figure 4: When looking at it in more detail, it can be seen that the difference between the two curves increase over time. At the end of April, it’s about half a mm; until end of June it might increase to 0.8 mm.  Blue line: business as usual. Red line: lower emissions due to the shutdown.


There is an important lesson to learn from this exercise: the Covid-19 shutdown has almost no influence on the increase of CO2 in the atmosphere. It’s still bad, only a little bit less bad – more about that at the end of this article. And we face the important question being asked several times during the pandemic already: Can we detect the imprint of the shutdown in the atmosphere?

The answer is, as very often in science: ‘in theory YES’. It would be simply the difference between the two curves, our instruments are sensitive enough to do so. However, in practice, there are unfortunately some problems that make the matter extremely complicated and difficult.

1.    We are measuring only one curve. We are not running a controlled experiment with two planets – one with and the other without the shutdown. Thus, we have only the red curve in Figure 4 and we have to relate this curve to either an artificial (modelled) blue curve or to previous years. Both approaches have serious problems. Having an artificial blue curve takes us away from measurements and can always be criticised. Comparing it to other years takes us to the next problem.

2.    The global carbon cycle is not functioning as a simple clockwork. The ups and downs shown in the Figure 1 are not regular, because the weather varies between the years. There might be a warm winter and an early spring in one year, in the next year a late spring, and there might be wet or dry summers, warm or cold autumns.

Figure 5: The natural fluctuation in the ‘atmospheric swimming pool’ shows some inter-annual variability and therefore looks more like this theoretical 5-year period with sometimes higher water table during  
 January and February and lower in July and August than in other years. The reason for this is weather fluctuation.


Figure 6: The human influence is changing the ‘atmospheric swimming pool’. The annual variations and the additional sources combine to a now slightly more irregular curve that still shows ups and downs and still a very clear trend (still an increase by about 6 cm over five years).


Figure 7: The very same curve but now with decreased emissions due to the Covid-19-related shutdown in the last year (red part of the curve). The signal of the shutdown is very subtle. 


Figure 8: The difference between the two curves remains the same as in Fig. 4. It increases over the first 6 months. At the end of April, it’s about 1 mm; until end of June it might increase to 1,5 mm.


Combining the two problems mentioned above (1. we don’t have the blue curve in our data and 2. the fluxes into and out of the ‘atmospheric swimming pool’ vary inter-annually) leads us to the most obvious approach to catch the shutdown signal in the observations. We compare year 5 with the shutdown to the other years.

Figure 9: The water table in the ‘atmospheric swimming pool’ over the five years in a comparative plot. The difference in the position of the plots comes from the trend (anthropogenic emissions) that constantly increases the water table.


Figure 10: The years become comparable by artificially moving them to the same water table in January. The thick blue line represents the Year 5 without the thick red line with the Covid-19-related shutdown. The problem of the approach becomes obvious: the effect of the shutdown is smaller than the inter-annual variability and thus, is difficult to confirm in a statistically significant way.


In addition to the two problems elaborated so far, there is a third problem: wind.

3.    Imagine the pool is outdoors. Then, wind would cause waves. These waves can be several cm in amplitude and disturb the measurements of the water table severely.

Summarising: it is a mission impossible to find a thin hair in a large swimming pool with changing water table and waves.

The answer is in the waves caused by the wind

However, we would not be scientists if we gave up here. And there is indeed a better approach than simply looking for the average concentration. In fact, the information is in the waves. To explain this, we will shortly be changing from the water table in the ‘atmospheric swimming pool’ to the real measurements of CO2 in the atmosphere, which the Integrated Carbon Observation System (ICOS) is providing. However, let’s stay a while longer at the swimming pool , and imagine that the inflow is not happening at only one place of the swimming pool but is distributed throughout the pool. In this setting, the waves might carry the information of the nearby inflow when they are measured constantly and over a longer time.

Now, we turn to the atmospheric measurements. We take a closer look at the atmospheric CO2 concentrations at one ICOS station, the atmospheric tower near Gartow in Germany. As all other ICOS stations it is fortunately up and running to continue monitoring the atmosphere during the shutdown. The concentration is measured in parts per million of CO2, ppm. We can see ups and downs of the concentration that are caused by the wind that – depending on the weather – transports the air masses from different areas in the vicinity of the tower. We can see the general curve with a decrease in spring and summer, and an increase in autumn and winter. And we can see the fluctuations that are caused by the wind transporting air from areas having different amount of emissions. We call these areas ‘footprints’, and for each moment in time we can calculate the footprint area that causes a high or low CO2 concentration. At first glance, the variation has become smaller during the past weeks. This could have two reasons: either the wind brings only air masses from areas with low fluctuations, or it is carrying the imprint of lower emissions. This requires thorough statistical analyses that have not been carried out so far. However, we are sure that imprint of the Covid-19 shutdown can be found in the variation of the atmospheric CO2 concentrations.

Figure 11: Near real time data of atmospheric concentration of CO2 at the ICOS tower near Gartow, Germany. The scatter is the result of the atmospheric transport, bringing air masses from different areas with higher or lower emissions. The variability has been decreased during the past two months (red square).

Join the race and find the hair in the atmospheric swimming pool!

ICOS data are provided openly and near real time from 22 atmospheric towers all over Europe. We are encouraging scientists all over the globe to analyse these data and find ‘the hair in the atmospheric swimming pool’. The prize will be a place in the hall of fame of greenhouse gas science, a highly ranked publication and a keynote lecture in the next ICOS Science Conference. To support this, we offer access to computing capacities at the ICOS Carbon Portal and further in-depth discussions with the scientific community and beyond. The race is open, please contact us for further information: We hope for interesting statistical approaches or innovative new ideas in data analysis. Here, at the end of this article, we want to revisit the swimming pool analogue because we have a dream. Our dream is that the billions of euros and dollars now being unlocked to support the economic recovery will be used wisely to steer the decarbonisation of our societies. To simulate this dream, we have varied our simulation: the year with the Covid-19 shutdown is now the first year of a five-year period. The following four years are characterised by a stepwise decrease of the anthropogenic CO2 emissions. Every three months, the daily increase is reduced by 1 µm. The hair becomes thinner and thinner, and at the end of the five-year period it is only 12 instead of 32 µm, because anthropogenic emissions are less than half of what they were in 2019. The society has the technologies for this, as well as the money to implement them. The result of what investing the recovery money wisely would look like is shown in Figure 12:

Figure 12: The result of a hypothetical decrease of the anthropogenic emissions based on wise use of the financial support for the economies after the Covid-19 crisis.
Blue line: business as usual
Red line: lower emissions due to the shutdown and wise use of the unlocked money thereafter.


The curve describing the water table in the ‘atmospheric swimming pool’ (the CO2 concentration in the atmosphere, respectively) would be considerably flattened and could be even turned around during the second half of the century. We are facing a historical chance that is extremely important not only for our but also for future generations. In a few decades, the history books will value politicians and CEO’s in terms of their successful management of both the Covid-19 and the climate crisis: Have their decisions been able to flatten only one, or perhaps both of these curves.