Quote of the Day
All problems become smaller if you don’t dodge them, but confront them. Touch a thistle timidly, and it pricks you; grasp it boldly, and its spines crumble.
— William S. Halsey
Introduction
Figure 1: NOAA Plot of the Atmosphere's CO2 Concentration.
My youngest son told me that I needed to watch the new Cosmos series with Neil deGrasse Tyson. I was immediately hooked – it is a masterpiece of scientific exposition for a general audience. I thought the original Cosmos with Carl Sagan was excellent, but the progress in computer graphics during the intervening decades makes the program visually stunning.
I was particularly interested in the part of the program that addressed the rise in global CO2 levels. Dr. Tyson stated that 30 billion tons of CO2 are being added to the atmosphere every year from human-related (i.e. anthropogenic) sources. I thought I would try to confirm this tonnage level using Figure 1, which is an atmospheric CO2 level chart from the National Oceanic and Atmospheric Administration (NOAA).
Background
For thousands of years, CO2 levels stayed at ~280 ppm (Figure 2) because the natural mechanisms of CO2 generation have been in equilibrium with the natural mechanisms of CO2 absorption (Source). Figure 2 shows data from both direct measurements and ice cores. Starting in about 1800 CE, this balance was upset and the atmosphere's CO2 level has been rising ever since. The start of rising global CO2 levels and the beginning of the industrial age (~1800 CE) appear to coincide . CO2 levels are now over 400 ppm and are rising at a rate of over 3 ppm per year – and the rate of increase is increasing.
The interesting aspect of Figure 2 is that we can separate out natural sources of CO2 from anthropogenic content by the carbon isotope content (
Figure 2: Natural Vs Human-Related CO2 Generation (Source).
According to the USGS, volcanoes release about 250 million tons of CO2 compared to 35 billion tons of CO2 from anthropogenic sources.
Analysis
Annual CO2 Concentration Rise
2016 started with a level of 404.02 ppm, with the concentration increasing by more than 3 ppm in 2015. I found a table of NOAA data for the annual increase in CO2 levels here. In Figure 3, I plotted the data and fit a linear curve to it. Not only is the CO2 concentration increasing every year, the rate of increase is increasing by 0.00275 ppm/year/year.
Figure 3: Annual CO2 Concentration Increase.
Annual Atmospheric CO2 Tonnage Increase
Figure 4 shows my rough enough for the tonnage being released into the atmosphere. It is reasonably close to Tyson's "30 billion tons per year" statement. You will notice a unit called "atm" in the analysis – this stands for a sea-level air pressure of 1 atmosphere or 101,335 Pascals.
Figure 4: Annual CO2 Tonnage Put into the Atmosphere.
My rough calculation shows ~27 billion tons of CO2 per year going into the atmosphere. This is within 10% of Tyson's 30 billion ton figure, so my approximations give results that are pretty close to his figure.
Conclusion
I was able to confirm the statement from Neil deGrasse Tyson that the annual increase in atmospheric CO2 tonnage is ~30 billion tons a year. Since volcanic activity releases ~250 million tons of CO2, the vast majority of the CO2 released into the atmosphere every year is from human sources.
Mark,
re CO2 tonnage:
Enjoyed the post. What's important to me is having a sense of the total annual CO2 of 30 billion tons---a standard against which to measure all the numbers that get thrown around about saving 200,00 or whatever.
But in the calculations, I don't see what you are using for atm.
Thanks,
Paul C
Any suggestions for clarity are greatly appreciated. I have updated the post to define "atm"– it means atmospheric pressure at sea level and is a Mathcad built-in unit. I also a link to a Wikipedia entry that confirms my value for the mass of the Earth's atmosphere.
mathscinotes
Only when the "man in the street" understands the danger to himself and his family will he demand emissions get lowered. Politicians value holding their seats over everything else. Voters must act in large numbers.
The key question is not proving some CO2 number to a certain decimal point. It is: How do we motivate average voters to demand change regarding energy production?
William Gloege
CGNP.org
thank you for these mathematical calculations this is what I was looking for this took some work and I appreciate it
Thank you for the note – it means a lot to me when people find this info useful.
mark
30 Billion tonnes added annually sounds scary, until you realise that equates to 2 parts / 1,000,000. 30B is suddenly tiny to the point of near insignificance. Which raise four questions for me:
1. What is the total weight of CO2 in the atmosphere?
2. The currently accepted average global temperature is 15°C (288°Kelvin). We are told that a 2°C (or 2K) rise in the average increase is dangerously warm and could result in catastrophic consequences.
What is your view on the theoretical ideal average temperature for the planet – and why?
3. The currently accepted average global concentration of CO2 is 412 ppm and rising at 2ppm annually. At 250ppm plants (on which we rely for food) stop growing.
Note: In a controlled experiment two identical crops of wheat were grown in identical sealed conditions (except for the concentration of CO2). The wheat crop grown at 410ppm produced 20% more grain than the one grown at a concentration of 286ppm.
Based on this empirical evidence what is your view on the theoretical ideal concentration of CO2 that would be most beneficial for the planet – and why?
3. As the atmosphere of Mars has a CO2 concentration of 96% (and it is a cold planet). Venus has a CO2 concentration of 97% (and it is an grossly overheated planet). Earth has a CO2 concentration of 0.041%
Based on these empirical facts, can you explain the perceived correlation between any planets average temperature and the concentration of CO2 – and how can this correlation be shown to be a causation of temperature?
I look forward to having these troubling issues explained to me (and everyone else who enjoys your blog).