As a part of a class during the fall of 1997, data on world population and atmospheric carbon dioxide (CO2) concentration were analyzed to see if a well defined relationship exists between them. It is found by methods of least squares inversion that there is in fact a very well defined relationship. The following equation (eq 1) accurately fits the population growth since 1950 :

Eq. 1. Population(billions) = 2.54*exp((year-1950)*0.0183)

(standard deviation between eq.1 and census data = .045 billion, or 45 million).

Atmospheric CO2 data from Hawaii is related to population by the equation:

Eq. 2. CO2(ppmv) = 264.77(ppmv) + 16.55(ppmv/(billion persons) * population(billions) + 2.8(ppmv)*cos(2*pi*f*year -1.75)

where f = 1 cycle/year, and the concentration of CO2 is given in parts per million by volume (ppmv). The cosine term in equation 2 describes the annual variation, which is thought to be due to seasonal activity of land biota (trees, people etc.) and the constant term 264.77(ppmv) describes the background CO2 level. The standard deviation between the Hawaii CO2 data and equation 2 is 0.95 ppmv.

Figure 1 shows the data and the CO2 calculated from equation 2.

The population data were obtained from the US census bureau at http://www.census.gov/ipc/www/worldpop.html , and the atmospheric CO2 data from file://cdiac.esd.ornl.gov/pub/ .

These data show that there is a very well defined empirical relationship between the growth in Earth’s human population and the growth in atmospheric CO2, at least for the last 40 years. From a simply mathematical viewpoint we can invert the problem and say that the atmospheric CO2, after removing the annual variation, is a very good proxy for the human population. This simple and rather naive approach overlooks the extreme complexities involved in the chemistry and physics of the processes controlling CO2 interchange, and the implications for the processes. However lack of a complete understanding of the processes is not an impediment to exploring this empirical relationship. The equation relating population growth to CO2 is then:

Eq. 3. Population(billions) = (CO2(ppmv) - 264.77(ppmv)-(annual variation))/16.55(ppmv/billion persons)

The population predicted from the CO2 data is compared to the census data in FIGURE_2 , and it fits very well, as of course it should. Given the difficulties and likely errors in measuring Earth’s population, the population predicted from the CO2 data may be more indicative of reality.

There are two other features of the data worth noting. The first is that the seasonal changes in atmospheric CO2 are not phase shifted with respect to the seasons by more than a few months, indicating that the atmosphere is rapidly affected by the terrestrial activity. We infer from this that human activity will also be rapidly communicated to the atmosphere. This implies that changes in population, or CO2 production by human activity, are reflected in the CO2 data with a time delay of order months. The second is related to the atmospheric CO2 production per person per year. Moore and Bolin (1986) calculate that a CO2 concentration of 346 ppmv is equivalent to a global atmospheric content of 740 billion metric tons of CO2 . Using this relationship and the time rate of change of the population from eq. 1 we get that on average the activity of each person produces 0.65 metric tons of CO2 per year. Multiplying this number by 6 billion (the present population) we get 3.9 billion tons of CO2/year, a number which is close to the estimated production from fossil fuels. It should also be noted that the CO2 exhaled by humans per year is not an insignificant fraction of this number (5% ?). The growth in atmospheric CO2 related to human activity is shown graphically in FIGURE_3 .

Accurate data records on atmospheric CO2 and population only go back to about 1950. Before this we must rely on indirect methods for estimating atmospheric CO2, such as ice core data, and population estimates that are not based on accurate census taking. Using the air trapped in Antarctic ice cores (see for example Bender et al 1997 in the Proceedings of the National Academy of Sciences (http://www.pnas.org /)) and population estimates from the US Census Bureau the correlation between CO2 and population since 1800 may be analyzed. FIGURE_4 shows the data from 1800 to the present. We see that the data from 1800 to 1950 are fit with a population growth rate and CO2 production rate that are different from the period 1950 to 1996. Prior to 1950 the population growth rate was .0081 as compared to the present rate of .0183. The CO2 production rate was about 18.97 ppmv/person prior to 1950 as compared to 16.55 at the present. Stated another way these results could be interpreted to infer that the rate of population growth has increased since 1950 and that we are putting slightly less CO2 per person per year into the atmosphere.

Given the complexity of natural processes controlling CO2 it is remarkable that atmospheric CO2 tracks the human population so closely. Although we cannot rigorously prove it, it seems highly probable that the growth in atmospheric CO2 over at least the past 40 years, and probably over the past 200 years, is directly related to human activity and not to natural variations.

Based on the data it appears that unless the production of CO2 per person is reduced, CO2 will remain an excellent proxy for population. Since most of the worlds population is looking forward to an increase in their standard of living, it seems unlikely that this rate will change, at least over the next decade.

References:

Moore, Berrien lll, and Bert Bolin, The Oceans, Carbon Dioxide, and Global Climate Change, Oceanus V29, N 4, 1986/87