Goodbye 400 ppm: The statistics of the Keeling Curve

Figure 1: The Keeling Curve: Monthly carbon dioxide values at Mauna Loa from 1956 to end of 2018. Data from:

There are two iconic graphs of climate science. The first of these is the “hockey-stick” curve of temperature since 1000 CE, originally published by Michael E. Mann and his colleagues in 1998. Despite decades of controversy, the general picture of an anomalously fast rise in temperature beginning in the 20th century still stands. The second iconic graph is that of atmospheric carbon dioxide measured at Mauna Loa since 1958 by the Scripps Institution of Oceanography, under the direction of Charles David Keeling (Keeling passed away in 2005, he was succeeded by his son Ralph Keeling). When Keeling first measured CO2, the December 1958 value was 314.7 parts per million (ppm); sixty years later, the value has reached 408.9 ppm. This more than 25% increase is the most direct and incontrovertible evidence we have of recent human impact on the chemistry of the atmosphere. We long ago passed 400 ppm and there is no looking back.

Figure 2: Keeling curve with linear regression (red line). Equaiton is above the graph.
Figure 3: Residuals of a linear regression on the Keeling curve.
Figure 4: Second degreee polynomial fit to the Keeling curve.Equation above the graph. Not a linear increase!
Figure 5: First-difference (month-to-month change) for the Keeling curve from 1970–1980. The large amplitude curve reflects Northern Hemisphere photosynthesis; the dips at the peaks are Southern hemisphere photosynthesis.
Figure 6: Autocorrelogram for the differenced data; values reflect sum of photosynthesis in the two hemispheres.
Figure 7: Fourier analysis of the differenced time series. There are two major peaks.

Paleontologist, geologist, ecologist, educator. Professor at the University of Illinois at Chicago. Author of Explorers of Deep Time.