This post is about a paper that was published 50 years ago:

Manabe, S. and Wetherald, R.T., 1967. Thermal equilibrium of the atmosphere with a given distribution of relative humidity.

Journal of the Atmospheric Sciences,24(3), pp.241-259.

That paper (hereafter referred to as MW67) was perhaps the first study of the earth’s climate using a modern radiative-convective numerical model, including the water vapor feedback. It is a classic paper in climate science and was extraordinarily important in inspiring future work on numerical modeling of the climate system.

Since this year is the 50th anniversary of MW67, let’s take a look at its findings and compare them to the past 50 years of observations. In their abstract, MW67 state that:

a doubling of the CO2 content of the atmosphere has the effect of raising the temperature of the atmosphere […] by about 2C.

More precisely, in Table 5 they show that doubling CO2 from 300 to 600 ppmv would raise the temperature by 2.36° C.

Using the methods described previously on this site, we can compare the actual change in CO2 concentration to the actual change in temperature, over the 50-year period since the paper was published. To do this, we will plot *the base-2 logarithm of CO2 concentration for each year* (X) against *the average of the six major global temperature datasets (from GISTEMP, Berkeley Earth, Cowtan&Way, NOAA, HADCRU, and JMA)* (Y).

##### Figure 1. Observed CO2 vs temperature, from 1967-2016 (blue) and the predicted slope of the regression line from MW67 (red).

The result is shown in Figure 1 above. The slope of the CO2-vs-temperature regression line in the 50 years of actual observations (blue line) is 2.57, only slightly higher than MW67’s prediction of 2.36 (red line). The error in their estimate of the rate of warming per doubling of CO2 was less than 10%.

This is even more impressive when one considers that at the time MW67 was published, there had been no detectable warming in over two decades. Their predicted warming appeared to mark a radical change with the recent past:

##### Figure 2. Observed CO2 vs temperature up to 1967 (blue) and the predicted warming from MW67 (red).

Note that MW67 did not provide a prediction for when CO2 would reach a given level, only for the amount of warming that would result once that level was reached. So the slope of the red line in Figure 2 is based on how CO2 increased after 1967, information that was not available at the time of MW67. In other words, the actual prediction only included the amount of warming from a given amount of CO2, not the specific year in which that CO2 level would be reached.

As it turns out, their prediction was remarkably successful:

##### Figure 3. Observed CO2 vs temperature up to 2016 (blue) and the predicted warming from MW67 (red).

As shown in Figure 3, the temperature in 2016 — half a century after MW67 was published — was almost exactly what MW67 would have predicted based solely on the atmospheric CO2 concentration. That really is quite astonishing. So, happy birthday and congratulations to MW67.