A couple of weeks ago, I discussed how a manager needs to be able to evaluate results from complex computer calculations with simple analytical models. Let’s take an example of how a “back-of-the-envelope” calculation can give you insight into one of the most controversial discussions of our time – global warming. A number of very smart scientists have developed what must be very complex computer programs that calculate the effect of CO2 emissions from man-made sources on the temperature of our atmosphere. Seems like something this complex would not lend itself to a simple analysis. But is that true?
To begin with, let’s look at the composition of our atmosphere, which is heated by the sun and, by radiant heat transfer, transfers additional heat to the earth’s surface. Now, radiant heat transfer is something an engineer in the heat-processing industry understands well. For instance, we all know that in a furnace atmosphere, any nitrogen or oxygen in the atmosphere has no impact on the radiant heat transfer since both have zero emissivity. The primary radiant energy is generated by the CO2 and water vapor in the combustion gases.
From the 1976 Standard Atmosphere Tables generated by the government, we know that 99% of the atmosphere is made up of oxygen and nitrogen. The trace elements present are the only elements that contribute to any radiant heat transfer from the atmosphere to the surface. From those tables, CO2 has a presence of 322 ppm. Up to an altitude of 2 km, water vapor is present at an average concentration of 2,843 ppm.
Now, from our knowledge of the science of radiation and using standard emissivity tables, we also know that water vapor has about 2.3 times the emissivity of CO2.
From the "expert's" global-warming discussions, we are told that about 3-4% of the CO2 in the atmosphere comes from man-made sources. Now let’s make our back-of-the-envelope calculation. We have a ratio of “man-made” CO2 to w.v. of 2,843/11.3 = 252. With w.v. having 2.3 times the impact on radiation of CO2, the impact of the man-made CO2 to radiant heat transfer in our atmosphere is only 0.17% of the w.v. contribution.
And if we eliminated all the man-made CO2, the impact on the atmospheric radiation from the combined effect of the CO2 and w.v. would be about 0.00006%. Does anyone really believe with all the variables involved with using average concentrations in the world’s atmosphere that this would have any impact? As a manager, what faith would you have in the result predicted from this program? How much of your company’s future would you put at risk from these results?