# Hayden: All you need is elementary algebra

Physics professor Howard Hayden offers the editors of Physics Today a simple algebraic exercise to alleviate climate alarmism.

October 13, 2011

Editor
Physics Today
AIP, Suite 1NO1
Melville, NY 11741-4502

Re: Two “climate change” articles in October 2011 issue

Gentle Folks:

In elementary algebra—oh, so long ago—we learned how to make graphs with the independent variable on the horizontal axis and the dependent variable on the vertical axis. Later on, in science classes we learned the usefulness of the technique: the independent variable is the cause and the dependent variable is the effect. In the fields of health physics and pharmacy, the graphs are called dose-response curves, but everybody who has done experimental science has made similar plots.

The discussions about whether—and how much—increases of CO2 concentration cause increases in temperature come down to such a cause-effect relationship. A reasonable approach would be to plot temperature rise (effect) on the vertical axis versus CO2 forcing on the horizontal axis. The reason I say “would be” is that climate alarmists have never done it. A pharmaceutical company that approached the FDA for a license to manufacture and distribute a drug for which they failed to produce dose-response curves would be laughed out of the hearing room.

The Somerville/Hassol article talks of “communicating the science of climate change.” There is, of course, no theory of climate, because the all-important Navier-Stokes equations can’t even be solved for turbulence in a 4-inch pipe. The causal relationship of temperature rise to CO2 concentration increase, could, however, be displayed in a simple graph using readily available data. Now that would be a way to communicate.

The Sherwood article is merely reasoning by analogy—giving some cases where good science was opposed by establishment opinion. Curiously, in the present case, he opines in favor of establishment opinion, dismissing opposition as “bogus counterarguments,” the same as was done to Copernicus and Galileo. In any case, reasoning by analogy is inherently illogical. Listing a million analogies would neither strengthen nor weaken the link between CO2 and temperature.

We need not sit helplessly by, waiting to climate modelers to connect effect with cause. I call upon readers to make the requisite graph, using the forcing function 2 5.35 Wm *ln(C/C0) from Table 6.2 of IPCC’s Third Assessment Report (http://ipcc.ch/), temperature data and CO2 data from NASA/GISS at http://data.giss.nasa.gov/gistemp/tabledata/GLB.Ts+dSST.txt and http://data.giss.nasa.gov/modelforce/ghgases/Fig1A.ext.txt respectively. The results may cause you to issue a sigh of relief.

Best Regards,

Howard C. Hayden
Prof. Emeritus of Physics, UConn

## 11 thoughts on “Hayden: All you need is elementary algebra”

1. Elgrau says:

“Elgrau, the climate won’t go into a runaway warming, but it will get warmer. A doubling of the CO2 concentration is expected to heat the Earth around 3K before a new equilibrium is reached.

Based on which PlaystationTM climate model? lol
Again, Thomas, you assume a lot….that ALL the other things that effect temps (and produce things like ice ages, etc., etc.) are all “nuetral” during this period and ONLY CO2 concentration changes (i.e., doubling) and ALL these other effects are a “wash”. That is just your (wishful?) assumption that (based on the extremely poor record of these climate models to predict CURRENT temp changes based on CO2 concentration) does not appear to be correct.

2. Thomas says:

Elgrau, the climate won’t go into a runaway warming, but it will get warmer. A doubling of the CO2 concentration is expected to heat the Earth around 3K before a new equilibrium is reached.

3. Elgrau says:

“If we block some energy from going out the system will heat up to
compensate.”

Yes, and then since “the system” is hotter, it will radiate MORE heat into space, and so on. If it were not a self-compensating (i.e., a stable) system, all life would have been frozen or fried (forever) by now…

4. Thomas says:

Rshearer, some aspects of climate may be chaotic, but the basic features are based on energy conservation and don’t seem to be. If we block some energy from going out the system will heat up to compensate.

Then you mix equations and models. There are countless models used in aerodynamics, not just one. They may for the most part be based on the same equations, but then so are the climate models. Not that climate models are anywhere near perfect, but they do give a rough estimate of AGW, and there is no reason to assume the overestimate rather than underestimate the problem. You don’t need perfect knowledge to realize that this is a serious problem.

5. RShearer says:

Thomas, notwithstanding that the Bernoulli principle is quite well understood now but was not during the early development of fixed-wing aircraft, Hayden’s point is that climate is much more complex and indeed chaotic, and cannot be modelled (with accuracy).

There is a single Bernoulli equation. IPCC recognizes 20 or so climate models. If this science were settled, there would only need to be one.

6. Thomas says:

There are a few problems with Hayden’s method. As Elgrau points out there are other factors affetcting temperature, such as cooling sulphate emissions from power plants. It also takes a long time to heat up the Earth, especially the oceans, so in a situation with increasing forcing the temperature will lag. Both of these factor ensure that Hayden will underestimate the climate sensitivity.

Climate scientists have used all kind of methods to estimate climate sensitivity, the reason they don’t like Hayden’s method may have more to do with that it isn’t useful rather than that they are incompetent.

Finally, to paraphrase Hayden “There is, of course, no theory of flight, because the all-important Navier-Stokes equations can’t even be solved for turbulence in a 4-inch pipe.”. Nevertheless we can build airplanes that fly. Usually you don’t need a perfect theory to get results that are good enough to be useful.

7. elgrau says:

If I were interested enough and thought it was even something to bother with (due to the fact that there is really nothing that man can do about the climate anyway at least for now…except to adapt to it or die!) I’d probably do an N dimensional least squares fit using “N” significant variables that are postulated to effect “mean global temperature” (whatever that is..) and the record of their values over as long a past period as data exists for all of them vs. the best estimate of said temperatures for this same period. The resulting LSQ coefficients of each variable might indicate the significance of each variable on temperature. You could also play around with the phasing (lead/lag time of each effect/variable) and perhaps come up with a pretty good idea of what (and how much) each of these variables effect temperature….but unless you included most all of the variables that drive mean temp (which might not even be known!), you’d probably fail….’cause climate is most likely chaotic and not likely prone to prediction anyway….on the other hand it does seem to be periodic (what with ice ages coming at pretty regular intervals and durations).

8. Dennis Sidwell says:

The largest variable, no the 95% variable in the room is water vapor. Doesn’t matter what you think about any or all the other gases in the atmosphere, water vapor is the most abundant green house gas on the planet. Sorry, I forgot to mention sun spots by that little guy in the sky.

Is anyone able to put “facts” on paper and show a graph how all the green house gases interact, including water vapor, in conjunction with sun spot activity over the years? Anyone.

9. Elgrau says:

I like his logic and know it to be a complex system (climate…). However, simply plotting Temp vs CO2 concentration (as a “cause/effect” relationship) makes the (bogus) assumption that CO2 concentration is the ONLY variable effecting temperature. You’d need to consider ALL (or most!) of the major variables that affect temperature and then show a plot wherein all of these variables were held constant with ONLY CO2 concentration changing to have a better idea of what CO2 concentration actually does to temperature. Some other variable that ALSO effects temperature might be changing more during your observation period and thus MASKING the effect of CO2 on temperature…just say’n. That said, I do know that man made CO2 is (very!) most likely not anything to be alarmed at re “climate change”. These “other variables” are FAR more significant than man made CO2…..IMO!

10. Jason Kolb says:

I don’t quite understand the significance, but with about 10 min of Excel work you can convert the text to columns and plot two alarming exponential curves on an X-Y graph and yeild a linear scatter plot. Doesn’t that just show that the future temp predicitons were developed using the forcing data, that’s typically the only reason you get a straight line correlation between two sets of data. I can’t post the graph, but the average temp data gives a linear fit with a 0.83 R^2 value, which is pretty linear.

11. Walter Sobchak says: