Archive for June, 2020

Lindzen’s new paper: An oversimplified picture

June 23, 2020

MIT Prof. Richard Lindzen (retired) has published (19 May 2020) a very interesting new paper in The European Physical Journal Plus (Springer) titled “An oversimplified picture of the climate behavior based on a single process can lead to distorted conclusions“. The full article is paywalled (a shockingly high 45€ for 10 pages!), but it is easy to find an accessible version by googling.

The article is written in very easy terms, at least concerning the first 3 chapters and the conclusion in chapter 5. I read it carefully several times and will try to summarize as best I can.

  1. Introduction

In the introduction Lindzen recall’s that greenhouse warming is a recent element in climate literature, and even if known and mentioned, played a minor role in climate science before 1980. He also repeats a mostly ignored argument, i.e. that even if there is some global warming now (from whatever causes) the claim that this must be catastrophic should be seen with suspicion.

2. Chapter 2

Chapter 2 is titled “The climate system” and on these less than 1.5 pages Lindzen excels in clarity. He writes nothing that could be controversial, but many of these facts are constantly ignored in the media: the uneven solar heating between the equator and the poles drives the motions of heat in the air and the oceans; in the latter there are changes in timescales ranging from years (e.g. El-Nino, PDO and AMO) to millenia, and these changes are present even if the composition of the atmosphere would be unchanging.

The surface of the oceans is never in equilibrium with space, and the complicated air flow over geographic landscapes causes regional variations in climate (not well described by climate models). Not CO2, but water vapor and clouds are the two most important greenhouse substances; doubling the atmospheric CO2 content would increase the energy budget by less than 2%.

He writes that the political/scientific consensus is that changes in global radiative forcing are the unique cause of changes of global temperatures, and these changes are predominantly caused by increasing CO2 emissions. This simplified picture of one global cause (global radiative forcing) and one global effect (global temperature) to describe the climate is mistaken.

It is water vapor that essentially blocks outgoing IR radiation which causes the surface and adjacent air to warm and so triggers convection. Convection and radiative processes result in temperature decreasing with height, up to level where there is so little water vapor left that radiation escapes unhindered to space. It is at this altitude where the radiative equilibrium between incoming solar energy and outgoing IR energy happens, and the temperature  there is 255 K. As the temperature has decreased with height, level zero (i.e. the surface) must be warmer. Adding other greenhouse gases (like CO2) increases the equilibrium height, and as a consequence the temperature of the surface. The radiative budget is constantly changed by other factors, as varying cloud cover and height, snow, ocean circulations etc. These changes have an effect that is comparable to that of doubling the CO2 content of the atmosphere. And most important, even if the solar forcing (i.e. the engine driving the climate) would be constant, the climate would still vary, as the system has autonomous variability!

The problem of the “consensus” climatology (IPCC and politics) is that they ignore the many variables at work and simplify the perturbation of energy budget of a complex system to the perturbing effect of a single variable (CO2).

3. History

In this short chapter Lindzen enumerates the many scientists that disagreed up into the eighties with the consensus view. But between 1988 and 1994, climate funding in the USA for example increased by a factor of 15! And all the “new” climate scientists understood very well that the reason for this extraordinary increase in funding was the global warming alarm, which became a self-fulfilling cause.

Let me here repeat as an aside what the German physicist Dr. Gerd Weber wrote 1992 in his book “Der Treibhauseffekt”:


4. Chapter 4

This is the longest chapter in Lindzen’s paper, also one that demands a few lectures to understand it correctly. Lindzen wants to show that the thermal difference between equatorial and polar region has an influence on global temperature, and that this difference is independent from the CO2 content of the atmosphere. He recalls the Milankovitch cycles and the important messages that variations in arctic (summer) insolation cause the fluctuations in ice cover. The arctic inversion (i.e. temperature increasing with height) makes the surface difference between equator and polar temperatures greater than they are at the polar tropopause ( 6 km). So one does not have to introduce a mysterious “polar amplification” (as does the IPCC) for this temperature differential.

Lindzen establishes a very simple formula which gives the change in global temperature as the sum of the changes of the tropical temperature (mostly caused by greenhouse radiative forcing) and that of the changes of the equator-to-pole temperature difference (which is independent of the greenhouse effect). This means that even in the absence of greenhouse gas forcings (what is the aim of the actual climate policies) there will be changes in global temperature.


5. Conclusion

The conclusion is that the basic premise of the conventional (consensus or not) climate picture that all changes in global (mean) temperature are due to radiative forcing is mistaken.


My personal remarks:

Will this paper by one of the most important atmospheric scientists be read by the people deciding on extremely costly and radical climate policies? Will it be mentioned in the media?

I doubt it. The climate train like the “Snowpiercer” in the Netflix series is launched full steam ahead, and political decisions become more and more the result of quasi religious emotions than that of scientific reasoning. But reality and physics are stubborn… and so as the Snowpiercer is vulnerable to avalanches and rockfall, the actual simplistic climate view could well change during the next decades, long before the predicted climate catastrophe in 2100 will occur.

COVID-19 Luxembourg, final remarks

June 6, 2020


by Francis Massen (
06 June 2020


1. Introduction

The COVID-19 pandemic (or epidemic)  started the 29th Feb 2020 in Luxembourg; this is day 0 or day 1, dependent on counting (I start at day 0).

I wanted to follow the evolution using a model (better: a formula) developed about 200 years ago by Benjamin GOMPERTZ, an English autodidact and later member of the Royal Society. The GOMPERTZ formula belongs to the category of sigmoid functions, which describe a phenomenon starting slowly, going through a quasi exponential development phase and than slowing down up to zero progression. The formula written in Excel notation is:

y = a*exp(-b*exp(-c*x)) with exp(x) = ex

It has only 3 parameters, and clearly a represents an horizontal asymptote when x tends to infinity:  y(inf) = a*exp(-b*0) = a

The Gompertz function is much in use in population dynamics, but also in the first phase of a developing epidemic.

All data and graphs are in the subdirectory Archive.


2. The situation at the end (31-May-20)

Fig.1 shows the Gompertz function modelled on the 92 days of the total infected in Luxembourg, starting 29-Feb-20 and ending 31-May-20.

Modeling means that the parameters a, b and c are mathematically choosen by a regression calculus (Levenberg-Marquardt algorithm) to give a best fit to the observations:

fig.1. Gompertz function fitted to the total infected after 92 days, extended to 100 days.

The next figure shows the previous fit and the observations:

fig.2. Deviations from Gompertz fit


Despite the visible differences, statistically all parameters are significant and the goodness of the fit R2 = 0.998 (the maximum possible is R2=1).


3. How does the Gompertz function fit at the start?

A first question is “when is the fit statistically significant?”.

Let’s take as an example the situation on 16-Mar. None of the 3 parameters were statistically significant; the uncertainty range for parameter a was a ridicule [-19621 … +22437 ]

Nevertheless the fit to the few data points was visually excellent:

fig.3 Gompertz fit to the 6 available data from 29-Feb to 16-Mar


If we would have taken this fit as a valid predictor for the future, we would have been in for a big surprise:

fig.4. The previous fit extended to 100 days (red line), compared to the observations (green dots).

The green curve shows what happened, the red is the predictor made the 16-May.

Conclusion #1: beware of predictions made too early in the development of the epidemic!


The 24-March (=day 24) was the first day where all parameters were statistically significant (alpha = 95%); if we use the Gompertz function calculated from the available data at that moment, the previous fig.4 will change (see fig.5):

fig.5. Gompertz fit made at day 24; the uncertainty range for a at that date shown by the green box was [1182 .. 3098]


 We see that the number of total infected is finally  1400 more that the prediction made the 24th March; the final total is even about 1000 cases more than the higher bound of the uncertainty range!


Conclusion #2: beware of predictions made too early in the development of the epidemic! (I repeat myself!)


4. Evolution of the number of death

Fig.6 shows the number of deaths on the first day where all parameters of the Gompertz fut are significant; the yellow rectangle corresponds to the borders of the uncertainty range, which is large, but not impossible large.

Fig.6. Death number of Gompertz curve prediction, 05-Apr-20 (=36th day)

The Gompertz curve does not fit very well, as the death number increases by jumps:

Fig.7. Death number and Gompertz fit on all observations until 5th Apr. 20


The uncertainty range does not narrow smoothly, but goes through some violent swings before narrowing continuously from about the 44th day ( 8 April) on, as shown by the next animation:

Fig. 8. Animation showing the evolution of death number and the uncertainty interval (upper and lower bounds by full and open squares)


Similar to what has been concluded above: if one had taken the prediction made the 9th April, the number of predicted deaths would have been about 250, to be compared to the final 110.


Conclusion #3: beware of predictions made too early in the development of the epidemic! (I repeat myself!)


5. Final remarks

1.  The 200 year-old Gompertz curve represents well the ongoing epidemic, independent from the political decisions to impose strict measures like shutting down schools and many economic actors, and imposing a relatively strict quarantine: the evolution of both total infected and total death number follows well this simple curve. The death numbers vary more by pause and jumps, so that deviation from the Gompertz curve is more apparent.

2. Even if all 3 parameters of the curve are found to be statistically significant, one can not rely on the prediction to have a correct estimate of the total number of infections and of death. These predictions are only valid when enough data are present, which represents a serious decision problem as this “enough” number is unknown a priori. In hind-cast, one can see that after about 50 days the total number of infected can be reasonable well predicted; this is the moment where the exponential increase is over and the progression begins to slow down. For the number of deaths the date where a valid prediction can be made is about 10 days later (i.e. 60 days after the start).

3. The sad conclusion is that this modeling, independent from its intellectual and scientific interest, is a poor instrument to help making political decisions at the earliest moment, a time when they are most urgently needed. Models are very good at the final development stages of the pandemic; but alas their usefulness is inversely proportional to the delay from the start of the epidemic. One should not be fooled by an extremely good R2: all models follow the past in an excellent way, but this is in general no guaranty on how good they are in predicting the future.



Francis Massen, meteoLCD

06 June 2020