Saturday, May 25, 2013

The tale of a tail

Due to budgetary constraints, the managing director of a climate research institute decided that the salaries had to be cut somewhat. She summoned all researchers and told them that, unfortunately, the current 5%-95% salary range of 1500-4500 €/month would have to be adjusted to 1200-3900 €/month. Their reaction was lukewarm. Each believed that their earnings lied somewhere in the middle of the range, and so the cut that each one had to suffer would probably be not as large as they once fretted. However, when they were about to sign the agreement, the managing director whispered:

well, .. you know that the wage distribution is not symmetrical and that the most likely wage, that so far was 3000 €/month, will turn to be 2000 €/month in the future.

- "What ? This is something completely different ! " one exclaimed.
- " Let us negotiate until the 7th IPCC report ! "  another suggested. "Perhaps the numbers may have changed by then".


lucia said...


hvw said...

Hi Eduardo,

You write in the UBA-thread:

Zur Sensitivität habe ich diese kleine Tabelle vorbereitet:
____ 5% 33% Mode 66% 95%

Can you or anybody else enlighten me why for ECS the mode is usually reported as a measure of central tendency and not the median, which would naively seem to be the more natural choice?

hvw said...

As nobody seems able to answer this, here is my best guess:
Among mode, median and mean, for the probability distributions of climate sensitivity, the mode is always lower than the other two measures. Reporting the mode just shows that the IPCC tends to choose the conservative alternative when in doubt.

eduardo said...



this is a good question. When the distributions are not symmetrical, a good practice would be to report all those measures to better characterize the distribution. However, the situation here may be more complex. The methods to estimate the sensitivity vary. They may range from simple linear regression models to Bayesian methods incorporating previous expert judgement and results from model ensembles. For some methods it may be easier to estimate the mean, for others the mode. The IPCC range, in my understanding, summarizes the results from all these methods and thus it is a final expert judgement after all , a degree of believe in Bayesian parlance . I will try to get a more definitive answer from the IPCC authors.

More technically, one has to bear in mind that some distributions simply do not have a mean value. The ratio of two Gaussian distributions is a Cauchy distribution that, for some values of its parameters, may have a mode but not a mean. The sensitivity is often expressed as a ratio of two quantities, a temperature change versus a change in forcing, both quantities with uncertainties attached. If the distribution of the denominator is in some sense too close to the value of zero, the mean of the ratio may not even exist. Because of the aerosols, the uncertainty in the forcing is wide, as we all know, and thus it resembles the situation that I just explained. I way out of this is, as James Annan advocates, to cap the Bayesian priors of the sensitivity by imposing a priori physical limits to the sensitivity

eduardo said...

This is an another example that although the imprint of anthropogenic forcing can be detected in the observations, the estimates of climate sensitivity do come down by including recent observed temperatures. Both assertions are not in contradiction, although they raise indirectly some other questions, like for instance why could high-sensitivity models also reproduce the observed evolution of temperatures in the 20th century

Observed 21st century temperatures further constrain likely rates of future warming

Peter A. Stott*, Gareth S. Jones


We carry out a detection and attribution analysis of observed near-surface temperatures to 2010 and demonstrate that the signal of human influence on climate has strengthened over the first decade of the 21st century. As a result, we show that global warming is set to continue, with the second decade of the 21st century predicted to be very likely warmer than the first. Estimates of future warming rates consistent with observations of past climate change are now better constrained than they were a decade ago. The highest rates of warming previously consistent with past warming now appear to be unlikely. © 2012 British Crown copyright, the Met Office. Published by John Wiley & Sons Ltd.