Watt about the mode?

There’s another post on Watts Up With That (WUWT) about climate sensitivity. It’s based, again, on the recent paper by Nic Lewis in which he finds that climate sensitivity is probably closer to 1.5oC than between 2oC and 3oC, which is what many other studies suggest. This could be and these post about climate sensitivity seem quite balanced. Having said that, one does have to be careful of “single study syndrome”. Just because someone publishes a paper that differs from the results of others, does not mean that the new result is correct. It simply adds to the body of evidence which, over time, will – as more data is collected and more models developed – converge towards a generally accepted result.

I thought I would make a couple of comments though. One is that there is statement in the post claiming that

Lewis finds that in recent years neither the global temperature nor ocean heat uptake have changed very much, while CO2 concentrations have continued to rise. Therefore, the climate sensitivity must be lower.

Firstly, we don’t know what global temperatures have done in recent years since the errors in the trend are too large. Secondly, other studies suggest that ocean heat content has risen quite dramatically in recent years. This may be wrong, but does suggest that one cannot then state that ocean heat content has not risen recently.

The other issue is that they seem to be focusing on the mode of the distribution of possible values. A figure showing the distribution of possible climate sensitivities from Lewis (2012), and from three other studies, is shown in the figure below (credit: Anthony Watts, WUWT). Each study produces a distribution of possible values, that peaks at some value. This peak is known as the mode of the distribution. Some regard it as the most likely number, and hence should be the value that we consider as the most likely climate sensitivity.

Climate sensitivity distributions from Lewis (2012) and from 3 other studies (credit : Anthony Watts, WUWT).

Climate sensitivity distributions from Lewis (2012) and from 3 other studies (credit: Anthony Watts, WUWT).


The mode, however, may not be the most likely climate sensitivity. If there were an infinite number of Earths each with a climate sensitivity such that the distribution of climate sensitivities matched one of the distributions shown in the figure above, there would be more Earths with climate sensitivities near the mode, than near any another possible number.

However, we don’t have an infinite number of Earths, we have a single Earth with a single climate sensitivity. Given that the climate sensitivity distributions are skewed (i.e., the mode is closer to the low-end than to the high-end, or, there is a tail extending to high values) there is a less than 50% chance that the actual climate sensitivity has a value as low as that of the mode. Another property of a distribution is the median value. This is the value that essentially divides the distribution in two such that there is a 50% chance that the actual value lies above the median and (obviously) a 50% chance that it lies below the median. Since these distributions are skewed, the median is at a higher value than the value of the mode. It seems to me, therefore, that the median number is a more appropriate number to consider than the mode. Admittedly, the Lewis (2012) distribution is less skewed than the rest and so the median will be quite close to the mode. Either way, however, the climate sensitivity is more likely to be at a value higher than the mode, than below the mode. Therefore, even Lewis (2012) suggests that climate sensitivity is bigger than 1.6oC and they’ve assumed a lower rate of heat uptake in the oceans than many would regard as reasonable.However, I do find this WUWT post quite interesting in that it is an example – in my view – of a perfectly reasonable discussion of the science surrounding global warming and climate change. When referring to CO2 it says yes, it warms the planet – just not as much as thought. I just find it confusing to find a post like this that seems quite balanced surrounded by others that seem to completely ignore well-established scientific knowledge. If there were more posts like this, a proper scientific discussion could actually take place. I’d certainly encourage this, but we’ll have to see if future posts remain as balanced or revert back to type.

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4 Responses to Watt about the mode?

  1. Rachel says:

    One thing I feel is absent from the climate sensitivity debate is the fact that 50 million years ago, the Earth was a lot hotter. Much hotter than just 2-3C. There were crocodiles off the coast of Greenland. A 2-3C warming is not going to provide an arctic habitat for crocodiles and 1.5C of warming is certainly not going to. And back then, there was about the same amount of CO2 in the atmosphere as there’s going to be in 100 years if we continue to twiddle our thumbs.

  2. I thought that as kind of the point though. There are those who think the positive feedback could lead to quite substantial increases in temperature. If you look at the 3 other models in the figure, there is a non-negligible chance that climate sensitivity could be higher than 3oC. Lewis (2012) essentially claim that this isn’t possible (based on their model) but it seems like they’ve chosen changes in ocean heat content lower than what others think is reasonable, so could well be underestimating the climate sensitivity.

    It seems like the issue is that anyone claiming that we could undergo some level of “catastrophic” warming is shot down because they’re being an alarmist and that no previous predictions of catastrophe have come true. The issue with this – IMO – is that there is always a first time and one of the reasons we’ve avoided previous catastrophes is that we’ve done something to avoid them (ozone hole, for example). It just seems that some are basically unwilling to consider some of the arguments being made by those who are concerned about climate change and try to use vague philosophical arguments about why there isn’t enough evidence to become alarmed, rather than actually considering the possibility that maybe this is the time to become alarmed and to act.

    I guess what I’m suggesting is that anyone who tried to make the argument that you’re suggesting would be shot down because someone would then claim that there’s not enough evidence to support your claims about the climate 50 million years ago (as they’re essentially trying to do now to any study that produces a hockey stick shape).

  3. Rachel says:

    What better evidence could there be than the discovery of bones belonging to a crocodile in the arctic? Matt Huber, who appears in the Thin Ice documentary makes this observation. Perhaps if I’m feeling brave, I’ll post a comment at WUWT.

  4. I agree, but I think the issue is that some will either dispute the evidence or dispute any claims about the climate at that time. It’s maybe worth a shot though. I keep living in hope that someone will comment on WUWT and some of the regular commentators will say “Ohhh, I hadn’t realised that. Good point.”

    I keep meaning to watch all of Thin Ice. I shall have to set some time aside to do so.

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